Spherical Shell Atmosphere Research Articles

Effects of the Earth curvature on Mie-scattering radiances at high solar-sensor geometries based on Monte Carlo simulations.

Given the importance of vector radiative transfer models in ocean color remote sensing and a lack of suitable models capable of analyzing the Earth curvature effects on Mie-scattering radiances, this study presents an enhanced vector radiative transfer model for a spherical shell atmosphere geometry by the Monte Carlo method (MC-SRTM), considering the effects of Earth curvature, different atmospheric conditions, flat sea surface reflectance, polarization, high solar and sensor geometries, altitudes and wavelengths. A Monte Carlo photon transport model was employed to simulate the vector radiative transfer processes and their effects on the top-of-atmosphere (TOA) radiances. The accuracy of the MC-SRTM was verified by comparing its scalar model outputs from Henyey-Greenstein (HG) phase function with the Kattawar-Adams model results, and the mean relative differences were less than 2.75% and 4.33% for asymmetry factors (g-values) of 0.5 and 0.7, respectively. The vector mode results of MC-SRTM for a spherical shell geometry with the Mie-scattering phase matrix were compared with the PCOART-SA model results (from Polarized Coupled Ocean-Atmosphere Radiative Transfer model based on the pseudo-spherical assumption), and the mean relative differences were less than 2.67% when solar zenith angles (SZAs) > 70 ∘ and sensor viewing zenith angles (VZAs) < 60 ∘ for two aerosol models (coastal and tropospheric models). Based on the MC-SRTM, the effects of Earth curvature on TOA radiances at high SZAs and VZAs were analyzed. For pure aerosol atmosphere, the effects of Earth curvature on TOA radiances reached up to 5.36% for SZAs > 70 ∘ and VZAs < 60 ∘ and reduced to less than 2.60% for SZAs < 70 ∘ and VZAs > 60 ∘. The maximum Earth curvature effect of pure aerosol atmosphere was nearly same (10.06%) as that of the ideal molecule atmosphere. The results also showed no statistically significant differences for the aerosol-molecule mixed and pure aerosol atmospheres. Our study demonstrates that there is a need to consider the Earth curvature effects in the atmospheric correction of satellite ocean color data at high solar and sensor geometries.

Spherical vector radiative transfer model for satellite ocean color remote sensing.

Atmospheric correction is the key step for satellite ocean color remote sensing. However, most of the existing atmospheric correction algorithms do not consider the effects of Earth curvature. In fact, Earth curvature has a significant impact on satellite observation signals under large solar zenith angles or large viewing zenith angles. In this study, based on the Monte Carlo method, a vector radiative transfer model with spherical shell atmosphere geometry (hereafter our SSA-MC model) considering the influence of Earth curvature was established, which can be applied to conditions with high solar zenith angles or high viewing zenith angles. Our SSA-MC model was first compared with the Adams&Kattawar model, and the results show that the mean relative differences are 1.72%, 1.36% and 1.28% for solar zenith angles of 0 ∘, 70.47 ∘ and 84.26 ∘, respectively. Moreover, our SSA-MC model was further validated by more recently benchmarks from Korkin's scalar and vector models, and the results show that the relative differences are mostly less than 0.5% even at extremely high solar zenith angles (84.26 ∘). Then, our SSA-MC model was verified with the Rayleigh scattering radiance calculated by the look-up tables (LUTs) in SeaDAS under low-to-moderate solar or viewing zenith angles, and the results show that the relative differences are less than 1.42% when solar zenith angles are less than 70 ∘ and viewing zenith angles are less than 60 ∘. Our SSA-MC model was also compared with the Polarized Coupled Ocean-Atmosphere Radiative Transfer model based on the pseudo-spherical assumption (PCOART-SA), and the results show that the relative differences are mostly less than 2%. At last, based on our SSA-MC model, the effects of Earth curvature on Rayleigh scattering radiance were analyzed for both high solar zenith angles and high viewing zenith angles. The result shows that the mean relative error between the plane-parallel (PP) geometry and spherical shell atmosphere (SSA) geometry is 0.90% when the solar zenith angle is 60 ∘ and the viewing zenith angle is 60.15 ∘. However, the mean relative error increases with increasing solar zenith angle or viewing zenith angle. When the solar zenith angle is 84 ∘ and the viewing zenith angle is 84.02 ∘, the mean relative error is 4.63%. Thus, Earth curvature should be considered in atmospheric corrections at large solar or viewing zenith angles.

