JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 11,352 11,359, doi:10.1002/jgrd.50844, 2013 Grvity wve ctivity in the troposphere nd lower strtosphere: An oservtionl study of sesonl nd internnul vritions Yongfu Wu, 1 Wei Yun, 1 nd Jiyo Xu 1 Received 21 April 2013; revised 13 Septemer 2013; ccepted 16 Septemer 2013; pulished 3 Octoer 2013. [1] An 11 yer (1998-2008) temperture nd wind dt set otined over Annette Islnd (55.03 N, 131.57 W) is used to exmine grvity wve ctivity nd their sesonl nd internnul vritions in grvity wve ctivity. Verticl wve numer spectr of normlized temperture nd wind fluctutions re clculted nd re compred with the predictions of grvity wve sturtion models. Results indicte tht there re serious discrepncies etween our mesurements nd erlier oservtionl results t present stge of study of verticl wve numer spectr. The correltion coefficients etween tropospheric nd strtospheric temperture spectrl prmeters re very smll, suggesting tht the result is in greement with previous studies. Time series of totl wve energy revel cler sesonl nd internnul vritions. Mximum wve energy mplitudes occur ner winter of ech yer in the troposphere ndnersummerofechyerinthestrtosphere.specificlly, the mximum wve energy mplitudes in the troposphere show close correspondence with the mximum occurrence rte of dynmicl instility. In ddition, the mximum wve energy mplitudes in the strtosphere lso show close correspondence with the mximum occurrence rte of convective instility. Cittion: Wu, Y., W. Yun, nd J. Xu (2013), Grvity wve ctivity in the troposphere nd lower strtosphere: An oservtionl study of sesonl nd internnul vritions, J. Geophys. Res. Atmos., 118, 11,352 11,359, doi:10.1002/jgrd.50844. 1. Introduction [2] Verticl profiles of tmospheric wind nd temperture in the troposphere nd middle tmosphere exhiit fluctutions with verticl scles rnging from few tens of meters to few tens of kilometers, which re now widely thought to e due principlly to field of grvity wves. VnZndt [1982] pointed out tht the oserved spectr tend to hve the sme shpe nd power spectrl density regrdless of sesons, meteorologicl conditions, nd geogrphicl loctions. Susequently, motivted y oservtions of universl spectrum, vrious grvity wve sturtion models hve een developed, including liner instility [Dewn nd Good, 1986; Smith et l., 1987], nonliner wve-wve interction [Weinstock, 1990], Doppler spreding [Hines, 1991; Grdner, 1994], nd sturted-cscde similitude theory [Dewn, 1997]. [3] During the pst two decdes, numer of uthors hve exmined the chrcteristics nd vriility of the tmospheric spectr using vriety of tmospheric wind nd temperture oservtions from different pltforms, including mesurements from rdiosondes [Tsud et l., 1991; Allen nd Vincent, 1995; Nstrom et l., 1997; Nstrom nd VnZndt, 2001], 1 Stte Key Lortory of Spce Wether, Center for Spce Science nd Applied Reserch, Chinese Acdemy of Sciences, Beijing, Chin. Corresponding uthor: W. Yun, Stte Key Lortory of Spce Wether, Center for Spce Science nd Applied Reserch, Chinese Acdemy of Sciences, Beijing 100190, Chin. (wyun@spcewether.c.cn) 2013. Americn Geophysicl Union. All Rights Reserved. 2169-897X/13/10.1002/jgrd.50844 MST rdr [Smith et l., 1985; Fritts et l., 1988; Tsud et l., 1989], rocket [Dewn et l., 1984; Wu nd Xu, 2006], nd stellite [Wng et l., 2000]. A universl spectrum nd severl grvity wve sturtion modes hve een proposed [VnZndt, 1982; Dewn nd Good, 1986; Smith et l., 1987; Weinstock, 1990; Hines, 1991; Grdner, 1994; nd Dewn, 1997]. However, oserved spectr re usully compred with the models of Dewn nd Good [1986] nd Smith et l. [1987], including slope nd mplitude. [4] Allen nd Vincent [1995] hve pointed out tht lthough the greement etween theory nd experiment ppers to hve een ccepted lredy, the shpes nd mplitudes of verticl wve numer power spectr cn vry with geogrphic position nd time. Moreover, the extent of these vritions is not well known t present nd the ville dt set of high-resolution rdiosonde mesurements is idel for ddressing the prolem. Therefore, our first purpose in this study is to use n 11 yer (Ferury 1998 to Decemer 2008) rdiosonde dt set conducted t Annette Islnd (55.03 N, 131.57 W), US, to exmine the chrcteristics of verticl wve numer spectr of normlized temperture nd wind fluctutions in the troposphere nd lower strtosphere. During the pst decde, the grvity wve ctivity nd its sesonl nd internnul vritions hve een studied primrily t tropicl-ocen sites nd t midltitude continentl sites, using rdiosonde oservtions [Alexnder nd Vincent, 2000;Vincent nd Alexnder, 2000; Zhng nd Yi, 2007].However,verylittleinformtion on the sesonl nd internnul vritions of totl wve energy E(=K E + P E ) t midltitude sites is currently ville. Therefore, our second purpose is to study the sesonl nd internnul vritions of totl wve energy E t this midltitude site using the sme high-resolution rdiosonde mesurements. 11,352
