Rossby wave propagation on potential vorticity fronts with finite width

B J Harvey,M H P Ambaum,J Methven

doi:10.1017/jfm.2016.180

B J Harvey, M H P Ambaum + Show 1 more

Open Access

https://doi.org/10.1017/jfm.2016.180

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Abstract

The horizontal gradient of potential vorticity (PV) across the tropopause typically declines with lead time in global numerical weather forecasts and tends towards a steady value dependent on model resolution. This paper examines how spreading the tropopause PV contrast over a broader frontal zone affects the propagation of Rossby waves. The approach taken is to analyse Rossby waves on a PV front of finite width in a simple single-layer model. The dispersion relation for linear Rossby waves on a PV front of infinitesimal width is well known; here, an approximate correction is derived for the case of a finite-width front, valid in the limit that the front is narrow compared to the zonal wavelength. Broadening the front causes a decrease in both the jet speed and the ability of waves to propagate upstream. The contribution of these changes to Rossby wave phase speeds cancel at leading order. At second order the decrease in jet speed dominates, meaning phase speeds are slower on broader PV fronts. This asymptotic phase speed result is shown to hold for a wide class of single-layer dynamics with a varying range of PV inversion operators. The phase speed dependence on frontal width is verified by numerical simulations and also shown to be robust at finite wave amplitude, and estimates are made for the error in Rossby wave propagation speeds due to the PV gradient error present in numerical weather forecast models.

Highlights

Large-scale Rossby waves are ubiquitous features of the extratropical atmosphere.They typically reside on, and propagate along, the region of large isentropic potential vorticity (PV) gradient at the tropopause
The region of large PV gradient is narrow, in the sense that its width is much smaller than the typical wavelengths of Rossby waves, and as such the jet stream itself meanders latitudinally
A simple model for this PV front is obtained in the limit of a single PV step separating two regions of uniform PV, representing the tropopause as a discontinuity between high PV stratospheric air on the poleward side and low PV tropospheric air on the equatorward side (e.g. Verkley 1994; Swanson, Kushner & Held 1997)

Summary

Introduction

Large-scale Rossby waves are ubiquitous features of the extratropical atmosphere. They typically reside on, and propagate along, the region of large isentropic potential vorticity (PV) gradient at the tropopause. This represents a broad baroclinic zone with no meridional jet structure Smoothing this basic state results in a continuous transition from low to high stratification across the tropopause, and the study shows that this acts to increase the Rossby wave phase speeds. 2. Linear waves on a sharp potential vorticity front The QGSW model (see, e.g., Vallis 2006) represents the large-scale dynamics of a single-layer fluid at small Rossby number. Increasing the frontal separation reduces the phase speeds of both modes, but the impact on the meandering mode is quadratic in due to a leading-order compensation between a reduction in advection by the basic state jet and the ability of the waves to propagate upstream (see (1.1)). It is shown that both of these results carry over to the continuous PV gradient case

Linear waves on a potential vorticity front of finite width

Findings

Conclusions and discussion