Atmospheric Angular Momentum Transport and Balance in the AGCM-SAMIL

ADVANCES IN ATMOSPHERIC SCIENCES, VOL. 27, NO. 5, 2010, 1183 1192 Atmospheric Angular Momentum Transport and Balance in the AGCM-SAMIL LI Jun 1,2,3 ( ) and WU Guoxiong 1 ( ) 1 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029 2 Graduate University of the Chinese Academy of Sciences, Beijing 100049 3 National Meteorological Center, Beijing 100081 (Received 11 September 2009 revised 18 December 2009) ABSTRACT NCEP/NCAR reanalysis data and the spectral atmospheric general circulation Model (AGCM) of IAP/LASG (SAMIL) are employed to investigate the transport and balance of atmospheric angular momentum (AAM). It is demonstrated that SAMIL depicts the general features of the AAM transport and balance reasonably well. The AAM sources are in the tropics and sinks are in the mid-latitudes. The strongest meridional transport occurs in the upper troposphere. The atmosphere gains westerly momentum and transports it upward in the areas of surface easterlies, and downward into the areas of surface westerlies. Consequently, AAM balance is maintained. Systematic biases of the model compared to the reanalysis and observations are revealed. Possible mechanisms for these biases are investigated. In SAMIL, the friction torque in the tropics is stronger compared to the observations, which is probably due to the excessive precipitation along the Inter-tropical convergence zone (ITCZ) in the model, since the simulated Hadley circulation is much stronger than observed. In the winter half of the year, the transport center is in the lower troposphere in the SAMIL model, but it is in the upper troposphere in the reanalysis and observations. These discrepancies also suggest that simulations of convection and tropical precipitation need to be improved and that higher resolution is necessary for a quantitative simulation of AAM transport and balance. Results also demonstrate that the analysis of the transport and balance of atmospheric angular momentum is a powerful tool in diagnosing climate models for potential improvement. Key words: angular momentum, friction torque, mountain torque Citation: Li, J., and G. X. Wu, 2010: Atmospheric angular momentum transport and balance in the AGCM-SAMIL. Adv. Atmos. Sci., 27(5), 1183 1192, doi: 10.1007/s00376-009-9157-5. 1. Introduction Atmospheric angular momentum (AAM) is one of the fundamental parameters used to characterize atmospheric general circulation and climate. Total angular momentum of the atmosphere ocean solid earth system is considered as a constant, although each component of this system may change. The transport and budget of AAM are two important issues to the atmospheric general circulation (Lorenz, 1967). Jeffreys (1926) pointed out that the meridional transport of AAM by transient and stationary eddies is significant in maintaining the AAM balance. Starr (1948) directly used observational data at high altitudes to compute the transport of AAM. White (1949), Priestley (1951), Ye and Yang (1955), Ye and Zhu (1958), Kung (1968), and Newton (1971a, b), etc., have calculated the production of AAM due to friction and terrain at the earth s surface. These results indicate that the AAM sources are in the tropics and the sinks are in midlatitudes. Atmospheric general circulation models (AGCMs) have been used to study the atmospheric circulation and climate variation by investigating their performance in simulating the AAM transport and budget. Because the atmospheric mean meridional circulation Corresponding author: WU Guoxiong, gxwu@lasg.iap.ac.cn China National Committee for International Association of Meteorology and Atmospheric Sciences (IAMAS), Institute of Atmospheric Physics (IAP) and Science Press and Springer-Verlag Berlin Heidelberg 2010

1184 ATMOSPHERIC ANGULAR MOMENTUM TRANSPORT AND BALANCE IN SAMIL VOL. 27 (MMC) can modulate the AAM and energy budgets (Wu and Tibaldi, 1988; Wu and Cai, 1993), investigating the MMC and AAM transport and balance can also help understand the behaviors of, and the systematic errors in, AGCMs. In this study, we evaluate the SAMIL model by diagnosing the AAM transport and balance. Section 2 briefly introduces the model and data. Section 3 provides some concepts and relevant equations concerning the AAM and its transport and balance. The budget and transport of the AAM in the SAMIL as well as in the NCEP/NCAR reanalysis are evaluated in sections 4 and 5, respectively. Comparison of these results with observations and the mechanism responsible for the identified systematic errors are also presented. Concluding remarks are given in section 6. 