Icy particles in the summer mesopause region: Three-dimensional modeling of their environment and two-dimensional modeling of their transport

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. A11, 1366, doi: /2001ja000316, 2002 Icy particles in the summer mesopause region: Three-dimensional modeling of their environment and two-dimensional modeling of their transport U. Berger and U. von Zahn Leibniz-Institute of Atmospheric Physics, Kühlungsborn, Germany Received 26 September 2001; revised 19 November 2001; accepted 29 November 2001; published 15 November [1] In summertime, layers of icy particles form in the high-latitude mesopause region, causing the phenomena of noctilucent clouds and polar mesosphere summer echoes. We study the formation of these layers by means of a 3-D general circulation model of the middle atmosphere (COMMA/IAP) including new modules for the mesospheric chemistry and for the microphysics of icy particles. We initialize the mesopause region with an ensemble of two million particles and investigate their time-dependent transport in a 2-D Lagrangian way. We use the model to study in considerable detail ice particle formation by heterogeneous nucleation on smoke particles, freeze-drying of the mesopause region by formation of ice particles, and the influences of tidal waves and particle eddy diffusion on ice particle and noctilucent cloud (NLC) layer behavior. We present model results on the requirements for adequate size of smoke particles to act as condensation nuclei in the mesopause region (directly after initialization > 0.7 nm radius; after 8 hours > 2 nm), the types of ice particle trajectories, the timescale for growth of particles (6 to 8 hours to radii > 20 nm) and sublimation of ice particles (duration of sublimation phase typically 6 hours), the typical altitude range of maximum NLC brightness ( km), the size distributions of ice particles (closer to Gaussian than lognormal in shape), the importance of the vertical component of the tidal winds on NLC layer behavior, and the dominance of semidiurnal over diurnal tidal effects. Furthermore, the model allows us to make predictions on a number of NLC features that are either currently under study or may become observable in the near future, such as properties of NLC at high arctic latitudes, and the development of layers with strongly enhanced water vapor mixing ratios near the lower border of the NLCs. INDEX TERMS: 0305 Atmospheric Composition and Structure: Aerosols and particles (0345, 4801); 0320 Atmospheric Composition and Structure: Cloud physics and chemistry; 0341 Atmospheric Composition and Structure: Middle atmosphere constituent transport and chemistry (3334); 3332 Meteorology and Atmospheric Dynamics: Mesospheric dynamics; KEYWORDS: Lagrangian transport, diffusion, ice particle, mesopause, NLC, mesospheric tides Citation: Berger, U., and U. von Zahn, Icy particles in the summer mesopause region: Three-dimensional modeling of their environment and two-dimensional modeling of their transport, J. Geophys. Res., 107(A11), 1366, doi: /2001ja000316, Introduction [2] Noctilucent clouds (NLCs) are clouds that occur in summer at altitudes between 82 and 85 km poleward of 50 latitude. If they occur in the latitude band between 50 and approximately 65, they may become visible to a human observer who is located on the nightside of the Earth while the clouds, due to their high altitude, are still illuminated by the sun. Poleward of 65, permanent day light throughout the summer prevents visual observations of NLCs. [3] Polar mesosphere summer echoes (PMSEs) are strong echoes received in summer by VHF radars (typically working near 50 MHz) which are located poleward of 50 latitude. The echo-producing layers extend typically from 82 to 88 km altitude. Copyright 2002 by the American Geophysical Union /02/2001JA [4] The strong similarities of the seasonal and spatial occurrence zones of NLCs and PMSEs make it highly likely that both phenomena have a common cause, even though the layering effects are detected at widely differing wavelengths (tenths of micrometers vs. many meters). Both types of layers develop and exist in an atmospheric region with temperatures below 150 K. Both phenomena, NLCs and PMSEs, are thus indicators for and products of an extremely cold state of our atmosphere. [5] The definition of an NLC given above is a classical one insofar as it refers to a phenomenon which is seemingly only observable for an observer in twilight. It has been proven, however, by two totally independent methods that these cloud layers also form and exist in daylight. The first proof for this fact came from satellite observations of NLCs in daytime by Donahue et al. [1972]. Later, the technique of groundbased observations of NLCs by lidar was extended to enable such SIA 10-1

2 SIA 10-2 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION observations also in full daylight [Nussbaumer et al., 1996; von Zahn et al., 1998]. Through these studies, it became amply clear that layers of noctilucent clouds exist not only in near-darkness, but also in full sun light. We will retain, nevertheless, the widely used designation of noctilucent clouds for both the nighttime and daytime scattering layers as well as for the so-called polar mesospheric clouds (PMCs). [6] The past decade has brought us new methods for studying NLC layers. Examples for new observing capabilities are those for (1) lidar soundings of NLCs in full daylight, (2) lidar soundings of NLCs at more than one wavelength, and (3) of simultaneous and common-volume observations of NLC layers by lidar and PMSE layers by radar. In addition, our knowledge about important ambient parameters such as the temperature and the water vapor mixing ratio in the critical altitude region 82 to 88 km was considerably improved during this period. These new observations (to be discussed in chapter 2) have so far not been considered or incorporated into models of the microphysics of NLC particles and layers. The recently obtained NLC and PMSE properties provide new and stringent inputs for models of the growth, transport, and sublimation of icy particles in the mesopause region. [7] Here we report on our effort to understand better than before the recently observed features of NLCs and PMSEs. For this we use our 3-D COMMA/IAP model [Berger and von Zahn, 1999] which has been expanded by a module for the growth, transport and evaporation of ice particles in the mesopause region. The model has allowed us to follow the complex trajectories (in 2-D) of ice particles as function of their size and to better understand the processes leading to the observed tidal variation of NLC altitude, of NLC particle sizes and of basic NLC and PMSE layer characteristics. [8] About 12 years ago, the results of NLC research were summarized in a book by Gadsden and Schröder [1989]. At that time, reasonably firm knowledge about NLCs was the following: The altitude of NLC is 83 ± 1 km; the cloud particles consist of ice; the particle size is smaller than 100 nm; the occurrence frequency of NLCs is anticorrelated with solar activity. Important unanswered questions were those about the nucleation processes for NLC particles, their median radius, size distribution and shape, the role of dynamics in the life cycle of NLC particles, and the relationships of NLC and PMSE layers. [9] Since appearance of the early papers by, for example, Hesstvedt [1961] on the sublimation of water vapor onto sublimation nuclei, considerable progress has been made in our understanding of NLC formation and properties by modeling the microphysical processes governing the formation, growth, and dissipation of NLC particles. In the past two decades, particularly noteworthy contributions have come from Turco et al. [1982], Thomas and McKay [1985], Jensen and Thomas [1988], Inhester et al. [1994], Sugiyama et al. [1996], and Klostermeyer [1998]. Following the conclusions of Turco et al. [1982] that heterogeneous nucleation is by far the most important nucleation process for NLC particle formation, all subsequent modelers have assumed only this process to be responsible for NLC particle formation (except for Sugiyama et al. [1996]). Another common and important feature of all these studies is their use of only 1-D models. This feature severely limits the usefulness of these models for studies of the impact of dynamical processes on the behavior of NLC particles and layers. To overcome part of this weakness, Jensen and Thomas [1988] and Klostermeyer [1998] implant into their 1-D models vertical winds taken from the 2- D atmosphere model of Garcia [1989], whereas Sugiyama et al. [1996] define their own vertical wind field which decreases to zero velocity at the mesopause. We note, though, that all modern 2-D [Garcia and Solomon, 1985; McIntyre, 1989] and 3-D [Berger and von Zahn, 1999] models predict a maximum of the upwards directed wind at, or little below, the mesopause. The upward directed winds are very important in prolonging the times available for NLC ice particles of a few nanometer size to grow by collection of water vapor to, say, 50 nm size. If these winds are not included in 1-D models, artifically modified temperature profiles [Turco et al., 1982; Jensen and Thomas, 1988; Sugiyama et al., 1996; Klostermeyer, 2001] or enhanced water vapor abundances [Sugiyama et al., 1996] must provide for a sufficiently fast growth rate of the ice particles. [10] When trying to summarize the achievements and shortcomings of previous NLC models, we would classify as correctly modeled parameters (1) the altitude difference between NLC and the mesopause and (2) the approximate mean radius of NLC particles (while assuming a lognormal size distribution). Large unknowns remain about the effects of dynamical processes on NLC particles and about the role of ion nucleation in NLC particle formation. Difficulties exist in predicting the tidal variations in altitude and backscatter ratio of NLC layers. Furthermore, there has never been a 3-D atmosphere model which calculated selfconsistently the thermal structure of the mesopause, the dynamics of the mesopause region, the water vapor abundances, and the microphysics of NLC particle formation, growth and sublimation. Nor has the large amount of observational data on PMSE layers been treated in NLC models. [11] The aim of this paper is to provide a progress report on modeling the development and results of NLC particle and layer formation. Our model permits the study of growth, 2-D transport, and dissipation of NLC particles in a 3-D, selfconsistently calculated background atmosphere including effects of tidal variations. Such an approach should yield considerably more realistic results than previous studies. 2. New Observations Since the Late 1980s [12] Due to the 2-D character of the transport code of our ice particle model, its strength lies in the description of microand mesoscale phenomena, yielding sub-kilometer altitude resolution and fractions-of-an-hour temporal resolution. The latter allows, e.g., detailed model studies of diurnal variations of NLC parameters. Observations of this kind come mostly, though not exclusively, from ground-based experiments. It is for that reason that we focus in the following short review on their contributions towards progress in NLC science. [13] Since the late 1980s, there was the development of groundbased lidars with the capability to perform measurements of NLCs in full daylight [von Zahn et al., 2000]. The development of this capability was essential for lidar studies of NLCs at Arctic latitudes because there NLCs occur almost exclusively in daylight conditions. An early highlight of these new observations was the discovery of an unexpectedly strong semidiurnal variation of the altitude of NLCs [von Zahn et al., 1998]. Subsequently, the singlecolor lidar observations were extended to multi-color lidar

