Determination of appropriate irrigation water depth and its sensitivity to water price using the production function

The use of drip irrigation systems for citrus orchards has become a standard method. Economically, drip irrigation is cost-effective for many fruit trees. But only using these systems cannot improve water productivity or net income, and the suitable irrigation water depth should be determined based on production-water and cost-water relationships. Deficit irrigation is one of the appropriate ways to optimize water use in water limitation conditions. However, its economic effects should be evaluated. The optimum applied water depths are used to enhance the product or the net income in water limiting conditions. Therefore, as the first step, the water-production and water-cost functions must be prepared. Production-water function is a quadratic function that relates production to the amount of applied water during the irrigation season. The cost-water function is a linear function that relates total production costs to total applied water. By optimizing these functions, the optimal depth of irrigation water is obtained. English method is an appropriate method to determine the optimal irrigation water depth, which is based on water-production and water-cost functions.

In order to determine water-production and water-cost functions, an experiment was conducted in an orange orchard in Sari. The trees were 25-year-old Thomson Navel oranges spaced in 6×6 meters, which were drip irrigated. The climate in the study area was mild with hot and humid summers and humid and mild winters. Four irrigation levels including 100, 80, 65 and 50% of irrigation water depth were applied in 5 replications. To determine the irrigation water depth, soil moisture was measured and the amount of irrigation water depth (D) and irrigation volume (V) were calculated. Applied water was considered in two cases. In the first case, irrigation water was considered as the applied water, and in the second case, irrigation water plus precipitation was considered as the applied water. Then, the optimal irrigation water depths were determined by mathematical optimization. Next, the economic evaluation of these optimal depths was carried out using 6 indices. It is worth mentioning that in deficit irrigation, the water use per unit of area (one hectare) is reduced compared to the full irrigation, and therefore the irrigated area will be more than one hectare. Thus, the amount of equivalent production and equivalent net income per unit of land increase.

This study showed that when water is not limited, applying full irrigation 〖"(W" 〗_"m" ) provides the highest amount of net income per unit of land. In water and land limiting conditions, if the water limitation is mild, using the optimum depth in water limiting condition 〖"(W" 〗_"w" ) leads to a 26 percent reduction in irrigation water use, which causes a 4 percent decrease in net income per unit of land. But it increases net income per unit of irrigation water by 16 percent. In addition, if the water limitation is severe, it is more useful to apply the equivalent optimum applied water depth 〖"(W" 〗_"ew" ). Although it causes a 17 percent decrease in net income per unit of land, it causes a 46 percent decrease in irrigation water use. Furthermore, when precipitation occurs, the sum of irrigation water and precipitation should be considered as applied water. However, in order to evaluate the effect of deficit irrigation, only irrigation water should be considered to determine the equivalent irrigated area. Therefore, in water limiting condition, if land is not limited, the use of 〖"(W" 〗_"ew" ) leads to the highest net income per unit of land. Because by using 〖"(W" 〗_"ew" ), more area can be irrigated. In addition, the highest water productivity is obtained from the optimal depth under water limiting conditions ("W" _"w" and W_ew). On the other hand, according to the current prices of fruit and water, the net income and optimal depth of applied water are not sensitive to the price of irrigation water. However, they are highly sensitive to the price of fruit. This is due to the large difference in the price of fruit compared to the price of water, which makes production play a more important role than water on the net income. Overall, the use of optimal depths in water limiting conditions can be a suitable solution to overcome the problems of water scarcity in Iran. Moreover, return on investment (ROI) is a key factor along with technical analysis that experts should consider in order to provide an acceptable irrigation schedule for farmers.