Robin Hogan, Julien Delanoë, Nicky Chalmers, Thorwald Stein, Nicola Pounder, Anthony Illingworth

1. Robin Hogan, Julien Delanoë, Nicky Chalmers, Thorwald Stein, Nicola Pounder, Anthony Illingworth University of Reading Thanks to Richard Forbes, Steve Woolnough, Alessandro Battaglia, Doug Parker What can we learn about clouds and their representation in models from the synergy of radar and lidar observations?

2. Spaceborne radar, lidar and radiometers The A-Train • NASA • 700-km orbit • CloudSat 94-GHz radar (launch 2006) • Calipso 532/1064-nm depol. lidar • MODIS multi-wavelength radiometer • CERES broad-band radiometer • AMSR-E microwave radiometer EarthCare • EarthCARE (launch 2013) • ESA+JAXA • 400-km orbit: more sensitive • 94-GHz Doppler radar • 355-nm HSRL/depol. lidar • Multispectral imager • Broad-band radiometer • Heart-warming name

3. Overview • What do spaceborne radar and lidar see? • Towards a “unified” retrieval of ice clouds, liquid clouds, precipitation and aerosol • Variational retrieval framework • Results from CloudSat-Calipso ice-cloud retrieval • Consistency with top-of-atmosphere radiative fluxes • Evaluation and improvement of models • Spatial structure of mid-latitude and tropical cirrus • CloudSat simulator to evaluate Unified Model over Africa • Challenges and opportunities from multiple scattering • Fast forward model • Multiple field-of-view lidar retrieval • First results from prototype unified retrieval • Outlook for model evaluation and improvement

4. What do CloudSat and Calipso see? • Radar: ~D6, detects whole profile, surface echo provides integral constraint • Lidar: ~D2, more sensitive to thin cirrus and liquid clouds but attenuated Cloudsat radar CALIPSO lidar Insects Aerosol Rain Supercooled liquid cloud Warm liquid cloud Ice and supercooled liquid Ice Clear No ice/rain but possibly liquid Ground Target classification Delanoe and Hogan (2008, 2010)

5. CloudSat and Calipso sensitivity • In July 2006, cloud occurrence in the subzero troposphere was 13.3% • The fraction observed by radar was 65.9% • The fraction observed by lidar was 65.0% • The fraction observed by both was 31.0%

6. Ingredients of a variational retrieval • Aim: to retrieve an optimal estimate of the properties of clouds, aerosols and precipitation from combining these measurements • To make use of integral constraints must retrieve components together • For each ray of data, define observation vector y: • Radar reflectivity values • Lidar backscatter values • Infrared radiances • Shortwave radiances • Surface radar echo (provides two-way attenuation) • Define state vector x of propertiesto be retrieved: • Ice cloud extinction, number concentration and lidar-ratio profile • Liquid water content profile and number concentration • Rain rate profile and number concentration • Aerosol extinction coefficient profile and lidar ratio • Forward model H(x) to predict the observations • Microphysical component: particle scattering properties • Radiative transfer component

7. The cost function Some elements of x are constrained by a prior estimate The forward model H(x) predicts the observations from the state vector x Each observation yi is weighted by the inverse of its error variance This term can be used to penalize curvature in the retrieved profile • The essence of the method is to find the state vector x that minimizes a cost function: + Smoothness constraints

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

9. Example ice cloud retrievals Lidar observations Visible extinction Lidar forward model Ice water content Radar observations Effective radius Radar forward model • MODIS radiance 10.8um • Forward modelled radiance Delanoe and Hogan (2010)

10. Evaluation using CERES TOA fluxes • Radar-lidar retrieved profiles containing only ice used with Edwards-Slingo radiation code to predict CERES fluxes • Small biases but large random shortwave error: 3D effects? Longwave Bias 0.3 W m-2, RMSE 14 W m-2 Shortwave Bias 4 W m-2, RMSE 71 W m-2 Nicky Chalmers

11. CERES versus a radar-only retrieval • How does this compare with radar-only empirical IWC(Z, T) retrieval of Hogan et al. (2006) using effective radius parameterization from Kristjansson et al. (1999)? Longwave Bias –10 W m-2, RMSE 47 W m-2 Shortwave Bias 48 W m-2, RMSE 110 W m-2 Bias 10 W m-2 RMS 47 W m-2 Nicky Chalmers

12. Remove lidar-only pixels from radar-lidar retrieval Change to fluxes is only ~5 W m-2 but lidar still acts to improve retrieval in radar-lidar region of the cloud How important is lidar? Longwave Bias 4 W m-2, RMSE 9 W m-2 Shortwave Bias –5 W m-2, RMSE 17 W m-2 Nicky Chalmers

