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 meters 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 neighbor 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 how differently that bargaining position can fall.
| System | Where the water comes from | Downstream exposure | The flashpoint |
|---|---|---|---|
| Indus South Asia | Snow and glacier melt from the Himalaya, Karakoram and Hindu Kush, with monsoon rain on the foothills — very little from the arid plains downstream | Extreme. Pakistan’s farming runs overwhelmingly on the Indus irrigation system, fed by rivers that rise or pass upstream of its border | The 1960 Indus Waters Treaty, brokered by the World Bank, split the system by river: the eastern rivers to India, the western rivers to Pakistan. India may build run-of-the-river hydropower on the western rivers within storage limits — so every new project’s storage becomes the argument |
| Mekong SE Asia | Tibetan snowmelt in the headwaters, then heavy monsoon rain over Laos, Thailand, Cambodia and Vietnam | Real but buffered. Most of the annual flow joins below China’s upper-Mekong dams — though the upstream share is much larger in the dry season | The upstream dam cascade: when it stores and releases water, how much sediment it traps before the delta, its effect on the Tonlé Sap flood pulse, and whether flow data is shared with the downstream Mekong River Commission |
That contrast is the whole point. Pakistan’s exposure is severe because the water that matters is generated in mountains upstream while its own plains are dry; the lower Mekong’s is real but partial because monsoon rain falling below the dams supplies most of the river. Where the water is generated relative to the border decides how much leverage exists — and seasons matter as much as annual totals, because control over the dry-season flow is control over the months that hurt.
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.