39
Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian Middle Atmosphère Mode! S.R. Beagley 1 , J. de Grandpré 1 , IN. Koshyk 2 , N.A. McFarlane 3 and T.G. Shepherd 2 1 Department ofEarth and Atmospheric Science, York University 2 Department of Physics, University of Toronto 3 CCCma, Atmospheric Environment Service, Victoria [Original manuscript received 4 September 1996; in révisée form 15 April 19971 ABSTRACT The Canadian Middle Atmosphère Modelling (MAM) project is a collaboration between thé Atmospheric Environment Service (AES) of Environment Canada and several Canadian universities. Its goal is thé development of a comprehensive General Circulation Model of thé troposphere-stratosphere-mesosphere System, starting from thé AES/CCCma third-génération atmospheric General Circulation Model. This paper describes thé basic features of thé first-generation Canadian MAM and some aspects ofits radiative-dynamical climatology. Standard first-order mean diagnostics are presentedfor monthly means and for thé annual cycle ofzonal-mean winds and températures. The mean méridional circulation is examined, and comparison is made between thé steady diabatic, downward controlled, and residual streamfunctions. It isfound thaï downward contrat holds quite well in thé monthly mean through most of thé middle atmosphère, even during equinoctal periods. The relative rôles of différent drag processes in determining thé mean downwelling over thé wintertime polar middle stratosphère is examined, and thé vertical structure of thé drag is quantified. RÉSUMÉ Le projet canadien de Modélisation de l'Atmosphère Moyenne (MAM) est une collaboration entre le Service de l'Environnement Atmosphérique (SEA) d'Environnement Canada et certaines universités canadiennes. Le but est de développer un modèle de circu- lation générale pour le domaine troposphère-stratosphère-mésosphère à partir du modèle canadien de circulation générale (SEA/CCCtna) de troisième génération. Cet article décrit les caractéristiques de base du MAM canadien de première génération et quelques aspects de sa climatologie radiative et dynamique. Les diagnostics standards du premier ordre sont présentés pour les moyennes mensuelles et le cycle annuel des vents zonaux moyens et des températures. La circulation méridionale moyenne du modèle est examinée et comparée avec la circulation diabolique stationnaire, résiduelle, et celle établie à partir des principes du contrôle vers le bas (downward control). Pour les moyennes mensuelles, la circulation du contrôle vers le bas correspond assez bien aux résultats du modèle dans l'ensemble de l'atmosphère moyenne et ce, même durant les êquinoxes. Le rôle relatif des différents ATMOSPHERE-OCEAN 35 (3) 1997, 293-331 0705-5900/97/0000-0293$ 1.25/0 © Canadian Meteorological and Océanographie Society

Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

  • Upload
    others

  • View
    3

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

Radiative-Dynamical Ciimatoiogy of théFirst-Generation Canadian Middle Atmosphère

Mode!

S.R. Beagley1, J. de Grandpré1, IN. Koshyk2, N.A. McFarlane3 andT.G. Shepherd2

1 Department ofEarth and Atmospheric Science, York University2Department of Physics, University of Toronto

3CCCma, Atmospheric Environment Service, Victoria

[Original manuscript received 4 September 1996; in révisée form 15 April 19971

ABSTRACT The Canadian Middle Atmosphère Modelling (MAM) project is a collaborationbetween thé Atmospheric Environment Service (AES) of Environment Canada and severalCanadian universities. Its goal is thé development of a comprehensive General CirculationModel of thé troposphere-stratosphere-mesosphere System, starting from thé AES/CCCmathird-génération atmospheric General Circulation Model. This paper describes thé basicfeatures of thé first-generation Canadian MAM and some aspects ofits radiative-dynamicalclimatology. Standard first-order mean diagnostics are presentedfor monthly means and forthé annual cycle ofzonal-mean winds and températures. The mean méridional circulation isexamined, and comparison is made between thé steady diabatic, downward controlled, andresidual streamfunctions. It isfound thaï downward contrat holds quite well in thé monthlymean through most of thé middle atmosphère, even during equinoctal periods. The relativerôles of différent drag processes in determining thé mean downwelling over thé wintertimepolar middle stratosphère is examined, and thé vertical structure of thé drag is quantified.

RÉSUMÉ Le projet canadien de Modélisation de l'Atmosphère Moyenne (MAM) est unecollaboration entre le Service de l'Environnement Atmosphérique (SEA) d'EnvironnementCanada et certaines universités canadiennes. Le but est de développer un modèle de circu-lation générale pour le domaine troposphère-stratosphère-mésosphère à partir du modèlecanadien de circulation générale (SEA/CCCtna) de troisième génération. Cet article décritles caractéristiques de base du MAM canadien de première génération et quelques aspectsde sa climatologie radiative et dynamique. Les diagnostics standards du premier ordre sontprésentés pour les moyennes mensuelles et le cycle annuel des vents zonaux moyens et destempératures. La circulation méridionale moyenne du modèle est examinée et comparéeavec la circulation diabolique stationnaire, résiduelle, et celle établie à partir des principesdu contrôle vers le bas (downward control). Pour les moyennes mensuelles, la circulationdu contrôle vers le bas correspond assez bien aux résultats du modèle dans l'ensemblede l'atmosphère moyenne et ce, même durant les êquinoxes. Le rôle relatif des différents

ATMOSPHERE-OCEAN 35 (3) 1997, 293-331 0705-5900/97/0000-0293$ 1.25/0© Canadian Meteorological and Océanographie Society

Page 2: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

294 / S.R. Beagley et al.

mécanismes de résistance qui déterminent la subsidence au cours de l'hiver dans les régionspolaire, est examiné et la structure verticale de ces processus est quantifiée.

1 IntroductionOur ability to understand any component of thé environment is ultimately testedby our ability to model its behaviour mathematically from first principles. Onlyby developing crédible models can we make informed prédictions of thé changesin our environment that will resuit from external perturbations such as anthro-pogenic influences. Thèse two statements summarize thé rationale behind thé de-velopment of comprehensive three-dimensional atmospheric General CirculationModels (GCMs).

GCMs hâve been under development at many différent research centres aroundthé world for several décades. They provide a critical component of our currentunderstanding of possible global change due to increased levels of greenhousegases (IPCC, 1995). Most GCMs do not extend up beyond thé lower stratosphère,or hâve strongly degraded stratospheric resolution. This is for thé simple reason thattheir focus is on thé troposphère, and their users wish to invest their computationalresources in other ways (e.g., longer simulations, higher resolution, coupling toan océan model). Until about ten years ago, thé only significant exception to thisraie was thé Geophysical Fluid Dynamics Laboratory's (GFDL) "SKYHI" GCM(Mahlman and Umscheid, 1984), which extended up to an altitude of 80 km with auniforni 2 km vertical resolution, and which therefore resolved thé stratosphère and(lower) mésosphère. Most GCMs also do not include a prognostic représentationof chemical constituents.

In thé last décade, however, there has been increasing interest in thé stratosphèreand mésosphère (which together constitute thé so-called middle atmosphère). Oneof thé principal drivers for this interest has been thé observed depletion of théozone layer, which has been most notable in polar régions but has also occurredin midlatitudes (WMO, 1995), The impact on thé ozone layer of émissions fromproposed high-altitude subsonic and supersonic civil aircraft is a further cause forconcern (NASA, 1995). In addition, it has recently become clear that greenhouse-gas induced surface warming is coupled to stratospheric ozone variations (IPCC,1995). In order to perform climate impact assessment studies that bear on anyof thèse issues, one clearly requires a model that can represent ozone and otherchemically active constituents in thé middle atmosphère. Until recently, however,thé only models available for this purpose hâve been two-dimensional (zonallyaveraged) models. While instructive, such models are ultimately limited by theirneed to parametrize ail eddy processes.

For thèse reasons, among many others, there has been considérable effort investedin récent years toward thé development of comprehensive GCMs that include théentire troposphere-stratosphere-mesosphere System and that contain a prognosticreprésentation of chemical constituents. In most cases, groups began with an ex-

Page 3: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 295

isting tropospheric GCM, and made the necessary modifications to enable it to sim-ulate the stratosphere and mesosphere. Not only is this strategy technically efficient,it also offers the advantage of beginning with a known tropospheric climate. Sincethe more massive troposphere provides the major dynamical driving of the strato-sphere and mesosphere, a good tropospheric simulation is evidently a prerequisitefor a good middle atmospheric simulation.

