Stochastic Modeling of Episode Duration, Magnitude, and Peak in Long Paleo Records

该项目利用资金帮助开发可应用于降水、河流、温度和干旱的长期古气候记录的随机模型，以量化气候系统中的不确定性，改善与气候相关的管理和研究。研究人员正在使用一个理论模型来回答以下问题：(1)比所有观测到的干旱时间更长的干旱的概率是多少？(2)两个暖期的差异是否有统计学意义？(3)低流量事件是否与高流量事件具有不同的性质？(4)给定规模的洪水的复发间隔是多少？研究人员将开展以下具体工作：1)建立持续时间与幅度、持续时间与峰值、幅度与峰值的所有联合二元分布模型；2)建立持续时间、幅度和峰值的联合三变量分布模型；3)测试这些随机模型是否适合长期的古气候记录，如北美帕尔默干旱严重指数（PDSI）的树木年轮重建；4)将新的建模工具应用于长期古气候记录，以提高对水文气候事件的概率估计，如百年一遇干旱的持续时间和规模；5)评价具有相同变量的两个时间序列之间的显著差异。该研究旨在量化西南地区水文气候事件（如干旱的持续时间、程度和峰值）的可能性，以便区域水资源管理者能够更有效地进行规划。一名地理研究生和一名数学研究生将通过这项研究得到支持，从而有助于弥合传统的学术学科鸿沟。

This project uses funds to help develop stochastic models that can be applied to long paleoclimatic records of precipitation, streamflow, temperature, and drought in order to quantify uncertainty in climate systems and improve climate-related management and research. The researchers are using a theoretical model to provide answers to questions like: (1) What is the probability of a drought longer than all observed droughts? (2) Is the difference between two warm periods statistically significant? (3) Do low-flow episodes have different properties than high-flow ones? and (4) What are the recurrence intervals for floods of a given size? The researchers will carry out the following specific tasks: 1) model all the joint bivariate distributions of duration and magnitude, duration and peak value, magnitude and peak value; 2) model the joint trivariate distribution of duration, magnitude, and peak value; 3) test how these stochastic models fit long paleoclimatic records, such as tree-ring reconstructions of the Palmer Drought Severity Index (PDSI) over North America; 4) apply the new modeling tools to long paleoclimatic records to improve probabilistic estimates of hydroclimatic episodes, such as duration and magnitude of 100-year droughts; and 5) evaluate how two time series of the same variable are significantly different from one another.The research aims to quantify the likelihood of hydroclimatic episodes (such as the duration, magnitude, and peak value of drought) in the Southwest so that regional water resource managers can plan more effectively. A graduate student in geography and one in mathematics will be supported through the research thereby helping to bridge traditional academic disciplinary divides.