The Mesospheric Ice Microphysics And tranSport model (MIMAS) is used to study
local time (LT) variations of polar mesospheric clouds (PMCs) in the Northern
Hemisphere during the period from 1979 to 2013. We investigate the tidal
behavior of brightness, altitude, and occurrence frequency and find a good
agreement between model and lidar observations. At the peak of the PMC layer
the mean ice radius varies from 35 to 45 nm and the mean number density
varies from 80 to 150 cm

Polar mesospheric clouds (PMCs), also known as noctilucent clouds (NLCs),
consist of water-ice crystals. They occur at midlatitudes to high latitudes, around
83 km altitude

A variety of spaceborne experiments have observed PMCs since the late 20th
century

In contrast to satellite measurements, ground-based measurements are
geographically restricted but have the ability to cover a full local time
cycle. For example, variations of PMC occurrence frequency and brightness as a function
of local time have been observed in detail with lidar instruments

In this paper we discuss results from a 3-D Lagrangian transport model for
PMCs called MIMAS (Mesospheric Ice Microphysics And tranSport model); see
also the data description in

The MIMAS model is a 3-D Lagrangian transport model designed
specifically to model ice particles in the mesosphere–lower thermosphere
(MLT) region. MIMAS is limited from midlatitudes to high latitudes
(45–90

Typically, MIMAS calculates a complete PMC season from mid-May to end of
August. Each of the seasonal simulations starts with the same water vapor
distributions on constant pressure levels

Simultaneously, 40 million condensation nuclei (dust particles) are
transported according to 3-D background winds, particle eddy diffusion, and
sedimentation. The radii of the dust particles in the model vary according to
a Hunten distribution between 1.2 and 3.6 nm

In MIMAS, temperatures, densities, pressure, and wind fields are prescribed
using hourly output data from the Leibniz Institute Middle Atmosphere (LIMA)
model which aims in particular to represent the thermal structure around
mesopause altitudes

Local time variation derived from monthly and zonal means of
temperature

LIMA is nudged to tropospheric and stratospheric reanalysis data available
from the European Centre for Medium-Range Weather Forecasts (ECMWF), Reading,
UK. LIMA incorporates the 40-year ECMWF reanalysis data set (ERA-40) from
1960 to 2002 and ECMWF operational analysis thereafter. The nudging
coefficient is altitude dependent with a constant value of
1 (3.5 day)

Background conditions of temperature and background water vapor
are certainly of overriding importance, controlling ice formation in the mesopause
region. In the following we will briefly summarize some of the main MIMAS results of
mean state and local time variation of the background. We show in
Fig.

Local time variation derived from daily data of temperature (K) for
two heights (km) at different latitudes for July 2009; see text for more
details. Mean: mean temperature over a daily cycle; Max.: maximum temperature
over a daily cycle; Min.: minimum temperature over a daily cycle; LT(Max.):
local time (LT) in hours of Max.; LT(Min.): local time (LT) in hours of Min.;

Another possibility to examine local time structures is to analyze
straightforward time series of a single day based on hourly data for
individual latitudinal and longitudinal grid points (“method 2”). We then
estimate from each daily data sample specific parameters of mean and
maximum/minimum values including corresponding times. Additionally,
sinusoidal fits are applied to this daily sample in order to calculate 24,
12, and 8 h tidal amplitudes and phases. This procedure is repeated for
every grid point, taking into account the difference in local time on various
longitudinal positions, and for every day during July. After averaging, we
finally get mean values of parameters that describe monthly local time
variations on the basis of local daily time series. Generally, method 1
generates smaller estimates of mean local time variations than method 2 since
local time parameters are determined from a highly smoothed state in method 1. Conversely, method 2 uses single-day time series and therefor also
records day-to-day variations of daily fluctuations which depend not only on
variable tidal wave activity but also on variable planetary and large-scale
gravity wave activity, e.g., as observed by

We begin with a short discussion of the general mean background state of
temperatures. Both averaging procedures from method 1
(Fig.

Figure

At PMC altitudes near 83 km diurnal tidal amplitudes are up to a factor of 2 stronger than semidiurnal amplitudes. This means that local variations of temperatures are mainly affected by diurnal tidal modes. At mesopause altitudes diurnal and semidiurnal amplitudes get larger and are of similar size.

