Model results of mesospheric ice layers and background conditions at 69°N from 1961 to 2008 are analyzed. The model nudges to European Centre for Medium-Range Weather Forecasts data below ∼45 km. Greenhouse gas concentrations in the mesosphere are kept constant. At polar mesospheric cloud (PMC) altitudes (83 km) temperatures decrease until the mid 1990s by -0.08 K/yr resulting in trends of PMC brightness, occurrence rates, and, to a lesser extent, in PMC altitudes (−0.0166 km/yr). Ice layer trends are consistent with observations by ground-based and satellite instruments. Water vapor increases at PMC heights and decreases above due to increased freeze-drying caused by the temperature trend. Temperature trends in the mesosphere mainly come from shrinking of the stratosphere and from dynamical effects. A solar cycle modulation of H2O is observed in the model consistent with satellite observations. The effect on ice layers is reduced because of redistribution of H2O by freeze-drying. The accidental coincidence of low temperatures and solar cycle minimum in the mid 1990s leads to an overestimation of solar effects on ice layers. A strong correlation between temperatures and PMC altitudes is observed. Applied to historical measurements this gives negligible temperature trends at PMC altitudes (∼0.01–0.02 K/yr). Strong correlations between PMC parameters and background conditions deduced from the model confirm the standard scenario of PMC formation. The PMC sensitivity on temperatures, water vapor, and Ly-α is investigated. PMC heights show little variation with background parameters whereas brightness and occurrence rates show large variations. None of the background parameters can be ignored regarding its influence on ice layers.
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 Ice layers in the polar summer mesosphere are eventually suitable for detecting climate change since they are very sensitive to temperature changes and have been observed for more than 100 years [see, e.g., Thomas, 1996; DeLand et al., 2006; Shettle et al., 2009]. Whether or not ice layers show trends is disputed in the literature [von Zahn, 2003; Thomas et al., 2003]. In this paper we concentrate on long-term optical signatures in ice layers detected in an atmosphere/ice model and observed by ground-based lidar (noctilucent clouds, NLC) or by satellites (polar mesospheric clouds, PMC). Since the physical process is similar in both phenomena (optical extinction of light passing through an ice layer) we will occasionally use “NLC” as referring to both NLC and PMC.
 The most comprehensive global PMC observations are currently performed by the AIM (Aeronomy of Ice in the Mesosphere) satellite [Russell et al., 2009]. The longest record of PMC observations (28 years) comes from SBUV instruments (Solar Backscatter in the Ultraviolet) on various satellites. The data set has been intensively analyzed for trends and solar cycle variations (see DeLand et al.  and Shettle et al.  for some recent results). A solar cycle modulation and an increase of PMC albedo and occurrence rates was found. The magnitude of the effects observed by SBUV increases with latitude which asks for trend studies at polar latitudes. In this paper we concentrate on 69°N since NLC observations are most frequent here. We will compare our model results in detail with SBUV observations. [Hervig and Siskind, 2006] have recently summarized temperature, water vapor, and PMC observations from HALOE (Halogen Occultation Experiment) which are available since 1991. They find lower temperatures during solar minimum conditions (compared to solar maximum), more precisely in the time period 1993–1995. As we will show later, the low temperatures around 1994 are at least partly due to a long-term trend which is not associated with solar activity.
 In this paper we present long-term and solar cycle variations of ice layers and background parameters based on 48 years (1961–2008) of model simulations. We do not investigate variations on smaller time scales caused by waves, quasi-biennial oscillations, etc. It is important to notice that the concentration of greenhouse gases such as CO2, O3, and CH4 is kept constant in the model. This is true for the mesosphere and also for the troposphere and stratosphere. However, the effect of increasing trace gas concentrations in the troposphere and lower part of the stratosphere is indirectly present in LIMA due to nudging to ECMWF (European Center for Medium-Range Weather Forecasts). For H2O we use the same profile in mid May for all 48 years, which is then exposed to varying Ly-α radiation, background temperatures, transport, etc., and also feeds back with ice particles. H2O therefore varies in time although the profile before the season (mid May) is the same in all years. All long-term variations of mesospheric ice layers observed in the model must ultimately come from the stratosphere (or below) or from indirect effects on water vapor. The model adapts to the real world below approximately 45 km, more precisely to data from ECMWF. This implies that all radiative and dynamical trend effects that are present in the lower atmosphere are implicitly included.
2. Progress With Leibniz-Institute Middle Atmosphere Model/Ice
2.1. Modeling With Leibniz-Institute Middle Atmosphere Model
 The LIMA (Leibniz-Institute Middle Atmosphere) model is a new general circulation model of the middle atmosphere which especially aims to represent the thermal structure around mesopause altitudes [Berger, 2008]. LIMA is a fully nonlinear, global, and three-dimensional Eulerian grid point model which extends from the ground to the lower thermosphere (0–150 km) taking into account major processes of radiation, chemistry, and transport. Different from most models of the middle atmosphere, LIMA applies a triangular horizontal grid structure with 41,804 grid points in every horizontal layer (Δ× ∼ Δy ∼110 km) and adapts to tropospheric and lower stratospheric data from ECMWF. We combine LIMA with data from ECMWF applying a simplified assimilation method. At every time step (150 s) LIMA gradually nudges the model to ECMWF data. The intensity of nudging depends on altitude. More precisely, it is constant from the ground to the middle stratosphere (35 km) and decreases to zero at and above 45 km. The ECMWF data used by LIMA are extracted with 1° × 1° resolution for 21 pressure levels from 1000 to 1 hPa every 6 h at 0000, 0600, 1200, and 1800 UT. For each time step of LIMA (150 s) the ECMWF data are linearly interpolated in time. Data are also interpolated in space to match the LIMA grid structure. Due to the nudging process the lower part of the atmosphere in LIMA is very close to reality and exhibits highly variable wave patterns which propagate into the upper atmosphere and, among others, influence ice formation.
