Combined Space-Time State Space Model for Field Soil Water Storage.

The spatial distribution of soil water storage over a spatial domain is usually based on the pattern of landscape topography, soil type, vegetation, plant water uptake and drainage conditions. The spatial pattern of soil water storage often times exhibits stability over time. In the temporal domain, describing the process of soil water storage requires knowing the upper and lower boundary conditions, evapotranspiration and drainage. Only a few approaches exist, that describe unsaturated zone soil water storage while combining both the spatial and temporal domain, e.g., Or and Hanks (1992). The objective of this study is to predict soil water storage processes in space and time simultaneously. Similar to the approach of Or and Hanks (1992), a balance equation is used for predicting soil water storage in the temporal domain for each of the known locations. Whenever a measurement for the spatial distribution of profile water storage exists, the temporal storage estimation is updated based on spatial relationships of soil water storage at neighboring locations and other soil processes such as soil texture. A combined space-time Kalman-Filter based algorithm is used in this approach. During the estimation in the temporal domain, prediction variance increases. At the time of measurement, the state and state variance are updated with a stochastic gain, called the Kalman gain as well as the state variance. At 45 locations in a Western-Kentucky farmer’s field, soil water storage were measured using a capacitance probe. The upper boundary was calculated using the FAO Penman Monteith approach. Various approaches are used for estimating the lower boundary, i.e., deep drainage. For the temporal error propagation, Taylor’s provisional rule was used. Deviations between temporal prediction and measurement were largest during rainfall periods, while periods of soil water redistribution resulted in smaller prediction variance and deviations between measurement and prediction.