AKA "That time Octavia calibrated roughness models to 129 separate rainfall runoff experiments" -- read it here.
Predicting how much runoff you'll get after rain is important, but hard. One of the many uncertainties in modeling runoff is applying a flow resistance measure to a given landscape. Flow resistance is like friction - it describes how energy is lost from flowing water to the underlying surface.
Most runoff models represent flow resistance with an equivalent roughness. You might have come across a Chezy coefficient, a "friction factor" or a Manning’s n. Modelers calibrate their model by adjusting this roughness measure until the model can reproduce available discharge observations at watershed scale. But it's always nice to have "real" measurements of things, not just calibrated numbers. So there have been a lot of experiments where flow amounts and velocities are measured together, which allows you to calculate the "real" equivalent roughness. The figure below shows an example of a rainfall - runoff plot - one of 129 used by the USDA for this purpose. The graph in the middle shows how rainfall simulators were used to estimate runoff -- the rainfall rate was increased (blue) until the runoff equilibrated (orange), and infiltration could be estimated from mass balance (green). The right hand plot shows how the data from the middle plot get re-arranged and the roughness is estimated as the slope of the lines. Different roughness measures (Manning etc) have different roughness parameter and are shown in different colours.
But here's the wacky thing. When reviewing the literature about roughness estimates there is a bit jump in the values of equivalent roughness obtained for short runoff plots versus long runoff plots. Small plots measured with rainfall simulators seemed to have up to 10 times the estimated roughness of large plots measured under rainstorms.
We don't usually think of flow resistance as being dependent on the scale that you measure it on. It's as if someone said: 'you get 10 times as much friction on your car wheels (per unit m driven) if you drive 10 km than if you drive 100 km'. It seems wacky - we think of friction as being a property of a surface, not something that cares about how long that surface goes on for.
Clever Octavia Crompton worked out how to resolve this conundrum by realising that the estimated roughness in a runoff experiment is related to, but different than the calibrated equivalent roughness obtained by taking flow data in a model. In experiments, velocities are obtained based on a tracer release, and so represents a path-averaged quantity. However, discharge itself is not path averaged in the same way and so estimates of roughness using discharge alone (through model calibration) are different to those based on the velocity and discharge measured at the outlet.
Octavia used her understanding of shallow flow to determine a correction factor that links these two measures of roughness, allowing us to harmonize roughness estimates from model calibration and from experiments.
She then used a Saint Venant Equation model to represent runoff in those 129 runoff plots. The correction factors needed to get the calibrated roughness to agree with experiment weren't enormous - experimental roughness was average of 0.46, and the. calibrated and average of 0.39 (that's panel A below). Using the correction factors allowed the experimentally determined discharge and velocity to be reconciled with the modeled versions (panels B and C, which show the cumulative distribution of these values across all the 129 runoff plots). The difference between predictions made with experimental and calinbrated roughness wasn't large for discharge, but was much larger for velocity.
So if you want to use runoff plots to estimate roughness, AND you want to use that roughness to predict flow velocities or runoff at larger scales - you should check out Octavia's correction factor!
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