Radiative Transfer In Cloudy Atmosphere Research Articles

A novel hybrid scattering order-dependent variance reduction method for Monte Carlo simulations of radiative transfer in cloudy atmosphere

We present a novel hybrid scattering order-dependent variance reduction method to accelerate the convergence rate in both forward and backward Monte Carlo radiative transfer simulations involving highly forward-peaked scattering phase function. This method is built upon a newly developed theoretical framework that not only unifies both forward and backward radiative transfer in scattering-order-dependent integral equation, but also generalizes the variance reduction formalism in a wide range of simulation scenarios. In previous studies, variance reduction is achieved either by using the scattering phase function forward truncation technique or the target directional importance sampling technique. Our method combines both of them. A novel feature of our method is that all the tuning parameters used for phase function truncation and importance sampling techniques at each order of scattering are automatically optimized by the scattering order-dependent numerical evaluation experiments. To make such experiments feasible, we present a new scattering order sampling algorithm by remodeling integral radiative transfer kernel for the phase function truncation method. The presented method has been implemented in our Multiple-Scaling-based Cloudy Atmospheric Radiative Transfer (MSCART) model for validation and evaluation. The main advantage of the method is that it greatly improves the trade-off between numerical efficiency and accuracy order by order.

Monte Carlo Simulations of Radiative Transfer in Cloudy Atmosphere over Sea Surfaces

A rigorous and modular Monte Carlo radiative transfer model MCRT has been developed to compute radiance for realistic cloudy atmosphere over sea surfaces in the visible and near-IR spectra. The simulation methods of the sample's trajectories are consistently described in the whole simulation spatial domain, which consists of a number of voxel cells for atmosphere and square cells for the sea surface. An inverse transformation method is applied in an atmospheric scattering event simulation and a rigorous accept/reject method is formulated for simulating a reflection event at Cox-Munk (CM) anisotropically and Nakajima-Tanaka (NT) isotropically roughened sea surface. Both methods have been implemented within the model and were tested as two individual modules achieving high accuracy. The model as a whole system was also validated by other codes. The mean difference is about 0.084% and 0.528% in comparison to the Spherical Harmonics code (SHARM) and Monte Carlo Atmospheric Radiative Transfer Simulator (MCARaTS) respectively for 1D atmosphere and the NT model. The comparisons of the Spherical Harmonic Discrete Ordinate Method (SHDOM) show that agreements are obtained in the sun glint regions for 1D atmosphere and the CM model and the mean differences are below 0.478% for a 3D cloud field with lambertian. In general, the major advantage of MCRT is that it could simulate more accurate reflection direction at sea surfaces in a shorter time and hence more accurate radiance in complex cloudy atmosphere over sea surfaces with high numerical efficiency especially on a small PC.

Multiple-scaling methods for Monte Carlo simulations of radiative transfer in cloudy atmosphere

Two multiple-scaling methods for Monte Carlo simulations were derived from integral radiative transfer equation for calculating radiance in cloudy atmosphere accurately and rapidly. The first one is to truncate sharp forward peaks of phase functions for each order of scattering adaptively. The truncated functions for forward peaks are approximated as quadratic functions; only one prescribed parameter is used to set maximum truncation fraction for various phase functions. The second one is to increase extinction coefficients in optically thin regions for each order scattering adaptively, which could enhance the collision chance adaptively in the regions where samples are rare. Several one-dimensional and three-dimensional cloud fields were selected to validate the methods. The numerical results demonstrate that the bias errors were below 0.2% for almost all directions except for glory direction (less than 0.4%) and the higher numerical efficiency could be achieved when quadratic functions were used. The second method could decrease radiance noise to 0.60% for cumulus and accelerate convergence in optically thin regions. In general, the main advantage of the proposed methods is that we could modify the atmospheric optical quantities adaptively for each order of scattering and sample important contribution according to the specific atmospheric conditions.

