Online computation of snow albedo using the two-stream and asymptotic radiative transfer theory
Snow TARTES is an educational and research purpose web application to compute the reflection (albedo) from multi-layered snowpack. It also computes the profile of light (irradiance) within the snowpack.

Getting started

First specify the properties of each layer of the snowpack: layer thickness, snow density and snow grain optical diameter (or SSA) are the three compulsary parameters. Soot can also be added. Then select the shape of the grains and if the illumination is diffuse or direct beam. In the latter case, setting the angle of incidence is compulsary. Soil, grass or ice can be also selected for the bottom interface but this only impacts albedo for ~10 cm of snow or less. Several ice absorption spectra are available, the effect on albedo is weak in the visible (400-600 nm) and near infrared (1550-1910 nm), null elsewhere. Press "Compute!" to plot the spectral albedo and the irradiance profile, or "Download albedo" or "Download irradiance" to get the data in csv format. For all numerical parameters, instead of using a single number, it is possible to use a range with the syntax: (start:end:step), which plots several curves. It is also possible to select a group of shapes or all bottom interface spectrum to explore the sensitivity to these parameters. The total number of curves per graph is limited to 10.

How does this work ?

The Two-streAm Radiative TransfEr in Snow (TARTES) model performs the calculation. This model describes the shape of the grains with two parameters (B and g) as in the asymptotic approximation of the radiative transfer theory (AART) (Kokhanovsky and Zege, (2004)) to compute the optical properties in each layer from the snow properties. The albedo is then calculated for the entire snowpack using the two-stream approximation with the delta-eddington correction. Detailled equations can be found in Libois et al. 2013. TARTES is implemented in Python and is open-source. Installation and documentation are available from TARTES web site or from TARTES is easy to use and can do more than this webapp. Give it a try if the webapp appears to be limited.


This webapp was implemented by Ghislain Picard using: TARTES python package, Flask and Bootstrap web framework, Bokeh plotting library and ASTER spectra (reproduced from the ASTER Spectral Library through the courtesy of the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California. Copyright © 1999, California Institute of Technology. ALL RIGHTS RESERVED).


  • Q. Libois, G. Picard, J. France, L. Arnaud, M. Dumont , C. Carmagnola , and M. D. King, Influence of grain shape on light penetration in snow, The Cryosphere, 7, 1803-1818, 2013, doi:10.5194/tc-7-1803-2013
  • Kokhanovsky, A. A., and Zege, E. P. (2004). Scattering optics of snow. Applied Optics, 43(7), 1589-1602, doi: 10.1364/AO.43.001589
  • Baldridge, A. M., S.J. Hook, C.I. Grove and G. Rivera, 2009.. The ASTER Spectral Library Version 2.0. Remote Sensing of Environment, vol 113, pp. 711-715, doi:10.1016/j.rse.2008.11.007
  • G. Picard, Libois, Q., and Arnaud, L., (2016) Refinement of the ice absorption spectrum in the visible using radiance profile measurements in Antarctic snow, The Cryosphere Discussion, doi:10.5194/tc-2016-146, in review
  • Warren, S. G., and R. E. Brandt (2008), Optical constants of ice from the ultraviolet to the microwave: A revised compilation. J. Geophys. Res., 113, D14220, doi:10.1029/2007JD009744
  • Warren, S. G. (1984) Optical constants of ice from the ultraviolet to the microwave, Applied Optics, 23, 8, 1206-1225, doi: 10.1364/AO.23.001206
  • A. Robledano, G. Picard, M. Dumont, F. Flin, L. Arnaud, Q. Libois, Unraveling the optical shape of snow, Nature Communication, 14, 3955, doi:10.1038/s41467-023-39671-3, 2023