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S. Kravtsov
,
D. Kondrashov
, and
M. Ghil

Abstract

Predictive models are constructed to best describe an observed field’s statistics within a given class of nonlinear dynamics driven by a spatially coherent noise that is white in time. For linear dynamics, such inverse stochastic models are obtained by multiple linear regression (MLR). Nonlinear dynamics, when more appropriate, is accommodated by applying multiple polynomial regression (MPR) instead; the resulting model uses polynomial predictors, but the dependence on the regression parameters is linear in both MPR and MLR.

The basic concepts are illustrated using the Lorenz convection model, the classical double-well problem, and a three-well problem in two space dimensions. Given a data sample that is long enough, MPR successfully reconstructs the model coefficients in the former two cases, while the resulting inverse model captures the three-regime structure of the system’s probability density function (PDF) in the latter case.

A novel multilevel generalization of the classic regression procedure is introduced next. In this generalization, the residual stochastic forcing at a given level is subsequently modeled as a function of variables at this level and all the preceding ones. The number of levels is determined so that the lag-0 covariance of the residual forcing converges to a constant matrix, while its lag-1 covariance vanishes.

This method has been applied to the output of a three-layer, quasigeostrophic model and to the analysis of Northern Hemisphere wintertime geopotential height anomalies. In both cases, the inverse model simulations reproduce well the multiregime structure of the PDF constructed in the subspace spanned by the dataset’s leading empirical orthogonal functions, as well as the detailed spectrum of the dataset’s temporal evolution. These encouraging results are interpreted in terms of the modeled low-frequency flow’s feedback on the statistics of the subgrid-scale processes.

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D. Kondrashov
,
S. Kravtsov
,
A. W. Robertson
, and
M. Ghil

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.

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S. Kravtsov
,
P. Berloff
,
W. K. Dewar
,
M. Ghil
, and
J. C. McWilliams

Abstract

A novel mechanism of decadal midlatitude coupled variability, which crucially depends on the nonlinear dynamics of both the atmosphere and the ocean, is presented. The coupled model studied involves quasigeostrophic atmospheric and oceanic components, which communicate with each other via a constant-depth oceanic mixed layer. A series of coupled and uncoupled experiments show that the decadal coupled mode is active across parameter ranges that allow the bimodality of the atmospheric zonal flow to coexist with oceanic turbulence. The latter is most intense in the regions of inertial recirculation (IR). Bimodality is associated with the existence of two distinct anomalously persistent zonal-flow modes, which are characterized by different latitudes of the atmospheric jet stream. The IR reorganizations caused by transitions of the atmosphere from its high- to low-latitude state and vice versa create sea surface temperature anomalies that tend to induce transition to the opposite atmospheric state. The decadal–interdecadal time scale of the resulting oscillation is set by the IR adjustment; the latter depends most sensitively on the oceanic bottom drag. The period T of the nonlinear oscillation is 7–25 yr for the range of parameters explored, with the most realistic parameter values yielding T ≈ 20 yr.

Aside from this nonlinear oscillation, an interannual Rossby wave mode is present in all coupled experiments. This coupled mode depends neither on atmospheric bimodality, nor on ocean eddy dynamics; it is analogous to the mode found previously in a channel configuration. Its time scale in the model with a closed ocean basin is set by cross-basin wave propagation and equals 3–5 yr for a basin width comparable with the North Atlantic.

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A. W. Robertson
,
C-C. Ma
,
C. R. Mechoso
, and
M. Ghil

Abstract

A multiyear simulation with a coupled ocean-atmosphere general circulation model (GCM) is presented. The model consists of the UCLA global atmospheric GCM coupled to the GFDL oceanic GCM; the latter is dynamically active over the tropical Pacific, while climatological time-varying sea surface temperatures (SST) are prescribed elsewhere. The model successfully simulates the main climatological features associated with the seasonal cycle, including the east-west gradient in SST across the equatorial Pacific. The most apparent deficiencies include a systematic cold bias (∼2 K) across most of the tropical Pacific and underestimated wind stress magnitudes in the equatorial band. Multichannel singular spectrum analysis is used to describe the multivariate structure of the seasonal cycle at the equator in both the model and observed data. The annual harmonic in equatorial SST is primarily wind driven, while air-sea interaction strongly affects the semiannual harmonic.

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A. W. Robertson
,
C-C. Ma
,
M. Ghil
, and
C. R. Mechoso

Abstract

Two multiyear simulations with a coupled ocean-atmosphere general circulation model (GCM)-totaling 45 years-are used to investigate interannual variability at the equator. The model consists of the UCLA global atmospheric GCM coupled to the GFDL oceanic GCM, dynamically active over the tropical Pacific. Multichannel singular spectrum analysis along the equator identifies ENSO-like quasi-biennial (QB) and quasi-quadrennial (QQ) modes. Both consist of predominantly standing oscillations in sea surface temperature and zonal wind stress that peak in the central or east Pacific, accompanied by an oscillation in equatorial thermocline depth that is characterized by a phase shift of about 90° across the basin, with west leading east. Simulated interannual variability is weaker than observed in both simulations. One of these is dominated by the QB, the other by the QQ mode, although the two differ only in details of the surface-layer parameterizations.

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