As noted above, a principal motivation behind the development of three-dimensional middle atmosphere GCMs is the simulation of chemical climate. Itis clear that the middle atmosphere is a region where dynamics, chemistry andradiation play equal roles, and interact strongly with each other (e.g., Pels, 1985;Andrews et al., 1987; Mahlman et al., 1994). Nevertheless, most three-dimensionalmodelling groups have begun by using specified (seasonally varying) chemicalfields, in order to try to develop a reasonable simulation of the radiative-dynamicalclimate before introducing the feedbacks that would arise from fully interactivechemistry. Given the extremely long (several year) overturning timescale for long-lived chemical constituents in the middle atmosphere, a simulation with fully inter-active chemistry would presumably take decades to equilibrate. (No group has yetmanaged to reach this stage.) In contrast, a "non-interactive" strategy allows one toobtain some information on the radiative-dynamical climate of the model after onlya few years of integration. Simulation of the chemical fields can then be performedessentially off-line, using the results of the radiative-dynamical calculation.

Within Canada, an effort to develop a comprehensive GCM of the troposphere-stratosphere-mesosphere system began in early 1993, starting from the third-generation GCM of the Canadian Centre for Climate Modelling and Analysis(CCCma). The scientific rationale behind this Canadian Middle Atmosphere Mod-elling (MAM) project, and a description of its structure and goals, is provided inShepherd (1995). The present paper provides the model description and some basicaspects of the radiative-dynamical climatology of the first-generation CanadianMiddle Atmosphere Model (CMAM). A description of the associated stratosphericchemical module and results from non-interactive simulation of stratosphericchemistry using the CMAM will be reported separately (de Grandpre et al.,1997).

Simulation of the radiative-dynamical climate of the middle atmosphere requiresan accurate representation of three main physical processes: (i) radiation; (ii) merid-ional circulation, including symmetric (inertial) overturning in the tropics; and (iii)dynamical forcing from the troposphere. An accurate representation of the firsttwo processes should be possible from first principles. (The radiation is normallyparametrized, but can be validated against accurate line-by-line calculations.) Thedynamical forcing, however, is another matter. Drag exerted by breaking and dissi-pating planetary waves is a major driver of the stratospheric Brewer-Dobson circu-lation, and this process should be explicitly resolvable. Large-scale tropical wavesshould also be resolvable, though may be sensitive to the nature of tropical convec-tion and thus somewhat dependent on the convective parametrization scheme being

Page 4: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

296 / S.R. Beagley et al.

used. The main problem arises with gravity waves, whose drag largely comes fromwaves having spatial scales well below the resolution currently available in a globalmodel. Although direct observational evidence does not exist to make a definitivestatement on this matter, indirect evidence strongly suggests that gravity-wave drag(GWD) is critical to driving the solstitial pole-to-pole mean meridional diabaticcirculation in the mesosphere (e.g., Andrews et al., 1987). GWD is also felt to beimportant to tropical zonal-wind oscillations, as well as in certain regions of theextratropical stratosphere. (There are also significant nonlinear feedbacks betweenGWD and planetary-wave drag (McLandress and McFarlane, 1993; Boville, 1995.)

Whatever GWD cannot be resolved must evidently be parametrized. However,the parametrization of GWD is an extremely challenging problem, because of thepaucity of direct observational or theoretical/modelling constraints. On the otherhand, resolving the GWD appears to be hopeless with current computational tech-nology. Both the GFDL (Hamilton et al., 1995) and National Center for Atmo-spheric Research (NCAR) (Boville, 1995) middle atmosphere models have beenrun at high (100-200 km) horizontal resolution, in order to see whether the explicitrepresentation of more gravity-wave activity can correct the strong cold, westerlybias that exists in the southern hemisphere polar night jet. (This bias is widely at-tributed to missing GWD.) Although some improvement does occur in comparisonto lower resolution simulations, a strong bias remains. Moreover, Hamilton (1993)has found that the resolved GWD falls off less steeply than k^ with horizontalwavenumber k, suggesting that no convergence is in sight.

Therefore the only option is to proceed with GWD parametrization. Parametriza-tion of orographic GWD (McFarlane, 1987) is now a standard feature of generalcirculation (and numerical weather prediction) models. Although some questionsremain concerning its implementation, orographic GWD is regarded as being rela-tively better understood than non-orographic GWD. However, it is clear that non-orographic gravity-wave sources, with generally non-zero phase speeds, are also im-portant. Their effect is expected to be greatest, relatively speaking, in the southernhemisphere (because of the lack of much topography in middle latitudes), and inthe lower thermosphere and summertime mesosphere (because of the existence ofzero-wind lines below those regions). Thus the Canadian MAM project is currentlyexamining GWD parametrization schemes that can represent non-orographic waves,including the schemes of Hines (1997) and Medvedev and Klaassen (1995). Sincethese schemes are expected to have a significant impact on the middle atmospherecirculation in the model, it seems appropriate to establish a benchmark climatologyagainst which their effects can be compared.

This, then, is the rationale behind the first-generation CM AM. The model in-cludes a state-of-the-art tropospheric climate (inherited from the CCCma third-generation GCM), and a state-of-the-art middle atmosphere longwave radiationcode (Fomichev and Blanchet, 1995). Its circulation is not intended to be the closestpossible approximation to the observed circulation. Rather, the model is meant toembody the current radiative-dynamical understanding of the middle atmosphere of

administrator
Page 5: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 297

which we have fairly high confidence. In this respect, the climatology of the first-generation CMAM is directly comparable to the recently published climatologies ofthe middle atmosphere GCMs from GFDL (Hamilton et al, 1995), NCAR (Boville,1995) and the Max Planck Institute for Meteorology (MPI) (Manzini and Bengtsson,1996), which likewise do not include a parametrization of non-orographic GWD.(These models do, however, differ in whether or not they include a parametrizationof orographic GWD.) A distinctive feature of the CMAM is that it extends to 0.001mb (approximately 95 km), higher than that which is typical of middle atmosphereGCMs. This means that the spurious effects of our upper sponge layer should haveless impact than in other models with diffusive or Rayleigh-drag sponge layers atlower altitudes (cf. Shepherd et al., 1996).

The plan of the paper is as follows. Section 2 contains a description of themodel, of the specification of our three-year simulation, and of the observationaldatasets that are used for comparison. A three-year simulation is clearly much tooshort to allow a quantitative analysis of interannual variability. Nevertheless, it islong enough to determine the major strengths and weaknesses of the model, andto provide a reference point for future improvements. Section 3 presents standardmonthly mean fields for the four cardinal months January, April, July and October.The annual cycle of the model, as it manifests itself in several fields, is exam-ined in Section 4. Various diagnostics of the mean meridional circulation are pre-sented in Section 5, and the paper concludes with a summary and discussion inSection 6.

2 Model description and observational datasetsThe CMAM is an upward extension of the CCCma third-generation atmosphericGCM. This latter model is itself still under development, and its detailed descriptionwill be published at a later date. The following discussion summarizes the mainfeatures of the CMAM version of the model. This version shares many features withthe Canadian Climate Centre's (CCC) second-generation model (GCMII) describedin McFarlane et al. (1992). The basic numerical formulation is essentially the sameas that used in GCMII. In particular, the spectral transform method is used torepresent the horizontal spatial structure of the main prognostic variables, whilethe vertical representation is in terms of rectangular finite elements defined for ahybrid vertical coordinate r| as described by Laprise and Girard (1990). The actualdefinition of the ambient pressure on coordinate surfaces is p = pof\+(ps —/>o)[Cn —rjr)/(l — r|7-)]3/2, where r\T = PT/PO with pT and p0 being specified constants,in this case pr = 0.0006 mb and p$ = 1013 mb, and ps is the (instantaneous)surface pressure. This definition is slightly different from that proposed by Lapriseand Girard (1990) and used in GCMII, in that the quadratic dependence on thecoordinate value is replaced by a three-halves power. This choice was made toensure a monotonic variation of pressure as a function of the vertical coordinateover high terrain.

