We infer from the observed occurrence frequency of polar mesosphere summer echoes and from the three-dimensional (3-D) modeling of conditions in the high-latitude mesopause region that a persistent layer of icy particles exists in midsummer at all latitudes poleward of about 60°N at and a few kilometers below the mesopause. All of these icy particles are transported equatorward by the climatological mean winds. At the same time, many of the larger icy particles possess a high enough sedimentation velocity to induce a net downward transport of water vapor. Both types of particle motions cause the mesopause region to become substantially dryer than without these transports of icy particles. We follow the interactions between water vapor and icy particles by means of a 3-D dynamical and chemical model, which includes a module for the formation, growth, and sublimation of icy particles. For midsummer conditions and poleward of 67°N latitude, the model predicts (1) a strongly dehydrated region, typically above 84 km, in which the water vapor mixing ratio can fall below 0.2 ppmv and (2) atmospheric regions with enhanced water vapor abundance near both the lower and the equatorward borders of the icy particle layer.
 We are used to consider noctilucent clouds (= NLC) to be a locally transient phenomenon throughout the high-latitude summer. In midsummer, say 15 June to 15 July, NLCs occur rather infrequently near 55°N, and their occurrence frequency near 70°N is still only in the order of 40% [Fiedler et al., 2003]. It is only poleward of 80°N that they may become a near-permanent feature of the midsummer mesopause region [Donahue et al., 1972; Thomas, 1984]. Furthermore, NLC observations from high inclination satellites show them to form patchy fields, not always a continuous “polar hood” [Donahue et al., 1972; Carbary et al., 1999]. The dependence of NLC brightness and occurrence frequency on the solar activity cycle leads to additional variability in their presence at high latitudes.
 The ephemeral nature of visually observed NLC has led many scientists to believe that a lack of a visible NLC indicates the absence of ice particles from the local mesopause region. This paper draws attention to the possibility, that at latitudes poleward of, say, 65° in midsummer icy particles may exist near-permanently in the summer mesopause region, regardless of whether or not they form visible NLC. A near-permanent existence of these ice particles should have important implications for basic parameters of and processes acting in the mesopause region.
 Here we predict the existence of such layer of ice particles based on (1) the observed occurrence frequency of polar mesosphere summer echoes of VHF radars and (2) our 3-D modeling of conditions in the summer high-latitude mesopause region. Included in the modeling effort is a study of the interactions of the two phases of water, gaseous and solid, which coexist in the mesopause region. We quantitatively evaluate the consequences of these interactions, which lead to the formation of atmospheric regions with significantly depleted water vapor abundance and others with enhanced water vapor abundance as compared to the undisturbed atmospheric state. A discussion of these implications is the second aim of this paper.
 In the following, we will deal with “icy particles” (and not ice crystals). This term is to emphasize that we assume that at NLC altitudes almost all, if not all, nanometer-sized particles contain a smoke particle (Figure 1) as a condensation nucleus (CN). A pure ice crystal may sublimate totally, whereas sublimation of the entire ice of an icy particle still leaves us with the original smoke particle (which may act as CN again). Finally, we emphasize that in the following we focus on atmospheric conditions near midsummer (not considering the beginning and end of the NLC season.
1.2. Introduction to Our Numerical Model
 The possibility that NLC particles may cause a certain amount of freeze-drying for the atmospheric region above the NLC has been indicated by a number of 1-D models of the mesopause region since the work of Reid , Turco et al.  and others. By necessity, these studies left unanswered many basic questions concerning the importance of horizontal transport for the life cycle and spatial distribution of icy particles. Berger and von Zahn  (hereinafter referred to as B&vZ) modeled the formation and the life cycle of icy particles in the polar mesopause region by means of a 3-D general circulation model [Berger and von Zahn, 1999] of the middle atmosphere (COMMA/IAP) including new modules for the mesospheric chemistry and for the microphysics of icy particles. They initialized the mesopause region with an ensemble of two million smoke particles and investigated their time-dependent transport in a 2-D latitudinal circle domain. An essential result of B&vZ was their prediction that in midsummer and near 70°N latitude (and probably at all higher latitudes) there exists a permanent layer of icy particles in the mesopause region. Above 85 km, their radius is below 20 nm and therefore these particles are too small in radius and number density to produce visible NLCs. The prediction of the existence of this permanent layer of icy particles is based on measured climatological mean parameters of the atmosphere, not on any forced variability in temperature or humidity.
 Here we expand the model of B&vZ by increasing the number of smoke particles from 2 to 20 million. This enables us to generalize the transport code to a 3-D scheme while maintaining a reasonable number of smoke or icy particles over the entire 3-D model domain (= 77.8 to 94.0 km in altitude, 49°N to 90°N in latitude). For this upgrade, there was no need to change the COMMA/IAP model of B&vZ. Hence its temperature, wind, and humidity fields still match closely the observations obtained at the ALOMAR facility and Andøya Rocket Range (69.3°N, 16.0°E) as described in more detail by B&vZ. Furthermore, the microphysical model has been upgraded by accounting for temperatures of the dust particles being higher than the ambient temperature. We took the parametrization of this process from Eidhammer and Havnes  with an accommodation coefficient β = 0.5.
