Bryson C. Bates

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.

Performance of conceptual rainfall-runoff models in low-yielding ephemeral catchments

Low-yielding catchments with ephemeral streams involve highly nonlinear relationships between rainfall and runoff, and there is much less documentation and appreciation of the ability to predict streamflow in these veiy difficult cases than in humid catchments. The predictions of three conceptual rainfall-runoff models are assessed in three low-yielding, emphemeral streams over a 10-year period. The models are a simple conceptual model, Generalized Surface inFiltration Baseflow (GSFB; eight parameters), a hybrid metric/conceptual model, Identification of Hydrographs and Components from Rainfall, Evaporation and Streamflow data (IHACRES; six parameters), and a complex conceptual model, the Large Scale Catchment Model (LASCAM; 22 parameters). The Salmon (0.82 km2), Stones (15 km2), and Canning (517 km2) catchments in Western Australia were selected for their range of sizes and low runoff yields (1.6–12.2% of rainfall). Their behavior is representative of a large part of Australia and semiarid regions, where antecedent conditions are critical determinants of streamflow response to rainfall. Such catchments provide a stern test of the capability of conceptual models. Five-year calibration and validation performances were assessed with a range of statistics. The models were run daily but performance was assessed on both a daily and monthly basis by aggregating daily model streamflows and observations up to monthly. The models performed well, particularly in the monthly case where often more than 90% of the variance of observed streamflow was explained in simulation on independent periods. However, while the simple conceptual model is adequate for monthly time periods, the daily simulation results indicate that a slightly more complex model (the hybrid model or the complex conceptual model) is required for daily predictions in these dry catchments. The model simulation results extend the following notion of Jakeman and Hornberger [1993] from humid to semiarid ephemeral catchments: that a model of about six parameters, albeit in an appropriate model structure, is sufficient to characterize the information in rainfall-discharge time series over a wide range of catchment sizes. Models of such modest complexity also predict runoff with good accuracy outside calibration periods, even in ephemeral, low-yielding catchments. The simulation results highlight the critical importance of the deep groundwater and antecedent moisture conditions on stream yields in ephemeral catchments and point to the desirability of accounting for these factors in arid-zone modeling.

A spatiotemporal model for downscaling precipitation occurrence and amounts

A stochastic model that relates synoptic atmospheric data to daily precipitation at a network of gages is presented. The model extends the nonhomogeneous hidden Markov model (NHMM) of Hughes et al. by incorporating precipitation amounts. The NHMM assumes that multisite, daily precipitation occurrence patterns are driven by a finite number of unobserved weather states that evolve temporally according to a first-order Markov chain. The state transition probabilities are a function of observed or modeled synoptic scale atmospheric variables such as mean sea level pressure. For each weather state we evaluate the joint distribution of daily precipitation amounts at n sites through the specification of n conditional distributions. The conditional distributions consist of regressions of transformed amounts at a given site on precipitation occurrence at neighboring sites within a set radius. Results for a network of 30 daily precipitation gages and historical atmospheric circulation data in southwestern Australia indicate that the extended NHMM accurately simulates the wet-day probabilities, survival curves for dry- and wet-spell lengths, daily precipitation amount distributions at each site, and intersite correlations for daily precipitation amounts over the 15 year period from 1978 to 1992.

Probabilistic optimization for conceptual rainfall-runoff models : A comparison of the shuffled complex evolution and simulated annealing algorithms

