Parameter interdependence and uncertainty induced by lumping in a hydrologic model

Throughout the world, watershed modeling is undertaken using lumped parameter hydrologic models that represent real-world processes in a manner that is at once abstract, but nevertheless relies on algorithms that reflect real-world processes and parameters that reflect real-world hydraulic properties. In most cases, values are assigned to the parameters of such models through calibration against flows at watershed outlets. One criterion by which the utility of the model and the success of the calibration process are judged is that realistic values are assigned to parameters through this process. This study employs regularization theory to examine the relationship between lumped parameters and corresponding real-world hydraulic properties. It demonstrates that any kind of parameter lumping or averaging can induce a substantial amount of ‘structural noise’ which devices such as Box-Cox transformation of flows and auto-regressive moving average (ARMA) modeling of residuals are unlikely to render homoscedastic and uncorrelated. Furthermore, values estimated for lumped parameters are unlikely to represent average values of the hydraulic properties after which they are named and are often contaminated to a greater or lesser degree by the values of hydraulic properties which they do not purport to represent at all. As a result, the question of how rigidly they should be bounded during the parameter estimation process is still an open one