A linear model of wintertime low-frequency variability

An alternate paradigm of low-frequency variability is investigated: variability in the extratropics is predominantly the result of low-frequency tropical diabatic heating which forces extratropical anomalies that can be additionally modified by transient eddy feedbacks. The zonally asymmetric time-mean basic state is necessary to organize the variability. However, its importance as an energy source/sink for the anomalies (as stressed by Simmons et al.) is secondary.

To test this hypothesis, we use a linear empirical-dynamical model (EDM) which is constructed using observations of the past 30 years. Notably, it includes tropical diabatic heating as an evolving model variable rather than as an externally specified forcing, and also includes, in effect, the feedback of extratropical weather systems on the more slowly varying circulation. Both of these features are shown to be important contributors to the model's realism.

The EDM is better at forecasting week 2 anomalies than a baroclinic model based on the linearized equations of motion, with many more than the EDM's 37 degrees of freedom, and forced with observed diabatic heating over the duration of the forecast. Indeed, at week 2 the EDM's skill is competitive with that of the nonlinear medium-range forecast (MRF) model with O(10^6) degrees of freedom in use at the National Centers for Environmental Prediction. Importantly, this encouraging model performance is not limited to years of El Nino or La Nina episodes in the eastern tropical Pacific.

The EDM presented here assumes that the statistics of extratropical low-frequency variability are Gaussian and that the dynamics are linear, stable, and stochastically forced. The approximate validity of these assumptions is demonstrated through several tests. A potentially limiting aspect of such a stable linear model with decaying eigenmodes concerns its ability to predict anomaly growth. It is nevertheless found, through a singular vector analysis of the model's propagator, that not only can predictable anomaly growth occur in this dynamical system through constructive modal interference, but actually occurs often. Examination of the dominant growing singular vectors further confirms the importance of tropical heating anomalies associated with El Nino/La Nina and Madden-Julian oscillation episodes in the predictable dynamics of the extratropical circulation. The analysis suggests that without inclusion of tropical heating, weekly averages may be predictable only about two weeks in the extratropics, but with tropical heating included, they may be predictable as much as seven weeks ahead.

The EDM is able to reproduce the observed lagged covariability statistics of low-frequency variability remarkably well. The power spectra of observed low-frequency anomalies also compares well with the prediction from the EDM. Both of these quantities are badly simulated by both barotropic and baroclinic models linearized about the time-mean flow. The spatial structure of the stochastic forcing necessary to maintain variability is discussed, and compared to that required in simpler models. The energy balance of the variability is analyzed to quantify the relative importance of the different mechanisms which contribute to variability.