Linear Reservoirs and Numerical Diffusion

The conceptual model of a cascade of linear reservoirs, in particular the SSAR routing equation, is reviewed in the light of the theory of numerical diffusion. The SSAR routing equation is a special case of the Muskingum routing equation. Since the latter simulates the diffusion processes by off-centering the temporal derivative in its discrete formulation, it follows that the same numerical diffusion mechanism underlies the SSAR routing equation and its associated linear reservoir assumption. The extension of the technique to a cascade of linear reservoirs, thus providing an additional parameter for simulation purposes, is readily envisaged. The use of a conceptual model such as the cascade of linear reservoirs remains a problem of system identification: given an excitation (excess rainfall) and system response (basin outflow), the overall system characteristics (model parameters) are sought by calibration.