We derive a minimal dynamical systems model for the Northern Hemisphere midlatitude jet dynamics by embedding atmospheric data and by investigating its properties (bifurcation structure, stability, local dimensions) for different atmospheric flow regimes. The derivation is a three-step process: first, we obtain a 1-D description of the midlatitude jet stream by computing the position of the jet at each longitude using ERA-Interim. Next, we use the embedding procedure to derive a map of the local jet position dynamics. Finally, we introduce the coupling and stochastic effects deriving from both atmospheric turbulence and topographic disturbances to the jet. We then analyze the dynamical properties of the model in different regimes: one that gives the closest representation of the properties extracted from real data; one featuring a stronger jet (strong coupling); one featuring a weaker jet (weak coupling); and one with modified topography. Our model, notwithstanding its simplicity, provides an instructive description of the dynamical properties of the atmospheric jet.

Jet streams are narrow, fast-flowing westerly air currents near the tropopause. They are a major feature of the large-scale atmospheric circulation and modulate the frequency, severity and persistence of weather events across the extratropics (e.g.,

Even though the climatological NHJ is a westerly flow, it can present large meanders on synoptic timescales

The dynamics of meanders and split jets has often been framed in terms of transitions between zonal and blocked flows since the seminal work by

In order to advance our understanding of the jet dynamics, we employ a low-dimensional dynamical systems model derived from reanalysis data. The best-known example of a low-dimensional model for atmospheric phenomena is Lorenz' simple three-dimensional system representing some features of Rayleigh–Bénard convection

Progress in data quality and availability and the advent of stochastic dynamical systems have renewed the attention for data embedding. Recently,

First, we provide the details of the reanalysis data and of the jet detection algorithm (Sect.

The analysis is based on the European Centre for Medium Range Weather Forecasts's ERA-Interim

The jet position is diagnosed through a modified version of the approach by

We define an index of large jet meanders, or breaks (breaking index, BRI), as the daily number of meridional variations in jet position of more than 10

Figure

Snapshot of the jet position extracted from the ERA-Interim data set on 4 February 1979 and time series of the jet position for the year 1979, recorded at longitude 120

In order to embed the data and derive the effective maps of the dynamics, we remove the seasonal cycle from the data by subtracting, longitude by longitude, the average meridional position for each calendar day and dividing by the standard deviation. For the deseasonalized data, the dimensionless threshold for the computation of the BRI corresponding to about 10

Our analysis leverages two recently developed dynamical systems metrics, namely the local dimension of the attractor

The local dimension is estimated by making use of extreme value statistics applied to Poincaré recurrences. The

Extreme value statistics also allow estimating the persistence of a given state

While not directly issued from the Navier–Stokes equations, our framework builds on concrete physical hypotheses, namely that (i) the physics of the jet is the same at every longitude and is only slightly modified by the presence of topographical constraints, (ii) the jet can experience sudden breaks and shifts from its central position (CJ) to northern (NJ) or southern latitudes (SJ), (iii) the jet must propagate to the west, and (iv) smaller-scale phenomena, such as turbulence and baroclinic waves, will be introduced in the model only if necessary to reproduce the effective dynamics in the data. This latter point is fundamentally different from the philosophy of direct numerical simulations.

We construct our model starting from the local time series of the non-dimensionalized jet position

The average return map extracted from the data at longitude

If we perform a numerical simulation of Eq. (

However, considering small-scale turbulent disturbances to the jet dynamics is not sufficient to reproduce the blocking and breaking of the jet. Even if the introduction of

Baroclinic activity is associated with extratropical cyclones and anticyclones, on scales of the order of 10

The minimal sub-grid parametrization can thus be written in the following form:

Schematic representation of noise contributions to the CML model (Eqs.

Bifurcation diagrams as a function of

Owing to the unidirectional coupling in our model and to the large

In this section we compare the ERA-Interim deseasonalized jet position data with numerical simulations of our model. In order to have the same statistical sample as for the reanalysis, we simulate 37 years of daily snapshots of the jet position. The best fit of our model to the data is obtained, by a trial and error procedure, for the parameters

We first consider the latitudinal distribution of the yearly median jet positions at each longitude (dots in Fig.

Single-year median location (dotted points) and multiyear average of medians (solid lines) of the meridional jet position for ERA-Interim

We next consider the NHJ's shifts from CJ towards NJ or SJ positions. We binarize the dynamics by the detecting all the events such that

We further assess our model by means of the

Figure

Box plots of the local dimension

The bifurcation diagram in Fig.

We have derived a minimal model of the jet stream position dynamics, based on a stochastic coupled map lattice, by embedding data extracted from ERA-Interim. This procedure innovates over earlier studies (e.g.,

Future analyses could apply this approach to the Southern Hemisphere, where the role of topography is less important than in its northern counterpart. This would allow us to better constrain the influence of topography on the dimension–persistence diagrams. Another possibility would be to use the low-dimensional model to build a surrogate data set of the jet positions and then apply this to atmospheric analogues, so as to construct realistic atmospheric dynamics. Finally, it would be interesting to study whether further projections of the atmospheric dynamics to a lower-dimensional space are possible, beyond the model developed here, and to test possible relations between different atmospheric blocking indices and the BRI defined here.

Bifurcation diagram of the global dynamics obtained for

The analysis we have conducted can, however, already answer some of the questions left open in

The data sets analyzed in this paper are available in the ERA-Interim repository:

A coupled map lattice (CML;

To extract the local jet dynamics, we construct an average return map. We first coarse-grain the state space into

An important ingredient of the jet dynamics is the presence of topographic obstacles to the midlatitude zonal flow. Mountain ranges and land–sea boundaries cause meridional deviations in the mean jet location

As discussed in Sect.

Owing to the unidirectional coupling in our lattice jet model and to the large

The supplement related to this article is available online at:

DF and YS performed the analysis and derived the conceptual model. GM computed the jet position data. All the authors participated in the writing and the discussions.

The authors declare that they have no conflict of interest.

Yuzuru Sato, Gabriele Messori and Nicholas R. Moloney thank the LSCE for hospitality.

All the authors were supported by the ERC grant no. 338965-A2C2. Davide Faranda and Yuzuru Sato were supported by the CNRS PICS grant no. 74774 and by London Mathematical Laboratory External Fellowships. Davide Faranda and Pascal Yiou were supported by an INSU-CNRS-LEFE-MANU grant (project DINCLIC). Yuzuru Sato was supported by the Grant in Aid for Scientific Research (C) no. 18K03441, JSPS, Japan. Gabriele Messori was supported by grant no. 2016-03724 from the Swedish Research Council Vetenskapsrådet and the Department of Meteorology of Stockholm University. This research has been supported by the H2020 European Research Council (grant no. A2C2 (338965)), the Centre National de la Recherche Scientifique (grant no. PICS 74774), the JSPS (grant no. 18K03441), the Swedish Research Council Vetenskapsrådet (grant no. 2016-03724) and the Department of Meteorology of Stockholm University.

This paper was edited by Andrey Gritsun and reviewed by two anonymous referees.