A variational cloud retrieval
scheme combining radar, lidar
and radiometer observations
Robin Hogan & Julien Delanoe
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
• Calipso lidar
7 June 2006
Aerosol from
China?
Molecular
scattering
• CloudSat radar
Mixed-phase
altocumulus
Drizzling
stratocumulus
Cirrus
Non-drizzling
stratocumulus
Rain
East China Sea
Japan
Sea of Japan
Eastern Russia
5500
km
Motivation
• Why combine radar, lidar and radiometers?
– Radar ZD6, lidar b’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 scheme
• Observation vector
– Elements may be missing
 ln b1 





 ln b 
n


Z1





y 



Zm





 I 8.7 m 



I
 8.7 12.0m 
Attenuated lidar
backscatter profile
Radar reflectivity
factor profile (on
different grid)
Visible optical depth
Infrared radiance
Radiance difference
• State vector
 ln 1ice 


  


ln

n


ice
 ln N1 





 ln N mice 
x

S


 LWP 
1


liq
 ln N1 
  


aer
 ln 1 





Ice visible extinction
coefficient profile
Ice normalized
number conc. profile
Extinction/backscatter
ratio for ice
Liquid water path and
number conc. for each
liquid layer
Aerosol visible
extinction coefficient
profile
Solution method
New ray of data
Locate cloud with radar & lidar
Define elements of x
First guess of x
• 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
Forward model
Predict measurements y from
state vector x using forward
model H(x)
Also predict the Jacobian H
Has solution converged?
2 convergence test
No
Yes
Calculate error in retrieval
Proceed to next ray
Gauss-Newton iteration step
Predict 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
Radar forward model and a priori
• 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 scattering
• 90-m footprint of Calipso
means that multiple
scattering is a problem
• Eloranta’s (1998) model
Narrow
field-of-view:
forward
scattered
photons escape
– 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)
Wide field-ofview:
forward
scattered
photons may be
returned
Ice cloud
Molecules
Liquid cloud
Aerosol
Hogan (2006, Applied Optics, in press). Code: www.met.rdg.ac.uk/clouds
Radiance 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 retrieval
Observations
State
variables
Derived
variables
Aircraftsimulated
profiles with
noise (from
Hogan et al.
(2006)
Optical
depth 13.9;
lidar sees
to 3.6
Retrieval is
accurate
but not
perfectly
stable
where lidar
loses signal
• Donovan et al. (2000) algorithm can only be applied where
both lidar and radar have signal
Variational radar/lidar retrieval
Observations
Lidar noise
matched by
retrieval
State
variables
Derived
variables
Noise
feeds
through to
other
variables
• Noise in lidar backscatter feeds through to retrieved extinction
…add smoothness constraint
Observations
State
variables
Retrieval
reverts to
a-priori N0
Derived
variables
Extinction
and IWC
too low in
radar-only
region
• Smoothness constraint: add a term to cost function to penalize
curvature in the solution (J’ = l
Si d2i/dz2)
…add a-priori error correlation
Observations
State
variables
Derived
variables
Vertical
correlation
of error in
N0
Extinction
and IWC
now more
accurate
• Use B (the a priori error covariance matrix) to smooth the N0
information in the vertical
…add visible optical depth constraint
Observations
State
variables
Derived
variables
Slight
refinement
to
extinction
and IWC
• Integrated extinction now constrained by the MODIS-derived
visible optical depth
…add infrared radiances
Observations
State
variables
Derived
variables
• Better fit to IWC and re at cloud top
Poorer fit
to Z at
cloud top:
information
here now
from
radiances
Observed
94-GHz
radar
reflectivity
Observed
905-nm lidar
backscatter
Forward
model radar
reflectivity
Forward
model lidar
backscatter
Ground-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

Radar only:
retrieval tends
towards a-priori
Lower error in
regions with both
radar and lidar
Conclusions and ongoing work
• 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!
Scotland
Lake
district
England
Isle of
Wight
CloudSat observations over the UK on 18th June 2006
France
MODIS RGB composite
13.10 UTC
June 18th
Scotland
Lake
district
England
Isle of
Wight
France
MODIS Infrared window
13.10 UTC
June 18th
(Sunday)
Scotland
Lake
district
England
Isle of
Wight
France
Met Office rain
radar network
13.10 UTC
June 18th
(Sunday)
Scotland
Lake
district
England
Isle of
Wight
France
Sd
Banda Sea
An island of
Indonesia