Bayesian hierarchical modelling: Incorporating spatial information in water resources assessment and accounting

Abstract

Water resources assessment and accounting research requires making the best use of multiple sources of data for producing reliable accounting predictions. For any given quantity of interest, e.g. soil moisture, available sources of data could be directly observed in situ, derived indirectly from a remotely-sensed surrogate (e.g. brightness temperature) using retrieval models, or output from deterministic hydrological models. Whether it be model-data fusion or the evaluation of remotely-sensed products, multiple data sources for individual quantities of interest must be assimilated to optimize the use of available information. Popular data assimilation techniques focus heavily on assimilating time series at fixed geographical locations. Yet, the resulting predictions typically show unrealistically large variability over space. This suggests the need to assimilate spatial maps at fixed time points, in addition to time series at fixed locations. Spatial statistical models, constructed in a Bayesian hierarchical framework, offer an intuitive and unifying approach for this purpose. It cohesively utilizes multiple data sources by addressing the mismatch in both spatial and measurement scales between ground-based and remotely-sensed products; it can also spatially interpolate missing data due to the remote sensor's "blind spots." In this paper, we use the evaluation of the remotely-sensed soil moisture product, AMSR-E, to illustrate this statistical framework. Specifically, a single statistical model can incorporate both point-level in situ data (benchmark) and pixel-based AMSR-E data (product), as well as other related variables such as precipitation. Show more