Retrieving stratocumulus drizzle parameters using Doppler radar and lidar
E WAN J. O’C ONNOR , ROBIN J. H OGAN
AND
A NTHONY J. I LLINGWORTH
Department of Meteorology, University of Reading, United Kingdom
Submitted to J. Appl. Meteorol., July 2003
ABSTRACT
Stratocumulus is one of the most common cloud types globally with a profound effect on the Earth’s radiation budget, and
the drizzle process is fundamental in understanding the evolution of these boundary-layer clouds. In this paper a combination of
94-GHz Doppler radar and backscatter lidar is used to investigate the microphysical properties of drizzle falling below the base
of stratocumulus clouds. The ratio of the radar to lidar backscatter power is proportional to the fourth power of mean size so
potentially can provide an accurate size estimate. Information about the shape of the drop size distribution is then inferred from
the Doppler spectral width. The algorithm estimates vertical profiles of drizzle parameters such as liquid water content, liquid
water flux and vertical air velocity, assuming that the drizzle size spectrum may be represented by a gamma distribution. The
depletion timescale of cloud liquid water through the drizzle process can be estimated when the liquid water path of the cloud is
available from microwave radiometers and our observations suggest that this timescale varies from a few days in light drizzle to
a few hours in strong drizzle events. We have used both radar and lidar observations from Chilbolton, and aircraft size spectra
taken during the Atlantic Stratocumulus Transition Experiment, to derive the following power law relationship between liquid
water flux (LWF) in g m 2 s 1 and radar reflectivity (Z ) in mm6 m 3 : LWF 0 0093 Z 0 69 . This is valid for frequencies up
to 94 GHz and therefore would allow a forthcoming spaceborne radar to measure liquid water flux around the globe to within a
factor of two for values of Z above 20 dBZ .
1. Introduction
bution from the vertical velocity of the air.
Wakasugi et al. (1986) proposed that clear air Doppler
radar provided the necessary air velocity information and
Gossard (1988), using a 915 MHz wind profiler, also
demonstrated that it is possible to separate the clear air
return from the drizzle return and thus obtain the vertical
air velocity directly. Millimeter-wave cloud radars have
the necessary sensitivity and narrow beamwidth to measure the Doppler spectrum of the smaller drizzle droplets
of interest but are no longer sensitive to the clear air return, so a method of estimating the vertical air velocity
accurately by some other means is required as the terminal velocity of the drizzle droplets is comparable to the expected updrafts and downdrafts. The airborne Wyoming
Cloud Radar aboard the University of Wyoming King Air
uses the aircraft inertial navigation system to attempt to
correct for the vertical air velocity (Vali et al., 1998; Galloway et al., 1999; French et al., 2000) but this is of course
not possible from the ground.
In addition to measuring the mean velocity and spectral width, Doppler radars are able to measure the full
spectrum of velocities within the radar sample volume. It
is therefore possible, in principle, to separate the cloud
droplet component of the spectrum (droplets less than
50 m in diameter) from the drizzle component (Gossard
et al., 1997; Babb et al., 1999). The terminal fall velocity of these cloud droplets is typically only a few cm s 1 ,
so that they can be considered as tracers of the air motion
and the air velocity can be inferred. However, due to the
sixth power dependence of the radar return on droplet diameter, the echo from the cloud mode tends to be much
smaller than that of the drizzle, and only a small amount
of turbulence is sufficient to smear the Doppler spectrum
Boundary-layer clouds are one of the most significant components of the shortwave radiation budget of the
Earth (Ramanathan et al., 1989; Harrison et al., 1990) and
the accurate representation of such clouds in numerical
models is crucial for understanding climate (Slingo and
Slingo, 1991; Jones et al., 1994). Observations (Miller
et al., 1998; Albrecht, 1989) and modelling studies (Albrecht, 1993; Wood, 2000) have shown that drizzle is important principally because it is involved in determining
the cloud lifetime and evolution. The drizzle process may
also have implications for the radiative properties of such
clouds (Feingold et al., 1996, 1997) through alteration of
the cloud droplet spectra. For the purposes of this paper,
we define drizzle as water droplets greater than 50 m
in diameter (e.g. French et al., 2000) which may or may
not evaporate before reaching the surface, rather than the
200 m in the American Meteorological Society glossary (1959).
Previous ground-based Doppler radar techniques for
measuring rain and drizzle droplets have attempted to exploit the direct relationship between terminal fall velocity
and droplet size. By assuming a model for the droplet size
distribution, such as lognormal or gamma, the radar reflectivity factor, mean Doppler velocity and Doppler spectral width can be used to estimate the number concentration and mean size of the drops (Atlas et al., 1973; Frisch
et al., 1995). However, an ambiguity arises because the
measured mean Doppler velocity has a significant contri-
Corresponding author address: Department of Meteorology, Earley
Gate, PO Box 243, Reading RG6 6BB, United Kingdom.
E-mail: [email protected].
1
6250 Hz, yielding a folding velocity of 5 m s 1 . The
first three moments of the Doppler spectrum are calculated from the average of thirty 256-point FFTs (fast
fourier transforms) which gives a temporal resolution of
1.25 s. The estimated sensitivity is 50 dBZ at 1 km. It
has been calibrated to within 1.5 dB by comparison with
the 3 GHz radar at Chilbolton which itself has been calibrated to better than 0.5 dB using the non-independence
of its polarimetric parameters (Goddard et al., 1994).
The radar used in the second case study was the zenithpointing 35 GHz Rabelais radar, on loan from the University of Toulouse. It is of the conventional pulsed type with
a pulse width of 0.33 s, a beamwidth of 0.4 , a PRF of
3125 Hz, has a folding velocity of 6 m s 1 and was sampled every 75 m. It has been calibrated to within 1.5 dB
by comparison with the 3 GHz radar at Chilbolton in the
same manner as the 94 GHz Galileo radar and the estimated sensitivity is 42 dBZ at 1 km.
Situated close to the radar during both case studies was
a zenith-pointing Vaisala CT75K ceilometer consisting of
an InGaAs diode laser operating at 905 nm with a divergence of 0.75 mrad and a field of view of 0.66 mrad (both
half angle). It is a fully automated system which produces
averaged profiles every 30 s with a range resolution of
30 m. Calibration of the lidar to within 5% is achieved
using the technique described by O’Connor et al. (2004).
so that the narrow cloud peak is lost in the larger drizzle
mode.
In this paper we combine the Doppler radar measurements with those of a backscatter lidar to retrieve the crucial drizzle parameters. The lidar backscatter signal is approximately proportional to the second power of the diameter so the ratio of the radar to lidar backscatter power
is a very sensitive function of mean size (Intrieri et al.,
1993). Once the size is known, concentration and higher
moments of the distribution can be derived from the observed radar reflectivity, which depends on the assumed
size distribution. However, the technique may only be applied in the drizzle below cloud base as the lidar beam is
strongly attenuated as soon as it penetrates the cloud. In
drizzle there is minimal attenuation of the lidar and radar
signals and cloud base is always well defined by the lidar, but cannot be detected using the radar echo which
is dominated by the drizzle droplets. The inferred drizzle droplet concentration and mean size are refined further
by using the Doppler spectral width to infer the shape of
the droplet size distribution. We also correct the observed
Doppler spectral width for turbulence by calculating the
standard deviation of the measured mean velocities and
assuming a 5 3 power law for the vertical velocity spectrum. We then calculate bulk parameters such as drizzle
liquid water content and liquid water flux, and if total liquid water path is available from microwave radiometers,
the timescale for the depletion of cloud water by drizzle
may be estimated.
