AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-11-5925-2018Combining cloud radar and radar wind profiler for a value added estimate of vertical air motion and particle terminal velocity within cloudsMeasuring vertical air motion and terminal fall velocity incloudsRadenzMartinradenz@tropos.dehttps://orcid.org/0000-0002-7771-033XBühlJohanneshttps://orcid.org/0000-0002-0354-3487LehmannVolkerGörsdorfUlrichLeinweberRonnyLeibniz Institute for Tropospheric Research (TROPOS), Leipzig, GermanyMeteorologisches Observatorium Lindenberg/Richard-Aßmann-Observatorium, Deutscher Wetterdienst, Tauche, GermanyMartin Radenz (radenz@tropos.de)26October201811105925594019April201824May201817September20181October2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://amt.copernicus.org/articles/11/5925/2018/amt-11-5925-2018.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/11/5925/2018/amt-11-5925-2018.pdf
Vertical-stare observations from a 482MHz radar wind profiler and a
35GHz cloud radar are combined on the level of individual Doppler
spectra to measure vertical air motions in clear air, clouds and
precipitation. For this purpose, a separation algorithm is proposed to remove
the influence of falling particles from the wind profiler Doppler spectra and
to calculate the terminal fall velocity of hydrometeors. The remaining error
of both vertical air motion and terminal fall velocity is estimated to be
better than 0.1ms-1 using numerical simulations. This
combination of instruments allows direct measurements of in-cloud vertical
air velocity and particle terminal fall velocity by means of ground-based
remote sensing. The possibility of providing a profile every 10s
with a height resolution of <100m allows further insight into the
process scale of in-cloud dynamics. The results of the separation algorithm
are illustrated by two case studies, the first covering a deep frontal cloud
and the second featuring a shallow mixed-phase cloud.
Introduction
Clouds are a key component of the Earth's climate system
. They drive the hydrological cycle
and influence the radiative balance
. The radiative effect of clouds and
the efficiency of precipitation formation depend strongly on the
microphysical structure of clouds,
i.e. number concentration, size, shape and phase of particles. Cloud
microphysics is strongly controlled by vertical velocity, as up- and
downdraughts control temperature and supersaturation of an air parcel
. Hence, cloud lifetime and the production rate
of cloud condensate is sensitively coupled to vertical motion
. However, only a few observations
of in-cloud vertical air motions are available, leaving a major driver of
cloud microphysics unconsidered. The current lack of process-level
understanding leads to large uncertainties in numerical climate simulations
and weather prediction models .
Cloudy air is a complex multiphase, multi-velocity and multi-temperature
physical system and there is an ongoing scientific discussion regarding the
correct equations for describing the motion of moist atmospheric air in the
presence of condensation . In this paper we explicitly distinguish between the
velocity of the homogeneous gaseous mixture of dry air and water vapour
(hereafter called air motion for brevity) and the velocity of liquid and
solid water particles with respect to the surrounding air (hydrometeor
terminal velocity). In the stationary case, the vertical velocity of
hydrometeors, which can be observed by ground-based radars, is simply the
superposition of air motion and terminal velocity.
Different radar-based methods have been proposed for the retrieval of the
vertical wind speeds in clouds, like the Mie notch retrieval
and the dual-frequency method
. This paper presents a dual-frequency approach
which combines Doppler spectra from a cloud radar and a radar wind profiler
(RWP) to obtain this information. RWPs are the only remote sensing
instruments which are sufficiently sensitive to scattering from the
particle-free “clear air” and can be used to
observe air motion directly. However, RWPs are not only sensitive to clear-air scattering but also to particle scattering from clouds and
precipitation. This particle scattering can mask the clear-air return and
leads to the so-called Bragg–Rayleigh ambiguity . An
algorithm is presented which tries to disentangle the contributions of both
scattering mechanisms through a combination of Doppler spectra obtained by
radars operating at two widely spaced frequencies. The simultaneous
observation of air motion and particle velocity furthermore makes it possible
to retrieve the particle terminal velocity.
The paper is structured as follows: first the theoretical background is
provided in Sect. . Campaign and technical details of the
instruments are presented in Sect. . Afterwards the algorithm
is introduced and illustrated by two case studies. Artificially generated
spectra, together with a Monte Carlo approach, are used to evaluate the
accuracy of the proposed algorithm and to provide an error estimate for each
spectrum operationally. This evaluation is presented in
Sect. followed by a short discussion, a summary and the
conclusions.
Theoretical background
The general form of the weather radar equation can be written as
P(r0)=∫VI(r0,r)η(r)d3r,
where r0 is the centre of a range bin and η denotes the volume
reflectivity. I(r0,r) is the instrument-weighting function.
It depends on the antenna radiation pattern, especially the beamwidth and the
characteristics of the pulse but most importantly pulse length. Its rather
complex form can, under certain assumptions, be simplified into the calibration
constant C/r2detailed derivation in.
Scheme illustrating the contribution of particle and clear-air
scattering to the Doppler spectra of the radars. Scattering from particles
(and their terminal fall velocity relative to the surrounding air) and the
clear-air return from the air motion are caused by completely different
processes and have to be considered separately in an ideal case (a).
