Comparison of modeled color ratios with observations
For comparison with model results we use 30 000 lidar measurements of
color ratios observed in the period 1998 to 2014. In order to compare
a wide range of NLC simulations with non-spherical shapes to these
measurements, model simulations were conducted using background
conditions from 5 days in mid-July of 2009, i.e., 120 time steps. July 2009 was selected
for compatibility to previous simulations .
For the model data, 5 latitude bands from 67 to 72∘ N
were used, as well as 120 longitudinal bands (zonal model resolution is 3∘).
The first simulation is the reference run with only spherical particle
shape. Six model runs using very different distributions of
non-spherical particles are also used, namely all shapes from highly
elongated to very flat (0.1<ε<10), moderately flat
(1.1<ε<3.2), moderately elongated (0.32<ε<0.87), moderately elongated to flat (0.32<ε<3.2),
and moderately elongated to very flat (0.32<ε<5.6
and 0.32<ε<10). For all simulations with cylindrical
particles, the initial particle shape is distributed uniformly in
logε; for instance the simulation with (0.1<ε<10) includes the same number of particles with (0.1<ε<0.2) as (0.75<ε<1.5) or (3<ε<6). The shape distribution is discussed in more detail
later, in Fig. . All simulations used exactly
the same atmospheric conditions (e.g., temperature, H2O, wind).
For all these model simulations, all model grid volumes
in the latitude range around ALOMAR (69∘ N)
are evaluated, ≈ 1 million in the peak backscatter range.
Since large particles are easier to distinguish using CRs (Sect. ),
the lidar statistic used here is restricted to strong NLCs with
β532>13×10-10 m-1sr-1. An equivalent
restriction is used for the modeled NLC, which also removes the need for explicit
altitude filtering. From the resulting volumes containing a strong NLC (≈100 000
per simulation), a distribution of modeled NLC color ratios is computed for each of the
seven simulations.
Figure shows modeled color ratios from one of
these simulations. Color ratios observed by lidar also include
measurement uncertainties, which have to be simulated for the modeled
NLC in order to compare color ratios directly. This is done by
applying a Gaussian smoothing filter to the modeled CRs, with a filter
width determined by the lidar measurement uncertainties, i.e., 0.01
(IR / Vis) and 0.3 (UV / Vis),
respectively. Figure shows the effect of the
smoothing filter on the modeled color ratios for a simulation
containing both needle- and disc-shaped particles. The unedited
(modeled) CR distribution for β>13×10-10 m-1sr-1 covers a relatively narrow strip
within the parameter space of IR / Vis and UV / Vis combinations, which
roughly follows the line for spherical particles. For large particles
(low UV / Vis) it diverges from the spherical particle line and becomes
broader. As discussed in Sect. , the true CR distribution
is sharply delimited by the spherical particle line: for ice particles
smaller than ≈100 nm, this line constitutes a minimum
IR / Vis ratio using standard Mie theory.
Filled contours: modeled distribution of color ratios for one NLC
simulation with cylindrical particles, normalized to 100 % for the
most common CR combination. Contour lines: same distribution after applying
a Gaussian smoothing filter determined by the uncertainty of lidar-measured
color ratios. Black line: color ratios for spherical particles; numbers show
CRs for particular spherical particle radii. These are very similar but not
identical to the ε=1 cylinders in Fig. .
After applying the smoothing filter, the distribution becomes broader
and resembles a drop-like shape, lying partially in the forbidden
area to the left of the spherical particle curve. Because of the
wedge shape of the true distribution, the probability density maximum
(innermost, red isolines) is also shifted toward lower UV / Vis values.
In Fig. we compare modeled color ratios for strong NLCs
in the spherical particle reference simulation to the lidar
observations. The modeled distribution is drop-shaped like the one in
Fig. , but with a steeper incline and aligned
along the black curve for spherical particles.
The ALOMAR-measured color ratios also form a drop shape, but both its
alignment and the position of its mode (the probability density
distribution maximum) differ considerably from the spherical model
simulation. In particular, the simulated mode in UV / Vis is higher (by
0.9) and the one in IR / Vis is lower (by 0.015) compared to the
lidar. Also, the measured CRs include a long tail with IR / Vis ratios
reaching up to 0.24, which is not adequately reproduced by the
spherical particle simulation (max IR / Vis: 0.13). In conclusion,
using spherical ice particles produces color ratios which are not
compatible with observations.
Figure shows an extensive comparison of color ratios
between the lidar data and six different cylindrical particle simulations,
in the following referred to by their panel number in Fig. .