The absolute value of the mean Doppler velocity is not
used in the retrieval of the drizzle droplet size distribution
but we are able to calculate the theoretical Doppler velocity that would be measured in still air for the derived size
distribution. The difference between this and the actual
Doppler velocity therefore yields the air vertical velocity.
A useful validation for the technique is that over a few
hours the mean of this inferred air velocity should be zero
providing there are no topographical effects.
The instrumentation used in this paper is described in
section 2. In section 3, the theoretical basis for the technique is explained in detail. The parameters that are available from the radar and lidar are presented, as are any necessary assumptions. The expected accurracy and possible
shortcomings of the technique are discussed in section 4.
In sections 5 and 6 results are presented from two case
studies undertaken at Chilbolton and a relationship between radar reflectivity and liquid water flux is proposed
in section 7.
3. Theory
a. Measured parameters
A Doppler radar commonly measures the first three
moments of the Doppler spectrum which, in principle,
contain the information required to derive the parameters
of a three-parameter droplet size distribution (Frisch et al.,
1995). However, although the radar reflectivity is directly
related to the droplet size distribution alone, the Doppler
velocity and Doppler spectral width may have significant
contributions from the air motion as well.
The radar reflectivity factor for spherical liquid water
droplets at frequency f , is defined as
Zf K f T 2
2
K f 0
n D D 6 f
D d D (1)
0
where K f T 2 is the dielectric factor of liquid water at
temperature T, K f 0 2 is the dielectric factor of liquid
water at 0 C, n D d D is the number concentration of
water droplets with diameters between D and D d D,
and f D is the Mie/Rayleigh backscatter ratio. The ratio of dielectric factors present in (1) ensures that radars
of different wavelengths will all measure the same Z for
a 0 C cloud containing Rayleigh-scattering liquid water
droplets. The dielectric constant varies with temperature
at 94 and 35 GHz and is calculated using the empirical
formula given by Liebe et al. (1989).
2. Instrumentation
The radar used in the first case study was the zenithpointing 94 GHz Galileo radar located at Chilbolton in
Southern England. It is of the conventional pulsed type
with a pulse width of 0.5 s, a beamwidth of 0.5 and is
operated with a range resolution of 60 m and a PRF of
2
d d
(2)
n D D 6 D f D d D
n D D 6 f D d D 0
0
log (vertical velocity spectral energy)
The mean Doppler velocity, , measured by a zenithpointing Doppler radar is the sum of the vertical air motion, , and the mean Z -weighted droplet terminal fall
velocity, d :
(3)
In this paper we adopt the convention that velocity is positive away from the radar. Beard (1976) provided semik
k
k
empirical formulae for calculating the terminal velocity
l
s
λ
log (horizontal wavenumber)
of individual water droplets, D .
The radar Doppler spectral width, , is the Z - F IG . 1: Theoretical turbulent spectrum plotted on a log-log scale where
weighted standard deviation of velocities within the pulse the dark shaded area is the turbulent energy affecting the radar in 1 secvolume. In the absence of turbulence a distribution of ond and the light grey area is the turbulent energy measured over 30
droplets will have an intrinsic Doppler variance due to the seconds.
range of terminal velocities given by
where a is the universal Kolmogorov constant, & is the
D!
" d 2 n D D 6 f D d D
0
2
(4) dissipation rate and k is the wavenumber which can be
d 6 n
D
D
D
d
D
related to a length scale, L, by k 2() L. The turbulent
f
0
contribution to the spectral width is then
Broadening of the spectrum can occur if the droplets expek*
rience additional random motion due to turbulence and for
S k dk (8)
t2 a vertically pointing radar with finite beamwidth there is
ks
a contribution from the component of the horizontal wind
3
along the beam. If it is assumed that the sources of spec(9)
a & 2' 3 k+ 2' 3 ks 2' 3 2
tral broadening are independent of one another, the ob2' 3
3a &
served spectral variance, 2 , is the sum of the variances
L s 2' 3 L + 2' 3 (10)
2
2
(
from each source (Doviak and Zrnić, 1993) such that
2
d
2
#
b
2
$
t
2
where k+ 2(, L + is the smallest scale probed by the
Doppler radar (L + is half the radar wavelength) and ks 2(, L s corresponding to the scattering volume dimension
which also includes large eddies travelling through the
sampling volume within the dwell time (1 second) for the
radar. For a beamwidth of 0 5 and no wind, L s is about
mm and the impact of L +
9 m at 1 km whereas L + is 1.6
appears negligible. The cut-off for the turbulent kinetic
energy spectrum in the viscous sub-range may be at larger
scales than the smallest scale probed by the Doppler radar
but, even if the cut off is at 10 cm, the second term in (10)
is only 5% of the first term and L + can be ignored.
The difficulty with this technique using the observed
Doppler width, , for a one second dwell is that we cannot separate the d and t components in (5). We now follow Bouniol et al. (2003) and consider a new parameter,
. - 2 , which is the variance of the individual mean Doppler
velocities measured each second, computed over 30 seconds, and show that . - 2 is dominated by turbulence and
can be used to estimate the t 2 component of the one second Doppler variance 2 in (5) which can be subtracted
so that d 2 can be derived.
Figure 1 displays the theoretical turbulent energy
spectrum as a function of wavenumber and the two in-
(5)
where b 2 is the contribution due to finite beamwidth and
t 2 is the contribution from air turbulence. We are interested in d 2 so we need to estimate b 2 and t 2 and remove
them. The value of b , assuming a circularly symmetric
Gaussian pattern, is given by (Doviak and Zrnić, 1993)
b
U%
4 ln 2
(6)
where % is the one-way, half-power beamwidth of the
radar antenna in radians and U is the horizontal wind. For
a typical wind speed (U 10 m s 1 ) in the boundary
layer, b 0 032 m s 1 for the 94 GHz Galileo radar.
Kollias et al. (2001) estimated the turbulence in fairweather cumuli by assuming that t 2 in (5) was the dominant contribution. We follow the method of Bouniol et al.
(2003), where it is assumed that turbulence is a homogeneous and isotropic process of energy dissipation. The
Kolmogorov hypothesis then states that the statistical representation of the turbulent energy spectrum S k is given
by
S k a & 2' 3 k 5' 3 (7)
3
0.5
0.4
Ratio of σt 2 to σ−v 2
The equations (7-15) are based on the assumption that
the length scales of turbulent eddies being probed by the
Doppler radar lie within the inertial subrange of the turbulence spectrum and that - 2 is dominated by turbulence
rather than any coherent fluctuations in droplet terminal
velocity. These assumptions have been shown to be valid
by Bouniol et al. (2003) who observed that, in drizzle, the
value of & derived from - 2 is independent of the integration time.
The lidar extinction coefficient, 4 (in m 1 ), is defined
as
(
(16)
n D D 2 d D
4 2 0
0.5 km
1 km
2 km
3 km
0.45
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
10
20
30
40
−1
Horizontal wind speed, U (m s )
50
where it is assumed that the lidar wavelength is small
compared to the particle size and the geometric optics apF IG . 2: Theoretical ratio of / t 2 to /12 0 2 as a function of horizontal wind
proximation can be applied. The relationship between 4
speed for a beamwidth of 0 53 at various altitudes.
and the lidar backscatter coefficient, 5 (in m 1 sr 1 ), is described by
tegrals that relate to - 2 and t 2 , where we assume the
(17)
4 S5!
turbulent contribution dominates . - 2 and is given by
where S (in sr) is termed the lidar ratio and varies with
ks
wavelength and droplet size. Raman lidars (Ansmann
(11) et al., 1992) and high spectral resolution lidars (Grund
S k dk - 2 kl
and Eloranta, 1990) can measure 4 directly but most li2' 3
3a &
2' 3
2' 3
dars
measure only the attenuated backscatter coefficient
Ll Ls
(12)
2 2(
5,6 which is related to the true backscatter coefficient, 5 ,
where kl 2(, L l and relates to the large eddies trav- by
z
elling through the sampling volume during the averaging
5 6 z 57 z exp 2
48 z 6 dz 6
(18)
0
time. If we take the ratio of (10) to (12) we have
Generally, the attenuation in drizzle is small (4
9
L s 2' 3
t2
1
0
5
km
)
and
therefore
4
can
be
retrieved
from
(17)
(13)
(18) without experiencing instability, providing S can
. - 2
L l 2' 3 L s 2' 3 and
be estimated with sufficient accuracy. The estimation of
The length scale is given by,
S using Mie theory is described below.
