We have identified a region of an ice cloud where a sharp transition of
dual-wavelength ratio occurs at a fixed height for longer than 20 min. In
this paper we provide evidence that rapid aggregation of ice particles
occurred in this region, creating large particles. This evidence comes from
triple-wavelength Doppler spectrum radar data that were fortuitously being
collected. Through quantitative comparison of the Doppler spectra from the
three radars we are able to estimate the ice particle size distribution (of
particles larger than 0.75 mm) at different heights in the cloud. This
allows us to investigate the evolution of the ice particle size distribution
and determine whether the evolution is consistent with aggregation, riming or
vapour deposition. The newly developed method allows us to isolate the signal
from the larger (non-Rayleigh scattering) particles in the distribution.
Therefore, a particle size distribution retrieval is possible in areas of the
cloud where the dual-wavelength ratio method would fail because the bulk
dual-wavelength ratio value is too close to zero.
The ice particles grow rapidly from a maximum size of 0.75 to 5 mm while
falling less than 500 m in under 10 min. This rapid growth is shown to
agree well with theoretical estimates of aggregation, with aggregation
efficiency being approximately 0.7, and is inconsistent with other growth
processes, e.g. growth by vapour deposition or riming. The aggregation occurs
in the middle of the cloud and is not present throughout the entire lifetime
of the cloud. However, the layer of rapid aggregation is very well defined
at a constant height, where the temperature is -15∘C and lasts
for at least 20 min (approximate horizontal distance: 24 km). Immediately
above this layer, the radar Doppler spectrum is bi-modal, which signals the
formation of new small ice particles at that height. We suggest that these
newly formed particles, at approximately -15∘C, grow dendritic
arms, enabling them to easily interlock and accelerate the aggregation
process. The large estimated aggregation efficiency in this cloud is
consistent with recent laboratory studies for dendrites at this temperature.
Introduction
Ice microphysical processes are an important part of cloud and precipitation
formation; most surface precipitation begins as ice particles
. However, numerical models, of either weather or climate,
have difficulty in accurately simulating ice cloud. For example, the CMIP5
models have regional cloud ice water paths that differ from observations by
factors of 2–10 . This challenge is partly because
observations of ice particles are sparse and because processes controlling
the formation and evolution of ice particles, such as aggregation, are poorly
understood and crudely parameterized in most models.
Additionally, measuring the number and size of ice particles within clouds is
challenging. The two main methods, in situ aircraft observations and active
remote sensing observations, both have their deficiencies. First, active
remote sensing instruments, such as the radar and lidar, are good at measuring
the bulk scattering quantities, such as radar reflectivity. However,
converting these bulk quantities to cloud microphysical properties requires
numerous assumptions (e.g. the shape of individual hydrometeors and the particle
size distribution). In contrast, aircraft observations measure the size and
number of ice particles directly, but only within a small sample volume, at a
single height at any given time and during sporadic case studies.
Furthermore, ice particle size distributions have been shown to be biased as
a result of shattering of ice particles on aircraft-mounted instrument inlets
, which results in an artificially
increased concentration of small ice crystals.
Nevertheless, cloud microphysical observations and in particular particle
size distributions are important for many applications. One important
application is the better understanding of processes that occur within
clouds. For example, size distributions measured from aircraft have been used
to study aggregation in cirrus clouds . Furthermore, the
size distribution itself affects the relative importance of vapour deposition,
riming and aggregation for ice particle growth. Vapour deposition and
evaporation rates are proportional to the first moment of particle size
distribution, while riming is related to higher moments (product of projected
area and fall speed), and aggregation rates depend on the breadth of the
particle size distribution through the difference in fall speeds. Thus the
shape and breadth of the particle size distribution are an important control
on the relative importance of the processes involved. Another important
application is to provide observations with which numerical models can be
evaluated and their parameterizations can be improved.
In this paper, we report radar observations of one cloud system, where
large vertical gradients in cloud microphysical properties were observed at a
fixed height for at least 20 min. By exploring the radar data beyond the
standard bulk quantities and exploiting observations from multiple radars
together with their Doppler spectra, we are able to estimate the size
distribution of particles at different heights and therefore diagnose the
most likely process for the rapid but consistent changes in cloud properties
with height. The changes of cloud microphysical properties with height
apparently result from rapid aggregation of ice particles. These observations
were made using three co-located, vertically pointing radars at different
frequencies (3, 35 and 94 GHz).
Analysis of the radar Doppler spectra has previously been performed for the
onset of drizzle in stratiform clouds , and
the application of multi-frequency Doppler spectra has been used to determine
the rain size distribution . For the ice phase,
the three different frequencies have been used simultaneously to categorize
rimed and unrimed particles from the surface
and from aircraft-based radar
observations
.
However, this is the first attempt to retrieve the ice particle size
distributions from multi-frequency Doppler spectrum observations. These
retrievals are then used to evaluate the microphysical processes active
within the clouds.
The aggregation process can be characterized by the aggregation kernel kEq. 9:
k=π4EaggD1+D22|v(D1)-v(D2)|,
where D1 and D2 are the diameters of the two potentially aggregating
particles and v(D) is the fall velocity of the particle. The aggregation
efficiency of ice particles (Eagg; the probability that two
particles experiencing a “close approach” will collide and stick together)
is typically low, although a large range of values has been reported and
understanding of how aggregation efficiency varies with environmental
parameters is still sparse. Eagg has previously been found to
depend on both the particle habit and the temperature at which the collisions
occur; however, a large range of values has been reported. An increase in
the aggregation efficiency at about -15∘C has been reported in
several laboratory studies. One such study , where small
particles were drawn past a large stationary ice target, showed a weak
temperature dependence of Eagg, with a broad peak around
-12∘C and maximum values of 0.1–0.2.
used a 10 m tall cloud chamber containing large concentrations of small ice
particles settling under gravity and reported a much sharper peak of
Eagg around -15∘C, with values of 0.4–0.9, but
the best estimate at other temperatures was below 0.2.