Tle 1. The Numer of Blloon Soundings in Ech Month Used in This Pper From Ferury 1998 to Decemer 2008 Yer J F M A M J J A S O N D 1998 0 44 51 48 58 47 0 30 29 35 42 26 1999 28 33 40 33 43 52 49 41 38 27 35 23 2000 31 42 42 41 50 51 54 48 33 45 38 32 2001 47 45 39 44 48 47 54 57 38 33 36 46 2002 48 36 41 45 50 50 47 37 38 37 39 42 2003 41 45 40 52 48 0 44 39 25 27 23 35 2004 35 31 27 43 48 51 51 47 36 35 22 28 2005 24 34 48 46 57 55 57 54 39 42 34 41 2006 50 35 40 46 55 53 47 56 36 37 38 40 2007 32 38 38 52 54 54 51 57 45 39 36 0 2008 48 36 0 43 49 44 47 45 45 26 36 32 [5] This pper is orgnized s follows. We egin y descriing the experimentl dt nd nlysis procedures in section 2. Our oservtionl results nd discussions re presented in section 3. The conclusions re given in section 4. 2. Experimentl Dt nd Anlysis Methods [6] An 11 yer (1998 2008) temperture nd wind dt set otined from 7590 high-resolution lloon soundings t Annette Islnd (55.03 N, 131.57 W), US, is used to study grvity wve ctivity nd sesonl nd internnul vritions of totl wve energy in the troposphere nd lower strtosphere. Tle 1 summrizes the numer of lloon soundings lunched in ech month used in this pper from Ferury1998 to Decemer 2008. The lloon soundings were lunched twice per dy t 1100 nd 2300 UT nd were recorded t 6 s intervls which correspond, pproximtely, to 30 m height resolution given the pproximte 5 m/s scending rte of the lloon. We interpolte the temperture nd wind dt set t 50 m height intervls using cuic spline function in order to otin eqully spced dt points. The temperture nd wind dt with height resolution of 50 m re used to derive verticl wve numer spectr of normlized temperture nd wind fluctutions s well s totl wve energy. [7] Further, we restrict the nlysis to the height rnges of 1.65 8.00 km in the troposphere nd 18.00 24.35 km in the lower strtosphere, giving 6400 m height rnge. This tropospheric height rnge eginning t 1.65 km is selected in order to exclude plnetry oundry lyer effects [Nstrom et l., 1997; Nstrom nd VnZndt, 2001]. This strtospheric height rnge eginning t 18.00 km is selected in order to exclude the possile effect of the tropopuse on the verticl wve numer spectr of the normlized temperture nd wind fluctutions. Between 1998 nd 2008, out 70% of ll lloon soundings reched height of 24.35 km. Figure 1 displys n exmple of temperture (Figures 1 nd 1c) nd Brunt-Väisälä frequency squred (Figures 1 nd 1d) profiles oserved on 14 Octoer 2000 (Figures 1 nd 1) nd 30 Octoer 2000 (Figures 1c nd 1d). The Brunt-Väisälä frequency squred N 2 is N 2 ¼ ðg=tþð T= z þ ΓÞ; (1) where T is the temperture, g is the ccelertion due to grvity, nd Γ is the ditic lpse rte. The temperture profile in Figure 1 is reltively simple. The temperture decreses from the surfce lyer to distinct tropopuse t round 10.35 km, which is mrked y lrge increse in N 2 profile in Figure 1. In contrst, the temperture nd N 2 profiles in Figures 1c nd 1d re complex nd re usully not clerly recognized. The min tropopuse is seen to occur t out 16.8 km, consistent with lrge increse in N 2 in Figure 1d. However, there is lso zone of high stility ( secondry tropopuse) locted t 11.3 km nd which hs corresponding mximum in N 2. The region etween 11.3 nd 16.8 km is trnsition region etween purely tropospheric ehvior elow nd purely strtospheric ehvior ove. [8] Now, we descrie our procedure for spectrl nlysis. Dewn nd Grossrd [2000] showed tht the nlysis procedure used y Nstrom et l. [1997] did not include prewhitening/postcoloring nd tht their results were contminted y n rtifct not previously discussed in the literture. Therefore, we pply the prewhitening/postcoloring procedure in this