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Abstract
The theory of empirical normal modes (ENMs) for a shallow water fluid is developed. ENMs are basis functions that both have the statistical properties of empirical orthogonal functions (EOFs) and the dynamical properties of normal modes. In fact, ENMs are obtained in a similar manner as EOFs but with the use of a quadratic form instead of the Euclidean norm. This quadratic form is a global invariant, the wave activity, of the linearized equations about a basic state. A general formulation is proposed for calculating normal modes from a generalized hermitian problem, even when the basic state is not zonal.
The projection coefficients of the flow onto a few leading ENWs generally have a more monochromatic behavior than that obtained for EOFS, which give them an intrinsically more predictable character. This property is illustrated by numerical experiments using the shallow water model on the sphere. It is shown, in particular, that the ENM coefficients, when used as predictors in a statistical linear model, provide better predictions of the behavior of the shallow water atmosphere than EOF coefficients. It is also shown that the choice of the basic state itself is crucial.
Abstract
The theory of empirical normal modes (ENMs) for a shallow water fluid is developed. ENMs are basis functions that both have the statistical properties of empirical orthogonal functions (EOFs) and the dynamical properties of normal modes. In fact, ENMs are obtained in a similar manner as EOFs but with the use of a quadratic form instead of the Euclidean norm. This quadratic form is a global invariant, the wave activity, of the linearized equations about a basic state. A general formulation is proposed for calculating normal modes from a generalized hermitian problem, even when the basic state is not zonal.
The projection coefficients of the flow onto a few leading ENWs generally have a more monochromatic behavior than that obtained for EOFS, which give them an intrinsically more predictable character. This property is illustrated by numerical experiments using the shallow water model on the sphere. It is shown, in particular, that the ENM coefficients, when used as predictors in a statistical linear model, provide better predictions of the behavior of the shallow water atmosphere than EOF coefficients. It is also shown that the choice of the basic state itself is crucial.
Abstract
The low-frequency variability in the midlatitudes is described through an analysis of the oscillatory phenomena. In order to isolate nearly periodic components of the atmospheric flow, the multichannel version of the singular spectrum analysis (M-SSA) is developed and applied to an NMC 32-year long set of 700-hPa geopotential heights. In the same way that principal component analysis identifies the spatial patterns dominating the variability, M-SSA identifies dynamically relevant space–time patterns and provides an adaptive filtering technique.
Three major low-frequency oscillations (LFOs) are found, with periods of 70 days, 40–45 days, and 30–35 days. The 70-day oscillation consists of fluctuations in both position and amplitude of the Atlantic jet, with a poleward-propagating anomaly pattern. The 40–45-day oscillation is specific to the Pacific sector and has a pronounced Pacific/North American (PNA) structure in its high-amplitude phase. The 30–35-day mode is confined over the Atlantic region, and consists of the retrogression of a dipole pattern. All these oscillations are shown to be intermittently excited, and M-SSA allows the localization of their spells. The two Atlantic oscillations turn out to be frequently phase locked, so that the 30–35-day mode is likely to be a harmonic of the 70-day mode. The phase locking of the Pacific 40–45-day with the Atlantic 30–35-day oscillations is also studied.
Next, the relationships between LFOs and weather regimes are studied. It is shown in particular that the occurrence of the Euro-Atlantic blocking regime is strongly favored, although not systematically caused, by particular phases of the 30–35-day mode. The LFOs themselves are able to produce high-amplitude persistent anomalies by interfering with each other.
The transition from a zonal regime to a blocking regime is also shown to be highly connected to the life cycle of the 30–35-day mode, indicating that regime transitions do not result only from the random occurrence of particular transient eddy forcing. There are preferred paths between weather regimes. This result leaves us with the hope that at least the large-scale environment-favoring weather regimes may be forecast in the long range. Conditional probability of occurrence of blocking, 30 days ahead, is enhanced, relative to climatological probability, by a factor of 2 if the phase of the 30–35-day oscillation is known. This also emphasizes the necessity of operational models to represent correctly the extratropical LFOs in order to produce skillful long-range and even medium-range forecasts of weather regimes.
