Determining the production function and optimal irrigation depth of Roselle in deficit irrigation conditions and using potassium fertilizer

The limitations of water resources in supplying the demands of consumer sectors including drinking, hygiene and healthcare, agriculture, industry, as well as environment well reflect the importance of proper use of water. Thus, it is essential to choose an optimal and superior strategy to use water under water deficit conditions. This experiment was implemented as split plot in a fully randomized block design in a research farm in the southeast of Iran on Roselle plant. The experimental treatments included three levels of potassium fertilizer 75 t ha(-1) (K-1), 112.5 t ha(-1) (K-2), and 150 t/ha(-1) (K-3) (equivalent to 50%, 75%, and 100% of potassium fertilizer requierment) and four levels of irrigation water including 40%, 60%, 80%, and 100% of the plant water requierment (11, 12, 13, and 14). The main aim of the research was to estimate the production function as well as to calculate the index and optimal depths of consumed water. Regression analyses were done by linear, Cobb-Douglas, Quadratic and Transcendental functional forms of Roselle production. The final production indicators in relation to the water depth and potassium fertilizer, the final rate of technical substitution for potassium fertilizer and water depth, and the final production value in relation to water depth and potassium fertilizer were calculated. The results indicated that the Quadratic function was chosen as the superior function. The final production index in relation to the minimum water depth was 1.4 and for maximum water depth was - 0.86 kg cm(-1) of water depth. The final production index in relation to the minimum and maximum potassium fertilizer was calculated as 3.92 and 1.77 kg respectively. The results also showed that by applying deficit irrigation under water constraint conditions, the optimal depths of consumed water in relation to the maximum depth at 75, 112.5 and 150 kg levels of potassium fertilizer per hectare had 13.29, 14.34, and 13.1 cm reduction of water consumption respectively. As can be seen, elevation of potassium fertilizer up to 75% resulted in more saving of water consumption. Use of potassium fertilizer can modify the damages resulting from drought stress in Roselle.