Code validation

The development and validation of this code owns to previous studies for laying out the path. In this section, we describe our attempts to replicate published results concerning APSFs. To avoid copyright infringement, our reconstruction of the results are presented here, with indication to the original figure numbers and links to the online article.

Validation 01

This validation attempts to reproduce the results presented by Dieder Tanré, Maurice Herman and Pierre-Yves Deschamps in their study Influence of the background contribution upon space measurements of ground reflectance (1981). The the same base data for aerosol size distribution and vertical profile were used for input to Mie calculations and as model atmospheres for Monte Carlo calculations. The phase function and vertical profile are reproduced below (equivalent to Fig. 1 and 2 in the original study).

There is a small difference in the aerosol profile, despite the same source. Our values are reproduced from Table 3 of McClatchey et al. (1971). Those small differences propagate to the integrated vertical aerosol extinction, (Table 1). To minimize differences between the studies, our vertical optical thickness profiles were normalized to the same values at surface as in the original study. Those changes are prior to the simulation of the APSFs. Only the standard profiles for 5 and 23 km visibility were used.

Table 1 - Vertical optical thickness calculated from the base data of McClatchey et al. (1971).

	Original	apsfs	Original	apsfs
Wavelength	MC23	MC23	MC05	MC05
450	0.2801	0.2929	0.9305	1.0224
850	0.1550	0.1637	0.5151	0.5713

The following figures are equivalent to the their Fig. 5 and 6, showing the normalized cumulative distribution function of the diffusely transmitted photons with respect to radial distance from point of observation. Results for models MC23 and MC05 include the interaction of Rayleigh and aerosol scattering.

Interestingly, the only clear difference between our results is the Rayleigh curve at 850 nm. In the original work, it reaches 0.5 at 5 km, but since the Rayleigh phase function is not dependent on wavelength, that difference would have to arise from the optical thickness effect alone, which their research show to be minor (in terms of spatial pattern of the APSF). Our values for the vertical Rayleigh optical thickness were the same. It could be an error during the production of the original image.

Validation 02

The same model used in the previous study was implemented on the radiative transfer code 6SV of Eric F. Vermote, Dieder Tanré, Jean-Luc Deuzé, Maurice Herman and Jean-Jacques Morcrette (Second Simulation of the Satellite Signal in the Solar Spectrum, 6S: An Overview, 1997). It was implemented as an average aerosol model. The vertical aerosol profile is not specified and the APSFs are computed here with the previous MC23 profile. The objective is to evaluate the effect of sensor altitude and view angle against the figures provided in the 6SV User Manual Part 2, section SUBROUTINE ENVIRO.

The images below show the effect of sensor altitude when close to the surface, for Rayleigh (left) and aerosols (right), and are equivalent to Fig. 2 and 3 of the SUBROUTINE ENVIRO section.

The images below show the effect of view angle, for Rayleigh (left) and aerosols (right), and are equivalent to Fig. 4a and 4b of the SUBROUTINE ENVIRO section.