3 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA 10-3 Table 1. Properties of Noctilucent Cloud and Polar Mesosphere Summer Echoes Near 69 N Latitude Parameter Noctilucent Cloud Polar Mesosphere Summer Echoes Reference Mean altitudes of layer maxima 83.2 km von Cossart et al. [1999b] 82.6 km Carbary et al. [2001a] 85 km Hoffmann et al. [1999] Lower boundary of layers close to 82 km and 150 ± 2 K Lübken et al. [1996] frequently colocated within a few 100 m von Zahn and Bremer [1999] Typical layer widths 1.4 km (FWHM) von Cossart et al. [1999b] 4 8 km (above 2 db) Hoffmann et al. [1999] Tidal variations in altitudes of the layer peaks total variation of about 2 km, von Zahn et al. [1998] being dominated by a semidiurnal tide Hoffmann et al. [1999] Particle size distribution (presumed lognormal) r med =51nm s = 1.42 von Cossart et al. [1999a] N =82cm 3 Particle composition ice particles Hervig et al. [2001] observations of NLCs, both in full daylight and in darkness. This development resulted in the first measurements of three-parameter size distributions, including the distribution width, of NLC particles [von Cossart et al., 1999a; Alpers et al., 2000]. Accurate measurements of NLC altitudes at high Northern latitudes were also provided by groundbased lidar observations at 67 N [Thayer et al., 1995, 2001] and 68 N [Stebel et al., 2000], as well as by the MSX satellite [Carbary et al., 2001a]. [14] Significant progress in our understanding of the layering phenomena occurring in the extremely cold region of the Arctic summer mesopause was achieved by use of a Rayleigh lidar together with a MST radar at the site of the Alomar observatory on the island Andoya, Norway (69 N, 16 E). Simultaneous and common-volume measurements of NLCs by lidar and of PMSEs by radar established for the first time the strong spatial and temporal relationships of the two layering phenomena [Nussbaumer et al., 1996; von Zahn and Bremer, 1999]. Observations with these instruments also established a firm record of the yearly occurrence frequency of NLCs and PMSEs at the Alomar site [von Cossart et al., 1999b; Hoffmann et al., 1999]. [15] One more important step towards a better understanding of the environment in which NLCs exist was the placement of a groundbased microwave spectrometer for soundings of mesospheric water vapor profiles at the Alomar observatory in This instrument acquires profiles of the water vapor mixing ratio between 40 and 85 km altitude [Seele and Hartogh, 1999]. At the summer solstices, the instrument determined a water vapor mixing ratio of 2.4 ppmv at 85 km. By August of 2000, the instrument observations covered 3 complete and continuous annual cycles of upper mesospheric water vapor mixing ratios [Hartogh, 2000]. Very relevant for our model study are also the most recent results of MAHRSI and UARS/ HALOE observations: The first confirmation that water ice is the primary component of NLC particles [Hervig et al., 2001] and the first observation of a layer of enhanced water vapor abundance at NLC altitudes [Summers et al., 2001]. [16] Large progress has been made in documenting the thermal structure of the Arctic summer mesopause region since the late 1980s. During the summer 1987, a series of 26 falling sphere experiments established the thermal structure and its variability of the mesosphere and mesopause at summer solstice and 69 N[von Zahn and Meyer, 1989]. For these conditions, the mesopause was found at 88 km altitude and 129 K. These data were more recently incorporated into a comprehensive empirical model of the thermal structure of the Arctic summer mesosphere at 69 N, 16 E [Lübken, 1999] which now provides a firm basis for comparisons of temperatures predicted by atmospheric models with observed ones. Last, but not least important, the structure and intensity of turbulent layers in the arctic mesopause region have been documented by quite a few experiments [see e.g., Thrane et al., 1985; Lübken, 1997; Czechowsky and Rüster, 1997]. [17] Finally, we note the more recent development of much improved capabilities for the in situ measurement of dust and icy particles [see e.g., Havnes et al., 1996, 2001; Mitchell et al., 2001]. These experiments have provided clear evidence for the existence of significant densities of heavy charged dust and icy particles (note that Havnes et al. designate both stony and icy particles as dust ) within the NLC and PMSE layers. Yet, the quality of determination of particle masses has not yet reached the stage that we could compare an in situ measured mass distribution with our modeled distributions. [18] These new observations of NLC properties call for an effort of upgrading models which are to simulate numerically the formation and life cycle of NLCs. Today, such models need to consider also the new knowledge about PMSE layers which so far has hardly be included in numerical modeling of NLCs. Here we will do so with respect to the parameters of PMSE layers and the estimated size of icy particles contributing to PMSEs. We will not consider, though, the interactions of these icy particles with the ambient plasma and the cause for its spatial variability. We summarize in Table 1 those properties of NLC and PMSE layers which we will consider in our modeling effort. [19] In our numerical description of a background atmosphere we attempt to reproduce the observed conditions of the mesosphere region over Andoya in a most realistic way at least in the sense of climatology means including tidal daily variations. 3. Model Description [20] In our model approach, we describe a multiple particle system containing a number of two million smoke particles presuming several initial size distributions between 1.0 and 3.5 nm radius which act as potential condensation nuclei in a supersaturated cold atmosphere. These smoke particles are transported in a background atmosphere which is specified

4 SIA 10-4 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 1. Diurnal means of (a) temperature, (b) vertical wind, (c) zonal wind, and (d) meridional wind versus latitude at summer solstice as calculated by the 3-D COMMA/IAP model. The latitude of Andoya/ Alomar is indicated by a thin line. The altitude of the mesopause is indicated by a thick line. by a self-consistent data set of 3-D time-dependent horizontal and vertical winds, temperature, pressure, and water vapor distributions. The numerical transport method is a Lagrangian scheme which is applied to each particle through computing the specific trajectory of each single particle. [21] During each transportation time step a simplified microphysical parameterization allows heterogeneous condensation of water vapor on condensation nuclei (CN), growth of ice shells around the CN, sedimentation of these particles, and later sublimation of the ice shells in warmer regions of the atmosphere. The entire ensemble of two million particles produces a large scale ice cloud event, in which the history and life cycle of each ice particle is well known. During growth and sublimation of ice particles we take into account the respective changes in the background water vapor which is itself advected in time by an Eulerian transport. [22] Although our proposed ice formation model is generally valid for time-dependent, 3-D conditions, we will apply our concept for a 2-D case of a longitudinal-height cross section for the latitudinal circle of Andoya (69 N). Because of numerical limits of computer storage and run time, our available computer capacity allows so far only a conditioning of a maximum number of two million individual particles. In order to provide a reasonable statistic of model results, we therefore presume a 2-D model domain. Here, the spatial grid ranges from km to 92 km in the vertical direction (z = 50 m) with a horizontal resolution of l = The integration in time of the ice model scheme takes place in steps of t =45s The COMMA/IAP Model [23] The atmospheric background conditions of winds, temperatures, and water vapor are calculated by means of the general circulation model of the middle atmosphere COMMA/IAP (Cologne Model of the Middle Atmosphere/ Institute of Atmospheric Physics, Kühlungsborn). This model is designed for studies of physical processes in the high latitude summer mesopause region [Berger and von Zahn, 1999]. [24] COMMA/IAP is a fully non-linear, global and three-dimensional Eulerian gridpoint model which extends from the ground to the lower thermosphere (0 150 km) using a vertical grid refinement (z ffi 0.8 km) to resolve the observed structures of minimum temperature layers at the mesopause. The model system consists of a dynamical core, and modules for radiation and for mesospheric chemistry-transport.

5 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA 10-5 Figure 2. Diurnal means of (a) water vapor, (b) water vapor saturation, and (c) minimal radius (nm) of CN which allows formation of an ice shell versus latitude at summer solstice as calculated by the full 3-D CTM module of COMMA/IAP model. The latitude of Andoya/Alomar is indicated by a thin line. The altitude of the mesopause is indicated by a gray line. [25] The gravity wave parametrization used in our model is based on the work of Holton and Zhu [1984]. We increased the number of gravity waves, which deposit gravity wave momentum near critical and breaking levels at mesospheric heights, from 12 to 33 with phase velocities (four azimuthal directions: 0, 90, 180, 270) from 5, 25, and 50 m/s to 0, 10, 20, 30, 40, 50, 60, 70, and 80 m/s. We also performed a careful tuning of sensitivity parameters in the gravity scheme (e.g., efficiency, horizontal wave length, excitational amplitude) in order to achieve a close match of model predictions and observations for the high-latitude summer mesopause region. [26] Figures 1a 1d show the zonal and diurnal means of temperature and vertical, zonal, and meridional wind components in the mesopause region (75 95 km) at high latitudes for 21 June conditions. The simulated temperature field shown in Figure 1a reproduces the mesopause altitude and mesopause temperature as observed with different measurement techniques. For the summer mesosphere at 69 N the model predicts the mesopause at 88 km and 128 K. For an altitude of 82 km the temperature is 150 K. These predictions agree closely with Lübken [1999]. For the North pole and 21 June the COMMA/IAP predicts a mesopause at 91 km and 113 K and the 150 K level is located again near 82 km. This might indicate that the lowest edges of ice particle clouds occur at almost the same heights at both latitudes. [27] The explanation for the existence of a very cold polar summer mesopause is a strong adiabatic cooling due to largescale vertical upward motions (see Figure 1b), which are forced by breaking gravity waves. Strongest vertical upward winds are predicted near the pole with velocities of more than 70 mm/s, corresponding to an adiabatic cooling rate of more than 70 K per day. Maximum vertical velocities occur about 5 km below the mesopause. In the structures of the zonal wind (see Figure 1c) we identify the upper part of the mesospheric summer jet at 60 N near 80 km with typical easterly (towards the west) wind speeds of 60 m/s. The zonal wind reversal is located slightly above the mesopause heights. A comparison with wind observations of the Alomar MF-radar facility shows an reasonable agreement of absolute wind values and reversal heights [Hoffmann et al., 2002]. The meridional wind (see Figure 1d) is blowing equatorward with maximum wind speeds of about 14 m/s at mesopause levels. Again the radar observations indicate similar climatological values [Nastrom et al., 1982; Rüster, 1992].

