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Vertical Structure of Ice Clouds and Vertical Air Motion from Vertically Pointing Cloud Radar Measurements
4.1 .property of Radar ParametersThefrequency distributions of z,vd,and SW were examined forthe classified ice clouds.Figure 4 shows the histograms o
4.1 .property of Radar Parameters
Thefrequency distributions of
z
,
vd
,and SW were examined forthe classified ice clouds.
Figure 4
shows the histograms of radar parameters by ice cloud type.Thebin size of the histogram was 2 dBz for
z
,0.2 m s
−1
for
vd
,and 0.02 m s
−1
forSW.Thefrequency was normalized with the total frequency of each type.The
z
of the anvil andstratiform were broadly distributed from −30 to 20 dBz,whereas that of cirrus had a narrow distribution of
z
from −30 to 5 dBz.The
z
distributions of the anvil andstratiform displayed similar features,but the
z
of the anvil was larger than that of stratiform.In addition,the second peak in anvil andstratiform coincided with the first peak in cirrus.Thevelocity distribution of cirrus was narrow with a peak of −0.6 m s
−1
that showed smaller absolute values than those of the peaks of the anvil andstratiform velocities (−1.2 m s
−1
).Although anvil had a larger
z
,it showed a smaller falling velocity (smaller negative values) than that of stratiform.Thepeak in SW distribution of cirrus was 0.04 m s
−1
,while that in stratiform was the largest at 0.14 m s
−1
.
To obtain detailed distributions of radar parameters by ice cloud type,the histograms were calculated in different intervals of cloud height (
Figure 5
).Thecirrus within a height of 10 to 12 km showed the highest frequency at −25 dBz for
z
,−0.6 m s
−1
for
vd
,and 0.03 m s
−1
forSW.This result was consistent with that of the work conducted by Ye et al.[
18
] since over 60% of cirrus cases were observed during the summer season (June to July).Theshape of
z
distribution in a cirrus that occurred at a height of 12 to 15 km was similar to that in cirrus at a height of 10 to 12 km.In contrast,the cirrus occurring at a height from 8 to 10 km had a right-skewed distribution with a peak at −7 dBz.In stratiform andanvil types,the highest frequencies occurred at a height range of 6 to 8 km,and the peaks of histograms moved to larger
z
andlarge negative (downward) velocity with decreasing heights,indicating the downward growth of precipitation.Themode of SW distributions systematically moved to larger values with a decrease in height (notably less in cirrus).This is likely an indication of the spread of particle size distribution toward the ground due to their steady growth as indicated by the change in
z
mode.
Figure 6
shows contoured frequency by altitude diagrams (CFAd) of
z
,
vd
,and SW forthe three ice cloud types.Cirrus typically occurred at a height range from 9 to 12 km.Thestratiform andanvil type clouds showed two modes at height ranges of 10–12 km (similar to cirrus) and5–9 km,respectively.This indicates the potential seeder–feeder effect in stratiform andanvil.Thesignificant growth of
z
and
vd
appeared in the layer from 8 to 10 km forall types of ice clouds.However,the
vd
of stratiform was nearly constant near a height of 7 to 8 km andseems to be an elongated “S” shape.In addition,SW rapidly increased in this layer due to the broadening of the power spectrum.Thus,this “S” shape of
vd
with an increase in
z
can be interpret as either ( 1 ) the existence of an upward air motion with induced turbulence or ( 2 ) broadening of snow particle size distribution due to an increase number concentration of small particle .
Themean vertical profiles of the radar parameters are shown in
figure 7
.The
z
slope is related to ice cloud growth.
z
in general increase with increase
vd
,and SW,indicating general growth of ice particles.Themean
z
forstratiform andanvil increased with a similar slope at the height range of 8 to 11 km,but the averaged
z
of the anvil was larger than the
z
of stratiform throughout the entire altitude.The
vd
profiles of cirrus andanvil were quite similar in the layer of 9–12 km andthen separated below the layer due to a rapid reduction in
z
in cirrus (that is,evaporation of ice particles).However,the falling velocity (negative
vd
) profiles of anvil were smaller than those of stratiform.In addition,the SW of the anvil was the largest due to the diverse size andvelocity of ice particles.This indicates that anvil is composed of a lower density andlarger sizes of ice particles than those of stratiform.One of the outstanding features in the averaged
vd
profile was the elongated “S” shape with reduced
vd
value in the layer of 7–8 km .It is is is notable that SW in stratiform andanvil dramatically increase at the 7–8 km height .