%
L U t 2z sin
(14) b. Drizzle parameters
2
We now have three independent measurables, Z , where t is the observation time and z is the height in m. and 4 from which to derive the three parameters (NW ,
For an averaging time of 30 seconds the second term in D0 and ) describing the droplet size distribution, n D ,
(14) can often be ignored and L l U t. For L s , t is 1 which we assume can be represented by a normalised
second and the correction for the beamwidth is necessary gamma distribution of the form
for low U.
:
D
[3 67 ] D
The theoretical ratio of t 2 to - 2 is displayed in Fig. 2
n D NW f exp
and shows the effect of the beamwidth correction at low
D0
D0
wind speeds. It also shows that for low altitudes and hori(19)
zontal winds greater than about 10 m s 1 the ratio is close where NW is the concentration normalised so that the liqto 0.14 so that for the Galileo radar at a height of 1 km the uid water content is independent of , D0 is the median
contribution of turbulence to 2 on a 1 second timescale equivolumetric diameter, represents the shape of the
is estimated as
distribution and
(15)
t 2 0 14 - 2
6 3 67 4
f
(20)
; The horizontal winds from the Met Office mesoscale
3 674
4
model are generally accurate to 1-2 m s 1 (Panagi et al.,
;
2001) so, in this study, we have used the model winds and where
denotes the gamma function. For a value of
Fig. 2 to provide a more precise estimate of the turbulent
0,
(19)
reduces to the familiar inverse-exponential
contribution.
distribution.
4
be determined accurately using Mie scattering theory by
including the factor f D from (1) in (21). For the purposes of this paper we define 6 to describe this departure from pure Rayleigh scattering in terms of distributions of droplet sizes rather than for single droplets (i.e.
Z Mie 6 Z Rayleigh ). Figure 3 shows theoretical values
of 6 at 94 and 35 GHz as a function of D0 and . For
D0 9 200 m, 6B D0 1 to within 2% at 10 C for all
, but at larger sizes Mie scattering effects become significant and, for certain sizes, Mie scattering is stronger than
the Rayleigh scattering assumption due to the influence
of the resonance region described by van de Hulst (1957).
The temperature profile obtained from observations or an
operational forecast model is used to account for the small
temperature dependence of 6 .
1.4
Mie−to−Rayleigh ratio, γ ’
1.2
1
0.8
0.6
0.4
µ= 0
µ= 2
µ= 5
µ = 10
0.2
0
10
100
Median volume diameter, D0 (µm)
1000
µ= 0
µ= 2
µ= 5
µ = 10
d
−1
Intrinsic Doppler spectral width, σ (ms )
F IG . 3: Theoretical Mie-to-Rayleigh ratio, <>= , at 94 GHz (black) and
35 GHz (grey) for gamma distributions of droplet sizes with different
values of ? at 103 C.
If we initially assume Rayleigh scattering so that
D
f
1 in (1) and that, in the absence of attenuation,
the lidar extinction coefficient can be obtained from the
observed lidar backscatter, then we can take the ratio of Z
to 4 defined in terms of (19) to remove the dependence on
NW f and obtain as a first approximation
Z
4
(
2
0
D 6@
0
D 2@
:
:
exp [3A 67@
D0
exp [3A 67@
D0
:
:
]D
dD
]D
dD
(21)
1
0.1
0.01
10
100
Median volume diameter, D (µm)
1000
0
F IG . 4: Intrinsic Doppler spectral width, / d , at 94 GHz for gamma distributions of droplet sizes with different values of ? at 103 C.
µ= 0
µ= 2
µ= 5
µ = 10
d
−1
Intrinsic Doppler spectral width, σ (ms )
where the slight variation of the dielectric factor with
temperature in (1) has been accounted for by using the
temperature profile obtained from observations (radiosondes) or numerical operational forecast models. Integration
over all sizes yields
;
Z
2 7 1
(22)
D0 4
;
4
(
3 3 67 4
and the potential accuracy of the technique is illustrated
by the fourth power dependence of the radar/lidar ratio
on D0 , which results in the relative error in retrieved size
being much less than the error in the input parameters Z
and 4 , and any small errors due to the truncation ratio
of the gamma function (Ulbrich and Atlas, 1998) will be
similarly reduced to negligible levels.
At high frequencies the Rayleigh scattering assumption can only strictly be applied when dealing with individual cloud and drizzle droplets smaller than around
300 m at 94 GHz and 1 mm at 35 GHz. Since we are
considering size distributions whose droplets are spherical (droplets are not significantly aspherical until they
are a few millimetres in diameter) and have a well defined refractive index, their backscattering properties can
1
0.1
0.01
10
100
Median volume diameter, D0 (µm)
1000
F IG . 5: Intrinsic Doppler spectral width, / d , at 35 GHz for gamma distributions of droplet sizes with different values of ? at 103 C.
Figures 4 and 5 display theoretical values of 5
d
as a
where S and 6 are functions of and D0 ( 6 also varies
very slightly with temperature), and are implemented as
look-up tables. A first estimate of D0 can be found by assuming a value of 0 in (23). This estimate can then
be refined iteratively by comparing the observed spectral
width (corrected for turbulence) with that calculated using (4), adjusting to agree with observations and recomputing D0 until convergence. Once D0 and are established, NW is derived from observed Z . Now that we
have derived the three parameters, NW , D0 and that define n D , d can be calculated independently of the mean
Doppler velocity, using (3), and the vertical air motion can be inferred. The drizzle liquid water content (LWCd and the drizzle liquid water flux (LWFd ) are defined as
follows;
(
n D D 3 d D (24)
LWCd F l
6 0
(
LWFd (25)
n D D 3 D d D F l
6 0
function of median volume diameter for various values of
at 94 and 35 GHz. These show the smooth transition
from the Stokes regime, where d C D 2 for the terminal
fall velocity of droplets 9 60 m, to a more linear regime.
Mie scattering effects are again noticeable when D0 D
200 m. It can be seen that d varies by about a factor of
two between 0 and 10, allowing retrieval of from after it has been corrected for turbulence and any
horizontal winds using (6).
The relationship between lidar extinction and
backscatter in stratocumulus clouds and drizzle can
also be derived using Mie theory. The value of the
lidar backscatter coefficient oscillates wildly with size
for individual droplets but once a realistic spectrum of
droplet sizes is present these oscillations are smoothed
out (O’Connor et al., 2004). Figure 6 displays the 905 nm
extinction-to-backscatter ratio, S, as a function of D0
and . Our computations show that the change in visible
refractive index is negligible for the range of temperatures
expected. For droplet median diameters ranging from
Extinction−to−backscatter ratio, S (sr)
where F l is the density of liquid water.
