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  • Author or Editor: K. N. Liou x
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K. N. Liou and N. Rao

Abstract

The effects of cloud geometry and inhomogeneity on the radiative properties of cirrus clouds are investigated by using the successive orders of scattering (SOS) approach for radiative transfer. This approach is an integral solution method that em be directly applied to specific geometry and inhomogeneous structure of a medium without the requirement of solving the basic differential radiative transfer equation. A specific interpolation scheme is developed for the intensity and source function iterations to reduce the computation effort, and its accuracies are checked with existing results from the plane-parallel adding-doubling method, a number of two-dimensional models, and the three-dimensional Monte Carlo method. The SOS approach is shown to be particularly useful for cirrus clouds with optical depths less than about 5. Some demonstrative results show that the importance of the cloud-side scattering is dependent on the cloud horizontal dimension relative to the vertical thickness and that the cloud inhomogeneity can play a significant role in determining the domain-averaged solar reflection and transmission patterns.

By employing the optical depth retrieved from AVHRR radiances and the ice crystal size distribution derived from replicator soundings during FIRE-II IFO, Kansas, November-December 1991, a means by which a 3D extinction coefficient field for cirrus clouds can be constructed is demonstrated. The SOS model is applied to finite, inhomogeneous cirrus clouds to investigate deviations of the radiation fields computed from the pixel by pixel (PBP) plane-parallel approximation. The authors show that the PBP approach is a good approximation for computing the domain-averaged reflected and transmitted fluxes if the cloud horizontal dimension is much larger than the vertical thickness. However, the PBP bidirectional reflectance patterns computed from the plane-parallel method deviate substantially from those from the 3D model because of the horizontal radiative energy exchanges coupled with the cloud optical inhomogeneity.

For finite clouds, the authors derive a physical equation using the Cartesian coordinates to define cloud absorption in terms of the absorbed solar flux per volume associated with the 3D flux divergence. The cloud absorption so defined is governed by the incident solar fluxes on three sides and reflection and transmission at the cloud top and bottom as well as radiation leakages out of the four sides. Using a solar wavelength of 2.22 µm as an example, it is shown that anomalous cloud absorption can occur if specific cloud geometries are involved, for example, cubic clouds with an oblique solar zenith angle. Compatibilities between radiometric measurements from aircraft and theoretical calculations are further discussed. To resolve the anomalous cloud absorption issue, from the physical perspective, it is essential that the cloud geometrical structure and cloud microphysics including aerosols be determined concurrently with radiometric measurements from the air.

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Yu Gu and K. N. Liou

Abstract

A two-dimensional cirrus cloud model has been developed to investigate the interaction and feedback of radiation, ice microphysics, and turbulence-scale turbulence, and their influence on the evolution of cirrus clouds. The model is designed for the study of cloud-scale processes with a 100-m grid spacing. The authors have incorporated a numerical scheme for the prediction of ice crystal size distributions based on calculations of nucleation, diffusional growth, advection, gravitational sedimentation, and turbulent mixing. The radiative effect on the diffusional growth of an individual ice crystal is also taken into account in the model. The model includes an advanced interactive radiative transfer scheme that employs 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. This radiation scheme is driven by ice water content and mean effective ice crystal size that represents the ice crystal size distribution. To study the effects of entrainment and mixing on the cloud, a second-order turbulence closure has been developed and incorporated into the model. Simulation results show that initial cloud formation occurs through ice nucleation associated with dynamic and thermodynamic forcings. Radiation becomes important for cloud evolution once a sufficient amount of ice water is generated. Radiative processes enhance both the growth of ice crystals at the cloud top by radiative cooling and the sublimation of ice crystals in the lower region by radiative heating. The simulated ice crystal size distributions depend strongly on the radiation fields. In addition, the radiation effect on individual ice crystals through diffusional growth is shown to be significant. Turbulence begins to play a substantial role in cloud evolution during the maintenance and dissipation period of the cirrus cloud life cycle. The inclusion of turbulence tends to generate more intermediate-to-large ice crystals, especially in the middle and lower parts of the cloud. Incorporation of the second-order closure scheme enhances instability below the initial cloud layer and brings more moisture to the region above the cloud, relative to the use of the traditional eddy mixing theory.

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Y. Takano and K. N. Liou

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 directions than do solid columns and plates and the single scattering albedo becomes larger when a crystal becomes more complex in shape. Results simulated for randomly oriented hollow columns can be used to interpret lidar backscattering observations. Moreover, the authors further illustrate that the computed phase matrix values for randomly oriented dendrites closely match with 1aboratory observed data for plate-type crystals generated in cold chambers. It is also shown that using equal volume or equal projected-area spheres 1eads to significant errors in the computation of scattering, absorption, and polarization properties for irregular ice crystals. The phase functions, the single scattering albedos and their parameterizations, as well as the polarization patterns presented in this paper are significant in terms of the interpretation of radiance and flux observations from the ground, the air, and space in cirrus cloudy conditions and for remote sensing applications.

