Numerical Simulation of the winter polar wave. clouds observed by Mars Global Surveyor. Mars Orbiter Laser Altimeter

Transcription

1 Numerical Simulation of the winter polar wave clous observe by Mars Global Surveyor Mars Orbiter aser Altimeter G. Tobie, F. Forget, an F. ott aboratoire e Métérologie Dynamique (MD), Université Pierre et Marie Curie, Tour ème étage, 4,place Jussieu, PARIS ceex 05, France tobie@lm.jussieu.fr, forget@lm.jussieu.fr, flott@lm.ens.fr Now at aboratoire e Planétologie et Géoynamique, UFR es Sciences et Techniques 2, rue e la Houssinière, BP NANTES ceex 03, France phone : +33 (0) fax : +33 (0) tobie@chimie.univ-nantes.fr 69 pages incluing 3 tables an 10 figures. Submitte to Icarus, 06/09/2002, Revise, 28/01/2003 1

2 Running hea : Simulation of Martian winter north polar wave clous Corresponing Author : Gabriel Tobie aboratoire e Planétologie et Géoynamique, UFR es Sciences et Techniques, 2, rue e la Houssinière, BP NANTES ceex 03, France phone : +33 (0) fax : +33 (0) tobie@chimie.univ-nantes.fr 2

3 Abstract In 1998, the Mars Orbiter aser Altimeter reveale the presence of isolate or quasi-perioic thick clous uring the Martian polar night. They are believe to be compose of CO ice particles an to be tilte against the win irection, a feature characteristic of vertically propagating orographic gravity waves. To support that interpretation, we present here numerical simulations with a two imensional anelastic moel of stratifie shear flow that inclues simple CO ice microphysics. In some of the simulations presente, the orography is an iealize trough, with imensions characteristic of the many troughs that shape the Mars polar cap. In others, it is near the real orography. In the polar night conitions, our moel shows that gravity waves over the north polar cap are strong enough to inuce aiabatic cooling below the CO frost point. From this cooling, airborne heterogeneous nucleation of CO ice particles occurs from the groun up to the altitue of the polar thermal inversion. Although the moel preicts that clous can be present above 15km, only low altitue clous can backscatter the aser beams of MOA at a etectable level. Accoringly, the shape of the aser echoes is relate to the shape of the clous at low level, but o not necessarily coincie with the top of the clous. The moel helps to interpret the clou patterns observe by MOA. Above an isolate orographic trough, an isolate extene sloping clou tilte against the win is obtaine. The moel shows that the observe quasi-perioic 3

4 clous are ue to the succession of small-scale topographic features, rather than to the presence of resonant trappe lee waves. Inee, the CO conensation greatly amps the buoyancy force, essential for the maintenance of gravity waves far from their sources. Simulations with realistic topography profiles show the clou response is sensitive to the win irection. When the win is irecte upslope of the polar cap, on the one han, a large scale clou, moulate by small-scale waves, forms just above the groun. On the other han, when the win is irecte ownslope, air is globally warme, an perioic ice clous inuce by small-scale orography form at altitues higher than 3-5km above the groun. In both cases, a goo agreement between the simulate echoes an the observe one is obtaine. Accoring to our moel, we conclue that the observe clous are quasistationary clous mae of moving ice particles that successively grow an sublimate by crossing col an warm phases of orographic gravity waves generate by the successive polar troughs. We also fin that the rate of ice precipitation is relatively weak, except when there is a large scale air ynamical cooling. Key wors: Mars, atmosphere; atmosphere, ynamics; clous; CO ices 4

5 1 Introuction Since 1998, the Mars Orbiter aser Altimeter (MOA) aboar the Mars Global Surveyor (MGS) orbiter has observe optically thick clous above the winter north an south polar caps (Zuber et al. 1998, Smith et al. 2001). The fact that they are only present uring the winter polar night suggests that they are constitute of CO ice particles (Ivanov an Muhleman 2001). These clous are etecte from the surface up to altitues of 15-20km above the groun. Some of them are isolate while others present quasi-perioic successive patterns. Typical isolate clous are foun to be extene from the surface to altitues of 4-6 km above the surface (Pettengill an For 2000). Whatever their shape an their vertical extension are, they all look tilte against the ominant win, with a slope between zero to twenty egrees (Ivanov an Muhleman 2001). These observations suggest that they are prouce by mountain waves an that their perioic patterns might be ue to the presence of trappe lee waves (Pettengill an For 2000, Zuber et al. 1998). The fact that these clous are triggere by the orography is further supporte by the fact that the topography on Mars presents large mesoscale irregularities near the poles. For instance, the north polar ice cap is elevate above its surrouning with a 3km maximum elevation near the pole (Zuber et al. 1998). It is sculpte by spiral troughs, whose typical epth an half-epth with are aroun 0.5km an 7km (Ivanov 2000), respectively. 5

6 For the last thirty years, CO ice clous attribute to mountain waves have been observe in the lee of craters or large volcanoes (Hunt an Pickersgill 1984). Before 1998, clous have never been irectly observe above the winter polar caps, although their presence uring the polar night ha been intuite for a long time (Gierash an Gooy 1968, Pollack et al. 1990, Forget et al. 1995). Inee, the clous optical properties can explain the low brightness temperature areas observe on the winter polar cap (Kieffer et al. 1977, Forget et al. 1995). They can also play a key role in the Martian climate, which greatly epens on the conensation of CO in polar night conitions (Yokohata et al. 2002). Accoringly, these clous may nee to be parameterize in General Circulation Moels, an a better unerstaning of their life cycles is essential for this purpose. Following the Mariner 9 an Viking observations, ynamical moels have been propose to explain the formation of clous by lee waves (Pirraglia 1976, Pickersgill an Hunt 1979). These stuies i not investigate (i) the occurence of lee waves when the atmosphere is near the frost point, an (ii) the ynamical coupling between CO ice conensation an the wave ynamics. The first objective of this paper is to aress these two issues. The secon objective is to give further evience that the organize structures, seen in the MOA echoes, are prouce by CO ice clous triggere by orographic gravity waves. For these purposes, we have evelope a moel that couples 2D stratifie flow ynamics with CO ice clou physics. The ynamical moel solves the anelastic equations of motion 6

