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Given a collection of science-based computational models that all estimate states of the same environmental system, we compare the forecast skill of the average of the collection to the skills of the individual members. We illustrate our results through an analysis of regional climate model data and give general criteria for the average to perform more or less skillfully than the most skillful individual model, the “best” model. The average will only be more skillful than the best model if the individual models in the collection produce very different forecasts; if the individual forecasts generally agree, the average will not be as skillful as the best model. [ABSTRACT FROM AUTHOR]

We study two-dimensional flow in a layered heterogeneous medium composed of two materials whose hydraulic properties and spatial distribution are known statistically but are otherwise uncertain. Our analysis relies on the composite media theory, which employs random domain decomposition in the context of groundwater flow moment equations to explicitly account for the separate effects of material and geometric uncertainty on ensemble moments of head and flux. Flow parallel and perpendicular to the layering in a two-material composite layered medium is considered. The hydraulic conductivity of each material is log-normally distributed with a much higher mean in one material than in the other. The hydraulic conductivities of points within different materials are uncorrelated. The location of the internal boundary between the two contrasting materials is random and normally distributed with given mean and variance. We solve the equations for (ensemble) moments of hydraulic head and flux and analyze the impact of unknown geometry of materials on statistical moments of head and flux. We compare the composite media approach to approximations that replace statistically inhomogeneous conductivity fields with pseudo-homogeneous random fields. [ABSTRACT FROM AUTHOR]

Explores ways to improve the status of stochastic theories and models as routine tools for studying hydrology. Reasons why stochastic approaches have not been extensively used as routine tools; Need for hydrogeologists to acknowledge the objective need for stochastic models in many applications; Need for more extensive methods of collecting data.