That depends on the nature of your study. Is it statistical, spatial, mathematical, etc.?

For statistics I would recommend looking in sourceforge in a list like this: http://sourceforge.net/directory/science-engineering/mathematics/statistics/os:windows/freshness:recently-updated/

I could not advise on any particular on that field because I've only used one or two many years ago specially for curve fitting. You can take a look on the same list for general purpose mathematics.

For general purpose spatial analysis and manipulation I would advise: SGeMS (http://sgems.sourceforge.net/), GeoMS (http://sourceforge.net/projects/geoms/?source=directory), or GEOMS2 (http://sourceforge.net/projects/geoms2/?source=directory). All of them are mainly or also geostatistics software.

You also have the GIS software: SAGA GIS (http://www.saga-gis.org/en/index.html) or QGIS (http://www.qgis.org/en/site/).

All of the examples above are free. Also there are great packages for several types of visual and data analysis if you consider doing programming.

http://sourceforge.net/directory/science-engineering/mathematics/statistics/os:windows/freshness:recently-updated/

http://sgems.sourceforge.net/

http://sourceforge.net/projects/geoms/?source=directory

http://sourceforge.net/projects/geoms2/?source=directory

http://www.saga-gis.org/en/index.html

http://www.qgis.org/en/site/

Hi Rodrigo,

Continuing with the very comprehensive response by Pedro Correia. I would add that the theoretical modeling of light pollution is extremely complex, as it involves atmospheric sciences usually based on the radiative transfer theory. We are looking for an approach that is a little simpler. Currently the paper is in development, but once finished I will send it to you.

Some models that could be considered, which are the most current, and are mathematically complex, but they are the more accurate:

Kocifaj, M. (2007). Light-pollution model for cloudy and cloudless night skies with ground-based light sources. Applied optics, 46(15), 3013-3022.

Aubé, M., Franchomme-Fossé, L., Robert-Staehler, P., & Houle, V. (2005, August). Light pollution modelling and detection in a heterogeneous environment: toward a night-time aerosol optical depth retreival method. InOptics & Photonics 2005 (pp. 589012-589012). International Society for Optics and Photonics.

Aubé, M., & Kocifaj, M. (2012). Using two light-pollution models to investigate artificial sky radiances at Canary Islands observatories. Monthly Notices of the Royal Astronomical Society, 422(1), 819-830.

Garstang, R. H. (1986). Model for artificial night-sky illumination. Publications of the Astronomical Society of the Pacific, 364-375.

Martín Aubé in his page has some interesting explanations including a user´s guide of his model and a google code.

http://cegepsherbrooke.qc.ca/~aubema/index.php/Prof/IllumEn

If you need something else please contact me.

Just an insignificant addition to the already quite comprehensive list provided here: The ULR (Upward Light Ratio) of customizable lighting scenarios can be calculated using the free light planning and simulation software DIALux provided by DIAL.

http://www.dial.de/DIAL/en/dialux/about.html