7 (ipps an Hemler 1991), an has been use for the Earth atmosphere to stuy mountain waves (ott 1998, Georgelin an ott 2001). The clou moel inclues simple CO ice microphysics, seimentation an win avection. In all the simulations presente, the backgroun flow is representative of the Martian winter north polar cap climatology. It is consistent with the climatologies of the MD Martian GCM (Forget et al. 1999) an the available MGS observations. To aress the relative importance of the ynamical an physical processes responsible of the existence of these clous, the simulations one are presente in orer of increasing complexity. In Section 2, we examine the generation of gravity waves by a single orographic trough in a non conensing north polar winter atmosphere as well as the impact of the release of latent heat ue to CO conensation. We examine to which extent the regular structure can be relate to resonant trappe waves, an to which extent their ynamics is affecte by the CO ice conensation. These simulations serve as a basis to interpret the more realistic ones, presente in Section 4. In Section 3, we give a escription of CO ice clou physics an the basis riving wave clou formation. Numerical simulations with these clou physics an realistic north polar cap topographies are presente in Section 4. In orer to compare with the MOA clou echo observation, we reconstruct from the moel outputs the echoes the simulate clous prouce. In Section 5, we iscuss these results an sum up the main points of our finings. 7

8 2 Dynamics of the mountain waves in the Martian north polar night 2.1 The Martian polar night atmosphere The characteristic of the Martian atmosphere within the polar night are quite unique. In the absence of solar energy, the temperature of the surface falls own to the conensation point of CO, leaing to the formation of the ry ice seasonal polar caps. Above the surface, the raiative-convective processes also ten to cool the atmosphere to the frost point of CO. Therefore, in the major part of the polar night atmosphere, the temperature profile follows the conensation temperature profile. The corresponing thermal structure is very stable, with a typical lapse rate (-1 K/km) much less steep than the aiabatic lapse rate (-5 K/km). Such stable conitions are favorable to gravity waves that occur in stratifie flows, as suggeste by the high resolution thermal profiles recore by the raio-occultation experiment of Mars Global Surveyor (Hinson et al. 2000). These profiles exhibit temperature oscillation with vertical wavelength of about 1 to 2 km an amplitue of the orer of a few kelvins. In some locations, the temperature of the polar night atmosphere can be significantly warmer than the frost point of CO if the atmosphere is aiabatically warme by the large-scale flow ynamics. On the one han, this can happen 8

9 near the surface when the win blows ownhill (Foehn win effect) as escribe in Forget et al. (1998) (conversely, ascening wins globally enhance the conensation). On the other han, spacecraft observations (Jakosky an Martin 1987, Smith et al. 2001, Pearl et al. 2001) as well as moelling stuies (Wilson 1997, Forget et al. 1999) have shown that above 15 to 50 km, epening on the latitue, season, an ust loaing, the atmosphere is always warme by a escent of air force by a convergence of mass above 50 km. This convergence results from a combination of a strong mean meriional circulation (Haley cell) an wave (mostly ties) -mean flow interaction (Forget et al. 1999, Wilson 1997). Another key parameter for the present stuy is the win profile. No irect observations are available, but analysis of simulations performe with the MD General Circulation Moel suggest that the win is near constant between a few tens of meters above the surface to at least 10 km, with a typical velocity of 10 m.s On the one han, this is ue to the the fact that the turbulent bounary layer is extremely thin, because of the high stability of the atmosphere. On the other han, in the free atmosphere, the win oes not strongly increase with altitue because the horizontal temperature graient are small, the temperature being everywhere that of the conensation point. This is very ifferent from what occurs at sunlit latitues, where the win increases with altitue to satisfy the thermal win balance.. 9

10 " " 2.2 Waves in a non conensing atmosphere Theory Gravity waves generate when a stratifie air flow passes over a mountain have been extensively stuie in the Earth atmosphere (Queney 1947; see Smith 1980 for a review). These waves are riven by the buoyancy force that acts on air parcels isplace vertically in a stably stratifie environment. They are usually referre to lee waves because they are observe in the lee of mountains. Their intrinsic frequency is between the Brünt-Väisällä frequency, (where is the gravity, is the backgroun potential temperature) an the Coriolis frequency,! (where is the rotation frequency of the planet an the latitue). In the 2D linear case, the response of the atmosphere to the mountain forcing can be analyze in the Fourier space, "$#&%(' *),+ "/#102!' ;: 02 (1) where "$#<%(' is the topography profile, - its Fourier transform an 02 the horizontal wavenumber associate with. The vertical propagation of each harmonic epens on the vertical structure of the incient flow, i.e. on its horizontal - velocity = #?>@' an potential temperature #1>@' profiles. Waves generate by a flow with uniform velocity = A 3 an uniform stratification BA 3, propagate freely 10

11 : D E : : > upwar along straight ray paths. When = an vary with altitue, the gravity waves are refracte an the shortest harmonics can be reflecte at some altitues an return to the groun where they are reflecte again (Scorer 1949). At these short wavelengths an through constructive or estructive interferences, only a finite number of moes can exist in the long term an ownstream of the obstacle. They are often referre to as resonant trappe moes, because they correspon to the only isturbances that exist in the long term an in the absence of orographic forcing. To stuy atmospheric lee waves, but excluing acoustic waves, the anelastic approximation is better aapte than the Boussinesq an hyrostatic approximations. In this approximation, freely propagating gravity waves an trappe mountain waves co-exist (the latter being exclue, for instance, in the hyrostatic approximation). In this framework, the two-imensional (x-z) equations of motion are (see for instance Scinocca an Shepher 1992): :C AFE C G # K ' IH K J C GQP #&R MON C D ' M (2) (3) where C D is the velocity fiel, c H is the constant pressure heat capacity, R the backgroun ensity. In Eq. (2) an Eq. (3), the Exner pressure, K, an the potential 11

