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A novel ensemble method for retrieving properties of warm cloud in 3-D using ground-based scanning radar and zenith radiances

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A novel ensemble method for retrieving propertiesof warm cloud in 3-D using ground-basedscanning radar and zenith radiances
Mark D. Fielding
1
, J. Christine Chiu
1
, Robin J. Hogan
1
, and Graham Feingold
2
1
Department of Meteorology, University of Reading, Reading, UK,
2
NOAA Earth System Research Laboratory, Boulder,Colorado, USA
Abstract
We present a novel method for retrieving high-resolution, three-dimensional (3-D) nonprecipitatingcloud
ﬁ
elds in both overcast and broken-cloud situations. The method uses scanning cloud radar andmultiwavelengthzenithradiancestoobtaingridded3-Dliquidwatercontent(LWC)andeffectiveradius(
r
e
)and2-D column mean droplet number concentration (
N
d
). By using an adaption of the ensemble Kalman
ﬁ
lter,radiancesareusedtoconstraintheopticalpropertiesofthecloudsusingaforwardmodelthatemploysfull3-Dradiative transfer while also providing full error statistics given the uncertainty in the observations. To evaluatethe new method, we
ﬁ
rst perform retrievals using synthetic measurements from a challenging cumuluscloud
ﬁ
eld produced by a large-eddy simulation snapshot. Uncertainty due to measurement error in overheadclouds is estimated at 20% in LWC and 6% in
r
e
, but the true error can be greater due to uncertainties in theassumed droplet size distribution and radiative transfer. Over the entire domain, LWC and
r
e
are retrievedwith average error 0.05
–
0.08gm
3
and ~2
μ
m, respectively, depending on the number of radiance channelsused. The method is then evaluated using real data from the Atmospheric Radiation Measurement programMobile Facility at the Azores. Two case studies are considered, one stratocumulus and one cumulus. Whereavailable, the liquid water path retrieved directly above the observation site was found to be in good agreementwith independent values obtained from microwave radiometer measurements, with an error of 20gm
2
.
1. Introduction
Boundary layer clouds are fundamental to the Earth
’
s radiation budget, their high re
ﬂ
ectance constituting asigni
ﬁ
cant contribution to the planetary albedo [
Hartmann et al
., 1992]. Even small changes in theirdistribution or composition can have a signi
ﬁ
cant effect on climate [
Oreopoulos and Platnick
, 2008]. Theirturbulent, complex structures, coupled with a strong susceptibility to aerosol, mean they remain a key sourceof uncertainty in climate projections [e.g.,
Randall et al
., 2007;
Turner et al
., 2007b]. To complement advancesin modeling studies, accurate observations of clouds and radiation are vital to improvement in theparameterization schemes of global circulation models (GCMs).Pro
ﬁ
ling instruments, such as vertically pointing cloud radar, are invaluable for obtaining long-term time seriesof clouds [e.g.,
Illingworth et al
., 2007] and give good vertical and partial horizontal information on cloudproperties. However, they are less well suited for inferring a whole-sky view. This problem is particularlyapparent when attempting to reproduce observed surface irradiances in radiation closure studies [
McFarlaneand Evans
, 2004;
Wang et al
., 2011] or analyzing cloud radiative effects, both of which are sorely needed asobservational constraints for realistic cloud and radiation parameterizations for GCMs [
Qian et al
., 2012]. Inparticular,the3-Dhorizontaltransportofphotons(henceforth
“
3-Deffects
”
)isanonnegligiblesourceoferrorinthe 1-D radiation schemes of current GCMs [e.g.,
Cahalan et al
., 1994;
Hogan and Shonk
, 2013], particularlyfor cumulus clouds [
Pincus et al
., 2005]. The ability to observe cloud structure and cloud microphysicalproperties in 3-D is also a key step to improving our understanding of cloud life cycle and cloud organization. Toaddressthisneedfor3-Dmeasurementsofclouds,theU.S.DepartmentofEnergy
’
sAtmosphericRadiationMeasurement (ARM) program [
Ackerman and Stokes
, 2003] has installed scanning polarimetric Doppler cloudradar [
Widener et al
., 2012] at their Climate Research Facilities. The radars can scan at up to 15° s
1
producingreasonable coverage over a 5min time period, which can then be interpolated to a 3-D gridded domain of radar re
ﬂ
ectivity. However, as radar re
ﬂ
ectivity is proportional to both the number and the size of clouddroplets, further information is required to deduce these microphysical properties inside the 3-D domain.FIELDING ETAL.
