impact of a simple parameterization of convective gravity ... · they also described a second...

Impact of a simple parameterization of convective gravity-wave dragin a stratosphere-troposphere general circulation modeland its sensitivity to vertical resolution

C. Bossuet, M. DeÂ queÂ , D. Cariolle

Centre National de Recherches MeÂ teÂ orologiques, 42 Av. Coriolis, Toulouse, France

Received: 3 January 1996 / Revised: 31 July 1997 /Accepted: 25 August 1997

Abstract. Systematic westerly biases in the southernhemisphere wintertime ¯ow and easterly equatorialbiases are experienced in the MeÂ teÂ o-France climatemodel. These biases are found to be much reduced whena simple parameterization is introduced to take intoaccount the vertical momentum transfer through thegravity waves excited by deep convection. These wavesare quasi-stationary in the frame of reference movingwith convection and they propagate vertically to higherlevels in the atmosphere, where they may exert asigni®cant deceleration of the mean ¯ow at levels wheredissipation occurs. Sixty-day experiments have beenperformed from a multiyear simulation with the stan-dard 31 levels for a summer and a winter month, andwith a T42 horizontal resolution. The impact of thisparameterization on the integration of the model isfound to be generally positive, with a signi®cantdeceleration in the westerly stratospheric jet and witha reduction of the easterly equatorial bias. The sensitiv-ity of the MeÂ teÂ o-France climate model to verticalresolution is also investigated by increasing the numberof vertical levels, without moving the top of the model.The vertical resolution is increased up to 41 levels, usingtwo kinds of level distribution. For the ®rst, the increasein vertical resolution concerns especially the troposphere(with 22 levels in the troposphere), and the second treatsthe whole atmosphere in a homogeneous way (with 15levels in the troposphere); the standard version of 31levels has 10 levels in the troposphere. A comparison ismade between the dynamical aspects of the simulations.The zonal wind and precipitation are presented andcompared for each resolution. A positive impact isfound with the ®ner tropospheric resolution on theprecipitation in the mid-latitudes and on the westerlystratospheric jet, but the general impact on the modelclimate is weak, the physical parameterizations usedappear to be mostly independent to the vertical resolu-tion.

Key words Meteorology and atmospheric dynamics áConvective processes á Waves and tides

1 Introduction

The study of the present climate and the investigation ofthe impact of changes in greenhouse gases and strato-spheric ozone on the future climate require the devel-opment of reliable, comprehensive atmospheric modelsand the coupling of such atmospheric models withcomprehensive ocean models. For realistic numericalsimulations many physical and dynamical processesmust be included, and a large variety of investigationsabout model sensitivity and model ability to reproduceobserved phenomena have to be performed. The grav-ity-wave drag e�ect on the large-scale ¯ow is importantfor the dynamic coupling of the troposphere andstratosphere. An improved understanding and a con-sideration of the vertical transfer of momentum viawaves generated in the troposphere are important forthe development of accurate global climate models.

The orographic gravity waves' generation and mech-anism are now well understood. Lindzen (1981), Palmeret al. (1986) and McFarlane (1987) showed an improve-ment by introducing an orographic gravity-wave dragparameterization. They reduce the polar night vortexintensity and have a realistic zonal wind over continents.However, observations of gravity waves in the middleatmosphere (Fritts, 1984) indicate that a large numberof gravity waves are not stationary but high-frequencywaves, and so display sources other than topographicones. A large part of them are likely to be excited byconvection and are linked to the convective cells.Indeed, in active convective regions (tropics) the cumu-lus convection involves strong transient vertical motionsand behaves like mountains in the environmentalhorizontal ¯ow, thus generating gravity waves. Clarket al. (1986) referred to this as the ``obstacle e�ect''.

Correspondence to: Dr. C. Bossuete-mail: [email protected]

Ann. Geophysicae 16, 238±249 (1998) Ó EGS ± Springer-Verlag 1998

They also described a second mechanism of convectivegravity-wave generation, the ``mechanical oscillatore�ect'': the interface disruption of two layers withdi�erent stabilities due to upward and downwardoscillation of convective eddies (next to the tropopause)is a source of waves.

Such waves have been observed by aircraft, rocketsand reported by Kuettner et al. (1987) above convectiveboundary layers in continental mid-latitudes and byJames (1959) and P®ster et al. (1993) above deepconvection in the tropics. These waves have earlier beenstudied numerically with two-dimensional simulationsby Clark et al. (1986) above shallow cumulus and byFovell et al. (1992) above a squall line. Three-dimen-sional simulations have also been performed by Haufand Clark (1989) and Kershaw (1995). Those studiesreveal that the strength of the vertical shear of thehorizontal wind determines the waves excitation.

The convective gravity waves generated in thetroposphere propagate vertically with westerly (easterly)phase speeds relative to the mean ¯ow and transferwesterly (easterly) momentum into the stratospherewhen they break, thus in¯uencing the environmental¯ow through wave drag and di�usion. This e�ect of thedrag exerted on the mean ¯ow by the gravity wavesexcited by convection has to be taken into account inatmospheric GCMs. The ®rst purpose of this work is tointroduce and to test a new parameterization whichvertically transfers momentum induced by these waves(in the upper atmosphere).

