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Robin Hogan, Julien Delanoë, Nicola Pounder, Nicky Chalmers, Thorwald Stein, Anthony Illingworth University of Reading Thanks to Alessandro Battaglia and Richard Forbes Towards unified retrievals of cloud, precipitation and aerosol from combined radar, lidar and radiometer observations

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Clouds in climate models 14 global models (AMIP) 90N S Latitude Vertically integrated cloud water (kg m -2 ) But all models tuned to give about the same top-of- atmosphere radiation The properties of ice clouds are particularly uncertain Via their interaction with solar and terrestrial radiation, clouds are one of the greatest sources of uncertainty in climate forecasts But cloud water content in models varies by a factor of 10 Need instrument with high vertical resolution… Stephens et al. (2002)

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Vertical structure of liquid water content Cloudnet: several years of retrievals from 3 European ground-based sites Observations in grey (with range indicating uncertainty) How do these models perform globally? –ECMWF has far too great an occurrence of low LWC values 0-3 km –Supercooled liquid water content from seven forecast models spans a factor of 20 Illingworth, Hogan et al. (2007)

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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 2012 –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? –Classification of targets from radar and lidar –Global distribution of supercooled clouds from the LITE lidar Towards a unified retrieval of cloud, 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 Challenges and opportunities from multiple scattering –Fast forward model –Multiple field-of-view lidar retrieval EarthCARE 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 but attenuated Radar-lidar ratio provides size D

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CloudSat and Calipso sensitivity 7 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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Distribution versus temperature & latitude No supercooled water colder than –40 ° C (as expected) Supercooled water more frequent in southern hemisphere storm track Hogan et al. (2004)

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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 (not yet implemented) –Surface radar echo providing two-way attenuation (ditto) 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 from the state vector –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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Unified retrieval Ingredients developed Work in progress 1. New ray of data: define state vector x Use classification to specify variables describing each species at each gate Ice: extinction coefficient, N 0, lidar extinction-to-backscatter ratio Liquid: extinction coefficient and number concentration Rain: rain rate, drop diameter and melting ice Aerosol: extinction coefficient, particle size and lidar ratio 2a. Radar model Including surface return and multiple scattering 2b. Lidar model Including HSRL channels and multiple scattering 2c. Radiance model Solar and IR channels 3. Compare to observations Check for convergence 4. Iteration method Derive a new state vector Adjoint of full forward model Quasi-Newton or Gauss- Newton scheme 2. Forward model Not converged Converged Proceed to next ray of data 5. Calculate retrieval error Error covariances and averaging kernel

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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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Gauss-Newton method Requires the curvature 2 J/x 2 –A matrix –More expensive to calculate Faster convergence –Assume J is quadratic and jump to the minimum Limited to smaller retrieval problems J x x1x1 J/x 2 J/x 2 Minimization methods - in 1D Quasi-Newton method (e.g. L-BFGS) Rolling a ball down a hill –Intelligent choice of direction in multi-dimensions helps convergence Requires the gradient J/x –A vector (efficient to store) –Efficient to calculate using adjoint method Used in data assimilation J x x2x2 x3x3 x4x4 x5x5 x6x6 x7x7 x8x8 x1x1 J/x x2x2 x3x3 x4x4 x5x5

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Ice retrieval First challenge: –How do we model radar scattering from complex ice particles? In Rayleigh regime (»D), backscatter proportional to mass squared –Particle shape irrelevant –Use a mass-D relationship But Rayleigh assumption often not valid at 94 GHz (=3 mm) –Most papers assume homogeneous ice-air spheres with a diameter equal to the maximum dimension D of the particle, and apply Mie theory Problems with this approach: –Non-Rayleigh behaviour depends on the vertical dimension of the particle –Most are irregular aggregates with an average axial ratio of 0.6 –They fall with their maximum dimension horizontal Alternative approach: –Approximate as horizontally aligned oblate spheroids

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Spheres versus spheroids Spheroid Sphere Transmitted wave Sphere: returns from opposite sides of particle out of phase: cancellation Spheroid: returns from opposite sides not out of phase: higher b Hogan et al. (2011)

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–Sphere produces ~5 dB error (factor of 3) –Spheroid approximation matches Rayleigh reflectivity (mass is about right) and non-Rayleigh reflectivity (shape is about right) Test with dual-wavelength aircraft data Hogan et al. (2011)

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Test with 3-GHz differential reflectivity Hogan et al. (2011) Horizontal polarization Z h –Differential reflectivity Z dr is larger for more extreme axial ratios –Agreement with Z and Z dr confirms the Brown & Francis (1995) mass-D relationship and axial ratio = 0.6 Z dr = 10log 10 (Z h /Z v )

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Ice cloud: non-variational retrieval Donovan et al. (2000) algorithm can only be applied where both lidar and radar have signal Observations State variables Derived variables Retrieval is accurate but not perfectly stable where lidar loses signal Donovan et al. (2000) Aircraft- simulated profiles with noise (from Hogan et al. 2006) Delanoe and Hogan (2008)

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Variational radar/lidar retrieval Noise in lidar backscatter feeds through to retrieved extinction Observations State variables Derived variables Lidar noise matched by retrieval Noise feeds through to other variables Delanoe and Hogan (2008)

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…add smoothness constraint Smoothness constraint: add a term to cost function to penalize curvature in the solution (J = i d 2 i /dz 2 ) Observations State variables Derived variables Retrieval reverts to a-priori N 0 Extinction and IWC too low in radar-only region Delanoe and Hogan (2008)

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…add a-priori error correlation Use B (the a priori error covariance matrix) to smooth the N 0 information in the vertical Observations State variables Derived variables Vertical correlation of error in N 0 Extinction and IWC now more accurate Delanoe and Hogan (2008)

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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? Chalmers (2011) 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 Chalmers (2011)

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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 Chalmers (2011)

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A-Train versus models Ice water content 14 July 2006 Half an orbit 150° longitude at equator Delanoe et al. (2011)

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Both models lack high thin cirrus ECMWF lacks high IWC values; using this work, ECMWF have developed a new prognostic snow scheme that performs better Met Office has too narrow a distribution of in-cloud IWC Evaluation of gridbox-mean ice water content In-cloud mean ice water content

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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) 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 Pounder, Hogan et al. (2011)

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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 Useful optical depth information from one 100-m- footprint lidar (e.g. Calipso)! Pounder, Hogan et al. (2011)

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THOR lidar

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EarthCARE The ESA/JAXA EarthCARE satellite is designed with synergy in mind We are currently developing synergy algorithms for its instrument specification

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EarthCARE lidar High Spectral Resolution capability enables direct retrieval of extinction profile

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EarthCARE radar: Doppler capability 94-GHz radar 10-GHz radar Example from NASA airborne cloud radar demonstrates –Can estimate ice fall-speed globally: important for radiation budget –Can identify strong updrafts in convective cores 94-GHz reflectivity in convection disappears very quickly: multiple scattering from CloudSat may be giving us a false impression of how far we are penetrating

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Unified algorithm: progress Bringing all the aspects of this talk together… 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 –Preliminary retrieval of ice, liquid, rain and aerosol –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: –Estimate and report error in solution and averaging kernel –Interface to radiance models –Test on a range of ground-based, airborne and spaceborne instruments

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Observations vs forward models –Radar and lidar backscatter are successfully forward modelled (at final iteration) in most situations –Can also forward model Doppler velocity (what EarthCARE would see) Radar reflectivity factor Lidar backscatter

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Three retrieved components Liquid water content Ice extinction coefficient Rain rate

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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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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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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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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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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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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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