February 1989 T. Iwasaki, S. Yamada and K. Tada 29. A Parameterization Scheme of Orographic Gravity Wave Drag

February 1989 T. Iwasaki, S. Yamada and K. Tada 29 A Parameterization Scheme of Orographic Gravity Wave Drag with Two Different Vertical Partitionings Part II: Zonally Averaged Budget Analyses Based on Transformed Eulerian Mean Method By Toshiki Iwasakil National Center for Atmospheric Research 2 Boulder, * 80307 Shinichi Yamada and Kazumasa Tada Japan Meteorological Agency, Ote-machi, Chiyoda-ku, Tokyo 100, Japan (Manuscript received,27 April 1988, in revised form 15 October 1988 Abstract The effects of orographic gravity wave drag (GWD) on zonal-mean fields of medium-range forecasts are analyzed by means of the transformed Eulerian-mean (TEM) method. Results show that the geostrophic adjustment to GWD behaves very differently between the stratosphere and troposphere. In the troposphere, both the tropospheric and stratospheric GWDs significantly change Eliassen- Palm (EP) flux divergence due to large-scale (model-resolvable) waves. The change in the EP flux divergence is much larger than the net change of tonal wind and GWDs themselves and it is almost balanced with the change in the Coriolis acceleration term due to meridional flows. Among wave activities, transient gravity waves resolved in the model are considered to play important roles in the vertical redistribution of additional wave moments due to GWD. In the stratosphere, the stratospheric GWD induces a hemispheric single cell meridional circulation. The vertical motions in this cell cause significant temperature changes. The Coriolis acceleration due to GWD-induced meridional flows is almost balanced with the GWD itself. In contrast with the troposphere, EP flux divergence is less affected by GWD. From the view of Lagrangian-mean meridional circulation, diabatic heating in the tropics and wave, mean-flow interaction due to planetary-scale waves have been recognized mainly to drive a hemispheric single cell circulation (the so-called Brewer-Dobson circulation) in the lower-stratosphere. Our results indicate that the stratospheric GWD contributes to the maintenance of the single cell circulation as well. Especially in the midlatitudes of the northern hemisphere, the GWD can be regarded as an important forcing and considerably enhances lower-stratospheric downward motions in the polar side of the subtropical jet stream. It might affect significantly the transport of trace constituents in the stratosphere. 1. Introduction In Part I by Iwasaki el al. (1989), the effects of orographic gravity wave drag (GWD) are parameterized in two ways by considering non-hydrostatic effects. The type A scheme for long waves (wavelength * 100km) distributes the drag forcing 1 Visiting Scientist at NCAR on leave from the Japan Me - teorological Agancy 2 The National Center for Atmospheric Research is sponsored by the National Science Foundation. 1989, Meteorological Society C of Japan mainly to the stratosphere and the type B scheme for short waves (*10km) mainly to the lower troposphere. A combination of these two schemes was clearly shown to reduce tonally averaged forecast errors of excessive westerlies both in the troposphere and stratosphere. The reduction in forecast errors suggests that the model without the GWD schemes underestimates the tropospheric and stratospheric dissipation of angular momentum. It is noted that the effects of GWD do not stay around the forced area but rapidly extend both in the vertical and horizontal. The following points in

30 Journal of the Meteorological Society of Japan Vol. 67, No. 1 Part I are of great interest: Most of the drag forcing given to the lower stratosphere (type A) and to the lower troposphere (type B) are rapidly redistributed throughout the troposphere and reduce tropospheric westerlies north of 40*N. Both schemes strengthen tropospheric westerlies south of 40*N, even when the zonal component of GWD is negative. The type A scheme significantly changes the lower-stratospheric temperature while the type B hardly does. These findings indicate that the drag forcings are expected to change zonal-mean fields considerably through the modification of mean-meridional circulations and wave activities. In this paper, we examine the response of zonal-mean fields by using the results of forecast experiments with and without GWD. Particular attempts are made to compare the responses to type A and B schemes with each other. Since GWD schemes significantly influence tonal means of not only tonal wind but also temperature, consistent analysis of the angular momentum transport and heat transport is desired. The representation based on the Lagrangian-mean