Model resolution is also an important aspect for theperformance of the simulations, and has been discussedearlier in the literature (Boville, 1991; Hayashi et al.,1989, and references therein), and illustrated by im-provements in simulations (Lindzen and Fox-Rabino-vitz, 1989; Mesinger et al., 1990; Warner and Seaman,1990). Advances in computer power and development ofnew observation systems are making it possible toincrease resolution in general circulation models(GCMs). These resolution studies may provide someinteresting features of the scale dependencies of themodel parameterizations.

The work of Boyle (1993) and DeÂ queÂ et al. (1994) onthe horizontal resolution showed that the role of theorography is improved by increasing resolution, and sohas an impact on the atmospheric circulation above thecontinents. The main improvements due to horizontalresolution occur in the stratospheric simulation (whenthe model has su�cient vertical resolution) as shown byKiehl and Williamson (1991) and Boyle (1993). How-ever, the improvement is not uniform for all aspects ofthe simulations; Boyle (1993) ®nds some degradationvisible from the ®rst 30 days of the simulation: theconvective parameterization appears to be resolutiondependent in certain regions and is more e�cient for aweak horizontal resolution (this impact is also found inthe work of DeÂ queÂ et al., 1994). The dynamic aspects ofthe circulation are not sensitive to the change inresolution. Although increasing resolution can improvethe accuracy of numerical models by decreasing discret-ization errors, it can also degrade some simulated ®elds

by destroying the equilibrium of compensating errors(Houghton et al., 1992).

The vertical resolution is also important for thenumerical simulations e�ciency, as shown by Palmer etal. (1986). In an another way, by extending the top of themodel up to the stratosphere, Boville and Cheng (1988)found an improvement in the tropospheric-stratosphericsimulation, with a reduction of the westerly winds and awarming of the polar lower stratosphere. These e�ectsare due to re¯ection of the vertically propagating waveactivity by the upper boundary of the model andin¯uence the mean tropospheric ¯ow.

The second purpose of this work is to examinethe impact of a smaller spacing of the levels within themodel's vertical domain without moving the top ofthe model. Increasing the number of levels may inducesigni®cant changes in the atmospheric circulation and inthe troposphere, as found by Williamson (1988).

We focus in this study on the tropospheric resolution.Indeed, two di�erent 41-vertical-level distributions areconsidered, which in the ®rst case of increased resolutionconcerns especially the troposphere (with 22 levels in thetroposphere), and in the second one the whole atmo-sphere in an homogeneous way (with 15 levels in thetroposphere). The impact of the vertical resolution iscompared with the simulation of the standard 31-levelversion of ARPEGE-Climat (with 10 levels in thetroposphere). We focus our analysis on the verticalshape of the general circulation and on the precipitation¯uxes.

Section 2 describes the GCM used and the main biasof the general circulation simulated with the standard31-level version of ARPEGE-Climat. Section 3 presentsthe new parameterization of the drag exerted on themean ¯ow by gravity waves excited by convection.Section 4 presents the results obtained with di�erentvertical level spacing and their impact on the generalcirculation. Conclusion and remarks appear in Sect. 5.

2 Description of the basic GCM

The atmospheric GCM used in this study is a climateversion of the model developed from the numericalmodel ARPEGE used by MeÂ teÂ o-France and ECMWFfor operational short- and medium-range forecast. Adescription of the basic climate version (Version 0) canbe found in DeÂ queÂ et al. (1994). This model is a spectralGCM that can be integrated at various horizontalspectral triangular truncations. The ARPEGE-Climatstandard vertical coordinate is a progressive hybridsigma-pressure coordinate extending from the surface tothe mesosphere (80 km). The semi-implicit integrationallows for a 15-min time-step for the spectral horizontalresolution of T42. The physical parameterizations arestate-of-the-art schemes that can be found in the otherGCMs. One original feature of this model is the fact thatthe ozone concentration is advected and interacts withthe rest of the model through the radiative code, andaccounts for the photochemical sources and sinks bymeans of a simple linear scheme. The modi®cations

C. Bossuet et al.: Impact of a simple parameterization of convective gravity wave drag 239

which have been made in the ARPEGE-Climat model inthis work (since DeÂ queÂ et al., 1994) are the following:

1. The radiation scheme (Morcrette, 1991) is calledevery 3 h; this scheme belongs to the physicalparameterization package of the ECMWF model. Ittakes into account four ®elds of aerosols and cloud-radiation interactions in detail.

2. The land surface processes are taken into accountwith the soil-vegetation scheme of Noilhan andPlanton (1989). This includes three water reservoirswhich reduce the overestimated surface temperatureover the continents during the summer. The geo-graphical distributions of the soil and vegetationproperties are taken into account.

3. The liquid and solid water phases are distinguished inthe precipitation scheme.

4. The atmospheric mass sources and sinks induced byevaporation and precipitation are taken into accountin order to improve the tropical rainfall simulation.

5. A new de®nition of the vertical levels has been given(see next section).

The experiments described in this paper were per-formed from a well-equilibrated state of the atmosphere.The initial conditions are the result of a 5-year integra-tion of the model with the standard 31 levels. Then aperturbation, the convective gravity-wave drag param-eterization and/or a change to 41 vertical levels, isintroduced. The length of the integrations is 60 days. Inorder to limit the dependence on the initial conditions,several 60-day integrations are averaged. Five winter 60-day runs are performed, starting on 29 November ofyears 1 to 5 of the reference integration, and ®ve summer60-day runs are performed, starting on 24 May of thesame years.

