Fraunhofer diffraction description in the approximation of the light field theory

The wavelength is that natural scale that determines the applicability domains of the ray approximation and the wave approximation of light. If the change of the radiation power spatial density is significant at the wavelength scale, we deal with the light diffraction phenomenon, which is a subject to the wave optics. Let us consider the diffraction phenomenon at the diaphragm. It is possible to distinguish the near zone with significant wave inhomogeneities (i.e. the Fresnel zone) and the far Fraunhofer diffraction zone, in which the wave becomes close to homogeneous (the so-called quasi-homogeneous) and the ray approximation is possible. The problem is that there is no explicit relationship between the radiance of the rays before and after diaphragm. Method for determining the boundary conditions for the radiance in the Fraunhofer zone through the radiance of the incident radiation is proposed in the paper. This approach for computing the radiance field in the Fraunhofer zone can be generalized to other problems of optics, thereby providing the possibility of using computationally efficient ray-approximation-based methods to determine the light fields

A Proof-of-Concept Algorithm for the Retrieval of Total Column Amount of Trace Gases in a Multi-Dimensional Atmosphere

An algorithm for the retrieval of total column amount of trace gases in a multi-dimensional atmosphere is designed. The algorithm uses (i) certain differential radiance models with internal and external closures as inversion models, (ii) the iteratively regularized Gauss-Newton method as a regularization tool, and (iii) the spherical harmonics discrete ordinate method (SHDOM) as linearized radiative transfer model. For efficiency reasons, SHDOM is equipped with a spectral acceleration approach that combines the correlated k-distribution method with the principal component analysis. The algorithm is used to retrieve the total column amount of nitrogen for two- and three-dimensional cloudy scenes. Although for three-dimensional geometries, the computational time is high, the main concepts of the algorithm are correct and the retrieval results are accurate

Analysis of the Discrete Theory of Radiative Transfer in the Coupled "Ocean-Atmosphere" System: Current Status, Problems and Development Prospects

In this paper, we analyze the current state of the discrete theory of radiative transfer. One-dimensional, three-dimensional and stochastic radiative transfer models are considered. It is shown that the discrete theory provides a unique solution to the one-dimensional radiative transfer equation. All approximate solution techniques based on the discrete ordinate formalism can be derived based on the synthetic iterations, the small-angle approximation, and the matrix operator method. The possible directions for the perspective development of radiative transfer are outlined

Evaluating the assimilation of S5P/TROPOMI near real-time SO2 columns and layer height data into the CAMS integrated forecasting system (CY47R1), based on a case study of the 2019 Raikoke eruption

The Copernicus Atmosphere Monitoring Service(CAMS), operated by the European Centre for Medium-Range Weather Forecasts on behalf of the European Com-mission, provides daily analyses and 5 d forecasts of atmospheric composition, including forecasts of volcanic sulfur dioxide (SO2) in near real time. CAMS currently assimilates total column SO2products from the GOME-2 instruments on MetOp-B and MetOp-C and the TROPOMI instrument on Sentinel-5P, which give information about the location and strength of volcanic plumes. However, the operational TROPOMI and GOME-2 data do not provide any information about the height of the volcanic plumes, and therefore some prior assumptions need to be made in the CAMS data assimilation system about where to place the resulting SO2increments in the vertical. In the current operational CAMS configuration, the SO2increments are placed in the mid-troposphere, around 550 hPa or 5 km. While this gives good results for the majority of volcanic emissions, it will clearly be wrong for eruptions that inject SO2at very different altitudes, in particular exceptional events where part of the SO2plume reaches the stratosphere.A new algorithm, developed by the German Aerospace Centre (DLR) for GOME-2 and TROPOMI, optimized in the frame of the ESA-funded Sentinel-5P Innovation–SO2Layer Height Project, and known as the Full-Physics Inverse Learning Machine (FP_ILM) algorithm, retrieves SO2 layer height from TROPOMI in near real time (NRT) in addition to the SO2column. CAMS is testing the assimilation of these products, making use of the NRT layer height information to place the SO2increments at a retrieved altitude. Assimilation tests with the TROPOMI SO2layer height data for the Raikoke eruption in June 2019 show that the resulting CAMSSO2plume heights agree better with IASI plume height data than operational CAMS runs without the TROPOMI SO2layer height information and show that making use of the additional layer height information leads to improved SO2 forecasts. Including the layer height information leads to higher modelled total column SO2values in better agreement with the satellite observations. However, the plume area and SO2burden are generally also overestimated in the CAMS analysis when layer height data are used. The main reason for this overestimation is the coarse horizontal resolution used in the minimizations. By assimilating the SO2layer height data, the CAMS system can predict the overall location of the Raikoke SO2plume up to 5 d in advance for about 20 dafter the initial eruption, which is better than with the operational CAMS configuration (without prior knowledge of the plume height) where the forecast skill is much more reduced for longer forecast lead times