13. A-Train versus models • Ice water content • 14 July 2006 • Half an orbit • 150° longitude at equator Delanoe et al. (2010)

14. Both models lack high thin cirrus Met Office has too narrow a distribution of in-cloud IWC ECMWF lacks high IWC values, remedied in new model version Gridbox mean: In-cloud mean:

15. Cascade project Mid-level outflow African easterly jet Saharan air layer Moist monsoon flow • How can we identify & cure errors in modelling African convection? • Unified Model simulations at a range of resolutions • Evaluate using A-Train retrievals • Also run “CloudSat simulator” to obtain radar reflectivity from model Location of African easterly jet Parker et al. (QJRMS 2005)

16. Frequency of occurrence of reflectivity greater than –30 dBZ Plot versus “dynamic latitude” (latitude relative to location of AEJ) Anvil cirrus too low in model Little sign of mid-level outflow Cascade 40-km model versus CloudSat Unified Model CloudSat (~01.30 LT) CloudSat (~13.30 LT) Thorwald Stein

17. Fairly similar behaviour to 40-km model Larger diurnal cycle in anvil Cascade 12-km model versus CloudSat Unified Model CloudSat (~01.30 LT) CloudSat (~13.30 LT) Thorwald Stein

18. Note increase from 38 to 70 levels Anvil cirrus now at around the right altitude Slightly more mid-level cloud Large overestimate of stratocumulus (and too low) Cascade 4-km model versus CloudSat Unified Model CloudSat (~01.30 LT) CloudSat (~13.30 LT) Thorwald Stein

19. Structure of Southern Ocean cirrus Observations • Note limitations of each instrument Retrievals

20. Hogan and Kew (QJ 2005) Outer scale 50-100 km -5/3: Cloud-top turbulence & upscale cascade Fall-streaks & wind-shear remove smaller scales lower in cloud: steeper power spectra • Slice through Hogan & Kew 3D fractal cirrus model • Southern Ocean cirrus is just like Chilbolton cirrus! 90 km

21. Tropical Indian Ocean cirrus Indian Ocean Burma Stratiform region in upper half of cloud? Turbulent fall-streaks in lower half of cloud?

22. Turbulent lower region Stratiform upper region dominated by larger scales • Sum of two fractal cirrus simulations • Fall-streak paradigm unsuitable for cloud top 600 km 120 km Thorwald performing spectral analysis on Cascade model

23. Unified retrieval: Forward model • From state vector x to forward modelled observations H(x)... Gradient of cost function (vector) xJ=HTR-1[y–H(x)] x Ice & snow Liquid cloud Rain Aerosol Lookup tables to obtain profiles of extinction, scattering & backscatter coefficients, asymmetry factor Ice/radar Ice/lidar Ice/radiometer Liquid/radar Liquid/lidar Liquid/radiometer Vector-matrix multiplications: around the same cost as the original forward operations Rain/radar Rain/lidar Rain/radiometer Aerosol/radiometer Aerosol/lidar Sum the contributions from each constituent Lidar scattering profile Radar scattering profile Radiometer scattering profile Adjoint of radiometer model Adjoint of radar model (vector) Adjoint of lidar model (vector) Radiative transfer models H(x) Adjoint of radiative transfer models Lidar forward modelled obs Radar forward modelled obs Radiometer fwd modelled obs yJ=R-1[y–H(x)]

24. First part of a forward model is the scattering and fall-speed model Same methods typically used for all radiometer and lidar channels Radar and Doppler model uses another set of methods Scattering models

25. Radiative transfer forward models • Infrared radiances • Delanoe and Hogan (2008) model • Currently testing RTTOV (widely used, can do microwave, has adjoint) • Solar radiances • Currently testing LIDORT • Radar and lidar • Simplest model is single scattering with attenuation: b’=b exp(-2d) • Problem from space is multiple scattering: contains extra information on cloud properties (particularly optical depth) but no-one has previously been able to rigorously make use of data subject to pulse stretching • Use combination of fast “Photon Variance-Covariance” method and “Time-Dependent Two-Stream” methods • Adjoints for these models recently coded • Forward model for lidar depolarization is in progress

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

27. Scattering regimes • Regime 2: Small-angle multiple scattering • Occurs when Ql~ x • Only for wavelength much less than particle size, e.g. lidar & ice clouds • No pulse stretching • Regime 3: Wide-angle multiple scattering (pulse stretching) • Occurs when l~ x Mean free path l • Regime 0: No attenuation • Optical depth d<< 1 • Regime 1: Single scattering • Apparent backscatter b’is easy to calculate from d at range r: b’(r) =b(r)exp[-2d(r)] Footprint x

28. Time-dependent 2-stream approx. • Describe diffuse flux in terms of outgoing stream I+ and incoming stream I–, and numerically integrate the following coupled PDEs: • These can be discretized quite simply in time and space (no implicit methods or matrix inversion required) Source Scattering from the quasi-direct beam into each of the streams Timederivative 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.)

