A Hierarchy of Data-Based ENSO Models

Abstract

Global sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset's statistics. These inverse models assume that the system's variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset's leading empirical orthogonal functions. Multiple linear regression has been widely used to obtain inverse stochastic models; it is generalized here in two ways. First, the dynamics is allowed to be nonlinear by using polynomial regression. Second, a multilevel extension of classic regression allows the additive noise to be correlated in time; to do so, the residual stochastic forcing at a given level is modeled as a function of variables at this level and the preceding ones. The number of variables, as well as the order of nonlinearity, is determined by optimizing model performance.The two-level linear and quadratic models have a better El Niño-Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models' simulated Niño-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Niño and negative La Niña events. The benefits of the quadratic model are less clear in terms of its overall, cross-validated hindcast skill; this model outperforms, however, the linear one in predicting the magnitude of extreme SST anomalies.Seasonal ENSO dependence is captured by incorporating additive, as well as multiplicative forcing with a 12-month period into the first level of each model. The quasi-quadrennial ENSO oscillatory mode is robustly simulated by all models. The "spring barrier" of ENSO forecast skill is explained by Floquet and singular vector analysis, which show that the leading ENSO mode becomes strongly damped in summer, while nonnormal optimum growth has a strong peak in December.

Extreme events: dynamics, statistics and prediction

“…This approach is based on constructing an Empirical Model Reduction (EMR) model of ENSO (Kondrashov et al, 2005b), which combines a nonlinear deterministic with a linear, but state-dependent stochastic component; the latter is often referred to as multiplicative noise. This EMR ENSO model has also been quite competitive in real-time ENSO forecasts.…”

An empirical stochastic model of sea-surface temperatures and surface winds over the Southern Ocean

“…The construction of the above statistical models is rooted in the empirical methodology of Kravtsov et al (2005b) and Kondrashov et al (2005; however, the model construction algorithm is substantially modified and improved here in a number of ways that help choose the optimal model structure (see the appendices). These modifications make Kravtsov et al (2005b) technique, previously used to identify low-dimensional behavior within high-dimensional noisy data, applicable to the analysis of the phenomena involving intermediate number of degrees of freedom.…”

“…Despite our having removed the explicit seasonal cycle from the SLW fields prior to constructing our empirical stochastic model, the parameters of this model may still have some seasonal dependence. Kondrashov et al (2005) found that the optimal way to incorporate such dependence is two include, at the main level of the model, two additional predictors, namely sin(2π t/365) and cos(2π t/365). The remainder of the procedure is unaltered, and the construction of the additional levels of the empirical stochastic models proceeds as described above.…”

Complicated ENSO models do not significantly outperform very simple ENSO models

“…It is evident from this paper that even the largest models running on amongst the largest computers in the world are presently not performing much better than models that can be run on a desktop computer. There seems to be no reason why using even faster computers will do any better than the present day supercomputers unless a fundamental breakthrough is made in understanding the processes that trigger the ENSO events (Eisenman et al, 2005;Kondrashov et al, 2005;Perez et al, 2005;Saynisch et al, 2006;Vecchi et al, 2006). Such an understanding would allow more targeted data collection to drive the models and would focus modifications to dynamical model codes to those processes that matter most.…”