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Energy dissipation rates: Observational data guides us in choosing an appropriate small vertical-wavenumber cutoff for an ultra-simple spectral gravity wave parametrization
Those involved are Chris D Warner and Michael E McIntyre.
Our ultra-simple spectral gravity wave parametrization (see Warner and McIntyre 1999) assumes that a spectrum of gravity waves of an idealized shape is launched from the lower stratosphere. This spectrum evolves and is modified by the changing density, buoyancy frequency and background wind as it propagates upward through the atmosphere. Pseudomomentum flux and energy flux are deposited as the spectrum evolves and lead to a wave-induced acceleration and a wave-induced heating of the atmosphere. A typical idealized launch spectral shape for our ultra-simple spectral gravity wave parametrization is shown in Figure 1. The spectrum is defined by two power laws in different ranges of vertical wavenumber m separated by a crossover wavenumber mlx. In this typical launch spectrum, there is no pseudomomentum from vertical wavenumbers in the range 0 to mmin, a power one dependence for vertical wavenumber in the range mmin to mlx and a power minus three dependence for vertical wavenumbers greater than mlx. The idea is to cut down on computational costs for GCM purposes.
For wavenumbers below mlx, the spectrum is hardly constrained by gravity wave observations, in particular, the value (or even the existence) of mmin cannot be determined as mmin corresponds to the largest vertical wavelengths that are hardest to distinguish from the background wind. However, it is possible to choose a "best value" for mmin by comparing the energy dissipation rates from our ultra-simple spectral parametrization for various values of mmin with observational energy dissipation rates such as those derived from the rocket measurements of Lübken (1997). Figure 2 shows such a comparison. The value of 20km for mmin that we showed in Figure 2 is seen to yield a peak energy dissipation rate and altitude comparable to Lübken's result. The observational energy dissipation rate is more localised in altitude than is the case for our parametrization. Part of the explanation may be that zonally averaged climatological atmospheres vary much more smoothly with altitude than is likely to be the case in reality at these altitudes. Our next step is to check this out.
References
Lübken, F.-J., 1997: Seasonal variation of turbulent energy dissipation rates at high latitudes as determined by in situ measurements of neutral density fluctuations, J. Geophys. Res., 102(D12), 13441-13456.
Warner, C. D., McIntyre, M. E., 1999: Toward an ultra-simple spectral gravity wave parametrization for general circulation models Earth, Planets, Space, (accepted for publication in DYSMER special issue).
Intermediate Gravity-Wave Modelling
Those involved are (in alphabetical order) Michael McIntyre, Karine Sartelet, Claude Souprayen, and Chris Warner, under funding from the EC and from NERC in responsive mode.
In order to improve our understanding of observed gravity wave spectra, and to help bridge the gap between observational data and GCM parametrization schemes, a new, "intermediate" level of process modelling, based on stochastic hypotheses, e.g. about spectral phase information, is being developed and compared with data. It is hoped that the resulting "intermediate models" will incorporate both monochromatic (orographic) and broadband (non-orographic) waves in a consistent way that allows for their mutual interaction. Parametrizations for GCMs will, in turn, be able to be checked using an intermediate model as a test-bench, in addition to direct comparisons with data. One issue is whether real gravity-wave fields are 'sparse' (with well separated wave packets) or 'dense' (with all wavenumbers superposed in physical space, producing strong 'Doppler spreading' effects, as the currently popular Hines gravity-wave scheme assumes).
We began with some simple tests with stochastic hypotheses applied to the commonly observed power-spectral behaviour, and then, finding that the confrontation with data was not sharp, moved toward building a hierarchy of simplified dynamical models that are phase-sensitive. Some of these are being built using recently discovered wavelet techniques. It is hoped that the latter might themselves provide a possible alternative building block for intermediate modelling, as well as a new view of, and new insights into, the wave dynamics.
Model Dynamical Experiments
Those involved are Bjorn Hassler, Peter Haynes, Michael McIntyre, and (earlier) David Sankey.
The group is continuing with model dynamical experiments, with shallow-water and stratified models, as part of a program to understand why, in the real atmosphere, the wave-driven or 'gyroscopically pumped' global-scale stratospheric circulation withdraws air mainly from the tropical rather than the subtropical troposphere. As was emphasized in the review of stratosphere-troposphere exchange by Holton et al. (1995), this is not in the slightest obvious from 'downward control' theory. We also want to understand whether the observed regime of tropical stratospheric upwelling is robust or fragile. As emphasized by Michael McIntyre in his talk to the recent UGAMP summer meeting, this too is far from obvious. There could be sensitivities to small wave-induced forces well below observationally constrained thresholds.
The experiments examine the nonlinear, steady-state response to a given zonal force field F, assuming zonal symmetry and emphasizing cases with no artificial friction. The problem is nonlinear because of the meridional advection of relative angular momentum. Nonzero values of F, and therefore the associated gyroscopic pumping action, are confined in these experiments to latitudes poleward of a 'subtropical cutoff latitude' Ys , typically lying between 10 and 30 deg. The latitude (Y) dependence of F is chosen such that a linear 'downward control' formula, ignoring relative angular momentum against earth angular momentum, would predict, unrealistically, an upwelling region concentrated wholly in the neighbourhood of Y = Ys.
Nonlinearity modifies the picture in two ways. First, the pumping action pulls tropospheric air up into the model stratosphere from latitudes equatorward of Y = Ys, including air from the far side of the equator in some cases when the pumping is from one hemisphere only and F is large enough or Ys small enough. Second, the robustness of the downward control principle in high latitudes, which, under typical parameter conditions, closely constrains the total mass flux M pulled into the stratosphere and the latitudes at which it is pushed back into the troposphere the 'pump' with prescribed F is like a constant-current circuit device gives way, in the zonally symmetric dynamics, to a certain low-latitude fragility of the pattern of withdrawal of air from different latitudes in the tropics and subtropics Y < Ys . The tropical pattern is sensitive to small changes in F (smaller than any changes that can be well characterized from observed wave fields in the tropics and subtropics), as well as to other factors such as the tropical distribution of radiative equilibrium temperatures.
References
Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Rood, R. B., Pfister, L., 1995: Stratosphere-troposphere exchange, Revs.Geophys., 33, 403-439.
Chris Warner
DAMTP, University of Cambridge
C.D.Warner@damtp.cam.ac.uk