Both processes are entangled when observed by real instruments (b).
Reflectivity of different scattering processes
following. Red lines indicate
typical values of hydrometeor reflectivity with the sensitivity threshold of
the cloud radar at -55dBZ. Orange
lines indicate the reflectivity for Cn2 typically observed in the
atmosphere e.g.. The grey line shows the
reflectivity of one liquid drop (N=1m-3) with a diameter of
d=3mm as derived from Mie theory.
Two atmospheric scattering mechanisms are relevant for RWP, clear-air
scattering caused by inhomogeneities of the refractive index at a scale of
half the radar wavelength (the Bragg scale) and scattering by hydrometeors.
Clear-air scattering, often called Bragg scattering for short, can be used to
assess vertical air motion without a particle proxy. While higher-order
effects like fluxes of the local refractive index parameter may introduce
differences between the observed Doppler velocity and true air velocity
, these effects are assumed
to be mainly relevant in the convective boundary layer
. The volume reflectivity of clear-air
ηair can be related to the refractive index structure
parameter by the Ottersten equation if the Bragg scale lies within
the inertial subrange of fully developed turbulence:
ηair=0.38λ-1/3Cn2.
In the case of incoherent scattering, i.e. random distribution of the
particles within the radar resolution volume, the volume reflectivity can be
described with the following:
ηparticle=∫σλ(D)N(D)dD=π5|K|2λ4Z,
where σλ(D) is the backscattering cross section of particles
with diameter D at a wavelength λ, N(D) is the particle number
distribution, Z is the reflectivity factor and |K|2 accounts for the
refractive index of the particle. A simple analytical relationship for
σλ is available if the Rayleigh approximation holds; i.e. the
particles are small compared to the wavelength. In the case of larger
particles more complex approaches are required to relate σλ to
particle size and shape. In the following, the signal from those particles is
referred to as non-Rayleigh scattering.
Cloud radar reflectivity (a), RWP SNR (c), cloud
radar velocity (b) and RWP velocity (d) on 17 June 2015
illustrating the Bragg–Rayleigh ambiguity. As soon as the particle return
dominates (high reflectivity in the cloud radar), the clear-air signal in the
RWP is masked by the falling particles. This case is presented in more detail
in Sect. .
Coherent radars are able to estimate the Doppler spectrum on the basis of the
demodulated and pre-processed receiver data. The use of classical spectral
estimators, like the discrete Fourier transform, is very well established in
radar meteorology. The obtained power spectrum describes the information
content of the raw signal as a function of Doppler frequency. The Doppler
spectrum contains the same amount of information as the raw data if the
assumption of a stationary random Gaussian process holds for the duration of
the dwell (note that this does not hold for some types of clutter echoes).
For RWP, clear-air and particle scattering act simultaneously and
independently; hence the processes are not correlated, which often leads to
the appearance of two distinct spectral peaks in the Doppler spectrum
. While this offers the
principal option of retrieving the vertical wind speed even in the presence of
precipitation, the applicability of this approach is rather limited since the
two scattering peaks are often entangled; i.e. they cannot be uniquely
separated in the Doppler spectrum as schematically illustrated in
Fig. . Heuristic models for the Doppler spectrum
have been proposed for the purpose of relating its properties to the physical
parameters describing the scattering medium; however no comprehensive theory
based on first principles is available. For particle scattering, the simple
model for the Doppler spectrum established by has
been widely used; see e.g. or
. The particle signal is always shifted by the
vertical air motion vair, resulting in a observed velocity v=vair+vt and it is furthermore broadened by turbulence within the
resolution volume. No such model is yet available for the Doppler spectrum of
a clear-air scattering signal. The classical assumption that the clear-air
peak has a Gaussian shape was suggested for simplicity by ;
however the author has also mentioned that deviations are not uncommon.
Scheme of the separation algorithm. The separation begins with the
raw measurements from cloud radar and RWP as denoted in the top row. The
separation between particle and clear-air signal is performed after adaption
of the different sampling characteristics and relative calibration. The
products are the quality flagged vertical air velocity and the particle
terminal velocity. Further description is in the text.
An unambiguous separation of both clear-air and particle peaks in a single
radar Doppler spectrum is sometimes possible, especially for
very-high-frequency radars operating near
50MHz (see e.g. ) due to the strong
increase in particle-scattering reflectivity towards smaller wavelength; see
Fig. . The dual-frequency method attempts
to resolve this entanglement by combining data from radars with sufficiently
different wavelengths. The choice of frequencies is crucial to achieve a good
separability. used a 1 and a 3GHz radar to
discriminate between clear-air and particle scattering, yielding a frequency
spacing factor of 3. Different methods were developed and further refined to
separate both contributions . This development led to the approach of
combining Doppler spectra from two radars operating at 50 and a
915MHz, having a frequency spacing factor of 18
. The combination of a 482MHz RWP
and a 35GHz cloud radar, as used in this study, provides a
strongly increased frequency spacing factor of 73. The additional advantage
of using a cloud radar operating at 35GHz is that this instrument
is de facto not sensitive at all to clear-air scattering, even for very high
values of Cn2. While a direct comparison of the theoretically calculated
volume reflectivities (as in Fig. ) would
not immediately support this statement it needs to be considered that the
Ottersten equation implicitly requires the existence of an inertial subrange
at the Bragg scale. However, the Bragg scale of the cloud radar is only about
4mm and therefore of the order of the Kolmogorov-length
microscale.
