Robin Hogan, Julien Delanoë, Nicola Pounder, Robin Hogan, Julien Delanoë, Nicola Pounder, Nicky Chalmers, Thorwald Stein, Anthony Illingworth Nicky Chalmers, Thorwald Stein, Anthony Illingworth University of Reading University of Reading Thanks to Alessandro Battaglia and Richard Forbes Thanks to Alessandro Battaglia and Richard Forbes Towards “unified” retrievals of Towards “unified” retrievals of cloud, precipitation and aerosol cloud, precipitation and aerosol from combined radar, lidar and from combined radar, lidar and radiometer observations radiometer observations
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Robin Hogan, Julien Delanoë, Nicola Pounder, Nicky Chalmers, Thorwald Stein, Anthony Illingworth University of Reading Thanks to Alessandro Battaglia and.
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• Lidar: ~D2, more sensitive to thin cirrus and liquid but attenuated
• Radar-lidar ratio provides size D
CloudSat and Calipso CloudSat and Calipso sensitivitysensitivity
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%
Distribution versus temperature & Distribution versus temperature & latitudelatitude
• No supercooled water colder than –40°C (as expected)• Supercooled water more frequent in southern hemisphere storm track
Hogan et al. (2004)
Ingredients of a variational Ingredients of a variational retrievalretrieval
• 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:
• 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
The cost functionThe cost function• The essence of the method is to find the state vector x that minimizes
a cost function:
TxxδxBδxδyRδy
x
T1T1T
1
2
211
12
2
12
2
2
1
2
1
2
1
22
1
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1)(
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n
iiiii
n
i bi
iim
i yi
ii xxxbxHy
J
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
Unified Unified retrievalretrieval
Ingredients developedWork in progress
1. New ray of data: define state vector x
Use classification to specify variables describing each species at each gateIce: extinction coefficient , N0’, lidar extinction-to-backscatter ratio
Liquid: extinction coefficient and number concentrationRain: rain rate, drop diameter and melting iceAerosol: 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 vectorAdjoint of full forward modelQuasi-Newton or Gauss-Newton scheme
2. Forward model
Not converged
Converged
Proceed to next ray of data5. Calculate retrieval error
• 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)
Lidar observations
Radar observations
Visible extinction
Ice water content
Effective radius
Lidar forward model
Radar forward model
Example ice Example ice cloud cloud
retrievalsretrievalsDelanoe and Hogan (2010)
Evaluation using CERES TOA Evaluation using CERES TOA fluxesfluxes
• 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)
ShortwaveBias 4 W m-2, RMSE 71 W m-2
LongwaveBias 0.3 W m-2, RMSE 14 W m-2
CERES versus a radar-only CERES versus a radar-only retrievalretrieval
• 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
ShortwaveBias 48 W m-2, RMSE 110 W m-2
LongwaveBias –10 W m-2, RMSE 47 W m-2
Chalmers (2011)
How important is lidar?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
ShortwaveBias –5 W m-2, RMSE 17 W m-2
LongwaveBias 4 W m-2, RMSE 9 W m-2
Chalmers (2011)
A-Train A-Train versus versus
modelsmodels• Ice water
content• 14 July 2006• Half an orbit• 150°
longitude at equator
Delanoe et al. (2011)
• 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 Evaluation of gridbox-mean ice water contentcontent
In-cloud mean ice water In-cloud mean ice water contentcontent
Radiative transfer forward Radiative transfer forward modelsmodels
• 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
Examples of multiple scattering
LITE lidar (<r, footprint~1 km)
CloudSat radar (>r)
StratocumulusStratocumulus
Intense thunderstormIntense thunderstorm
Surface echoSurface echoApparent echo from below the surface
• 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 Scattering regimesregimes
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
• 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
Unified algorithm: progressUnified 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
Observations vs forward Observations vs forward modelsmodels
– 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
Three retrieved componentsThree retrieved components• Liquid water content
• Ice extinction coefficient
• Rain rate
OutlookOutlook• 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
• 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 modelsScattering models
Particle type Radar (3.2 mm) Radar Doppler Thermal IR, Solar, UVAerosol Aerosol not
Time-Dependent Two-Stream (TDTS) method (Hogan and Battaglia 2008)
Lidar & radar, wide-angle multiple scattering
N2 N3 N2
Depolarization capability for TDTS Lidar & radar depol with multiple scattering N2 N2
Radiometer model Applications Speed Jacobian Adjoint
RTTOV (used at ECMWF & Met Office) Infrared and microwave radiances N N
Two-stream source function technique (e.g. Delanoe & Hogan 2008)
Infrared radiances N N2
LIDORT Solar radiances N N2 N
• Infrared will probably use RTTOV, solar radiances will use LIDORT• Both currently being tested by Julien Delanoe
• 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
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
Minimizing the cost functionMinimizing 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
112 BHRHxTJ
axBaxxyRxy 11
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2
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axBxyRHx 11 )(HJ T
JJii xxxx
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Comparison of convergence Comparison of convergence ratesrates
• 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
Unified algorithm: first results for Unified algorithm: first results for ice+liquidice+liquid
Ob
serv
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s
Retr
ieval
But lidar noise degrades retrieval
TruthRetrieval
First guessIterations
ObservationsForward modelled retrievalForward modelled first guess