UCLA Vector Radiative Transfer Model for Application to Satellite Data

Assimilation

K. N. Liou, S. C. Ou, and Y. Takano

Department of Atmospheric Sciences and Institute of Radiation and Remote Sensing

University of California, Los Angeles

• Coupling the vector delta-four-stream method with the adding principle

• Computation of radiance derivative

• Thin cirrus cloud parameterization incorporating OPTRAN transmittances

• Analysis of AIRS data

Scientific Objectives

• Couple a vectorized –4–stream with the adding principle for application to satellite data assimilation.

• Determine and compute radiance derivative terms based on the –4–stream/adding principle and examine its sensitivity to optical depth and cloud water content.

• Utilize OPTRAN’s transmittances in association with the single-scattering parameterization for thin cirrus cloudy radiance calculations for selected AIRS channels.

• Analyze AIRS spectra for validating the cirrus parameterization

Polarized Delta-Four Stream (D4S) Method for Thermal Emission

• Starting with the basic equation governing the transfer of diffuse Stokes vector I=(I, Q)T in an azimuthal-average form, we solve the radiative transfer problem by considering 4 directional streams and the expansion of the scattering phase matrix in terms of Legendre polynomials.

• Following the standard procedure for solving the scalar equations using the D4S method (Liou 2002), the vector equation set is decomposed into 8 differential equations.

• Mathematical manipulation yields two 4th-order differential equation for which the solution for polarization parameters at the 4 Gaussian zenith angles is obtained by the eigenvalue approach.

• The source function technique is used to obtain the polarization parameters at arbitrary zenith angles.

• The D4S is applied to each vertical model layer, followed by the adding procedure to obtain the radiance at the top of atmosphere.

• An analytical expression for radiance derivative with respect to cloud optical depth has been derived to reduce computation time.

• A paper entitled “A Polarized Delta-Four-Stream Approximation for Infrared and Microwave Radiative Transfer: Part 1” (Liou, Ou, Takano, and Liu) is to appear in JAS

,

Construct a Module RTSolution in CRTM

• Work closely with NOAA personnel to construct a module RTSolution in CRTM

• Use a simplified adding module framework:

i) compile and execute CRTM modules

ii) isolate the -4-stream module

iii) convert the current -4-stream code into f95 format

iv) identify I/O links between the -4-stream routine and CRTM

v) test run the combined program to assure speed and accuracy

Calculation and Parameterization of Radiance Derivatives

• For the assimilation of cloudy radiances, the variational analysis of Weng and Liu (2003) has been followed.

• For thermal infrared and microwave radiation, the radiance derivative can be expressed from the D4S/adding method as follows:

where the boldface parameters are obtained from the D4S method using the source function technique.• This expression can be used to obtain the radiance derivative with respect to cloud water content, which is a prognostic variable in the

NCEP’s GFSA model.

1* *1exp / 1ab

a a u b a u d b u d

T R R S F B R B F

II I I I I

Sensitivity of Radiance Derivatives With Respect to Cloud Optical Depth

Thin Cirrus Cloud Parameterization Incorporating OPTRAN Transmittances

• Using AIRS high-spectral-resolution measurements of radiances and atmospheric states, we have developed a new fast radiative transfer model to simulate high resolution IR spectral radiances in thin cirrus cloudy conditions.

• We combine the OPTRAN and a radiation parameterization involving spectral cloud optical properties. • A cirrus radiation model has been built based on the single-scattering properties for ice crystals of various

shapes (plate, solid and hollow columns, bullet rosette, aggregate, and irregular and rough surface) and sizes computed from the unified theory for light scattering for ice crystals.

• Twenty two size bins with maximum ice crystal dimensions varying from 17.5 to 1550 m have been used along with the shape distributions defined for a number of atmospheric conditions.

• Calculations have been performed for 3151 wavelengths covering a spectral region from 100 to 3250 cm -1 and degraded to the AIRS spectral resolution.

Single-Scattering Properties for Tropical Ice Crystal Size Distribution

Sensitivity of Thermal IR Window Brightness Temperature Spectra to Cirrus Optical Depth and Ice Crystal Size

A MODIS/Aqua visible composite (RGB) calibrated radiance image at 1km resolution for May 28, 2003 at 1550 UTC, showing a distinctive clear area around 2o South, and 147o East around the island north of Papua New

Guinea.

A Scene for AIRS Spectra Analysis

Domain analyzed

Comparison of Observed and Computed (OPTRAN) AIRS Spectra for Clear Sky May 28, 2003 at 1550 UTC near ARM-TWP site

Research for the Next Reporting Period

• Develop a polarized multi-layer D4S program

• Develop a method to compute radiance derivatives with respect to other cloud and surface parameters in the D4S program

• Compile the optical properties of cirrus clouds for representative ice crystal size distributions for AIRS wavelengths

• Compare the observed and computed AIRS spectra in cirrus cloudy conditions

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