Kuo-Nan Liou

An Introduction to Atmospheric Radiation

Fundamentals of Radiation for Atmospheric Applications. Solar Radiation at the Top of the Atmosphere. Absorption and Scattering of Solar Radiation in the Atmosphere. Thermal Infrared Radiation Transfer in the Atmosphere. Light Scattering by Atmospheric Particulates. Principles of Radiative Transfer in Planetary Atmospheres. Application of Radiative Transfer Principles to Remote Sensing. Radiation and Climate.

Parameterization of the Radiative Properties of Cirrus Clouds

Abstract A new approach for parameterization of the broadband solar and infrared radiative properties of ice clouds has been developed. This parameterization scheme integrates in a coherent manner the δ-four-stream approximation for radiative transfer, the correlated k-distribution method for nongray gaseous absorption, and the scattering and absorption properties of hexagonal ice crystals. A mean effective size is used, representing an area-weighted mean crystal width, to account for the ice crystal size distribution with respect to radiative calculation. Based on physical principles, the basic single-scattering properties of ice crystals, including the extinction coefficient divided by ice water content single-scattering albedo, and expansion coefficients of the phase function, can be parameterized using third-degree polynomials in terms of the mean effective size. In the development of this parameterization the results computed from a light scattering program that includes a Geometric ray-tracing progr...

On the Correlated k-Distribution Method for Radiative Transfer in Nonhomogeneous Atmospheres

Abstract The correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres is discussed in terms of the physical and mathematical conditions under which this method is valid. Two correlated conditions are necessary and sufficient for the exact transformation of the wavenumber integration to an integration over the cumulative probability (g), a monotonically increasing and smooth function in the absorption coefficient space. These conditions involve the use of a reference condition to define the absorption coefficient and an assumption concerning the ordering of the absorption coefficient. The correlated conditions are exact in the context of a single line, periodic lines, and the strong- and weak-line limits. In realistic atmospheres, these assumptions are best for adjacent levels but produce increasing blurring or deviations for distant levels. We investigate the blurring of the correlated assumptions on the computations of fluxes and heating rates based on “exact” line-by-line re...

Solar Radiative Transfer in Cirrus Clouds. Part I: Single-Scattering and Optical Properties of Hexagonal Ice Crystals

Abstract We have developed an efficient light scattering and polarization program, based on a ray-tracing technique, for hexagonal ice crystals randomly and horizontally oriented in space. Improvements have been made on the ray-tracing computations through a proper treatment of the δforward transmission by geometric rays and incorporation of the effect of birefringence of ice. Using this program, computations of the scattering phase matrix are made from the observed ice crystal size distributions for four typical cirrus clouds. The results for single-scattering parameters, including the phase function, single-scattering albedo, extinction cross section, and asymmetry factor for five solar wavelengths, are presented and discussed. Moreover, we show that the assumption of equivalent spheres with the same surface areas as hexagonal ice crystals leads to leads to larger asymmetry factors for all wavelengths and smaller single-scattering albedos for near IR wavelengths. The computed phase matrix elements compa...

Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals

A new geometric-optics model has been developed for the calculation of the single-scattering and polarization properties for arbitrarily oriented hexagonal ice crystals. The model uses the ray-tracing technique to solve the near field on the ice crystal surface, which is then transformed to the far field on the basis of the electromagnetic equivalence theorem. From comparisons with the results computed by the finite-difference time domain method, we show that the novel geometric-optics method can be applied to the computation of the extinction cross section and single-scattering albedo for ice crystals with size parameters along the minimum dimension as small as ~6. Overall agreement has also been obtained for the phase function when size parameters along the minimum dimension are larger than ~20. We demonstrate that the present model converges to the conventional ray-tracing method for large size parameters and produces single-scattering results close to those computed by the finite-difference time domain method for size parameters along the minimum dimension smaller than ~20. The present geometric-optics method can therefore bridge the gap between the conventional ray-tracing and the exact numerical methods that are applicable to large and small size parameters, respectively.

CERES Edition-2 Cloud Property Retrievals Using TRMM VIRS and Terra and Aqua MODIS Data—Part I: Algorithms