If we can estimate how much liquid water is in the
cloud and the rate at which drizzle is leaving the cloud,
then the timescale for cloud liquid water depletion by
drizzle is given by
100
G
LWP
LWFd
(26)
10
where LWP is the total liquid water path (i.e. cloud plus
drizzle) obtained from coincident radiometers and LWFd
is the liquid water flux immediately below cloud base.
µ= 0
µ= 2
µ= 5
µ = 10
1
10
100
Median volume diameter, D0 (µm)
4. Error analysis
1000
In this section we estimate the error in the retrieval
of D0 , drizzle liquid water content, drizzle liquid water
flux and vertical air velocity. We first assume that the
shape of the droplet size distribution (i.e. the value of in
Eq. 22) is known and the droplets are Rayleigh scattering
with respect to the radar. If we integrate the appropriately
weighted gamma function over the drop size distribution
then we have
F IG . 6: Theoretical lidar ratio, S, at 905 nm as a function of D0 for
gamma distributions of droplet sizes with different values of ? .
10 to 50 m the value of S D0 is almost constant
with a value of 18 8 sr. Typical droplet diameters for
stratocumulus with significant
liquid water content (Miles
et al., 2000) lie between 8 and 20 m. It is this feature
of stratocumulus clouds that can be used to calibrate the
lidar (O’Connor et al., 2004). The median diameter of the
droplet size distribution for drizzle droplets falling below
the cloud (D0 D 50 m) lie in the range where S D0 can no longer be assumed constant and needs to be taken
into account.
Z
5
LWCd
LWFd
d
C
C
C
C
C
N W D0 7 N W D0 3 N W D0 4 N W D0 5 D0 (27)
(28)
(29)
(30)
(31)
c. Algorithm
Equation 22 can now be written as
;
Z
2 7 S D0 6E D0 D0 4
;
5
(
3 3 67 4
where it has been assumed that for LWFd , the terminal velocity distribution D in (25) is adequately represented
by C D. The weak functional dependence on is ad(23) dressed later.
6
The random error in Z can be expressed, in linear and is about 18%.
space, as
The Z -weighted droplet terminal velocity, d , is proH
1
portional to D0 according to (31) and will therefore have
Z I
(32)
the same error characteristics as D0 with a relative error
MI
of 12%. If D0 is very low, then the contribution of drops
where M I is the number of equivalent independent samfalling in the Stoke’s regime could lead to d C D0 2 , and
ples, given by Doviak and Zrnić (1993):
a consequent error in d of 24%. The mean Doppler ve1
locity is measured directly by the radar and the error
4 G d ( 2
(33) in is better than the bin width of the Doppler spectrum
MI J
produced by the FFT as part of the coherent processing
J
where is the spectral width, G d the dwell time and the algorithm. For the Galileo radar the velocity resolution
radar wavelength. In this paper the radar data are averaged is on the order of 4 cm s 1 . The error in the vertical air
over 30 seconds to match the temporal resolution of the li- velocity is given by
H
H
H
dar data. With a typical spectral width of 0 5 m s 1 , the
1
2
random error in Z is about 0 02 dB, or 0.5%, at 94 GHz
(38)
d 2 2
H
35 GHz. A larger systemand close to 0 04 dB, or 1%, at
atic error may be present due to the difficulty of accurately and as is so low, the error in is the same magnitude
calibrating a radar of this wavelength. We estimate the as the error in d .
accuracy of the calibration to be around 1.5 dB (Hogan
The Doppler spectral width contains the information
et al., 2003) or 40%.
about the shape of the droplet size distribution. Figures 4
The lidar is a commercial instrument and the errors and 5 show that estimating the value of to within one
are difficult to determine. However, the signal to noise element of the sequence 0, 2, 5, 10, requires that d can be
ratio is good at low altitudes and the lidar has been obtained to within 30%. In principle, the Doppler spectral
calibrated to within 5% using the technique described width, , can be measured to much better than 30%, but
by O’Connor et al. (2004) so that we estimate the error in the error in deriving d depends on the relative size of the
lidar backscatter, 5 , for individual rays to be about 10%. other contributing terms to plus their associated error.
From (22), if S is constant, D0 C Z K5) 1' 4 but for
It was shown in section 3 that b is typically a few
drizzle the factor S D0 from (23) should also be in- cm s 1 and can be neglected. We observe that typical valcluded; the slope of the curves in Fig. 6 for D0 D 100 m ues of M - in drizzle are of the order 0 1 m s 1 so from (15)
indicates this can be approximated by S C D0 0A 5 so the estimated value of t is about 0 04 m s 1 . From Figs. 4
that
and 5, the terminal velocity component
of the Doppler
2
1
7
(34) width, d , is above 0 1 m s once D0 D 100 m, and so
D0 C Z L5M
is less than 15%. Consequently,
the turbulent correction
The fractional error in the median volume diameter is then
we should be able to distinguish changes in from 0 to 2,
H
H
H
1
2 to 5 or 5 to 10 quite easily for D0 D 100 m and obtain
2
5 2
D0
2
Z 2
(35) an indication of the value of for D0 D 50 m. The effect
D0
7
Z
5
of these changes in can be derived by an appropriately
weighted integration of the normalised gamma function
so that if the fractional error in Z is about 40% and the (19) to give the dependence in equations (27-31), and
fractional error in 5 is about 10%, the relative error in D0 reveals that these step changes in lead to a change in D0
is about 12% when is known.
and LWFd of about 7% and minimal change in the liquid
For the drizzle liquid water content, LWCd C NW D0 4 , water content. Hence we conclude that, for the instrument
which can be written as LWCd C Z D0 3 or LWCd C
errors considered, the overall error in D0 and is about
Z 1' 7 5 6' 7 and the fractional error,
14%, LWCd about 10% and LWFd about 20%. These erH
H
H
rors are valid provided that, at 94 GHz, D0 is less than
1
2
2
around 500 m, and at 35 GHz, D0 is less than around
LWCd
1
Z
6 5 2
(36) 1 mm.
LWCd
7
Z
5
is about 10%. Considering the drizzle liquid water flux, 5. 11 September 2001 Case Study
LWFd C
NW D0 5 , which can be written as LWFd C
We now apply the technique described in section 3 to
2
Z D0 or LWFd C Z 3' 7 5 4' 7 , the fractional error is given
data taken by the Galileo Doppler radar and the Vaisala
by
lidar ceilometer at Chilbolton. Figure 7 shows 3 hours of
H
H
H
1
data taken on the morning of 11 September 2001 during
2
2 2
LWFd
1
3 Z
4 5
typical
stratocumulus conditions with appreciable drizzle
(37)
5
LWFd
7
Z
falling beneath the base of the cloud. Panel (a) shows
7
1
dBZ
Height (km)
2
(a) Chilbolton 94 GHz Galileo radar − Radar Reflectivity Factor
m
−1
2
10−4
(b) Chilbolton 905nm CT75K Lidar Ceilometer − Attenuated backscatter coefficient
−1
1
sr
Height (km)
0
−7
10
−1
−1
0
−2
0.1
−1
1
0
5:30
−1.5
1
(d) Chilbolton 94 GHz Galileo radar − Doppler Spectral Width
ms
Height (km)
10−6
−0.5
1
2
10−5
0
(c) Chilbolton 94 GHz Galileo radar − Mean Doppler Velocity
ms
Height (km)
0
2
10
0
−10
−20
−30
−40
−50
6:00
6:30
7:00
Time (UTC)
7:30
8:00
8:30
0.01
F IG . 7: Observed variables for 11 September 2001. Time-height plots of (a) radar reflectivity factor, (b) attenuated lidar backscatter, (c) radar
Doppler velocity (positive away from the radar) and (d) radar Doppler spectral width. The black line in each panel indicates cloud base derived
from the lidar.
radar reflectivity, Z , and panel (b) coincident attenuated
lidar backscatter 5,6 . The lidar shows a prominent cloud
base at all times, while the radar appears unable to discriminate between drizzle in cloud and drizzle falling beneath the cloud. Cloud base remains relatively constant
at 1.5 km with occasional departures to 1 km which may
indicate pannus, and cloud top appears constant for long
periods with a typical cloud depth of 350 m.
