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

1. Towards “unified” radar/lidar/radiometer retrievals for cloud radiation studies Robin Hogan Julien Delanoe Department of Meteorology, University of Reading, UK

2. Motivation • 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

3. Broadband radiometers used only to test retrievals made using the other instruments Surface/satellite observing systems

4. Radar and lidar • Advantages of combining radar, lidar and radiometers • Radar ZD6, 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

5. 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

6. First step: target classification 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

7. Formulation of variational scheme 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

8. The cost function 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

9. 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 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

10. 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)

11. Lidar forward model: multiple scattering 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

12. Poster P3.10: Multiple scattering • To extend to precip, need to model radar multiple scattering CloudSat multiple scattering New model agrees well with Monte Carlo

13. Radiance 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 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)

14. Ice cloud: non-variational retrieval 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

15. Variational radar/lidar retrieval • 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

16. …add smoothness constraint • 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

17. …add a-priori error correlation • 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

18. …add visible optical depth constraint • Integrated extinction now constrained by the MODIS-derived visible optical depth Observations State variables Derived variables Slight refinement to extinction and IWC

19. …add 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

20. 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

21. Ground 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

22. Example from the AMF in Niamey 94-GHz radar reflectivity Forward model at final iteration 532-nm lidar backscatter 94-GHz radar reflectivity Observations 532-nm lidar backscatter

23. Results: radar+lidar only 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)

24. Results: radar, lidar, SEVERI radiances 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

25. CloudSat/CALIPSO retrieval Oct 13, 2006 0352-0358 AVHRR Radar Reflectivity from CloudSat Height [km] 0352 0355 0358 Attenuated lidar backscatter from CALIPSO Height [km]

26. Forward model Observed radar reflectivity, 95 GHz Attenuated lidar backscatter, 532 nm Radar reflectivity forward model Attenuated lidar backscatter forward model

27. Preliminary results (radar+lidar) 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

28. MODIS radiances 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

29. CloudSat/CALIPSO example 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

30. Conclusions and ongoing work • 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