meridional circulation is more suitable to reform the budget analysis than the representation based on the Eulerian-mean. Because periodic waves without drift motions, which never cause net heat and momentum transports, produce Eulerian-mean flows (see for example, Matsuno, 1980), we use the transformed Eulerian-mean (TEM) method which approximates the Lagrangian-mean circulation (Andrews and McIntyre, 1976). In the TEM, the tendency of the zonal wind is reasonably separated into the Coriolis acceleration due to net mean-meridional motion and the wave activity (EP flux divergence) and the adiabatic terms of thermodynamic equation are dominated by mean-meridional advections (Dunkerton, 1978). As to the response to stratospheric drag forcings, Palmer et al. (1986, hereafter referred to as PSS) proposed a simple model based on a 2-dimensional linear solution. It will be compared to our full analyses based on the forecast experiments. 2. TEM diagnosis procedure Dynamically consistent forecast fields produced by NWP models allow us to diagnose tonal means using fully primitive TEM equations without a geostrophic approximation. Following Dunkerton et al.(1981) and Andrews et al.(1983), the TEM tonal momentum and thermodynamic equations are written in a log-pressure spherical coordinate as follows: and Variables are listed in the Appendix. The overbars and primes denote zonal means and deviations from the zonal means, respectively. The subscripts of z and * indicate partial derivatives. The ADV* (u) represents the advective tendency of zonal wind due to the residual circulation including the Coriolis acceleration. Here, the Eliassen-Palm flux divergence DF denotes the wave, mean-flow interaction only of the model-resolvable waves and the interaction of parameterized subgrid-scale gravity waves is represented as an external forcing XGWD* The external forcing X denotes horizontal and vertical diffusions in the free atmosphere. In order to get physical insights into the impacts of the GWD schemes, we decompose the difference between the two forecasts with and without GWD into each term of equations (1) and (2). Integrating these equations with time and dividing by the forecast period t, we have

February 1989 T. Iwasaki, S. Yamada and K. Tada 31 where * and [ ] indicate differences between two forecasts and time-averaged tendencies [A]= from common initial conditions, we used the relations of *u(0)=0 and *(0)=0. These equations relate the changes in the tonal wind and in the potential temperature at forecast time t with the averaged tendencies of TEM. In order to reduce numerical errors, we take the full forecast period of t=8 days and composite 3 cases. The time-averaged tendencies are evaluated from field variables with a time interval of 24 hours but for [XGWD] with the interval of 6 hours. These analyses may be subjected to time-sampling errors, vertical-interpolation errors and finite-difference errors. Hence, the dissipation term (Loss) is defined to assess these errors as follows: If the errors and changes in the external forcings (except for GWD) are negligibly small, the term of Loss becomes equal to the parameterized GWD. The change in the external forcing (vertical and horizontal diffusion) [*X] is thought to be much less than the numerical error in the TEM analyses, at least in the free atmosphere. Hence, its effects are neglected in the discussions below. 3. Results 3.1 Meridional circulation induced by the parameterized GWD The upper panel of Figure 1 shows the difference in the mass streamfunction between run A and control run C, i. e., (A-C), where the mass streamfunctions are calculated from integrating residual vertical velocities, as given by definition (8), with respect to latitude. In the stratosphere of the Northern Hemisphere, the type A scheme induces a meridional circulation with a single-cell structure, whose ascending, poleward and descending flows are located in low, mid- and high latitudes, respectively. In the troposphere, the residual circulation induced by the type A scheme is roughly separable into two cells. South of 40*N, flows form a direct cell whose stream lines almost close at the lower boundary. In the northern cell, a number of stream lines do not close and the mass stream function does not become zero at the lowest level. This roughly indicates that the latitudinal distribution of surface pressure of run A becomes considerably different from that of the control run as the forecast period t progresses. In the conventional Eulerian-mean analysis, the difference in the mass streamfunction at each latitude * holds where *P is the difference in tonally averaged surface pressure between two forecasts