The National Aeronautics and Space Administrations Clouds and the Earths Radiant Energy System (CERES) Project was designed to improve our understanding of the relationship between clouds and solar and longwave radiation. This is achieved using satellite broad-band instruments to map the top-of-atmosphere radiation fields with coincident data from satellite narrow-band imagers employed to retrieve the properties of clouds associated with those fields. This paper documents the CERES Edition-2 cloud property retrieval system used to analyze data from the Tropical Rainfall Measuring Mission Visible and Infrared Scanner and by the MODerate-resolution Imaging Spectrometer instruments on board the Terra and Aqua satellites covering the period 1998 through 2007. Two daytime retrieval methods are explained: the Visible Infrared Shortwave-infrared Split-window Technique for snow-free surfaces and the Shortwave-infrared Infrared Near-infrared Technique for snow or ice-covered surfaces. The Shortwave-infrared Infrared Split-window Technique is used for all surfaces at night. These methods, along with the ancillary data and empirical parameterizations of cloud thickness, are used to derive cloud boundaries, phase, optical depth, effective particle size, and condensed/frozen water path at both pixel and CERES footprint levels. Additional information is presented, detailing the potential effects of satellite calibration differences, highlighting methods to compensate for spectral differences and correct for atmospheric absorption and emissivity, and discussing known errors in the code. Because a consistent set of algorithms, auxiliary input, and calibrations across platforms are used, instrument and algorithm-induced changes in the data record are minimized. This facilitates the use of the CERES data products for studying climate-scale trends.

Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space

The finite-difference time domain (FDTD) method for the solution of light scattering by nonspherical particles has been developed for small ice crystals of hexagonal shapes including solid and hollow columns, plates, and bullet rosettes commonly occurring in cirrus clouds. To account for absorption, we have introduced the effective permittivity and conductivity to circumvent the required complex calculations in the direct discretization of the basic Maxwell equations. In the construction of the finite-difference scheme for the time-marching iteration for the near field the mean values of dielectric constants are defined and evaluated by the Maxwell–Garnett rule. In computing the scattered field in the radiation zone (far field) and the absorption cross section, we have applied a new algorithm involving the integration of the electric field over the volume inside the scatterer on the basis of electromagnetic principles. This algorithm removes the high-angular-resolution requirement in integrating the scattered energy for the computation of the scattering cross section. The applicability and the accuracy of the FDTD technique in three-dimensional space are validated by comparison with Mie scattering results for a number of size parameters and wavelengths. We demonstrate that neither the conventional geometric optics method nor the Mie theory can be used to approximate the scattering, absorption, and polarization features for hexagonal ice crystals with size parameters from approximately 5 to 20.

Spectrally Consistent Scattering, Absorption, and Polarization Properties of Atmospheric Ice Crystals at Wavelengths from 0.2 to 100 um

AbstractA data library is developed containing the scattering, absorption, and polarization properties of ice particles in the spectral range from 0.2 to 100 μm. The properties are computed based on a combination of the Amsterdam discrete dipole approximation (ADDA), the T-matrix method, and the improved geometric optics method (IGOM). The electromagnetic edge effect is incorporated into the extinction and absorption efficiencies computed from the IGOM. A full set of single-scattering properties is provided by considering three-dimensional random orientations for 11 ice crystal habits: droxtals, prolate spheroids, oblate spheroids, solid and hollow columns, compact aggregates composed of eight solid columns, hexagonal plates, small spatial aggregates composed of 5 plates, large spatial aggregates composed of 10 plates, and solid and hollow bullet rosettes. The maximum dimension of each habit ranges from 2 to 10 000 μm in 189 discrete sizes. For each ice crystal habit, three surface roughness conditions (i...

Multiple Scattering Parameterization in Thermal Infrared Radiative Transfer

Abstract A systematic formulation of various radiative transfer parameterizations is presented, including the absorption approximation (AA), δ-two-stream approximation (D2S), δ-four-stream approximation (D4S), and δ-two- and four-stream combination approximation (D2/4S), in a consistent manner for thermal infrared flux calculations. The D2/4S scheme uses a source function from the δ-two-stream approximation and evaluates intensities in the four-stream directions. A wide range of accuracy checks for monochromatic emissivity of a homogeneous layer and broadband heating rates and fluxes in nonhomogeneous atmospheres is performed with respect to the “exact” results computed from the δ-128-stream scheme for radiative transfer. The computer time required for the calculations using different radiative transfer parameterizations is compared. The results pertaining to the accuracy and efficiency of various radiative transfer approximations can be utilized to decide which approximate method is most appropriate for ...

Radiative Transfer in Cirrus Clouds. Part III: Light Scattering by Irregular Ice Crystals

Abstract A new Monte Carlo/geometric ray-tracing method has been developed for the computation of the scattering, absorption, and polarization properties of ice crystals with various irregular structure, including hollow columns, bullet rosettes, dendrites, and capped columns. The shapes of these ice crystals are defined by appropriate geometric models and incident coordinate systems. The incident photons are traced with a hit-and-miss Monte Carlo method and followed by geometric reflection and refraction on the crystal boundary. Absorption has been accounted for by means of stochastic procedures. Computation of the phase matrix elements and normalization of the phase function have been carried out using the results derived from rays that undergo reflections and refractions and from Fraunhofer diffraction using projected cross section areas for irregular ice crystals. Numerical results are presented for visible and near-infrared wavelengths. It is shown that irregular ice crystals scatter more in forward ...