12 [ b > e e % e E E b % e P temperature,, have been written: K TSVU UOWXZY \[ K K #1>@' #?>@' J K #&% N > N4A ' N J #<% N > N]A ' N (4) (5) where the zero subscript refers to the flui at rest, the tiles represent perturbations, U^W is a constant reference pressure, _ T` IH, ` is the gas constant an the temperature. If we assume that the flui at rest is in hyrostatic balance, an invoke the ieal gas law U R à[ are uniquely etermine once [ #1>@' allows to efine the mass flux streamfunction b,, all the backgroun thermoynamic fiels is specifie. The continuity equation Eq. (3) c R fe Nhg jib R e (6) At the lower bounary, we impose that, g = # ' "#<%(' N (7) a linearization of the general free-slip bounary conition that is only vali when the nonimensional parameter kml Iprq lon s Iput n, where H is the maximum elevation (see for instance, Smith 1979). When this conition is satisfie, the waves 12

13 Š # b - e % e b b # : : > e e b - S x b e % X e e % e E b - b - : : 3 2 % e x b % e i b - force by the obstacle are well escribe by the linearize set: e e AVE = 'wvox i A E R = K iyih > e ' x i R ye xw# ' ji R # ' = # '4"#<%(' at x *ON *ON > ON (8) (9) (10) where the primes replace the tiles in Eq. (2) an Eq. (3) to inicate that only the linear part of the total isturbance is consiere, an v {z { 2 is the vorticity. To escribe the flow response, it is conventional to consier the steay limit. In this case, one particular harmonic force at the groun, x #<% N >@' R 1} ` 3~# #?>@' ' N (11) has a vertical structure which is governe by the Taylor Golstein equation: Oƒ E l s i s Is i ƒ E # ' s # V#1>@' i 0 2 ' i ˆ *ON i 0 2; M (12) (13) where S(z) is the Scorer parameter (i.e., the inex of wave refraction). For V#1>@' i 0 2FŒ, the solution is of the form: it is of the form: x 3 Ž 7 E x 3 \ 3;Ž 57 E 7, where 0 574, an for V#1>@' i 0 2 t # #?>@' i 0 2 '. For the, 13

14 first case, there is vertical propagation, an for the secon one, there is no vertical propagation an the harmonic is evanescent in the vertical irection. Because the Scorer parameter varies with altitue, there are circumstances where an harmonic propagates vertically at low level an becomes evanescent above a turning point hš with V# š ' 0 2 where they are reflecte towar the groun. It is the basic mechanism riving the trappe moes mentione before Backgroun profiles an analysis of the Scorer parameter profiles Figure 1 The main characteristics of the north polar winter lower atmosphere are that the temperature profile is usually near the CO conensation temperature profile an that the win profile is almost constant with altitue (see Section 2.1). In our analysis, the temperature is assume to follow the CO conensation temperature up to the polar thermal inversion altitue. We have assume two profiles for the backgroun win conitions (Fig. 1a): a constant win, =, an a more realistic one, =, that takes into account a win graient above 8km. For the temperature, we have consiere three ifferent profiles (Fig. 1b): [ without thermal polar inversion, [ with a thermal inversion at >!œ km, an [ with a thermal inversion at > j œ km. These various backgroun conitions yiel to totally ifferent Scorer parameter profiles (Fig. 1c). In all cases, only harmonics with horizontal wavelength larger than K V# ' km can propagate upwar at the groun. 14

15 For # = N][ ', the Scorer parameter increases faintly with altitue, so there is no level where an harmonic that propagates vertically near the groun can become evanescent at some level above. For # = N4[ ', harmonics with horizontal wavelengths between 6km an K V# 50km ' ž km encounter a turning height between 10 an 50 km, an a large number of wavelengths are trappe at low altitue. 2.3 Dynamical moel The ynamical moel solves the linear equations (8) an (9) in spectral space in the horizontal irection an in finite-ifferences in the vertical irection (ott 1998). In time, the evolution equations are solve by one Euler step, followe by successive eapfrog steps. After each time step, an Asselin filter is applie (Asselin 1972). The height of the omain is 50 km an its with range between 200km to 1000km. The horizontal an vertical resolution equals 500m. At the upper bounary, a amping layer (15km thick) is use in orer to eliminate artificial reflections. The timestep is equal to 1s. The backgroun surface pressure is fixe to 7.5 mbar. 15

16 k Simulation with an isolate relief We make here a set of four simulations with an iealize trough, which is characteristic of the north polar cap topography. Its profile is given by: "#<%(' Bi 2 }wÿ N (14) where k is the epth an the half with. In all simulations, we take k P œ km an km, values that are characteristic of the troughs in the polar cap accoring to Ivanov (2000). In the first two simulations, the CO ice conensation is neglecte. The backgroun flows are such that in one case, there is no trappe resonant moes (backgroun profile (0)) while in the other case, trappe moes can occur (backgroun profile (1)). The thir an fourth simulations repeat the first two, but forbiing the temperature to go below the CO frost point. Figure 2 Dynamic simulation Fig. 2a an 2b present the velocity an the temperature anomalies fiel after four hours of integration an for the backgroun profiles (0) an (1) respectively. On both figures, the win an temperature fiels above the trough present a well efine upwar an freely vertically propagating wave, as inicate by the tilt against the backgroun win of the wave patterns. In these patterns, the positive (negative) temperature anomalies are locate above where air 16