The radar reflectivity is dependent on the sixth power
of the diameter and so the larger, but far less numerous, drizzle droplets in cloud and below cloud dominate
the radar return even though their liquid water content is
neglible compared to that of the small but numerous cloud
droplets. This also explains why, in regions where it is
not drizzling (such as before 05:40 and after 08:20 UTC),
cloud base is detected by the lidar but not the radar as it
is not so sensitive to the small cloud droplets. Reflectivity
values reach 0 dB both in cloud and below cloud while
5,6 values reach 5 N 10 5 sr 1 m 1 below cloud and jump
rapidly to 5 6 D 2 N 10 4 sr 1 m 1 when penetrating the
cloud. The drizzle evaporates completely before reaching
the ground. The background lidar signal of 10 6 sr 1 m 1
is due to boundary layer aerosol.
The radar Doppler velocity, displayed in panel (c),
shows a large variation in the velocity of the drizzle,
ranging from 0 5 to 2 m s 1 , and the pattern of ve
locities is characterized
by narrow fall streaks, indicating the stongly inhomogeneous nature of drizzle. These
streaks usually coincide with the increases seen in radar
reflectivity and lidar backscatter below cloud. Within the
cloud the velocities are generally of a smaller magnitude
and decrease towards cloud top where they are close to
0 m s 1 . Cloud droplets have terminal velocities of only a
few cm s 1 and as the drizzle droplets grow a corresponding increase in terminal fall velocity is observed.
The Doppler spectral width, depicted in panel (d), is
also characterized by streaks which coincide with the increases in radar reflectivity and lidar backscatter below
cloud. The high values seen just prior to 07:00 UTC coincide with the strong negative values in the Doppler velocity.
The derived microphysical parameters are displayed
in Fig. 8. Panel (a) shows D0 , the median volume diameter of the derived drizzle droplet size distribution, varying from 40 m to 250 m, similar sizes to those found
by Vali et al. (1998). The value of which describes
the shape of the size distribution is shown in panel (b).
The derived distributions are consistently broad although
8
(a) Drizzle Median Diameter
200
1
100
0
Height (km)
50
µm
Height (km)
2
2
10
8
6
4
2
0
−1
(b) Drizzle Shape Parameter
1
2
10−1
(c) Drizzle Liquid Water Content
−2
10
−3
1
0
10−4
−1
2
10
(d) Drizzle Liquid Water Flux
10−2
−2 −1
1
gm s
Height (km)
10−3
gm
Height (km)
0
0
5:30
6:00
6:30
7:00
Time (UTC)
7:30
8:00
−3
10
−4
10
8:30
F IG . 8: Drizzle parameters derived from the radar and lidar for 11 September 2001: (a) median diameter D0 , (b) shape parameter
water content and (d) liquid water flux.
?
, (c) liquid
(b) Estimated air velocity, w
1
0.5
5 10 15
5
10
−1
U (ms )
Velocity (ms−1)
0.5
15
Distance (km)
20
10−2
(c) Correlation
−3
10
0
10−4
−0.5
10−5
5
10
15
Distance (km)
20
−1
25
−2 −1
0
0
0
LWF (g m s )
1.5
1
(a)
w (ms−1)
Height (km)
2
25
F IG . 9: (a) Horizontal wind speed, U , taken from sondes at Larkhill at 05Z (solid) and 11Z (dashed) on 11 September 2001. (b) Time series of
vertical air velocity, O , for a selected region (0712 to 0748 UTC) is shown with an aspect ratio of 3:1 (horizontal:vertical). Velocity is positive
away from the radar. Cloud top as measured by the radar is shown by the black line. (c) Time series showing correlation of vertical air velocity, O ,
(black) and drizzle liquid water flux, LWFd , (red) at an altitude of 720 m for the same region as in (b).
9
there are occasions when much narrower distributions are
observed (i.e higher values of ), particularly between
and towards the base of the drizzle streaks. Preferential
evaporation of the smaller drizzle droplets is a possible
explanation. Liquid water content values (panel c) reach
0 2 g m 3 and liquid water flux values (panel d) reach
0 02 g m 2 s 1 (0 07 mm hr 1 ) which are consistent with
et al. (1998) who found maximum drizzle rates of
Vali
0.1-0 2 mm hr 1 . The background vertical air velocity, ,
can be estimated using (2) and (3) and the derived up and
downdrafts reach 1 m s 1 with an error of up to 0 2 m s 1 .
Radiosonde ascents at Larkhill (25 km to the west of
Chilbolton) were available for 05:00 UTC and 11:00 UTC
and were indicative of a decoupled cloud layer capped by
a strong inversion at about 2 km and a boundary layer
reaching 1 km below a transition layer which remained
in place throughout the day. The mean horizontal wind
measured by the radiosondes (Fig. 9a) at cloud level has
been used to transform the time axis into a length scale
and a section of (from 07:12 to 07:48 UTC) is shown in
Fig. 9b. Wind shear is present below cloud and manifests
itself by causing the drizzle streaks to fall at a significant
angle to the vertical, up to 2.5 km in the horizontal for a
1 km fall in the vertical. There is a strong impression of a
cellular structure which, if it extended through the whole
boundary layer, had horizontal-vertical aspect ratios ranging from 1:1 to 3:1 but if confined to the cloud layer had
horizontal-vertical aspect ratios of 2:1 to 6:1. The cloud
top and base remain relatively constant throughout this
period. A time series of and LWFd at 720 m are depicted together in Fig. 9c to show that an increase in drizzle liquid water flux is seen in the vicinity of updrafts. The
mean vertical velocity during this period is 0 2 m s 1
and considering the error in this is not significantly
different from zero. Thus far topography has been neglected
and around Chilbolton the ground slopes up to 20 m over
a distance of 1 km (a gradient of 2%). A steady horizontal
airflow of 10 m s 1 could give rise to a vertical motion of
0 2 m s 1 .
6. 20 October 1998 Case Study
An opportunity to estimate the drizzle depletion
timescale occured during the Cloud Lidar and Radar Experiment, CLARE ’98 (ESA, 1999) , at Chilbolton in October 1998 using data from the 35 GHz Rabelais radar and
Vaisala CT75K ceilometer. Estimates of LWP from microwave radiometers at 21.3, 23.8 and 31.7 GHz were provided by the Technical University of Eindhoven, Netherlands.
The 35 GHz Rabelais did not measure Doppler spectral width during this period and so a constant value of
0 for n D was used when estimating D0 , LWCd and
LWFd . This seems a reasonable assumption based on the
values obtained on 11 September 2001 and any error in
deriving values based on this assumption is not expected
to significantly alter the results, as explained in section 4.
For instance, if 5 when it has been assumed that
0, then LWFd is in error by only 20% whereas the
depletion timescale varies over orders of magnitude. With
no mean Doppler velocity available, it was not possible to
estimate the vertical air velocity.