 An important question for any model of the NLC region is that about the nucleation process of ice particles. Ice particles may nucleate from gas phase water vapor by (1) (uncharged) homogeneous nucleation, (2) ion nucleation, or (3) heterogeneous nucleation on any kind of condensation nucleus. Early during these nucleation and growth processes, the growing particle is required to overcome the so-called Kelvin barrier of Gibbs free energy of the particle-vapor system [see, e.g., Gadsden and Schröder, 1989]. In the mesopause region, this barrier prohibits stable growth of a pure ice crystal by homogeneous nucleation or ion nucleation for water vapor saturation ratios S smaller than about 1000 or 200, respectively. How often and over what spatial regions such high-saturation ratios may occur can be assessed currently only by numerical models of the mesopause region because no reliable water vapor measurements at the mesopause exist. Gumbel et al.  and others have argued that neither homogeneous nor ion nucleation play a significant role in formation of the ice particles near the summer mesopause. A much more efficient process of nucleation appears to be that of heterogeneous nucleation on nanometer-sized aerosols. Such aerosols may be produced by the immediate recondensation of silicates after their evaporation from meteoroids within meteor trails. Aerosols of this origin were designated “smoke particles” by Hunten et al. . Following B&vZ we base our models on the assumption that smoke particles exist in number density and size distribution as calculated by Hunten et al. . This assumption allows our COMMA/IAP model to correctly predict a large number of observed properties of NLC and PMSE. This certainly does not constitute proof of the correctness of our assumption of heterogeneous nucleation, but does qualify it as a very useful tool for modeling NLC and PMSE layers (see also section 3.5.2).
2. Arguments for a Persistent Summer Upper Mesosphere Ice Cloud (SUMIC)
2.1. Polar Mesosphere Summer Echoes as a Monitor for the Presence of Icy Particles
 Radars operating near 50 MHz in the VHF band and at high latitudes observe in midsummer regularly strong echoes from the 81 to 90 km region, the so-called polar mesosphere summer echoes (PMSE). For a review of the phenomenon of PMSE, see Cho and Röttger . The spatial and seasonal coincidences of the occurrences of PMSE and NLC make it very likely that both phenomena have a common cause even though they are observed at greatly different wavelengths (6 m versus 0.4 μm). Today, it is well established that the common cause for the two phenomena is the occurrence of extremely low ambient temperatures (125 to 150 K), which are low enough to allow the ubiquitous formation of icy particles. These icy particles interact with the plasma of the lower ionosphere in a way that the electromagnetic waves emitted by the radars become backscattered with significant efficiency producing the PMSE echoes, while the larger of the ice particles scatter enough solar radiation to make these layers of icy particles under favorable conditions visible for the naked eye as NLC. Recent models, which aim at an understanding of the scatter process producing PMSE echoes, assume the existence of icy particles in the scattering layer [e.g., Reid, 1990; Inhester et al., 1994; Cho and Röttger, 1997; Rapp and Lübken, 2003]. Therefore we suggest that the occurrence of PMSE, similar to that of NLC, is a very good indicator for the existence of icy particles in the mesopause region. An important difference between the two phenomena is, however, that the occurrence frequency of PMSE is much higher than that of NLC. Hence accepting PMSE as an indicator for icy particles yields a considerably higher occurrence frequency for these particles than deriving this frequency from NLCs. It is this point-of-view which we will further deliberate below.
 In Table 1 we list the occurrence frequencies of PMSE in midsummer 2001 at three different latitudes. At 54°N, these radar echoes are observed only sporadically and then solely under sunlit conditions [Zecha et al., 2003]. Poleward of the Arctic Circle at 67°N, however, PMSEs are a near-continuous phenomenon during midsummer. Figure 2 shows the occurrence frequency of PMSE versus signal-over-noise ratio (SNR) as observed between 15 June and 15 July 2001 by the ALWIN VHF radar at 69°N latitude (J. Bremer, personal communication, 2002). Echoes yielding a SNR ≥ 5 db are present for 97% of all times. If one raises the SNR level to ≥ 10 db, the occurrence frequency is still 90%. For a detailed discussion of ALWIN radar results, see Bremer et al. . We wish to take PMSE as an indicator for icy particles of any size, even for those that may be too small or too large to contribute to the formation of PMSE. We therefore select here the more “sensitive” level of 5 dB as criterion for the occurrence of PMSE and hence the presence of icy particles in the mesopause region. We take these radar observations as strong support for our assumption that during midsummer the entire polar region is continuously hooded by a layer of icy particles at mesopause altitudes.
Table 1. Observed Occurrence Frequencies of PMSE in Midsummer 2001 at Various Latitudes
 The question about the average size of icy particles that are involved in the formation of PMSE is still difficult to answer. So far, the size of these particles has just never been measured directly. There are, however, a number of estimations in the literature (see Table 2) that suggest that a good estimate for a typical radius is 10 nm.
