Momentum balance and gravity wave forcing in the mesosphere and lower thermosphere

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1 GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L07805, doi: /2009gl037252, 2009 Momentum balance and gavity wave focing in the mesosphee and lowe themosphee H.-L. Liu, 1 D. R. Mash, 2 C.-Y. She, 3 Q. Wu, 1 and J. Xu 4 Received 15 Januay 2009; evised 3 Mach 2009; accepted 10 Mach 2009; published 8 Apil [1] Gavity wave focing (GWF), which is the pimay dive of the mesospheic and lowe themospheic (MLT) ciculation, is difficult to measue diectly. In this wok, the zonal mean GWF at extatopical MLT is deduced fom measued winds using momentum balance. With the GWF dominating in the MLT, the zonally aveaged zonal momentum equation can be simplified to a balance elation between the GWF and the Coiolis foce in the extatopics. The meidional advection of zonal momentum makes a highe ode contibution to the momentum balance, especially at places whee the GWF maximizes. This method is tested with WACCM3 model and peliminay esults ae obtained fom wind measuements by CSU Na lida and TIMED/TIDI. Citation: Liu, H.-L., D. R. Mash, C.-Y. She, Q. Wu, and J. Xu (2009), Momentum balance and gavity wave focing in the mesosphee and lowe themosphee, Geophys. Res. Lett., 36, L07805, doi: /2009gl Intoduction [2] Gavity wave focing (GWF) plays a key ole in the mesosphee and lowe themosphee (MLT) by contolling the ciculation and the wind, themal and compositional stuctues of this egion [e.g., Gacia and Solomon, 1985]. In spite of thei impotance, diect measuement o infeence of the gavity wave (GW) impacts, namely the mean flow acceleation and eddy mixing fom GW beaking, have been difficult. Thee wee a few significant eseach effots in this espect. Alexande and Rosenlof [2003] calculated the esidual focing due to GWs in the statosphee fom UARS data and UKMO esults. Fo that calculation, the diabatic heating ate is needed as an input fo deiving esidual ciculation velocities and the total zonal momentum foce. The foce fom dissipation of esolved waves is detemined fom UKMO fields and then substacted fom the total zonal momentum to obtain the foce of unesolved GWs. Khattatov et al. [1997] deived an effective eddy diffusion coefficient by fitting the diunal tide deived fom UARS/HRDI measuements to a linea tidal model. Moe ecently, J. Xu et al. (Estimation of the equivalent Rayleigh fiction in MLT egion fom the migating diunal tides obseved by TIMED, submitted to Jounal of Geophysical Reseach, 2009) deduced 1 High Altitude Obsevatoy, National Cente fo Atmospheic Reseach, Boulde, Coloado, USA. 2 Atmospheic Chemisty Division, National Cente fo Atmospheic Reseach, Boulde, Coloado, USA. 3 Depatment of Physics, Coloado State Univesity, Fot Collins, Coloado, USA. 4 State Key Laboatoy fo Space Weathe, Chinese Academy of Sciences, Beijing, China. Copyight 2009 by the Ameican Geophysical Union /09/2009GL037252$05.00 an effective dag coefficient fom tempeatue measuements by the Sounding of the Atmosphee using Boadband Emission Radiomety (SABER) instument and zonal and meidional wind measuements by the TIMED Dopple Intefeomete (TIDI) instument on boad the NASA Themosphee Ionosphee Mesosphee Enegetics and Dynamics (TIMED) satellite. Zhu et al. [2001] developed a diagnostic method to deive all the dynamical and chemical tace fields fom tempeatue and ozone measuements, based on a globally balanced 2D diagnostic model. The method uses the linea satuation theoy to elate GWF and eddy diffusion, and the net heating fom GW beaking is also consideed. The pimay balance elationship used theein is a balance between the meidional gadient of GWF and the vetical gadient of total heating. [3] In this study we examine the momentum balance in the MLT egion using scale analysis and model simulations, and the feasibility of applying this balance elation to deduce GWF fom gound-based and satellite wind measuements. It is well known that the gadient wind appoximation [Randel, 1987] in the meidional diection still holds well in the MLT at middle and high latitudes [Liebeman, 1999; Obeheide et al., 2002], so that the zonal wind can be calculated fom the latitudinal gadient of geopotential (thus tempeatue). In the zonal diection the GWF becomes inceasingly impotant in the MLT, and its elative significance compaed with othe tems is studied hee in the zonal mean sense based on scale analysis, and