17 e e k escen (ascen), consistent with them being ue to aiabatic warming (cooling). Notice that, as altitue increases, the wave amplitue above the trough increases, which is consistent with the fact that the air ensity ecreases with altitue. The two simulations strongly iffer in the lee of the rige. With constant backgroun win (profile (0), Fig. 2a), the isturbances ownstream are very weak. When the backgroun win an temperature vary (profile (1), Fig. 2b), the waves exten ownstream an the isturbance fiel in the lee compares in amplitue with its value above the trough. This result comes from the fact that a significant fraction of the harmonics excite at the groun, meets a turning point above > km an can be reflecte ownstream. In this simulation with profile (1), the wave pattern ownstream has a rather well efine horizontal wave length, 2 km. Although the wave pattern ownstream is not steay, the ominance of this particular wavelength illustrates the existence of at least one resonance in the backgroun profile (1). However, as the turning level of this moe is quite high ( > km), it takes a rather long time to evelop an several hours are necessary before it ominates the wave fiels ownstream. Since the resonant moe amplitue compares to that of the freely propagating wave, we can assume that the vertical win amplitue is everywhere given by its value near the groun: g x = # ' "$#&%(' % = # ' in temperature variations that are roughly given by: [ x (see Eq. (7)). It results [ # ' k (see Eq. (5) an Eq. (9)), a value consistent with those in Fig. 2a an Fig. 2b. If we apply 17

18 œ these scalings to the Martian north polar cap topography, which is mae of successive troughs of characteristic scales, k ž m an ª km (Ivanov, 2000), temperature anomalies of near 2K can be expecte. This value is large enough to force clou formation. Figure 3 Impact of the conensation on the wave ynamic In reality the waves occur in an atmosphere close to the frost point, an the waves are affecte by the release of latent heat when CO is conensing. To stuy this effect, we have re-conucte the first two experiments assuming that the temperature T I«cannot fall below the conensation temperature T &. This is an extreme case use to serve as a theoretical basis to unerstan the impact of CO ice conensation on the ynamics. More realistic cases incluing simple clou microphysics are presente in Section 4. Results for the two ifferent backgroun conitions are shown on Fig. 3a an Fig. 3b. The impact on the wave fiel is very strong. Wherever ascent ue to wave isturbances tens to prouce a cooling below the conensation temperature, CO ice conensation keep the air parcel near T & 6 which is also the backgroun temperature. The parcel is just as heavy as its environment an no restoring force rives it own. For this funamental reason, the isturbance fiels in Fig. 3a an Fig. 3b only see the ascent an escent near the groun irectly force by the trough. The gravity 18

19 wave ynamics only act in proucing the first escent along the upstream sie of the trough (positive temperature anomaly) an the ascent escribe before an where the conensation annihilates the wave. Following this picture, it seems natural that the isturbances o not see the backgroun flow variations locate above 10 km an the isturbance patterns in Fig. 3a an Fig. 3b are near one from the other: the conensation annihilates the resonance. 3 A parameterization of CO ice clou formation The above simulations with simplifie conensation scheme have proven that the ynamics of mountain waves is strongly affecte by the conensation of CO, at least within a near saturate atmosphere. Accoringly, a better escription of the conensation process incluing nucleation of the ice particles, growth rate, win avection an seimentation, an sublimation, is neee to accurately moel the formation of wave clous as well as the feeback of the conensation-sublimation processes on the wave ynamics. Compare to the results in Section 2, CO ice microphysical processes can inee elay the onset an the evelopment of CO ice clous, allowing a more complete evelopment of the gravity waves isturbance. 19

20 + ' + P 3.1 Microphysics of CO ice As for water clous on Earth, the microphysics of CO ice clou primarily epen on the supersaturation ( Œ ) or subsaturation ( t ) of the atmosphere: * $± i (15) In Eq. (15), + is the ambient partial pressure of CO (on Mars it is near the ambient total pressure), ± is the equilibrium vapor pressure of CO : # & ~³µ i? [, with & P¹ žº ¼» Pa an & º P¹½@º $±² K (James et al. 1992). The formation of ice particles requires some egree of supersaturation. Homogeneous nucleation nees very high supersaturation (s ), while heterogeneous nucleation, which involves a foreign substrate (ust or water ice particle) occurs at relatively low supersaturation. For two reasons, heterogeneous nucleation is likely to occur within the polar night atmosphere. First, the Martian northern mile latitues in fall an winter are often swept by regional ust storms (Cantor et al. 2001), which probably inject a large amount of aerosols into the polar night atmosphere. Secon, it is even more likely that water ice coate ust particles (or even almost pure water ice particles) serve as conensation nuclei for the CO ice : the ege of the polar night is known to contain relatively thick water ice clous (the polar hoo) which are probably present in the entire polar night atmosphere (see, e.g. Smith et al. 2001). Thermal infrare observations 20

21 Å e A e Å e A E E performe at the limb at 80 N suggest that water ice particles are present from above 40 km throughout the region where the CO conensation curve is reache, proviing a relatively constant source of nuclei for CO conensation though vertical seimentation in aition to horizontal transport (Pearl et al. 2001). On the basis of theoretical consieration base primarily on Gooing s (1986) calculations of the crystallographic isregistry between CO an caniate Martian ust minerals, Woo (1999) estimates the minimum critical value of nucleation supersaturation z &À. He showe that, for a typical ust loaing of 0.1Á m aerosol particles atmosphere (visible optical epth  ± 5Äà P ), heterogeneous nucleation coul occur at supersaturation as low as 10 ¾. Experimental stuies (Glanorf et al. 2001), in which water ice is use as a nucleator of CO ice, suggest that critical supersaturations of ¾ are require. In our stuy, we consier both values (10 an 35 ¾ ) as possible values for the critical nucleation supersaturation s z &À. Once nucleation has occurre, the growth of the ice particles is controlle by microphysical processes. In analogy to Ohm s law (McKenzie an Haynes 1992), the growth rate of the particle raius Å, e Å, can be moele by: ÆÇ # [VN{ ' iyèé # [VN 'IÊ Æ àë ` Ì ` 7 Ê N (16) where the constants àë, ` Ì an ` 7 represent the resistances to the growth ue to heat transfer, mass transfer an crystal surface kinetic, respectively. In Eq. (16), 21