Figure 10 shows two hours of data taken on the morning of 20 October 1998. Panel (a) shows radar reflectivity factor, Z , and cloud base derived from the lidar is
superimposed. Panel (b) shows attenuated lidar backscatter and, as in the previous case, the cloud base is prominent in the lidar data but not in the radar data. Again,
wind shear was present and affected the angle at which
the drizzle fell although it does not appear to have been
as strong within cloud. The cloud top remained constant
at about 2.25 km while the cloud base had more variation
and cloud depth ranged from 400 m to 800 m. The drizzle
completely evaporated before reaching the ground.
The derived microphysical parameters are shown in
Fig. 11. Values of D0 (panel a) reach 300 m in the
strong drizzle streaks near 08:00 UTC with LWCd values
reaching 0 1 g m 3 (panel b) and LWFd values reaching
0 05 g m 2 s 1 (panel c).
Values of the total column liquid water path, LWP, obtained from the microwave radiometers, range from 100300 g m 2 which are typical of stratocumulus (Greenwald
et al., 1995) and distinct increases in cloud LWP correlate well with the strong drizzle streaks and associated
increases in drizzle LWP. Comparison of the cloud LWP
with the liquid water path of the drizzle in panel d indicates the relative partitioning of liquid water between
cloud mode and drizzle mode; the drizzle LWP is often
two orders of magnitude lower than the cloud LWP in
light drizzle. This confirms that the drizzle LWP makes a
negligible contribution to the total LWP measured by the
radiometer which is dominated by the cloud. The value
of G derived using (26) is shown in panel e and varies
from several days for the weaker drizzle to two hours in
the stronger drizzle events (the period after 07:35 UTC).
The scatter in G matches the inherent variable nature of
drizzle.
7. Relation between drizzle flux and radar reflectivity
factor
Observed values of radar reflectivity factor versus derived values of drizzle flux, LWFd , are plotted together
with the line of best fit and its standard deviation, in
Fig. 12 for the 94 GHz case on 11 September 2001, and
in Fig. 13 for the 35 GHz case on 20 October 1998. The
fits for the two cases agree quite well and we suggest that
the power law relationship derived from the 11 September
2001 case;
10
LWF 9 3 N 10
6
Z 0A 69 (39)
2
dBZ
Height (km)
(a) 35 GHz Rabelais radar − Radar Reflectivity Factor
0
10
0
−10
−20
−30
−40
−50
−5
2
0
6:00
sr−1 m−1
Height (km)
−4
10
(b) Chilbolton 905nm CT75K Lidar Ceilometer − Attenuated backscatter coefficient
6:30
7:00
Time (UTC)
7:30
8:00
10
−6
10
−7
10
2
(a) Drizzle Median Diameter
200
100
1
µm
Height (km)
F IG . 10: Observed variables for 20 October 1998: (a) radar reflectivity factor and (b) attenuated lidar backscatter. The black line indicates cloud
base derived from the lidar.
0
50
2
−2
10
1
g m−3
Height (km)
−1
10
(b) Drizzle Liquid Water Content
0
−3
10
−4
10
2
g m−2s−1
Height (km)
−1
10
(c) Drizzle Liquid Water Flux
1
500
−2
LWP (gm )
0
10−3
−4
10
(d) Liquid water path
LWP cloud
LWP drizzle x 20
0
3
τ (hrs)
10−2
10
(e) Depletion timescale
2
10
1
10
0
10
6:00
6:30
7:00
Time (hrs)
7:30
8:00
F IG . 11: Drizzle parameters derived from radar, lidar and microwave radiometer for 20 October 1998: (a) median diameter D0 , (b) liquid water
content, (c) liquid water flux, (d) liquid water path and (e) drizzle depletion timescale.
11
−3
−3
10
10
−2 −1
log (LWF[kg m s ]) = 0.06889Z[dBZ] −5.031
10
Liquid water flux (kg m−2 s−1)
Liquid water flux (kg m−2 s−1)
10
−4
−5
10
−6
10
−7
10
−8
v (m s−1)
2
−5
10
1.5
−6
10
1
−7
10
0.5
−8
10
−40
−4
10
10
−30
−20
−10
0
10
Radar reflectivity factor Z (dBZ)
20
−40
F IG . 12: Drizzle liquid water flux and radar reflectivity values derived
for the 94 GHz case on 11 September 2001 with mean (solid) and P 1
standard deviation (dashed) fits to the data.
0
−30
−20
−10
0
10
Radar reflectivity factor Z (dBZ)
20
F IG . 14: Liquid water flux and radar reflectivity calculated from FSSP
and 2DC size spectra measured by the Met Office C-130 during ASTEX.
The shading of each point indicates the Z -weighted mean terminal velocity calculated from the spectra.
−3
10
−3
log (LWF[kg m−2s−1]) = 0.07643Z[dBZ] −4.854
10
log (LWF[kg m−2s−1]) = 0.0673Z[dBZ] −4.754
10
−4
10
Liquid water flux (kg m−2 s−1)
Liquid water flux (kg m−2 s−1)
10
−5
10
−6
10
−7
10
−4
10
−5
10
−6
10
−7
10
−8
10
−8
10
−40
−30
−20
−10
0
10
Radar reflectivity factor Z (dBZ)
20
−40
F IG . 13: Drizzle liquid water flux and radar reflectivity values derived
for the 35 GHz case on 20 October 1998 with mean (solid) and P 1 standard deviation (dashed) fits to the data.
where LWF is in kg m 2 s 1 and Z has units of
mm 6 m 3 , would, from the scatter in Fig. 12, allow LWF
to be measured to within a factor of two from Z alone.
This is similar to the relationship derived for the 20th October 1998 case, where the shape of the size distribution
was not known, and implies that the relationship is also
valid at 35 GHz.
It has been proposed that spaceborne radar will be able
to retrieve liquid water content by using a Z -LWC relationship that also incorporates visible optical depth when
available (Austin and Stephens, 2001; Stephens et al.,
2002). This may be possible in drizzle-free clouds but
ignores the fact that drizzle can dominate Z , especially
in marine stratocumulus, while having a negligible impact on the liquid water content (Fox and Illingworth,
1997), so a Z -LWC relationship should be limited to nonprecipitating liquid water clouds (Papatsoris, 1994). A
Z -LWF relationship is likewise limited to precipitating
liquid water clouds, i.e. those that contain drizzle but,
−30
−20
−10
0
10
Radar reflectivity factor Z (dBZ)
20
F IG . 15: Liquid water flux and radar reflectivity values calculated from
FSSP and 2DC size spectra measured by the Met Office C-130 during
ASTEX with thick lines indicating mean (solid) and P 1 standard deviation (dashed) fits to the data. To remove pure cloud droplet spectra, only
values with a Z -weighted mean terminal velocity greater than 0 1 m s 1
are plotted and considered for the regression fit.
since the presence of drizzle droplets greatly enhances the
reflectivity, these are the clouds that are easily detected
by a spaceborne cloud radar (Fox and Illingworth, 1997)
whereas the reflectivity of non-precipitating liquid water
clouds will usually be below the detection limit.
No direct in situ validation was available for the radar
studies in this paper, so, for the purposes of comparison,
we have looked at aircraft observations of particle size
spectra taken during the Atlantic Stratocumulus Transition Experiment (ASTEX) (Albrecht et al., 1995). Figure 14 shows drizzle flux, LWFd , versus radar reflectivity
factor, Z , calculated from 10 second averages of the size
distributions obtained by the Forward Scattering Spectrometer Probe (FSSP) and the 2D cloud probe (2DC)
aboard the Met Office C-130 aircraft. It should be noted
that the ASTEX data include events both in and below
12
cloud and the large scatter is due to the presence of both
small cloud droplets and larger drizzle droplets. Any direct fit to the data will be biased by the high number
of spectra containing cloud droplets only. However, the
Z -weighted mean terminal velocity, d , calculated from
10 second averages of the size spectra using the formulae
given by Beard (1976), and indicated by the shading of
each point in Fig. 14, provides an objective means of separating the cloud and drizzle components so that a comparison can be made with the values of LWFd derived from
the radar/lidar technique. Potentially, the velocity information in Fig. 14 could be used by a Dopplerised spaceborne radar, such as that proposed for EarthCARE (ESA,
2001) , to discriminate between drizzle and cloud.
