Sergey Kravtsov

Multilevel Regression Modeling of Nonlinear Processes: Derivation and Applications to Climatic Variability

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 proce...

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 Nino–Southern Oscillation (ENSO) hindcas...

Multidecadal Climate Variability in Observed and Modeled Surface Temperatures

Abstract This study identifies interdecadal natural climate variability in global surface temperatures by subtracting, from the observed temperature evolution, multimodel ensemble mean based on the World Climate Research Programmes (WCRP) Coupled Model Intercomparison Project phase 3 (CMIP3) multimodel dataset. The resulting signal resembles the so-called Atlantic multidecadal oscillation (AMO) and is presumably associated with intrinsic dynamics of the oceanic thermohaline circulation (THC). While certain phases of the oscillation are dominated by the anomalies in the North Atlantic region, other phases are characterized by global teleconnections to the North Pacific Ocean, tropical Atlantic Ocean, as well as the Southern Ocean. In particular, natural variability of sea surface temperature in the Atlantic hurricanes’ main development region has a peak-to-peak amplitude comparable in magnitude to this region’s surface temperature increase over the past century, for all seasons. Evidence suggests that the...

Connecting past and present climate variability to the water levels of Lakes Michigan and Huron

[1] The water levels of Lakes Michigan and Huron have been monitored since 1865, and numerous attempts have since been made to connect their variations to potentially predictable large-scale climate modes. In the present study, the levels are analyzed after outflow-related damping effects were removed, increasing the transparency of the lake level fluctuations and potential climate connections. This filtering exposes a large oscillation which is connected to the Atlantic Multidecadal Oscillation (AMO), and a ∼27-yr periodicity that is likely resulting from the intermodulation of two near-decadal cycles originating in the North Atlantic region. While the lake level fluctuations prior to 1980 were predominately driven by changes in precipitation, it is now found that for the first time in our years of record, evaporation has begun to significantly contribute to lake level changes. Summertime evaporation rates have more than doubled since 1980 as a result of increasing water-surface temperatures, which are significantly correlated with decreasing wintertime ice cover.

The Effects of Mesoscale Ocean-Atmosphere Coupling on the Large-Scale Ocean Circulation

Abstract Small-scale variation in wind stress due to ocean–atmosphere interaction within the atmospheric boundary layer alters the temporal and spatial scale of Ekman pumping driving the double-gyre circulation of the ocean. A high-resolution quasigeostrophic (QG) ocean model, coupled to a dynamic atmospheric mixed layer, is used to demonstrate that, despite the small spatial scale of the Ekman-pumping anomalies, this phenomenon significantly modifies the large-scale ocean circulation. The primary effect is to decrease the strength of the nonlinear component of the gyre circulation by approximately 30%–40%. This result is due to the highest transient Ekman-pumping anomalies destabilizing the flow in a dynamically sensitive region close to the western boundary current separation. The instability of the jet produces a flux of potential vorticity between the two gyres that acts to weaken both gyres.

Ocean eddy dynamics in a coupled ocean-atmosphere model

Abstract The role of mesoscale oceanic eddies is analyzed in a quasigeostrophic coupled ocean–atmosphere model operating at a large Reynolds number. The model dynamics are characterized by decadal variability that involves nonlinear adjustment of the ocean to coherent north–south shifts of the atmosphere. The oceanic eddy effects are diagnosed by the dynamical decomposition method adapted for nonstationary external forcing. The main effects of the eddies are an enhancement of the oceanic eastward jet separating the subpolar and subtropical gyres and a weakening of the gyres. The flow-enhancing effect is due to nonlinear rectification driven by fluctuations of the eddy forcing. This is a nonlocal process involving generation of the eddies by the flow instabilities in the western boundary current and the upstream part of the eastward jet. The eddies are advected by the mean current to the east, where they backscatter into the rectified enhancement of the eastward jet. The gyre-weakening effect, which is due...