The spectral representation currently used in the CMAM is the same as that

Page 6: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

298 / S.R. Beagley et al.

in GCMII: namely a 32-wave triangularly truncated (T32) spherical harmonic ex-pansion with an associated quadratic Gaussian transform grid of 96 x 48 points,uniformly spaced in longitude and nearly so in latitude, giving a grid spacing ofapproximately 3.75°. Following standard practice this grid is used to evaluate con-tributions of nonlinear (advective) terms to the tendencies of the main prognosticvariables, and transform them into the spectral domain. In GCMII this grid is alsoused to evaluate contributions from parametrized physical processes. However, inthe CMAM these are evaluated on the linear (64 x 32) Gaussian transform gridhaving a grid spacing of approximately 5.625°. This procedure, though requiring anadditional transform to evaluate the corresponding contributions in the spectral do-main, produces a net saving of computational resources because of the substantialreduction in the number of points at which computationally intensive algorithms,such as those used to evaluate contributions due to radiative heating and latent heatrelease, are used. Results of test simulations show that use of the linear grid forthese computations does not incur significant loss of accuracy or adverse effectsdue to aliasing arising from nonlinearity in the parametrization of the physicalprocesses.

The vertical domain of the CMAM, which includes all of the region betweenthe surface and 0.0006 nib (PT), approximately 100 km, is spanned by 50 layers ofunequal thickness. The model prognostic fields are carried on levels placed at themidpoints of the layers, with the top level being at 0.001 mb (approximately 95 km).Throughout the upper stratosphere and the mesosphere the layers are approximatelyequally spaced in In (p) giving an approximate layer depth of 3 km. The verticalresolution in the troposphere is finer than in GCMII, and the spacing of the levelsis uniform in r\ between level 30 (T| = 0.175) and level 41 (T| = 0.725). Below thislevel the layer depths decrease monotonically toward the surface, with the lowestlevel being at t| = 0.995, approximately 50 m above the surface at sea level.

There are some parametrized physical processes that are new to GCMII andhence to CMAM. These include the introduction of the Canadian Land SurfaceScheme (CLASS), a new module for treatment of the land surface processes(Verseghy et al., 1993). This new land surface scheme is considerably more com-prehensive than the simple single soil layer scheme used in GCMII. In particular,the new scheme includes three soil layers, a snow layer where applicable, and avegetative canopy treatment. Both liquid and frozen forms of soil moisture arecarried as prognostic variables. Soil surface properties, such as surface rough-ness heights for heat and momentum (which differ from each other in general)and surface albedos, are taken to be functions of the primary and secondarysoil and vegetation types and the soil moisture conditions within a given gridvolume.

Surface exchanges of heat, moisture and momentum are represented usingstability-dependent bulk transfer coefficients. Although similar in form to thoseused in GCMII, these have been modified over land, as discussed in Verseghy etal. (1993). The treatment of turbulent transfer within the planetary boundary layer is

administrator
Page 7: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 299

as in GCMII, except that an additional direct non-local mixing of heat and moistureis carried out in circumstances where the buoyancy flux at the surface is upward. Inthose cases it is assumed that the boundary layer will tend to become well mixed,on a timescale of one hour, to a depth determined such that the virtual potentialtemperature of the mixed layer does not exceed that of the layer directly above it.In practice this mixed layer is always comprised of the lowest model layer and anintegral number of adjacent layers, rarely more than one or two.

In GCMII, latent heat release due to cumulus convection is parametrized usinga soft convective adjustment scheme while that due to stratiform clouds is treatedusing a large-scale condensation algorithm (McFarlane et al., 1992). In the CMAMthe moist convective adjustment algorithm has been replaced by the cumulusparametrization of Zhang and McFarlane (1995). This parametrization is a bulkmass-flux scheme that includes a representation of convective-scale updrafts anddowndrafts, and is designed to account for the effects of penetrative convection ina manner that is more physically sound than is the moist convective adjustmentscheme.

Solar radiative heating in the CMAM is treated using the scheme of Fouquartand Bonnel (1980) as in GCMII. The treatment of terrestrial radiation makes use ofa combination of the Morcrette (1991) scheme and the scheme of Fomichev et al.(1993). These schemes are designed to have acceptable accuracy in different regionsin the vertical, with the Morcrette scheme being reliable in the lower stratosphereand the troposphere. The new CMAM combined scheme is discussed in detail byFomichev and Blanchet (1995).

Gravity-wave drag is an important component of the wave driving in the middleatmosphere. The parametrization of the drag due to breaking of orographicallyexcited gravity waves is parametrized, as in GCMII, following McFarlane (1987).This scheme does not deal with gravity waves that may arise from a variety of othersources, including moist convection, the development of dynamical instabilitiesin regions of strong wind shear, geostrophic adjustment, and frontal zones. Inparticular, it completely misses the effect of gravity waves with non-zero phasespeeds. Within the past decade a considerable body of published observationalwork lends support to the idea that there is a nearly universal spectrum of verticallypropagating gravity waves throughout the middle atmosphere. As discussed in theIntroduction, we feel that it is useful to determine a reference climatology of theCMAM before introducing further gravity-wave parametrizations to deal with thisspectrum. However, a simple Rayleigh-drag sponge layer is employed in the currentversion of the CMAM, which switches on smoothly above 0.01 mb such that thedamping time constant becomes 0.5 days at the top of the model. In additionto absorbing upward-propagating (resolved) waves — and thereby preventing theoccurrence of significant downward reflection at the upper boundary — the spongelayer might be regarded as a (very) crude representation of gravity-wave drag inthe mesopause region.

A significant difference between the second- and third-generation GCMs is in

Page 8: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

300 / S.R. Beagley et al.

their treatment of water vapour transport. While the spectral transport algorithm isretained as in the earlier generation models, the quantity that is transported is thehybrid moisture variable proposed by Boer (1995). This variable S, which is usedin the spectral domain, is related to specific humidity q according to

c 1 r t / ^ q<qn mS = < 1 + ln(go/<?) (1)I q q*31 qo

where, in the CMAM, qo is given the fixed value of 10 g/kg. As noted by Boer(1995), use of this variable alleviates, to a considerable extent, the undesirableeffects that accompany the development of unphysical negative values from spectraltransport of specific humidity, and the ad hoc procedures that must be used to fillsuch "holes" while maintaining appropriate conservation constraints.

A semi-Lagrangian transport algorithm for use in the CMAM has been developedand is currently being tested. This algorithm will be used for transport of watervapour and other trace species in a later version of the model.

Since the current version of the CMAM does not have an active chemical sourceof water vapour, moisture (in terms of the hybrid variable S) is not evaluatedprognostically above the 30 mb level. For the purpose of evaluating radiative heatingin this region of the model domain, the water vapour content is specified as afunction of the local potential temperature using an empirical relationship derivedfrom observational data. Ultimately the model's chemically and physically evolvedwater vapour will be used throughout the CMAM to replace this simple empiricalfit.

The model simulation presented in this paper is initialized from FGGE-IIIb (FirstGARP Global Experiment) data for 12z 2 January. Since these data extend onlyto 10 mb, initial values of temperature and winds above this level are set equalto those at the 10 mb level. The initial four months of the run are discarded anddata archived every 18 hours for a three-year run beginning OOz 1 May. Many ofthe surface fields are saved as running time averages to avoid sampling problems(see McFarlane et al., 1992). Monthly mean climatological sea surface temperatures(SSTs) are prescribed from Shea et al. (1990), which is based on a climatologyspanning the period 1950-1979.