©2014. American Geophysical Union. All Rights Reserved.
1
PUBLICATIONS
Journal of Geophysical Research: Atmospheres
RESEARCH ARTICLE
10.1002/2014JD021742
Key Points:
•
New method for retrieving 3-Dcloud
ﬁ
elds
•
Three-dimensional radiative transfer isused as a forward model
•
Evaluations against other retrievalsshow good agreement
Correspondence to:
M. D. Fielding,m.d.
ﬁ
elding@pgr.reading.ac.uk
Citation:
Fielding, M. D., J. C. Chiu, R. J. Hogan,and G. Feingold (2014), A novelensemblemethodforretrievingpropertiesofwarmcloud in 3-D using ground-basedscanning radar and zenith radiances,
J. Geophys. Res. Atmos.
,
119
, doi:10.1002/ 2014JD021742.Received 12 MAR 2014Accepted 21 AUG 2014Accepted article online 26 AUG 2014
Several existing methods to retrieve cloud microphysical properties using vertically pointing cloud radar andother sources of information could be adapted for a scanning radar retrieval. First, one could add priorknowledgebased oninsitu observations[e.g.,
McFarlane et al
., 2002]orbased on theory,forexample, usingasimple model to predict droplet sizes given certain atmospheric conditions [e.g.,
Rémillard et al
., 2013].Second, an additional active sensor could be added to the retrieval. For example,
Hogan et al
. [2005] and
Huang et al
. [2009] showed that differential attenuation with dual-wavelength radar could retrieve liquidwatercontent(LWC).Finally,passivesensorscouldbeaddedtotheretrieval.Themostwidelyusedconstraintis liquid water path (LWP) measurements from microwave radiometers [e.g.,
Frisch et al
., 1995;
Frisch et al
.,1998;
Lohnert et al
., 2001]. Additionally,
Dong and Mace
[2003] combined radar measurements and cloudoptical depth retrieved from solar irradiances, which works best for relatively overcast, horizontallyhomogeneous clouds due to the hemispheric
ﬁ
eld of view of radiometers.In contrast to irradiances,zenith radiances are collected from a narrow
ﬁ
eld-of-view,which can capture cloudvariability at higher spatial resolution and therefore are a more appealing choice for the retrieval of heterogeneouscloud.Byusingawavelengththatisabsorbedbyliquidwaterandonethatisnotabsorbedbyliquid water, zenith radiance measurements have previously been used to simultaneously constrain dropletsize(usingtheabsorbingwavelength)andcloudopticaldepth(usingthenonabsorbingwavelength)withoutradar measurements [e.g.,
McBride et al
., 2011;
Chiu et al
., 2012]. These retrievals use a plane parallelapproximation;
Marshak et al
. [2004] showed that 3-D effects in heterogeneous cloud conditions can lead to
“
unretrievable
”
combinations of radiance measurements. The greater the heterogeneity in the cloud
ﬁ
eld,the greater the 3-D effects, which increases the potential for error in both the retrieved microphysical andradiative properties of the cloud.As scanning cloud radar provides information on the 3-D cloud structure, it appears possible to utilize theseformerly unwelcome 3-D effects, provided that 3-D radiative transfer is used as a forward model. A potentialstumbling block is that modeling 3-D radiative transfer is a dif
ﬁ
cult problem and typically their adjoints(models that specify the sensitivity of their output to their input) do not exist, which rules out many standardtechniques for solving inverse problems. By using an ensemble-based method, we will show that we canovercome this issue and use 3-D effects to our advantage.Inthispaper,weproposeanovelENsembleClOudREtrievalmethod(ENCORE)toretrievethe3-Dmicrophysicalproperties of clouds using scanning cloud radar and zenith radiances. The method has three key features.First,byusinganensemble-basedmethod,wecanusefull3-Dradiativetransferasaforwardmodelwithouttheneed forits adjoint. Asfar as weareaware, the only previous use ofa similar method for a meteorological radarretrieval is that described by
Grecu and Olson
[2008]. Second, while satellite-based radiance-radar retrievalshave been developed for CloudSat and Moderate Resolution Imaging Spectroradiometer (MODIS) [
Austinand Stephens