A simple model for a single RWP Doppler spectrum S(v) is given by
:
S(v)=Sair(v)+Sparticle(v)+N(v),
where Sair(v) and Sparticle(v) are the spectra of clear-air and particle scattering, and N(v) is the system noise.
Following and , the received
power can be decomposed through the Doppler spectrum S(r0,v) as
P(r0)=∫S(r0,v)dv=∬I(r0,r)η′(r,v)d3rdv,
where η′(r,v) is the spectral reflectivity. For
simultaneously acting clear-air and particle scattering, the volume
reflectivities are additive η=ηair+ηparticle; hence
∫S482(r0,v)dv=∬I482(r0,r)ηair′(r,v)+ηparticle′(r,v)d3rdv
∫S35(r0,v)dv=∬I35(r0,r)ηparticle′(r,v)d3rdv.
These two relationships provide the basis for a combination of the cloud radar
and RWP Doppler spectra as described in the following sections.
Collocated observations with a 35 GHz cloud radar and a 482 MHz radar wind profiler
For this study we combine the data from the 35GHz cloud radar
and the powerful, narrow beamwidth 482 MHz RWP
e.g.,
both operated by the German Meteorological Service at Richard Aßmann
Observatory in Lindenberg, Germany. Both radars were closely collocated to
achieve maximum overlap of the observation volumes. In the following, RWP
is used as an abbreviation for the 482MHz radar and “cloud
radar” is used as a shorthand for the 35GHz Doppler radar. It is
worth mentioning that the proposed methods are not restricted to these
frequencies.
The RWP is used with two configurations or operating modes. The first mode is
used for intensive observation periods (IOPs), during which the RWP beam is
pointing only into the vertical direction. During the second observation
mode, 30 min of vertical measurements are alternated with 30 min of Doppler
beam swinging (DBS). This configuration was chosen to fulfil operational
requirements and it also has the benefit that measurements of horizontal wind
are available. The cloud radar is by design operating in the vertical mode only.
The technical parameters of cloud radar and RWP are given in
Table . The measurements were performed between June and
September 2015 in the framework of the COLRAWI campaign combined
observations with lidar, radar and wind profiler;.
Configuration settings of the major instruments used in the COLRAWI
campaigns based on. The second number indicates
the setting used for the RWP during IOPs.
Daily median (dot) and the median absolute deviation (bar) of the
RWP calibration for the whole campaign when appropriate conditions were
present. The IOP settings are marked in red, the intermitting mode in blue.
Measurement gaps due to maintenance are marked in grey. Note that the
ordinate is linearly scaled.
Figure shows the measurements of both
systems for an example case (17 June 2015; covered in detail in
Sect. ), in which the Bragg–Rayleigh ambiguity
becomes strikingly evident. A frontal system approaches Lindenberg with
the cloud base continuously decreasing from 6km to the ground
as can be seen in the cloud radar reflectivity factor Z35 GHz
(hereafter reflectivity). The RWP is able to measure the clear-air signal
and hence the vertical velocity of clear air during the cloud free period
(Fig. d). As expected, the strongest
clear-air return is observed at the top of the atmospheric boundary layer
(Fig. c at around 2.0km) but
also at local maxima of refractive index gradients higher aloft. As soon as
hydrometeors are present, the particle signal dominates and masks the air
motion.
A synergistic algorithm to use cloud radar Doppler spectra for a suppression of particle echoes in RWP Doppler spectra
An overview of the proposed algorithm is given in Fig. .
The Doppler spectra produced by the standard signal processing algorithm from
the cloud radar and the RWP are used as input.
In a first step, the effect of the differing sampling characteristics of both
radars (especially beamwidth and pulse length) is accounted for: the signal
peaks in the cloud radar spectra are artificially broadened and the range
resolution is also coarsened. Furthermore, the power density in the RWP
spectra are relatively calibrated based on the cloud radar data. The actual
removal of the Bragg–Rayleigh ambiguity is performed by suppressing the parts
of the RWP spectra which are influenced by a particle signal. A peak finder
is used with a moment estimation algorithm based on Gaussian fitting to
estimate reflectivity, mean velocity and spectral width of the clear-air
return. The particle terminal fall velocity is calculated by subtracting the
vertical air velocity (first moment of the particle suppressed RWP spectrum)
from the cloud radar vertical velocity.
Doppler spectrum for 1 August 2015 16:57 UTC at
4160 m (a), the associated weighting function (b) and the
fuzzy membership function (c).