An improved pseudo spherical shell algorithm for vector radiative transfer

The radiative transfer solution in a plane-parallel geometry is a good approximation for many applications in the Earth or other planetary systems as the Earth’s radius is quite large (∼6371 km). The plane-parallel geometry is however problematic in polar regions where the solar zenith angle is usually large (>60∘) and the spherical shell effect is significant. One simple solution is the so-called pseudo-spherical shell (PSS) approximation, which treats the solar beam attenuation exactly along the nadir in the spherical shell atmosphere while keeping the plane parallel geometry for multiple scattering calculation. The PSS approximation improves the solution for intermediately large solar zenith angles, though the error is still large for large viewing zenith angles. In order to further improve the treatment of a spherical shell geometry, we have developed an improved pseudo spherical shell (IPSS) approximation. In the method, we used the following techniques: I.) The single scattering solution is solved exactly for the spherical shell atmosphere; II.) The multiple to single scattering solution ratio is solved using the plane-parallel geometry with our radiative transfer code based on successive order of scattering method; III.) The ratio of the multiple to single scattering solution is assumed to be the same for both the plane parallel and spherical shell geometry. We tested the performance of IPSS with two benchmark cases involving the Rayleigh scattering matrix. If the Rayleigh optical thickness is 0.25, the error is smaller than 1% for most of the viewing directions (<70∘). If the Rayleigh optical thickness is 1.0, the error is bounded within ±2%. The error does not show obvious dependence on the viewing zenith angle. Our newly developed IPSS scheme is highly accurate and can be used in the remote sensing applications of the polar regions.

The Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 aerosol extinction retrieval algorithm: theoretical basis

Abstract. The theoretical basis of the Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 aerosol extinction retrieval algorithm is presented. The algorithm uses an assumed bimodal lognormal aerosol size distribution to retrieve aerosol extinction profiles at 675 nm from OMPS LP radiance measurements. A first-guess aerosol extinction profile is updated by iteration using the Chahine nonlinear relaxation method, based on comparisons between the measured radiance profile at 675 nm and the radiance profile calculated by the Gauss–Seidel limb-scattering (GSLS) radiative transfer model for a spherical-shell atmosphere. This algorithm is discussed in the context of previous limb-scattering aerosol extinction retrieval algorithms, and the most significant error sources are enumerated. The retrieval algorithm is limited primarily by uncertainty about the aerosol phase function. Horizontal variations in aerosol extinction, which violate the spherical-shell atmosphere assumed in the version 1 algorithm, may also limit the quality of the retrieved aerosol extinction profiles significantly.

A new method of measuring aerosol optical properties from digital twilight photographs

Abstract. An optimal-estimation algorithm for inferring aerosol optical properties from digital twilight photographs is proposed. The sensitivity of atmospheric components and surface characteristics to brightness and color of twilight sky is investigated, and the results suggest that tropospheric and stratospheric aerosol optical thickness (AOT) are sensitive to condition of the twilight sky. The coarse–fine particle volume ratio is moderately sensitive to the sky condition near the horizon under a clean-atmosphere condition. A radiative transfer model that takes into account a spherical-shell atmosphere, refraction, and multiple scattering is used as a forward model. Error analysis shows that the tropospheric and stratospheric AOT can be retrieved without significant bias. Comparisons with results from other ground-based instruments exhibit reasonable agreement on AOT. A case study suggests that the AOT retrieval method can be applied to atmospheric conditions with varying aerosol vertical profiles and vertically inhomogeneous species in the troposphere.

