## Appendix A  
The five models found by [5] to be highly performant and considered in this study as references are briefly introduced next. _PB model_  
PB [11] estimates the diffuse fraction utilizing only two predictors: the clearness index \(k_{t}\) and the daily average of the clearness index \(k_{day}\). The latter captures the variability in solar irradiance time series during a day. \(k_{day}\) is defined as:  
\[k_{day}=\frac{1}{n}\sum_{i=1}^{n}k_{t,i} \tag{1}\]  
where \(n\) is the daylight duration expressed in minutes. The model was built with data from the BSRN station in Palaiseau, France. The model is defined by a linear piecewise equation [11]:  
\[ \begin{split} k_{d}=1.011925-0.0316193k_{t}-0.0293827\ k_{day}-1.656 7278(k_{t}-0.367)\theta(k_{t}-0.367)+\\ +1.8982144(k_{t}-0.734)\ \theta(k_{t}-0.734)-0.8547682\Big{(}k_{day}-0. 462\Big{)}\theta\Big{(}k_{day}-0.462\Big{)}\end{split}  \tag{2}\]  
\[\text{where }\theta(x)= \begin{cases}0,&x<0\\ 1,&x\geq 0\end{cases} \text{ denotes the Heaviside step function. }\]  
_E2 model_  
The first minute-scale separation models were reported by the author of [20]. The models were built using data collected from six stations included in the Australian Meteorology Bureau's meteorological network. Among the proposed models in [20], the best is Engerer2, here denoted E2. The model estimates \(k_{d}\) based on the following predictors: \(k_{t}\), the zenithal angle \(\theta_{z}\), the apparent solar time \(AST\), and the deviation of the measured clearness index \(k_{t}\) from its estimation under clear skies \(k_{tc}\):  
\[\Delta k_{tc}=k_{tc}-k_{t} \tag{3}\]\(\Delta k_{tc}\) provides information about cloud enhancement (\(\Delta k_{tc}<0\)). The last predictor used by E2 is \(k_{de}\), the part of \(k_{d}\) that is attributable to cloud enhancement. It is given by the equation:  
\[k_{de}=\max\biggl{(}0,1-\frac{G_{cs}}{G}\biggr{)}\] (A4)  
where \(G_{cs}\) is the clear-sky global horizontal irradiance. E2 is defined by a logistic equation [20]:  
\[k_{d}=C+\frac{1-C}{1+\exp(\beta_{0}+\beta_{1}k_{t}+\beta_{2}AST+\beta_{3} \theta_{z}+\beta_{4}\Delta k_{tc})}+\beta_{5}k_{de}\] (A5)  
\(C\), \(\beta_{0}\), \(\beta_{1}\), \(\beta_{2}\), \(\beta_{3}\), \(\beta_{4}\), and \(\beta_{5}\) are empirical coefficients [20]. In this study, for running E2, the clear-sky solar irradiance components, _DNI_ and _DHI_, have been estimated with the Biga and Rosa model [28]. _S1 model_  
The authors of [21] also proposed a logistic model, referred to in this study as S1. Unlike E2, S1 replaces the predictors that capture the cloud enhancement events with predictors that manage the variability in the state of the sky. Cloud enhancement is still accounted for, but as an indicator that switches between two branches of the model. Two different sets of empirical coefficients are fitted on the basis of two sets of data collected from Australia and Brazil, respectively. The model equation is [21]:  
\[k_{d}= \begin{cases}\left[1+\exp\Bigl{(}\beta_{7}+\beta_{8}k_{t}+\beta_{9}AST+ \beta_{10}h+\beta_{11}k_{day}+\beta_{12}\psi+\beta_{13}G_{cs}\Bigr{)}\right]^{ -1}&\text{IF }K_{csi}\geq 1.05\text{ AND }k_{t}>0.65\\ \left[1+\exp\Bigl{(}\beta_{0}+\beta_{1}k_{t}+\beta_{2}AST+\beta_{3}h+\beta_{4} k_{day}+\beta_{5}\psi+\beta_{6}G_{cs}\Bigr{)}\right]^{-1}&\text{OTHERWISE}\end{cases} \] (A6)  
where \(AST\) denotes the apparent solar time in hours, \(h\) is the solar elevation angle in degrees, \(\psi\) is the persistence factor, \(G_{cs}\) is the clear sky solar irradiance, in \(MJ/\left(hour\cdot m^{2}\right)\), and \(K_{csi}\) is the ratio of the measured global horizontal irradiance and the modeled global clear sky irradiance. In this study, the model was implemented using the coefficients fitted to data collected in Australia. _S3 model_  
S3 [25] is an alternative version of S1. An additional predictor, the hourly clearness index, \(k_{hour}\) was introduced:  
\[k_{d}=