2. Data and model The NCEP/NCAR reanalysis monthly mean data set from 1979 to 1988 (Kalnay et al., 1996) is employed for the study. A ten-year period is selected for comparison purposes since the results obtained by (Oort and Peixoto, 1983) are based on observations during a period of less than ten years. The analysis data set includes 17 vertical layers from 1000 to 10 hpa. Grid spacing is 2.5 2.5 in the horizontal. The atmospheric general circulation model SAMIL developed at LASG/IAP is used to simulate the observed angular momentum transport and its balance. The model atmosphere is divided into 9 vertical layers in a σ coordinate system, and the resolution is rhomboidally truncated at wave number 42 in the horizontal. A standard atmosphere subtraction scheme is used in the model dynamical framework (Wu et al., 1996) to increase the accuracy in calculating pressure gradient forces. Physical processes include the K-distribution radiation scheme (Wang, 1996), the SSIB land surface schemes (Xue et al., 1991), a moist convective parameterization (Manabe et al., 1965), and horizontal and vertical diffusion. Sea surface temperature and sea ice are interpolated from the monthly mean data set provided by the Atmospheric Model Inter-comparison Program (AMIP). The model has been validated to simulate the climate characteristics reasonably well (Wu et al., 2003). In this study, the model was integrated for 10 years, and results from the last 8 years were extracted for analysis. In nature, the atmosphere interacts with the underlying ocean and solid earth incessantly. Exchange of angular momentum between the atmosphere and the underlying surface should become another source of AAM and results in oscillations of the earth system with various frequencies. However, the use of an atmospheric circulation model alone and a constant mean angular velocity (Ω) as adopted in the model do not allow such an interaction process. Therefore, the results from this study can merely account for the long-term averaged state at which the total AAM could be considered as nearly conserved. 3. The concept of atmospheric angular momentum 3.1 Definition The earth rotates around its axis at a mean angular velocity Ω. The component of angular momentum along the direction of this axis is M n, where n denotes the unit vector in the direction of Ω ( Ω = Ωn). For a unit atmospheric mass, the absolute angular momentum (M) along the axis of rotation is: M = ΩR 2 cos 2 ϕ + ur cos ϕ, (1) where R is the mean radius of the earth, u is the zonal wind component, and ϕ is latitude. The first term on the right-hand side represents the atmospheric angular momentum due to the earth s rotation. The second term is the relative angular momentum. 3.2 AAM balance equation Multiplying both sides of zonal momentum equation by R cos ϕ, and after manipulation, we can obtain the AAM balance equation for a unit volume: ρm t = divρmc p λ + ρf λr cos ϕ, (2) where ρ is density, p is pressure, F λ is zonal friction, c is three-dimensional wind vector, and λ is longitude. By integration over the total volume, and using the relation between frictional stress (τ 0 ) and friction ( F λ = 1 ρ t where τ z ρmdv = sfc ), Eq. (2) can be expressed as: p λ dv + τ 0 R 3 cos 2 ϕdλdϕ. sfc (3) τ 0 R 3 cos 2 ϕdλdϕ denotes the integration of frictional stress on the earth surface. The first term on the right-hand side of Eq. (3) is the pressure or mountain torque, and the second term is friction torque. These are positive if the resultant eastward angular momentum of the atmosphere is increased. In the free atmosphere, ( p/ λ)dλ is zero when it is integrated zonally. In the presence of mountains and at a fixed altitude, the zonal integration of p/ λ equals the sum of the east west pressure difference across various

NO. 5 LI AND WU 1185 mountain ranges, which reflects the fact that mountains resist the resulting pressure gradient force of the atmosphere and do work against the atmosphere in the opposite direction. Therefore, this term is known as mountain torque. Wherever there is a mountain, there is a mountain torque. By virtue of the pressure difference between the eastern and western sides of various mountains on the earth, the mountain torque can change the atmospheric angular momentum. Equation (3) then indicates that the AAM can be changed by the effects of either terrain or by surface friction. Additionally, the parameterization of the subgridscale orographic gravity wave drag in a numerical model is another important source of mountain torque which can significantly influence the AAM in the model as reported by Huang and Sardeshmukh (1999) and Brown (2004). However, the version of the SAMIL AGCM used in this study does not consider this parameterization, and the associated mountain torque is not included in Eq. (3). 