Physical Geography

Start with the wrong answer

On the Mercator world map that still hangs in a great many classrooms, Greenland and Africa look about the same size. Greenland covers 2.16 million square kilometres. Africa covers 30.37 million. Africa is roughly fourteen times larger, and the map has told you otherwise without misplacing a single coordinate. Every point on that map is in exactly the right relationship to every other point in one specific respect. The trouble is which respect.

This is the right place to begin a course in physical geography, because it is a compact demonstration of the discipline's central habit: before you can say anything about the Earth's surface, you have to say how you measured it, and what that method of measuring throws away.

Where the Mercator error actually comes from

Gerardus Mercator published his world map in 1569 for a specific job: ocean navigation. He wanted a chart on which a straight line drawn between two ports would be a line of constant compass bearing, so a pilot could set one heading and hold it. To make that work, the map has to be conformal, meaning angles are preserved locally, so a small shape on the ground keeps its shape on the paper.

Preserving angles has an arithmetic consequence. On a globe, lines of longitude converge toward the poles; on a Mercator map they are drawn parallel, which stretches every east-west distance by a factor of 1 divided by the cosine of the latitude. To keep shapes right rather than squashing them, the north-south spacing has to be stretched by the same factor. At 60 degrees north, cosine 60 is 0.5, so the stretch is 2 in both directions. At 80 degrees north, cosine 80 is about 0.174, so the stretch is about 5.8 in both directions.

Area is the product of the two, so area is exaggerated by the square of that factor: four times at 60 degrees, about 33 times at 80 degrees. Greenland spans roughly 60 to 83 degrees north. Africa straddles the equator, where the stretch factor is 1. The apparent equality of the two is not an error in the map. It is the map working exactly as designed, read for a purpose it was never designed for.

Key idea: A projection is not right or wrong. It is a trade, and the only real error is using a map for a question it does not answer.

Why you cannot escape the trade

Carl Friedrich Gauss proved in 1827 what is now called the Theorema Egregium, the remarkable theorem: the Gaussian curvature of a surface is intrinsic, so a surface with curvature cannot be flattened onto a plane without stretching. A sphere has curvature. A sheet of paper does not. No projection, however clever, escapes this. Peel an orange and try to press the peel flat; it tears or it wrinkles, and there is no third option.

So mapmakers choose which property to keep. Four are on offer, and no projection keeps more than a couple of them at once.

Family	Preserves	Sacrifices	Good for
Conformal (Mercator, Lambert conformal conic, stereographic)	Local angles and shapes	Area, badly, away from the standard line	Navigation, aeronautical charts, large-scale topographic sheets
Equal-area (Albers, Mollweide, Lambert azimuthal, sinusoidal)	Area everywhere	Shape, and usually angles	Thematic maps of density, land cover, population, anything you will compare by size
Equidistant (azimuthal equidistant, plate carree)	Distance from one point or along set lines	Everything else	Range rings, seismic distance, radio propagation
Compromise (Robinson, Winkel tripel, Natural Earth)	Nothing exactly	A little of each, spread thin	General reference world maps, where no single property dominates

Notice what this means in practice. If you are about to calculate the area of a burn scar, a watershed or a habitat patch, you must reproject into an equal-area system first, or your number is decorative. If you are digitising a coastline for a navigation product, you want conformal. The question determines the projection, never the other way round.

What the coordinates are attached to

Latitude and longitude feel absolute in a way that projections plainly are not, and this is the second place a beginner goes wrong. A coordinate is a position relative to a mathematical model of the Earth's shape, and there is more than one model.

Three surfaces are in play. The topographic surface is the actual ground, with its mountains and trenches. The geoid is the equipotential surface of Earth's gravity field that best matches global mean sea level, and because Earth's mass is unevenly distributed it is lumpy, rising and falling by tens of metres relative to a smooth shape. The reference ellipsoid is a smooth mathematical figure, an oblate spheroid flattened at the poles, chosen to approximate the geoid.

A datum pins an ellipsoid to the Earth, fixing its size, shape, orientation and origin. The modern global datum is WGS 84, which your phone reports positions in. The older North American Datum of 1927 used a different ellipsoid tied to a survey station in Kansas. Convert a NAD 27 coordinate to WGS 84 and the position can move by more than a hundred metres, in places by a couple of hundred. That is the difference between the correct parcel and the neighbour's. Older USGS topographic sheets carry the shift printed in the margin for exactly this reason.

Elevation has its own version of the problem. A GNSS receiver natively measures height above the ellipsoid, which is not the height above sea level anyone means by elevation. Converting between them requires a geoid model, and in the continental United States the separation between ellipsoid and geoid runs to roughly negative 30 metres. Report an ellipsoid height as an elevation and you are out by the height of a ten-storey building.

Reading a scale without getting it backwards

Scale is written as a representative fraction: 1:24,000 means one unit on the map equals 24,000 of the same units on the ground. One centimetre is 240 metres. One inch is 2,000 feet, which is why the USGS 7.5-minute quadrangle series settled on that number for the United States.

Here is the reversal that catches everyone. A 1:24,000 map is a large-scale map. A 1:1,000,000 map is a small-scale map. The fraction 1/24,000 is a larger number than 1/1,000,000, and the naming follows the fraction, not the area covered. Large scale means small area and lots of detail; small scale means big area and little detail. Say it to yourself twice, because it will come up in every professional context you meet.

Scale has a second, deeper meaning in geography: the scale at which you aggregate data changes the answer you get. The modifiable areal unit problem is the demonstration that redrawing the boundaries of your reporting units, without changing a single underlying observation, changes correlations and even flips their sign. Related is the ecological fallacy: a relationship measured across counties does not license a claim about individuals within them. Neither of these is a technicality. Both have decided real arguments about the causes of things.

The upshot: Scale is a choice, and the pattern you find is partly a product of the choice, so a competent analyst reports the units and tests whether the finding survives changing them.

The instruments that measure the surface now

Physical geography stopped depending on the theodolite and the barometer some time ago. Four technologies do most of the modern measuring, and each answers a different question.

• Global navigation satellite systems. The United States GPS constellation, joined by Galileo, GLONASS and BeiDou, lets a receiver trilaterate its position from satellite timing signals. A handheld unit is good to a few metres. A permanently installed geodetic station, differenced against a network over months, resolves motion at the millimetre scale, which is how plate velocities and volcanic inflation are now measured directly rather than inferred.
• Optical and multispectral imaging. Landsat 1 launched on 23 July 1972 and the series has run continuously since, with Landsat 8 and 9 currently returning imagery at 30 metres per pixel in the visible, near-infrared and shortwave-infrared bands, 15 metres in the panchromatic band, and a repeat cycle of 16 days for a single satellite. Since 2008 the whole archive has been free, which is why long-term land-cover change is a solved measurement problem and was not one before.
• Radar. Synthetic aperture radar supplies its own illumination and penetrates cloud, so it works at night and through weather. Interferometric SAR compares the phase of two passes over the same ground and detects displacement of a centimetre or less, which is how subsidence from groundwater pumping, inflation of magma chambers and coseismic ground motion are now mapped over whole regions.
• Lidar. A pulsed laser flown over terrain returns millions of ranges per second. Because some pulses find gaps in a forest canopy, filtering the returns produces a bare-earth digital elevation model under the trees. The USGS 3D Elevation Program is building this coverage for the United States, and lidar has already revealed fault scarps, ancient river channels and archaeological earthworks that a century of field walking had missed.

Two things are worth noticing about that list. First, none of these instruments produces a photograph in the everyday sense. A Landsat scene is a grid of calibrated radiance values in several wavelength bands, most of which the eye cannot see, and the pretty picture is a rendering choice made afterwards. Second, every one of them has a resolution, and resolution decides what can exist in your data. A process operating at 5 metres is invisible in 30 metre pixels, and no amount of analysis recovers it.

A worked case: measuring the area of a lake

Suppose you want the surface area of a reservoir from satellite imagery. Walk it through. You obtain a Landsat scene, which arrives in a Universal Transverse Mercator projection, a conformal system that divides the globe into 60 zones six degrees of longitude wide. Conformal is wrong for area, so step one is to reproject into an equal-area system appropriate to the latitude, such as an Albers equal-area conic with standard parallels chosen for the region.

Step two is to separate water from land, usually with a normalised difference water index built from the green and shortwave-infrared bands, since water absorbs shortwave infrared almost completely and vegetation reflects it strongly. Step three is to count the water pixels and multiply by pixel area, 900 square metres for a 30 metre pixel.

Now the honest part. Your answer inherits three errors: mixed pixels along the shoreline, where a single cell is partly water and partly mud; the date of the image, since a reservoir at the end of a dry season is not the same object as the same reservoir in spring; and any residual geometric error in the scene's registration. A result reported without those three caveats is not a measurement, it is a number. Getting into the habit of naming the error terms is most of what separates a geographer from someone with software.

Common misconceptions

• Some projection somewhere gets everything right. Gauss proved otherwise in 1827. Choosing a projection is choosing which distortion you can live with.
• The Gall-Peters projection is the honest alternative to Mercator. It is equal-area, which fixes one problem, but it badly distorts shape, stretching the tropics vertically and the high latitudes horizontally. It is one trade among many, not a correction.
• Latitude and longitude are absolute. They are relative to a datum. The same physical point has different coordinates in NAD 27 and WGS 84, differing by up to a couple of hundred metres.
• A large-scale map covers a large area. The opposite. Large scale means a large representative fraction, so a small area in high detail.
• Satellite images show what a camera would see. Most bands are outside visible light, and the colours in a published image are assigned, not observed.

Where this leaves us

• Every flat map distorts, because curvature is intrinsic; projections differ only in which property they keep and which they surrender.
• Mercator's area exaggeration grows as the square of 1 over the cosine of latitude, which is why Greenland at 60 to 83 degrees north swells to look like an equatorial continent fourteen times its size.
• Coordinates and elevations mean nothing without a stated datum and, for heights, a geoid model; datum errors run to hundreds of metres horizontally and tens of metres vertically.
• Representative fractions run counter to intuition: 1:24,000 is large scale, 1:1,000,000 is small scale, and the analytical unit you choose can change the correlation you find.
• GNSS, multispectral imaging, interferometric radar and lidar each measure a different quantity at a different resolution, and resolution sets a hard limit on what your data can contain.

Sources

1. United States Geological Survey. (n.d.). National Geospatial Program. usgs.gov
2. United States Geological Survey. (n.d.). Landsat missions. usgs.gov
3. National Aeronautics and Space Administration. (n.d.). Landsat science. landsat.gsfc.nasa.gov
4. United States Geological Survey. (n.d.). 3D Elevation Program. usgs.gov
5. National Coordination Office for Space-Based Positioning, Navigation, and Timing. (n.d.). GPS.gov: Official U.S. government information about the Global Positioning System. gps.gov
6. Snyder, J. P. (1987). Map projections: A working manual (U.S. Geological Survey Professional Paper 1395). U.S. Government Printing Office.

A town where the sun sets in November

Utqiagvik sits on the Arctic coast of Alaska at 71.3 degrees north. In late November the sun goes below the horizon and does not come back for roughly two months. In summer the reverse happens: from mid-May until early August it never sets, and the town works, plays baseball and sleeps under continuous daylight for something close to eighty days.

Nothing about the Sun changes during those months. The Sun does not move closer, dim, or shift its output. Everything that happens at Utqiagvik is produced by the geometry of a tilted ball going round a star, and once you can reconstruct that geometry you can predict the length of the day and the strength of the sunlight anywhere on Earth, on any date, with a calculator. That is the aim of this lesson.

The explanation that almost everybody starts with, and why it fails

Ask a hundred adults why summer is warm and a large share will say the Earth is closer to the Sun in summer. Test it. Earth's orbit is very slightly elliptical. Perihelion, the closest approach, occurs in early January at about 147.1 million kilometres. Aphelion, the farthest point, occurs in early July at about 152.1 million kilometres. The difference is about 3.4 percent in distance, which by the inverse square law gives roughly 7 percent in the energy arriving at the top of the atmosphere.

Now notice the dates. Earth is nearest the Sun in January, which is the depth of northern winter, and farthest in July, in the middle of northern summer. If distance drove the seasons, the northern hemisphere would have its winter and summer the wrong way round. It also fails a second test: the southern hemisphere has summer in January and winter in July, exactly opposite the north. A single global distance cannot produce two opposite seasons at once.

The 7 percent is real, and it does something. It makes southern summers marginally more intense at the top of the atmosphere and northern summers marginally less so. But the southern hemisphere is mostly ocean, which stores heat and damps the swing, so the effect is small in observed temperature. Distance is a minor term. It is not the mechanism.

The point: Seasons are a hemispheric phenomenon happening in opposite directions at the same moment, so their cause has to be something that differs between the hemispheres. Distance from the Sun does not.

The actual mechanism: tilt plus a fixed direction

Earth's rotational axis is tilted 23.44 degrees from the perpendicular to its orbital plane. That angle is called the obliquity. Crucially, the axis keeps pointing in the same direction in space as Earth goes round; it currently points near Polaris, and it does not swing to follow the Sun. This is called parallelism of the axis, and it is the half of the explanation that most diagrams leave out.

Put the two together. In June the northern end of the axis leans toward the Sun, so the northern hemisphere gets steeper sunlight and longer days. Six months later Earth is on the other side of its orbit, the axis still points the same way in space, and now the northern end leans away. Tilt supplies the angle; parallelism supplies the fact that the angle reverses over half an orbit.

The consequences fall out as a set of latitudes you already know the names of, and every one is a number derived from 23.44 degrees.

Line	Latitude	Where the number comes from	What happens there
Tropic of Cancer	23.44 N	The obliquity itself	Sun directly overhead at noon on the June solstice, the northern limit of the subsolar point
Tropic of Capricorn	23.44 S	The obliquity itself	Sun directly overhead at noon on the December solstice
Arctic Circle	66.56 N	90 minus 23.44	At least one day of 24-hour daylight and one of 24-hour darkness each year
Antarctic Circle	66.56 S	90 minus 23.44	The same, in the opposite season
Equator	0	The rotation axis	Day length near 12 hours all year; subsolar point passes twice, at the equinoxes

Utqiagvik at 71.3 north is 4.7 degrees inside the Arctic Circle, and that is the whole explanation for its two dark months. The further inside the circle you go, the longer the polar night, until at the pole itself it runs half the year.

Two reasons steep sunlight is stronger

Latitude and season control temperature through the angle of the incoming beam, and the angle works in two ways at once.

The first is beam spreading. A shaft of sunlight of fixed width lands on a small patch of ground when it comes in steeply and smears across a much larger patch when it comes in at a slant. The energy per square metre falls with the sine of the solar altitude. At an altitude of 90 degrees the beam is concentrated; at 30 degrees the same beam covers twice the area, so each square metre gets half as much.

The second is path length, expressed as air mass. A vertical beam passes through one atmosphere's thickness. A beam at 30 degrees altitude passes through about twice that, and near the horizon through many times more. Every extra kilometre of air scatters and absorbs a little more, which is why you can look at a setting sun and not at a noon one, and why the sun looks red at the horizon: the short blue wavelengths have been scattered out of the beam.

Working an actual number

The solar altitude at local solar noon follows one line of arithmetic. Take 90 degrees, and subtract the absolute difference between your latitude and the Sun's declination, which is the latitude of the subsolar point on that date.

Try Chicago, at 41.9 degrees north. On the June solstice the declination is plus 23.44, so noon altitude is 90 minus the difference between 41.9 and 23.44, that is 90 minus 18.5, which gives 71.5 degrees. On the December solstice the declination is minus 23.44, so the difference is 41.9 plus 23.44, that is 65.3, and the noon altitude is 24.7 degrees.

Convert those to energy. The sine of 71.5 degrees is about 0.95; the sine of 24.7 degrees is about 0.42. So at midday in June, before any atmospheric losses, each square metre of level ground in Chicago receives about 2.3 times the direct solar energy it receives at midday in December. Then multiply by day length: about 15 hours 14 minutes in June against 9 hours 8 minutes in December, a ratio of about 1.7. The two effects compound, so the daily total in June is roughly four times the December total. That factor of four, not the 3.4 percent of orbital distance, is what makes a season.

Why this matters: Insolation is set by two multiplying quantities, beam angle and day length, and both peak together in the summer hemisphere. That is why the seasonal swing grows with latitude and nearly vanishes at the equator.

Why the hottest day is not the longest day

The June solstice is the day of maximum insolation in the northern hemisphere, yet in most places the warmest average temperatures arrive in late July or August. The gap is called the seasonal lag, and it happens because the surface keeps taking in more energy than it loses for weeks after the solstice, so stored heat continues to accumulate. The peak of temperature comes when incoming and outgoing energy balance, not when the input peaks.

The size of the lag depends on what the surface is made of. Water has a high specific heat capacity, mixes to depth, and is partly transparent, so it warms and cools slowly; coastal and island stations can lag by two months or more. Land warms and cools in a thin skin, so continental interiors lag by only about a month. This one difference, the thermal inertia of water against land, will reappear in several later lessons, because it also produces monsoons, maritime climates and the muted seasonality of the southern hemisphere.

Solar time is not clock time

One more complication, because it trips up field measurements. Solar noon, when the Sun crosses your meridian, is not usually 12:00 on the clock. Two things pull them apart. Time zones are broad political stripes, so a place at the eastern edge of a zone reaches solar noon well before a place at the western edge. And Earth's orbit is elliptical and its axis tilted, so the apparent Sun runs fast at some times of year and slow at others; the correction is called the equation of time and reaches about plus 16 minutes in early November and about minus 14 minutes in mid-February.

Plot the Sun's position at the same clock time every day for a year and the two effects trace a figure-eight in the sky called the analemma. For practical work, the National Oceanic and Atmospheric Administration publishes a solar position calculator that handles all of this from a latitude, longitude and date, and it is the sensible thing to use before you install a solar panel, model a shadow, or interpret a temperature record.

The same geometry on a very long clock

Nothing in the geometry is permanent. Three orbital parameters vary on long cycles, first worked out quantitatively by Milutin Milankovitch in the early twentieth century. Eccentricity, the shape of the orbit, varies on roughly 100,000 and 400,000 year cycles. Obliquity, the tilt, oscillates between about 22.1 and 24.5 degrees on a 41,000 year cycle; more tilt means stronger seasons in both hemispheres. Precession, the slow wobble of the axis, changes which season coincides with perihelion on a cycle of roughly 19,000 to 23,000 years.

These do not change the total annual energy Earth receives by much. They redistribute it by latitude and season, and the summer insolation at high northern latitudes turns out to be the quantity that governs whether continental ice sheets survive the summer. That link between orbital geometry and the ice ages is developed properly in the Atlas course on climate systems; here the point is narrower. The tilt that gives Utqiagvik its dark December is itself a variable, and it has been the pacemaker of Quaternary glaciation.

Common misconceptions

• Seasons are caused by distance from the Sun. Earth is closest in January, during northern winter, and the two hemispheres have opposite seasons simultaneously, which no distance explanation can produce.
• The Earth's axis tips back and forth toward the Sun. The axis holds a fixed direction in space. It is Earth's position in the orbit that changes which hemisphere leans sunward.
• Day and night are exactly equal at the equinox. Close, but not exact: atmospheric refraction lifts the Sun's image and day length is measured to the upper limb, so equal day and night falls a few days off the equinox.
• The longest day is the hottest day. Thermal inertia delays the temperature peak by about a month inland and two months or more near oceans.
• The Sun is overhead at noon everywhere in summer. Only between the tropics does the Sun ever pass through the zenith, and even there only on two dates a year.

What to carry forward

• Seasons come from a 23.44 degree axial tilt combined with an axis that keeps a fixed direction in space, not from the 3.4 percent variation in orbital distance.
• The tropics and polar circles are arithmetic consequences of that one angle: 23.44 and 90 minus 23.44.
• Noon solar altitude equals 90 degrees minus the difference between your latitude and the solar declination; the energy per square metre follows the sine of that altitude.
• Beam spreading and day length multiply, giving Chicago roughly four times as much daily solar energy in June as in December.
• Temperature lags insolation by weeks because surfaces store heat, and orbital parameters themselves drift on cycles of 20,000 to 400,000 years.

Sources

1. National Aeronautics and Space Administration. (n.d.). The Sun. NASA Science. science.nasa.gov
2. National Oceanic and Atmospheric Administration, Global Monitoring Laboratory. (n.d.). NOAA solar calculator. gml.noaa.gov
3. United States Naval Observatory. (n.d.). Astronomical applications: Sun and moon data. aa.usno.navy.mil
4. National Centers for Environmental Information. (n.d.). Paleoclimatology data and orbital forcing. NOAA. ncei.noaa.gov

The number the whole planet runs on

A square metre held perpendicular to the Sun just outside the atmosphere intercepts about 1,361 watts. That figure, the total solar irradiance, has been measured continuously by satellite radiometers since 1978, and it varies by only about one watt across the eleven-year sunspot cycle. Everything in this lesson is an accounting exercise on that 1,361 watts: where it goes, what fraction comes back out, and what the residual does to the temperature of the ground under your feet.

We are going to do the accounting as an actual calculation, because the calculation produces a striking result. Done correctly with nothing but the solar constant, Earth's reflectivity and a law from 1879, it predicts a planet whose average surface temperature is 18 degrees below freezing. The real average is about 15 degrees Celsius. The 33 degree gap is not an error. It is the atmosphere, and it is the reason there is liquid water.

What the air is made of

Dry air is remarkably uniform up to about 80 kilometres because turbulence keeps it mixed. By volume it is 78.08 percent nitrogen, 20.95 percent oxygen and 0.93 percent argon. Those three account for 99.96 percent of the whole. Carbon dioxide runs at roughly 420 parts per million, which is 0.042 percent, and the NOAA baseline record at Mauna Loa shows it climbing by two to three parts per million every year.