Adaption of the cloud radar spectra to match the sampling characteristics of the RWP
Both radars have significantly different
instrument-weighting functions, because of different antenna radiation
patterns and different pulse lengths (Table ), which
result in different resolution volumes. The pulse length is matched by
summing the spectral reflectivities of the cloud radar spectra within a RWP
range gate. A Gaussian window of 90m width is used to account for
the range-weighting function of the RWP. The different beamwidth of the RWP
is accounted for by an artificial broadening of the cloud radar Doppler spectrum.
A larger beamwidth is more susceptible to spectral broadening caused by the
radial component of the horizontal wind at the edges of the beam. A full
theoretical treatment is provided by with an
analytical formula, which is used to artificially broaden the
cloud radar spectrum. This adapted cloud radar spectrum matches the sampling
characteristics of the RWP and is referred to as S35(v) in the
following and r0 is omitted for brevity. The profile of the
horizontal wind required for this correction is taken from numerical weather
prediction model data from the European Centre for Medium-Range Weather
Forecasts.
Before the broadening, bins in the cloud radar that are dominated by plankton
(like insects or pollen) are removed by using the linear depolarization ratio
(LDR) to identify highly depolarizing targets
. All bins with a LDR higher than
-13dB are filtered, because hydrometeors exhibit a smaller LDR
e.g..
Furthermore, both radars operate with different temporal sampling (also Table ), which results in different frequency or equivalently
velocity resolutions of their Doppler spectra. The slightly different
velocity resolution of the cloud radar is matched by linear interpolation,
assuming uniformly distributed energy within each spectral bin. Additionally,
the RWP spectrum is smoothed in a pre-processing step by convolution with a
Gaussian window (σ=1bin) to reduce the variance of the
estimated spectral power densities caused by the small number of incoherent
averages. It is referred to as S482(v).
Relative calibration of the RWP Doppler spectra
For a meaningful comparison of the RWP and cloud
radar spectra, a relative calibration of the RWP with the cloud radar as
the reference is performed. When selecting a small velocity interval
[vmin,vmax], where the Rayleigh approximation
holds for the cloud radar and no clear-air scattering contribution is present
in the RWP, Eqs. () and
() combine to
C482=C35∫vminvmaxS482(v)dv∫vminvmaxS35(v)dv,
with C482 and C35 as the calibration constants of the RWP and the
cloud radar. S482(v) and S35(v) are the for the
sampling characteristics adapted Doppler spectra of RWP and cloud radar. This
relationship holds because the reflectivity factor Z is independent of
wavelength under the Rayleigh approximation. The calibration of the cloud
radar is assumed to be correct with an accuracy of 1.3dB. Attenuation by gases is corrected by using the
model of . In this relative calibration scheme
highly accurate absolute calibration of the cloud radar is not required; hence attenuation is not a primary concern.
Above the boundary layer and in the absence of deep convection and strong
gravity waves, the clear-air signal of the vertical beam is always close to
0ms-1 and therefore excluded if vmax is set to
-0.9ms-1. The lower boundary of the velocity interval is
intended to exclude non-Rayleigh scattering from large particles, which are
characterized by a large terminal velocity .
Hence, vmin is set to -3.0ms-1, which corresponds
to the terminal velocity of a liquid sphere with a diameter of
1mm.
Flow chart of the quality flag decision logic.
For each Doppler spectrum the calibration is additionally checked by
comparing the calibrated Doppler spectra S482(v) and S35(v) within
the boundaries of the particle peak. If the difference between the spectral
reflectivities is less than 2dB in 4 bins around the maximum of
the particle peak and less than 2dB at its minimum the calibration
is considered valid. Otherwise a correction factor is calculated by averaging
S482(v)-S35(v) in 4 bins around the maximum of the particle peak.
The corrected calibration is applied if this correction factor is less than
20dB and the standard deviation less than 10dB. For
larger correction factors, the calibration is flagged as unreliable.
This allows the automated estimation of the calibration constant within a
wide range of atmospheric conditions and also a continuous monitoring of this
relative calibration. Within the 3 months of the COLRAWI campaign 2015
the daily calibration constant showed a standard deviation of less than
1dB (Fig. ).
Suppression of the particle scattering contribution in the RWP Doppler spectra and estimation of the clear-air momentsWeighting function
A weighting function
Pair is used to suppress the particle influence in the
RWP spectrum. It describes the relative contribution of clear-air scattering
to the whole spectral reflectivity
Pair=1-S35(v)S482(v).
The weighting function is defined as being equal to 1 if a bin in the Doppler
spectrum is dominated by clear-air scattering and 0 if particle scattering
dominates. It is constructed as follows: the adapted cloud radar Doppler
spectrum is cut off at the RWP noise level. The relative contribution is
calculated from this cloud radar spectrum and the RWP spectrum using Eq. (). Afterwards the weighting function is set to 1
at all bins where there is no cloud radar signal and is smoothed by a 5 bin
wide running mean to reduce noise. It is scaled with the inverse SNR of the
cloud radar for all bins with a weight less than 0.5. This reduces the
spectral reflectivity in the bins strongly dominated by particle return down
to the noise level and provides a clear suppression of the particle
contribution. The clear-air reflectivity spectrum Sair(v) is then
calculated by
Sair(v)=Pscaled, air(v)⋅S482(v).