6 SIA 10-6 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION [28] These background conditions provided by COMMA/ IAP represent a self-consistent data set of winds and temperatures which will be employed in the following simulations Chemistry Transport Module [29] The chemistry transport module of the mesosphere and lower thermosphere provides the radiative module of COMMA/IAP with trace gas contributions like ozone, water vapor, atomic oxygen, nitric oxide etc. The characteristics of the chemistry-transport module are described in detail by Körner and Sonnemann [2001]. So far, the dynamical core and the chemistry transport module are not completely interactively coupled for every time step. Dynamics and temperature fields calculated by COMMA /IAP are used as preprocessed 3-D and time-dependent fields for the chemistry transport module within a 10 day interval of model time in order to compute actual chemical species distributions. [30] We are particularly interested in the mesospheric water vapor distribution valid for mid and high latitudinal summer conditions. The water vapor distribution above 75 km is determined mainly by three processes which we mention in decreasing order of importance: The most dominant one is the upward transport of water vapor due to the synoptic vertical upward wind; The second process is photolysis of water vapor by solar Lyman a; The third process is vertical turbulent diffusion. [31] Figure 2a shows the calculated water vapor distribution from the chemistry-transport module. At 75 km a typical water mixing ratio is 5 ppmv. This result is supported by ground-based microwave observations of Seele and Hartogh [1999] who measured water vapor contents over Alomar between 75 and 80 km of 4 5 ppmv for summer conditions. Above these heights the chemistry-transport module predicts a decrease of water vapor down to at 0.8 ppmv at 90 km. We also note from Figure 2a an increase in water vapor mixing ratios towards the summer pole, which is mainly due to the vertical wind being the strongest above the pole. [32] The water vapor volume mixing ratio X H2 O is used to calculate the local water partial pressure p H2 O as p H2O ¼ X H2O p where p is pressure of air. Then the saturation pressure of water vapor p 1 over a plane ice surface is expressed with the simplified version of the Kirchhoff formula [Gadsden and Schröder, 1989] ð1þ log e p 1 ¼ 28: :4 : ð2þ T The saturation of the ambient atmosphere with water vapor is defined by the saturation ratio S S ¼ p H 2O p 1 : ð3þ Whenever an air volume is supersaturated (S > 1), such a condition will allow the existence of an ice phase. According to equation (2) these conditions depend crucially on very low temperatures which exist at mesopause heights. As we see in Figure 2b, regions of supersaturated air extend from 83 to 93 km, depending on latitude. The value of S =1 coincides closely with a temperature of 147 K at 83 km for any latitude poleward of 65 N. This S value divides altitude ranges of either growth or sublimation of ice particles. Whenever an ice particle falls across the S = 1 level, the ice particle has reached its maximum size and will start to sublimate below that level. [33] Near the pole, S values become sufficiently large to allow homogeneous nucleation on small molecule clusters with radii 0.3 nm (Figure 2c). This process will be limited, however, to rather small ranges of latitudes and altitudes. Hence, in the current model we consider only particle formation through heterogeneous nucleation on CN (see also section 3.4) Initialization of 2-D Background Conditions at Andoya Initialization of Winds and Temperatures at Andoya [34] Figures 3a 3c shows the initial fields of temperature, vertical wind, and zonal wind versus local time at Andoya (69 N) for 21 June. A semidiurnal tide dominates the LT-dependence. The thermal tide attains amplitudes of only 1 and 2 K at 80 and 88 km altitude, respectively. The tidal components in the wind field attain typical amplitudes of 30 mm/s and 20 m/s for the vertical and zonal component of the wind. Note that at the altitude of NLCs (83 km) the amplitude of the vertical tidal wind is just about as large as the upward synoptic wind Adjusted Initialization of Water Vapor at Andoya [35] Because of the importance of large-scale, upward transport of water from the lower mesosphere, we will first describe our numerical advection scheme used for water vapor volume mixing ratios as an Eulerian volume method. Within this study we are using a positive-definite advection algorithm by Bott [1989] which yields very good results for tracer distributions with strong spatial gradients. We expect strong gradients, e.g., when ice clouds sublimate in very localized altitude zones. In order to avoid artificial over- and undershooting tracer values, this scheme was further developed to a more restrictive monotonic flux version which eliminates this deficiency [Bott, 1992]. In addition, this transport scheme produces only a minute numerical diffusion, an advantage which now will allow us to introduce reasonable physical diffusion constants derived from real observations (see below). [36] We want to achieve two objectives with such an quasi-exact transport algorithm: First, we aim to adjust the initial water profiles to the actual dynamical background. So far, the chemistry transport module of COMMA/IAP provides us with water vapor concentrations which belong to climatology means over 10 days. Thus this predescribed profile has still to be fitted to the actual tidal variations. Second, we want to describe the contributions of growing and sublimating ice clouds which subtract and add water molecules from and to the background water vapor. This variable change in the background water now has to be accommodated by the dynamical advection scheme. [37] Figure 4 summarizes the characteristics of the pure transport algorithm for a 1-D case (zonal wind equal zero) of a constant vertical wind transporting water vapor volume mixing ratios upwards with a velocity of 34.7 mm/s (= 3 km/d). The spatial grid has a grid resolution of

7 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA 10-7 Figure 3. Local time (also longitude) dependencies of (a) temperature, (b) vertical wind, and (c) zonal wind at 69 N at summer solstice as calculated by the 3-D COMMA/IAP model. In Figure 3b, solid lines indicate upward winds, dashed lines downward winds. The thick line indicates the location of the mesopause. 50 m in vertical direction in combination with a time step of t = 45 s. As a lower boundary condition for the transport scheme we assume at 80 km a constant water vapor mixing ratio of 4.3 ppmv. In Figure 4, the initial state of water vapor (thin dashed line) coincides with the profile of Figure 1 at latitude 69 N in addition with a postulated rectangle superimposed. The rectangle is introduced to investigate the transport behavior of steep gradients in a general water vapor distribution. After a transport time of 2 days (3840 iterations) the initial rectangular distribution of our tracer is expected to be shifted 6 km upward under ideal circumstances (thin solid line). The used transport scheme provides a transport behavior changing only slightly the shape of the rectangular distribution of water vapor, hence maintaining its steep gradients (thick solid line). The influence of the lower boundary condition on the transport behavior is indicated by the constant values 4.3 ppmv up to 86 km after 2 days. [38] The photodissociation rate k photo [s 1 ] of water vapor by solar Lyman a flux and the Schuman-Runge band (daily mean solar zenith angle = 68, mean solar activity) are available, e.g., from Jensen [1989]. The functional dependence is expressed as follows log 10 k photo ¼ 33:7081 þ 0:1 þ 0: z 0: z 2 dn H2O dt ¼ k photo n H2O; where z is the geometric altitude [km], n H2O number density of water molecules (cm 3 ). In Figure 4 the process of photodissociation (thick dotted line) decreases the rectangular distribution by 30% and also the underlying background water vapor content. [39] As the third process, we introduce an eddy diffusion transport in addition to advection as dx H2O dt ð4þ ð5þ ¼ K zz ðþ z d2 X H2O dz 2 : ð6þ

8 SIA 10-8 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 4. One-dimensional transport of rectangular water vapor profile with a constant vertical wind (w = 3 km/d) for 2 days (3840 iterations, time step t = 45 s) with the monotonic Bott scheme (see text). Thin dashed line: initial state of water vapor. Thin solid line: theoretical expected water vapor after 2 days transportation time. Thick line: water vapor after 2 days transportation time. Dotted line: water vapor after 2 days transportation time taking into account photolysis destruction. We have adopted a time-independent eddy diffusion profile from Lübken [1997], who derived eddy diffusion coefficients from rocket experiments with ionization gauges over Andoya for summertime conditions (Figure 5). A significant property of this eddy profile is its steep positive gradient between 82 and 90 km. The eddy diffusion is only in the range of 5 10 m 2 /s at altitudes near 82 km, where we expect the lower edges of ice clouds. The eddy diffusion coefficient maximizes at 90 km altitude with values of 200 m 2 /s. Figure 6 shows the effects of this eddy diffusion on a Figure 5. Vertical profile of the eddy diffusion coefficient K zz for summer conditions at Andoya/Alomar (from Lübken [1997]). Figure 6. One-dimensional transport with a constant vertical wind (w = 3 km/d) of a rectangle for 2 days (3840 iterations, t = 45 s) with the monotonic Bott scheme taking into account photolysis destruction and turbulent eddy diffusion (see text). The various curves indicate the tracer distribution for every 6 hours. layer of enhanced water vapor with 12 ppmv mixing ratio. After its initial start at 82 km altitude, this layer has been totally dissipated 2 days later. As we see in Figure 6, eddy diffusion is a very efficient process for mixing layered structures. Note that the transport and photolysis schemes are still running in parallel with diffusion. [40] Finally we introduce the modeled zonal and vertical wind fields from Figures 3a and 3b, which we apply in the transport scheme (grid resolution: z = 50 m, l = 2.25 ) to calculate the tidal wind induced structure of the background water vapor for a latitudinal circle of Andoya. Because we are not able to incorporate our full chemistry transport module of COMMA/IAP in our time-dependent ice cloud formation model, we need a simplified chemistry, the results of which differ hopefully only slightly from those of the full chemistry-transport module. This simplified chemistry includes vertical transport, photolysis, and eddy diffusion as previously discussed. Local time dependencies of winds and temperature are achieved for every time interval of 9 min. We postulate the equivalence of longitudinal directed structures to local time dependencies over a day. To this end, we shift wind- and temperature fields westwards by l = 2.25 per 9 min. This procedure ensures cyclical boundary conditions and repeats the atmospheric background condition from one day to another. We assume as an initial guess of a water vapor state the profile from the full chemistry transport module valid for the latitude of Andoya (Figure 2a). Then we compute, taking into account the simplified chemistry, the converging quasi-static state of the water vapor distribution after 10 days simulation time. Figure 7 shows the new quasi-static state including the daily (or longitudinal) variation of water vapor. It is evident that the dominant semidiurnal tide in the wind field has been transferred to the water distribution. Both states, that of initialization from the full chemistry-transport module and of the 10-day state from the simplified chemistry run, contains almost identical amounts of water vapor. This

9 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA 10-9 where m = kg is the mass of a water molecule, k B = JK 1 is the Boltzmann constant, T is the temperature of surrounding air, r = 932 kg m 3 is the density of ice, and s the surface tension of ice-water vapor. [43] In the case of very small water droplets and icy spheres the surface tension reduces and is expressed in terms if the radius r [Tolman, 1949] s ¼ s 1 1 þ 2d=r : ð8þ d is a empirical factor which Turco et al. [1982] specify as d = m. s 1 (J m 2 ) denotes the surface tension over a plane ice surface and is a function of temperature (K). Hale and Plummer [1974] quote a linear fit with Figure 7. Quasi-static state of water vapor volume mixing ratio ( ppmv) at 69 N after 10 days of transport time at the summer solstice versus local time and longitude taking into account dynamical transport (dynamics from Figures 4b and 4c), photolysis destruction, and eddy diffusion. indicates that water vapor in the summer mesopause region at high latitudes is mostly determined by the three processes of vertical transport, photolysis, and eddy diffusion. We will use the adjusted water vapor profile of Figure 7 as an initial guess of the background water vapor X H2 O for starting the model of ice cloud formation. Any subsequent evolution of the background water vapor will be calculated using our simplified chemistry scheme which is linked to the Eulerian transport module Microphysics of Ice Particles [41] In principle, ice particles can form by either ion nucleation, homogeneous or heterogeneous condensation of water vapor. The first two condensation processes need, however, very large values of supersaturation. Therefore heterogeneous nucleation onto meteoric smoke particles should be the most realistic process of ice particle formation provided some kind of condensation nuclei are indeed available [Gadsden, 1982]. Like Turco et al. [1982] we presume that the required CN are continuously formed in the km region by the recondensation of meteoric material which was previously vaporized during the highspeed entry of meteoroids into the Earth s atmosphere. This latter process was extensively modeled by Hunten et al. [1980] who designated these CN as smoke particles. [42] If the atmospheric temperature is low enough and sufficient water vapor is available, supersaturated air conditions will allow ice formation to proceed on these CN. The saturation pressure depends, however, not only on temperature, but on the particle radius too, the so-called Kelvin effect. We apply a standard formula, which gives the saturation pressure of water vapor p sat (r) over a sphere with radius r in terms of saturation pressure of water vapor over a plane ice surface p 1 from equation (2) as 2ms p sat ðþ¼p r 1 exp k B Tr r ð7þ s 1 ¼ 0:141 1: T: As an example the correction of the surface tension is about 23% for an icy sphere of radius 1 nm. [44] Now we are able to quote a saturation ratio S(r) related to spherical CN in terms of radius r Sr ðþ¼ p H 2O p sat ðþ r : ð9þ ð10þ According to equations (7) (10), a minimum radius of a smoke particle can be calculated that allows ice condensation to proceed onto this nucleus. Figure 2c shows the distribution of such minimum radii assuming the background conditions of Figures 1a and 2a. At 69 N latitude, only CN with radii larger than about 0.7 nm allow the formation of ice particles, still requiring ambient saturation values (3) of S 70. With formation of an initial layer of ice particles, freeze-drying of the mesopause region shifts the radii of CN required for heterogeneous nucleation rapidly towards higher values, as will be shown below. [45] According to Hesstvedt [1961], the growth rate dr/dt of a spherical ice particle is given by dr dt ¼ a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m=2pk B T r p sat ðsr ðþ 1Þ; ð11þ where a is a so-called condensation coefficient which describes the probability that a free water molecule sticks on the surface of the ice particle. Its value has been assumed to fall between 0.5 [Reid, 1975] and 1 [Turco et al., 1982; Klostermeyer, 1998]. Our choice will be the one of Gadsden [1998] with a = For local conditions of S(r) < 1, the growth rate (11) becomes negative with the physical meaning that ice growth changes to ice sublimation. [46] Due to its mass the proposed spherical ice particle will own a sedimentation velocity w s which depends on the radius of the ice particle, and density and temperature of the surrounding air w s ¼ grr rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ; ð12þ 2n atm 2 m atm k B T where g = 9.55 m/s 2 is the gravitational acceleration, m atm = kg is the average mass of an air

