An Information-Theoretic Approach to Reconciling Historical Climate Observations and Impacts on Agriculture

Decision-makers in climate risk management often face problems of how to reconcile diverse and conflicting sources of information about weather and its impact on human activity, such as when they are determining a quantitative threshold for when to act on satellite data. For this class of problems, it is important to quantitatively assess how severe a year was relative to other years, accounting for both the level of uncertainty among weather indicators and those indicators’ relationship to humanitarian consequences. We frame this assessment as the task of constructing a probability distribution for the relative severity of each year, incorporating both observational data—such as satellite measurements—and prior information on human impact—such as farmers’ reports—the latter of which may be incompletely measured or partially ordered. We present a simple, extensible statistical method to fit a probability distribution of relative severity to any ordinal data, using the principle of maximum entropy. We demonstrate the utility of the method through application to a weather index insurance project in Malawi, in which the model allows us to quantify the likelihood that satellites would correctly identify dam-aging drought events as reported by farmers, while accounting for uncertainty both within a set of commonly used satellite indicators and between those indicators and farmers’ ranking of the worst drought years. This approach has immediate utility in the design of weather-index insurance schemes and forecast-based action programs, such as assessing their degree of basis risk or determining the probable needs for postseason food assistance. SIGNIFICANCE STATEMENT: We present a novel statistical method for synthesizing many indicators of drought into a probability distribution of how bad an agricultural season was likely to have been. This is important because climate risk analysts face problems of how to reconcile diverse and conflicting sources of information about drought—such as determining a quantitative threshold for when to act on satellite data, having only limited, ordinal information on past droughts to validate it. Our new method allows us to construct a probability distribution for the relative severity of a year, incorporating both kinds of data. This allows us to quantify the likelihood that satellites would have missed major humanitarian droughts due to, for example, mistimed observations or unobserved heterogeneity in impacts.