AO3D: A Monte Carlo code for modeling of environmental light propagation

A Monte Carlo radiative transfer program (Atmosphere–Ocean 3-Dimensional, AO3D) for modeling the coupled atmosphere–ocean environment has been developed. The code allows for the specification of optical properties for the atmosphere, land and ocean. Light rays are tracked as they pass between the atmosphere and the ocean, reflect off the ocean surface, the ocean floor, and off land, or are absorbed. In this version the polarization of light rays is not considered. The optical properties of each horizontally homogeneous layer within the atmosphere and ocean can be set on a layer-by-layer basis with a choice of phase functions, absorption and scattering coefficients, and index of refraction. A wind-dependent Cox and Munk ocean surface realization (with whitecaps) is implemented to model refraction and reflection from surface waves. Either spherical- or flat-Earth models can be used, and all refraction and reflection are accounted for. The AO3D model has been tested by parts, and as a whole by comparison with single- and total-scattering calculations from other radiative transfer codes. Comparisons with Monte Carlo calculations by Adams and Kattawar (agreement in TOA radiance within the published precision ∼2%), MODTRAN4 (agreement in spherical-shell atmosphere (SSA) sky radiance within about 2%) and Coupled DIScrete Ordinate Radiative Transfer (COART) (agreement in plane-parallel (PP) sky radiance within 2%) are shown. Sun photometer measurements (including large air mass values) at the Mauna Loa Observatory are compared to AO3D simulations (for a spherical Earth) and suggest that a thin aerosol layer was present above the observatory at the time of the measurements.

Simulation of solar radiation during a total eclipse: a challenge for radiative transfer

Abstract. A solar eclipse is a rare but spectacular natural phenomenon and furthermore it is a challenge for radiative transfer modelling. Whereas a simple one-dimensional radiative transfer model with reduced solar irradiance at the top of the atmosphere can be used to calculate the brightness during partial eclipses a much more sophisticated model is required to calculate the brightness (i.e. the diffuse radiation) during the total eclipse. The reason is that radiation reaching a detector in the shadow gets there exclusively by horizontal transport of photons in a spherical shell atmosphere, which requires a three-dimensional radiative transfer model. In this study the first fully three-dimensional simulations for a solar eclipse are presented exemplified by the solar eclipse at 29 March 2006. Using a backward Monte Carlo model we calculated the diffuse radiation in the umbra and simulated the changing colours of the sky. Radiance and irradiance are decreased by 3 to 4 orders of magnitude, depending on wavelength. We found that aerosol has a comparatively small impact on the radiation in the umbra. We also estimated the contribution of the solar corona to the radiation under the umbra and found that it is negligible compared to the diffuse solar radiation in the wavelength region from 310 to 500 nm.

McSCIA: application of the Equivalence Theorem in a Monte Carlo radiative transfer model for spherical shell atmospheres

Abstract. A new multiple-scattering Monte Carlo 3-D radiative transfer model named McSCIA (Monte Carlo for SCIAmachy) is presented. The backward technique is used to efficiently simulate narrow field of view instruments. The McSCIA algorithm has been formulated as a function of the Earth's radius, and can thus perform simulations for both plane-parallel and spherical atmospheres. The latter geometry is essential for the interpretation of limb satellite measurements, as performed by SCIAMACHY on board of ESA's Envisat. The model can simulate UV-vis-NIR radiation. First the ray-tracing algorithm is presented in detail, and then successfully validated against literature references, both in plane-parallel and in spherical geometry. A simple 1-D model is used to explain two different ways of treating absorption. One method uses the single scattering albedo while the other uses the equivalence theorem. The equivalence theorem is based on a separation of absorption and scattering. It is shown that both methods give, in a statistical way, identical results for a wide variety of scenarios. Both absorption methods are included in McSCIA, and it is shown that also for a 3-D case both formulations give identical results. McSCIA limb profiles for atmospheres with and without absorption compare well with the one of the state of the art Monte Carlo radiative transfer model MCC++. A simplification of the photon statistics may lead to very fast calculations of absorption features in the atmosphere. However, these simplifications potentially introduce biases in the results. McSCIA does not use simplifications and is therefore a relatively slow implementation of the equivalence theorem.

