## 1 Introduction  
Clean energy generation is a very important issue in the development of any community that aspires to become sustainable. In this context, we are witnessing an exponential development of the photovoltaic (PV) energy sector [1]. The feasibility study as well as the technical design of a PV system are based on an on-site, detailed simulation of the system's operation. For running such simulations, accurate in-plane estimates of solar irradiance are required. Even today, measurements of solar irradiance in various spatial directions are very scarce. Thus, in-plane solar irradiance is commonly estimated on the basis of solar irradiance measured on the horizontal surface [2]. To apply a transposition model, both direct-normal (_DNI_) and diffuse (_DHI_) solar irradiance components are required [3]. However, the component of solar radiation measured with the highest spatial density at the planetary level is global horizontal solar irradiance (_GHI_). This fact assigns the separation models a privileged place in modeling solar resources at the Earth's surface. In a broad sense, a separation model estimates _DNI_ and _DHI_ from _GHI_ measurements (see, e.g., [4] for a recent treatment of the topic). The term irradiance defines the solar energy flux, expressed in W/m\({}^{2}\). _GHI_ denotes the incoming solar energy flux incident on a unitary horizontal surface from the entire celestial vault. _GHI_ is the result of summing two components in the horizontal plane: the beam and the diffuse solar irradiance. The solar irradiance beam is the solar energy flux coming directly from the Sun disk to the Earth, measured on a horizontal plane. If \(\theta_{z}\) denotes the zenithal angle, then the solar irradiance beam is expressed by the cosine law: \(DNI\cdot\cos\theta_{z}\). Diffuse solar irradiance, or _DHI_, defines the solar radiation that has been scattered by the atmospheric constituents but still reaches the surface of the Earth. The three components are related by the closure equation:  
\[GHI=DNI\cos\theta_{z}+DHI \tag{1}\]  
The problem of separating global irradiance into its direct and diffuse components is a current topic of interest in solar energy research (see, e.g., [5]), with the stated aim of increasing the performance of the separation process. Generally, the output of a separation model is the diffuse fraction, defined by equation [6]:  
\[k_{d}=\frac{DHI}{GHI} \tag{2}\]  
Technically speaking, _GHI_ is directly measured, then _DHI_ is straightforwardly obtained from the estimated diffuse fraction, and finally _DNI_ is estimated through Equation (1):  
\[DNI=\frac{1-k_{d}}{\cos\theta_{z}}GHI \tag{3}\]  
Along with this basic application, the evaluation of _DHI_ and _DNI_ on the basis of _GHI_, which is currently the diffuse fraction, acquires new values, such as its use as a quantifier of the uncertainty induced by aerosols in estimating clear-sky _DHI_[7] or as a proxy for classifying the sky conditions into clear, intermediate, and overcast [8]. The key stage in _DHI_ estimation is the choice and application of a separation model, i.e., the estimation of diffuse fraction from one or more atmospheric parameters, frequently called predictors. The accuracy level in diffuse fraction estimation determines the overall accuracy of a separation model. The diffuse fraction is typically estimated as a function of clearness index [6]:  
\[k_{t}=\frac{GHI}{G_{ext}} \tag{4}\]  
where \(G_{ext}\) represents the solar irradiance deterministically computed in a horizontal plane at the top of the atmosphere. The clearness index encapsulates information about atmospheric transparency, and its measured time series captures the stochastic part of solar irradiance [9]. In the last few decades, separation models have experienced continuous development [6]. The main engine of the development was constituted by the needs of the solar industry, with the research focusing on the practical modeling of the diffuse fraction based on the atmospheric clearness index.