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**Radar/lidar/radiometer retrievals of ice clouds from the A-train**

Robin Hogan, Julien Delanoe Department of Meteorology, University of Reading, UK Richard Forbes European Centre for Medium Range Weather Forecasts Alejandro Bodas-Salcedo Met Office, UK

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Motivation Clouds are important for climate due to interaction with radiation A good cloud retrieval must be consistent with broadband fluxes at surface and top-of-atmosphere (TOA) Advantages of combining radar, lidar and radiometers Radar ZD6, lidar b’D2 so the combination provides particle size Radiances ensure that the retrieved profiles can be used for radiative transfer studies How do we do we combine them optimally? Use a “variational” framework: takes full account of observational errors Straightforward to add extra constraints and extra instruments Allows seamless retrieval between regions of different instrument sensitivity In this talk a new variational radar-lidar-radiometer algorithm is applied to a month of A-Train data Comparison with MODIS retrievals Evaluation of Met Office and ECMWF model ice clouds Investigation of the morphology of tropical cirrus

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**Surface/satellite observing systems**

Ground-based sites ARM and Cloudnet NASA A-Train Aqua, CloudSat, CALIPSO, PARASOL ESA EarthCARE For launch in 2013 Radar 35 and/or 94 GHz Doppler, Polarization 94 GHz CloudSat 94 GHz CPR Doppler Lidar Usually 532 or 905 nm Polarization 532 & 1064 nm CALIOP 355 nm ATLID Polarization, HSRL VIS/IR radiometers Some have infrared radiometer, sky imager, spectrometer MODIS, AIRS, CALIPSO IIR (Imaging Infrared Radiometer) Multi-Spectral Imager (MSI) Microwave radiometers Dual-wavelength radiometer (e.g. 22 & 28 GHz) AMSR-E (6, 10, 18, 23, 36, 89 GHz) None Broadband radiometers Surface BBR Europe/Africa sites have GERB overhead CERES (TOA only) BBR (TOA only) Broadband radiometers used only to test retrievals made using the other instruments

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**Why not invert the lidar separately?**

“Standard method”: assume a value for the extinction-to-backscatter ratio, S, and use a gate-by-gate correction Problem: for optical depth d>2 is excessively sensitive to choice of S Exactly the same instability for radar (Hitschfeld & Bordan 1954) Better method (e.g. Donovan et al. 2000): retrieve the S that is most consistent with the radar and other constraints For example, when combined with radar, it should produce a profile of particle size or number concentration that varies least with range Implied optical depth is infinite

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**Formulation of variational scheme**

For each ray of data we define: Observation vector • State vector Elements may be missing Logarithms prevent unphysical negative values Attenuated lidar backscatter profile Ice visible extinction coefficient profile Ice normalized number conc. profile Extinction/backscatter ratio for ice Radar reflectivity factor profile (on different grid) Visible optical depth Infrared radiance Radiance difference (TBD) Aerosol visible extinction coefficient profile (TBD) Liquid water path and number conc. for each liquid layer

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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 an a priori estimate This term penalizes curvature in the extinction profile + Smoothness constraints

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**xk+1= xk+A-1{HTR-1[y-H(xk)]**

Solution method New ray of data Locate cloud with radar & lidar Define elements of x First guess of x An iterative method is required to minimize the cost function Forward model Predict measurements y from state vector x using forward model H(x) Predict the Jacobian H=yi/xj Gauss-Newton iteration step Predict new state vector: xk+1= xk+A-1{HTR-1[y-H(xk)] -B-1(xk-b)-Txk} where the Hessian is A=HTR-1H+B-1+T Has solution converged? 2 convergence test No Yes Calculate error in retrieval Proceed to next ray

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**Radar forward model and a priori**