with and without GWD. In fact, the zonally averaged surface pressure predicted by the run A is about 10mb more than the control run in high latitudes at t=8 days. In the TEM analysis, the difference in mass streamfunctions does not correspond exactly to the surface pressure difference, because residual velocities add heat flux terms to Eulerian-mean velocities (e.g., Trenberth,1987). However, the [*(50*N, xsurface)] calculated from the surface pressure differences with the relation (14) is comparable with (strictly a little less than) [*x(50*n, 850mb)] calculated from residual velocities. Even in the TEM analysis, a considerable part of non-zero differences in the mass streamfunctions in lower levels comes from the surface pressure difference. The lower panel of Figure 1 shows the response of residual circulations to the type B scheme. In the stratosphere, the type B scheme hardly affects the flow. Of course, the type B scheme does not directly force the stratospheric circulation but significantly modifies stratospheric planetary-scale waves through the wave propagation in a medium-range time scale as shown in the Part I. However, their wave, mean-flow interactions seem still too weak to change the mean-meridional circulations in the stratosphere. In the troposphere, the type B scheme induces two cell circulations as does the type A scheme. In the northern cell, open stream lines, corresponding to the latitudinal redistribution of zonally averaged surface pressure, appear as well. The tropospheric circulation induced by the type B scheme is rather weaker than that by the type A scheme. It seems to be due to the fact that the surface gravity wave stress generated by the type B scheme is smaller (see section 4.1 of Part I) Here, we note that the ensemble means of forecasts within a medium-range time scale are not close to an equilibrium state of the model atmosphere, but are in transition from the initial climate (the ensemble mean of initial conditions) to the model climate. If the forecast period t is much longer than a medium-range time scale, *P(t) must be saturated at a surface pressure difference between two model

32 Journal of the Meteorological Society of Japan Vol.67, No.1 climates with and without GWD schemes. Hence, for a long term average, *p(t)t in the right hand side of the relation (14) approaches zero and most stream lines are expected to close at the lower boundary. In this sense, the open cell structure in the response of the meridional circulation should be regarded as a reflection of the transition stage from the ensemble mean of initial values (actual climate) to the model climate. 3.2 Angular momentum balance According to Eq. (10), the tonal wind change u(t) due to GWD is decomposed into the * contributions of mean-meridional motion [*ADV*(u)], wave driving (EP flux divergence) [DF] and forcing itself [XGWD] The mean-meridional term is dominated by the Coriolis acceleration * In the northern-hemispheric stratosphere, the [*ADV*(u)] due to the type A becomes positive, since this scheme induces poleward flows as shown in the previous subsection. In the lower troposphere, both schemes change [*ADV* (u)] in their signs around 40*N, reflecting the two-cell structure in the GWD-induced residual circulation, i, e., poleward flows in the north and equatorward flows in the south. Figure 2 shows the differences in Eliassen-Palm flux divergence [*DF] between two runs with and without GWD together with the difference in the flux vectors [*F] by arrows. Both type A and B schemes increase EP flux in the high-latitude lower troposphere. This additional flux converges and reduces westerlies throughout the whole troposphere north of 40*N. As shown later, the flux Fig. 1. Meridional cross sections of GWD-induced residual circulation. Mass streamfunctions are averaged during the whole forecast period of 8 days and composited for three cases. Contour interval is 2*109 kg/s and negative areas are shaded. (top: for run A minus control run, bottom: for run B minus control run)

