## 2 Materials and Methods
### Quality Control Procedure
#### 2.5.2 BSRN Quality Control Procedure  
Tests on increments (or step tests) in irradiation is very difficult to define due to the very nature of the solar radiation, since the appearance of a cloud may induce a sudden drop in irradiance which may reach several hundred W/m\({}^{2}\). Fluctuations from moment to moment can be very large, and this prevents from setting effective upper and lower bounds. A maximum difference of 1000 W/m\({}^{2}\) could be imposed on the irradiance, but this limit is so high that the test would be ineffective. [PERSON] et al., (2011) [41] have suggested a value of 555 W/m\({}^{2}\), which is the case for at least 95% of measurements.  
The BSRN QC procedure for the one component tests is based on three tests: the Physically Possible Limits (PPL), the Extremely Rare Limits (ERL) and the Configurable Climatological Limits (CCL) [33]. The PPL procedure is introduced for detecting extremely large errors in radiation data, while the ERL procedure is used to identify measurements exceeding the extremely rare limit. Radiation data exceeding these limits normally occur under very rare conditions and over very short time periods (Table 3). The configurable climatological limits are based on long period of records in the Southern Great Plains of United States. The analysis of the tests was implemented through various software packages, such as Windographer Ver. 4, Minitab ver. 20 and Excel. For each test, a QC flag is defined. If the test is successful, the corresponding flag takes the value of zero, otherwise it takes the value of 1. Thus, a flag of one indicates that the variables involved in the test are erroneous or at least suspect.  
The PPL tests check the maximum and minimum limits that can be physically reached by irradiance and aim at detecting extremely large errors in the radiation data. The upper limits of short-wave irradiances depend on the solar zenith angle. The minimal value of solar irradiance must be 0 W/m\({}^{2}\), although because of the radiative cooling at night, the limit is set at \(-4\) W/m\({}^{2}\). The test is applied independently to each of the solar radiation  
Figure 5: Two-dimensional representation of global radiation (\(G\)).  
components shown in Table 3[33]. \(G_{0n}\) is the normal irradiance at the top of the atmosphere and \(\theta_{z}\) is the solar zenith angle (SZA). The horizontal irradiance at the top of the atmosphere is estimated by Equation (6), while the clear sky irradiance was estimated by Equation (11) using data from the study station. The model of clear sky irradiance underestimates the global irradiances at low solar elevation angles. Any measurements outside the PPL limits are excluded from the analysis. As indicated from the graphs of Figure 6, all the data are within the said PPL limits. The blue line represents the PPL limit and the red line the ERL limit, respectively.  
The graphs show that a very large majority of values pass the said tests. Some values of global irradiances are closed to the ERL limits (Figure 6). As explained earlier, these values occur during partially cloudy conditions, when total irradiance may be enhanced due to the reflection of solar irradiance from the base of the clouds and from scattering of direct irradiance due to cloud particles.  
The suggested climatological limits are based on data obtained from Great Plains in the United States. The limits are classified in two levels. The '1 st level' have the'smallest' testing limits, while those referred as '2 nd level' gives the second lower limits. The graphical representation of PPL, ERL, and CCL limits of all the shortwave components are shown in Figures 6 and 7. Both global and diffuse irradiances show some values above the 1 st and 2 nd level limits. Regarding the global radiation there are only 21 and 64 cases above the limits of 1 st and 2 nd level, respectively. Diffuse irradiances showed lower cases (6 and 33, respectively).