Each panel includes a mean square deviation χ2 to quantify
the degree of similarity between simulation and measurements:
χ2=1n∑i=1n(Xi-Xi^)2,
where Xi is the probability density of the modeled color ratios and
Xi^ that of the lidar-measured CRs in a given CR bin. Lower
values of χ2 indicate a better agreement.
Filled contours: measured multi-year statistic of color ratio
distribution observed by ALOMAR RMR lidar for strong NLCs (β>13×10-10 m-1sr-1). Contour lines: modeled CR distribution
for spherical particle simulation from 67 to 72∘ N with simulated
measurement error. χ2 refers to the difference between model and
measurements; see Fig. . All distributions are normalized to
100 % for their respective probability density maximum.
Filled contours, all panels: lidar CR statistic as in
Fig. . Contour lines: modeled color ratio distribution including
simulated measurement errors for six different cylindrical particle shape
distributions. All distributions are normalized to 100 % for their
respective maximum. χ2 values are calculated by averaging the squared
deviations between model and observation (in %) over the plot area,
0< UV / Vis < 6 and 0 < IR / Vis < 0.3.
The first simulation (a) represents a wide range of highly
non-spherical cylinders (0.1<ε<10). While this
reproduces the measured distribution's tail adequately, the mode of
the distribution is shifted towards higher IR / Vis to such an extent
that χ2 is even larger than for the spherical
run. Figure shows that highly elongated particles
around 60 nm leave a characteristic signature in color ratios,
in the form of strongly increased IR / Vis compared to spherical
particles, accompanied by relatively high UV / Vis values. The position
of the lidar-measured CR mode thus counter-indicates the presence of
such strongly needle-shaped ice particles to any great extent.
In the second model run (b), both disc- and needle-shaped particles
are limited to moderate axis ratios (0.32<ε<3.2). The
comparison to the lidar data is much better with very similar
distribution modes. The distribution tail is not reproduced very
accurately, although considerably better than for the spherical
reference run. This shape distribution is also consistent with satellite
measurements, with the SOFIE instrument indicating mean
axis ratios around 2. However, SOFIE is not able to distinguish
between needle- and disc-shaped particles with the same ratio of
longest to shortest axis. For this reason two additional simulations
were conducted, one with only flattened particles (1.1<ε<3.2) and another using only elongated cylinders (0.32<ε<0.87).
Neither of the simulations (c) and (d) are an improvement compared to (b).
In particular, the distribution tail is largely unchanged with
only a slight improvement for (d). For the needle-shaped cylinders (d), the distribution mode is shifted away from the measurements,
while the color ratios of the flattened particle simulation (c) are
stretched out along the UV / Vis axis more than the lidar data set. The
preliminary conclusion is that a combination of discs and needles is
needed to accurately replicate both the mode and the tail of the lidar-measured distribution.
The remaining question is how to improve on (b) (0.32<ε<3.2), primarily to get a better match for the distribution tail, like
in (a). The two simulations (e) and (f) include more flattened ice
particles while leaving the elongated part of the distribution
unchanged compared to (b). The simulation (e) (0.32<ε<5.6) shows even a slightly better match of the distribution modes than (b)
while achieving a good approximation of the distribution tail. On
the other hand, very highly flattened particles with ε up
to 10 (Fig. f) cause an exaggerated distribution tail and
a shifting of the mode at the same time. The reason for the good match
with (e) can be seen in Fig. : the relatively rare
very large disc-shaped particles >80 nm have much higher
IR / Vis ratios compared to spheres or needles, which causes the tail
and thus the drop shape of the color ratio distribution.
The analysis in Fig. is qualitative to some extent
because of its limited number of simulations, since the parameter
space of possible particle shape distributions is much larger
especially if non-uniform (e.g., Gaussian) distribution shapes are
considered. A robust result is that cylindrical particles with axis
ratios consistent with SOFIE are also consistent
with the ALOMAR lidar, that a mix of needle and disc shapes is
required and that a slight emphasis on discs produces the best match.
Effects on ice layers
Since particle shape affects NLC microphysics in addition to optical
cloud properties, the switch from spherical to cylindrical shape may
affect the ice cloud morphology. Those effects are studied in this
section, both in the average cloud morphology during mid-season and
in the size distribution during a single, bright NLC event.
Average NLC parameters north of 60∘ N during July of 2009,
from the reference simulation (spherical particles) and six sensitivity runs
with different distributions of cylindrical particles. Left panel:
backscatter coefficient (532 nm); right panel: ice mass density
(g km-3). No threshold is used; i.e., zero values are included in
the average.