 We note that the dynamical core and chemistry-transport module (CTM) of LIMA are not yet coupled interactively. As an intermediate step we performed CTM simulations of chemical tracer distributions with high temporal resolution and dynamical LIMA background conditions [Sonnemann et al., 2007, 2008]. The comparison with observations is very satisfying. For example, LIMA shows nice agreement with mesospheric water vapor profiles measured up to ∼80 km by a microwave instrument based at ALOMAR (Arctic Lidar Observatory for Middle Atmosphere Research, 69°N). This concerns the magnitude of the concentrations and its variations with altitude and season (P. Hartogh et al., Water vapor measurements at ALOMAR over a solar cycle compared with model calculations by LIMA, submitted to Journal of Geophysical Research, 2009).
2.2. Modeling With LIMA/Ice
 A 3-D Lagrangian ice transport model is superimposed on LIMA to study the formation and life cycle of ice particles in the polar mesopause region. The main ideas regarding simplified mesospheric chemistry, transport of water vapor, Lagrangian transport, and microphysics of ice particles are taken from a former version of the model called COMMA/IAP (Cologne Model of the Middle Atmosphere/Institute of Atmospheric Physics, Kühlungsborn) [Berger and von Zahn, 2002; von Zahn and Berger, 2003a]. We have made various improvements in the ice module, some of which are described in the following. The combination of the Lagrangian ice transport model with LIMA background conditions is called LIMA/ice. Once per hour LIMA/ice uses LIMA results of 3-D winds, temperatures, densities, pressures, and water vapor concentrations varying with altitude, latitude, longitude, and time. To cover the entire summer season LIMA/ice runs from 25 May to 15 August in the Northern Hemisphere, and from 25 November to 15 February in the Southern Hemisphere. Forty million condensation nuclei (CN) are transported in LIMA according to background winds, particle eddy diffusion, and sedimentation. In the real world there are many more CN in the polar cap. Therefore, each CN represents many dust particles of the same size (see Berger and von Zahn  for more details). This is later used to determine the number of dust or ice particles per unit volume. If the particles traverse regions of supersaturation ice particles may form. We have determined water vapor saturation pressures following Murphy and Koop . Applying the expression from Mauersberger and Krankowsky  instead would not significantly affect the main results regarding long-term trends. For example, the mean NLC altitudes would decrease by basically the same amount (∼300 m) in all 48 years and the length of the seasons would increase by 2–3 days only. The fact that ice particle temperatures may differ from ambient temperatures is considered in the model [Espy and Jutt, 2002; Rapp and Thomas, 2006]. The formation and sublimation of ice is interactively coupled to background water vapor which thereby leads to a redistribution of H2O known as “freeze-drying.” In addition, the background water vapor is photolyzed applying actual Lyman-α fluxes updated once per day [Chabrillat and Kockarts, 1997].
 In Figure 1a we show as an exemplarily snapshot the location of all condensation nuclei (CN) and ice particles which happened to be within a latitude band of 69.0°N–69.2°N at a certain time (17 July 2008, 0000 UT). There are a total of 187.571 CN and 91.255 ice particles represented in this plot; that is, many pixels are plotted on top of each other. We have chosen a rather small latitude band width to limit the number of particles in the plot. In Figure 1b we show distributions of ice particle parameters at the same point in time. We have expanded the latitude band to 69.0°N–69.99°N to cover enough particles for deriving statistically meaningful values. In reality there are many more particles in the atmosphere compared to the upper part of Figure 1a. In order to arrive at reasonable numbers for ice radii, number densities, and backscatter coefficients, we therefore take each of the particles in Figure 1a representing many particles. The “representative factor” is constant in time and altitude [Berger and von Zahn, 2002]. Within the NLC layer shown in Figure 1, we observe the following range of ice particle parameters: brightness (β): ∼1–20 × 10−10/(m sr−1); radius (r): 15–75 nm; number density(N): 50–400/cm3. These numbers are consistent with lidar observations at ALOMAR and also with recent satellite observations [Baumgarten et al., 2008; Hervig et al., 2009].
 The appropriateness of LIMA/ice to study ice particle morphology is best demonstrated by comparison with observations. In former publications we have demonstrated that LIMA/ice is capable of reproducing the temporal and spatial variation of the most important ice layer parameters such as altitudes, occurrence rates, and brightness [Berger and Lübken, 2006; Lübken et al., 2008, 2009]. As an example Figure 2 shows the mean NLC height distribution from 48 summer seasons (1961–2008) in comparison with lidar observations from ALOMAR (1997–2008) [updated from Fiedler et al., 2009]. As can be seen from Figure 2 the mean NLC height from LIMA nicely agrees with ALOMAR within the combined vertical resolution of the model and measurements. We note that the variability of NLC heights in LIMA is somewhat smaller compared to observations. This may be caused by small-scale processes such as short-period gravity waves which are not present in LIMA. Since we want to investigate mean and long-term characteristics of ice layers in this paper the reduced short-term variability is of minor importance here.
 LIMA/ice results for 48 years (1961–2008) are now available (for both hemispheres) and allows us to study climatological behavior of NLC parameters. In this paper we concentrate on 69°N since NLC observations are most frequent here. It is important to realize that we have used the same H2O profile for all years at the beginning of the season (25 May). This profile is then exposed to varying Ly-α radiation, transport, and redistribution by freeze-drying.
