Cosine Of Zenith Angle Research Articles

Inversion method of target gas cloud transmittance based on atmospheric profile synthesis background

The sky infrared background radiation varies greatly with spatial distribution and time. When scanning Fourier transform infrared remote sensing imaging system scans the target gas cloud with the sky as the background, the background radiation corresponding to each scanned pixel is different, and the background does not have a constant baseline. It is extremely difficult to obtain the background spectrum of each pixel in real time, which affects the inversion accuracy of the target gas cloud transmittance. An inversion method of target gas cloud transmittance based on atmospheric profile synthesis background is proposed in this work. The temperature, humidity, pressure, and ozone profiles of the measured locations and the atmospheric model are used to generate the sky infrared background in order to solve the problem, i.e. the difficulty in measuring the clean sky infrared background spectrum in the chemical industry park. This paper proposes that there is a continuous derivable relationship between the sky infrared background spectrum and the cosine of zenith angle at each wavenumber, so a small amount of sky infrared background spectrum with a zenith angle gradient can quickly generate a sky infrared background spectrum at any elevation angle. The proposed method is verified by the moderate resolution atmospheric radiative transfer model (MODTRAN) software simulation and the remote sensing imaging experiment of SF<sub>6</sub> gas. The proposed method can quickly generate the sky infrared background spectrum corresponding to any angle within a gradient elevation angle and accurately invert the target gas cloud transmittance at each pixel. The results show that the distribution trend of the column concentration of the SF<sub>6</sub> gas cloud is consistent with the actual distribution, and the correlation is 0.99979.

Estimating Photosynthetically Active Radiation Intercepted by Almond and Walnut Trees using UAV-Captured Aerial Images and Solar Zenith Angle

Highlights Measurement of canopy light interception data using a ground-based mobile system. Using UAV-captured aerial images and zenith angle to estimate canopy light interception at different times of the day. Identifying boundaries of individual trees using the maximum likelihood estimator and the watershed algorithm. Abstract. Photosynthetically Active Radiation (PAR) absorbed by the leaves is a key piece of information to study the crop response to environmental conditions that could be used to estimate crop production potential. Canopies in a commercial orchard present differences in their capability to intercept light mainly due to the spatial variability in canopy development. There is a need for developing tools that could capture spatial variability in PAR interception to predict potential yield. Unmanned Aerial Vehicles (UAV) present an interesting alternative to provide this information, as they cover a larger area than ground-based systems in a shorter period with high spatial resolution. The objective of this study was to determine the relationship between the shadow of a tree derived from a ground-based canopy light interception scan obtained using a lightbar mounted on a mobile platform and that acquired from UAV Red-Green-Blue (RGB) images. Information acquired by an UAV was classified to separate canopy from its shadow, grass and sunlit soil using maximum likelihood estimator. Boundaries of individual trees were identified based on their positions using watershed transform algorithm. The relationship between canopy PAR interception data, sun angle in the sky (zenith angle), and the information derived from aerial images was analyzed. Coefficient of determination (R2) values of 0.92 and 0.88 were found for the multiple linear regression between PAR, the shadow area and the cosine of zenith angle obtained for almond and walnut crops, respectively. Moreover, R2 values of 0.81 and 0.86 were found for the relationship between the shadow’s area obtained underneath the canopy and the shadow’s area obtained from the UAV images and the cosine of the zenith angle for almond and walnut crops, respectively. The results show that the PAR interception can be estimated using the zenith angle and the area of the shadow, which can be obtained from a RGB aerial image. Keywords: Almond, Canopy segmentation, Image classification, PAR interception, Shadow area, UAV, Walnut.

15-digit accuracy calculations of Chandrasekhar’s H $H$ -function for isotropic scattering by means of the double exponential formula

This work shows that it is possible to calculate numerical values of the Chandrasekhar $H$-function for isotropic scattering at least with 15-digit accuracy by making use of the double exponential formula (DE-formula) of Takahashi and Mori (Publ. RIMS, Kyoto Univ. Vol. 9, 721, 1974) instead of the Gauss-Legendre quadrature employed in the numerical scheme of Kawabata and Limaye (Astrophys. Space Sci. Vol. 332, 365, 2011) and simultaneously taking a precautionary measure to minimize the effects due to loss of significant digits particularly in the cases of near-conservative scattering and/or errors involved in returned values of library functions supplied by compilers in use. The results of our calculations are presented for 18 selected values of single scattering albedo $\varpi_0$ and 22 values of an angular variable $\mu$, the cosine of zenith angle $\theta$ specifying the direction of radiation incident on or emergent from semi-infinite media.

An evolutionary artificial neural network ensemble model for estimating hourly direct normal irradiances from meteosat imagery

A new evolutionary design of an ANN (artificial neural network) ensemble model is developed to generate hourly DNI (direct normal irradiance) estimates. The procedure combines a genetic algorithm for selecting the best inputs with an ANN ensemble method. The ensemble model was calibrated and evaluated using three years of Meteosat-9 images and data measured at 28 high-quality ground stations over an extensive area, mainly in Europe. The most valuable inputs for DNI estimation are shown to be the following: all Meteosat-9 channels except ch08 and ch11; relative air mass m, integral Rayleigh optical thickness δr, extraterrestrial global irradiance G0, beam clear-sky index Bcs, and the cosine of zenith angle θ. No additional atmospheric information such as turbidity, aerosol optical depth or water vapor content are required for the model. Ensemble estimates were nearly unbiased (MBE = 1.98%) and overall RMSE (root mean square error) was 24.29% across an independent spatial and temporal dataset. This represents an improvement of 35% over other common methods for estimating DNI. The estimates were reasonably reliable in all seasons, and were more accurate in clear-sky conditions.

