Bayesian model averaging assessment on groundwater management under model structure uncertainty

Abstract

This study introduces Bayesian model averaging (BMA) to deal with model structure uncertainty in groundwater management decisions. A robust optimized policy should take into account model parameter uncertainty as well as uncertainty in imprecise model structure. Due to a limited amount of groundwater head data and hydraulic conductivity data, multiple simulation models are developed based on different head boundary condition values and semivariogram models of hydraulic conductivity. Instead of selecting the best simulation model, a variance-window-based BMA method is introduced to the management model to utilize all simulation models to predict chloride concentration. Given different semivariogram models, the spatially correlated hydraulic conductivity distributions are estimated by the generalized parameterization (GP) method that combines the Voronoi zones and the ordinary kriging (OK) estimates. The model weights of BMA are estimated by the Bayesian information criterion (BIC) and the variance window in the maximum likelihood estimation. The simulation models are then weighted to predict chloride concentrations within the constraints of the management model. The methodology is implemented to manage saltwater intrusion in the ''1,500-foot'' sand aquifer in the Baton Rouge area, Louisiana. The management model aims to obtain optimal joint operations of the hydraulic barrier system and the saltwater extraction system to mitigate saltwater intrusion. A genetic algorithm (GA) is used to obtain the optimal injection and extraction policies. Using the BMA predictions, higher injection rates and pumping rates are needed to cover more constraint violations, which do not occur if a single best model is used.

Sensitivity analysis of the probability distribution of groundwater level series based on information entropy

“…There are many literatures about the methods of uncertainty analysis, for example, classical Bayesian techniques (Rojas et al 2010;Singh et al 2010;Tsai 2010), pseudoBayesian (Beven and Binley 1992;Beven and Freer 2001;Hassan et al 2008), geostatistics techniques (Feyen and Caers 2006;Feyen et al 2003;Liang et al 2009), and others. Generally, these methods are mainly focus on inversion of model parameters and uncertainty assessment of model output.…”

Hierarchical Bayesian model averaging for hydrostratigraphic modeling: Uncertainty segregation and comparative evaluation

“…When developing a conceptual model to represent a subsurface formation, uncertainties in model data, structure, and parameters always exist. To accommodate for different sources of uncertainty, strategies as model selection, model elimination, model reduction, model discrimination, and model combination are commonly used to reach a robust model, using single‐model approaches [ Cardiff and Kitanidis , ; Demissie et al ., ; Engdahl et al ., ; Feyen and Caers , ; Kitanidis , ; Gaganis and Smith , ; Irving and Singha , ; Nowak et al ., ; Wingle and Poeter , ] or multimodel approaches [ Doherty and Christensen , ; Li and Tsai , ; Morales‐Casique et al ., ; Neuman , ; Refsgaard et al ., ; Rojas et al ., ; Singh et al ., ; Troldborg et al ., ; Tsai and Li , ; Tsai , ; Ye et al ., ; Wöhling and Vrugt , ].…”

“…Wagener and Gupta [] remark that an uncertainty assessment framework should be able to account for the level of contribution of the different sources of uncertainty to the overall uncertainty. In the groundwater area, to advance beyond collection multimodel methods, Li and Tsai [] and Tsai [] present a BMA approach that can separate two sources of uncertainty, which arise from different conceptual models and different parameter estimation methods. These were the first two studies to extend the collection BMA formulation of Hoeting et al .…”

“…[] to two levels. The current study generalizes the work of Li and Tsai [] and Tsai [] to a fully hierarchical BMA method. To our knowledge, this is the first work that extends the BMA formulation in Hoeting et al .…”

Statistical summer mass-balance forecast model with application to Brúarjökull glacier, South East Iceland

“…This technique, called model averaging, incorporates the uncertainty associated with model selection into predictions of unknown variables (Hjort and Claeskens, 2003). The model averaging approach has in recent years been applied to several hydrological model applications (Diks and Vrugt, 2010;Tsai, 2010).…”