Robin HoganJulien DelanoëNicola Pounder

Chris WestbrookUniversity of Reading

Approaches for Approaches for variational liquid-cloud variational liquid-cloud retrievals using radar, retrievals using radar, lidar and radiometerslidar and radiometers

Fox and Illingworth (1997)

• Maritime airmassesx Continental airmasses

Drizzle dominates Z

Liquid cloud

dominates Z

The drizzle problemThe drizzle problem

What other obs can be What other obs can be exploited?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

Dual-Dual-wavelength wavelength

radar for LWCradar 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)

Examples of multiple scattering

LITE lidar (<r, footprint~1 km)

CloudSat radar (>r)

StratocumulusStratocumulus

Intense thunderstormIntense thunderstorm

Surface echoSurface echoApparent echo from below the surface

Fast multiple scattering fwd Fast multiple scattering fwd modelmodel

CloudSat-like example

• New method uses the time-dependent two-stream approximation

• Agrees with Monte Carlo but ~107 times faster (~3 ms)

• Added to CloudSat simulator

Hogan and Battaglia (J. Atmos. Sci. 2008)

CALIPSO-like example

Multiple FOV lidar retrievalMultiple 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

600 m100 m

10 m

Results for a sine profileResults 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

THOR

lidar

Forward model for depolarization Forward model for depolarization subject to multiple scatteringsubject to multiple scattering

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 tot = || + T

1 21

1 I II I S

c t r

1 21

1 I II I S

c t r

Time derivative Remove this and we have the time-independent two-stream approximation

Spatial derivative Transport of radiation from upstream

Loss by absorption or scatteringSome of lost radiation will enter the other stream

Gain by scattering Radiation scattered from the other stream

Source

Scattering from the quasi-direct beam into each of the streams

Hogan and Battaglia (J. Atmos. Sci., 2008.)

...with depolarization• Define “co-polar weighted” streams K+ and K– and use them to calculate the

co-polar backscatter co = || – T:

• 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, ,represents the rate of loss due to absorption used in calculating , so this may be achieved simply by

multiplying 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

T

||

tot co

tot co

1.2

op

tical d

ep

ths

12

op

tical d

ep

ths

totco

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

Unified algo. work since PM2Unified 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)

Unified Unified retrievalretrieval

Ingredients developed beforeNot yet developed

1. New ray of data: define state vector

Use classification to specify variables describing each species at each gateIce: extinction coefficient , N0’, lidar extinction-to-backscatter ratio

Liquid: extinction coefficient and number concentrationRain: rain rate and mean drop diameterAerosol: 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 vectorEither 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

Lidar and forward modelLidar and forward model

• Only forward-model molecular signal where it has been affected by attenuation

Radar and forward modelRadar and forward model

• Note: no rain retrieved yet

Retrieved ice and liquidRetrieved ice and liquid

• Liquid clouds rather weakly constrained by observations at the moment

Remaining tasks...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…