Comparison of models for calculating daytime long-wave irradiance using long term data set

Abstract

Twenty simple and widely used models for calculating clear sky daytime long-wave irradiance were tested against measured long-wave irradiance data. As input the models required only air temperature or air temperature and water vapour pressure, all measured at screen height. Meteorological data and long-wave irradiance measurements from 32 consecutive years at the Climate and Water Balance Station at Taastrup in eastern Denmark and from 7 consecutive years at the Agrometeorological Station at Foulum in western Denmark were used. The long time series of the data sets ensured all weather conditions and extreme events were captured. Clear sky conditions were assumed when the ratio of measured global radiation at the surface to the extraterrestrial exceeded approximately 0.75. A set of statistical procedures was used to evaluate the performance of the models. The mean bias errors ranged from −23 to +12 W m −2 and −18 to +15 W m −2 and root mean square errors from 39 to 45 W m −2 and 30–36 W m −2 in Taastrup and Foulum, respectively. Model performance improved when using average daily daytime clear sky data and a more strict definition of clear sky conditions. No improvements were found when the data sets were subdivided by season or upwind surface cover type. Four of the clear sky models were superior to the other models tested. These models were combined with two all sky daytime long-wave irradiance models and compared to actual all sky daytime long-wave irradiance data included in the Foulum and Taastrup data sets. The mean bias errors ranged from −8 to +5 W m −2 and −6 to +8 W m −2 and root mean square errors from 29 to 30 W m −2 and 23–24 W m −2 in Taastrup and Foulum, respectively. Based on the results of this study and the fact that the Prata and Brutsaert clear sky models were founded on a physical basis these models were recommended for use with the Crawford and Duchon all sky model when calculating daytime long-wave irradiance in a temperate climate.