@article {Kondrashov.Kravtsov.ea.2005,
title = {A hierarchy of data-based ENSO models},
journal = {Journal of climate},
volume = {18},
number = {21},
year = {2005},
pages = {4425{\textendash}4444},
abstract = {Global sea surface temperature (SST) evolution is analyzed by constructing predictive models that best describe the dataset{\textquoteright}s statistics. These inverse models assume that the system{\textquoteright}s variability is driven by spatially coherent, additive noise that is white in time and are constructed in the phase space of the dataset{\textquoteright}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 Ni{\~n}o{\textendash}Southern Oscillation (ENSO) hindcast skill than their one-level counterparts. Estimates of skewness and kurtosis of the models{\textquoteright} simulated Ni{\~n}o-3 index reveal that the quadratic model reproduces better the observed asymmetry between the positive El Ni{\~n}o and negative La Ni{\~n}a 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 {\textquotedblleft}spring barrier{\textquotedblright} 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.},
doi = {10.1175/JCLI3567.1},
author = {Kondrashov, Dmitri and Kravtsov, S and Robertson, Andrew W. and Ghil, Michael}
}