 In Figure 3 we show the seasonal and latitudinal extent of ice layers in the Northern Hemisphere, more precisely mean occurrence rates (per day in percent) defined as follows. At a certain time we determine radii and number densities of dust/ice particles in each box given by the vertical, longitudinal, and latitudinal grid of 100 m × 3° × 1°. This yields hourly values of backscatter coefficients β assuming a certain lidar wavelength (532 nm in our case). For each latitude/longitude grid we count the number of hours per day where β exceeds a certain threshold (here: 1 × 10−10/(m sr−1)) anywhere in a vertical column. This gives occurrence rates on every horizontal grid point for every day. Averaging within a given latitude band (i.e., over 120 longitudes) results in the mean occurrence rates shown in Figure 3. For example, an occurrence rate of 100 percent in Figure 3 means that NLC with β > 1 × 10−10/(m sr−1) is observed somewhere in a vertical column at every hour of that particular day at that particular latitude at all 120 longitudes. We will later use seasonal mean occurrence rates in this paper. These are determined by further averaging within a certain latitude band for the core of the ice season, namely 6 June to 21 July (46 days).
 As can be seen from Figure 3, there is quite some year-to-year variability in the ice layer. This concerns not only occurrence rates but basically all ice layer parameters, namely altitude, brightness, mean radius, latitudinal extent, etc. There is a tendency for occurrence rate in Figure 3 to increase over the years. This will be discussed further in section 5.2 along with other comparisons of trend results. Note that occurrence rates in 2002 are considerably smaller compared to adjacent years which is due to the exceptionally large planetary wave activity in the Southern Hemisphere in that particular year [Becker et al., 2004]. The main purpose of this paper is to analyze the properties of ice layers and the background conditions in these 48 years. Furthermore, we have performed special sensitivity tests regarding the influence of temperatures, water vapor, and Ly-α on ice layers.
 We chose to pick ice layer and background parameters at 83 km in most cases for various reasons. Most important, some of the effects described in the paper are largest at the lower boundary of the height layer with supersaturation, for example the accumulation of water vapor. We will occasionally discuss the altitude dependence of our results.
3. Decadal-Scale Variations of Ice Layer Parameters
 In Figure 4 we show mean temperatures from 1 to 31 July at 83 km, and seasonal mean (6 June to 21 July) NLC altitudes (zNLC) from 1961 to 2008. A general trend is visible in temperatures and in zNLC. Note that the long-term trend is not uniform in time but changes sign in the mid 1990s. We have fitted straight lines to temperatures and altitudes from 1961–1994 and find slopes of −0.080 ± 0.016 K/yr, and −0.0166 ± 0.0048 km/yr, respectively. Temperatures in 1975 and 1976 are considerably higher compared to the general trend which is due to a bias in satellite temperatures [Gleisner et al., 2005]. As will be seen later these “outliers” can be used as an unintended case study to give detailed insight into stratospheric temperature effects on ice layers. We have ignored the 1975/1976 data points when calculating the fits. It is obvious from Figure 4 that altitudes and temperatures are closely correlated. More details will be discussed later.
 There is no Ly-α variation of temperatures detectable in Figure 4. This is not surprising since in the current version of LIMA/ice Ly-α acts on H2O only. Variations in H2O do not feed back on temperatures and dynamics. We do not expect a significant influence of H2O modulation on temperatures since radiative effects and chemical heating rates are presumably small.
 To study interannual variability we have smoothed the time series of zNLC in Figure 4 by a spline fit and determined the root mean square (RMS) of the deviations between the original data and the spline fit. We find a RMS deviation of ±0.33 km which characterizes the year-to-year variability. This is somewhat smaller but still consistent with year-to-year variability detected in lidar observations of NLC [Fiedler et al., 2009]. Variability from year to year can best be investigated by models because currently available optical instruments cannot monitor ice layers continuously in time and space: lidars observe at one location only, whereas satellites are often hampered by incomplete sampling. We note that radars measure PMSE continuously but the signal depends on further background parameters (turbulence, ionization, etc.) some of which are only poorly known.
 In Figure 5 we show water vapor profiles for all 48 years both from the end of May and from the center of the NLC season (1–10 July). Growth, transport, and evaporation of ice particles leads to a redistribution of water vapor (freeze-drying) and an accumulation in the height range ∼81–84 km. Figure 5 demonstrates that the magnitude of this effect varies from year to year. As expected such an effect does not occur in May since it is still too warm for ice particle formation. We note that a typical time constant for the redistribution of water vapor is only a few hours [see Berger and von Zahn, 2002, Figure 28]. In Figure 6 we show yearly values of zonal mean water vapor concentrations at 83 km both for 30–31 May and from 1 to 10 July, i.e., in the middle of the season. The data have been smoothed by running mean over 2 years. There is a general increase in H2O in July, not so in May. A straight line fit shows an average increase of H2O(July) of 0.053 ± 0.01 ppmv/yr. We will discuss potential reasons for this increase in section 6. A statistically significant anticorrelation of H2O with Ly-α (both in May and in July) can clearly be seen in Figure 6. The correlation coefficients and their upper/lower limits for a confidence level of 95% are r = −0.77−0.62−0.86 and r = −0.54−0.30−0.71, respectively. This suggests an influence of solar radiation on water vapor. The initial H2O profile on 25 May is exposed to solar UV radiation varying with solar cycle. Since the photochemical time-constant in the summer upper mesosphere is a few days only the water vapor profiles at 30–31 May and in July vary nearly “instantaneously” with Ly-α [Körner and Sonnemann, 2001; Sonnemann and Grygalashvyly, 2005]. We will see later that redistribution of water vapor by freeze-drying smears out the anticorrelation in July to a certain extent.