found aggregation efficiencies for planar snow
crystals drawn past a cylindrical target of 0.3–0.85 depending on the
particle size. reported that both the maximum dimension of
ice aggregates and the probability of seeing aggregates increased at around
-15∘C, which was linked to the preferred formation of dendritic
particles at this temperature. This is supported by other studies showing a
larger Eagg in the presence of dendritic particles.
found an Eagg of around 0.55 for clouds
dominated by dendrites at the cloud top but much lower values around 0.07 when
dendrites were not present. Low Eagg values of 0.09 were also
found for tropical anvil clouds where dendritic particles were not present at
temperatures of -3 to -11∘C . In the early
stage of aggregation, reported that the aggregates were
made up of a small number of dendritic particles. These studies seem to
suggest that dendrites, which typically form at around -15∘C, can
significantly increase the aggregation efficiency because the dendritic
branches interlock with other particles, whereas the aggregation efficiency
is much lower when dendritic particles are not present. In this study,
retrievals from radar observations will be used to estimate the aggregation
efficiency and will be compared with the laboratory-derived values.
showed that the assumed particle size distribution is
the single-largest sensitivity in the model physics for mixed-phase
altocumulus clouds. The importance of correctly simulating the ice particle
size distribution has been shown in several other studies
.
Therefore understanding and correctly implementing the aggregation process in
numerical models of cloud physics is important for the overall development of
the cloud system.
This paper is organized with an overview of the instruments and data in
Sect. 2, an overview of the case study in Sect. 3, and details about the
retrieval in Sect. 4. Section 5 details the cloud properties retrieved and
their uncertainties, and Sect. 6 summarizes the evidence for aggregation, with
conclusions drawn in Sect. 7.
Data and methods
We use data from three co-located radars at the Chilbolton Observatory in
Hampshire, southern England, on the afternoon of 17 April 2014. The radars
operate at frequencies of 3 GHz 9.75 cm wavelength, 25 m antenna,
0.28∘ beamwidth;, 35 GHz 8.58 mm
wavelength, 2.4 m antenna, 0.25∘ beamwidth; and
94 GHz 3.19 mm wavelength, 0.46 m antenna, 0.5∘
beamwidth;. The 35 and 94 GHz cloud radars are situated
immediately next to one another, whereas the 3 GHz radar is sited less than
50 m away (Fig. ). The sampling of the three radars was
synchronized to within 0.1 s, and full pulse-to-pulse power and phase
measurements were recorded. For the 3 GHz radar, Doppler spectra were
calculated every second and incoherently averaged over 10 s. For the 35 and
94 GHz cloud radars, spectra were calculated every 0.11 and 0.08 s
respectively and again incoherently averaged over 10 s. Assuming typical
wind speeds of 20 m s-1 aloft, the averaged spectra correspond to a
200 m section of cloud. Ground clutter was removed from the spectra by
masking returns with velocity being near zero. Noise levels were estimated from
measurements beyond the range of meteorological echoes (>10 km) and
subtracted from the individual spectra prior to averaging. The data from each
radar were interpolated onto a common range and velocity grids (60 m range by
0.0195 m s-1 velocity).
Dual-wavelength ratios as a function of
ice particle diameter for the three pairs of radar frequencies used in this
study. Dual-wavelength ratios from the
scattering model are shown with solid
lines. For comparison, mean dual-wavelength ratios of unrimed aggregates
within 250 µm wide diameter bins from are
shown by points for four different aggregate-monomer types.
A photograph of the three co-located radars at the Chilbolton
Observatory, Hampshire, England. From left to right: the 3 GHz CAMRa radar,
94 GHz radar and 35 GHz radar.
Because of the large antenna, it is necessary to apply a near-field
correction to the 3 GHz data at heights below about 6 km
. This correction factor was derived empirically by
comparing 3 GHz reflectivity profiles against those measured by the 35 GHz
instrument (which has a much smaller antenna) in a number of Rayleigh-scattering ice clouds. The magnitude of the correction was 1 dB at 5 km,
rising to 3 dB at 3 km.
A summary of the terminology used throughout this paper, where “F”
denotes the radar frequency.
SymbolVariable nameVariable definitionUnitZFRadar reflectivityTotal radar cross-sectional area of scatterers within the target volumedBZ (Z= mm6 m-3)DWRF1/F2Dual-wavelength ratioZF1–ZF2dBsZFSpectral reflectivityRadar reflectivity per Doppler spectrum velocity bindBX (X=mm6m-3(ms-1)-1)sDWRF1/F2Spectral dual-wavelength ratiosZF1–sZF2dBData quality, calibration and attenuation correction
To account for potentially imperfect calibration and attenuation by
atmospheric gases and liquid water in the lower troposphere, the 35 and
94 GHz reflectivity is corrected relative to a 3 GHz radar. The 3 GHz radar
is absolutely calibrated to within 0.5 dB, using the method of
. The radar reflectivity value from the cloud radars (35
and 94 GHz) was adjusted to match the 3 GHz radar reflectivity in each
profile so as to remove any calibration or attenuation offsets. The
adjustment amount was estimated in regions where Rayleigh scattering was
expected at all three wavelengths
Based on an analysis of
reflectivity differences, Rayleigh scattering is assumed where the 3 GHz
reflectivity is below 5 dBZ, and the absolute difference between the 3 and
94 GHz velocity measurements is less than 0.025 m s-1. Measurements
were also excluded where the 3 GHz reflectivity was less than -10 dBZ to
avoid effects of residual ground clutter.
and hence where the reflectivity
should be the same from each radar. The adjustments reduce the median
difference in reflectivity (Z) in the Rayleigh-scattering areas to 0 dB.
The same adjustment to Z (in dB) is made throughout the profile. A
different correction is applied individually to each 10 s profile; the
equivalent dB correction is also applied to the Doppler spectrum power within
each profile. This adjustment works well because the majority of the
attenuation by atmospheric gases and liquid water occurs below the cloud base. In
other cases, where the cloud base is lower or with embedded liquid water layers,
a different treatment would be necessary.
