• Introduction
• Gravity Waves from Fronts: Parameterization
• General Circulation Model and Design of the Simulations
• Results
• Conclusions
• References

FIGURES

• Figure 1
• Figure 2
• Figure 3
• Figure 4

1. Introduction

Current parameterizations of the gravity wave processes that are relevant to middle atmosphere general circulation modeling need to have specified somewhere in the lower atmosphere a number of characteristics of the gravity wave spectrum that arise from different possible gravity wave sources (i.e. the so-called gravity wave source spectrum). The aim of this work is to take into account in the specification of the gravity wave source spectrum a space and time modulation of the gravity wave wind variance and propagation directions associated with the occurrence of frontal systems. Given that fronts are poorly resolved at the truncations commonly used in middle atmosphere models (T30 or T42), first a method is devised to diagnose conditions that are considered to be the precursor of frontogenesis in a space and time dependent low resolution flow. This is achieved by evaluating horizontal isotherm compression due to flow deformation and convergence. Second, when particular conditions are satisfied, the precursor to frontogenesis is used as an indicator of subgrid scale gravity wave emission in the model. Third, the wind variance and the propagation directions of the gravity wave source spectrum are specified according to empirical evidences of frontal generation of gravity waves. The model middle atmosphere response to this gravity wave forcing is presented. We restrict our study to fronts since they are thought to be one of the major non-stationary gravity wave sources in the extra-tropics, other gravity wave source mechanisms being left for later examination.

2. Gravity Waves from Fronts: Parameterization

Frontogenesis is most likely to occur when a strong deformation wind field acts to increase the horizontal temperature gradient. In two dimensions (latitude-longitude), the evolution of the horizontal potential temperature (b) gradient is given by the so-called frontogenesis function (Hoskins 1982)

High values of the right-hand side of Eq. 1

at some selected vertical level can be interpreted as a possible precursor to frontogenesis when b, u, and v are interpreted as large scale (or resolved) fields. In the context of a numerical simulation at relatively low resolution, frontogenesis may not occur, but high values (greater than some selected threshold) of the frontogenesis function could indicate that it would have occurred at a sufficiently high resolution. The approach followed here assumes that the frontogenesis function calculated at a single vertical level in the troposphere suffices to determine the possible occurrence of frontogenesis. Charron and Manzini (2000) showed that the frontogenesis function is indeed a good front indicator and that it can be useful as a tool for parameterizing gravity wave sources.

The parameters that are necessary to completely specify a spectrum of gravity waves emerging from frontal disturbances being mostly unknown, the approach followed here is based on two empirical evidences gathered from measurements and high resolution numerical simulations. The first one is that bursts of high horizontal wind variance linked to gravity wave motion is observed on the passage of fronts (Fritts and Nastrom 1992, Eckermann and Vincent 1993), the second one being that gravity waves are emitted, at least, in the cross-front directions (Griffiths and Reeder 1996). Based on these observations and high resolution idealized numerical results, it is assumed that the total variance, the orientation of propagation, and the launching height of the gravity wave source spectrum are specified in the following way:

(1) At the launching level located at around 600 hPa, the right-hand side of Eq. 1 is evaluated. This fixed launching level is chosen a priori in the scope of representing gravity waves that are emerging from low level fronts.

(2) If the threshold of 0.1 (K/100km)2/hour at some horizontal grid point and time step is reached, a subgrid scale total gravity wave wind variance of 4 m2 s-2 is imposed at that horizontal grid point and time step. The horizontal propagation directions of the equally bi-partitioned vertical flux of horizontal momentum in a frame of reference moving with the flow are chosen to be given by the two cross-front directions.

(3) If the threshold is not reached, an isotropic total gravity wave wind variance of 0.64 m2 s-2 is instead imposed with the aim of representing other possible gravity wave sources.