4.2.Estimation of Terminal velocity andvertical Air Motion
When a
vt
–
z
relationship was calculated by the various temporal average intervals,the coefficient
a
andexponent
b
changed depending on averaging time andice cloud types.In the cirrus case on 25 September 2014,the coefficient slightly decreased from 0.794 to 0.779 with an increase in the average time by up to 20 min andthen increased from 0.779 to 0.816 at an average time longer than 20 min (
Figure 8
).Theexponent increased from 0.104 to 0.138 with an average time of 5–60 min.In contrast,the coefficients decreased from 0.848 to 0.835 with an increase in average time forthe anvil case on 16 June 2014 (not shown).As the average time increased,smaller-scale variabilities were eliminated,and only mean characteristics remained.It was necessary to select the average time in which the coefficient andexponent representing the properties of ice clouds did not significantly change.Protat andWilliams [
20
] found that the error of estimated terminal fall velocity can be most reduced when the average time is set at 20 min.In addition,Matrosov et al.[
13
] anddelanoë et al.[
10
] propose that it is possible to approximate
vd
as the
vt
in this time average since
vair
can be neglected with an average of 20 min.Therefore,the average time forthe calculation of the
vt
–
z
relationship was set as 20 min.
The
vt
–
z
relationships were derived forall ice cloud cases (
figure 9
).Themean coefficient andmean exponent forcirrus (filled green dot) were 0.65 (0.29 to 1.5) and0.09 (−0.04 to 0.17),respectively.Thecirrus clouds had larger differences in
z
and
vt
depending on the height of the cloud echo andthe wide distribution of the values of coefficients andexponents.As cloud height decreased,the coefficient andexponent became larger (
figure 9
c,d).Although cirrus showed a wide variation of coefficients andexponents,the variation of
vt
in cirrus was relatively small with
z
varying (
figure 9
b ) .These results is were were similar to those of previous study on cirrus cloud [
20
,
26
] .accord to Kalesse et al .[
26
],the empirical relationship relates dominant microphysical processes in different parts of ice clouds,and exponent
b
can be explained in terms of moments of particle size distributions.In addition,they showed that a negative (or close to zero) exponent
b
near the cloud top indicates a rapid increase in number concentration (low moment) rather than reflectivity (high moment).This coefficient was the smallest in cirrus.
For stratiform cases,the coefficient
a
was from 0.95 to 1.37 (mean of 1.07) andthe exponent
b
was from 0.08 to 0.16 (mean of 0.12).Thecoefficients andexponents of anvil cases were from 0.63 to 0.90 andfrom 0.12 to 0.19,respectively.With the same
z
,the
vt
of stratiform was always high than the
vt
of the anvil.However,anvil had a larger
b
than that of the exponent of stratiform,indicating that the
vt
of anvil increased more rapidly than that of stratiform as
z
increased.This implies that the density of anvil increased more quickly than that of stratiform forthe same
z
increment [
31
,
32
].
vt
was calculated from the observed
z
using pre-determined
vt
–
z
relationships by ice cloud types,and
vair
was then estimated by comparing
vd
with derived
vt
.
figure 10
,
Figure 11
and
figure 12
show the time–height cross-section of observed
z
and
vd
as well as the estimated
vt
and
vair
.In the case of cirrus on 9 August 2015 (
figure 10
),
z
increased from −25 to 5 dBz and
vd
increased from 0 to −1.5 m s
−1
as the
vt
of ice particles increased.Interestingly,the vertical andtemporal structure of
vd
is much small than that of
z
and
vt
,which is due to the added smaller scale variation in vertical air motion.
According to Protat andWilliams [
20
],the
vt
–
z
relationship technique has a high level of accuracy,in which the residual between retrieved
vt
andreference
vt
is less than 0.1 m s
−1
above a height of 9 km.Given this error,the retrieval technique of
vair
in this study will contribute to understanding the microphysical anddynamical processes in the ice clouds.
vair
had an upward air motion up to 0.4 m s
−1
in the upper part of the cloud where
vd
was small andthe estimated
vt
range from −0.8 to −0.4 m s
−1
.However,
vair
in the lower part of the cloud appeared to be a downward air motion from −0.8 to 0 m s
−1
.Thebottom part of the cloud was repeatedly modulated by upward anddownward motions.
Thecase of stratiform on 5 July 2014 developed vertically to a height of 13 km (
Figure 11
).A dramatic growth appeared with an increase in
z
of about 8 db km
−1
andan increase in
vt
of about 0.3 m s
−1
km
−1
at the height of 10–13 km.Strong upward air motions (up to 1.5 m s
−1
) appeared in this layer.Strong
z
was prominent andvertically well developed at 1200–1330 UTC.This is related to a vertically stacked updraft with strong hot spots of
vair
in the top of the precipitation system.There exists a significant reduction in
vd
in the layer with a height of 7–8 km (−17–−15 °C) (
Figure 11
b).This is consistent with the mean vertical profiles of
vd
in
figure 7
b.This appeared as the layer of upward motion with some periodicity (
Figure 11
d).Similar characteristics appeared in different stratiform cases,leading to average statistical characteristics (shown below).