then evaluated using esults fom the NCAR Whole Atmosphee Community Climate Model (WACCM3). The applicability of the balance elation fo deiving GWF fom wind measuements fom both gound-based and satellite measuements is demonstated. WACCM3 solves the pimitive equations fom the Eath suface to the lowe themosphee ( hpa, appoximately 140 km), and is thus appopiate fo this study. GWF in WACCM3 is paameteized based on the linea satuation theoy [Lindzen, 1981]. Detailed infomation of WACCM3 can be found by Gacia et al. [2007]. The gound-based wind obsevations used ae fom the monthly mean winds fom the two-beam Na lida at Coloado State Univesity (41 N, 105 W), which has been obseving full diunal cycles of the mesopause egion tempeatue and hoizontal wind in campaign mode since May 2002, weathe pemitting [She et al., 2004; Yuan et al., 2008]. TIDI zonal mean winds ae also used to infe GWF. The TIDI zonal mean winds ae obtained by emoving the tidal components and then aveaging the esidual winds ove all longitudes. Details of the TIDI instument and TIDI tidal analysis ae given by Killeen et al. [2006] and Wu et al. [2008]. [4] The deivation of the momentum balance in the pesence of stong GWF and the test of the balance using WACCM3 ae pesented in Section 2. The application of the L of5

2 Figue 1. Zonal mean gavity wave focing (a) fom WACCM on Decembe 17, (b) deduced fom model winds using (2), and (c) deduced fom model winds using (4). Contou inteval: 20 ms 1 d 1 ; solid contou line: eastwad focing. balance elation to deducing GWF fom wind measuements is discussed in Section 3. Conclusions ae given in Section Momentum Balance in the Pesence of Stong Gavity Wave Focing [5] The full momentum equation in the zonal diection is: Du Dt F x ¼ f þ u tan f v 1 þ 2 whee D/Dt is the Lagangian time deivative, u and v the zonal and meidional winds, f the Coiolis paamete, the Eath adius, f the latitude, l the longitude, F x the total body foce, and n the total viscosity (eddy plus molecula) coefficient. Fom standad scale analysis [e.g., Holton, 2004], the Coiolis foce and the geopotential gadient tems in (1) ae 10 3 ms 2 and dominate ove othe tems in the lowe atmosphee. In the MLT egion, howeve, the zonal mean zonal GWF is on the same ode of magnitude (100 ms 1 d 1 o 10 3 ms 2 ), although locally the GWF may o may not be compaable to the Coiolis foce given the lage spatial and tempoal vaiability of GWF. With n 100 m 2 s 1 2 u/@z m 1 s 1 (assuming a 50 ms 1 change within 10 km) in the MLT, the viscous tem is thus ms 2. It is much smalle than the zonal mean GWF and will be ignoed in the following discussion. Theefoe the pimay foce balance in the zonal diection in the MLT is between the zonal mean GWF and the Coiolis foce (the geopotential gadient tem becomes zeo when integated along the longitude cicle): F x GW u tan f ¼ f þ v with the assumption that ion dag is not impotant below 100 km so that F x F x GW. This simple foce balance allows the detemination of zonal mean GWF solely fom the zonal mean winds. It should be noted that the advective tems in the full zonal mean þ F x ¼ f þ u tan f v ð1þ ð2þ ð3þ ae fom mean and eddy advection, and thei impact on the mean flow is geneally seconday compaed to the GWF in the MLT egion, unlike that in the statosphee. This will be futhe examined using numeical model esults. [6] To test this momentum balance and to bette undestand the elative significance of the tems in (3), WACCM3 simulation esults unde Decembe solstice conditions ae examined. The simulation esults fist confim that the zonal mean of the gadient wind is in good ageement with the zonal mean of the actual zonal wind u below 100 km in the extatopics, with the maximum diffeence less than 5 ms 1 (10%) (not shown). Because of this good ageement, u is intechangeable with the gadient wind in the following analysis. Figues 1a and 1b show the paameteized zonal mean GWF in WACCM and the zonal mean GWF obtained fom (2), espectively. It is seen that the estimated GWF epoduces the geneal mophology of the paameteized GWF in both hemisphees in the MLT egion. The two ae in good quantitative ageement except at places whee the paameteized GWF maximizes (80 85 km aound 50 in the summe hemisphee and aound 70 and 80 km at mid to low latitudes in the winte hemisphee). The infeed GWF thee is weake than the maximum GWF. This discepancy at the maximum GWF is educed if the meidional advection tem is included: F x