RT Modelling for All-Weather Microwave Radiance Assimilation

1. RT Modelling for All-Weather Microwave Radiance Assimilation Albin J. Gasiewski Bob L. Weber Dean F. Smith • Center for Environmental Technology – University of Colorado, Boulder, CO Collaborators: T. Meissner, J. Johnson, V. Irisov, A. Voronovich, B. Stankov, and J. Zelenak

2. Objectives • Develop a fast accurate forward RT model providing tangent linear capability and compatible with the JCSDA CRTM • Incorporate full-Stokes ocean surface emission model with Jacobian applicable for all microwave satellites • Demonstrate precipitation “locking” of regional- scale NWP models onto satellite microwave radiances. • Improve snow surface emission models over ~10-89 GHz.

3. Anticipated capabilities include: Extended thermodynamic information (water vapor and temperature fields) within the forecast-sensitive and economically important cloud-covered regions. Improved accuracy of cloud and radiation products. Short-term prediction of mesoscale convection for warnings with high specificity (precipitation “locking”). Tracking of latent heat exchange within precipitation for improved thermodynamic knowledge. All-Weather Microwave Assimilation

4. DOTLRT Evolution

5. DOTLRTv1.0b (January 2005, August 2005) Discrete ordinate layer adding solution Polydispersive with 5-hydrometeor phases (cloud, rain, graupel, snow, cloud ice) Henyey-Greenstein phase function with Mie absorption, scattering, and asymmetry Liebe 87 and 93 attenuation models Fast multistream radiation and geophysical Jacobian, compatible with satellite streams Selective incorporation of scattering in layer solution CTRM compatible Intercompared with RTTOVS v7 (Oct 2005) DOTLRTv2.1 (~October 2006) Exact Mie phase matrix model with Mie library Full Stokes ocean surface model with Jacobian Full Stokes (surface-generated) radiance product DOTLRT* Attributes Voronovich et al., "A Fast Multistream Scattering-Based Jacobian for Microwave Radiance Assimilation," IEEE Trans. Geosci. Remote Sensing, August, 2004.

6. H=HI HR HG H =Total Jacobian HI= Instrument Jacobian HR= Radiation Jacobian HG= Geophysical Jacobian Jacobian Components

9. Exact Mie Library (DOTLRTv2.1) • Input Parametrization • Mean size parameter k<a> (with exponential polydisperson) • Complex effective dielectric constant εeff = εr - jεi • Complex effective dielectric constant temperature derivative dεeff/dT = dεr/dT - jdεi/dT • Total 5x real*8 input parameters with nonlinear indexing • Output (Product) Parameterization • Absorption coefficient • Multistream scattering matrix (6 streams, 2 polarizations = 72 numbers) • Derivatives of above WRT temperature and k<a> • Total 3(1x+72x)=219x real*8 output parameters • Library Size • 2.5 GB for 0.1K error over Hurricane Bonnie run • Size parameters up to k<a> = 4 • Goal of 50 MB currently exceeded by ~50x (needs work!)

10. Absorption Cross Section vs. Dielectric Constant (6 stream) k<a>=0.02 k<a>=0.1 k<a>=1.0 k<a>=9.0 Imaginary Part of ε Real Part of ε (Note: color ranges vary)

11. Scattering Cross Section Matrix Element (1,1) vs. Diel. Const. (6 stream) k<a>=0.02 k<a>=0.1 k<a>=1.0 k<a>=9.0 Imaginary Part of ε Real Part of ε (Note: color ranges vary)

12. Mie Library Forward Error - Hurricane Bonnie – Full Mie vs Mie Library Upwelling TB

13. Full Stokes Ocean Surface Emission Model

14. Goal Develop a standardized fast full-Stokes ocean surface emissivity module for a wind-driven ocean surface applicable at arbritrary microwave frequencies and incidence angles, and thus relevant to all existing and planned conically and cross-track scanned sensors (WindSat, AMSR-E, TMI, SSMI, SSMIS, and CMIS as well as AMSU-A, NPP ATMS, and NPOESS ATMS, and GPM).

