A hierarchical Bayesian network (HBN) algorithm is developed for data assimilation (DA) and tested with an instance of soil moisture assimilation from a hydrological model and ground observations. In essence, the HBN is a framework that can statistically describe Bayesian models and capture the dependencies in the models more realistically than non-hierarchical Bayesian models. In this work, DA divided into three levelsdata, process, and parameter -and conditional probability models are defined for each level. The data model mainly deals with the scale differences of multi-source data in DA, while the process model is designed to take account of the non-stationary process. Moreover, both the temporal auto-correlation and the spatial correlation are considered in the process model. Soil moisture observations from the Soil Moisture Experiment in 2003 (SMEX03) and Variable Infiltration Capacity (VIC) model are sequentially assimilated with HBN. The result shows that the assimilation with HBN provides spatial and temporal distribution information of soil moisture and the assimilation result agrees well with the ground observations. IntroductionThe basic tenet of data assimilation (DA) is to combine complementary information from measurements and dynamic models into an optimal estimate of the geophysical fields of interest, generally defined as states (Reichle 2008). In doing so, DA systems interpolate and extrapolate observations and provide estimates at the scales required by the applicationboth in the temporal and spatial domains. Meanwhile, DA estimates the states when the unobserved physical parameters have a complicated functional dependence on the states estimated. These characteristics make DA one of the indispensable methods in Earth system science. DA has wide applications also across the range of the Earth sciences. One of the major applications is in the production of operational weather forecasts; other applications include oceanography, atmospheric chemistry, climate studies, and hydrology. Currently, DA is a key technique for obtaining spatial-temporal distribution and variation information of multiple Earth science parameters in the global, continental, and regional scales with the aid of a long time series of data records.The goal of DA is to effectively combine multi-source data with the associated uncertainty to estimate the state of interest. The theory of DA rests on the mathematical
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