Engineering topics

Loeb, N. G.

Publications and source records attributed to Loeb, N. G..

At least 19 records

NASA NTRS2015

On the Relative Stability of CERES Reflected Shortwave and MISR and MODIS Visible Radiance Measurements During the Terra Satellite Mission

Fifteen years of visible, near-infrared, and broadband shortwave radiance measurements from Clouds and the Earth's Radiant Energy System (CERES), Multiangle Imaging Spectroradiometer (MISR), and Moderate Resolution Imaging Spectroradiometer (MODIS) instruments on board NASA's Terra satellite are analyzed in order to assess their long-term relative stability for climate purposes. A regression-based approach between CERES, MODIS, and MISR (An camera only) reflectances is used to calculate the bias between the different reflectances relative to a reference year. When compared to the CERES shortwave broadband reflectance, relative drift between the MISR narrowbands is within 1%/decade. Compared to the CERES shortwave reflectance, the MODIS narrowband reflectances show a relative drift of less than −1.33%/decade. When compared to MISR, the MODIS reflectances show a relative drift of between −0.36%/decade and −2.66%/decade. We show that the CERES Terra SW measurements are stable over the time period relative to CERES Aqua. Using this as evidence that CERES Terra may be absolutely stable, we suggest that the CERES, MISR, and MODIS instruments meet the radiometric stability goals for climate applications set out in Ohring et al. (2005).

Corbett, J. G.↗

NASA NTRS2011

Clouds and Earth Radiant Energy System (CERES), a Review: Past, Present and Future

The Clouds and Earth Radiant Energy System (CERES) project s objectives are to measure the reflected solar radiance (shortwave) and Earth-emitted (longwave) radiances and from these measurements to compute the shortwave and longwave radiation fluxes at the top of the atmosphere (TOA) and the surface and radiation divergence within the atmosphere. The fluxes at TOA are to be retrieved to an accuracy of 2%. Improved bidirectional reflectance distribution functions (BRDFs) have been developed to compute the fluxes at TOA from the measured radiances with errors reduced from ERBE by a factor of two or more. Instruments aboard the Terra and Aqua spacecraft provide sampling at four local times. In order to further reduce temporal sampling errors, data are used from the geostationary meteorological satellites to account for changes of scenes between observations by the CERES radiometers. A validation protocol including in-flight calibrations and comparisons of measurements has reduced the instrument errors to less than 1%. The data are processed through three editions. The first edition provides a timely flow of data to investigators and the third edition provides data products as accurate as possible with resources available. A suite of cloud properties retrieved from the MODerate-resolution Imaging Spectroradiometer (MODIS) by the CERES team is used to identify the cloud properties for each pixel in order to select the BRDF for each pixel so as to compute radiation fluxes from radiances. Also, the cloud information is used to compute radiation at the surface and through the atmosphere and to facilitate study of the relationship between clouds and the radiation budget. The data products from CERES include, in addition to the reflected solar radiation and Earth emitted radiation fluxes at TOA, the upward and downward shortwave and longwave radiation fluxes at the surface and at various levels in the atmosphere. Also at the surface the photosynthetically active radiation and ultraviolet radiation (total, UVA and UVB) are computed. The CERES instruments aboard the Terra and Aqua spacecraft have served well past their design life times. A CERES instrument has been integrated onto the NPP platform and is ready for launch in 2011. Another CERES instrument is being built for launch in 2014, and plans are being made for a series of follow-on missions.

Smith, G. L.↗

NASA NTRS2004

Light Scattering by an Infinite Circular Cylinder Immersed in an Absorbing Medium

Analytic solutions are developed for the single-scattering properties of an infinite dielectric cylinder embedded in an absorbing medium with normal incidence, which include extinction, scattering and absorption efficiencies, the scattering phase function, and the asymmetry factor. The extinction and scattering efficiencies are derived by the near-field solutions at the surface of the particle. The normalized scattering phase function is obtained by use of the far-field approximation. Computational results show that while the absorbing medium significantly reduces the scattering efficiency, it has little effect on absorption efficiency. The absorbing medium can significantly change the conventional phase function. The absorbing medium also strongly affects the polarization of the scattered light. However, for large absorbing particles the degrees of polarization change little with the medium s absorption. This implies that if the transmitting lights are strongly weakened inside the particle the scattered polarized lights can be used to identify objects even when the absorption property of the host medium is unknown, which is very important for both active and passive remote sensing.

