Overcast sky luminance is dependent on the physical state of the atmosphere below cloud level

Abstract

An approximate formula for sky luminance under overcast conditions taking into account different pollution content of the atmosphere is determined. The homogeneous cloud layer is considered to be a constant source of light, while the undercloud atmosphere is taken as a single scattering medium. The final mathematical expressions depend on turbidity and scattering ability of the undercloud atmosphere as well as on the altitude of the clouds. Such a parameterised model is therefore easily scalable and well adjusted to the actual meteorological situation (contrary to empirical models in current use). The derived analytical formula is suitable for engineering practice to perform rapid simulations of sky luminance.

Let the sunshine in? The effects of luminance on economic preferences, choice consistency and dominance violations

“…The altitude of the clouds, their thickness, the under-cloud atmosphere, the incident angle and intensity of solar radiation and pollution are additional factors that determine the amount of light that passes through clouds. Under many circumstances increases in cloud cover can actually increase surface luminance, for example a surface fog which can often trap photons and lead to oddly bright conditions [ 24 ]. Overall, cloud coverage alone has little to do with the light exposure at the earth surface level, a point relevant to previous studies of this issue.…”

“…These seemingly contradicting results become less inconsistent when one realizes that we know from the meteorology literature that cloud coverage alone does not accurately predict light exposure at the earth surface level (e.g. [ 24 ]). Indeed, in our dataset CloudCoverage does explain some daily variation in luminance, but only 7% of that variation.…”

The influence of ground reflectance on the overcast sky luminance

“…Overcast sky luminance and ground reflectance 47 luminous energy directed toward the Earth within an elementary solid angle dX given in Kocifaj 20 as:…”

“…The symbols are described in the paper undercloud atmosphere and is given as a sum of molecular m and aerosol a optical thicknesses. 20 Note that the well-known turbidity factor T V is directly linked to the ratio ( m þ m )/ m . It is convenient to use an approximate relation T V ffi 0:1.…”

“…Although a very approximate formula for D 2 (, m) was introduced in Kocifaj 20 the exact expression is as follows:…”