Kalman Filter in Open Channel Flow Estimation

In computing water surface profiles in open channels, uncertainties often arise in selection of resistance coefficients, such as Manning's n. In this paper the Kalman filtering approach is developed to deal with such uncertainties. This approach combines a mathematical system model and an observation model. The former consists of (1)A stochastic nonlinear differential equation governing the steady one-dimensional open channel flow; and (2)one of three possible stochastic differential equations expressing Manning's n (constant, function of the location of channel cross section, or function of both the location and the water depth). The observation model simply shows the observed water depth as the sum of true water depth and error. The estimation technique was tested for its accuracy in generating estimates of water depth and Manning's n at several different schemes of sampling or measuring water depths. Results with Kalman filtering are compared with two paralle methods normally used today.