Investigating biological response in the UVB as a function of ozone variation using perturbation theory

In order to determine a biological response to ultraviolet radiation, calculations of biologically weighted dose rates are required, which in turn involve the integral over wavelength of an action spectrum multiplied by appropriate surface flux data. To determine a biologically weighted dose rate accurately, a reasonable wavelength resolution is required, involving a full radiative transfer solution to be performed for each wavelength in order to obtain the surface flux information. If biologically weighted dose rates are needed as a function of ozone variation, then the number of radiative transfer solutions quickly makes a large number of ozone variations cumbersome. This paper shows that the perturbation theory developed for atmospheric radiative transfer by Box and co-workers can predict surface fluxes and hence biologically weighted dose rates for a large range of ozone variations very efficiently. The method is then extended to calculate radiation amplification factors. Results for biologically weighted dose rates are presented for a large range of solar zenith angles and ozone loadings using perturbation theory and a full radiative transfer code and show that the perturbation predictions never deviate very far from the radiative transfer solutions.