Search Results

You are looking at 11 - 20 of 30 items for

  • Author or Editor: M. Ghil x
  • Refine by Access: Content accessible to me x
Clear All Modify Search
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.

Full access
A. W. Robertson
,
M. Ghil
, and
M. Latif

Abstract

The response of the Max Planck Institute’s ECHAM3 atmospheric general circulation model to a prescribed decade-long positive anomaly in sea surface temperatures (SSTs) over the North Atlantic is investigated. Two 10-yr realizations of the anomaly experiment are compared against a 100-yr control run of the model with seasonally varying climatological SST using a model spatial resolution of T42. In addition to the time-mean response, particular attention is paid to changes in intraseasonal variability, expressed in terms of North Atlantic–European weather regimes. The model regimes are quite realistic.

Substantial differences are found in the 700-mb geopotential height field response between the two decadal realizations. The time-mean response in the first sample decade is characterized by the positive (zonal) phase of the North Atlantic oscillation (NAO); this response can be identified with changes in the frequency of occurrence of certain weather regimes by about one standard deviation. (Preliminary results of this numerical experiment were reported at the Atlantic Climate Variability Workshop held at the Lamont–Doherty Earth Observatory of Columbia University, Palisades, New York, 24–26 September 1997.) By contrast, the second SST anomaly decade shows a localized trough centered over the British Isles; it projects less strongly onto the model’s intrinsic weather regimes. The control run itself exhibits pronounced decade-to-decade variations in the weather regimes’ frequency of occurrence as well as in its NAO index. The two 10-yr anomaly experiments are insufficient, in length and number, to identify a robust SST response above this level of intrinsic variability.

Full access
S. Kravtsov
,
A. W. Robertson
, and
M. Ghil

Abstract

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.

Full access
S. Kravtsov
,
A. W. Robertson
, and
M. Ghil

Abstract

Atmospheric low-frequency variability (LFV) is studied in a two-layer quasigeostrophic model. The model geometry is a periodic β channel with flat bottom and zonally inhomogeneous thermal forcing. As a result of the idealized land–sea contrast, the model produces a zonally modulated climatological jet with realistic amplitude. The model's LFV is equivalent barotropic; principal component analysis reveals that it consists of (i) dominant stationary patterns with red-noise-like temporal behavior and (ii) propagating waves with periods of 37 and 50 days superimposed on the former.

The vorticity forcing due to synoptic eddies is dominated by self-interaction of high-pass filtered model fields. Applying a phase-randomized, stochastic analog of this forcing to a version of the full model in which fast baroclinic instability and, therefore, synoptic eddies are suppressed, produces a climatology and LFV that are very similar to those in the full model. Synoptic eddies are solely represented in the simplified model version by means of stochastic forcing that is independent of the low-frequency flow. It follows that, while fast synoptic eddies are modulated in the full model by the LFV, this modulation is fairly passive: anomalous generation of the synoptic eddies in the course of the full system's low-frequency evolution, the so-called synoptic-eddy feedback, is not essential in selecting the system's low-frequency modes; the main role of synoptic eddies is to supply energy to these modes.

Further analysis indicates that the LFV in this thermally driven model originates from the barotropic mode's dynamics. The baroclinic mode passively follows, to first order, the low-frequency changes in the barotropic mode. The latter changes are due to stochastically excited, weakly damped linear eigenmodes of the barotropic-mode equation. Two distinct stationary eigenmodes, as well as two pairs of propagating modes with periods of 27 and 36 days, respectively, dominate the low-frequency behavior. The leading empirical orthogonal functions in this model are associated with these six particular eigenmodes. The latter are not well separated, however, from the other eigenmodes in terms of damping time scale, and it is the barotropic nonlinearity that selects the six dynamically important modes over the others. Interactions between these six modes also result in the occurrence of probability density maxima in two-dimensional subspaces of the model's phase space.

Full access
S. Kravtsov
,
A. W. Robertson
, and
M. Ghil

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 with the mean flow and, consequently, dominate the lowest-frequency behavior in the model. The leading stationary mode resembles the observed annular mode in the Southern Hemisphere.

The bimodality is due to nonlinear interactions between nearly equivalent barotropic, stationary, and propagating modes, while the synoptic eddies play a modest role in determining the relative persistence of the two states. The role of synoptic eddies is very substantial only at unrealistically high values of the bottom drag, where they give rise to ultralow frequency variability by modifying the jet in a way that reinforces generation of the eddy field. This type of behavior is related to the presence of a homoclinic orbit in the model’s phase space and is not apparent for more realistic, lower values of the bottom drag.

Full access
K. Bhattacharya
,
M. Ghil
, and
I. L. Vulis

Abstract

We present a simple, deterministic energy-balance model with possible relevance to climatic variations on the time scale of glaciation cycles. The lag between ice-sheet extent and zonally-averaged temperature is modeled as a time delay in the ice-albedo feedback. The model exhibits self-sustained oscillations which are quasi-periodic or aperiodic in character. Fourier spectra of solutions have the features of many paleo-climatic records: peaks of variable height and width superimposed on a continuous, red-noise type background.