10 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION molecule, and n atm denotes the number density of air (1/m 3 ). The above formula of the fall speed is a derivation by Chapman and Kendall [1965] and Reid [1975]. Later Turco et al. [1982] introduced a correction factor of 8/(8 + p) accounting for inelastic collisions which decrease the fall speed by a factor of about 0.7. We decided to adopt the simpler formalism of Reid due to physical uncertainties how the genuine sedimentation velocities should be correctly described. [47] The above formalism (11), (12) is a description for spherical particles as a key ingredient to our simplified microphysical model. In fact, condensation coefficients, ice growth rate, or sedimentation velocity would change for a more general assumption of nonspherical ice particles. This generalization involves, however, too many new parameters and unknowns to deal with it at this time Multiple Particle System Lagrangian Transport Scheme of Particles [48] In the following we introduce an ensemble of particles and investigate their time-dependent transport in a Lagrangian way. This classical trajectory problem can be solved by estimating the actual spatial coordinates for every time step t for each particle. We compute the 2-D coordinates (x, z) in our 2-D domain of the latitudinal circle over Andoya (69 N) from time step i to i +1forthenth par-ticle as with x n iþ1 ¼ x i n þ u n i t ziþ1 n ¼ z i n þ w n i t u n i ¼ u n b ; wn i ¼ w n b i þ w n s i þ ~w n e i : ð13þ The actual vertical wind w n i, acting on particle n, consists of three components: The synoptic vertical background wind w bi (Figure 3b), the sedimentation velocity w si, and an eddy velocity ~w ei which takes into account turbulent small-scale motions. The background velocity (u bi, w bi ) is defined as the exact velocity at the exact location of the particle n at time i. At these coordinates (x n i, z n i ) the components (u bi, w bi ) have to be be computed by interpolation procedures (e.g., method of finite elements of second order) from values of the background wind at the edges of our volume element which encloses the particle. The edge values are provided by the original grid (not necessarily equidistant) of the background atmosphere, by, e.g., COMMA/IAP. Generally, such an interpolation scheme delivers the actual value of each requested parameter as winds, temperature, air pressure, and density, or water vapor for an arbitrary location in our gridded model domain. [49] The sedimentation velocity w s is described by equation (12). The estimation of eddy velocity ~w e will be discussed in the next subsection Eddy Diffusion Scheme for Turbulent Motions of Particles [50] The eddy velocity ~w e is to parameterize the process of turbulent diffusion which an individual microscopic particle should experience. In the upper mesosphere turbulent mixing mostly occurs on scales in the order of several 10 m. Lübken [1997] derived turbulent velocities which in summer maximize near 90 km altitude at a few m/s. These velocities, which exhibit a chaotic behavior, produce turbulent height displacements. [51] In the following we introduce a self-consistent concept for combining the classical volume eddy diffusion (K zz mixing) approach with particle eddy diffusion. [52] For the approach of classical volume diffusion we rewrite equation (6) as Fick s second law d C d t ¼ D d2 C dz 2 ð14þ with concentration C of a tracer where the diffusion coefficient D is assumed to be constant. There exists an analytical solution for the problem of a diffusing d-function [Moore, 1975]. Starting at time t = 0, the initial concentration C described by a d-peak with C d(z =0)=N (N number per unit length) diffuses in time and space with C ¼ ffiffiffiffiffiffiffiffiffiffi 1 p exp z2 : ð15þ 4pDt 4Dt The diffusion coefficient D characterizes the speed that the distribution C spreads over the domain z with time. Formally, equation (15) is the mathematical description of a statistical Gaussian normal distribution C ¼ pffiffiffiffiffi 1 2p exp z2 s 2s 2 ð16þ with variance s 2 and s being the half width of the Gaussian distribution. Hence, the substitution becomes s 2 ¼ 2 Dt: ð17þ The analytic solution (15) will be used to test our numerical approaches of solving diffusivity problems for both cases of volume and particle mixing and to investigate their relationship. For a 1-D case we define two initial distributions as d(t =0, 1/2z z 1/2z) = 50,000 for classical volume diffusion and d(t =0,z = 0) = 50,000, d(t =0,z 6¼ 0) = 0 for particle diffusion. The latter initial value of 50,000 defines the number N of particles which are initialized at one single point at z = 0 whereas the former initial field describes the concentration value of a passive tracer (N = 50,000/z) which is defined over one full grid element with width z = 50 m. If now the peak distributions start to diffuse with time we will expect that under ideal circumstances both distributions should diffuse with same velocities sustaining their same shape at least in the limit of a infinitely large number of particles where a mean mixing of a statistic ensemble should converge to a volume mixing process described by Fick s second law or equation (6). The numerical solution of the differential equation (14) can be obtained by using an implicit time step scheme (Crank-Nicholson method), here with a time step of t = 45 s. In order to relate quantitatively eddy volume diffusion with eddy particle diffusion we need to define a transformation from diffusion coefficients D into particle velocities ~w e. Furthermore, we need to find a statistical probability function how particle

11 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 8. Diffusion of a particle distribution with N = 50,000 initialized as a d peak with d(0) = 50,000 after 1 and 2 day simulation time. Particles diffuse with a maximum turbulent random velocity w e = 0.5 m/s per time step t = 45 s. The distribution is defined as a histogram which counts the number of particles per z = 50 m (polygonally solid line) with an equivalent eddy diffusion coefficient D = m 2 /s. Two smooth solid lines (overplotted at this scale) base on the analytic solution of eddy volume diffusion after equation (15), and the Crank-Nicholson scheme of equation (14), see text. velocities are statistically distributed (e.g., Maxwell distribution, Gaussian distribution, uniform distribution). [53] Indeed, we performed numerical experiments testing several probability distributions. These tests showed that only the uniform distribution of random velocities in the interval with boundarys ±w e meets the statistical relation. Therefore, we generate a random number P r inside our numerical code that has a uniformly distributed probability in the interval between ±1 (such a software generator is itself uniformly random). This random number expresses the statistical likeliness that a discrete actual turbulent velocity exists over the range of ±w e (z) with [54] Figure 8 contains the diffusion profiles of an initial d-peaked distribution obtained from three different approaches after 1 and 2 days of simulation time: The particle diffusion (polygonally solid line), the numerical volume diffusion by iterations with the Crank-Nicholson scheme of equation (14) (first smooth solid line), and the equivalent analytic solution (15) (second smooth solid line). The two smooth solid lines, the curve of the analytic solution (15) of Fick s second law (14) and the numerical curve, are undistinguishable at the scale of the plot, and are overplotted. This indicates that the numerical volume diffusion procedure works almost exactly in terms of numerical accuracy describing identically the analytic solution. [55] The diffusive particle (polygonally curve) distribution is computed in the following way. We make an arbitrary choice of, e.g., w e = 0.5 m/s which defines the uniformly random distributed values of vertical winds in the interval [ w e ; w e ]. At time i the iterative path lengths z i n = z i 1 n + P r w e t of particles n 2 N are randomly distributed with mean z and variance s 2 z as z ¼ XN zn i N ¼ 0 ; s2 z ¼ XN zn i 2 z N 1 : ð19þ n¼1 Using equation (17) we get the respective eddy diffusion coefficient D = s z 2 /(2it) which is applied in the analytic function and in the numerical volume scheme. At every time step i, this numerically computed D is almost independent of time as expected within small statistical errors of 1% (Figure 9). As Figure 8 indicates, a total number of N = 50,000 particles almost generates a statistical distribution. The histogram counts the number of particles per z = 50 m, which is in good agreement with the analytical, or numerical volume method, respectively. If once N, w e, and D are properly chosen, the particle ensemble and volume characteristics of diffusion coincide at every time. Indeed, this approach is only successful due to the availability of a computer software providing a random generator (uniform probability function) of high quality. Obviously, D is a function of w e. Larger values of n¼1 ~w e ¼ P r w e ðþ; z P r 2 ½ 1; 1Š: ð18þ The random procedure generates for every event new and unrepeatable values for every particle at each time step. Generally, we will allow incidental large turbulent velocities up to several meters per seconds even though we will always use a fixed time increment of t =45s. Turbulent distance changes larger as a grid box diameter will only occur for cases when the random generator picks a turbulent velocity of more than approximately 1 m/s. At these cases we allow for a violation of the Levy-Courant criteria of numerical stability that a single trajectory will overjump a box within a single timestep. Nevertheless, all physics and transports sensitive to such a particle will be well-defined, an advantage of our particle approach. Figure 9. Numerically computed variance after equation (21) s 2 z of randomly distributed pathlengths of 50,000 particles as a function of time (solid dots) against theoretical variance (solid line).