Linearizations of the Spherical Harmonic Discrete Ordinate Method (SHDOM)

Linearizations of the spherical harmonic discrete ordinate method (SHDOM) by means of a forward and a forward-adjoint approach are presented. Essentially, SHDOM is specialized for derivative calculations and radiative transfer problems involving the delta-M approximation, the TMS correction, and the adaptive grid splitting, while practical formulas for computing the derivatives in the spherical harmonics space are derived. The accuracies and efficiencies of the proposed methods are analyzed for several test problems

Differential inverse inelastic mean free path and differential surface excitation probability retrieval from electron energy loss spectra

Quantitative interpretation of the electron spectroscopy data requires the information on differential inverse inelastic mean free paths (DIIMFP) and differential surface excitation probabilities (DSEP). In this paper, we test an algorithm of extracting DIIMFP and DSEP from reflected electron energy loss spectra (REELS) and photo-electron spectra (PES) in which the desired functions are parametrized on the base of a classical Lorentz oscillator. Unknown parameters are found by using the fitting procedure. To account for surface excitations, the investigated samples are considered as multi-layer systems. Simulations of REELS and PES are performed by making use of the partial intensity approach. The partial intensities for the reflection function and the photo-electron density flux are computed on the base of the invariant imbedding method. Extracted DIIMFPs and DSEPs are compared with those obtained by other authors. Finally, REELS and PES spectra for Be, Mg, Al, Si, Nb and W are computed using the retrieved DIIMFPs and DSEPs, and compared with the experimental spectra. All comparisons show good agreement

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

Methods Calculating the Slab Radiance Factor

One of the most critical problems of realistic visualization of the real-world objects is physically adequate modeling of their reflection of light. Reflection of light by objects occurs both from the surface and the bulk of matter (scattering). Accounting for the light reflection from the surface of objects was solved almost a century ago based on its representation as a Fresnel randomly rough surface. Scattering by a bulk of matter is the subject of radiation transfer theory, which has only recently received its known completion in the form of discrete transfer theory. Strict analytical methods for solving the radiation transport equation (RTE) are often not highly effective for calculating the radiance factor. For a long time, in the absence of effective numerical methods for solving problems and the unavailability of high-speed computers for practical calculations, approximate methods for solving RTE were developed. However, their accuracy and applicability limits were poorly defined. The discrete transfer theory allowed us to evaluate the existing approximate methods for solving the UPI, their accuracy, and the efficiency of application for calculating the radiance factor. It is shown that the most effective method is the method of synthetic iterations. The method is based on the selection of the solution anisotropic part based on a small-angle approximation of the RTE solution. The solution regular part can be calculated by any approximation. Then a simple iteration from the complete solution is performed to refine the angular distribution of the radiance factor

Cluster Low-Streams Regression Method for Hyperspectral Radiative Transfer Computations: Cases of O2 A- and CO2 Bands

Current atmospheric composition sensors provide a large amount of high spectral resolution data. The accurate processing of this data employs time-consuming line-by-line (LBL) radiative transfer models (RTMs). In this paper, we describe a method to accelerate hyperspectral radiative transfer models based on the clustering of the spectral radiances computed with a low-stream RTM and the regression analysis performed for the low-stream and multi-stream RTMs within each cluster. This approach, which we refer to as the Cluster Low-Streams Regression (CLSR) method, is applied for computing the radiance spectra in the O2 A-band at 760 nm and the CO2 band at 1610 nm for five atmospheric scenarios. The CLSR method is also compared with the principal component analysis (PCA)-based RTM, showing an improvement in terms of accuracy and computational performance over PCA-based RTMs. As low-stream models, the two-stream and the single-scattering RTMs are considered. We show that the error of this approach is modulated by the optical thickness of the atmosphere. Nevertheless, the CLSR method provides a performance enhancement of almost two orders of magnitude compared to the LBL model, while the error of the technique is below 0.1% for both bands

Accuracy Enhancement of the Two-Stream Radiative Transfer Model for Computing Absorption Bands at the Presence of Aerosols

The two-stream model is the fastest radiative transfer model among those based on the discrete ordinate method. Although its accuracy is not high enough to be used in applications, the two-stream model gets more attention in computationally demanding tasks such as line-by-line simulations in the gaseous absorption bands. For this reason, we designed the cluster low-streams regression (CLSR) technique, in which a spectrum computed with a two-stream model, is refined by using statistical dependencies between two- and multistream radiative transfer models. In this paper, we examine the efficiency of this approach for computing Hartley-Huggins, O2 A-, water vapour and CO2 bands at the presence of aerosols. The numerical results evidence that the errors of the CLSR method is not biased and around 0.05 %, while the performance enhancement is two orders of magnitude