A variational cloud retrieval scheme combining radar, lidar and radiometer observations Robin Hogan & Julien Delanoe University of Reading, UK. The CloudSat.

A variational cloud retrieval A variational cloud retrieval scheme combining radar, lidar scheme combining radar, lidar and radiometer observationsand radiometer observations

Robin Hogan & Julien DelanoeRobin Hogan & Julien DelanoeUniversity of Reading, UK .University of Reading, UK .

• The CloudSat radar and the Calipso lidar were launched on 28th April 2006

• They join Aqua, hosting the MODIS, CERES, AIRS and AMSU radiometers

• An opportunity to tackle questions concerning role of clouds in climate

• Need to combine all these observations to get an optimum estimate of global cloud properties

Eastern RussiaJapanSea of JapanEast China Sea

• Calipso lidar

• CloudSat radar

Molecular scattering

Aerosol from China?

CirrusMixed-phase

altocumulus

Drizzling stratocumulus

Non-drizzling stratocumulus

Rain

7 June 2006

5500 km

MotivationMotivation• Why combine radar, lidar and radiometers?

– Radar ZD6, lidar ’D2 so the combination provides particle size– Radiances ensure that the retrieved profiles can be used for

radiative transfer studies

• Some limitations of existing radar/lidar ice retrieval schemes (Donovan et al. 2000, Tinel et al. 2005, Mitrescu et al. 2005)– Only work in regions of cloud detected by both radar and lidar– Noise in measurements results in noise in the retrieved variables– Eloranta’s lidar multiple-scattering model is too slow to take to

greater than 3rd or 4th order scattering– Other clouds in the profile are not included, e.g. liquid water clouds– Difficult to make use of other measurements, e.g. passive radiances – Difficult to also make use of lidar molecular scattering beyond the

cloud as an optical depth constraint– Some methods need the unknown lidar ratio to be specified

• A “unified” variational scheme can solve all of these problems

Formulation of variational Formulation of variational schemescheme

m

m

m

n

I

I

Z

Z

0.127.8

7.8

1

1

ln

ln

y

aer1

liq1

1

ice

ice1

ice1

ln

ln

LWP

ln

ln

ln

ln

N

S

N

N

m

n

x

• Observation vector • State vector– Elements may be missing

Attenuated lidar backscatter profile

Radar reflectivity factor profile (on different grid)

Ice visible extinction coefficient profile

Ice normalized number conc. profile

Extinction/backscatter ratio for ice

Visible optical depth

Aerosol visible extinction coefficient profile

Liquid water path and number conc. for each liquid layerInfrared radiance

Radiance difference

Solution methodSolution method• Find x that minimizes a cost function J

of the form J = deviation of x from a-priori + deviation of observations from

forward model + curvature of extinction profile

New ray of dataLocate cloud with radar & lidarDefine elements of xFirst guess of x

Forward modelPredict measurements y from state vector x using forward model H(x)Also predict the Jacobian H

Has solution converged?2 convergence test

Gauss-Newton iteration stepPredict new state vector:

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

-B-1(xi-xa)-Txi}where the Hessian is

A=HTR-1H+B-1+T

Calculate error in retrieval

No

Yes

Proceed to next ray

Radar forward model and Radar forward model and a a prioripriori• 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)

Lidar forward model: multiple Lidar forward model: multiple scatteringscattering

• 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)

Hogan (2006, Applied Optics, in press). Code: www.met.rdg.ac.uk/clouds

Ice cloud

Molecules

Liquid cloud

Aerosol

Narrow field-of-view:

forward scattered

photons escape

Wide field-of-view:

forward scattered

photons may be returned

Radiance forward modelRadiance forward model• MODIS solar channels provide an estimate of optical depth

– Only very weakly dependent on vertical location of cloud so we simply use the MODIS optical depth product as a constraint

– Only available in daylight

• MODIS, Calipso and SEVIRI each have 3 thermal infrared channels in 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)

Ice cloud: non-variational Ice cloud: non-variational retrievalretrieval

• 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

Aircraft-simulated profiles with noise (from Hogan et al. (2006)

Optical depth 13.9; lidar sees to 3.6

Variational radar/lidar Variational radar/lidar retrievalretrieval

• 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

……add smoothness constraintadd smoothness constraint

• Smoothness constraint: add a term to cost function to penalize curvature in the solution (J’ =

id2i/dz2)

Observations

State variables

Derived variables

Retrieval reverts to a-priori N0

Extinction and IWC too low in radar-only region

……add a-priori error add a-priori error correlationcorrelation

• 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

……add visible optical depth add visible optical depth constraintconstraint

• Integrated extinction now constrained by the MODIS-derived visible optical depth

Observations

State variables

Derived variables

Slight refinement to extinction and IWC

……add infrared radiancesadd infrared radiances

• Better fit to IWC and re at cloud top

Observations

State variables

Derived variables

Poorer fit to Z at cloud top: information here now from radiances

Observed94-GHz

radar reflectivity

Observed 905-nm

lidar backscatter

Forward model radar

reflectivity

Forward model lidar backscatter

Ground-based exampleGround-based example

Lidar fails to penetrate deep ice cloud

Retrieved extinction

coefficient

Retrieved effective radius re

Retrieved normalized

number conc.

parameter N0

Error in retrieved

extinction

Lower error in regions with both radar and lidar

Radar only: retrieval tends towards a-priori

Conclusions and ongoing Conclusions and ongoing workwork

• A variational method has been described for combining radar, lidar, radiometers and any other relevant measurements, to retrieve profiles of cloud microphysical properties

• In progress:– Testing radiance part of retrieval using geostationary-satellite

radiances from Meteosat/SEVIRI above ground-based radar & lidar– Add capability to retrieve properties of liquid-water layers, drizzle

and aerosol

• Then apply to A-train data!

CloudSat observations over the UK on 18th June 2006

Scotland EnglandLakedistrict

Isle of Wight France

13.10 UTC 13.10 UTC June 18June 18thth

Scotland EnglandLakedistrict

Isle of Wight France

MODIS RGB composite

Scotland EnglandLakedistrict

Isle of Wight France

MODIS Infrared window

13.10 UTC 13.10 UTC June 18June 18th th

(Sunday) (Sunday)

Scotland EnglandLakedistrict

Isle of Wight France

Met Office rain radar network

13.10 UTC 13.10 UTC June 18June 18th th

(Sunday) (Sunday)

SdSd

Banda SeaAn island of Indonesia