3.3 AAM transport equation In the p-coordinate system, the time-mean and zonal-mean of Eq. (3) is expressed as (Peixoto and Oort, 1992): t [M] = 1 ( [ ϕ ] cos ϕ ) R cos ϕ ϕ [ ] [ ] z τ p [ pλ p] g R cos ϕ, (4a) λ p with [ ϕ ] = R 2 cos 2 ϕω[v]+ R cos ϕ ( [u][v] + [u v ] + [u v ] ) [ p ] = R 2 cos 2 ϕω[ω]+ R cos ϕ ( [u][ω] + [u ω ] + [u ω ] ), (4b) where [ ] and * represent the zonal-mean and its anomalies, and and represent the time-mean and perturbations thereof, respectively. [ ϕ ] denotes the meridional transport of AAM, and [ p ] denotes the vertical transport of angular momentum. The first term on the right-hand side of Eq. (4b) is the transport of Ω-angular momentum by MMC ([v],[ω]). The remaining three terms, i.e., [u][v], [u v ], and [u v ] represent, respectively, the northward flux of relative momentum brought about by MMC, stationary eddies, and transient eddies. To analyze the vertical transport of AAM, following Peixoto and Oort (1992), we introduce a gross friction τpλ. It comprises the third and fourth terms on the right-hand side of Eq. (4a): τpλ p = g R cos ϕ z λ + τ pλ p. (5) Since the temporal variations of the AAM are usually small, the left-hand side of Eq. (4a) can be considered to be zero in the long-term average. Therefore, we can define a stream function ψ M for the zonal-mean transport of AAM. Following Starr et al. (1970), these equations are: 2πR cos ϕ [ ϕ ] = ψ M p, (6a) 2πR cos ϕ([ p ] + R cos ϕ[τ pλ]) = ψ M R ϕ. (6b) Assuming ψ M is equal to zero at the top level, and integrating Eq. (6a) downward, we can obtain the ψ M distribution in the (ϕ, p) plane. Then based on Eq. (6b), the vertical transfer of AAM [ p ] + R cos ϕ[τpλ ] can be calculated (Hantel and Hacker, 1978). 4. The budget of the AAM We show next the mountain and friction torques which generate the AAM and therefore can significantly influence the AAM balance. By integration in λ over the mountain ranges, the first term on the righthand side of Eq. (3) becomes: { ( ) } p P λ dv = dλ dzr 2 cos ϕdϕ λ = ( p) i dzr 2 cos ϕdϕ, (7) i where ( p) i is the east-west pressure difference across the ith mountain range, and its vertical integration starts from the geopotential height at the bottom pressure level to that at the top pressure level across the mountain range. Therefore, the pressure torque is also known as mountain torque. The second term on the right hand side of Eq. (3) ( sfc τ 0R 3 cos 2 ϕdλdϕ) is the friction torque due to wind stress. Hellerman and Rosenstein (1983) computed the surface stress over the oceans from cruise reports and using the following aerodynamic formula (Priestley, 1951) τ 0 = ρc D V u, (8) where the drag coefficient C D equals to 0.0013. They calculated the meridional profiles of the surface torque and mountain torque integrated over each 5 latitude belt (Figs. 11, 12 of Peixoto and Oort, 1992). We will show that results from the model and NCEP/NCAR reanalysis data are similar to their study. Figure 1 shows the annual-mean mountain and friction torques, where the solid line represents the model and the dashed line is for the reanalysis. For both data

1186 ATMOSPHERIC ANGULAR MOMENTUM TRANSPORT AND BALANCE IN SAMIL VOL. 27 Fig. 1. Annual-mean meridional distributions of (a) mountain torque (upper panel), and (b) friction torque (lower panel). Solid line is for the SAMIL model, dashed is for the NCEP/NCAR Reanalysis. Units: Hadleys (1 Hadley=10 18 kg m 2 s 1 ). sets, friction torque is generally positive in the low latitudes from 30 S to 30 N, and negative in the midlatitudes (Fig. 1b). This result also agrees with previous studies (Newton, 1971a, b; Oort and Peixoto, 1983). Because there are few large-scale mountains in Southern Hemisphere and in low latitudes, the mountain torque in SAMIL agrees, in general, with that in the reanalysis. However, in the middle latitudes of the Northern Hemisphere where the largest mountains exist, SAMIL has a distinct mountain torque result that departs from the reanalysis due to coarse horizontal resolution as well as differences in circulation around the mountains. Figure 1a demonstrates that the mountain torque in Northern Hemisphere also presents some deviation from that given by Newton (1971b), and shows the significant difference between the model and the reanalysis. Although the maximum mountain torque exists in Northern Hemisphere in both the model and reanalysis results, the torque is more than 2 Hadley units (1 Hadley=10 18 kg m 2 s 1 ) around 40 N in the SAMIL modeling, but about 1.5 Hadley at 57 N in the reanalysis. North of 60 N, the mountain torque is negative in the reanalysis but positive in SAMIL