Incorporating Uncertainty in Spatial Decision-Making for Agronomy

By Sriram Jallu

Abstract
Decision making under uncertainty is a complex task, requiring not only a quantification of the uncertainty concerning the outcomes upon choosing between options, but also the perception of the said uncertainty by the decision maker. While there are methods to support decision making in the presence of uncertainty, the integration of decision-makers' risk perception is less common. The current study presents a methodological framework for spatial decision making under uncertainty, which accounts for risk attitudes of decision makers. The framework is composed of four components; 1) identifying and quantifying uncertainty, 2) uncertainty propagation, 3) accounting for risk attitude, and 4) optimization under uncertainty. The framework was applied to a case study concerning optimal fertilizer application in west Cameroon under uncertainty for three typical levels of risk attitude: 1) risk-neutral, 2) weak risk-aversive and 3) strong risk-aversive. The results of the case study show that, as the aversion towards risk increased, there was an increase in the optimized fertilizer amounts in areas with high uncertainty. In contrast, the risk attitude had no significant effect in areas with low uncertainty. Although these results may seem counterintuitive, a close examination of the yield distributions at selected locations provides insights that explain the findings. At the location with high uncertainty, the optimization seeks to reduce the low-yield events, for strong risk-aversive individual, even at the cost of high fertilizer gifts. On the other hand, at low uncertainty location, the optimization algorithm is able to produce low variance yield distributions, resulting in similar optimal fertilizer gifts for all the three personas. The practical applicability of the results is constrained by factors such as the considered input uncertainties and spatial aggregation level, highlighting opportunities for future research. However, the design of the framework makes it a versatile tool that can be applied across domains and to various decision problems, beyond those of agronomy and farming.