Using transfer functions to quantify El Niño Southern Oscillation dynamics in data and models

Abstract

Transfer function tools commonly used in engineering control analysis can be used to better understand the dynamics of El Niño Southern Oscillation (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 be used first to assess whether the underlying relationship is or is not frequency dependent, and if so, to diagnose the underlying differential equations that relate the variables, and hence describe the dynamics of individual subsystem processes relevant to ENSO. Estimating process parameters allows the identification of compensating model errors that may lead to a seemingly realistic simulation in spite of incorrect model physics. This tool is applied here to the TAO array ocean data, the GFDL-CM2.1 and CCSM4 general circulation models, and to the Cane–Zebiak ENSO model. The delayed oscillator description is used to motivate a few 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 for model improvement. The transfer function methodology is also useful in understanding the dynamics and evaluating models of other climate processes.

A collection on ‘Climate dynamics: multiple scales and memory effects’

“…MacMartin & Tziperman [8] apply here transfer function methodology to help understand ENSO dynamics, compare data with models and identify systematic model errors. Transfer functions represent the frequency-dependent input-output relationship between a pair of variables.…”

Technical note: Simultaneous fully dynamic characterization of multiple input–output relationships in climate models

“…Analyzing the response to a different perturbed region (not shown) can help ascertain whether that response is particular to perturbations in a single region or whether this is the result of excitation of a natural mode of variability; in the latter case, information about the timescale of response can aid in identifying which mode of variability is being excited. In addition, one could isolate particular spatial areas that one wishes to analyze (for example, by spatial averaging over the midlatitudes) and compute the transfer function (MacMartin and Tziperman, 2014) to ascertain magnitude, phase, and spectral coherence of the relationship between that feature and the input signal. Through these explorations, one has a much Figure 9.…”

Modelos estadísticos para la interacción océano-atmósfera

“…Como en MacMartin y Tziperman (2014), pudimos comparar cuantitativamente diferentes procesos individuales entre las observaciones. Nótese que las ecuaciones (10) y (11) describen, de manera implícita, las relaciones de un sistema de retroalimentación que contiene los elementos clave presentados en la mayoría de los modelos dinámicos utilizados en la predicción canónica de ENSO (Fernández y (Graham et al, 2015) o el modelo de oscilador retrasado (MacMartin y Tziperman, 2014). Comenzando con un frío (anomalías SOI positivas) o una condición ENSO normal, los vientos alisios ecuatoriales pueden generar una ola Kelvin ascendente hacia el este en el Pacífico occidental.…”