February 1989 T. Iwasaki, S. Yamada and K. Tada 33 convergence balances mostly with Coriolis acceleration due to GWD induced meridional motion. Between 30* and 40*N, EP flux divergence induced by GWD is positive and enhances tropospheric westerlies. Thus, model resolvable waves play important roles in the tropospheric redistribution of drag forcings produced in the parameterization. Figure 3 shows contributions of [*ADV*(u)], [*DF] and [XGWD] to net changes in tonal momentum tendency *u(t)t of Eq. (10) due to the type A scheme at 70mb and 700mb levels. In midlatitudes, the type A scheme produces the largest drag forcing around 70mb. Since the quantity [Loss] calculated by the definition (12) is almost equal to [XGWD], numerical errors and [*X] do not seem to seriously affect this TEM analysis. At the 70 mb level, the change in the Coriolis acceleration (*[*ADV*(u)]) highly compensates for the drag forcing [XGWD] and then net tendency *u(t)t is very small compared to these two terms. North of 30N, the drag forcings prevail against the change in the Coriolis acceleration and contribute to the reduction in westerlies as suggested by Tanaka and Yamanaka (1985). South of 30*N, the Coriolis term prevails against the drag forcing and accelerates the westerlies. The EP flux divergence due to large-scale waves is hardly changed by the inclusion of the type A scheme except for north of 70*N. At the 700mb, the change in the EP flux divergence [*DF] and in Coriolis acceleration [*ADV* (u)] are much larger Fig. 2. Meridional cross sections of GWD-induced Eliassen-Palm fluxes (arrows) and their divergences (contours) averaged during 8 days and composited for three cases. The magnitudes of flux intensities are shown by arrows at the lower left corner of the figure (units: kg/sec2). Contour interval of flux divergence is 0.5m/(sec*day) and negative (deceleration) areas are shaded. (top: for run A minus control run, bottom: for run B minus control run)

34 Journal of the Meteorological Society of Japan Vol.67, No.1 Fig. 3. Contributions of each term in Eq. (10) to the net tendency change in mean zonal wind *u(t)t due to the type A scheme at 70mb (top) and 700mb (bottom). The time period t is the full forecast length of 8 days. The [Loss] defined by Eq. (12) is also shown to indicate numerical errors. Heavy solid, thin solid, broken, chain and dotted lines indicate *u(t)t[*adv*(u)], [xgwd], [*DF] and [Loss], respectively. [vertical unit: m/(sec*day)] Fig. 4. Same as Figure 3, except for type B scheme. than GWD [XGWD] and almost balance each other. Both terms change in sign around 40*N. The [*DF] dominates a little over the [*ADV*(u)] in all latitudes and the net tendency *u(t)t becomes positive (negative) south (north) of 40*N. Figure 4 shows the contributions to the net tendency change *u(t)t in the type B scheme. In the stratosphere, the type B scheme hardly changes either the Coriolis acceleration or the EP flux divergence. In the troposphere, the EP flux divergence and Coriolis acceleration term strongly respond to the type B scheme. Even at the level of 700mb, where large GWD forcings are distributed by the type B scheme, these two terms become larger in magnitude than the drag forcings. Both terms change in sign around 40*N and compensate for each other as well, as observed in the case of incorporating the type A scheme. 3.3 Heat balance Since the zonally averaged diabatic heating rate Q in the model are hardly affected by the introduction of GWD schemes at least within a mediumrange time scale, temperature differences between two forecasts with and without GWD schemes are considered to be adiabatically induced'. Figure 5 shows the meridional cross sections of the advection term [*ADV* (*)] in the thermodynamic equation (11). The eddy term [*EDDY (*)] is found to be

February 1989 T. Iwasaki, S. Yamada and K. Tada 35 much less than the heat advection due to residual velocities. The difference between [*ADV* (*)] and net temperature change shown in Figure 12 of Part I may arise from numerical errors in the TEM diagnosis. A comparison between [*ADV* (*)] and the net temperature change confirms that significant temperature changes are induced in the lower stratosphere by the heat advection due to the residual flow, i. e., heatings around (50*N, 200mb) and coolings around (30*N, 100mb). From further decor position of the advection term, the vertical component appears to be dominant in these stratospheric temperature changes. As is well-known, the representation of heat balance in the TEM is very different from that in a conventional Eulerian-mean diagnosis where eddy terms play important roles in heat transports in midlatitudes. In this TEM analysis, the finding that vertical advections are dominant in GWD-induced temperature change is also consistent with the concept on the stratospheric thermal balance in terms of the Lagrangian-mean circulation. Then, we can straightforwardly understand the relation of heat transport to the meridional circulation. 4. Discussion 4.1 Geostrophic adjustment to the ageostrophy induced by GWD schemes The above analyses lead us to the following physical picture on the geostrophic adjustment of the zonal mean fields to the ageostrophy induced by the parameterized GWD. Figure 6 shows a schematic Fig. 5. Meridional cross sections of [*ADV* (*)] with contour interval of 0.5K/day. negative. (top: for run A minus control run, bottom: for run B minus control run) Shaded areas are