 Our knowledge about the average size of NLC particles is much better than that for PMSE-causing particles. In recent years, it became possible to measure the size distribution of NLC particles by ground-based lidar. The median radii derived from these observations fall typically in the range from 30 to 50 nm [von Cossart et al., 1999; Alpers et al., 2000], their number density in the order of 102 cm−3. In order for particle layers of the mesopause region to become visible to the naked eye, their particles should have radii larger than, say, 25 nm.
 Differences exist in characteristic parameters of PMSE and NLC. As stated above, the typical median radii are likely 10 and 40 nm for PMSE and NLC icy particles, respectively. The number densities of the two types of particles are in the order of 103 and 102 cm−3 in PMSE and NLC layers, respectively. Note that in the visible, the scatter cross section of these particles increases with almost the 6th power of the particle size. Hence a 40 nm particle scatters sunlight more than 2000 times stronger than a 10 nm particle.
 The presence of PMSE in midsummer at polar latitudes implies therefore that icy particles in the 10 nm size range reside near-continuously in the altitude range of PMSE (typically 82–88 km). Now and then, the size distribution of these persistent icy particles develops a tail toward larger sizes, which makes the largest particles visible as NLC. The transient character of NLC therefore implies only a variability in the size distribution of the icy particles, NOT an on/off existence of icy particles (“no” particles versus “many” particles). We do not explain here, WHY that variability in the size distribution occurs (one could speculate that it is due to wave-driven changes of temperature [Rapp et al., 2002], changes of water vapor, changes of the vertical winds, variations in the production and/or size distribution of smoke particles, and/or aurora-induced enhancements of NO abundance).
 The lower border of NLC and PMSE layers occur at the same altitude [von Zahn and Bremer, 1999]. This indicates a total evaporation of the ice of all icy particles, independent of their size. This evaporation is caused by rapid warming of the particles which are either sedimenting and/or are blown downward. The upper border of PMSE layers is, however, typically many kilometers higher than that of NLC layers. This indicates that the upper border of NLC layers is a region of only a gradual diminution of the mean particle size and not a region of complete loss of icy particles.
Figure 4 shows modeled zonally averaged values of the water vapor mixing ratio, the saturation ratio S, and the minimum radius of CNs versus latitude and altitude for an atmosphere, which is assumed free of CNs of any kind. The ambient water vapor distribution (Figure 4a) is characterized by approximately 3 ppmv water in the NLC altitude range (82 to 83 km) and slightly less than 2 ppmv at the mesopause between 50°N and 80°N. Between 80°N and 90°N it becomes slightly dryer than at the lower latitude mesopause. The saturation ratio S (Figure 4b) reaches at the 69°N mesopause a maximum value of 100 and increases to larger than 10000 at the North Pole. The minimum radius of CNs (Figure 4c), required to overcome the Kelvin barrier for ice formation, is below 1 nm for a considerable range in altitude near 69°N and well below 0.3 nm at the North pole.
 In this study we aim at simulating a quasi-steady state of icy particle formation, growth, transport, and sublimation. To this end we need to supply the mesopause region with a steady rate of fresh CNs. Numerically, we approach this goal by seeding at time t = 0 the dust-free atmosphere with 20 million smoke particles (details to be given below). At later times, individual smoke particles will arrive at a vertical or horizontal boundary of the model domain at which times we relocate them into randomly chosen locations within the initial seeding domain. By this procedure, a continuous seeding process is realized and a quasi-steady state of the number, spatial distribution and size distribution of the icy particle number is reached about 3.5 days after the initial seeding event. In addition, the total number of particles analyzed by the model is kept constant, and the fate of any individual particle can be followed. Before we will provide two examples which demonstrate how the quasi-steady state of icy particle distributions is approached, we need, however, to give details of our choices for CN properties at time t = 0.
 We take the size and altitude distributions for our 20 million smoke particles directly from Hunten et al. . The size distribution comprises particles with radii between 1.0 and 3.5 nm with a large majority of all particles being in the radius class 1.0 to 1.5 nm (see B&vZ, section 3.5.3). The altitude distribution of smoke particles is shown in Figure 5. The seeding domain extends from 83 to 93 km in altitude and 65°N to 90°N in latitude (longitude-independent) and is thus smaller than our model domain (to economize computing time).
 After individual smoke particles have arrived at a vertical or horizontal boundary of the model domain, they are relocated into randomly chosen locations within the initial seeding domain. The rate at which these relocations proceed is shown in Figure 6. During the first day, the rate is given by smoke particles initially located above the mesopause and now reaching the upper border of the model domain (94 km altitude). At day 2.0, a peak in the relocation rate is produced by those smoke particles which started to arrive at the low latitude border of the model domain (50°N). After an initial adjustment period of about 3.5 days, the rate of relocations of smoke particles into the seeding domain (= re-seeding) attains a steady value of about 85 particles per second. In this steady state, about 5 million of the smoke particles carry an ice layer (= icy particle), whereas the remaining 15 million are without ice (= bare CNs) due to being either too small to form a stable icy particle or being in regions of the model domain with S < 1. These numbers imply that in our model CNs need on average 2.7 days to be transported from their seeding location to a border of the model domain.