and according to Newton (1971b). The minimum mountain torque in the Northern Hemisphere is about 0.6 Hadley in the reanalysis, 1.6 Hadley in the SAMIL, and 2 Hadley in Newton s calculations. The reason for these differing results may be due to the fact that Newton (1971a) used only 4 months to generate the annual mean and the data resolution is at 5 degrees, which is too rough to calculate the mountain torque accurately. The appearance of negative mountain torque between 20 N and 40 N in SAMIL seems unusual and needs further investigation. Based on the spectral European Center for Medium-Range Weather Forecasts (ECMWF) model with different resolutions, Brown (2004) calculated the model resolved mountain torque in each 10-degree latitude belt, and demonstrated that in 2001 the negative mountain torque was located between 15 60 N in July (refer to their Fig. 8a) and between 27 60 N in January (refer to their Fig. 7a). The corresponding maximum is about 2 Hadley at T95 resolution, and gradually reduces as the resolution is increased. Using observational data, Ye and Zhu (1958) calculated the AAM budget and found that the mountain torque between 28 40 N possesses a unique and remarkable seasonal change, with strong negative values in the summer months between April and August and extremes of more than 3 Hadley along 35 N in April, May, and June, but with weaker positive torques in winter months between September and February with extremes of just over +2 Hadley along 35 N in December and January. This latitude zone contains the Tibetan Plateau and the Plateau of Iran in Asia, and the Appalachian Mountains and Rocky Mountains in North America. Due to continental scale thermal forcing (Wu et al., 2009) to the east of these mountain ranges and in the near surface layers, there is low pressure in summer and high pressure in winter. In addition, in winter the mechanically induced barotropic and/or baroclinic mountain waves generate surface lows to the east of ranges and surface highs to the west Wu (1984). Whereas in summer, the thermally induced stationary mountain Rossby waves also generate surface lows to the east of ranges and highs to the west (Wu et al., 2003, 2009). As a combination of the effects of the aforementioned regional-scale mountain forcing and the continental-scale thermal forcing, it seems that the negative mountain torque in summer should be greater than the positive mountain torque in winter. Thus, the annual mean negative mountain torque appearing within the latitude range between 20 N and 40 N in SAMIL might be acceptable, despite the existence of discrepancies compared with the NCEP results. The sum of mountain and friction torques shows positive values in low latitudes as the principal source of AAM, but negative values in mid-latitudes as the

NO. 5 LI AND WU 1187 principal sink of AAM. Since surface stress is directed against surface winds, it is positive when the surface wind is easterly and negative when the surface wind is westerly. Therefore surface friction always generates AAM in the surface easterlies while it always consumes AAM in the middle and high latitudes where surface westerlies prevails. It should be pointed out that the relative contribution of the mountain torque and friction torque to the total torque depends on the time scale (Weickmann at al., 1997). For example, Swinbank (1985) produced daily global values of mountain and friction torques by using the orography field and a boundary layer scheme intrinsic to the UKMO general circulation model (GCM) and discovered that the mountain torque appears to be responsible for most of the shortterm variability. On interannual time scales, where most of the variability is associated with ENSO-related changes in AAM, Stefanick (1982), Rosen and Salstein (1984), and Rosen (1993) suggested that the mountain torque is more important, in concert with the dramatic rearrangement of atmospheric mass across the Pacific that characterizes the Southern Oscillation. Our results as shown in Fig. 1 indicate that the friction torque is more dominant on a decadal-mean time scale. This result is in agreement with previous calculations such as by Priestley (1951) and Newton (1971a and b), and to some extent modifies the view of White (1949) that the two torques are comparable in magnitude. 