 In Figure 7 we show yearly values (mean of 6 June to 21 July) of NLC brightness and occurrence rates from LIMA/ice. The data have been smoothed by running mean over 2 years. A general increase is visible both in brightness and occurrence rates. The occurrence rate has increased by more than a factor of 2 since the early 1960s. There is a period of large brightness and occurrence rates in 1994–1999 which is due to a combination of very low temperatures (the lowest in the entire period; see Figure 4) and high H2O during solar minimum (see Figure 6). In earlier periods of solar minimum, for example, around 1986/1987, H2O was also high, but temperatures were higher compared to the mid 1990s which results in less intense ice clouds. There is an obvious modulation of occurrence rates and brightness with Ly-α in Figure 7. This is caused by a modulation of H2O by Ly-α (see Figure 6) and the dependence of occurrence rates and brightness on H2O (discussed later).
 We have studied in detail various correlations of background atmosphere and ice layer parameters. The results are summarized in Table 1. Note that we have excluded the years 1975/1976 from the correlation analysis because of the bias in ECMWF in these years mentioned earlier. In Figure 8 we show the correlation between temperatures at 83 km and NLC heights. A nearly perfect and statistically highly significant correlation (r = 0.930.870.96 for a 95% confidence level) exists between zNLC and T(83 km). A straight line fit (ignoring the outliers from 1975 and 1976) gives a slope of 0.263 ± 0.016 km/K. Note that the outliers perfectly match the straight line fit which suggests that the main processes controlling the correlation between temperature and NLC height do not change when rather larger excursions are considered.
Table 1. Correlation Between Ice Layer Parameters and the Background Atmosphere
 In Figure 9 we show the correlation between NLC heights and brightness. NLC are generally brighter if they appear at lower altitudes (correlation coefficient: −0.81). This is in agreement with observations [e.g., Fiedler et al., 2003; Chu et al., 2006] and concurs with the generally accepted understanding of ice particle growth and sedimentation. Roughly speaking, when the altitude range of supersaturation extends to lower altitudes, more water vapor is available for particle growth. For a constant water vapor mixing ratio the available number of water vapor molecules increases exponentially. In reality (and in LIMA/ice) the situation is much more complicated because of freeze-drying, horizontal and vertical transport, etc. The fact that the logarithm of NLC brightness varies roughly with NLC altitude (see Figure 9) suggests that the simple considerations presented above cover the main physical process. The two outliers from 1975/1976 produce brightness values within the normal range of values, but at too high altitudes (∼84.8 km).
 In Figure 10 we show the correlation between NLC heights and occurrence rates. Note that we consider seasonal mean ice layers for a given brightness threshold (here β > 1 × 10−10/(m sr−1)). Each occurrence rate summarizes the results from 1,589,760 data points, namely 1 latitude band (1 degree) × 120 longitudes (3 degrees) × 120 altitudes (100 m) × 24 hours × 46 days. Ice layers appear more often at lower altitudes, of course only within the height range of supersaturation. Indeed, NLC observations at ALOMAR show that NLC with a brightness larger than a certain threshold appear more frequently at lower altitudes [e.g., Fiedler et al., 2003]. The two outliers at ∼84.8 km are due to the high and unrealistic temperatures in 1975/1976.
 We observe an anticorrelation between occurrence rates and temperatures (not shown here) which is statistically significant (r = −0.75−0.59−0.85 for a 95% confidence level). Furthermore, an anticorrelation between brightness and temperature is detected. Brightness increases with lower temperatures, T(83 km), but mainly for temperatures lower than 150 K.
 In Figure 11 we show NLC brightness versus occurrence rates. A large and statistically highly significant correlation is obtained (r = 0.940.890.96 for a 95% confidence level). We recall that the brightness value for a certain year is the mean of all brightness values detected in a season and in a given latitude band averaged over all longitudes. We refer to section 2 for a definition of occurrence rates. The correlation in Figure 11 implies that if the mean brightness increases so does the total number of NLC. This means that the brightness of all clouds (from faint to strong) increases so that more and more clouds appear above the threshold. This result is in agreement with SBUV observations where a high correlation between yearly mean brightness and occurrence variations is observed [see DeLand et al., 2007, Figure 7; Shettle et al., 2009, Figure 2]. In Figure 12 we show the correlations between water mixing ratios and NLC occurrence rates and brightness. There is a strong and significant correlation between H2O concentration at 83 km in July on the one hand and NLC brightness and occurrence rates on the other hand; the correlation coefficients are r = 0.890.810.94 and r = 0.920.860.95, respectively, for a confidence level of 95%. The interpretation of this result is somewhat complicated. We recall that the water vapor profile on 25 May is the same for all 48 years. Certainly, if ice particles are brighter and more frequent (e.g., because it is cold in a particular year) they collect more water vapor which is then dumped at ∼83 km (i.e., brighter NLC lead to more H2O). At the same time if more water vapor is available for ice particle condensation (e.g., because the vertical and/or horizontal area of supersaturation has increased because of cooling) this will certainly lead to brighter and more frequent NLC (i.e., more H2O leads to brighter NLC). We tried to distinguish between these two cases by studying the correlation between H2O at 83 km (melting region) and at 87 km (collecting region). The result is not conclusive but suggests that both explanations are partly true. This implies that the contribution of water vapor changes to the long-term PMC brightness trend is difficult to address. This subject requires a detailed investigation of the temporal and spatial intensity of freeze-drying, etc., which is beyond the scope of this paper. The correlation of brightness and occurrence rates with H2O at the beginning of the season (30–31 May) is considerably smaller (r = 0.63 and r = 0.60, respectively). This is because the interaction between water vapor and NLC particles is more intense in the peak NLC season.
 There is no statistically significant correlation of Ly-α with temperatures (r = −0.06) nor with NLC altitudes (r = 0.19) consistent with observations [Fiedler et al., 2009]. In LIMA/ice there is no feedback of Ly-α on temperatures and therefore no effect on NLC altitudes. There is a small and statistically nonsignificant anticorrelation between Ly-α and occurrence rates (r = −0.34) and brightness (r = −0.41), both determined from the raw unsmoothed data. This is explained by the modulation of water vapor by Ly-α (Figure 6) and the strong correlation between water vapor and occurrence rates and brightness (Figure 12). However, the strong correlation of H2O and Ly-α in May (r = −0.77) is partly destroyed by redistribution of H2O due to freeze-drying which leaves a relatively weak correlation of Ly-α and water vapor (r = −0.54). This in turn results in a rather weak correlation of Ly-α with occurrence rates and brightness. In summary, higher temperatures in the upper mesosphere lead to higher and weaker NLC. Brighter, more frequent, and lower NLC are associated with more H2O.
4. Sensitivity of Ice Layer Parameters on Temperatures, Water Vapor, and Ly-α
 We have studied in detail the sensitivity of ice layer parameters to background conditions, namely to temperatures, water vapor, and Ly-α. From the 48 years of LIMA results we have selected certain years with mean, “cold” and “warm” conditions at 83 km; these years are 2007, 1998, and 1970, respectively, where the July mean temperatures are 148.3 K, 147.3 K, and 149.3 K, respectively (see Figure 4). For these years we have applied mean/high/low water vapor concentrations (, and ± 25%) before the NLC season has started (May 25). Furthermore, we have chosen Ly-α values of 4.75, 3.5, and 6.0 Ly-α units (1 Ly-α unit = 1011 photons/(cm2 s−1)) according to mean, solar minimum, and maximum conditions. These values were kept constant for the entire season. We have treated the influence of H2O and Ly-α separately since Ly-α is not the only process modifying water vapor. Other mechanisms, for example, horizontal and vertical transport also play a role.
 In Figure 13 we show the sensitivity of NLC heights to temperatures, water vapor, and Ly-α. As can be seen from Figure 13 the entire range of height variation is rather small (∼1 km). Heights vary approximately linearly with temperature, consistent with Figure 4. For any given temperature the range of zNLC variation due to H2O or Ly-α is very small (0.4–0.6 km) and decreases with increasing temperature.
 In Figure 14 we show the sensitivity of occurrence rates to temperatures, water vapor, and Ly-α. As can be seen, occurrence rates generally vary as expected, i.e., they increase with increasing water vapor, decreasing temperatures, and decreasing Ly-α. The total range of occurrence rates is large, namely from roughly 0 to 40%. None of the background parameter influence is much smaller compared to others; that is, neither temperature nor water vapor nor Ly-α can be ignored. Therefore, an increase of occurrence rates cannot directly be related to a change in one of these parameters. It might well be due to a combination of several. For example, a 10% increase of occurrence rates from approximately 14% to 24% may be caused by various variations: from (Tmax, Lymin, H2Omean) to (Tmean, Lymax, H2Omax), or from (Tmean, Lymean, H2Omin) to (Tmin, Lymax, H2Omean), and various other combinations.
 In Figure 15 we show the sensitivity of brightness to temperatures, water vapor, and Ly-α. Again, brightness values vary strongly with temperatures, water vapor, and Ly-α and none of these background parameters can be neglected. It is interesting to note that the range of β values increases (for given Ly-α radiation) with decreasing temperatures. This means that the sensitivity of brightness is largest (smallest) in the center (at the beginning/end) of the season where temperatures are low (high). Furthermore, for a given temperature the variability of β is largest for minimum Ly-α radiation (blue crosses in Figure 15).
 We conclude that different ice layer parameters (altitude, brightness, occurrence rates) have different sensitivity to changes in temperatures, H2O, and Ly-α. NLC altitudes primarily reflect temperatures and are less sensitive to H2O and Ly-α. Occurrence rates and brightness are both sensitive to temperature, water vapor, and Ly-α variations. This implies that for a given observation of occurrence or brightness variations one usually cannot unambiguously infer changes in background parameters.
5. Comparison With Measurements
 We have shown in previous publications that the main morphology of ice layers from LIMA/ice is in excellent agreement with observations [e.g., Berger and Lübken, 2006; Lübken et al., 2008, 2009]. This regards, for example, the mean NLC altitude, its variation with latitude, and interhemispheric differences of occurrence rates, brightness, etc. Regarding temperatures, the long-term variation shown in Figure 4 is small: the peak-to-peak variation from 1961 to 2008 is only 3–4 Kelvin. Unfortunately, little is known about long-term changes of the thermal structure in the polar upper mesosphere in summer. Lübken  found a very small and nonsignificant negative temperature trend from a comparison of historical rocket grenade temperatures (mid 1960s) to recent measurements by falling spheres. Below the mesopause trends of approximately −0.05 to −0.1 K/yr were derived [see Lübken, 2001, Figure 6]. A straight line fit to the LIMA/ice temperatures in Figure 4 from 1961–1991 results in a trend of only −0.080 ± 0.016 K/yr, in remarkable agreement with Lübken .
 In Figure 6 we also show H2O values from Hervig and Siskind  for 65°N–70°N, 20 days from solstice, and at 80 km (i.e., slightly below the LIMA/ice altitude). As can be seen the agreement is very good, both for absolute values and for the modulation with solar cycle. This suggests that the most important photochemical processes affecting H2O are well presented in LIMA/ice. We have also compared HALOE extinction coefficients with LIMA/ice backscatter coefficients β. Indeed, the extinction coefficients in HALOE peak around 1995–1998 similar to β values derived from LIMA/ice. However, the amplitude of this modulation is larger in HALOE compared to LIMA/ice which is presumably due to the difference between extinction and backscatter as well as other systematic differences caused by observation geometry, wavelength, sampling, etc. In the future we plan to expand our LIMA/ice analysis to study these differences further.