Sun, W.↗

NASA NTRS2004

On the Retrieval of Ice Cloud Particle Shapes from POLDER Measurements

Shapes of ice crystals can significantly affect the radiative transfer in ice clouds. The angular distribution of the polarized reflectance over ice clouds strongly depends on ice crystal shapes. Although the angular-distribution features of the total or polarized reflectance over ice clouds implies a possibility of retrieving ice cloud particle shapes by use of remote sensing data, the accuracy of the retrieval must be evaluated. In this study, a technique, which applies single ice crystal habit and multidirectional polarized radiance to retrieve ice cloud particle shapes, is assessed. Our sensitivity studies show that the retrieved particle shapes &om this algorithm can be considered good approximations to those in actual clouds in calculation of the phase matrix elements. Although a fractal poly-crystal shape or an inhomogeneous hexagonal column may also produce this type of phase functions, more representative single-scattering properties from combinations of natural particle shapes and size distributions may still be necessary in accurate retrieval of other cloud properties such as optical thickness and particle size.

Sun, W.↗

NASA NTRS2004

Light Scattering by Coated Sphere Immersed in Absorbing Medium: A Comparison between the FDTD and Analytic Solutions

A recently developed finite-difference time domain scheme is examined using the exact analytic solutions for light scattering by a coated sphere immersed in an absorbing medium. The relative differences are less than 1% in the extinction, scattering, and absorption efficiencies and less than 5% in the scattering phase functions. The definition of apparent single-scattering properties is also discussed. (C) 2003 Elsevier Ltd. All rights reserved.

Sun, W.↗

NASA NTRS2004

Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Terra Satellite: Methodology - Part 1

The Clouds and Earth's Radiant Energy System (CERES) provides coincident global cloud and aerosol properties together with reflected solar, emitted terrestrial longwave and infrared window radiative fluxes. These data are needed to improve our understanding and modeling of the interaction between clouds, aerosols and radiation at the top of the atmosphere, surface, and within the atmosphere. This paper describes the approach used to estimate top-of-atmosphere (TOA) radiative fluxes from instantaneous CERES radiance measurements on the Terra satellite. A key component involves the development of empirical angular distribution models (ADMs) that account for the angular dependence of Earth's radiation field at the TOA. The CERES Terra ADMs are developed using 24 months of CERES radiances, coincident cloud and aerosol retrievals from the Moderate Resolution Imaging Spectroradiometer (MODIS), and meteorological parameters from the Global Modeling and Assimilation Office (GMA0) s Goddard Earth Observing System DAS (GEOS-DAS V4.0.3) product. Scene information for the ADMs is from MODIS retrievals and GEOS-DAS V4.0.3 properties over ocean, land, desert and snow, for both clear and cloudy conditions. Because the CERES Terra ADMs are global, and far more CERES data is available on Terra than was available from CERES on the Tropical Rainfall Measuring Mission (TRMM), the methodology used to define CERES Terra ADMs is different in many respects from that used to develop CERES TRMM ADMs, particularly over snow/sea-ice, under cloudy conditions, and for clear scenes over land and desert.

Loeb, N. G.↗

NASA NTRS2004

Examination of Surface Roughness on Light Scattering by Long Ice Columns by Use of a Two-Dimensional Finite-Difference Time-Domain Algorithm

Natural particles such as ice crystals in cirrus clouds generally are not pristine but have additional micro-roughness on their surfaces. A two-dimensional finite-difference time-domain (FDTD) program with a perfectly matched layer absorbing boundary condition is developed to calculate the effect of surface roughness on light scattering by long ice columns. When we use a spatial cell size of 1/120 incident wavelength for ice circular cylinders with size parameters of 6 and 24 at wavelengths of 0.55 and 10.8 mum, respectively, the errors in the FDTD results in the extinction, scattering, and absorption efficiencies are smaller than similar to 0.5%. The errors in the FDTD results in the asymmetry factor are smaller than similar to 0.05%. The errors in the FDTD results in the phase-matrix elements are smaller than similar to 5%. By adding a pseudorandom change as great as 10% of the radius of a cylinder, we calculate the scattering properties of randomly oriented rough-surfaced ice columns. We conclude that, although the effect of small surface roughness on light scattering is negligible, the scattering phase-matrix elements change significantly for particles with large surface roughness. The roughness on the particle surface can make the conventional phase function smooth. The most significant effect of the surface roughness is the decay of polarization of the scattered light.