GW u tan f ¼ f þ v þ Figue 1c shows excellent ageement with Figue 1a. Theefoe, by compaing to WACCM simulations, (2) is a good fist-ode appoximation to the momentum balance in the MLT egion, and the meidional advection tem can povide coection to this appoximation. The advection tem includes both advection by the mean flow and the v eddy advection tem 1. It is woth noting that the gadient wind balance could still be easonable in the zonal diection fo the eddy components [Obeheide et al., 2002]. Theefoe, the eddy advection tem can be appoximated using both zonal and meidional gadient winds. Equations (2) and (4) allow us to infe zonal mean GWF fom meidional wind measuement and zonal wind o tempeatue measuement in the MLT egion in the extatopics. This is valuable given ð4þ 2of5

3 Figue 2. Monthly mean (a) zonal and (b) meidional wind climatology fom the Na lida at CSU. (c) Monthly mean gavity wave focing deduced fom the climatological winds using (2). Contou intevals: 10 ms 1 (Figue 2a), 5 ms 1 (Figue 2b), and 25 ms 1 d 1 (Figue 2c). Solid contou lines: eastwad in Figues 2a and 2c, nothwad in Figue 2b. the impotance of this quantity in the MLT and the difficulty of measuing it diectly. 3. Gavity Wave Focing Infeed Fom Obsevations [7] The mean zonal and meidional wind climatology between km above Fot Collins is obtained fom multiple yeas of 24-hou Na-lida measuements at CSU [Yuan et al., 2008]. Affoded by the 24-hou measuements of this lida system, tidal waves have been emoved in pocessing the data to obtain the mean winds. The mean winds can still have contibutions fom planetay waves (PWs), though the magnitudes of the taveling PWs should be significantly educed afte aveaging ove each month fom multiple yeas. The quasi-stationay PWs (QSPWs) ae usually not vey lage above 80 km. Theefoe, the monthly climatological winds obtained should be appoximately equal to the zonal mean winds, and (2) can be applied to deive the zonal GWF climatology. It should be noted that the method can intoduce lage eo if applied duing peiods with enhanced QSPWs (e.g. statospheic sudden waming), because of the lage diffeence between tempoal mean and zonal mean winds. [8] Figues 2a and 2b ae the monthly climatological zonal and meidional winds, espectively, fom the CSU lida measuements, and Figue 2c is the zonal GWF deived fom these winds using (2). The GWF is eastwad duing most of the summe months (Apil Octobe) between km, and is westwad in pat o all of that height ange duing the winte months. The eastwad GWF duing the summe months is geneally stonge than the westwad GWF duing the winte months. The maximum eastwad GWF occus in May at 87 km with a magnitude of 130 ms 1 d 1, and the maximum westwad GWF is found in Januay at 83 km with a magnitude of 100 ms 1 d 1. The GWF changes apidly fom Apil to May within the obseved altitude ange. As agued by Liu and Roble [2004], a change of GWF is a likely cause of the atomic oxygen sping equinox tansition, and this deived GWF lends suppot to that agument. By compaing the GWF with the monthly zonal wind in Figue 2a, it is clea that the GWF geneally coesponds well to the vetical wind shea aound the wind evesal. The apid change in the mean zonal wind afte sping equinox is also consistent with the apid incease in GWF. [9] The deived GWF also suppots model studies of GWF, which ae mostly paameteized and tuned in global models so that the zonal winds match obsevations [e.g., Gacia and Solomon, 1985] (also Figue 1). The model esults suggest that the GWF in the summe hemisphee is stong and has a pominent peak aound the mesopause egion, while in the winte hemisphee the GWF is elatively weak and moe unifomly distibuted ove altitude. The magnitudes of the GWF aound June and Decembe/Januay shown in Figue 2c ae simila to those fom WACCM (Figue 1a) at 41 S and 41 N, espectively. [10] At 41 latitude, a 1 ms 1 eo in the mean meidional wind tanslates to an eo of ms 2 o 8.2 ms 1 d 1 of mean GWF, accoding to (2). The eo ba of the monthly mean meidional wind fom the lida measuement is ±2 ms 1 between km, mainly due to geophysical vaiability, and inceases to ±5 ms 1 at 100 km with inceasing measuement eos [Yuan et al., 2008, Figue 2]. Theefoe, the eo of GWF between km is ±16.4 ms 1 d 1 and inceases to ±41 ms 1 d 1 at 100 km. An additional eo comes fom neglecting the meidional advection tem, especially at altitudes whee the GWF maximizes, as discussed in the pevious