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

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

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 • 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

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

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 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: 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 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

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

…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)

…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 Poorer fit to Z at cloud top: information here now from radiances Better fit to IWC and re at cloud top

Radar-only retrieval Observations State variables Derived variables

Radar plus optical depth Observations State variables Derived variables

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

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

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

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

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

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

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

Sd sdf An island of Indonesia Banda Sea

Antarctic ice sheet Southern Ocean