Water vapour is deliberately left out of that list because it is not uniform. It ranges from almost nothing over Antarctica in winter to about 4 percent of the air by volume in a humid tropical afternoon, and its concentration is set by temperature, since warmer air can hold more. Hold on to that variability. It makes water vapour both the strongest greenhouse gas in the atmosphere and a feedback rather than a control.

Notice a strange fact about the list. The two dominant gases, nitrogen and oxygen, do almost nothing thermally. Their molecules are symmetric pairs of identical atoms, so vibrating or rotating does not change the distribution of electrical charge along the molecule. A molecule can only absorb infrared radiation if the vibration changes its dipole moment. Nitrogen and oxygen cannot, so they are transparent to the infrared the Earth emits. The trace gases, which have three or more atoms arranged asymmetrically, can. That is why 0.042 percent of the atmosphere does more thermal work than the 78 percent above it.

What matters here: The greenhouse effect is a property of molecular geometry, not of abundance, which is why trace gases at parts-per-million concentrations set the temperature of a planet.

The vertical structure, and why temperature keeps reversing

Pressure falls smoothly with height, roughly halving every 5.5 kilometres, so about half the atmosphere's mass sits below the summit of Denali and about 90 percent below 16 kilometres. Temperature does something more interesting: it falls, then rises, then falls, then rises again, and each reversal marks a change in what is absorbing energy.

Layer	Approximate range	Temperature trend	Why
Troposphere	Surface to 8 km at the poles, 16 to 18 km at the equator	Falls, on average 6.5 degrees per kilometre	Heated from below by the surface; contains nearly all weather and water vapour
Stratosphere	Tropopause to about 50 km	Rises	Ozone between roughly 15 and 35 km absorbs ultraviolet, warming the layer from within
Mesosphere	About 50 to 85 km	Falls	Too little ozone to heat it; the mesopause is the coldest place in the atmosphere
Thermosphere	Above about 85 km	Rises steeply	Scarce molecules absorb extreme ultraviolet and X-rays; the air is so thin the high temperature carries little heat

The troposphere is where physical geography lives, and its defining property follows from being heated from below. Warm air at the bottom is buoyant, so it rises; the layer overturns, and that overturning is what we call weather. The stratosphere is heated from within at its upper levels, which puts warm air above cool air. That is a stable arrangement, it resists vertical motion, and it is why airliners climb into the lower stratosphere to find smooth air, and why volcanic aerosols injected above the tropopause linger for years instead of raining out in a week.

The calculation, step by step

Now the accounting. Follow each step, because every one is a place a mistake gets made.

Step one: spread the beam over the whole planet. Earth intercepts sunlight as a disc of area pi times the radius squared, but it radiates from a sphere of area four pi times the radius squared. So the average incoming energy per square metre of surface is the solar constant divided by four: 1,361 divided by 4, which is about 340 watts per square metre.

Step two: subtract what is reflected. Earth's albedo, the fraction of sunlight reflected straight back to space, averages about 0.30, most of it from clouds, with contributions from ice, snow, deserts and the atmosphere itself. So 340 times 0.30, about 100 watts per square metre, leaves again without ever being absorbed. Absorbed energy is 340 minus 100, which is about 240 watts per square metre.

Step three: set emission equal to absorption. In steady state the planet must radiate away exactly what it takes in, or its temperature would run away. So Earth must emit about 240 watts per square metre as infrared.

Step four: invert the Stefan-Boltzmann law. A body radiates energy proportional to the fourth power of its absolute temperature: E equals sigma times T to the fourth, with sigma, the Stefan-Boltzmann constant, equal to 5.67 times ten to the minus eight watts per square metre per kelvin to the fourth. Rearranged, T equals the fourth root of E divided by sigma. Dividing 240 by 5.67 times ten to the minus eight gives about 4.23 times ten to the ninth. Its fourth root is about 255. So Earth's effective radiating temperature is 255 kelvin, which is minus 18 degrees Celsius.

Step five: compare with the world. The measured global mean surface temperature is about 288 kelvin, or 15 degrees Celsius. The calculation is out by 33 degrees, and it is out in a very specific way. The 255 kelvin figure is not wrong about the planet; it is the temperature of the level in the atmosphere from which infrared actually escapes to space, roughly 5 kilometres up. The surface is warmer than that level because the troposphere has a lapse rate, and the greenhouse gases in between force the escape level upward and therefore the surface temperature with it.

Change one input and watch the answer flip

Redo step two with a different albedo and the procedure becomes a lesson in feedback. Suppose ice sheets advance far enough that global albedo rises from 0.30 to 0.62, the sort of value a heavily glaciated Earth might reach. Absorbed energy falls to 340 times 0.38, which is about 129 watts per square metre. Divide by sigma and take the fourth root: about 218 kelvin, or minus 55 degrees Celsius.

A change of 32 percentage points in reflectivity drops the radiating temperature by 37 degrees. And here is the vicious part: cold makes more ice, ice raises albedo, higher albedo makes it colder. That is the ice-albedo feedback, and it is why the geological record contains episodes of extraordinarily extensive glaciation and why sea ice loss in the Arctic is watched so closely today. Reverse the sign and the same feedback runs the other way, which is one reason the Arctic is warming faster than the global mean.

The surface budget: where the 240 watts actually goes

Averaging over the globe hides most of the interesting behaviour, so drop to a single patch of ground. Its energy budget balances like this. Net radiation is what remains after incoming shortwave, reflected shortwave, incoming longwave from the atmosphere and emitted longwave from the surface are added up. That net radiation is then spent in three ways.

• Latent heat flux. Energy used to evaporate water, about 2.5 million joules per kilogram, which leaves the surface as vapour and is released again, somewhere else, when the vapour condenses. Over the ocean and over a wet forest this term dominates.
• Sensible heat flux. Energy transferred to the air by conduction and then carried off by convection, warming the air you can feel. Over a desert, where there is no water to evaporate, almost all of the net radiation goes here, which is why deserts get very hot by day.
• Ground heat flux. Energy conducted into or out of the soil or water below. Small on a daily average over land, large in the ocean, and the reason a lake in October is warmer than the air above it.

The split between latent and sensible heat, called the Bowen ratio, explains a great deal of local climate at a glance. An irrigated field and a bare field beside it receive identical radiation and reach completely different afternoon temperatures, because one spends its energy evaporating and the other spends it heating the air. The same logic explains why the diurnal temperature range in a desert can exceed 25 degrees Celsius while a humid tropical station varies by less than 8: water vapour absorbs outgoing infrared at night, and dry air does not.

The core of it: Radiation sets how much energy a surface has; the availability of water decides whether that energy becomes temperature or becomes evaporation.

The imbalance, and where the energy goes sideways

Two refinements matter before we move on. First, the global budget is not exactly balanced. Satellite measurements from NASA's Clouds and the Earth's Radiant Energy System instruments show Earth absorbing roughly one watt per square metre more than it emits. That sounds trivially small against 340. Spread over the planet's surface and accumulated over years it is an enormous quantity of energy, and more than 90 percent of it has gone into the ocean.

Second, the budget is wildly unbalanced by latitude. Between roughly 35 north and 35 south, the surface absorbs more solar energy than it radiates away. Poleward of that, the reverse. If nothing moved, the tropics would keep heating and the poles keep cooling without limit. They do not, because the atmosphere and ocean carry energy poleward at a rate measured in petawatts, peaking near 35 degrees in each hemisphere. That transport is not an afterthought to the circulation. It is the reason the circulation exists, and every wind belt, storm track and ocean current in the next several lessons is a mechanism for moving heat out of the tropics.

Common misconceptions

• The greenhouse effect works like a greenhouse. A glasshouse warms mainly by preventing convective mixing with outside air. The atmosphere warms the surface by absorbing and re-emitting infrared, a different mechanism that happens to share a name.
• Carbon dioxide is too scarce at 0.042 percent to matter. Absorption depends on molecular geometry, not abundance; nitrogen and oxygen are transparent to infrared no matter how much of them there is.
• Higher in the atmosphere is closer to the Sun, so it should be warmer. The troposphere is heated from below by the surface, not from above, which is why it cools with height. The stratosphere, heated internally by ozone, does warm with height.
• The thermosphere is hot, so a satellite there would burn. Temperature measures the kinetic energy of individual molecules; at that density there are too few molecules to transfer meaningful heat.
• Earth's energy budget is in balance. It is close, but CERES measurements show a persistent surplus of roughly one watt per square metre, over 90 percent of which has been absorbed by the ocean.

Putting it together

• The solar constant is about 1,361 watts per square metre; averaged over the sphere that is 340, of which about 100 is reflected and about 240 absorbed.
• Inverting the Stefan-Boltzmann law on 240 watts per square metre gives an effective radiating temperature of 255 kelvin, 33 degrees below the observed surface mean of 288 kelvin.
• That 33 degree gap is the greenhouse effect, produced by asymmetric molecules such as water vapour, carbon dioxide, methane and ozone, and not by the nitrogen and oxygen that make up 99 percent of the air.
• Temperature reverses at each atmospheric boundary because the heating source changes: surface heating below the tropopause, ozone absorption above it.
• At a point on the ground, net radiation is partitioned into latent, sensible and ground heat fluxes, and the availability of water decides the split and therefore the local climate.
• Energy is in surplus equatorward of about 35 degrees and in deficit poleward, and closing that gap is what the winds and currents are for.

Sources

1. National Aeronautics and Space Administration. (n.d.). Clouds and the Earth's Radiant Energy System (CERES). NASA Langley Research Center. ceres.larc.nasa.gov
2. National Oceanic and Atmospheric Administration, Global Monitoring Laboratory. (n.d.). Trends in atmospheric carbon dioxide. gml.noaa.gov
3. National Aeronautics and Space Administration. (n.d.). Earth Observatory. earthobservatory.nasa.gov
4. National Oceanic and Atmospheric Administration. (n.d.). JetStream: An online school for weather. noaa.gov

Norway, cut off, 1917

When the First World War closed the North Sea, Norwegian forecasters lost the British weather telegrams they had depended on. Storms arrived at the fishing fleets unannounced. Vilhelm Bjerknes, who had come home to found the Bergen Geophysical Institute in 1917, responded by doing the opposite of what a shortage usually produces: he built a much denser observing network inside Norway, dozens of stations reporting several times a day, and set his students to look at what the crowded data showed.

What it showed was that the boundaries between warm and cold air were not fuzzy transition zones spread over hundreds of kilometres, as the textbooks then assumed. They were sharp. Temperature, humidity and wind direction all changed across a line you could draw on a map, and storms grew along those lines. In 1919 Vilhelm's son Jacob Bjerknes published the structure of a moving cyclone built on exactly this idea, and Halvor Solberg and Tor Bergeron worked out how such a storm is born, matures and dies. The group needed a word for the sharp boundary. With the Western Front in every newspaper, they called it a front, and the metaphor of two armies of air contesting a line has stuck for more than a century.

What follows is that model, which is still the basis of the weather map you look at on your phone.

Air masses: where the armies come from

An air mass is a large body of air, often more than 1,600 kilometres across, that has sat over a uniform surface long enough to take on its temperature and moisture. The surface it sat over is the source region, and the naming follows two letters: a lower-case letter for moisture, from the source being continental (c, dry) or maritime (m, humid), and a capital for temperature, from arctic (A), polar (P), tropical (T) or equatorial (E).

Air mass	Source region	Character	Weather it brings
cP, continental polar	Northern Canada, Siberia	Cold, dry, stable	Clear cold snaps; lake-effect snow if it crosses open water
mP, maritime polar	North Pacific, North Atlantic	Cool, moist, conditionally unstable	Low cloud, drizzle, orographic rain on windward coasts
cT, continental tropical	Northern Mexico, the Sahara, interior Australia	Hot, very dry	Heat waves, drought, dust
mT, maritime tropical	Gulf of Mexico, Caribbean, subtropical oceans	Warm, very moist, unstable	The moisture supply for most heavy rain and severe storms in mid-latitudes
cA, continental arctic	Arctic Basin, Greenland ice sheet	Bitterly cold, extremely dry	The most severe outbreaks of winter cold

Two air masses of different origin do not blend readily, because differences in temperature mean differences in density. That reluctance to mix is what maintains the sharp boundary.

Four kinds of front, distinguished by geometry

What matters about a front is not which air is advancing but the slope of the boundary, because slope decides how fast the warm air is lifted and therefore what clouds form.

A cold front is cold air pushing under warm air. The dense air behaves like a plough and the boundary is steep, on the order of 1 in 50 to 1 in 100. Warm air is forced up quickly, so cloud grows vertically into cumulonimbus, and the precipitation is intense, narrow and short-lived, often with thunder. Passage is abrupt: wind veers, temperature drops, pressure that had been falling begins to rise, and within an hour the sky can clear.

A warm front is warm air riding up over retreating cold air. It cannot plough, only climb, and the slope is gentle, 1 in 100 to 1 in 200. The lifting is slow, so cloud is layered rather than towering. You see the arrival long before you feel it: high cirrus first, perhaps a day ahead and a thousand kilometres out, thickening through cirrostratus and altostratus to nimbostratus, then many hours of steady, moderate rain or snow. The passage is gradual, with a slow temperature rise and clearing to a warm, often muggy air mass behind.

A stationary front is a boundary neither air mass can push, and it can sit for days, delivering repeated rounds of rain along the same line. That is the classic setup for river flooding, because the same catchment is rained on again and again. An occluded front forms when the faster cold front overtakes the warm front and lifts the entire warm sector clear of the ground. The occlusion marks maturity and the beginning of the end for a cyclone, because once the warm air is aloft the temperature contrast that powered the storm is gone.

Remember: Cold front means a steep boundary, brief violent weather; warm front means a shallow boundary, long gentle weather. Everything else about frontal weather follows from that one difference in slope.

Why the storm turns, and why it deepens

Three forces set the wind. The pressure gradient force pushes air from high pressure toward low, at right angles to the isobars, and it is the only one that actually initiates motion. The Coriolis effect, which arises because the ground beneath a moving parcel is itself rotating, deflects that motion to the right in the northern hemisphere and to the left in the southern. It is zero at the equator and strongest at the poles, and it grows with wind speed. Friction acts only in the lowest kilometre or so.

Above the friction layer, the pressure gradient force and the Coriolis effect come into balance and the wind blows parallel to the isobars rather than across them. That is the geostrophic wind, and it is why upper-air charts show flow following the contours. Near the ground, friction slows the air, which weakens the Coriolis deflection and lets the pressure gradient win slightly, so surface wind crosses the isobars inward toward a low at 20 to 30 degrees.

That inward crossing is the crucial piece. Air spiralling into a surface low has nowhere to go but up. Rising air cools, condenses, forms cloud and releases latent heat, which makes it more buoyant still. Around a high, air sinks, warms, and dries, which is why anticyclones bring clear skies. A single fact about surface friction thus separates storm from calm.

But convergence at the surface can only continue if something removes the air at the top. That something is the polar front jet stream, a ribbon of fast wind at 9 to 12 kilometres altitude where the temperature contrast between polar and tropical air is sharpest. The jet is not straight; it meanders in long Rossby waves, and in certain positions within those waves the flow spreads apart, creating divergence aloft. A surface low sitting beneath a zone of upper-level divergence deepens, because more mass is being exhausted at the top than is being imported at the bottom. Cyclogenesis is a partnership between the ground and the tropopause.

The life of one storm

The Bergen model gives the sequence. It starts as a wave on a stationary polar front, a small kink where cold air begins to push south at one point and warm air north at another. Pressure falls at the kink. Over a day the wave amplifies into an open wave cyclone, with a clear warm sector between a trailing cold front and a leading warm front, the whole system 1,000 to 2,500 kilometres across and moving east at 30 to 50 kilometres an hour.

The cold front, being steeper and faster, gains on the warm front. When it catches it, the storm occludes: the warm sector is lifted entirely off the surface and the low is now surrounded by cold air at ground level. The occlusion often produces the heaviest precipitation of the storm's life, but it is a terminal condition, since the horizontal temperature contrast the cyclone fed on has been converted to potential energy and spent. The low fills over the following two to four days. The whole cycle runs three to ten days, and the front left behind waits for the next wave.

Storms at smaller scales

Fronts organise weather at a thousand kilometres. Three other systems operate below that, and each has its own recipe.

Thunderstorms need three ingredients: moisture at low levels, instability so that a lifted parcel keeps rising on its own, and a lifting mechanism to start it, whether a front, a mountain slope, or daytime heating. An ordinary air-mass storm lasts under an hour, because its own downdraught cuts off the inflow that feeds it. A supercell escapes that fate through vertical wind shear: because wind speed and direction change with height, the updraught is tilted away from the downdraught and can persist for hours, rotating as a mesocyclone. Supercells produce most large hail and nearly all violent tornadoes.

Tornadoes are rated after the fact on the Enhanced Fujita scale, in use since February 2007, which estimates wind speed from damage to specific structures. The United States records roughly 1,200 tornadoes a year, more than any other country, because the continent has an unobstructed corridor allowing dry continental air from the southwest to override moist Gulf air from the south beneath a strong jet.

Tropical cyclones run on entirely different physics from mid-latitude storms: no fronts and no temperature contrast, but a warm core fed by latent heat released from ocean evaporation. The requirements are specific. Sea surface temperature of at least about 26.5 degrees Celsius through the upper 50 metres, weak vertical wind shear so the storm can stay vertically stacked, a pre-existing disturbance, and enough distance from the equator, roughly 5 degrees of latitude, for the Coriolis effect to organise rotation. That last condition is why no hurricane forms on the equator.

The Saffir-Simpson scale rates them by sustained wind, from Category 1 at 74 miles per hour to Category 5 at 157 and above. It is worth knowing that the scale is a poor guide to danger, because the largest death tolls come from water rather than wind. Hurricane Katrina in 2005 came ashore in Mississippi and Louisiana with a storm surge that reached more than 8 metres in places along the Mississippi coast, and the great majority of the more than 1,800 deaths were from flooding.

In short: Mid-latitude cyclones extract energy from horizontal temperature contrasts; tropical cyclones extract it from warm water through latent heat. Same word, opposite engines.

Common misconceptions

• The Coriolis effect determines which way water spins down a drain. At the scale of a sink the force is millions of times weaker than the effects of basin shape and residual motion. It governs systems hundreds of kilometres across, not domestic plumbing.
• A cold front means the weather turns cold, a warm front means it turns warm. The names describe which air mass is advancing. The distinctive weather comes from the slope of the boundary, and a cold front in July can be followed by a pleasant afternoon.
• Hurricanes and tornadoes are the same phenomenon at different sizes. A hurricane is a warm-core system hundreds of kilometres across drawing energy from ocean heat over days. A tornado is a vortex tens or hundreds of metres across, lasting minutes, embedded in a thunderstorm.
• Low pressure causes rain directly. Low pressure causes surface convergence, which forces ascent; the ascent causes cooling, condensation and rain. The pressure is a symptom of the circulation, not the cause of the cloud.
• Opening windows equalises pressure and saves a house from a tornado. It does not, and it wastes time that should be spent getting to an interior room on the lowest floor.

The short version

• The Bergen school, working from a dense Norwegian observation network in 1917 to 1922, established that air masses meet along sharp fronts and that storms grow on them.
• Air masses are labelled by moisture and temperature of their source region, and maritime tropical air is the moisture supply for most heavy mid-latitude rain.
• Cold fronts are steep and produce narrow, intense, convective weather; warm fronts are shallow and produce broad, prolonged, layered precipitation.
• Surface friction turns the geostrophic balance into inflow, inflow forces ascent, and a surface low deepens when upper-level divergence beneath a jet stream removes the rising air.
• A cyclone runs from wave to open wave to occlusion over three to ten days, and occlusion ends it by removing the temperature contrast that fed it.
• Supercells persist because wind shear separates updraught from downdraught; tropical cyclones need warm water, low shear and enough latitude for Coriolis to work.

Sources

1. National Oceanic and Atmospheric Administration. (n.d.). JetStream: An online school for weather. National Weather Service. noaa.gov
2. NOAA National Hurricane Center. (n.d.). Tropical cyclone climatology and the Saffir-Simpson scale. nhc.noaa.gov
3. NOAA Storm Prediction Center. (n.d.). Severe weather and tornado data. spc.noaa.gov
4. NOAA National Severe Storms Laboratory. (n.d.). Severe weather 101. nssl.noaa.gov
5. Bjerknes, J. (1919). On the structure of moving cyclones. Geofysiske Publikasjoner, 1(2). Norwegian Academy of Science and Letters.

A city that averages less than a millimetre of rain

Arica sits on the Pacific coast of northern Chile at 18 degrees south. Its long-term average annual rainfall is under a millimetre, which is the driest figure recorded for any inhabited place with a long instrumental record. Inland, in the core of the Atacama, some weather stations have gone for years at a stretch without measuring rain at all. The desert is fogbound most mornings. Moisture is not absent from the air over Arica; it is abundant. It simply never falls.

Now look at a globe. The Sahara sits at 15 to 30 north. The Arabian, Kalahari and Great Australian deserts occupy the same latitude band. Cross to North America and the Sonoran and Chihuahuan sit there too. That band of aridity encircling the planet at roughly 20 to 30 degrees in both hemispheres is too regular to be an accident, and explaining it is the first job of this lesson. But Arica will not fit the explanation, and neither will the Gobi, and neither will Death Valley. There is more than one way to make a desert, and telling them apart is the second job.

Three cells, and where the air comes down

The previous lesson ended on a surplus of energy in the tropics and a deficit at the poles. The atmosphere closes that gap with a circulation that is not one giant overturning loop, because the Earth rotates and the Coriolis effect will not permit it, but three loops per hemisphere.

Intense solar heating near the equator drives ascent along a band called the intertropical convergence zone. Rising air cools, condenses, and rains, which is why the equatorial belt holds the world's rainforests. That air, now stripped of moisture, spreads poleward at altitude, cools by radiating to space, grows dense and descends at 20 to 35 degrees latitude. The loop is the Hadley cell, named for George Hadley, who proposed a version of it in 1735.

