Philip Gabriel

Statistical radiative transport in one-dimensional media and its application to the terrestrial atmosphere

Abstract This paper describes radiative transfer through a single cloud layer that is horizontally uniform but statistically distributed in the vertical and compares the radiative transfer in such a statistical cloud to its deterministic counterpart. Specific examples of the derivation of the probability density functions of cloud reflection and transmission by single cloud layers are described for given observed statistical distributions of cloud optical depth and single scattering albedo. Numerical results of the probability density functions for cloud albedo, transmission and absorption are presented, as are the moments of these distributions. Although the computations apply to a hypothetical statistical medium that only approximate clouds in the atmosphere to a limited extent, results of this study demonstrate that radiative transfer in the statistical cloud is substantially different from that of its deterministic counterpart having the same ensemble mean properties. It is also demonstrated that the ...

Simple Radiative Transfer Methods for Calculating Domain-Averaged Solar Fluxes in Inhomogeneous Clouds

Abstract The use of cloud fraction as a means of incorporating horizontal cloud inhomogeneity in radiative transfer calculations is widespread in the atmospheric science community. This study addresses some issues pertaining to the use of cloud fraction by performing radiative transfer in inhomogeneous two-dimensional media. Two approximation techniques are developed to solve the equation of transfer for the spatial averages of diffuse flux. The first is based on a first-order closure technique that leads to a one-dimensional equation of transfer with a modified source term. The computational speed of this technique is equivalent to the plane-parallel method. The second method of approximation performs a full two-dimensional computation of the direct solar beam that is used as the pseudo-source in an independent pixel diffuse radiative transfer calculation. Both methods require a knowledge of the spatial distribution of the direct solar transmission, rather than cloud fraction, for their specification. Te...

A Fourier–Riccati Approach to Radiative Transfer. Part I: Foundations

Abstract The three-dimensional equation of radiative transfer is formally solved using a Fourier-Riccati approach while calculations are performed on cloudy media embedded in a two-dimensional space. An extension to Stephens’ work, this study addresses the coupling between space and angle asserted by the equation of transfer. In particular, the accuracy of the computed radiation field as it is influenced by the angular resolution of the phase function and spatial discretization of the cloudy medium is discussed. The necessity of using a large number of quadrature points to calculate fluxes even when the phase function is isotropic for media exhibiting vertical and horizontal inhomogeneities is demonstrated. Effects of incorrect spatial sampling on both radiance and flux fields are also quantified by example. Radiance and flux comparisons obtained by the Fourier-Riccati model and the independent pixel approximation for inhomogeneous cloudy media illustrate the inadequacy of the latter even for tenuous clouds.

Performance assessment of a five‐channel estimation‐based ice cloud retrieval scheme for use over the global oceans

[1] This work determines the performance of a five-channel ice cloud retrieval scheme in context of numerical synthetic experiments and real-world data and examines the implications of these results on the global retrieval of ice cloud microphysical properties over the global oceans. This estimation-based scheme, designed from information content principles, uses a rigorous, state-dependent error analysis to combine measurements from the visible, near-infrared, and infrared spectral regions. In the synthetic experiments, the five-channel scheme performed as well or better in terms of retrieval bias and random error than the traditional split-window and Nakajima and King bispectral retrieval techniques for all states of the atmosphere. Although the five-channel scheme performed favorably compared to the other methods, the inherently large uncertainties associated with ice cloud physics dictate typical retrieval uncertainties in both IWP and effective radius of 30–40%. These relatively large uncertainties suggest caution in the strict interpretation of small temporal or spatial trends found in existing cloud products. In MODIS and CRYSTAL-FACE applications, the five-channel scheme exploited the strengths of each of the bispectral approaches to smoothly transition from a split-window type approach for thin clouds to a Nakajima and King type approach for thick clouds. Uniform application of such a retrieval scheme across different satellite and field measurement campaigns would provide a set of consistent cloud products to the user community, theoretically allowing the direct comparison of cloud properties for the climate processes studies found throughout the literature.