There do not exist comprehensive observational datasets covering the full domainof the CMAM, and it is therefore necessary to use a variety of data sources forvalidation purposes. For zonal mean zonal wind and temperature through the depthof the atmosphere (Figs 2 and 4) we use the COSPAR International ReferenceAtmosphere (CIRA) dataset (Fleming et al., 1990), which is a combination ofOort's data in the troposphere (1963-73), Nimbus 5 Selective Chopper Radiometermeasurements in the stratosphere (1973-74), and Nimbus 6 Pressure ModulatorRadiometer measurements in the mesosphere (1975-78). It provides monthly andzonal mean temperatures, together with zonal winds obtained from gradient windbalance. Although limited in a number of respects, the CIRA dataset has become a

administrator
Page 9: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 301

standard point of comparison for middle atmosphere models because of its uniquevertical extent. For all other middle atmospheric fields we use the recent UnitedKingdom Meteorological Office (UKMO) dataset (Swinbank and O'Neill, 1994),which although limited in vertical extent is far more comprehensive than is CIRA.It provides objectively analyzed three-dimensional fields of wind, temperature andgeopotential up to 0.3 mb for the three-year period January 1993 to December1995 inclusive. Both the CIRA and UKMO datasets are limited by the shortnessof the records on which they are based. For surface fields, therefore, we havechosen to use standard tropospheric datasets based on long-term records: 10 years oftwice-daily National Centers for Environmental Prediction (NCEP) analyses for themean sea level pressure (Fig. 8), and Jaeger's (1976) climatology for precipitation(Fig. 9).

3 Monthly mean fieldsIn this section, monthly mean model fields over the three-year run for the fourcardinal months January, April, July and October are presented for some basicquantities, together with corresponding observed fields.

We begin with a basic characterization of the middle atmosphere. In all fig-ures, except where otherwise noted, the model fields are only shown belowthe sponge layer. The vertical axes are labelled in terms of both pressure and(effective) height, the latter being calculated using a fixed density scale height of7 km. Figure 1 shows the zonal mean temperature from the model. Basic featuresto be noted are: a well-defined tropopause (where the lapse rate changes drasti-cally); a local temperature minimum in the tropics at about 16 km (the elevatedtropical tropopause); a temperature maximum in the vertical around 50 km (thestratopause); a local temperature maximum at the summertime polar stratopause; aseparated wintertime polar stratopause; a local temperature minimum in the win-tertime polar middle stratosphere; and a reversal of the pole-to-pole meridionaltemperature gradient, during solstice seasons, between the stratosphere and meso-sphere. All these features correspond qualitatively to observations.

Difference fields between the model and the CIRA climatology are shown in Fig.2. The most striking model biases are found in polar regions, although there is alsoa general warm bias of around 5K in the lower mesosphere, as well as a general coldbias of around 5K in the upper mesosphere. In the polar regions, the wintertimepolar stratopause is much too cold, most particularly in the southern hemisphere(July). This southern pole cold bias persists into austral spring (October), with itsmaximum descending into the middle stratosphere. Precisely the same behaviouris seen in the GFDL "SKYHI" model (Hamilton, 1995).

Figure 3 shows the zonal mean zonal wind from the model. To a very goodapproximation, the zonal mean zonal wind is in gradient wind balance with thezonal mean temperature, so the features seen in this figure are closely related tofeatures seen in Fig. 1. The most notable basic features are the westerly wintertimeand easterly summertime jets in the mesosphere. The CIRA climatology is shown in

Page 10: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

302 / S.R. Beagley et al.

Fig. 1 Zonally averaged temperature lield calculated from a 3-year run with the CMAM. Contourinterval = 10K.

Fig. 4. (There is no need for difference fields in this case!) The agreement betweenthe model and the observations can be said to be at best qualitative, though itshould be noted that since the zonal wind is roughly the vertical integral of thetemperature gradient, it tends to magnify the biases seen in the temperature. Thesouthern hemisphere cold bias in wintertime polar temperatures translates into anenormous westerly bias, with maximum zonal winds in the polar vortex reaching180 m/s in July — more than a factor of two stronger than observations. Thiswesterly bias is also present in both equinoctal seasons. Although the magnitudes

administrator
Page 11: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 303

Fig. 2 The difference between the field in Fig. 1 and the zonally averaged temperature field obtainedfrom the CIRA climatology. Contour interval = 5K.

of the northern hemisphere winds are rather better, the wintertime jet is too farpoleward.

The fact that the southern hemisphere zonal mean fields exhibit such a cold, west-erly bias is common to all middle atmosphere general circulation models that — likethe first-generation CMAM — do not include a parametrization of non-orographicGWD (e.g., Boville, 1995; Hamilton et al., 1995; Manzini and Bengtsson, 1996).In the northern hemisphere, the influence of planetary-wave drag together with oro-graphic GWD is largely determinative of stratospheric temperatures. In the southernhemisphere, in contrast, the relative absence of planetary waves and orographic

Page 12: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

304 / S.R. Beagley et al.

Fig. 3 Zonally averaged zonal wind field calculated from a 3-year run with the CMAM. Contourinterval = 10 m/s.

GWD (because of the relative absence of large-scale zonal inhomogeneities in thesurface conditions at middle and high latitudes) means that any non-orographicGWD that might be present has much greater relative importance (Garcia andBoville, 1994). The current belief is that the cold, westerly bias seen in modelslike the CMAM is due to an inadequate representation of non-orographic GWD.

We now turn to a basic characterization of some tropospheric circulation features.Since the middle atmosphere is driven significantly by the drag exerted by plane-tary waves emanating from the troposphere, a prerequisite for a reasonable middleatmosphere climate is the representation of a reasonable tropospheric climate —

administrator
Page 13: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 305

100090N 60N 30N 0 303 60S 90S 90N 60N 30N 0 308 60S 90S

Latitude Latitude

Fig. 4 Zonally averaged zonal wind lield calculated from the CIRA climatology. Contour interval10 m/s.

particularly as it pertains to planetary-scale zonal inhomogeneities. Figure 5 showsthe zonal wind at 200 mb from the model, and Fig. 6 the corresponding field fromthe UKMO observations. Overall the agreement is quite good, although the modelappears to have more longitudinal structure in the tropics than do the observations.Figure 1 shows the mean sea level pressure from the model, and Fig. 8 the corre-sponding field from the NCEP observations. As with the 200-mb zonal wind, themodel fields are quite good overall; in particular the subtropical highs are apparent(in fact they are generally too strong), as well as the strong midlatitude gradient inthe southern hemisphere. It is worth remarking that the discrepancies noted above

Page 14: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

180W 0 180E 180W 0 180E

Fig. 5 Zonal wind field at 200 mb calculated from the CMAM. Contour interval = 10 m/s. Regions where the wind speed exceeds 30 m/s are shaded.

Page 15: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

Fig. 6 Zonal wind field at 200 mb obtained from UKMO assimilated data for the 3-year period 1993-1995. Contour interval = 10 m/s. Regions where the windspeed exceeds 30 m/s are shaded.

Page 16: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

Fig. 7 Mean sea level pressure (mslp) as calculated from the CMAM. Contour interval = 5 mb. Regions where the mslp is less than 980 mb are heavily shadedand regions where the mslp is greater than 1020 mb are lightly shaded.

administrator
Page 17: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

Fig. 8 Mean sea level pressure (mslp) obtained from twice-daily NCEP anaylses over a 10-year period. Contour interval = 5 mb. Regions where the mslp is lessthan 980 mb are heavily shaded and regions where the mslp is greater than 1020 mb are lightly shaded.

Page 18: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

310 / S.R. Beagley et al.

are also apparent in simulations with the third-generation tropospheric GCM, bothat its usual T48 resolution as well as at T63. The apparent weakness of the JanuaryAzores high, and the associated overly zonal upper tropospheric jet structure overthe North Atlantic, stand in contrast to this pattern. Since there is considerable in-terannual variability in these particular circulation features, we cannot say whetherthese apparent model errors are robust features of the model climatology. The finaltropospheric feature to be considered is the zonally averaged precipitation, whichis shown in Fig. 9 for both the model and Jaeger's (1976) climatology. Apart froma moist bias in the model in northern hemisphere midlatitudes, the agreement isfairly good.

4 Annual cycleIn this section, we examine the annual cycle of the model as it manifests itself inseveral middle atmosphere fields.

