## 2 A Survey on the Separation Model's Performance  
A general perspective on the separation models' equation is given by [10]. Almost all the separation models have an empirical basis, ranging from purely empirical models [11] to the very rare models incorporating physical features [12]. Many empirical models are fitted to data collected from a single station (e.g., [13]), but there are also models fitted to data collected from stations spread all over the world (e.g., [14]). The practical separation models consist of linear or non-linear equations (see, e.g., the large variety of separation models gathered by [4]). The most populated classes of the separation model equations' are polynomial and logistic.  
The first separation model proposed by [PERSON] and [PERSON] in 1960 [15] linearly relates the daily diffuse solar irradiation to the daily global solar irradiation. After this opening work, hundreds of single-predictor polynomial models have been proposed, e.g., [16] in 1977, [17] in 1982, [18] in 2006, and so on. Most of the polynomial separation models contain a single equation defined over the entire range of the clearness index. Some separation models comprise more than one equation, each equation being defined over a sub-domain of the clearness index [11]. The first logistic model was proposed in 2001 [19]. It was motivated by the attempt to abandon the branched structure of many previous models. Some of the latest and most popular separation models are from the class of logistic models ([5; 20; 21]).  
The separation models are not significantly distinctive in their formal nature. What differentiates them mainly is the number and nature of the predictors. The search for an ideal combination of predictors can be easily understood by looking at the scattering of the diffuse fraction with respect to the clearness index (e.g., Figure 1, Figure 2a). Because single predictor models cannot explain the dispersion of the diffuse fraction at a fixed value of the clearness index, the proposed polynomial models started to operate with more predictors [21; 22; 23].  
From a timescale perspective, there is a large variety of separation models that are applicable to GHI time series sampled from 1 min [11] to monthly [24] intervals.  
The separation models are comprehensively reviewed in [6]. The paper compares the performance of 140 separation models using data from 54 stations spread across all climate zones. The authors claim an exhaustive study, involving all separation models published prior to 2016. The paper concluded that no separation model can outclass all the others in every location. However, the model Engerer2 [20] (further denoted E2) was indicated to be quasi-universal based on the statistical results in different climate zones. The current state-of-the-art in separation models is highlighted by recent work [5]. It compares the 10 separation models that claimed to perform better than E2 against a huge dataset collected from all climate zones. The study identifies four minute-scale separation models, developed after 2016, that outperform Engerer2: Yang4 (Y4) [5], Starke1 (S1) [21], Starke3 (S3) [25], and Paulescu (PB) [11]. The abbreviation used in this study is indicated in brackets.  
On the basis of the outcomes from [5; 6], in the present study we considered only the top five models from [5]. The ensemble of the five models represents the state-of-the-art in separating diffuse from global solar irradiance. The performance of these models is considered a benchmark in the evaluation of the performance of the separation models proposed in this study. The five models are briefly introduced in Appendix A.