Sun, W.↗

NASA NTRS2004

Top-of-Atmosphere Shortwave Broadband Observed Radiance and Estimated Irradiance over Polar Regions from Clouds and the Earth's Radiant Energy System (CERES) Instruments on Terra

Empirical angular distribution models for estimating top-of-atmosphere shortwave irradiances from radiance measurements over permanent snow, fresh snow and sea ice are developed using CERES measurements on Terra. Permanent snow angular distribution models depend on cloud fraction, cloud optical thickness, and snow brightness. Fresh snow and sea ice angular distribution models depend on snow and sea ice fraction, cloud fraction, cloud optical thickness, and snow and ice brightness. These classifications lead to 10 scene types for permanent snow and 25 scene types for fresh snow and sea ice. The average radiance over clear-sky permanent snow is more isotropic with satellite viewing geometry than that over overcast permanent snow. On average, the albedo of clear-sky permanent snow varies from 0.65 to 0.68 for solar zenith angles between 60$logical and\circ$ and 80 deg, while the corresponding albedo of overcast scenes varies from 0.70 to 0.73. Clear-sky permanent snow albedos over Antarctica estimated from two independent angular distribution models are consistent to within 0.6%, on average. Despite significant variability in sea ice optical properties with season, the estimated mean relative albedo error is -1 % for very dark sea ice and 0.1% for very bright sea ice when albedos derived from different viewing angles are averaged. The estimated regional root-mean-square (RMS) relative albedo error is 5.6% and 2.6% when the sea ice angular distribution models are applied to a region that contains very dark and very bright sea ice, respectively. Similarly, the estimated relative albedo bias error for fresh snow is -0.1% for very dark snow.

Kato, S.↗

NASA NTRS2004

Top-of-Atmosphere Direct Radiative Effect of Aerosols over Global Oceans from Merged CERES and MODIS Observations

The direct radiative effect of aerosols (DREA) is defined as the difference between radiative fluxes in the absence and presence of aerosols. In this study, the direct radiative effect of aerosols is estimated for 46 months (March, 2000 to December, 2003) of merged CERES and MODIS Terra global measurements over ocean. This analysis includes the contribution from clear regions in both clear and partly cloudy CERES footprints. MODIS-CERES narrow-to-broadband regressions are developed to convert clear-sky MODIS narrowband radiances to broadband SW radiances, and CERES clear-sky Angular Distribution Models (ADMs) are used to estimate the corresponding TOA radiative fluxes needed to determine the DREA. Clear-sky MODIS pixels are identified using two independent cloud masks: (i) the NOAA-NESDIS algorithm used for inferring aerosol properties from MODIS on the CERES Single Scanner Footprint TOA/Surface Fluxes and Clouds (SSF) product (NOAA-SSF); and (ii) the standard algorithm used by the MODIS aerosol group to produce the MODO4 product (MODO4). Over global oceans, direct radiative cooling by aerosols for clear scenes identified from MODO4 is estimated to be 5.5 W m-2, compared to 3.8 W m-2 for clear scenes from NOAA-SSF. Regionally, differences are largest in areas affected by dust aerosol, such as oceanic regions adjacent to the Saharan and Saudi Arabian deserts, and in northern Pacific Ocean regions influenced by dust transported from Asia. The net total-sky (clear and cloudy) DREA is negative (cooling) and is estimated to be -2.0 W m-2 from MOD04, and -1.6 W m-2 from NOAA-SSF. The DREA is shown to have pronounced seasonal cycles in the Northern Hemisphere and large year-to-year fluctuations near deserts. However, no systematic trend in deseasonalized anomalies of the DREA is observed over the 46-month time series considered.

