Application of the Viterbi Algorithm in Hidden Markov Models for Exploring Irrigation Decision Series

Abstract:

Anticipating farmers’ irrigation decisions can provide the possibility of improving the efficiency of canal operations in on-demand irrigation systems. Although multiple factors are considered during irrigation decision making, for any given farmer there might be one factor playing a major role. Identification of that biophysical factor which led to a farmer deciding to irrigate is difficult because of high variability of those factors during the growing season. Analysis of the irrigation decisions of a group of farmers for a single crop can help to simplify the problem. We developed a hidden Markov model (HMM) to analyze irrigation decisions and explore the factor and level at which the majority of farmers decide to irrigate. The model requires observed variables as inputs and the hidden states. The chosen model inputs were relatively easily measured, or estimated, biophysical data, including such factors (i.e., those variables which are believed to affect irrigation decision-making) as cumulative evapotranspiration, soil moisture depletion, soil stress coefficient, and canal flows. Irrigation decision series were the hidden states for the model. The data for the work comes from the Canal B region of the Lower Sevier River Basin, near Delta, Utah. The main crops of the region are alfalfa, barley, and corn. A portion of the data was used to build and test the model capability to explore that factor and the level at which the farmer takes the decision to irrigate for future irrigation events. Both group and individual level behavior can be studied using HMMs. The study showed that the farmers cannot be classified into certain classes based on their irrigation decisions, but vary in their behavior from irrigation-to-irrigation across all years and crops. HMMs can be used to analyze what factor and, subsequently, what level of that factor on which the farmer most likely based the irrigation decision. The study shows that the HMM is a capable tool to study a process which is not memory-less like irrigation behavior.