22 Î Å Å R N È s ÈÉ is the Kelvin correction that accounts for the effect of the particle curvature on the vapor pressure, it is given by : ;È1É # [VN ' ³µ # ží Î 5 È [ ` ' i (17) where Í is the molecular weight of CO, ` is the gas constant, R 5 is the ensity of the CO ice, an Î is the surface energy of the CO ice crystal. We take = Î ÏÏ =0.080 J.m, Ð 111Ñ being the lowest energy crystallographic face of CO ice (Woo 1999). Below ;È1É, the supersaturation is not large enough for conensation, an sublimation occurs. As CO is the major component of the Martian atmosphere, the resistance associate with mass transfer ` Ì is negligible (` ÌªÒ ` Ë@N{` 7 ). The growth rate epens mainly on the crystal growth mechanism (Woo 1999). This author has shown that if crystals grow with the Screw Dislocation growth mechanism, the crystal surface kinetic resistance is negligible as well, an the limiting factor is the heat transfer: àë Ó ` 7. If they grow with the 2-D Nucleation growth mechanism, it is the other way roun, the surface kinetic is the limiting factor: àë Ò ` 7. In fact, this secon mechanism requires very high supersaturation, sô 200%, which is unlikely to be satisfie. Between these two extreme mechanisms, growth mechanism may also be 2D heterogeneous nucleation, stacking fault or other processes. These epen a lot on the crystal structure of both conensation nuclei an CO ice, factors that are not well-ocumente for 22

23 œ Å R È e [ : X : Ì the Martian atmosphere. In orer to inclue the effect of CO ice microphysics on the formation of wave clous, two extreme growth rate scenarios are efine an teste in our 2D moel : a fast growth scenario an a slow growth one. These two scenarios give an assessment of the upper an lower bouns for the growth rate of CO ice particles. In the fast growth scenario, the growth-rate-limiting process is only the heat transfer àë, an in the slow growth scenario, it is mainly the surface kinetic resistance ` 7. In both cases, the heat transfer resistance is estimate with the following formula: R ËÕ 5 0Ö Ë! $± # [ ' S e ± (18) where 0Ö Ë is the gas thermal conuctivity, 0Ö Ë \ OØhH Å, where Å is the Prantl number, Å PÙº (Woo 1999), is the ynamic viscosity, m ÛÚ K # Ü Ì 0 [ Ì ' N wà (19) with Ü Ì the CO molecule mass, 0 the Boltzmann constant, an wà the CO molecule iameter. The surface kinetic resistance ` 7 is fixe to zero in the fast growth scenario, an to 10Ý s.m in the slow growth scenario. Although Eq. 18 is only vali in the continuum regime, i.e. where the iameter of the ice particles is larger than the mean free path of air molecules in the surrouning atmosphere, 23

24 it is also use in the kinetic regime to give an upper boun for the growth rate of the smallest ice particles. More quantitatively, the ifference between the two scenarios is the growth rate of the ice particles smaller than Á m. In the slow growth scenario, the growth rate is controlle by the surface kinetic for particles smaller than 20-40Á m, an it is controlle by the heat transfer for larger ice particles. In the fast growth scenario, whatever the size of ice particles is, its growth rate is controlle by heat transfer. As a consequence, the fast growth scenario overestimates the growth rate of ice particles with raius below 10-20Á m, while the slow growth one unerestimates it. Table I An other process of importance is the coagulation of the CO ice particles as they collie through Brownian motion. At small particle concentrations, coagulation oes not have a significant effect on the clou properties an o not moify the growth of particles. From Rossow (1978), the coagulation time constant for CO ice epens on the concentration of CO ice particles. Assuming that CO ice particles nucleate on airborne (ust an water ice) particles greater than P Á m, the number ensity of ice particles is irectly relate to the number ensity of aerosol particles initially present in the atmosphere. Table I presents the number mixing ratio of the aerosol particles greater than 0.1Á m for ifferent visible optical epths assuming an aerosol size istribution 24

25 as in Ockert-Bell et al.(1997). In this aerosol size istribution, most of the aerosol particles are inclue below 1Á m. The mean raius of aerosol particles is about 0.5Á m. For a typical ust loaing atmosphere (Â ± 5ÄÃ P ), if all the aerosol particles lea to CO ice particles an grow to 50Á m raius, the coagulation time is aroun 10Þ -10ß s. As a comparison, the conensation growth time for 50Á m CO ice particles is aroun 10-10ˆ s. The coagulation of ice particles is negligible, an the number of ice particles remains constant with time, once they nucleate. 3.2 Basis of wave clous formation Figure 4 The fact that the formation of the clous epens on both wave patterns an CO ice microphysics, is summarize in Fig. 4. Airborne nuclei are avecte horizontally by the backgroun flow an cross the orographic waves. When an air parcel loae with ust or water ice particles passes over a trough, ynamical cooling inuce by orographic wave leas to nucleation if the temperature has ecaye enough, i.e., if the temperature variation creates supersaturation as high as the critical nucleation supersaturation ( z &À ). As here, the backgroun temperature at low altitue follows the CO conensation temperature, the backgroun saturation equals zero an the super(sub)saturation is irectly relate to the temperature isturbance. For a 2K temperature perturbation which is a typical temperature 25