Loeb, N. G.↗

NASA NTRS2004

2004: Finite-Difference Time Domain Solution of Light Scattering by an Infinite Dielectric Column Immersed in an Absorbing Medium

The two-dimensional (2-D) finite-difference time domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions, extinction and absorption efficiencies, are derived using an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approx .1%. The errors in the scattering phase functions are typically smaller than approx .4%. Using the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.

Sun, W.↗

NASA NTRS2003

Light Scattering by Gaussian Particles: A Solution with Finite-Difference Time Domain Technique

The understanding of single-scattering properties of complex ice crystals has significance in atmospheric radiative transfer and remote-sensing applications. In this work, light scattering by irregularly shaped Gaussian ice crystals is studied with the finite-difference time-domain (FDTD) technique. For given sample particle shapes and size parameters in the resonance region, the scattering phase matrices and asymmetry factors are calculated. It is found that the deformation of the particle surface can significantly smooth the scattering phase functions and slightly reduce the asymmetry factors. The polarization properties of irregular ice crystals are also significantly different from those of spherical cloud particles. These FDTD results could provide a reference for approximate light-scattering models developed for irregular particle shapes and can have potential applications in developing a much simpler practical light scattering model for ice clouds angular-distribution models and for remote sensing of ice clouds and aerosols using polarized light. (copyright) 2003 Elsevier Science Ltd. All rights reserved.

Sun, W.↗

NASA NTRS2003

Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Tropical Rainfall Measuring Mission Satellite: Validation - Part II

Top-of-atmosphere (TOA) radiative fluxes from the Clouds and the Earth s Radiant Energy System (CERES) are estimated from empirical angular distribution models (ADMs) that convert instantaneous radiance measurements to TOA fluxes. This paper evaluates the accuracy of CERES TOA fluxes obtained from a new set of ADMs developed for the CERES instrument onboard the Tropical Rainfall Measuring Mission (TRMM). The uncertainty in regional monthly mean reflected shortwave (SW) and emitted longwave (LW) TOA fluxes is less than 0.5 W/sq m, based on comparisons with TOA fluxes evaluated by direct integration of the measured radiances. When stratified by viewing geometry, TOA fluxes from different angles are consistent to within 2% in the SW and 0.7% (or 2 W/sq m) in the LW. In contrast, TOA fluxes based on ADMs from the Earth Radiation Budget Experiment (ERBE) applied to the same CERES radiance measurements show a 10% relative increase with viewing zenith angle in the SW and a 3.5% (9 W/sq m) decrease with viewing zenith angle in the LW. Based on multiangle CERES radiance measurements, 18 regional instantaneous TOA flux errors from the new CERES ADMs are estimated to be 10 W/sq m in the SW and, 3.5 W/sq m in the LW. The errors show little or no dependence on cloud phase, cloud optical depth, and cloud infrared emissivity. An analysis of cloud radiative forcing (CRF) sensitivity to differences between ERBE and CERES TRMM ADMs, scene identification, and directional models of albedo as a function of solar zenith angle shows that ADM and clear-sky scene identification differences can lead to an 8 W/sq m root-mean-square (rms) difference in 18 daily mean SW CRF and a 4 W/sq m rms difference in LW CRF. In contrast, monthly mean SW and LW CRF differences reach 3 W/sq m. CRF is found to be relatively insensitive to differences between the ERBE and CERES TRMM directional models.

Loeb, N. G.↗

NASA NTRS2003

Angular Distribution Models for Top-of-Atmosphere Radiative Flux Estimation from the Clouds and the Earth's Radiant Energy System Instrument on the Tropical Rainfall Measuring Mission Satellite: Methodology - Part 1

Clouds and the Earth s Radiant Energy System (CERES) investigates the critical role that clouds and aerosols play in modulating the radiative energy flow within the Earth-atmosphere system. CERES builds upon the foundation laid by previous missions, such as the Earth Radiation Budget Experiment, to provide highly accurate top-of-atmosphere (TOA) radiative fluxes together with coincident cloud and aerosol properties inferred from high-resolution imager measurements. This paper describes the method used to construct empirical angular distribution models (ADMs) for estimating shortwave, longwave, and window TOA radiative fluxes from CERES radiance measurements on board the Tropical Rainfall Measuring Mission satellite. To construct the ADMs, multiangle CERES measurements are combined with coincident high-resolution Visible Infrared Scanner measurements and meteorological parameters from the European Centre for Medium-Range Weather Forecasts data assimilation product. The ADMs are stratified by scene types defined by parameters that have a strong influence on the angular dependence of Earth's radiation field at the TOA. Examples of how the new CERES ADMs depend upon the imager-based parameters are provided together with comparisons with existing models.

