Modeling Plant Height and Biomass Production of Cluster Bean and Sesbania across Diverse Irrigation Qualities in Pakistan's Thar Desert

Plant height (PH) plays a crucial role in determining per-plant growth and biomass production. Various characteristics of PH, along with the formulation of mathematical growth models, can provide a theoretical yield or biomass production based on water quality, fruit quality, and yields. The aim of this study was to investigate the relationship between PH and biomass per-plant production of two fodder crops (Cluster bean and Sesbania) under different water quality irrigation parameters in the Thar desert of Pakistan. Universal models of PH were established in which growing degree days (GDDs) and different water quality irrigation techniques have been applied as independent variables to calculate the maximum plant height of both of these crops. For this purpose, the logistic growth model, Gaussian growth model, modified Gaussian growth model, and Cubic polynomial growth model were used. Furthermore, universal biomass per plant production models have been developed for both crops, between biomass per plant, GDDs, and PH. However, among all these developed models, the modified Gaussian and Cubic polynomial growth models produced the best results. The Cubic polynomial model has meaningless parameters that make the model not very accurate, so the modified Gaussian growth model is the best among all models. Furthermore, the relationship between biomass per plant and different water qualities was established using Michaelis-Menten equations for both crops. It was observed that an increase in salt concentration within the water quality led to a decline in biomass per plant, indicating a negative linear relationship between these factors. The growth of Cluster bean and Sesbania ceased when the electrical conductivity (EC) reached or exceeded 12.34 ds/m and 11.51 ds/m, respectively. Furthermore, the results show that Cluster bean and Sesbania have the maximum plant height under brackish water irrigation when the GDD is at 1500 degrees C, while in freshwater irrigation, the maximum plant height of Sesbania and Cluster bean was observed when the GDD is at 1444 degrees C and 1600 degrees C. It was concluded that these developed mathematical models can provide crucial insights for enhancing production in desert conditions by improving water use efficiency across diverse irrigation water qualities.