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Werner Metz

Abstract

This paper is concerned with the forcing of the low-frequency variability (10 days up to 3 months) of the barotropic planetary waves (wavenumbers 1 to 4) for wintertime conditions in the Northern Hemisphere. In particular, the forcing by the transient vorticity fluxes arising from the interactions between the planetary waves and the synoptic-scale eddies is considered. This forcing effect is stochastically modeled in terms of a combined Markov-complex EOF approach. The performance of these stochastically modeled vorticity fluxes is evaluated in the framework of a simple barotropic dynamical model.

It turns out that the forcing is highly coherent in wavenumber space, i.e., local in physical space, and that this organization is largely associated with its low-frequency components. The simple dynamical model with the modeled forcing is able to reproduce reasonably well the spatial structure of the observed low-frequency variance of the planetary waves. The performance is best if only the low-frequency components of the stochastically modeled forcing are prescribed. In this case the observed variance maximum over the Atlantic is well simulated, in position and in intensity, while the model variance over the Pacific is weaker than observed and shifted to the west.

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Werner Metz

Abstract

Nine winters of Northern Hemisphere observations are used for a statistical analysis of the relation between the mountain forcing of the zonally-averaged barotropic wind and blocking. Thereby, the temporal variability of the phenomenon “blocking” is expressed by a blocking index lime series. It is demonstrated that the zonally averaged wind exhibits statistically significant negative anomalies at midlatitudes (40°N, 53°N) for the early blocking stage. The mountain drag is anomalously negative (corresponding to a slow-down of the zonal mean wind) at high (53°N, 70°N) and at middle (40°N, 53°N) latitudes. These significant negative mountain drag anomalies are found before the onset or at the very first stage of blocking. In terms of a signal-to-noise ratio, the strongest impact of the mountain drag on the zonal mean wind tendency occurs at the latitudes (30°N, 40°N), where the main mountain ranges of the earth are located.

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Werner Metz

Abstract

The forcing of Northern Hemisphere blocking highs by the transient vorticity transfer from the cyclone-scale eddies into the planetary flow is investigated. Thereby, a barotropic prediction model for the planetary modes is numerically integrated. The time-dependent cyclone-scale vorticity forcing is evaluated from the observations.

The blocking activity in the forced model flow is examined by means of an objective analysis scheme. It is found that the model flow exhibits frequent blocking with some regional preference for the Atlantic and Pacific oceans. The mean structure of the model blocks compares well with the observations, particularly in the case of Atlantic blocking. However, the mean amplitude of the model blocks is only about two-thirds of those observed. Furthermore, it is found that the time-mean part of the forcing does not support the blocking pattern, so that the model blocking activity is due only to the transient forcing.

The significance of the cyclone-scale vorticity forcing for the occurrence of observed blocks is established in terms of model flow pattern averaged over days of actually observed blocking. In the case of Atlantic blocks, the model reproduces the correct mean structure of the observed flow with about one-third of the observed intensity. On the other hand, this mechanism fails in the Pacific. It is believed that this shortcoming is partly due to poor data resolution in the Pacific.

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Werner Metz

Abstract

Canonical correlation analysis is applied to investigate the relationship between the low-pass filtered (barotropic) streamfunction and the effects of cyclone-scale eddies. The eddy effects are evaluated in terms of flux convergences using a spectral quasi-geostrophic twolevel formulation. The analysis is based on six winters of ECMWF observations. In particular only the intraseasonal low-frequency components of the streamfunction and the eddy effects having oscillation periods from 10 days to one season are considered.

The canonical correlation analysis identifies canonical modes in terms of spatial streamfunction patterns that are optimally correlated with associated patterns of the eddy effects, together with amplitude time series that determine the instantaneous projections of analyzed variables onto the mode patterns.