pper. First, the mens nd liner trends re removed from the normlized temperture, zonl wind, nd meridionl wind profiles. Then the normlized temperture, zonl wind, nd meridionl wind profiles re prewhitened y mens of differentiting filter given y y i ¼ x i βx i 1 (2) where x i nd y i re the dt series efore nd fter prewhitening, nd β is tken to e 1. Second, cosine tpe window is pplied to the differenced dt. The differenced profiles re then trnsformed to the power spectrl density using the fst Fourier trnsform routine. Finlly, the power spectr densities of the prewhitened dt, F pw, re djusted to compenste the effect of the differencing nd the cosine tper window. [9] The post-colored spectr, F pwpc (m), re given y F pwpc ðm i Þ ¼ F pw ðm i Þ 21 ½ cosð2πi=mþš ; (3) where pwpc is prewhitening/postcoloring, m i is the ith wve numer, nd M is numer of dt points. c Figure 1. ( nd c) An exmple of temperture, nd ( nd d) N 2 profiles mesured on 14 Octoer (Figures 1 nd 1) 2000 nd 30 Octoer (Figures 1c nd 1d) 2000. The thick verticl rs on the N 2 profiles show the men vlues of N 2 nd the height rnges used in spectrl nlysis. d 11,353
3. Oservtionl Results nd Discussions Figure 2. Men verticl wve numer spectr of normlized temperture fluctutions in the () troposphere nd in the () lower strtosphere. The dshed stright line in Figures 2 nd 2 is predicted y the liner sturtion theory of Dewn nd Good [1986] nd Smith et l. [1987]. [10] Our purposes in this section re to exmine the chrcteristics of verticl wve numer spectr of normlized temperture nd zonl nd meridionl wind fluctutions nd to ssess the sesonl nd internnul vritions of totl wve energy using ll verticl profiles of temperture nd zonl nd meridionl wind in the troposphere nd the lower strtosphere. To do this, we first clculte individul verticl wve numer spectr of ech normlized temperture nd zonl nd meridionl wind fluctutions. Then these individul verticl wve numer spectr of normlized temperture nd zonl nd meridionl wind fluctutions re verged rithmeticlly to increse confidence level in the spectrl power. Finlly, the totl wve energy is otined from the verticl wve numer spectr of normlized temperture nd zonl nd meridionl wind fluctutions. 3.1. Men Spectr [11] The men spectr of normlized temperture fluctutions in the troposphere nd the lower strtosphere otined from 5287 lloon soundings re shown in Figure 2. The dshed stright line in Figure 2 is predicted y the liner sturtion theory of Dewn nd Good [1986] nd Smith et l. [1987] with the spectrl slope of 3.0. The two men normlized temperture spectr in Figures 2 nd 2 exhiit severl significnt fetures. First, in the wve numer rnge of 1.09 10 3 5.00 10 3 cyc/m, the two men normlized temperture spectr hve slopes ner 2.73 in the troposphere nd 2.70 in the lower strtosphere, which is consistently smller thn the slope of 3 predicted y the liner sturtion theory. The wve numer of 5.00 10 3 cyc/m corresponds to hlf the Nyquist wve numer due to the 50 m resolution. In this wve numer rnge of 1.09 10 3 5.00 10 3,the lising effects should e insignificnt. The sudden decrese in the slope t the right-hnd end of the spectr is proly due to lising, s descried y Allen nd Vincent [1995]. Second, the spectrl mplitude in the troposphere is consistently lrger thn the expected prediction y s much s fctor of out 2.0 ut the spectrl mplitude in the lower strtosphere is consistently less thn theoreticl prediction. Third, the two men spectr exhiit cler discontinuities in the slopes to less negtive vlues t smll wve numers of 3.13 10 4 (cyc/m) in the troposphere nd of 4.69 10 4 (cyc/m) in the lower strtosphere. This yields n estimte of the dominnt verticl wvelength t these heights of λ ¼ 1 m ¼ 3:2kminthetroposphere nd λ ¼ 1 m ¼ 2:1km in the lower strtosphere. The dominnt verticl wvelengths of 3.2 km in the troposphere nd 2.1 km in the lower strtosphere re consistent with erlier oservtionl results. Fritts et l. [1988] showed tht the dominnt verticl wvelength ws λ * =2 1/3 /m * =2.5 3.0 km in the troposphere nd λ * =2 1/3 /m * =2.5 2.9 km in the lower strtosphere for velocity nd temperture dt, respectively. They re lso close to the vlue of λ * = 2.0 km in the temperture field in the troposphere nd the lower strtosphere reported y Tsud et l. [1991] s well s to the vlue of λ * =2.4kmndλ * = 2.7 km in the temperture field in the troposphere nd the lower strtosphere reported y Allen nd Vincent [1995]. It must e pointed out, however, tht the conversion from dominnt verticl wve numer m * to dominnt verticl wvelength λ * is not the sme s used y other uthors, some, including the oservtions presented here, use λ * =1/m * [Tsud et l., 1991; Allen nd Vincent, 1995], othersuse λ * =2 1/3 /m * [Fritts et l., 1988]. This is importnt to er in mind when we discuss the dominnt verticl wvelength. [12] We exmine the normlized temperture spectr sorted y seson (winter nd summer). We first group the individul normlized temperture spectr into summer (June, July, nd August) nd winter (Decemer, Jnury, nd Ferury) efore verging. Then the sesonl men spectr of normlized temperture fluctutions re clculted. The sesonl men spectr re displyed in Figure 3. We cn see tht in the wve numer rnge of 1.09 10 3 5.00 10 3 cyc/m, there is no sesonl vrition. [13] The men verticl wve numer spectr of zonl nd meridionl wind fluctutions in the troposphere nd the lower strtosphere re shown in Figure 4. The dshed stright line in Figure 4 is predicted y the liner sturtion theory of Dewn nd Good [1986] nd Smith et l. [1987] with the spectrl slope of 3.0. In the wve numer rnge of 1.09 10 3 5.00 10 3 cyc/m, the tropospheric slopes in Figure 3. Sesonl men verticl wve numer spectr of normlized temperture fluctutions in the () troposphere nd in the () strtosphere. The curves leled summer nd winter re men spectr otined from June, July, nd August nd from Decemer, Jnury, nd Ferury. 11,354
c Figure 4. Men verticl wve numer spectr of () zonl nd (c) meridionl wind fluctutions in the troposphere nd () zonl nd (d) meridionl wind fluctutions in the lower strtosphere. The dshed stright line is predicted y the liner sturtion theory of Dewn nd Good [1986] nd Smith et l. [1987]. Figures 4 nd 4c re 4.09 nd 4.44 nd the strtospheric slopes in Figures 4 nd 4d re 3.50 nd 3.51, which is significntly steeper thn the slope of 3 predicted y the liner sturtion theory. The spectrl mplitudes in Figures 4 4d show lrge difference etween oservtion (the solid line) nd theory (dshed stright line). At the wve numer 5.00 10 3 (cyc/m), the oservtionl mplitudes re out 1 order of mgnitude smller thn the theoreticl mplitudes. The reson for this is not fully understood ecuse we do not know how these wind dt re otined from originl record. [14] Except for the oservtionl results of verticl wve numer spectr of wind fluctutions discussed y Pfenninger et l. [1999], the uthors re wre of no such steeper slopes occurring in the troposphere nd lower strtosphere. Pfenninger et l. [1999] gve review of their wind spectr nd noted the wind spectr hve much steeper slope thn the temperture spectr. We suspect tht this is result of the proprietry filtering process employed during the dt cquisition which excessively ttenutes the high verticl d wve numer components of the spectrum. Our wind spectr re very similr to those otined y Pfenninger et l.[1999]. Thus, we think tht it is lso possile tht our wind dt used in this pper gretly ttenute the high verticl wve numer components of the wind spectr. 3.2. Correltion Slopes nd Amplitudes Between the Troposphere nd Strtosphere [15] If grvity wves generted in the troposphere propgte upwrd without reking or sturtion processes, filtering effects, there should e significnt correltion in the spectrl properties of the two regions. Pfenninger et l. [1999] exmined their temperture spectr nd otined the correltion vlues of 0.11 for the slope nd 0.19 for the mplitude [see Pfenninger et l., 1999, Figure 8]. The two correltion coefficients re very smll, suggesting tht little coherence exists etween wves in the troposphere nd wves in the strtosphere. In contrst, Nstrom et l. [1997] exmined their F u + v spectr nd otined significnt correltion vlues of 0.40 for the slope nd 0.52 for the mplitude, suggesting tht the tropospheric nd strtospheric spectr re composed of wves tht hve common source. Following Pfenninger et l.[1999]ndnstrom et l. [1997], we exmine the correltion coefficients of the normlized temperture spectr. The result of nlysis is illustrted in Figure 5. Figure 5 shows the correltion coefficient is 0.04 for the slope nd 0.05 for the mplitude. The t test shows tht t the 99% level of significnce, there is no detectle significnce of the slope nd mplitude. The insignificnt correltions show tht the spectr in the troposphere nd the lower strtosphere re composed of wves tht hve different source. 