Friday, December 7, 2012

Solar Radiation Physics and Geometry for hydrologists

I started to realize that a hydrologist has to learn about radiation, since the first moment I put my sight a little beyond rainfall-runoff moedelling, at least fifteen years ago. This was in building the first bricks of GEOtop: the first problem we faced was to avoid give radiation to point in shadows, i.e. calculating shadows. At the time this was not very much documented, even if the papers by Ralph Dubayah, Jeff Dozier, and others were already out since a few years. I started with giving a look to IPW and I tried to understand what and how it works, but eventually I finish to try my own modules.  To summarise some of the topic,  I renovated my slides on slideshare, which now better cover the notation, and can be considered as a preliminary reading before going to the Formetta et al. 2012 paper (see it on GMDD).
Radiation  treated in the slides mostly regards: geometry (where we finally followed the work of Javier Corripio), shortwave radiation treatment, and longwave radiation.
If, from many points of view working  with a real model of atmospheric absorption would be more exciting, hydrologists use mostly parameterizations, and that is what I mostly summarised in my slides together with a little of astronomical geometry.

Anyway, I found really useful the papers you see listed below.


(Mostly about short-wave radiation)

Bird, R. and Hulstrom, R.: Simplified clear sky model for direct and diffuse insolation on horizontal surfaces, Tech. rep., Solar Energy Research Inst., Golden, CO (USA), 1981.

Bird, R. E.,  Riordan, C, 1986: Simple Solar Spectral Model for Direct and Diffuse Irradiance on Horizontal and Tilted Planes at the Earth's Surface for Cloudless Atmospheres. J. Climate Appl. Meteor., 25, 87–97. doi:<0087:SSSMFD>2.0.CO;2

Boland, J., Scott, L., and Luther, M.: Modelling the diffuse fraction of global solar radiation on a hori- zontal surface, Environmetrics, 12, 103–116, 2001.

Corripio, J.: Modelling the energy balance of high altitude glacierised basins in the Central Andes., PhD dissertation, University of Edinburgh, 2002.

Corripio, J.: Vectorial algebra algorithms for calculating terrain parameters from DEMs and solar radi- ation modelling in mountainous terrain, International Journal of Geographical Information Science, 17, 1–24, 2003.

Dozier, J. and Frew, J.: Rapid calculation of terrain parameters for radiation modeling from digital elevation data, Geoscience and Remote Sensing, IEEE Transactions on, 28, 963–969, 1990.

Dubayah, R.: Modeling a solar radiation topoclimatology for the Rio Grande River Basin., Journal of vegetation science : official organ of the International Association for Vegetation Science, 5, 627–640,, 1994.

Dubayah, R. and Paul, M.: Topographic solar radiation models for GIS, International Journal of Geo- graphical Information Systems, 9, 405–419, 1995.

Duguay, C.: Radiation modeling in mountainous terrain review and status, Mountain Research and Development, pp. 339–357, 1993.

Erbs, D., Klein, S., and Duffie, J.: Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation, Solar Energy, 28, 293–302, 1982.

Gubler, S., Gruber, S., and Purves, R.: Uncertainties of parameterized surface downward clear-sky shortwave and all-sky longwave radiation., Atmos. Chem. Phys, 12, 5077–5098, 2012.

Helbig, N., Lowe, H., Mayer, B., and Lehning, M.: Explicit validation of a surface shortwave radiation
balance model over snow-covered complex terrain, Journal of Geophysical ResearchAtmospheres, 115, D18 113, 2010.

Long, C. and Ackerman, T.: Surface measurements of solar irradiance: A study of the spatial correlation between simultaneous measurements at separated sites, Journal of Applied Meteorology, 34, 1995. Mikla ́nek, P.: The estimation of energy income in grid points over the basin using simple digital elevation model, in: Annales Geophysicae, vol. 11, 11 European Geophysical Society, Springer, 1993.

Orgill, J. and Hollands, K.: Correlation equation for hourly diffuse radiation on a horizontal surface,
Solar energy, 19, 357–359, 1977.

Ranzi, R. and Rosso, R.: Distributed estimation of incoming direct solar radiation over a drainage basin, Journal of Hydrology, 166, 461–478, 1995.
Spencer, J.: Fourier series representation of the position of the sun, Search, 2, 172, 1971.

Tovar, J., Olmo, F., and Alados-Arboledas, L.: Local-Scale Variability of Solar Radiation in a Mountainous Region., Journal of Applied Meteorology, 34, 2316–2328, 1995.


  1. This is a new concept for me, I have not considered solar radiation until an upcoming evaporation project we are installing a net pyrometer to estimate evaporation. I would like to potentially use this data for other purposes and will lookthrough some of these papers. It is interesting, thankyou.

    1. You can also find other nformation in one of the most recent posts