As shown by Dreveton et al. (1993), the GCM isallowed 30 days to reach a new equilibrium to the per-turbation imposed and the last 30 days of the integrationare used for the time-averaged results. The horizontalresolution is a spectral T42 triangular truncation equiv-alent to a Gaussian grid with a mesh of about 2:8� in

latitude and longitude. The ®rst experiment with thestandard 31 levels is used as a reference (hereafterREF31).

Figures 1 and 2 show the height±latitude sections ofthe zonal average of zonal wind for REF31 and aclimatology of the European Centre for Medium-rangeWeather Forecasts (ECMWF) daily analyses (whichextend only up to 10 hPa). This climatology has beenobtained by averaging 6 years of 6-hourly analysesbetween 1985 and 1991, for which the ECMWF modelused a T106 truncation. The ®gures present the mainbiases of the ARPEGE-Climat model.

In the July reference experiment (Fig. 1) the positionsof the jet stream agree well with climatology, althoughthe westerly stratospheric jet is too strong by about10 m sÿ1 near the tropopause (100 hPa) and 20 m sÿ1 inthe stratosphere. The easterly jet intensity is alsooverestimated by about 10 m sÿ1 in the lower strato-sphere; this equatorial easterly bias is common to manyGCMs.

In the January reference experiment (Fig. 2) thewesterly stratospheric jet is too strong by 10 m sÿ1. Inthe southern hemisphere, the easterly jet is overestimat-ed with an equatorial easterly bias, in the low strato-sphere, of 10 m sÿ1.

3 The convective gravity-wave drag parameterization

Before increasing the vertical resolution, we try toreduce these systematic biases in the zonal average ofzonal wind shown in the previous section. A simpleparameterization of the drag exerted on the mean ¯owby gravity waves excited by convection is introduced inthe same way as Palmer et al. (1986), who implementedan orographic gravity-wave drag parameterization.

This parameterization deals with the e�ect on themean ¯ow of the gravity waves excited by convection.Indeed, we only take into account the vertical transfer ofmomentum induced by these waves and not theirpossible di�usion e�ects on heat. We consider a frame

Fig. 1a, b. Zonal mean of zonalwind for July for a the ECMWFclimatology and b the referenceexperiment REF31; contour interval10 m sÿ1

240 C. Bossuet et al.: Impact of a simple parameterization of convective gravity-wave drag

moving with the cumulus convection. In this frame,linked to the cloud base, we can assume that the wavesare stationary (they have a phase speed equal to thewind speed at the bottom of the cloud) and have avertical propagation. For the interaction with the large-scale ¯ow, the wave is assumed to be activated in theplane de®ned by the direction of the absolute wind at thetop of the cloud (source of convective gravity waves)and the vertical.

In this given reference frame with respect to theconvective eddies, we can treat the convective gravity-wave drag like the orographic one, and follow Lindzen(1981) in applying linear theories of propagation.

The intensity of momentum transported by thegravity waves excited by the convection is chosen todepend on the precipitation ¯ux, which is an index ofconvective activity in the model, as shown by Tiedtke(1984) in his parameterization of cumulus convection.

At the top of the cloud, the convective gravity waveinduces a momentum ¯ux given by the empiricalrelation:

sT!� ÿKPconv

vT!kvT!k ; �1�

where K is an empirical coe�cient, Pconv is the convec-tive precipitation and vT

! is the wind at the top of thecloud.

Above the cloud, away from critical levels anddissipative e�ects, the convective momentum ¯ux re-mains constant. There is no interaction with the large-scale ¯ow. The wave propagates vertically and remainslinear. As the air density decreases with height, thegravity-wave magnitude increases until a critical level ofbreaking is reached (where the magnitude and thewavelength are about the same order). At this level thereis saturation and the wave exchanges momentum withthe mean ¯ow.

Following the instability criterion of Lindzen (1981)for the orographic gravity wave breaking, we havesaturation when:

C�q;N ;U� � qqT

NT

NUUT

� �3

� 1 ; �2�

where qT is the air density at the top of the cloud, NT theBrunt±VaõÈ ssaÈ laÈ frequency at the top of the cloud and UTis the component of the relative wind (in the givenreference frame) in the direction of the wind at the top ofthe cloud. The expression of U (at a level l) is:

U � � v!ÿ vb!�: vT!

k vT! k ; �3�

where vb! is the wave phase speed.

The momentum ¯ux at level l is given by:

sl � ClsT : �4�At the top of the cloud (level lT ) the wave is saturated(ClT � 1). As height increases, l decreases (since l � 41at the surface and l � 0 at the top of the model) and Clremains constant as a function of l until a critical level isencountered; above this level C decreases monotonicallyfollowing:Cl � min

ÿCl�1�ql�1;Nl�1;Ul�1�;Cl�ql;Nl;Ul�

�.

Once zero value is attained, it remains constant up to thetop of the model (the wave is completely absorbed).

Inside the cloud, in contrast to the orographic GWD,which exchanges momentum with the solid earth, weassume that the convective gravity-wave stress is zero atthe surface. For the sake of simplicity, we take a linearempirical pro®le such that the ¯ux s decreases linearlyfrom the top of the cloud to its base, where it is ®xed tozero value. Indeed, the momentum derived from theatmosphere is given back to the lower atmosphericlayers (inside the cloud). The stable layers below thecloud base are not supposed to be a�ected by themomentum deposition.

