Exact Sensitivity Equation for One-Dimensional Steady-State Shallow Water Flow (Application to Model Calibration)

Abstract

Sensitivity analysis is an important tool that can be used for calibration of river flow models. Generally, friction coefficient is used as a calibration parameter for steady-state one-dimensional shallow water flow models. In this study, the local sensitivity analysis is used to derive a general rule for calibration of prismatic open channel models. For this, the sensitivity of the water depth to the friction coefficient is analytically derived for one-dimensional steady flow conditions in a wide rectangular channel. Also, the parameter of influence distance is defined to calibrate a channel reach using stage measurement at a given location. This characteristic distance allows 90% of the maximum possible variation in the sensitivity of the water depth to the friction coefficient to be captured. This parameter estimates the optimal length of a channel reach over which the friction coefficient can be calibrated from stage measurement. This length locates downstream of the stage measurement point in subcrit...