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Qiang Fu and K. N. Liou

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 results, using a variety of atmospheric profiles and spectral intervals containing principal absorbing gases. In the thermal infrared, errors in fluxes are less than 0.2% for H2O, CO2, CH4, and N2O, and ∼2% for O3. Errors in heating rates are less than 0.01 K day−1 for these gases below ∼30 km. Larger errors of ∼0.1 K day−1 can occur at some levels above this height. For H2O lines in the solar region, errors in fluxes and heating rates are within 0.05% and 0.01 K day−1, respectively. Based on numerical experimentation, we find that the number of g values ranging from 1 (for weak bands) to ∼10 (for strong bands) are usually sufficient to achieve acceptable accuracy for flux and heating rate calculations.

The correlated k-distribution method differs fundamentally from the traditional approach that employs scaling approximations and band models to separate height and wavenumber integrations for transmittance calculations. The equivalent k values for various gases computed from this approach can be directly incorporated in the multiple-scattering program involving cloud and aerosol particles.

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Qiang Fu and K. N. Liou

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 program for size parameters larger than 30 and the exact spheroid solution for size parameters less than 30 are used. The computations are carried out for 11 observed ice crystal size distributions and cover the entire solar and thermal infrared spectra. Parameterization of the single-scattering properties is shown to provide an accuracy within about 1%. Comparisons have been carried out between results computed from the model and those obtained during the 1986 cirrus FIRE IFO. It is shown that the model results can be used to reasonably interpret the observed IR emissivities and solar albedo involving cirrus clouds. The newly developed scheme has been employed to investigate the radiative effects of ice crystal size distributions. For a given ice water path, cirrus clouds with smaller mean effective sizes reflect more solar radiation, trap more infrared radiation, and product stronger cloud-top cooling and cloud-base beating. The latter effect would enhance the in-cloud heating rate gradients. Further, the effects of ice crystal size distribution in the context of IR greenhouse versus solar albedo effects involving cirrus clouds are presented with the aid of the upward flux at the top of the atmosphere. In most cirrus cases, the IR greenhouse effect outweigh the solar albedo effect. One exception occurs when a significant number of small ice crystals are present. The present scheme for radiative transfer in the atmosphere involving cirrus clouds is well suited for incorporation in numerical models to study the climatic effects of cirrus clouds, as well as to investigate interactions and feedbacks between cloud microphysics and radiation.

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J. K. Roskovensky and K. N. Liou

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The importance of separating thin cirrus and aerosols from satellite remote sensing to produce broader and more accurate fields for the determination of respective radiative forcings is highlighted. This has been accomplished through the development of a new methodology for retrieving both thin cirrus and aerosol optical depths simultaneously over oceans from the Moderate Resolution Imaging Spectroradiometer (MODIS) data. This method employs a procedure to quantify and remove the thin cirrus contribution to the observed reflectance through a correlation of visible and 1.38-μm reflectances so that the aerosol signal can be extracted. Aerosol optical depths are then retrieved through comparisons with the simulated reflectances created a priori. Using the aerosol optical depth along with the specific viewing geometry and surface reflectance as pointers to locations in a lookup table of modeled reflectances, cirrus optical depth and an effective ice crystal size can be retrieved. An iterative scheme has been created that uses the retrieved effective cirrus ice crystal size to account for the effect that the particle size distribution has on the correlation of visible and 1.38-μm reflectance. Retrievals of both aerosol and thin cirrus optical depths over the Atmospheric Radiation Measurement (ARM) Tropical Western Pacific (TWP) site of Nauru performed on a limited number of cases have proven to be consistent with values determined from ground measurements. Also, comparisons with the MODIS aerosol retrievals over a broad area of ocean have highlighted the potential usefulness of this procedure in increasing the amount of potential aerosol information recovered and removing the ever-present thin cirrus contamination.

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Y. Takano, K. N. Liou, and P. Minnis

Abstract

Using a model that combines single-scattering properties for spheroidal and hexagonal ice crystals, the thermal infrared radiative properties of cirrus clouds have been investigated. Infrared scattering and absorption properties for randomly oriented spheroids and hexagons are parameterized based on the anomalous diffraction theory and a geometric ray-tracing method, respectively. Using observed ice crystal size distributions, upwelling radiances at the top of cirrus cloudy atmospheres have been computed. Results show that the presence of small ice crystals can produce significant brightness temperature differences between two infrared wavelengths in the 10-μm window. Theoretical results have been compared with observed brightness temperature differences between 8.35 and 11.16 μm and between 11.16 and 12 μm. The observed values were obtained from the High-Spectral Resolution Interferometer Sounder. It is shown that the use of the present nonspherical model for ice crystals in radiative transfer calculations leads to a significantly better interpretation of the observed data than does the use of the spherical model.

