Relationship between UVB and broadband solar radiation in Spain

The daily values of UVB irradiation (290-315 nm), I-UVB, and the broadband total irradiation (300-2800 nm), I-T, measured on a horizontal plane have been correlated for the period 2000-2008 at 16 measurement sites in Spain. The results have been compared with the daily experimental values registered at the same sites during the period 2009-2011. The coefficients of determination R-2 obtained by applying a linear regression are higher than 0.88 for all sites and increase to 0.94 when using a quadratic regression. When all data are considered together, the values of R-2 are 0.91 and 0.97 for the linear and quadratic regressions, respectively. Three different clearness indices, which are dimensionless parameters, have been also used in order to reduce the uncertainties of the estimations and to reduce the local nature of the coefficients: (1) the UVB clearness index, k(TUVB)=I-UVB/I-0UVB; (2) the modified UVB clearness index, k(TUVB)' and (3) the estimated UVB clearness index, k(TUVB)(*). The results show a strong dependence on the solar zenith angle. The bi-dimensional regression of k(TUVB) as a function of the solar zenith angle and the clearness index, k(T), substantially improves the correlation, with R-2 values higher than 0.81 for all sites. Finally, a formula relating k(TUVB) and k(T), valid for latitudes between 36 degrees N and 44 degrees N, has been obtained: k(TUVB) = 0.064 k(T) -0.0011 theta(z) -1.24 E-05 phi + 7.6 E-05 lambda + 0.063, where theta(z) represents the solar zenith angle (in degrees), phi is the latitude (in degrees) of the site and.. is the distance to the sea (in km). We have compared the experimental values for the period 2009-2011 with those estimated using this expression. For this, the coefficient of determination (R-2) is 0.87, with a MBD of -3.4%, a RMSE of 21% and a NRMSE of 8.7%.