36 Journal of the Meteorological Society of Japan Vol.67, No.1 Stratospheric response to stratospheric GWD Tropospheric response both to stratospheric GWD and to tropospheric GWD Fig. 6. Schematic diagram of geostrophic adjustments to GWD in tonal-mean fields. Broken lines connect mainly balanced terms. diagram of the angular momentum balance associated with the GWD in the stratosphere (top) and the troposphere (bottom). In the stratosphere, the zonal-mean fields respond only to stratospheric drag forcings (type A). As was shown in Section 3.2, the zonal component of the type A GWD is almost balanced with the change in the Coriolis acceleration. Although planetary-scale waves are significantly modified by both the type A and B schemes, the change in wave, mean-flow interactions of these waves (EP flux divergence) contribute little to the net change in the zonal wind except for north of 70*N. In the case of the type A scheme, the EP flux divergence seems to be relatively important north of 70*N. However, numerical errors (the difference between [XGWD] and [Loss]) become so large in high latitudes that detailed discussions on momentum balance should be left untouched. The heat advections due to mean-vertical motion change the temperature distributions in the lower stratosphere so as to achieve thermal wind balance to the change in the vertical shear. In contrast, in the troposphere, the EP flux divergence plays an important role in geostrophic adjustment to both the stratospheric and tropospheric forcings. In the case of run A, the major portion of the drag forcings generated in the stratosphere is rapidly transmitted to the troposphere and change the tropospheric mean tonal flow, as discussed in Part I. This vertical transfer of momentum seems to be made mainly not through the mean-meridional circulation but through the vertical propagation of waves. This is seen from the fact that the contribution of mean meridional circulation to *u(t)t is very different in sign from the net tendency change which is positive (negative) south (north) of 40*N as shown in the previous section, but that it almost has the same sign as the change in the EP flux divergence. The rapid vertical transfer of momentum implies that the group velocities of waves which contribute to the momentum transfer are much faster than those of Rossby waves. They must be gravity waves resolved in the model. As mentioned in Section 2.1 of Part I, stationary gravity waves cannot effectively transfer momentum owing to inertial effects. Hence, transient gravity waves, which can easily interact with mean flows, may transfer most of the momentum given to the stratosphere by the type A scheme back to the troposphere. Simultaneously, mean-meridional flows may change so that the mass field may geostrophically adjust to changes in the tropospheric tonal wind field. Tropospheric drag produced by the type A scheme is less effective to the tropospheric flow fields. Special experiments omit-

February 1989 T. Iwasaki, S. Yamada and K. Tada 37 Fig. 7. EP flux (arrows) and its divergence (contours) of run A averaged for the forecast period of 8 days and composited for three cases. The magnitudes of flux intensities are shown by the arrows at the lower left corner of the figure. Contour interval is 5m/(sec.day) and negative areas are shaded. ting the tropospheric component of the type A drag (below 300mb) have similar tropospheric momentum balance to the run A. Thus, the change in tropospheric flows due to the type A scheme is considered to result mostly from the stratospheric component. In run B, the drag forcing generated mainly in the lower troposphere may be redistributed throughout the troposphere by model-resolvable waves as well. Consequently, impacts of both the type A and B schemes on the tropospheric zonal wind become rather barotropic even though the vertical partitionings of drag forcings are not vertically uniform. As to the response of tonal-mean fields to stratospheric drag forcings, a simple solution based on a 2-dimensional linear model was attempted by PSS. Since this was solved as an initial value problem, it can be directly compared to the impacts on forecasts. Their solution can almost describe the stratospheric response analyzed in this work. However, their solution is insufficient to describe the tropospheric response, because it neglects changes in the EP flux divergence which is shown to be significantly larger in this analysis. Another shortcoming arises from the lower boundary condition of *x=0. That is, the zonal mean of surface pressure is unchanged. This