Loeb, N. G.↗

NASA NTRS2003

Estimation of Instantaneous TOA Albedo at 670 nm over Ice Clouds from POLDER Multidirectional Measurements

An algorithm that determines the 670-nm top-of-atmosphere (TOA) albedo of ice clouds over ocean using Polarization and Directionality of the Earth's Reflectance ( POLDER) multidirectional measurements is developed. A plane-parallel layer of ice cloud with various optical thicknesses and light scattering phase functions is assumed. For simplicity, we use a double Henyey-Greenstein phase function to approximate the volume-averaged phase function of the ice clouds. A multidirectional reflectance best-fit match between theoretical and POLDER reflectances is used to infer effective cloud optical thickness, phase function and TOA albedo. Sensitivity tests show that while the method does not provide accurate independent retrievals of effective cloud optical depth and phase function, TOA albedo retrievals are accurate to within similar to 3% for both a single layer of ice clouds or a multilayer system of ice clouds and water clouds. When the method is applied to POLDER measurements and retrieved albedos are compared with albedos based on empirical angular distribution models (ADMs), zonal albedo differences are generally smaller than similar to 3%. When albedos are compared with those on the POLDER-I ERB and Cloud product, the differences can reach similar to 15% at small solar zenith angles.

Sun, W.↗

NASA NTRS2002

Early Radiometric Validation Results of the Ceres Flight Model 1 and 2 Instruments Onboard NASA's Terra Spacecraft

The CERES Flight Model 1 and 2 instruments were launched aboard NASA's Earth Observing System (EOS) Terra Spacecraft on December 18, 1999 into a 705 Km sun-synchronous orbit with a 10:30 a.m. equatorial crossing time. These instruments supplement measurements made by the CERES Proto Flight Model (PFM) instrument launched aboard NASA's Tropical Rainfall Measuring Mission (TRMM) spacecraft on November 27, 1997 into a 350 Km, 38-degree mid-inclined orbit. An important aspect of the EOS program is the rapid archival and dissemination of datasets measured by EOS instruments to the scientific community. On September 22, 2000 the CERES Science Team voted to archive the Edition 1 CERES/Terra Level 1b and Level 2 and 3 ERBE-Like data products. These products consist of instantaneous filtered and unfiltered radiances through temporally and spatially averaged TOA fluxes. CERES filtered radiance measurements cover three spectral bands including shortwave (0.3 to 5 micron), total (0.3 to less than 100 microns) and an atmospheric window channel (8 to 12 microns). The current work summarizes both the philosophy and results of validation efforts undertaken to quantify the quality of the Terra data products as well as the level of agreement between the Terra and TRMM datasets.

Priestley, K. J.↗

NASA NTRS2002

Estimate of Top-of-Atmosphere Albedo for a Molecular Atmosphere over Ocean using Clouds and the Earth's Radiant Energy System (CERES) Measurements

The shortwave broadband albedo at the top of a molecular atmosphere over ocean between 40deg N and 40deg S is estimated using radiance measurements from the Clouds and the Earth's Radiant Energy System (CERES) instrument and the Visible Infrared Scanner (VIRS) aboard the Tropical Rainfall Measuring Mission (TRMM) satellite. The albedo monotonically increases from 0.059 at a solar zenith angle of 10deg to 0.107 at a solar zenith angle of 60deg. The estimated uncertainty in the albedo is 3.5 x 10(exp -3) caused by the uncertainty in CERES-derived irradiances, uncertainty in VIRS-derived aerosol optical thicknesses, variations in ozone and water vapor, and variations in surface wind speed. The estimated uncertainty is similar in magnitude to the standard deviation of 0.003 that is derived from 72 areas divided by 20deg latitude by 20deg longitude grid boxes. The empirically estimated albedo is compared with the modeled albedo using a radiative transfer model combined with an ocean surface bidirectional reflectivity model. The modeled albedo with standard tropical atmosphere is 0.061 and 0.111 at the solar zenith angles of 10deg and 60deg, respectively. This empirically estimated albedo can be used to estimate the direct radiative effect of aerosols at the top of the atmosphere over oceans.

