Using Transfer Functions to Quantify ENSO Dynamics in Data and Models

Transfer function tools commonly used in engineering control analysis can be used to better understand the dynamics of ENSO, compare data with models, and identify systematic model errors. The transfer function describes the frequency-dependent input-output relationship between any pair of causally-related variables, and can be estimated from time series. This can then be used to diagnose the underlying differential equations that relate the variables, and hence to describe the dynamics of individual subsystem processes that are relevant to the overall dynamics of ENSO. Estimating process parameters allows the identification of compensating model errors that may lead to a seemingly realistic simulation for the wrong reason. This tool is illustrated here using the TAO array for ocean data, the GFDL CM2.1 general circulation model (GCM), and the Cane-Zebiak ENSO model. The delayed oscillator description of ENSO is used to motivate a few of the relevant processes involved in the dynamics, although any other ENSO mechanism could be used instead. We identify several differences in the processes between the models and data that may be useful in improving the models. The same methodology may also be useful in understanding the dynamics and evaluating models of other climate processes.