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The radiative transfer in a scattering plane-parallel atmosphere is discussed, considering the exact analytical, the computational and the approximate methods. Some results of numerical comparisons are given. Finally, the difficulties of realistic atmospheric models are emphasized.
The inter-comparison of the reflective solar bands (RSB) between the instruments onboard a geostationary orbit satellite and a low Earth orbit satellite is very helpful in assessing their calibration consistency. Himawari-8 was launched 7 October 2014 and GOES-R was launched on 19 November 2016. Unlike previous GOES instruments, the Advanced Himawari Imager (AHI) on Himawari-8 and the Advanced Baseline Imager (ABI) on GOES-R have onboard calibrators for the RSB. Independent assessment of calibration is nonetheless important to enhance their product quality. MODIS (Moderate Resolution Imaging Spectroradiometer) and VIIRS (Visible Infrared Imaging Radiometer Suite) can provide good references for sensor calibration. In this work, the inter-comparison between AHI and VIIRS is performed over a pseudo-invariant target. The use of stable and uniform calibration sites provides comparison with accurate adjustment for band spectral difference, reduction of impact from pixel mismatching, and consistency of BRDF (Bidirectional Reflectance Distribution Function) and atmospheric correction. The site used is the Strzelecki Desert in Australia. Due to the difference in solar and view angles, two corrections must be applied in order to compare the measurements. The first is the atmospheric scattering correction applied to the top of atmosphere reflectance measurements. The second correction is applied to correct the BRDF effect. The atmospheric correction is performed using a vector version of the Second Simulation of a Satellite Signal in the Solar Spectrum (6SV) model and the BRDF correction is performed using a semi-empirical model. Our results show that AHI band 1 (0.47 microns) has a good agreement with VIIRS band M3 within 0.15 percent. AHI band 5 (1.61 microns) shows the largest difference (5.09 percent) with VIIRS band M10, while AHI band 5 shows the least difference (1.87 percent) in comparison with VIIRS band I3. The methods developed in this work can also be directly applied to assess GOES-16/ABI (Geostationary Operational Environment Satellite16 / Advanced Baseline Imager) calibration consistency, a topic we will address in the future.
Sky brightness measurements in visual and ultraviolet regions of spectrum - multiple light scattering
A technique for the inversion of satellite auroral brightness observations is developed, which takes into account the backscattering of light from the snow-covered ground and atmospheric scattering. The theory includes parallax effects. Parallax arises when a point in the aurora is observed from different angles against a background with a variable brightness. It is shown that observations from a spinning satellite at any given angle from nadir are sufficient to recover the auroral form.
Voyager images of Triton indicate considerable spatial variability in the concentration of at least two different scattering components in the atmosphere. Data from high phase angle limb scans were fit to Mie scattering models to derive mean particle sizes, number densities, and vertical extent for both types of scattering material at ten different locations between 15 deg S and 70 deg S. These fits reveal a thin haze at latitudes equatorward of 25-30 deg S. The imaging data can be fit reasonably well by both conservatively scattering and absorbing hazes with particle sizes near 0.18 micron and optical depths of order 0.001-0.01. Rayleigh scattering haze fits the imaging data somewhat less well, and can be totally ruled out by combining the imaging and UVS measurements. At high southern latitudes, Triton displays clouds below an altitude of approximately 8 km, as well as the haze at higher altitudes. The clouds have particle sizes which may range from 0.7-2.0 microns, or may be near 0.25 micron. The atmospheric optical depth poleward of 30 deg S must be generally greater than 0.1, but need not be more than 0.3. Horizontal inhomogeneities are quite noticeable, especially at longitudes east of (i.e., higher than) 180 deg.
A theory is developed for discretizing the vector integro-differential radiative transfer equation including both solar and thermal radiation. A complete solution and boundary equations are obtained using the discrete-ordinate method. An efficient numerical procedure is presented for calculating the phase matrix and achieving computational stability. With natural light used as a beam source, the Stokes parameters from the model proposed here are compared with the analytical solutions of Chandrasekhar (1960) for a Rayleigh scattering atmosphere. The model is then applied to microwave frequencies with a thermal source, and the brightness temperatures are compared with those from Stamnes'(1988) radiative transfer model.
The paper discusses an analytical solution for the nadir radiance as measured from a satellite, based on a simplified single-scattering approximation in which the scattered radiation is not subject to extinction. In the solution, terms can be identified as due to a reflection from the vicinity of the object pixel, and respectively, (1) upward scattering to zenith above the object pixel (cross radiance), and (2) downward scattering from the entire atmosphere to the object pixel (cross irradiance). It is shown that the cross radiance is proportional to the forward scattering optical thickness, as defined, and the cross irradiance to the backscattering optical thickness. In addition, explicit expressions and computer solutions for the cross radiance from annular or from rectangular reflecting areas are presented. It is concluded that the effect depends on the height distribution and on the sharpness of the forward peak of the scattering particles.
