1. Robin Hogan & Julien Delanoe
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

3. 7 June 2006 Calipso lidar CloudSat radar Molecular scattering
Aerosol from China?
Cirrus
Mixed-phase altocumulus
Drizzling stratocumulus
Non-drizzling stratocumulus
5500 km
Rain
Japan
Eastern Russia
East China Sea
Sea of Japan

4. 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

5. Formulation of variational scheme
Observation vector • State vector
Elements may be missing
Ice visible extinction coefficient profile
Ice normalized number conc. profile
Extinction/backscatter ratio for ice
Attenuated lidar backscatter profile
Radar reflectivity factor profile (on different grid)
Aerosol visible extinction coefficient profile
Liquid water path and number conc. for each liquid layer
Visible optical depth
Infrared radiance
Radiance difference

6. xi+1= xi+A-1{HTR-1[y-H(xi)]
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
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
Has solution converged?
2 convergence test No
Yes
Calculate error in retrieval
Proceed to next ray

7. 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)

9. Lidar forward model: multiple scattering
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)
Narrow field-of-view: forward scattered photons escape
Wide field-of-view: forward scattered photons may be returned
Ice cloud
Molecules
Liquid cloud
Aerosol
Hogan (2006, Applied Optics, in press). Code:

10. 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)

11. Ice cloud: non-variational retrieval
Aircraft-simulated profiles with noise (from Hogan et al. (2006)
Donovan et al. (2000)
Observations
State variables
Derived variables
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

12. Variational radar/lidar retrieval
Observations
State variables
Derived variables
Lidar noise matched by retrieval
Noise feeds through to other variables
Noise in lidar backscatter feeds through to retrieved extinction

13. …add smoothness constraint
Observations
State variables
Derived variables
Retrieval reverts to a-priori N0
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 d2ai/dz2)

14. …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

15. …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

16. …add infrared radiances
Observations
State variables
Derived variables
Poorer fit to Z at cloud top: information here now from radiances
Better fit to IWC and re at cloud top

17. Radar-only retrieval
Observations
State variables
Derived variables

18. Radar plus optical depth
Observations
State variables
Derived variables

19. Radar, optical depth and IR radiances
Observations
State variables
Derived variables

20. Ground-based example Observed 94-GHz radar reflectivity
Observed 905-nm lidar backscatter
Forward model radar reflectivity
Forward model lidar backscatter
Lidar fails to penetrate deep ice cloud

21. Retrieved extinction coefficient a
Retrieved effective radius re
Retrieved normalized number conc. parameter N0
Error in retrieved extinction Da
Radar only: retrieval tends towards a-priori
Lower error in regions with both radar and lidar

22. 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!
CloudSat observations over the UK on 18th June 2006
Scotland
England
Lake
district
Isle of Wight
France

23. 13.10 UTC June 18th MODIS RGB composite France Scotland England Lake
district
Isle of Wight
France
13.10 UTC June 18th

24. 13.10 UTC June 18th (Sunday) MODIS Infrared window France Scotland
Lake
district
Isle of Wight
Scotland
England
France

25. 13.10 UTC June 18th (Sunday) Met Office rain radar network France
Lake
district
Isle of Wight
Scotland
England
France

26. Sd
sdf
An island of
Indonesia
Banda Sea

27. Antarctic ice sheet
Southern Ocean