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

Robin Hogan Julien Delanoë Nicola Pounder Chris Westbrook University of Reading

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**The drizzle problem Drizzle dominates Z Liquid cloud dominates Z**

Maritime airmasses x Continental airmasses Fox and Illingworth (1997)

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**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

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**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)

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**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

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**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

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**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

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**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

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THOR lidar

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

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**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.)

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**...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

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1.2 optical depths btot bco 12 optical depths

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**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

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**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)

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**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

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**Lidar and forward model**

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

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**Radar and forward model**

Note: no rain retrieved yet

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**Retrieved ice and liquid**

Liquid clouds rather weakly constrained by observations at the moment

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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…

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Robin Hogan, Nicola Pounder University of Reading, UK

Robin Hogan, Nicola Pounder University of Reading, UK

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