What descends is the key. Sinking air is compressed as pressure increases, and compression warms it at about 10 degrees Celsius per kilometre. Warming air can hold more water vapour, so its relative humidity collapses even though its absolute moisture content does not change. Cloud evaporates. Precipitation becomes essentially impossible. The result is a belt of persistent high pressure, the subtropical highs, and beneath it, on every continent that reaches those latitudes, a desert.

Two more cells complete the pattern. The polar cell has cold dense air sinking at the pole and flowing equatorward as the polar easterlies. Between them, the Ferrel cell is a thermally indirect circulation driven by the two on either side, with the surface flow moving poleward and being deflected into the prevailing westerlies of the mid-latitudes. Where polar and tropical air meet, at roughly 60 degrees, sits the polar front, and that is where the cyclones of the previous lesson are born.

Latitude	Vertical motion	Surface pressure	Surface winds	Consequence
0 to 5	Rising	Equatorial low	Convergent, light and variable	Rainforest; heavy convective rain most afternoons
20 to 35	Sinking	Subtropical high	Trade winds equatorward, westerlies poleward	The world's great subtropical deserts
50 to 60	Rising	Subpolar low	Convergent along the polar front	Storm tracks; the wettest mid-latitude coasts
85 to 90	Sinking	Polar high	Polar easterlies	Polar desert; Antarctica is the driest continent

The whole pattern migrates with the seasons, following the subsolar point with a lag of a few weeks. That migration is what produces seasonally wet and dry tropical climates: a place at 12 degrees north sits under the intertropical convergence zone in July and under the edge of the subtropical high in January, so it has a monsoon and a dry season rather than year-round rain.

Worth holding on to: Rain requires ascent. Anywhere air is descending on average, whether at 30 degrees latitude, on the lee side of a mountain, or over cold water, it is dry, and no amount of nearby moisture changes that.

The four recipes

Subtropical subsidence is only the first mechanism. Here are all four, with the diagnostic that tells them apart.

1. Subtropical subsidence. Sinking limb of the Hadley cell. Diagnostic: the desert lies in a band at 15 to 35 degrees and extends across an entire continent regardless of terrain. The Sahara, at over 9 million square kilometres, is the type case, along with the Arabian, Kalahari and Australian deserts.

2. Rain shadow. A mountain range forces air to rise, wringing out its moisture on the windward side, so the lee side receives descending, dried, warmed air. Diagnostic: extreme rainfall contrast over a short horizontal distance, with the wet side upwind. Death Valley receives about 55 millimetres a year in the lee of the Sierra Nevada, whose western slopes take more than 1,500 millimetres in places. Patagonia sits in the lee of the Andes for the same reason.

3. Cold ocean current and coastal upwelling. Cold water offshore chills the air above it from below, creating a temperature inversion, which is the most effective possible suppressor of ascent. Fog forms readily, because the air is at saturation, but the inversion caps convection, so nothing grows deep enough to rain. Diagnostic: a coastal desert with fog, high humidity and no rain. This is Arica and the Atacama with the Humboldt Current, and the Namib with the Benguela Current.

4. Continentality. Some places are simply too far from any ocean, and often shielded by mountains from what moisture might reach them. Diagnostic: an interior location deep inside a large landmass with an enormous annual temperature range. The Gobi and the Taklamakan qualify, the latter also sitting behind the Himalaya, which the summer monsoon cannot cross.

Several deserts run on more than one mechanism. The Atacama is a coastal cold-current desert that also sits in the subtropical belt and in the rain shadow of the Andes, which is why it is not merely dry but the driest non-polar place on Earth. Explaining a desert well usually means ranking mechanisms rather than choosing one.

Working a rain shadow with numbers

The rain shadow is worth doing arithmetically, because the result is counterintuitive: the air that comes down the far side is not just drier than the air that went up, it is warmer.

Two lapse rates do the work. Unsaturated air rising and cooling by expansion changes temperature at the dry adiabatic lapse rate, about 10 degrees Celsius per kilometre. Once the air reaches saturation and condensation begins, the latent heat released partly offsets the cooling, so it follows the saturated adiabatic lapse rate, roughly 5 degrees per kilometre in warm air.

Take a parcel at the coast at 20 degrees Celsius, forced up a 3 kilometre range, with its lifting condensation level at 1 kilometre.

• Sea level to 1 km, unsaturated: 20 minus 10, giving 10 degrees at the condensation level. Cloud forms.
• 1 km to 3 km, saturated: 10 minus 5 times 2, giving 0 degrees at the summit. Between the condensation level and the summit the parcel has been raining out its moisture.
• 3 km down to sea level on the lee side. The parcel is no longer saturated, because it lost its water on the way up, so it warms at the dry rate for the whole descent: 0 plus 10 times 3, giving 30 degrees.

The parcel left the coast at 20 degrees and arrives on the far side at 30 degrees, having lost most of its water. That 10 degree gain is the latent heat released on the windward side, now carried down as sensible heat. This is the mechanism of the foehn of the Alps, the chinook of the eastern Rockies, and the Santa Ana of southern California. Chinook winds have raised temperatures by more than 20 degrees Celsius in a few hours, and the same physics is why the fire weather of the American West arrives with offshore downslope flow.

Turning weather records into a map of climate

Individual weather is not climate. Climate is the statistical description of weather over a standard period, conventionally 30 years, including its variability and extremes and not only its averages. Turning those statistics into a world map requires a classification, and the one still in use was built by a botanist.

Wladimir Koppen published his first version in 1884 and the mature form around 1900, later revised with Rudolf Geiger. His governing idea was elegant: rather than drawing arbitrary lines through temperature and rainfall, use the boundaries that vegetation already draws, since plants integrate the whole climate including its seasonality and extremes. Then work backwards to find the temperature and precipitation thresholds that coincide with those vegetation limits.

Group	Name	Defining criterion	Example
A	Tropical	Every month averages 18 degrees Celsius or warmer	Singapore (Af), Mumbai (Aw)
B	Dry	Precipitation below a threshold set by temperature and rainfall seasonality	Cairo (BWh), Denver (BSk)
C	Temperate	Coldest month between 0 and 18 degrees Celsius	London (Cfb), Rome (Csa)
D	Continental	Coldest month below 0, warmest above 10	Chicago (Dfa), Moscow (Dfb)
E	Polar	Warmest month below 10 degrees Celsius	Barrow (ET), Vostok (EF)

The B group is the interesting one, because it is defined differently from all the others. Groups A, C, D and E are thermal: they ask how warm it is. Group B is defined by a comparison between precipitation received and precipitation needed, so a place is dry if it loses more water to evaporation than it gains from rain. That threshold rises with temperature, because warmer air evaporates more. The consequence is that 400 millimetres a year makes a semi-arid steppe in hot Texas and a comfortably humid climate in cool Ireland. Aridity is a ratio, never an amount, and this is the single most useful thing the Koppen system teaches.

Within B, the split is arithmetic: below half the threshold is BW, a true desert; between half and the full threshold is BS, a steppe or semi-arid climate. A third letter, h or k, marks hot or cold varieties.

Bottom line: A climate is dry when evaporative demand exceeds supply, which is why the same rainfall total can describe a desert in one place and a pasture in another.

Where the classification creaks

Koppen's scheme has survived 140 years because it is simple and because its categories match things people can see. It has real limits, and knowing them is part of using it well.

It is built on monthly means, so it is nearly blind to variability, and two stations with identical monthly averages can have completely different growing seasons if one gets its rain in reliable weekly increments and the other in three storms. Its boundaries are drawn as hard lines through what are actually gradients. Its vegetation logic is partly circular, since it uses vegetation to define climate and is then used to explain vegetation. And it says nothing about soils, which often matter more to what grows than the last few millimetres of rainfall.

Alternatives address some of these. Thornthwaite's system, from 1948, works from a water balance, computing potential evapotranspiration explicitly rather than approximating it. Modern classifications built from gridded reanalysis data give finer resolution than the sparse station network Koppen had. And because the thresholds are fixed while the climate is not, mapping Koppen zones for different decades makes shifts visible: comparisons of recent decades against the mid-twentieth century show substantial areas reclassified, mostly poleward and mostly out of colder groups into warmer ones.

Common misconceptions

• Deserts are defined by being hot. They are defined by aridity. Antarctica is a desert, and much of the Gobi is a cold desert with winter temperatures below minus 30 degrees Celsius.
• Deserts are places where the air is dry. On the Atacama and Namib coasts the air is often at saturation, with fog most mornings. What is missing is ascent, not moisture.
• All deserts are made the same way. Four independent mechanisms operate, and the Atacama runs on three of them at once.
• Air on the lee side of a mountain is cooler because it has lost its heat as rain. It arrives warmer than it started, because the latent heat released during windward condensation is carried over and reappears as sensible heat during the dry descent.
• A given rainfall total tells you whether a place is arid. Only relative to evaporative demand. Four hundred millimetres is steppe in Texas and humid in Ireland.

What to remember

• Three circulation cells per hemisphere move heat poleward and set the surface wind belts; rain follows ascent and drought follows descent.
• The subtropical highs at 20 to 35 degrees are the descending limb of the Hadley cell, and they put a desert belt around the planet on every continent that reaches them.
• The other three desert mechanisms are rain shadow, cold coastal current with inversion, and continentality, each with a diagnostic signature.
• Air crossing a range cools at 10 degrees per kilometre while unsaturated and about 5 while raining, then warms at 10 all the way down, arriving hotter and drier than it began.
• Koppen's classification uses vegetation boundaries to fix thermal thresholds, but defines its dry group by the ratio of precipitation to evaporative demand rather than by an amount.
• The scheme is blind to variability and draws hard lines through gradients, and its fixed thresholds make climate shifts visible when it is remapped decade by decade.

Sources

1. Beck, H. E., Zimmermann, N. E., McVicar, T. R., Vergopolan, N., Berg, A., and Wood, E. F. (2018). Present and future Koppen-Geiger climate classification maps at 1-km resolution. Scientific Data, 5, 180214. doi.org
2. National Centers for Environmental Information. (n.d.). Climate data and normals. NOAA. ncei.noaa.gov
3. National Park Service. (n.d.). Death Valley National Park: Weather and climate. nps.gov
4. Encyclopaedia Britannica. (n.d.). Desert. britannica.com

Twenty percent of all river water, from one river

The Amazon delivers roughly 209,000 cubic metres of water to the Atlantic every second. That single river carries something like a fifth of all the fresh water that all the world's rivers deliver to all the world's oceans. Its discharge is greater than the next seven largest rivers combined, and the plume of fresh water it pushes offshore is detectable in surface salinity hundreds of kilometres out to sea.

Numbers like that make rivers feel like the main event in the water cycle. They are not. Every river on Earth, at any instant, holds about two thousandths of one percent of the planet's fresh water. Rivers are conspicuous because water moves through them fast, not because much water is in them. Understanding that distinction, between how much of something there is and how quickly it turns over, is the first move in hydrology and the organising idea of this lesson.

The budget, and the far more useful second column

Start with the stocks. Of all the water on Earth, about 96.5 percent is ocean salt water. Of the small remainder that is fresh, roughly 69 percent is locked in glaciers and ice caps, about 30 percent is groundwater, and everything else, all lakes, all soil moisture, all wetlands, all atmospheric vapour and every river, shares just over 1 percent of the fresh water. Rivers alone hold about 0.006 percent of the fresh total.

Now add the second column, which is residence time: the average length of time a water molecule stays in a reservoir, calculated as the volume in storage divided by the rate of throughput.

Reservoir	Share of all water	Typical residence time	What that implies
Oceans	About 96.5 percent	Roughly 3,000 years	Enormous thermal and chemical inertia; changes are slow but very hard to reverse
Glaciers and ice sheets	Roughly 1.7 percent of all water	Decades to hundreds of thousands of years	An archive of past climate, and a slow but enormous contributor to sea level
Groundwater	Roughly 1.7 percent of all water	Days near a stream to tens of thousands of years in deep aquifers	Some of it is effectively non-renewable on human timescales
Atmosphere	About 0.001 percent	Roughly 9 days	Tiny stock, colossal flux; the whole atmospheric store is replaced about 40 times a year
Rivers	About 0.0002 percent	Weeks to months	Fast turnover makes them responsive, and therefore the visible face of drought and flood

Global precipitation runs at roughly half a million cubic kilometres a year. Most of it falls straight back into the ocean it evaporated from. The land receives more precipitation than it evaporates, and the surplus, on the order of 40,000 cubic kilometres a year, returns to the sea as river flow and groundwater discharge. That surplus is the entire renewable freshwater resource of the planet, and every river in this lesson is a piece of it in transit.

So what?: A reservoir's importance is set by its flux, not its volume. The atmosphere holds almost no water and moves nearly all of it.

The drainage basin as the unit of analysis

Hydrology does not work in political units. It works in the drainage basin, also called a watershed or catchment: all the land from which water drains to a single outlet, bounded by a divide along the ridge line. Basins nest. The Ohio basin sits inside the Mississippi basin; a hillslope gully sits inside a first-order stream's catchment.

The Mississippi basin drains about 3.2 million square kilometres, roughly 41 percent of the land area of the contiguous United States, taking water from 31 states and two Canadian provinces to one outlet below New Orleans. That is why an agricultural decision in Iowa becomes a water quality problem in the Gulf of Mexico: the basin, not the state, is the connected system.

Basins are described by measurable properties. Stream order, in the scheme Arthur Strahler set out in 1952, numbers the smallest unbranched headwater channels as first order; where two first-order streams join they make a second order, and only the meeting of two channels of equal order raises the order. This has a useful consequence: order rises slowly, so the Mississippi is only about tenth order, and first-order streams make up the great majority of total channel length in any basin. Whatever happens in headwater streams happens to most of the river network.

Drainage density, total channel length divided by basin area, measures how finely dissected a landscape is. It is high on impermeable shales and clays where water cannot infiltrate, and low on permeable sandstone or fractured basalt where it can. Drainage pattern reflects underlying structure: a branching dendritic pattern over uniform rock, a trellis pattern where alternating hard and soft beds have been folded, a radial pattern off a volcano, a rectangular pattern where joints and faults control the channels. Read a drainage map and you are partly reading the geology beneath it.

Measuring a river, step by step

Discharge is the volume of water passing a cross-section per unit time, and it is calculated from two things you can measure with a tape and a current meter. Discharge equals cross-sectional area multiplied by mean velocity.

Work an example. A stream is 30 metres wide, with a mean depth of 1.5 metres and a mean velocity of 0.8 metres per second. Area is 30 times 1.5, that is 45 square metres. Discharge is 45 times 0.8, which is 36 cubic metres per second. In practice a hydrographer does not use one mean depth and one mean velocity; the channel is divided into perhaps twenty vertical sections, each measured separately, and the results summed, because velocity varies enormously across a channel, being fastest just below the surface near the centre and near zero against the bed and banks.

Nobody wades into a river in flood, so gauging stations do it differently. Many careful discharge measurements at different water levels build a rating curve, a relationship between stage, which is the water surface height, and discharge. After that the station only has to record stage, which a pressure sensor does continuously and cheaply, and discharge is read off the curve. The United States Geological Survey runs a national network of streamgages on this principle, with data published in near real time, and that network is the raw material for almost every flood forecast, water supply decision and river restoration design in the country.

The caution worth knowing is that rating curves fail at the extremes. A flood larger than any measured flow requires extrapolating the curve past its data, and a flood that rearranges the channel bed invalidates the curve entirely. The largest and most consequential discharges are the least reliably measured, which is a general feature of extreme events and not just a river problem.

The hydrograph, and what a parking lot does to it

Plot discharge against time through a storm and you get a storm hydrograph. Rain begins; discharge stays flat for a while as water infiltrates and fills depressions; then the rising limb climbs steeply; discharge reaches a peak some time after peak rainfall, and that delay is the lag time; then a long recession limb falls away as the basin drains, eventually settling back to baseflow, the groundwater-fed component that keeps a stream running between storms.

The shape encodes the basin. A steep, small, impermeable, sparsely vegetated basin gives a short lag and a high sharp peak, called a flashy response. A large, flat, permeable, forested basin gives a long lag and a broad low peak. Now urbanise it. Roofs, roads and car parks are impervious, so infiltration collapses and overland flow rises. Storm drains replace the slow overland path with a fast pipe. Both changes push the same direction: shorter lag, higher peak, and a lower baseflow afterwards, because the groundwater that used to be recharged never got into the ground. The same rainfall on the same land produces a substantially larger flood after development than before, which is why stormwater detention is required by ordinance in most jurisdictions.

Key idea: Land cover changes the hydrograph without changing the rainfall. Most of what we call a flood problem is a runoff problem.

What the water carries

A river moves three kinds of load. Dissolved load is material in solution, invisible, and often the largest component in a chemically weathered humid basin. Suspended load is fine sediment held up by turbulence, and it is what makes a river brown. Bed load is coarse material rolling, sliding and bouncing along the bottom, a small fraction of the total mass but responsible for most of the abrasion that cuts a channel.

Two terms are often confused. Competence is the largest particle a river can move, and it depends on velocity, rising very steeply with it. Capacity is the total quantity it can carry, and it depends mostly on discharge. A small fast mountain stream has high competence and low capacity: it rolls boulders but carries little total sediment. A large slow lowland river is the reverse.

There is a genuine surprise in the erosion data, summarised in the curve Filip Hjulstrom published in 1935. You might expect finer particles to be easier to lift, all the way down. They are not. Sand of about 0.2 to 0.5 millimetres is entrained at the lowest velocity of anything. Finer silts and clays need higher velocities to erode, because their flat particles pack tightly and are held by electrostatic cohesion. That is why a clay bank stands in a current that is stripping sand from beside it, and why once fine sediment is suspended it stays suspended almost indefinitely, since the velocity needed to keep it moving is very much lower than the velocity needed to lift it.

Why rivers refuse to run straight

Leave a river alone on an alluvial floodplain and it will not run straight for long. Any slight bend concentrates the fastest thread of flow against the outer bank, where velocity and turbulence are highest, so the outer bank is eroded into a steep cut bank. Flow on the inner side is slower, so sediment is deposited as a point bar. Erosion outside and deposition inside means the bend migrates sideways and grows more curved, which increases the effect. The feedback is self-reinforcing, and the resulting meanders settle into a remarkably consistent geometry: meander wavelength is typically ten to fourteen times channel width, across rivers spanning six orders of magnitude in size.

Eventually a meander loop grows so tight that the river cuts across its neck in a flood and abandons the loop, leaving an oxbow lake. Meander migration and cutoff are what build a floodplain: the river sweeps across its valley, reworking sediment, and overbank flows deposit fine material and build natural levees along the channel edges.

Not every river meanders. A braided channel, a network of shifting bars and shallow threads, forms where sediment supply is high, banks are non-cohesive and discharge is highly variable, which describes the outwash rivers in front of glaciers exactly. Change the sediment supply or bank strength and the same river changes pattern, which is why braiding and meandering are best read as responses to conditions rather than as types of river.

Reading a flood correctly

One piece of vocabulary causes more public confusion than anything else in hydrology. A 100-year flood is not a flood that happens once a century. It is a flood with a 1 percent probability of being equalled or exceeded in any given year, estimated by fitting a statistical distribution to the annual maximum discharges on record. Two of them can occur in consecutive years without anything being unusual, because the events are treated as independent draws.

Over a 30 year mortgage, the probability of experiencing at least one 1 percent flood is one minus 0.99 raised to the thirtieth power, which is about 26 percent. That is the number a homeowner actually needs, and it is nothing like the intuition the phrase creates. The estimates also assume the statistics are stationary, meaning the underlying distribution is not changing, and both land use change and climate trends undermine that assumption. Modern practice increasingly reports the annual exceedance probability directly and updates it, rather than repeating a recurrence interval that invites the wrong reading.

Common misconceptions

• A 100-year flood happens once a century. It has a 1 percent annual chance, so two in successive years is unremarkable, and the chance of at least one in 30 years is about 26 percent.
• Rivers hold most of the world's fresh water. They hold about 0.006 percent of it. Their importance comes from flux, not storage.
• Finer sediment is always easier to erode. Sand entrains at the lowest velocity; clays resist erosion because they are cohesive, even though they stay suspended once lifted.
• Rivers erode fastest on the inside of a bend, where the water piles up. The opposite: the fastest thread swings to the outer bank, cutting it back, while the slower inner side builds a point bar.
• Building in a floodplain is safe once a levee is there. Levees raise the threshold rather than removing the hazard, and by encouraging development behind them they can raise the damage from the flood that eventually overtops or breaches them.

Pulling it together

• Water is overwhelmingly stored in the ocean and in ice, but the atmosphere, with a nine day residence time, does nearly all the moving.
• The drainage basin is hydrology's working unit; stream order, drainage density and drainage pattern describe it and reflect the geology beneath it.
• Discharge equals cross-sectional area times mean velocity, and gauging stations convert continuously measured stage into discharge through a rating curve that is least reliable at the extremes.
• The storm hydrograph's lag and peak encode basin properties, and impervious cover shortens the lag, raises the peak and lowers baseflow without altering the rainfall.
• Rivers carry dissolved, suspended and bed load; competence depends on velocity and capacity on discharge, and cohesive clays resist erosion more strongly than sand.
• Meanders arise from a self-reinforcing outer-bank erosion feedback with wavelengths ten to fourteen times channel width, and a 100-year flood is a 1 percent annual probability, not a schedule.

Sources

1. United States Geological Survey. (n.d.). Water Science School. usgs.gov
2. United States Geological Survey. (n.d.). National Water Information System: Web interface. waterdata.usgs.gov
3. United States Geological Survey. (n.d.). Water Resources Mission Area. usgs.gov
4. Leopold, L. B., Wolman, M. G., and Miller, J. P. (1964). Fluvial processes in geomorphology. W. H. Freeman and Company.