Figure 7 shows the temporal development of the water vapor distribution from t = 0 to t = +5 days for (1) a polar latitude and (2) a high-latitude location. During the first half day of our model simulation, a dramatic freeze-drying process develops in close vicinity of the mesopause because the ambient conditions and our choice of seeding domain allow a large majority of all our smoke particles to form icy particles right after t = 0. The water vapor mixing ratios recover somewhat in the period until about model day 3.5. Now the smoke particles are distributed over the model domain, which is larger in volume than the seeding domain (but the CNs are still mostly above 84 km), and the low water vapor mixing ratios near the mesopause prevent some of the small CNs from forming stable icy particles. Both the rate at which bare smoke particles are re-seeded (see Figure 6) and the contours of water vapor mixing ratio (see Figure 7) indicate that in our model calculations we reach at day 4.0 a quasi-steady state of ice formation and sublimation. In order to be conservative, we allow another day for “settling down” of all processes and parameters to steady state conditions. Thus, in the following we will consider our results from model day 5.0 as representative for conditions in the midsummer mesopause region under steady state conditions.
 We show in Figure 8a the locations of 20,000 randomly chosen icy particles at the time 5.0 days and their trajectories in the following 30 min. While a smoke particle is embodied in an icy particle, its trajectory is shown as black line. If it has changed to bare smoke particles in the following 30 min, its trajectory is shown as gray line. The SUMIC can be clearly recognized in the altitude range between 82 and 92 km and extending from about 60°N latitude to the North Pole. Figure 8b shows the same kind of trajectories, but now throughout the period 5.0 to 6.0 days and for only 1000 particles (for a larger number of particles, the plot becomes too black). By far the largest number of smoke particles, which are carried for good out of the SUMIC by the background winds, leave the SUMIC vertically toward the lower, warmer thermosphere and meridionally toward the warmer middle latitudes. A comparatively small number of icy particles exits the SUMIC temporarily at its lower border. However, as soon as evaporation of their ice shells has made them light enough, they are carried upwards again into the SUMIC by the climatological mean winds. Hence the lower border of the SUMIC does not act as a permanent sink for smoke particles or other types of condensation nuclei. A few gray trajectories inside the SUMIC are produced by smoke particles that are too small to overcome the Kelvin barrier for formation of an icy particle (see chapter 3).
 The trajectories of individual smoke and icy particles are affected by the mean climatological winds (in vertical, meridional, and zonal directions), by the tidal winds, by eddy diffusion, and (if the particles are heavy enough) by their intrinsic sedimentation velocities. The influences of the various components of vertical motion on the distributions of water vapor mixing ratio, water vapor saturation ratio, and particle density have been discussed in depth by B&vZ. An influence of the mean meridional wind is to transport the particles away from the pole toward the midlatitudes in the entire model region. In the mesopause region, the maximum lifetime of icy particles is limited by their meridional transport into warmer regions of the MLT. According to our model, the zonal mean meridional winds are in the order of (−10 ± 4) m/s or (−8 ± 3)°/days between 60°N and 80°N latitude at the mesopause and a few kilometers below. Thus, even icy particles formed close to 80°N can stay in the SUMIC area for no more than three days.
 We note that our model does not account explicitly for the local small-scale effects of gravity waves passing through the mesopause region. These have been discussed by, e.g., Jensen and Thomas , Gerrard et al. , and Rapp et al. . In our model, short-term temperature variations impressed upon the icy particles by the passage of gravity waves are in kind simulated by the process of eddy diffusion, which produces pronounced vertical excursions for the particles too. More importantly, we suggest that the cited studies have not established in a quantitative fashion any strong modification of the mean state of the NLC layer due to the local effects of gravity waves. In fact, the study of Rappet al.  could be used to argue that we may expect only minor modifications, if any. Their numerical simulations show that gravity waves with periods longer than 6.5 hours tend to amplify NLC, while waves with shorter periods tend to destroy NLC. At the same time, the nine events of gravity waves that they observe and analyze have a mean period of 6.9 hours which is very close to the period of waves which supposedly effect NLCs very little. As we address here only the mean state of NLC (including tidal variability), we will not deal with phenomena of shorter than tidal timescales.
 We point out that the trajectories calculated by our model deviate significantly in character from the “classical” picture of NLC particle motions as developed in earlier 1-D NLC models [e.g., Turco et al., 1982; Jensen and Thomas, 1988; Sugiyama et al., 1996]. These particles formed close to the mesopause and had only vertical motions caused by sedimentation and presumed vertical winds. Our model results indicate that the area of production of icy particles is far larger than just the close vicinity of the mesopause, that the trajectories are heavily modified in vertical direction by tidal winds and eddy diffusion, that the largest number of icy particles are evaporating in the lower thermosphere and not in the upper mesosphere, and that the net transport of water through the SUMIC is dominated by a meridional transport, not a vertical transport. Furthermore, after their nucleation icy particles can live many days (= many tidal cycles) and their mean lifetime is probably determined more by the meridional than the vertical transport times.