26 isturbance above the north polar cap (Section 2.4), the supersaturation is near 30-35% below 10km, a value for which nucleation of CO ice particles is possible. The nucleation starts in the winwar sie of the clous where conensation nuclei avecte by the mean flow continuously come into. Once the ice particles have nucleate, they grow more or less quickly epening on the microphysical assumption. The nucleate particles are avecte by the win out of the nucleation front an continue to grow ownstream as long as they stay in a region where Œ ;È1É. The size of the CO ice particles an consequently their seimentation velocity epen on the growth rate: for fast growth, large particles are expecte, while for slow growth, small ones are expecte. Once outsie the conensation area ( Œ ÈÉ ), the ice particles start sublimating. On the one han, if the particles are sufficiently large, they o not entirely sublimate an can fall to the groun. The clous then look like long snow tails (Colaprete et al. 2002). On the other han, if the particles are small, they weakly precipitate an can totally sublimate ownstream of the conensation area, since t ÈÉ there. The clous then resemble stationary clous mae of horizontally moving particles. In this circumstance, the shape of the clous is likely to be impose by the orographic gravity waves. 26

27 Ö Ö W Ö W Ö Ö 3.3 Description of the clou moel The number mixing ratio of ice particles N Hà W (i.e., particle number per mass unit) remains constant all along the simulation an in the whole omain, it is fixe at the beginning of the simulation. Nevertheless, the amount of CO ice in each elementary square box (500m» 500m) varies with time, it epens on the amount of ice avecte from or towar the ajacent boxes an on the growth or sublimation rate of the mean ice particle raius, Å Hà, in each box. The initial mean ice particle raius is fixe to 0.5Á m, which is the mean value of the aerosol particle size (section 3.1). In aition to r Hà W, in each box, CO ice is also escribe by the mean mixing ratio of CO ice, á, which is the mass ratio between the ice phase an the gaseous phase. Ice particle transport The avection of á from a box to the next ownstream an below is compute with a Vanleer Scheme (Hourin an Armengau 1999), using the velocity fiel given by the ynamical part of the moel plus a vertical velocity ue to the seimentation of ice particles, â Ã È. In each box, VÃ È is erive from the mean ice particle raius Å Hà, by using a Stokes law correcte for low pressure by the Cunningham slip-flow correction (Rossow 1978). At each timestep, the istribution of CO ice mixing ratio á is re-calculate with this avection scheme, an a new mean ice particle raius r Hà W is estimate in each box. After that stage, the conensation or sublimation of these ice particles is com- 27

28 E Ö W : E : š n E : E : : e A pute. conensation-sublimation processes In each box, a value of the supersaturation is estimate after each ynamical time step, at A E, using Eq. (15): # A A ' # A A ' $± # A A ' i (20) where $± # A is the equilibrium vapor pressure (see section 3.1), A ' Õã ã 3 } ä åå n Ö p Ž š n } Ö päæçwèé Ö p is the ambient pressure, an # [ e A ' Ï«is the ynamical tenency of the temperature euce from the potential temperature by Eqs. (5) an (9). On the one han, if CO ice is avecte in the box from its ajacent boxes, the further growth of the mean ice particle raius is allowe, an the growth rate is calculate with Eq. (16). On the other han, if no CO ice is avecte in the box, the conition Œ z &À is require to allow the growth of the mean ice particle raius Å Hà. Inee, if no CO ice is avecte into the box, that means that non-ice particles, which are continuously avecte by the mean flow, come into. The growth of these non-ice particles is only possible if the critical nucleation supersaturation z &À is reache. In fact, Œ z &À shoul be require only in the winwar part of the box, where non-ice particles are concentrate. To accurately escribe this phenomenon, a submeshgri woul be necessary. But, by simplicity, 28

29 : Ö W : A : [ A e : e A á P E : ' this requirement is impose on the whole mesh. The calculation of the amount of conense or sublimate CO ice leas to a new value of the super(sub)saturation. i\ Œ ½ If the saturation variation is large, typically, numerical errors on the conense or sublimate ice quantity can become significant. To reuce these errors, a physical subtimestep A is impose with iê # ½ '. For each subtimestep, [ # A is estimate from the ynamical temperature tenency, constant all along the ynamical timestep, an from the conensation temperature tenency, which is calculate from the quantity of CO ice conense (or sublimate) uring the previous subtimestep A : A S e X & ØhH» ë (21) In Eq. (21), is the latent heat of CO ice conensation, ØhH is the heat capacity of CO gas, an ë á the amount of ice mixing ratio conense in the previous subtimestep. To summarize, the input ata of the clou moel are : 1. the critical nucleation supersaturation z &À an the number mixing ratio Hà of ice particles that are allowe to grow. 2. the ynamical temperature tenency # e [ A ' Ï«4, the pressure, the tem- 29

30 Å Ö W À R Ö W A perature [ :, the vertical an horizontal win velocities at each timestep. The output ata is the temperature after conensation [ ì, the ice particle raius Hà, an the ice mixing ratio á. 4 Results 4.1 Simulations with a 2D-isolate trough In a first set of experiments, we stuy the formation of wave clous over the 2Disolate Gaussian trough use in Section 2 an investigate the sensitivity of the results to (i) the ifferent microphysical assumptions (see section 3.1) an (ii) the assume backgroun flows (see section 2.2.2). To establish if the clous are optically ense enough to reflect the MOA laser beam, we follow Pettengill an For (2000) an compare the moel particle number ensity to the value, W Èwí M P Ûß Å # Ü ' N (22) where Å is the particle raius in Á m. The first level, starting from the top, where the ice particle number ensity Hµà ì Ö W threshol, is consiere as the aser reflecting level. Hà ( R is the air ensity) is above that 30

