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

干旱是自然灾害中代价最高、人们了解最少的灾害之一。目前通过干旱监测系统确定干旱具体情况的过程是以干旱指数为基础的，这些指数是根据各种单独的数据来源，主要是降雨量、土壤湿度和径流量建立的。然而，这些指数不占水文变量的空间和时间结构。由于缺乏合理的方法来表示水文变量之间的相关性，并将这些数据集的维数降低到可管理的水平，研究人员在建立高度相关的水文变量的统计模型时受到了阻碍。本研究将开发创新的方案，利用Copula模型水文分布下的一组条件独立的假设稀疏图形模型表示。在Copula方法中，变量的联合分布被建模为变量的变换后的边缘分布的函数，因此可以将变量的联合性质与单个变量的无条件概率分开考虑。 该项目将利用这一统计技术制定一个联合干旱指标，该指标利用多个空间来源的信息，并保持水文变量之间的适当依赖关系。关键的假设是，基于copula的方法将1）提供干旱的联合描述，这种描述将使我们能够在一系列时间窗口内研究这些干旱的空间尺度，以建立时间依赖性，2）使干旱状态的概率分类和从当前干旱中恢复的机会评估成为可能。这一为期两年的项目将专门针对印第安纳州不同时间尺度上的干旱，尽管所开发的方法将适用于所有地区和所有空间尺度上的干旱，鉴于干旱对人类和经济的巨大影响，这项研究对社会具有很大的潜在效益，这项研究的结果将引起广大用户的兴趣。 特别是，研究将开发易于解释的地图和缺水和干旱的特征，这将被开发用于国家和州机构以及更广泛的气候学家，水文学家和利益相关者社区。 该项目还将支持研究生和本科生的教育，他们将接受统计水文学多学科领域的培训。

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.