Wade the section, and at each vertical record how far across you are, how deep it is, and how fast it is going. Each vertical owns half the distance to its neighbour on each side — that is the mid-section method, and it is what a gauging station does.
In water shallower than about 0.75 m, one reading at six tenths of the depth below the surface is taken as the mean for that vertical. Deeper than that, read at two tenths and eight tenths and average them. Both rules exist because the velocity profile through a natural channel is roughly logarithmic, and those are the depths where the local velocity equals the mean.
A flood you did not see can still be measured: the slope of the water surface, the shape of the channel and how rough it is. Manning's n is the weak link and everybody knows it — the answer is as good as that guess and no better.
| channel | n |
|---|
Groundwater moves because the head falls, and how fast depends on the rock. Darcy velocity is not the speed of the water — it is the flow spread over the whole cross section, rock included. Divide by the porosity that actually connects and you get the speed a contaminant travels, which is several times higher and the number that matters.
| material | K, m/day |
|---|
Pump a well at a steady rate, watch the drawdown in an observation well, and plot it against the logarithm of time. After the early minutes it becomes a straight line, and the line is the aquifer: its slope gives transmissivity, where it crosses zero gives storage.
What is in the water is a separate question with its own instrument — Water chemistry for the ions, hardness, saturation and whether it can be drunk or irrigated with. This one only deals with how much of it moves and how fast.