Comparative analysis of the error of the single scattering approximation when solving one inverse problem in two-dimensional and three- dimensional cases

The inverse problem for the nonstationary radiative transfer equation is considered, which consists in finding the scattering coefficient for a given time-angular distribution of the solution to the equation at a certain point. To solve this problem, the single scattering approximation in the pulsed sounding mode is used. A comparative analysis of the error in solving the inverse problem in the single scattering approximation for two-dimensional and three-dimensional models describing the process of high-frequency acoustic sounding in a fluctuating ocean is carried out. It is shown that in the two-dimensional case the error of the approximate solution significantly exceeds the error in the three-dimensional model.

Empirical model of multiple scattering effect on single-wavelength lidar data of aerosols and clouds

We performed extensive Monte Carlo (MC) simulations of single-wavelength lidar signals from a plane-parallel homogeneous layer of atmospheric particles and developed an empirical model to account for the multiple scattering in the lidar signals. The simulations have taken into consideration four types of lidar configurations (the ground based, the airborne, the CALIOP, and the ATLID) and four types of particles (coarse aerosol, water cloud, jet-stream cirrus and cirrus). Most of simulations were performed with the spatial resolution of 20 m and the particles extinction coefficient εp between 0.06 km−1 and 1.0 km−1. The resolution was of 5 m for high values of εp (up to 10.0 km−1). The majority of simulations for ground-based and airborne lidars were performed at two values of the receiver field-of-view (RFOV): 0.25 mrad and 1.0 mrad. The effect of the width of the RFOV was studied for the values up to 50 mrad. The proposed empirical model is a function that has only three free parameters and approximates the multiple-scattering relative contribution to lidar signals. It is demonstrated that the empirical model has very good quality of MC data fitting for all considered cases. Special attention was given to the usual operational conditions, i.e., low distances to a particles layer, small optical depths and quite narrow receiver field-of-views. It is demonstrated that multiple scattering effects cannot be neglected when the distance to a particles layer is about 8 km or higher and the full RFOV is of 1.0 mrad. As for the full RFOV of 0.25 mrad, the single scattering approximation is acceptable for aerosols (εp ≲ 1.0 km−1), water clouds (εp ≲ 0.5 km−1), and cirrus clouds (εp ≤ 0.1 km−1). When the distance to a particles layer is of 1 km, the single scattering approximation is acceptable for aerosols and water clouds (εp ≲ 1.0 km−1, both RFOV = 0.25 and RFOV = 1 mrad). As for cirrus clouds, the effect of multiple scattering cannot be neglected even at such low distance when εp ≳ 0.5 km−1.

Effective moduli of rocks predicted by the Kuster–Toksöz and Mori–Tanaka models

Natural rocks are polymineral composites with complex microstructures. Such strong heterogeneities significantly affect the estimation of effective moduli by some theoretical models. First, we have compared the effective moduli of isotropic rocks predicted by the Kuster–Toksöz (KT) model and the Mori–Tanaka (MT) model. The widely used KT model only has finite precision in many cases because of its assumption that is restricted to the first-order scattering approximation. However, the MT model based on the Eshelby tensor in mesomechanics has the advantage of predicting effective moduli of rocks, especially when the volume fraction of embedded inclusions is sufficiently large. In addition, the MT model can be used to predict the effective modulus of anisotropic rocks, but the KT model cannot. For a certain kind of shale or tight sandstones, which are viewed as isotropic composites, both the models work well. For the medium containing spherical pores, both the models produce the same results, whereas for ellipsoidal pores the MT model is more accurate than the KT model, validated by the finite element simulations. In what follows, the applicable ranges of simplified formulas for pores with needle, coin and disk shapes, widely used in engineering, are quantitatively given based on the comparison with the results according to the reduced ellipsoidal formulas of the MT and KT models. These findings provide a comprehensive understanding of the two models in calculating the effective modulus of rocks, which are beneficial to such areas as petroleum exploration and exploitation, civil engineering, and geophysics.

