A Joint Approach Combining Correlation and Mutual Information to Study Land and Ocean Drivers of U.S. Droughts: Methodology

Abstract

Abstract Normalized mutual information (NMI) is a nonparametric measure of the dependence between two variables without assumptions about the shape of their bivariate data distributions, but the implementation and interpretation of NMI in the coupled climate system is more complicated than for linear correlations. This study presents a joint approach combining correlation and NMI to examine land and ocean surface forcing of U.S. drought at varying lead times. Based on the distribution of correlation versus NMI between a source variable (local or remote forcing) and target variable [e.g., summer precipitation in the southern Great Plains (SGP)], newly proposed one-tail significance levels for NMI combined with two-tailed significance levels of correlation enable us to discern linearity and nonlinearity dominant regimes in a more intuitive way. Our analysis finds that NMI can detect strong linear relationships like correlations, but it is not exclusively tuned to linear relationships as correlations are. Also, NMI can further identify nonlinear relationships, particularly when there are clusters and blank areas (high density and low density) in joint probability distributions between source and target variables (e.g., detected between soil moisture conditions in eastern Montana from mid-February to mid-August and summer precipitation in the SGP). The linear and nonlinear information are found to be sometimes mixed and rather convoluted with time, for instance, in the subtropical Pacific of the Southern Hemisphere, revealing relationships that cannot be fully detected by either NMI or correlation alone. Therefore, this joint approach is a potentially powerful tool to reveal complex and heretofore undetected relationships.