A water table that has been falling since 1950

The High Plains aquifer, of which the Ogallala Formation is the largest part, underlies about 450,000 square kilometres beneath parts of eight states from South Dakota to Texas. It supplies close to 30 percent of all the groundwater used for irrigation in the United States, and the centre-pivot circles you see from an aeroplane over Nebraska and Kansas are drawing on it right now.

The United States Geological Survey has tracked its water levels since large-scale pumping began around 1950. Averaged across the whole aquifer, the water table has fallen about 16 feet. Averages hide the problem. In parts of the Texas Panhandle and southwestern Kansas the decline exceeds 150 feet, and some wells that once produced have been abandoned because the saturated thickness beneath them no longer supports a pump.

Here is the question that organises this lesson. Rain falls on Kansas every year. Why does pumping deplete an aquifer at all, rather than simply drawing on an annually renewed supply? Answering that properly requires understanding how water is stored underground, how fast it actually moves, and why some of the water in the southern High Plains fell as rain during the last ice age and has not been replaced since.

Two properties that sound the same and are not

Every rock and sediment has void space. Porosity is the percentage of a material's volume that is void, and it measures how much water the material can hold. Permeability is the ease with which fluid moves through the connected voids, and it measures how much water the material will actually give up.

These come apart dramatically, and the divergence is the single most important fact in groundwater geology. Clay can have a porosity of 50 percent or more, higher than most sandstone, because its platy particles pack loosely. But the pores between clay particles are microscopic, poorly connected, and their walls hold water by molecular attraction that a pump cannot overcome. Clay stores a great deal of water and yields almost none. Well-sorted sand and gravel, by contrast, have porosity around 25 to 35 percent and large, well-connected pores, so they yield water freely.

This distinction sorts the subsurface into two categories. An aquifer is a body of rock or sediment permeable enough to supply useful quantities of water: sand and gravel, porous sandstone, fractured limestone, jointed basalt. An aquitard restricts flow: shale, unfractured igneous rock, and above all clay.

The point: How much water a formation holds and how much it will give you are different questions with different answers, and confusing them is how dry wells get drilled.

The water table and what sits above it

Dig down through soil and you pass through the zone of aeration, where the pores hold both air and water, water clinging as films around the grains. This is where plant roots draw from and where a contaminant spill first sits. Below it is the zone of saturation, where every pore is full of water. The boundary between the two is the water table, marked in a well by the level the water stands at.

The water table is not flat. It is a subdued replica of the land surface above it: higher under hills, lower under valleys, because recharge on the hills adds water faster than it can drain sideways. Where the land surface cuts below the water table you get a spring, a lake, a wetland or a gaining stream, one fed by groundwater and therefore able to run between storms. This is the baseflow of the previous lesson, and it is why an aquifer decline eventually shows up as a dry creek even where nobody pumped from the creek.

An unconfined aquifer is open to the surface, so its upper limit is the water table and it recharges directly from above. A confined aquifer is sandwiched between aquitards, recharged only where its permeable layer reaches the surface, sometimes hundreds of kilometres away. Water in a confined aquifer is under pressure, so when a well penetrates the confining layer, water rises above the top of the aquifer to the level of the potentiometric surface. If that level is above the ground, the well flows without pumping, and it is called artesian, after the province of Artois in France. The Great Artesian Basin of Australia, covering more than 1.7 million square kilometres, is the classic example, and the pastoral settlement of inland Australia depended on it.

How fast does groundwater actually move?

Henry Darcy, working on the municipal water supply of Dijon, published in 1856 the experimental relationship that still governs the subject. Flow through a porous medium is proportional to the cross-sectional area and to the hydraulic gradient, which is the drop in head divided by the distance over which it drops, with a constant of proportionality called hydraulic conductivity that describes the material.

Put numbers to it. Take a gravel aquifer with hydraulic conductivity of 10 metres per day, a hydraulic gradient of 0.01, meaning the water table falls one metre every hundred metres, and a cross-section 100 square metres in area. Discharge is conductivity times area times gradient: 10 times 100 times 0.01, which is 10 cubic metres per day through that cross-section.

Now convert that to a velocity, which is the number people find startling. Divide the flux per unit area by the porosity, because the water is only moving through the void fraction, not the whole rock. Ten metres per day times 0.01 gives 0.1 metres per day of specific discharge; divide by a porosity of 0.25 and the actual water velocity is 0.4 metres per day, or about 146 metres a year. And that is a good aquifer. In fine sand it might be a few metres a year; in clay, centimetres per century.

Two consequences follow immediately. First, a contaminant that reaches groundwater will still be there decades later, and will move as a slow plume rather than flushing out. Second, and this answers the question that opened the lesson, recharge in the southern High Plains is measured in a few millimetres a year, because the climate is semi-arid and the shallow subsurface is often capped by low-permeability material. Water pumped out at rates set by irrigation demand cannot be replaced at rates set by Darcy's law and a dry climate. Radiocarbon dating of water from parts of the aquifer gives ages in the thousands of years. It is fossil water, recharged under wetter Pleistocene conditions, and pumping it is mining, not harvesting.

What pumping does to the ground itself

Pumping a well lowers the water table around it into a cone of depression, steep near the well and flattening outward. Two wells close together interfere, each deepening the other's cone, which is why well spacing is regulated. Sustained regional pumping merges thousands of cones into a regional decline.

There are three further consequences, all documented at scale.

• Land subsidence. Water in the pores of a compressible aquitard helps carry the weight of everything above. Remove it and the clay compacts, permanently. In California's San Joaquin Valley, subsidence near Mendota reached about 8.5 metres between the 1920s and the 1970s, a figure documented by the USGS in a famous photograph of a pole marked with successive land surface levels well above a person's head. The compaction is largely irreversible: the storage capacity is destroyed along with the elevation.
• Saltwater intrusion. In coastal aquifers, fresh groundwater floats on denser salt water, and the interface sits well below sea level. Lower the freshwater head by pumping and the interface rises, salting wells that were fresh. Recovery, if it happens, takes decades.
• Loss of baseflow. Because gaining streams are the surface expression of the water table, regional decline reduces or ends the flow of springs and small streams, converting perennial channels to ephemeral ones.

Where the rock dissolves

One landscape type breaks most of the rules just described, and about a quarter of the world's population drinks from it. Karst develops where soluble rock, usually limestone, is dissolved by slightly acidic water.

The chemistry is simple and worth carrying. Rainwater absorbs carbon dioxide from the air and much more from soil, where root respiration and decay raise concentrations far above atmospheric. Dissolved carbon dioxide forms weak carbonic acid. Carbonic acid attacks calcium carbonate to make calcium bicarbonate, which is soluble and is carried away. Limestone does not crumble; it disappears into solution, molecule by molecule, along whatever fractures the water can reach.

Because the process widens the fractures it uses, it is self-accelerating. A hairline joint becomes a millimetre channel, which carries more water, which dissolves faster, which becomes a passage, which becomes a cave. Mammoth Cave in Kentucky, the longest known cave system on Earth, has more than 400 miles of surveyed passage, all of it dissolved out of Mississippian limestone beneath a protective sandstone cap.

The surface landscape that results is distinctive: closed depressions called sinkholes, streams that disappear underground at swallow holes, dry valleys, large springs where the water re-emerges, and in the tropics, residual towers left where dissolution has removed everything around them. Inside the caves, water that has dissolved limestone loses carbon dioxide as it drips into air-filled passages, so calcite comes back out of solution and builds speleothems. Their layered growth records past rainfall and temperature, which makes them valuable climate archives.

Remember: Karst water does not seep through pores, it runs through conduits. That single difference reverses most of the safety assumptions people carry about groundwater.

In a normal porous aquifer, water travels metres per year through small pores, and that slow passage filters out bacteria and adsorbs many contaminants. In karst, water can move kilometres per day through open conduits, with almost no filtration. A spill at a sinkhole can reach a spring used for drinking water within hours, still carrying its bacteria and its sediment. Dye tracing, in which harmless fluorescent dye is introduced at a sinkhole and monitored at springs, routinely shows connections nobody would have predicted from surface topography, because the underground drainage divide need not follow the surface one. Karst also produces sudden collapse: a cavity roof weakened by dissolution can fail without warning, and in central Florida such collapses swallow roads and buildings, most spectacularly at Winter Park in 1981.

Common misconceptions

• Groundwater flows in underground rivers. Except in karst conduits it moves through pore spaces at centimetres to metres per day. The image of a subterranean river is wrong nearly everywhere.
• Clay holds no water because it is impermeable. Clay has very high porosity and holds a great deal of water. It simply will not yield it, which is a different property.
• Artesian means the water is especially pure or comes from great depth. It means the potentiometric surface stands above the top of the aquifer, so water rises without pumping. It says nothing about quality.
• An aquifer refills as soon as it rains. Recharge rates are set by climate and by the permeability of the shallow subsurface; parts of the southern High Plains hold water thousands of years old and receive a few millimetres a year.
• Land that subsides from pumping will rise again if pumping stops. Compaction of clay layers is largely permanent, and the lost storage capacity does not come back.

The takeaway

• Porosity measures how much water a material holds; permeability measures how much it will yield, and clay scores high on the first and near zero on the second.
• The water table is a subdued replica of the topography, and where the land cuts below it you find springs, wetlands and gaining streams.
• Confined aquifers carry pressure, so wells rise to the potentiometric surface and flow unaided where that surface is above ground.
• Darcy's law gives flux from conductivity, area and hydraulic gradient; dividing by porosity converts it to real velocity, typically well under a metre a day.
• Because recharge is slow and pumping is fast, parts of the High Plains aquifer are being mined rather than harvested, with regional declines exceeding 150 feet and irreversible subsidence elsewhere.
• Karst aquifers move water through dissolved conduits at kilometres per day with almost no filtration, which makes them productive, valuable and unusually easy to contaminate.

Sources

1. United States Geological Survey. (n.d.). Water Science School: Groundwater. usgs.gov
2. United States Geological Survey. (n.d.). Water Resources Mission Area. usgs.gov
3. National Park Service. (n.d.). Mammoth Cave National Park. nps.gov
4. Encyclopaedia Britannica. (n.d.). Karst. britannica.com
5. Ford, D. C., and Williams, P. W. (2007). Karst hydrogeology and geomorphology (revised edition). John Wiley and Sons.

The highest tide on Earth

At Burntcoat Head in the Minas Basin, at the far end of the Bay of Fundy in Nova Scotia, the difference between low water and high water reaches about 16 metres. Boats sit on mud in the morning and float five storeys higher by afternoon. Three hundred kilometres away in the open Atlantic, the same tidal forcing produces a range of roughly a metre. The Moon does not pull harder on Nova Scotia.

The difference is resonance, and getting to it will take us through the whole physical ocean: the currents that carry the planet's heat, the wind-driven upwelling that feeds a fifth of the world's fisheries, the waves that shape every coast, and finally the tides. The Atlas course on oceanography goes deeper on marine chemistry and biology; here the interest is the ocean as a component of the physical geography of the land it touches.

The setting: a layered, salty, mostly cold ocean

Seawater covers about 71 percent of Earth's surface to an average depth of roughly 3,700 metres. Average salinity is about 35 grams of dissolved salt per kilogram of water, varying from around 40 in the evaporation-dominated Red Sea to about 10 in the river-fed Baltic. Sodium and chloride dominate, but the proportions of the major ions are essentially constant everywhere, which tells you the ocean is thoroughly mixed on timescales shorter than the residence times of its salts.

Vertically, the ocean is layered by density, and density is set by temperature and salinity together, which is why the deep circulation is called thermohaline. A wind-stirred mixed layer, tens to a couple of hundred metres thick, sits on top. Below it the thermocline is a zone of rapid temperature decrease, and it acts as a barrier to vertical exchange. Beneath the thermocline lies the deep ocean, which is uniformly cold, between about 0 and 4 degrees Celsius, everywhere on Earth including under the tropics. More than 90 percent of ocean water sits below the thermocline in that cold, dark, slow-moving mass.

Gyres, and why the western side is different

Surface currents are driven by wind, modified by the Coriolis effect, and steered by continents. The trade winds push water westward in the tropics; the mid-latitude westerlies push it eastward at 40 degrees; continents block the flow at both ends. The result is a closed loop in each ocean basin, a subtropical gyre, turning clockwise in the northern hemisphere and anticlockwise in the southern. There are five major ones.

Gyres are not symmetric, and the asymmetry is dramatic. Look at the North Atlantic. On the eastern side, the Canary Current is broad, slow, shallow and cool, spread over hundreds of kilometres and drifting at a few centimetres per second. On the western side, the Gulf Stream is narrow, deep, warm and fast, confined to under a hundred kilometres and running at more than two metres per second.

This western intensification happens because the Coriolis parameter increases with latitude rather than being constant. The consequence, worked out by Henry Stommel in 1948, is that the return flow required to close the gyre is compressed against the western boundary. Every ocean shows it: the Kuroshio off Japan, the Agulhas off southeast Africa, the Brazil Current, the East Australian Current.

The transport involved is difficult to intuit. Since 1982 a submarine telephone cable across the Florida Straits has measured the Florida Current continuously through the voltage its flow induces, and the mean transport is about 30 million cubic metres per second. That is roughly twenty-five times the combined discharge of every river on Earth, in one strait, all the time. Downstream the Gulf Stream entrains more water still. That flow carries tropical heat northeast, and it is a substantial part of the reason northwest Europe is warmer than its latitude would suggest.

In short: Western boundary currents are the ocean's express lanes, narrow and fast because the Coriolis parameter varies with latitude, and they carry a large share of the planet's poleward heat transport.

Ekman transport, upwelling, and a fifth of the world's fish

Wind blowing over water does not push the water straight downwind. Vagn Walfrid Ekman worked out why in 1905, after Fridtjof Nansen noticed that Arctic sea ice drifted 20 to 40 degrees to the right of the wind. Surface water is dragged by the wind and deflected by the Coriolis effect; the layer below is dragged by the surface layer and deflected again; and so on downward, tracing an Ekman spiral. Integrated over the whole affected depth, the net Ekman transport is 90 degrees to the right of the wind in the northern hemisphere, and 90 degrees to the left in the southern.

Now apply that to a coast. Along the coast of Peru, in the southern hemisphere, the prevailing wind blows equatorward, roughly parallel to the shore. Ekman transport is 90 degrees to the left of the wind, which points away from the land. Surface water is pushed offshore, and water must rise from below to replace it. That is coastal upwelling.

What rises is cold, and, far more importantly, it is loaded with nitrate and phosphate, because the deep water has accumulated the nutrients released by sinking organic matter over centuries. Delivering those nutrients into the sunlit surface layer supports enormous phytoplankton growth and everything above it in the food web. The four great eastern boundary upwelling systems, off Peru and Chile, California, northwest Africa and Namibia, occupy well under 1 percent of ocean area and yield roughly a fifth of the global marine fish catch. It is also why those same coasts are foggy deserts: the cold water creates the inversion described two lessons ago.

Why this matters: The wind does not have to blow offshore to drive upwelling. Alongshore wind is enough, because Ekman transport turns it. That one rotation supports some of the most productive water on the planet.

When the upwelling stops

Every few years the trade winds across the tropical Pacific weaken. Warm surface water that they normally pile up in the western Pacific slides back east; the thermocline, normally shallow off South America and deep near Indonesia, flattens; and the water upwelling off Peru is drawn from above the thermocline, which means it is warm and nutrient-poor. Fisheries collapse. Peruvian fishermen named the phenomenon El Nino because it typically peaked around Christmas.

The atmospheric half of the same system, the seesaw in surface pressure between the eastern and western tropical Pacific, is the Southern Oscillation, and the coupled phenomenon is now called ENSO. Its effects reach far beyond Peru through atmospheric teleconnections: shifted storm tracks, drought in Australia and Indonesia, heavy rain along the coast of Ecuador and in the southern United States, altered Atlantic hurricane activity. The opposite phase, La Nina, exaggerates the normal pattern instead. The strong events of 1982 to 1983, 1997 to 1998 and 2015 to 2016 are the reference cases, and ENSO is the single largest source of year-to-year climate variability on Earth after the seasons themselves.

The deep circulation, on a thousand-year clock

Below the wind-driven surface layer, the ocean turns over on a completely different timescale. In the Nordic and Labrador Seas, surface water is cooled by frigid air and made saltier still by sea ice formation, which expels salt as it freezes. It becomes dense enough to sink, forming North Atlantic Deep Water, which flows south at depth through the Atlantic. Around Antarctica the same process produces the even denser Antarctic Bottom Water. That sinking water eventually mixes upward elsewhere in the world ocean and returns as surface flow, a circuit taking on the order of a thousand years.

The Atlantic branch of this system, the Atlantic Meridional Overturning Circulation, has been monitored continuously since 2004 by a moored array across the Atlantic at about 26 degrees north. It matters to physical geography for two reasons: it carries heat northward on top of what the Gulf Stream does at the surface, and its strength depends on the density of high-latitude surface water, which fresh meltwater reduces. That dependence is why the paleoclimate record contains abrupt regional temperature swings associated with meltwater pulses, and why the circulation's future behaviour is closely watched.

Waves: what actually moves

Wind waves grow with three things: wind speed, the duration the wind blows, and fetch, the distance of open water over which it blows. A gale on a small lake cannot build a big sea because the fetch is too short.

The crucial physical point is that a water wave transmits energy, not water. A parcel of water in a deep-water wave travels in a circular orbit and returns close to where it started, which is why a floating gull rises and falls but does not travel with the crest. Those orbits shrink with depth, becoming negligible below about half the wavelength, a depth called the wave base. Below wave base, a passing storm does nothing.

When the wave reaches water shallower than half its wavelength, the orbits touch bottom and are flattened into ellipses. Friction slows the wave, the wavelength shortens, and because the energy has to go somewhere the height grows. The crest steepens until the front face can no longer support itself, and the wave breaks, generally when height is roughly four fifths of the water depth. That is the entire life of a wave from generation to surf, and it is why surf zones sit where they do.

Two consequences shape coastlines. Wave refraction: because a wave slows in shallow water, a crest approaching at an angle bends toward the shallows. Off a headland, where the sea floor shoals early, wave energy is focused; in the bay next door it is spread out. Headlands are therefore attacked hardest and bays accumulate sediment, and over time an irregular coast is straightened. Longshore drift: waves that still arrive at an angle after refraction push water and sediment obliquely up the beach face, while the backwash runs straight down the slope. Repeat a few thousand times a day and sand migrates steadily along the shore, sometimes tens of thousands of cubic metres a year. Interrupt that current with a groyne or a jetty and sand accumulates on the updrift side while the downdrift beach starves, which is the origin of a large fraction of the world's coastal engineering disputes.

Tides, and why Fundy

Tides come from gravity acting differentially. The Moon pulls hardest on the near side of Earth, less on the centre, and least on the far side. Working in the Earth-Moon system's rotating frame, that difference produces a bulge of water on the side facing the Moon and, from the same asymmetry, a second bulge on the opposite side. Earth rotates through both, giving most coasts two high tides and two low tides in about 24 hours and 50 minutes, the extra 50 minutes accounting for the Moon's own motion along its orbit.

The Sun does the same thing with about 46 percent of the Moon's tide-raising force, being far more massive but very much farther away. When Sun, Earth and Moon line up at new and full moon, the two effects add and produce the large spring tides. At first and last quarter they partly cancel, giving the smaller neap tides. The cycle takes about 14 days, and it has nothing to do with the season, despite the name.

None of that explains 16 metres. Range depends on the shape of the basin the tide enters. In a funnel-shaped bay that narrows and shallows, the same volume of water is squeezed into a smaller cross-section, so it must rise higher. Beyond that, if the natural period of oscillation of the basin is close to the roughly 12.4 hour tidal period, the basin resonates, and each tidal push reinforces the last. The Bay of Fundy has almost exactly that natural period. The Bristol Channel and Ungava Bay do too, and they show comparable ranges. Meanwhile a nearly enclosed basin like the Mediterranean, too small to develop its own tide and connected only through a narrow strait, has ranges of a few tens of centimetres. Tidal range is a property of the coast, not of the Moon.

Common misconceptions

• Water travels along with a wave. Water parcels move in closed orbits and stay put; only energy propagates. The wave that reaches your beach did not bring water from the storm.
• Tides are high because the Moon is overhead. There are two bulges, one facing the Moon and one on the opposite side, so a high tide occurs when the Moon is overhead and again when it is underfoot.
• Spring tides happen in spring. They occur twice a month, at new and full moon, when solar and lunar forcing align.
• Upwelling requires wind blowing off the land. Alongshore wind is enough, because Ekman transport acts at 90 degrees to the wind.
• The Gulf Stream is what keeps Europe mild, on its own. Ocean heat transport contributes, but atmospheric transport and the prevailing westerlies bringing maritime air across the Atlantic account for a large share of the effect.

Summing up

• The ocean is layered by density, with a wind-mixed surface layer over a thermocline and a cold deep mass that holds more than 90 percent of the water.
• Wind, Coriolis and continents organise surface flow into five subtropical gyres, and western intensification makes the western boundary currents narrow, deep and fast, with the Florida Current alone moving about 30 million cubic metres per second.
• Ekman transport at 90 degrees to the wind turns alongshore wind into coastal upwelling, and the four eastern boundary upwelling systems supply roughly a fifth of the world fish catch from under 1 percent of ocean area.
• ENSO is the coupled ocean-atmosphere oscillation that shuts that upwelling down every few years and reorganises weather across much of the planet.
• Waves transmit energy through orbital motion, break when height reaches about four fifths of depth, refract to concentrate energy on headlands, and drive longshore drift that coastal structures interrupt.
• Tides arise from differential gravity with two bulges, vary on a fortnightly spring and neap cycle, and reach 16 metres in the Bay of Fundy because the basin resonates at the tidal period.

