RT Modelling for All-Weather Microwave Radiance Assimilation

Greenbelt, MDMay 31-June 1, 2006JCSDA 2006 Science Workshop

RT Modelling for All-Weather Microwave Radiance

AssimilationAlbin J. Gasiewski

Bob L. WeberDean 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


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.


All-Weather Microwave Assimilation

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.


DOTLRT Evolution


DOTLRT* Attributes 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 productVoronovich et al., "A Fast Multistream Scattering-Based Jacobian for Microwave Radiance Assimilation," IEEE Trans. Geosci. Remote Sensing, August, 2004.


Jacobian Components

H=HI HR HG

H = Total Jacobian

HI = Instrument Jacobian

HR = Radiation JacobianHG = Geophysical

Jacobian


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!)


Absorption Cross Section vs. Dielectric Constant (6 stream)

Real Part of ε

Ima

gin

ary

Par

t o

f ε

(Note: color ranges vary)

k<a>=0.02 k<a>=0.1

k<a>=1.0 k<a>=9.0


Scattering Cross Section Matrix Element (1,1) vs. Diel. Const. (6 stream)

Real Part of ε

Ima

gin

ary

Par

t o

f ε

k<a>=0.02 k<a>=0.1

k<a>=1.0 k<a>=9.0

(Note: color ranges vary)


Mie Library Forward Error - Hurricane Bonnie – Full Mie vs Mie Library

Upwelling TB


Full Stokes Ocean Surface Emission Model


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).


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.


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.

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.

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.

Strategy (cont’d)


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…


Meissner-Wentz vs. Our Results

M-WWindSat

1st Azimuthal Harmonic 2nd Azimuthal Harmonic

TV 18.7



M-WWindSat

1st Azimuthal Harmonic 2nd Azimuthal Harmonic

TH 18.7



M-WWindSat

1st Azimuthal Harmonic

2nd Azimuthal Harmonic

TU 18.7



M-WWindSat

1st Azimuthal Harmonic(-1x)

2nd Azimuthal Harmonic(-1x)

T4 18.7

(Note EE vs physics sign conventions!)


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 tabularizedmodel characteristics


Precipitation Locking


All Wx Precipitation Locking Simulator

DOTLRTv2SOSFilled ApertureSynthetic Aperture

NWP (MM5)Assimilation StepError Covariance Model


+

n___

…

Σ

…

+

-

NMS-CLEANState Vector Update

ECU

Observed LEO/GEO Data

…

Truth Radiances

Innovations

…

Initial State

……

Iterate State

Converged State

…

Forecast State

Simulated Truth State Sequence

NWP Model Radiances

…

…

Error Covariance

Jacobian






+

n___

…

Σ

…

+

-


ECU


…

Truth Radiances

Innovations

…

Initial State

……

Iterate State

Converged State

…

Forecast State


NWP Model Radiances

…

…

Error Covariance

Jacobian

Implemented





+

n___

…

Σ

…

+

-


ECU


…

Truth Radiances

Innovations

…

Initial State

……

Iterate State

Converged State

…

Forecast State


NWP Model Radiances

…

…

Error Covariance

Jacobian

ImplementedIn progress



Hydrometric Error Covariance Models

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


Snow Emission Modeling


Gridded Corrected Emissivity Maps CLPX 37 GHz North Park


CLPX ISA – PSR Comparison


Future Plans


Year-3 (FY 06) Plans

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


Summary

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.


[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 andSea Water from Micorwave Satellite Observations”, IEEE Trans. Geosci. Remote Sens., vol. 42, 1836-1849, 2004.

References (Ocean Emission)

RT Modelling for All-Weather Microwave Radiance Assimilation

Documents

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