section. Calculation of this tem equies knowledge of the meidional shea of the zonal wind. This infomation may be deived fom netwoks of gound based measuements at diffeent latitudes, o the ability to make wind measuements at multiple azimuth angles at appopiate accuacy. [11] Equation (2) can also be applied to wind measuements fom satellite to estimate zonal mean GWF and its latitude distibution. Figues 3a and 3b ae the zonal mean zonal and meidional wind, espectively, calculated fom TIMED/TIDI measuements. These ae 61-day aveage zonal mean winds centeed on day 352 of 2005 [Wu et al., 2008]. The zonal mean zonal wind has been compaed with the zonal mean geostophic zonal wind deived fom TIMED/SABER tempeatue measuements fo the same time peiod. It is found that the two ae in geneal ageement at middle to high latitudes, though the TIDI zonal wind displays a westwad bias of about 10 ms 1 compaed with the geostophic zonal wind (not shown). Figue 3c is the zonal mean GWF deived fom the winds using (2). The GWF in the southen (summe) hemisphee is eastwad between km (mid-latitudes) o km (polewad of 40 S), 3of5

4 Figue 3. Zonal mean (a) zonal wind and (b) meidional wind calculated fom 61 days of TIDI measuements aound day 352, (c) Zonal mean gavity wave focing deived fom the measued winds using (2). Contou intevals: 10 ms 1 (Figue 3a), 5 ms 1 (Figue 3b), and 25 ms 1 d 1 (Figue 3c). Solid contou lines: eastwad in Figues 3a and 3c, nothwad in Figue 3b. and the maximum eastwad GWF at southen mid-latitudes is 75 ms 1 d 1. In the nothen (winte) hemisphee midlatitudes the GWF is westwad between km and becomes weakly eastwad above, while westwad above 85 km polewad of 50 N. At mid-latitudes the westwad GWF is elatively weak (below 50 ms 1 d 1 ), and it eaches lage values (about 100 ms 1 d 1 ) at highe latitudes. The values and the vetical vaiation of GWF at nothen midlatitudes ae in geneal ageement with those obtained fom CSU lida measuements (Figue 2c) fo winte (Decembe and Januay). The values at southen mid-latitudes above 85 km ae weake than those fom WACCM (Figue 1a). The GWF below 85 km in the southen hemisphee is significantly diffeent fom the model climatology, which could esult fom geophysical vaiability and/o bias in TIDI analysis. [12] The pecision of the TIDI zonal mean wind is 1.5 ms 1 [Wu et al., 2008], which tanslates to 3.3 ms 1 d 1 at 10 and 17.8 ms 1 d 1 at 70. In addition to the eo fom neglecting meidional advection, thee could also be a systematic bias in meidional wind (as well as zonal wind) due to uncetainty of the zeo wind. Given the dependence of GWF on the mean meidional wind, futue studies will seek bette methods to detemine the zeo meidional wind, so that the latitudinal distibution and tempoal vaiability of GWF can be bette quantified. 4. Conclusions [13] In this wok we have shown that in the extatopical MLT the pimay zonal balance is between the zonal mean GWF and the zonal mean Coiolis foce. The meidional advection of zonal momentum povides highe ode coection to this balance elationship, especially at places whee the GWF maximizes. This is pobably because maximum GWF coesponds to a lage shea of zonal wind and zonal wind evesal, whee PWs ae likely to inteact with the mean wind. This simple balance elation affods the deduction of GWF, at least to leading ode, fom wind measuements in the MLT at extatopical latitudes. This is in contast to that in the statosphee, whee the focing by the PWs is most significant and the calculation of GWF equies knowledge of these PWs and the esidual ciculation [e.g., Alexande and Rosenlof, 2003]. [14] The feasibility of this method is demonstated using climatological zonal and meidional winds fom CSU Na lida and wind measuements fom TIMED/TIDI. The estimated zonal GWF fom these measuements show weak westwad focing duing winte and stong eastwad focing duing summe between km, and thei peak values coespond to lage vetical shea and evesal of mean zonal wind. The GWF estimated fom the CSU wind climatology also displays apid change fom westwad to eastwad aound Apil. [15] It is impotant to extact and emove the tides and PWs when applying this method. Fo gound-based measuements, the emoval of these waves is essential fo the tempoal mean to be a good appoximation of the zonal mean. It is thus impotant to make 24-hou measuements fo tidal emoval, and to eithe have netwoks of gound-based measuements to extact PWs o pefom long time aveaging