5.2. Ice Layers From Satellites and Lidar
 In Figure 16 we show the time series of PMC occurrence rates from LIMA/ice in comparison with measurements from SBUV. Note that both the LIMA/ice and SBUV data have been smoothed by running mean over 2 years. The SBUV occurrence rates are taken for the latitude band 64°N–74°N [see Shettle et al., 2009, Figure 2]. Since LIMA/ice does not attempt to consider the instrumental sensitivity of SBUV nor other factors which might cause a systematic shift between LIMA/ice and PMC observations (scattering angle, sampling issues, etc.), we have multiplied SBUV occurrence rates by a factor of 6 to get similar absolute numbers for SBUV and LIMA/ice. As can be seen from Figure 16 there is general agreement between LIMA/ice and SBUV regarding the large values in the mid 1990s, the variation with solar cycle, and the general trend. We note that the correlation between LIMA/ice and SBUV increases considerably when smoothed data over 2 years are used (see Table 1). This suggests that biennial processes play a role in the variability of PMC.
Fiedler et al.  has recently summarized lidar measurements of NLC performed at ALOMAR for nearly a solar cycle. For strong NLC they find record high occurrence rates in the first year of their observations (1997), in nice agreement with Figure 16. Surprisingly, occurrence rates at ALOMAR dropped from 2004 to 2007 although an increase was expected (and observed by SBUV) because of decreasing solar activity. In the same time period the occurrence rates of all NLC (including faint clouds) increased. We plan to study this subject further in the future taking into account instrument specifications (sensitivity, sampling, etc.) and their effect on long-term variations. It is interesting to note that NLC altitudes from ALOMAR do not vary substantially over a solar cycle, in agreement with LIMA/ice results shown in Figure 4.
 There are some very strong correlations in LIMA/ice, for example between NLC altitudes and temperatures at NLC altitudes. The slope of 0.26 km/K shown in Figure 8 is practically identical to results deduced from the Community Aerosol and Radiation Model for Atmospheres (CARMA) [Turco et al., 1979; Toon et al., 1979; Lübken et al., 2007]. In contrast to CARMA the simulations in LIMA/ice use consistent wind fields, horizontal transport, and variability introduced from the stratosphere. The agreement between results from CARMA and LIMA/ice suggests that microphysical processes related to local supersaturation conditions (CARMA) prevail in determining mean NLC altitudes, whereas mechanisms related to horizontal transport and variability (LIMA/ice) are less influential. This is important when comparing local temperature measurements, for example by lidar, to NLC heights.
 The correlations shown above suggest a general dependence of ice layer morphology on background parameters: whether or not ice layers appear critically depends on supersaturation, i.e., primarily on low temperatures, whereas the visibility of clouds, i.e., brightness and occurrence rates, is basically influenced by the amount of water vapor available for particle growth. Water vapor can generally be neglected for supersaturation considerations, but determines the ultimate size of the ice particles and thereby the ability to scatter light. This implies that one must be careful in comparing results from instruments with different sensitivities.
 We have studied in detail the potential influence of time lags on the correlations and have applied lags of up to ±2 years in steps of one year. In all cases of significant correlation coefficients at zero time lag it drops drastically and is nonsignificant if a time lag is introduced. This is in agreement with findings from SBUV which are consistent with zero time lag [see, e.g., Shettle et al., 2009].
 One of the main points of this paper is to demonstrate the strong link between the mesosphere and the stratosphere. This link is demonstrated by an unintended case study: in the years 1975 and 1976 the satellite temperatures in the stratosphere were biased toward too large values [Gleisner et al., 2005]. This led to too large temperatures in ECMWF. As can be seen from Figure 4 this directly resulted in too large temperatures at NLC altitudes (by ∼3 Kelvin). Consequently this led to low NLC occurrence rates, high altitudes, etc. This unintended cases study demonstrates the strong coupling of the mesosphere in LIMA/ice to the stratosphere and the sensitivity of ice layer parameters to small temperature changes in the mesosphere. Note that the two outliers from 1975/1976 perfectly match the line fitted to the ‘normal’ points in Figure 8 which demonstrates that the feedback of temperatures and related background parameters (winds) on the morphology of ice layers is valid even for comparatively large deviations from the mean state. On the other hand, the two outliers from 1975/1976 clearly deviate from the normal correlations of brightness and occurrence rates (see Figures 9 and 10). This is presumably because H2O does not follow the unrealistic conditions in these years. For example, given their brightness these ice layers should have appeared 1 km lower as they actually do in LIMA/ice.
6.2. Solar Cycle Effects in Water Vapor and Ice Layers
 LIMA/ice produces solar cycle variations of H2O at 83 km of approximately 2.5 ppm in midsummer which is in agreement with HALOE (see Figure 6). The modulation is in the same order (but slightly higher) compared to CTM calculations by Sonnemann and Grygalashvyly . The modulation of H2O results in a modulation of chemical heating rates which, however, is small (∼0.01 K/d) and will therefore not affect temperatures (M. Grygalashvyly, personal communication, 2009).
 In general a solar cycle effect in ice layers is expected since Ly-α affects H2O through photodissociation which in turn affects brightness and occurrence rates. It has been speculated from simulations with COMMA/IAP (Cologne Model of the Middle Atmosphere/Institute of Atmospheric Physics, Kühlungsborn) that freeze-drying will significantly reduce the potential influence of Ly-α on H2O above ∼82 km, whereas the effect is enhanced at 80–82 km [von Zahn et al., 2004]. As can be seen from Figure 6 there is a statistically significant effect of Ly-α on water vapor at 83 km (r = −0.54−0.30−0.71). From the slope we derive a sensitivity of −1.6 ppmv/Ly-α unit. We have expanded this analysis and determined the sensitivity at all altitudes. As can be seen from Figure 17, water vapor is reduced by Ly-α in the entire height range of our ice domain, where the largest reduction by up to 2 ppmv/Ly-α units occurs around 82 km. We also show relative reductions in Figure 17 to account for the decrease of undisturbed water vapor concentration with altitude. Since the total variation of Ly-α during a solar cycle is approximately 2 Ly-α units, the 25 percent maximum reduction at 82 km implies a total decrease of ∼50%. Different to COMMA/IAP a significant sensitivity of H2O to Ly-α is observed in the entire upper mesosphere, namely up to 92 km. We explain this effect by “episodic mixing” events in LIMA/ice which bring back water vapor into the dried region by variable background winds.