3.3. Slope nd Amplitude of the Normlized Temperture Spectr [16] The spectrl slope nd mplitude re two min prmeters descriing the chrcteristics of the spectrum. We clculte the spectrl slopes in the wve numer rnge from 1.09 10 3 to 5.00 10 3 cyc/m nd the spectrl mplitudes t m = 2.5 10 3 cyc/m for ll soundings. The histogrms of the spectrl slope re reveled in Figure 6, which shows tht they oth re pproximtely normlly distriuted. Further, Figure 6 shows tht the steepest nd shllowest slopes re 5.75 nd 0.50 in the troposphere nd 5.02 nd 0.31 in Figure 5. () Slope nd () mplitude of normlized temperture spectr in the troposphere versus those in the lower strtosphere. Figure 6. Histogrms of the spectrl slopes of normlized temperture spectr nd their est fit Gussin distriution in the () troposphere nd in the () lower strtosphere. 11,355
Figure 7. Histogrms of the spectrl mplitudes of normlized temperture spectr nd their est fit Gussin distriution in the () troposphere nd in the () lower strtosphere. the lower strtosphere, respectively. These dt show tht there is considerle vriility in the slope from one flight to nother. [17] The histogrms of the spectrl mplitude in Figure 7 lso show tht they oth re pproximtely normlly distriuted. Figure 7 shows tht t m = 2.5 10 3 cyc/m, the mximum nd minimum mplitudes re 5.55 nd 5.63 in the troposphere nd 3.34 nd 3.13 in the lower strtosphere, respectively. These dt lso show tht there is considerle vriility in the mplitude. [18] Similr vriility in oth slope nd mplitude to Figures 6 nd 7 is lso otined y lloon, lidr, nd rocket [Senft nd Grdner, 1991; Nstrom et l., 1997; Pfenninger et l., 1999; Wu nd Xu, 2006]. As descried y Fritts nd Alexnder [2003] There re, in ddition, mny resons to expect tht the spectrum will lso exhiit considerle vriility sptilly nd temporlly ecuse of vrious sources, filtering environments, qusi-discrete wves, nd grvity wve interctions with lrger scles of motion, it is therefore not surprising tht there is considerle vriility in oth slope nd mplitude of the individul spectrum. 3.4. Wve Energy [19] We exmine the sesonl nd internnul vriility in wve energy y computing the monthly-men vlues of potentil nd kinetic energies. [20] The potentil energy density is given y PE ¼ g2 2N 2 T =T 2: (4) overrs in equtions (4) nd (5) show the totl zonl, meridionl, nd normlized temperture vrinces in the wve numer rnge of 1.09 10 3 5.00 10 3 cyc/m. [23] Wefirst clculte the monthly-men vlues of u 2, v 2, nd T 2 =T in the wve numer rnge of 1.09 10 3 5.00 10 3 cyc/m from the monthly-men spectr of the zonl, meridionl, nd normlized temperture fluctutions. Then we sustitute the monthly-verged vlues of u 2 ; v 2 ; 2 T =T, N 2, nd g into equtions (4) nd (5). Finlly, the sesonl nd internnul vritions in E re smoothed y pplying five-point running men. The resulting monthlymen profiles of wve energy re shown in Figure 8. It is the wve energy time series, shown in Figure 8 tht exhiits sesonl nd internnul vritions with time, with mximum wve energy mplitudes occur ner winter of ech yer in the troposphere in Figure 8 nd ner summer of ech yer in the lower strtosphere in Figure 8. [24] Fritts nd Alexnder [2003] showed tht two most importnt grvity wve sources for the middle tmosphere re convection nd wind sher. Following Fritts nd Alexnder [2003], we exmine the tmospheric stility. The Richrdson numer, Ri, cn e used s convenient mesure of convective nd dynmicl stility, respectively. The Richrdson numer Ri is N 2 Ri ¼ 2 2 ; (7) u þ v z z where u nd v re the zonl nd meridionl winds. Convective instility occurs when N 2 < 0, while dynmicl instility [21] The kinetic energy density is given y KE ¼ 1 2 u 2 þ v 2 : (5) [22] The totl wve energy density is given y E ¼ PE þ KE; (6) where u 2 nd v 2 re the monthly-men vlues of zonl nd meridionl wind vrinces nd re otined from the zonl 2 nd meridionl wind spectr, respectively, T =T is the monthly-men vlues of the normlized temperture vrince nd is otined from the normlized temperture spectr. The Figure 8. Time series of monthly-men wve energy in the () troposphere nd in the () lower strtosphere oserved during n 11 yer period. 11,356