We begin with the mean annual march of temperature averaged over the tropicaland extratropical lower stratosphere, shown in Fig. 10 for both the model and theUKMO observations. As noted by Yulaeva et al. (1994), there is a pronouncedannual cycle, with almost complete cancellation between tropical and extratropicalvariations. (By taking the boundary between the regions at 30°, the two regions haveequal mass.) This cancellation suggests that the temperature variations are associ-ated with the annual cycle in the mean meridional (diabatic) circulation. In fact, thetropical lower stratosphere is always cooled below radiative equilibrium, consistentwith the upwelling branch of the Brewer-Dobson circulation, and what one is seeingis a modulation of this process, with more cooling occurring in northern hemispherewinter than in southern hemisphere winter. Yulaeva et al. (1994) attribute this tothe fact that wintertime planetary-wave drag is stronger in the northern than inthe southern hemisphere. Some support for this claim is provided by the study ofRosenlof (1995), although the way in which extratropical drag reaches into the deeptropics remains an open question. Interestingly, the difference between model andobservations also exhibits this near cancellation between tropical and extratropicalvariations, suggesting that the model bias is associated with an insufficiently strongBrewer-Dobson circulation through most of the year. This bias is particularly largein austral spring (September through November), leading to a several-month delayin the timing of the temperature extreme during this half of the year.

The mean annual march of middle stratosphere (10 mb) zonal mean temperature,as a function of latitude, is shown in Fig. 11 for both model and observations. Thefield is evidently dominated by the midlatitude and polar variations. Summertimemodel temperatures are quite reasonable in both hemispheres. Northern hemispherewintertime temperatures are fairly realistic, although they are too warm in the fall:the northern hemisphere polar night vortex does not form rapidly enough. As forthe southern hemisphere, wintertime model temperatures are clearly much too cold,and the vortex breaks up much too late. This delayed vortex break-up is presumablyrelated to the fact that the extratropical lower stratospheric temperatures continue

Page 19: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 311

January April

Fig. 9 Zonally averaged precipitation obtained from CMAM (solid) and from Jaeger's (1976) clima-tology (dashed).

to cool into austral spring, rather than reaching their minimum in late austral winter(Fig. 10). Individual time-series of 10-mb temperatures over the North Pole (NP)and South Pole (SP), for the three model years, are shown in Fig. 12 (centredin mid-winter), and those for the UKMO observations are shown in Fig. 13. Themodel realistically exhibits multiple sudden warmings over the wintertime NP, andthe absence of any sudden warmings over the wintertime SP. The model warmingsappear to begin earlier in the winter than in the observations, but it must be bornein mind that the run is only three years long. A run of this duration is far frombeing long enough to perform any kind of systematic study of sudden warmings.

Page 20: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

312 / S.R. Beagley et al.

Fig. 10 Climatological mean annual march of temperature averaged over the layer between 30 and150 mb. Solid lines are derived from a 3-ycar CMAM climatology and dashed lines fromUKMO data for the period January 1993 - December 1995. The lower curves correspond toaverages over the tropics (30°S—30°N) and the upper curves to averages over the extratropics(poleward of 30°S and 30°N).

On the other hand, the warmings that do occur appear to have realistic physicalcharacteristics.

The mean annual march of subpolar (60° latitude) zonal mean zonal wind, asa function of height, is shown in Fig. 14 for the model, and in Fig. 15 for theUKMO observations. For 60°S, about all that can be said is that the model fieldis qualitatively correct, being westerly for about the right fraction of the year,and exhibiting the descent of the westerly wind maximum with time from latewinter (August) through the austral spring. For 60°N, the model correctly exhibitsa shorter westerly regime compared with the southern hemisphere, and no descent ofthe westerly wind maximum. Instead, it correctly reveals intermittent decelerationsassociated with occasional sudden warmings.

Figure 16 shows the time-series of zonal mean zonal wind at the equator, as afunction of height, for the three-year CMAM integration, together with a rocket-sonde climatology. A semiannual oscillation (SAO) is clearly evident in the CMAMat the stratopause, extending (backward in time) into the middle mesosphere. Thisis in general accord with the observations (see also Hirota, 1980), although themodel's westerly phase is too weak and does not descend far enough. This defi-ciency is a common feature of other MAMs (e.g., Hamilton and Mahlman, 1988;Sassi et al., 1993; Jackson and Gray, 1994). The current understanding of thestratopause SAO (e.g., Andrews et al., 1987) is that it is driven by a semiannualmodulation of the (easterly) planetary-wave drag extending non-linearly into the

administrator
Page 21: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 313

10 mb temperature (Model)

Fig. 11 Mean annual march of zonally averaged temperature at 10 mb from a 3-year CMAM clima-tology and from UKMO assimilated data for the 3-year period 1993-1995. Contour interval= 5K.

tropics, acting against a relatively uniform (westerly) drag from equatorial Kelvinwaves. The CMAM, like most MAMs, appears (based on preliminary analysis) tocontain equatorial Kelvin waves, in addition to planetary waves, although we havenot performed sufficient analysis to deduce that this mechanism is, in fact, what isdriving our stratopause SAO. On the other hand, there is not much evidence of themesopause SAO in the model. The mesopause SAO is attributed to GWD (e.g.,Andrews et al., 1987), presumably non-orographic, so it is not surprising that itwould fail to appear in the CMAM. In any case the mesopause SAO would haveto occur largely within the model sponge layer.

Page 22: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

314 / S.R. Beagley et al.

NP Temperature at 10 mb (Model)

J F M A M J J A S O N D

Fig. 12 March of temperature along the 10 mb level at the poles, from a 3-year CMAM climatology.Different curves indicate the different years in the integration.

5 Meridional circulationThe mean meridional circulation provides the link between diabatic (principallyradiative) heating and dynamical forcing. In this section, the mean meridional cir-culation of the CMAM is examined within the framework of the TransformedEulerian Mean (TEM) system of equations (e.g., Andrews et al., 1987). Withinthis framework, the zonal momentum, continuity, and thermodynamic equationsare written

administrator
Page 23: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 315

NP Temperature at 10 mb (Obs.)

SP Temperature at 10 mb (Obs.)

J F M A M J J A S O N D

Fig. 13 As Fig. 12 but from UKMO data for the period 1993-1995.

du(2a)

(2b)

(2c)

Page 24: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

316 / S.R. Beagley et al.

Zonally averaged zonal wind at 60S (Model)

Fig. 14 Mean annual march of zonally averaged z.onal wind at 60°S and 60°N from a 3-year CM AMclimatology. Contour interval = 10 m/s.

where z is a log-pressure vertical coordinate and the residual velocities (z>*,w*)are defined by

The overbar is used to denote a zonal mean, while deviations from the zonal meanare denoted by a prime. When evaluated using model data, the Eliassen-Palm (EP)flux divergence V'F/(p0a cos ()>) represents the resolved adiabatic eddy forcing of thezonal mean zonal flow (based on 18-hour sampling of the eddies), while X includes

administrator
Page 25: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 317

Zonally averaged zonal wind at 60S (Obs.)

.010

Zonally averaged zonal wind at 60N (Obs.)

1000J F M A M J J A S O N D

Fig. 15 As Fig. 14 but from UKMO data for the period January 1993 - December 1995.

all other forcing elements in the model (including numerical dissipation). Thus Xmight be regarded as representing the parametrized sub-grid scale or unresolvedforcing. The term Q is the total diabatic heating, and all other symbols have theirusual meaning. The continuity equation (2b) allows the introduction of a massstreamfunction *F according to

(4a,b)

In the case of model data, one can of course compute v * and w*, and hence*¥, directly from their definition. In the case of atmospheric observations, however,reliable direct measurements of the components of v * and w* are not available.

Page 26: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

318 / S.R. Beagley et al.

Fig. 16 a) March of z.onally averaged zonal wind at the equator from a 3-year CMAM integration.A semi-annual oscillation is clearly evident above 1mb. b) As in a) but a composite basedon several years of rocketsonde observations at Kwajalein (8.7°N, 167.7°E), reproduced fromHamilton and Mahlman (1988). Shaded regions in b) correspond to regions with solid contoursin a), i.e., to westerlies. Contour interval = 10 m/s in both panels.

Instead, various approximate methods have been used in the past to infer the residualcirculation. It is therefore of interest to use the CMAM data to examine the accuracyof those approximations relative to the direct calculation of *F.

The direct calculation of XP, denoted *¥dir, consists of calculating v* from (3a),and then integrating (4a) downward from the model lid assuming *P vanishes there.The results from CMAM are shown in Fig. 17 for ensemble mean January, April,July and October. (Note that different contour intervals are used in the troposphere,stratosphere and mesosphere, so that the streamfunction is visible in each region.)

administrator
Page 27: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 319

Fig. 17 Ensemble mean residual streamfunction ¥,/,> from a 3-year CMAM integration, calculatedfrom the expression for v *. Contour interval = 500 kg/m/s between 1000 mb and 100 mb; 25kg/m/s between 100 mb and 1 mb; 2 kg/m/s above 1 mb.

