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Piero Malguzzi and Paola Malanotte Rizzoli


Many recent studies have been devoted to atmospheric Patterns that persist beyond the synoptic time scale, such as those known as blocking events. In the present paper we explore the possibility that blocking patterns can be modeled with a local approach. We propose a truncated model that is a time-dependent, highly nonlinear extension of our earlier analytical theory. In this theory, stationary coherent structures were found as asymptotic solutions of the inviscid, quasi-geostrophic potential vorticity equation with a mean zonal wind with vertical and horizontal shear, in the limit of weak dispersion and weak nonlinearity. The truncated model is obtained by projecting the potential vorticity equation onto the orthonormal basis defined by the lowest order problem of the asymptotic theory and then suitably truncating the number of modes. The time-evolution of the model is investigated numerically with different truncations.

The steady solutions were antisymmetric dipoles, with the anticyclone north of the cyclone; they have an equivalent barotropic vertical structure and are meridionally as well as zonally trapped. We suggest that this solution could model the persistent patterns associated with blocking events that satisfy Rex's definition. An extensive series of numerical experiments is carried out to investigate the persistence of the steady solutions and their stability to different superimposed perturbations. The result is that, in an environment as turbulent as the real atmosphere, a typical estimate of the robustness (predictability) of the solution is of the order of 10 to 12 days. Such persistence is consistent with observations of blocking patterns.

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Paola Malanotte-Rizzoli and Piero Malguzzi


In this paper we exploit a nonlinear baroclinic theory of atmospheric Rossby waves superimposed on westerly winds with meridional and vertical shear which was proposed in two earlier studies, Parts I and II. In Part I, nonlinear, stationary Rossby wave solutions were found consisting of a localized vortex pair and having an equivalent barotropic structure. These solutions, found in the context of an asymptotic theory for the quasi-geostrophic baroclinic potential vorticity equation, were proposed as a model for atmospheric blocking. In Part II, the theory was extended to the time-dependent, highly nonlinear case, removing the weak-amplitude limitations of the asymptotic theory of Part I. The localized highly nonlinear dipole solution of Part II was found to be remarkably robust to different energetic perturbations, even with a baroclinically unstable mean zonal wind. A typical persistence (predictability) time for the solution of Part II was of the order 10 to 15 days, consistent with observations of blocking patterns.

In this paper we investigate two further aspects of the high-amplitude solution of Part II. First, we study the formation of the coherent dipole starting from rather different initial conditions. We establish a necessary and sufficient criterion for the formation of the coherent structure. This criterion involves the preexistence of a zonal low wavenumber component (wavenumber one) in an antisymmetric meridional mode having a large enough amplitude. If this condition is satisfied, the evolution into the block configuration is assured by the model internal dynamics that is of the Korteweg-deVries type.

Second, we study the effect of short-scale, transient eddies upon the blocking dipole. We include dissipative effects and find that the eddy forcing is such to maintain the coherent structure against both mean advection and dissipation. The eddy forcing pattern resulting from the numerical experiments compares well with the observational evidence, given the high truncation of the model used.

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Piero Malguzzi and Paola Malanotte-Rizzoli


Many recent theoretical and observational studies have been devoted to the understanding of atmospheric patterns that persist beyond the synoptic time scale. These patterns are known as blocking events.

Properties of blocking events emerging from the observational evidence are consistent with the properties of nonlinear, i.e., coherent, localized structures characterized by locking of phases and phase speeds which are amplitude dependent.

In the present paper we develop a nonlinear, analytical theory with solutions in the form of stationary, coherent structures superimposed on a mean westerly wind. The model is the inviscid, quasi-geostrophic potential vorticity conservation equation with a mean zonal wind having vertical as well as horizontal shear. The used mean wind profile is typical of the atmosphere at midlatitude. The stationary, coherent solution is an antisymmetric dipole, with the anticyclone north of the cyclone; it has an equivalent barotropic vertical structure, is meridionally as well as zonally trapped and obeys a nonlinear dynamics in the zonal wave guide.

This pattern, even though idealized, exhibits a strong similarity and is consistent with observations of blocking patterns.

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Paola Malanotte-Rizzoli and Paul J. Hancock


In a series of previous papers, a local theory was formulated to model the persistent atmospheric patterns known as blocking events. The adopted model was the fully nonlinear, baroclinic quasi-geostrophic potential vorticity equation with a mean zonal wind having vertical and horizontal shear. Solutions were found consisting of localized dipole structures with an equivalent barotropic vertical structure. The basic “recipe” provided by the theory was that, in order to form a block characterized by a split flow with an embedded vortex pair, the upstream mean zonal wind ū(y, z) must have a structure which allows for local confinement. Specifically, the function V = ¼ − y/ū, with y, the meridional gradient of mean potential vorticity, must have the shape of a potential well. The bound states of this potential well are structures localized in the (y, z) plane and trapped by the well's positive barriers.

The data analysis carried out here and the results presented are designed to establish whether such a trapping structure exists for the positive blocking cases when compared with the winter climatological mean or other patterns such as the negative anomaly cases of Dole. The unambiguous and robust results emerging from the data analysis are: (i) the composite of the positive anomaly cases shows a strong northern barrier centered in the latitude band 62° to 72°N, in agreement with the northern confinement of the block. The southern barrier, if present, is not covered by the available data. The northern, positive barrier is not present in the climatology. Its presence and significance are doubtful and debatable for the negative anomaly composite. (ii) For the individual positive cases of blocking in which the vortex pair is sufficiently north to be fully covered by the analysis and for which a smooth and zonal upstream wind can be defined, the V-function shows both northern and southern positive brriers at the latitudes of block confinement.

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