5. Transport of the AAM 5.1 Meridional transport Since the angular momentum component due to Ω is much larger than the relative angular momentum, its meridional transport dominates north-south transport of the absolute angular momentum. Conservation of mass requires that the vertical mass integral of the first-term on the right-hand side of Eq. (4b) vanishes in the long-term mean. Therefore, the flux of relative angular momentum must be important for the horizontal transport of absolute angular momentum from the source regions to the sink regions. In the following we use the output of SAMIL and the NCEP/NCAR reanalysis to analyze each component of the second term on the right-hand side of Eq. (4b) to show the meridional transport. Figures 2 and 3 display zonal-mean cross sections of the annual-mean northward flux of momentum by all motions and its components calculated from the reanalysis data and the model output, respectively. First, both data sets show an overall symmetry with Fig. 2. Zonal-mean cross sections of the annual-mean northward flux of momentum (based on NCEP/NCAR reanalysis data) by (a) all motions, (b) transient eddies, (c) stationary eddies, and (d) MMC. Units: m 2 s 2. respect to the equator in the transport by all components except the stationary eddies, which is consistent with observational data (Oort and Peixoto, 1983). At the upper levels, the transient eddies dominate the total transport (Figs. 2b and 3b), and the maxima are located between the latitudes of 30 and 35 at the 200-hPa level. This indicates that the poleward transport by transient eddies is mostly important in the upper troposphere in the tropics and mid-latitudes. The centers of the stationary eddy flux are also located in the subtropics at the 200-hPa level (Figs. 2c and 3c). In the Southern Hemisphere, as shown by Oort and Peixoto based on observational data, the maximum of stationary eddy flux is much weaker than the transient eddy flux. However, in the Northern Hemisphere there is no significant difference in intensity between the two eddy fluxes; i.e., both possess strong positive centers in the subtropics in the upper troposphere. Compared with previous data diagnosis (Oort and Peixoto, 1983), the transient eddy transport is weaker and the stationary eddy transport

1188 ATMOSPHERIC ANGULAR MOMENTUM TRANSPORT AND BALANCE IN SAMIL VOL. 27 port in the Southern Hemisphere is stronger than in the Northern Hemisphere. This distinction is due to the contribution of the transient eddy flux. Figures 4 and 5 demonstrate the meridional profiles of the vertical- and zonal-mean northward transport of momentum, respectively, from the NCEP/NCAR reanalysis data and SAMIL model. The two figures show that in spite of the fact that the stationary eddies are not important in the Southern Hemisphere, the total angular momentum transport by transients, stationary eddies, and MMC are quite similar in the two hemispheres. This differs from the observational results (Oort and Peixoto, 1983) showing that the total transport in the Southern Hemisphere is somewhat stronger than in the Northern Hemisphere because the transient transport in the Southern Hemisphere is stronger. Even for individual seasons the bulk of the momentum transport is accomplished by transient eddies. The cause for this distinction may be that the low-resolution model fails to describe the transient eddies well enough. For all seasons the stationary eddy Fig. 3. Zonal-mean cross sections of the annual-mean northward flux of momentum (based on SAMIL output) by (a) all motions, (b) transient eddies, (c) stationary eddies, and (d) MMC. Unit: m 2 s 2. is much stronger in the reanalysis (Fig. 2). Such differences are more distinct in SAMIL (Fig. 3). The reason may be that the resolution of the models is not fine enough to resolve the transient eddies and their transport properties. In addition, the stationary eddy flux in the Northern Hemisphere is much greater than in the Southern Hemisphere, indicating the significance of terrain and land-sea contrast in the Northern Hemisphere in influencing the formation of stationary waves. In the tropics the two eddy transports are small and in agreement with the observations. The MMC transport shows the effects of the three-cell structure in each hemisphere. Except in the boundary layer and close to the tropopause, its contribution to the total transport is relatively small compared to the two eddy fluxes. Although there are some differences in angular momentum transport between the two hemispheres, the stationary eddy transport is very small in the Southern Hemisphere and the total angular momentum transport by various components are comparable. In the high latitudes, the maximum of equator-ward trans- Fig. 4. Meridional profiles of the vertical- and zonalmean northward transports of momentum (based on NCEP/NCAR reanalysis data) by (a) all motions, (b) transient eddies, (c) stationary eddies, and (d) mean meridional circulation for annual (solid curve), DJF (dashed curve), and JJA (long-dashed curve) mean conditions. Units: m 2 s 2.