Kato, S.↗

NASA NTRS2002

Top-of-Atmosphere Direct Radiative Effect of Aerosols from the Clouds and the Earth's Radiant Energy System Satellite Instrument (CERES)

Nine months of CERES/TRMM broadband fluxes combined with VIRS high-resolution imager measurements are used to estimate the daily average direct radiative effect of aerosols for clear-sky conditions over the tropical oceans. On average, aerosols have a cooling effect over the tropics of 4.6 +/- 1 W/sq m. The magnitude is approx.2 W/sq m smaller over the southern tropical oceans than it is over northern tropical oceans. The direct effect derived from CERES is highly correlated with coincident aerosol optical depth retrievals inferred from 0.63 microns VIRS radiances (correlation coefficient of 0.96). The slope of the regression line is approx. -32 W/sq m/t over the equatorial Pacific Ocean, but changes both regionally and seasonally, depending on the aerosol characteristics. Near sources of biomass burning and desert dust, the aerosol direct effect reaches -25 W sq m to -30 W/sq m. The direct effect from CERES also shows a dependence on wind speed. The reason for this dependence is unclear-it may be due to increased aerosol (e.g. sea-salt or aerosol transport) or increased surface reflection (e.g. due to whitecaps). The uncertainty in the tropical average direct effect from CERES is approx. 1 W/sq m (approx. 20%) due mainly to cloud contamination, the radiance-to-flux conversion, and instrument calibration. By comparison, uncertainties in the direct effect from the ERBE and CERES "ERBE-Like" products are a factor of 3 to 5 larger.

Loeb, N. G.↗

NASA NTRS2002

Defining Top-of-Atmosphere Flux Reference Level for Earth Radiation Budget Studies

To estimate the earth's radiation budget at the top of the atmosphere (TOA) from satellite-measured radiances, it is necessary to account for the finite geometry of the earth and recognize that the earth is a solid body surrounded by a translucent atmosphere of finite thickness that attenuates solar radiation differently at different heights. As a result, in order to account for all of the reflected solar and emitted thermal radiation from the planet by direct integration of satellite-measured radiances, the measurement viewing geometry must be defined at a reference level well above the earth s surface (e.g., 100 km). This ensures that all radiation contributions, including radiation escaping the planet along slant paths above the earth s tangent point, are accounted for. By using a field-of- view (FOV) reference level that is too low (such as the surface reference level), TOA fluxes for most scene types are systematically underestimated by 1-2 W/sq m. In addition, since TOA flux represents a flow of radiant energy per unit area, and varies with distance from the earth according to the inverse-square law, a reference level is also needed to define satellite-based TOA fluxes. From theoretical radiative transfer calculations using a model that accounts for spherical geometry, the optimal reference level for defining TOA fluxes in radiation budget studies for the earth is estimated to be approximately 20 km. At this reference level, there is no need to explicitly account for horizontal transmission of solar radiation through the atmosphere in the earth radiation budget calculation. In this context, therefore, the 20-km reference level corresponds to the effective radiative top of atmosphere for the planet. Although the optimal flux reference level depends slightly on scene type due to differences in effective transmission of solar radiation with cloud height, the difference in flux caused by neglecting the scene-type dependence is less than 0.1%. If an inappropriate TOA flux reference level is used to define satellite TOA fluxes, and horizontal transmission of solar radiation through the planet is not accounted for in the radiation budget equation, systematic errors in net flux of up to 8 W/sq m can result. Since climate models generally use a plane-parallel model approximation to estimate TOA fluxes and the earth radiation budget, they implicitly assume zero horizontal transmission of solar radiation in the radiation budget equation, and do not need to specify a flux reference level. By defining satellite-based TOA flux estimates at a 20-km flux reference level, comparisons with plane-parallel climate model calculations are simplified since there is no need to explicitly correct plane-parallel climate model fluxes for horizontal transmission of solar radiation through a finite earth.

Loeb, N. G.↗