In Fig. we compare observable parameters
of simulated NLC layers at 69∘ N over a time period of 1 month
(July of 2009). NLCs consisting of non-spherical particles are up to
50 % brighter than those in the spherical particle
simulation, resulting from both increased growth rates and reduced
sedimentation compared to spheres (see
Fig. ). The brightness of the various
non-spherical particle simulations are more similar: those favoring
discs tend toward higher brightness than simulations with primarily
needles, with differences in β of up to 30 %. This
disparity is caused by the stronger microphysical effects on
growth and sedimentation for disc shapes as compared to needles (Fig. ). The
ice mass density of NLCs in simulations with cylindrical particles is
also up to ≈30 % higher than in the spherical particle
run. As for the backscatter coefficient, the increase in ice mass is
larger for simulations with disc-shaped cylinders than for needle shapes.
The rather low values in average brightness and ice mass density result
from the lack of a threshold. As minor changes in the mass density make
some populations of clouds fall below the threshold in one simulation or
the other, omitting a threshold gives more accurate comparisons for the
different model runs.
Mean values for MIMAS NLC brightness north of 60∘ N using
different particle shape distributions.
Particle shape
βmax
βint
Δz
[10-10 m-1sr-1 ]
[10-7 sr-1]
[km]
Spherical
6.26
9.58
1.53
Cylindrical
0.1<ε<10
8.53
14.44
1.69
0.32<ε<3.2
8.20
13.01
1.59
1.1<ε<3.2
9.06
14.38
1.59
0.32<ε<0.87
7.41
11.67
1.57
0.32<ε<5.6
8.86
14.37
1.62
0.32<ε<10
9.46
16.21
1.71
The altitude of the NLC layer is much less affected by particle shape:
all distributions have their brightness maximum within 100 m
of each other, with the cylindrical particle simulations peaking at
marginally higher altitude than the spherical reference run. Another
parameter is the width of the mean ice layer, calculated as
Δz=βintβmax, where
βmax is the maximum brightness and
βint the column-integrated brightness at
532 nm e.g.,. It varies between
1.53 km for spherical particles and 1.71 km for the
distribution favoring highly flattened particles; see
Table . Generally, the layer width increases with
the axis ratios present in the shape distribution: the slower
sedimentation and faster growth of non-spherical particles (especially
disc-shaped) shifts the upper edge of the NLC region further up, while
lower NLC edge and maximum altitude are less affected.
The altered particle shape also affects the particle size distribution
and thus indirectly the backscatter signal in
Fig. . In Fig. we show the ice
particle size and number density for a single strong NLC around
69∘ N at one time step (16 July 2009, 24:00 UT). In
simulations with non-spherical ice particles, these grow ≈5–10 nm larger on average, depending on altitude and the
simulation in question. Among the non-spherical shapes, those with the
highest aspect ratios form the largest particles, and flattened
particles grow noticeably larger than elongated ones. The width of the
particle size distribution is also larger for non-spherical shapes in
general, with a strong increase in the presence of very large
particles (r>80 nm, not shown in Fig. ).
Simulated volume-equivalent radius and number density for a bright
NLC event within 135–150∘ E, 67–72∘ N on 16 July 2009 at
24:00 UT, with different shape distributions. Only particles
>15 nm are included in the average of size and number density.
Microphysical parameters for the same strong NLC as in
Fig. , compared between simulations with different particle
shape distributions. The altitude of maximum brightness used for
nmax, rmax and σ(rmax) is
82–83 km, and only particles larger than 15 nm are
considered for all parameters.
Particle shape
nmax
rmax
σ(rmax)
r‾
IWC
βmax
βint
[cm-3]
[nm]
[nm]
[nm]
[gkm-2]
[10-10 m-1sr-1]
[10-7 sr-1]
Spherical
151.3
57.6
11.5
31.7
266
63.7
67.3
Cylindrical
0.1<ε<10
122.4
64.2
14.2
35.0
328
59.5
73.3
0.32<ε<3.2
105.9
63.6
13.6
32.7
293
66.8
77.0
1.1<ε<3.2
99.8
67.4
13.6
32.9
305
73.8
90.5
0.32<ε<0.87
133.0
60.8
13.7
32.7
299
64.8
74.6
0.32<ε<5.6
98.3
66.4
14.5
33.4
309
65.1
81.9
0.32<ε<10
108.2
67.4
14.2
35.3
338
63.1
83.7
On the other hand, the number of ice particles in the main layer of
this strong NLC is generally lower for the non-spherical shapes
compared to the spherical shapes, by 20–35 %. As with
particle size, the largest differences in number density are seen for
simulations including highly flattened particles. The increased size
and decreased number density for non-spherical shape are linked to the
availability of water vapor. For all simulations, the same initial
H2O was used; this constrains the growth of NLC particles. The
increased relative importance of turbulent transport compared to the
(reduced) sedimentation rate results in a more effective
differentiation of the ice layer into those particles growing visible
(r>20 nm) and those staying at small size. For this reason, the larger particle
size due to improved growth conditions for cylindrical ice is
accompanied by a reduced number density in the NLC layer. Since the
backscatter signal depends on particle size as
r5 to r6, NLCs made of
non-spherical particles are brighter than those with spherical
particles in spite of the lower number density and reduced backscatter
coefficient of single particles with the same equivalent radius.