condition implies equatorial winds in the troposphere, which are the returning flows of the stratospheric poleward winds. They explained that the tropospheric westerlies were decelerated through the Coriolis effects due to these returning equatorial flows. However, the surface pressure is different between run A and the control run. Therefore, our results differ from PSS's solution in the lower-tropospheric meridional flows and their Coriolis accelerations. The lower boundary condition of x=0 is not appropriate for the initial value problem. * 4.2 Role of the type A GWD in the lower stratospheric and tropospheric general circulation The Lagrangian-mean flows form a Hadley-like single cell circulation (the so-called Brewer-Dobson circulation) in a hemispheric lower stratosphere and troposphere, as was clearly shown by Kida (1977, 1983). It has been recognized that this structure is maintained not only by diabatic heating, but also by wave, mean-flow interactions. Pfeffer (1987) showed that the EP flux divergence due to large-scale waves significantly contributes to the formation of the single cell circulation especially in high latitudes. Of course, neither numerical experiments by Kida nor observational analyses by Pfeffer included effects of subgrid-scale gravity waves. However, as shown in Section 3.1, the type A GWD considerably enhances the single cell structure in the stratosphere. Here, we compare the role of subgrid-scale gravity waves to the role of large-scale waves. Figure 7 shows the EP flux divergence of run A. It is found that large-scale waves do not produce large EP flux convergence deceleration in the mid-latitudinal stratosphere where the large GWD is produced. In this region, the GWD seems to be relatively important. In fact, systematic forecast errors of lower-stratospheric temperature are significantly reduced by incorporating the GWD scheme. On the other hand, in higher latitudes, the GWD becomes small because the excita-

38 Journal of the Meteorological Society of Japan Vol.67, No.1 Fig. 8. Schematic diagram showing how effects of GWD influence the distribution of trace constituents in the mid-latitude lower stratosphere. tion of gravity waves is rather inactive due to weaker westerlies in the lower troposphere. Planetary-scale waves, which may have larger coherence length and are more easily propagated in the horizontal than gravity waves, are thought to act more effectively on the mean flow in higher latitudes. Therefore, it seems that diabatic beatings, wave, mean-flow interactions of large-scale waves and subgrid-scale gravity waves contribute to the maintenance of the lowerstratospheric single cell circulation in different ways..3 Effects of GWD on Me dower-stratosphere tracer 4 transports It is well-known that some stratospheric trace constituents have very asymmetric distributions and annual marches between the southern and northern hemispheres. Atmospheric circulations associated with the earth's orography are believed to be one of the major causes of these asymmetries. Among them, the roles of planetary-scale waves in meridional circulations and eddy diffusions of stratospheric species have interested many authors. From the above discussion, we can expect that GWD also plays an important role in the stratospheric tracer transport especially in the mid-latitudes. As was symbolically represented by Holton (1980), in the Lagrangian-mean framework, stratospheric tracers are mainly transported in the vertical by advections due to mean-motions, while in the horizontal by eddy diffusion. In the case of ozone, the distribution in the lower stratosphere is primarily determined by dynamical effects, because its chemical lifetime is very long, except in the tropics. Between 300mb and 100mb levels, the atmosphere is stable (as a part of the stratosphere) on the polar side of the subtropical jet stream, while it is rather convective (as a part of the troposphere) on the equatorial side. At this altitude in mid-latitudes, the ozone mixing ratio is increased by the downward advection of ozone-rich air from the upper stratosphere but decreased by horizontal mixing with the ozone-poor tropospheric air from lower latitudes on isentropic surfaces. Figure 1 shows that the type A GWD significantly enhance the lower-stratospheric downward motion in the Northern Hemisphere. It must increase the ozone mixing ratio at least below the 100mb level in mid-latitudes (just north of the jet stream). Next, we point out that the level of the tropopause is also important for the distribution of trace constituents. In the troposphere, vertical diffusion coefficients become noticeably larger than those in