Gamma ray scattering gauge design optimum parameters to measure Mars atmospheric density
The orbiting Burst and Transient Source Experiement (BATSE) will locate gamma ray burst sources by analysis of the relative numbers of photons coming directly from a source and entering its prescribed array of detectors. In order to accurately locate burst sources it is thus necessary to identify and correct for any counts contributed by events other than direct entry by a mainstream photon. An effort is described which estimates the photon numbers which might be scattered into the BATSE detectors from interactions with the Earth atmosphere. A model was developed which yielded analytical expressions for single-scatter photon contributions in terms of source and satellite locations.
Using parameters recently measured in the laboratory, the shapes of manifolds belonging to the R-branch of Saturn's 3 nu 3 CH4 band were analyzed in terms of a homogeneous scattering model of Saturn's atmosphere, and the results were compared with those of an earlier analysis in terms of a reflecting-layer model. The resulting effective pressure is an order of magnitude smaller than for the reflecting-layer analysis, and the C/H ratio is an order of magnitude higher than the solar value. The overall fit of the theoretical profiles to the observed manifold shapes is distinctly worse, especially for R(7). Scattering evidently plays only a minor role in the formation of this band along Saturn's south-central meridian.
A study is presented of the solar radiation transfer in the complete earth-atmosphere system, and numerical results are compared with satellite data obtained during the Earth Radiation Budget Experiment on Nimbus 6, in August, 1975. Emphasis is placed on the upwelling radiance distribution at the top of the atmosphere, assumed to be at 50 km. The numerical technique is based on the finite difference method, which includes azimuth and spectral variations for the entire solar wavelength range. Detailed solar properties, atmospheric physical properties, and optical properties are used. However, since the property descriptions are based on a trade-off between accuracy and computational realities, aerosol and cloud optical properties are treated with simple approximations. The radiative transfer model is in good agreement with the satellite radiance observations. The method provides a valuable tool in analyzing satellite- and ground-based radiation budget measurements and in designing instrumentation.
A method for calibrating satellite sensors (such as the AVHRR visible and NIR bands) is proposed by which the sensors are calibrated using well-known physical characteristics of the atmosphere, ocean, and deserts, as well as the digital satellite imagery. The approach, independent of ground support, used the following three phenomena: molecular scattering over the ocean for absolute visible band calibration; ocean glint, to transfer the calibration from the visible band to the NIR band; and desert reflectance to monitor, independently, the stability of the visible and NIR bands. The method was applied to NOAA-7, -9, and -11 sensors. The results of the ocean and the desert calibration methods were found to differ in the brightness range and the spectral response of the radiance source (molecular scattering over the ocean versus the desert reflectance).
Whenever a solar radiometer is used to measure direct solar radiation, some diffuse sky radiation invariably enters the detector's field of view along with the direct beam. Therefore, the atmospheric optical depth obtained by the use of Bouguer's transmission law (also called Beer-Lambert's law), that is valid only for direct radiation, needs to be corrected by taking account of the scattered radiation. This paper discusses the correction factors needed to account for the diffuse (i,e., singly and multiply scattered) radiation and the algorithms developed for retrieving aerosol size distribution from such measurements. For a radiometer with a small field of view (half-cone angle of less than 5 deg) and relatively clear skies (optical depths less than 0.4), it is shown that the total diffuse contribution represents approximately 1% of the total intensity.
The period covered by this cooperative agreement included the analysis of data from the Voyager encounter with Neptune and Triton and the primary Galileo mission to Jupiter (including the Galileo Probe entry into Jupiter's atmosphere), as well as continued work on Uranus' seasonal variability using the Voyager encounter data as a baseline.
Morphological studies of nighttime dark current data from the Nimbus 4 backscattered UV experiment indicate enhancements during the period of a full moon. The nature and magnitude of these lunar UV radiance enhancements are determined, and their potential use as a measure of nighttime ozone is considered. The data were grouped into five-day study intervals centered about each full moon sequence, and about each corresponding new moon interval. The analysis was performed in a magnetic frame of reference (McIlwain, 1961) in order to evaluate magnetospheric perturbation effects and to minimize the effects of charged energetic particle contamination or precipitation. All isolated elements showing spurious or abnormal enhancements were removed selectively (about 3%) to further screen the data. Results demonstrate the presence and uniqueness of a lunar signal, induced by atmospherically backscattered UV radiation. This signal was not sufficiently strong, however, to accurately map global nighttime ozone on the Nimbus 4 instrument.
A series of aircraft flights has been initiated to measure the spectral reflectance of ocean waters containing various concentrations of chlorophyll. The results of both the theoretical and experimental investigations indicate that satellite-borne radiometers can sense ocean color. However, the accuracy to which the chlorophyll concentration can be measured appears to be 0.1 to 0.4 mg/cu m depending upon solar zenith angles. These accuracies are less than desired by many of the oceanographers and an effort is being made to improve the quality of the chlorophyll concentration determination. Further measurements will be made in areas with higher chlorophyll concentration in order to better understand the relationship between chlorophyll concentration and ocean color. Also the effects of high water turbidity will be investigated.
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