Space-Time Variance Propagation of Biophysical Processes.
Ole Wendroth, Univ of Kentucky, Dept of Plant and Soil Sciences, N-122M Agr. Sci. North, Lexington, KY 40546 and Donald R. Nielsen, Univ of California, Dept LAWR Hydrologic Science, 113 Veihmeyer Hall, Davis, CA 95616.
For the description of a large variety of biophysical processes, model equations have been derived to predict the processes as a function of time subject to initial and boundary conditions. To date, little attempt has been made to estimate the variances associated with such predictions. On the other hand, spatial estimation techniques are now commonly used that are based on the spatial covariance structure of one or several variables and their relation to each other. Kriging and cokriging are examples of such spatial estimation techniques which provide spatial distribution maps of the estimation error. Very few attempts have been made in which a process of a variable or a vector is described simultaneously in both space and time. Therefore, little is known about the prediction variance behavior when the development of a process is considered simultaneously in both spatial and temporal domains. A large prediction variance of a process in the temporal domain may result from a simplified model equation, a limited representation of site specific properties affecting the process, or a large uncertainty in the knowledge of physical functions that govern the process. The spatial uncertainty depends on the local variance compared to the global variance, and the spatial sampling distance. Because Kriging and cokriging estimation variances are dominated by the variance-lag distance behavior, increasing the spatial density of observations frequently causes a reduction of the spatial estimation uncertainty. The objective of this study is, to incorporate spatial estimation variance in the temporal prediction of field profile soil water storage in order to reduce the prediction variance. This is achieved using a Kalman filter set up in both the temporal and spatial domains, and in combination with a kriging estimation. The measurement variance usually applied in the stochastic weighting matrix for the update of the predicted state and its variance is replaced by the spatial estimation variance. The above framework is applied to estimate field profile soil water storage based on precipitation and evapotranspiration at a particular location. For each location, soil water storage is estimated based on the neighboring observations and their covariance structure. The impact of spatial uncertainty on the temporal prediction uncertainty is quantified with implications for experimental design.