Analysis of the polar vortex oscillations in a shallow water model of the stratosphere using quasi−Lagrangian diagnostics
Polar vortex oscillations are investigated using the long−term run of the potential-vorticity-based shallow water (SW) models for the stratosphere. In the SW models examined here, the combined effects of mechanical forcing, thermal forcing, and dissipation are the factors that can cause polar vortex oscillation. The mechanical forcing is provided by a time-independent topography, mimicking tropospheric excitation of the stratosphere. The thermal forcing is provided by a linear relaxation of the mass field to a time-independent equilibrium state mimicking the radiative relaxation taking place in the stratosphere. The SW equations in the potential vorticity (PV), velocity divergence and acceleration divergence representation are solved for a range of resolutions using the "diabatic contour-advective semi-Lagrangian" (DCASL) algorithm and a standard pure semi-Lagrangian (SL) algorithm. Using vastly different numerical algorithms makes it possible to uncover the degree of numerical sensitivity and the properties of the zonal vacillations with much greater accuracy than previous studies based on the SW model of the stratosphere. The equations for velocity and acceleration divergence are solved using spectral transform in longitude and compact fourth-order finite differencing in latitude. The spatial resolution is indicated by M Ï N, M and N being the number of grid points in the longitudinal and latitudinal directions, respectively. The results for the pure SL algorithm with spatial resolutions of 256 Ï 256, 512 Ï 512, and 1024 Ï 1024 are presented and compared with the corresponding results for the DCASL algorithm with a spatial resolution of 256 Ï 256. The results for the quasi-Lagrangian diagnostics indicate the superiority of the DCASL algorithm, since it can give results in 256 Ï 256 resolution comparable with those of the SL in the vastly more expensive 1024 Ï 1024 resolution. This accuracy occurs despite a clear difference in the topology of the quasi-equilibrium state to which the long-term solutions tend to approach, a strong vortex for DCASL as opposed to a diffuse vortex for the SL, indicating the possibility of multiple equilibrium solutions depending on the degree of diffusion. The present research focuses on a Lagrangian viewpoint to the evolution of the polar vortex by looking at the behavior of the quasi-Lagrangian diagnostics of the equivalent latitude, the mass enclosed by PV contours and the terms involved in its time evolution. The PV field forms the basis for calculating the quasi-Lagrangian diagnostics. The time evolution of the mass enclosed by PV contour is associated with nonconservative processes such as diabatic heating, friction, and irreversible small-scale mixing. Generally, the mass of the polar vortex increases (decreases) due to the action of diabatic (dissipative) mass flux. The results of this study are in contrast with the results reported at T42 resolution by Rong and Waugh in 2004, where the spectral transform algorithm was used to solve the SW equations in vorticity, divergence, and mass representation, wherein dissipation was produced by explicitly damping vorticity using hyperdiffusion. Except for the first large-amplitude oscillation, there is no sign of a clear, systematic phase shift between the dissipative and diabatic mass fluxes across the edge of the polar vortex, though such a shift is proposed by Rong and Waugh as the main mechanism responsible for the vacillations. Concomitant with the absence of the phase shift, the oscillations tend to be decaying and occur rather intermittently. Rather than the phase shift, the inherent fluctuations in both the diabatic and dissipative mass fluxes across the edge of the polar vortex seem to play the dominant role in generating the vacillations. Further diagnostics and numerical experiments are needed to assess the latter mechanism.
Iranian Journal of Geophysics, Volume:4 Issue:2, 2011
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