, 2001], we are unaware of an equivalent ground-based method. Finally, the retrieval isindependent of microwave-based LWP retrievals, permitting their use for validation. The paper is organized as follows. We present the methodology of our 3-D retrieval for nonprecipitatingboundary layer clouds in section 2. In section 3 we evaluate the retrieval using synthetic cloud
ﬁ
elds fromlarge-eddy simulations. Section 4 contains an analysis of two case study retrievals, one for a cumulus cloud
ﬁ
eld and one for a stratocumulus cloud
ﬁ
eld. A discussion follows in section 5, and the conclusions andsummary are in section 6.
2. Methodology of ENCORE
2.1. Overview of Retrieval Method
The method retrieves 2-D
ﬁ
elds of cloud droplet number concentration
N
d
(assumed constant with height)and 3-D LWC and
r
e
. Our retrieval is built on a
ﬂ
exible ensemble framework that allows for the easy additionor removal of any observational data set. In this paper, the framework is used to maximize the synergybetween zenith radiances and radar re
ﬂ
ectivity from scanning radar. The required observational data sets are available from colocated instruments at various ARM
ﬁ
eld sites.Ground-based scanning ARM cloud radars (SACRs) provide radar re
ﬂ
ectivity [
Widener et al
., 2012]. At each
ﬁ
eldsite,tworadarsofdifferentfrequencyaremountedontoasinglepedestal,typicallyKaandWband. Boththese radars have very narrow
ﬁ
elds of view (~0.3°) making them ideal for cloud studies [
Kollias et al
., 2014].
Journal of Geophysical Research: Atmospheres
10.1002/2014JD021742
FIELDING ETAL.
©2014. American Geophysical Union. All Rights Reserved.
2
Zenith radiance measurements areavailable from ARM narrow
ﬁ
eld of viewradiometers (2NFOV) or ARM shortwavearray spectroradiometers (SAS-Ze). Bothof these instruments are ground basedwith 1s temporal resolution. The 2NFOV has channels at 673 and 870nm with a1.2°
ﬁ
eld of view. The SAS-Ze measuresradiances across the whole shortwavespectrum (350
–
1700nm) at a spectralresolution of 2.4nm in the visible and6nm in the near infrared with a 1°
ﬁ
eld-of-view. For clarity, in the rest of the paper we will refer to wavelengthsof radiation that are absorbed by liquidwater as
“
absorbing
”
(e.g., 1640nm) andthose that are not as
“
nonabsorbing
”
(e.g., 440, 673, and 870nm). Since thezenith radiances are local column-averaged measurements and do notprovide detailed cloud information forthe full 3-D domain, our retrievalprocedurecontainsthreemajorsteps,asillustrated in Figure 1 and outlined next. The
ﬁ
rst step is to place all observationson to a common grid. Scanning radarobservations are mapped to a regular3-D grid, using linear interpolation via aDelaunay triangulation [see
Fieldinget al
., 2013]. Figure 1a illustrates anexample of radar scans made with theCross Wind Range Height Indicator(CWRHI) strategy from a radar located inthe center of the domain. Similarly,zenith radiance observations are alsocollected at the center of the domainand are linearly interpolated to a 1-Dtrack. Both data sets are placed on aspatial grid by assuming the commonlyused frozen turbulence hypothesis,with wind speed and direction obtainedfrom a colocated wind pro
ﬁ
ler.Each zenith radiance observation ismainly a function of the overhead cloudproperties due to the narrow
ﬁ
eld of view of the radiometers; however, when 3-D effects are not negligible, 1-D radiative transfer calculations areinsuf
ﬁ
cient to satisfactorily simulate zenith radiances and thus cannot provide proper constraints for ourretrievals. Therefore, 3-D radiative transfer calculations need to be incorporated in our algorithm. Due to thetrade-off between computational cost and the inclusion of 3-D effects, the second step of the retrieval isrestricted to a series of subsets of the full domain; each subset domain, dubbed a
“
supercolumn,
”
is selectedalongtheaforementioned1-D
“
radiance
”
track.Thesizeof thesupercolumn(magentasquaresinFigure1b)ischosen to reduce computational cost while encompassing most 3-D effects. This second step is a keycomponent of our retrieval method and will be detailed in section 2.2.