The multi-wavelength approach allows us to measure the diameter of ice
particles that are comparable in size to the shortest radar wavelength or
larger e.g.. For ice particles comparable
in size to the radar wavelength, non-Rayleigh scattering becomes important.
For suitably large particles, it becomes possible to size the particles based
on the different radar returns at different wavelengths.
In contrast to the bulk retrieval that makes a single retrieval for particles
of all fall velocities together, the Doppler spectrum approach allows for
retrievals of particle size and number concentration to be made separately on
particles of distinct fall velocities. We can use the multi-wavelength
approach to determine the representative particle size from the “spectral
dual-wavelength ratio” (sDWR; i.e. the difference in reflectivity of
particles within a small range of fall velocities; see Table for
a full summary of radar quantities used in the paper) but can additionally
separate the particles based on their fall velocity, allowing us to retrieve
the ice particle size distribution.
A correction to the velocities measured by the radar is also applied.
Unfortunately, the three radars were not pointing precisely vertically for this case (as determined by
biases in the mean Doppler velocity in the Rayleigh-scattering part of the
cloud), and initial testing suggested that there was a large sensitivity to
the velocity offsets in the spectra (see Sect. ). The
3 GHz radar was pointing vertically, but after analysing the data, the 35
and 94 GHz radars were determined to be off zenith by approximately 0.2 and
0.15∘ respectively in opposing directions. These offsets were
determined by assessing the mean Doppler-velocity differences between the
three radars as a function of height. The correlation of these velocity
differences with the atmospheric wind profile (determined from ECMWF forecast
fields) enabled an estimation of the pointing angle errors.
The mispointing of the radars is small and likely does not result in a
substantial mismatch in sample volume given the 10 s integration time.
However, this small mispointing means that the radar detects a small
component of the horizontal wind in addition to the fall velocities of the
ice particles. Although the pointing angle error is small, the horizontal
wind component detected is of the order of a few centimetres per second,
which is large enough to affect our comparison of the Doppler spectra
from the three radars. Therefore, we have made a correction to the velocity
measurements for the 35 and 94 GHz radars to ensure that the spectra are
well aligned and can be compared. This correction is important because even a
small shift in velocity can substantially affect the estimates of sDWR. In
practice, the correction applied is +0.0585 m s-1 (three velocity bins)
for the 35 GHz radar and -0.0390 m s-1 (two velocity bins) for the
94 GHz radar throughout the cloud layer. This correction is imperfect;
however, we do not have independent measurements of the horizontal wind speed
with sufficient accuracy and a high enough vertical resolution to make a
reliable height-dependent correction or indeed any direct measurement of the
mispointing. Radiosonde data and the ECMWF model output show that the horizontal
wind speed was near-constant with height throughout the cloud layer on this
day, and inspection of many individual Doppler spectra indicates that our
simple correction aligns to the spectra very well in this case.
To reduce the noise in the spectra, each individual spectrum has been
smoothed in velocity space by averaging over a 0.0585 m s-1 window,
which equates to three velocity bins. We mask out regions where significant
turbulence is present because the vertical air motions are large and vary on
small timescales and space scales compared to the particle fall velocities that we
are trying to measure. Near the cloud base, there is a layer of substantial
turbulence caused by sublimation of ice particles as they fall into
subsaturated air, and this leads to destabilization of the atmosphere in this
layer. In this turbulent layer, the implicit assumption that measurements at
a specific velocity are of a single particle size is invalid. Hence, we
identify regions where turbulence alters the spectra by calculating the
contribution of turbulence to spectral width using
Eqs. 10–15. Points where the velocity variance from
turbulence exceed a threshold value of 10-3 m2 s-2 are not
considered when performing our retrievals. This threshold value was chosen
such that all affected regions were suitably masked and, in the remaining
data, that the width of the Doppler spectrum was determined by microphysical rather
than turbulent contributions. Additionally, any points in the spectra that
are 20 dB down from the peak of the spectra are removed in order to minimize
the impact of noise.
The case – 17 April 2014
Figure a shows the radar reflectivity measured at Chilbolton for
the thick stratiform ice cloud observed on 17 April 2014. This cloud formed
in north-westerly flow, ahead of a cold front. The surface cold front reached
Chilbolton at about 18:00 UTC. The front was not associated with any surface
precipitation at Chilbolton and only very light precipitation across some
other parts of southern England.
The evolution of the cloud reflectivity and the ratio of 35 and 94 GHz
reflectivity are shown in Fig. . The cloud top height was
approximately 9 km, where 35 GHz reflectivity values are around -15 dBZ
and increase to 19 dB at approximately 4 km altitude near the cloud base. The
temperature at the cloud top was -45∘C, and the freezing level was at
about 2.7 km. Throughout most of the cloud the DWR values are below 1 dB.
However, at around 4 km altitude there is a rapid increase in DWR with
decreasing height, which indicates an increase in particle size such that the
backscattered return at 94 GHz is no longer from Rayleigh scattering. The
region of these large DWR values is consistent in height (onset at 4.5 km
altitude; Fig. c) and is evident for at least 35 min. The
largest DWR values occur at around 16:15 UTC, with peak values reaching
7 dB. The profile of DWR values at 16:15 UTC is shown in Fig. c.
Radar data from a larger portion of the same cloud were analysed in
. Earlier in the day (before 15:40 UTC), the cloud did not
show this sharp transition to high DWR values around 4.5 km.
also used the triple-frequency radar data to determine that
the cloud contained primarily aggregate snowflakes, consistent with the
scattering model (lines in
Fig. ). Scattering properties of unrimed aggregates
from are also consistent with observations and give
very similar characteristics to the
scattering model (points in Fig. ). We focus on the
time from 15:45 to 16:20 UTC, where there are dual-wavelength ratios of up to
8 dB below 4.5 km (Fig. b and c).