Shape distribution of simulations with non-spherical particles on
16 July 2009 at 24:00 UT; panels (a) to (f) are arranged
analogous to Fig. . Black lines are the initial
(logε) uniform distributions including all ice particles;
colored lines show shape distributions for particles larger than a given
threshold. For each radius threshold the distributions are individually
normalized to the most common particle shape, and mean ε values
(〈ε〉) are calculated using 1ε
for ε<1.
Table lists a number of additional microphysical
parameters for the case of a strong cloud as shown in
Fig. for the (spherical) reference run and the
various non-spherical particle simulations. The ice water content
(IWC), defined as the column mass density of particles in the ice
phase, shows a slight increase for cylindrical particle shapes, by
10–20 %. High axis ratio particles appear to increase IWC
more than only slightly non-spherical shapes. The small increase
supports the earlier statement that a limited supply of water vapor
results in larger particles but reduced number density during
strong growth conditions, i.e., when temperatures are low enough that a
high fraction of the water vapor within the growth region is depleted by
particle growth.
IWC values for this event are generally high compared to satellite measurements
, due to the choice of a very
bright NLC. From Table we see that the increase in
backscatter signal for cylindrical particles is considerably weaker
for this bright NLC example than for the statistic in
Table . Only βint is consistently
larger, similar to the results when analyzing all NLCs. As for the
statistic in Table , flattened particles lead to
brighter ice clouds, by 15–25 % compared to the spherical simulation.
Finally, Fig. shows the development of ice particles
within the six simulations with cylindrical ice particles. When
counting all particles, the uniform initial distribution shapes
(see Sect. ) within the
respective ε limits are evident in all panels; minor
deviations are due to statistical variability caused by the random-number
generator. However, when counting only particles larger than
specific radius thresholds, the resulting distributions are no longer
uniform but constitute a U shape: strongly non-spherical particles
are considerably more common than those with ε close to 1
if only large particles are considered. For the simulation (a) with
(0.1<ε<10), highly flattened particles
(ε=10) are around 70 % more common than
ε=1 particles, if the radius threshold is set at
5 nm. ε=10 is 3 times more common than
ε=1 for particles with r>10 nm and nearly 6
times more common for r>20 nm. This imbalance is smaller
but still distinct for elongated or more moderately flattened
cylinders. It also appears to be largest for size thresholds around
20 nm, since the imbalance is slightly smaller for a threshold
of 40 nm (visible NLC particles).
These differences in Fig. are much larger
than those between simulations in
Figs. and : with their larger
surface-to-volume ratio, strongly non-spherical particles outperform
low ε particles in growing to large size in a common
volume. This is observed both for elongated and flattened
high-ε particles but is most pronounced for the flattened
(disc-shaped) case. The prevalence of high axis ratios among
large particles is most likely due to the increased growth rates, with
the reduced fall speed contributing slightly at most. Otherwise we would
expect the center of the U shape shifted to elongated particles, like
for the correction factor Φsedi; see Fig. .
Shape inhomogeneities in the general particle distribution tend to get
amplified within the NLC layer: Fig. includes the average
axis ratio 〈ε〉 for each radius threshold,
calculated using 1ε for ε<1.
〈ε〉 is shifted to higher values when only large
(r>20 nm) particles are considered, by ≈0.1 in
simulations (b), (c), and (d) and by 1.2 and 1.4 in simulations
(a) (0.1<ε<10) and (f) (0.32<ε<10),
respectively. This helps to explain the large effects on the optical
NLC properties in Sect. seen for simulations including highly
aspheric particles. For simulation (e) (0.32<ε<5.6),
where we find the best agreement to the ALOMAR lidar, the
〈ε〉 value of 2.8 for r>20 nm is more suitable
for comparing mean axis ratios to SOFIE satellite measurements than
the lower value of 2.4 for the initial distribution since the backscatter
signal is caused by large ice particles. Our analysis thus yields
a somewhat higher estimate for mean axis ratio than the value of 2.0
by .