Positive contours represent a circulation in the counterclockwise sense. The modelcorrectly reproduces the persistent two-cell Brewer-Dobson circulation in the strato-sphere, with the winter hemisphere cell being stronger than the summer hemispherecell during solstitial seasons. It is evident that the total tropical upwelling in themodel is greater in January than in July, which is consistent with the hypothesisof Yulaeva et al. (1994) concerning the annual cycle of tropical lower stratospheretemperatures shown in Fig. 10. The model also correctly reproduces the single-cellwinter-to-summer-pole meridional circulation in the mesosphere.

Page 28: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

320 / S.R. Beagley et al.

An indirect way of estimating 4/, which presumes steady-state conditions, isto neglect the first and last terms in (2c), and then solve for *F from knowledgeof Q using the iterative method introduced by Murgatroyd and Singleton (1961).The method consists of computing w* from (2c), assuming initially that v * — 0,and then calculating v * from (2b). A new estimate of w* is then obtained from(2c), and the process repeated until it converges. A constraint on the calculation isprovided by the horizontally integrated mass continuity equation (2b), which statesthat the net vertical mass flux across a pressure surface must vanish. In this paper,the vertical residual velocity is corrected by a fixed amount at each latitude and ateach iteration in order to satisfy this constraint. (This correction method is clearlynot unique. Shine (1989) discusses the sensitivity of the estimated circulation todifferent correction methods.) The steady diabatic streamfunction obtained in thisway, denoted *PJ£/, is shown in Fig. 18. Evidently *¥slt is quite similar in character to^¥(iir. There is reasonable quantitative agreement in January, but there are significantquantitative differences in the other months shown. In the equinoctal months, someof these differences are attributable to the steady-state assumption used to derive^Pjrf, as has been verified by repeating the calculation for *?.«; but with the transientterm 30/8? included. (The final term of (2c) was found to be extremely small,except in the very lowest part of the northern hemisphere mid-latitude stratosphere.)However, it appears that the mass-flux correction procedure itself introduces errorsin the estimate of *P. The most notable such errors in this case are a factor of twooverestimate of the strength of the mesospheric circulation in April, anomalousmesospheric upwelling north of 40°N in July, and a factor of two underestimate ofthe downwelling in the summertime polar lower stratosphere in July.

The mean diabatic heating field Q that was used to determine *¥sd is shown inFig. 19, weighted by (7"/0) to give a diabatic temperature tendency. This quantityrepresents the sum of solar heating, infrared cooling, horizontal and vertical diffu-sion, and the heat generated by mechanical drag processes. The dominant featuresinclude cooling in the wintertime mesosphere and warming in the summertimemesosphere, with the cooling largely confined to the polar regions. This pattern is,of course, consistent with the mesospheric residual circulation seen in Fig. 17.

Another indirect way of estimating *P, which also presumes steady-state condi-tions, is to neglect the first term in (2a), and then solve for *F by combining (2a)with (2b). This yields the downward control streamfunction, ^V* defined by

(5)

(Haynes et al., 1991), where m is the zonally averaged absolute angular momentumand f = V'F/(pofl cos <|))+X is the total forcing on the zonal mean zonal flow. Theresults from CMAM are shown in Fig. 20 (with the upper limit of integration in (5)replaced by the height of the model lid). Since (5) fails in regions where surfacesof constant angular momentum do not span the vertical domain of the model, thoseareas (which cover most of the tropics) have been heavily shaded. It is evident that

administrator
Page 29: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 321

90N 60N SON 0 30S 60S 90S 90N 60N SON 0 SOS 60S 90S

Latitude Latitude

Fig. 18 Ensemble mean steady diabatic residual streamfunction *FS^ from a 3-year CMAM integration.Contour intervals as in Fig. 17.

*¥dc agrees very well with *?</„., especially for solstitial seasons. This confirms thatthe downward control calculation is inherently much better conditioned than is thediabatic heating calculation.

One implication of the above results is that a quantitative comparison between theCMAM residual circulation and observations is problematical. Direct observationalestimates can be obtained of the diabatic heating Q, and there have been a numberof calculations of ^¥sd (or of its transient counterpart, when the temperature tendencyterm is also included) from observations (e.g., Solomon et al., 1986; Shine, 1989;Rosenlof, 1995). Unfortunately, this kind of calculation invariably requires the

Page 30: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

322 / S.R. Beagley et al.

Diabatic 3T/3t (K/day) - Jan. Diabatic 3T/3t (K/day) - Apr.0.01... • . v -=—i i ^_ - i r^—<; ^z—^ v^ ̂ .,.,|B1

100090N 60N 30N 0 30S 60S 90S 90N 60N SON 0 30S 60S 90S

Latitude Latitude

Fig. 19 Ensemble mean diabatic temperature tendency Held, (f/Q)Q from a 3-year CMAM integration.Contour interval = 1 K/day.

use of a mass-flux correction, whether explicitly or implicitly, which renders theresults somewhat uncertain; even when using model data, the results are seen tobe contaminated by the mass-flux correction. In contrast, the downward controlcalculation is robust; unfortunately, however, direct observational estimates of yare not available.

The components of the zonal force 7 used to determine *¥dc are shown inFigs 21 and 22 for January and July, respectively. Negative contours denote aneasterly (or westward) force, which represents a drag for a westerly flow. (Notethat the domain of these plots includes the model sponge.) With the exception of

administrator
Page 31: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 323

100090N 60N SON 0 303 60S 90S 90N 60N SON 0 SOS 60S 90S

Latitude Latitude

Fig. 20 Ensemble mean residual streamfunction *Pjc from a 3-year CMAM integration, calculated viathe method of downward control. Shading in each panel indicates regions where surfaces ofconstant angular momentum, m, do not span the vertical and values of 4V cannot be defined.Contour intervals as in Fig. 17.

the diffusive terms (which are fairly small), the forces are drag-like everywhere,i.e., westerly where the flow is easterly, and easterly where the flow is westerly.There is significant "resolved" drag V'F/(p0acost))) in both hemispheres, includinga positive-negative dipole in the southern hemisphere mesospheric polar night jetwhich may be indicative of mixed barotropic-baroclinic instability. The region ofpositive V'F/(po« cos <))) below the sponge layer in the summertime upper meso-sphere may be indicative of the two-day wave, as discussed by Norton and Thuburn

Page 32: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

324 / S.R. Beagley et al.

V-F/(p0a cos?)) Orographic GWD

Fig. 21 January ensemble mean resolved zonal forcing VF/(pQfl cos <j>) and components of unresolvedzonal forcing (orographic gravity-wave drag, sponge drag and horizontal + vertical diffusion)from a 3-ycar CMAM integration. Contour interval = 5 m/s/day.

(1996). The orographic gravity-wave drag, which is part of the "unresolved" forcingX, provides a significant negative drag in the winter hemisphere over certain latitudebands.

The fairly close agreement between 4V and ¥</,> in the extratropical middleatmosphere suggests that the downward control arguments of Haynes et al. (1991)are relevant to the CMAM behaviour in this region of the model. The downwardcontrol formula (5) can therefore be used to estimate the effect of the differentcomponents of J on the vertical mass flux at a given model level. A particularly

administrator
Page 33: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 325

90N 60N 30N 0 308 60S 90S 90N 60N SON 0 303 60S 90S

Latitude Latitude

Fig. 22 As Fig. 21 but for July and with contour interval = 10 m/s/day.

interesting region to examine is the wintertime polar stratosphere: an accurate de-termination of the vertical mass flux in this region is critical for middle atmospheremodels, in part because it strongly affects the wintertime polar stratospheric tem-peratures upon which ozone-depleting chemistry relies. The total vertical mass fluxpoleward of latitude fa at a height zo is given by

for the SP

for the NP.(6)

Page 34: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

326 / S.R. Beagley et al,

Using (4), and assuming that *P vanishes at the poles, (6) leads to

•W (4>o, 3>) = ±2na*P(<J>o5 zo), (7)

where the plus sign is taken for the SP and the minus sign for the NP. We nowassume *P fc* ¥rfc and combine (5) with (7) in order to estimate the fraction of'W that is controlled by drag processes between heights ZQ and z > ZQ, following

(9)

administrator
Page 35: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 327

January (60N-90N).001

dwm

ft£<u

OTW(Dt-,

.01

.2 .4 .6 .8 1.0Fraction of vertical mass flux

July (60S-90S).001

.01

.2 .4 .6 .8Fraction of vertical mass flux

1.0

Fraction of the CMAM total vertical mass flux at 10 mb controlled by drag processes actingbetween 10 mb and the values along the ordinate. Separate curves indicate the flux controlledby all drag components together (solid), by the EP flux divergence alone (dashed), and byparametrized orographic gravity-wave drag alone (dash-starred). Other drag processes providenegligible contributions to the flux at 10 mb. The upper panel represents the average verticalflux over the latitude band 60°N-90°N for model January, and the lower panel the averageover the 60°S-90°S band for model July.

