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.

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.

The Effect Of Scattered Radiation On Capabilities Of Laser Beam Guidance

The paper discusses the possibility of remote detection of a continuous laser beam propagating in a scattering continental and coastal atmosphere, when it is recorded outside the axial zone. In the single scattering approximation, estimates of the radianceat the registration site are carried out, which are compared with the threshold characteristics of existing photodetectors in the visible and IR spectral regions. It is shown that the laser radiation (LR) of the beam is reliably recorded in the range of angles (0–180)° at metrological range of visibility equal (5–20) km at night conditions. At twilight, under the same conditions, detection capabilities are significantly reduced. A significant increase of the LR beam radiance contrast with a decrease in its divergence has been shown experimentally in the field observations. At twilight, a decrease in the beam’s radiance contrast is seen. A beam with a divergence equal to 2 ceases to be distinguishable at angles equal to (80–90)°, and a beam with a divergence of 4 – at angles (60–70)°.In this case, the contrast difference reaches up to 10 times.

Seismo-Acoustic Benchmark Problems Involving Sloping Solid–Solid Interfaces and Variable Topography

The accuracy of the seismo-acoustic parabolic equation is tested for problems involving sloping solid–solid interfaces and variable topography. The approach involves approximating the medium in terms of a series of range-independent regions, using a parabolic wave equation to propagate the field through each region, and applying a single-scattering approximation to obtain transmitted fields across the vertical interfaces between regions. The accuracy of the parabolic equation method for range-dependent problems in seismo-acoustics was previously tested in the small slope limit. It is tested here for problems involving larger slopes using a finite-element model to generate reference solutions.