To zeroth order, the global atmospheric circulation may be construed as arising from the three-way interaction between the mean meridional circulation, mid-latitude zonal jet streams and baroclinically unstable eddies. Advection of planetary angular momentum by the mean meridional circulation, specifically by the thermally direct Hadley cell, supports so-called “thermally driven” jets . Convergence of eddy momentum flux by baroclinic eddies supports so-called “eddy-driven” jets . Purely thermally driven or eddy-driven jets are largely theoretical constructs: the former would require an eddy-less, axisymmetric atmosphere , while the latter can only exist in the absence of a thermally driven meridional advection of zonal-mean angular momentum e.g.. However, there are atmospheric flows that approximate these two limiting cases to a good degree, albeit with the caveats discussed below. These are often termed “subtropical” and “polar-front” jets in reference to their geographical locations.

The subtropical jet is an upper-tropospheric jet with a strong vertical shear located at the poleward edge of the Hadley cell. While the observed tropical circulation is distinctly zonally asymmetric e.g., the underlying physical drivers of this flow may be related to the idealized axisymmetric scenario of . Poleward of the Hadley cell, the Ferrel cell corresponds to a region of strong baroclinic activity. Here, an equivalent barotropic polar-front jet exists e.g.. While the meridional advection of zonal-mean angular momentum in the region is clearly non-zero, we can again relate this jet to one of the idealized limiting cases described above. Specifically, two-layer quasi-geostrophic models show that in this region, when a geophysical background flow is perturbed, the growing baroclinic waves that result from the perturbations can spontaneously generate a jet through converging westerly momentum flux e.g..

The distinction between the subtropical and polar-front jets is not always evident, and the jets display different characteristics depending on geographical location and season. In the Northern Hemisphere, the two flows are mostly separate during wintertime over the North Atlantic basin, while over parts of Asia and the Pacific the default atmospheric configuration is of a single or “merged” jet. This terminology is supported by evidence that a single jet results from the (quasi-)collocation of the regions of eddy generation with the subtropical jet such that the driving mechanisms are both thermal and eddy-related . In the Southern Hemisphere (SH), the austral summertime circumpolar jet is located around 40–50∘ S, collocated with regions of enhanced surface baroclinicity e.g.. During austral winter, a single jet is seen in the Indian Ocean sector, while two distinct branches emerge in the Pacific sector: a subtropical jet at around 30∘ S and a polar-front jet at around 60∘ S e.g.. At upper levels, the strongest flow is seen for the Pacific subtropical jet, while at lower levels the flow over the Indian Ocean sector is strongest e.g.see also Fig. a. While the climatological picture shows two distinct jets co-existing in the Pacific sector, these are not well-separated every year . On shorter timescales (e.g. days or weeks), we further expect periods when the two jets are merged and others when they are distinct.

The different locations and drivers of the two jet structures, plus the intermediate merged jet, arise from very different underlying mechanisms. They in turn result in very different flow characteristics, for example in terms of the jet's variability properties, the wave spectrum and the degree of non-linearity e.g.. However, our understanding of the dynamical maintenance mechanisms mostly relies on conceptual or idealized models e.g.. Linking these to the phenomena observed in the real atmosphere is therefore key to further our understanding of this major component of the climate system. Our goal in the present study is precisely to provide a concise quantitative overview of the jet characteristics in an idealized atmospheric model and relate them to the large-scale flows in the real atmosphere, as reproduced by reanalysis products. We specifically focus on developing a unitary analysis framework which may be applied to both the idealized model and reanalysis data, allowing for direct intercomparison.

An idealized model fit for the task at hand should be able to maintain three distinct jet regimes: a thermally driven subtropical jet, an eddy-driven polar-front jet and a merged jet. Just as in the real atmosphere, these regimes should differ in the location and variability of the jet stream, as well as in the structure, zonal wavenumber and phase speed of the dominant modes. Here, we use the two-layer modified quasi-geostrophic (QG) spherical model of . Unlike other QG models, our setup includes advection of the zonal-mean momentum by the ageostrophic mean meridional circulation. This enables the model to resolve the momentum balance of the subtropical jet. The model can therefore reproduce the three different jet regimes and their distinct wave-mean flow feedback mechanisms .

