Maximum Likelihood Estimators for Coarsely Resolved Precipitation Data

Abstract

Most of the literature dealing with hydrologic frequency analysis treats data as being exact and error free. This paper demonstrates that the use of common estimators for distribution parameters and quantiles can lead to serious biases and inadequate assessments of uncertainties when data are coarsely resolved, which is often the case for short-duration precipitation data. Alternative estimators are presented for cases of both data truncation and data rounding and are shown to be superior to common estimators for fitting of exponential and Gumbel probability distributions. A technique is also recommended for determination of the fraction of a data set that would be expected to consist of zeros, enabling an objective approach to augmentation of nonzero data.