## 3 Review and Evaluation of Solar Irradiance Forecasting Methods
### Numerical Models  
Ground-based pyranometer stations cannot provide full coverage, and traditional statistical models based on time series have limited applicability, making numerical weather predictions (NWPs) a viable alternative on a global, regional, and national scale. NWP involves modeling the temporal development of the atmospheric state using differential equations that describe the physical laws of climate. Data from radiosondes, meteorological satellites, and ground-based meteorological observations are utilized for this purpose. These observations are processed using data assimilation and analysis methods, which perform quality control to obtain values that can be used by the mathematical algorithms of numerical models. These algorithms are typically based on a uniform spacing grid. The resulting data are then used as a starting point for forecasting. The set of equations used in NWP are known as the primitive equations. In terms of size and grid spacing, numerical weather prediction models are typically differentiated by their spatial scale. Additionally, a variety of methodologies are employed in the development of these models, resulting in a multitude of different models. Some noteworthy global and regional models include the Global Forecast System (GFS), the National Oceanic and Atmospheric Administration (NOAA), and the European Centre for Medium-Range Weather Forecasts (ECMWF). Mesoscale models such as MM5 and WRF are also widely used. Irradiance forecasts vary in their models, with differences in data assimilation techniques (such as 3D-Var, 4D-Var, and EnKF), the number of vertical layers of the atmosphere handled, consideration of concentration values for aerosol, H\({}_{2}\)O, O\({}_{2}\), O\({}_{3}\), and CO\({}_{2}\), the number of parameterizations for different physical processes, and the degree of sophistication of scattering/absorption schemes used, as well as the number of updates per day and loop time steps. Independently of the spatial resolution that different methods may provide, the solar forecasting research that is exclusively based on numerical models generally performs this when searching for forecasts at a time horizon longer than 6 h, whereas, if the aim of the study is a shorter forecast, the numerical methods are applied as backup systems to improve accuracy. There are a number of studies that utilize forecasts provided by various numerical models to evaluate the effectiveness of different forecasting methods. For instance, Ref. [156] shows the importance of developing a seasonal and site-specific model output statistics (MOS) approach to improve forecast accuracy in the evaluation of the GHI forecasts from the WRF model in southern Nevada. In addition, Ref. [157] evaluates the irradiance forecast accuracy at time horizons of about 24 h from the ECMWF model and demonstrates that NWP forecasts can be an essential tool for the operation of solar power generation systems. The same author of [53] goes on to describe the use of various post-processing methods, especially multivariate regression models, in numerical ECMWF forecasting for day-ahead forecasts. Moreover, Ref. [158] analyses performance improvement by incorporating hourly aerosol estimates into the ECMWF model, while Ref. [159] proposes a method to forecast the GHI and DNI up to 6 h in advance by inserting the Meteosat Second Generation (MSG) cloud index estimates into the vertical layer of the WRF model. On the other hand, there are several studies that use numerical models as a verification or backup system for other methods. For instance, Ref. [160] supports the use of a stochastic differential equation model with an NWP for modeling the uncertainty associated with a GHI forecast. Similarly, Ref. [161] establishes a methodology to shorten the 24 h forecasts provided by the WRF model through an ANN technique. Ref. [162] combines three implementations of the WRF model with multivariate statistical learning techniques.