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Title: Reflected solar radiance seen by satellite

Abstract

We derive the integral expression for the reflected solar flux F (W/m2) seen by a sensor deployed on a satellite circling the earth at elevation ht. The sensor’s responsivity is that of a Si photodiode, (0.3, 1.1) µm. We first ignore atmospheric absorption, but account for light emanating from all angles, zenith up to parallel to earth surface. The expression, which holds for all “Solar–Earth–Sensor” (elevation) angles φe, corrects a long-used equation in the USNDS program, that models “background irradiance,” Ramsey [3], Eq.(2.2). Flux striking the sensor is proportional to the sea-level solar radiance I0 and the average earth albedo A. Results are displayed for ht = 2.02 · 104 km. The integral varies with angle φe, i.e., F = F(φe). When sensor and sun are aligned with earth center, F = F(0) = 0.620 I0AR2, where R = re/(re + ht) and re is the average earth radius. For the specified ht, |φe| < 180 - θ0 deg, where θ0 = 13.90. For larger angles, F = 0 since the sensor cannot see any part of earth illuminated by the sun. The flux F(φe) decays as ϵ3.5 when φe = 180-θ0- ϵ and ϵ→ 0, i.e., as the sensormore » enters darkness. Our ϵ3.5 result differs from Ramsey’s [3], Eq.(2.2), which has ϵ4.3. We conclude Eq.(2.2) is incorrect for two reasons: the erroneous decay and, more importantly, that it vanishes only at φe = 180. Our result, Eq.(14), presents a simple approximation to F(φe), accurate to better than 0.5%. The approximation blends Ramsey’s expression for small φe with an ϵ3.5 decay for large angles. Assuming a solar radiance I0 = 1120, W/m2 Wikipedia [7], and albedo A = 0.3, NASA, yields F(0) = 3.8 W/m2 , which is 80% less than the leading term in Ramsey [3], Eq.(2.2). If atmospheric absorption is not ignored our integrand is modified by the factor exp(-τ Natm), where τ is the atmosphere’s optical depth and Natm accounts for slant path absorption. The result is spectrally dependent. Absorption significantly decreases the flux as φe → 180 - θ0.« less

Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1579619
Report Number(s):
LLNL-TR-799529
986251
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
Physics - Nuclear physics and radiation physics

Citation Formats

Shestakov, A. I. Reflected solar radiance seen by satellite. United States: N. p., 2019. Web. doi:10.2172/1579619.
Shestakov, A. I. Reflected solar radiance seen by satellite. United States. https://doi.org/10.2172/1579619
Shestakov, A. I. 2019. "Reflected solar radiance seen by satellite". United States. https://doi.org/10.2172/1579619. https://www.osti.gov/servlets/purl/1579619.
@article{osti_1579619,
title = {Reflected solar radiance seen by satellite},
author = {Shestakov, A. I.},
abstractNote = {We derive the integral expression for the reflected solar flux F (W/m2) seen by a sensor deployed on a satellite circling the earth at elevation ht. The sensor’s responsivity is that of a Si photodiode, (0.3, 1.1) µm. We first ignore atmospheric absorption, but account for light emanating from all angles, zenith up to parallel to earth surface. The expression, which holds for all “Solar–Earth–Sensor” (elevation) angles φe, corrects a long-used equation in the USNDS program, that models “background irradiance,” Ramsey [3], Eq.(2.2). Flux striking the sensor is proportional to the sea-level solar radiance I0 and the average earth albedo A. Results are displayed for ht = 2.02 · 104 km. The integral varies with angle φe, i.e., F = F(φe). When sensor and sun are aligned with earth center, F = F(0) = 0.620 I0AR2, where R = re/(re + ht) and re is the average earth radius. For the specified ht, |φe| < 180 - θ0 deg, where θ0 = 13.90. For larger angles, F = 0 since the sensor cannot see any part of earth illuminated by the sun. The flux F(φe) decays as ϵ3.5 when φe = 180-θ0- ϵ and ϵ→ 0, i.e., as the sensor enters darkness. Our ϵ3.5 result differs from Ramsey’s [3], Eq.(2.2), which has ϵ4.3. We conclude Eq.(2.2) is incorrect for two reasons: the erroneous decay and, more importantly, that it vanishes only at φe = 180. Our result, Eq.(14), presents a simple approximation to F(φe), accurate to better than 0.5%. The approximation blends Ramsey’s expression for small φe with an ϵ3.5 decay for large angles. Assuming a solar radiance I0 = 1120, W/m2 Wikipedia [7], and albedo A = 0.3, NASA, yields F(0) = 3.8 W/m2 , which is 80% less than the leading term in Ramsey [3], Eq.(2.2). If atmospheric absorption is not ignored our integrand is modified by the factor exp(-τ Natm), where τ is the atmosphere’s optical depth and Natm accounts for slant path absorption. The result is spectrally dependent. Absorption significantly decreases the flux as φe → 180 - θ0.},
doi = {10.2172/1579619},
url = {https://www.osti.gov/biblio/1579619}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {11}
}