Figure 9 shows the same (zonally averaged) parameters as Figure 4, but at model day 5.0. The formation of icy particles within the SUMIC and the subsequent sedimentation of these particles to lower altitudes (where they sublimate and return the water to the ambient atmosphere) leads to a removal of substantial amounts of water vapor from the mesopause region, a so-called freeze-drying process. At the mesopause this process causes the water vapor mixing ratio to drop from about 2 ppmv to <0.1 ppmv and 0.2 ppmv at 80°N and 70°N, respectively. We shall discuss the consequences of this strong decrease of humidity in the next chapter. The water vapor that is removed from the SUMIC by the icy particles is later returned as water vapor to the ambient atmosphere predominantly at the midlatitude border of the SUMIC and its lower border near 82 km. Within the latter area, an increase of the water vapor mixing ratio up to 6 ppmv is recognizable in the zonal averages of Figure 9a and up to 9 ppmv in the local values of Figure 7b.
 Comparison of Figures 4b and 9b shows that the freeze-drying process decreases the maximum saturation ratio at the polar mesopause by one order of magnitude to 103. This substantial decrease of the saturation ratio raises in turn the minimum radius for CNs throughout the SUMIC (Figure 9c).
3. Consequences of the Freeze-Drying Effect
3.1. Dehydrated Mesopause: Degree of Dehydration and Time Constant for Its Development
Figure 7 presented examples of the temporal and altitude-dependent development of the water vapor mixing ratio after an aerosol-free atmosphere has been seeded with the condensation nuclei. At 80°N, 90°W (Figure 7a), the drop in water vapor mixing ratio occurs initially with a time constant of <6 hours. The mixing ratio bottoms out about days after initialization at the very low value to 0.02 ppmv. Hence the condensation of ambient water vapor on icy particles causes a drop in the saturation ratio S by about a factor 100. Figure 7b shows the same scenario at 65°N, 90°W. Here minima of the mixing ratio develop slightly below the local mesopause and exhibit a pronounced semidiurnal structure. The water vapor mixing ratios in the local minima are about 0.2 ppmv during the initial two days and 0.3 ppmv in the steady state past day 4.0. These ratios are thus significantly larger than at 80°N. Although the initial seeding act in our model is a purely theoretical “experiment,” the computational results still teach us that freeze-drying at mesopause altitudes is a quite dynamic process. For the real mesopause region the results imply that the degree of dehydration will react rather quickly to any temporal or local changes in the input of CNs.
3.2. Regions With Enhanced Water Vapor
 The water vapor taken up by the formation of icy particles in the SUMIC is transported with the icy particles into warmer regions where the ice is sublimated and returned as water vapor to the ambient atmosphere. Our model indicates two general areas which develop such enhanced water vapor levels (see Figure 10 for zonal means of the change): (1) At the lower border of the SUMIC between 82 and 84 km altitude with a maximum effect in the 65° to 70°N latitude band; (2) At the low latitude border of the SUMIC South of 60°N in the 83 to 90 km altitude range. Area (1) is much smaller in volume than area (2). We suggest that the total amount of water vapor released from icy particles is larger in area (1) than in area (2), although the absolute enhancement is smaller in area (1) than in area (2). The enhancement in area (1) was predicted by von Cossart et al.  based on their measurements of the ice density in NLCs. The zonally averaged enhancement was modeled and discussed previously by B&vZ. Summers et al.  reported on the first case studies of this enhancement through observations taken in summer 1997 near 70°N by the satellite instruments MAHRSI and HALOE. Here we draw attention to the feature in Figure 7b that the layer of enhanced water vapor near 83 km, which is a product of the sublimation of NLCs, should exhibit a strong semidiurnal variation of its mixing ratio. This feature as predicted by our model may be difficult to verify by satellite-based instruments because tidal effects are generally difficult to observe from high-inclination satellites.
 The built-up of the layer of enhanced water vapor near 83 km can only start after NLC have been formed. The NLCs in turn are an indication for the presence of large, sublimating icy particles. In the B&vZ model, after seeding of a dust-free atmosphere with CNs, icy particles need about 10 hours to grow large and dense enough to form a visible NLC (see their Figure 33). This timescale for formation of NLCs is similar to the ones derived before by, e.g., Gadsden  and Jensen and Thomas . We can identify in Figure 7b the onset of the water vapor enhancement near 83 km at approximately +0.8 days, or in other words, about half a day after formation of the first visible NLC. At +1.8 days the mixing ratio shows a tidal maximum of 6 ppmv. It is only at time +2.8 days and later, that the tidal maxima exhibit the steady state value of 8 ppmv. Therefore the time constant for development of areas with enhanced water vapor is significantly larger than that for development of the dehydrated area.
