Analysis of a parameter estimation technique for linear hydrologic systems using Monte Carlo simulation

Abstract

A large number of approaches have been suggested to attempt to determine the response of a watershed to precipitation. One manner of classification divides these into physically-based and non-physically-based models. The former attempts to incorporate into a mathematical model the physical processes and parameters (infiltration, evaporation, channel length, etc.) that influence watershed response. The latter uses a solely mathematical representation of the watershed response based on developing a transfer function between input (precipitation) and output (runoff) data sets, and are commonly known as black-box models. The subject of this study is a recently developed black-box linear system model that uses parametric programming to execute a bicriterion approach in creating a family of solutions to the response of a watershed during a given storm event. The two criteria employed were the physical plausibility (smoothness) of a response function and the error between the computed and actual runoff. A so-called "preferred" solution would then be selected that represents the most acceptable trade-off between these two criteria from amongst all those generated by the method. In the study presented here this approach was analyzed using the Monte Carlo simulation technique. Three types of Gaussian-based random error with known statistical parameters were imposed on an actual effective precipitation-direct surface runoff data set, and the resulting "noisy" data sets analyzed using the parametric programming technique. Additional selection criteria (based on the residuals between the computed and observed runoff) were developed to select the so-called "preferred" response function. The variance of the error of estimate was then computed separately using the "preferred" response function chosen from the actual input-output data set and various sets of response functions chosen from the "noisy" data sets. The lowest variance occurred for response functions designated as "preferred" using the selection criteria, and for response functions very slightly more and less plausible than the "preferred." In general, the value of variance of error of estimate was in proportion to the magnitude and complexity of the type of random error employed.