709 
Figure 1 Schematic representation of the 
illumination and viewing geometry 
Figure 2 SKYL curves for lightly-laden 
continental and heavily-laden urban/industrial 
type aerosol concentrations (662 and 826 nm). 
In fact, the direct solar irradiance will be distributed over the angular subtense of the sun, but since this is very 
small (about 0.533° at the Earth surface), the sun is generally considered to be a point illumination source. In 
equation (3), L sky is the sky radiance due to scattering of solar radiation in the atmosphere, as well as localized 
irradiance due to adjacency effects (Tanré et al. 1990). 
The total incident irradiance on the surface, E; (Wm' ! ) is defined as: 
It should be noted that p,(£2) is commonly cited as a definition of albedo (e.g. Kimes and Sellers (1985)), but 
it should be understood that it is only equivalent to albedo if one assumes that there is no diffuse component to 
the irradiance field (L sky in equations (3) and (5) is zero). It will be shown below how p ¡(O) can be used to 
model the effects of diffuse irradiance in deriving albedo, given certain assumptions, but shortwave energy values 
calculated using p,(£2) alone make the implicit assumption that all irradiance is incident from the direction of 
the Sun. Thus, whilst p,(£2) can be considered as an intrinsic surface property, the albedo is not strictly 
so. 
2.1. Isotropic Sky 
If L sky is assumed to be constant (i.e. an isotropic sky) then equation (3) becomes: 
(4) 
(5) 
where E sun (Wm' ! ) = n L sun . The albedo (a, unitless) of the surface is then defined as: 
( 6 ) 
The hemispherical-directional reflectance , p,(i2) (unitless) is defined: 
(7) 
L e (a,Q su „) = L sk ,(£0 (Q) + E sunPl (iO fiGA-n) IG^.NI 
If 
( 8 ) 
J Jl+ L sky (Q sun ,Q / ) IQ'.NI d£T = SKYL(Q sun ) E.jQ^J 
where SKYL is the proportion of diffuse irradiance (unitless) and where, if the sky is isotropic: 
(9)