Abstract
The low-frequency variability in the midlatitudes is described through an analysis of the oscillatory phenomena. In order to isolate nearly periodic components of the atmospheric flow, the multichannel version of the singular spectrum analysis (M-SSA) is developed and applied to an NMC 32-year long set of 700-hPa geopotential heights. In the same way that principal component analysis identifies the spatial patterns dominating the variability, M-SSA identifies dynamically relevant space–time patterns and provides an adaptive filtering technique.
Three major low-frequency oscillations (LFOs) are found, with periods of 70 days, 40–45 days, and 30–35 days. The 70-day oscillation consists of fluctuations in both position and amplitude of the Atlantic jet, with a poleward-propagating anomaly pattern. The 40–45-day oscillation is specific to the Pacific sector and has a pronounced Pacific/North American (PNA) structure in its high-amplitude phase. The 30–35-day mode is confined over the Atlantic region, and consists of the retrogression of a dipole pattern. All these oscillations are shown to be intermittently excited, and M-SSA allows the localization of their spells. The two Atlantic oscillations turn out to be frequently phase locked, so that the 30–35-day mode is likely to be a harmonic of the 70-day mode. The phase locking of the Pacific 40–45-day with the Atlantic 30–35-day oscillations is also studied.
Next, the relationships between LFOs and weather regimes are studied. It is shown in particular that the occurrence of the Euro-Atlantic blocking regime is strongly favored, although not systematically caused, by particular phases of the 30–35-day mode. The LFOs themselves are able to produce high-amplitude persistent anomalies by interfering with each other.
The transition from a zonal regime to a blocking regime is also shown to be highly connected to the life cycle of the 30–35-day mode, indicating that regime transitions do not result only from the random occurrence of particular transient eddy forcing. There are preferred paths between weather regimes. This result leaves us with the hope that at least the large-scale environment-favoring weather regimes may be forecast in the long range. Conditional probability of occurrence of blocking, 30 days ahead, is enhanced, relative to climatological probability, by a factor of 2 if the phase of the 30–35-day oscillation is known. This also emphasizes the necessity of operational models to represent correctly the extratropical LFOs in order to produce skillful long-range and even medium-range forecasts of weather regimes.
Abstract
We present a new statistical-dynamical approach to the concept of weather regimes, including the effect of tralisients, without any assumption other than scale separation. The method is applied to a quasi-geostrophic channel model without topography and forced by a local baroclinic jet. Baroclinic perturbations grow and decay along a storm track which is linked with a maximum of low-frequency variability towards its exit, in agreement with the observations.
The weather regimes are searched within the subspace spanned by the large scales only. They are identified through the resolution of a stationary problem in which the feedback of the transients is included as an ensemble average over analogs of the large-scale flow. In this way, the feedback is a continuous function of the large-scale flow only, and the system of equations is closed, taking into account the whole coupling. The solution is obtained using a nonlinear optimization technique.
Several regimes are identified corresponding to zonal and blocking situations. The blocking flow is characterized by a well-marked barotropic dipole at the end of the storm track of synoptic perturbations. The feedback term is shown to act positively in both cases though there are major differences between zonal and blocking regimes. In particular we show that the dipole of the blocking flow is essentially maintained against dissipation by the small-scale fluxes. It is shown that full nonlinearity is required to explain the observed behavior.
The efficiency of the method in this simple case allows us to discuss its extension to a more ambitious diagnostic of regimes in atmospheric observations as well as GCM simulations.
Abstract
We present a new statistical-dynamical approach to the concept of weather regimes, including the effect of tralisients, without any assumption other than scale separation. The method is applied to a quasi-geostrophic channel model without topography and forced by a local baroclinic jet. Baroclinic perturbations grow and decay along a storm track which is linked with a maximum of low-frequency variability towards its exit, in agreement with the observations.
The weather regimes are searched within the subspace spanned by the large scales only. They are identified through the resolution of a stationary problem in which the feedback of the transients is included as an ensemble average over analogs of the large-scale flow. In this way, the feedback is a continuous function of the large-scale flow only, and the system of equations is closed, taking into account the whole coupling. The solution is obtained using a nonlinear optimization technique.