New models to compute solar global hourly irradiation from point cloudiness

The Kasten–Czeplak (KC) model [16] is tested against data measured in five meteorological stations covering the latitudes and longitudes of Romania (South-Eastern Europe). Generally, the KC cloudy sky model underestimates the measured values. Its performance is (marginally) good enough for point cloudiness C=0–1. The performance is good for skies with few clouds (C<0.3), good enough for skies with medium amount of clouds (C=0.3–0.7) and poor on very cloudy and overcast skies. New very simple empirical cloudy sky models are proposed. They bring two novelties in respect to KC model. First, new basic clear sky models are used, which evaluate separately the direct and diffuse radiation, respectively. Second, some of the new models assume the atmospheric transmission factor is a nonlinear function of the cosine of zenith angle Z. The performance of the new models is generally better than that of the KC model, for all cloudiness classes. One class of models (called S4) has been further tested. The sub-model S4TOT has been obtained by fitting the generic model S4 to all available data, for all stations. Generally, S4TOT has good accuracy in all stations, for low and intermediate cloudy skies (C<0.7). The accuracy of S4TOT is good and good enough at intermediate zenith angles (Z=30–70°) but worse for small and larger zenith angles (Z=0–30° and Z=70–85°, respectively). Several S4 sub-models were tested in stations different from the origin station. Almost all sub-models have good or good enough performance for skies with low and intermediate cloud amount (C=0–0.7) and when all available data are considered (C=0–1).

Generalization of Marshak boundary condition for non-Lambert reflection

In this paper we generalize the Marshak lower boundary condition in the method of spherical harmonics (MSH) for an arbitrary law of surface reflection. The obtained analytical solution is based on the bilinear interpolation of surface bidirectional reflection distribution function (BRDF). Recurrent formulas presented here allow to avoid numeric integration and calculate matrices of boundary conditions for arbitrary orders of azimuthal and Legendgre polynomial expansions of MSH. For practical applications, we have studied the effect of discretization of the BRDF angular grid on the accuracy of calculation of reflected diffuse radiance. Simulations conducted for a large number of vegetative covers, soils and sand, show that an accuracy of 0.2% can be achieved with M=11 azimuthal harmonics at N=21 grid knots in cosine of zenith angle. Calculations over a ruffled water surface are much more demanding. For wind speed v≥10 m/ s , an accuracy of 0.2% requires discretization of M≥40, N≥51.

Influence of humidity on the aerosol scattering coefficient and its effect on the upwelling radiance during ACE-2

Aerosol scattering coefficients (σsp) have been measured over the ocean at different relative humidities (RH) as a function of altitude in the region surrounding the Canary Islands during the Second Aerosol Characterization Experiment (ACE-2) in June and July 1997. The data were collected by the University of Washington passive humidigraph (UWPH) mounted on the Pelican research aircraft. Concurrently, particle size distributions, absorption coefficients and aerosol optical depth were measured throughout 17 flights. A parameterization of σsp as a function of RH was utilized to assess the impact of aerosol hydration on the upwelling radiance (normalized to the solar constant and cosine of zenith angle). The top of the atmosphere radiance signal was simulated at wavelengths corresponding to visible and near-infrared bands of the EOS-AM )“Terra” (detectors, MODIS and MISR. The UWPH measured σsp at 2 RHs, one below and the other above ambient conditions. Ambient σsp was obtained by interpolation of these 2 measurements. The data were stratified in terms of 3 types of aerosols: Saharan dust, clean marine (marine boundary layer background) and polluted marine aerosols (i.e., 2- or 1-day old polluted aerosols advected from Europe). An empirical relation for the dependence of σsp on RH, defined by σsp(RH)=k. (1−RH/100)−γ, was used with the hygroscopic exponent γ derived from the data. The following γ values were obtained for the 3 aerosol types: γ(dust)=0.23±0.05, γ(clean marine)= 0.69±0.06 and γ(polluted marine)=0.57±0.06. Based on the measured γ's, the above equation was utilized to derive aerosol models with different hygroscopicities. The satellite simulation signal code 6S was used to compute the upwelling radiance corresponding to each of those aerosol models at several ambient humidities. For the pre-launch estimated precision of the sensors and the assumed viewing geometry of the instrument, the simulations suggest that the spectral and angular dependence of the reflectance measured by MISR is not sufficient to distinguish aerosol models with various different combinations of values for dry composition, γ and ambient RH. A similar behavior is observed for MODIS at visible wavelengths. However, the 2100 nm band of MODIS appears to be able to differentiate between at least same aerosol models with different aerosol hygroscopicity given the MODIS calibration error requirements. This result suggests the possibility of retrieval of aerosol hygroscopicity by MODIS.