Linear stochastic conceptual response models for small catchments
By randomizing the inputs to the deterministic Nash-Dooge linear reservoir cascade, linear stochastic conceptual response models suitable for small catchments are formulated as simple linear stochastic dynamical systems within the formalism of stochastic differential equations (SDE’s). The system driving processes, rainfall and evapotranspiration losses, the latter regarded as a negative input, are modeled respectively as a compound Poisson process and a mean zero white Gaussian noise superposed on a deterministic mean. Elementary stochasticized Nash-Dooge cascades of n equal linear reservoirs and two reservoirs in parallel are given as potential models of surface and subsurface response. On consideration of recent discoveries concerning streamflow generation, a more conceptually plausible coarse-grained dynamical model of parallel quick and slow response regimes is developed by confining all evapotranspiration losses to the slow reservoir, modeling evapotranspiration fluctuations as mean zero colored Gaussian noise and rationalizing a linearized infiltration model dependent on slow regime outflow just prior to an event. In essence, the effort is directed towards generalizing the deterministic Nash-Dooge theory of the unit hydrograph to a linear stochastic theory of catchment response.