Mathematical Models of how the Transpiration Affects Rainfall through Agriculture Crops

Abstract

The water vapor in the atmosphere is mainly formed through the vaporization of water from oceans, open land water sources, and transpiration through forests and agricultural crops. In the present study, our aim was to formulate a mathematical model to see the effect of transpiration from agricultural crops on rainfall. In the model formulation, it is assumed that clouds are formed in the atmosphere through the transpiration of agricultural crops proportional to the crops apart from the oceans and other sources (assumed constant). It is observed that in the presence of agriculture crops, the average rainfall increases. In the presence of clouds, cloud seeding techniques (use of conducive aerosols) are used to stimulate rainfall, which increases the agricultural crops with saturated type functional form. To capture the impact of environmental fluctuations, the stochastic version of the proposed model is also studied. The analysis of the model reveals that cloud seeding not only increases the rainfall, but it also increases the agricultural crops and clouds in the atmospheric environment.