## 1 Introduction  
Spatial and temporal variability, as well as measurements and modeling techniques of solar radiation, a primary factor affecting the Earth's climate, are subjects of interest of many studies.  
However, in Poland, possibly mainly due to the limited data accessibility, solar radiation studies are rare and based on individual data series [1; 2; 3; 4; 5]. The exception is a paper concerning changes in solar radiation in the years 1961-1995 at six stations [6]. Analysis of relationships between solar radiation and meteorological elements for more than one observation series has been conducted, for example, by [7; 8; 9] and concerned the calibration of coefficients for an Angstrom-type formula, describing linear correlation between sunshine duration and global solar radiation.  
The best source of information on global solar radiation is its measurement results; however, due to the lack of sufficiently dense actinometric network, a modeling approach is a common practice. There are different types of models based on meteorological elements, including those which use sunshine duration as an input variable, i.e., the classic Angstrom formula [10; 11] and its modified versions [12; 13; 14]; those based on the relationship between solar radiation and air temperature [15; 16; 17]; and models utilizing cloudiness [18; 19], relative air humidity [20], or precipitation [21].  
Although the aforementioned models are commonly used, sometimes no meteorological data are available. In this case, the solution can be provided by a model based on relative geometric position between the sun and the earth, where the only variable is the day of the year.  
Additionally, such a solution does not need time-consuming input data processing (quality analysis, homogenization, gap filling).  
As the cloudiness is usually the most variable and influential factor affecting atmospheric transmissivity for shortwave radiation [20], simple day-of-the-year models, based on trigonometric functions or \(n\)th degree polynomials have been mainly developed for locations with relatively large global solar radiation (H) and slight and hardly variable cloud cover, i.e., in Turkey [22], Greece [23], China [24], Morocco [25], Egypt [26], Algeria [27], and Iran [28].  
In the temperate transitional climate typical for Poland, which is affected by considerable and variable cloudiness, these types of models are expected to be less accurate than those based on meteorological elements, especially referring to day-by-day model performance evaluation, since they do not consider variability of meteorological conditions. However, some authors apply also long-term analysis [28] based on mean monthly daily values, and this type of estimation (helpful for the simulation study of the long-term performances of solar energy utilization techniques [29]) was applied in this study.  
As in practice, the simple model, requiring as little input data as possible and involving no preliminary data processing procedure, seems to be useful for the end user, and the authors made an attempt to calibrate local coefficients and assess prediction accuracy of selected global solar radiation models to answer the question of whether or not such an approach can be used in Poland.