Optimal Irrigation Control Using Stochastic Cluster Point Processes for Rainfall Modelling and Forecasting

Abstract

Optimal irrigation control is performed. The control accounts for the intraseasonal variation of the crop water requirements and for tie dynamics of soil moisture depletion process. The clustering dependence structure of rainfall occurrences is explicitly accounted for. Stochastic rainfall inputs to the soil-plant system are characterized by storm intensities, storm durations, interarrival times, and number of storms in a given period of time. Precipitation occurrences are modelled as a Neyman-Scott cluster process; and using Palm-Khinchin theory conditional distributions of the time to the next rainfall events are derived. These distributions are conditional on part of the immediate history of storm arrivals. The derived distributions are seen to possess characteristics desired for short term forecasting of rainfall occurrences. Particularly, they exhibit the ability to detect short term trends in precipitation occurrences. The probabilistic description of precipitation is coupled with a probabilistic description of cumulative infiltration from storms and a Markov chain approach to the dynamics of soil moisture throughout the growing season. Conditional probabilities of soil moisture are derived and used within a Stochastic Dynamic Programming algorithm to obtain irrigation decisions. The control is obtained in the form of decision functions which yield the optimal irrigation depth as a function of soil moisture content at the root zone, volume of irrigation water available, and number of days since the last rainfall occurrence. Case study results confirm the existence of a clustering dependence structure in rainfall occurrences as well as the goodness of the Neyman- Scott process in its modelling. However, there appears to be no significant difference in expected maximum net benefits when comparing results obtained with the control model under the homogeneous Poisson assumption and under the conditional Neyman-Scott model. Furthermore, slightly lower expected benefits are obtained with the conditional Neyman- Scott model than with the non-homogeneous Poisson model.