Efficient unbiased variance reduction techniques for Monte Carlo simulations of radiative transfer in cloudy atmospheres: The solution

We present five new variance reduction techniques applicable to Monte Carlo simulations of radiative transfer in the atmosphere: detector directional importance sampling, n-tuple local estimate, prediction-based splitting and Russian roulette, and circum-solar virtual importance sampling. With this set of methods it is possible to simulate remote sensing instruments accurately and quickly. In contrast to all other known techniques used to accelerate Monte Carlo simulations in cloudy atmospheres – except for two methods limited to narrow angle lidars – the presented methods do not make any approximations, and hence do not bias the result. Nevertheless, these methods converge as quickly as any of the biasing acceleration techniques, and the probability distribution of the simulation results is almost perfectly normal. The presented variance reduction techniques have been implemented into the Monte Carlo code MYSTIC (“Monte Carlo code for the physically correct tracing of photons in cloudy atmospheres”) in order to validate the techniques.

Radiative transfer in the cloudy atmosphere

Radiative transfer in clouds is a challenging task, due to their high spatial and temporal variability which is unrivaled by any other atmospheric species. Clouds are among the main modulators of radiation along its path through the Earth’s atmosphere. The cloud feedback is the largest source of uncertainty in current climate model predictions. Cloud observation from satellites, on a global scale, with appropriate temporal and spatial sampling is therefore one of the top aims of current Earth observation missions. In this chapter three-dimensional methods for radiative transfer in cloudy atmospheres are described, which allow to study cloud-radiation interaction at the level needed to better understand the fundamental details driving climate and to better exploit remote sensing algorithms. The Monte Carlo technique is introduced which allows to handle nearly arbitrarily complex atmospheric conditions. The accuracy of the method is discussed by comparison between different models and with observations. Finally, we show some examples and discuss under which conditions three-dimensional methods are actually needed and when commonly-used one-dimensional approximations are applicable. This chapter builds upon the excellent overview of one-dimensional radiative transfer in ERCA Volume 3 [B. Pinty and M.M. Verstraete, ERCA 3, 67 (1998)].

Implications of the Observed Mesoscale Variations of Clouds for the Earth's Radiation Budget

The effect of small-spatial-scale cloud variations on radiative transfer in cloudy atmospheres currently receives a lot of research attention, but the available studies are not very clear about which spatial scales are important and report a very large range of estimates of the magnitude of the effects. Also, there have been no systematic investigations of how to measure and represent these cloud variations. We exploit the cloud climatology produced by the International Satellite Cloud Climatology Project (ISCCP) to: (1) define and test different methods of representing cloud variation statistics, (2) investigate the range of spatial scales that should be included, (3) characterize cloud variations over a range of space and time scales covering mesoscale (30 - 300 km, 3-12 hr) into part of the lower part of the synoptic scale (300 - 3000 km, 1-30 days), (4) obtain a climatology of the optical thickness, emissivity and cloud top temperature variability of clouds that can be used in weather and climate GCMS, together with the parameterization proposed by Cairns et al. (1999), to account for the effects of small-scale cloud variations on radiative fluxes, and (5) evaluate the effect of observed cloud variations on Earth's radiation budget. These results lead to the formulation of a revised conceptual model of clouds for use in radiative transfer calculations in GCMS. The complete variability climatology can be obtained from the ISCCP Web site at http://isccp.giss.nasa.gov.

Super-exponential extinction of radiation in a negatively correlated random medium

It was shown in recent work that spatial correlations among obstacles of a random, absorbing medium can lead to slower-than-exponential (sub-exponential) extinction of radiation with propagation distance. Exponential decay, described by the Beer–Lambert law, arises in a special case when the medium contains no correlations. A third possibility, examined here, is that of negative correlations which can lead to faster-than-exponential (super-exponential) extinction. Using a Monte Carlo approach, we confirm that sub-exponential decay occurs when the volume-averaged pair correlation function is greater than zero at the scale of interest and that the Beer–Lambert law is recovered when correlations vanish. We also find that when the volume-averaged pair correlation function is negative, super-exponential extinction with propagation distance occurs. These results are of special interest to the problem of radiative transfer in cloudy atmospheres, where the pair correlation function previously has been shown to be negative and positive at different scales.