Local time variation derived from daily data of

We also compared the phase structures as calculated by the two averaging
procedures from method 1 and 2, and find that phases of maximum and minimum
values as well as tidal phases remain almost unchanged. Interestingly,
temperature phases change with latitude at PMC altitudes. Particularly, the
local time of the daily minimum (Table

Besides temperatures, water vapor plays an essential role for PMC formation.
Figure

MIMAS results indicate that local time variations of water vapor in terms of
absolute values are much stronger than thermal local time variations. At
69

Generally, modeled PMCs in MIMAS exist approximately poleward of
54

It was found that for most of the time that supersaturation exists, the
saturation ratio only falls below

Hourly mean values of the saturation ratio (

Mean seasonal variations of PMC occurrence
frequency

During the northern hemispheric summer PMCs typically occur from end of May
until mid-August

Figure

In order to convert the model output from MIMAS to specific lidar
measurements, we apply spherical Mie-theory calculations to modeled ice
particle distributions while taking into account the laser wavelength
(532 nm) and scatter geometry (180

Figure

Figure

Figure

Mean local time variations of PMC occurrence
frequency

We summarize that the modeled seasonal distributions of occurrence, altitude, and brightness are fairly consistent with the ALOMAR RMR lidar observations, especially for July conditions. Therefore we will concentrate our discussion of model results in the following sections on this core period of the northern PMC season.

PMCs preferentially occur during morning hours which is attributed to thermal
tides of background temperatures in the mesopause region

Ratio of diurnal to semidiurnal amplitudes (

Figure

In order to investigate these different structures we calculated the ratios
of diurnal to semidiurnal tidal amplitudes (

In summary, observed local time variations of PMC occurrence and brightness at ALOMAR are fairly well reproduced by MIMAS.

Comparison of PMC brightness values between different instruments is affected
by observational constraints, e.g., viewing geometry, lighting conditions,
temporal overlap, and wavelength.

In Fig.

We summarize that the MIMAS model results of PMC ice water content are compatible to a high degree with the satellite observations.

Hourly median values of IWC from 2007–2013 (July) for
67–71

Figure

Hourly median values of IWC from 2007–2013 (July) for
67–71

In the previous sections we compared MIMAS simulations of backscatter and ice water content with observations in order to show that MIMAS provides realistic model results. Now we investigate in more detail the local time variations in different ice parameters as ice particle number density, ice particle radius, and ice mass density in comparison to backscatter.

Ice parameters at 67–71

Our model simulations of PMCs show that the number of ice particles is largest
at mesopause altitudes between 86 and 89 km, where the highest chance of
nucleation is found. This altitude region serves as a reservoir of small ice
particles. Then, slightly below mesopause altitudes, the MIMAS model predicts
the largest number density of ice particles to fall in the range 500 to 1500 cm

In Fig.

Mean ice radii vary between 35 and 45 nm. These numbers are in good
agreement with AIM–SOFIE observations, which also indicate ice radii of
35–40 nm

Investigating the local time dependence of ice parameters we find that the
ice number density maximizes in the morning hours between 03:00 and 05:00 LT, which
corresponds with the maxima of ice mass density and

In MIMAS local time dependencies in ice parameters are mainly forced by tidal
variations in background temperature and water vapor, as has been discussed
in Sect. 2.2. Local time dependence of brightness in terms of

Our numerical simulations indicate that the local time variations of PMCs are
subject to significant latitudinal dependencies. Figure

Median IWC values for July 2007–2013 as a function of latitude for different local times. No threshold has been applied, IWC values of zero (no PMCs) are included. The vertical bars represent the lower and upper quartile of the data.

Ratios of IWC tidal amplitudes for July 2009 and different latitude bands. No threshold has been applied, IWC values of zero (no PMCs) are included. The ratios of maximum to minimum IWC indicate the variability throughout the day. For details see text.

IWC median values at midlatitudes are much smaller (about 100 times) than
those at high latitudes. Therefore we also use the ratio of daily maximum to
minimum IWC values as an additional indicator for local time variations; see
Table

Diurnal variation of hourly median IWC values for July 2007–2013 for different latitude bands. No threshold has been applied, IWC values of zero (no PMCs) are included. Dots indicate the data and solid lines are harmonic fits using periods of 24, 12, and 8 h.

