A Nonstationary Framework for Studying Weather/Climate Extremes

The study of weather and climate extremes often uses the theory of extreme values. Such a detection method has a major problem: to obtain the probability distribution of extremes, one has to implicitly assume the Earth's climate is stationary over a long period within which the climatology is defined. While such detection makes some sense in a purely statistical view of stationary processes, it can lead to misleading statistical properties of weather and climate extremes caused by long term climate variability and change, and may also cause enormous difficulty in attributing and predicting these extremes. To alleviate this problem, here we report a novel non-stationary framework for studying weather and climate extremes in a non-stationary framework. In this new framework, the weather and climate extremes will be defined as timescale-dependent quantities derived from the anomalies with respect to non-stationary climatologies of different timescales. With this non-stationary framework, the non-stationary and nonlinear nature of climate system will be taken into account; and the attribution and the prediction of weather and climate extremes can then be separated into 1) the change of the statistical properties of the weather and climate extremes themselves and 2) the background climate variability and change. The new non-stationary framework will use the ensemble empirical mode decomposition (EEMD) method, which is a recent major improvement of the Hilbert-Huang Transform for time-frequency analysis. Using this tool, we will adaptively decompose various weather and climate data from observation and climate models in terms of the components of the various natural timescales contained in the data. With such decompositions, the non-stationary statistical properties (both spatial and temporal) of weather and climate anomalies and of their corresponding climatologies will be analyzed and documented.