How Do You Measure a River? Height Is Easy and Flow Is Not

The quantity people want is discharge, meaning the volume of water passing a point each second, and it cannot be measured continuously by any practical instrument. What can be measured continuously and cheaply is stage, meaning the height of the water surface, which a float in a stilling well, a pressure sensor or a radar looking down all record reliably and automatically. Converting one into the other requires a relationship between them, established by measuring discharge directly on a number of occasions across a range of levels and fitting a curve through the results. That curve is the rating, and everything published about a river's flow depends on it being right.

Direct measurement is laborious, which is why it is done occasionally rather than continuously:

• •Dividing the channel into vertical sections and measuring velocity and depth in each
• •Velocity sensors lowered from a bridge, a cableway or a boat
• •Acoustic instruments that profile velocity across the whole section at once
• •Dilution gauging, releasing a tracer and measuring its concentration downstream
• •Weirs and flumes of known geometry, where level alone gives discharge by calculation
• •Each method has a range of conditions it suits and none covers a flood safely

A rating is not permanent, and keeping it current is most of the work. The channel changes, since sediment is deposited and scoured, banks erode and vegetation grows, and any of those alters the depth at which a given flow passes. Structures are built. Debris accumulates and is cleared. The relationship also differs between a rising and a falling river, since water on the rise has a steeper surface slope and therefore moves faster at the same depth. And the highest flows are the least well determined, because measuring during a flood is dangerous and rarely done, so the upper part of the curve is extrapolated beyond any measurement, which is exactly the part flood warnings depend on.

Several traditional indicators tell an observer something about a river without any equipment, and they remain useful. Debris caught in vegetation and against structures marks the height of the last significant flood and stays visible for months. A distinct line of staining, moss or scour on a bank or bridge pier marks the level water regularly reaches. Vegetation zonation up a bank records how often each level is submerged. Old flood marks cut into walls and buildings record exceptional events, sometimes across centuries, and in several European towns those marks are the longest flood record available. Local names for fields and features frequently record flooding, which is why a house on a plot with a watery name is worth asking about.

Long series from these stations underpin a great deal. Flood risk is estimated by fitting a distribution to the annual maximum flows recorded at a station and extrapolating to the rarer events that determine design standards for defences, bridges and planning decisions, which means an error in the rating propagates into everything built on it. Water resource planning depends on knowing what flows are reliably available. Abstraction licences are set against measured flows. Ecological assessment depends on whether flows stay within a range. Detecting change over decades requires records long enough to separate a trend from ordinary variability, which is why the oldest stations are disproportionately valuable and why losing a long record is a permanent loss.

Water level is measured continuously and cheaply while discharge is not, so flow is inferred through a curve established by occasional direct measurements. Channels shift and the relationship changes, and the highest flows are extrapolated beyond any measurement because gauging a flood is dangerous. Flood defence design rests on extrapolating those records to rarer events.