February 1989 T. Iwasaki, S. Yamada and K. Tada 39 the stratosphere and dominate vertical transports of constituents. Then, mixing ratios of constituents sharply change around the tropopause. As is wellknown, total ozone amounts (vertically integrated ozone mass) are much larger on the polar side of the subtropical jet stream than on the equatorial side, reflecting the difference in the tropopause height. Iwasaki and Kaneto (1984) showed that the altitude of the tropopause primarily determines the seasonal variation of total ozone amounts in midlatitudes. In the control run without GWD schemes, the tropopause height in mid-latitudes (northern side of the subtropical jet stream) cannot be maintained realistically, but it becomes higher with the forecast period because cooling biases in the lower stratosphere reduce static stability just above the tropopause. These errors are clearly reduced by incorporating the type A GWD. Therefore, subgridscale gravity-wave drags are thought to affect significantly the distribution of trace constituents through the lowering of the tropopause. The stratospheric temperature change is induced mainly by mean vertical heat advections as discussed in Section 3.3. Thus, we can say that the GWD enhances the downward Lagrangian motion on the polar side of the subtropical jet stream and affects the distributions of lower-stratospheric trace constituents in two ways; i, e., enhancements of vertical advective transports and lowering the polar tropopause (suppressing vertical diffusion) as schematically shown in Figure 8. In the case of ozone, both effects must contribute to the increase of total amounts in midlatitudes. The vertical residual velocities w* averaged north of 40*N is about -0.5mm/sec (downward) at 100mb in run A and run AB. It is comparable with values estimated under the assumption of radiative-advective balance (e.g., Murgatroyd and Singleton, 1961 and Gille et al. 1987). On the other hand, the vertical velocity of the control run at the same level is almost zero. Of course, this model might produce downward motion through wave, mean-flow interactions of large-scale waves, if the forecast period were extended and the model reached its equilibrium stage. In the model climate of the control run, however, the cooling bias would be more apparent than in the forecast in the mid-latitude lower stratosphere and the downward motion would still be slower compared to the actual climate. Therefore, the stratospheric GWD is thought to be very important for the forecast and climate simulation of conservative stratospheric species, such as water vapor, ozone and so on. 5. Conclusions The TEM analyses of the impacts on the type A and B GWD schemes are summarized as follows; In the stratosphere: The type A scheme induces a single-cell residual circulation with its upward branch on the equatorial side and the downward branch on the polar side of the subtropical jet stream. The Coriolis acceleration due to the meridional flow of this cell highly compensates for the drag forcing. Net change in the tonal wind is almost explained by the sum of these two terms. The heat advection due to the vertical motion in this cell roughly accounts for the temperature change induced by the GWD. The type B scheme induces less residual flows in the stratosphere. In the troposphere: Both schemes change the EP flux divergence of model-resolvable waves. These changes are much larger than the accelerations due to the drag forcings themselves and highly compensate for the Coriolis acceleration. Most of the drag forcing given to the stratosphere (type A) and to the lower troposphere (type B) may be rapidly redistributed throughout the troposphere through the momentum transport by the transient gravity waves (phase speed C*0) resolved in the model. The response of zonal-mean fields to the type A GWD has been compared to the simple solution obtained by PSS. The stratospheric response agrees well with their solution. However, PSS's solution is insufficient to represent the tropospheric response. Deficiency arises from (i) the shortcomings associated with the lower boundary condition and (ii) the neglect of eddy effects. In particular, even zonalmean (two-dimensional) models should include the effects of GWD-induced large-scale eddies in the troposphere. The stratospheric GWD contributes to the maintenance of a lower-stratospheric single-cell circulation (in the sense of Lagrangian-mean) as well as diabatic heating and wave, mean-flow interactions of planetary-scale waves. The GWD is relatively important in the mid-latitudes. The changes in the meridional circulation by the GWD are thought to influence tracer transports in the lower stratosphere through the enhancement of vertical advection and the suppression of vertical diffusion around the tropopause north of the subtropical jet stream. The asymmetric distributions of trace constituents and their annual marches between the southern and northern hemispheres is due partly to the excitation of gravity waves by subgrid-scale orography. Acknowledgments Numerical calculations of both parts in this study were carried out at the Numerical Prediction Division of the Japan Meteorological Agency. The authors wish to express their sincere thanks to Drs. K. Ninomiya and T. Kitade and the staff members of