Properties of reflected sunlight derived from a Green's function method

The inference of optical depth and particle size of clouds and aerosols using remotely sensed reflected radiance at solar wavelengths has received much attention recently. The information these measurements provide is path integrated. However, very little is known about the vertical distribution of this weighting. To characterize it, we first solve the radiative transfer equation (RTE) by a Greens function approach, and then investigate the sensitivity of the weighting to vertical inhomogeneities in the extinction by introducing a function that is closely related to the Greens function, herein called the contribution function. This function calculates the contributions to the radiance at the upper boundary of the medium by underlying layers. Three hypothetical clouds of identical optical depth but exhibiting different extinction profiles were used in this study. The contribution function was found very sensitive to the extinction profile. The global reflection and transmission matrices used to construct the Greens function, derived using an eigenmatrix method, resulted in an efficient, stable, and accurate method for calculating the emerging radiances that can be extended to multi-layered media.

Parameterization of Atmospheric Radiative Transfer. Part II: Selection Rules

Abstract This paper describes simple, computationally efficient methods of calculating 2-stream broadband fluxes and heating rates in the shortwave and longwave for multilayered media. The method, herein referred to as selection rules, is used in conjunction with conventional 2-stream solvers to reduce the number of full-up radiative transfer calculations, thus decreasing the computation time.

Adjoint perturbation and selection rule methods for solar broadband two-stream fluxes in multi-layer media

Abstract This paper describes computationally efficient methods of solving the two-stream plane-parallel equation of radiative transfer in multi-layered media using adjoint perturbations in combination with selection rules. Semi-analytical results are obtained for the perturbed fluxes in atmospheres illuminated by solar radiation. The perturbation approach is useful in media dominated by multiple scattering whereas selection rules apply when absorption is dominant or if the media is weakly scattering. Selection rules can be applied with conventional two-stream solvers to reduce the number of radiative transfer calculations. For example, clear sky broadband fluxes computed with selection rules for a 30 layer atmosphere using the k -distribution method were obtained in about one-seventh the time taken by the standard solvers. An 12-fold increase in computational speed over the standard solvers was achieved when selection rules were used with the perturbation method for the same atmosphere. Fluxes so computed were within 10% of those calculated using standard, full up two-stream radiative transfer codes.

ADJOINT PERTURBATION METHOD APPLIED TO TWO-STREAM RADIATIVE TRANSFER

Abstract This paper describes a computationally efficient method for solving the plane parallel equation of radiative transfer for the two-stream fluxes based on the adjoint perturbation formulation. Analytical results for the perturbed fluxes are presented for a single layer atmosphere containing both solar and thermal sources. Simple linear and exponential corrections to the base state fluxes are explored. For the solar radiative transfer problem, the exponential form of the perturbation correction can accommodate deviations exceeding 400% in the base state optical properties while maintaining accuracy to within a few percent. For thermal radiative transfer, the linear form of perturbation relation is the more accurate, but unlike the solar problem, deviations from the base state optical properties must remain relatively small (less than 20%) if the errors in the computed fluxes are to remain within a few percent of the true fluxes. The method is applied to the calculation of broadband solar fluxes in a layer of scatterers embedded in an absorbing gas, where the absorption is modeled via the k-distribution method.

Effects of Tunable Data Compression on Geophysical Products Retrieved from Surface Radar Observations with Applications to Spaceborne Meteorological Radars

AbstractThis paper presents results and analyses of applying an international space data compression standard to weather radar measurements that can easily span eight orders of magnitude and typically require a large storage capacity as well as significant bandwidth for transmission. By varying the degree of the data compression, the nonlinear response of models that relates measured radar reflectivity and/or Doppler spectra to the moments and properties of the particle size distribution characterizing clouds and precipitation was analyzed. Preliminary results for the meteorologically important phenomena of clouds and light rain indicate that for a ±0.5-dB calibration uncertainty, typical for the ground-based pulsed-Doppler 94-GHz (or 3.2 mm, W band) weather radar used as a proxy for spaceborne radar in this study, a lossless compression ratio of only 1.2 is achievable. However, further analyses of the nonlinear response of various models of rainfall rate, liquid water content, and median volume diameter ...

Improving Estimates of the Earth’s Radiation Budget with Multispectral and Hyperspectral Satellite Observations

This presentation explores the potential benefits of combining satellite-based hyperspectral radiances with active measurements for refining estimates of the many factors that influence the Earth’s radiation budget.