a variational cloud retrieval scheme combining radar, lidar and radiometer observations robin hogan...
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A variational cloud retrieval A variational cloud retrieval scheme combining radar, lidar scheme combining radar, lidar and radiometer observationsand radiometer observations
Robin Hogan & Julien DelanoeRobin Hogan & Julien DelanoeUniversity of Reading, UK .University of Reading, UK .
• The CloudSat radar and the Calipso lidar were launched on 28th April 2006
• They join Aqua, hosting the MODIS, CERES, AIRS and AMSU radiometers
• An opportunity to tackle questions concerning role of clouds in climate
• Need to combine all these observations to get an optimum estimate of global cloud properties
Eastern RussiaJapanSea of JapanEast China Sea
• Calipso lidar
• CloudSat radar
Molecular scattering
Aerosol from China?
CirrusMixed-phase
altocumulus
Drizzling stratocumulus
Non-drizzling stratocumulus
Rain
7 June 2006
5500 km
MotivationMotivation• Why combine radar, lidar and radiometers?
– Radar ZD6, lidar ’D2 so the combination provides particle size– Radiances ensure that the retrieved profiles can be used for
radiative transfer studies
• Some limitations of existing radar/lidar ice retrieval schemes (Donovan et al. 2000, Tinel et al. 2005, Mitrescu et al. 2005)– Only work in regions of cloud detected by both radar and lidar– Noise in measurements results in noise in the retrieved variables– Eloranta’s lidar multiple-scattering model is too slow to take to
greater than 3rd or 4th order scattering– Other clouds in the profile are not included, e.g. liquid water clouds– Difficult to make use of other measurements, e.g. passive radiances – Difficult to also make use of lidar molecular scattering beyond the
cloud as an optical depth constraint– Some methods need the unknown lidar ratio to be specified
• A “unified” variational scheme can solve all of these problems
Formulation of variational Formulation of variational schemescheme
m
m
m
n
I
I
Z
Z
0.127.8
7.8
1
1
ln
ln
y
aer1
liq1
1
ice
ice1
ice1
ln
ln
LWP
ln
ln
ln
ln
N
S
N
N
m
n
x
• Observation vector • State vector– Elements may be missing
Attenuated lidar backscatter profile
Radar reflectivity factor profile (on different grid)
Ice visible extinction coefficient profile
Ice normalized number conc. profile
Extinction/backscatter ratio for ice
Visible optical depth
Aerosol visible extinction coefficient profile
Liquid water path and number conc. for each liquid layerInfrared radiance
Radiance difference
Solution methodSolution method• Find x that minimizes a cost function J
of the form J = deviation of x from a-priori + deviation of observations from
forward model + curvature of extinction profile
New ray of dataLocate cloud with radar & lidarDefine elements of xFirst guess of x
Forward modelPredict measurements y from state vector x using forward model H(x)Also predict the Jacobian H
Has solution converged?2 convergence test
Gauss-Newton iteration stepPredict new state vector:
xi+1= xi+A-1{HTR-1[y-H(xi)]
-B-1(xi-xa)-Txi}where the Hessian is
A=HTR-1H+B-1+T
Calculate error in retrieval
No
Yes
Proceed to next ray
Radar forward model and Radar forward model and a a prioripriori• Create lookup tables
– Gamma size distributions– Choose mass-area-size relationships– Mie theory for 94-GHz reflectivity
• Define normalized number concentration parameter– “The N0 that an exponential
distribution would have with same IWC and D0 as actual distribution”
– Forward model predicts Z from extinction and N0
– Effective radius from lookup table
• N0 has strong T dependence– Use Field et al. power-law as a-priori– When no lidar signal, retrieval
relaxes to one based on Z and T (Liu and Illingworth 2000, Hogan et al. 2006)
Field et al. (2005)
Lidar forward model: multiple Lidar forward model: multiple scatteringscattering
• 90-m footprint of Calipso means that multiple scattering is a problem
• Eloranta’s (1998) model – O (N m/m !) efficient for N
points in profile and m-order scattering
– Too expensive to take to more than 3rd or 4th order in retrieval (not enough)
• New method: treats third and higher orders together– O (N 2) efficient – As accurate as Eloranta
when taken to ~6th order– 3-4 orders of magnitude