Light scattering from the spherical‐shell atmosphere: Earth curvature effects measured by SeaWiFS

It is commonly known that the Earth's atmosphere is a spherical‐shell atmosphere (SSA) rather than a plane‐parallel atmosphere (PPA). Thus, the light scattered by the Earth's atmosphere is governed by physics of the radiative transfer equation (RTE) with proper boundary conditions in the SSA system. In satellite and aircraft remote sensing, however, the PPA model is usually assumed to compute the lookup tables and convert the sensor‐measured signals to the desired physical and optical quantities.The PPA assumption is a simple yet very good approximation for solar and sensor zenith angles &lt; ∼80°. Note that the solar and sensor zenith angles here are defined as a measure at the local surface. In the PPA assumption, however, the solar zenith angles ≥90° is not defined. When the solar zenith angles ≥90° in the PPA system; i.e., when the Sun is below the horizon, there will be no light scattered out to the top of the atmosphere (TOA) or at the bottom of the surface. We would experience complete darkness in this situation.

A vector radiative-transfer model for the Odin/OSIRIS project

A vector radiative-transfer code has been developed that is able to accurately and efficiently calculate radiance and polarization scattered from Earth's limb. A primary application of this code will be towards generating weighting functions, based on calculated limb radiances, for the retrieval of trace gases (O3, NO2, BrO, OClO, and O4) from the optical spectrograph and infrared imaging system (OSIRIS). OSIRIS is a UV–visible instrument on board the Odin satellite that measures limb-scattered light. This model solves the vector radiative-transfer equation using an iterative technique simultaneously in both plane-parallel and spherical-shell atmospheres. OSIRIS simulated limb radiance and polarization and OSIRIS weighting functions are presented along with a discussion of the numerical solution parameters, model intercomparisons and timings, and necessary model improvements. Overall agreement with other models was found to be very good and model speed is comparable to a fast finite-difference code. A set of OSIRIS reference atmospheres have been compiled for use with radiative-transfer models. Each of the 216 atmospheres (18 latitudes × 12 months) include profiles of air, pressure, temperature, ozone, NO2, BrO, and stratospheric aerosols.PACS Nos.: 42.68-w, 94.10Gb

A pseudo three‐dimensional resonance line radiative transfer model with overlapping lines

A description of a resonance line Feautrier radiative transfer (RT) code which allows for coupling between closely spaced emission lines is presented. This code has been used to model closely spaced H and D Lyman α 1215.67 Å and 1215.34 Å emission lines, respectively, in the Jovian thermosphrre. There is no direct interaction between these lines, but coupling and energy transfer may occur as the Voigt broadened lines overlap. The RT method is pseudo three‐dimensional in that a spherical shell atmosphere is accounted for in direct solar beam scattering but with one‐dimensional (1‐D) plane‐parallel multiple scattering. In addition, allowance is made for a varying solar zenith angle along the line of sight in calculating intensities. Using a model atmosphere for thermospheric D and H produced by a 1‐D photochemical‐diffusion model, we present results illustrating the relative importance of including coupling of H and D Lyman α emission lines in radiative transfer calculations for both the disk and limb of Jupiter. These results suggest that the spectral contrast between the H and D Lyman α features is reduced in long limb path geometries and that the disk measurement provides better detection possibilities.

Combined differential‐integral approach for the radiation field computation in a spherical shell atmosphere: Nonlimb geometry

A new combined differential‐integral approach (CDI) has been developed, which is more accurate than commonly used pseudospherical models but not so complicated and computer time‐consuming as a fully spherical model. The radiative transfer equation is solved in its integral form. The multiple‐scattering source function is obtained by solving the integrodifferential radiative transfer equation in a pseudospherical atmosphere. Relative differences between the new model and the pseudospherical model for a variety of solar zenith angles, viewing angles, and azimuth angles for a set of wavelengths are presented. Furthermore, the GDI model is compared with a Gauss‐Seidel spherical model (GSS) and with MODTRAN. The difference between GDI and GSS is found to be less than 2% and between GDI and MODTRAN up to 12%.