Page 36: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

328 / S.R. Beagley et al.

of the first-generation Canadian Middle Atmosphere Model. This version of themodel contains a state-of-the-art tropospheric climate (inherited from the CCCmathird-generation GCM from which it was developed) and a state-of-the-art middleatmosphere longwave radiation code (Fomichev and Blanchet, 1995), and it has itshighest model level at 0.001 mb (approximately 95 km), substantially higher thanthat which is typical of middle atmosphere GCMs. The philosophy behind such amodel configuration was to provide a reference run to serve as a point of comparisonfor future model improvements. The goal was not to obtain the closest possibleimitation of the observed circulation, but rather to determine the consequence ofcertain fundamental model ingredients. It is well known that middle atmospheremodel results can be "improved" by the inclusion of Rayleigh drag or enhanceddiffusion. (For example, a prototype version of the CMAM with an ad hoc excessivevelocity drag — some results from which were presented in Shepherd (1995) — hadin many respects a better-looking climate than the present version.) Such devicesmay be necessary in the short term, but they must be regarded as "training wheels",to be removed when the rest of the model is able to stand on its own. Our experiencehas been that relaxational drag processes, in particular, interact strongly with othermodel components (Shepherd et al., 1996). Their presence therefore complicates theprocess of model improvement, and casts doubt on climate sensitivity experiments.

Our climatology has been obtained from a three-year simulation. This is shortby most standards, and certainly precludes a quantitative analysis of interannualvariability. Nevertheless, it is long enough to reveal the model's major strengthsand weaknesses with regard to its mean climate.

Monthly mean fields from CMAM have been presented in Section 3 for thefour cardinal months January, April, July and October. The model captures thebasic features of the middle atmosphere temperature distribution (Figs 1 and 2),although there is a general warm bias in the lower mesosphere and a general coldbias in the upper mesosphere. There is also a serious cold bias in the wintertimepolar stratosphere, most particularly in the southern hemisphere (July). This feature,known as the "cold pole" problem, is common to all middle atmosphere modelswithout parametrized non-orographic GWD (e.g., Boville, 1995; Hamilton et al.,1995; Manzini and Bengtsson, 1996).

The annual cycle of the CMAM has been examined in Section 4. Tropical lowerstratospheric temperatures follow an annual cycle that is qualitatively like obser-vations (Fig. 10), although there is a cold bias in austral spring. A correspondingwarm bias in the extra-tropics suggest that this bias is due to an insufficientlystrong Brewer-Dobson circulation in the model during this part of the year. Theannual cycle of northern hemisphere polar stratospheric temperatures is fairly re-alistic (Fig. 11), with reasonable sudden warming behaviour (Figs 12 and 13). Thesouthern hemisphere, in contrast, has a wintertime cold bias and a delayed vortexbreakdown (Figs 11-13). The CMAM tropical zonal wind exhibits a stratopausesemiannual oscillation (Fig. 16), although its westerly phase is too weak and doesnot descend far enough.

administrator
Page 37: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 329

The mean meridional circulation of the CMAM has been examined in Section5 within the framework of the TEM equations. The residual circulation (Fig. 17)exhibits the expected features in the stratosphere and mesosphere. An attempt toreconstruct the residual circulation directly from the diabatic heating was only par-tially successful (Fig. 18), raising doubts about the reliability of such calculations.In contrast, the downward control estimate of the residual circulation worked quitewell, at least outside tropical regions (Fig. 20). This motivated further investigationof the impact of the various zonal momentum forcing (or drag) mechanisms in theCMAM. Mid-stratospheric downwelling over the wintertime pole was examined indetail (Fig. 23), since this process is closely linked to wintertime stratospheric polartemperatures. In the northern hemisphere, the downwelling poleward of 60°N wasfound to depend strongly on both resolved EP flux divergence and parametrizedorographic GWD; in the southern hemisphere, in contrast, the GWD played a minorrole. In both cases, there was a significant effect from drag located well above thelevel of interest; this was particularly true in the southern hemisphere, where 50%of the downwelling could be attributed to drag exerted more than two scale heightsabove the level of interest.

The model biases in the current version of the CMAM are serious enough thatobtaining a reasonable simulation of the chemical climate would seem unlikely.This is particularly the case for heterogeneous chemistry, which has an extremelystrong temperature dependence. The problem is most acute in the polar night,where heterogeneous reactions are critical for ozone-hole chemistry, yet wherethe model temperature bias is most severe. Clearly a prerequisite for compre-hensive chemical climate modelling in the middle atmosphere is to cure this"cold pole" problem. Significant improvement to the CMAM climate in this re-spect is expected to come from the parametrization of a full spectrum of GWD.However, this GWD is believed to occur principally in the upper mesosphere, muchof which is close to or within our present sponge layer. The results of Shepherdet al. (1996) show that a fixed drag force imposed within a sponge layer is nearlycompletely absorbed by the sponge, thereby largely nullifying its expected impacton temperatures below (Garcia and Boville, 1994). This suggests that testing meso-spheric GWD schemes with the present CMAM configuration is of questionablevalue. (The problem can only be worse for models with lower lids.) Thus our fu-ture plans include raising the model lid even higher, and modifying the treatmentof the sponge. This should also begin to allow a simulation of large-scale neutralphenomena in the upper mesosphere/lower thermosphere region, including thermaltides.

AcknowledgementsThe Canadian MAM project has been supported by a Strategic Grant from theNatural Sciences and Engineering Research Council of Canada, which was com-plemented by direct support of the MAM Core Group from the Atmospheric En-vironment Service, as well as by additional support provided through the AES's

Page 38: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

330 / S.R. Beagley et al.

Climate Research Network. The authors are grateful to the reviewers for theirthoughtful and constructive suggestions.

References

ANDREWS, D.G.; J.R. HOLTON and C.D. LEOVY. 1987.

Middle Atmosphere Dynamics. Academic Press.489 pp.

BOER, G.J. 1995. A hydrid moisture variable suit-able for spectral GCMs. In: Research Activitiesin Atmospheric and Oceanic Modelling. ReportNo. 21, WMO/TD-No. 665, World Meteorolog-ical Organization, Geneva, pp. 4.1-4.2.

BOVILLE, B.A. 1995. Middle atmosphere version ofCCM2 (MACCM2): annual cycle and interan-nual variability. J. Geophys. Res. 100: 9017-9039.

DE GRANDPRE, J.; J.W. SANDILANDS, J.C. McCONNELL,

S.R. BEAGLEY, P.C. CROTEAU and M.Y. DANILIN.

1997. Canadian Middle Atmosphere Model:Preliminary results from the chemical transportmodule. ATMOSPHERE-OCEAN, 35: in press.

PELS, s. 1985. Radiative-dynamical interactions inthe middle atmosphere. Adv. Geophys. 28A:277-300.

FLEMING, E.L.; S. CHANDRA, J.J. BARNETT and M.

CORNEY. 1990. Zonal mean temperature, pres-sure, zonal wind and geopotential height asfunctions of latitude. Adv. Space Res. 10(12):11-59.

FOMiniEV, v.i. and J.P. BLANCIIET. 1995. Develop-ment of the new CCC/GCM longwave radiationmodel for extension into the middle atmosphere.ATMOSPHERE-OCEAN, 33: 513-529.