Several regimes are identified corresponding to zonal and blocking situations. The blocking flow is characterized by a well-marked barotropic dipole at the end of the storm track of synoptic perturbations. The feedback term is shown to act positively in both cases though there are major differences between zonal and blocking regimes. In particular we show that the dipole of the blocking flow is essentially maintained against dissipation by the small-scale fluxes. It is shown that full nonlinearity is required to explain the observed behavior.
The efficiency of the method in this simple case allows us to discuss its extension to a more ambitious diagnostic of regimes in atmospheric observations as well as GCM simulations.
Abstract
A low-order deterministic qualitative model is formulated in order to simulate extratropical low-frequency variability. This deterministic model is based on a filtering of the potential vorticity equation on the 315-K isentrope and a projection onto its leading empirical orthogonal functions. The model has an empirical formulation, and the feedback of unresolved scales is taken into account. The model building procedure is novel, since it is not based on a severe truncation of the physical evolution equations but on an empirical analog averaging of each relevant dynamical process. It can be applied to any geophysical system for which long observational data series are available.
The model is used to diagnose weather regimes with its multiple equilibria and intraseasonal oscillations as periodic orbits. These equilibria result from the balance between large-scale advection, transient feedback, and residual forcing. The authors analyze their forcing budgets and show in particular that transient feedback tends to amplify and advect upstream the regime anomaly patterns. However, the key forcing turns out to be the large-scale advection, since the other forcing terms only reshape the regime anomalies. The maintenance of observed intraseasonal oscillations is also examined by means of forcing budgets. Results show that large-scale advection and transient feedback are also key dynamical factors in the maintenance of their life cycle.
Finally, the low-order model is integrated and qualitatively simulates two of the three identified oscillations, those with periods of 70 and 28 days. The intraseasonal oscillations show up as unstable periodic orbits in the low-order model. This indicates that these oscillations are mostly driven by the internal dynamics of the extratropical atmosphere.
Abstract
A low-order deterministic qualitative model is formulated in order to simulate extratropical low-frequency variability. This deterministic model is based on a filtering of the potential vorticity equation on the 315-K isentrope and a projection onto its leading empirical orthogonal functions. The model has an empirical formulation, and the feedback of unresolved scales is taken into account. The model building procedure is novel, since it is not based on a severe truncation of the physical evolution equations but on an empirical analog averaging of each relevant dynamical process. It can be applied to any geophysical system for which long observational data series are available.
The model is used to diagnose weather regimes with its multiple equilibria and intraseasonal oscillations as periodic orbits. These equilibria result from the balance between large-scale advection, transient feedback, and residual forcing. The authors analyze their forcing budgets and show in particular that transient feedback tends to amplify and advect upstream the regime anomaly patterns. However, the key forcing turns out to be the large-scale advection, since the other forcing terms only reshape the regime anomalies. The maintenance of observed intraseasonal oscillations is also examined by means of forcing budgets. Results show that large-scale advection and transient feedback are also key dynamical factors in the maintenance of their life cycle.
Finally, the low-order model is integrated and qualitatively simulates two of the three identified oscillations, those with periods of 70 and 28 days. The intraseasonal oscillations show up as unstable periodic orbits in the low-order model. This indicates that these oscillations are mostly driven by the internal dynamics of the extratropical atmosphere.
Abstract
Two different definitions of midlatitude weather regimes are compared. The first seeks recurrent atmospheric patterns. The second seeks quasi-stationary patterns, whose average tendency vanishes. Recurrent patterns are identified by cluster analysis, and quasi-stationary patterns are identified by solving a nonlinear equilibration equation. Both methods are applied on the same dataset: the NMC final analyses of 700-hPa geopotential heights covering 44 winters. The analysis is performed separately over the Atlantic and Pacific sectors.
The two methods give the same number of weather regimes—four over the Atlantic sector and three over the Pacific sector. However, the patterns differ significantly. The investigation of the tendency, or drift, of the clusters shows that recurrent flows have a systematic slow evolution, explaining this difference. The patterns are in agreement with the ones obtained from previous studies, but their number differs.
