Bayesian model averaging with fixed and flexible priors: theory, concepts, and calibration experiments for rainfall-runoff modeling

This paper introduces for the first time the concept of Bayesian Model Averaging (BMA) with multiple prior structures, for rainfall‐runoff modeling applications. The original BMA model proposed by Raftery et al. (2005) assumes that the prior probability density function (pdf) is adequately described by a mixture of Gamma and Gaussian distributions. Here we discuss the advantages of using BMA with fixed and flexible prior distributions. Uniform, Binomial, Binomial‐Beta, Benchmark, and Global Empirical Bayes priors along with Informative Prior Inclusion and Combined Prior Probabilities were applied to calibrate daily streamflow records of a coastal plain watershed in the South‐East USA. Various specifications for Zellner's g prior including Hyper, Fixed, and Empirical Bayes Local (EBL) g priors were also employed to account for the sensitivity of BMA and derive the conditional pdf of each constituent ensemble member. These priors were examined using the simulation results of conceptual and semi‐distributed rainfall‐runoff models. The hydrologic simulations were first coupled with a new sensitivity analysis model and a parameter uncertainty algorithm to assess the sensitivity and uncertainty associated with each model. BMA was then used to subsequently combine the simulations of the posterior pdf of each constituent hydrological model. Analysis suggests that a BMA based on combined fixed and flexible priors provides a coherent mechanism and promising results for calculating a weighted posterior probability compared to individual model calibration. Furthermore, the probability of Uniform and Informative Prior Inclusion priors received significantly lower predictive error whereas more uncertainty resulted from a fixed g prior (i.e. EBL)

Application of acceptance probability approach for determination of optimal rain gauge network density (Case study: South Khorasan province)

For accurate estimation of rainfall, as a key element in agricultural and water balance studies, an optimum density of raingauges is required. Although many approaches based on geostatistic are developed to optimize raingauges network, but majority of them suffer from drawbacks. This study aimed to assess a newly developed method in geostatistic based on acceptance probability, for designing the raingauge network with least error in South Khorasan province. The linear moment method was used for testing the homogeneity of the study stations. Then, by choosing a suitable semi-variogram, the acceptance probability in the region was calculated. Based on the spatial pattern of annual rainfall, the acceptance probability was worked out for various parts of the province and the acceptance accuracy (AP) values were analyzed at different levels of probability. The results showed that 20 stations of existing network had no significant effect on estimating the rainfall and it can be recommended to shift their location in order to obtain an optimal network. Also, similar to the existing network of 63 stations, the remaining 43 stations could cover 36% of the province at the probability acceptance level of 80%. Besides, the results indicated that by adding 27 rain gauges to the locations specified in the optimal density, the performance of the optimized network will be approximately doubled comparing to previously existing one, which means 65% coverage of province