Overview of the cloud structure on 17 April 2014 showing the
(a) 35 GHz radar reflectivity and (b) the ratio of 35 GHz
reflectivity to 94 GHz reflectivity throughout the sampling period.
(c) The vertical profile of DWR at 16:15 UTC.
We attempt to understand what causes the rapid change in cloud properties
during this period of substantial DWR35/94 and the rapid change in
height. Looking at the spectral reflectivity at each height (sZ35;
Fig. a) together with the spectral dual-wavelength ratio
(sDWR35/94; Fig. b) reveals the changes of the cloud
properties with altitude. From these data, the origin of the large changes in
the sharp transition can be identified. At 5.4 km, there is an increase in
the signal coming from slow-falling particles (0.4–0.6 m s-1;
Fig. a). At this height, only the fastest-falling particles
have sDWR35/94>1 dB. At 4.5 km, the reflectivity and spectral
reflectivity of the slow-falling particles have increased. The
sDWR35/94 increases up to 8 dB for the fastest-falling particles, and
by 4 km the increase in sDWR35/94 is seen for the majority of
particles. Interestingly, the fall velocity of these particles does not
increase as the particles grow larger and produce large sDWR35/94
values.
Height profile of (a) spectral reflectivity at 35 GHz
(sZ35) and (b) spectral dual-wavelength ratio
(sDWR35/94) recorded at 16:15 UTC. Temperatures from the ECMWF model
at 16:00 UTC are shown every 1 km and at 5.3 km, where the small-particle
mode is first evident.
Illustration of the retrieval method and the retrieved size
distribution at three heights at 16:15 UTC. (a)–(c) are
just above the layer of secondary ice nucleation,
(d)–(f) are within that layer and
(g)–(i) are below this layer, where the dual-wavelength
differences are largest. (a), (d) and (g) show
the 3, 35 and 94 GHz spectra at that height. (b), (e) and
(h) show the distribution of sDWR35/94 data points within a
window around the central time (90 s by 300 m), with the black line
denoting the median power difference for each velocity bin. (c),
(f) and (i) show the retrieved ice particle size
distribution, with the colour of the line relating to the velocity of the data
used to determine that data point. The grey shaded region marks particle
diameters smaller than 0.75 mm, where there is no reliable information
available to size the ice particles. The higher altitude plots are from
earlier times to account for an approximately 1 m s-1 fall velocity of
the ice particles.
Retrieval of the ice particle size distribution
To retrieve the ice particle size distribution from the cross-calibrated and
velocity-matched Doppler spectra (see Sect. ) at three
wavelengths, we use the method described below. The method is illustrated at
three separate heights in Fig. . The following is
calculated for each individual velocity bin, within each radar range gate and
at all times:
Calculate the spectral dual-wavelength ratio (sDWR=sZ35-sZ94).
This is simply calculated as the difference between the spectral reflectivity
(sZ) at 35 and 94 GHz (Fig. a, d and g).
Determine the particle diameter D from sDWR. The relationship between
particle diameter and particle DWR from the
scattering model
(Fig. ) is used to convert the sDWR value to
particle diameter. We use this scattering model based on its good agreement
with observational data for this case ; other scattering
models may be more appropriate for different cases.
Calculate the mass m of an ice particle with diameter D, assuming the
mass–size relationship of m=0.0185D1.9 for all
ice particles. Use of this mass–diameter relationship is supported by
, who found that the fractal dimension of snowflakes on this
day was 1.9, and hence the exponent of 1.9 is appropriate; other
mass–diameter relationships may be more appropriate for different cases.
Determine the radar reflectivity of a single ice particle with diameter D and mass
m using the scattering model.
Determine the total number of particles within the velocity bin. This is calculated by
dividing the total spectral reflectivity sZ by the single-particle reflectivity calculated in the previous step.
The size and number of ice particles within the velocity bin is now known.
The particle size distribution can be estimated by performing this same
process for each velocity bin.
Up to this point, we have determined the diameter D of the ice particles
within each velocity bin and also the particle size distribution
dN/dV (where dN is the concentration of ice
particles with velocity between V and V+dV). We can convert
dN/dV to the ice particle size distribution
dN/dD (concentration of ice particles with diameter between
D and D+dD). This is the common way to express a particle size
distribution that is independent of the measuring sample interval
(dD or dV). To do so, we need to know the relationship
between the velocity bin width dV and the diameter bin width
dD. To determine this, we use a 300 m by 90 s window (five range
gates by nine individual averaged spectra) centred on the current radar pixel
and compute the power-law fit to the measured Doppler velocity and retrieved
diameter values, of the form V=cDd. A power-law relationship is used
because it is both easily differentiable and common in microphysical scaling
relationships e.g.. We use the differential of this
power-law fit to compute dVdD – the diameter bin
width for each velocity bin. The size distribution is then calculated as
dNdD=dNdVdVdD.
There is a relatively large sensitivity of the retrieved size distribution to
the power-law fit, but this is primarily in terms of the number
concentration rather than the diameter of the particles or the shape of the
size distribution (see Sect. for a complete sensitivity
analysis).
Retrieval of the size and number concentration of ice particles is only
possible for particles larger than about 0.75 mm in diameter (corresponding
to a sDWR35/94 of about 1 dB; Fig. ). For
smaller particles, sZ is very similar at all three radar frequencies, and
differences are not easily distinguished from noise in the spectra. For
particles larger than about 3 mm in diameter, the sDWR35/94 saturates
at about 8–9 dB (Fig. ) as a result of the fractal
geometry of the aggregates see, and therefore retrieval
of particle diameter from sDWR35/94 is no longer possible. Therefore,
where sDWR35/94 is larger than 6 dB, the diameter and number
concentration are retrieved using sDWR3/35 instead, following the same
method as above. This pair of frequencies does not saturate until
significantly larger particle diameters and therefore, for larger particles,
have a larger sensitivity to change in diameter than for the 35/94 GHz pair.