NO. 5 LI AND WU 1189 Fig. 5. Meridional profiles of the vertical- and zonal-mean northward transport of momentum (based on SAMIL output) by (a) all motions, (b) transient eddies, (c) stationary eddies, and (d) mean meridional circulation for annual (solid curve), DJF (dashed curve), and JJA (long-dashed curve) mean conditions. Units: m 2 s 2. transport is considerably stronger in the Northern Hemisphere than in the Southern Hemisphere. Particularly in winter, the stationary eddies in the midlatitudes of the Northern Hemisphere are the major contributor to the total flux of AAM. 5.2 Vertical transport of AAM Following Eq. (6a) or Eq. (6b), the streamfunctions of the zonal mean transport of absolute angular momentum are calculated and shown in Fig. 6. Panels (a), (b), and (c) are, respectively, the annualmean, DJF-, and JJA-mean based on the reanalysis data. Correspondingly, panels (d), (e), and (f) in Fig. 6 are from the SAMIL model. Figure 6 depicts the characteristics of the AAM flow along the MMC and the distribution of angular momentum sources and sinks on the surface. This pattern is similar to that obtained from observational data (Oort and Peixoto, 1983). For example, the absolute angular momentum transport is quasi-symmetric with respect to the equator in Fig. 6a and Fig. 6d. In the winter hemisphere, as the Hadley cell gets stronger, the associated angular momentum transport is larger. However, there are some differences between the results from either SAMIL or the reanalysis versus the observational data. For instance, the observed annual mean shows that the transport center in the Southern Hemisphere is stronger ( 270 10 18 kg m 2 s 1 ) than in the Northern Hemisphere (220 10 18 kg m 2 s 1 ), as in NCEP/NCAR, and 390 10 18 kg m 2 s 1 in the Southern Hemisphere but 280 10 18 kg m 2 s 1 in the Northern Hemisphere in SAMIL. However in observational data, Oort and Peixoto (1992) estimated the maximum in the Southern Hemisphere is 183 10 18 kg m 2 s 1 and 200 10 18 kg m 2 s 1 in the Northern Hemisphere. This bias is consistent with the fact that the friction torque in the Southern Hemisphere tropics is greater than in the Northern Hemisphere both in the model and in the reanalysis (Fig. 1). Another discrepancy in SAMIL compared to the reanalysis is the altitude of the transport center in the tropics. In winter, in both the observational data and the reanalysis, the transport centers are in the upper troposphere, but in SAMIL these maxima are in the lower troposphere. Because the angular momentum transport in the tropics is closely connected with the Hadley cell and the altitude of the Hadley circulation center is related to the diabatic heating maximum in the tropics (Wu and Cai, 1993), we can infer that the bias of the lower transport center in the tropics is associated with the convection parameterization scheme. In addition, the intensity of the transport center in the tropics in SAMIL is stronger than in the reanalysis or observations. This is consistent with the results shown in Fig. 1 where the friction torque in the tropics in the model is stronger than in the reanalysis. This can be attributed to the excessive latent heating release near the equator in SAMIL (Wu et al., 2003). Figure 6 also shows that the transport is strengthened in winter, which corresponds to the enhanced generation of AAM near the surface and enhanced upward transport. These features are also in good agreement with observations as analzyed by Peixoto and Oort (1992). Figure 7 shows the streamlines of the non-divergent component of the zonal-mean transport of relative angular momentum. This is obtained by dropping the Ω[v] term from the internal source term [ ϕ ] in Eq. (4b) and then integrating Eq. (6). Similar to Fig. 6, panels (a), (b), and (c) of Fig. 7 show, respectively, the annual-mean, DJF-, and JJA-mean from the reanalysis data. Correspondingly, panels (d), (e), and (f) of Fig. 7 are from the SAMIL model. The distinc-

