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

干旱是代价最高、也是最不为人所知的自然灾害之一。目前通过干旱监测仪进行干旱指定的过程是基于干旱指数，这些指数是从各种独立的数据来源构建的，主要是降雨量、土壤湿度和径流。然而，这些指数没有考虑到水文变量的时空结构。研究人员在建立高度相关的水文变量的统计模型方面受到阻碍，因为缺乏可靠的方法来表示水文变量之间的相关性并将这种数据集的维度降低到可管理的水平。这项研究将开发创新的方案，利用Copulas在稀疏图形模型表示的一组条件独立性假设下模拟水文分布。在Copula方法中，变量的联合分布被建模为变量的变换边缘分布的函数，因此变异性的联合性质可以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开发一个联合干旱指标，该指标利用来自多个空间来源的信息，并保留水文变量之间的适当依赖关系。关键假设是，基于Copula的方法将1)提供对干旱的联合描述，这种描述将使我们能够研究这些干旱在一系列时间窗口中的空间尺度，以建立时间相关性，以及2)能够对干旱状况进行概率分类，并评估从当前干旱中恢复的机会。这个为期两年的项目将在不同的时间尺度上专门研究印第安纳州的干旱问题，尽管所开发的方法将适用于所有地区和所有空间尺度的干旱。鉴于干旱造成的巨大人力和金钱后果，这项研究对社会具有很大的潜在益处，这项研究的结果将引起广泛用户的兴趣。特别是，这项研究将编制易于解释的缺水和干旱地图和特征，供国家和州机构以及更广泛的气候学家、水文学家和利益攸关方使用。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.