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Due to the uneven density of the Earth’s atmosphere, the light propagation path bends, destroying the collinearity condition of the ground object, camera projection center, and image point and introducing the atmospheric refraction error of optical satellite. The atmospheric refraction error seriously affects the geometric positioning accuracy and restricts the application of remote sensing imagery. This study proposes a novel and generalized atmospheric refraction correction method based on the rational function model (RFM) to compensate for refraction errors in various optical satellites without the complex satellite ephemeris and protected camera parameters. By using globally measured atmospheric parameters and the imaging characteristics of optical satellites, global atmospheric refraction indices with 400 height layers were stored. A compensation model of atmospheric refraction error was proposed, based on a limited number of key points, to improve processing efficiency. Based on the projection relationship in optical satellite imaging, the satellite position and object direction of key points were determined through backward calculation of the RFM, eliminating the need for complex and undisclosed satellite auxiliary data. Atmospheric refraction error was compensated by conducting iterative geometric positioning and refraction correction using an atmospheric model with 400 height layers. Experimental results show that the proposed method can be applied to sub-meter-level resolution and large swath-wide optical images for atmospheric refraction error correction. The average processing time is less than 2 s. Moreover, the improvement in geometric positioning accuracy of optical images ranges from 0.057 m to 2.985 m. This method is as accurate as the refraction correction method using a rigorous model.

Atmospheric refraction is one of the most significant factors that affect the geolocation accuracy of high-resolution remote sensing images. However, most of the current atmospheric refraction correction methods based on empirical data neglect the spatiotemporal variation of pressure, temperature, and humidity of the atmosphere, inevitably resulting in poor geometric positioning accuracy. Therefore, in terms of the problems mentioned above, this study proposed a spatiotemporal atmospheric refraction correction method (SARCM) based on global measured data to avoid the uncertainty of traditional empirical models. Initially, the atmosphere was stratified into 42 layers according to their pressure property, and each layer was divided into 1,042,560 grid cells with intervals of 0.25 longitude and 0.25 latitude. Then, the atmospheric refractive index of each grid in the imaging region was accurately calculated using the high-precision Ciddor formula, and the result was interpolated using three splines. Subsequently, according to the rigorous geometric positioning model, the line-of-sight of each pixel and the viewing zenith angle outside the atmosphere in WGS84 were derived to provide input for atmospheric refraction correction. Finally, the coordinates of the ground control points were corrected with the calculated atmospheric refractive index and Snell’s law. The experimental results showed that the proposed SARCM could effectively improve the positioning accuracy of the image with a large viewing zenith angle, and especially, the improvement percentage for a viewing zenith angle of 34.2426° in the x-direction was 99.5%. Moreover, the atmospheric refraction correction result of the SARCM was better than that of the primary state-of-the-art methods.

The refraction error compensation model for ground object detection is established. Firstly, based on a 100-meter interval, the area between the aircraft and the ground objects is stratified, and the Hopfield model of the atmospheric refractive index is combined with the e-index model to achieve an accurate simulation of the atmospheric refractive index profile. Then, based on the information such as the line-of-sight direction, flight altitude, and observation wavelength of the ground object observation target by the aircraft, combined with Snell’s law, the distance from the projection of the aircraft on the Earth’s surface to the true position of the ground object is given, and the true elevation angle is derived. Finally, by calculating the difference between the apparent elevation angle and the true elevation angle of the aircraft, the elevation angle error model of the aircraft is established to correct the elevation angle error of the aircraft caused by atmospheric refraction and is applied to the precise identification and positioning of the observed target.

This paper proposes a simple physics-based method for estimating the C n 2 profile in the lower atmosphere, using the Ellison scale as a measure of the outer turbulence scale. The new approach only Requires the temperature profile as an input to obtain the profile of the outer turbulence scale, followed by the C n 2 profile. Using sounding data from Lhasa (Tibet) C n 2 profiles were estimated using three outer scale models (Thorpe, HMNSP99, and Ellison) and compared with the measured C n 2 profile. Results show that the Ellison scale method offers better results as a profile estimator than the other two methods. Compared with the measured C n 2 profile, the average relative error of the Ellison scale method is generally lower than 8%, with a correlation coefficient larger than 0.5.

Optical turbulence limits the angular resolution of ground-based astronomical telescopes. The key parameter of optical turbulence is seeing. In this study, seasonal variations of seeing estimated from differential image motion monitor measurements at the Large Solar Telescope site are discussed. The Large Solar Telescope will be located at an elevation of 2000 m above sea level ( 51 ° 37 ′ 18 ″ N, 100 ° 55 ′ 07 ″ E ). The highest seeing values are observed in winter. The median of seeing is 2.″1. In summer, the median decreases to 1.″1. The best atmospheric conditions are observed in April–May, when the medians of seeing are low and the standard deviations are high. During this period, atmospheric situations with low values of seeing (∼0.″5–0.″6) are often observed. We simulated multilayer neural networks for the measured seeing by applying a group method of data handling. Modeled seeing is well described in terms of mean meteorological parameters, which include wind speed components and large-scale vorticity of air flows at different altitudes in the atmosphere. The 12-layer optimal neural network obtained has a high correlation coefficient between modeled and measured seeing values. The linear correlation coefficient is 0.77.