We do not use the 3/35 GHz pair for the full range of particle diameters
because the 3 GHz is affected more by noise than the 35 GHz spectra and
therefore negatively impacts the retrieval of particle sizes when the DWR is
small. It would be equally valid to calculate the size and number
concentration of the larger particles using the 3 / 94 GHz pair instead,
and this indeed enables a consistency check that the retrieval works well and
that the input Doppler spectra are well matched.
Retrieved cloud properties and validation
Throughout most of the cloud, the 35/94 GHz dual-wavelength ratio
(DWR35/94) is near zero (<1 dB; Fig. b), implying that
the ice particles are relatively small and are still in the Rayleigh-scattering regime at 94 GHz (maximum diameter 0.75 mm). DWR only exceeds
2 dB after 15:45 UTC and between 4.3 km and the cloud base.
From 16:00 to 16:20 UTC, there is a sharp transition from
DWR35/94<1 dB at 4.5 km to peak DWR35/94 values at 4 km, with
the maximum DWR35/94=8 dB. The altitude of this sharp transition is
consistent after 16:02 UTC, with the largest DWR35/94 values being
present after 16:10 UTC. There is also evidence of this transition layer as
early as 15:45 UTC.
More detail can be seen by examining the Doppler spectra for the different
radars at a few fixed heights in detail. The Doppler spectra measured at
5.89, 4.81 and 4.15 km (Fig. a, d and g) show three spectra
with rather different shapes. At 4.15 km, the spectra have only a single
mode,
but throughout most of the velocity range, sZ35 is much greater than
sZ94. The sDWR35/94 reaches 8 dB (Fig. h), and
the largest particles are sized at around 5 mm. The retrieved size
distribution is approximately inverse exponential (Fig. i).
At 5.89 km (Fig. 5a–c), in contrast, the spectra
for all three radars are very similar with a single peak; all
sDWR35/94 values are below 1 dB (Fig. b). The small
sDWR35/94 values mean that it is not possible to reliably size the ice
particles here, other than to say that they are all smaller than 0.75 mm.
About 1 km lower in the cloud, at 4.81 km (Fig. d–f), the mean velocity and reflectivity have both
increased, but there is also a bi-modal structure to the spectra captured at
both frequencies. This second mode is related to newly formed, small ice
particles that are falling slower than the majority of older, larger ice
particles. Furthermore, at 4.81 km, there are larger and faster-falling
particles present than at 5.89 km. The largest sDWR35/94 values now
approach 4 dB (Fig. e), and particles larger than 0.75 mm
are present, with the largest retrieved diameter of 1.2 mm. The size
distribution (Fig. f) of the reliably sized particles
(those larger than 0.75 mm and outside the grey region of the plot) is
inverse exponential.
The consistent and narrow range of heights over which this rapid change in
size occurs is just below the region where new particles are seen around
5.4 km and the Doppler spectra are bi-modal (Fig. d). These
new particles fall slowly, which suggests that they are small and are formed
at this level. These particles begin to fall faster as they grow in size.
Particles forming around -15∘C would initially grow as dendrites
. As these particles grow, the sDWR35/94 starts
to increase for the larger (faster falling) particles, which we take to be
aggregates. This increase in sDWR35/94 implies an acceleration of the
aggregation process at this height.
The reduction of the size distribution slope between 4.81 and 4.15 km
remains consistent for at least 30 min from 15:45 UTC onwards but is not
present earlier in the cloud. The observations shown in
Fig. are similar throughout this time period, which
explains the sharp increase in DWR of between 4.8 and 4.1 km (Fig. )
during this time period.
Evolution and validation of retrieved size distributions
To evaluate how accurate the retrieved ice particle size distributions are,
we would ideally like to compare them against in situ data. However, in situ
observations are not available for this case. Therefore, we evaluate the
retrievals against other retrieval methods.
Time–height plots of Λ, the slope of the ice particle size
distribution derived from the (a) multi-wavelength Doppler spectrum
method and (b) the dual-wavelength ratio (DWR) method. The grey
regions mark areas of the cloud where no retrieval of Λ was possible.
See text for details. Panel (c) shows a profile of values averaged
over 2 min centred on 16:15 UTC. The grey lines show the expected changes
in Λ for three different values of aggregation efficiency (1.0, 0.7,
0.2), assuming that the ice particle size distribution at 4.5 km evolves due
to aggregation alone.
By fitting an inverse-exponential curve to the retrieved particle size distribution data from our Doppler
spectrum method, we can estimate the slope of the size distribution,
Λ in dN/dD=N0exp(-ΛD)
(Fig. a). By means of verification, we also calculate
the slope of a purely inverse-exponential size distribution fitted to match
the DWR35/94 values only (Fig. b). There is
excellent agreement between the two methods in the regions where the size
distribution is broader and less steep. Figure c
shows a 2 min average of Λ, which again shows the excellent
agreement throughout the whole profile, particularly the height of the rapid
change of Λ between 5 and 4 km. The only region of disagreement is
just below 4 km, where the spectra method suggests even broader size
distribution than the DWR method. This could be evidence that the
inverse-exponential size distribution approximation in this region is not
appropriate because DWR35/94 was
almost saturated at 8–9 dB. However, both methods agree that there is a
rapid increase in ice particle size occurring as they fall from 4.5 to
3.6 km and a broadening of the ice particle size distribution. In the next
section, we present evidence that this rapid change is occurring as a result
of aggregation and not occurring through vapour deposition or riming.
The spectral method developed here is more sensitive to the presence of a few
large particles than the DWR method. With the spectral method, the influence
of a few non-Rayleigh scatterers can be seen in the spectra before the
reflectivity of the individual scatterers is large enough to contribute
significantly to the total reflectivity (which is a weighted average of
sDWR over all particles). Therefore, the retrieved particle size
distributions higher in the cloud are more reliable with the spectral method
than the DWR method because we are able to isolate the signal from the
larger particles in the distribution. However, the spectral method is
sensitive to noise in the spectra, and hence when the overall signal becomes
weak, and the noise is therefore a more significant contributor, the
retrieved particle size distributions are also noisy.