12 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION w e imply an increase of s z 2 and so D producing a stronger mixing. [56] In the following, we want to look for the fundamental dependence of w e and D in our approach. Therefore we performed a sensitivity study running several numerical experiments where we changed the presumed values of w e e.g. from 0 m/s to 5 m/s (N = 50,000, t = 45 s, and z =50 m remained unchanged). As a result we obtain that D and w e are related as follows: D w 2 e ; D ¼ aw2 e ; a ¼ 7:5 s: ð20þ This means, uniformly distributed random velocities within a interval of maximum turbulent velocity of, e.g., w e =±1 m/s give rise to a mixing of an ensemble which is equivalent to a volume mixing with D = 7.5 m 2 /s. Eddy diffusion coefficients in the order of 180 m 2 /s near the mesopause region at high summer latitudes would be matched vice versa by uniformly distributed random velocities between ±4.9 m/s, whereas Lübken [1997] derives about ±2.5 m/s for the same strength of eddy diffusion. [57] So far, we derived the expression (20) based solely on the argument that diffusion behavior is identical for both volume systems and multiple particle systems. We will now discuss the influence of the size of the time increment t which determines the relation between D and w e. Therefore we interpret the physical meaning of our somewhat artificially specified constant a and its dependence on the assumed time interval t =45s in which an individual random turbulent velocity remains constant. In general the variance of uniform randomly picked values from the interval ±w e can be expressed by s 2 w ¼ Z we w e ðw w Þ 2 fðwþ dw; where the probability density function f(w) of an uniform distribution is given by f(w) = 1/(2w e ). Performing the integration (w = 0), we get s 2 w ¼ 1 3 w 2 e : Now we are able to combine the analytic velocity variance s w 2 of a single particle in a random walk with the resulting spatial variance of an ensemble of N particles. This variance s z 2 (it) in the space domain z is a function of time it (Figure 9) and can be expressed as a sum of unique variances s 2 z ðitþ ¼ XN n¼1 zn i 2 z N 1 ¼ i XN n¼1 z 1 2 n z N 1 ¼ 1 3 iw2 e ðtþ2 ð21þ presuming that the random process is statistically independent from one time step to the next. Inserting equation (21) in equation (20), the coefficient a is given as a ¼ D w 2 e ¼ s2 1 z 6 2tw 2 ¼ w2 e iðt e itw 2 e Þ2 ¼ 1 6 z t w e ; where the path scale z t is defined as z t w e t. ð22þ [58] Therefore the constant a expresses also the ratio of the turbulent path scale over the turbulent velocity (times a factor of 1/6). For every specific value of w e, e.g., 1 m/s, and time increment t, e.g., 45 s, the turbulent path scale z t is nonambiguous resulting in, e.g., a = 7.5 s. [59] With D ¼ aw 2 e ¼ 1 6 z t w e ¼ 1 6 tw2 e ð23þ we can identify the unique parameter combination within the parameter triple D, w e, and either z t or t which determines D. For example, only the product of z t w e is sensitive to D. That means increasing the free time t between collisions of particles allows a smaller turbulent velocities to result in eddy diffusion coefficients of same size. [60] We summarize these results as follows: (1) Eddy diffusion processes described by Fick s law can only be reproduced in multiple particle systems assuming uniformly random distributed turbulent velocities. (2) Eddy diffusivity and turbulent velocities are connected through equation (23). (3) A rule of thumb says that the spreading of atmospheric layers expressed by its half width is proportional to the square root of the eddy diffusion coefficient (17) Initialization of Smoke Particle Size Distributions [61] The Earth s atmosphere is continuously bombarded by a flux of extraterrestrial meteoroids, a major fraction of which evaporates in the km altitude range. Rosinski and Snow [1961] called attention to the possibility that much of the so-formed refractory vapor could quickly recondense, forming a multitude of tiny particles. For these, Hunten et al. [1980] coined the term smoke particles and studied the properties and size distributions of them in considerable detail. We presume that these smoke particles are the condensation nuclei (CN) which in our model study initialize the process of ice formation at and below the mesopause. [62] Hunten et al. [1980] determined the absolute concentration of smoke particles created in the mesosphere by assuming an initial smoke particle size (r 0 ) which then fixes the total number of all other sizes at later times. In their study these authors present several equilibrium profiles of dust particle densities which illustrate the physical processes involved like coagulation, sedimentation, eddy diffusion, or presence of micrometeorites. Our Figure 10 shows such altitude profiles of the total number of smoke particles of three initial sizes in the km range. We note that we have scaled here the absolute number of smoke particles to be compatible with a meteoric mass influx of 110 t/d [Love and Brownlee, 1993]. [63] In our model simulations we use an ensemble of two million smoke particles for which their size distribution starts with a minimum initial radius of 1 nm. The number densities of smoke particles with larger sizes decrease rapidly [Hunten et al., 1980]. We assume the following partioning of the whole set of two million CN into 5 size classes: particles in class [1 nm; 1.5 nm], particles in class [1.5 nm; 2.0 nm], particles in class [2.0 nm; 2.5 nm], particles in class [2.5 nm; 3.0 nm], and 400 particles in class [3.0 nm;

13 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA studies. The first case is our standard model (zero background water vapor diffusion and zero particle diffusion) and the second is the diffusion model (with background water vapor and particle diffusion). [67] In the past, authors neglected eddy diffusivity of ice particles with the argument that particle diffusion should be of minor importance compared to turbulent eddy diffusion of air volumes [see e.g., Jensen and Thomas, 1988; Klostermeyer, 1998]. It was reasoned that the diffusion of particles of finite sizes by large-scale eddies can be described by D particle ¼ D eddy =Sc ð24þ Figure 10. Smoke particle (CN) concentrations described by Hunten et al. [1980] presuming a meteoric flux of 110 t/d. Concentration profiles are shown for three initial smoke particle radii, r 0 = 0.5, 1, and 2 nm. 3.5 nm]. Furthermore, within each size class the initial size distribution of smoke particles is uniform randomly distributed. [64] In the spatial initialization of CN the local positions of each particle are uniformly spread by means of the same random generator over the latitudinal circle of Andoya (69 N) in a km altitude sub-range of the vertical model range ( km) taking into account the proposed height dependence (Figure 10). [65] Two of our aims are to calculate the absolute number and size statistics of ice particles, and to account quantitatively for the interaction of ice particles with the ambient background water vapor. To this end, we have introduced in our ice particle model a proxy factor which relates our modeled CN number density to the ambient number densities of several thousands CN per cm 3. In our 2-D model domain of initialization of CN [1 cm 10 km 2p R Earth cos 69 ], we introduce a virtual thickness of 1 cm for reasons of a volume unit 1/cm 3, the entire ensemble of two million particles provides a CN density of smoke particles per cm 3 at z = 80 km and smoke particles per cm 3 at z = 90 km. At first sight, the difference between ambient and modeled numbers of CN appears very large, but we will show in subsection that a mean statistic is sufficiently documented by counting and scaling (proxy factor) the numbers of ice particles over neighbored model grid boxes (z = 50 m,l = 2.25 ). 4. Results of Modeling [66] We investigate the process of ice particle formation for the latitude of Andoya (69 N) in two different model with the Schmidt number Sc being the inverse of the molecular Prandtl number as the ratio of molecular viscosity to molecular particle diffusion. The Schmidt number Sc can be obtained from empirical derived diffusion coefficients of aerosols with Sc =6.5 r p 2, r p radius of particle/aerosol in nm by Lübken et al. [1998]. According to (24), particle diffusion should be orders of magnitudes smaller than D eddy, and therefore negligible. Although this concept was developed originally on molecular or microscopic scales, the argument has been carried over to large-scale eddy turbulence (macroscale of 10 m). It implies that eddy diffusion processes would be sensitive to the mass and size of particles. As a consequence, large masses would experience no significant eddy diffusivity within a eddy diffusive molecular background. [68] Here we argue that particle diffusivity caused by large scale eddy diffusion is independent from the mass of the particle. Eddy diffusion should mix both ice particles and water vapor concentrations by the same amount. With this assumption, we expect that turbulent diffusion becomes a major process which strongly affects the process of ice cloud formation. Such approach yields considerably more realistic results than a zero particle diffusion model. However, with particle diffusion included, many parameters describing the growth of ice particles become statistically disturbed which makes the interpretation of model results more complicated. Therefore we introduce our standard model first, as it permits a clearer view than the diffusion model of the processes governing the life cycle of particles Results of the Standard Model [69] In this section we discuss our model results which presume the absence of eddy diffusion for both particles and background water vapor Growth and Sublimation of Ice Particles [70] First, we present the behavior of a few individual particles and demonstrate different types of life cycles. The initial size of a CN determines strongly the altitude at which an ice particle is able to start growing due to supersaturated air conditions (see Figures 11a and 11b). For large CN (r > 3 nm) particle growth due to ice formation is allowed above altitudes of approximately 84 km with saturation values S > 4. Such large CN are, however, not available in significant numbers in our simulation because of the steep exponential decay in the adopted Hunten et al. distribution of CN. For smoke particles with r < 1.5 nm, ice formation can only start at supersaturation conditions S > 10.

14 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 11. Local time (also longitude) dependencies of (a) water vapor saturation versus altitude with initialized water vapor from Figure 7a and temperatures from Figure 3a at 69 N at summer solstice, and (b) minimum radius (nm) of condensation nuclei that allows formation of an ice shell. The altitude of the mesopause is indicated by a gray line. [71] As examples for life cycles, we follow in Figure 12 the trajectories of five individual CN during three days of transport. All five trajectories show a sort of swinging behavior due to the vertical and zonal components of the tidal wind (plotted time interval of 30 min). The first three smoke particles (1 3) with radii of 1.09, 2.28, and 2.36 nm, respectively, are released at altitudes km near 150 W longitude. Here, the smoke particle 1 is transported upwards and never experiences conditions with high enough S to accumulate any ice. In contrast, the CN 2 and 3 (with larger radii) start instantaneously to form ice because for them S is sufficiently large to allow condensation of ice. These two particles grow to a maximum ice size of 43 nm and 55 nm over 18 hours, reaching a maximum sedimentation speed in the order of 10 cm/s (Figure 13). The latter speed clearly overcomes the synoptic upward wind. After the ice particles fall through the S = 1 level, they sublimate quickly, hence reducing their ice masses and falling with smaller sedimentation velocities. Subsequently two cases may occur: Either a local upward background wind boosts the sublimating ice particle again upwards (against its sedimentation velocity) into supersaturated altitude regions where it survives. For example, 2 sublimates partially down to 7 nm radius during 15 hours, and oscillates around 7 10 Figure 12. Trajectories of 5 individual particles with radii of 1.09, 2.28, 2.36, 1.03, and 2.30 nm during 3 days. Gray and colored dots define smoke state and ice size, respectively. The black circles indicate the initial location.