Figure 1.
Diagram showing the main steps of the ENsemble ClOudREtrieval method (ENCORE). (a) Gathering of radiance (red dashed lines)and radar re
ﬂ
ectivity (hemispherical slices) observations, (b) retrieveddrop number concentration and effective radius within each supercol-umn (magenta boxes), (c) re
ﬂ
ectivity matching of donor columns (solid)to recipient columns (translucent), and (d) completed retrieval.
Journal of Geophysical Research: Atmospheres
10.1002/2014JD021742
FIELDING ETAL.
©2014. American Geophysical Union. All Rights Reserved.
3
Once the retrievals for the supercolumns are complete, the third step, illustrated in Figure 1c, is to retrievecloud properties for the rest of the domain by matching their radar re
ﬂ
ectivity with the clouds inside thesupercolumns. Details are given in section 2.3.
2.2. Retrieval for Supercolumns2.2.1. State Vector and Forward Models
The state vector,
x
, which contains the variables we wish to retrieve, is de
ﬁ
ned as
x
¼
log
N
i
¼
1
…
m
;
j
¼
1
…
n
ð Þ
d
;
log
r
i
¼
1
…
m
;
j
¼
1
…
n
;
k
¼
1
…
l
ð Þ
e
T
;
(1)
where
i
and
j
are grid indices in the horizontal;
k
is the vertical index; and
n
,
m
, and
l
de
ﬁ
ne the number of horizontalandverticalgridpointsinthesupercolumn,respectively.Thevariablesin
x
arede
ﬁ
nedinlogspaceto keep their values positive in linear space. Cloud droplet number concentration
N
d
is forced to be heightinvariant, whereas
r
e
is allowed to vary with height. LWC is de
ﬁ
ned as
LWC
¼
43
πρ
w
N
d
r
3e
exp
3
σ
2
;
(2)
where
σ
is the shape parameter or geometric standard deviation (standard deviation of the log of dropletradius), and
ρ
w
isthe densityofliquid water. As
σ
isnot retrieved, wechooseto keepitconstant; wediscusstheimpact of this assumption on retrievals in section 3.3. From LWC and
r
e
, cloud optical depth,
τ
, can be given as
τ
¼
32
ρ
w
∫
H
T
H
B
LWC
h
ð Þ
r
e
h
ð Þ
d
h
;
(3)
where
H
B
is the height of cloud base and
H
T
is the cloud top and the extinction ef
ﬁ
ciency has been assumedto be 2 (valid in the visible part of the spectrum).Using
N
d
,
r
e
,andalognormalclouddropletdistribution,wecanalsonowforwardmodelradarre
ﬂ
ectivityandzenith radiance, needed to map the state variables to observation space. We can safely use the Rayleighscattering approximation for cloud droplets since the SACRs operate at Ka or W band, but at these highfrequencies we must account for gas and liquid water attenuation. As a result, radar re
ﬂ
ectivity is given as
Z
¼
64
N
d
r
6e
exp 3
σ
2
ð Þ
10
0
:
2
∫
L
0
α
f
þ
κ
f
LWC
ð Þ
d
L
′
;
(4)
where
α
f
(dBkm
1
) is the one-way speci
ﬁ
c attenuation coef
ﬁ
cient due to atmospheric gases,
κ
f
(dBkm
1
(gm
3
)
1
) is the one-way speci
ﬁ
c attenuation coef
ﬁ
cient of liquid water [
Hogan et al
., 2005], and
L