To elucidate the intrinsic dynamical characteristics of the different jet regimes, we interpret atmospheric flows as representative of the evolution of chaotic atmospheric attractors. Recent advances in dynamical systems theory have demonstrated that any instantaneous state of a chaotic system may be described by two metrics: the local dimension – related to the system's active degrees of freedom around that particular state – and a local measure of persistence . This approach can easily be applied to a variety of datasets, including suitably processed reanalysis data, and may thus be used to provide a direct analogy between modelled and observed flows. Here, we apply it for the first time to the study of atmospheric jets in both idealized model and reanalysis data. In doing so, we underscore the links that can be made between the dynamical systems metrics and the physical characteristics of the atmospheric flow.

The connection between the dynamical systems characteristics of the flow and the jet regimes arises from the wave spectrum and its interaction with the zonal-mean flow. According to , the flow in the idealized two-layer modified QG model transitions from a subtropical jet regime to a merged jet regime and then to an eddy-driven jet regime as the eddy energy is increased. At the transition between the merged and eddy-driven jet regimes, the wave energy spectrum becomes turbulent and an inverse energy cascade takes place. At this transition, an increase in the jet's latitudinal variability and a decrease in its characteristic variability timescale are also seen . We expect these changes to be reflected in the dynamical systems metrics, which capture the active degrees of freedom and the persistence of the flow.

We first provide a brief overview of the data, model and analysis approaches in Sect. . Sections  and outline the dynamical characteristics of the different flow regimes in the model and reanalysis, respectively. Finally, we discuss these results in the context of both idealized models and studies of the observed atmospheric jet, and we draw our conclusions in Sect. .

As discussed in the Introduction, purely thermally driven or eddy-driven jets are largely theoretical constructs. Moreover, for a given region and season, the jet typically displays large intraseasonal variability and a range of different flow characteristics e.g.. On this basis, we expect the jets observed in the real atmosphere to blend the dynamical characteristics of the different jet regimes reproduced in the QG model.

To verify whether our dynamical systems approach can distinguish between different jet regimes in the real atmosphere, we therefore take a slightly different angle from that used in our idealized model, although the analysis tools are identical to those used above. We compute d and θ on barotropic zonal wind (see Sect. ) but consider flow anomalies associated with concurrent low or high values of d and θ. We define these as values beyond the 10th or 90th percentiles of the respective distributions. The choice of joint high or low percentiles is dictated by the fact that the different jet regimes in Fig.  b and d align chiefly along a d–θ diagonal. The analysis focuses on austral winter (JJA) over the Pacific domain shown in Fig. , which is chosen because it displays a variety of jet regimes. During the austral winter, the signature of the subtropical – and predominantly thermally driven – jet is evident at upper levels around 30∘ S, while that of the polar – and predominantly eddy-driven – jet emerges most clearly at lower levels around 60∘ S (Fig. ). Periods when these flows are well-separated alternate with periods dominated by a single nearly barotropic flow, akin to a merged jet.

When both d and θ are anomalously low, the upper-level zonal wind (300 hPa) displays a clear maximum around 30∘ S, coincident with the climatological location of the subtropical jet and characterized by above-average speeds (Fig. a). The signature of this jet extends to the lower troposphere, where a low-level (850 hPa) zonal wind maximum located slightly poleward of the 300 hPa maximum is clearly visible on the same days, especially in the eastern part of the domain (Fig. c). This inference is confirmed by analysing the vertical cross section of the zonal flow, which evidences a poleward displacement of the location of the zonal wind maximum at 850 hPa compared to 300 hPa (Fig. e). The EKE shows widespread negative anomalies across the central and southern portions of the domain and localized positive anomalies at 300 hPa matching the latitude of the jet (Fig. a, c). We interpret the above characteristics as the signature of a merged jet.