Empirical mode reduction in a model of extratropical low-frequency variability

This paper constructs and analyzes a reduced nonlinear stochastic model of extratropical low-frequency variability. To do so, it applies multilevel quadratic regression to the output of a long simulation of a global baroclinic, quasigeostrophic, three-level (QG3) model with topography; the model’s phase space has a dimension of O(10 4 ). The reduced model has 45 variables and captures well the non-Gaussian features of the QG3 model’s probability density function (PDF). In particular, the reduced model’s PDF shares with the QG3 model its four anomalously persistent flow patterns, which correspond to opposite phases of the Arctic Oscillation and the North Atlantic Oscillation, as well as the Markov chain of transitions between these regimes. In addition, multichannel singular spectrum analysis identifies intraseasonal oscillations with a period of 35–37 days and of 20 days in the data generated by both the QG3 model and its low-dimensional analog. An analytical and numerical study of the reduced model starts with the fixed points and oscillatory eigenmodes of the model’s deterministic part and uses systematically an increasing noise parameter to connect these with the behavior of the full, stochastically forced model version. The results of this study point to the origin of the QG3 model’s multiple regimes and intraseasonal oscillations and identify the connections between the two types of behavior.

Multiple Regimes and Low-Frequency Oscillations in the Northern Hemisphere’s Zonal-Mean Flow

This paper studies multiple regimes and low-frequency oscillations in the Northern Hemisphere zonal-mean zonal flow in winter, using 55 yr of daily observational data. The probability density function estimated in the phase space spanned by the two leading empirical orthogonal functions exhibits two distinct, statistically significant maxima. The two regimes associated with these maxima describe persistent zonal-flow states that are characterized by meridional displacements of the midlatitude jet, poleward and equatorward of its time-mean position. The geopotential height anomalies of either regime have a pronounced zonally symmetric component, but largest-amplitude anomalies are located over the Atlantic and Pacific Oceans. High-frequency synoptic transients participate in the maintenance of and transitions between these regimes. Significant oscillatory components with periods of 147 and 72 days are identified by spectral analysis of the zonal-flow time series. These oscillations are described by singular spectrum analysis and the multitaper method. The 147-day oscillation involves zonal-flow anomalies that propagate poleward, while the 72-day oscillation only manifests northward propagation in the Atlantic sector. Both modes mainly describe changes in the midlatitude jet position and intensity. In the horizontal plane though, the two modes exhibit synchronous centers of action located over the Atlantic and Pacific Oceans. The two persistent flow regimes are associated with slow phases of either oscillation.

Bimodal Behavior in the Zonal Mean Flow of a Baroclinic β-Channel Model

Abstract The dynamical origin of midlatitude zonal-jet variability is examined in a thermally forced, quasigeostrophic, two-layer channel model on a β plane. The model’s behavior is studied as a function of the bottom-friction strength. Two distinct zonal-flow states exist at realistic, low, and intermediate values of the bottom drag; these two states are maintained by the eddies and differ mainly in terms of the meridional position of their climatological jets. The system’s low-frequency evolution is characterized by irregular transitions between the two states. For a given branch of model solutions, the leading stationary and propagating empirical orthogonal functions are related to eigenmodes of the model’s dynamical operator, linearized about the climatological state on this branch. Nonlinear interactions between these modes are instrumental in determining their relative energy level. In particular, the stationary modes’ self-interaction is shown to vanish. Thus, these modes do not exchange energy wit...

Interdecadal Variability in a Hybrid Coupled Ocean–Atmosphere–Sea Ice Model

Interdecadal climate variability in an idealized coupled ocean-atmosphere-sea-ice model is studied. The ocean component is a fully three-dimensional primitive equation model and the atmospheric component is a two-dimensional (2D) energy balance model of Budyko-Sellers-North type, while sea ice is represented by a 2D thermodynamic model. In a wide range of parameters the model climatology resembles certain aspects of observed climate. Two types of interdecadal variability are found. The first one is characterized by northward-propagating upper-ocean temperature anomalies in the northwestern part of the ocean basin and a westward-propagating, wavelike temperature pattern at depth. The other type has larger-scale temperature anomalies that propagate westward in both the upper and deep ocean, along the sea ice edge. Both types of oscillations have been found previously in similar models that do not include sea ice. Therefore, the oscillation mechanism does not depend on sea-ice feedbacks nor is it modified very much by the inclusion of sea ice. For some parameter values, the interdecadal oscillations are self-sustained, while for others they are damped. Stochastic-forcing experiments show that, in the latter case, significant interdecadal signals can still be identified in the time series of oceanic heat transport. The periods of these signals, however, do not closely match those identified in a stability analysis of the deterministic model when linearized about its steady state. The authors show that linearization around the actual climatology of the stochastically forced integrations provides a better match for some of the modes that were poorly explained when linearizing about the deterministic models steady state. The main difference between the two basic states is in the distribution of climatological convective depth, which is affected strongly by intermittent atmospheric forcing.