Sources

1. National Oceanic and Atmospheric Administration. (n.d.). National Ocean Service education. oceanservice.noaa.gov
2. NOAA Atlantic Oceanographic and Meteorological Laboratory. (n.d.). Western boundary current observations. aoml.noaa.gov
3. NOAA Center for Operational Oceanographic Products and Services. (n.d.). Tides and currents. tidesandcurrents.noaa.gov
4. National Aeronautics and Space Administration. (n.d.). Sea level change portal. sealevel.nasa.gov
5. Stommel, H. (1948). The westward intensification of wind-driven ocean currents. Transactions, American Geophysical Union, 29(2), 202-206.

Two dates and five hundred kilometres

The shield-building lavas of Kauai date to roughly 5.1 million years ago. Kilauea, on the island of Hawaii about 500 kilometres to the southeast, has erupted repeatedly in the last decade. Between them the islands of Oahu, Molokai, Lanai and Maui line up in order, and their ages line up too, oldest in the northwest and youngest in the southeast.

Divide the distance by the time. Five hundred kilometres is 50 million centimetres; divide by 5.1 million years and you get roughly 10 centimetres a year. Now put a continuously recording GNSS receiver on any of those islands and leave it for a decade. It reports the Pacific plate carrying Hawaii northwest at a speed in the same range. A calculation from million-year-old rock and a measurement from a satellite receiver agree, which is the sort of convergence that turns a hypothesis into a framework.

That agreement is recent. For most of the twentieth century the idea that continents move was considered not merely unproven but faintly disreputable. This lesson is about how that changed, and about what the theory lets you predict once you have it. The Atlas physical geology course treats the rock record and the mineralogy in detail; here the interest is the surface: where the mountains, trenches, volcanoes and fault zones are, and why they are there and not somewhere else.

Wegener's case, and the hole in it

Alfred Wegener, a German meteorologist, set out continental drift in 1912 and expanded it in a book of 1915. He proposed that the continents had once been assembled into a single mass he called Pangaea and had since separated. His evidence was better than he is usually given credit for.

• Fit. The coastlines of South America and Africa match, and the fit is markedly better at the edge of the continental shelf than at the shoreline, which is what you would expect if the shelf is the true continental margin.
• Fossils. Mesosaurus, a small freshwater reptile incapable of crossing an ocean, is found in Permian rocks in both Brazil and southern Africa and nowhere else. The seed fern Glossopteris, with seeds too heavy for wind dispersal across an ocean, occurs across South America, Africa, India, Australia and Antarctica.
• Mountain belts. The Appalachians of eastern North America continue, in age and structure, into the Caledonides of Scotland, Ireland and Scandinavia. Reassemble the continents and the range is continuous.
• Ancient glaciation. Late Palaeozoic glacial deposits and striated pavements occur in India, Australia, southern Africa and South America, all now in tropical or temperate latitudes. Reassemble them around a south polar centre and the striations point outward from one ice cap.

The objection that sank him was mechanical. Wegener suggested the continents ploughed through oceanic crust, driven by tidal and rotational forces. Geophysicists calculated that those forces were far too weak and that the crust was far too strong, and they were right. Without a plausible engine, a great deal of good evidence sat unused for forty years.

The upshot: Evidence without a mechanism does not persuade a science, and the mechanism, when it came, was found at the bottom of the ocean rather than on the continents Wegener had studied.

What the seafloor turned out to look like

Wartime and post-war ocean surveying, much of it by echo sounder and magnetometer, produced three findings in about a decade.

First, the shape. Working from sounding profiles at Lamont, Marie Tharp and Bruce Heezen mapped a continuous mountain range running through the middle of the Atlantic and on through every ocean basin, some 65,000 kilometres in all, with a deep rift valley along its crest. Tharp noticed that the rift lined up with earthquake epicentres, which suggested the ridge was actively pulling apart.

Second, the mechanism. Harry Hess proposed in 1962 that new ocean floor is created at the ridge, spreads outward, and is destroyed at the deep trenches. The continents do not plough through the ocean floor; they ride on it.

Third, the proof. Earth's magnetic field reverses polarity at irregular intervals, and lava cooling at the ridge locks in the field direction of its moment. Frederick Vine and Drummond Matthews, with Lawrence Morley independently, pointed out in 1963 that if Hess was right the seafloor should carry a record of those reversals as stripes of alternating magnetisation, symmetrically arranged on both sides of the ridge. Magnetometer surveys found exactly that pattern. It is one of the cleanest confirmed predictions in the earth sciences, and the seafloor drilling programme that followed added the closing argument: sediment thickness and basement age both increase steadily away from the ridges, and the oldest oceanic crust anywhere is only about 180 million years old, against continental rocks approaching 4 billion.

Three ways plates can meet

The lithosphere, the rigid outer shell of crust plus uppermost mantle, is broken into about a dozen major plates that move over the weaker, ductile asthenosphere below. Almost everything geologically dramatic happens at the edges.

Boundary	Motion	Setting	Landforms	Hazards
Divergent	Plates separate	Mid-ocean ridge; continental rift	Ridge and rift valley; fissure eruptions; new ocean basin	Shallow, moderate earthquakes; effusive volcanism
Convergent, ocean to ocean	One plate subducts	Western Pacific	Deep trench; volcanic island arc	Great earthquakes; explosive volcanoes; tsunami
Convergent, ocean to continent	Denser ocean plate subducts	Andes, Cascades	Trench; continental volcanic arc; folded and thrust belt	The largest earthquakes recorded; explosive volcanoes
Convergent, continent to continent	Neither subducts	Himalaya, Alps	Extreme crustal thickening; high plateaux; no volcanic arc	Large shallow earthquakes; landslides
Transform	Plates slide past	San Andreas, Alpine Fault	Linear valleys, offset streams, sag ponds	Shallow, damaging earthquakes; no volcanism

Two features of this table are worth pausing on. Continent to continent collision produces no volcanic arc, because neither buoyant continental plate will descend far enough to trigger melting; instead the crust doubles in thickness and rises. The Himalaya and the Tibetan Plateau, averaging around 5,000 metres over an area of some 2.5 million square kilometres, are what that looks like. India began colliding with Eurasia roughly 50 million years ago, and the convergence is still running at around 4 to 5 centimetres a year, which is why the range is still rising and still seismically dangerous.

Transform boundaries produce no volcanoes at all, because nothing is being created and nothing subducted, only offset. The San Andreas system, about 1,200 kilometres of it, accommodates the Pacific plate sliding northwest past North America at roughly 5 centimetres a year, and the entire hazard there is seismic.

What actually moves the plates

Mantle convection is the usual one-line answer, and it is incomplete. Current understanding gives most of the force to the plates themselves.

Slab pull is the dominant term. Oceanic lithosphere cools as it ages, becomes denser than the asthenosphere beneath it, and once subduction starts the sinking slab drags the rest of the plate behind it. The evidence is in the rates: plates with long subducting margins, like the Pacific and Nazca, move several times faster than plates with little or no subducting edge, like the North American and African. Ridge push is a smaller contribution, the gravitational sliding of elevated young lithosphere away from the ridge crest. Basal drag from mantle flow can help or hinder depending on the direction of flow beneath a given plate.

Rates vary accordingly. The Mid-Atlantic Ridge spreads at about 2.5 centimetres a year, roughly the rate fingernails grow. The East Pacific Rise, with vigorous subduction on its eastern side, spreads at up to 15. Those differences change the shape of the ridge itself: slow ridges have deep median rift valleys and rugged flanks; fast ridges are smoother and lack a pronounced central valley.

Hotspots, and the plates as a clock

Hawaii sits nowhere near a plate boundary, which is exactly why it is useful. A hotspot is a persistent source of melt, probably fed by a mantle plume, that stays roughly fixed while the plate slides over it. Each volcano is built, carried off the heat source, goes extinct, subsides and erodes, while the next one grows behind it. The result is a chain whose ages increase with distance, which is a direct record of the plate's speed and direction.

The Hawaiian chain continues northwest as a line of submerged seamounts and then turns sharply north as the Emperor chain, with the bend dated to roughly 47 million years ago. Whether the bend records a change in plate direction, a shift of the plume, or both is still argued, and it is a good example of a case where the framework is secure and a specific interpretation within it is not. Yellowstone works the same way on a continent, with a track of progressively older calderas running southwest across the Snake River Plain.

Why crust floats, and why it rises when unloaded

One more principle belongs here, because half the later landform lessons depend on it. Isostasy is the buoyant equilibrium between the lithosphere and the denser mantle beneath. Continental crust is less dense than mantle, so it floats, and like an iceberg, a thicker piece floats higher and also extends deeper. Mountain ranges therefore have roots, columns of crust extending well below the surrounding crust.

The important consequence is dynamic. Add load, and the crust subsides; remove load, and it rises. Pile a three kilometre ice sheet onto Scandinavia and the crust sinks; melt the ice and it rebounds, which it is still doing at up to about a centimetre a year around the Gulf of Bothnia, ten thousand years after the ice left. Strip a kilometre of rock off a mountain range by erosion and the range rises in response, exposing rocks that formed far deeper. Erosion therefore does not simply lower mountains; it also drives their uplift, and the two processes reach a rough balance.

The core of it: Plates are moved mainly by the weight of their own sinking edges, and the crust that rides on top floats, so it rises and falls as loads are added and removed.

The long cycle

J. Tuzo Wilson recognised in the 1960s that ocean basins open and close repeatedly, and the sequence named after him supplies a way to place any region in a life cycle. A continent rifts, as East Africa is rifting now. The rift floods and becomes a narrow sea, as the Red Sea has. Seafloor spreading widens it into a mature ocean, as in the Atlantic today. Eventually subduction begins at its margins and the ocean starts to close, as the Pacific is doing. The closing ocean narrows to a remnant, as the Mediterranean is. Finally the continents collide and the ocean is destroyed, leaving a suture and a mountain range, as at the Himalaya. Every stage exists somewhere on Earth right now, which is why the cycle can be read directly from a world map.

Common misconceptions

• Continents plough through the ocean floor. This was Wegener's proposal and it is wrong; continents are carried passively on plates that include the ocean floor.
• Plate boundaries coincide with continental margins. Most do not. The Atlantic margins are geologically passive, sitting in the middle of plates, while the boundary runs down the ridge in mid-ocean.
• Mantle convection drags the plates along from below. Slab pull from the plates' own sinking edges dominates, which is why plates with long subducting margins move fastest.
• All convergent boundaries produce volcanoes. Continent to continent collision produces none, because neither buoyant plate descends deep enough to generate melt.
• Erosion simply wears mountains down. Isostatic rebound lifts the range as load is removed, which is how deeply formed rocks reach the surface.

What you now know

• Hotspot track arithmetic and satellite geodesy independently give Pacific plate motion of roughly 10 centimetres a year, and their agreement is what makes the theory quantitative.
• Wegener assembled strong evidence from fit, fossils, mountain belts and ancient glaciation, and was rejected because his proposed mechanism was physically impossible.
• Seafloor mapping, Hess's spreading hypothesis and the symmetric magnetic stripes predicted by Vine and Matthews supplied the mechanism and the proof between 1957 and 1963.
• Divergent, convergent and transform boundaries each generate a distinctive set of landforms and hazards, and continent to continent collision is the case with no volcanism.
• Slab pull dominates the driving forces, so spreading rates vary from about 2.5 centimetres a year in the Atlantic to about 15 on the East Pacific Rise.
• Isostasy makes the crust float, giving mountains roots and driving rebound when ice or rock is removed, and the Wilson cycle places every ocean basin somewhere between rifting and collision.

Sources

1. Kious, W. J., and Tilling, R. I. (1996). This dynamic Earth: The story of plate tectonics. United States Geological Survey. pubs.usgs.gov
2. United States Geological Survey. (n.d.). Hawaiian Volcano Observatory. usgs.gov
3. United States Geological Survey. (n.d.). Earthquake Hazards Program. usgs.gov
4. Encyclopaedia Britannica. (n.d.). Plate tectonics. britannica.com
5. Vine, F. J., and Matthews, D. H. (1963). Magnetic anomalies over oceanic ridges. Nature, 199(4897), 947-949.

Two mornings, thirty-one years apart

At 8:32 on the morning of 18 May 1980, a magnitude 5.1 earthquake shook Mount St Helens in Washington State. The volcano's north flank, which had bulged outward more than a hundred metres over the preceding two months as magma pushed into it, lost its support and slid. About 2.5 cubic kilometres of mountain came away in seconds, the largest debris avalanche in recorded history. Removing that weight uncorked the pressurised system beneath, and a lateral blast tore north across roughly 600 square kilometres of forest, flattening mature trees like mown grass. Fifty-seven people died. When the ash cleared, the summit was 400 metres lower than it had been at breakfast.

At 14:46 on 11 March 2011, about 130 kilometres off the Pacific coast of Tohoku in northern Japan, a section of the boundary where the Pacific plate descends beneath Japan slipped. The rupture ran for hundreds of kilometres with displacements of up to tens of metres, released a magnitude 9.0 to 9.1 earthquake, lifted the seafloor, and sent a tsunami into a coastline defended by seawalls built for a smaller event. Run-up exceeded 10 metres along long stretches and reached far higher in places. Nearly 20,000 people died or went missing. Honshu itself moved about 2.4 metres east.

Both events are the crust releasing stored energy. They release it by different mechanisms, produce different hazards, and demand different responses, and this lesson works through both.

Why some volcanoes flow and others explode

The single most useful predictor of how a volcano behaves is the silica content of its magma, because silica controls viscosity and viscosity controls whether gas can escape gently or must escape violently.

Magma	Silica	Viscosity	Eruption style	Landform	Example
Basaltic	About 50 percent	Low, runny	Effusive; gas bubbles escape freely; lava fountains and flows	Broad shield volcano, gentle slopes	Mauna Loa, Kilauea, Icelandic fissures
Andesitic	About 60 percent	Intermediate	Alternating explosive and effusive	Steep-sided stratovolcano of interlayered lava and ash	Mount St Helens, Fuji, Cotopaxi
Rhyolitic	Over 70 percent	Extremely high	Violently explosive; gas cannot escape until pressure fails the rock	Lava domes and collapse calderas	Yellowstone, Long Valley, Toba

Silica tetrahedra link into chains and networks in the melt, and the more silica there is, the more polymerised and the stickier the magma. In runny basalt, dissolved gas nucleates into bubbles and rises out. In stiff rhyolite it cannot, so the gas stays dissolved under pressure until decompression allows it to expand faster than the melt can flow, and the magma shatters itself into ash. The chemistry also maps onto tectonic setting: divergent boundaries and hotspots deliver basalt, subduction zones deliver andesite and rhyolite, because water carried down with the slab and assimilation of continental crust both push the composition toward silica.

Bottom line: Ask what the magma is made of and you can predict the shape of the mountain, the style of the eruption, and the way it is most likely to kill people.

Ranking the hazards honestly

Lava flows are the image most people carry, and they are among the least dangerous volcanic hazards, because they usually move slowly enough to walk away from. They destroy property comprehensively and take very few lives. The real killers are these.

• Pyroclastic density currents. Ground-hugging avalanches of hot gas and volcanic particles, moving at highway speeds or faster at temperatures of several hundred degrees Celsius. They are unsurvivable within their path, cannot be outrun, and are the principal cause of death in explosive eruptions.
• Lahars. Volcanic mudflows with the consistency of wet concrete, formed when ash mixes with water from melting snow and ice or from rain. They follow valleys, travel tens of kilometres, and can occur years after an eruption. In 1985 a comparatively small eruption of Nevado del Ruiz in Colombia melted part of its ice cap and sent lahars down river valleys into the town of Armero, killing roughly 23,000 people, most of them in their homes, dozens of kilometres from the crater.
• Tephra fall. Ash accumulating on roofs to the point of collapse, contaminating water, destroying crops and disabling jet engines.
• Sector collapse. The Mount St Helens mechanism: a flank fails and the depressurisation triggers a lateral blast.
• Gas and climate effects. Sulphur dioxide injected into the stratosphere forms sulphate aerosol that reflects sunlight. Pinatubo in 1991 lofted roughly 20 million tonnes of sulphur dioxide and cooled global mean surface temperature by a few tenths of a degree for about two years. Tambora in 1815, a much larger eruption, produced the northern hemisphere summer failure of 1816.

Eruption size is ranked on the Volcanic Explosivity Index, a logarithmic scale from 0 to 8 based mainly on erupted volume. Mount St Helens rates 5. Pinatubo rates 6. Tambora rates 7. The rarity rises as steeply as the scale: VEI 5 events occur somewhere on Earth roughly once or twice a decade, VEI 7 events once or twice a millennium.

How a fault stores and releases energy

Harry Fielding Reid, studying the surface offsets left by the 1906 San Francisco earthquake, arrived at the explanation still used. Rocks on either side of a locked fault are being driven past each other by plate motion, but friction holds the fault surface in place, so the rock deforms elastically, storing strain energy exactly as a bent stick stores it. When accumulated stress exceeds the fault's frictional strength, the fault slips, the rock springs back to its unstrained shape, and the stored energy radiates as seismic waves. That is elastic rebound. The focus, or hypocentre, is where rupture begins at depth; the epicentre is the point on the surface directly above it.

Three kinds of wave leave the focus. P waves are compressional, push and pull along the direction of travel; they are fastest, arrive first, and pass through solids and liquids alike. S waves are shear, moving material perpendicular to travel; they are slower and cannot pass through liquid at all, which is how the liquid outer core was discovered. Surface waves travel along the ground rather than through it, arrive last, decay more slowly with distance, and cause most of the damage to buildings.

The wave speeds give you a free distance meter. Because P and S waves travel at different speeds, the interval between their arrivals grows with distance from the focus. One station converts that interval into a distance and can draw a circle. Three stations produce three circles that intersect at one point, which is the epicentre. This is why seismic networks need geographic spread rather than just sensitivity.

Two different questions: how big, and how bad

Magnitude and intensity are constantly confused, and they answer different questions.

Moment magnitude measures the energy released at the source, and it has one value per earthquake. It is computed from the seismic moment, which is the rigidity of the rock multiplied by the area of fault that slipped multiplied by the average slip. Because it is built from the physical size of the rupture, it does not saturate at large events, which is why it replaced the older Richter local magnitude for anything above about magnitude 7. The scale is logarithmic in amplitude and each whole unit corresponds to roughly 32 times the energy, so a magnitude 7 releases about a thousand times the energy of a magnitude 5.

That relationship explains why only subduction zones produce the very largest earthquakes. Moment is proportional to rupture area, and only a shallow-dipping plate interface offers a fault surface hundreds of kilometres wide and a thousand long. The five largest instrumentally recorded earthquakes, Chile in 1960 at 9.5, Alaska in 1964, Sumatra in 2004 and Tohoku in 2011 among them, are all subduction events. A transform fault like the San Andreas, which is nearly vertical and limited to the depth at which rock behaves brittly, cannot generate a rupture area of that size.

Intensity measures the shaking experienced at a place, on the Modified Mercalli scale, and it has many values per earthquake because it falls off with distance and depends on the ground. That last dependence is not a minor correction. Loose, water-saturated sediment amplifies shaking severely compared with bedrock, and can also liquefy, losing its strength entirely and letting buildings sink or tilt while remaining structurally intact. In 1985 an earthquake off the Pacific coast of Mexico caused catastrophic destruction in Mexico City some 350 kilometres away, because the city sits on the sediments of a drained lake bed whose natural resonant period matched that of its mid-rise buildings. Distance did not protect it; the subsurface condemned it.

What matters here: Where the shaking is felt matters as much as how much energy was released, and the difference is made by what the ground is made of.

Tsunami, and why Tohoku was worse than its seawalls

A tsunami is generated when the seafloor itself is displaced vertically, usually by a subduction earthquake but also by submarine landslides and volcanic collapse. In the open ocean the wave has a very long wavelength, sometimes hundreds of kilometres, a small height, often under a metre, and a speed set by water depth, which in 4,000 metres of water is around 700 kilometres per hour. A ship at sea does not notice it.

Approaching shore, the same physics that governs ordinary waves applies but at colossal scale. Depth falls, the wave slows, the wavelength shortens, and the energy is compressed into a much greater height. The result arrives not as a breaking wave but as a fast, sustained rise of the sea that keeps coming for many minutes, then withdraws with equal force.

The lesson Tohoku drove home was about the limits of design assumptions. Japanese coastal defences were built to the largest events in the historical record for each stretch of coast. The 2011 rupture was larger than that record contained, and geological work afterwards found evidence of comparable predecessors, including a very large event in 869, in deposits that had not been given sufficient weight in the design standards. A hazard estimate is only as long as its record, and instrumental records are decades old while the relevant recurrence intervals are centuries to millennia.

What can and cannot be predicted

Short-term earthquake prediction, naming a place, time and magnitude in advance, remains impossible, and decades of effort on precursors have not produced a reliable one. What does work is different and useful.

Probabilistic hazard assessment estimates the chance that a given level of shaking will be exceeded at a site over a stated period, which is what building codes need. Early warning exploits the speed difference between waves and electronics: a network detects P waves near the epicentre, estimates the size, and transmits an alert that outruns the damaging S and surface waves. Warning times are seconds to tens of seconds, which is enough to stop trains, close valves, halt surgery and get people away from windows. Japan and Mexico have operated such systems for years, and the United States west coast now runs one.

Volcanoes are more forecastable than earthquakes, because magma moving toward the surface announces itself: swarms of small earthquakes, measurable ground deformation as the edifice inflates, and changes in the composition and rate of gas emission. The two months of bulging at Mount St Helens before 18 May were exactly this, and monitoring produced an evacuation zone that saved a great many lives, even though the lateral direction of the blast was not anticipated.

