Reflected solar radiance seen by satellite
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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.
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1579619
- Report Number(s):
- LLNL-TR-799529; 986251
- Country of Publication:
- United States
- Language:
- English
Similar Records
A reverse shock in GRB L60509A
Coupling sky images with radiative transfer models: a new method to estimate cloud optical depth