Evidence for rapid aggregation of dendrites
In this section we examine whether the changes in particle size and size
distribution could be explained by processes other than aggregation.
Specifically we address whether vapour deposition or riming could lead to the
observed changes.
Ice particles grow from smaller than 0.75 mm in diameter (DWR < 1 dB),
above this transition layer, to larger than 5 mm by the time they reach
4 km (Fig. c). Mean radar Doppler velocities just above this
transition layer are 1–1.2 m s-1 (Fig. d),
indicating that, on average, ice particles will take 400–500 s to fall from
4.5 to 4 km, although the largest particles responsible for the large DWR
values will fall faster than the average particle.
The growth of ice particles by vapour deposition cannot produce large ice
particles quickly enough to match our observations. Calculations using
the vapour deposition growth equation from are
presented to demonstrate this. The equations used were
dmdt=4πCSSiFLsRvT-1LsKT+RvTesi(T)D,m=0.0185D1.9,
where the rate of change of particle mass m with time t is a function of
the ice particle capacitance C (assumed to be D/4 here, following
, where D is the diameter), supersaturation with respect
to ice SSi and the ventilation coefficient F=0.65+0.44×0.60.33Re0.5. Re is the Reynolds number; Re=ρDV(D)/μ, calculated from the air density ρ, particle diameter D,
terminal velocity V(D) and dynamic viscosity of air μ. Terms in the
denominator are the latent heat of sublimation Ls, the specific gas
constant for vapour Rv, temperature T, thermal conductivity of air
K and saturated vapour pressure over ice esi;
Eq. () is the mass–size
relationship.
These calculations, for a liquid-saturated atmosphere at -10∘C,
show that typical ice particles would, at their absolute fastest, take over
40 min (2534 s) to grow from 0.75 to 5 mm in diameter. Similarly,
calculate that it takes over 30 min to grow a particle of
3 mm through vapour deposition. We therefore can rule out pure vapour
deposition as the source of the largest particles, which develop in less than
10 min.
Riming of the ice particles by collecting liquid water is another possible
explanation; however, there is no evidence of significant supercooled liquid
water present at this height. There were no strong backscatter returns in the
lidar measurements (not shown) which would indicate the presence of liquid
droplets, and the liquid water path measured by the microwave radiometer is
below the noise level of the instrument (about 20 g m-2) throughout
the observation period. Furthermore, the triple-frequency analysis for the
scattering models in do not show agreement with the
expected triple-wavelength signature of rimed particles
but rather for aggregate snow crystals.
The sharp and consistent transition of cloud properties with height after
15:45 UTC is therefore likely a result of aggregation. The first indication
that aggregation is the most important process in this part of the cloud is
the continual decrease in Λ (the slope of the ice particle size
distribution) with height down from the top of the transition layer. This
change with height indicates that there are more large particles and fewer
small particles as the particle size distribution evolves, consistent with
aggregation:
5dΛdz=Λbχfdχfdz1-2Γb+δ+1Γ(b+d+1)Γδ+1Γ2b+d+1-πEaggIlχfΛb+d-14abcΓ(b+d+1)Γ(2b+d+1).
We calculated the expected change of Λ with height using
Eq. (), following , for several
different values of aggregation efficiency (Eagg). In
Eq. (), a, b, are constants in the mass–diameter
relationship m=aDb; c, d, are constants from the fall
velocity–diameter relationship V=cDd; δ=1.0 following
; Γ is the gamma function; χf is the
snow flux in kg m-2 s-1; and Il is calculated from
Eq. (20) of , dependent on b and d. In our
calculations, it takes the value of 11.524. These calculations assume that
aggregation and vapour deposition together are the primary processes affecting
the evolution of the size distribution and that changes to the total mass
are only due to vapour deposition or sublimation, not the accretion of liquid
drops.
To estimate the aggregation efficiency in this part of the cloud, we need to
know the slope of the particle size distribution at the top of the layer and
the vertical profile of snow flux. The Λ value is estimated from the
retrieved size distribution. The snow flux profile is estimated from the
retrieved particle diameters, which are converted to a mass, multiplied by the measured
Doppler velocity and then integrated across the spectra. Using the retrieved
profile of size distribution properties and snow flux profile at 16:15 UTC
as input, the expected change of Λ with height for Eagg
values of 0.2, 0.7 and 1.0 are shown in Fig. c. The
evolutions of Λ between 4.5 and 4.0 km altitude, as calculated by
either the Doppler spectrum method or the simpler DWR method, are both
consistent with theoretical evolution, with an Eagg of around 0.7. The
Eagg=0.2, reported in , cannot reproduce the
observed broadening of the size distribution through this shallow layer of
cloud and leads to Λ being overestimated by almost an order of
magnitude at 3.5 km. Eagg=0.7 is at the higher end of values
reported in the literature. However, found 0.4<Eagg<0.9 at -15∘C, whereas for all other
temperatures sampled, the best estimate was Eagg≤0.2.
Similarly, reported that Eagg values greater
than unity were required for small particles for a good fit to observed
aggregation within tropical cirrus anvils. Our results are consistent with
the high values of Eagg of at
-15∘C but do not support the Eagg<0.2 reported by
. This suggests that the free-fall experiments in the 10 m
cloud chamber may be more representative of the natural aggregation in the
atmosphere than the stationary target experiments of .
speculate that the higher Eagg at
-15∘C is because the dendritic branches of the crystals are able
to interlock and that this can increase Eagg by at least a factor
of 3. Increased aggregation efficiency in the presence of dendritic crystals
also agrees with observations by . Our observations are
consistent with these hypotheses.
Further evidence to support the hypothesis of rapid aggregation in this part
of the cloud is seen in the vertical profiles of snow flux and number flux
(Fig. ). These quantities have been calculated
by determining the number and total mass of ice particles at each height and
for each velocity bin from the Doppler spectrum retrieval. The mass (or
number) in each velocity bin is then multiplied by the Doppler velocity
measured by the radars in order to determine the flux. Only flux values of
particles > 0.75 mm in diameter are shown because the number of smaller
particles cannot be reliably estimated with this combination of radars.
