Surface water · hydrology
Every river is measured, predicted, dammed and argued over — usually in that order.
A stream is the easiest part of the water cycle to see and among the hardest to pin down. Its discharge has to be inferred from a stick in the water; its floods have to be predicted from records too short to contain the flood you care about; and the moment anyone builds a dam, the river stops being a physical system and becomes a political one.
Nobody measures a river’s discharge directly. You measure how deep and how fast, in strips across the channel, and add them up — then you do it often enough to never have to do it again.
Velocity and depth both vary across a channel — fastest near the middle and just below the surface, near zero at the bed and banks. So the section is split into strips, each one measured separately with a current meter, and the discharges summed. Edit any cell.
| Strip | width (m) | depth (m) | velocity (m/s) | area (m²) | q (m³/s) |
|---|---|---|---|---|---|
| Total discharge | — | — | |||
Measuring discharge is slow, wet and occasionally dangerous. Measuring stage — the water level — is trivial: a staff gage is a ruler bolted to a bridge pier. So you measure discharge at many stages once, fit a stage–discharge relation, and from then on read a number off a ruler and convert.
Two cautions that matter
The high end is the guessed end. There are very few measurements at extreme flows — nobody is wading a river in a flood — so the curve is extrapolated exactly where the numbers matter most. The discharge of a big flood always carries real error.
The channel moves. Erosion and deposition change the cross-section, so the same stage stops meaning the same discharge. Rating curves have to be re-checked and re-fitted, and a big flood usually invalidates the one you had.
A rating curve is a power law, Q = a(h − h0)b, where h0 is the stage at which flow would stop. Plotted on log axes it becomes a straight line, which is why gaging data are almost always shown that way.
A hydrograph is discharge plotted against time, and its shape is a readout of the whole catchment — how steep it is, what it is made of, how much of it is roofs and roads, and whether the ground was already wet when the rain came.
The same rainfall over the same basin produces very different hydrographs depending on what the water lands on. Change the catchment and watch the peak move.
Flood planning asks a question the data cannot quite answer: how big is the flood we should build for? The method is to rank the floods you have recorded, fit a line, and extrapolate past the end of your own record — which is exactly as uncomfortable as it sounds.
Take the largest discharge from each year, rank them biggest first, and assign each a recurrence interval by the Weibull formula. Plot discharge against log recurrence interval and the points fall close to a line you can extend.
A “100-year flood” is not a flood that happens once a century. It is a flood with a 1% chance in any given year — and that is a very different thing, as the arithmetic shows.
| Flood | 1 year | 2 years | 10 years | 30 years | 50 years | 100 years |
|---|
A dam converts a river into a schedule. That is its purpose and also its problem — because a river was already doing several jobs, and most of them depended on the timing it just lost.
| Run-of-the-river | Large reservoir | |
|---|---|---|
| Storage | Little or none — passes flow through as it arrives | Large, often years of flow |
| Power | Varies with the river; output drops in the dry season | Firm, dispatchable output year-round |
| Flood control | Essentially none | Substantial — the main civil justification |
| Land taken | Small footprint, few people displaced | Large inundation, often mass displacement |
| Evaporation | Negligible | Can be a major loss — a big shallow reservoir in a hot dry place loses metres a year |
| Sediment | Passes much of it; still traps some | Traps nearly all of it |
| Downstream effect | Modest — timing largely preserved | Large — the operator now controls the hydrograph |
| Geopolitics | Harder to weaponise: little ability to withhold | Filling it, and operating it, are both negotiable acts |
The distinction matters most on a shared river. A run-of-the-river dam upstream is a smaller threat to a downstream neighbour because there is little capacity to hold water back — though it still traps sediment, and the reassurance depends on the operator not later adding storage.
A transboundary river crosses borders, which means the country with the water is rarely the country that needs it most. Two systems show the two extremes of that bargaining position.
| System | Where the water comes from | Downstream exposure | The flashpoint |
|---|---|---|---|
| Nile NE Africa | Overwhelmingly the Blue Nile, from the Ethiopian highlands — the White Nile contributes far less | Extreme. Egypt has almost no rainfall of its own and depends on flow generated entirely outside its borders | The GERD in Ethiopia. Its reservoir gives an upstream state real control over a river a downstream state cannot live without — and the filling rate alone is a negotiation |
| Brahmaputra GBM system | Himalayan snowmelt and monsoon rain, gathered across Tibet, India, Bhutan, Nepal and Bangladesh | Significant but buffered. Much of the flow is generated below the upstream dams, from monsoon rain falling on the lower basin | Upstream dams such as Zangmu, and — just as contentious — whether upstream states share the flow data that downstream flood warning depends on |
That contrast is the whole point. Egypt’s vulnerability is near-total because essentially all its water is generated upstream; Bangladesh’s is real but partial because a large share of the Brahmaputra’s flow enters below any dam a neighbour can build. Where the rain falls relative to the border decides how much leverage exists — which is why the precipitation maps from the last module are not a separate topic from the politics.
Streams, floods & dams
Evaporation, and why altitude matters
Reservoir evaporation scales with surface area, temperature, humidity, solar radiation and wind. So the same volume of water loses far less if it is stored deep and cool than broad and hot.
A reservoir in cool, humid highlands loses much less than a wide, shallow one in a hot desert — which is a real argument that storing a shared river’s water upstream wastes less of it. It is also, unavoidably, an argument that hands the upstream country the storage.
Physical efficiency and political control point the same direction here, and that is precisely what makes the dispute hard.