A stable estimator for linear models: 1. Theoretical development and Monte Carlo Experiments

Instant unit hydrograph (IUH) type linear models have been widely used to simulate many hydrologic systems. Unfortunately, the classical parameter estimators used to calibrate this type of model often fail to give a reliable and meaningful solution. It has been suggested that a set of constraints that can be deduced from the physics of the hydrologic system be imposed on the IUH in order to reduce the high sensitivity of the classical estimators to errors in the available data. Therefore a mathematically correct constrained estimator has been devised, and its solution is obtained by using quadratic programing. The higher degree of efficiency of this estimator (smaller dispersion of the estimates about the true value) is shown numerically through Monte Carlo experiments.