Advancing stochastic modeling and diagnostics of change for hydroclimatic processes and extremes

我们生活在一个前所未有的全球水文气候和环境变化的时代，需要可靠的工具来模拟和改进极端水文气候的预测，量化它们的不确定性，并评估自然变化和人为强迫下的环境变化。*这项研究计划的长期目标是推进平稳和非平稳时空随机模拟，将其扩展和应用到降尺度方法、缺失值填充(MVS)和对水文气候变化的稳健诊断。*这项研究的四个短期目标是：(1)增加我们对多尺度降水和温度的时空结构的了解，并提供新的平稳和非平稳随机模型；(2)采用新的填充方法，通过使用随机方法，从缺失数值的记录中推进当前的最大值提取计划；(3)为气候模型预测和历史数据制定新的时空缩减计划；以及(4)建立准确的诊断方法，以检测和评估所观察到的极端水文气候变化和趋势的重要性。为了实现这些目标，将使用数千个现场站点、再分析网格产品和气候模型输出进行大数据分析。降水和温度的时空结构将由一组简约的参数空间和时间相关结构来数学描述。将使用与这些过程的性质一致的一组扩展的熵派生分布来探索多个尺度上的边际分布的特性。一个先进的时空随机建模框架将通过扩展上级高斯方案来开发，以便包括时变边缘并纳入重要的场特征，包括各向异性和风暴运动学。这些进展将体现在MVS的填充方法、缩小尺度方案以及通过利用降水和温度的时空结构以及边际分布的精确表示和模拟来诊断水文气候变化。*开发的随机建模工具和汇编的数据库将免费提供，并通过以下方式惠及科学界：(1)产生科学知识，因为开发的方法适用于水文气候学领域以外的领域；(2)通过对降水等复杂过程进行精确的随机建模，改进水文建模；(3)通过可靠的水文气候变化诊断和多尺度的可靠降水和温度强迫数据的现成数据库支持明智的决策；以及(4)改进极端天气事件风险和严重程度的概率预测。

We live in an era of unprecedented global hydroclimatic and environmental change that requires reliable tools to model and improve predictions in hydroclimatic extremes, quantify their uncertainty, and assess environmental changes under natural variability and human forcings.******The long-term goal of this research program is to advance stationary and non-stationary spatiotemporal stochastic modeling with extensions and applications into downscaling methods, infilling of missing values (MVs), and robust diagnostics of hydroclimatic change. ******The four short-term objectives of this research are to: (i) increase our understanding of the spatiotemporal structure of precipitation and temperature at multiple scales and provide novel stationary and non-stationary stochastic models; (ii) introduce novel infilling methods and advance current maxima extraction schemes from records with missing values through the use of stochastic approaches; (iii) develop novel spatiotemporal downscaling schemes for climate model projections and historical data; and, (iv) create accurate diagnostics to detect and assess the significance of observed changes and trends in hydroclimatic extremes. To fulfill the objectives, big-data analyses will be performed using thousands in situ stations, reanalysis grid products, and climate model outputs. The spatiotemporal structure of precipitation and temperature will be mathematically described by a set of parsimonious parametric spatial and temporal correlation structures. The properties of the marginal distribution at multiple scales will be explored using an extended set of entropy-derived distributions that are consistent with the nature of these processes. An advanced spatiotemporal stochastic modeling framework will be developed by extending the parent Gaussian scheme in order to include time varying marginals and incorporate important field features, including anisotropy and storm kinematics. These advances will be embodied in infilling methods for MVs, downscaling schemes, and diagnostics of hydroclimatic change by exploiting the precise representation and simulation of the spatiotemporal structure as well as the marginal distribution of precipitation and temperature.******The developed stochastic modeling tools and compiled databases will be freely available and benefit the scientific community through: (i) generating scientific knowledge as the developed methods are applicable beyond the field of hydroclimatology; (ii) improving hydrological modeling through precise stochastic modeling of complex processes such as precipitation; (iii) supporting informed decision making with robust diagnostics of hydroclimatic change and ready-to-use databases of reliable precipitation and temperature forcing data at multiple scales; and, (iv) improving the probabilistic prediction of risk and severity of extreme weather events.**