Relationship between the effective cloud optical depth and different atmospheric transmission factors

• This study allows us to estimate the cloud optical depth for overcast conditions on the basis of the transmission factors.
• The results were obtained for both the ultraviolet erythema radiation and the broadband in 2011 and tested with data in 2012.
• The results obtained can be adjusted by using different expressions, such as power and exponential equations.

This study examines the sensitivity of cloud optical depth (COD) for overcast conditions to radiation transmission using data collected in Valencia, Spain. These relationships are provided as simple empirical functions, therefore avoiding the need to apply complex model minimisation schemes to obtain COD. Comparisons are presented between COD obtained by a minimization method and several radiation transmission factors comprising a clearness index (kt), a modified version (kt'), a cloud modification factor (CMF) and its modified version (CMF'). Additionally, a statistical model of COD proposed by J.C. Barnard and C.N. Long (2004) is tested with our data. Statistical relationships between COD and these variables were developed for measurements in the ultraviolet Erythema Radiation (UVER) range as well as for broadband measurements covering the full solar spectrum. Measurements collected in 2011 were used to develop power and exponential relationships relating COD to the above transmission factors, and subsequently tested with independent data collected in 2012. In general, expressions relating COD to CMF perform better and exhibit a higher correlation than equivalent expressions relating COD to clearness indices, especially in the UVER range. The expression of Barnard and Long is potentially adequate for the estimation of COD for both UVER and broadband solar radiation in Valencia, but the regression coefficients need tuning for local conditions.