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

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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.