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A. Navarra

Abstract

An anomaly model linearized around the observed winter climatology is used to study the steady response of the atmosphere to diabatic heating. The model is an R7, nine vertical levels, primitive equations, fully spectral model, derived from the GFDL GCM (Geophysical Fluid Dynamics Laboratory's General Circulation Model). The anomaly model is capable of treating basic states that depend on latitude, longitude and height. The Krylov technique is used to solve the linear equations. This generality allows the treatment of the important problem of linear waves in the atmosphere from a more general paint of view; a larger class (zonally asymmetric) of basic states can now be treated for the baroclinic primitive equations. The (R7) linear anomaly model is used to investigate the linear response to equatorial and midlatitude prescribed heating. The results indicate that the solution is affected by the presence of the stationary waves in the basic state. In particular, in the case of midlatitude heating large responses can be obtained for some locations of the heating. However, because of the low resolution used in these experiments no firm conclusion can be drawn on the role of baroclinic effects.

The most sensitive areas are identified in some preliminary sensitivity experiments. In the equatorial heating case they correspond to equatorial heating positioned south of the main jet stream. In the midlatitude heating case, a large response is obtained with shallow heating placed at the beginning of the Asian jet stream.

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A. Betti and A. Navarra

Abstract

The Schmidt decomposition is applied to the evolution operator of the linearized barotropic equation on a sphere (in the following referred to as the barotropic propagator) to study the evolution of the variance, that is, of the collective evolution of a cloud of trajectories centered around the initial condition. The variance can give reliable information on the tendency that some initial conditions may have to generate large spreads in the subsequent time evolution, especially when many modes with similarly large amplifying rates exist. It appears rather arbitrary, under these circumstances, to pick a particular mode just because it happens to have the largest rate for that particular numerical formulation and resolution setting. It is also shown that the Golden-Thompson generalized inequality and other indicators can be used to estimate the linear variance from the analysis of the initial condition itself, without the need for performing the costly explicit calculation of the propagator.

Numerical experiments performed on a set of initial conditions obtained from a simulation experiment and from observations show that in a barotropic model a spread index based on an indicator of non-self-adjointness, as the Golden-Thompson index, is capable of detecting with good reliability initial conditions with a tendency to produce large spreads.

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A. Navarra and J. Tribbia
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A. Navarra and K. Miyakoda

Abstract

Anomally models based on a spectral general circulation model (GCM) are formulated and applied to study of low-frequency atmospheric variability in the extratropics, and long-range forecasting research. A steady linear version of the anomaly model is treated by a matrix method. This model consists of nine vertical levels, 15 wave rhomboidal truncation, primitive equation system, and a fixed basic state, which is three-dimensionally variable. The matrix to be handled is extremely large, but can be solved using Krylov's technique. The solutions represent various teleconnection patterns known in the observed atmosphere. The sensitivity of the response of this anomaly model to zonally variability of the temporally fixed basic fields and to the geographical position of tropical heatings is investigated. The solutions of the steady linear anomaly model are compared with those of the original GCM, revealing that there are a few similarities among the solutions, but considerable discrepancies are also evident. A time-dependent nonlinear anomaly model is applied to further investigate the discrepancy. It appears that transient are crucial for explaining the disagreement, although the study with the time-dependent anomaly model is preliminary.

A noteworthy aspect of the overall approach is that the anomaly models are derived, with only small modifications, from the full GCM, and therefore, their relationship can be readily investigated. It is concluded that the steady linear model may be used as a diagnostic tool for investigating the characteristics of the full GCM and the dynamics of a particular state of the atmosphere. However, caution is needed when there is a significant role played by transient eddies, and in the treatment of tropical Rayleigh friction.

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A. Navarra and J. Tribbia

Abstract

A new method is presented to detect the portion of variability connected between two climatic fields. The method is a realization of the Procrustes problem, and it is a generalization of methods for analysis of variance such as the singular value decomposition (SVD) or canonical correlation analysis (CCA). The Procrustes formulation offers a general framework to link together variance analysis methods, and regression methods, including as special cases SVD and CCA.

Using this approach two fields can be divided into a subspace where variations of one field are connected to variations of the other field, the coupled manifold, and a subspace where variations are independent, the free manifold. The unified approach can be applied to prescribed SST experiments, in which case it recovers consistent results with other methods designed to identify the forced portion of variance, but it can now be extended also to the coupled case or to observations.

Some examples from prescribed SST simulation experiments and observations are discussed.

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