The cluster analysis algorithm used here is a partitioning algorithm, which agglomerates data around randomly chosen seeds and iteratively finds the partition that minimizes the variance within clusters, given a prescribed number of clusters. The authors develop a classifiability index, based on the correlation between the cluster centroids obtained from different initial pullings. By comparing the classifiability index of observations with that obtained from a multivariate noise model, an objective definition of the number of clusters present in the data is given. Although the classifiability index is maximal by prescribing two clusters in both sectors, it only differs significantly from that obtained with the noise model using four Atlantic clusters and three Pacific clusters. The partitioning clustering method turns out to give more statistically stable clusters than hierarchical clustering schemes.
Abstract
Two different definitions of midlatitude weather regimes are compared. The first seeks recurrent atmospheric patterns. The second seeks quasi-stationary patterns, whose average tendency vanishes. Recurrent patterns are identified by cluster analysis, and quasi-stationary patterns are identified by solving a nonlinear equilibration equation. Both methods are applied on the same dataset: the NMC final analyses of 700-hPa geopotential heights covering 44 winters. The analysis is performed separately over the Atlantic and Pacific sectors.
The two methods give the same number of weather regimes—four over the Atlantic sector and three over the Pacific sector. However, the patterns differ significantly. The investigation of the tendency, or drift, of the clusters shows that recurrent flows have a systematic slow evolution, explaining this difference. The patterns are in agreement with the ones obtained from previous studies, but their number differs.
The cluster analysis algorithm used here is a partitioning algorithm, which agglomerates data around randomly chosen seeds and iteratively finds the partition that minimizes the variance within clusters, given a prescribed number of clusters. The authors develop a classifiability index, based on the correlation between the cluster centroids obtained from different initial pullings. By comparing the classifiability index of observations with that obtained from a multivariate noise model, an objective definition of the number of clusters present in the data is given. Although the classifiability index is maximal by prescribing two clusters in both sectors, it only differs significantly from that obtained with the noise model using four Atlantic clusters and three Pacific clusters. The partitioning clustering method turns out to give more statistically stable clusters than hierarchical clustering schemes.
Abstract
Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
Abstract
Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.
Abstract
The forcing of low-frequency variability by synoptic transient traveling perturbations is investigated within a quasi-geostrophic channel forced by a localized baroclinic jet. Spontaneously generated baroclinic perturbations grow and decay along a storm track; at the end of the track a maximum of low-frequency variability is obtained, in agreement with atmospheric observations. The structure of low-frequency variability is studied with a combination of statistical methods, using a multivariate red noise model as a random reference. We show that the anomalies are preferentially linked with local stationary structures or long-wave vacillations according to their location and their sign.
A systematic study of persistence is conducted with a criterion based on rms of the streamfunction variations. The interesting quantity is the probability of persistence which shows a very inhomogeneous distribution in phase space and several separated maxima. The composites based on these maxima exhibit the characters of zonal and blocking regimes. The transient feedback has a positive role in extending the jet downstream but the primary effect is the maintenance of the blocking circulation.
Abstract
The forcing of low-frequency variability by synoptic transient traveling perturbations is investigated within a quasi-geostrophic channel forced by a localized baroclinic jet. Spontaneously generated baroclinic perturbations grow and decay along a storm track; at the end of the track a maximum of low-frequency variability is obtained, in agreement with atmospheric observations. The structure of low-frequency variability is studied with a combination of statistical methods, using a multivariate red noise model as a random reference. We show that the anomalies are preferentially linked with local stationary structures or long-wave vacillations according to their location and their sign.
A systematic study of persistence is conducted with a criterion based on rms of the streamfunction variations. The interesting quantity is the probability of persistence which shows a very inhomogeneous distribution in phase space and several separated maxima. The composites based on these maxima exhibit the characters of zonal and blocking regimes. The transient feedback has a positive role in extending the jet downstream but the primary effect is the maintenance of the blocking circulation.
Abstract
The long-term predictability of 70-kPa geopotential heights is examined by a series of hindcast experiments over a validation period of 40 years using empirical models. Only the North Atlantic sector is considered. Significant skill is found up to lead times of one to two months for forecasts of time averages and of weather regime occurrence frequencies.
