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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?

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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 (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 EarthCare

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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

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What do CloudSat and Calipso see? Cloudsat radar CALIPSO lidar Target classification Insects Aerosol Rain Supercooled liquid cloud Warm liquid cloud Ice and supercooled liquid Ice Clear No ice/rain but possibly liquid Ground Delanoe and Hogan (2008, 2010) Radar: ~D 6, detects whole profile, surface echo provides integral constraint Lidar: ~D 2, more sensitive to thin cirrus and liquid clouds but attenuated

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CloudSat and Calipso sensitivity 5 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%

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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 properties to 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

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

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Retrieval framework Ingredients developed before In progress Not yet developed 1. New ray of data: define state vector Use classification to specify variables describing each species at each gate Ice: extinction coefficient, N 0, 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 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

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

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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? Nicky Chalmers Shortwave Bias 4 W m -2, RMSE 71 W m -2 Longwave Bias 0.3 W m -2, RMSE 14 W m -2

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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)? Bias 10 W m -2 RMS 47 W m -2 Shortwave Bias 48 W m -2, RMSE 110 W m -2 Longwave Bias –10 W m -2, RMSE 47 W m -2 Nicky Chalmers

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How important is lidar? 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 Shortwave Bias –5 W m -2, RMSE 17 W m -2 Longwave Bias 4 W m -2, RMSE 9 W m -2 Nicky Chalmers

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

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Gridbox mean: In-cloud mean: 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

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Cascade project 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 Moist monsoon flow African easterly jet Saharan air layer Mid-level outflow Parker et al. (QJRMS 2005) Location of African easterly jet

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Cascade 40-km model versus CloudSat 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 Unified ModelCloudSat (~01.30 LT)CloudSat (~13.30 LT) Thorwald Stein

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

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Cascade 4-km model versus CloudSat Unified ModelCloudSat (~01.30 LT)CloudSat (~13.30 LT) 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) Thorwald Stein

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Structure of Southern Ocean cirrus Observations -Note limitations of each instrument Retrievals

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

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

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

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

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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 Particle typeRadar (3.2 mm)Radar DopplerThermal IR, Solar, UV AerosolAerosol not detected by radar Mie theory, Highwood refractive index Liquid dropletsMie theoryBeard (1976)Mie theory Rain dropsT-matrix: Brandes et al. (2002) shapes Beard (1976)Mie theory Ice cloud particles T-matrix (Hogan et al. 2010) Westbrook & Heymsfield Baran (2004) Graupel and hailMie theoryTBDMie theory Melting iceWu & Wang (1991) TBDMie theory

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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: = exp(-2 ) –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

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Examples of multiple scattering LITE lidar (

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Regime 0: No attenuation –Optical depth << 1 Regime 1: Single scattering –Apparent backscatter is easy to calculate from at range r : (r) = (r) exp[-2 (r)] Scattering regimes Footprint x Mean free path l Regime 2: Small-angle multiple scattering – Occurs when l ~ 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

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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) Time derivative Remove this and we have the time- independent two- stream approximation Spatial derivative Transport of radiation from upstream Loss by absorption or scattering Some 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.)

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Fast multiple scattering forward model CloudSat-like example New method uses the time- dependent two-stream approximation Agrees with Monte Carlo but ~10 7 times faster (~3 ms) Added to CloudSat simulator Hogan and Battaglia (J. Atmos. Sci. 2008) CALIPSO-like example

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Multiple field-of-view 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 m 100 m 10 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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Optical depth from multiple FOV lidar 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 Nicola Pounder

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

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

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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

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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 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

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Unified algorithm: state variables State variableRepresentation with height / constraintA-priori Ice clouds and snow Visible extinction coefficientOne variable per pixel with smoothness constraintNone Number conc. parameterCubic spline basis functions with vertical correlationTemperature dependent Lidar extinction-to-backscatter ratioCubic spline basis functions20 sr Riming factorLikely a single value per profile1 Liquid clouds Liquid water contentOne variable per pixel but with gradient constraintNone Droplet number concentrationOne value per liquid layerTemperature dependent Rain Rain rateCubic spline basis functions with flatness constraintNone Normalized number conc. N w One value per profileDependent on whether from melting ice or coallescence Melting-layer thickness scaling factorOne value per profile1 Aerosols Extinction coefficientOne variable per pixel with smoothness constraintNone Lidar extinction-to-backscatter ratioOne value per aerosol layer identifiedClimatological type depending on region 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? Proposed list of retrieved variables held in the state vector x

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and 2 nd derivative (the Hessian matrix): Gradient Descent methods –Fast adjoint method to calculate x J means dont need to calculate Jacobian –Disadvantage: more iterations needed since we dont 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 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

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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

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Computational cost can scale with number of points describing vertical profile N; we can cope with an N 2 dependence but not N 3 Radiative transfer forward models Radar/lidar modelApplicationsSpeedJacobianAdjoint Single scattering: = exp(-2 ) Radar & lidar, no multiple scatteringNN2N2 N Platts approximation = exp(-2 ) Lidar, ice only, crude multiple scatteringNN2N2 N Photon Variance-Covariance (PVC) method (Hogan 2006, 2008) Lidar, ice only, small-angle multiple scattering N or N 2 N2N2 N Time-Dependent Two-Stream (TDTS) method (Hogan and Battaglia 2008) Lidar & radar, wide-angle multiple scatteringN2N2 N3N3 N2N2 Depolarization capability for TDTSLidar & radar depol with multiple scatteringN2N2 N2N2 Radiometer modelApplicationsSpeedJacobianAdjoint RTTOV (used at ECMWF & Met Office)Infrared and microwave radiancesNN Two-stream source function technique (e.g. Delanoe & Hogan 2008) Infrared radiancesNN2N2 LIDORTSolar radiancesNN2N2 N Infrared will probably use RTTOV, solar radiances will use LIDORT Both currently being tested by Julien Delanoe Lidar uses PVC+TDTS (N 2 ), radar uses single-scattering+TDTS (N 2 ) Jacobian of TDTS is too expensive: N 3 We have recently coded adjoint of multiple scattering models Future work: depolarization forward model with multiple scattering

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