at a single site to educe PWs. Futhe, simultaneous measuements of the meidional gadient of zonal wind, eithe fom multiple sites o by wind measuements at multiple azimuth angles, will enable calculation of meidional advection of zonal momentum and thus efinement of the GWF calculation. It is thus desiable fo futue studies to apply this method to moe gound-based facilities that ae capable of 24-hou wind measuements (e.g. lida, meteo ada) to bette quantify GWF at extatopical latitudes. [16] Global wind measuements fom TIDI cetainly have the advantage of making it possible to deduce GWF ove extended extatopical latitudes, although the slow pecessing ate of the satellite obit equies multiple days (60 days) of data fo complete local time coveage to sepaate tides, PWs and zonal mean winds. The extacted wind tides and PWs fom TIDI and gadient wind components deived fom SABER will be used to calculate the meidional advection of zonal momentum fo highe ode coection of the GWF in futue studies. The key poblem in applying this method to TIDI wind measuement, howeve, is that systematic bias may stem fom uncetainty in detemining the zeo wind. Removal of the systematic bias equies caeful coss-validation with gound-based measuements. [17] Acknowledgments. We thank Rolando Gacia fo helpful discussions. HLL s effot is suppoted in pat by the Office of Naval Reseach 4of5

5 (N C-0209). QW s effot is suppoted by a NASA gant NAG to NCAR. The National Cente fo Atmospheic Reseach is opeated by the Univesity Copoation fo Atmospheic Reseach unde sponsoship of the National Science Foundation. Refeences Alexande, M. J., and K. H. Rosenlof (2003), Gavity wave focing in the statosphee: Obsevational constaints fom the Uppe Atmosphee Reseach Satellite and implications fo the paameteization in global models, J. Geophys. Res., 108(D19), 4597, doi: /2003jd Gacia, R. R., and S. Solomon (1985), The effect of beaking gavity waves on the dynamics and chemical composition of the mesosphee and lowe themosphee, J. Geophys. Res., 90, Gacia, R. R., et al. (2007), Simulation of secula tends in the middle atmosphee, , J. Geophys. Res., 112, D09301, doi: / 2006JD Holton, J. R. (2004), An Intoduction to Dynamic Meteoology, 535 pp., Elsevie Acad., Bulington, Mass. Khattatov, B. V., et al. (1997), Diunal migating tide as seen by the High- Resolution Dopple Image UARS: 1. Monthly mean global meidional winds, J. Geophys. Res., 102, Killeen, T. L., et al. (2006), Timed Dopple Intefeomete: Oveview and ecent esults, J. Geophys. Res., 111, A10S01, doi: / 2005JA Liebeman, R. S. (1999), The gadient wind in the mesosphee and lowe themosphee, Eath Planets Space, 51, Lindzen, R. S. (1981), Tubulence and stess owing to gavity wave and tidal beakdown, J. Geophys. Res., 86, Liu, H.-L., and R. G. Roble (2004), Dynamical pocesses elated to the atomic oxygen equinox tansition, J. Atmos. Sol. Te. Phys., 66, Obeheide, J., et al. (2002), Geostophic wind fields in the statosphee and mesosphee fom satellite data, J. Geophys. Res., 107(D23), 8175, doi: /2001jd Randel, W. J. (1987), The evaluation of winds fom geopotential height data in the statosphee, J. Atmos. Sci., 44, She, C.-Y., et al. (2004), Tidal petubations and vaiability in mesopause egion ove Fot Collins, CO (41N, 105W): Continuous multi-day tempeatue and wind lida obsevations, Geophys. Res. Lett., 31, L24111, doi: /2004gl Wu, Q., et al. (2008), Global distibution and inte-annual vaiations of mesospheic and lowe themospheic neutal wind diunal tide: 1 Migating tide, J. Geophys. Res., 113, A05308, doi: /2007ja Yuan, T., C.-Y. She, D. A. Kuege, F. Sassi, R. Gacia, R. G. Roble, H.-L. Liu, and H. Schmidt (2008), Climatology of mesopause egion tempeatue, zonal wind, and meidional wind ove Fot Collins, Coloado (41 N, 105 W), and compaison with model simulations, J. Geophys. Res., 113, D03105, doi: /2007jd Zhu, X., J.-W. Yee, and E. R. Talaat (2001), Diagnosis of dynamics and enegy balance in the mesosphee and lowe themosphee, J. Atmos. Sci., 58, H.-L. Liu and Q. Wu, High Altitude Obsevatoy, National Cente fo Atmospheic Reseach, P.O. Box 3000, Boulde, CO , USA. (liuh@uca.edu) D. R. Mash, Atmospheic Chemisty Division, National Cente fo Atmospheic Reseach, P.O. Box 3000, Boulde, CO , USA. C.-Y. She, Depatment of Physics, Coloado State Univesity, Fot Collins, CO 80526, USA. J. Xu, State Key Laboatoy fo Space Weathe, Chinese Academy of Sciences, P.O. Box 8701, Beijing , China. 5of5