This empirical scheme does not take into account thepossible e�ects of resonance and trapped waves due tomultiple re¯ection of the wave. Experiments have beenperformed with di�erent values of the empirical coe�-cient K in Eq. (1). No attempt has been made to obtainimprovements in the zonal wind by excessive tuning of

Fig. 2. As Fig. 1 for January


the gravity-wave drag parameter K: a weak coe�cientmakes the parameterization inoperative, and a strongcoe�cient produces too strong a warming in the highestlayers of the model, in the polar regions. Finally,realistic simulation is obtained with a coe�cient K equalto 103.

The experiment performed with 31 levels and with theconvective gravity-wave drag parameterization is re-ferred to hereafter as GWD31.

The impact of the Convective Gravity Wave Drag(CGWD) parameterization on the vertical structure ofthe general circulation is shown in the height±latitudesections of Fig. 3. The statistics are calculated with ®veindependent July months. The isolines represent themonthly zonal average of zonal wind and the shadedpatterns represent the total zonal wind tendency due toconvection (in m sÿ1 dayÿ1) for both experiments,REF31 and GWD31. It has to be noted that this zonalwind tendency also takes into account the impact of theconvection scheme (Bougeault, 1985) which is respon-sible for the zonal wind tendency in the troposphere forthe experiment REF31, Fig. 3a. The two parameteriza-tions are coupled. The convection scheme is activatedunder two conditions: a convergence of humidity in thelower layers and an unstable vertical temperaturepro®le. The momentum ¯ux is redistributed within thecloud by an adjustment of the pro®le to a cloudy windpro®le, supposed to be constant in the vertical.

The CGWD parameterization extends this phenom-enon above the convective cloud, as shown by Fig. 3b,for the GWD31 experiment, where just a weak impact isfound on the zonal wind in the troposphere (theparameterization is operative above the cumulus cloudbase). At the equator, the high convective activitygenerates gravity waves which vertically transfer mo-mentum in the upper atmosphere, translated in Fig. 3bby a zonal wind tendency due to convection. Looking atFig. 4a, which represents the zonal mean total precip-itation for July (for the climatology, the REF31 andGWD31 experiments), one can see that this zonal windtendency due to convection in the northern hemisphere

corresponds to the maximum of the precipitation(10�±20� in the northern hemisphere), in agreement withthe empirical momentum ¯ux de®nition.

The wave drag stress decelerates the easterly zonalwind. Near the tropopause, the 20-m sÿ1 isoline isthrown back at 40 hPa in the GWD31 experimentinstead of 80 hPa in the reference REF31. The system-atic equatorial easterly bias is substantially reduced byabout 10 m sÿ1, in better agreement with the climatol-ogy (as seen in the previous section). In the upperstratosphere, the easterly stratospheric jet in theGWD31 experiment is reduced by 10 m sÿ1.

The tropical oceans also represent an importantsource of convective gravity waves, and the stratospher-ic drag induced is a signi®cant contributor to the

Fig. 3a, b. Zonal average of zonalwind response to the convectivegravity-wave drag parameterizationfor a REF31 and b GWD31 for July.The dotted and solid contour lines(with 10-m sÿ1 interval) representthe zonal average of zonal wind, andthe shaded values represent the zonalaverage of zonal wind tendency dueto convection (m sÿ1 dayÿ1). Thelight shading represents the positivevalues over 0:1 m sÿ1 day ÿ1 and thedark shading the negative values overÿ0:1 m sÿ1 day ÿ1

Fig. 4. Zonal mean precipitation �mm dayÿ1� for July: REF31(dotted ), GWD31 (dashed ) and the climatology (solid )


momentum budget in the southern hemisphere. Thewesterly stratospheric jet is found to be reduced by40 m sÿ1 (in the middle atmosphere), a change in theright direction if compared with the climatology.

For January (not shown), the stratospheric jetstrength is slightly reduced. The impact of the CGWDparameterization on the zonal average of the zonal windis weak compared to July, especially on the westerlystratospheric jet. Indeed the critical levels are furtherdown in the northern hemisphere, due to the occurrenceof planetary waves, which are non-existent in thesouthern hemisphere.

An impact is seen in July on the total precipitation¯ux (including the solid, liquid, convective and strati-form precipitation). Figure 4 presents the distribution ofthe precipitation as a function of latitude in July for theexperiments GWD31 and REF31 compared to theclimatology of Legates and Willmot (1990) based onrain gauge observations.

The global monthly mean precipitation decreases inthe GWD31 experiment (3:20 mm dayÿ1) comparedto the reference REF31 (3:30 mm dayÿ1). We observea decrease in precipitation in the mid-latitudes and in thenorthern hemisphere (30�N), in agreement with theclimatology, which is signi®cant respectively at 99% and95% according to t-tests (with a degree of liberty of 4).This feedback on the total precipitation ¯ux mostlyconcerns the convective precipitation (the stratiform oneis not a�ected), and is especially important in regions ofhigh convective activity, where the parameterization isparticularly active. Figure 5 presents the precipitationerrors for July, between the experiments REF31,GWD31 and the climatology, in the monsoon area.

The maxima of the precipitation error are less intense inthe GWD31 experiment. The convective precipitationare reduced in good agreement with the climatology,however the simulated precipitation cores are locatedtoo far south with respect to observations, and this biasis ampli®ed when the empirical coe�cient K is increased(i.e. when the intensity of convective gravity waves isincreased).