Create lookup tables Gamma size distributions Choose mass-area-size relationships Mie theory for 94-GHz reflectivity Define normalized number concentration parameter “The N0 that an exponential distribution would have with same IWC and D0 as actual distribution” Forward model predicts Z from extinction and N0 Effective radius from lookup table N0 has strong T dependence Use Field et al. power-law as a-priori When no lidar signal, retrieval relaxes to one based on Z and T (Liu and Illingworth 2000, Hogan et al. 2006) Field et al. (2005)

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**Lidar forward model: multiple scattering**

90-m footprint of Calipso means that multiple scattering is a problem Eloranta’s (1998) model O (N m/m !) efficient for N points in profile and m-order scattering Too expensive to take to more than 3rd or 4th order in retrieval (not enough) New method: treats third and higher orders together O (N 2) efficient As accurate as Eloranta when taken to ~6th order 3-4 orders of magnitude faster for N =50 (~ 0.1 ms) Narrow field-of-view: forward scattered photons escape Wide field-of-view: forward scattered photons may be returned Ice cloud Molecules Liquid cloud Aerosol Hogan (Applied Optics, 2006). Code:

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**Wide-angle multiple scattering**

CloudSat multiple scattering To extend to precip, need to model radar multiple scattering Talk on Wednesday, session B! New model agrees well with Monte Carlo

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**Radiance forward model**

MODIS and CALIPSO each have 3 thermal infrared channels in the atmospheric window region Radiance depends on vertical distribution of microphysical properties Single channel: information on extinction near cloud top Pair of channels: ice particle size information near cloud top Radiance model uses the 2-stream source function method Efficient yet sufficiently accurate method that includes scattering Provides important constraint for ice clouds detected only by lidar Ice single-scatter properties from Anthony Baran’s aggregate model Correlated-k-distribution for gaseous absorption (from David Donovan and Seiji Kato) MODIS solar channels provide an estimate of optical depth Only available in daylight Likely to be degraded by 3D radiative transfer effects Only usable when no liquid clouds in profile … currently not used

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**Ice cloud: non-variational retrieval**

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

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**Variational radar/lidar retrieval**

Observations State variables Derived variables Lidar noise matched by retrieval Noise feeds through to other variables Noise in lidar backscatter feeds through to retrieved extinction

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**…add smoothness constraint**

Observations State variables Derived variables Retrieval reverts to a-priori N0 Extinction and IWC too low in radar-only region Smoothness constraint: add a term to cost function to penalize curvature in the solution (J’ = l Si d2ai/dz2)

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**…add a-priori error correlation**

Observations State variables Derived variables Vertical correlation of error in N0 Extinction and IWC now more accurate Use B (the a priori error covariance matrix) to smooth the N0 information in the vertical

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**…add visible optical depth constraint**

Observations State variables Derived variables Slight refinement to extinction and IWC Integrated extinction now constrained by the MODIS-derived visible optical depth

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**…add infrared radiances**

Observations State variables Derived variables Poorer fit to Z at cloud top: information here now from radiances Better fit to IWC and re at cloud top

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**Radar-only retrieval Retrieval is poorer if the lidar is not used**

Observations State variables Derived variables Use a priori as no other information on N0 Profile poor near cloud top: no lidar for the small crystals Retrieval is poorer if the lidar is not used

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**Radar plus optical depth**

Observations State variables Derived variables Optical depth constraint distributed evenly through the cloud profile Note that often radar will not see all the way to cloud top

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**Radar, optical depth and IR radiances**

Observations State variables Derived variables

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**CloudSat-CALIPSO-MODIS example**

Lidar observations Radar observations 1000 km

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**CloudSat-CALIPSO-MODIS example**

Lidar observations Lidar forward model Radar observations Radar forward model

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**Radar-lidar retrieval**

Extinction coefficient Ice water content Effective radius Forward model MODIS 10.8-mm observations

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**…add infrared radiances**

Radiances matched by increasing extinction near cloud top Forward model MODIS 10.8-mm observations

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**Retrievals with different radar and lidar detection**

Lidar observations 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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One orbit in July 2006

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**Comparison with Met Office model**

log10(IWC[kg m-3]) A-Train Model Antarctica Central Pacific Arctic Ocean Atlantic South Russia

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**Effective radius versus temperature**

All clouds An effective radius parameterization?