Full access
R. Balgovind
,
A. Dalcher
,
M. Ghil
, and
E. Kalnay

Abstract

A simple model that yields the spatial correlation structure of global atmospheric mass-field forecast errors is derived. The model states that the relative potential vorticity of the forecast error is forced by spatially multi-dimensional white noise. The forecast error equation contains a nondimensional parameter c 0, which depends on the Rossby radius of deformation. From this stochastic-dynamic equation, a deterministic equation for the spatial covariance function of the 500 mb geopotential error field is obtained.

Three methods of solution are examined: 1) an analytic method based on spherical harmonics, 2) a numerical method based on stratified sampling of Monte-Carlo realizations of the stochastic-dynamic equation, and 3) a combined analytic-numerical method based on two successive applications of a fast Poisson solver to the deterministic covariance equation. The three methods are compared for accuracy and efficiency, and the third (combined) method is found to be clearly superior.

The model's covariance function is compared with global correlation data of forecast-minus-observed geopoteniial fields for the DST-6 period February–March 1976. The data are based on the GLAS forecast-assimilation system in use at that lime (Ghil et al., 1979).

The model correlations agree well with the latitude dependence of the data correlations. The fit between model and data confirms that the forecast error between 24 and 36 h is largely random, rather than systematic; the value of the parameter c 0 which gives the best fit suggests that much of this error can be attributed to baroclinic, rather than barotropic effects. Deterministic influences not included in the model appear at 12 and 48 h. They suggest possibilities of improving the forecast system by a better objective analysis and initialization procedure, and a better treatment of planetary-wave propagation, respectively.

An analytic formula is obtained which locally approximates well the model's global correlations. This formula is convenient to use in the calculation of weighting coefficients for analysis and assimilation schemes. It shows that Gaussian functions are a poor approximation for the forecast error correlations of the mass field, and their derivatives an even poorer approximation to wind field correlations.

Full access
P. Bernardet
,
A. Butet
,
M. Déqué
,
M. Ghil
, and
R. L. Pfeffer

Abstract

Experiments were performed in a rotating, differentially heated annulus, with and without bottom topography of azimuthal wavenumber 2. Both water and a viscous glycerol-water mixture were used as a working fluid. In one series of experiments, measurements of azimuthal velocity u were carded out by Doppler-laser velocimetry at midradius and at ⅓ and ⅔ depth. In the other, temperature measurements were made by a set of thermistors at three different heights and three different radii. Results were analyzed by Fourier transformation, separately in space and in time, and in terms of complex empirical orthogonal functions (CEOFs).

In the experiments with topography, a standing wave 2 is generated, with larger amplitude at the upper level and a tilted wave structure. The two leading CEOFs contain a very large fraction of the variance, and give an excellent picture of the spatial modulation of the traveling baroclinic waves. The dominant baroclinic wave has azimuthal wavenumber 4, 5 or 6, according to the nondimensional parameters of the given experiment, and pronounced sidebands due to the topography. The modulation of this wave is such that its largest amplitude occurs at the lower level upstream of the two topographic ridges. At the upper level, the modulation is weaker, with the maximum wave amplitude located downstream of the ridges. Partial decoupling of the two wave trains attached to the two ridges is evident in one experiment.

Low-frequency vacillation of the entire flow pattern is apparent; this vacillation has a period of about 50 annulus rotations in the viscous mixture. The possible relevance of this topographically induced vacillation to the extratropical 30–60 day oscillation is discussed.

Full access
T. M. Chin
,
M. J. Turmon
,
J. B. Jewell
, and
M. Ghil

Abstract

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Full access
A. Deloncle
,
R. Berk
,
F. D’Andrea
, and
M. Ghil

Abstract

Two novel statistical methods are applied to the prediction of transitions between weather regimes. The methods are tested using a long, 6000-day simulation of a three-layer, quasigeostrophic (QG3) model on the sphere at T21 resolution.

The two methods are the k nearest neighbor classifier and the random forest method. Both methods are widely used in statistical classification and machine learning; they are applied here to forecast the break of a regime and subsequent onset of another one. The QG3 model has been previously shown to possess realistic weather regimes in its northern hemisphere and preferred transitions between these have been determined. The two methods are applied to the three more robust transitions; they both demonstrate a skill of 35%–40% better than random and are thus encouraging for use on real data. Moreover, the random forest method allows one, while keeping the overall skill unchanged, to efficiently adjust the ratio of correctly predicted transitions to false alarms.

A long-standing conjecture has associated regime breaks and preferred transitions with distinct directions in the reduced model phase space spanned by a few leading empirical orthogonal functions of its variability. Sensitivity studies for several predictors confirm the crucial influence of the exit angle on a preferred transition path. The present results thus support the paradigm of multiple weather regimes and their association with unstable fixed points of atmospheric dynamics.

Full access