31 œ W œ Baseline case Figure 5 Fig. 5a shows the temperature an velocity anomalies fiel for the backgroun flow profiles(0) ( = = an [B j[ & 6 ), in the case of the fast growth scenario with z &À % an Hà Ö Ý kg. ike in the simulations with a simple conensation parameterization (Fig. 3), the clou formation has a strong impact on the wave fiel. Nevertheless, the inclusion of the realistic microphysics make the resulting wave an clou fiels quite ifferent from those presente in Section 2. The successive conensation an sublimation of the ice particles blown by the win create a large area where the temperature isturbance is near zero because [î u[ &. Both conensation an sublimation annihilate the gravity waves far above an ownstream the trough. Figure 6 The four pictures on Fig. 6 present successive phases ( AV, 100, 150 an 200 minutes) of the evelopment of the clou features corresponing to Fig. 5a. In all the figures, the black crosses represent the altitue of the expecte MOA echoes, accoring to Eq. (22). These four successive snapshots show that the wave perturbations increase in amplitue above the trough in function of time. Nevertheless, this growth is rapily limite by the evelopment of the clous. After Ah mn (Fig. 6a), the wave perturbations have propagate upwar an the 31

32 supersaturation has reache the critical nucleation supersaturation s z &À between 1 an 3 kilometers above the trough. At that time (Fig. 6a), a small clou has alreay forme. Where the ice particles start growing, supersaturation ecreases, except in a narrow ban on the winwar sie of the clou. In this ban, supersaturation remains quite high an allows the non-ice particles to start growing. The supersaturation in the clou rapily falls to 0%. The ice particles stop to grow, an they are just avecte by the win an fall own. The ice particles sublimate ownstream where s t s ÈÉ, which limits the horizontal extension of the clou. Before starting to sublimate, the mean ice particle raius within the clou reaches about 60Á m. After 100 minutes (Fig. 6b), a large clou is forme. Above this primary clou, other clous evelop as well. As they are mae of smaller particle than the primary low level clou an as the number ensity Hà ì Ö W of particles ecreases with altitue, they remain unetectable. Only the main extene clou near aloft the trough is etectable by MOA. Thereafter, this primary clou keeps growing (Fig. 6c) an, at A už mn (Fig. 6), a sloping clou extene from the surface to near 7 km above it, is obtaine. The slope of its echoes ë &À¹ z is near 8, a value close to the echoes of isolate clous observe by the MOA experiment (see Table 3 in Pettengill an For (2000) for a comparison). It is noteworthy that the moel clou echoes o not necessarily correspon to the top of the clou but to a region within the clou 32

33 where the ice particles are large an ense enough to backscatter the aser pulse at a level etectable by MOA. Nevertheless, the shape of the echo backscatters is irectly relate to the clou shape. Note as well that the clou an the echoes are tilte against the win irection, following the vertically propagating gravity wave Sensitivity to backgroun conitions Fig. 5a an Fig. 5b show moel results for the backgroun flow profiles (0) an (1), respectively, with = m.s, after four hours of integration. The comparison between these two figures shows that the presence of a win shear at mile altitue (win profile (1)) has no influence on the wave fiel pattern. This follows that the waves are strongly ampe at low altitue, so they mainly prouce an extene etectable clou above the trough. At altitues higher than 10km above the surface, the wave pattern an the clou shape are near inistinguishable, only the main clou at low altitue is etectable, an the echoes are almost the same for the two backgroun conitions (not shown in Fig. 5 but they are those presente in Fig. 6 an Fig. 7). Table II presents the general characteristics of the extene clou (its MOA etectability, its maximum value of the mean ice particle raius, ` Ì/à 2, the slope of its echoes, ë &ÀÇ z, an the vertical extension of the echoes, D 3 &ÀÇ z, i.e. the vertical istance between the base an the top of its echoes) obtaine for ifferent 33

34 Ö Ö W input parameters. The results corresponing to Fig. 6 are presente in column 5. These show that simulations performe with two ifferent values for the low altitue win amplitue ( = features. For = than for = œ m.s m.s. œ m.s or = m.s ) lea to ifferent echo, the clou echoes are more extene an more sloping We then mae sensitivity tests to ifferent altitues of the polar thermal inversion: 12.5km, 25km an 50km, corresponing to the temperature profiles [, [ an [, respectively. The maximum altitue of clou formation is sensitive to the inversion altitue, but the maximum altitue of clou echoes oes not epen on it: all clou echoes are obtaine below altitues of km above the surface Sensitivity to microphysical parameters To examine the robustness of our results, sensitivity tests to values of the critical nucleation supersaturation s z?à an of the number mixing ratio Hà of ice particles, an to the growth scenario (slow or fast) have been mae. In all the cases presente in this section, those tests are limite to the uniform backgroun profiles (0). Figure 7, Table II, Table III Critical nucleation supersaturation s z &À clou formation corresponing to Fig. 6, i.e. with N Hµà W Fig. 7 presents the time evolution of =10Ý kg, for the fast 34

35 grow scenario, but with s z &À =35%. Comparison with Fig. 6 shows that a higher critical nucleation supersaturation elays the onset of clou formation by about one hunre minutes. This elay permits a larger evelopment of the wave fiels (Fig. 7a) an consequently moifies slightly the resulting clou pattern. Fig. 7b show that nucleation starts after about 100 minutes only, between 1 an 3km above the trough, like in Fig. 6a. After 150 minutes (Fig. 7c), a secon clou appears between 10 an 15 km above the surface. After 200 minutes (Fig. 7), an extene clou is forme above the trough. It prouces echoes from the groun up to a altitue of 6 km. The slope of the echo feature is aroun ike in the simulation with s z &À =10% (Fig. 6), the higher altitue clous are not etectable by the MOA instrument. The general characteristics of the resulting clou are summarize in column 5 an 6 of Table II, for the runs in Fig. 6 an Fig. 7 respectively. For these two cases, the maximal value of the mean ice particle raius ` Ì à 2, the vertical extension D 3 &ÀÇ z of the echoes an their slope ë &À¹ z o not significantly epen on z &À. This result is quite systematic (see the other columns in Table II an Table III), note nevertheless that when z &À œ % an for = œ m.s, no clous are forme ( i.e., there are no assigne values to ` Ì/à 2, ë &ÀÇ z an D 3?ÀÇ z for these input values). This comes from the fact that supersaturation never excees the threshol for particles to start growing, at least after four hours of integration. 35