Figure 15 shows drizzle flux versus radar reflectivity
factor calculated from the ASTEX data, for the drizzle
component only, obtained by selecting the spectra with
0 1 m s 1 . The Z -LWFd relationship that is derived
d D
drizzle component of the data is relatively insenfrom the
sitive to the value of d chosen as the threshold. The fit derived from the ASTEX data is reasonably consistent with
those in Figs. 12 and 13 which are derived from below
cloud base only. The bias of the ASTEX fit is probably
due to the fact that some mixed drizzle and cloud droplet
spectra have been included, and also because the aircraft
probes provided a poor sample of the low concentration
of the larger drizzle droplets. The 30 s averaging of the
radar and lidar data corresponds to a horizontal distance
of approximately 300 m, assuming a typical horizontal
wind speed of 10 m s 1 , and 60 m in the vertical. The ASTEX data were averaged over 10 s, which corresponds to
a horizontal distance of approximately 1 km, and was regarded as the shortest averaging period that would provide
enough drizzle sized drops to form representative drizzle
droplet spectra. This may account for the larger spread
seen in Fig. 15, compared to Figs. 12 and 13, since longer
averaging periods may have produced better spectra but
would have encompassed regions with markedly different
drizzle rates and concentrations.
These plots show that a future spaceborne radar will
be able to make much more accurate measurements of
liquid water flux than liquid water content for values of
Z above 20dBZ , where the radar reflectivity and liquid
water flux is dominated by drizzle droplets and the liquid
water content is dominated by cloud droplets. For lower
values of Z , an ambiguity may arise in deriving liquid
water flux or liquid water content, because both cloud and
drizzle droplets can make a significant contribution to Z
and liquid water flux; the ambiguity could be removed if
the radar had a Doppler capability as envisaged for EarthCARE.
ing radar and lidar to provide continuous measurements
of drizzle. The technique only requires temporal averaging for matching the two data streams, thus 30 second
temporal timescale (and smaller) is possible. This allows
detection of the cellular structure and investigation of the
inhomogeneities present in drizzle.
An advantage of the technique is that there is no reliance on the mean Doppler velocity to obtain the droplet
size distribution, in contrast to existing radar-only techniques. It has the potential to retrieve vertical profiles of
D0 , drizzle LWC and drizzle LWF below cloud base to
within 15-20% with the assumption that a gamma function fits the size distribution, and can also estimate the
vertical wind and the shape parameter, , of the size distribution. The spatial scales of updrafts and downdrafts
can also be derived and it was found that updrafts tended
to coincide with the occurrence of the strongest drizzle
streaks. This indicates that drizzle production may be
enhanced by the evaporative cooling experienced below
cloud which can have a feedback effect into stimulating
the production of more drizzle. Vali et al. (1998) also
observed upward transport of drizzle drops in cloud.
Observations in the first case study suggest that, except at the edges of drizzle regions, the shape parameter,
, tends to be close to zero and appears to confirm the
findings of Ichimura et al. (1980) and Wood (2000), who
both indicated that observations could be sufficiently well
described by an exponential distribution. Therefore, the
technique could be used by an un-Dopplerised radar assuming a fixed value of .
There also appears to be a correlation between drizzle
LWP and cloud LWP in the strong drizzle regions. Previous observations have stated that there is no relationship
between the two and a long timeseries of data would be
required to see if this is a regular occurrence. The drizzle
LWP is affected by wind shear but the timescale for depletion of liquid water is derived from values of LWF taken
directly below cloud base and is unaffected. The minimum value for this timescale is about 2 hours; more observations need to be made to link this timescale to other
meteorological parameters.
The presence of drizzle droplets enhances the reflectivity of liquid water clouds sufficiently so that they can
be detected by a spaceborne cloud radar and, although
it is not possible to retrieve the LWC of such clouds,
a Z -LWF relationship has been shown to be robust enabling the drizzle beneath climatically important marine
stratocumulus to be monitored routinely for the first time.
Acknowledgements
We thank the Radiocommunications Research Unit
at the Rutherford Appleton Laboratory, Henri Sauvageot
8. Conclusion
(University of Toulouse, France), Phil Brown (Met Office)
A technique has been demonstrated that uses the in- and Suzanne Jongen (Technical University of Eindhoven,
herent sensitivity of radar/lidar synergy with zenith point- Netherlands) for providing the data. The Galileo radar
13
was developed for the European Space Agency (ESA) by
REFERENCES
Officine Galileo, the Rutherford Appleton Laboratory and Albrecht, B. A., 1989: Aerosols, cloud microphysics, and
the University of Reading, under ESTEC Contract No.
fractional cloudiness. Science, 245, 1227–1230.
10568/NL/NB. This research was funded by NERC grant
NER/T/S/1999/00105 and EU CloudNet contract EVK2- Albrecht, B. A., 1993: The effects of precipitation on the
CT-2000-00065. The CLARE ’98 campaign was funded
thermodynamic structure of trade-wind boundary layby ESA (grant 12957/98).
ers. J. Geophys. Res., 98, 7327–7337.
Albrecht, B. A., Bretherton, C. S., Johnson, D., Schubert,
W. H., and Frisch, A. S., 1995: The Atlantic Stratocumulus Transition Experiment — ASTEX. Bull. Amer.
Meteorol. Soc., 76(6), 889–904.
American Meteorological Society, 1959: Glossary of Meteorology. American Meteorological Society, 45 Beacon St. Boston, MA.
Ansmann, A., Wandinger, U., Riebesell, M., Weitkamp,
C., and Michaelis, W., 1992: Independent measurement of extinction and backscatter profiles in cirrus
clouds by using a combined Raman elastic-backscatter
lidar. Appl. Opt., 31(33), 7113–7131.
Atlas, D., Srivastava, R. C., and Sekon, R. S., 1973:
Doppler radar characteristics of precipitation at vertical incidence. Rev. Geophys. Space Phys., 11, 1–35.
Austin, R. T. and Stephens, G. L., 2001: Retrieval of stratus cloud microphysical parameters using millimetric
radar and visible optical depth in preparation for CloudSat, Part I: Algorithm formulation. J. Geophys. Res.,
106, 28,233–28,242.
Babb, M. B., Verlinde, J., and Albrecht, B. A., 1999: Retrieval of cloud microphysical quantities from 94-GHz
radar Doppler power spectra. J. Atmos. Ocean. Technol., 16, 489–503.
Beard, K. V., 1976: Terminal velocity and shape of cloud
and precipitation drops aloft. J. Atmos. Sci., 33, 851–
864.
Bouniol, D., Illingworth, A. J., and Hogan, R. J.,
2003: Deriving turbulent kinetic energy dissipation
rate within clouds using ground based 94 Ghz radar. In
31st Conference on Radar Meteorology, Seattle, USA.
Amer. Meteor. Soc., 193-196.
Doviak, R. J. and Zrnić, D. S., 1993: Doppler radar and
weather observations. Academic Press, 2nd edition.
ESA (European Space Agency), 1999: International
Workshop Proceedings, CLARE ’98, Cloud Lidar And
Radar Experiment, ESA WPP-170. European Space
Agency, ESTEC, Nordwijk, The Netherlands.
