Edward P. Campbell

A Markov Chain Monte Carlo Scheme for parameter estimation and inference in conceptual rainfall-runoff modeling

A fully Bayesian approach to parameter estimation and inference in conceptual rainfall-runoff models (CRRMs) is presented. Computations are performed using a Markov chain Monte Carlo (MCMC) method based on the Metropolis-Hastings algorithm. Single-site and block updating schemes are used for model parameters subject to nonnegativity restrictions as well as interval, equality, and order constraints. Diagnostics for the convergence of the Markov chain and CRRM assessment are also considered. The MCMC approach produces samples from the joint posterior distribution of the model parameters. This provides more information than single-point estimates and avoids the need to use a normal approximation to the posterior as the basis for inference. The methodology is demonstrated using an eight-parameter conceptual rainfall-runoff model and two case studies from southeastern Australia. The first case study considers a watershed with high runoff yield over a 12-year period. The second case study considers a watershed with low yield over a 17-year period. The results indicate that (1) Bayesian methods provide an objective framework for model criticism and choice, (2) the proposed strategies for handling constraints on model parameters are effective, (3) the model parameters are sensitive to likelihood function selection, (4) the conventional approach of using a power transformation and an autoregressive process to stabilize error variance and model dependence in the residuals may have limited success, and (5) some care is required in the implementation of the MCMC approach and reliable results will be difficult to obtain when CRRM complexity exceeds the limitations of the rainfall-runoff data at hand. A key finding is that the MCMC scheme presented herein provides a powerful means of identifying specific inadequacies in the structure of CRRMs.

A Bayesian Approach to parameter estimation and pooling in nonlinear flood event models

A Bayesian procedure is presented for parameter estimation in nonlinear flood event models. We derive a pooling diagnostic using Bayes factors to identify when it is reasonable to pool model parameters across storm events. A case study involving a quasi-distributed, nonlinear flood event model and five watersheds in the southwest of Western Australia is presented to illustrate the capabilities and utility of the procedure. The results indicate that Markov chain Monte Carlo methods based on the Metropolis-Hastings algorithm are useful tools for parameter estimation. We find that pooling is not justified for the model and data at hand. This suggests that current practices in nonlinear flood event modeling may be in need of urgent review.

Characterizing and Modeling Temporal and Spatial Trends in Rainfall Extremes

Abstract A hierarchical spatial model for daily rainfall extremes that characterizes their temporal variation due to interannual climatic forcing as well as their spatial pattern is proposed. The model treats the parameters of at-site probability distributions for rainfall extremes as “data” that are likely to be spatially correlated and driven by atmospheric forcing. The method is applied to daily rainfall extremes for summer and winter half years over the Swan–Avon River basin in Western Australia. Two techniques for the characterization of at-site extremes—peaks-over-threshold (POT) analysis and the generalized extreme value (GEV) distribution—and three climatic drivers—the El Nino–Southern Oscillation as measured by the Southern Oscillation index (SOI), the Southern Hemisphere annular mode as measured by an Antarctic Oscillation index (AOI), and solar irradiance (SI)—were considered. The POT analysis of at-site extremes revealed that at-site thresholds lacked spatial coherence, making it difficult to ...

Bayesian learning and predictability in a stochastic nonlinear dynamical model

Bayesian inference methods are applied within a Bayesian hierarchical modeling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple nonlinear marine biogeochemical model. A novel approach is proposed to the formulation of the stochastic process model, in which ecophysiological properties of plankton communities are represented by autoregressive stochastic processes. This approach captures the effects of changes in plankton communities over time, and it allows the incorporation of literature metadata on individual species into prior distributions for process model parameters. The approach is applied to a case study at Ocean Station Papa, using particle Markov chain Monte Carlo computational techniques. The results suggest that, by drawing on objective prior information, it is possible to extract useful information about model state and a subset of parameters, and even to make useful long-term forecasts, based on sparse and noisy observations.

Regionalization of rainfall-runoff model parameters using Markov Chain Monte Carlo samples

A general approach to the regionalization of rainfall-runoff model parameters is developed that uses posterior calibration samples derived by Markov Chain Monte Carlo methods. For each watershed the posterior calibration samples are used to define the second-order properties of the posterior distribution of the model parameters. Regionalization of the model parameters is accomplished for all parameters simultaneously via a regional link function that links the posterior means to watershed characteristics. A linear model is a particular case of our general approach, and we examine its performance in some detail. We indicate nonlinear and nonparametric extensions that may also be accommodated. A case study involving a quasi-distributed, nonlinear flood event model and 39 watersheds in southwestern Australia is presented. We find that the regional model has substantial predictive ability.