Common misconceptions

• Lava flows are the deadliest volcanic hazard. They are among the least deadly. Pyroclastic density currents and lahars cause most volcanic deaths.
• Each step on the magnitude scale means ten times more energy. Ten times the wave amplitude, but about 32 times the energy, so two steps is roughly a thousandfold.
• Small earthquakes relieve stress and prevent large ones. Because energy scales so steeply, it would take about 32,000 magnitude 4 events to release the energy of one magnitude 7.
• Being farther from the epicentre always means less damage. Mexico City in 1985 was devastated 350 kilometres away because lake-bed sediments amplified and resonated with the shaking.
• A tsunami is a single giant breaking wave. It is a series of long-period surges that keep rising for many minutes, and the first arrival is often not the largest.

Looking back

• Silica content sets magma viscosity, which sets eruption style and volcano form, from runny basaltic shields to explosive rhyolitic calderas.
• Pyroclastic density currents and lahars, not lava, cause most volcanic deaths, as Armero in 1985 showed at a distance of tens of kilometres from a modest eruption.
• Elastic rebound stores strain in rock either side of a locked fault and releases it as P, S and surface waves, whose arrival differences locate the epicentre.
• Moment magnitude measures energy at the source and depends on rupture area, which is why only subduction zones generate magnitude 9 events.
• Intensity depends on distance and above all on ground conditions, since soft saturated sediment amplifies shaking and can liquefy.
• Short-term earthquake prediction is not possible, but probabilistic hazard mapping, seconds-scale early warning and volcano monitoring by seismicity, deformation and gas all work.

Sources

1. United States Geological Survey. (n.d.). Volcano Hazards Program. usgs.gov
2. United States Geological Survey. (n.d.). Mount St. Helens. usgs.gov
3. Smithsonian Institution. (n.d.). Global Volcanism Program. volcano.si.edu
4. United States Geological Survey. (n.d.). Earthquake Hazards Program. earthquake.usgs.gov
5. Reid, H. F. (1910). The mechanics of the earthquake: The California earthquake of April 18, 1906 (Report of the State Earthquake Investigation Commission, Vol. 2). Carnegie Institution of Washington.

A hillside with a file

On the morning of 22 March 2014, a hillside above the North Fork Stillaguamish River near Oso, Washington, gave way. Roughly 7.6 million cubic metres of glacial sediment came down. Forty-three people died, making it the deadliest single landslide in United States history.

The hillside was not a surprise. It had failed in 1937, 1942, 1951, 1967, 1988 and again in 2006, and after the 2006 event engineers had built a log crib wall at its toe. It was known locally, and in the technical literature, as an unstable slope. The area had just recorded an extraordinarily wet forty-five days.

So what was missed? Not that the slope would fail. What was missed was how far the debris would go. The 2014 failure did not stop at the base of the hill, as previous ones had. It mobilised into a fast, fluid debris flow that crossed the valley floor, crossed the river, and ran out roughly a kilometre into a residential area on the far side that lay outside the mapped hazard zone. Reconnaissance teams afterwards concentrated on exactly this: the failure was foreseeable, the mobility was not adequately anticipated.

This lesson works from that gap outward. To understand why a slope fails and how far the debris travels, you first need to know how solid rock becomes loose material at all.

Breaking rock without changing it

Physical weathering reduces rock to smaller pieces of the same composition. Four processes do most of it.

Frost wedging works because water expands by about 9 percent when it freezes. Water in a crack freezes, exerts pressure on the crack walls, widens it, and admits more water on the next thaw. What matters is not how cold a place gets but how often it crosses the freezing point with liquid water available, which is why frost action is fiercest in high mountains and in maritime cold climates rather than in the deep-frozen continental interior of Antarctica.

Salt crystallisation is the arid equivalent. Water carrying dissolved salts penetrates pores, evaporates, and the growing salt crystals exert pressure. It hollows out the alcoves and honeycomb cavities characteristic of desert sandstone and it is a persistent problem for stone buildings near the sea.

Unloading, or pressure release, matters more than it looks. Granite crystallises kilometres deep under enormous confining pressure. When erosion removes the overburden, the rock expands slightly upward and cracks parallel to the surface, producing curved sheeting joints. Slabs then peel away in a process called exfoliation, which is what gives Half Dome in Yosemite and the granite domes of Georgia their shape.

Biological and thermal action complete the set: roots wedging into joints, burrowing animals, and the differential expansion of minerals under repeated heating and cooling, which contributes in deserts though less than was once believed.

Breaking rock by changing it

Chemical weathering alters the minerals themselves, and it produces the clays and dissolved ions that make soil possible.

Hydrolysis is the most important reaction on the planet by volume. Slightly acidic water attacks feldspar, the most abundant mineral group in the crust, converting it into clay minerals while releasing potassium, sodium or calcium ions into solution along with silica. Granite does not so much crumble as rot: its feldspar becomes clay, its mica alters, and its quartz, which is nearly immune, is released as loose sand grains. That is where the sand on most beaches comes from and where most of the clay in most soils comes from.

Dissolution removes soluble minerals entirely, which is the karst process of an earlier lesson. Oxidation attacks iron-bearing minerals, converting iron to rust-coloured oxides, weakening the crystal structure and staining the rock red or orange. Hydration incorporates water into a mineral's structure, causing expansion that helps break the rock apart.

Rates depend on four things. Climate dominates: chemical reactions roughly double in rate for every ten degrees of warming, and they need water, so hot wet tropics weather chemically at many times the rate of cold or dry regions, producing deep, intensely leached soils. Rock type matters, since minerals that crystallise at high temperature are furthest from equilibrium at the surface and weather fastest, with olivine and calcium feldspar going first and quartz last. Surface area matters, and it explains why jointed rock rounds off into spheroidal forms: corners are attacked from three sides, edges from two, faces from one. Time matters, and so does vegetation, whose roots and decaying litter raise soil carbon dioxide and organic acid concentrations far above atmospheric levels.

Key idea: Physical and chemical weathering are not competitors but collaborators. Breaking rock into pieces multiplies the surface area available for chemical attack, and chemical attack weakens rock so that it breaks more easily.

Sorting the ways material goes downhill

Mass wasting is the downslope movement of rock and soil under gravity, without a transporting medium like a river or a glacier doing the carrying. Classification uses two axes, what the material is and how it moves.

Motion	Name	Speed	Diagnostic
Fall	Rockfall	Free fall, very fast	Talus cone of angular blocks at a cliff base
Slide, rotational	Slump	Slow to moderate	Curved failure surface; the block back-tilts, leaving a crescent scarp above and a bulging toe below
Slide, translational	Rock slide, debris slide	Fast	Movement along a planar weakness such as a bedding plane or joint dipping out of the slope
Flow, slow	Creep	Millimetres per year	No scarp; tilted poles and fence posts, curved tree trunks, bowed walls
Flow, rapid	Debris flow, mudflow	Metres per second	Channelised, water-saturated, long runout onto an alluvial fan

Creep deserves more attention than it gets, because it moves the largest total volume of material of any of these. It has no dramatic event to mark it, only the slow ratcheting of soil particles that are heaved perpendicular to the slope by frost or wetting and then settle vertically under gravity, netting a small downslope displacement each cycle. Every leaning gravestone and bulging retaining wall on a hillside is a record of it.

The arithmetic of a slope

Slope stability reduces to a ratio called the factor of safety: the forces resisting movement divided by the forces driving it. Above 1, the slope holds. At 1 it is on the point of failure. Below 1 it moves.

The driving force is the downslope component of the weight of the material, which grows with slope angle and with mass. Resistance comes from shear strength, which is the sum of cohesion, meaning the material's internal stickiness, and friction, which is proportional to the normal force pressing the potential failure surface together.

Now walk through what water does, since water is the trigger in the great majority of landslides, and it works in three ways at once.

• It adds weight. Saturated soil is substantially heavier than dry soil, so the driving force rises.
• It raises pore water pressure. This is the big one, and it is not intuitive. Water in the pores of a soil pushes outward, which reduces the effective stress pressing the grains together. Friction depends on that effective stress, so as pore pressure rises, frictional resistance falls, and it can fall to almost nothing. This is why heavy rain and rapid snowmelt trigger landslides, and why a rising water table can destabilise a slope that has stood for decades.
• It destroys apparent cohesion. Damp sand holds a vertical face because surface tension in thin water films binds the grains, which is why sandcastles work. Fully saturate it and the films disappear, and so does the cohesion.

Everything else that triggers a landslide works through the same equation. Undercutting, whether by a river eroding the outside of a meander bend or by a road cut, steepens the slope and removes support from the toe. Vegetation removal takes away root reinforcement, which acts as real cohesion, and reduces the evapotranspiration that kept the soil drier; the effect is delayed, since roots take years to decay, which is why landslide rates in logged catchments peak several years after felling. Loading the top of a slope with fill or a building raises the driving force. Earthquake shaking adds a transient horizontal force and can liquefy saturated sediment outright.

Back to Oso: why runout is the hard part

With the mechanics in hand, return to the question the lesson opened on. Predicting whether a slope will fail is a matter of geology, geometry and groundwater, and it is difficult but tractable; a slope with a documented history of six failures in eighty years is not a puzzle. Predicting how far the debris will travel is a different problem, and it is much harder.

Runout depends on whether the failed mass stays coherent or turns into a fluid. A block that slides intact stops when the slope flattens. A mass that disaggregates and mobilises, especially one that is already saturated, behaves like a dense fluid, retains its momentum, and can travel many times the height it fell. At Oso the material was glacial sediment, saturated after an exceptional wet period, and it mobilised. The runout ratio, distance travelled divided by height dropped, was far higher than the local record of previous failures on the same slope suggested.

The general lesson is one that recurs across hazard geography. Hazard zones drawn from the historical record capture the events that have already happened. A physical process capable of a different behaviour, in this case rapid mobilisation instead of coherent sliding, produces an event outside the mapped zone. This is the same failure of imagination that put Japanese seawalls at the height of the largest known tsunami rather than the largest possible one, and it is why modern hazard practice increasingly models the process rather than extrapolating the record.

Worth holding on to: A slope's history tells you it can fail. It does not tell you the maximum distance the debris can reach, and that is usually the number that decides who dies.

What actually stabilises a slope

Because pore pressure is the dominant variable, drainage is the most cost-effective mitigation available: horizontal drains driven into the slope, surface ditches to intercept runoff before it infiltrates, and sealing of cracks that would otherwise channel water into the mass. Regrading works on the geometry, either flattening the slope or, more efficiently, removing material from the top and placing it as a buttress at the toe, which reduces the driving force and increases resistance in one operation. Structural measures, retaining walls, rock bolts, anchored mesh and shotcrete, are effective at small scale and expensive at large scale. Vegetation reinforces shallow soils with roots and reduces pore pressure through transpiration, though it does nothing for deep-seated failures.

And avoidance remains the cheapest and most reliable option. Landslide susceptibility mapping, when it is used to guide zoning rather than filed after the permits are issued, prevents more damage than every engineering measure combined.

Common misconceptions

• Landslides happen mainly on very steep slopes. Deep-seated failures in weak or saturated material occur on gentle slopes, sometimes under 10 degrees, and quick clays have failed on ground that looks almost flat.
• Water lubricates the failure surface. The dominant mechanism is pore pressure reducing the effective stress that generates friction, not lubrication in the everyday sense.
• Removing vegetation causes landslides immediately. The effect is delayed by several years while root systems decay, which is why post-logging failure rates peak well after the felling.
• Frost weathering is strongest in the coldest places. It is strongest where the temperature crosses freezing frequently with liquid water present, not where it stays deeply frozen.
• Chemical weathering is unimportant in cold or dry places. It is slower, not absent, and even in deserts salt and dew-driven reactions do measurable work.

Recap

• Physical weathering breaks rock without changing it, through frost wedging, salt crystallisation, unloading and biological action; chemical weathering alters the minerals themselves.
• Hydrolysis of feldspar into clay is the single most voluminous weathering reaction, and it supplies most soil clay and most beach sand.
• Weathering rate is controlled by climate, rock type, surface area and time, and physical and chemical processes accelerate one another.
• Mass movements classify by material and motion into falls, rotational slumps, translational slides and flows, with slow creep moving the greatest total volume.
• Failure occurs when the factor of safety falls below one, and water triggers most landslides by adding weight, raising pore pressure and removing apparent cohesion.
• At Oso the failure was foreseeable from the slope's history, but the mobilised debris ran out roughly a kilometre beyond the mapped hazard zone, which is the part hazard mapping most often gets wrong.

Sources

1. United States Geological Survey. (n.d.). Landslide Hazards Program. usgs.gov
2. National Park Service. (n.d.). Yosemite National Park: Rockfall and geology. nps.gov
3. Encyclopaedia Britannica. (n.d.). Weathering. britannica.com
4. National Aeronautics and Space Administration. (n.d.). Earth Observatory: Landslides. earthobservatory.nasa.gov
5. Keaton, J. R., Wartman, J., Anderson, S., Benoit, J., delaChapelle, J., Gilbert, R., and Montgomery, D. R. (2014). The 22 March 2014 Oso landslide, Snohomish County, Washington (GEER Association Report No. GEER-036). Geotechnical Extreme Events Reconnaissance Association.

Neuchatel, 1837

Louis Agassiz opened the annual meeting of the Swiss Society of Natural Sciences with an argument his audience found close to absurd. Granite boulders lie scattered across the Jura mountains, some the size of cottages, and the granite they are made of outcrops nowhere nearer than the Alps, tens of kilometres away across a valley. The prevailing explanation was a great flood. Agassiz said ice: a sheet that had once covered much of northern Europe, carried the boulders, scratched the bedrock, and piled up the ridges of unsorted rubble that farmers ploughed around.

He had the sequence of evidence right and some of the details wrong, and it took a generation for the idea to be accepted. But the observations he pointed at are the observations you can still make. Rocks that do not match their surroundings, called erratics. Parallel scratches, striations, on polished bedrock. Ridges of unsorted debris where no river could have put them. Every one of them says ice, and this lesson works through what ice does, both where it currently is and across the enormous areas where it used to be.

From snowfall to flowing ice

A glacier is not frozen water in the sense a pond is. It begins as snow that survives a summer. Under the weight of successive years the delicate crystals compact, sublimate at their points and refreeze at their contacts, becoming granular firn, and then, as air is squeezed out, dense glacial ice. The process takes years to decades depending on how much snow falls, and the resulting ice is a metamorphic rock made of a single mineral.

Whether a glacier exists at all is decided by mass balance: accumulation, mostly snowfall, against ablation, which is melting, sublimation and calving. Where they balance, the equilibrium line runs across the glacier; above it is the zone of accumulation, below it the zone of ablation. A glacier with a positive annual balance thickens and its terminus advances; a negative balance thins it and the terminus retreats. This is why a retreating glacier is still flowing forwards. The ice continues to move downvalley the whole time; it is simply melting away at the snout faster than it arrives.

The ice moves two ways. Below roughly 50 metres, the pressure lets ice deform plastically, so crystals slip past one another and the mass flows. Above that depth, ice is brittle, which is why the upper 50 metres of a glacier cracks into crevasses as it passes over irregularities. Second, where meltwater is present at the bed, the whole glacier can slide over its bed, and that basal sliding can be far faster than internal deformation. Typical valley glaciers move metres to a few hundred metres a year. Fast outlet glaciers draining ice sheets, with abundant basal water and a marine terminus, can exceed ten kilometres a year.

Remember: Retreat describes the position of the terminus, not the direction of flow. Ice in a retreating glacier is still moving downhill.

The two ways ice erodes

Glaciers erode by plucking and by abrasion, and the two produce different marks.

Plucking works where meltwater seeps into joints in bedrock beneath the glacier and refreezes, welding blocks to the base of the ice, which then carries them away as it moves. It produces steep, rough, quarried faces. Abrasion works because those entrained rocks are dragged across the bedrock like the teeth of a rasp, scratching striations and grinding out extremely fine rock flour. That flour, suspended in meltwater, is what gives glacial rivers and lakes their opaque turquoise colour.

Both act on the same knob of rock and produce a roche moutonnee: gently sloped and polished on the upglacier side where abrasion dominates, steep and jagged on the downglacier side where plucking does. Find one and you know which way the ice was moving, without any other evidence.

What alpine glaciation leaves behind

Where glaciers occupied mountain valleys, the landform assemblage is distinctive enough to read from a photograph.

• Cirque: the armchair-shaped hollow at a glacier's head, excavated by rotational flow and headwall plucking. Once the ice is gone it often holds a small lake, a tarn.
• Arete and horn: where two cirques cut back toward each other they leave a knife-edged ridge, an arete; where three or more meet, they leave a pyramidal peak, a horn. The Matterhorn is the type example.
• Glacial trough: a valley cross-section changed from the V of a river to a U, because ice erodes the whole width of its channel rather than a narrow line at the bottom. Spurs that once interlocked are cut off as truncated spurs.
• Hanging valley: a tributary glacier erodes less deeply than the trunk glacier, so after the ice goes its floor is left high above the main valley. Yosemite's waterfalls pour from exactly this.
• Fjord: a glacial trough eroded below sea level and drowned when the ice melted. Sognefjord in Norway exceeds 1,300 metres in depth, far below the sill at its mouth, which is only possible because ice, unlike a river, can erode below sea level.

What continental ice sheets leave behind

Ice sheets covered northern North America and northern Europe, and their deposits are the ground much of the population of both now lives on.

Everything a glacier deposits directly, without water sorting it, is till: unsorted, unstratified, containing everything from clay to boulders in one mass. That texture alone distinguishes glacial from river deposits at a glance.

Moraines are ridges of till. A terminal moraine marks the furthest advance, built where the conveyor of ice delivered debris to a stationary snout for a long period. Long Island and Cape Cod are terminal moraine complexes of the Laurentide ice sheet, which is why the geology of those places is a pile of transported rubble rather than local bedrock. Recessional moraines mark pauses during retreat; lateral moraines line the valley sides; a medial moraine forms where two glaciers merge and their inner laterals join.

Drumlins are streamlined hills of till, tens of metres high and up to a kilometre or two long, with the blunt end facing the direction the ice came from. They occur in fields of hundreds, and they give the ice direction as reliably as striations. Eskers are sinuous ridges of sorted, stratified sand and gravel, deposited by streams running in tunnels beneath the ice, so they wind across the landscape like an embankment built by no one. Beyond the ice margin, meltwater spreads sorted sediment across an outwash plain, and blocks of ice buried in that outwash melt later to leave depressions called kettles, which fill with water as ponds.

The larger effects reorganised whole drainage systems. The Great Lakes occupy basins scoured and deepened by the Laurentide ice sheet, and they hold roughly a fifth of the world's surface fresh water. The Ohio and Missouri rivers run approximately along the limit of glaciation, having been pushed there by the ice. Fine silt blown off the barren outwash plains accumulated downwind as loess, which weathers into some of the most productive agricultural soil on the planet, in Iowa, in Ukraine and above all on the Loess Plateau of China.

The world at the last glacial maximum

The Quaternary began about 2.58 million years ago, and it has contained dozens of glacial and interglacial cycles paced by the orbital variations of an earlier lesson. The most recent maximum peaked roughly 26,000 to 19,000 years ago.

At that point ice covered around 25 percent of land area, against about 10 percent today. The Laurentide ice sheet reached three kilometres and more in thickness over Hudson Bay. Because that water came out of the ocean, global sea level stood roughly 120 to 130 metres lower than now, which exposed continental shelves, joined Britain to continental Europe, joined New Guinea and Tasmania to Australia, and opened the Bering land bridge between Siberia and Alaska.

Today about 90 percent of the world's ice by volume sits in Antarctica and about 8 percent in Greenland. If all of it melted, sea level would rise on the order of 65 metres. That is not a forecast for any human timescale; it is a statement of the size of the reservoir, and it is why the mass balance of those two ice sheets is one of the most closely monitored quantities in earth science.

Frozen ground without glaciers

Periglacial environments are cold regions near but not under ice, where freezing and thawing rather than glacier flow does the geomorphic work. The defining condition is permafrost: ground that remains at or below zero degrees Celsius for at least two consecutive years. It underlies roughly 15 percent of the exposed land area of the northern hemisphere, running through Siberia, northern Canada and Alaska, and reaching depths of hundreds of metres.

Above the permafrost lies the active layer, which thaws each summer and refreezes each winter, from a few tens of centimetres to a couple of metres thick. Because the permafrost beneath is impermeable, meltwater cannot drain, so the active layer becomes saturated. That is why the Arctic, despite low precipitation, is full of ponds and boggy ground, and why the landforms of periglacial regions are dominated by what happens when saturated soil freezes.

• Patterned ground. Repeated freezing sorts stones from fines and cracks the ground into polygons, producing ice-wedge polygons and sorted circles and stripes that look designed.
• Pingos. Ice-cored hills, sometimes tens of metres high, raised where water is injected under pressure beneath the surface and freezes.
• Solifluction lobes. The saturated active layer creeps downslope over the frozen base, producing tongue-shaped terraces on slopes of only a few degrees.
• Thermokarst. Where ice-rich permafrost thaws, the ground collapses into an irregular terrain of hollows and lakes, resembling limestone karst but produced by melting rather than dissolving.

Two consequences reach beyond geomorphology. The first is engineering. A heated building set directly on permafrost thaws the ground beneath it, which then settles unevenly, so northern construction is placed on piles with an air gap, or on gravel pads thick enough to insulate. The Trans-Alaska Pipeline is carried above ground over much of its length on supports fitted with heat pipes that pull warmth out of the ground in winter, precisely to keep the permafrost frozen.

The second is carbon. Cold, waterlogged, frozen soils have accumulated organic matter for tens of thousands of years without fully decomposing it. Estimates put the organic carbon stored in permafrost region soils on the order of 1,500 billion tonnes, roughly twice the amount currently in the atmosphere. Thaw allows microbial decomposition to resume, releasing carbon dioxide where conditions are dry and methane where they are waterlogged, which is a feedback the Atlas climate course examines in detail.