Figure 9. () Time series of monthly-men wve energy nd () occurrence rte of dynmicl instility in the troposphere oserved during n 11 yer period. occurs when 0 < Ri < 0.25. First, we determine the grdients T/ z, u/ z, nd v/ z y cuic spline function over 300 m using vlues for every 50 m. Then we sustitute the N 2, u/ z,nd v/ z into eqution (5) nd clculte the occurrence rte of dynmicl instility, which is defined y N di N o, where N di denotes the numer of occurrences of dynmicl instility in month nd N o denotes the totl numer of oservtions in month. A similr exercise using N 2, u/ z, nd v/ z yields the occurrence rte of convective instility, which is defined y N ci N o,wheren ci denotes the numer of occurrences of convective instility in month nd N o denotes the totl numer of oservtions in month. Finlly, the occurrence rte of dynmicl instility or convective instility is smoothed y pplying five-point running men [25] The smoothed profile of occurrence rte of dynmicl instility, together with the oserved vrition in E in the troposphere, is shown in Figure 9. There is cler positive correltion etween the occurrence rte of dynmicl instility nd E. The correltion coefficient is 0.79. The t test shows tht the correltion coefficient of 0.79 is significnt t the 99% level. This suggests tht in the troposphere the lrger vlue of wind sher nd smller positive vlue of Brunt-Väisälä frequency squred, N 2, re the min excittion source of the sesonl nd internnul vritions in E. It must e noted, however, tht since the high wve numer components of the wind fluctutions re excessively filtered, the ctul occurrence rte of dynmicl instility my e underestimted. A similr nlysis is lso mde for studying the reltionship etween the convection instility nd E in the troposphere, ut no cler correltion is found. Thus, they will not e shown. [26] To investigte the reltionship etween the occurrence rtes of convective or dynmicl instility with E in the lower strtosphere, we further clculte the occurrence rte of convective nd dynmicl instility similr to those in the troposphere. The smoothed profile of occurrence rte of convective instility, together with the oserved vrition in E in the lower strtosphere, is shown in Figure 10. We see from Figure 10 tht there is lso cler positive correltion etween the occurrence rte of convective instility nd E. The correltion coefficient is 0.64. The t test shows tht the correltion coefficient of 0.64 is significnt t the 99% level. This suggests tht in the lower strtosphere the convective instility is the min excittion source of the sesonl nd internnul vritions in E. As descried ove, since the high wve numer components of the wind fluctutions re excessively filtered, the ctul occurrence rte of convective instility my e underestimted. A similr nlysis is lso mde for studying the reltionship etween the dynmicl instility nd E in the lower strtosphere, ut we do not find cler correltion etween dynmicl instility nd E. Thus, they will not e shown. 3.5. The Rtio of Kinetic Energy to Potentil Energy [27] As descried in section 3.4, the monthly-men vlues of kinetic energy nd potentil energy hve een clculted in the troposphere nd lower strtosphere. Now, we use five-point running men to remove smll-scle noise in the profiles of kinetic energy nd potentil energy. The rtio of kinetic energy to potentil energy (R) is shown in Figure 11. The men rtio is 0.73 in the troposphere, which is the sme vlue s Zhng nd Yi [2007] reported t Wuhn sttion, Chin, nd is difficult to e explined from the grvity wve theory. This implies more complex wve field thn wht is ssumed in most current models. On the other hnd, more interesting Figure 10. () Time series of monthly-men wve energy nd () occurrence rte of convective instility in the lower strtosphere oserved during n 11 yer period. 11,357
