.. _approximations:

Approximations
==============

.. _sloppyillum:

.. figure:: pics/illum_xkcd.png 
   :width:  67%                
   :align: center              
     
   A quite sloppy but more honest comic like style illumination
   graphic
	   
#. **NO ARTIFICIAL ILLUMINANCE**

   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.:

   * The night sky in the world: http://www.lightpollution.it/dmsp/

   * Lichtverschmutzung in Österreich: http://www.nightsky.at/Obs/LP/

#. **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.

#. **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.

#. **Constant turbidity**

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

#. **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.

#. **Constant moon distance**

   The moon distance ranges from perigee :math:`r_p \approx
   363\;000\;km` to apogee :math:`r_a \approx 405\;500\;km`. That
   means a maximum variation of illuminance by the factor
   :math:`(r_p/r_a)^2 \approx 0.8`, so a variation of the moon
   luminance of :math:`\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.

#. **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.
      
#. **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.

#. **Very rough estimates of sun light (twilight) illuminance**
      
   Twilight brightness at sun altitudes higher then nautical twilight
   (:math:`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!*

#. **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.

===================================================================
   
.. warning::
      
   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.