15. Strategy 1. Analyze a sufficiently long sequence of WindSat data to derive the wind induced isotropic and anisotropic emissivity variations for all four Stokes parameters. This was done by T. Meissner and F. Wentz [1], and corroborated by this JCSDA study.

16. Strategy (cont’d) 2. Extend the WindSat results to other frequencies and incidence and angles using the two-scale model [e.g., S. Yueh, 2]. This model has recently been cast into a computationally efficient form by J. Johnson [3] who has sent us a copy of his code. This code not only produces both the geometrical optics emission from a smooth surface and the enhancement of this emission due to wind, but also the Ω factor [4] which describes the modification of downwelling reflected radiation over simple specular reflection due to tilted surface facets reflecting radiation from other parts of the sky into the direction in question (related to Maetzler’s and Rosenkranz’ “Lambertivity”). Thus the code provides everything necessary for complete full Stokes emission modelling of the surface.

17. Strategy (cont’d) 3. A modification of the Johnson code [3] was needed to reproduce the results of [1] for the second harmonic. The code originally used the Durden-Vesecky model for the sea surface spectrum [5], which is known to have an incorrect wind speed dependence. It does, however, incorporate an adequate angular spreading function. Thus the isotropic component of the Durden-Vesecky spectrum [5] was replaced by the Elfouhaily spectrum [6], but with the Durden-Vesecky angular spreading function retained.

18. Strategy (cont’d) 4. However, the Elfouhaily angular spreading function produced non-physical values for Ω in the Johnson model.No existing sea spectrum model was able to reproduce the WindSat result [1] that the second harmonic of the 3rd Stokes parameter U decreased for wind speeds greater than 12 m/s. The model sea spectrum was thus tuned in both the isotropic and angular spreading parts to reproduce the WindSat first and second harmonic U results.

19. Other Spectrum Modifications 5. The high-frequency portion of the Elfouhaily spectrum was also multiplied by the Pierson-Moskowitz shape spectrum to correct an error in [6]. 6. The generalized Phillips-Kitaigorodskii equilibrium range parameter for short waves was modeled as continuous function of the friction velocity at the water surface to eliminate a discontinuous jump in the [6] formulation. The following results are for an increase in power of the isotropic Elfouhaily spectrum by 25% compared to the Durden-Vesecky spectrum and a multiplier of the exponential factor in the Durden-Vesecky angular spreading function…

20. Meissner-Wentz vs. Our Results TV 18.7 M-W WindSat 1st Azimuthal Harmonic 2nd Azimuthal Harmonic

21. Meissner-Wentz vs. Our Results TH 18.7 M-W WindSat 1st Azimuthal Harmonic 2nd Azimuthal Harmonic

22. Meissner-Wentz vs. Our Results TU 18.7 M-W WindSat 2nd Azimuthal Harmonic 1st Azimuthal Harmonic

23. Meissner-Wentz vs. Our Results T4 18.7 M-W WindSat (Note EE vs physics sign conventions!) 2nd Azimuthal Harmonic (-1x) 1st Azimuthal Harmonic (-1x)

24. With the Johnson code modified and tuned to the Meissner Wentz WindSat results there are a few more model adjustments/optimizations needed: A small adjustment needed for total consistency – replacement of the present dielectric constant of sea water code by the Meissner Wentz dielectric constant [7]. With this change all of the emission values in the following table will be generated by July 2006. Adjustment of slope pdf of the long-wave portion of the spectrum to converge closer to the WindSat 1st harmonic behavior Use automated gradient search to jointly optimize model parameters (multiplier for D-V spreading function, amplitude of short- and long wave portions of Elfouhaily spectrum) based upon WindSat 2-look data. Tabularize model and derivatives over wind speed and incidence angle range to generate ocean surface emission library: Ocean Emission – Next Steps Desired tabularized model characteristics

25. Precipitation Locking

26. _ _ _ Observed LEO/GEO Data n … Simulated Truth State Sequence … … … … … SOS Filled Aperture Synthetic Aperture Truth Radiances DOTLRTv2 + + ECU Innovations Σ - NWP Model Radiances SOS Filled Aperture Synthetic Aperture Jacobian DOTLRTv2 Iterate State … … NMS-CLEAN State Vector Update Initial State Forecast State Converged State NWP (MM5) Assimilation Step Error Covariance Model … Error Covariance All Wx Precipitation Locking Simulator

