Nonlinear climatology and paleoclimatology: Capturing patterns of variability and change with Self-Organizing Maps

Self-Organizing Maps (SOMs) provide a powerful, nonlinear technique to optimally summarize complex geophysical datasets using a user-selected number of " icons" or SOM states, allowing rapid identification of preferred patterns, predictability of transitions, rates of transitions, and hysteresis/asymmetry in cycles. For example, SOM-based patterns concisely capture the spatial and temporal variability in atmospheric circulation datasets. SOMs and the SOM-based methodology are reviewed here at a practical level so as to encourage more-widespread usage of this powerful technique in the atmospheric sciences. Usage is introduced with a simple Antarctic ice core-based dataset to show analysis of multiple variables at a single point in space. Subsequent examples utilize a 24-year dataset (1979-2002) of daily Antarctic meteorological variables and demonstrate usage with 2-D, gridded data, for single and multiple variable scenarios. These examples readily show how SOMs capture nonlinearity in time series data, concisely summarize voluminous spatial data, and help us understand spatial and temporal change through, for example, pattern frequency analysis and identification of preferred pattern transitions.