Climatology of local time variations of IWC in units of grams per
square kilometer (g km

Table

Now we investigate the local time structure of IWC and its latitudinal
dependence in terms of different IWC thresholds. In the following, IWC data
are not frequency weighted. Additionally we extend the time period to range
from 1979 to 2013, thereby presenting a 35-year climatology of daily
fluctuations which aims to describe mean local time variations. Such
specifications might be useful for satellite data analysis in order to
perform local time corrections. The results are shown in
Table

Maximum values of IWC occur in general during the early morning hours, whereas
minimum values are present in the afternoon hours. Local times of IWC maximum
and minimum are independent of the selected threshold. There exists a time
shift in latitudinal direction, e.g., at polar latitudes
74–82

Lidar observations of daily variations of mid-latitude NLCs (54

As shown in Sect. 2.2, phase positions of minimum temperature at PMC altitudes move to some extent during early morning hours backwards in time in the poleward direction. Also, the phase of the daily water vapor maximum tends to follow this time shift. We conclude that both temperature and water vapor phases cause the general early morning hour structure in IWC and its shift towards higher latitudes.

Generally, the time difference between IWC maximum and minimum is
approximately constant, with 12 h at all latitudes and for all three
thresholds. This indicates that a tidal decomposition of daily data reveals
the significant role of the diurnal tidal oscillation. Indeed, all daily time
series of IWC are approximated to a high degree by harmonic fits of a
dominant 24 h and a minor 12 h component, the ratio

We summarize that these results highlight the importance of taking tidal PMC
variations into account when compiling data sets which are distributed over
latitude and local time. It turns out that for IWC (1) local time variations
depend on threshold conditions, e.g., relative local time variations decrease
with larger thresholds; (2) local time variations depend on latitude, e.g.,
absolute local time variations increase towards the pole; and (3) a phase shift
exists towards the pole which is independent of the threshold value, e.g., the
IWC maximum moves backward in time from 08:00 LT at midlatitudes to 02:00 LT at
high latitudes. The IWC local time behavior presumably exhibits year-to-year
as well as long-term variability which may effect the 35-year mean state given
in Table

In this paper we presented a detailed investigation of tidal effects on PMC
occurrence, altitude, brightness, and microphysical properties of ice
particles as calculated by the MIMAS model. As already discussed in several
publications, the interpretation of PMC observations requires a careful
treatment of the local time of the observations even for the investigation of
long-term records

Our analysis shows that the local time dependence becomes the most evident when
concentrating on one single season. When limiting the analysis to the season
2009 we find that local time variations of temperature at 69

We calculated a climatology of IWC local time variations from a 35-year average
from 1979 to 2013 for different thresholds and latitude bands, which might be
useful for satellite data analysis in order to perform local time
corrections. Local time variations are found to depend on latitude and
threshold conditions. For the latitude band 64–74

It should be noted that gravity waves could mask the influence of tides, especially for the terdiurnal component. Gravity waves are partly included in the MIMAS model, but a detailed investigation regarding their effects on the tidal behavior of PMCs is beyond the scope of this paper. However, we expect that the latitudinal variations of tidal amplitudes are robust and will help in interpreting long-term observations with varying latitudes and fixed or variable local times.

The model data are available upon request from the
corresponding author, and ALOMAR lidar data are available upon request from
Jens Fiedler. The AIM community provided access to the SOFIE version 1.3
downloaded from

Francie Schmidt drafted the paper. All the authors reviewed the paper and interpreted the data. Uwe Berger conducted the LIMA and MIMAS modelling. Jens Fiedler had provided the lidar data from ALOMAR.

The authors declare that they have no conflict of interest.

This article is part of the special issue “Sources, propagation, dissipation and impact of gravity waves (ACP/AMT inter-journal SI)”. It is not associated with a conference.

We appreciate the financial support from the German BMBF for the ROMIC/TIMA project. This research was supported by the European Union's Horizon 2020 Research and Innovation program under grant agreement no. 653980. The European Centre for Medium-Range Weather Forecasts (ECMWF) is gratefully acknowledged for providing ERA-40 and operational analysis data. Edited by: Jörg Gumbel Reviewed by: two anonymous referees