For January (Fig. 4b), the impact of the CGWDparameterization on the total precipitation ¯ux is weak,with a slight decrease in the precipitation in the mid-latitudes (in both hemispheres).

The introduction of the convective gravity-wave dragparameterization has a positive impact on the strengthof the stratospheric jets and reduces the easterlyequatorial bias. In the troposphere an impact is seenon the convective precipitation, in high convectiveactivity area, with a decrease in the precipitation. Themonsoon tends to shift equatorwards and the precipi-tation anomalies are reduced.

4 Impact of vertical resolution

4.1 The distribution of the vertical levels

Using the version of ARPEGE-Climat including theCGWD parameterization, integrations with 41 verticallevels instead of 31 have been performed with thevertical resolution increased uniformly over the vertical(GWDS41 experiment) and with an increase in thenumber of levels especially in the troposphere (experi-ment GWDT41). The choice of 41 levels was motivatedby constraints on the calculation time and computercost. The purpose of this study was to determine thepossible impact of a ®ner tropospheric resolution, inorder to test the stability of parameterizations (clouds,di�usion, etc) with regard to vertical resolution.

Figure 6 presents the vertical resolution in the threeversions of the model. The top of the model is ®xed at0.01 hPa. The three level distributions which are com-pared in this paper are the following: GWD31 ± thestandard 31-level model has a pressure-level distributionso as to have 21 levels in the stratosphere and 10 in thetroposphere (with three levels in the boundary layer).GWD31 is the reference experiment in this section.GWDS41 ± the ®rst 41-level con®guration, where thestratospheric and the tropospheric resolution are en-hanced, has 26 levels in the stratosphere and 15 levels inthe troposphere (with four levels in the boundary layer).GWDT41 ± the second 41-level con®guration, whereonly the tropospheric resolution is increased, has 19levels in the stratosphere and 22 levels in the tropo-sphere (with six levels in the boundary layer). However,the reference stratospheric resolution (of GWD31) is notexactly conserved in order to ensure a continuouspressure-level distribution with this new troposphericresolution (as one can see in Fig. 6). The method used todetermine the distribution of the vertical levels ispresented in the Appendix.

Fig. 5a, b. Precipitation error for July in mm dayÿ1 between a thereference REF31 and the climatology and b the experiment GWD31and the climatology; values over 5mm dayÿ1 are shaded


Five 60-days runs are performed and averaged (asseen in Sect. 2), starting from a stabilized atmosphericstate. The horizontal resolution is kept at T42, in orderto isolate the impact of the vertical resolution. The time-step, largely controlled by the horizontal resolution, iskept at 15 min. The hybrid vertical coordinate g used isa terrain following sigma coordinate close to the surfaceand a pressure coordinate in the higher levels, to be welladapted to stratospheric modelling (Simmons and Bur-ridge, 1981); g varies from 0 at the model top to 1 at thesurface. (See Appendix for more details). No singlecharacterization of the consistency of the vertical tohorizontal resolution can be applied throughout thedepth of the atmosphere in this paper, as had beenpossible in previous consistency studies, which used aconstant vertical increment with height (Lindzen andFox-Rabinovitz, 1989) since the layer thickness varieswith height.

For each level distribution con®guration some tuningis required in order to compare the di�erent simulations.The cloud cover is diagnosed at each level by combining

the stratiform and the convective cloudiness fractionswith maximum overlap. The stratiform cloudiness iscalculated from the di�erence between the relativehumidity and a critical humidity pro®le given by:

hc�k� � 1ÿ a1p�k�ps

1ÿ p�k�ps

� �� 1� ��

a2p p�k�

psÿ 1

2

� �� ; �5�

where p�k� is the pressure of the k-th level and ps thesurface pressure, a1 and a2 are empirical coe�cients,which are, respectively, equal to 1.7 and 1 (in thestandard, 31-level version). The empirical parameters a1and a2 must be adapted to each change in the model (inparticular a change in resolution) in order to ensure aglobal planetary albedo of 0.3 and a global radiativeequilibrium at the top of the atmosphere in annual mean(they are equal, respectively, to 1.5 and 1 in theGWDS41 version and to 1.6 and 2 in GWDT41).

Fig. 6. Vertical layer structure of the experiments GWD31, GWDS41and GWDT41, in a linear scale below level 100 hPa (in thetroposphere) and in a logarithmic scale above level 100 hPa. Pressure

thicknesses shown for each layer (without parentheses) are in hPa andassume a surface value of 1000 hPa. Approximate height thicknessesin metres are shown for each layer in parentheses


4.2 Impact of increased vertical resolutionon the general circulation

Figure 7 presents the di�erence between the 41-levelexperiments and the reference GWD31 for the zonalaverage of zonal wind for July. The impact of verticalresolution enhancement is not very striking. The maindi�erences between the experiments GWDT41,GWDS41 and the reference experiment GWD31 occurin the upper part of the atmosphere. In the southernhemisphere stratospheric polar night, the westerly jetintensity is reduced by 20 m sÿ1 when the verticalresolution is increased (a change in the right directionif compared to the climatology).