 The correlation of Ly-α and ice layer parameters is generally small (see Table 1) if we consider the entire 41 years of LIMA/ice simulations. The anticorrelation of Ly-α and occurrence rates in SBUV and in LIMA/ice is most likely exaggerated because very low temperatures accidentally occurred around 1995 which happened to coincide with a period of minimum solar activity (see Figure 4). Consequently the NLC occurrence rates are very high in this period. We repeat that Ly-α cannot influence temperatures in LIMA/ice. Such an effect does presumably exist and will most likely modify the effect of Ly-α on ice particle parameters. From our studies we see that an accidental coincidence of minimum temperatures and solar minimum conditions can lead to an overestimate of solar cycle effects on ice layers.
 Ice layers follow the background change of temperatures and H2O. There are still some open questions regarding the microphysics of ice nucleation, for example on the role of meteoric dust [Rapp and Thomas, 2006]. The general agreement between LIMA/ice and ice layers, including the solar cycle variation and long-term trend suggests that these uncertainties are either of minor importance or they cancel out each other for the temporal and spatial scales investigated here.
6.3. Trends in Temperatures, Water Vapor, and Ice Layers
 Trends in background concentrations of trace gases are ignored in the current version of LIMA/ice and will be dealt with in the future. We note that LIMA/ice still covers major features of observed ice layer trends which highlights the importance of other influences on long-term appearance of ice layer (e.g., stratospheric effects on temperatures). Regarding trace gas trends in the polar summer mesosphere little is known from observations and some of the measurements differ substantially from expectations (see section 6.3.2).
6.3.1. Trends in Temperatures
 Since there are no trace gas trends implemented in the current version of LIMA/ice, trends in mesospheric temperatures and H2O (and subsequently in ice layers) must have their origin in the lower atmosphere. Regarding temperature trends the results presented in this paper are presumably valid also if mesospheric greenhouse gas trends are added because practically all models predict very small (negative) or even positive temperature trends around the polar summer mesopause (see Bremer and Berger , Akmaev et al. , Schmidt et al. , and Garcia et al.  for some recent examples). As mentioned earlier little is known about trends in photochemically active gases in the summer polar mesosphere.
 The linear relationship between NLC heights and temperatures (at 83 km) shown in Figure 4 allows us to estimate temperature changes from a comparison of altitudes. Jesse  summarized NLC height measurements performed around 1890 by triangulation from Berlin and arrives at a mean value of 82.08 km. von Zahn and Berger [2003b] argue that a mean value of 82.4 ± 0.4 km (at 53°N) is probably more representative for these observations. Lübken et al.  have recently compiled NLC heights from various stations and reported a mean value of 82.75 km at 54°N with a variability (standard deviation) of 1.58 km. The difference of mean heights from 1890 and today is therefore very small (350–670 m) and corresponds to a very small temperature change (at 83 km) of 1.3–2.5 K and negligible trends of 0.11–0.22 K/decade. We realize that the zNLC/T(83 km) slope of 0.263 km/K was derived for 69°N and not for midlatitudes. The low occurrence rates of NLC at midlatitudes makes it rather difficult to study a similar dependence here. On the other hand, the similarity of the slopes derived from LIMA/ice and CARMA [see Lübken et al., 2007] suggests that this result is of general relevance and may therefore also be used at midlatitudes.
 What causes the temperature trend in the mesosphere? In Figure 18 we show height profiles of temperature trends both on geometric and log-pressure altitude scales. We have considered the time period 1961 to 1994 only since the temperature trend changes sign after 1994 (see Figure 4). Largest trends on both height scales occur around 35–45 km. In the mesosphere temperature trends maximize around 85 km (geometrical heights) and reach ∼−0.9 K/decade (see also Figure 4). Temperature trends in the mesosphere are much smaller on log-pressure heights which is in agreement with our assumption of zero trends in trace gases. In Figure 18 we also show trends of geometrical heights in log-pressure coordinates (red curve). Due to stratospheric cooling the mesosphere is shrinking by approximately 50–100 m, an effect which increases with height. At NLC heights (approximately 80 km) atmospheric shrinking has summed up to ∼70–80 m/decade corresponding to a cooling of −0.3–0.4 K/decade, i.e., nearly 50% of the total cooling (see blue line in Figure 18). Atmospheric shrinking at lower altitudes (mainly stratosphere) therefore constitutes a considerable part of the total effect in the upper mesosphere. The remaining cooling comes from dynamics, which includes a trend in wave activity and/or a variation of filtering by background winds, and/or a trend in planetary wave activity in the Southern Hemisphere. For the latter increasing evidence in measurements and modeling is now available [e.g., Becker et al., 2004; Karlsson et al., 2007].
 A detailed discussion on the physical reasons for trends in the stratosphere is beyond the scope of this paper. There are several candidates causing such a trend, for example ozone, carbon dioxide, planetary wave activity, etc. Note that stratospheric trends in trace gases are implicitly considered in LIMA/ice because of nudging to ECMWF. The change of trends in the mid 1990s (see Figure 4) is detected in several stratospheric parameters, for example in the annual total ozone values at mid and polar latitudes [World Meteorological Organization, 2007]. We realize that long-term variations of stratospheric temperatures is a complex subject depending on various photochemical and dynamical processes, and not only on ozone.
