Optimal Allocation of the Irrigation Water Through a Non Linear Mathematical Model

Abstract

A study on the optimal allocation of the irrigation water among 9 crops (autumnal and spring sugar beet, spring and summer grain maize, dry and shell bean, eggplant, pepper and processing tomato) has been carried out, utilizing experimental data of yield response to irrigation obtained in different years in Southern Italy (Policoro MT, 40° 12’ Northern Lat.; 16° 40’Western Long.). Fitting Mitscherlich’s equation modified by Giardini and Borin to the experimental data of each crop, the curve response parameters have been calculated: A = maximum achievable yield in the considered area (t ha-1); b = extra-irrigation water used by the crop (m3 ha-1); c = water action factor (ha m- 3); K, calculated only for tomato crop. ,decreasing factor due to the water exceeding the optimal seasonal irrigation volume (100% of the Crop Maximum Evapotranspiration less effective rainfall, ETMlr). The A values, using the prices of the agricultural produces and the irrigation water tariffs applied by the Consorzio Irriguo della Capitanata, have been converted in Value of Production (VP) less the fixed and variable irrigation costs (VPlic). The equation parameters were used in a non linear mathematical model written in GAMS (General Algebraic Modelling System), in order to define the best irrigation water allocation amongst the 9 crops across the entire range of water availability and the volume of maximum economical advantage, hypothesising that each crop occupied the same surface (1 ha). This seasonal irrigation volume, that corresponded to the maximum total VPlic, was equal to 37000 m3. Moreover, the model allowed to define the best irrigation water distribution among the crops also for total available volumes lower than that of maximum economical advantage (37000 m3). Finally, it has been underlined that the vegetable crops should be irrigated with seasonal irrigation volumes equal to 100% of the ETM, whereas the summer and spring maize and the autumnal and spring sugar beet with volumes equal to 78; 62; 48 and 41 % of the ETM, respectively. This research work has confirmed the validity of the model, that can also be adopted to study other yield factors.