3. General Circulation Model and Design of the Simulations

The main reference simulation, hereafter labeled GWRF1, is carried out with the MAECHAM4 model with the abovementionned parameterization of the gravity wave emission from frontal disturbances applied to the input source spectrum of the Hines parameterization (Hines 1997a,b). The GWRF1 employs T30 truncation and includes a few other modifications to the input source spectrum with respect to the configuration used by Manzini and McFarlane (1998). As the GWRF1 simulation evolves, the right-hand side of Eq. 1 is computed at each grid point and time step at the launching level near 600 hPa in order to determine whether or not conditions favorable to frontogenesis are met and to specify the gravity wave variance and directions of propagation accordingly.

In addition, two sensitivity simulations have been carried out with MAECHAM4, respectively labeled UNI1 and UNI2. They serve as a mean of directly evaluating the impact of including a representation of fronts in the gravity wave source. Both UNI1 and UNI2 simulations are carried out at T30 truncations. The source spectrum of the UNI1 and UNI2 simulations is assumed to be isotropic. The total gravity wave wind variance at the same launching level as GWRF1 is set to 0.64 m2 s-2 for UNI1 and to 1 m2 s-2 for UNI2, uniform in space and constant time. The UNI1 source spectrum would therefore be identical to the one specified in simulation GWRF1 if the minimum threshold of the frontogenesis function was never reached in this latter simulation. The UNI2 source spectrum is very close to the monthly zonal mean source spectrum of GWRF1 in the extra-tropics.

The results from the GWRF1, UNI1, and UNI2 simulations are each one from 12 year integrations.

4. Results

This parameterization based on resolved deformation and convergence fields in the model middle troposphere leads to a gravity wave source intensity that has local maxima at known storm track locations. Moreover, a seasonal modulation of the monthly and zonal mean total gravity wave wind variance at the model launching level is observed with minima in summer, especially in the Northern Hemisphere. Instantaneous values of the total gravity wave wind variance entering the lower stratosphere seem to mimic relatively well the wind variances calculated from measurements made by instruments installed on commercial aircrafts.

When comparing GWRF1 to UNI1 in summer, the monthly and zonal mean vertical flux of zonal momentum carried by gravity waves reaching the middle atmosphere is almost unchanged when gravity waves from fronts are suppressed, but the winter values are more than doubled when gravity waves from fronts are parameterized.

The second sensitivity test (UNI2) consists in imposing a uniform and constant gravity wave wind variance at launching level that is very close to the monthly and zonal mean extra-tropical variance observed in the simulation in which fronts are acting as gravity wave sources. It turns out that even though the mean strength of the gravity wave forcing and the mean characteristics of the propagating medium in the two experiments are essentially the same in winter, the mean negative vertical flux of zonal momentum reaching the middle atmosphere is found to be more important when gravity waves from fronts are present, especially at 60S in July. This is essentially caused by the fact that tropospheric filtering effects by critical levels are reduced when gravity waves emerge from frontal zones since the gravity wave propagation directions and the wind direction are generally perpendicular in the model troposphere of GWRF1.

The mean mesospheric zonal gravity wave induced force per unit mass of the two sensitivity experiments tends to be higher near the model top in winter than in the GWRF1 simulation. On the other hand, the mean winter zonal induced force per unit mass of the GWRF1 simulation acts lower in the mesosphere than for the sensitivity tests, in accordance with the fact that the initial amplitude of the parameterized gravity waves emerging from frontal zones is greater than the selected constant amplitude in the sensitivity tests, and despite the relatively small amplitude of waves emerging from non-frontal zones.

The seasonal modulation of the monthly and zonal mean gravity wave wind variance at launching level in experiment GWRF1 is found to be helpful in simulating a more realistic zonal mean middle atmospheric jet in the Northern Hemisphere in July. During that month, a simulation with a gravity wave forcing that is uniform at launching level suffers from too strong middle atmospheric jet in the Southern Hemisphere (simulation UNI1) or a slightly too weak jet in the Northern Hemisphere (simulation UNI2). Moreover, the observed equatorward tilt of the mean zonal middle atmospheric jet in the Southern Hemisphere in July is more pronounced and closer to observations in GWRF1 than in UNI1 and UNI2. Figs. 1 and 2 depict NCEP and CIRA86 zonal wind data (OBS) in January and July, as well as the ensemble mean of GWRF1, UNI1, and UNI2.