Radiative analysis of luminescence in photoreactive systems: Application to photosensitizers for solar fuel production

Most chemical reactions promoted by light and using a photosensitizer (a dye) are subject to the phenomenon of luminescence. Redistribution of light in all directions (isotropic luminescence emission) and in a new spectral range (luminescence emission spectrum) makes experimental and theoretical studies much more complex compared to a situation with a purely absorbing reaction volume. This has a significant impact on the engineering of photoreactors for industrial applications. Future developments associated with photoreactive system optimization are therefore extremely challenging, and require an in-depth description and quantitative analysis of luminescence. In this study, a radiative model describing the effect of luminescence radiation on the calculation of absorptance is presented and analyzed with the multiple inelastic-scattering approach, using Monte Carlo simulations. The formalism of successive orders of scattering expansion is used as a sophisticated analysis tool which provides, when combined with relevant physical approximations, convenient analytical approximate solutions. Its application to four photosensitizers that are representative of renewable hydrogen production via artificial photosynthesis indicates that luminescence has a significant impact on absorptance and on overall quantum yield estimation, with the contribution of multiple scattering and important spectral effects due to inelastic scattering. We show that luminescence cannot be totally neglected in that case, since photon absorption lies at the root of the chemical reaction. We propose two coupled simple and appropriate analytical approximations enabling the estimation of absorptance with a relative error below 6% in every tested situation: the zero-order scattering approximation and the gray single-scattering approximation. Finally, this theoretical approach is used to determine and discuss the overall quantum yield of a bio-inspired photoreactive system with Eosin Y as a photosensitizer, implemented in an experimental setup comprising a photoreactor dedicated to hydrogen production.

Fast Hyper-Spectral Radiative Transfer Model Based on the Double Cluster Low-Streams Regression Method

Fast radiative transfer models (RTMs) are required to process a great amount of satellite-based atmospheric composition data. Specifically designed acceleration techniques can be incorporated in RTMs to simulate the reflected radiances with a fine spectral resolution, avoiding time-consuming computations on a fine resolution grid. In particular, in the cluster low-streams regression (CLSR) method, the computations on a fine resolution grid are performed by using the fast two-stream RTM, and then the spectra are corrected by using regression models between the two-stream and multi-stream RTMs. The performance enhancement due to such a scheme can be of about two orders of magnitude. In this paper, we consider a modification of the CLSR method (which is referred to as the double CLSR method), in which the single-scattering approximation is used for the computations on a fine resolution grid, while the two-stream spectra are computed by using the regression model between the two-stream RTM and the single-scattering approximation. Once the two-stream spectra are known, the CLSR method is applied the second time to restore the multi-stream spectra. Through a numerical analysis, it is shown that the double CLSR method yields an acceleration factor of about three orders of magnitude as compared to the reference multi-stream fine-resolution computations. The error of such an approach is below 0.05%. In addition, it is analysed how the CLSR method can be adopted for efficient computations for atmospheric scenarios containing aerosols. In particular, it is discussed how the precomputed data for clear sky conditions can be reused for computing the aerosol spectra in the framework of the CLSR method. The simulations are performed for the Hartley–Huggins, O2 A-, water vapour and CO2 weak absorption bands and five aerosol models from the optical properties of aerosols and clouds (OPAC) database.

Statistical estimates of the effect of the sea water scattering phase function on the characteristics of airborne hydrooptical lidar signals

The effect of the scattering phase functions of sea water types by the Petzold classification on the characteristics of signals of an airborne lidar is investigated using the Monte Carlo method. It is shown that for pure and coastal waters, the single scattering approximation is applicable for solving the laser sensing equation. Based on the analysis of the results obtained in the closed numerical experiment, the method of reconstruction of the extinction coefficient of lidar signals by pure and coastal sea waters in the mixing water layer is proposed and substantiated. The obtained results can be used to expand the possibilities of lidar signal interpretation, especially in complex and ambiguous situations.

Generalized optical theorem for Rayleigh scattering approximation

A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results is revisited the classical and standard scattering elastic problem of a dielectric sphere for which the incident field can be any arbitrary invariant beam.