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**Frequency of IWC vs. temperature**

log10(IWC) Radar+lidar only Mean and variance of IWC both increase with temperature Clearly need both radar and lidar to detect full range of ice clouds log10(IWC [kg m-3]) log10(IWC) Lidar only Radar only

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**Comparison of mean effective radius**

July 2006 mean value of re=3IWP/2tri from CloudSat-CALIPSO only Just the top 500 m of cloud MODIS/Aqua standard product

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**Comparison of ice water path**

Mean of all skies Mean of clouds CloudSat-CALIPSO MODIS Need longer period than just one month (July 2006) to obtain adequate statistics from poorer sampling of radar and lidar

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**Comparison of optical depth**

Mean of all skies Mean of clouds CloudSat-CALIPSO MODIS Mean optical depth from CloudSat-CALIPSO is lower than MODIS simply because CALIPSO detected many more optically thin clouds not seen by MODIS Hence need to compare PDFs as well

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**Differences between hemispheres**

No obvious differences in the general trend IWC shifted to low temperatures in southern hemisphere Temperature [˚C] Temperature [˚C] Boreal Summer Austral Winter Such information is crucial for global atmospheric modelling

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**Comparison with model IWC**

A-Train Met Office ECMWF Temperature (°C) Temperature (°C) Global forecast model data extracted underneath A-Train A-Train ice water content averaged to model grid Met Office model lacks observed variability ECMWF model has artificial threshold for snow at around 10-4 kg m-3

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**Structure of Southern Ocean cirrus**

Observations Note limitations of each instrument Retrievals

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**Tropical Indian Ocean cirrus**

MODIS infrared window radiance Turbulent fall-streaks in lower half of cloud? Stratiform region in upper half of cloud? Observations Note limitation of each instrument Retrievals

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**Mid-latitude cirrus Tropical cirrus**

1300 km 320 km 600 km 120 km Stratiform upper region dominated by larger scales A-Train data show quite different structure above ~12.5 km in tropical cirrus: gravity waves? Outer scale 90 km -5/3 law Hogan and Kew (QJ 2005) found that mid-latitude cirrus structure affected by cloud top turbulence with a typical outer scale of km

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**Summary and future work**

New dataset provides a unique perspective on global ice clouds Planned retrieval enhancements Retrieve liquid clouds and precipitation at the same time to provide a truly seamless retrieval from the thinnest to the thickest clouds Incorporate microwave and visible radiances Adapt for EarthCARE satellite (ESA/JAXA: launch 2013) Model evaluation How can Met Office and ECMWF model cloud schemes be improved? High-resolution simulations of tropical convection in “CASCADE” Use CERES to determine the radiative error associated with misrepresented clouds in model Cloud structure and microphysics What is the explanation for the different regions in tropical cirrus? What determines the outer scale of variability? Can we represent tropical cirrus in the Hogan & Kew fractal model? Can we resolve the “small crystal” controversy?

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Convergence The solution generally converges after two or three iterations When formulated in terms of ln(a), ln(b’) rather than a, b’, the forward model is much more linear so the minimum of the cost function is reached rapidly

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**Enforcing smoothness 1 Cubic-spline basis functions**

Let state vector x contain the amplitudes of a set of basis functions Cubic splines ensure that the solution is continuous in itself and its first and second derivatives Fewer elements in x more efficient! Forward model Convert state vector to high resolution: xhr=Wx Predict measurements y and high-resolution Jacobian Hhr from xhr using forward model H(xhr) Convert Jacobian to low resolution: H=HhrW Representing a 50-point function by 10 control points The weighting matrix

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Enforcing smoothness 2 Twomey matrix, for when we have no useful a priori information Add a term to the cost function to penalize curvature in the solution: ld2x/dr2 (where r is range and l is a smoothing coefficient) Implemented by adding “Twomey” matrix T to the matrix equations

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