An example of a spectrum and the associated weighting function is shown in
Fig. a and b. This weighting function approach
is similar to with the difference that our
weighting function is calculated for each bin individually without any
cumulative distribution, and the inverse SNR is used for scaling instead of a
fixed 40dB factor. The estimates for the first three moments
(reflectivity, mean velocity and width) are the calculated using a standard
moment estimator e.g..
Peak fitting
A second method used to isolate the clear-air contribution is fitting a
Gaussian-shaped function the part of the RWP spectrum which is not influenced
by particle return. The peak-fitting method is based on the assumption of a
Gaussian shape of the clear-air peak . The
fitting algorithm is constrained by a priori information from the combined
spectra, together with long-term statistical properties of the clear-air peak.
Measurements and value added products during the evening of
17 June 2015. Cloud radar reflectivity (a) and vertical
velocity (c). RWP reflectivity (b), quality
flag (d) and retrieved vertical air motion (f). The
particle terminal velocity calculated from the air velocity and the cloud
radar velocity (e). For the impact of the separation algorithm
compare (a) and (f) to
Fig. . Areas flagged for quality reasons
are coloured white.
The bins without particle influence are identified a priori by using a fuzzy-membership-like approach and a peak-finding algorithm. A region in the
spectrum is dominated by clear-air return if
1-pcloud radar⋅pRWP>pcloud radar⋅pRWP,
where p is the spectral reflectivity of each instrument scaled to
0,1. All of the signal left from the cloud radar peak maximum is
neglected. From this membership function (example in
Fig. c), the peak with the highest SNR is
selected and its moments (reflectivity, mean velocity and width as calculated
by a standard moment estimator) are used as a priori information for the
fitting algorithm. The Gaussian peak is then fitted to this part of the
spectrum using a trust region reflective algorithm
. This fitting algorithm constrains the parameter
space to physically reasonable values for the mean properties of the clear-air peak in the absence of hydrometeors. The reflectivity Zair and
the spectral width σair are assumed to lie in the ranges
between -50 and 10dBZ and 0.07 and 0.45ms-1
respectively. The resulting fitting parameters are then identified as the
moments of the clear-air peak.
Quality flag
A threshold-based decision tree is used to determine
the quality flag (Fig. ). A RWP Doppler
spectrum is considered to be particle influenced if the cloud radar spectrum
contains bins where the cloud radar reflectivity is higher than the RWP noise
level. Furthermore, spectra of the RWP with a SNR of less than
10dB are flagged as low SNR. Spectra with low SNR are not
necessarily less reliable, but during further processing, they have to be
treated with care.
Histogram of RWP vertical velocities for the evening of 17 June
(same period as shown in Fig. ). n denotes
the number of spectra that contributed to each class. The minimum at
0ms-1 in the clear-air and in-cloud raw spectra is caused by
the stationary clutter filtering procedure in the original RWP signal
processing.
As stated in Sect. a LDR threshold of
-13dB is used to separate scattering from hydrometeors from
atmospheric plankton. The plankton flag is set when the LDR of the whole
cloud radar spectrum is above the LDR threshold and the total reflectivity is
low but above the RWP noise level. For scattering by plankton the cloud
radar frequently shows the same vertical air velocity as the RWP.
The melting layer is characterized by high reflectivities combined with high
LDR values in the cloud radar or an elevated noise level in the RWP. Due to
the complex scattering processes within the melting layer (water coated
irregular spheres), a meaningful separation is not (yet) possible. The
remaining thresholds are subjectively estimated based on visual inspection of
the Doppler spectra.
Mixed-phase layered cloud in the afternoon of 1 August 2015.
Temperature T and dew point temperature Td(a) as well
as potential temperature and wind profile from the 18 UTC radiosonde ascent.
Cloud radar reflectivity (b), vertical velocity retrieved with the
standard RWP signal processing (c), cloud radar vertical
velocity (e) and the retrieved vertical air motion (f).
Values exceeding the velocity colour scale are shown in dark blue and red.
ExamplesCase study 1: frontal clouds on 17 June 2015
In the following section, the separation
algorithm is applied to the example case shown in
Fig. . During the afternoon of 17 June 2015, an occlusion with warm-front characteristics passed over Lindenberg. First
high clouds appeared at about 16:00 UTC. The cloud base slowly descended from
above 6km until liquid precipitation reached the ground at 23:00 UTC.
The melting layer at around 2.8km height is visible from
approximately 19:30 onwards. Comparing Figs. f
and d, the impact of the separation
algorithm becomes visible. As shown in Fig. b, high RWP reflectivity can be observed at strong gradients of temperature
and/or humidity, both at the top of the atmospheric boundary layer at
2km, where reflectivities of up to 10dBZ are visible, as
well as at the air mass boundary between 2.5 and 6km.
It also becomes visible how precipitation alters the strong reflectivity
feature at the top of the boundary layer at about 22:20 UTC. The vertical air
motion (Fig. f) reveals that the structure of
successive up- and downdraughts sustain within the thinner parts of the cloud,
especially before 19:30 UTC. Afterwards this pattern is less pronounced above
the melting layer, whereas within the liquid precipitation the pattern of
successive up- and downdraughts continues.