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Wei-Liang Lee and K. N. Liou

Abstract

A coupled atmosphere–ocean radiative transfer model based on the analytic four-stream approximation has been developed. It is shown that this radiation model is computationally efficient and at the same time can achieve acceptable accuracy for flux and heating rate calculations in the atmosphere and the oceans. To take into account the reflection and transmission of the wind-blown air–water interface, a Monte Carlo method has been employed to simulate the traveling of photons and to compute the reflectance and transmittance of direct and diffuse solar fluxes at the ocean surface. For the ocean part, existing bio-optical models, which correlate the concentration of chlorophyll and the absorption and scattering coefficients of phytoplankton and other matters, have been integrated into this coupled model. Comparing to the values computed by more discrete streams illustrates that the relative accuracies of the surface albedo and total transmission in the ocean determined from the present model are generally within 5%, except in cases of the solar zenith angle larger than 80°. Observational data have also been used to validate this model and the results show that the relative differences of downward and upward shortwave fluxes and albedo are within 10% of the observed values. This computationally efficient and physically based radiative transfer model is well suited for consistent flux calculations in a coupled atmosphere–ocean dynamic system.

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Qiang Fu, Steven K. Krueger, and K. N. Liou

Abstract

A two-dimensional cumulus ensemble model is used to study the interactions of radiation and convection in tropical squall cloud clusters. The model includes cloud-scale and mesoscale dynamics, an improved bulk ice microphysics parameterization, and an advanced interactive radiative transfer scheme. The life cycle of a tropical squall line is simulated over a 12-h period using thermodynamic and kinematic initial conditions as well as large-scale advective forcing typical of a GATE Phase III squall cluster environment. The focus is on the interaction and feedback between longwave (or IR) radiation and cloud processes.

It will be shown that clew-sky IR cooling enhances convection and, hence, surface precipitation. Simulation results reveal an increase of surface precipitation by ∼15% (∼1.7 mm) over a 12-b period due to this clear-sky cooling. With fully interactive IR radiative heating, direct destabilization of clouds via IR radiative top cooling and base warming generates more turbulence and contributes to the longevity and extent of the upper-tropospheric stratiform (anvil) clouds associated with deep convection. The greater extent of anvil clouds decreases the outgoing IR flux at the top of the atmosphere by as much as 20 W m−2.

With fully interactive IR radiative heating, the anvil cirrus reduces the IR cooling of the troposphere with respect to the clear-sky values. This cloud IR radiative forcing has a negative feedback on tropical deep convection, which will be referred to as “anvil cloud IR radiative feedback.” This feedback decreases surface precipitation by ∼10% (∼1.3 mm). It will also be shown that IR radiative processes modify the hydrometer profiles by affecting convection. On changing the cloud particle size distributions prescribed in radiation calculations, it is further demonstrated that the size distributions significantly influence the convective activity through their effects on the cloud IR radiative forcing.

The impact of clear-air IR cooling and cloud radiative forcing on deep convection is further examined by using the cloud-work function, which is a generalized number of the moist convective instability in die large-scale environment. The clear-air IR cooling tends to increase the cloud-work function, but the cloud IR radiative forcing tends to reduce it, especially for the deposit clouds.

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

Abstract

The delta-four-stream polarized (vector) thermal radiative transfer has been formulated and numerically tested specifically for application to satellite data assimilation in cloudy atmospheres. It is shown that for thermal emission in the earth’s atmosphere, the [I, Q] component of the Stokes vector can be decoupled from the [U, V] component and that the solution of the vector equation set involving the four-stream approximation can be expressed in an analytic form similar to the scalar case. Thus, the computer time requirement can be optimized for the simulation of forward radiances and their derivatives. Computations have been carried out to illustrate the accuracy and efficiency of this method by comparing radiance and polarization results to those computed from the exact doubling method for radiative transfer for a number of thermal infrared and microwave frequencies. Excellent agreement within 1% is shown for the radiance results for all satellite viewing angles and cloud optical depths. For polarization, differences between the two are less than 5% if brightness temperature is used in the analysis. On balance of the computational speed and accuracy, the four-stream approximation for radiative transfer appears to be an attractive means for the simulation of cloudy radiances and polarization for research and data assimilation purposes.

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