Figs. 1 and 2 depict NCEP and CIRA86 zonal wind data (OBS) in January and July, as well as the ensemble mean of GWRF1, UNI1, and UNI2. The stratospheric mean polar cold bias in the Southern Hemisphere in winter obtained in the absence of gravity waves emerging from frontal zones can reach 25--30 K near 5 hPa in simulation UNI1, but is reduced to 2--4 K when these gravity waves are included. Among the four simulations performed for this study, the temperature biases at the poles is found to be minimal when part of the parameterized gravity wave activity is modulated by frontogenesis.

The stratospheric mean polar cold bias in the Southern Hemisphere in winter obtained in the absence of gravity waves emerging from frontal zones can reach 25-30 K near 5 hPa in simulation UNI1, but is reduced to 2-4 K when these gravity waves are included. Among the four simulations performed for this study, the temperature biases at the poles is found to be minimal when part of the parameterized gravity wave activity is modulated by frontogenesis. Figs. 3 and 4 show the mean temperature at 87N and 87S in the stratosphere throughout a year cycle obtained from 15 years of NCEP data. Figs. 3 and 4 also depict the difference between the three simulations described earlier and the NCEP data. Note that part of the simulated biases can be due to the specified ozone climatology employed in the simulations.

Figs. 3 and 4 show the mean temperature at 87N and 87S in the stratosphere throughout a year cycle obtained from 15 years of NCEP data. Figs. 3 and 4 also depict the difference between the three simulations described earlier and the NCEP data. Note that part of the simulated biases can be due to the specified ozone climatology employed in the simulations.

5. Conclusions

Gravity waves being a major mesospheric forcing that can greatly impact on the stratospheric circulation, establishing a source parameterization that is based on our dynamical knowledge of their generation mechanisms should help in obtaining realistic simulations of the middle atmosphere. In the MAECHAM4 model, the medium in which parameterized gravity waves are propagating is surely very important in determining the broad characteristics of these waves that reach the middle atmosphere, but this study shows that a gravity wave source spectrum that is related, even though somewhat crudely, to dynamical a mechanism leading to gravity wave emission can actually improve simulations of the middle atmosphere in terms of zonal mean fields. Convective and jet stream gravity wave excitation are mechanisms that would also need to be taken into account in order to get a more complete picture of the impact of modulating the gravity wave emission by relevant dynamical phenomena in middle and upper atmospheric general circulation models.

References

Charron, M., and E. Manzini, 2000: Gravity waves from fronts: Parameterization and middle atmosphere response in a general circulation model. Submitted.

Eckermann, S. D., and R. A. Vincent, 1993: VHF radar observations of gravity-wave production by cold fronts over southern Australia. J. Atmos. Sci., 50, 785-806.

Fritts, D. C., and G. D. Nastrom, 1992: Sources of mesoscale variability of gravity waves. Part II: Frontal, convective, and jet stream excitation. J. Atmos. Sci., 49, 111-127.

Griffiths, M., and M. J. Reeder, 1996: Stratospheric inertia-gravity waves generated in a numerical model of frontogenesis. I: Model solutions. Quart. J. Roy. Meteor. Soc., 122, 1153-1174.

Hines, C. O., 1997a: Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. Part 1: Basic formulation. J. Atmos. Solar-Terr. Phys., 59, 371-386.

Hines, C. O., 1997b: Doppler-spread parameterization of gravity-wave momentum deposition in the middle atmosphere. Part 2: Broad and quasi monochromatic spectra, and implementation. J. Atmos. Solar-Terr. Phys., 59, 387-400.

Hoskins, B. J., 1982: The mathematical theory of frontogenesis. Ann. Rev. Fluid Mech., 14, 131-151.

Manzini, E., and N. A. McFarlane, 1998: The effect of varying the source spectrum of a gravity wave parameterization in a middle atmosphere general circulation model. J. Geophys. Res., 103, 31,523-31,539.