Quantifying outcomes in agricultural planning

Abstract

The availability of ground water to irrigate crops is a key component in food security, particularly in developing regions such as the Indo-Gangetic Basin. Policy settings implemented by governmental authorities can have longer term impact on the livelihoods of farming communities in the region, particularly under the uncertainty of future climate conditions. For example, government policies imposing a minimum level on the ground water table in an agriculture region may result in insufficient ground water available to irrigate a given area of crop, and so the cropped area may have to be reduced consequently. We have developed a model that computes the cropped area that keeps the water table level above a critical value under the uncertainty of future rainfall scenarios. We use a water balance model to predict the change in water table level caused by growing a fixed area of a particular crop over one year with a given annual rainfall. We then model the annual rainfall as a stochastic process and use Monte Carlo simulations to generate stochastic annual rainfall paths, and adjust the cropped area to maintain the underground water table above a critical level in response to each stochastic annual rainfall path by using the water balance model. We have implemented an optimization procedure that maximises the Sharpe ratio for each year that allows farmers in a region to allocate land to crops in a manner that maximises returns while minimising risk. Starting with land allocations determined through a simple portfolio optimization, we found that considering the effects of rainfall on cropping allocations in addition to accumulating the future cash-flows with a penalty for switching cropping allocations causes a significant difference in cropping allocations when compared to the simple single period optimization scheme. Our results suggest that the effect of uncertain climate through rainfall in conjunction with certain policy settings may cause a change in optimal cropping land allocations. Further work will focus on developing an optimization model that computes a globally optimal solution, taking into account scenarios where the crop prices do not follow the expected future trajectories.