; A.A. KUTEPOV, R.A. AKMAEV and Ci.M. SHVED.

1993. Parameterization of the 15 Jim CO2 bandcooling in the middle atmosphere (15-115 km)./. Atmos. Terr. Phys. 47: 1037-1049.

FOUQIIART, Y. and B.BONNEL. 1980. Computation ofsolar heating of the earth's atmosphere: a newparameterization. Beitr. Phys. Atmos. 53: 35-62.

GARCIA, R.R. and B.A. BOVILLE. 1994. "Downwardcontrol" of the mean meridional circulationand temperature distribution of the polar winterstratosphere. J. Atmos. Sci. 51: 2238-2245.

HAMILTON, K. 1993. What can we learn from gen-eral circulation models about the spectrum ofmiddle atmosphere motions? In: Coupling Pro-cesses in the Lower and Middle Atmosphere,

E. Thrane et al. (Eds), Kluwcr Academic, Dor-drecht, The Netherlands, pp. 161-174.

-. 1995. Comprehensive simulation of themiddle atmosphere climate: some recent results.Cllm. Dyn. 11: 223-241.

and J.D. MAIILMAN. 1988. General Circu-lation Model simulation of the semiannual os-cillation of the tropical middle atmosphere. J.Atmos. Sci. 45: 3212-3235.

; RJ. WILSON, J.D. MAHLMAN and L..I.

liMSCHEiD. 1995. Climatology of the SKYHITropospherc-Stratosphere-Mesosphere GeneralCirculation Model. /. Atmos. Sci. 52: 5-43.

IIAYNES, P.M.; CJ. MARKS. M.E. McINTYRE, T.O. SHEP-HERD and K.P. SHINE. 1991. On the "downwardcontrol" of extratropical diabatic circulations byeddy-induced mean zonal forces. /. Atmos. Sci.48: 651-678.

IIINES, c.o. 1997. Dopplcr-spread parameterizationof gravity-wave momentum deposition in themiddle atmosphere. Part I: Basic formulation.J. Atmos. Sol-Terr. Phys. 59: 371-386.

IIIROTA, I. 1980. Observational evidence of thesemiannual oscillation in the tropical middleatmosphere — a review. Pure Appl. Geophys.118: 217-238.

IPC'C (Intergovernmental Panel on Climate Change).1995. Climate Change, Radiative Forcing ofClimate Change, and an Evaluation of theIPCC IS92 Emission Scenarios, J.T. Houghtonet al. (Eds), Cambridge University Press,572 pp.

JACKSON, D.R. and L..I. GRAY. 1994. Simulation of thesemi-annual oscillation of the equatorial middleatmosphere using the Extended UGAMP Gen-eral Circulation Model. Q. J. R. Meteorol. Soc.120: 1559-1588.

JAEGER, L. 1976. Monatskartcn des Nicderschlagsfur die ganz Erde. Ber. Deusch. Wetterdienstes.139: 1-38.

LAPRISE, R. and c. GIRARD. 1990. A spectral generalcirculation model using a piecewisc-constant f i -nite element representation on a hybrid verticalcoordinate system. J. dim. 3: 32-52.

MAIILMAN, J.D. and L..I. UMSCHEID. 1984. Dynamics

administrator
Page 39: Radiative-Dynamical Ciimatoiogy of thé First-Generation Canadian …atmosp.physics.utoronto.ca/~tgs/Beagley1997.pdf · 2008-06-10 · Radiative-Dynamical Ciimatoiogy of thé First-Generation

The First-Generation Canadian Middle Atmosphere Model / 331

of the middle atmosphere: successes and prob-lems of the GFDL "SKYHI" general circulationmodel. In: Dynamics of the Middle Atmosphere,J.R. Holton and T. Matsumo (Eds), Terrapuh,Tokyo, Japan, pp. 501-525.

; J.P. PINTO and L.J. UMSCHEID. 1994. Trans-

mean meridional circulation in the stratosphere.J. Geophys. Res. 100: 5173-5191.

and J.R. HOLTON. 1993. Estimates of the

port, radiative, and dynamical effects of theAntarctic ozone hole: a GFDL "SKYHI" modelexperiment. /. Atmos. Sci. 51: 489-508.

MANZINI, E. and L. BENGTSSON. 1996. Stratosphericclimate and variability from a general circula-tion model and observations. Clim. Dyn. 12:615-639.

MCFARLANE, N.A. 1987. The effect of orographicallyexcited gravity wave drag on the general circu-lation of the lower stratosphere and troposphere./. Atmos. Sci. 44: 1775-1800.

; Ci.J. BOER, J.-P. BLANCHE! and M. LAZARE.

1992. The Canadian Climate Centre second-generation atmospheric general circulationmodel and its equilibrium climate. J. Clim. 5:1013-1044.

MCLANDRESS, c. and N.A. MCFARLANE. 1993. Inter-actions between orographic gravity wave dragand forced stationary planetary waves in thewinter northern hemisphere middle atmosphere.J. Atmos. Sci. 50: 1966-1990.

MEDVEDEV, A.S. and G.P. KLAASSEN. 1995. Verticalevolution of gravity wave spectra and the pa-rameterization of associated wave drag. J. Geo-phys. Res. 100: 25,841-25,853.

MORCRETTE, i.-j. 1991. Radiation and cloud ra-diative properties in the ECMWF operationalweather forecast model. J. Geophys. Res. 96:9121-9132.

MURGATROYD, RJ. and F. SINGLETON. 1961. Possiblemeridional circulations in the stratosphere andmesosphere. Q. J. R. Meteorol. Soc. 87: 125-135.

NASA. 1995. 1995 Scientific Assessment of theAtmospheric Effects of Stratospheric Aircraft.National Aeronautics and Space AdministrationReference Publication 1381, 64 pp.

NORTON, W.A. and j. THUBURN. 1996. The two-daywave in a middle atmosphere GCM. Geophys.Res. Lett. 23: 2113-2116.

ROSENLOF, K.H. 1995. Seasonal cycle of the residual

stratospheric residual circulation using thedownward control principle. J. Geophys. Res.98: 10,465-10,479.

SASSI, F.; R.R. GARCIA and B.A. BOVILLE. 1993. The

stratopause semiannual oscillation in the NCARCommunity Climate Model. J. Atmos. Sci. 50:3608-3624.

SHEA, D.J.; K.E. TRENBERTII and R.W. REYNOLDS. 1990.

A global monthly sea surface temperature cli-matology. NCAR Technical Note NCAR/TN-345+STR, 167 pp.

SHEPHERD, T.G. 1995. The Canadian MAM project.CMOS BULLETIN, 23(1): 3-10.

; K. SEMENIUK and J.N. KOSHYK. 1996.

Sponge-layer feedbacks in middle-atmospheremodels. /. Geophys. Res. 101: 23,447-23,464.

SHINE, K. 1989. Sources and sinks of zonal mo-mentum in the middle atmosphere diagnosedusing the diahatic circulation. Q. J. R. Mete-orol. Soc. 115: 265-292.

SOLOMON, S.; J.T. KIEIIL. R.R. GARCIA and W. GROSE.

1986. Tracer transport by the diabatic circu-lation deduced from satellite observations. J.Atmos. Sci. 43: 1603-1617.

SWINBANK, R. and A. O'NEILL. 1994. A stratosphere-troposphere data assimilation system. Man.Weather Rev. 122: 686-702.

VERSEGHY, D.L.; N.A. McFARLANE and M. LAZARE.

1993. A Canadian Land Surface Scheme forGCMs: II. Vegetation model and coupled runs.Int. J. Climatol. 13: 347-370.

WMO. 1995. Scientific Assessment of Ozone De-pletion: 1994. Report No. 37, World Meteo-rological Organization Global Ozone Researchand Monitoring Project, 451 pp.

YULAEVA, E.; J.R. HOLTON and J.M. WALLACE. 1994.

On the cause of the annual cycle in tropicallower stratospheric temperatures. J. Atmos. Sci.51: 169-174.

ZHANG, G.J. and N.A. MCFARLANE. 1995. Sensitivityof climate simulations to the parameterizationof cumulus convection in the CCC-GCM.ATMOSPHERE-OCEAN, 33: 407-446.