1. Approaches for variational liquid-cloud retrievals using radar, lidar and radiometers
Robin Hogan
Julien Delanoë
Nicola Pounder
Chris Westbrook
University of Reading

2. The drizzle problem Drizzle dominates Z Liquid cloud dominates Z
Maritime airmasses
x Continental airmasses
Fox and Illingworth (1997)

3. What other obs can be exploited?
From space no single instrument provides water content and size
Need synergy of multiple instruments, for example from space:
Solar radiances provide optical depth and near-cloud-top mean radius
Surface radar return from the oceans provides LWP
High spectral resolution lidar provides extinction at cloud top
Multiple FOV lidar provides extinction profile (in principle)
Rate of increase of depolarization related to cloud-top extinction via multiple scattering
Very difficult to estimate cloud base height
…from the ground:
Zenith-pointing sun photometer for optical depth
Multi-wavelength microwave radiometer for LWP
Radar Doppler spectra for liquid clouds embedded in drizzle or ice
AERI infrared spectrometer
Dual-wavelength radar for LWC profile
Can be difficult to identify multiple layers

4. Dual-wavelength radar for LWC
Radar reflectivity factor dominated by drizzle
Lidar sees cloud base
Dual-wavelength ratio
DWR[dB] = dBZ35 – dBZ94
Increases with range due to liquid attenuation
Derivative provides LWC
For radiative studies and model evaluation, how important is the vertical structure?
Is the Cloudnet “scaled adiabatic” method good enough?
Hogan et al. (2005)

5. Examples of multiple scattering
LITE lidar (l<r, footprint~1 km)
CloudSat radar (l>r)
Stratocumulus
Intense thunderstorm
Surface echo
Apparent echo from below the surface

6. Fast multiple scattering fwd model
Hogan and Battaglia (J. Atmos. Sci. 2008)
New method uses the time-dependent two-stream approximation
Agrees with Monte Carlo but ~107 times faster (~3 ms)
Added to CloudSat simulator
CloudSat-like example
CALIPSO-like example

7. Multiple FOV lidar retrieval
To test multiple scattering model in a retrieval, and its adjoint, consider a multiple field-of-view lidar observing a liquid cloud
Wide fields of view provide information deeper into the cloud
The NASA airborne “THOR” lidar is an example with 8 fields of view
Simple retrieval implemented with state vector consisting of profile of extinction coefficient
Different solution methods implemented, e.g. Gauss-Newton, Levenberg-Marquardt and Quasi-Newton (L-BFGS)
lidar
Cloud top
100 m
10 m
600 m

8. Results for a sine profile
Simulated test with 200-m sinusoidal structure in extinction
With one FOV, only retrieve first 2 optical depths
With three FOVs, retrieve structure of extinction profile down to 6 optical depths
Beyond that the information is smeared out
Nicola Pounder

9. THOR lidar

10. Forward model for depolarization subject to multiple scattering

11. Time-dependent 2-stream
Describe diffuse flux in terms of outgoing stream I+ and incoming stream I–, and numerically integrate the following coupled PDEs:
I+ and I– are used to calculate total (unpolarized) backscatter btot = b|| + bT
Source Scattering from the quasi-direct beam into each of the streams
Time derivative Remove this and we have the time-independent two-stream approximation
Gain by scattering Radiation scattered from the other stream
Loss by absorption or scattering
Some of lost radiation will enter the other stream
Spatial derivative Transport of radiation from upstream
Hogan and Battaglia (J. Atmos. Sci., 2008.)

12. ...with depolarization Robin Hogan and Chris Westbrook
Define “co-polar weighted” streams K+ and K– and use them to calculate the co-polar backscatter bco = b|| – bT:
Evolution of these streams governed by the same equations but with a loss term related to the rate at which scattering is taking place, since every scattering event randomizes the polarization and hence reduces the memory of the original polarization
But the single scattering albedo, w,represents the rate of loss due to absorption used in calculating g1, so this may be achieved simply by multiplying w by a factor , where 0 < < 1
This factor can be determined by comparison with Monte Carlo calculations provided by Alessandro Battaglia
Depolarization ratio is then calculated from
Robin Hogan and Chris Westbrook

13. 1.2 optical depths
btot
bco
12 optical depths

14. Backscatter Depolarization ratio
Comparison to Monte Carlo in isotropic clouds shows promising agreement for  = 0.8
Need to refine behaviour for few scattering events – does double scattering depolarize?
If we can forward model this behaviour, we can exploit it in a retrieval

15. Unified algo. work since PM2
Interface to generic “merged observation” files
Flexible configuration control to adapt to very different input data without recompiling
A-Train, EarthCARE, airborne, ground-based (in principle)
Applied to Julien’s A-Train files
Radar, lidar, MODIS and classification on the same grid
Basic liquid and ice properties retrieved from radar and lidar
Alternative minimizers implemented
Nelder-Mead simplex method (no gradient info required)
Gauss-Newton method with numerical Jacobian is being implemented
Simple code profiling to locate the slowest part of the algorithm
Parts could be sped-up, e.g. look-up of scattering properties is currently slower than radiative transfer!
With numerical adjoint, currently takes ~1 s per ray (expect large speed-up with analytic adjoint)

16. Ingredients developed before Not yet developed
Unified retrieval
1. New ray of data: define state vector
Use classification to specify variables describing each species at each gate
Ice: extinction coefficient , N0’, lidar extinction-to-backscatter ratio
Liquid: extinction coefficient and number concentration
Rain: rain rate and mean drop diameter
Aerosol: extinction coefficient, particle size and lidar ratio
3a. Radar model
Including surface return and multiple scattering
3b. Lidar model
Including HSRL channels and multiple scattering
3c. Radiance model
Solar and IR channels
4. Compare to observations
Check for convergence
6. Iteration method
Derive a new state vector
Either Gauss-Newton or quasi-Newton scheme
3. Forward model
Not converged
Converged
Proceed to next ray of data
2. Convert state vector to radar-lidar resolution
Often the state vector will contain a low resolution description of the profile
5. Convert Jacobian/adjoint to state-vector resolution
Initially will be at the radar-lidar resolution
7. Calculate retrieval error
Error covariances and averaging kernel
Ingredients developed before
Not yet developed

19. Lidar and forward model
Only forward-model molecular signal where it has been affected by attenuation

20. Radar and forward model
Note: no rain retrieved yet

21. Retrieved ice and liquid
Liquid clouds rather weakly constrained by observations at the moment

22. Remaining tasks...
Forward models for liquid clouds observed by EarthCARE
Implement LIDORT for solar radiances
Path-integrated attenuation model for radar using sea surface
Fix adjoints of various forward models
Finalize model of multiple scattering effect on depolarization
Other tasks
Include appropriate constraints for liquid retrievals (e.g. gradient constraint)
Apply to ground-based observations
Add aerosol and rain retrieval
Lots more things to do…