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Towards “unified” radar/lidar/radiometer retrievals for cloud radiation studiesPowerPoint Presentation

Towards “unified” radar/lidar/radiometer retrievals for cloud radiation studies

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Towards “unified” radar/lidar/radiometer retrievals for cloud radiation studies

Robin Hogan

Julien Delanoe

Department of Meteorology, University of Reading, UK

Motivation cloud radiation studies

- 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

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

Surface/satellite observing systemsRadar and lidar using the other instruments

- 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

- 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 separately? using the other instruments

- “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

First step: target classification using the other instruments

Ice

Liquid

Rain

Aerosol

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)

Example from

US ARM site:

Need to

distinguish

insects from

cloud

Formulation of variational scheme using the other instruments

Ice visible extinction coefficient profile

Attenuated lidar backscatter profile

Ice normalized number conc. profile

Radar reflectivity factor profile (on different grid)

Extinction/backscatter ratio for ice

Infrared radiance

Liquid water path and number conc. for each liquid layer

Visible optical depth

Radiance difference

Aerosol visible extinction coefficient profile

For each ray of data we define:

- Observation vector • State vector
- Elements may be missing
- Logarithms prevent unphysical negative values

The cost function using the other instruments

Some elements of x are constrained by an a priori estimate

The forward model H(x) predicts the observations from the state vector x

Each observation yi is weighted by the inverse of its error variance

This term penalizes curvature in the extinction profile

- The essence of the method is to find the state vector x that minimizes a cost function:

+ Smoothness constraints

Solution method using the other instruments

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 modelH(x)

Predict the JacobianH=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

No

Has solution converged?

2 convergence test

Yes

Calculate error in retrieval

Proceed to next ray

Radar forward model and using the other instruments 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)

Lidar forward model: multiple scattering using the other instruments

Wide field-of-view: forward scattered photons may be returned

Narrow field-of-view: forward scattered photons escape

- 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)

Ice cloud

Molecules

Liquid cloud

Aerosol

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

Poster P3.10: Multiple scattering using the other instruments

- To extend to precip, need to model radar multiple scattering

CloudSat multiple scattering

New model agrees well with Monte Carlo

Radiance forward model using the other instruments

- 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 thermalinfrared 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 retrieval using the other instruments

Donovan et al. (2000)

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

- 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

Variational radar/lidar retrieval using the other instruments

- 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 constraint using the other instruments

- Smoothness constraint: add a term to cost function to penalize curvature in the solution (J’ = l Sid2ai/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 correlation using the other instruments

- 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 constraint using the other instruments

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

Observations

State variables

Derived variables

Slight refinement to extinction and IWC

…add infrared radiances using the other instruments

- 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

Convergence using the other instruments

- 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

Ground based example using the other instruments

- 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 Niamey using the other instruments

94-GHz radar reflectivity

Forward model at final iteration

532-nm lidar backscatter

94-GHz radar reflectivity

Observations

532-nm lidar backscatter

Results: radar+lidar only using the other instruments

Large error where only one instrument detects the cloud

Retrievals in regions where radar or lidar detects the cloud

Retrieved visible extinction coefficient

Retrieved effective radius

Retrieval error in ln(extinction)

Results: radar, lidar, SEVERI radiances using the other instruments

Cloud-top error greatly reduced

Retrieval error in ln(extinction)

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

Retrieved visible extinction coefficient

Retrieved effective radius

CloudSat/CALIPSO retrieval using the other instruments

Oct 13, 2006 0352-0358

AVHRR

Radar Reflectivity from CloudSat

Height [km]

0352 0355 0358

Attenuated lidar backscatter from CALIPSO

Height [km]

Forward model using the other instruments

Observed radar reflectivity, 95 GHz

Attenuated lidar backscatter, 532 nm

Radar reflectivity forward model

Attenuated lidar backscatter forward model

Preliminary results (radar+lidar) using the other instruments

Retrieved visible extinction coefficient, log10(m-1)

Height [km]

Retrieved effective radius

Height [km]

Retrieved number concentration

Height [km]

Supercooled water?

Retrieved error in ln(extinction)

Height [km]

October 13th 2006

Granule 2006286023036_02443 between 3h52 and 3h58 UTC

MODIS radiances using the other instruments

Radiances not used in retrieval, just forward modeled for comparison

Radar Reflectivity from CloudSat

Height [km]

Attenuated lidar backscatter from CALIPSO

Height [km]

Radiances W sr-1 m-2

Forward model

MODIS

8.4–8.7 micron

10.78–11.25 micron

11.77 – 12.27 micron

CloudSat/CALIPSO example using the other instruments

Radar fails to detect thin cirrus

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

2006 Day 286

Radar Reflectivity from CloudSat

Attenuated lidar backscatter from CALIPSO

Conclusions and ongoing work using the other instruments

- 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

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