Three‐dimensional solar radiative transfer in small tropical cumulus fields derived from high‐resolution imagery

Since three‐dimensional (3‐D) radiative transfer in cloudy atmospheres is too expensive for large‐scale atmospheric models, approximate radiative transfer methods are used. The accuracy of these approximations for a large sample of realistic cloud fields has not been determined. This study examines 150 fields of small marine tropical cumulus to assess the magnitude of 3‐D effects on domain average solar fluxes and to evaluate the accuracy of these approximations in actual cumulus fields. The cloud fields are derived from Moderate‐Resolution Imaging Spectroradiometer Airborne Simulator (MAS) visible and thermal infrared imagery. Domain average broadband solar fluxes in these fields are simulated with a Monte Carlo radiative transfer model using four radiative transfer methods: full three‐dimensional, the independent pixel approximation (IPA), the tilted IPA, and the plane‐parallel approximation. The average 3‐D radiative effects of these cumulus cloud fields are small, with mean reflected flux errors up to 3 W/m2 for overhead Sun and less than 1 W/m2 for the daytime average. The mean errors for column‐absorbed fluxes are less than 0.3 W/m2 for all Sun angles. The small absolute flux errors are a result of the average field having small cloud fraction (10%), low cloud optical depth (4.4), and shallow clouds. Some individual fields have large 3‐D absolute reflected flux effects, and the normalized reflected flux errors are significant. The errors correlate well with the cloud fraction; so it may be possible to make corrections to the approximations.

Model for an investigation of radiative transfer in cloudy atmosphere

Parameterization of droplet size distributions using a composition of three gamma functions is suggested to simulate a wide spectrum of cloud droplets including drizzle and rain. It should be stressed out that this parameterization is based on extensive material (accumulated in the Russian Central Aerological Observatory) of aircraft observations in clouds and dependent on the cloud type, temperature and other factors. Effective computation technique using the geometric optics approach for the calculations of the parameters of electromagnetic scattering on spherical polydispersions and the database containing these parameters for a wide set of aerosol and cloud mediums are described. The parameterization, computation technique and the database are applied to create different optical atmospheric models with scattering properties rather close to reality for theoretical investigations of the atmospheric radiative transfer. Some examples of cloud radiation forcing studies are also considered in this paper. Their principal feature was the use of the original effective line-by-line and Monte-Carlo codes to take into account rigorously both the cloud/molecular scattering and a detailed spectral structure of water vapor, ozone, carbon dioxide and oxygen. It has been found: (a) variations of the mean droplet radius depending on the cloud temperature and other factors lead to essential changes in shortwave fluxes (tens of W/m 2), cloud radiation absorption (tens of W/m 2) and the Liquid Water Path (LWP) (by several times); (b) In continental clouds short wave fluxes mainly depend on small droplets. The existence of large (drizzle) drops perturbs slightly the fluxes and rather strongly affects the liquid water path and the cloud radiation absorption; (c) The solar radiation absorption and scattering by cloud media are generally defined only by the extinction coefficient and the effective radius and are slightly affected by other details of cloud size droplet distributions. These statements are in good agreement with other investigations. Thus, these parameterization and database should be good enough for the cloud optical properties simulation in the majority of practical applications. Moreover, the developed codes may be recommended for exact simulation of atmospheric radiative transfer in satellite and full-scale experiments, for testing and improving the radiation codes being used in climate models, etc.

Two-Dimensional Radiative Transfer in Cloudy Atmospheres: The Spherical Harmonic Spatial Grid Method

A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.

Parameterization of Infrared Radiative Transfer in Cloudy Atmospheres

Parameterization of the transfer of infrared fluxes is developed for an atmosphere containing nonblack and semi-transparent clouds. The concept of parameterization makes use of the predetermined broadband cloud emissivity, transmissivity and reflectivity as functions of the cloud liquid water/ice content. In conjunction with the cloud radiative properties, broadband emissivities for water vapor, carbon dioxide and ozone are derived from band parameters in which the effects of pressure and temperature on absorption are accounted for in the path length based on a number of physical adjustments. Infrared cooling rates computed from the parameterized broadband model for clear and cirrus cloudy atmospheres show close agreement with those obtained from a more sophisticated band-by-band model with accuracy within about 0.2°C day−1.