Close-up of the mixed-phase layered cloud between 16:30 and
17:00 UTC. Vertical velocity retrieved with the standard RWP signal
processing (a), retrieved vertical air motion (b), vertical
velocity of the cloud radar (c) and the terminal
velocity (d). Values exceeding the velocity colour scale are shown in
dark blue and red.
The effect of the Bragg–Rayleigh ambiguity also becomes obvious in
Fig. , which shows the frequency distribution of
RWP vertical velocities for the period shown in
Fig. . The shapes of the distributions for
clear-air and raw RWP spectra differ significantly. The hydrometeors' fall
velocity causes a second mode at -1.0ms-1. After
separation, the distribution of vertical velocities within the cloud is
rather similar to that of clear-air velocities (in terms of mean and width).
Dependency of the vertical velocity (a) and the
width (b) on the reflectivity as observed by the cloud radar during
COLRAWI. Clearly visible are the two clusters formed by cloud particles (low
reflectivity and slowly falling) and precipitation (high reflectivity and
fast falling).
Case study 2: mixed-phase cloud on 1 August 2015
On 1 August 2015, a small-scale low-pressure system over the eastern part of
France initiated the development of high and mid-level clouds in the southern
part of Germany. During the day these clouds were advected towards the north-east.
From 15:30 to 17:45 UTC a single-layer mixed-phase cloud was observed at
Lindenberg. The RWP was operated in the intermitting mode on that day,
meaning that 30 min of vertical stare is interrupted by 30 min of
DBS. As the 18:00 UTC radiosonde ascent
(Fig. a and d) reveals, a moist layer was
present between 4 and 6km with a stable air mass aloft. Near
the cloud top (around 6km height), the temperature was around
-17∘C (Fig. a).
Velocity error before the separation (a), with the
weighting function (b) and peak fitting (c). Shown is the
bin mean for all Monte Carlo spectra within the respective bins. The black
outline marks bins containing more than seven values. Bins without any
simulations are marked in grey.
Portion of successfully separated spectra depending on the peak
separation and contrast for the weighting function (a) and peak
fitting (b).
Error estimate for the weighting function (a) and the peak
fitting (b) methods during the period covered in case study 1
(Sect. ). Areas where no error estimate is
possible are marked in grey.
During the first part of the period shown in
Fig. the liquid water path (LWP) observed
with a collocated microwave radiometer ranged between 70 and 120gm-2, which later it peaked at 190gm-2. Beginning at 16:45 UTC
ice production increased, forming a virga with a clear signature in the cloud
radar reflectivity and vertical velocity below the liquid layer. The virga
dissolves rather quickly in the dry layer below the cloud. In the radiosonde
ascent (Fig. a) the relative humidity
decreases from 100% between 4.7 and 5.5km down to
below 10% at 3.8km. This dry layer is also visible in the RWP
as a gap in the measurements.
As the vertical air motion reveals in Fig. b, the
cloud exists under a background of strong vertical motion. Regrettably only
the intermittent mode observations are available for this case. But,
nevertheless, it is visible that the cloud gap at 16:30 UTC is caused by a
downdraught. Before and after that downdraught the particles form or
grow when the liquid layer is lifted. It can also be seen that a short delay
exists between the maximum of the vertical velocity and the response (growth)
of the particles (maximum of reflectivity and terminal velocity). This
example also emphasizes the importance of the separation algorithm. The
downward air motion at 16:35 UTC at 3.5km and the virga 20 min
later at 4.5km could not be distinguished in the raw RWP
measurement (Fig. a). It may also be possible
that the downdraught at 16:55 UTC was amplified by evaporation cooling.
Collocated observations of a vertical staring Doppler lidar (not shown)
augments these findings by also observing the updraught in the liquid layer at
cloud top.
From an estimate for in-cloud vertical air velocity, the terminal velocity
of the particles can be calculated (Fig. d). For a
first investigation, the mean velocity of the cloud radar peak was used, but
the Doppler spectra could also be used. When the updraught strengthens at
16:45, the terminal velocity increases as the particles grow. The particles
evaporate rather quickly when reaching the dry layer at 4km.
Evaluation of the separation algorithm
The accuracy of the separation algorithm is estimated
with a Monte Carlo approach. Doppler spectra of cloud radar and RWP are
generated numerically from a particle and a clear-air peak:
S482v=PGaussZparticle,v‾particle,σparticle+PGaussZair,v‾air,σairS35v=PGaussZparticle,v‾particle,σparticle,
where the Gaussian-shaped peak PGauss has the first three moments,
Z, v‾ and σ These spectra are used as input for the
separation algorithm. The output of the algorithm is then compared with the
input parameters of the synthetic Doppler spectra.
