7. Approximations


A quite sloppy but more honest comic like style illumination graphic


    In populated areas artificial brightness is one of the most important sources of light. Generally it improves the brightness given by natural sources. Of coarse illumination by forest fire and vulcanoes etc .. is also negelcted.

    For artificial night sky brightness see e.g.:

  2. No spectral calibration for sensors

    It is tacitly assumed that the daylight spectral effciancy for the human eye is also valid for any night vision sensor (photopic lux) although it is known, both, that night light is more redish than daylight and sensors differ in there spectral sensitivity.

  3. No shadowing, no terrain

    Directed light is more or less treated as a spatially constant source of diffuse light. Possible shadowing and horizon narrowing by the terrain is neglected.

  4. Constant turbidity

    No varying atmospheric clear sky turbidity due to dust, haze, mist etc.. is taken into consideration.

  5. No explicit absorption

    Absorption is only implicitely considerated by the parameterisation of the clear sky illuminace. No cloud absorption is calculated. Radiative extinction by clouds is only calculated by (multiple) scattering.

  6. Constant moon distance

    The moon distance ranges from perigee r_p \approx
363\;000\;km to apogee r_a \approx 405\;500\;km. That means a maximum variation of illuminance by the factor (r_p/r_a)^2 \approx 0.8, so a variation of the moon luminance of \approx +/- 10\;\% about the mean value can be assumed. This is negligible compared with other errors. Anyway this approximation could be prevented in further releases of the program with little to medium effort.

    In consistency with the approximation from above the moon parallax (varying aspect angle with the geographic position on earth) is also neglected.

  7. No lunar eclipses

    Lunar eclipses are rare events, and the calculation within the frame of the astronomic libraries used is beyond a reasonable effort. Lunar eclipses have to be communicated within the general briefing without a qualitative estimate of illuminance.

  8. No moon (or sun) altitude dependent albedo

    For clouds and the surface the albedo values are not taken as function of the moon altitude angle, although albedo is known to be higher for low altitude angles. Because of the generally rough estimates of albedo values this variation is not considered to be vital.

  9. Very rough estimates of sun light (twilight) illuminance

    Twilight brightness at sun altitudes higher then nautical twilight (h_s > -12^{\circ}) is considered to be so high, that the rough order of magnitude for the illuminance values is sufficient for night vision purposes. - So do not use the program to estimate illuminances above nautical twilight!

  10. The moon and the sun are the only reason for varying natural night illuminace

    Stars, planets, etc.. are considered to be constant. No polar light!

… and probably a lot of other implicit approximations and inaccuracies the author is not aware of.


Everybody must be aware that all calculated night time illuminance values are at its best an educated guess for real night time situations. Observed values can vary due to a manifold of reasons that are not coverd by this approach.