Robin Hogan Julien Delanoe Department of Meteorology, University of Reading, UK Towards unified...

Robin HoganJulien Delanoe

Department of Meteorology, University of Reading, UK

Towards “unified” Towards “unified” radar/lidar/radiometer radar/lidar/radiometer

retrievals for cloud retrievals for cloud radiation studiesradiation studies

MotivationMotivation• Clouds are important due to their role in radiative transfer

– A good cloud retrieval must be consistent with broadband fluxes at surface and top-of-atmosphere (TOA)

• Increasingly, multi-parameter cloud radar and lidar are being deployed together with a range of passive radiometers– We want to retrieve an “optimum” estimate of the state of the

atmosphere that is consistent with all the measurements– But most algorithms use at most only two instruments/variables and

don’t take proper account of instrumental errors

• The “variational” framework is standard in data assimilation and passive sounding, but has only recently been applied to radar– Mathematically rigorous and takes full account of errors– Straightforward to add extra constraints and extra instruments

• In this talk it will be shown how radar, lidar and infrared radiometers can be combined for ice cloud retrievals– Demonstrated on ground-based and satellite (A-train) observations– Discuss challenges of extending to other clouds and other instruments

Surface/satellite observing Surface/satellite observing systemssystems

Ground-based sites

ARM and Cloudnet

NASA A-TrainAqua, CloudSat,

CALIPSO, PARASOL

ESA EarthCAREFor launch in 2013

Radar 35 and/or 94 GHzDoppler, Polarization

94 GHz CloudSat 94 GHz CPRDoppler

Lidar Usually532 or 905 nm

Polarization

532 & 1064 nm CALIOP

Polarization

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)Polarization

None

Broadband radiometers

Surface BBREurope/Africa sites

have GERB overhead

CERES (TOA only) BBR (TOA only)

– Broadband radiometers used only to test retrievals made using the other instruments

Radar and lidarRadar and lidar• Advantages of combining 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)– They 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

Why not invert the lidar Why not invert the lidar separately?separately?

• “Standard method”: assume a value for the extinction-to-backscatter ratio, S, and use a gate-by-gate correction – Problem: for optical depth >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

Example fromUS ARM site:Need todistinguishinsects fromcloud

First step: target First step: target classificationclassification

Ice

LiquidRainAerosol Insects

• Combining radar, lidar with temperature from a model allows the type of cloud (or other target) to be identified– Example from Cloudnet processing of ARM data (Illingworth et al., BAMS

2007)

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

For each ray of data we define:• Observation vector • State vector

– Elements may be missing– Logarithms prevent unphysical negative values

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 layer

Infrared radiance

Radiance difference

The cost functionThe cost function• The essence of the method is to find the state vector x that

minimizes a cost function:

2 2

2 21 1

( )y x

i i

n ni i i

i iy b

y H x bJ

x+ Smoothness

constraints

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

Solution methodSolution method• An iterative method is required

to minimize the cost function

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)Predict the Jacobian H=yi/xj

Has solution converged?2 convergence test

Gauss-Newton iteration stepPredict 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

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 (Applied Optics, 2006). 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

Poster P3.10: Multiple Poster P3.10: Multiple scatteringscattering

CloudSat multiple scattering

• To extend to precip, need to model radar multiple scatteringNew model agrees well

with Monte Carlo

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– Likely to be degraded by 3D cloud effects

• 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 and Seiji Kato)

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)

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

ConvergenceConvergence• The solution generally

converges after two or three iterations– When formulated in terms

of ln(), ln(’) rather than ’ the forward model is much more linear so the minimum of the cost function is reached rapidly

Ground based exampleGround based example• Radagast Campaign (AMMA)

– Based in Niamey, Niger

• ARM Mobile Facility– MMCR cloud radar – 532-nm micropulse lidar– SEVIRI radiometer aboard

MeteoSat 2nd Generation: 8.7, 10.8, 12µm channels

• Ice cloud case, 22 July 2006

Example from the AMF in Example from the AMF in NiameyNiamey

94-GHz radar reflectivity

532-nm lidar backscatter

Forward model at

final iteration

94-GHz radar reflectivity

532-nm lidar backscatter

Observations

Retrievals in regions where radar or lidar detects the cloud

Retrieved visible extinction coefficient

Retrieved effective radius

Results: radar+lidar Results: radar+lidar onlyonly

Large error where only one instrument detects the cloud

Retrieval error in ln(extinction)

TOA radiances increase retrieved optical depth and decrease particle size near cloud top

Cloud-top error greatly reduced

Retrieval error in ln(extinction)

Retrieved visible extinction coefficient


Results: radar, lidar, SEVERI Results: radar, lidar, SEVERI radiancesradiances

CloudSat/CALIPSO retrievalCloudSat/CALIPSO retrieval

0352 0355 0358

Oct 13, 2006 0352-0358

Radar Reflectivity from CloudSatRadar Reflectivity from CloudSat

Attenuated lidar backscatter from CALIPSOAttenuated lidar backscatter from CALIPSO

Heig

ht

[km

]H

eig

ht

[km

]

AVHRR

Forward modelForward modelObserved

radar reflectivity,

95 GHz

Attenuated lidar

backscatter, 532 nm

Radar reflectivity

forward model

Attenuated lidar

backscatter forward model

Preliminary results Preliminary results (radar+lidar)(radar+lidar)October 13th 2006

Granule 2006286023036_02443 between 3h52 and 3h58 UTC

Retrieved error in ln(extinction)

Heig

ht

[km

]

Retrieved number concentration

Heig

ht

[km

]


Heig

ht

[km

]

Retrieved visible extinction coefficient, log10(m-1)

Heig

ht

[km

]

Supercooled water?

MODIS radiancesMODIS radiances



Radiances W sr-1 m-2

Forward model

MODIS

8.4–8.7 micron

10.78–11.25 micron

Heig

ht

[km

]H

eig

ht

[km

]Radiances not used in retrieval, just forward modeled for comparison

CloudSat/CALIPSO exampleCloudSat/CALIPSO example


2006 Day 286


Supercooled water: strong signal from lidar, weak (or nothing) from radar

Radar fails to detect thin cirrus

Conclusions and ongoing Conclusions and ongoing workwork

• New radar/lidar/radiometer cloud retrieval scheme – Applied to ground based or satellite data– Appropriate choice of state vector and smoothness constraints

ensures the retrievals are accurate and efficient– Can include any relevant measurement if forward model is

available– Could provide the basis for cloud/rain data assimilation

• Extension to other cloud types– Retrieve properties of liquid-water layers, drizzle and aerosol– Incorporate microwave radiances and “wide-angle” radar/lidar

multiple-scattering forward models for deep precipitating clouds• Other activities

– Validate using aircraft underflights– Use in radiative transfer model to compare with TOA & surface

fluxes– Build up global cloud climatology to evaluate models

Robin Hogan Julien Delanoe Department of Meteorology, University of Reading, UK Towards unified...

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