Sensitivity Equations for the One-Dimensional Shallow Water Equations: Practical Application to Model Calibration

A local perturbation approach is presented for the sensitivity analysis of the one-dimensional shallow water equations. Under steady state conditions the sensitivity of the water depth to the Strickler coefficient is shown to obey a first-order ordinary differential equation that becomes linear under uniform conditions. This allows a “half-distance” to be defined, which indicates the size of the region over which the Strickler coefficient can be calibrated from stage measurements. This region extends downstream of the stage measurement point under subcritical conditions and upstream under supercritical conditions. The validity of the approach is checked against typical backwater curve calculations. The sensitivity obtained by the local perturbation approach is very close to the empirical sensitivity, even when the Strickler coefficient is perturbed by $\pm 25\%$ , which validates the use of the approach in practical applications.