A slightly poleward drift of the polar stratospheric jetis also observed in the winter hemisphere for July. Thisfeature can be explained by the sensitivity of theorographic gravity-wave drag to the vertical resolution.Figure 8 presents the vertical structure of zonal windtendency (due to orographic gravity waves) for the threeexperiments in July, and shows a zonal wind tendencydecrease in the southern-hemisphere stratosphere withresolution (in GWDS41 and GWDT41). Dreveton et al.(1993) have shown in their work on the feedbacksbetween the parameterization schemes that the westerlystratospheric jet shifts polewards when the gravity-wavedrag decreases. This feature is enhanced when thetropospheric vertical resolution is increased. The zonalwind tendency (due to orographic gravity waves) inGWDT41 (Fig. 8c) is weaker by about 4 m sÿ1 dayÿ1 inthe southern-hemisphere stratospheric height-latitudescompared to GWDS41 (Fig. 8b).

Some work on the orographic gravity-wave dragparameterization is in progress in order to reduce thepoleward drift. This poleward shift of the westerlystratospheric jet produces a warming in the polar nightstratosphere that one can see in Fig. 9, which presentsthe zonal mean temperature di�erence between the

41-level experiments and the reference experiment stillfor July. This warming is increased in GWDT41, withthe tropospheric resolution. A warming by about 3� atthe top of the model is also observed in the 41-levelexperiments.

The easterly jet (Fig. 7) in the northern hemispherefor July is not sensitive to vertical resolution, except inthe upper stratosphere, where the jet is accelerated byabout 10 m sÿ1 in the 41-level experiments. However, atleast 10 years, simulation is required in the northernhemisphere for a stable climatology, owing to theimportant variability (Boville and Randel, 1986), so inspite of the t-test agreement, some more experimentshave to be performed to determine a stable impact of thevertical resolution.

For January, one can notice in Fig. 10, where thezonal average of zonal wind for 41-level and 31-levelexperiments is plotted, no impact on the easterly jet inthe southern hemisphere.

In the northern hemisphere, the westerly stratospher-ic jet is increased with resolution, in the upper strato-sphere by 20 m sÿ1 for the GWDS41 experiment and10 m sÿ1 for GWDT41 experiment, compared to thereference GWD31. However, in GWDS41 (Fig. 10b),with a vertical resolution increased in the whole atmo-sphere, the westerly stratospheric jet is strongly reducedin the middle atmosphere (compared to GWD31) andbecomes no more realistic. No systematic impact is seenon the zonal mean temperature for January (not shown)in the 41-level experiment, except for a warming (byabout 2�) at the top of the model.

The impact of increased vertical resolution on thegeneral circulation model is characterized (in both41-level experiments) by a poleward shift of the polarstratospheric jet in the winter hemisphere for July,induced by an orographic gravity-wave drag increase.For January, the impact is weak. A degradation of thewesterly stratospheric jet in GWDS41 is noticed,

Fig. 7a, b. Zonal mean di�erence ofzonal wind in m sÿ1 for July,between a the experiments GWD41and GWD31, and b the experimentsGWDT41 and GWD31; contourinterval 4 m sÿ1 and the dotted linesrepresent negative values


although more experiments have to be performedbecause of the important variability in the northernhemisphere due to the planetary waves.

4.3 Precipitation

The total precipitation simulated with the di�erentvertical resolution, including solid, liquid, stratiformand convective precipitation, is compared to the Legatesand Willmot (1990) climatology. The global meanprecipitation remains constant with vertical resolution;however, an impact in the 41-level experiments is seen

on the precipitation at the equator and mid-latitudes, asshown in Fig. 11a, b, where the distribution of theprecipitation as a function of latitude in July andJanuary is presented.

In July (Fig. 11a) the main impact on the precipi-tation is found in the northern hemisphere in themid-latitudes, where the precipitation decreases withresolution with respect to the observations. The decreaseis signi®cant at 99% (according to t-tests, with a degreeof liberty of 4). In the southern hemisphere the decreasein the tropical precipitation is stable at 95%; however,the precipitation was already underestimated in thereference experiment GWD31.

Fig. 8a±c. Zonal average of the zonal wind tendency due to the orographic gravity-wave drag in m sÿ1 dayÿ1 for July for the experiments aGWD31, b GWDS41 and c GWDT41; contour 0.1, 0.2, 0.5, 1 and 5 m sÿ1 dayÿ1, and positive values over 0.1 are shaded

Fig. 9a, b. Zonal mean di�erence oftemperature for July between a theexperiments GWDS41 and GWD31,and b the experiments GWDT41 andGWD31; contour interval 2�, thedotted lines represent negative values


In January (Fig. 11b), the maximum equatorial pre-cipitation shifts northwards in the GWDT41 experiment,compared to the reference GWD31, and is in betteragreement with the climatology. However, in GWDS41this maximum is reduced. Both impacts are signi®cant at99%. The impact of increased vertical resolution on theprecipitation is positive when the tropospheric resolu-tion is ®ner.

5 Concluding remarks

The GCM has a high resolution in the stratosphere(with respect to other GCMs) and su�ers from over-strong stratospheric winds and in particular from anequatorial easterly bias. A simple parameterization ofconvective gravity-wave drag has been introduced inARPEGE-Climat GCM which reduces these biases bytaking into account vertical momentum transfer throughconvective gravity waves from the troposphere to thestratosphere. The equatorial easterly bias is signi®cantlyreduced and the stratospheric winds are slowed down. Inthe troposphere an impact is seen on the monsoon,where the precipitation anomalies are reduced and shiftsouthwards compared to the climatology.