36 Ö W Ô œ P W W Þ t P œ Ö W Ö W W Ô P œ Ice particle number mixing ratio N Hà Ö W Hà Ö Œ ï in Table II that one nees kg slow growth scenario (Table III), one nees for increasing ice particle number mixing ratio raius, ` Ì à 2 It is clear from the first two columns to obtain etectable clous. For the Hà Ö Œ Hà Þ kg. Note as well that, the maximum ice particle, an the clou slope, ë?àç z, ecrease (see the raws 3, 4, 5 an 6 in Table II an Table III). In the fast growth case, for feature correspons to a haze transporte by the win ( ë?àç z Hà ß kg, the clou ). In this case, no clous with sloping top form, the nucleate ice particle number mixing ratio is too large, so the release of latent heat when they nucleate an start growing is very strong an the wave perturbation is completely attenuate ownstream. In the slow growth scenario (Table III), the same kin of results is obtaine for Hà ð kg. It is one of the few circumstances where the moele clous o not have the characteristics of the observe isolate clous (Pettengill an For 2000, Ivanov an Muhleman 2001), while for Hà Ö t Ý kg with the fast growth scenario, the moel clou echoes are similar to the observe ones. Growth rate: fast or slow The comparison between Table II (fast) an Table III (slow) shows that the maximal value of the mean ice particle raius, ` Ì à 2 epens strongly on the growth limiting factor. ` Ì/à 2 is quite systematically larger, for the fast growth scenario ( Table II) than for the slow growth scenario (Table III). Accoringly, in the fast growth case (Table II), less ice particles, 36

37 Ö W Ô Ö Ô P œ W ( Hà case (N Hà W Þ kg ) are neee for the etection by MOA than in the slow growth Ý kg ). Note as well that the slope of the clou echoes is higher for the fast growth scenario because the ice particles are larger an consequently seimentate more. Nevertheless, even in this case, there is only a small amount of ice that falls own to the groun. In the slow growth scenario, the ice particle transport is mainly controlle by horizontal avection, making the slopes rather small. In this scenario, it is ifficult to obtain slopes near the observe by MOA (Ivanov an Muhleman 2001) Summary of the isolate trough simulations The above simulations have shown that the clous triggere by a single trough are near always tilte against the win, at least the primary clou below > km, i.e. within the layer where the win is constant. This primary clou is relate to vertically propagating gravity waves force by the trough an extents from the surface up to > iñ km. Above this primary clou near the surface, other clous at higher altitues are generally foun, but they cannot be etecte by MOA, at least for realistic number mixing ratio of ice particles ( is also a lower limit, aroun 10Þ kg Hà Ö t ð kg ). There, for the ice particle number mixing ratio for the etectability of the primary clou by MOA. The slope of the primary clou echoes correspons to the slope of the clou but oes not necessarily correspon to the top of the clou. These last results are not much sensitive to the 37

38 backgroun flow profiles above 10km an to the critical value of the nucleation supersaturation, s z &À : whatever this value is, the temperature anomalies inuce by a 10m.s win over a 0.5 km epth trough in an atmosphere with [óòb[? are large enough to create CO ice clous below 20km. The vertical extension an the slope of the echoes mainly epen on both the growth rate assumption an on the win amplitue at low level. In the fast growth scenario, the clou echoes are more incline than in the slow growth scenario. The win amplitue at low altitue also increases the slope an the vertical extension of the clous. The simulate clou echoes forme above a iealize single trough successfully reprouce the echoes of the isolate clous observe by the MOA experiment (Pettengill an For 2000). Finally, these simulations have also allowe us to constrain the values of the moel parameters, before proceeing to simulations with realistic north polar cap topographies. 4.2 Simulation with realistic topographies In this section, the wave clou moel is use in the presence of realistic topographies, an even more quantitative comparisons with the MOA observations are mae. As the simulation in Section 4.1 only reveal a weak sensitivity of the moel response to the backgroun flow structure above 12.5 km, simulations with profiles (0) only are presente in the next three subsections. Three topography pro- 38

39 œ files that correspon roughly to the three MOA observations: Passes 207, 260 (Pettengill an For 2000) an 222 (Ivanov 2000) are consiere. Note however that the exact topography that triggere the clous cannot be use since the exact irection of the win is not known. Nevertheless, the global irection of the win which correspons to the three MOA observations can be estimate from the shape of the clou echoes (if we assume that they are tilte against the win, see Section 4.1.4). On this basis, the win irection will lea to a large-scale upslope air ascent for Pass 222 (Fig. 9) an to a large-scale ownslope air escent for Pass 207 (Fig. 10). arge scale cooling an warming will be inuce by these large-scale upslope an ownslope air motion, respectively (Forget et al. 1998) arge-scale flat topography Figure 8 Fig. 8 compares the MOA observations (upper panel) for Pass 260, with the simulate clous an echoes after two hours of integration (lower panel). On this figure an for comparison with the MOA ata, the altitue is efine as the altitue above the 6 mbar reference level, contrary to the results presente in the previous section, where the altitue was the istance from the surface. Above each trough or rige, at low altitue, extene sloping clous are forme, they resemble to the clous in the single trough simulation (compare for instance the thick clous near %!œ km an % ô km in Fig. 8 to that in Fig. 6). Nevertheless, as 39