The analysis is carried out between the barotropic components of the streamfunction and the eddy effects and the robustness of the canonical modes is tested. Two robust canonical modes are obtained. The leading mode (CCA mode α) shows significant, regionally very confined, eddy effects only over the Pacific, while the second mode (CCA mode β) is characterized by significant eddy effects over the Atlantic. The associated streamfunction patterns are larger-scale with the largest anomalies over the Pacific and Atlantic, respectively. In addition, the CCA mode α is also accompanied by significant patterns of the thermal streamfunction and baroclinic eddy effects. The temporal variability of the modes may be characterized by an integral time scale of about 20 days.

Episodes of large positive amplitudes or the CCA mode α may be associated with (rare) cases of Pacific blocking, in which case the barotropic eddy effects tend to maintain the blocking high. On the other hand, for episodes of large negative amplitudes the mode is related to a highly baroclinic regional anomaly of the subtropical Pacific jet that occurs near the date line. Upstream of the center of this jet anomaly significant baroclinic eddy effects can be observed tending to dissipate its thermal component, while significant barotropic eddy effects are found downstream of the jet center that feed back onto the barotropic jet component. The streamfunction pattern for this phase of the mode is very reminiscent of the cases of the persistent Pacific anomalies of the low-pass filtered 500 mb height of Dole.

The CCA mode β is less pronounced than the leading mode. It may be related to a regional jet anomaly over the Atlantic, where the positive phase is characterized by a jet anomaly southwards and to the east of the climatological mean Atlantic jet while the negative phase shows the jet anomaly more northwards In both cases the barotropic eddy effects tend to feed back upon the barotropic jet anomaly. For this mode no significant patterns of the thermal flow and the baroclinic eddy effects were obtained.

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Werner Metz

Abstract

A canonical correlation analysis is used to study the optimal relationship between low-frequency variations of the 500 mb height and the barotropic feedback effect in terms of cyclone-scale eddy-induced height tendencies. The analysis is performed separately for the Atlantic and Pacific sector using eight winters of observed data.

Three significant modes consisting of pairs of optimally correlated height patterns and associated height tendency patterns are obtained for the Atlantic sector but only one mode for the Pacific sector. These modes are found to be related to the EA, WA and PNA teleconnection patterns and to Atlantic blocking highs. Generally, the mutual orientation of the height and the height tendency patterns is such that a center in the height pattern is associated with an eddy tendency center of the same polarity, i.e., both variables are positively correlated. Maximal canonical correlations are obtained if the height field lags the height tendency field by one to two days. The efficiency of the eddy-induced height tendency to force the canonical height modes is evaluated as the ratio of the associated barotropic kinetic energy conversion to that due to the conversion from the time-mean flow. This ratio is about 0.4, and the characteristic time scale of the eddy tendency forcing is of the order of 14 days while that due to the time-mean flow conversion is about 6 days.

It is suggested that the obtained canonical correlation structure is primarily due to a steering effect of the teleconnections on the baroclinic eddies, and to a close coupling between the maximal cyclone-scale eddy activity and the barotropic eddy feedback effect.

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Werner Metz

Abstract

Recently, it has been shown that the EOFs (empirical orthogonal functions) of the solutions of a stationary linear model to an ensemble of white noise forcing fields are the Schmidt modes (singular modes) of the model' linear operator. If the forcing is not pure white noise, this exact association breaks down. In this paper, the role of these singular modes for the recurring modes of the solutions in the latter case is investigated.

First, a steady-state barotropic model, linearized about a wavy 300-mb basic state, is forced by a large sample of quasi-stationary vorticity forcings where the basic state and the forcing are both derived from a climate control run of the Hamburg ECHAM2 GCM. The EOFs of this sample of solutions are explicitly calculated and the leading EOF obtained turns out to be very similar to the leading singular mode of the model. The primary energy source of this mode is the conversion of the kinetic energy of the zonally asymmetric components of the basic state to the mode. On the other hand, the second EOF matches closely to the leading mode of the GCM's low-frequency variability. This second EOF occurs primarily due to the action of the forcing.