3.3. Spatial Extent of the Areas With Depleted and With Enhanced Water Vapor
 In Figure 11a we show the spatial extent of the area of dehydration at the 88 km level and five days after initialization in a North pole-centered projection. If, for the sake of argument, we define “severely” dehydrated conditions as those exhibiting water vapor mixing ratios below 0.5 ppmv, then the area of severe dehydration reaches from the pole to about 65°N. This model result is the basis for our thesis that strong effects of freeze-drying should be permanently present throughout the midsummer mesopause region down to latitudes of 65°N. Furthermore, within the dehydrated area the contour lines of constant mixing ratio show remarkably small tidal perturbations (= near-circular shape). This suggests that these contour lines are in fact controlled by the ambient temperature, which exhibits likewise small tidal perturbations (B&vZ). To prove this case we plot in Figure 11b the isotherms for the same conditions as chosen for Figure 11a. The 0.5 ppmv contour line falls close to a 134 K isotherm (±2K). This and Figure 9b indicate that within the dehydrated area, the increase of water vapor toward the low-latitude boundary occurs under conditions of S > 1. Hence it is not caused by a general sublimation of ALL icy particles. Rather, it is caused by sublimation of those icy particles, which are transported meridionally out of the extremely cold polar cap and have radii in the 1 to a few nanometer range. Due to the increase of temperature with decreasing latitude, the minimum radius of stable icy particles increases away for the North Pole. South of 65°N this makes all particles with r < 4 nm unstable against the Kelvin barrier (see Figure 9c) well before they reach a S = 1 condition.
Figure 12a shows a cross section through the area of enhanced water vapor mixing ratio at 82 km altitude. Quite different from the dehydrated area, the distribution of enhanced water vapor shows a strong semi-diurnal tidal variation (= westward propagating with zonal wave number 2). This variation is very likely driven by the vertical component of the tidal winds, which we illustrate in Figure 12b. The maximum enhancement of 12.7 ppmv is reached at a location (time) where (when) the vertical tidal wind changes sign from downward to upwards or, in other words, where (when) the icy particles experience the warmest environment. This semidiurnal variation can be clearly recognized also in the temporal behavior of the water vapor mixing ratio at a fixed longitude as shown in Figure 7b.
3.4. Spatial Distributions of the Icy Particles and Bare Smoke Particles
Figures 13a and 13b show the zonally averaged number densities and mean radii of icy particles, respectively, at t = +5 days. We emphasize that the particle count, required for the densities of Figure 13a, was made independent of the particle sizes. Our model predicts the largest number density of icy particles to fall in the range 500 to 1000 cm−3. At NLC altitudes of 83 km, the particle densities fall in the range 50 to 200 cm−3, which agrees reasonably well with the results of von Cossart et al. .
 It seems remarkable that in our model, which is based on climatological means, icy particles extend down to 56°N at 86 km altitude, whereas a saturation ratio S > 1 is found only at latitudes ≥59°N (see Figure 9b). Figure 3 indicates that the zonally averaged temperature at 56°N and 86 km is 149 K. The low latitude border of icy particles therefore occurs at the same “canonical” temperature of 150 ± 2 K, frequently observed at 69°N for the low altitude boundary of NLCs [Lübken et al., 1996]. The latitudinal distribution of icy particles shown in Figure 13a goes also a long way toward explaining the sporadic observations of mesospheric summer echoes (MSE) by 50 MHZ radar at 54°N (see Table 1).
Figure 13b shows the mean radius of the icy particles. In general terms, the mean radius increases from the top of the SUMIC downward and from the low-latitude boundary toward the pole. We suggest that contributing factors to this specific latitude dependence are the larger vertical path lengths available to the icy particles for condensation and the larger upward velocities of the climatological winds at polar latitudes. Figure 13b also indicates that at altitudes above 85 km the mean radius of icy particles stays generally below 20 nm and over a large portion of that area below 10 nm. Thus, all these particles are candidates to cause PMSE, but are too small to produce visible NLCs.
Figure 14 shows the zonally averaged distribution of bare smoke particles (those which have never formed an icy particle plus those which had collected ice, but later lost it again by sublimation) five days after the initial seeding act. This distribution is distinctly different from that of the icy particles (see Figure 13a). Bare smoke particles are re-generated from icy particles when the latter sublimate their ice in warmer regions. This occurs in our model, as pointed out before, above the high-latitude mesopause where substantial numbers of icy particles are blown upwards into the warmer thermosphere and at the lower latitude border of the SUMIC region where icy particles are carried by the meridional winds toward the warmer midlatitudes. It is noteworthy that below the NLC region, there is never a marked accumulation of re-generated bare smoke particles because those are immediately carried upwards again back into the ice-forming region by the climatological vertical wind. Another feature is a notable dearth of bare smoke particles near the pole. This is due to the fact that there the saturation ratio S is so large, even under dehydrated conditions, that all our smoke particles form icy particles very quickly.
 At t = +5 days, as applicable for Figure 14, the total number of bare smoke particles is about 15 million, while Figure 13a represents 5 million icy particles. The much larger number of bare smoke particles is caused by their accumulation at middle latitudes.
 As our model allows us to calculate not only the densities and mean radii of the ice particles, but also their particle size distribution, we can also calculate the absolute volume backscatter coefficient β at a typical lidar wavelength such as 523 nm following von Cossart et al. .