The consequences of increasing the vertical resolu-tion on the mean climate are generally weak, with apoleward drift of the stratospheric jet in the winterhemisphere for July, due to an orographic gravity-wavedrag decrease (as shown by Dreveton et al., 1993). ForJanuary, the high variability in the northern hemisphere(due to planetary waves) has no signi®cant impact.However, a warming at the top of the model occurs inboth experiments. Improvements are found on theprecipitation, when the vertical resolution is increased,at the equator and in the mid-latitudes.

Although the length of the integrations is 60 days, theaverage of the ®ve experiments limits the dependence onthe initial conditions and the interannual variability.These features are quite stable, as can be checked by thet-tests. It is to be noted that in spite of the doubling theresolution in the troposphere, the mean features do notchange much, maybe because of the readjustment ofclouds performed in order to obtain the same globalradiative forcings at the top of the atmosphere. It is alsoan indication that the physical parameterizations usedare resolution independent, at least in the range 10±20levels in the troposphere. An experiment was performed

Fig. 10a±c. Zonal average of zonal wind in m sÿ1 for January for a GWD31, b GWDS41 and c GWDT41; contour interval 10 m sÿ1

Fig. 11a, b. Zonal mean precipitation (mm dayÿ1) for a July andb January GWD31 (thin solid ), GWDT41 (dashed ), GWDS41(dotted ) and climatology (thick solid )


with 21 levels, chosen such that 7 levels are in thetroposphere and 14 in the stratosphere. Some degrada-tions were observed in the dynamics and in theprecipitation (in particular the tropical precipitation).

Despite the fact that the resolution increase is notfollowed by important model improvements, the use ofthe 41-level distribution with a ®ner troposphericresolution is planned in the next versions of theARPEGE-Climat GCM. The parameterizations whichwe are presently using have been developed during the1980s within GCMs using about 10 vertical levels in thetroposphere. The present study shows that the param-eterizations used are robust to vertical discretizationwithout arti®cial equilibrium or compensating errors.The present generation of atmospheric models use ahigher vertical and horizontal resolutions, and newparameterizations are developed starting from realisticrepresentation of the troposphere. We intend to developparameterizations with better representations of somekey physical process. A cloud prognostic scheme willreplace the present scheme and a more physically baseddi�usion scheme that takes into account the turbulentkinetic energy budget will be implemented.

Appendix

The vertical level distribution is controlled by aprogressive variation, with level number k, of functionsAk�1=2 and Bk�1=2, which determine the pressure pk�1=2 ofthe half model levels (these functions are analytical ineach interval). This method allows any distribution ofthe L levels.

The pressure at the layer interface is calculated by:

pk�1=2 � Ak�1=2 � Bk�1=2ps ; �6�where ps is the surface pressure and with the boundaryconditions, at the model top A0 � 0, B0 � 0 and at thesurface AL � 0, BL � 1.

Level pressure pk (where the main model variables arede®ned) is given by:

pk � 0:5�pk�1=2 � pkÿ1=2� : �7�Any choice of Ak�1=2 and Bk�1=2 which ensures theincrease with k of pk can be used.

The analytical functions A�g� and B�g� depend onadjustable parameters which control the vertical leveldistribution. The limit between the sigma coordinateand the pressure coordinate is chosen at p0, for thepressure coordinate g0 � k=L, then B is de®ned by:

B�g� � 0; g � g0 ;

B�g� � r0�gÿ g0�2�gÿ g2��g1 ÿ g0�2�g1 ÿ g2�

; g0 � g � g1 ;

B�g� � 1ÿ �1ÿ r0� 1ÿ g1ÿ g1

� �; g1 � g � 1 ;

�8�

where r0 determines the lowest layer thickness (betweenthe earth's surface and the last level) with a pressure r0(0.99) times the surface pressure, and the last level

pressure coordinate g1 � �Lÿ 1�=L; g2 ensures the Bderivative continuity in g1.

A is de®ned by:

A�g� � p0exp a�gÿ g0� � b1

gÿ 1

g0

� �� ; g � g0 ;

A�g� � p0�gÿ g1�2�gÿ g3��g0 ÿ g1�2�g0 ÿ g3�

; g0 � g � g1 ;

A�g� � 0; g1 � g � 1 ;

�9�

where a and b control the vertical level distribution inthe stratosphere such that A�1=L� � pa and A�l=2L� � pb(pa and pb are given pressures); g3 is chosen to ensure theA derivative continuity in g0.

Acknowledgements. The authors are grateful to their colleaguesfrom MeÂ teÂ o-France and to all the people who contributed to thedevelopment of ARPEGE/IFS model, and in particular to J. F.Geleyn. Thanks are also due to J. P. Piedelievre for providing theinitial situation of the integrations and to Dr. P. J. Gleckler and toB. Murphy for their help in reading the manuscript. The Europeancommission (contract HIRETYCS ENV4 CT95 0184), thePNEDC (French National Program for the Study of ClimateDynamics) and the higher education and research o�ce (contract94-3-1414) partly supported this study.

The Editor-in-chief thanks two referees for their help inevaluating this paper.

References

Bougeault, P., A simple parameterization of the large-scale e�ectsof deep cumulus convection, Mon. Weather Rev., 113,2108±2121, 1985.

Boville, B. A., Sensitivity of simulated climate to model resolution,J. Clim., 4, 469±485, 1991.

Boville, B. A., and X. Cheng, Upper boundary e�ects in a generalcirculation model, J. Atmos. Sci., 45, 2591±2606, 1988.

