NOTES AND CORRESPONDENCE Advanced Doubling-Adding Method for Radiative Transfer in Planetary Atmospheres

The doubling–adding method (DA) is one of the most accurate tools for detailed multiple-scattering calculations. The principle of the method goes back to the nineteenth century in a problem dealing with reflection and transmission by glass plates. Since then the doubling–adding method has been widely used as a reference tool for other radiative transfer models. The method has never been used in operational applications owing to tremendous demand on computational resources from the model. This study derives an analytical expression replacing the most complicated thermal source terms in the doubling–adding method. The new development is called the advanced doubling–adding (ADA) method. Thanks also to the efficiency of matrix and vector manipulations in FORTRAN 90/95, the advanced doubling–adding method is about 60 times faster than the doubling–adding method. The radiance (i.e., forward) computation code of ADA is easily translated into tangent linear and adjoint codes for radiance gradient calculations. The simplicity in forward and Jacobian computation codes is very useful for operational applications and for the consistency between the forward and adjoint calculations in satellite data assimilation. ADA is implemented into the Community Radiative Transfer Model (CRTM) developed at the U.S. Joint Center for Satellite Data Assimilation.

[1]  Ping Yang,et al.  Extinction efficiency and single‐scattering albedo for laboratory and natural cirrus clouds , 1997 .

[2]  James P. Hollinger,et al.  Passive Microwave Measurements of Sea Surface Roughness , 1971 .

[3]  J. Hovenier.  Symmetry Relationships for Scattering of Polarized Light in a Slab of Randomly Oriented Particles , 1969 .

[4]  Lihang Zhou,et al.  AIRS near-real-time products and algorithms in support of operational numerical weather prediction , 2003, IEEE Trans. Geosci. Remote. Sens..

[5]  G. G. Stokes.  IV. On the intensity of the light reflected from or transmitted through a pile of plates , 1862, Proceedings of the Royal Society of London.

[6]  Clemens Simmer,et al.  A general analytical expression for the radiation source function of emitting and scattering media within the matrix operator method , 1991 .

[7]  J. Fischer,et al.  Radiative transfer in an atmosphere-ocean system: an azimuthally dependent matrix-operator approach. , 1984, Applied optics.

[8]  Fuzhong Weng,et al.  A Microwave Polarimetric Two-Stream Radiative Transfer Model , 2002 .

[9]  Christian D. Kummerow,et al.  On the accuracy of the Eddington approximation for radiative transfer in the microwave frequencies , 1993 .

[10]  Albin J. Gasiewski,et al.  A fast multistream scattering-based Jacobian for microwave radiance assimilation , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[11]  Fuzhong Weng,et al.  Retrieval of sea surface wind vectors from simulated satellite microwave polarimetric measurements , 2003 .

[12]  F. Weng,et al.  A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere—I. Theory , 1992 .

[13]  Johannes Schmetz,et al.  On the parameterization of the radiative properties of broken clouds , 1984 .

[14]  Fuzhong Weng,et al.  A microwave land emissivity model , 2001 .

[15]  Quanhua Liu,et al.  A Polarized Delta-Four-Stream Approximation for Infrared and Microwave Radiative Transfer: Part I , 2005 .

[16]  J. Hansen,et al.  Multiple Scattering of Polarized Light in Planetary Atmospheres. Part I. The Doubling Method , 1971 .

[17]  Graeme L. Stephens,et al.  A new polarized atmospheric radiative transfer model , 1991 .

[18]  Thomas P. Kurosu,et al.  A linearized discrete ordinate radiative transfer model for atmospheric remote-sensing retrieval , 2001 .

[19]  Peter W. Gaiser,et al.  Polarimetric Emission Model of the Sea at Microwave Frequencies and Comparison with Measurements , 2002 .

[20]  Fuzhong Weng,et al.  Satellite Data Assimilation in Numerical Weather Prediction Models. Part I: Forward Radiative Transfer and Jacobian Modeling in Cloudy Atmospheres , 2003 .

[21]  Christopher W. O'Dell,et al.  The Successive-Order-of-Interaction Radiative Transfer Model. Part I: Model Development , 2006 .

[22]  Stephen J. English,et al.  Estimation of Temperature and Humidity Profile Information from Microwave Radiances over Different Surface Types , 1999 .

[23]  K. Stamnes,et al.  Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media. , 1988, Applied optics.

[24]  G. Plass,et al.  Matrix operator theory of radiative transfer. 1: rayleigh scattering. , 1973, Applied optics.

[25]  Xiaozhen Xiong,et al.  Alternative to the effective transmittance approach for the calculation of polychromatic transmittances in rapid transmittance models. , 2005, Applied optics.

[26]  J. Hovenier.  Multiple Scattering of Polarized Light in Planetary Atmospheres , 1971 .