Fuzzy evapotranspiration deficit model for crop water allocation

In this paper a fuzzy evapotranspiration deficit model is developed, for use in crop water allocations. Crop yield response to change in temperature and the farm practices followed by the farmers are not quantifiable precisely, and thus introduces uncertainty due to imprecision. This uncertainty is especially predominant in developing countries where agriculture is mainly practiced by small and poor farmers with widely varying farm practices. Most crop production functions relate the crop yield to evapotranspiration deficit of a crop. Evapotranspiration deficit of a crop depends on temperature and farm practices, in addition to the amount of water allocated. This dependence is not exactly quantifiable and is therefore modeled in this paper with fuzzy inference. A crop requires a desirable range of temperature during its different growth stages. If, during a particular growth stage, the temperature is well above or well below the desirable range, then even though the crop is satisfied on all other requirements such as water, manure, fertilizers, etc., the yield will still be adversely affected. Similarly the farm practices followed for a crop will affect the crop yield by affecting the evapotranspiration. Fuzzy sets provide a mechanism to address the imprecision associated with the evapotranspiration deficit of a crop. To address the imprecision associated with the weighted evapotranspiration deficit of a crop, a Fuzzy Evapotranspiration Deficit Model (FETDM) is developed, to obtain a weighted evapotranspiration deficit of a crop, in time period, for known values of irrigation allocation, rainfall, initial soil moisture, temperature and farm practice. The weighted evapotranspiration deficit is used as an input to the water allocation model, which allocates a known quantity of water optimally among the crops in an intra-seasonal time period. The model is developed specially for use in irrigation reservoir operation models that address water allocations across time periods. Application of the methodology is demonstrated with a case study in India.