CMG Research: A Copula-Based Probabilistic Approach for Space-Time Characterization of Droughts

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Drought is one of the most expensive and the least understood of natural disasters. The current process of drought specification through the Drought Monitor is based on drought indices that are constructed from various individual data sources, primarily rainfall, soil moisture, and streamflows. However, these indices do not account for spatial and temporal structure of the hydrologic variables. Researchers have been thwarted in building statistical models of the highly correlated hydrologic variables because of lack of sound methods for representing dependence between hydrologic variables and for reducing the dimensionality of such datasets to manageable levels. This research will develop innovative schemes that utilize copulas for modeling hydrologic distributions under a set of conditional independence assumptions represented by sparse graphical models. In the copula approach, the joint distribution of variables is modeled as a function of the transformed marginal distributions of the variables, so that the joint nature of the variability can be considered separately from the unconditional probabilities of the individual variables. The project will use this statistical technique to develop a joint drought indicator that draws on information from multiple spatial sources and preserves the proper dependence relationships among the hydrological variables. The key hypothesis is that a copula-based approach will 1) provide a joint description of droughts and that such a description will enable us to study the spatial scales of these droughts over a range of time-windows to establish temporal dependence, and 2) enable probabilistic classification of drought status and evaluation of the chance of recovering from a current drought. This two-year project will specifically address drought in Indiana at different temporal scales, although the methods developed will be applicable to droughts in all regions and on all spatial scales.The research has strong potential benefit for society given the enormous human and monetary consequences of drought, and the results of this research will be of interest to a wide user community. In particular, the research will develop easily interpretable maps and characterizations of water deficit and drought, which will be developed for use by national and state agencies as well as a broader community of climatologists, hydrologists, and stakeholders. The project will also support the education of graduate and undergraduate students, who will receive training in the multidisciplinary field of statistical hydrology.