Boville, B. A., and Randel W. J., Observations and simulation ofthe variability of the stratosphere and troposphere in January,J. Atmos. Sci., 43, 3015±3034, 1986.

Boyle, J. S., Sensitivity of dynamical quantities to horizontalresolution for a climate simulation using the ECMWF (Cycle33) model. J. Clim., 6, 796±815, 1993.

Clark, T. L., T. Hauf, and J. P. Kuettner, Convectively forcedinternal gravity waves: results from two-dimensional numericalexperiments, Q. J. R. Meteorol. Soc., 112, 899±925, 1986.

DeÂ queÂ , M., C. Dreveton, A. Braun, D. Cariolle, The ARPEGE/IFSatmosphere model: a contribution to the French communityclimate modelling, Clim. Dyn., 10, 249±266, 1994.

Dreveton C., M. DeÂ queÂ , and J. F. Geleyn, Interactions of physicalparameterizations in the climate version of the ARPEGE/IFSmodel, Beitr. Phys. Atmos., 66, 283±303, 1993.

Fovell, R., D. Durran, and J. R. Holton, Numerical simulations ofconvectively generated stratospheric gravity waves, J. Atmos.Sci., 49, 1427±1442, 1992.

Fritts, D. C., Research status and recommendations from theAlaska workshop in gravity waves and turbulence in themiddle atmosphere, Bull. Am. Meteorol. Soc., 65, 149±159,1984.

Hauf, T., and Clark, T. L., Three-dimensional numerical experi-ments on convectively forced internal gravity waves, Q. J. R.Meteorol. Soc., 115, 309±333, 1989.

Hayashi, Y., D. G. Golder, J. D. Malhman, and S. Miyahara, Thee�ect of horizontal resolution on gravity waves simulated by theGFDL SKYHI general circulation model, P. A. Geophys., 130,421±443, 1989.


Houghton, D. D., R. A. Petersen, and R. L.Wobus, Spatial resolutionimpacts on National Meteorological Center Nested Grid ModelSimulations, Mon. Weather Rev., 121, 1450±1466, 1992.

James, D. G., Observations from aircraft of temperatures andhumidities near stratocumulus clouds, Q. J. R. Meteorol. Soc.,85, 120±130, 1959.

Kershaw, R., Parameterization of momentum transport by con-vectively generated gravity waves, Q. J. R. Meteorol. Soc., 121,1023±1040, 1995.

Kiehl, J. T., and D. L. Williamson,Dependence of cloud amount onhorizontal resolution in the National Center for AtmosphericResearch community climate model, J. Geophys. Res., 96,10955±10980, 1991.

Kuettner, J. P., P. A. Hildebrand, and T. L. Clark, Convectionwaves: observations of gravity wave systems over convectivelyactive boundary layers, Q. J. R. Meteorol. Soc., 113, 443±467,1987.

Legates, D. R., and C. J. Willmott, Mean seasonal and spatialvariability in gauge-corrected global precipitation, Int. J. Clim.,10, 111±127, 1990.

Lindzen, R. S., Turbulence and stress owing to gravity wave andtidal breakdown, J. Geophys. Res., 86, 9707±9714, 1981.

Lindzen, R. S., and M. Fox-Rabinovitz, Consistent vertical andhorizontal resolution, Mon. Weather Rev., 117, 2575±2583,1989.

McFarlane, N. A., The e�ect of orographically excited gravity wavedrag on the general circulation of the lower stratosphere andtroposphere, J. Atmos. Sci., 44, 1775±1800, 1987.

Mesinger, F., T. L. Black, D. W. Plummer, and J. H. Ward, Etamodel precipitation forecasts for a period including TropicalStorm Allison, Weather Forecasting, 5, 483±493, 1990.

Morcrette, J. J., Radiation and cloud radiative properties in theEuropean Center for Medium Range Weather Forecasts fore-casting system, J. Geophys. Res., 96, 9121±9132, 1991.

Noilhan, J., and Planton S., A simple parameterization of landsurface processes for meteorological models, Mon. WeatherRev., 117, 536±549, 1989.

Palmer, T. N., G. J. Shutts, and R. Swinbank, Alleviation of asystematic westerly bias in general circulation and numericalweather prediction models through an orographic gravitywave drag parameterization, Q. J. Roy Meteorol. Soc., 112,1001±1039, 1986.

P®ster, L., S. Scott, and M. Loewenstein,Mesoscale disturbances inthe tropical stratosphere excited by convection: observationsand e�ects on the stratospheric momentum budget, J. Atmos.Sci., 50, 1058±1075, 1993.

Simmons, A. J., and D. M. Burridge, An energy and angular-momentum conserving vertical ®nite-di�erence scheme andhybride vertical coordinates, Mon. Weather Rev., 109, 758±766,1981.

Tiedtke, M., The e�ect of penetrative cumulus convection on thelarge-scale ¯ow in a general circulation model, Beitr. Phys.Atmos., 57, 216±239, 1984.

Warner, T. T., and N. L. Seaman, A real-time, mesoscale numericalweather prediction system used for research, teaching, andpublic service at the Pennsylvania State University, Bull. Am.Meteorol. Soc., 71, 792Ð805, 1990.

Williamson, D. L., The e�ect of vertical ®nite di�erence approx-imations on simulations with the NCAR Community ClimateModel, J. Clim., 1, 40±58, 1988.


impact of a simple parameterization of convective gravity ... · they also described a second...

Documents