Figure 11. Rtio (R) of kinetic energy to potentil energy in the () troposphere nd in the () lower strtosphere. The dshed lines show the men vlues of R. result is tht the men rtio is 1.75 in the lower strtosphere, which is close to 1.6 otined y Vincent nd Alexnder [2000]. This men rtio of out 1.6 otined from rdiosonde shows the wve field is dominted y inerti-grvity wves (the intrinsic frequency ω the inertil frequency f ) rther thn high-frequency wves (the intrinsic frequency ω >> the inertil frequency f ), s descried y Vincent nd Alexnder [2000]. [28] There re some other rdiosonde oservtions of the rtio of kinetic energy to potentil energy (R). Geller nd Gong [2010] showed the men R is out 2 to 3 in the troposphere nd out 1.5 to 2.5 in the lower strtosphere. Pfenninger et l. [1999] reported tht the kinetic energy ws lmost lwys lrger thn potentil energy y t lest fctor of 4 in the troposphere nd lower strtosphere. Nstrom et l. [1997] showed tht the men R ws out 2.5 in the troposphere nd 5 in the strtosphere. Nstrom nd VnZndt [2001] further showed tht the men R ws 3.1 in the troposphere nd 6.2 in the strtosphere s suggested. Zhng nd Yi [2007] rgued tht the oserved men R vried from 0.46 to 0.73 in the troposphere nd from 1.31 to 3.44 in the strtosphere. De l Torre et l. [1999] found tht the men R ws out 5 in the strtosphere. These oservtionl results re oviously inconsistent with our oservtionl results. 4. Conclusions [29] We hve presented spectrl nlysis of temperture nd zonl nd meridionl wind profiles sed on n 11 yer dt set from Ferury 1998 to Decemer 2008 oserved in the troposphere nd lower strtosphere over Annette Islnd (55.03 N, 131.57 W), US. The oservtions re used to exmine grvity wve ctivity nd its vritions with time. The spectrl nlysis leds to the following conclusions. [30] 1. The slopes of the men verticl wve numer spectr of the normlized temperture fluctutions in the wve numer rnge from 1.09 10 3 to 5.00 10 3 cyc/m re out 2.73 in the troposphere nd out 2.70 in the lower strtosphere, which is consistently smller thn the slope of 3 predicted y current grvity wve sturtion models. The spectrl mplitude in the troposphere is found to e consistently lrger thn expected y s much s fctor of out 2.0, ut the spectrl mplitude in the lower strtosphere is consistently less thn expected y theoreticl prediction. The results from our nlysis re inconsistent with some erlier oservtionl results. [31] 2. The zonl nd meridionl wind spectr revel much steeper slope compred to the theoreticl prediction. At the wve numer 5.00 10 3 cyc/m, the oservtionl mplitudes re out 1 order of mgnitude smller thn the theoreticl mplitudes. These oserved results re inconsistent with erlier oservtionl results. [32] 3. For the normlized temperture spectr, the correltion coefficient etween slopes is out 0.04 nd etween the mplitudes is out 0.05. The insignificnt correltion shows tht the tropospheric nd strtospheric normlized temperture spectr my e composed of wves tht hve different source. [33] 4. Time series of totl wve energy revel cler sesonl nd internnul vritions. Mximum wve energy mplitudes occur ner winter of ech yer in the troposphere nd ner summer of ech yer in the strtosphere. [34] 5. The mximum wve energy mplitudes in the troposphere show close correspondence with the mximum occurrence rte of dynmicl instility. The correltion coefficient is 0.79. This suggests tht in the troposphere the lrger vlue of wind sher nd smller positive vlue of Brunt-Väisälä frequency squred, N 2, re min excittion source of the sesonl nd internnul vritions in totl wve energy. [35] 6. The mximum wve energy mplitudes in the strtosphere lso show close correspondence with the mximum occurrence rte of convective instility. The correltion coefficient is 0.64. This suggests tht the convective instility is the min excittion source of the sesonl nd internnul vritions in totl wve energy. [36] 7. The rtio of kinetic energy/potentil energy is out 0.73 in the troposphere nd is difficult to e explined from the grvity wve theory. On the other hnd, the rtio of kinetic energy/potentil energy is out 1.75 in the lower strtosphere, which is close to 1.6. This suggests tht wve field is dominted y inerti-grvity wves, rther thn high-frequency wves. [37] Acknowledgments. The provision of dt y Ntionl Wether Service Sounding is grtefully cknowledged. We lso thnk the three nonymous reviewers for their vlule suggestions. This work is supported y the Chinese Acdemy of Sciences (KZZD-EW-01-2), the Ntionl Science Foundtion of Chin (41274153, 41229001), the Ntionl Importnt Bsic Reserch Project of Chin (2011CB811405), nd the project is lso supported y the Specilized Reserch Fund for Stte Key Lortories. References Alexnder, M. J., nd R. A. Vincent (2000), Grvity wves in the tropicl lower strtosphere: A model study of sesonl nd internnul vriility, J. Geophys. Res., 105, 17,983 17,993. Allen, S. J., nd R. A. Vincent (1995), Grvity wve ctivity in the lower tmosphere: Sesonl nd ltitudinl vritions, J. Geophys. Res., 100, 1327 1350. 11,358