Confidence is given to the reliability of our retrievals by the coherent
structures seen in time and height (Fig. a and b).
The vertical profile of snow flux and number flux
(Fig. c) also supports our rapid aggregation
hypothesis because the decrease in number flux from 4.5 km downwards is
substantially larger than the decrease in snow flux over the same heights.
The decrease in number (flux) relative to mass (flux) is exactly what is
expected from aggregation. The overall decrease in snow flux with height
could be explained by sublimation of the ice particles in subsaturated air
(included in our calculations in Eq. ) or through some
process where large particles become significantly smaller (e.g. collisional
breakup; not included in Eq. ). Nevertheless, these
properties also support rapid aggregation in this part of the cloud.
Time–height plots of the retrieved quantities of (a) snow
flux and (b) number flux. These quantities are calculated for
particles with retrieved diameter > 0.75 mm only and therefore
underestimate the true snow and number flux. Panel (c) shows the
profile of these two quantities retrieved at 16:15 UTC.
Sensitivity to uncertainties in the retrieval
The retrieval of the properties of the ice particle size distribution is
naturally sensitive to uncertainties in the input quantities. To determine the extent to which our retrieval is sensitive to these uncertainties, the retrieval
has been repeated with a range of different assumptions. The sensitivity
analysis looks at three different aspects: (1) the impact of improperly
aligning the Doppler spectra from the radars along the velocity axis, (2) the
impact of improperly aligning the Doppler spectra based on reflectivity or
calibration errors, and (3) the impact of using a different mass–diameter
relationship in the retrieval. The details of the different sensitivity tests
are given in Table .
The ice particle size distribution at 4.15 km (equivalent to
Fig. i) under various uncertainty assumptions. See
Table for details about the uncertainties included in these
retrievals.
Panels (a)–(d) show the vertical profile of
Λ at 16:15 UTC (equivalent to Fig. c) under
various uncertainty assumptions. Panel (e) shows the mean (solid
line) and range (shaded region) as a function of height for all individual
retrievals shown in panels (a)–(d). The mean is calculated
from the base-10 logarithm of the plotted values. The unperturbed retrieval
is plotted on panels (a)–(d) in black for comparison. The
theoretical curves for changes of Λ with height due to aggregation
and starting from 4.5 km altitude for Eagg values of 1.0, 0.7
and 0.2 are shown on panel (e), as in Fig. c.
Vertical profiles of c and d from the power-law fits to the
velocity and diameter retrievals between 16:14 and 16:16 UTC. The mean
(solid) and the spread approximated by the standard deviation of c and
d values in time at each height (dashed) are shown.
Details of the changes to the retrieval input or parameters for the
sensitivity testing.
AspectNameDescription1V35-4 cm s-1Doppler spectra from 35 GHz radar shifted to the left by two velocity bins (0.04 m s-1)1V35-2 cm s-1Doppler spectra from 35 GHz radar shifted to the left by one velocity bin (0.02 m s-1)1V35+2 cm s-1Doppler spectra from 35 GHz radar shifted to the right by one velocity bin (0.02 m s-1)1V35+4 cm s-1Doppler spectra from 35 GHz radar shifted to the right by two velocity bins (0.04 m s-1)2Z35-1 dB1 dB subtracted from Z35 and sZ352Z35+1 dB1 dB added to Z35 and sZ352Use -10<dBZ<+5Calibration of Z35 and Z94 to match Z3 in regions where -10<Z3<+5 dBZ2Use -20<dBZ<-10Calibration of Z35 and Z94 to match Z3 in regions where -20<Z3<-10 dBZ2Use -20<dBZ<+5Calibration of Z35 and Z94 to match Z3 in regions where -20<Z3<+5 dBZ3m=0.1048D2.148Replaces the mass–diameter relationship from with that from Heymsfield (2013) for aggregate snowflakes
Figure shows how the retrieved ice particle
size distribution at 4.15 km altitude and at 16:15 UTC varies under the
different uncertainty assumptions. There are some large variations in the
maximum ice particle diameters retrieved – in particular for uncertainties
related to changing the velocity (aspect 1; blue lines) and also in the
number concentration retrieved at a particular diameter,
which can vary by an order of magnitude.
However, the overall character of the size distribution is usually unchanged,
and when the characteristic slope of the size distribution Λ is
calculated, it is largely insensitive to the uncertainties.
This insensitivity of Λ to these uncertainties can be seen in
Fig. . In Fig. 9a–d, the vertical profile of
Λ at 16:15 UTC is shown for each of the different uncertainties.
This can be compared with Fig. c, and the retrieved
Λ profile from the unperturbed set-up is plotted in black in
Fig. 9a–d. Although there is some variation in
Λ for the different uncertainty assumptions, the vertical profile
continues to show rapid decreases in Λ with height down from 4.5 km,
consistent with large aggregation efficiency values
(Fig. e). The largest deviation is seen for the
uncertainty where Z35 and sZ35 are reduced by 1 dB. This change
results in larger Λ values at all heights due to a reduction of
DWR35/94 by 1 dB. The lower sDWR results in the retrieved
particle diameters being smaller such that the largest particles have lower
number concentrations and therefore a steeper slope is diagnosed.
Nevertheless, the change of Λ with height for this uncertainty is
also consistent with rapid aggregation. Therefore we conclude that none of
the uncertainties assessed substantially change the conclusion that
aggregation is likely the dominant mechanism for changing the ice particle
size distribution from 4.5 km downwards between 15:45 and 16:20 UTC.