1190 ATMOSPHERIC ANGULAR MOMENTUM TRANSPORT AND BALANCE IN SAMIL VOL. 27 Fig. 6. Streamlines of the zonal-mean transport of absolute angular momentum calculated based on the NCEP/NCAR reanalysis data (a c) and from the output of SAMIL (d f): (a) and (d) annual-mean; (b) and (e) DJF-mean; (c) and (f) JJA-mean. Units: 10 18 kg m 2 s 1. tion between Figs. 7 and 6 is the Ω angular momentum which has been removed in computing the stream function. Thus, the influence of MMC is removed since it is not related to the cross-latitude transport. Figure 7 explains more clearly the AAM cycle and its sources and sinks. In general, in the tropics where surface easterlies prevail there is ascending transport, and in the middle and high latitudes where surface westerlies prevail there is descending transport. In the winter Hemisphere, AAM transport is much stronger than in the other seasons, which agrees well with observations, as well. However, a strong transport area occurs in the upper tropics in the model (Fig. 7d), but not in the reanalysis (Fig. 7a) and observations (Figs. 11, 13 of Peixoto and Oort, 1992). Since Fig. 7d generally resembles Fig. 7f, we may infer that in SAMIL, the generation of absolute angular momentum in summer has too strong of weighting in the annual mean. 6. Concluding remarks In this study we diagnose the transport and balance of atmospheric angular momentum in SAMIL and in NCEP/NCAR reanalysis data and compare these results with those based on observations (Oort and Peixoto, 1983). Firstly, the mountain and friction torques which influence the balance of the AAM are reasonably simulated in SAMIL, except that the mountain torque is too large between 25 45 N where the Tibetan Plateau and the Rockies are located. The sources of AAM are in the tropics and the sinks are in mid- and high-latitude regions. The friction torque is stronger in the tropics compared to the observations, which is probably due to the excessive precipitation simulated along the ITCZ in the model. Second, SAMIL can simulate the angular momentum cycle reasonably well. AAM transport shows that the horizontal transport center is in the upper troposphere and the sources and sinks are on the surface, in concordance with the surface winds. Therefore the upward transport is in the tropics associated with surface easterlies, and the downward transport is in the middle and high latitudes associated with surface westerlies. Thus, a balance of AAM is maintained. Third, the features of the transport and balance of the AAM produced by SAMIL agree well with those from the NCEP/NCAR reanalysis and observational data. Nevertheless there are some discrepancies. For example, in the winter half of the year the transport center is in the lower troposphere in the SAMIL model, but it

NO. 5 LI AND WU 1191 Fig. 7. Streamlines of the non-divergent component of the zonal-mean transport of absolute angular momentum calculated based on the NCEP/NCAR reanalysis data (a c) and from the output of SAMIL (d f): (a) and (d) annual-mean; (b) and (e) DJF-mean; (c) and (f) JJA-mean. Units: 10 18 kg m 2 s 1 ; long-dashed denotes [u]/ cos ϕ in units of m s 1. is in the upper troposphere in the reanalysis and in the observations. These discrepancies suggest that simulations of the convection and tropical precipitation need to be improved. Results in this study indicate that the transport and balance of the atmospheric angular momentum are of great importance in understanding the atmospheric dynamics as well as in validating the model performance. Acknowledgements. This study is jointly supported by the CAS program KZCX2-YW-Q11-01, MOST GYHY200806006, and the National Science Foundation of China (Grant Nos. 40875034 40821092, and 40810059005). REFERENCES Brown, A. R., 2004: Resolution dependence of orographic torques. Quart. J. Roy. Meteor. Soc., 130, 3029 3046. Hantel, M., and J. M. Hacker, 1978: On the vertical eddy transports in the Northern atmosphere: II. On the vertical eddy momentum transport for summer and winter. J. Geophys. Res., 83, 1305 1318. Hellerman, S., and M. Rosenstein, 1983: Normal monthly wind stress over the World Ocean with error estimates. J. Phys. Oceanogr., 13, 1093 1104. Huang, H.-P., and P. D. Sardeshmukh, 1999: The balance of global angular momentum in a long-term atmospheric data set. J. Geophys. Res., 104(D2), 2031 2040. Jeffreys, H., 1926: On the dynamics of geostrophic winds. Quart. J. Roy. Meteor. Soc., 52, 85 104. Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40- year reanalysis project. Bull. Amer. Meteor. Soc., 77, 437 471. Kung, E. C., 1968: On the momentum exchange between the atmosphere and earth over the northern hemisphere. Mon. Wea. Rev., 96, 337 341. Lorenz, E. N., 1967: The Nature and Theory of the General Circulation of the Atmosphere. WMO-No. 218, Geneva, 161pp. Manabe, S., J. Smagorinsky, and R. F. Strickler, 1965: Simulated climatology of a general circulation model with a hadrologic cycle. Mon. Wea. Rev., 93, 769 798. Newton, C. W., 1971a: Moutain torque in the global angular momentum balance. J. Atmos. Sci., 28(4), 623 628. Newton, C. W., 1971b: Global angular momentum: Earth torque and atmospheric fluxes. J. Atmos. Sci.,

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