Multiple scattering radiance in limb‐viewing geometry

At present, satellite‐based limb‐viewing measurements in near‐UV, visible, and near‐IR wavelength range are based on the attenuation of direct solar light (the Stratospheric Aerosol and Gas Experiment instruments). This paper studies a new technique: the measurement of backscattered solar radiance spectrum in limb‐viewing geometry. A multiple‐scattering backward Monte Carlo algorithm “Siro” has been constructed for realistic radiative transfer modeling of these measurements. By Monte Carlo simulation the difficult spherical geometry of limb‐viewing can be accurately modeled, as can constituent densities and boundary conditions that vary in three dimensions. Previous multiple‐scattering models applicable to limb‐viewing all assume a spherical shell atmosphere. The backward technique is very efficient for simulating a receiver that has a narrow field of view. In this paper the role of multiple scattering is studied by the Siro model in an atmosphere including scattering by molecules and aerosols and absorption by O3. Simulations show that the multiple to total scattering ratio increases from almost zero at 300 nm to ∼5–60% at visible and near‐IR wavelengths (depending on solar geometry and albedo of Earth's surface). A single‐scattering model is not sufficient for the analysis of limb radiance measurements. When the solar zenith angle is small, limb radiance is very sensitive to the surface albedo. A bright spot of diameter 50 km on an otherwise dark surface already causes a noticeable increase of intensity.

Atmospheric correction of ocean-color sensors: effects of the Earth’s curvature

We investigate the influence of the curvature of the Earth on a proposed atmospheric-correction scheme for the Sea-Viewing Wide-Field-of-View Sensor (SeaWiFS) by simulating the radiance exiting the top of a spherical-shell atmosphere and inserting the result into the proposed correction algorithm. The error in the derived water-leaving reflectance suggests that the effects of the curvature are negligible for solar zenith angles (θ(0)) ≤ 70°. Furthermore, for θ(0) > 70° the error in atmospheric correction can usually be reduced if the molecular-scattering component of the top of the atmosphere reflectance (ρ(r)) is computed with a spherical-shell atmosphere radiative transfer code. Also, for θ(0) > 70° the error in atmospheric correction in a spherical-shell atmosphere, when ρ(r) is computed with a spherical-shell model, can be predicted reasonably well from computations made with plane-parallel atmosphere radiative transfer codes. This implies that studies aimed at improving atmospheric correction can be made assuming plane-parallel geometry and that the investigator can be confident when θ(0)> 70° that any improvements will still be valid for a spherical-shell atmosphere as long as ρ(r) is computed in spherical-shell geometry. Finally, a scheme for computing ρ(r) in a spherical-shell atmosphere in a relatively simple manner is developed.

Numerical technique for solving the radiative transfer equation for a spherical shell atmosphere

A method for numerically solving the equation of radiative transfer in a spherical shell atmosphere is presented. The method uses a conical boundary and a Gauss-Seidel iteration scheme to solve for all orders of scattering along a single radial line in the atmosphere. Tests of the model indicate an accuracy better than 1% for most Earth-atmosphere situations. Results from this model are compared with flat-atmosphere model results for a scattering-only atmosphere. These comparisons indicate that excluding spherical effects for solar zenith angles greater than 85° leads to errors larger than 5% at optical depths as small as 0.10.

High altitude Venus haze from Pioneer Venus limb scans

High vertical resolution scans of the Venus limb made by the Pioneer Venus Orbiter Cloud Photopolarimeter at 365 nm and 690 nm wavelengths are used to investigate the level of the haze top, and haze particle properties and scale height. Haze particle vertical optical depth 0.01 occurs at altitude 80 to 85 km based on knowledge of instrument pointing. The lowest haze tops were observed close to subsolar longitudes but the data set supports a longitude dependence no more than a temporal variation. Single scattering computations for a spherical shell atmosphere show good agreement with observed intensities for particles smaller than 0.3 μm radius and refractive index less than 1.7, consistent with, but not limited to, concentrated sulfuric acid. Particle scale height in the 0.5 to 2 mbar pressure regions varies between 1 and 3 km over the season (12 of 92 days), latitude (15–45°N), and local time (0900–1800) ranges of the observations. Detached layers of haze are sometimes present. An average particle scale height of 2.2 km at 84 km altitude yields an eddy diffusion coefficient of 1.3 × 10 5 cm 2 sec −1.