ESA (European Space Agency), 2001: The Five Candidate Earth Explorer Core Missions - EarthCARE —
Earth Clouds, Aerosols and Radiation Explorer, ESA
14
SP-1257(1). European Space Agency, ESTEC, Nord- Harrison, E. F., Minnis, P., Barkstrom, B. R., Rawijk, The Netherlands.
manathan, V., Cess, R. D., and Gibson, G. G., 1990:
Seasonal variation of cloud radiative forcing derived
Feingold, G., Stevens, B., Cotton, W. R., and Frisch, A. S.,
from the Earth Radiation Budget Experiment. J. Geo1996: The relationship between drop in-cloud resiphys. Res., 95, 18687–18704.
dence time and drizzle production in numerically simulated stratocumulus clouds. J. Atmos. Sci., 53(8), 1108– Hogan, R. J., Bouniol, D., Ladd, D. N., O’Connor, E. J.,
and Illingworth, A. J., 2003: Absolute calibration of
1122.
94/95-GHz radars using rain. J. Atmos. Ocean. Technol., 20(4), 572–580.
Feingold, G., Boers, R., Stevens, B., and Cotton, W. R.,
1997: A modeling study of the effect of drizzle on
cloud optical depth and susceptibility. J. Geophys. Res. Ichimura, I., Fujiwara, M., and Yanase, T., 1980: The size
distribution of cloud drops measured in small maritime
— Atmos., 102(D12), 13527–13534.
cumulus clouds. J. Meteorol. Soc. Jpn., 58, 403–415.
Fox, N. I. and Illingworth, A. J., 1997: The retrieval
Intrieri, J. M., Stephens, G. L., Eberhard, W. L., and Uttal,
of stratocumulus properties by ground based radar. J.
T., 1993: A method for determining cirrus cloud partiAppl. Meteorol., 36, 485–492.
cle sizes using lidar and radar backscatter technique. J.
Appl. Meteorol., 32, 1074–1082.
French, J. R., Vali, G., and Kelly, R. D., 2000: Observations of microphysics pertaining to the development Jones, A., Roberts, D. L., and Slingo, A., 1994: A cliof drizzle in warm, shallow cumulus clouds. Q. J. R.
mate model study of indirect radiative forcing by anMeteorol. Soc., 126, 415–443.
thropogenic sulfate aerosols. Nature, 370, 450–453.
Frisch, A. S., Fairall, C. W., and Snider, J. B., 1995: Mea- Kollias, P., Albrecht, B. A., Lhermitte, R., and
surement of stratus cloud and drizzle parameters in ASSavtchenko, A., 2001: Radar observations of updrafts,
TEX with a KQ -band Doppler radar and a microwave
downdrafts, and turbulence in fair-weather cumuli. J.
radiometer. J. Atmos. Sci., 52(16), 2788–2799.
Atmos. Sci., 58, 1750–1766.
Galloway, J., Pazmany, A., Mead, J., McIntosh, R. E., Liebe, H. T., Manabe, T., and Hufford, G. A., 1989:
Leon, D., French, J., Haimov, S., Kelly, R., and Vali,
Millimeter-wave attenuation and delay rates due to
G., 1999: Coincident in situ and W-band radar meafog/cloud conditions. IEEE AP, 37, 1617–1623.
surements of drop size distribution in a marine stratus
cloud and drizzle. J. Atmos. Ocean. Technol., 16, 504– Miles, N. L., Verlinde, J., and Clothiaux, E. E., 2000:
Cloud droplet size distributions in low-level stratiform
517.
clouds. J. Atmos. Sci., 57, 295–311.
Goddard, J. W. F., Tan, J., and Thurai, M., 1994: Technique for calibration of meteorological radars using dif- Miller, M. A., Jensen, M. P., and Clothiaux, E. E., 1998:
Diurnal cloud and thermodynamic variations in the
ferential phase. Electron. Lett., 30, 166–167.
stratocumulus transition regime: A case study using in
situ and remote sensors. J. Atmos. Sci., 55, 2294–2310.
Gossard, E. E., 1988: Measuring drop-size distributions
in clouds with a clear-air-sensing Doppler radar. J. AtO’Connor, E. J., Illingworth, A. J., and Hogan, R. J.,
mos. Ocean. Technol., 5, 640–649.
2004: A technique for autocalibration of cloud lidar
and for inferring the lidar ratio for ice and mixed phase
Gossard, E. E., Snider, J. B., Clothiaux, E. E., Martner, B.,
clouds. J. Atmos. Ocean. Technol., 21(5), 777–786.
Gibson, J. S., and Kropfli, R. A., 1997: The potential
of 8-mm radars for remotely sensing cloud drop size Panagi, P., Dicks, E., Hamer, G., and Nash, J., 2001: Predistributions. J. Atmos. Ocean. Technol., 14, 79–87.
liminary results of the routine comparison of wind profiler data with the Meteorological Office Unified Model
Greenwald, T. J., Stephens, G. L., Christopher, S. A., and
vertical wind profiles. Phys. Chem. Earth (B) - Hydrol.
Von der Haar, T. A., 1995: Observations of the global
Oceans Atmos., 26, 187–191.
characteristics and regional radiative effects of marine
cloud liquid water. J. Climate, 8, 2928–2946.
Papatsoris, A. D., 1994: Implication of super-large drops
in millimeter-wave radar observations of water clouds.
Grund, C. J. and Eloranta, E. W., 1990: The 27-28 OcElectron. Lett., 30(21), 1799–1800.
tober 1986 FIRE IFO cirrus case-study - cloud opticalproperties determined by High Spectral Resolution Li- Ramanathan, V., Cess, R. D., Harrison, E. F., Minnis, P.,
dar. Mon. Weather Rev., 118(11), 2344–2355.
Barkstrom, B. R., Ahmad, E., and Hartmann, D., 1989:
15
Cloud-radiative forcing and climate: Results from the
Earth Radiation Budget Experiment. Science, 243, 57–
63.
Slingo, A. and Slingo, J. M., 1991: Response of the National Center for Atmospheric Research community climate model to improvements in the representation of
clouds. J. Geophys. Res. — Atmos., 96, 15341–15357.
Stephens, G. L., Vane, D. G., Boain, R. J., Mace, G. G.,
Sassen, K., Wang, Z., Illingworth, A. J., O’Connor,
E. J., Rossow, W. B., Durden, S. L., Miller, S. D.,
Austin, R. T., Benedetti, A., Mitrescu, C., and the
CloudSat Science Team, 2002: The CloudSat mission
and the A-train. Bull. Amer. Meteorol. Soc., 83(12),
1771–1790.
Ulbrich, C. W. and Atlas, D., 1998: Rainfall microphysics
and radar properties: Analysis methods for drop size
spectra. J. Appl. Meteorol., 37(9), 912–913.
Vali, G., Kelly, R. D., French, J., Haimov, S., and Leon,
D., 1998: Finescale structure and microphysics of
coastal stratus. J. Atmos. Sci., 55, 3540–3564.
van de Hulst, H. C., 1957: Light scattering by small particles. Wiley and Sons.
Wakasugi, K., Mizutani, A., Matsuo, M., Fukao, S., and
Kato, S., 1986: A direct method for deriving dropsize distribution and vertical air velocities from VHF
Doppler radar spectra. J. Atmos. Ocean. Technol., 3,
623–629.
Wood, R., 2000: Parametrization of the effect of drizzle upon the droplet effective radius in stratocumulus
clouds. Q. J. R. Meteorol. Soc., 126, 3309–3324.
16