40 Journal of the Meteorological Society of Japan Vol.67, No.1 the Numerical Prediction Division for their continuous encouragements. In particular, Mr. M. Kudo, Mr. K. Kurihara and Dr. H. Nakamura gave us useful suggestions on the characteristics of gravity waves. This report was completed while one of the authors (T. I.) visited the National Center of Atmospheric Research (NCAR) with partial support from the National Oceanic and Atmospheric Administration under NA85AAG02575. He had several stimulating discussions with the scientists of NCAR. He is very grateful to Dr. A. Kasahara for arranging the visit to NCAR, his critical reading and valuable comments on this manuscript. Comments and discussions with Profs. J. Wallace and J. Holton and Drs. N. McFarlane, B. A. Boville, M. D. Yamanaka and two anonymous reviewers are appreciated. We are pleased to acknowledge Miss R. Bailey for her skillful typesetting. Appendix List of symbols a earth's radius Coriolis * parameter g gravitational acceleration z(=-h ln p/ps) altitude in log-pressure coordinate H scale height (=7000m) ps reference surface pressure (=1000mb) * latitude u zonal wind component meridional wind v component w vertical wind component potential temperature * air density *0 (=-*sexp(-z/h)) *s reference surface air density x external forcing Q external heating x mass streamfunction References Andrews, D. G., J. D. Mahlman and R. W. Sinclair, 1983: Eliassen-Palm diagnosis of wave-mean flow interaction in the GFDL "SKYHI" general circulation model. J. Atmos. Sci., 40, 2768-2784. Andrews, D. G. and M. E. McIntyre, 1976: Planetary waves in horizontal and vertical shear: The generalized Eliassen-Palm relation and the mean-zonal acceleration. J. Atmos. Sci., 33, 2031-2048. Dunkerton, T., 1978: On the mean meridional mass motions of the stratosphere and mesosphere. J. Atmos. Sci., 35, 2325-2333. Dunkerton, T. J., C. -P. F. Hsu and M. E. McIntyre, 1981: Some Eulerian and Lagrangian diagnostics for a model stratospheric warming, J. Atmos. Sci., 38, 819-843. Gille, J. C., L. V. Lyjak and A. K. Smith, 1987: The global residual mean circulation in the middle atmosphere for northern winter period. *. Atrnos. Sci., 44, 1437-1452. Holton, J. R., 1980: Wave propagation and transport in the middle atmosphere. Phil. Trans. Roy. Soc. London, A296, 73-85. Iwasaki, T. and S. Kaneto, 1984: Photochemical and dynamical contributions to the seasonal variation of total ozone amount over Japan. J. Meteor. Soc. Japan, 62, 343-356. Iwasaki T, S. Yamada and K. Tada, 1989: A parameterization scheme of orographic gravity wave drag with two different vertical partitionings. Part I: Impacts on medium-range forecasts. J. Meteor. Soc. Japan, 67, 11-27. Kida, H., 1977: A numerical investigation of the atmospheric general circulation and stratospherictropospheric mass exchange II: Lagrangian motion of the atmosphere. J. Meteor. Soc. Japan, 55, 71-88. Kida, 1983: General circulation of air parcels and transport characteristics derived from a hemispheric GCM. Part 2: Very long-term motions of air parcels in the troposphere and stratosphere. J. Meteor. Soc. Japan, 61, 510-523. Matsuno, T., 1980: Lagrangian motion of air parcels in the stratosphere in the presence of planetary waves. PAGEOPH, 118, 189-216. Murgatroyd, R. J. and F. Singleton, 1961: Possible meridional circulation in the stratosphere and mesosphere. Quart. J. Roy. Meteor. Soc., 87 125-135. Palmer, T. N., G. J. Shutts and R. Swinbank, 1986: Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parameterization. Quart. J. Roy. Meteor. Soc., 112, 1001-1039. Pfefl'er, R. L., 1987: Comparison of conventional and transformed Eulerian diagnostics in the troposphere. Quart. J. Roy. Meteor. Soc., 113, 237-254. Tanaka, H. and M. D. Yamanaka, 1985: Atmospheric circulation in the lower stratosphere induced by the mesoscale mountain wave breakdown. J. Meteor. Soc. Japan, 63, 1047-1054. Trenberth, K. E., 1987: The role of eddies in maintaining the westerlies in the southern hemisphere winter. J. Atmos. Sci., 44, 1498-1508.

February 1989 T. Iwasaki, S. Yamada and K. Tada 41