Figure 15 shows the zonal mean of the calculated volume backscatter coefficient versus latitude at four different altitude levels. Due to the approximate r6-dependence of this coefficient, both the latitude as well as altitude distribution of β are reflecting mostly the size distribution of the particles as shown in Figure 13b. Our model predicts the brightest NLCs at about 75°N (at the same time, we suggest that the fine structure seen in the β-profiles of Figure 15 for latitudes >85°N is an artifact of our model). Fiedler et al.  deduce from 5 summers of lidar observations at the ALOMAR observatory (69°N) a median NLC brightness of β = 6.2 × 10−10 m−1 sr−1 for an altitude of 83.4 km under midsummer conditions. For similar conditions, our model predicts β = 1 × 10−10 m−1 sr−1 which is in fair agreement with the observed value considering the limited capabilities of the lidar to detect low-brightness NLCs and our model assumption of mean climatological conditions.
 The geographical distribution of icy particles with radii >40 nm, hence typical NLC particles, at t = +5 days and residing in the altitude range 84.0 ± 0.1 km are shown in Figure 16 (our model contains in this altitude range 85308 particles with radii >40 nm). The equatorward border of the NLC layer falls close to 65°N.
 The visibility of NLCs is, however, much more dependent on particle radii than particle number densities. Therefore we calculated also the latitude- and longitude-dependent volume backscatter coefficient of the NLC particles for a wavelength of 523 nm and for 0.2 km wide altitude ranges centered on the altitudes 82, 83, 84, and 85 km (Figures 17a, 17b, 17c, and 17d, respectively). The shading is light for 0.05 < β < 1, dark for β > 2, and medium for β values in between. A strong longitude dependence of β is indicated only at the very lowest altitudes of the NLC layer (here near 82 km). Otherwise, the spatial distribution of β shows only weak longitude variations and a certain patchiness. Potential causes for the patchiness of transpolar NLC layer as observed by numerous satellite experiments are mentioned in our section 2.1. It is, however, mostly up to future and improved observations to identify the major sources for this patchiness.
3.5. Formation Processes of Icy and Ice Particles
3.5.1. Heterogeneous Nucleation of Icy Particles
 Here we presume, like many others authors, that smoke particles are the basic condensation nuclei at which the formation and subsequent growth of icy particle starts. This process allows us to overcome the Kelvin barrier for particle formation by providing condensation nuclei in the nanometer size range. Figure 4c shows the minimum radius that a smoke or icy particle needs to have in order to experience stable growth by ice formation at its surface [Gadsden, 1982] for ambient conditions as present in our model atmosphere just before seeding it with CNs. At 70°N, for example, this minimum radius is 0.5 nm at the mesopause. At the same time, the size distribution of smoke particles as calculated by Hunten et al.  contains large numbers of particles with radii larger than this minimum radius. Thus at the time of initialization, there are plenty of CNs available even at the mesopause and ice formation proceeds vigorously right after the initial seeding act. The situation changes considerably after the freeze-drying effect has lowered the saturation ratio by an order of magnitude. According to Figure 9c, the minimum radius is >1.5 nm at any altitude near 70°N latitude. As in the Hunten distribution less than 14% of all particles have radii >1.5 nm (see BvZ, section 3.5.3.), production of new icy particles from smoke particles is slowed down very considerably (this statement relies heavily on the very steep gradient df/dr in the size distributions modeled by Hunten et al. ). Losses of icy particles due to sedimentation or meridional transport into warmer regions are counter-acted mostly by meridional transport of larger icy particles from latitudes >80°.
 Not unexpectedly, the extremely low temperatures at the mesopause cause the highest saturation ratios S to occur close to the mesopause (see Figure 9b). Although this situation leads to smaller minimal radii for CNs (and hence a higher density of available CNs) than above and below the mesopause, the number density of icy particles maximizes about 1 km below the mesopause as shown in Figure 13a.
3.5.2. Homogeneous and Ion Nucleation of Ice Particles
 As pointed out in the Introduction, homogeneous and ion nucleation can proceed only under conditions of rather high-saturation ratios S. For nucleation mediated by singly charged ions, S needs to be larger than 200, for homogeneous nucleation S must be much larger still. According to Figure 9b, these ambient conditions are found in an atmosphere with our steady state CN density only very close to the mesopause poleward of 80°. The prediction then is that the freeze-drying effect makes both homogeneous and ion nucleation negligible processes for the formation of ice crystals at mesopause altitudes. We admit that this conclusion is based on an extrapolation of classical thermodynamics to molecule-size scales. A more sophisticated analysis of ion nucleation that included ion chemistry, but assumed the undisturbed water vapor mixing ration of 3 ppmv, has been given recently by Gumbel et al. . Even neglecting the freeze-drying process, these authors also conclude “we deem ionic nucleation not be feasible under average conditions near the high-latitude summer mesopause.” Future refinements of the theoretical description of the nucleation process may change this picture to some extent. Yet, if our claim is indeed correct that in midsummer icy particles in the 10 nm size range are continuously present at PMSE altitudes, then the mysteries about nucleation processes at subnanometer scales lose much of their importance for modeling and understanding observed NLC layer properties.