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

30. lidar Multiple field-of-view lidar retrieval Cloud top • 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) 100 m 10 m 600 m

31. 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

32. Despite vertical smearing of information, the total optical depth can be retrieved to ~30 optical depths Limit is closer to 3 for one narrow field-of-view lidar Optical depth from multiple FOV lidar Nicola Pounder

33. Unified algorithm: first results for ice+liquid But lidar noise degrades retrieval Convergence! Truth Retrieval First guess Iterations Observations Retrieval Observations Forward modelled retrieval Forward modelled first guess

34. Add smoothness constraint Smoother retrieval but slower convergence Truth Retrieval First guess Iterations Observations Retrieval Observations Forward modelled retrieval Forward modelled first guess

35. Unified algorithm: progress • Done: • Functioning algorithm framework exists • C++: object orientation allows code to be completely flexible: observations can be added and removed without needing to keep track of indices to matrices, so same code can be applied to different observing systems • Code to generate particle scattering libraries in NetCDF files • Adjoint of radar and lidar forward models with multiple scattering and HSRL/Raman support • Interface to L-BFGS quasi-Newton algorithm in GNU Scientific Library • In progress / future work: • Implement full ice, liquid, aerosol and rain constituents • Estimate and report error in solution and averaging kernel • Interface to radiance models • Test on a range of ground-based, airborne and spaceborne instruments, particularly the A-Train and EarthCARE satellites

36. Outlook • Use of radiances in retrieval should make retrieved profiles consistent with broadband fluxes (can test this with A-Train and EarthCARE) • EarthCARE will take this a step further • Use imager to construct 3D cloud field 10-20 km wide beneath satellite • Use 3D radiative transfer to test consistency with broadband radiances looking at the cloud field in 3 directions (overcome earlier 3D problem) • How can we use these retrievals to improve weather forecasts? • Assimilate cloud products, or radar and lidar observations directly? • Assimilation experiments being carried out by ECMWF • Still an open problem as to how to ensure clouds are assimilated such that the dynamics and thermodynamics of the model are modified so as to be consistent with the presence of the cloud • How can we use these retrievals to improve climate models? • We will have retrieved global cloud fields consistent with radiation • So can diagnose in detail not only what aspects of clouds are wrong in models, but the radiative error associated with each error in the representation of clouds

38. Proposed list of retrieved variables held in the state vector x Unified algorithm: state variables Ice clouds follows Delanoe & Hogan (2008); Snow & riming in convective clouds needs to be added Liquid clouds currently being tackled Basic rain to be added shortly; Full representation later Basic aerosols to be added shortly; Full representation via collaboration?

39. Minimizing the cost function Gradient of cost function (a vector) Gauss-Newton method Rapid convergence (instant for linear problems) Get solution error covariance “for free” at the end Levenberg-Marquardt is a small modification to ensure convergence Need the Jacobian matrix H of every forward model: can be expensive for larger problems as forward model may need to be rerun with each element of the state vector perturbed • and 2nd derivative (the Hessian matrix): • Gradient Descent methods • Fast adjoint method to calculate xJ means don’t need to calculate Jacobian • Disadvantage: more iterations needed since we don’t know curvature of J(x) • Quasi-Newton method to get the search direction (e.g. L-BFGS used by ECMWF): builds up an approximate inverse Hessian A for improved convergence • Scales well for large x • Poorer estimate of the error at the end

42. Comparison of convergence rates Solution is identical Gauss-Newton method converges in < 10 iterations L-BFGS Gradient Descent method converges in < 100 iterations Conjugate Gradient method converges a little slower than L-BFGS Each L-BFGS iteration >> 10x faster than each Gauss-Newton one! Gauss-Newton method requires the Jacobian matrix, which must be calculated by rerunning multiple scattering model multiple times

43. Computational cost can scale with number of points describing vertical profile N; we can cope with an N2dependencebut not N3 Radiative transfer forward models • Lidar uses PVC+TDTS (N2), radar uses single-scattering+TDTS (N2) • Jacobian of TDTS is too expensive: N3 • We have recently coded adjoint of multiple scattering models • Future work: depolarization forward model with multiple scattering • Infrared will probably use RTTOV, solar radiances will use LIDORT • Both currently being tested by Julien Delanoe