A single iteration in this Monte Carlo simulation consists of the following
steps: first, the input parameters (reflectivity, mean velocity and
spectrum width) for both peaks are randomly chosen. The frequency
distributions for the clear-air peak is derived from RWP observations within
clear air (Table ). The parameters of the particle peak are closely coupled to each
other and the parameters cannot be drawn from independent random
distributions. Large reflectivity values are more common at higher fall
velocities and spectral widths (Fig. ). All cloud
radar observations during the COLRAWI campaign are used to assemble a
three-dimensional histogram. The randomly chosen reflectivity is based on the
whole frequency distribution. Then a slice through the histogram at this
reflectivity is used to obtain the frequency distribution for which the
velocity is drawn. The spectral width is chosen accordingly.
From these set of parameters, the synthetic Doppler spectra are calculated
(Eqs. and ). For the cloud radar
spectrum only the particle peak is used, whereas for the RWP particle and
clear-air peak are added. Afterwards the noise floor and optionally
multiplicative noise are added. In the next step these two synthetic Doppler spectra are used as input for the separation algorithm
described in Sect. . The randomly drawn input parameters and the output from
the algorithm are stored for each step. If the separation algorithm fails to
reveal the clear-air peak, this is also stored.
Input settings for the Monte Carlo simulation. The values are based
on the clear-air properties of the RWP peak. Square brackets denote the range
from which the random numbers are drawn.
By running multiple Monte Carlo steps, all combinations of input parameters
are covered. Here, for each method (weighting function and peak fitting)
150 000 Monte Carlo steps were used and the error of the vertical air
velocity estimate of the algorithm is calculated:
verr=v‾air, input-v‾air,
corr,
where vair, input is the clear-air velocity used as input and
vair, corr is the result of the separation process. If the obtained
vertical velocity is larger than the actual one, verr becomes
negative, indicating an upward bias of the algorithm. If verr is
positive, there is a downward bias. This error decreases if both
contributions can be better distinguished in the spectrum. As a measure for
the distance of the peaks we define the peak separation S:
S=|v‾air-v‾particle|σair+σparticle,
where v‾ and σ are the first and second moments of the Doppler spectrum. For example, a particle peak at
v‾particle=-1.5ms-1 with
σparticle=0.8ms-1 and a clear-air peak at
v‾air=+0.5ms-1 with σair=0.3ms-1 give a peak separation of 1.8. The spectral contrast
C at v‾air is used as a second measure for
peak distinguishability.
C=Sairv‾air-Sparticlev‾air
The spectral contrast falls back to the RWP SNR when the reflectivity of the
particle signal is below the noise level at v‾air.
Figure a shows how the error depends on
S and C for the particle influenced measurement. As
it becomes clear from Fig. b and c the error
reduces with increasing S and C. For peak separations
S above 2 and spectral contrasts C above
15dB the possible errors of both separation methods are
negligible. The peak-fitting approach performs slightly better if both
S and C are small, but at the cost of larger errors
for small C and S above 1.8. Altogether the bias
for the weighting function is on average -0.023ms-1 (median
-0.005ms-1, interdecile range 0.072ms-1), and
for the peak fitting it is +0.003ms-1 (0.001,
0.058ms-1).
A detection rate can be calculated from the portion of spectra for which the
separation was successful. The weighting function approach is able to
separate 86 % of all synthetically generated spectra and performs slightly
better than the peak-fitting approach (80 %). As evident from
Fig. , the lowest detection rates occur
at low-peak separations S and spectral contrasts C.
Especially for peak separations around 1 the weighting function is more
robust compared to the fitting approach.
In addition to statistical error of the retrieval (averaged over all Monte
Carlo simulations), it is useful to estimate the potential error for a single
spectrum based on its properties. The measurements during the first case study
(Sect. ) for a error estimate for each spectrum.
The observed Doppler spectra from cloud radar and RWP are used to calculate
S and C. The error is then taken from the binned
results from the Monte Carlo simulation (Fig. b or
c). The frontal cloud observed on 17 June 2015
(Sect. ) is used to illustrate the error estimate
for each spectrum (Fig. ). Within liquid
precipitation (below 3km), the error is negligibly small as
clear-air and particle contribution are clearly distinguishable in the
spectrum. Above the melting layer the error is larger because of low terminal
velocities, with the particle peak being very close to the clear-air peak.
The error of the weighting function is mostly negative, indicating a slight
upward bias. Contrarily the errors of the peak-fitting method are mostly
positive, meaning a slight downward bias.
Discussion
The discussion will concentrate on three issues. The
calibration is assessed and compared to previous work. Secondly the selection
of frequencies is briefly discussed and the weighting function approach is
also compared to prior work. Finally the error as estimated by the Monte
Carlo simulation is shortly reviewed.
The accuracy of the relative calibration depends on the calibration of the
cloud radar. According to , the internal budget
calibration is accurate to 1.3dB. Neglecting all issues in the
cloud radar calibration and including the variability of the RWP calibration
constant (Sect. ), the uncertainty in the RWP
calibration is roughly 2dB. applied a
similar relative calibration approach as used in this study by calculating
the reflectivity of the full spectrum within light rain events. The approach
used here has two advantages. Firstly it is not required to manually
select of the events where calibration is possible. Secondly non-Rayleigh
contributions are excluded, which would otherwise mix into the SNR of the RWP
and obscure the true calibration constant. The check of the calibration
constant mitigates effects that decrease the observed reflectivity, like
partial beam filling. Furthermore, the correction factor may be used as a
first assessment of attenuation due to liquid water.
