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John Thuburn
and
Vincent Lagneau

Abstract

A shallow water model is used to simulate a case of planetary wave breaking in the lower winter stratosphere. The simulation is diagnosed in terms of zonal mean mass and zonal momentum budgets, and also in terms of potential vorticity (PV) contour mass and circulation budgets. The time evolution of the PV contour diagnostics depends only on nonconservative processes such as diabatic heating, friction, and irreversible small-scale mixing;transient but essentially reversible events such as a temporary displacement of the vortex from the pole are effectively filtered out. The PV contour diagnostics show unambiguously and quantitatively aspects of the evolution such as shrinking of the vortex and sharpening of the vortex edge. The cross-contour mass flux gives a radically different view of meridional transport from that given by the mass-weighted Eulerian mean poleward velocity, both in terms of its qualitative behavior and in terms of the physical mechanisms that cause it. The PV contour diagnostics can be used to define a balanced, zonally symmetric state, whose evolution can be compared directly with that of the Eulerian zonal mean state. A new expression is presented for finite-amplitude wave activity in terms of the PV contour diagnostics. Wave activity diagnostics for the wave-breaking simulation are shown. There are large differences between the zonal mean wave activity flux and its small-amplitude approximation, the Eliassen–Palm (EP) flux; some of the implications for interpreting EP flux diagnostics in the stratosphere are discussed.

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John Thuburn
and
George C. Craig

Abstract

Earlier theoretical and modeling work introduced the concept of a radiative constraint relating tropopause height to tropospheric lapse rate and other factors such as surface temperature. Here a minimal quantitative model for the radiative constraint is presented and used to illustrate the essential physics underlying the radiative constraint, which involves the approximate balance between absorption and emission of thermal infrared (IR) radiation determining tropopause temperature.

The results of the minimal model are then extended in two ways. First, the effects of including a more realistic treatment of IR radiation are quantified. Second, the radiative constraint model is extended to take into account non-IR warming processes such as solar heating and dynamical warming near the tropopause. The sensitivity of tropopause height to non-IR warming is estimated to be a few kilometers per K day−1, with positive warming leading to a lower tropopause. Sensitivities comparable to this are found in GCM experiments in which imposed changes in the ozone distribution or in the driving of the stratospheric residual mean meridional circulation lead to changes in tropopause height. In the Tropics the influence of the stratospheric circulation is found to extend down at least as far as the main convective outflow level, some 5 km below the temperature minimum.

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John Thuburn
and
George C. Craig

Abstract

The sensitivity of the tropopause height to various external parameters has been investigated using a global circulation model (GCM). The tropopause height was found to be strongly sensitive to the temperature at the earth’s surface, less sensitive to the ozone distribution, and hardly sensitive at all to moderate changes in the earth’s rotation rate. The strong sensitivity to surface temperature occurs through changes in the atmospheric moisture distribution and its resulting radiative effects. The radiative and dynamical mechanisms thought to maintain the tropopause height have been investigated in some detail. The assumption that the lower stratosphere is close to radiative equilibrium leads to an easily computed relationship between tropospheric lapse rate and tropopause height. This relationship was found to hold well in the GCM in the extratropics away from the winter pole. Possible reasons for the breakdown of the relationship in the Tropics and near the winter pole are discussed. Simple relationships predicted by two different baroclinic adjustment theories, between parameters such as potential temperature gradients, the Coriolis parameter, and tropopause height, were examined. When some of these parameters were changed explicitly in GCM experiments, the remaining parameters, determined internally by the GCM, did not respond in the predicted way. These results cast doubt on the relevance of baroclinic adjustment to the height of the tropopause.

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John Thuburn
and
Georgios A. Efstathiou

Abstract

We hypothesize that the convective atmospheric boundary layer is marginally stable when the damping effects of turbulence are taken into account. If the effects of turbulence are modeled as an eddy viscosity and diffusivity, then an idealized analysis based on the hypothesis predicts a well-known scaling for the magnitude of the eddy viscosity and diffusivity. It also predicts that the marginally stable modes should have vertical and horizontal scales comparable to the boundary layer depth. A more quantitative numerical linear stability analysis is presented for a realistic convective boundary layer potential temperature profile and is found to support the hypothesis.

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John Thuburn
,
Hilary Weller
,
Geoffrey K. Vallis
,
Robert J. Beare
, and
Michael Whitall

Abstract

A new theoretical framework is derived for parameterization of subgrid physical processes in atmospheric models; the application to parameterization of convection and boundary layer fluxes is a particular focus. The derivation is based on conditional filtering, which uses a set of quasi-Lagrangian labels to pick out different regions of the fluid, such as convective updrafts and environment, before applying a spatial filter. This results in a set of coupled prognostic equations for the different fluid components, including subfilter-scale flux terms and entrainment/detrainment terms. The framework can accommodate different types of approaches to parameterization, such as local turbulence approaches and mass flux approaches. It provides a natural way to distinguish between local and nonlocal transport processes and makes a clearer conceptual link to schemes based on coherent structures such as convective plumes or thermals than the straightforward application of a filter without the quasi-Lagrangian labels. The framework should facilitate the unification of different approaches to parameterization by highlighting the different approximations made and by helping to ensure that budgets of energy, entropy, and momentum are handled consistently and without double counting. The framework also points to various ways in which traditional parameterizations might be extended, for example, by including additional prognostic variables. One possibility is to allow the large-scale dynamics of all the fluid components to be handled by the dynamical core. This has the potential to improve several aspects of convection–dynamics coupling, such as dynamical memory, the location of compensating subsidence, and the propagation of convection to neighboring grid columns.

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