The empirical schemes produce forecasts of the conditional probability of occurrence of a predictand within its natural terciles. These probabilistic forecasts are compared for two sets of predictors. The (spatial) principal components of the Atlantic large-scale flow (S-PCs) and its space–time principal components (ST-PCs) obtained from multichannel singular spectrum analysis (MSSA). These latter predictors achieve a good compromise between explained variance and predictability. In particular, the skill of a one-step model, where predictand's conditional probabilities are obtained directly from an analog method, is compared with a two-step model, which first forecasts the ST-PCs and then specifies the predictand's conditional probabilities. The one- step model is systematically beaten by the ST-PC scheme for lead times beyond 10 days.
An attempt is made to explain why ST-PCs perform better than S-PCs in the long run by applying the forecast schemes to a simple low-order chaotic dynamical system. The key factor seems to be that for a dynamical system displaying low-frequency behavior and nonlinear spells of oscillations, the MSSA expansion gathers these phenomena into a few leading ST-PCs. These ST-PCs are therefore good candidates to quantify the concept of atmospheric “predictable” components.
Abstract
The long-term predictability of 70-kPa geopotential heights is examined by a series of hindcast experiments over a validation period of 40 years using empirical models. Only the North Atlantic sector is considered. Significant skill is found up to lead times of one to two months for forecasts of time averages and of weather regime occurrence frequencies.
The empirical schemes produce forecasts of the conditional probability of occurrence of a predictand within its natural terciles. These probabilistic forecasts are compared for two sets of predictors. The (spatial) principal components of the Atlantic large-scale flow (S-PCs) and its space–time principal components (ST-PCs) obtained from multichannel singular spectrum analysis (MSSA). These latter predictors achieve a good compromise between explained variance and predictability. In particular, the skill of a one-step model, where predictand's conditional probabilities are obtained directly from an analog method, is compared with a two-step model, which first forecasts the ST-PCs and then specifies the predictand's conditional probabilities. The one- step model is systematically beaten by the ST-PC scheme for lead times beyond 10 days.
An attempt is made to explain why ST-PCs perform better than S-PCs in the long run by applying the forecast schemes to a simple low-order chaotic dynamical system. The key factor seems to be that for a dynamical system displaying low-frequency behavior and nonlinear spells of oscillations, the MSSA expansion gathers these phenomena into a few leading ST-PCs. These ST-PCs are therefore good candidates to quantify the concept of atmospheric “predictable” components.
Abstract
The statistical model proposed by Vautard et al. is applied to the seasonal prediction of surface air temperatures over North America (Canada and the United States). This model is based on sea surface temperature predictors filtered by multichannel singular spectrum analysis (MSSA), which is equivalent here to a nonseasonal version of extended EOF analysis. Several versions of the MSSA model are proposed. The most successful one is based on a two-step procedure consisting in a prior prediction of filtered sea surface temperatures followed by a predictand specification stage.
The MSSA model is compared with the recent prediction technique based on canonical correlation analysis (CCA). The former model turns out, in this application, to be more skillful in most seasons than the latter. The differences are, however, marginal. The authors argue that these differences are due to the nonseasonal nature of the MSSA model and to overfitting problems inherent to CCA. Another advantage of the MSSA model relative to CCA is the possibility of easily transforming deterministic continuous forecasts into probabilistic categorical forecasts.
The geographical distribution of prediction skill across North America is studied. Canada turns out to be the country where skill is most significant. During winter, high skill values are also found over the southeastern United States.
Abstract
The statistical model proposed by Vautard et al. is applied to the seasonal prediction of surface air temperatures over North America (Canada and the United States). This model is based on sea surface temperature predictors filtered by multichannel singular spectrum analysis (MSSA), which is equivalent here to a nonseasonal version of extended EOF analysis. Several versions of the MSSA model are proposed. The most successful one is based on a two-step procedure consisting in a prior prediction of filtered sea surface temperatures followed by a predictand specification stage.
The MSSA model is compared with the recent prediction technique based on canonical correlation analysis (CCA). The former model turns out, in this application, to be more skillful in most seasons than the latter. The differences are, however, marginal. The authors argue that these differences are due to the nonseasonal nature of the MSSA model and to overfitting problems inherent to CCA. Another advantage of the MSSA model relative to CCA is the possibility of easily transforming deterministic continuous forecasts into probabilistic categorical forecasts.
The geographical distribution of prediction skill across North America is studied. Canada turns out to be the country where skill is most significant. During winter, high skill values are also found over the southeastern United States.