15 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 13. Sedimentation velocity w s versus particle radius at different altitudes. nm ice radius for the following 39 hours. Or, as particle 3, an ice particle sublimates totally, however, taking about 5 hours from the time of its maximum ice size of 55 nm radius back to a bare smoke particle. Although the bare smoke particle starts again to move upwards due to the mean vertical advection and even surpasses its former condensation altitude, it now fails to start a new ice formation process. This behavior is due to the freeze-drying process of the mesopause region (see also chapter 4.1.3). Last, we watch the trajectories of CN 4, r = 1.03 nm, and 5, r = 2.30 nm which are initially located at heights near 87.5 km. At the beginning of the simulation here the original air is so much supersaturated that even small smoke sizes between 0.7 and 1 nm radii are allowed to form spontaneously ice. Again we observe the process of ice growth while the particles slowly sediment down to approximately 85.5 km after 3 days. Their growth rate is, however, rather small, because freeze-drying has already decreased significantly the local S value. [72] In summary, to form icy particles small CN need strong supersaturation conditions given only at higher altitudes near the mesopause. Nevertheless, only the first wave of incoming small CN has the chance to act as condensation nuclei robbing the available background water for the following ones. Once ice formation has been started, the process of ice growth is running straight forward yielding largest particle sizes near 83 km altitude (S = 1). The maximum size of an ice particle is less determined by the absolute vertical path length of sedimentation but more by the specific point of time when ice formation starts for an individual particle. Relatively large CN of 2 nm need lower supersaturation values located at lower heights, hence they sediment as first ones across original air masses with a rich water vapor content which enables their fast growth. [73] If for any reason the absolute number of available CN in the atmosphere is very low, little background water vapor will be converted to ice. In this scenario, small CN forming ice particles at high altitudes will later yield large Figure 14. Local positions of 650,457 ice particles from an two million smoke particle ensemble after 2 day simulation time over the latitudinal circle of Andoya 69 N. The colored dots define the actual ice particle size. This simulation uses zero eddy diffusion.

16 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 15. (a) Local positions of 539,734 ice particles from Figure 14 with ice radius less than 15 nm. (b) Local positions of 27,460 ice particles from Figure 14 with ice radius larger than 30 nm. ice particles because of long sedimentation paths, and vice versa. But we expect that for real atmospheric conditions a marked freeze-drying effect will always be present. This process limits the growth rate for late ice particles. [74] Figure 14 shows the state of the entire ice particle system after 48 hours when 650,457 particles carry an ice shell with largest radii of approximately 50 nm. The other 1,349,543 particles remain bare smoke particles (see Figure 18). The sub-ensemble of ice particles can be identified as a large scale ice cloud where the lower edge of the ice cloud exhibits a significant height variation with a semidiurnal oscillation over longitude and local time, respectively (longitude 0 = : 1200 LT), see subsection Generally, small ice particles dominate at upper heights, whereas large ice particles are found only at lower altitudes. For purposes of a more distinct visualization, we separate two size classes of ice particles with a radius less than 15 nm (see Figure 15a) and those with a radius larger than 30 nm (see Figure 15b). Most of the small ice particles (Figure 15a) are distributed approximately 2 km above the NLC from 84.5 up to 87 km with the upper boundary one kilometer below the mesopause altitude. This fraction of ice sizes encompasses almost 80% of all ice particles (N = 539,734). Therefore PMSE signals, commonly attributed to the existence of smaller ice particles (10 nm), should only be detectable at upper heights and hardly overlapping with the NLC layers. Nevertheless, some small ice particles exist also within the region of the NLC. [75] In Figure 15b, the fraction of about 27,460 large ice particles should represent those particles which give rise to visually observable NLCs and are responsible for the Mie scattering of lidar photons (see subsection 4.2.2). The large ice particles attain maximum densities at certain local times and exhibit significant height variations over a day. The typical layer width is about 1.5 km. [76] Figures 16a 16i show the particle size distributions (in 1 nm intervals) for three different altitudes each with three longitudes, or local times. At altitudes near 86 km (Figures 16a 6c) we observe almost monodisperse distributions of ice particle which started originally at mesopause

17 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 16. (a i) Histograms of absolute ice number densities (1/cm 3 ) at three altitude regions versus 3 longitude regions from Figure 14. This simulation uses zero particle diffusion. altitudes 2 days ago. Figures 16g 16i show ice particle size distributions at altitudes near 83 km which maximize at radii of 58, 30, and 46 nm, depending on local time. Furthermore, at this height two size modes develop each having a more or less irregular size distribution. The smaller (secondary) mode is a vestige of survived sublimating ice particles like our particle 3 in Figure 12. At midaltitudes near 84.5 km (Figures 16d 16f ) the influence of this secondary mode diminishes because the spatial source for such particles is the sublimation zone and sedimentation prevents movements to higher altitudes. Generally, absolute ice particle densities increase with higher altitudes and density distributions become more and more rectangular and narrower. This analysis highlights a merit of our numerical scheme of a

18 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 17. The effects of freeze-drying after 2 days of simulation time on (a) water vapor, (b) saturation ratio, and (c) minimum radius (nm) of condensation nuclei that allows formation of an ice shell versus local time. The altitude of the mesopause is indicated by a gray line. single particle code where for each particle its origin and complete history is well traceable. [77] In summary, the calculated particle size distributions turn out to be highly variable in time and space and do not fit the commonly presumed lognormal distribution. In subsection we will show that particle eddy diffusion modifies substantially these size distributions Meridional Transport [78] In our study we mainly focus our discussion on a snapshot of the multiple particle system at a simulation time after 48 hours. We argue that such a time scale is a typical one for real atmospheric NLC events at 69 N. If one takes into account 3-D, time-dependent transport processes, a smoke particle released at the pole will be transported southwards to midlatitudes within approximately 5 days (see Figure 1d). Preliminary 3-D modeling results indicate that typical life times of ice particles are approximately 2 4 days. Hence our 2-D simulations should stay within that time frame. Furthermore, the 3-D results suggest that typical numbers of life cycles (smokeice-smoke) are in the range of 1 2 (CN of 1 nm radii). Figure 1a shows the 150 K isotherm almost latitudeindependent at a height of 82.5 km. This indicates that at, say 78 N, the lower edge of an NLC should appear at the same altitude as for other latitudes down to 65 N during midsummer. Furthermore, Figure 2b shows that the level of S = 1 (peak of NLC layer) is also constant in height between, say, 78 N and 68 N (Alomar). Yet, the total brightness of NLCs should be the stronger the more poleward the NLC layers are located, because the lower temperatures and increasing water vapor content should allow the formation of larger ice sizes. Similiar results have been obtained by observations of the MSX satellite [Carbary et al., 2001b]. But recent satellite observations from OGO 6 to MSX report of small scale structures, e.g., a horizontal patch and streamer structure in the brightness, which cannot be modeled with our 2-D approach. But we are able to predict that tidal signatures, especially 12 hours modes, should be again present at polar latitudes (Svalbard 78 N) with local time dependencies very similar to that observed at high latitudes (Andoya 69 N). These expectations follow from the fact that any semidiurnal structures of the vertical wind fields simulated by COMMA/IAP stay almost in phase from high to polar latitudes in summer.

19 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 18. (a) Local positions of 1,348,810 bare particles of the two million particle ensemble after 2 days. (b) Local positions of 24,942 bare particles which already fulfilled an ice cycle after 2 days Interactions of Ice Particles With the Ambient Background Water Vapor [79] As we had discussed in subsection the effect of freeze-drying influences enormously the size and number density of ice particles. In addition to this sink process for water vapor, ice particles should deliver their condensed water back to the environment when and where they sublimate. Thus a local source of water vapor is expected to develop in a narrow zone of sublimation below the altitude level with S =1. [80] Figure 17a presents the water vapor mixing ratios 48 hours after starting the ice cloud formation. In comparison to the initial conditions of Figure 7, we observe at mesopause altitudes (88 km) a decrease of water vapor from 1.7 to below 0.1 ppmv (= freeze-drying), and at the lower boundary of the NLC layer (82 km) an increase of water vapor mixing ratios from about 3 ppmv to a maximum of 10 ppmv at certain local times. [81] Figure 17b shows contours of saturation values with the thick line representing S = 1. Especially at a local time near 1400 LT there exist a sort of tongue with a region of undersaturated (dry) air extending from 82 km up to 87 km. Its domain almost coincides with the local tidal phase of a downward vertical wind regime which advects air volumes with low water vapor mixing ratios from higher to lower altitudes. The major portion of sublimated water is accumulated at the bottom of this tongue, up to 10 ppmv at 82 km. Such a supply of sublimated water vapor happens again near midnight conditions where a second downward semidiurnal tidal wind phase exists. However, here the process is weaker and yields water vapor mixing ratios of only 6 ppmv. Figure 17c shows the minimum radius that a CN particle needs to accumulate any ice. Only CN with radii > 3 nm may experience saturation conditions to initiate new ice particles. [82] Similiar to the local time dependence of water supply, particles which sublimate totally their ice shells, release their smoke nuclei preferentially at special local times and altitudes. Figure 18a shows the distribution of (still or again) bare smoke particles 48 h after the start of the model simulation. A number of 1,348,810 smoke particles populate the km height region, the remaining 733 smoke particles are located above 90 km. The sum of all smoke and ice particles (see Figure 14) totals to two million particles. Generally, all smoke particles have been transported upwards with a mean velocity of 2.7 km/day. The lower edge of the dust cloud near 85 km is the former lower boundary of dust initialization at 80 km. It exhibits a semidiurnal height variation due to its transport in the tidal background winds. At mesopause heights we find a region of dust-free air where all available CN had been removed by earlier ice formation. Below the main dust cloud we see thin layers of smoke particles, which are foot prints of past sublimation regions indicating one or even more full life cycles of bare smoke particle to ice particle and back. If these layers of smoke particles reach condensation conditions once more, such dense smoke particle structures will enhance inhomogeneous structures in the layer of ice particles. In support of this argument, Figure 18b shows only the fraction of smoke particles (a number of 24,942) which completed of

20 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 19. Study with particle diffusion: Trajectories of 5 single particles with radii of 1.09, 2.28, 2.36, 1.03, and 2.30 nm during 3 days. Gray and colored dots define smoke state and ice size, respectively. The black circles indicate the initial location. already one or more ice life cycles. We also observe a group of CN above the mesopause which is generated by sublimation events above the mesopause Results of the Diffusion Model [83] We now turn to our diffusion model of ice particle formation and dissipation. We expect this model to become more realistic by inclusion of eddy diffusion for both background water vapor (molecules) and smoke/ice particles. As noted before we consider the results of the diffusion model to match the observations better than the standard model with zero eddy diffusion. We choose a timeindependent profile for the eddy coefficient, the altitude dependence we take from the summer profile of Lübken Figure 20. Study with particle diffusion: Local positions of ice particles from an two million smoke particle ensemble after 2 day simulation time over the latitudinal circle of Andoya 69 N. The colored dots define the actual ice particle size.