The estimation of the aggregation efficiency value is largely dependent on
the mass–size and velocity–size relationships used, because these control the
values a, b, c and d, which are the main terms in Eq. ()
determining the change of Λ with height. b
and d also contribute substantially to change of I1. These values are,
however, relatively well constrained. First, Eq. () is
totally insensitive to a because it appears only once and is cancelled out
because it also contributes to the mass flux χf. Second, b=1.9
is known for this case . Therefore no sensitivity exists to
the choice of mass–size relationship. c and d have been estimated from
the power-law fits as part of the retrieval process and are quite well
constrained within the aggregation region (Fig. ).
Conclusions
We have shown that the use of radar Doppler spectrum data from three
co-located, vertically pointing radars at frequencies of 3, 35 and 94 GHz
can produce estimates of the ice particle size distribution and can be used to
identify and explore processes such as aggregation. Different radar
reflectivity for different radar frequencies shows evidence that there are
particles present that are large enough that they are no longer within the
Rayleigh-scattering regime. Using the Doppler spectra from the three radars,
we can determine the size and estimate the number of these ice particles.
In the case presented in this paper, we identify a region where the 35 to
94 GHz dual-wavelength ratio (DWR) increases rapidly with decreasing height,
indicative that large ice particles are forming quickly. We have ruled out
vapour deposition as the cause of these large particles because that process
is too slow. Similarly the rapid growth is not a result of riming because
there was no evidence of significant liquid water. We therefore argue that
these large particles, up to 5 mm in diameter, are a result of aggregation.
Our observations are consistent with theoretical calculations of ice particle
size distribution evolution resulting purely from aggregation. In this case
an aggregation efficiency around 0.7 fits the observations.
Aggregation as the cause of the rapid growth of ice particles is supported by
the consistent and narrow range of heights over which this change occurs. The
rapid aggregation occurs just below the region where the Doppler spectra are
bi-modal, indicating the presence of small, newly formed ice particles. It
appears that the small ice particles forming at approximately 5.3 km
(-15.4∘C) and appearing clearly in the Doppler spectra at
4.8 km (Fig. d) grow into dendritic ice particles at
temperatures around -15∘C and either aggregate with other
similarly formed particles or initiate aggregation with pre-existing ice
particles falling through this layer. The aggregation initiated by these
particles is then evident in the large particles present at 4.1 km, which
could not have been formed by vapour deposition or riming.
These observations of rapid aggregation at temperatures around
-15∘C add support to cloud chamber studies
, which also suggest that aggregation at around
-15∘C is much more efficient that at other temperatures. The
resulting changes to the ice particle size distribution through this
aggregation process strongly affect many microphysical process rates (e.g.
vapour deposition, sedimentation velocity and further aggregation), and therefore
failure to capture these aggregation regions in models can lead to
significant errors in the simulated cloud fields.
This multi-wavelength Doppler spectrum technique shows the ability to
determine the size distribution of ice particles in large portions of ice
clouds simultaneously. Previously, ice particle sizes have been determined
using ice particle sizing instruments attached to aircraft, which suffer from
two issues: small sample sizes and shattering of large ice particles on the
instrument inlet, resulting in many small particles in the sample volume and
leading to unreliable estimates of both large and small ice particle
concentrations . Therefore further
studies of cloud microphysical structure and processes using this method are
encouraged.
For the benefit of future studies, we give some advice here for achieving the
best results. To achieve reliable, quantitative results from this method, the
radars need to be very precisely pointed vertically. We find that
mispointing by 0.2∘ is sufficient in resolving a non-negligible
contribution from the horizontal wind in the Doppler spectra, which adds
extra challenges to comparing the spectra from the three radars. Ideally the
three radars should also have the same beamwidth; spectral broadening
increases for wider beams and again makes comparing spectra from different
radars more challenging, especially in the tails of the spectra where the
largest DWR values are expected. Despite these challenges, we have shown that
this technique enables the generation of ice particle size distributions from
remote sensing data. We were unable to make reliable retrievals in regions of
strong turbulence (e.g. due to instability created by sublimation) because
the assumption that the spectra were unchanged over the 10 s averaging window
was violated. Although no low-level clouds were present on this day, the
technique to cross-calibrate the radars near the cloud top enables the retrieval
to be performed even when supercooled-liquid or liquid clouds or rain are
partially attenuating the radar signal at lower levels. Retrievals of this
type have the potential to benefit the cloud microphysics community through
both statistical sampling of clouds and aiding studies of individual
processes such as the aggregation process detailed in this paper. Further
studies comparing the retrieved size distributions against data obtained from
aircraft are currently being performed.
One weakness of our current experimental set-up is that we can only size
particles larger than 0.75 mm. Particles smaller than 0.75 mm are in the
Rayleigh-scattering regime at all three wavelengths, and therefore their size
cannot be determined. The addition of an extra shorter wavelength (e.g. at
frequencies of 150 or 220 GHz, as advocated by )
would enable sizing of particles down to approximately 0.45 or 0.3 mm (for
150 and 220 GHz respectively). Such observations would provide a unique
opportunity for increasing our understanding of cloud microphysics, both
statistically and through process studies, as demonstrated in this paper.
Data availability
The radar data used in this paper can be accessed at the
Centre for Environmental Data Archival (http://www.ceda.ac.uk/) or by
contacting the authors.
Author contributions
AB performed most of the data analysis,
analysed the radar data and wrote the main part of the text. CW conceived and
led the research project, contributed code for the Westbrook scattering
model, and assisted with the radar data analysis. JN created the
pre-processing code for the radar data. TS provided code and experience from
previous work with the data. All authors discussed the scientific findings
and contributed to the final paper.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
This research was funded by the Natural Environment Research Council, grant
NE/K012444/1. We are grateful to the staff at the Chilbolton Facility for
Atmospheric and Radio Research for operating and maintaining the radars and,
in particular, Alan Doo, Allister Mallett, Chris Walden, John Bradford and
Darcy Ladd for their assistance in collecting the triple-wavelength
measurements.The article processing charges for
this open-access publication were covered by a Research
Centre of the Helmholtz Association.
Review statement
This paper was edited by Timothy Garrett and reviewed by
Paul Connolly and three anonymous referees.
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