The point: Permafrost is not simply frozen soil. It is a structural material that buildings depend on and a carbon store larger than the atmosphere, and both of those properties depend on it staying below zero.

Common misconceptions

• A retreating glacier flows backwards. The ice always flows downvalley; retreat means the snout melts back faster than ice is delivered to it.
• Glaciers gouge valleys because ice is hard. Ice alone would polish. The cutting is done by rock fragments frozen into the base, which is why abrasion and plucking, not the ice itself, do the erosion.
• Till and outwash are the same material. Till is deposited directly by ice and is unsorted; outwash is deposited by meltwater and is sorted and stratified. The difference is visible in a road cut.
• Permafrost means permanently frozen all the way to the surface. An active layer thaws every summer, and it is that layer that does nearly all the geomorphic work.
• The last glacial maximum simply made everywhere colder. It also lowered sea level by roughly 120 metres, exposed shelves and land bridges, and rerouted major rivers, changes that persist in today's geography.

Where this leaves us

• Snow becomes firn and then glacial ice under its own weight, and mass balance across the equilibrium line decides whether the terminus advances or retreats.
• Ice flows by plastic deformation below about 50 metres and by basal sliding where meltwater reaches the bed, at speeds from metres to over ten kilometres a year.
• Plucking and abrasion carve cirques, aretes, horns, U-shaped troughs, hanging valleys and fjords, and a roche moutonnee records the direction of flow.
• Ice sheets deposit unsorted till as moraines and drumlins, and meltwater deposits sorted sand and gravel as eskers and outwash, with kettles marking buried ice blocks.
• At the last glacial maximum, ice covered about a quarter of land and sea level stood roughly 120 to 130 metres lower, exposing the Bering land bridge and joining Britain to Europe.
• Permafrost underlies about 15 percent of northern hemisphere land, supports northern infrastructure, and holds on the order of 1,500 billion tonnes of organic carbon.

Sources

1. National Snow and Ice Data Center. (n.d.). Cryosphere: Glaciers, ice sheets and frozen ground. nsidc.org
2. National Park Service. (n.d.). Glacier National Park. nps.gov
3. National Aeronautics and Space Administration. (n.d.). Vital signs: Ice sheets and sea level. climate.nasa.gov
4. Encyclopaedia Britannica. (n.d.). Glacier. britannica.com
5. Schuur, E. A. G., McGuire, A. D., Schadel, C., and colleagues. (2015). Climate change and the permafrost carbon feedback. Nature, 520(7546), 171-179.

A lighthouse that had to be moved

The Cape Hatteras Lighthouse was lit in 1870, a brick tower 198 feet high standing about 1,500 feet back from the Atlantic. By the late 1990s the surf reached to within roughly 120 feet of its base. In the summer of 1999 the National Park Service jacked the whole tower off its foundation, set it on steel beams and rolled it 2,900 feet inland, a journey that took 23 days.

Nothing had gone wrong with the lighthouse. What moved was the island. Hatteras is part of the Outer Banks, a chain of barrier islands, and barrier islands migrate landward. The tower had been built on a surface that was in transit, and the engineering question in 1999 was not how to stop the shoreline but how far to get out of its way and for how long.

Deserts and coasts look nothing alike and are usually taught in separate chapters, but they run on the same accounting. In both, a moving fluid picks up loose grains, carries them a certain distance and drops them where it slows. The landforms are the ledger of that transfer.

Getting a grain of sand into the air

Wind is a poor lifter and an excellent sorter. Air is roughly 800 times less dense than water, so for the same speed it exerts far less force on a grain, which is why wind moves nothing coarser than sand while a river in flood rolls boulders. What wind does have is the ability to work on a dry, unprotected surface for months at a time.

Grains move three ways. Surface creep rolls the coarsest particles along the ground, driven partly by the wind and partly by the impacts of other grains. Saltation is the main event: a grain lifts, arcs downwind, and lands hard enough to knock further grains into the air, so the process is self-sustaining once started. Nearly all of that traffic happens within a metre of the ground, which is why the paint on a car in a sandstorm is stripped from the lower panels and the windows survive. Suspension carries the finest material, silt and clay, high into the atmosphere, where it can stay for days.

The threshold wind speed for moving a grain is lowest at around a tenth of a millimetre and rises in both directions from there. Coarser grains are heavier. Finer ones are harder to lift, which is counterintuitive: clay and fine silt cling to one another through electrostatic and moisture films, and they sit inside the thin calm layer of air right at the surface. Something has to disturb them first, and a tyre, a plough or the impact of saltating sand does it, which is why dust storms usually begin where sand is already moving.

That sorting sends the two fractions to different landscapes. Saltating sand travels metres to kilometres and piles up near its source as dunes. Suspended dust crosses oceans. NASA satellite work using CALIPSO estimated that roughly 182 million tonnes of dust leave North Africa each year and about 27.7 million tonnes of it falls in the Amazon basin, carrying phosphorus to a rainforest whose own soils are stripped of it. The largest single source is the Bodele Depression in Chad, the dry floor of a former lake.

So what?: Wind does not move a sediment mixture as a mixture. It splits it by size and sends the fractions to different continents, which is why dune sand is so uniformly graded and why the dust that lands on a Caribbean car came off a lake bed in Chad.

Why most of the Sahara is not sand

The Sahara of photographs is rolling dunes. The Sahara you would actually walk across is mostly gravel and rock. Sand seas cover only about a fifth of the world's desert area; the rest is stony plain, bare bedrock and dry mountain.

Wind erosion does that. Deflation is the removal of loose fine material, leaving the coarse behind. Where it works on mixed sediment for long enough, the surface becomes a single close-packed layer of pebbles known as desert pavement, which then protects everything below it. Break the pavement, with a vehicle track or a construction site, and the fines beneath begin to blow immediately; tank tracks cut across the Libyan desert in the Second World War are still visible from orbit.

How pavement forms is a live disagreement worth knowing, because it shows how a landform can have two plausible histories. The traditional account is deflation: wind strips the fines from the top down and the stones settle together as a lag. The competing account, argued by McFadden and colleagues in the 1980s from soils in the Mojave, is the reverse: the stones began at the surface on a fresh lava flow or alluvial fan, wind-blown silt sifted down between and beneath them, and the stone layer rode upward on the accumulating dust. The evidence that separates the two is under the pavement. A deflation lag should sit on the same mixed material it was winnowed from. An accretionary pavement sits on a layer of fine, well sorted, wind-delivered silt that could not have been left by winnowing at all, and that layer is exactly what the Mojave excavations found.

Where wind carries sand against rock, it abrades. The blasting is concentrated in the lowest metre, so telephone poles in sandy deserts are undercut at the base and boulders are faceted on their windward faces, producing ventifacts whose flat faces record wind directions. Sustained abrasion along a dominant wind carves streamlined ridges called yardangs, kilometres long in the Lut Desert of Iran, with the blunt end facing the wind and a tapering keel downwind.

Reading a dune field

A dune forms where saltating sand meets an obstacle or a drop in wind speed, deposits on the gentle windward slope, is pushed over the crest and avalanches down the steep lee face at the angle of repose, close to 34 degrees for dry sand. The dune therefore migrates downwind while individual grains cycle from its front to its back, leaving steeply inclined cross-beds that identify fossil dune fields such as the Navajo Sandstone in Zion.

Dune shape is not decorative. It is a readout of three variables: how much sand is available, how many directions the wind blows from, and whether vegetation is holding anything down.

Dune	Shape in plan	Wind regime	Sand supply	Example
Barchan	Crescent, horns pointing downwind	One dominant direction	Limited, on a firm floor	Coastal Peru; margins of the Namib
Transverse	Long ridges at right angles to the wind	One dominant direction	Abundant	Interiors of large sand seas
Linear or seif	Long parallel ridges, sinuous crests	Two directions, with a resultant	Moderate	Simpson Desert; much of the Sahara
Star	Central peak with three or more radiating arms	Many directions, no resultant	Abundant	Grand Erg Oriental; Great Sand Dunes, Colorado
Parabolic	U-shape with horns pointing upwind	One dominant direction	Moderate, with vegetation	Coastal dune belts; semiarid plains

Two rows of that table deserve a second look. Star dunes barely migrate, because no wind direction dominates long enough to push them anywhere; they grow instead, and they are the tallest dunes on Earth. Star Dune in Great Sand Dunes National Park in Colorado rises about 230 metres above the valley floor, the tallest in North America, and it is high precisely because the winds there come from several directions across the year.

Parabolic dunes are the useful trap. They look like barchans and they are the opposite. In a barchan the thin horns move fastest and run ahead; in a parabolic dune vegetation pins the horns while the bare centre blows out ahead of them, so the crescent opens upwind. Get that backwards and you will reconstruct the wind direction of a coastal dune field exactly 180 degrees wrong.

The rain that shapes a place with no rain

Now the part that surprises people. Most of the erosional work in most deserts is done by running water, not by wind.

Rain in a desert is rare, but when it comes it is often intense, and the surface it lands on is hostile to infiltration: little vegetation to slow the flow, thin or crusted soil, and in many places a hardpan of calcium carbonate. So a high proportion of the rainfall becomes runoff within minutes. Channels that are dry for years, called wadis or arroyos, fill in a rush that carries boulders, and they do it far downstream of where the rain fell. Flash floods kill hikers in slot canyons under a blue sky above them for exactly that reason.

Because the flow is short-lived, it dies quickly once it leaves confinement. Where a channel emerges from a mountain front onto a basin floor, it spreads, slows and dumps its load as an alluvial fan, coarse at the apex and fine at the toe. Fans from neighbouring canyons merge along the range front into a continuous apron, a bajada. Water that reaches the centre of a closed basin forms a shallow, temporary lake that evaporates and leaves a flat salt-crusted floor, a playa. Badwater Basin in Death Valley, at 86 metres below sea level, is one, and the salts on it were delivered by water and left behind by the sun.

Two more forms complete the desert assemblage. A pediment is a gently sloping bedrock surface at the foot of a retreating mountain front, thinly veneered with sediment and easily mistaken for a fan until you dig. An inselberg is an isolated steep-sided residual hill left standing as the surrounding surface wears back, Uluru being the example everyone has seen.

The same accounting on a coast

Turn now to the shoreline, where the fluid is water and the budget is easier to measure. An earlier lesson worked out how waves are generated, why they refract onto headlands and how longshore drift moves sediment along the shore. Build on that with one organising idea: the littoral cell, a stretch of coast with its own inputs, transport path and outputs, which can be balanced like a bank account. The inputs are rivers, which supply most of the sand on most coasts, plus eroding cliffs and, in places, sediment moved in from offshore. The transport is longshore drift. The outputs are permanent losses: sand blown inland into dunes, sand carried into an estuary, and above all sand funnelled into a submarine canyon whose head reaches close inshore, where it drops into deep water and never returns.

Coastal erosion then stops being mysterious. A beach narrows when withdrawals exceed deposits. In southern California, dams and concrete flood-control channels on the rivers cut the sand delivered to the coast while submarine canyons went on removing it at the far end, and the beaches have been maintained by imported sand ever since. That account was not attacked by the sea. It was defunded upstream.

What the waves cut, and what they build

On a coast where the budget is negative or the rock is exposed, wave energy does the cutting. Waves break against the base of a cliff, excavate a notch along the most vulnerable band of rock, and the overhang eventually collapses, so the cliff retreats parallel to itself and leaves behind a gently sloping shore platform cut into bedrock at about the level of low tide. That platform is the single best field evidence that a cliff has retreated, and its width is a measure of how far.

In rock with joints or faults, the retreat is selective and produces a well known sequence: waves exploit a weakness to open a cave; a cave cut through a headland from both sides becomes an arch; the arch roof falls and leaves a stack standing offshore; the stack is undercut and reduced to a stump awash at high tide. The Twelve Apostles on the Victorian coast of Australia are stacks in soft limestone, and one of them collapsed without warning in 2005, which is the sequence running at human speed.

Where the budget is positive, the same energy builds. Long low swells in summer push sand up the beach into a broad berm; short steep storm waves in winter strip it and store the sand offshore in a bar, which the next calm season returns, so a beach that looks destroyed in February is often just filed offshore. Where a coast turns a corner, drift carries sand out into open water and deposits it as a spit, often hooked landward at the end by refracted waves, as at Sandy Hook in New Jersey and Provincetown on Cape Cod. A spit that reaches an island becomes a tombolo; a ridge that seals a bay becomes a bay-mouth bar with a lagoon behind it.

The largest depositional forms are the barrier islands, long sand islands separated from the mainland by a lagoon or sound, fringing something like ten to fifteen percent of the world's coasts and almost the whole United States Atlantic and Gulf shoreline. They are not fixed. As sea level rises, storm waves wash over the island and carry sand from the ocean side to the back side, so the whole island rolls landward while keeping its shape, a process called overwash rollover. That is precisely what carried the shoreline up to the Cape Hatteras Lighthouse.

Holding the line, and what it costs

People build on coasts, and the shoreline moves, so a body of engineering exists to argue with it.

• Groynes are walls built out across the drift. Sand piles against the updrift side and the downdrift beach starves, so the problem is not solved but relocated to the neighbours, who then build their own groyne.
• Seawalls protect what is behind them and frequently destroy what is in front. A wall reflects wave energy rather than absorbing it as a beach does, scouring sand from its toe, and it cuts off the cliff or dune that was supplying sediment to the beach in the first place. Many walled shorelines end up with no beach at high tide at all.
• Beach nourishment imports sand, usually dredged from offshore. It preserves the beach, which is both the amenity and the natural defence, and it does not deprive the neighbours. It also washes away, so the cost recurs every few years, which makes it a subscription rather than a purchase.
• Managed retreat moves the asset instead of the water. It is politically the hardest and physically the only one that works indefinitely.

Which brings the lesson back to Hatteras. The Park Service considered a seawall and a jetty field, and moved the lighthouse instead, at a cost far lower than defending the site would have been and with an expected life of a century or so before the island catches up again. The decision was not a defeat. It was a correct reading of a sediment budget.

In short: Shoreline structures do not create sand. They redistribute it, and the redistribution is always paid for by somebody downdrift or by the beach in front of the wall.

Common misconceptions

• Deserts are shaped mainly by wind. Running water does most of the erosional work in most deserts; wind dominates only where sand is abundant and dry. The fans, wadis and playas are water landforms in a place with almost no water.
• Deserts are mostly sand. Sand seas cover roughly a fifth of the world's desert area. Stony pavement and bare rock cover far more.
• A parabolic dune is a barchan pointing the other way by chance. The reversal is caused by vegetation anchoring the horns while the centre blows out, so the two forms record opposite relationships between wind and plant cover.
• A seawall protects the beach. It protects the property behind it. By reflecting wave energy and cutting off the sediment supply from the cliff or dune, it frequently removes the beach in front of it.
• Barrier islands are permanent land. They migrate landward by overwash as sea level rises, which is why structures on them need either relocation or continual replenishment.

What to carry forward

• Wind sorts sediment by size: sand saltates within a metre of the ground and builds dunes near its source, while silt travels in suspension for thousands of kilometres, with roughly 182 million tonnes leaving North Africa each year.
• Deflation leaves desert pavement, which may form as a winnowed lag or by dust accreting beneath a stone layer; abrasion in the lowest metre makes ventifacts and yardangs.
• Dune form records sand supply, wind directionality and vegetation: barchan and transverse for one wind, linear for two, star for many, parabolic where plants pin the horns.
• Desert landscapes are largely water-cut, with wadis, alluvial fans, bajadas, playas, pediments and inselbergs produced by rare intense runoff on surfaces that will not infiltrate.
• A littoral cell balances river and cliff inputs against longshore transport and losses to dunes, estuaries and submarine canyons; erosion usually means the account was defunded upstream.
• Wave erosion cuts notches, shore platforms and the cave-arch-stack-stump sequence, while deposition builds berms, spits, tombolos and barrier islands that roll landward through overwash.
• Groynes and seawalls move the problem or trade the beach for the property; nourishment is a recurring cost and retreat is the only permanent answer, which is why the Cape Hatteras Lighthouse now stands 2,900 feet from where it was built.

Sources

1. National Park Service. (n.d.). Cape Hatteras National Seashore: Moving the lighthouse. nps.gov
2. United States Geological Survey. (n.d.). Coastal and Marine Hazards and Resources Program. usgs.gov
3. National Aeronautics and Space Administration. (n.d.). Earth Observatory: Dust and sand. earthobservatory.nasa.gov
4. Encyclopaedia Britannica. (n.d.). Dune. britannica.com
5. Bagnold, R. A. (1941). The physics of blown sand and desert dunes. Methuen.
6. McFadden, L. D., Wells, S. G., and Jercinovich, M. J. (1987). Influences of eolian and pedogenic processes on the origin and evolution of desert pavements. Geology, 15(6), 504-508.

Nizhny Novgorod, 1882

The provincial assembly of Nizhny Novgorod had a tax problem. It needed to value farmland, the values it had were wrong, and after a run of bad harvests nobody could agree on which land was actually good. So it hired a geologist, Vasily Dokuchaev, to go and find out.

Dokuchaev and his students spent four summers digging pits across the province and looking at the walls. What they found under the steppe grass was a body of black earth, in places more than a metre thick, dark all the way down rather than merely stained at the top, and organised into layers that repeated from pit to pit wherever the grassland and the climate repeated. He published the result in 1883 as Russian Chernozem, and the argument it made is the reason soil science exists as a discipline. Soil, he said, is not crushed rock and it is not geological debris. It is a natural body in its own right, formed at the meeting of climate, organisms, relief, parent material and time, and it can be mapped because those factors can be mapped.

What a pit face tells you

Cut a clean vertical face through a soil and you are looking at a profile: a set of roughly horizontal layers called horizons, each the record of what has been added, lost, moved or altered at that depth.

From the top down, the standard sequence runs like this. The O horizon is organic litter, leaves and needles in various stages of decay, which may be absent in a ploughed or arid soil. The A horizon is topsoil: mineral grains mixed with humus, dark, biologically busy, the layer roots and earthworms occupy. Below that, in soils where water moves steadily downward, sits an E horizon, pale and often close to ash grey because eluviation has washed the clay, iron and aluminium out of it and left the bleached quartz behind. Whatever left the E arrives in the B horizon, where illuviation deposits it: accumulated clay, or iron oxides, or in dry climates a band of calcium carbonate. The C horizon is weathered parent material that has not yet become soil, and R is the bedrock beneath.

Four processes generate all of that. Additions, mostly organic matter from above and dust and rainfall solutes. Losses, mostly leaching downward and erosion off the top. Translocation, the movement of material from one horizon to another, which is what E and B horizons record between them. And transformation, the chemical weathering of minerals and the decay of organic matter in place. When you read a profile, you are reading the balance of those four at each depth.

What matters here: A pale horizon is not a poor one by accident. It is the account of everything that has been washed out of it, and the dark or clay-rich band beneath it is where that material stopped.

Five factors, one equation

Hans Jenny put Dokuchaev's insight into a form you can work with in 1941, writing soil as a function of five factors: climate, organisms, relief, parent material and time. The value of the formulation is that you can hold four of them fixed and watch the fifth.

Climate dominates at continental scale, which is why a soil map of a large country looks unnervingly like its climate map. Temperature sets the rate of chemical weathering and of organic decay; precipitation sets the direction water moves through the profile. Where rainfall exceeds evaporation, the net movement is down, and soluble material leaches out. Where evaporation exceeds rainfall, the net movement over the year is up, and salts and carbonates accumulate at the depth where wetting fronts stop.

Organisms supply the organic matter and mix the profile. The difference between grassland and forest soil is mostly this: a tree drops its litter on the surface, while a grass grows a dense root system through the top metre and renews a large part of it every year, adding humus at depth rather than on top. That is why chernozem is black to a metre and forest soil is dark only in a thin band.

Relief works through drainage and erosion, and it produces a repeating sequence down any hillside that geographers call a catena: thin, young, well drained soil on the convex crest where material is being lost; deeper soil on the mid-slope; and at the foot, thick, poorly drained, often gleyed soil where everything from upslope has accumulated. The parent material and the climate are identical across all three. Only the position differs.

Parent material dominates locally, especially early on. Sandstone gives sandy, acidic, droughty soil; basalt gives clay-rich, base-rich, fertile soil; limestone gives thin soil, because dissolution removes most of the rock as solution and leaves only the insoluble residue behind.

Time is the factor people most often underestimate. A soil on a fresh lava flow may be a few centimetres of gritty material with lichen on it. On a stable surface a million years old in a wet tropical climate, the same basalt has become tens of metres of deeply leached clay. Estimates of how long it takes to build a centimetre of topsoil range from a few decades under ideal conditions to several centuries under ordinary ones, which sets the terms of every argument about erosion in the next lesson.

Texture decides most of the rest

Before the classification, one physical property does more work than any other. Texture is the proportion of sand, silt and clay in the mineral fraction, and it is defined purely by grain size: sand from 2 down to 0.05 millimetres, silt from 0.05 down to 0.002, and clay below 0.002. The United States Department of Agriculture texture triangle turns any three percentages into a name, and the centre of the triangle, roughly 40 percent sand, 40 percent silt and 20 percent clay, is loam.

Property	Sand	Silt	Clay
Drainage	Rapid	Moderate	Slow, waterlogs easily
Total water held	Little	Moderate	Most, but much of it held too tightly for roots
Surface area per gram	Very small	Small	Enormous
Nutrient holding, or cation exchange capacity	Very low	Low	High
Working it	Easy but droughty	Easy, erodes readily	Heavy when wet, brick-hard when dry

The clay column explains most of soil chemistry. Clay particles are not merely small; they are plate-shaped, they carry a negative surface charge, and a single gram can present a surface area measured in hundreds of square metres. Positively charged nutrient ions, calcium, magnesium, potassium, ammonium, cling to those surfaces instead of washing away, and the soil's capacity to hold them is its cation exchange capacity. Sand has almost none, which is why loam is prized: enough clay to hold nutrients and water, enough sand to drain and be worked.