De l Torre, A., P. Alexnder, nd A. Girldez (1999), The kinetic to potentil energy rtio nd spectrl seprility from high-resolution lloon soundings ner the Andes mountins, Geophys. Res. Lett., 26, 1413 1416. Dewn, E. M. (1997), Sturted-cscde similitude theory of grvity wve spectr, J. Geophys. Res., 102, 29,799 29,817. Dewn, E. M., nd R. E. Good (1986), Sturtion nd the universl spectrum for verticl profiles of horizontl sclr winds in the tmosphere, J. Geophys. Res., 91, 2742 2748. Dewn, E. M., nd N. Grossrd (2000), Power spectrl rtifcts in pulished lloon dt nd implictions regrding sturted grvity wve theories, J. Geophys. Res., 105, 4667 4683. Dewn, E. M., N. Grossrd, A. F. Quesd, nd R. E. Good (1984), Spectrl nlysis of 10 m resolution sclr velocity profiles in the strtosphere, Geophys. Res. Lett., 11, 80 83. Fritts, D. C., nd M. J. Alexnder (2003), Grvity wve dynmics nd effects in the middle tmosphere, Rev. Geophys., 41(1), doi:10.1029/ 2001RG000106. Fritts, D. C., T. Tsud, T. Sto, S. Fuko, nd S. Kto (1988), Oservtionl evidence of sturted grvity wve spectrum in the troposphere nd lower strtosphere, J. Atmos. Sci., 45, 1741 1759. Grdner, C. S. (1994), Diffusive filtering theory of grvity wve spectr in the tmosphere, J. Geophys. Res., 99, 20,601 20,622. Geller, M. A. nd J. Gong (2010), Grvity wve kinetic, potentil, nd verticl fluctution energies s indictors of different frequency grvity wves, J. Geophys. Res., 115, D11111, doi:10.1029/2009jd012266. Hines, C. O. (1991), The sturtion of grvity wves in the middle tmosphere. II. Development of Doppler-spred theory, J. Atmos. Sci., 48, 1360 1379. Nstrom, G. D., nd T. E. VnZndt (2001), Sesonl vriility of the oserved verticl wve numer spectr of wind nd temperture nd the effects of prewhitening, J. Geophys. Res., 106, 14,369 14,275. Nstrom, G. D., T. E. VnZndt, nd J. M. Wrnock (1997), Verticl wvenumer spectr of wind nd temperture from high-resolution lloon soundings over Illinois, J. Geophys. Res., 102, 6685 6701. Pfenninger, M., A. Z. Liu, G. C. Ppen, nd C. S. Grdner (1999), Grvity wve chrcteristics in the lower tmosphere t south pole, J. Geophys. Res., 104, 5963 5984. Senft, D. C., nd C. S. Grdner (1991), Sesonl vriility of grvity wve ctivity nd spectr in the mesopuse region t Urn, J. Geophys. Res., 96, 17,229 17,264. Smith, S. A., D. C. Fritts, nd T. E. VnZndt (1985), Comprison of mesospheric wind spectr with grvity wve model, Rdio Sci., 20, 1331 1338. Smith, S. A., D. C. Fritts, nd T. E. VnZndt (1987), Evidence of sturtion spectrum of tmospheric grvity wves, J. Atmos. Sci., 44, 1404 1410. Tsud, T., T. Inoue, D. C. Fritts, T. E. VnZndt, S. Kto, T. Sto, nd S. Fuko (1989), MST rdr oservtions of sturted grvity wve spectrum, J. Atmos. Sci., 46, 2440 2447. Tsud, T., T. E. VnZndt, M. Mizumoto, S. Kto, nd S. Fuko (1991), Spectrl nlysis of temperture nd Brunt-Väisälä frequency fluctutions oserved y rdiosondes, MST rdr oservtions of sturted grvity wve spectrum, J. Geophys. Res., 96, 17,265 17,278. VnZndt, T. E. (1982), A universl spectrum of uoyncy wves in the tmosphere, Geophys. Res. Lett., 9, 575 578. Vincent, R. A., nd M. J. Alexnder (2000), Grvity wves in the tropicl lower strtosphere: An oservtionl study of sesonl nd internnul vriility, J. Geophys. Res., 105, 17,971 17,982. Wng, D. Y., W. E. Wrd, B. H. Solheim, nd G. G. Shepherd (2000), Wvenumer spectr of horizontl wind nd temperture mesured with WINDII. Prt I: Oservtionl results, J. Atmos. Sol. Terr. Phys., 62, 967 979. Weinstock, J. (1990), Sturted nd unsturted spectr of grvity wves nd scle-dependent diffusion, J. Atmos. Sci., 47, 2211 2225. Wu, Y. F., nd J. Y. Xu (2006), Comprison of horizontl velocity spectr derived from chff rockets with sturtion models, J. Geophys. Res., 111, D13109, doi: 10.1029/2005JD006065. Zhng, S. D., nd F. Yi (2007), Ltitudinl nd sesonl vritions of inertil grvity wve ctivity in the lower tmosphere over centrl Chin, J. Geophys. Res., 112, D05109, doi:10.1029/2006jd007487. 11,359