Developing a New Deconvolution Technique to Model Rainfall-Runoff in Arid Environments

Abstract

The primary accomplishment of this research has been demonstrating the power of the deconvolution technique developed by Neuman and de Marsily (1976) in dealing with noisy rainfall- runoff records of short duration. Such records are encountered in arid environments where rainfall often occurs in short isolated bursts and the data are measured with a considerable margin of error. Our research work consisted of superimposing known noise on synthetic rainfall- runoff data and examining the ability of the Neuman -de Marsily deconvolution method to estimate the correct impulse response of the system when the data include only a single storm event. Approximately 50 Monte Carlo simulation runs were performed for each of three different noise models considered in our work. The results clearly demonstrated that the deconvolution model leads to reliable estimates and can be used with confidence in the presence of realistic noise levels. In addition to the Monte Carlo simulation tests and their analysis, certain improvements were introduced into the original deconvolution technique. In particular, the original version of the technique required that the hydrologist exercise subjective judgement in choosing the "best" solution for the deconvolution problem from a large number of admissible solutions. Our new method of selecting the "best" result is based on a comparative analysis of residuals and is more reliable than the earlier subjective approach. The improved method has been applied to real as well as synthetic rainfall -runoff data.