Automatic optimization algorithms are used routinely to calibrate conceptual rainfall-runoff (CRR) models. The goal of calibration is to estimate a feasible and unique (global) set of parameter estimates that best fit the observed runoff data. Most if not all optimization algorithms have difficulty in locating the global optimum because of response surfaces that contain multiple local optima with regions of attraction of differing size, discontinuities, and long ridges and valleys. Extensive research has been undertaken to develop efficient and robust global optimization algorithms over the last 10 years. This study compares the performance of two probabilistic global optimization methods: the shuffled complex evolution algorithm SCE-UA, and the three-phase simulated annealing algorithm SA-SX. Both algorithms are used to calibrate two parameter sets of a modified version of Boughtons [1984] SFB model using data from two Australian catchments that have low and high runoff yields. For the reduced, well-identified parameter set the algorithms have a similar efficiency for the low-yielding catchment, but SCE-UA is almost twice as robust. Although the robustness of the algorithms is similar for the high-yielding catchment, SCE-UA is six times more efficient than SA-SX. When fitting the full parameter set the performance of SA-SX deteriorated markedly for both catchments. These results indicated that SCE-UAs use of multiple complexes and shuffling provided a more effective search of the parameter space than SA-SXs single simplex with stochastic step acceptance criterion, especially when the level of parameterization is increased. Examination of the response surface for the low-yielding catchment revealed some reasons why SCE-UA outperformed SA-SX and why probabilistic optimization algorithms can experience difficulty in locating the global optimum.

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 ...

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.

Short communication: Statistical downscaling of rainfall data using sparse variable selection methods

In many statistical downscaling methods, atmospheric variables are chosen by using a combination of expert knowledge with empirical measures such as correlations and partial correlations. In this short communication, we describe the use of a fast, sparse variable selection method, known as RaVE, for selecting atmospheric predictors, and illustrate its use on rainfall occurrence at stations in South Australia. We show that RaVE generates parsimonious models that are both sensible and interpretable, and whose results compare favourably to those obtained by a non-homogeneous hidden Markov model (Hughes et al., 1999).

Stochastic Down-Scaling of General Circulation Model Simulations

Modelling the response of agricultural and natural ecosystems to climate forecasts requires daily data at local and regional scales. General circulation models (GCMs) provide reasonable simulations of atmospheric fields at the synoptic scale. However, they tend to over-estimate the frequency and under-estimate the intensity of daily precipitation. Stochastic downscaling techniques provide a means of linking the synoptic scale with local scales. They can be used to quantify the relation of climate variables at small space scales to the larger scale atmospheric patterns produced by GCMs. This paper reviews downscaling techniques from an applications perspective. It then presents a case study involving the use of a downscaling technique known as the nonhomogeneous hidden Markov model (NHMM). A NHMM fit to a 15-year record of daily atmospheric-precipitation data is used to downscale GCM atmospheric fields for South-West Western Australia. We compare the downscaled and observed ‘winter’ precipitation statistics at six stations near Perth, Western Australia. The results show that a downscaled GCM simulation provides credible reproductions of observed precipitation probabilities and the frequencies of wet and dry spells at each station.

Simulated Impacts of Climate Change on Groundwater Recharge in the Subtropics of Queensland, Australia

Increased atmospheric concentrations of CO2 could affect Australia’s groundwater resources via changes in rainfall and potential evapotranspiration regimes. The extent to which groundwater resources are affected by climate change will depend upon the local soils and vegetation. As a case study, we assess the potential impacts of climate change on groundwater recharge beneath North Stradbroke Island off the subtropical east coast of Queensland, Australia The simulated climates come from equilibrium (constant CO2 concentration) runs of the CSIRO9 general circulation model (GCM) for present and double-CO2 conditions. Based on the GCM output for each climate, a stochastic point weather generator, MWGEN, produces realisations of the daily climate variables. This climate “data” drives a numerical simulator, WAVES, of rainfall infiltration, variably saturated flow and evapotranspiration, producing temporal distributions of the daily groundwater recharge rate for various soil-vegetation environments. The transformation from rainfall infiltration to groundwater recharge can amplify the effects of climate change because of flow and storage in soils and dynamic plant water use. The simulation results indicate that double-CO2 climate change could more than double the net groundwater recharge; this increase is disproportionate to a 37 percent rise in mean annual rainfall, with ratios of the change in recharge to change in rainfall ranging from 0.76 to 1.05 for different soil-vegetation combinations. Such increases in recharge are enhanced by the dynamic growth and die-back of vegetation. The mean recharge rate, inter-annual variability and persistence in deviations from the mean are related to the soil and vegetation characteristics. Further improvements in estimating future climate and plant-water use should increase our understanding of the sensitivity of groundwater resources to expected climate change and climate variability.