Vertical transport and photochemistry in the terrestrial mesosphere and lower thermosphere (50–120 km)

The coupled effects of kinetics, solar cycle flux variations and vertical transport on the distribution of long‐lived hydrogen‐carbon‐oxygen compounds in the terrestrial mesosphere and lower thermosphere are studied using a one‐dimensional aeronomy model. The calculations account for the important chemical reactions and use rocket measurements of the solar flux at solar minimum and maximum. Photodissociation rates appropriate for the mesosphere are determined with a spherical shell atmosphere formalism; detailed corrections for the O2 Schumann‐Runge bands and the temperature dependence of the CO2 cross sections are used. Then an eddy diffusion profile is derived which gives agreement with the Aladdin 74 mass spectral measurements of atomic O, O2, CO2, and Ar in the lower thermosphere and observations of the O3 minimum at ∼80 km. The 115 GHz CO radio emission line computed for the CO mixing ratio profile predicted with the new eddy diffusion profile compares well with recent observations of W. J. Wilson. Differences between the calculated CO mixing ratio profile and previous theoretical and observational determinations are discussed. Our derived eddy diffusion profile has a sudden decrease at 92 km which is necessary to produce the atomic O peak at 98 km that appears in the Aladdin 74 measurements. This stagnant region apparently is a recurrent or persistent feature of the upper atmosphere since an atomic O peak around 98 km has been seen by different techniques in different seasons over several years. Slow eddy diffusion in the lower thermosphere through the homopause was also the conclusion of earlier Ar/N2 rocket measurements studies. The analytic approach of this paper could be used in the future to monitor variations in middle atmosphere dynamics, if regularly conducted simultaneous observations of various groups of species were available.

Radiative transfer in spherical shell atmospheres: II. Asymmetric phase functions

In this paper we investigate the effects of sphericity on the radiation reflected from a planet with a homogeneous, conservative scattering atmosphere of optical thicknesses of 0.25 and 1.0. We considered a Henyey-Greenstein phase function with asymmetry factors of 0.5 and 0.7. Significant differences were found when these results were compared with the plane-parallel calculations. Also, large violations of the reciprocity theorem, which is only true for plane-parallel calculations, were noted. Results are presented for the radiance versus height distributions as a function of planetary phase angle. These results will be useful to researchers in the field of remote sensing and planetary spectroscopy.

Monte Carlo Studies of the Sky Radiation at Twilight

Results are presented in several wavelengths of the sky intensity and polarization along the solar vertical at twilight, as calculated using the backward Monte Carlo method applied to spherical shell atmospheres. Molecular scattering with anisotropy of molecules, ozone absorption, and refraction are taken into account. The dependence of the intensity on the solar depression angle is in general agreement with calculations based upon single plus second order scattering, but the degree of polarization is much higher. It is verified that the molecular plus ozone atmosphere does not explain the purple light. The elongation of the Babinet neutral point from the sun is determined as a function of solar depression angle.

Backward Monte Carlo Calculations of the Polarization Characteristics of the Radiation Emerging from Spherical-Shell Atmospheres

A Monte Carlo procedure, designated as FLASH, was developed for use in computing the intensity and polarization of the radiation emerging from spherical-shell atmospheres and is especially useful for investigating the sunlit sky at twilight time. The procedure utilizes the backward Monte Carlo method and is capable of computing the Stokes parameters for discrete directions at the receiver position. Both molecular and aerosol scattering are taken into account as well as ozone, aerosol, water vapor, and carbon dioxide absorption within the atmosphere. The curvature of the light path due to the changing index of refraction with altitude is taken into account. Some comparisons are made between FLASH calculations for a pure Rayleigh atmosphere, a combined Rayleigh and aerosol atmosphere, and calculations reported by other authors for plane-parallel atmospheres. The comparisons show that the FLASH calculations for spherical-shell atmospheres are in good agreement with those for plane-parallel atmospheres within the range of zenith angles for which no differences could be attributed to the difference in the geometries of the two atmospheric models.