Theoretic Studies in Geophysical Fluid Dynamics and Climate Dynamics

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The principal investigator develops and studies mathematical models of geophysical processes important for weather and climate. A major aim is to better understand sources of climate variability and the extent of their influences. The work involves new mathematical theory and techniques for dynamic transitions between states of a system described by a set of partial differential equations, and for memory effects -- differences in any particular state's features that depend on the chain of states through which the system arrives at that state. The system may be deterministic or stochastic. The mathematical issues are motivated by climate problems, and in turn the theory and the techniques are applied to the understanding of fundamental issues in climate dynamics and prediction. This project leads to improved predictions and new insights into weather, climate, and environmental phenomena of central importance to our economy. One such phenomenon to be studied in this project is the El Nino-Southern Oscillation (ENSO), which is the dominant mode of inter-annual climate variability, and which has global impacts on temperature, precipitation, tropical cyclones, human health, and even conflict. The project involves scientists as well as graduate students from the related scientific disciplines. Graduate students are included in the work of the project. The principal investigator and his collaborators work on dynamic transition theory for both deterministic partial differential equations and stochastic partial differential equations (SPDEs), and on developing theory and methods to establish effective non-Markovian reduced models for SPDEs. The goal is to quantify the sensitivity and dynamic transitions associated with typical sources of climate low frequency variability. Major goals include quantifying the role played by the memory effects, and identifying the key nonlinear interactions between low and high modes and the memory effects caused by noise. A few typical sources of climate variability that will be studied include ENSO, tropical convections, and the thermohaline circulations. Their variability, independently and interactively, may play a significant role in climate changes, past and future. The project involves specific collaborations with active atmosphere/ocean scientists in different institutions, and graduate students are included in the project work as well.