As stated above, the choice of the frequencies governs the whole separation
process. In contrast to a lower-frequency radar, the 35GHz system
is completely insensitive to clear-air scattering. Hence, its Doppler
spectrum can be regarded as reference for the particle influence. A large
frequency spacing factor of 73 supports an even stronger discrimination of
clear-air and particle signal.
Compared to , the separation scheme had to be
modified in several aspects. The beamwidth of the cloud radar is rather small
(0.28∘, Table ); hence the beamwidth-broadening
effect had to be included (see Sect. ). During
construction of the weighting function, the fixed scaling factor of
40dB was replaced by the inverse SNR, which provides a better
suppression of the particle contribution. With the instruments used in this
study, the resolution in terms of velocity (<0.1ms-1), height
(<100m) and time (10s) is considerably improved
compared to prior work e.g., making the
scale of cloud processes accessible.
The Monte Carlo approach can only provide a first estimate of the possible
error. For single Doppler spectra the error in velocity according to the
Monte Carlo simulation can be up to ±0.3ms-1, whereas on
average this error is much smaller. These large errors are typically caused
by spectra where scattering from clear-air and particles is hardly separable.
The prediction of the error based on parameters computed from the Doppler
spectrum makes it possible to obtain an error estimate
for quasi-instantaneous values of the vertical air velocity. This offers the
possibility of including the error estimate in all following analysis steps,
which is an improvement on prior work.
Summary, conclusions and outlook
An synergistic algorithm based on a combination of Doppler spectra of a RWP
and a 35GHz cloud radar was developed with the goal of resolving
the Bragg–Rayleigh ambiguity, which can mask the vertical air motion when
particles are present. It was evaluated with a Monte Carlo approach using
synthetically generated Doppler spectra. The bias in the vertical air
velocity estimate for both methods is close to 0ms-1 with a
interdecile range of below 0.1ms-1. The results of the Monte
Carlo simulations are used to provide an error estimate for single Doppler
spectra. To automate the algorithm a continuous relative calibration
procedure and a quality control flag were also included. The relative
calibration proved to be quite stable over the 3 months of observations
available so far.
The application of the separation algorithm for vertical air velocity
estimate within clouds was shown for two case studies. They illustrate that
the algorithm can be applied to real measurements under various atmospheric
conditions, offering a deeper insight into the formation and evolution of
clouds.
The Cloudnet retrieval provides a proven
synergistic method for evaluation of numerical weather prediction models e.g., and the long-term quality-controlled data set also makes detailed cloud
microphysics studies possible . However,
continuous information on vertical air motion is not yet available in
Cloudnet, which means that a major constraining factor of cloud microphysics
is disregarded. The presented combination of a RWP and a cloud radar,
together with the separation algorithm, is able close this gap and can
provide a data set for further studies on aerosol–cloud dynamics and model
evaluation.
The calibrated RWP can provide information besides the air motion. Being less
susceptible to attenuation, quantitative measurements of the reflectivity are
possible under nearly all conceivable weather conditions. For long-term
measurements the combination of a 30 min DBS-based wind measurement mode
followed by a 30 min high-resolution vertical wind measurement mode turned
out to be a good compromise between frequent profiles of horizontal wind and
long-enough periods of vertical observation. By combining the
intermitting mode with standard Cloudnet methodology long-term observations
of vertical air motion on the scale of clouds become possible. Such a data
set would allow for model evaluation and studies on cloud-dynamics interactions over statistically
significant time periods.
The processing software “spectra mole” as used for
this publication is available under 10.5281/zenodo.1419486 (Radenz and
Bühl, 2018). The most recent version is available via GitHub:
https://github.com/martin-rdz/spectra_mole (last access:
15 October 2018). The raw and processed data are available from the
corresponding author on request.
MR developed the algorithm and wrote the paper.
JB initiated the COLRAWI project and performed synergistic integration of
data from cloud radar and wind profiler. UG performed the Cloudnet
measurements at Lindenberg. RL performed the special RWP measurements at
Lindenberg. VL performed the special RWP measurements at Lindenberg,
supervised the work and contributed to the manuscript. All authors
contributed continuously to the scientific discussion, planning and timing of
the measurements and implementation of the project.
The authors declare that they have no conflict of
interest.
Acknowledgements
The research leading to these results has received funding from the European
Union's Horizon 2020 research and innovation programme under grant agreement
no. 654109 (ACTRIS), the European Union Seventh Framework Programme
(FP7/2007–2013) under grant agreement no. 603445 (BACCHUS) and from the
HD(CP)2 project (FKZ 01LK1209C and 01LK1212C) of the German
Ministry for Education and Research. The publication of this article was funded
by the Open Access Fund of the Leibniz Association.
Edited by: S. Joseph Munchak
Reviewed by: two anonymous referees
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