Estimation of Probability Distributions for Hydrometeorological Applications

Abstract

Hydrometeorologists use imperfect (i.e., incomplete and/or partially erroneous) measurements and imperfect models to make predictions, both for forecasting and to support scientific inference. Because no models or data are ever perfect, forecasting and hypothesis testing must account for uncertainty. The probability calculus is unarguably the most common quantitative framework used for this purpose. This article presents probabilistic methods for estimating and reducing uncertainty that are common in hydrometeorological applications. The major focus is on Bayesian methods and approximations of those methods based on ensembles (i.e., Monte Carlo methods). The article includes a brief overview of both parametric and nonparametric methods, a brief introduction to inverse methods, and a brief introduction to data assimilation from a Bayesian perspec- tive. It is important to caution that although the probability calculus can be used to estimate predictive uncertainty and to aid scientific reasoning, all applications of probabilistic reasoning necessarily contain some amount of subjectivity.