ORIGINAL PAPER Procedure of embedding biological action functions into the atmospheric transmittance Eugenia Paulescu & Nicoleta Stefu & Paul Gravila & Remus Stefan Boata & Nicolina Pop & Marius Paulescu Received: 3 August 2011 / Accepted: 22 December 2011 / Published online: 13 January 2012 # Springer-Verlag 2012 Abstract In order to perform calculations of biologically effective irradiance, the usual procedure is to modulate the ground-measured spectral solar irradiance with a specific biological action function. The inconvenience is that only a few meteorological stations worldwide are equipped to measure the spectral solar irradiance in the ultraviolet range. This motivates the search for a numerical substitute, which constitutes the subject of this report. An innovative ap- proach based on generalized mean is used to infer the effective atmospheric transmittance. Its illustration resulted in a new parametric model for computing the biological dose under clear sky. The action spectrum for the growth response of plants, as a carrier of biological effects, is encapsulated into the atmospheric transmittance, leading to the calculation of the effective irradiance by simple algebra. The overall results indicate that the new parametric model performs accurately enough to be routinely used in practice. The procedure is general; therefore, it is described in detail to guide potential users in developing similar models incorporating other biological action spectra as needed. For speed-intensive applications, an executable file intended to run on any PC, which computes the effective irradiance with the proposed model, is provided. 1 Introduction Ultraviolet (UV) solar radiation, designating the spectral range from 0.28 to 0.4 μm, affects many natural processes related to the environment and human activities. Any increase in the UV radiation intensity is of concern due to potential harmful effects on the biosphere. Life is shielded from the adverse effects of UV radiation by the stratospheric ozone, but in the last decades, a decrease of the ozone concentration was detected (Herman 2010), mainly linked to anthropogenic ac- tivities. Erythema, DNA damage, and skin cancer are fre- quently related to UV exposure, causing a great concern for humans. UV radiation also influences vegetation growth, as well as dexterous materials like wood and polymers. Photon absorption is the primary event in a biological response to radiation. Since the probability of photon ab- sorption is strongly dependent on wavelength, the effective- ness of radiation in producing a biological response will also be wavelength-dependent. To obtain a result that is usable in predicting effects in nature, a spectral weighting function should be applied to relate quantitatively an experimental measured response to the UV dose. Thus, the study of the effects of UV solar radiation on the biosphere is an interdis- ciplinary research area, with the UV radiation itself being the common subject of both the radiative transfer through the atmosphere and photon-induced biological processes. A key question in photobiology is what wavelength of light elicits a particular response. The answer resides in the action spectrum, a graph that plots the efficiency with which electromagnetic radiation produces the biological effect as a function of the wavelength of the radiation. Basically, the spectral response of the biological endpoint is measured experimentally under well-defined conditions and then is formalized in the form of action function (for an example, E. Paulescu : N. Stefu : P. Gravila : R. S. Boata : M. Paulescu (*) Physics Department, West University of Timisoara, V Parvan Ave. 4, 300223 Timisoara, Romania e-mail: marius@physics.uvt.ro N. Pop Department of Physical Foundations of Engineering, “Politehnica” University of Timisoara, V Parvan Ave. 2, 300223 Timisoara, Romania Theor Appl Climatol (2012) 109:323–332 DOI 10.1007/s00704-011-0581-y