faster for N =50 (~ 0.1 ms)
Hogan (2006, Applied Optics, in press). Code: www.met.rdg.ac.uk/clouds
Ice cloud
Molecules
Liquid cloud
Aerosol
Narrow field-of-view:
forward scattered
photons escape
Wide field-of-view:
forward scattered
photons may be returned
Radiance forward modelRadiance forward model• MODIS solar channels provide an estimate of optical depth
– Only very weakly dependent on vertical location of cloud so we simply use the MODIS optical depth product as a constraint
– Only available in daylight
• MODIS, Calipso and SEVIRI each have 3 thermal infrared channels in atmospheric window region– Radiance depends on vertical distribution of microphysical
properties– Single channel: information on extinction near cloud top– Pair of channels: ice particle size information near cloud top
• Radiance model uses the 2-stream source function method– Efficient yet sufficiently accurate method that includes scattering– Provides important constraint for ice clouds detected only by lidar– Ice single-scatter properties from Anthony Baran’s aggregate
model– Correlated-k-distribution for gaseous absorption (from David
Donovan)
Ice cloud: non-variational Ice cloud: non-variational retrievalretrieval
• Donovan et al. (2000) algorithm can only be applied where both lidar and radar have signal
Observations
State variables
Derived variables
Retrieval is accurate but not perfectly stable where lidar loses signal
Aircraft-simulated profiles with noise (from Hogan et al. (2006)
Optical depth 13.9; lidar sees to 3.6
Variational radar/lidar Variational radar/lidar retrievalretrieval
• Noise in lidar backscatter feeds through to retrieved extinction
Observations
State variables
Derived variables
Lidar noise matched by retrieval
Noise feeds through to other variables
……add smoothness constraintadd smoothness constraint
• Smoothness constraint: add a term to cost function to penalize curvature in the solution (J’ =
id2i/dz2)
Observations
State variables
Derived variables
Retrieval reverts to a-priori N0
Extinction and IWC too low in radar-only region
……add a-priori error add a-priori error correlationcorrelation
• Use B (the a priori error covariance matrix) to smooth the N0 information in the vertical
Observations
State variables
Derived variables
Vertical correlation of error in N0
Extinction and IWC now more accurate
……add visible optical depth add visible optical depth constraintconstraint
• Integrated extinction now constrained by the MODIS-derived visible optical depth
Observations
State variables
Derived variables
Slight refinement to extinction and IWC
……add infrared radiancesadd infrared radiances
• Better fit to IWC and re at cloud top
Observations
State variables
Derived variables
Poorer fit to Z at cloud top: information here now from radiances
Observed94-GHz
radar reflectivity
Observed 905-nm
lidar backscatter
Forward model radar
reflectivity
Forward model lidar backscatter
Ground-based exampleGround-based example
Lidar fails to penetrate deep ice cloud
Retrieved extinction
coefficient
Retrieved effective radius re
Retrieved normalized
number conc.
parameter N0
Error in retrieved
extinction
Lower error in regions with both radar and lidar
Radar only: retrieval tends towards a-priori
Conclusions and ongoing Conclusions and ongoing workwork
• A variational method has been described for combining radar, lidar, radiometers and any other relevant measurements, to retrieve profiles of cloud microphysical properties
• In progress:– Testing radiance part of retrieval using geostationary-satellite
radiances from Meteosat/SEVIRI above ground-based radar & lidar– Add capability to retrieve properties of liquid-water layers, drizzle
and aerosol
• Then apply to A-train data!
CloudSat observations over the UK on 18th June 2006
Scotland EnglandLakedistrict
Isle of Wight France
13.10 UTC 13.10 UTC June 18June 18thth
Scotland EnglandLakedistrict
Isle of Wight France
MODIS RGB composite
Scotland EnglandLakedistrict
Isle of Wight France
MODIS Infrared window
13.10 UTC 13.10 UTC June 18June 18th th
(Sunday) (Sunday)
Scotland EnglandLakedistrict
Isle of Wight France
Met Office rain radar network
13.10 UTC 13.10 UTC June 18June 18th th
(Sunday) (Sunday)
SdSd
Banda SeaAn island of Indonesia