Bayesian estimation of erosion parameters. Part I. Theoretical development

This is the first of two articles that develop procedures for combining site measurements of erodibility with those contained in the Water Erosion Prediction Project (WEPP). Theoretical relationships are derived herein to estimate parameters using Bayesian estimation theory. Prior information is represented with a regression equation. Probability density functions are developed to represent the uncertainty in mean and variance assuming both normally and log-normally distributed erodibilities. For normally distributed values, the prior and posterior joint distributions are a normal-gamma distribution and the marginal distribution for the mean is a t-distribution. For log-normally distributed values, these relationships apply to the mean and variance of the log-transformed erodibility. Conversion relationships are given to determine the distributions of the untransformed data.