Then, the sensitivity of the singular modes to variations of the dissipation parameters and the basic state is investigated. Thereby, it is found that it is essential to retain the zonally inhomogeneous components of the basic state. With the wavy basic state, it is found that for sufficiently strong dissipation the leading singular mode becomes very similar to the leading mode of the GCM's low-frequency variability if an equivalent-barotropic basic state is used. Such a similarity cannot be achieved for a 300-mb basic state. Moreover, it also turns out that the quasi-stationary forcing associated with the GCM variability mode is able to excite the leading singular mode of the linear model.

It is suggested that the linear singular modes, via the conversion of kinetic energy of the wavy basic state, provide some of the fundamental structures into which observed low-frequency modes are organized in the real (nonlinear) world, too.

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Andrew W. Robertson and Werner Metz

Abstract

Linear baroclinic instability theory is used to investigate the subweekly time scale transient eddies (TEs) and their feedbacks associated with three-dimensional basic flows on the Northern Hemisphere, in terms of a two-layer quasi-geostrophic model. We consider an eight-winter time–mean flow as well as four composites of North Atlantic large-scale quasi-stationary patterns.

The structures of the two fastest-growing normal modes associated with the eight-winter climatology are found to compare very well in many aspects with the leading complex empirical orthogonal functions (CEOFs) of the observed bandpass filtered flow, with pattern correlations up to 0.65; although the normal modes are less localized than the CEOFs. The barotropic feedback implied by the linear modes is also found to compare quite reasonably with the observations, especially over the west Atlantic, but the baroclinic (negative) feedback is less well represented.

Composites coresponding to blocking (BL), zonal (ZO), Greenland anticyclone (GA), and Atlantic ridge (AR) weather regimes are next used to define basic states and composite maps of TE feedback. In all four cases the principal displacements of TE activity over the North Atlantic are captured by the fastest-growing Atlantic cyclogenesis modes. The structure of the barotropic feedback associated with the quasi-stationary anomalies is also reasonably simulated by the linear modes in many respects in the BL and ZO cases, but in the GA and AR cases the linear model is less successful.

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Andrew W. Robertson and Werner Metz

Abstract

The linear baroclinic instability of three-dimensional basic flows on the Northern Hemisphere is examined in terms of a simple two-level, quasi-geostrophic model. The basic flows considered comprise an observed six-winter mean flow, as well as anomalous flows which represent episodes where large-scale persistent flow anomalies, such as the Pacific/North American (PNA), East Atlantic (EA), or North Atlantic Oscillation (NAO) patterns exhibit large amplitudes.

For the climatological basic state, the fastest-growing normal modes with periods of around 4 days consist of regionally confined, synoptic-scale, baroclinic wave trains. These are considered as cyclogenesis modes, characterizing the linear synoptic-scale eddy activity associated with a given basic flow. This eddy activity has a pronounced maximum over the Pacific, close to the position of the observed Pacific storm track, but the second maximum over the Atlantic, corresponding to the Atlantic storm track, is considerably underestimated. Nevertheless, comparing the structure of the cyclogenesis modes with that of the leading complex EOFs of the observed bandpass-filtered flow, a pattern correlation squared of up to 0.4 is obtained. Truncating the basic state to comprise only the ultralong waves (zonal wavenumber m ≤ 4) results in rather little change in the cyclogenesis modes obtained.

Finally, the sensitivity of the cyclogenesis modes to the anomalous basic flows is investigated, using persistent anomaly patterns (PNA, EA, NAO) obtained from a rotated principal component analysis of the observed lowpass-filtered flow. The anomalous basic states are evaluated by adding or subtracting these patterns to/from the winter climatological mean flow. It turns out that the normal-mode wave trains are significantly deflected from their climatological positions, particularly in the EA and NAO cases. This model response is verified against composite maps of observed bandpass variance, obtained for episodes of strong PNA, EA or NAO anomalies respectively. It is found that, although the normal-mode wave trains are still relatively too weak over the Atlantic (compared to the Pacific), the structural differences in the observed bandpass eddy activity between positive and negative anomaly cases are captured quite well by the normal modes.

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