Detailed measurements of atmospheric humidity in the lower atmosphere are currently difficult and expensive to obtain. For this reason, there is interest in the development of low-cost, high-volume opportunistic technologies to acquire measurements of tropospheric humidity. We demonstrate the use of interferometry to measure the atmospheric refraction of the Automatic Dependent Surveillance-Broadcast (ADS-B) radio transmission routinely broadcast by commercial aircraft. Atmospheric refraction is strongly influenced by changes in humidity, and refractivity observations have proved to be an effective source of humidity information for numerical weather prediction models. A prototype ADS-B interferometer has been developed that can simultaneously perform angle-of-arrival (AoA) interferometry and decode ADS-B signals. Combining the measured AoA of the ADS-B signal with the known position of the aircraft (information contained within the ADS-B signal) allows the bending of the signal due to refraction to be determined. Combining the measured bending of numerous ADS-B signals allows for information concerning the refractivity structure to be extracted. An adjoint model is derived and used to retrieve synthetic one-dimensional refractivity profiles in a variety of atmospheric conditions. The results from an experiment using a prototype ADS-B interferometer are shown, and initial refractivity profiles are retrieved. Sources of uncertainty in the observations and the retrieved refractivity profiles are explored, and future work is suggested.

A comprehensive inter-comparison of seven radiative transfer models in the limb scattering geometry has been performed. Every model is capable of accounting for polarization within a spherical atmosphere. Three models (GSLS, SASKTRAN-HR, and SCIATRAN) are deterministic, and four models (MYSTIC, SASKTRAN-MC, Siro, and SMART-G) are statistical using the Monte Carlo technique. A wide variety of test cases encompassing different atmospheric conditions, solar geometries, wavelengths, tangent altitudes, and Lambertian surface reflectances have been defined and executed for every model. For the majority of conditions it was found that the models agree to better than 0.2 % in the single-scatter test cases and better than 1 % in the scalar and vectorial test cases with multiple scattering included, with some larger differences noted at high values of surface reflectance. For the first time in limb geometry, the effect of atmospheric refraction was compared among four models that support it (GSLS, SASKTRAN-HR, SCIATRAN, and SMART-G). Differences among most models with multiple scattering and refraction enabled were less than 1 %, with larger differences observed for some models. Overall the agreement among the models with and without refraction is better than has been previously reported in both scalar and vectorial modes.

Inaccurate stellar atmospheric refraction models impair the attainable accuracy of the refraction-based celestial navigation, leading to performance degradation in Strapdown Inertial Navigation System/Refractive Celestial Navigation System (SINS/RCNS) integrated navigation. This paper proposes a new SINS/RCNS integrated navigation algorithm aided by dual-band starlight refraction observations for near-Earth flight vehicles. In an analogy with the dual-frequency error correction in GNSS positioning, this algorithm exploits dual-band starlight measurements to estimate the atmospheric density error. Then, the measurement equation is established between the dual-band refraction angles and both position error and atmospheric density error. Moreover, the Extended Kalman Filter (EKF) is utilized to estimate the atmospheric density error online, which is then used for navigation error compensation. The simulation results indicate that the proposed algorithm can effectively mitigate navigation accuracy degradation by online correction for the atmospheric density error, enhancing integrated navigation performance for near-Earth flight applications.

Atmospheric refraction is a significant challenge to accurate distance and angle measurements in open-air environments, often limiting the precision of measurements obtained using electro-optic geodetic instruments despite their nominal accuracies. This study introduces a novel model, 3D-RM, designed to mitigate atmospheric effects on both distance and vertical angle measurements. The 3D-RM integrates in situ meteorological data from a network of automatic data-loggers, terrain information from a digital terrain model (DTM), and sensible heat flux from the fifth generation of European Centre for Medium-Range Weather Forecast reanalysis (ERA5), which is used in the application of the Turbulence Transfer Model (TTM) for estimating vertical refractivity gradients at various height levels. The model was tested with total station observations to 10 target points during two field campaigns. The results show that applying the model for distance correction leads to improvements in terms of closeness to reference values when compared to the standard method, which relies only on meteorological data collected at the station. Furthermore, the model has been additionally tested by removing the station meteorological data (3D-RM2). The results demonstrate that accurate corrections can be obtained even without the need of meteorological sensors specifically installed at the station point, which makes it more flexible. The 3D-RM is a cost-effective and relatively easy-to-implement solution, offering a promising alternative to existing methodologies, such as measuring meteorological values at both station and target points or the development of new instruments that can compensate the refractivity (such as a multiple-color electronic distance meter).

Terrestrial laser scanners (TLS) are widely used for deformation monitoring due to their ability to rapidly generate 3D point clouds. However, high-precision deliverables are increasingly required in TLS-based remote sensing applications to distinguish between measurement accuracies and actual geometric displacements. This study addresses the impact of atmospheric refraction, a primary source of systematic error in long-range terrestrial laser scanning, which causes laser beams to deviate from their theoretical path and intersect different object points on the target surface. A comprehensive study of two physical refractive index models (Ciddor and Closed Formula) is presented here, along with further developments on 3D spatial gradients of the refractive index. Field experiments were conducted using two long-range terrestrial laser scanners (Leica ScanStation P50 (Leica Geosystems, Heerbrugg, Switzerland) and Maptek I-Site 8820 (Maptek, Adelaide, Australia)) with reference back to a control network at two monitoring sites: a mine site for long-range measurements and a dam site for vertical angle measurements. The results demonstrate that, while conventional physical atmospheric models provide moderate improvement in accuracy, typically at the centimeter- or millimeter-level, the proposed advanced physical model—incorporating refractive index gradients—and the hybrid physical model—combining validated field results from the advanced model with a neural network algorithm—consistently achieve reliable millimeter-level accuracy in 3D point coordinates, by explicitly accounting for refractive index variations along the laser path. The robustness of these findings was further confirmed across different scanners and scanning environments.