21 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 21. Study with particle diffusion: (a) Local positions of 354,956 ice particles from Figure 20 with ice radius less than 15 nm. (b) Local positions of 41,579 ice particles from Figure 20 with ice radius larger than 30 nm. [1997]. As regards the absolute values of the eddy coefficients we decided after some numerical experiments to multiply the Lübken [1997] values with a factor of Hence, in our diffusion model, the eddy coefficients maximize at 90 km altitude at 46 m 2 /s. Employing the original Lübken [1997] values leads in our diffusion model to a far too strong smearing of vertical structures in comparison to those observed by lidar and radar. [84] The particle trajectories of Figure 19 have the same initial conditions with CN sizes of 5 members as in Figure 12. Yet, we observe different transport paths in comparison to the standard case with no particle diffusion. The random vertical displacements become the larger the higher in altitude the particle is located in accordance with the presumed eddy profile. Ice formation takes place as a function of smoke particle size as discussed in the subsection Particle 3 again experiences a total sublimation after 2 days. Particle 4 shoots off into the lower thermosphere. We take care of numerical provisions that no particle is allowed to abandon the vertical model range ( km). For such cases the particle is relocated at the upper or lower boundary so that the particle reenters the model domain. Perhaps the most obvious change undergoes particle 5 which has started from mesopause levels but here sediments very fast into the sublimation zone due to its randomly induced diffusive path. [85] Figure 20 shows the locations of all formed ice particles from the entire ensemble of two million CN particles 48 h after initialization. By comparison with Figure 14 it becomes clear that particle eddy diffusion (1) smoothes out in vertical direction the localized sub-layers, (2) diminishes slightly the amplitude of the tidal altitude variation, and (3) extends the altitude region filled with small ice particles by

22 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 22. Study with particle diffusion: (a) Local positions of 1,291,840 bare smoke particles of the two million particle ensemble after 2 days. (b) Local positions of 115,258 bare smoke particle which already fulfilled an ice cycle. 2 to 3 km into the lower thermosphere. We note that the total number of ice particles is 585,339 (in the altitude range km) which is only a quarter of the number of smoke particles at the time of initialization. [86] Figure 21a shows only the ice particles with radii < 15 nm ( N = 354,956). This figure indicates that the layer of small ice particles has expanded not only towards higher altitudes but also towards lower ones. Thus we find now both large and small particles at NLC altitudes. [87] Figure 21b demonstrate that NLC layers consisting of ice particles with radii about 40 nm radius are located at lowest heights. In comparison with the standard model the total numbers of these large ice particles (N = 41,579) has increased but absolute maximum sizes have decreased (e.g., particle 5 in Figure 19). Forty-eight hours after initialization, bare smoke particles (total number N dust = 1,291,840 in the altitude range km) are almost uniformly distributed over the entire altitude because of a diffusive random walk of CN (see Figure 22a). Thin layers of smoke particles have been smeared out in comparison to the zero eddy diffusion case (Figures 18a and 18b). But the fraction of bare smoke particles is increased to N = 115,258 (see Figure 22b) which were released after total sublimation of ice particles. We conclude that the process of ice particle eddy diffusion enhances sublimation processes and restricts the maximum growth of ice particles. [88] Again, ice particles sublimate preferentially at specific local times during a day. The water vapor distribution (Figure 23a) shows semidiurnal structures which are similar to the standard run. Even in the presence of particle diffusion the freeze-drying effect generates an extremely dry atmosphere with mixing ratios down to less than 0.1 ppmv in the mesopause region. The largest saturation values are in the order of only 2, and a sort of tongue exist for S = 1 similar to the model study assuming no particle diffusion (Figure 23b). A large fraction of our postulated CN ensemble has no chance to stimulate renewed ice formation due to a too small size (Figure 23c). This argument leads to the conclusion that this model predicts for this point of time a gradual, but steady loss of ice particles from the ice cloud. The ice cloud still looses ice particles by sublimation but hardly any new ice particles are formed. [89] In summary, our results suggest that ice particles, especially with sizes around 15 nm, become almost uniformly distributed over a large-altitude region due to the process of eddy diffusion. [90] Our use of a time-independent eddy diffusion profile is not necessarily in conflict with our understanding that turbulence in the upper atmosphere occurs intermittently [Hocking, 1990] and in layers [Lübken et al., 2002]. Our diffusion model still produces sensible results as long as the typical time and altitude scales for upper mesosphere turbulence are small in comparison to those of the ice particle forming processes. We argue that this is indeed the case. We also note that with our diffusion model we have introduced a turbulent diffusion profile which consists of comparatively low values, but even so it influences ice formation to a large degree.

23 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 23. Study with particle diffusion: The effects of freeze-drying after 2 days of simulation time on (a) water vapor, (b) saturation ratio, and (c) minimum radius (nm) of condensation nuclei that allows formation of an ice shell versus local time. The altitude of the mesopause is indicated by a gray line Temporal Development and Time Constants of Ice Formation [91] In this section we will study the temporal development of ice particles and estimate the life times of these ice particles. For this particular study our previous time frame starting at initialization and ending 48 h later appears somewhat short. For the current study we extend this frame to 120 h and extend the altitude range to 92 km. We argue that no individual ice particle is likely to survive much longer because the mean meridional wind will carry ice particles even from the summer pole into the warmer midlatitudes over such time scale. [92] Figure 24 as a schematic diagram helps to define the various phases that the smoke/ice particle experiences during one life cycle. Period (a) is the phase between the start of ice formation on the surface of the smoke particle until the ice particle has reached its maximum size (note that the change of ice radius does not need to be proceed uniformly in one direction). Period (b) is the phase between the time that the particle had attained its maximum radius and that when total sublimation had occurred (= a bare smoke particle is reproduced). Period (c) is the sum of periods (a) and (c) or in other words, the life cycle time that an individual smoke particle is covered by ice. Period (d) is the phase in which a smoke particle that has already completed a full ice cycle, waits as bare particle before it enters a second ice cycle. Figure 24. Definitions of different time scales of a particle life cycle: (a) between start of ice formation and the time that the ice particle has reached its maximum ice size, (b) between time of maximum ice size and total sublimation, (c) phase between start and end of ice state, and (d) between end of first ice state and start of second ice formation.

24 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 25. Study with particle diffusion: (a) histogram of normalized numbers of ice particles (N = 357,814) versus the duration of ice growth up to r max per 60 min interval. (b) Same as Figure 25a but numbers of ice particles versus the duration of total sublimation phase staring after the time of r max.(c) Same as Figure 25a but numbers of ice particles versus the duration of one complete ice cycle (growth and total sublimation). (d) Histogram of numbers of smoke particles (N = 7,336) of bare phase between ice cycle 1 and 2. [93] In the following we investigate those smoke/ice particles which have completed, within the time frame of 120 hours, at least one complete ice cycle from bare smoke particle to ice particle and back to bare smoke particle. Out of our initial ensemble of two million particles, a number of 357,814 fulfill this condition. Figure 25a shows the distribution of the duration of the growth phase (a) of these particles. After a sharp initial peak in the Figure 26. Study with particle diffusion: (a) Normalized histogram of the numbers of ice particles (N = 563,952) which grew up to a maximum ice radius per 1 nm interval. (b) Maximum radius of ice versus altitude where r max is reached. Plotted is every 10th particle of N = 563,952.

25 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 27. Study with particle diffusion: (a) Number of ice particles which form the entire ice cloud up to 92 km height for the first 3 days simulation time. Solid line: total number of all ice particles; dashed line: ice particles with r < 20 nm; dotted line: ice particles with r > 20 nm. (b) Total ice mass M ice of ice cloud for the first 3 days simulation time (thick solid line), growth rate (dashed line), sublimation rate (dotted line), and change of total ice mass dm ice /dt (sum of growth and sublimation rate) as thin solid line. first 6 hours after initialization, the distribution of durations becomes very uniform out to 120 hours. It is interesting to note that the initial peak is caused by those particles of small maximum ice radii which sublimate above (!) the mesopause. Figure 25b shows the distribution of the duration of the sublimation phase b. It indicates that sublimation, once it has started, proceeds rather rapidly to complete sublimation. The duration of the ice phase c is shown in Figure 25c and is obviously dominated by the wide distribution of growth durations. Figure 25d shows the length of the waiting time of smoke particles before they can start a second ice cycle. We draw attention to the fact, however, that in the scenario of our diffusion model, very few smoke particles ever enter a second ice cycle. We have mentioned that 357,814 particles complete one ice cycle. At the end of our 120 h time frame, an additional number of 378,816 smoke particles had started to form ice. Thus 736,630 smoke particles where involved in forming the upper mesospheric ice layer. Yet, only 7,336 out of those had started a second ice cycle. Therefore such second ice cycle can be considered a very rare event. From all the particles that had entered or gone through an ice phase, 536,952 ice particles had already reached a maximum ice size terminating of the ice growth phase. For this fraction the distribution of maximum radii of any ice particle is shown in Figure 26a. The distribution maximizes near 40 nm and extends to small sizes down to 4 nm of radii. These small ice particles are the result of short growth durations. Figure 26b shows the distribution of maximum radii versus altitude, where the maximum radius was reached. It shows the expected peak of large ice particles at NLC altitudes between 82 and 83 km. The figure reveals, however, also another region of maximum radii which is located above the mesopause and produced by particles with radii < 10 nm. These ice particles are those of short growth times and very likely escape (sublimate) into the lower thermosphere. [94] In order to derive the timescales of formation of ice particles and of total ice mass, we introduce Figures 27a and 27b, respectively. We also need Figure 28, which shows the temporal development of water vapor mixing ratio (zonal mean) in the altitude range 80 to 92 km from initialization until 72 h thereafter. As indicated in Figure 27a, almost all ice particles in our study domain have been formed instantaneously after initialization (thick line). The dashed and dotted lines indicate the number of particles with radii smaller and larger than 20 nm, respectively. The first particles with radii larger than 20 nm appear 3.5 hours after initialization. But even before that event, about 3 hours after initialization, a rapid decrease of the amount of condensible water vapor starts, indicating the onset of the freeze-drying effect (Figure 28). Subsequently, the growth rate of large particles is slowed down noticeably starting 5 to 6 hours after initialization (Figure 27a). A peak in water vapor consumption 3 hours after initialization is also easily recognizable in Figure 27b, which shows the following parameters: the total mass of ice carried by the smoke particles as thick line; the rate of change of the total ice mass as thin line; the rate of newly formed ice as dashed line and the rate of ice sublimation as dotted line. Evidently, the thin solid line must be the sum of the dashed and dotted lines. In this figure, we can identify the peak in growth rate of ice mass, 3 hours after initialization, as the onset of a significant freeze-drying effect. We also recognize that our particle ensemble comes into a sort of equilibrium 12 hours after initialization, at which time the sublimation rate is able to balance a fair share of the growth rate of total ice mass. Finally we note, that over the 3-day-period discussed here, the total number of ice particles decrease somewhat while the total ice mass still increases. This indicates a slow transfer of ice mass from small to larger particles.