6.3.2. Trends in Water Vapor
 What causes the trend in water vapor in July (Figure 6)? We argue that it comes from increased freeze-drying caused by the temperature decrease shown in Figure 4. To support this idea we show in Figure 19 the water vapor trend as a function of altitude. As can be seen the trend is largest in the height region of ice particle evaporation (∼81–83 km), whereas the trend is negative above due to increased collection of water vapor by ice particles. In principle a trend would also be caused by increasing vertical winds which brings more water vapor up from below. However, since the trend is zero at ∼80 km such a speculation can be ruled out. We note that long-term simulations including trace gas trends show increasing water vapor similar to LIMA/ice [Grygalashvyly et al., 2007]. But these models do not take into account freeze-drying and interaction of H2O with ice particles and can therefore not be used for trend analysis at NLC altitudes.
 A microwave instrument measuring water vapor is available at ALOMAR. It gives H2O concentrations up to approximately 80 km since 1996 and has been used for trend analysis [von Zahn et al., 2004]. A more recent study shows a general decrease of water vapor in the summer mesosphere just below NLC altitudes (Hartogh et al., submitted manuscript, 2009). This is surprising because from the anthropogenic increase of methane an increase in middle atmosphere humidity was expected. We conclude that not enough is known about water vapor trends in the upper summer mesosphere at polar latitudes.
6.4. Conclusion and Outlook
 We have analyzed 48 years (1961–2008) of LIMA/ice model results on temperatures, water vapor, and ice layer parameters (altitude, brightness, occurrence rates) at polar latitudes (69°N). The main morphology of NLC and PMC derived from LIMA/ice is in agreement with lidar and satellite observations. At NLC/PMC altitudes (83 km) a general temperature decrease by ∼2.5 K is observed from 1961 until the mid 1990s (rate: −0.08 K/yr). In the same time period mean NLC altitudes have decreased by approximately 0.5 km (rate: −0.0166 km/yr). After the mid 1990s temperatures and mean NLC heights increase. We find a water vapor increase at NLC heights and a decrease above. This trend is caused by the temperature trend mentioned above which leads to increased freeze-drying. The temperature and H2O trends are consistent with rocket borne and satellite observations of temperatures and water vapor, respectively. We note that observations around the polar summer mesopause are sparse and often uncertain.
 Trends in temperature and water vapor lead to trends in NLC brightness, occurrence rates, and (to a lesser extent) also in NLC altitudes. Long-term variations of PMC from LIMA/ice are consistent with satellite observations from SBUV. In the mid 1990s PMC are very strong and frequent which is due to an accidental coincidence of low temperatures (the lowest in the entire period) and solar cycle minimum. This exaggerates the correlation between SBUV ice layer parameters and solar cycle.
 The current version of LIMA/ice does not include trends in greenhouse gases. Temperature trends at NLC altitudes observed in LIMA/ice mainly come from the stratosphere or below. Shrinking of the atmosphere below NLC heights plays a major role in cooling the mesosphere. Dynamics and radiation also contributes. The strong link between mesospheric temperatures and the stratosphere is demonstrated in the years 1975/1976 when ECMWF temperatures in the stratosphere were biased toward too large values which directly resulted in too large temperatures at NLC altitudes and associated deviations in NLC parameters.
 We have determined correlations between background atmospheric parameters and ice layer characteristics. There is a strong correlation between temperature and NLC altitude. This allows us to deduce a temperature change from a comparison of actual NLC heights to historic measurements from the 1890s. We arrive at a maximum temperature decrease of only ∼−2.5°K. We have thereby assumed that the z/T dependence for polar latitudes also holds for lower latitudes and that other atmospheric parameters affecting NLC heights have not changed. We find further strong correlations between NLC brightness, occurrence rates, atmospheric temperatures, and water vapor. In summary, these correlations are consistent with the standard picture of NLC formation, sedimentation, growth, and evaporation.
 We have investigated the sensitivity of NLC parameters on variations in temperatures, water vapor, and Ly-α. NLC heights show only little variation with background parameters, whereas brightness and occurrence rates show large variations. None of the background parameters is dominant when influencing ice layers; that is, neither temperature nor water vapor nor Ly-α can be ignored. Therefore, an observed variation of, for example, occurrence rates cannot directly be related to a change in one of these parameters. It might well be due to a combination of several. More generally, temperatures must be low enough for ice layers to exist, but their visibility (affecting brightness and occurrence rates) is mainly determined by the amount of H2O available for condensation.
 We observe a statistically significant modulation of water vapor with Ly-α in May (i.e., before the NLC season has started) which is reduced in the NLC season due to redistribution of H2O by freeze-drying. Consequently, there is only a small and nonsignificant correlation of NLC brightness and occurrence frequency with Ly-α. Water vapor collected in the evaporation region of ice particles (around 83 km) is redistributed to higher altitudes by dynamics (“episodic mixing”) and is therefore exposed to larger solar cycle variations of Ly-α. The modulation of H2O by Ly-α is consistent with satellite observations.
 The general agreement between the main features and trends of ice layers in LIMA/ice and observations suggests that the microphysical and photochemical processes present in LIMA/ice cover the most important processes relevant for NLC formation, or, alternatively, that processes ignored in LIMA/ice cancel out.
 In the future we plan to introduce long-term trends in greenhouse gases in the mesosphere and study the effect on the background atmosphere and on ice layers. We will also expand the comparison of LIMA/ice results with lidar and satellite observations, for example considering other latitudes and instrumental constraints.
 We thank Jens Fiedler for providing an update on the NLC altitudes from ALOMAR. This research is supported by the Deutsche Forschungsgemeinschaft (DFG) under the CAWSES SPP grant LU 1174/3-1 (SOLEIL).