3.5.3. Growth Rate of Particles
 The low water vapor pressures remaining under freeze-drying conditions affect also the rate of growth dr/dt of icy particles, which is proportional to the ambient water vapor pressure. Due to the persistent freeze-drying effect, the water vapor pressure is reduced permanently by an order of magnitude at the mesopause, which will make there the growth rate of any icy particle even slower than under no-freeze-drying conditions. An opposite situation persists within and below the NLC layers where water vapor released from the icy particles increases the regular background water vapor pressure by factors up to 3 or so. This will make the rate of growth of particles in the upper part of NLC layers faster than under conditions with no icy particles being around. In addition, a transition from invisible (PMSE) particles to visible (NLC) particles involves a change of median radius from, say, 15 nm to, say, 30 nm. This change can take place in less time than required for an increase of the radius from 1 to 30 nm. Hence NLCs can come into being on shorter timescales than 12 hours (B&vZ).
3.6. Energetics and Chemistry of the Neutral and Ionized Atmosphere
 The extremely low water vapor pressure in the midsummer high-latitude mesopause region should have an impact on the energetics of the neutral atmosphere. Substantial changes in water vapor pressure lead to significant changes in the mixing ratios of trace constituents which in turn effect the local heating rates. According to Mlynczak and Solomon  and Sonnemann et al.  the reactions that produce the largest heating rates in the 80 to 90 km region are:
Of those three, (1) is potentially the single largest source of heat in the vicinity of the mesopause. The profile of H, however, could be substantially modified by a freeze-drying process acting in the mesopause region over a period of a few months. Under high-latitude midsummer conditions, H is mainly produced by photodissociation of H2O. Hence the questions arises whether or not the sum of vertical diffusive and advective transport of H into the freeze-dried region dominates the local H profile over the production of H due to water vapor dissociation. If not only the abundance of H2O, but also that of H is significantly lowered by the freeze-drying process, it would imply a weakening of a local heating source and hence decrease of ambient temperature. We note, though, that a potential feedback of H2O freeze-drying on the thermal structure of the mesopause region is not yet included in our COMMA/IAP model.
 As briefly mentioned above, the chemistry of the mesopause region should also be effected by drastically reduced water vapor abundances because the abundances of many important trace constituents such as O, O3, OH, HO2, and H are influenced by reactions of HOx with Oy [see, e.g., Smith and Brasseur, 1991; Körner and Sonnemann, 2001]. Furthermore, Summers and Siskind  and Havnes et al.  have proposed that the budgets of mesopause trace constituents are not only determined by gas-phase reactions, but by heterogeneous reactions involving smoke particles too. In addition, not only the neutral atmosphere chemistry is expected to react to strongly dehydrated ambient conditions, the chemistry of the lower ionosphere should be impacted too. The absolute densities and profiles of a number of specific ions are predicted to depend significantly on the ambient water vapor pressure. Measurements of water cluster ions [Swider and Narcisi, 1975; Arnold and Krankowsky, 1977; Kopp, 1984, 1990] and of silicon ions [Solomon et al., 1982] using rocketborne mass spectrometers combined with models of the ion chemistry [e.g., Reid, 1989] have yielded a number of times sub-ppm mixing ratios of water vapor. Yet from the published literature we do not see a consistent picture emerging that these sub-ppm values are typical for the midsummer high-latitude mesopause region. All these topics certainly deserve a separate in-depth study.
 Primarily based on the observation that PMSE persist near-continuously at high latitudes in midsummer and supported by numerical modeling we predict that in midsummer a persistent cloud of icy particles covers the summer pole down to about 60° latitude at mesopause heights. Most of these particles are far too small to cause visible NLC. The particles in this cloud take up the ambient water vapor, which in turn causes substantial freeze-drying within the cloud. By way of numerical modeling we quantify the spatial distribution of the icy particles and strength of the freeze-drying conditions as well as the subsequent formation of areas with enhanced water vapor. We point out that the areas of dehydration should exhibit little tidal variations, whereas the areas of enhanced water vapor exhibit strong semidiurnal tidal signatures.
 Is there any evidence for a dehydrated state of the midsummer polar mesopause? Ground-based microwave experiments as well as rocketborne and satelliteborne IR instruments still have a difficult time to measure a few ppmv of water vapor at 80 km altitude. They cannot yet provide evidence for the feature that we predict here: Water vapor mixing ratios less than 0.2 ppmv at 88 km. This means that convincing observational proof for a persistently freeze-dried midsummer polar mesopause is outstanding. The situation for observational proof of the existence of areas with enhanced water vapor is further developed, though. As outlined in section 3.2, the first observational evidence for water vapor mixing ratio in the order of 10 ppmv in the altitude range 82 to 84 km has been reported.
 Next recommended steps in the observational studies could be searches for (1) the predicted semidiurnal signatures in these layers of enhanced water vapor and (2) sharp gradients in the water vapor mixing ratio profiles right above these layers. Next steps in our modeling studies will be to study the behavior of the SUMIC throughout the summer season.
 We thank M. Rapp for valuable discussions and the two reviewers for most helpful suggestions for improvements of our manuscript. This work was in part supported by the Bundesministerium für Bildung und Forschung, Bonn, Germany, through the AFO 2000 program.