About the Relation between Sunshine Duration and Cloudiness on the Basis of Data from Hamburg

The aim of this paper is to relate the two meteorological parameters known as relative (bright) sunshine duration and cloudiness using the data from two stations of the city of Hamburg, Germany. We test the classic linear relationship, as well as newer polynomial extensions suggested in the literature. The results of regression are interpreted against a theoretical background recently put forward by Badescu. The suggested relations can be borne out, but we also point out difficulties due to data quality and insufficiency. 1. Introduction Knowledge of the relationship between sunshine duration and cloudiness is very important for the practical forecast of insolation [1]. In solar energy technology there are key meteorological parameters on both short and longer time scales. Datasets with sunshine duration are widespread and easily available for many parts of the world and long time intervals. In contrast, cloudiness has been slow in being estimated or measured reliably. For use in solar energy technologies, cloudiness is fundamental [1] because the insolation reaching the ground depends on the amount and type of the clouds blocking the direct solar radiation [2]. Due to the fact that cloudiness is much more difficult to measure accurately, it has since long been found necessary to look for a relationship between the widely available sunshine duration measurements and the formerly rather elusive estimation of cloudiness. This short work draws on data from one single German city, Hamburg. We shall use as our data source only two stations located in this city. The first one is a transmitter mast of the “Norddeutscher Rundfunk” (Northern German Broadcasting Corporation, NDR), while the second is Hamburg’s airport. At first, the data from these locations are evaluated separately and then they are compared with each other. We expect that both stations should deliver similar relations as Hamburg is a flat and rather homogeneous city. Correlations of both quantities from many cities have been used in proposing a relationship between them. In recent times, the level of sophistication has been raised by Badescu, who carried out many case studies for Romania, from at least 1990 on. He summarized the findings of his collaborators in a book he edited recently [3]. The general conclusion is that one may use a linear relationship between cloudiness and cloud shade for Romania. But he also has summarized a probabilistic theory that can lead to more general relationships, which had been explored or proposed earlier but on uncertain grounds. This theory of Badescu’s will