## 6 Conclusions  
This paper introduced two new separation models, which share global solar irradiance GHI into its direct-normal DNI and diffuse horizontal DHI components. The models effectively estimate the diffuse fraction at minute-scale resolution. Different from the already established minute-scale equations, the new models are differently formulated, being defined by rational polynomial equations. The first model, M1, operates with eight predictors. The M1 equation fails the beauty test but successfully passes the performance test. By contrast, the second model, M2, is defined by a beautiful equation. It operates with only three predictors defined on GHI measurements, which gives it high accessibility.  
Validation of the new models was carried out against data collected from 36 stations covering the four major climatic zones. Five current top minute-scale separation models were considered references. The tests were performed on the final product estimations,  
\begin{table}
\begin{tabular}{c|c|c c c c c|c} \hline \hline \multicolumn{1}{c|}{**Model**} & **PB** & **E2** & **S1** & **S3** & **Y4** & **M1** & **M2** \\ \hline \multirow{2}{*}{Mean rank} & _DNI_ & 4.86 & 6.58 & 2.30 & 3.44 & 4.30 & 2.02 & 4.47 \\  & _DHI_ & 4.83 & 6.94 & 4.33 & 2.11 & 4.61 & 2.05 & 3.11 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mean rank (Equation (7)) of the proposed (M1 and M2) and the reference (PB, E2, SI, S3, and Y4) separation models evaluated for the estimation of direct-normal _DNI_ and diffuse _DHI_ irradiances at all 36 stations from D_TEST.  
Figure 5: Ranking of the proposed (M1 and M2) and the reference (PB, E2, S1, S3, and Y4) separation models built on the basis of _nRMSE_ reached at the estimation of (**a**) direct-normal _DNI_ and (**b**) diffuse _DHI_ irradiances at every station from D_TEST. The stations are clustered by climate [27]: (A) tropical, (B) arid, (C) temperate and (D) continental.  
i.e., DNI and DHI. Based on a statistical linear ranking method according to the models' performance at every station, M1 leads the hierarchy, ranking first in both DNI and DHI estimation. The high accessibility of the M2 does not compromise accuracy. The results place M2 among the best-performing current models.  
Finally, we can conclude that all the models, both the proposed and the reference ones, seem to evolve in tandem (more or less similarly accurate), which could suggest a limit that cannot be crossed in the traditional estimation process. In order to further increase the accuracy of separating the global solar irradiance into its primary components, a new approach to the development of algorithms is necessary. Future work will be directed in this direction.  
Conceptualization E.P.; methodology, E.P. and M.P.; software E.P.; formal analysis, E.P. and M.P.; data curation, E.P.; writing--original draft preparation, E.P. and M.P.; writing--review and editing, E.P. and M.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
Publicly available data from BSRN ([[https://bsrn.awi.de/](https://bsrn.awi.de/)]([https://bsrn.awi.de/](https://bsrn.awi.de/)) accessed on 15 May 2023) were processed and analyzed in this study.  
The authors declare no conflict of interest.