27. _ _ _ Observed LEO/GEO Data n … Simulated Truth State Sequence … … … … … SOS Filled Aperture Synthetic Aperture Truth Radiances DOTLRTv2 + + ECU Innovations Σ - NWP Model Radiances SOS Filled Aperture Synthetic Aperture Jacobian DOTLRTv2 Iterate State … … NMS-CLEAN State Vector Update Initial State Forecast State Converged State NWP (MM5) Assimilation Step Error Covariance Model … Error Covariance All Wx Precipitation Locking Simulator Implemented

28. _ _ _ Observed LEO/GEO Data n … Simulated Truth State Sequence … … … … … SOS Filled Aperture Synthetic Aperture Truth Radiances DOTLRTv2 + + ECU Innovations Σ - NWP Model Radiances SOS Filled Aperture Synthetic Aperture Jacobian DOTLRTv2 Iterate State … … NMS-CLEAN State Vector Update Initial State Forecast State Converged State NWP (MM5) Assimilation Step Error Covariance Model … Error Covariance All Wx Precipitation Locking Simulator Implemented In progress

29. Spatial gradient mapping Hydrometric variable error proportional to spatial variance of prognostic field. Error covariance proportional to joint spatial variance Temporal gradient operator Requires tangent linear NWP time-operator Hydrometric Error Covariance Models

30. Snow Emission Modeling

31. Gridded Corrected Emissivity MapsCLPX 37 GHz North Park

32. CLPX ISA – PSR Comparison

35. Future Plans

36. Complete compact Mie library for DOTLRTv2.1 Compress in dielectric space by ~(3x)(3x)=9x Compress in d/dT space by ~1.5x Compress in product space by ~4x using integer log mapping If necessary: Can compress in product space using Henyey-Greenstein phase function by ~73x Complete comprehensive ocean surface emission model and integrate into DOTLRTv2.1 Minimize error over long wave spectrum and modulation function to fit WindSat first azimuthal harmonic Develop harmonic coefficient table with Jacobian Develop and demostrate precipitation locking testbed Develop/test hydrometric error covariance estimator Incorporate snow emission spectral model Regress PSR aircraft emissivity data to dense media RT model Year-3 (FY 06) Plans

37. DOTLRTv2.1 will contain major improvements over v1.0b, and is being designed to be directly usable within or readily transferable to operational environments. All-weather precipitation locking demonstration anticipated to provide insight into use of microwave data under arbitrary cloud/precipitation conditions. RT modeling effort transferred to and ongoing within the CU Center for Environmental Technology. Summary

38. References (Ocean Emission) [1] Meissner, T., and F. Wentz, “Physical Ocean Retrievals for WindSat”, Proc. MicroRad ’06, in press. [2] Yueh, S.H., “Modeling of Wind Direction Signals in Polarimetric Sea Surface Brightness Temperatures”, IEEE Trans. Geosci. Remote Sens., vol. 35, pp. 1400-1418, 1997. [3] Johnson, J.T., “An Efficient Two-scale Model for the Computation of Thermal Emission and Atmospheric Reflection From the Sea surface”, IEEE Trans. Geosci. Remote Sens., vol. 44, pp. 560-568, 2006. [4] Wentz, F.J., and T. Meissner, “Algorithm Theoretical Basis Document: AMSR Ocean Algorithm, version 2, report from Remote Sensing Systems, available at www.remss.com. [5] Durden, S.L., and J.F. Vesecky, “A Physical Radar Cross-Section Model for a Wind Driven Sea with Swell, IEEE Trans. Geosci. Remote Sens., vol. OE-10, pp.445-451, 1985. [6] Elfouhaily, T., B. Charon, K. Katsaros, and D. Vandemark, “A Unified Directional Spectrum for Long and Short Wind-driven Waves”, J. Geophys. Res., vol. 102, C7, pp. 15781-15796, 1997. [7] Meissner, T., and F. Wentz, “The Complex Dielectric constant of Pure and Sea Water from Micorwave Satellite Observations”, IEEE Trans. Geosci. Remote Sens., vol. 42, 1836-1849, 2004.