When both d and θ are anomalously high, the upper-level zonal flow evidences two maxima: a weaker-than-climatology jet around 30 ∘S and an anomalous secondary maximum at around 55∘ S, associated with large positive zonal wind speed anomalies (Fig. b). At low levels, there is a single jet located just to the north of 60 ∘S associated with large positive zonal flow anomalies (Fig. d). The southern jet therefore has a more pronounced barotropic structure than its northern counterpart, as also seen in the vertical cross section of the zonal flow (Fig. f). The EKE anomalies are predominantly positive across the central and southern portions of the domain (Fig. b, d). The above points to a primarily eddy-driven jet in the south and a primarily thermally driven jet further north, in agreement with the theoretical framework of and . It also suggests that the persistence of the double-jet configuration, with a strong eddy-driven jet, is lower (high θ) than that of the single merged jet (low θ).

We have analysed different jet regimes in a set of idealized simulations with a QG model and reanalysis data. The QG model reproduces the full range of theoretically derived jet regimes e.g.. These are an eddy-driven jet, a merged jet and a subtropical jet. It additionally reproduces transition states between a merged and eddy-driven jet, which we term mixed jets. Pure eddy-driven or thermally driven jets are largely theoretical constructs, and in the real atmosphere the separation between them is often blurred. Nonetheless, it is possible to identify primarily eddy-driven, primarily thermally driven and merged jets e.g.. The South Pacific sector is of particular interest in this context, since it is a region where the three main jet regimes may be observed at the same longitude e.g..

Relating the different jet regimes identified in idealized models to those identified in reanalysis data is far from immediate. Here, we have proposed an analysis approach which may be applied to both datasets and which provides a direct link between the characteristics of the jets in the QG model and those seen in the ERA-Interim dataset. Such an approach is grounded in dynamical systems theory and is based on two metrics, d and θ, which characterize the instantaneous (local in phase space) dynamical characteristics of the jet. The local dimension d is a proxy for the number of active degrees of freedom of the system. The persistence θ-1 is a measure of the typical residence time of the system in the neighbourhood of a given state. Their computation arises from an analysis of recurrences of the system, and both may be related to the concept of predictability. Indeed, one may expect low d, high θ-1 states to be more predictable than high d, low θ-1 situations (see Sect. ). This interpretation is confirmed by ongoing work by some of the authors, which finds a direct link between precipitation forecast skills at single stations in France and the values of d and θ computed for 500 hPa geopotential height fields in the preceding days. Unlike conventional approaches which diagnose the driving mechanisms of the jet in terms of complex physical processes, such as convection or eddy momentum flux convergence, the dynamical systems metrics allow us to delineate the dynamical properties of the jet uniquely from computing d and θ on the wind itself. Differently from previous studies using this approach, here we have thus attempted to link the dynamical systems metrics directly to the physical mechanisms of jet maintenance. As a caveat, we note that the absolute values of these metrics should be interpreted in a relative sense within each dataset they are computed on and that direct comparison of their magnitudes across datasets should be treated with caution. From a theoretical standpoint, there are cogent arguments supporting the use of recurrences of observables of a system to investigate the properties of the system's underlying phase space, even though all the variables defining said phase space cannot be considered e.g.. This makes our analysis affordable in terms of computational and data requirements – indeed, d and θ for a single variable from a reanalysis dataset may be computed by a modern laptop computer in a matter of hours – and versatile in terms of applicability to very different datasets see. Moreover, d and θ do not require prior knowledge of the exact location of the jet.

