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Unified Retrievals of Cloud, Precipitation, and Aerosol from Combined Radar, Lidar, and Radiometer Observations

This study aims to develop a unified retrieval method for cloud, precipitation, and aerosol properties using data from radar, lidar, and radiometer observations. The results will contribute to improving climate models and reducing uncertainties in climate forecasts.

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Unified Retrievals of Cloud, Precipitation, and Aerosol from Combined Radar, Lidar, and Radiometer Observations

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  1. Robin Hogan, JulienDelanoë, 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

  2. Clouds in climate models But all models tuned to give about the same top-of-atmosphere radiation 14 global models (AMIP) 0.25 0.20 0.15 Vertically integrated cloud water (kg m-2) The properties of ice clouds are particularly uncertain 0.10 0.05 90N 80 60 40 20 0 -20 -40 -60 -80 90S Latitude • 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)

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

  4. 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 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 2013 2015 2016 2017 2018 2019 2014

  5. 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

  6. 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 but attenuated • Radar-lidar ratio provides size D 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)

  7. 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%

  8. 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)

  9. 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 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 from the state vector • Microphysical component: particle scattering properties • Radiative transfer component

  10. The cost function Some elements of x are constrained by a prior estimate The forward modelH(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

  11. 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 , N0’,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 2. Forward model 4. Iteration method Derive a new state vector Adjoint of full forward model Quasi-Newton or Gauss-Newton scheme 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 Not converged 3. Compare to observations Check for convergence Converged 5. Calculate retrieval error Error covariances and averaging kernel Proceed to next ray of data

  12. 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)]

  13. Minimization methods - in 1D • Gauss-Newton method • Requires the curvature 2J/x2 • A matrix • More expensive to calculate • Faster convergence • Assume J is quadratic and jump to the minimum • Limited to smaller retrieval problems 2J/x2 J J/x J/x x1 x1 x2 x3 x2 x4 x3 x5 x6 x4 x7 x8 x5 x 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

  14. Ice retrieval • First challenge: • How do we model radar scattering from complex ice particles? • In Rayleigh regime (l»D), backscatter proportional to mass squared • Particle shape irrelevant • Use a mass-D relationship • But Rayleigh assumption often not valid at 94 GHz (l=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

  15. Spheres versus spheroids Transmitted wave Spheroid Sphere 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)

  16. Test with dual-wavelength aircraft data • 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) Hogan et al. (2011)

  17. Test with 3-GHz differential reflectivity Horizontal polarization Zh Differential reflectivity Zdr is larger for more extreme axial ratios Agreement with Z and Zdrconfirms the Brown & Francis (1995) mass-D relationship and axial ratio = 0.6 • Zdr= 10log10(Zh/Zv) Hogan et al. (2011)

  18. Ice cloud: non-variational retrieval Donovan et al. (2000) Aircraft-simulated profiles with noise (from Hogan et al. 2006) • 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 Delanoe and Hogan (2008)

  19. 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)

  20. …add smoothness constraint • Smoothness constraint: add a term to cost function to penalize curvature in the solution (J’ = l Sid2ai/dz2) Observations State variables Derived variables Retrieval reverts to a-priori N0 Extinction and IWC too low in radar-only region Delanoe and Hogan (2008)

  21. …add a-priori error correlation • Use B (the a priori error covariance matrix) to smooth the N0 information in the vertical Observations State variables Derived variables Vertical correlation of error in N0 Extinction and IWC now more accurate Delanoe and Hogan (2008)

  22. 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)

  23. 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 Chalmers (2011)

  24. 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 Chalmers (2011)

  25. 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 Chalmers (2011)

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

  27. Evaluation of gridbox-mean ice water content • 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 In-cloud mean ice water content

  28. 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

  29. 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)

  30. 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

  31. 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)

  32. 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) CloudSat-like example CALIPSO-like example

  33. 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

  34. 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)

  35. 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)! Optical depth from multiple FOV lidar Pounder, Hogan et al. (2011)

  36. THOR lidar

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

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

  39. EarthCARE radar: Doppler capability 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 10-GHz radar 94-GHz radar

  40. 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

  41. 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

  42. Three retrieved components • Liquid water content • Ice extinction coefficient • Rain rate

  43. 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

  44. 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

  45. 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?

  46. 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

  47. 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

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