is thedistance to the radar. Note that the assumed unimodal lognormal droplet distribution is only suitable fornonprecipitating clouds. Indeed, the success of the retrieval is strongly dependent on the validity of ourassumed droplet distribution; we are inferring the zeroth, second, and third moments from observations of the second and sixth moments.Zenith radiances are computed using fully 3-D radiative transfer. The effective radius from the state vectorandLWC determined from equation (2) are used to determine cloud extinction, single-scattering albedo, andphasefunction.Tointerpretrealobservations,theseneedtobecombinedwithsimilarpropertiesforaerosolsand gases, but since absorption is small at the wavelengths considered, we ignore gaseous attenuation.Aerosol properties are not included in the large-eddy simulations (LES) experiments. Radiative transfer iscomputed using the Spherical Harmonics Discrete Ordinated Method [
Evans
, 1998]. The surface albedo isspeci
ﬁ
ed using estimates from MODIS operational products [
Schaaf et al
., 2002].
2.2.2. Finding the Best Estimate of the State Vector
To
ﬁ
nd the best estimate of the state vector, we use an adaption to the ensemble Kalman
ﬁ
lter (EnKF, see
Evensen
[2003])similar to
Grecu and Olson
[2008]and
Iglesias et al
. [2013].Weoutlinethetheoreticalbasis
ﬁ
rstand then use Figure 2 to explain the practical details.Let us de
ﬁ
ne an ensemble
X
of individual state vectors,
x
, containing
N
members, i.e.,
X
¼
x
1
;
…
;
x
N
ð Þ
;
(5)
wherethesubscript referstotheparticularensemblemember.Themeanof
X
representsthebest estimateof the state vector, and the spread of the ensemble members around the mean represents the uncertainty in
Journal of Geophysical Research: Atmospheres
10.1002/2014JD021742
FIELDING ETAL.
©2014. American Geophysical Union. All Rights Reserved.
4
the best estimate. For each set of observations
y
, the ensemble is updated (subscript
“
new
”
) from the currentestimate of the state (subscript
“
old
”
) by applying the Extended Kalman Filter update equations [
Gelb
, 1974],to each ensemble member
q
, i.e.,
x
q
;
new
¼
x
q
;
old
þ
K
^
y
q
H
x
q
;
old
;
and (6)
K
¼
PC
T
CPC
T
þ
R
1
;
(7)
where the function
H
(
x
) is the forward model;
C
is the Jacobian of the forward model and is the sensitivity of the forward model to its input;
P
is the error covariance matrix of the current state;
R
is the observationerror covariance matrix, which represents the uncertainty in the observations; and
^
y
represents theobservations perturbed with random noise withvariance speci
ﬁ
ed by
R
.
K
, known as the Kalman gain matrix,controls how much weight is placed on the observations compared to the current state. As we do not know
C
for a 3-D radiative transfer forward model, we approximate
K
via the ensemble as follows:
E
x
¼
x
1
X
;
⋯
;
x
N
X
(8)
E
y
¼
H
x
1
ð Þ
H
x
ð Þ
;
⋯
;
H
x
N
ð Þ
H
x
ð Þ
h i
;
(9)
where
E
x
representstheensemblespread,
E
y
representsthespreadinpredictedobservationvalues,and
H
x
ð Þ
is the mean of the forward modeled observations. We then use
PC
T
≅
1
N
1
E
x
E
y
T
;
and (10)
CPC
T
≅
1
N
1
E
y
E
y
T
;
(11)
Figure 2.
Flowchart describing the ensemble state estimation method.
Journal of Geophysical Research: Atmospheres
10.1002/2014JD021742
FIELDING ETAL.
©2014. American Geophysical Union. All Rights Reserved.
5

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