In the QG model, d and θ allow us to characterize the different jet regimes. Specifically, when computed on barotropic zonal-mean zonal wind they highlight the eddy-driven jet as being a low-persistence, high-dimensional regime, the subtropical jet as being a high-persistence, low-dimensional regime and the merged jet as having intermediate dynamical characteristics. This reflects the wide wave spectrum and large latitudinal fluctuations in the eddy-driven jet versus the lower latitudinal variability of the subtropical jet. Indeed, in the former regime the energetic wave activity, the comparatively broad wave spectrum and the range of wave phase speeds offer a variety of different temporal evolutions of the atmospheric flow. In the latter regime, the flow instead displays a weak eddy kinetic energy and a narrow wave spectrum, with a correspondingly narrow range of wave phase speeds and meridional excursions. Moreover, the typically similar wavelength and phase speed of the waves implies that the temporal evolution of the atmospheric flow is relatively repetitive. further analysed the EKE budgets of different jet regimes in terms of the contributions by linear versus eddy–eddy interactions and found that the degree of linearity of the dynamics changes. The subtropical regime is comparatively linear, the merged regime's variability is dominated by wave-mean flow interactions, and the eddy-driven regime is non-linear with a turbulent upscale energy cascade. Intuitively, we expect the predictability of the flow to decrease and the jet structure to vary more strongly in time as the flow becomes more non-linear. The dynamical systems metrics thus reflect the theoretical expectations of the role of increased EKE in decreasing predictability . In contrast to the jet variability, the model's jet speed (Fig. ) is not related to the degree of non-linearity of the flow. Because of this, changes in jet speed may not map directly onto differences in d and θ.

A natural question to ask is whether d and θ also reflect variability within the individual simulations in the QG model. A preliminary analysis of the barotropic zonal-mean zonal wind for one of the simulations classified as an eddy-driven regime (simulation no. 2; see Table ) shows that, when d and θ are very low, the jet has large variability (red line in Fig. c) and a narrow profile reminiscent of the merged jet regime (compare the red line in Fig. b with the amber line in Fig. ). This may be contrasted with the average jet structure for this simulation, which is quite wide with an inflection suggestive of a separation between the eddy-driven and subtropical jets (grey line, Fig. b). During low d and θ time steps, the jet also displays a much sharper EKE spectrum (not shown) and a more equatorward lower-level jet (red line, Fig. d) than climatology. On the other hand, when d and θ are anomalously large, the lower-level jet is slightly more poleward and intense than usual (compare the grey and blue lines in Fig. d), and the spread in jet profiles is unusually low (blue line in Fig. c). The resemblance between low d and θ time steps in an eddy-driven jet simulation and the flow characteristics seen in merged jet regime simulations is consistent with inter-regime differences in the two dynamical systems indicators. Indeed, simulations classified as merged jet regimes generally display lower d and θ values than simulations within the eddy-driven regime (Fig. b). also found that the temporal variability of the eddy-driven jet includes a merged-jet-like state.

The results for reanalysis data largely mirror those found for the idealized simulations. Focusing on the Pacific sector of the Southern Ocean, d and θ computed on the barotropic zonal wind again discriminate between different jet regimes. Specifically, high d, high θ days display both a thermally driven subtropical jet and a strong eddy-driven polar-front jet, while low d, low θ days display a merged jet. A key difference from the results in the QG model is that, in the reanalysis data, the South Pacific sector we consider does not display a purely thermally driven nor a purely eddy-driven jet. Indeed, both jet regimes co-occur at different latitudes during winter. The upper-level jet is stronger in the single-jet merged configuration compared to the double-jet configuration (compare Fig. a and b), consistent with the idealized results of .

The distinction between eddy-driven, merged and subtropical jets also applies to the Northern Hemisphere (NH) e.g.. Moreover, within the same ocean basin the jet can transition between different regimes. Therefore, there is no a priori reason that our analysis framework should not be applicable to NH dynamics. For example, in the North Atlantic sector one may expect the climatological co-existence of an eddy-driven jet and a subtropical jet to correspond to high d and θ states and the rarer merged jet conditions e.g. to correspond to lower d and θ values. However, zonal asymmetries linked to land–sea contrast and orography are more prominent than in the SH e.g.. The observed separation in d–θ space between the different jet regimes may be affected by this, although it is not straightforward to infer exactly how without conducting a full analysis. Here, our intention is not to provide a systematic analysis of atmospheric jet characteristics in different geographical regions. Rather, by building upon both idealized simulations and reanalysis data, we illustrate the potential of dynamical systems indicators to diagnose jet regimes in a conceptually intuitive fashion.