Four soils and the climates that built them

The United States system sorts the world's soils into twelve orders. Four of them make the point.

Order	Where	Diagnostic feature	For farming
Mollisol	Mid-latitude grassland: the Corn Belt, the Ukrainian steppe, the pampas, the Canadian prairies	Thick dark base-rich A horizon built by grass roots	The best in the world; these regions feed a large share of the planet
Oxisol	Humid tropics on old stable surfaces	Deeply weathered, red, dominated by kaolinite and iron and aluminium oxides, very low exchange capacity	Poor and quickly exhausted despite the vegetation above
Spodosol	Cool humid conifer forest on sandy parent material	Bleached E horizon over a dark B stained by illuviated iron and organic matter	Acidic and infertile without heavy amendment
Aridisol	Deserts and semi-deserts	Little organic matter; a carbonate or gypsum band where wetting fronts stop, hardening into caliche	Productive with irrigation, and at permanent risk of salinisation

Read the table as four answers to one question: what happens to water in the profile. In the mollisol, water moves down far enough to leach the top but not far enough to strip it. In the oxisol, it moves down through everything for a very long time. In the spodosol, acidic conifer litter makes the percolating water aggressive enough to strip iron out of the upper profile and drop it lower down. In the aridisol, water barely moves at all, so nothing leaves and salts arrive.

Why the richest forest grows on the poorest soil

Now the fact that catches almost everyone. The Amazon rainforest, the densest concentration of terrestrial biomass and species on the planet, grows largely on oxisols and ultisols: soils so leached that in agricultural terms they are close to worthless.

The resolution is that in a tropical rainforest, the nutrients are not in the soil. They are in the living vegetation, and they are being recycled fast enough that they almost never enter the mineral soil at all. A leaf falls, is decomposed within weeks by warm, wet, intensely active fungi and invertebrates, and the released nutrients are captured on the spot by a mat of fine roots and their associated mycorrhizal fungi, often within centimetres of the surface. The loop is closed and tight. Very little leaks downward, which is a good thing, because anything that does leak is leached away for good.

Cut the forest and you cut the loop. Burning releases the nutrients as ash, which is a real fertiliser, and a cleared plot in the Amazon will give two or three decent harvests. Then the ash is used up or washed out, the exchange capacity beneath is too low to hold anything you add, and yields collapse. Shifting cultivation dealt with that by moving on and allowing decades of fallow. Permanent clearance has no such option, and iron-rich soil exposed to alternating wetting and drying can harden irreversibly into laterite, a material good enough to build with and useless to plant in.

There is a striking exception in the same basin. Scattered along the rivers are patches of terra preta, dark earth a metre or more deep, created by pre-Columbian populations who worked charcoal, pottery, bone and organic waste into the ground over centuries. Those patches are still markedly more fertile than the surrounding oxisols, hundreds of years after the people who made them were gone. It is the clearest demonstration available that soil is something that can be built, on a timescale of centuries rather than seasons.

The upshot: Vegetation density tells you about the nutrient cycle, not about the soil. Where recycling is fast and closed, spectacular forest sits on soil that will not grow maize for four years.

What sets the edge of a species range

Soil is one control on where a plant grows. Turn now to what decides where any organism lives.

Every species has a range of tolerance for each variable that matters to it: temperature, moisture, salinity, soil pH, light. Performance is best in the middle and falls toward the ends, and the factor closest to its limit sets the range regardless of how favourable everything else is, which is why a plant with ample water, warmth and light still fails on a soil short of one nutrient.

A second distinction matters more than it first appears. The fundamental niche is the set of conditions in which a species could survive with the place to itself. The realised niche is where it actually occurs once competitors, predators and dispersal barriers have had their say, and it is always smaller. Field experiments show a consistent pattern: the limit at the harsh end of a gradient is set by physiology, the limit at the benign end by competition. A species is often absent from good habitat not because it cannot live there but because something else does it better.

At the scale of continents, though, climate does most of the sorting, and it does it so reliably that unrelated floras converge on the same forms. The five regions with a Mediterranean climate, coastal California, central Chile, the Mediterranean basin, the Cape of South Africa and southwestern Australia, are separated by oceans and share almost no plant families. All five have produced dense, low, hard-leaved evergreen shrubland adapted to summer drought and periodic fire: chaparral, matorral, maquis, fynbos and mallee. Same climate, same solution, five separate times.

Bali and Lombok, 35 kilometres apart

Which makes the following observation genuinely strange. In 1859 Alfred Russel Wallace, working through the Malay Archipelago, described a line running between Borneo and Sulawesi and then south between Bali and Lombok. West of it the animals are Asian: woodpeckers, barbets, pheasants, and mammals including monkeys, squirrels and, on Bali until the twentieth century, a tiger. East of it, beginning on Lombok, the birds are cockatoos, honeyeaters and megapodes, and the mammals include marsupials.

Bali and Lombok are separated by about 35 kilometres of water. Their climates are the same, their vegetation is broadly the same, and a bird can see one island from the other. No environmental factor explains the difference.

The explanation is history plus bathymetry, and the earlier lesson on glaciation supplies it. Through the Pleistocene, sea level repeatedly fell roughly 120 metres. When it did, the shallow Sunda Shelf emerged and joined Bali, Java, Sumatra and Borneo into a single land mass continuous with mainland Asia, while the Sahul Shelf joined Australia, New Guinea and Tasmania. The Lombok Strait, however, is deep. It never dried. For millions of years animals could walk across most of the archipelago and never across that one channel, and the faunas evolved on either side of a gap that a map of climate cannot show. The islands between the two lines, which biogeographers call Wallacea, hold a mixture of both, assembled by whatever managed to cross water.

Islands, and why the theory left the islands

Wallace's observation grew into a general theory. In 1967 Robert MacArthur and Edward Wilson proposed that the number of species on an island settles at a balance between two rates: immigration of new species, which falls as the island fills up and is higher for islands near a source of colonists, and extinction, which rises as the island fills and is lower on large islands where populations are bigger. The equilibrium is dynamic. The number of species stays roughly constant while the identity of them turns over.

The empirical backbone is the species-area relationship, S proportional to A raised to the power z, with z commonly near 0.25 for islands. That exponent is worth feeling. A tenfold increase in area brings not ten times the species but roughly 1.8 times, and run the other way it is bleak arithmetic: destroy 90 percent of a habitat and, at equilibrium, expect to keep about half its species.

That reversal is why the theory matters far beyond islands. A reserve surrounded by farmland, a woodland cut in two by a motorway, an alpine community on a warming mountain top: each is an island in a hostile sea. It is why reserve design argues about size, shape and connectivity, and why the losses from a clearance keep arriving for decades afterwards, as populations too small to persist work their way down to zero.

Common misconceptions

• Rainforest soils must be rich because the forest is. Most are deeply leached and low in nutrients; the nutrient stock is in the living biomass and is recycled before it reaches the mineral soil.
• Soil is just weathered rock. It is an organised body with horizons produced by additions, losses, translocation and transformation, which is exactly the point Dokuchaev established in 1883.
• Clay soils give plants the most water. They hold the most water in total, but a large share of it is held so tightly that roots cannot extract it, which is why loam beats clay for available water.
• Topsoil grows back in a few seasons. Estimates run from decades to several centuries per centimetre, which is why erosion is treated as a permanent loss rather than a temporary one.
• Species live wherever the climate suits them. Climate sets what is possible; competition, dispersal and history set what is present, which is why Bali and Lombok differ across 35 kilometres of identical climate.

Putting it together

• Dokuchaev established in 1883 that soil is a natural body formed by climate, organisms, relief, parent material and time, and Jenny formalised those five factors in 1941.
• Horizons record what has been added, lost, moved and transformed at each depth, with eluviation stripping the E horizon and illuviation building the B.
• Texture controls drainage, available water and cation exchange capacity, and mollisols, oxisols, spodosols and aridisols are four answers to what water does in the profile: partial leaching, total leaching, acid stripping and no movement at all.
• Tropical forest holds its nutrients in biomass on a tight recycling loop, so clearance gives two or three harvests and then failure, while pre-Columbian terra preta shows soil can be built deliberately.
• Range limits come from the factor nearest its tolerance limit, with physiology setting the harsh edge and competition the benign one, and identical climates produce convergent vegetation in five separate Mediterranean regions.
• Wallace's Line separates Asian from Australasian faunas across 35 kilometres of identical climate, because the deep Lombok Strait stayed wet through every glacial low stand.
• Island biogeography balances immigration against extinction, and its species-area exponent near 0.25 means removing 90 percent of a habitat costs roughly half its species.

Sources

1. United States Department of Agriculture, Natural Resources Conservation Service. (n.d.). Soils. nrcs.usda.gov
2. Encyclopaedia Britannica. (n.d.). Soil. britannica.com
3. Encyclopaedia Britannica. (n.d.). Alfred Russel Wallace. britannica.com
4. Food and Agriculture Organization of the United Nations. (n.d.). Global Soil Partnership. fao.org
5. Jenny, H. (1941). Factors of soil formation: A system of quantitative pedology. McGraw-Hill.
6. MacArthur, R. H., and Wilson, E. O. (1967). The theory of island biogeography. Princeton University Press.

A fishing port with no sea

Moynaq, in Uzbekistan, had a fish cannery, a harbour and a fleet. The rusting hulls of that fleet are still there, lying on sand. The water is now more than a hundred kilometres away.

In 1960 the Aral Sea covered roughly 68,000 square kilometres and was the fourth largest lake on Earth. Two rivers fed it, the Amu Darya and the Syr Darya, and from the early 1960s Soviet planners diverted them to irrigate cotton across the desert of Central Asia. The engineering worked exactly as designed: cotton production rose, and the Karakum Canal carried water hundreds of kilometres across sand, losing a large share of it to seepage along the way. What nobody had a budget line for was the lake, which received the remainder.

A lake with no outlet is a balance between inflow and evaporation. Cut the inflow and the surface must shrink until evaporation from the smaller area matches what still arrives. The Aral did that. It fell, split into separate basins, and by the summer of 2014 NASA imagery showed the eastern basin of the southern Aral completely dry for the first time in the modern record. Salinity in the remaining southern water rose from around 10 grams per litre to well over 100, which is several times seawater, and the fishery of two dozen native species that had supported Moynaq was gone by the early 1980s. The exposed bed became a salt desert, and wind now lifts salt and agricultural residues from it and deposits them across the surrounding farmland and towns.

Every element of that story is physical geography from the earlier lessons in this course, run in reverse. This lesson is about what happens when people alter one term in a system they have measured only partially.

The same arithmetic on the southern plains

Thirty years earlier and eleven thousand kilometres away, the United States ran an unintentional version of the same experiment.

The southern Great Plains are semi-arid, with rainfall that swings hard between wet and dry decades. Their native cover was deep-rooted perennial grass whose root systems held the soil in place through droughts that had come and gone for millennia. Between about 1914 and 1930, high wheat prices, cheap land and the tractor turned tens of millions of acres of that sod over. The wet years of the 1920s made it look like sound judgement.

Drought arrived in 1931 and stayed. With no crop cover, no roots and no grass, the topsoil of a region the size of a country was loose, dry and exposed to a wind regime that had always been there. It went into the air. On 14 April 1935, remembered as Black Sunday, a dust cloud rolled across Oklahoma and the Texas panhandle and turned midday into darkness. Hugh Hammond Bennett, who had spent years arguing that soil erosion was a national emergency, was testifying in Washington that spring as plains dust dimmed the light over the capital. The Soil Conservation Act was signed on 27 April 1935, creating what is now the Natural Resources Conservation Service. Around two and a half million people left the Plains states during the decade.

The response was technical and it largely worked: contour ploughing so furrows run across the slope rather than down it, terracing, strip cropping, crop rotation, retirement of the most marginal land back to grass, and the Prairie States Forestry Project, which planted more than 200 million trees in shelterbelts between 1935 and 1942 to break the wind at ground level.

Bottom line: The drought was the trigger, not the cause. Droughts of that severity had crossed the same ground repeatedly without producing dust storms, because the sod was there. What changed was the cover, and the cover was the only variable under human control.

What a dam does downstream

A reservoir is a place where a river stops moving. Water can be released again; the sediment cannot, because the moment the current slows below the threshold for transport, the load drops to the reservoir floor and stays there. Global assessments put the share of river sediment intercepted by large reservoirs on the order of a quarter of the world total, and much higher in heavily regulated basins.

The Aswan High Dam, completed in 1970, is the case everyone learns, and the reason is that the Nile's silt had been the basis of Egyptian agriculture for five thousand years. It now settles in Lake Nasser. Egyptian farming shifted to manufactured fertiliser, and the delta, which had been maintained by that silt against the erosive work of the Mediterranean, began to lose the argument. The Rosetta and Damietta promontories have retreated at rates measured in tens of metres a year, and the delta is subsiding while receiving nothing to build it back.

The Colorado does the same thing with a different ending. Glen Canyon Dam closed in 1963, and between the dams and the irrigation withdrawals the river has almost never reached the Gulf of California since. Its delta, once a vast wetland, shrank to a fraction of its former area. In March 2014, under an agreement between the United States and Mexico, a deliberate pulse of water was released and, for the first time in many years, the Colorado reached the sea that May.

Louisiana shows what sediment starvation costs when it is added to subsidence. The Mississippi is leveed for navigation and flood control, so the sediment that once spread across the delta plain during floods is now delivered down a channel and off the edge of the continental shelf. USGS mapping puts coastal wetland loss in Louisiana since the 1930s at roughly 4,800 square kilometres. A delta is not a place; it is a process, and the process has been switched off while subsidence and sea level continue.

Levees, and the flood that gets worse

Levees deserve their own treatment, because they are the clearest example of a defence that changes the thing it defends against.

Confine a river between walls and you have removed its floodplain, so the same discharge must now pass through a narrower cross-section, which it does by running deeper and faster. Stage rises for a given flow, both there and upstream. Meanwhile the sediment that would have spread across the floodplain is deposited within the confined channel instead, so the bed aggrades, and the levees must be raised to keep pace. The Yellow River in China is the extreme case: in places its bed now sits many metres above the surrounding plain, held in by embankments, which is a stable arrangement only for as long as the embankments hold.

There is a social term in the equation as well, sometimes called the levee effect. A protected floodplain looks safe, so it gets built on, so the value at risk behind the levee rises, so a failure that is rarer is also far more expensive. The 1927 Mississippi flood and the 1993 Midwest floods both delivered that lesson, and both were followed by arguments about whether the answer was higher levees or setback levees and restored floodplain.

Ground that sinks and does not come back

An earlier lesson followed the water table under the High Plains down. Here is the geomorphic consequence.

When water is pumped out of an aquifer faster than it is replaced, the pressure that helped support the weight of the overlying sediment falls, and the fine-grained clay and silt layers compact. The surface drops. In California's San Joaquin Valley, USGS surveys documented subsidence of up to about 8.5 metres near Mendota between 1925 and 1977, a figure preserved in Joseph Poland's photograph of a telephone pole with the successive land surfaces marked on it above his head. Parts of central Mexico City have dropped roughly nine metres over the past century, wrecking drainage, sewers and colonial buildings. Parts of Jakarta have been subsiding by more than a decimetre a year, which is one reason Indonesia decided to build a new capital.

The important property is that this is largely irreversible. Sand and gravel layers rebound when pressure returns. Clay layers do not; their compaction is permanent, and with it goes a permanent loss of the aquifer's capacity to store water at all. You do not simply lower the water table and then refill it. You destroy part of the container.

Cities as physical systems

A city changes the surface energy balance and the water balance at the same time, and both effects are measurable with the tools from Module 1.

Replace vegetation and soil with asphalt, concrete and roofing and you lower the albedo of the surface, remove the evaporative cooling that transpiring plants provided, add thermal mass that stores heat through the day and releases it at night, and add waste heat from engines and air conditioning. The result is the urban heat island. The United States Environmental Protection Agency puts the annual mean air temperature of a city of a million or more at roughly 1 to 3 degrees Celsius above its rural surroundings, with the gap on a clear, calm evening reaching as much as 12 degrees. That is not a curiosity: it raises cooling demand, worsens heatwave mortality, and shifts the timing of frost and the growing season across the metropolitan area.

The water balance changes in parallel. Impervious surfaces cut infiltration to near zero and storm drains deliver the runoff to the channel in minutes rather than hours, so the hydrograph you built in the drainage-basin lesson grows a much higher peak with a much shorter lag. The same rainfall produces a flood that the pre-urban catchment would have absorbed. The engineering response, detention basins, permeable paving, green roofs and swales, works by restoring storage and delay rather than by enlarging pipes.

How much rock people move

Step back and ask how humans rank as a geomorphic agent. Roger Hooke put numbers to it: earth moved deliberately by construction, mining and agriculture amounts to something on the order of 40 billion tonnes a year, which exceeds the total sediment all the world's rivers carry to the sea. Add the material moved unintentionally through accelerated soil erosion and the imbalance grows.

The land-cover figures are of the same order. Agriculture occupies something close to 38 percent of the world's land surface. Mountaintop removal mining has reshaped ridge lines across central Appalachia and buried headwater streams under valley fill. Roughly two thirds of the world's long rivers no longer run freely from source to sea. When geologists argue about whether the present interval deserves its own name in the geological timescale, this is the sort of evidence they are arguing over, and the physical case is stronger than the terminology dispute suggests.

Why this matters: Humans are not one influence among many on the Earth's surface. Measured in tonnes moved per year, we are the largest single geomorphic agent operating on the continents.

Three reversals

It would be dishonest to end there, because some of these changes have been undone, and knowing which ones is the practical part of the subject.

At the northern end of the Aral, Kazakhstan built the Kok-Aral dam in 2005, sealing the North Aral Sea off from the drying southern basin so that the Syr Darya's flow accumulated in one place. The level rose by several metres within a few years, salinity fell far enough for native fish to survive again, and commercial fishing resumed in ports that had been stranded. The southern basin was not saved, and was not intended to be. A budget that could not close for the whole lake could close for part of it.

On the Olympic Peninsula, two dams on the Elwha River, in place since 1913 and 1927, were removed between 2011 and 2014, the largest dam removal ever undertaken in the United States. Millions of cubic metres of trapped sediment moved downstream, rebuilding the river mouth and the beaches beside it, and salmon were recorded above the former dam sites within a year of the barriers coming out. The river reassembled itself faster than most people predicted.

And on the southern plains, the shelterbelts, contour ploughing and conservation tillage that followed 1935 held through the drought of the 1950s, which was in some places drier than the 1930s and produced nothing like the same catastrophe. That is the strongest available evidence that the Dust Bowl was a land-management failure rather than a weather event.

What separates the reversible cases from the others is whether the physical capacity to recover survived. A river still has its sediment and its fish, so it can rebuild a delta once you stop holding the material back. A compacted clay aquifer has lost its pore space permanently, and no amount of subsequent restraint returns it.

Common misconceptions

• The Aral Sea dried up because of climate change. Its inflow was diverted for irrigation. The physical cause is an inflow term that was reduced deliberately, and the lake shrank until evaporation matched what was left.
• The Dust Bowl was caused by drought. Comparable droughts had crossed the same plains without stripping them. What changed was the removal of deep-rooted sod, and the proof is that the drought of the 1950s, with conservation measures in place, did not repeat it.
• A dam affects only the river above it. Trapping sediment starves deltas and beaches hundreds of kilometres downstream, which is why the Nile delta and southern California beaches are both retreating.
• Levees reduce flood risk. They reduce flood frequency at the protected spot while raising stage elsewhere, forcing the bed to aggrade, and increasing the value exposed when they eventually fail.
• Land that has subsided from groundwater pumping will rise again if pumping stops. Clay compaction is permanent, and the aquifer's storage capacity is destroyed along with the elevation.
• Damage on this scale cannot be undone. The North Aral Sea and the Elwha River both recovered substantially within a decade, because in each case the physical capacity for recovery was still present.

The takeaway

• The Aral Sea fell from roughly 68,000 square kilometres in 1960 to a dry eastern basin by 2014 because its two feeder rivers were diverted, and salinity rose from about 10 grams per litre to over 100.
• The Dust Bowl followed the ploughing of deep-rooted sod on a semi-arid plain, and the conservation measures adopted after 1935 prevented a repeat in the drier 1950s.
• Reservoirs trap sediment permanently, starving deltas and coasts; the Nile delta retreats at tens of metres a year and Louisiana has lost roughly 4,800 square kilometres of wetland since the 1930s.
• Levees raise flood stage, force the channel bed to aggrade, and concentrate value behind a defence that fails rarely and expensively.
• Groundwater overdraft compacts clay layers irreversibly, producing up to about 8.5 metres of subsidence in the San Joaquin Valley and destroying aquifer storage capacity.
• Cities raise mean temperature by roughly 1 to 3 degrees Celsius, up to about 12 on a calm clear night, and convert rainfall into rapid runoff with a high, early hydrograph peak.
• Deliberate human earth moving, on the order of 40 billion tonnes a year, exceeds the sediment delivered by all the world's rivers combined.
• Recovery is possible where the physical capacity for it survives, as at the North Aral Sea after 2005 and on the Elwha after the dams came out.

Sources

1. National Aeronautics and Space Administration. (n.d.). Earth Observatory: World of change, the shrinking Aral Sea. earthobservatory.nasa.gov
2. Encyclopaedia Britannica. (n.d.). Aral Sea. britannica.com
3. United States Geological Survey. (n.d.). Water Science School: Land subsidence. usgs.gov
4. United States Environmental Protection Agency. (n.d.). Heat islands. epa.gov
5. National Park Service. (n.d.). Olympic National Park: Elwha River restoration. nps.gov
6. Hooke, R. LeB. (2000). On the history of humans as geomorphic agents. Geology, 28(9), 843-846.