To investigate this unique feature in detail,we examined the doppler power spectra of vertically pointing X-band radar (vertiX,detail specification in [
18
]).When upward air motion appeared at a height of 7–8 km,the doppler spectra at a height of 7.5–7.7 km (layer near −15 °C) showed bi-modality with peaks at −1.0–−0.8 and−0.2–0.2 m s
−1
(
figure 12
).Thesecond peaks at a smaller fall velocity (smaller particles) became more pronounced from 1424 UTC to 1618 UTC on 5 July 2014.In addition,the
vd
(
z
) of the first peak decreased (increased) from 9.5 to 8.4km,indicating the growth of larger ice particles.Then,
vd
increased from a height of 8.4 to 7.3 km,where the second peak completely merged with the first peak.This increase was induced by the upward air motion.Furthermore,as shown by the second peak,numerous smaller ice particles of low
vt
were produced in this layer,grew,and merged afterward with existing larger ice particles.This layer had a temperature range of −16 °C to −13 °C,which was favorable forthe growth of pristine crystals to planar types [
33
,
34
,
35
,
36
].Thus,further investigation of the physical causes of upward motion andthe following microphysical processes with dual-polarimetric radar data andsnow habits from aircraft in situ measurements is recommended.
In the case of anvil on 16 July 2014,the
z
and
vd
increased with a decrease in height andshowed fall streaks of cloud particles (
Figure 13
).
vt
also showed a clear fall streak below 8 km.A rapid increase in
z
was observed in the layer of 7–8 km,which was consistent with the rapid decrease in
vd
at 1100–1300 UTC.The
vair
showed positive values (upward) in this layer andthe upper part of this system.After 13 UTC,the upward air motion appeared in the entire clouds,and the rapid growth started from the upper layers.
Thesame retrieval procedure of
vt
and
vair
forall cases (
Table 2
) was repeated,and the averaged
vd
,
vt
,and
vair
forall cases are shown in
figure 14
.In cirrus,average
vt
showed the smallest values (of −0.7 to −0.4 m s
−1
),although its
vd
was similar to that of the anvil,which is due to the slow growth of particles (
figure 7
a) anda smaller slope in the
vt
–
z
relationship (
figure 9
b).
vt
showed dramatic increases (from −0.5 to −1.1 m s
−1
) in anvil due to large value of
z
,as shown in
figure 7
a.The
vt
values of the stratiform were the largest (from −0.7 to −1.2 m s
−1
).Thesmallest mean upward air motion of less than 0.03 m s
−1
appeared in the top layer above 11 km in cirrus andthe downward motion was dominant below this layer.Theaverage
vair
of stratiform andanvil showed a similar trend: upward motion in the top layer,followed downward motion below,dramatic upward motion in the layer with a height of 7 km,and then downward motion below.In particular,the elongated “S” shape of the average
vair
was remarkable,with dramatic upward motion in the layer at around 7 km,particularly in the case of stratiform.
vair
was further examined via its CFAd,as shown in
Figure 15
.Stratiform andanvil showed the clear feature of an elongated “S” shape with a significant upward movement in the layer of 7 km.
vair
reach 0.5 m s
−1
forsome cases in this layer.Thephysical reasons forthis upward motion layer,which corresponds to about −15 °C,are yet to be determined.In addition,the quantile range of
vair
was the largest in the case of stratiform,indicating the existence of active dynamical processes.
4.3.variability of vertical Air Motion in a Case of Kelvin–Helmholtz (K–H) Wave on 18 June 2013
Theestimations of
vt
and
vair
were performed fora cloud case associated with a heavy precipitation system from 0400 to 0440 UTC on 18 June 2013 (
figure 16
).This system was associated with the stationary front,Changma front.Themelting layer of precipitation occurring at 4.5–5 km showed a rapid increase in
z
and
vd
.Above the melting layer,the large variability of
vd
occurred,in particular,a smaller scale structure in the layer of 5–6 km.Thepositive
vd
(warm colors andupward motion) also appeared in the layer of 6 to 7.5 km at 0432 UTC.As a result of estimations of
vt
and
vair
,
vt
gradually increased with a decrease in height,whereas
vair
appeared with large variability in time andheight.
Thethree major layers of upward motion were observed at around 10.5,9,and 7 km.Theupward motion was observed near the cloud echo top with a maximum of 0.5 m s−1 at 0418 UTC.After 0418 UTC,a large upward motion occurred in the layer of 6 to 8 km until 0437 UTC.Thealternating feature of downward andupward motions near 6 km was observed with high-resolution data (2 s data set),indicating K–H wave development associated with dynamical instability.A similar periodic motion was shown in the layer between 7.5 and9.5 km with a less pronounced andlonger period.
These upward motions were clear in CFAds of observed
z
andretrieved
vair
(
Figure 17
).As ice particles grew andfell,
z
rapidly increases from −20 to −2dBz at 7.5 km.While the
vair
of about 0.1 m s
−1
appeared at a height of 11 km,it gradually decreased until reaching a height of 8.5 km.When a significant increase in
z
from −2 to 5 dBz appeared in the layer from 7.5 to 7 km,a dramatic increase in
vair
up to about 1 m s
−1
was observed.This significant increase in
z
is relate to the rapid growth of hydrometeor due to the strong updraft .