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What can we learn about clouds and their representation in models from the synergy of radar and lidar observations? 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

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**Spaceborne radar, lidar and radiometers**

EarthCare 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

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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 Radar: ~D6, detects whole profile, surface echo provides integral constraint Lidar: ~D2, more sensitive to thin cirrus and liquid clouds but attenuated 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)

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**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%

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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 + Smoothness constraints**

The essence of the method is to find the state vector x that minimizes a cost function: Each observation yi 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 + Smoothness constraints

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**Ingredients developed before In progress Not yet developed**

Retrieval framework 1. New ray of data: define state vector Use classification to 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 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 Ingredients developed before In progress Not yet developed

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**Example ice cloud retrievals**

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

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

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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)? Shortwave Bias 48 W m-2, RMSE 110 W m-2 Longwave Bias –10 W m-2, RMSE 47 W m-2 Bias 10 W m-2 RMS 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 Location of African easterly jet Parker et al. (QJRMS 2005) Moist monsoon flow African easterly jet Saharan air layer Mid-level outflow

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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 Model CloudSat (~01.30 LT) CloudSat (~13.30 LT) Thorwald Stein

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**Cascade 12-km model versus CloudSat**

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

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**Cascade 4-km model versus CloudSat**

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) Unified Model CloudSat (~01.30 LT) CloudSat (~13.30 LT) Thorwald Stein

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**Structure of Southern Ocean cirrus**

Observations Note limitations of each instrument Retrievals

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**Slice through Hogan & Kew 3D fractal cirrus model**

90 km -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!

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**Tropical Indian Ocean cirrus**

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

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**Sum of two fractal cirrus simulations**

600 km 120 km Stratiform upper region dominated by larger scales Turbulent lower region 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 & snow Liquid cloud Rain Aerosol x Adjoint of radar model (vector) Adjoint of lidar model (vector) Adjoint of radiometer model Gradient of cost function (vector) xJ=HTR-1[y–H(x)] Vector-matrix multiplications: around the same cost as the original forward operations Adjoint of radiative transfer models yJ=R-1[y–H(x)] Ice/radar Liquid/radar Rain/radar Ice/lidar Liquid/lidar Rain/lidar Aerosol/lidar Ice/radiometer Liquid/radiometer Rain/radiometer Aerosol/radiometer Lookup tables to obtain profiles of extinction, scattering & backscatter coefficients, asymmetry factor Radar scattering profile Lidar scattering profile Radiometer scattering profile Sum the contributions from each constituent Radar forward modelled obs Lidar forward modelled obs Radiometer fwd modelled obs H(x) Radiative transfer models

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Scattering models 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 Particle type Radar (3.2 mm) Radar Doppler Thermal IR, Solar, UV Aerosol Aerosol not detected by radar Mie theory, Highwood refractive index Liquid droplets Mie theory Beard (1976) Rain drops T-matrix: Brandes et al. (2002) shapes Ice cloud particles T-matrix (Hogan et al. 2010) Westbrook & Heymsfield Baran (2004) Graupel and hail TBD Melting ice Wu & Wang (1991)

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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: 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

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**Examples of multiple scattering**

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

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**Scattering regimes Regime 2: Small-angle multiple scattering**

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)] Mean free path l 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 Footprint x 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 Source Scattering from the quasi-direct beam into each of the streams 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.)

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**Fast multiple scattering forward model**

Hogan and Battaglia (J. Atmos. Sci. 2008) New method uses the time-dependent two-stream approximation Agrees with Monte Carlo but ~107 times faster (~3 ms) Added to CloudSat simulator CloudSat-like example 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 100 m 10 m 600 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**

But lidar noise degrades retrieval Convergence! Truth Retrieval First guess Iterations Observations Retrieval Observations Forward modelled retrieval Forward modelled first guess

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**Add smoothness constraint**

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

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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**

Proposed list of retrieved variables held in the state vector x State variable Representation with height / constraint A-priori Ice clouds and snow Visible extinction coefficient One variable per pixel with smoothness constraint None Number conc. parameter Cubic spline basis functions with vertical correlation Temperature dependent Lidar extinction-to-backscatter ratio Cubic spline basis functions 20 sr Riming factor Likely a single value per profile 1 Liquid clouds Liquid water content One variable per pixel but with gradient constraint Droplet number concentration One value per liquid layer Rain Rain rate Cubic spline basis functions with flatness constraint Normalized number conc. Nw One value per profile Dependent on whether from melting ice or coallescence Melting-layer thickness scaling factor Aerosols Extinction coefficient One value per aerosol layer identified Climatological 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?

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**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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**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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**Radiative transfer forward models**

Computational cost can scale with number of points describing vertical profile N; we can cope with an N2 dependence but not N3 Radar/lidar model Applications Speed Jacobian Adjoint Single scattering: b’=b exp(-2t) Radar & lidar, no multiple scattering N N2 Platt’s approximation b’=b exp(-2ht) Lidar, ice only, crude multiple scattering Photon Variance-Covariance (PVC) method (Hogan 2006, 2008) Lidar, ice only, small-angle multiple scattering N or N2 Time-Dependent Two-Stream (TDTS) method (Hogan and Battaglia 2008) Lidar & radar, wide-angle multiple scattering N3 Depolarization capability for TDTS Lidar & radar depol with multiple scattering 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 Radiometer model Applications Speed Jacobian Adjoint RTTOV (used at ECMWF & Met Office) Infrared and microwave radiances N Two-stream source function technique (e.g. Delanoe & Hogan 2008) Infrared radiances N2 LIDORT Solar radiances Infrared will probably use RTTOV, solar radiances will use LIDORT Both currently being tested by Julien Delanoe

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