A Bayesian methodology is developed to evaluate parameter uncertainty in catchment models fitted to a hydrologic response such as runoff, the goal being to improve the chance of successful regionalization. The catchment model is posed as a nonlinear regression model with stochastic errors possibly being both autocorrelated and heteroscedastic. The end result of this methodology, which may use Box-Cox power transformations and ARMA error models, is the posterior distribution, which summarizes what is known about the catchment model parameters. This can be simplified to a multivariate normal provided a linearization in parameter space is acceptable; means of checking and improving this assumption are discussed. The posterior standard deviations give a direct measure of parameter uncertainty, and study of the posterior correlation matrix can indicate what kinds of data are required to improve the precision of poorly determined parameters. Finally, a case study involving a nine-parameter catchment model fitted to monthly runoff and soil moisture data is presented. It is shown that use of ordinary least squares when its underlying error assumptions are violated gives an erroneous description of parameter uncertainty. INTRODUCTION The catchment models referred to in this two paper sequence accord with the definition given by Moore and Clarke [1981]; namely, (1) they describe conceptually land-based hydrologic processes which are spatially averaged or lumped, and (2) some of their parameters are estimated by fitting to observed hydrologic data such as rainfall, pan evaporation, and streamflow. Such models have become important tools aiding water resources management. Recent state-of-the-art reviews including those of Chapman [1975], Sittner [1976], and Mein and McMahon [1982] have identified the following five major applications of catchment models: (1) extension of streamflow records, (2) generation of runoff satistics, (3) assessment of the effects of land use changes, (4) prediction at ungauged catchments, and (5) prediction of the effects of land use change on hydrologic regime. Of the five, it is generally agreed that only the first three have been successfully implemented. To succeed in the first three applications, it suffices to identify and fit a model capable of satisfactorily converting hydrologic inputs such as rainfall into outputs such as runoff. However, implementation of the last two applications is considerably more difficult. For catchment models fitted to rainfall-runoff data, the approach typically attempted is to develop regression relationships between optimized parameters and catchment characteristics. But success with such a regionalization approach has been limited. For example, Magette et el. [1976] developed regression relationships between six fitted parameters of the Kentucky watershed model and 15 measurable catchment characteristics. Independent tests revealed that errors in prediction of mean annual flows ranged from less than 1% to 860%. At least two reasons can be advanced to explain this limited success: 1. Poorly determined optimized parameters can obscure a useful regionalization relationship. XNow at Water Supply Division, Melbourne and Metropolitan Board of Works.