Spatial and temporal soil water estimation considering soil variability and evapotranspiration uncertainity

Lack of accurate information stemming from soil variability and climatic uncertainty obstructs efficient irrigation management. State-space models of soil water balance and potential evapotranspiration were used in the application of spatial-temporal estimation methods to reduce uncertainty. Temporal soil water storage estimates and estimation errors were obtained by the Kalman filter (KF). Spatial estimates were obtained by the conditional multivariate normal method. These spatial and temporal estimates were combined by an additional KF step that considers spatial estimates as measurements. Time-dependent soil water spatial covariance was approximated by assuming a constant correlation range and by using measurements variance to estimate the variogram "sill." Simulation and field results indicate that soil water storage estimates by the proposed method agreed better with measurements than estimates based on either spatial or temporal information only. The proposed estimation scheme can be extended to other systems with a simple physical model and a known spatial structure where only a few field measurements are available.