26 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 28. Study with particle diffusion: Time dependent background water vapor as zonally averages during 5 days simulation time. The zonal mean altitude of the mesopause is indicated by a gray line. [95] In summary, we derive from our smoke/ice particle model the following timescales after initialization of the model in air with original water vapor content: (1) Formation of more than 90% of all ice particles: < 0.5 hours; (2) Development of a significant freeze-drying effect: 3 hours; (3) Growth of particles to sizes larger than 20 nm ( NLC particles ): 6 to 8 hours; and (4) Start of substantial ice sublimation and buildup of a layer with enhanced water vapor near 82 km: 12 hours. [96] These numbers give us considerable guidance in understanding the sequence of events that lead to the formation of PMSE and NLC layers. In reality there is, however, never a state of the mesosphere as assumed in our model right before initialization: unperturbed, with all ingredients for the formation of ice, but no actual ice being formed. If our model atmosphere is a realistic simulation of the ambient atmosphere, the model tells us that the formation of ice particles is possible and ongoing at any time: in summer, the polar upper mesosphere must be loaded with smoke and ice particles continuously. Support for this conclusion comes from the observation of a the near-continuous presence of PMSE layers at arctic latitudes [Hoffmann et al., 1999]. A more delicate question is under which conditions and how fast can the ice particles grow in the ambient atmosphere to sizes which make the particles visible as NLCs? We argue that the time scale for particle growth to NLC sizes may be much shorter than the above derived 6 to 8 h depending on how large those ice particles are which we have just postulated to reside there at any summer time. Furthermore, in subsection we derive from our model that at 69 N NLCs should be observable by ground-based lidar in the order of 40% of the time. On the one hand, this is not far from the observations by von Cossart et al. [1999b]. On the other hand, this percentage must depend on a number of temporal variabilities which are not included in our model such as those of temperature, vertical winds, smoke particle density, turbulence activity, or solar activity. Even though we are quite pleased with the general level of agreement between model predictions and observations, it seems too early to put much emphasis on a quantitative comparison of modeled and observed occurrence rate of NLCs Particle Size Distributions and Backscatter Ratios [97] In this subsection we present size distributions of ice particles as calculated with our diffusion model and the resulting backscatter ratios as they may be observed with a ground-based lidar at the wavelength of 532 nm. As we had shown in subsection and Figure 16, our standard model (zero particle diffusion) predicts sharply peaked or nearly rectangular size distributions. Not unexpected, these structures are significantly smoothed out when we add particle diffusion to the model code. Figure 29 presents the size distributions after a simulation time of 48 h with particle diffusion for the same altitude regions and longitudes as Figure 16. The particle histograms are in most cases quite well represented by Gaussian normal distributions (solid lines). We also show best fits of lognormal distributions to the histograms (dotted lines). Lognormal distributions are commonly used to describe the size distribution of NLC particles. We also recognize that the modeled particle ensembles will give a slightly larger median radius if described by a normal distributions than by a lognormal distribution. Note that the particle density increases with height, but less strongly than in the case of the standard model. [98] The differences between the particle size distributions under nonturbulent and turbulent conditions might be understood as follows: We assume an ensemble of CN with

27 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 29. Study with particle diffusion: (a i) Histograms of absolute ice number densities (1/cm 3 )at3 altitude regions versus 3 longitude regions from Figure 20, day 2. In addition the solid line shows the corresponding Gaussian normal distribution, the dotted line presents the corresponding lognormal distribution. a monodisperse size distribution, released under zero turbulence conditions at a single altitude. In this scenario, the size distribution of the CN will remain monodisperse because all particles would grow at the same rate. For this to occur, an added assumption is that each ice particle grows independently of its size which is guaranteed by our simplified microphysics. Active turbulence induces, however, a broadening of the size distribution into a Gaussian normal

28 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 30. Figure 20. Study with particle diffusion: Computed backscatter ratios (l = 532 nm) with conditions of distribution (see subsection 3.5.2). If, on the other hand, large particles grow faster than small ones (multiplicative instead of additive probability), lognormal distributions can develop. Such process can be induced by coagulation of ice particles, a mechanism which we neglect in our study. The distributions will also be effected if particles attain at the same altitude different sedimentation velocities due to different ice masses. However, in any way, large random (turbulent) velocities in the order of meters per second will drive the size distribution towards a normal rather than a lognormal distribution. [99] In a last step we have calculated the Rayleigh/Mie backscatter ratio (BSR) from the derived particle size distributions at the wavelength of 532 nm, the latter being typical for a Rayleigh lidar [von Cossart et al., 1999a]. To this end, we adopted the numerical computed backscatter cross sections of Bohren and Huffman [1983]. The result is shown as Figure 30. The total width of the layer is about 2 km (for BSR > 10), the maximum backscatter ratio is of the order of 40 and occurs close to 83 km altitude, the altitude of maximum backscatter is closer to the lower border of the layer than the upper one, and the layer exhibits clear semidiurnal variations in altitude and backscatter ratio. All these features match closely the lidar observations of NLCs by von Zahn et al. [1998] and von Cossart et al. [1999a, 1999b]. This includes the maximum BSR in the order of 40, which is to represent climatological mean conditions for NLCs at the Alomar site. Any zero eddy diffusion model yields in general considerably larger ice particles and backscatter ratios. In addition, we mention that higher values of modeled BSRs might be obtained also by a possible choice of a slower sedimentation velocity due to the uncertainty of equation (12). [100] An interesting detail are the phases of the semidiurnal variation of backscatter ratio and altitude of the layer. The model predicts a positive correlation of the phases. The antarctic lidar observations of Chu et al. [2001] agree with this prediction, while the arctic lidar observations of von Zahn et al. [1998] show the two parameters to be anticorrelated. The arctic PMSE observations of Hoffmann et al. [1999] show strong tidal signatures, but again an in-phase relationship of power and altitude of the maximum radar echo. Clearly, further studies of the tidal phases are highly desirable Semidiurnal Variations of Ice Cloud Parameters [101] We return to the main tidal signatures of various parameters of an ice cloud located at 30 W longitude and as they develop over a time span of 72 hours. We start with the temporal evolution of the background water vapor (Figure 31a) which at mesopause heights rapidly decreases from 2 ppmv to 0.1 ppmv during the first 6 hours of ice formation. A first period of significant ice sublimation occurs after 14 hours delivering water vapor back to the atmosphere near 82 km altitude. In the following such a water supply occurs every 12 hours at local times of 1400 and 0200 LT increasing the water vapor from 4 up to 10 ppmv. Indeed, these regions of enhanced water vapor coincide with height sections and local time intervals when ice particle sublimate (S < 1) partially or even totally (Figure 31b). Bare smoke nuclei (black dots) are created by total sublimation of ice below the S = 1 condition near 83 km as well as above 1 km of the mesopause. For a LT of about 1400 sublimation zones in form of a tongue exist well inside the ice cloud. Such dry regions have been created by two facts: Firstly, freeze-drying effects due to previous ice growth have reduced water vapor. Secondly, the previous downward vertical winds have advected dryer air from above to lower altitudes hence decreasing S values inside the tongue. [102] Beside the tongue regions, the major sublimation processes happen below 83 km where temperatures exceed a threshold limit of 147 K. One identifies two local times per day with an enhanced total sublimation which happens subsequent to a local downward vertical wind phase. In such cases we get enhanced downward velocities for an ice

29 BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION SIA Figure 31. Study with particle diffusion: (a) Time-dependent water vapor at a fixed longitude (30 W) during 3 days simulation time. Start is at 1000 LT at summer solstice. (b) Time dependent vertical wind (gray lines: isolines in 20 mm/s steps), mesopause altitudes (gray diamonds), saturation level of S = 1 (solid black line), and single bare smoke particles released by total sublimation (black dots). particles which superposition to sedimentation and diffusive random velocities hence decreasing the probability that an ice particle may sediment through the S = 1 level. [103] The phase of the vertical component of the semidiurnal tidal wind affects significantly the structure of the ice cloud. Both the maximum ice particle size and the lower edge of the ice cloud are semidiurnally perturbed (Figure 32). The lower and upper edges of the ice cloud are always located around the phase of the maximum downward and upward vertical tidal wind phases, respectively. [104] If we compare the modeled tidal structures in Figure 33 with observations of NLCs, we see that some of the major characteristics fit to observational results. For example, the maximum backscatter signal experiences height variations of 1 km within 4 hours, the signal strength increases in time, and a so-called afternoon hole (model times: 30 and 54 hours = 1600 LT) exists where ice particles sublimate inside the cloud [Balsley et al., 1983]. [105] Evidently semidiurnal tidal variations should be observable for almost every ice cloud parameter, e.g., maximum size of ice particle, lower and upper edge of the ice cloud, altitude zone of major sublimation, dust distribution, backscatter ratio, and background water vapor. All these parameters are sensitive to the sign and strength of the tidal vertical wind. Especially the semidiurnal and diurnal change of largest ice particle radii and absolute altitude of the NLC is due to the local time-dependent behavior of the synoptic vertical background wind in combination with the actual value of the individual sedimentation velocity and turbulent random path fluctuations. Temperature tides play a minor role in causing the observed tidal variations of NLC parameters. 5. Conclusions [106] We have demonstrated a new approach to modeling the properties of ice particles in the mesopause region. This approach is based (1) on providing a 3-D global circulation model, including a chemistry-transport module, with high fidelity for the mesopause region, and (2) on introducing an ensemble of two million condensation nuclei, subjecting those to turbulent transport, and investigating their time-dependent transport in a Lagrangian way. The model allows us to follow the life cycle of each condensation nuclei/ice particles in time and space in great detail and to derive basic properties of the layers formed

30 SIA BERGER AND VON ZAHN: ICY PARTICLES IN SUMMER MESOSPHERE REGION Figure 32. Study with particle diffusion: Time dependent local positions of ice particles from an two million smoke particle ensemble at a fixed longitude (30 W) during 3 days simulation time. Starting time is 1000 LT at summer solstice. The colored dots define the actual ice size. by these particles. The model enables us to give a comprehensive description of the strong influences which the processes of freeze-drying of the mesopause region, of vertical tidal winds, and of particle diffusion have on the observable properties of NLC particles and layers. [107] We present model results on the requirements for adequate size of smoke particles to act as condensation nuclei in the mesopause region (directly after initialization > 0.7 nm radius; after 8 hours > 2 nm), on the time scale for growth of particles (6 to 8 hours to radii > 20 nm) and sublimation of ice particles (duration of sublimation phase typically 6 hours), and on the typical altitude range of maximum NLC brightness ( km). The model allows to predict a number of NLC features which are either currently under study or may become observable in the near future: (1) Properties of NLC layers at high arctic latitudes; (2) The dominance of semidiurnal over diurnal structures in a number of NLC layer parameters; (3) The development of layers with strongly enhanced water vapor mixing ratios near the lower border of NLCs; (4) The size distributions of NLC particles being closer to a normal than to a lognormal distribution. Figure 33. Figure 32. Study with particle diffusion: Computed backscatter ratios (l = 532 nm) with conditions of