A stochastic model of soil water regime in the crop root zone

Abstract

The soil water regime in a crop root zone is critical to crop growth. Understanding the dynamics of the soil water regime is a prerequisite to proper irrigation management. However, due to the random nature of weather conditions, the soil water regime tends to be highly variable, which makes irrigation scheduling a difficult task. To better characterize the dynamic variability of soil water regime, we developed a stochastic model of soil water storage (SWS) by treating the evapotranspiration (ET) as an explicit random process. While developing this model, first of all, a root zone water balance model for SWS was established, parameterized, and validated with lysimeter data collected at Yucheng comprehensive experimental station (YCES) in Shandong Province, North China. We then employed 14 years of daily meteorological data collected at YCES to compute the daily reference evapotranspiration (ET r ) data series and performed time series analysis, established a discrete AR(1) model for ET r and derived its continuous form by employing an even point sampling hypothesis. The stochastic model of SWS was formulated by incorporating the continuous AR(1) model into the deterministic model of SWS, which results in a system of two first-order temporal stochastic differential equations. Further, the Fokker-Planck equation of the probability density function (PDF) of SWS was derived and solved numerically. Consequently, the joint PDF of SWS and ET r , the marginal PDF,mean, and deviation of SWS were obtained. These numerical solution results compare favorably with two years of SWS measurements. This indicates that the stochastic model can be a useful tool for irrigation scheduling and the associated risk assessment. © 2006 Elsevier B.V. All rights reserved.