## 2 Materials and Methods  
### Data and Pre-Process  
#### 2.1.1 In Situ Measurements  
The \(R_{n}\) measurements were collected from 105 globally distributed sites in three radiative measuring networks (Table 1) from 1994 to 2017. Note that \(R_{n}\) was obtained directly or by adding the four radiative components measurements as Equation (1). Figure 1a shows the geographic locations of all sites and their land cover types classified according to International Geosphere-Biosphere Program (IGBP) [23]. These sites mainly distributed over North America (Figure 1c) and Europe (Figure 1d), with ten main land cover types, including deciduous broadleaf forest (DBF), evergreen broadleaf forest (EBF), evergreen needleleaf forest (ENF), mixed forest (MF), croplands (CRO), grasslands (GRA), close shrublands (CSH), open shrublands (OSH), woody savannas (WSA), and permanent wetlands (WET). The statistics of the main land cover types of these sites are given in Figure 1b. All original \(R_{n}\) measurements underwent strict quality control and were converted to local time format first, and then they were aggregated into two time scales instantaneous and daily. As Table 1 shows, the sampling frequency at different sites is different; hence, the \"instantaneous\" scale was defined as half-hour (30 min) according to the study of [PERSON] et al. [24] to ensure their consistency. Thereby, the \(R_{n}\) measurements at each site sampled at the frequency less than half hour were aggregated into half hour without any missed out, and then all half-hour samples (\(R_{ini}\)) were aggregated into daily means without any missing in one day. In addition, to satisfy the requirements of the \(R\) model, the hourly averages of \(R_{n}\) measurements during 10:00-11:00 hours were calculated by averaging the corresponding \(R_{ni}\). Afterwards, since all sites are on flat surfaces, the \(R_{n}\) measurement at 12:30 hour of each day was determined as the \(R_{nmax}\) for all sites, as [PERSON] et al. [14] suggested. Note that only the \(R_{ni}\) during 9:30-14:30 hours were used. Therefore, a piece of sample for one day \begin{table}
\begin{tabular}{c c c c c} \hline
**Abbr.** & **Number of Sites** & **Time Period** & **Temporal Resolution** & **Reference** \\ \hline ARM & 29 & 1994–2017 & 1 min & [21] \\ La & 70 & 1996–2015 & 30 min & [8] \\ Thuile & 6 & 1995–2017 & 1 or 3 min & [22] \\ \hline ARM: Atmospheric Radiation Measurement ([[http://www.archive.arm.gov/](http://www.archive.arm.gov/)]([http://www.archive.arm.gov/](http://www.archive.arm.gov/))), La Thuile: Global Fluanet (La Thuile dataset) ([[https://fluxnet.org/](https://fluxnet.org/)]([https://fluxnet.org/](https://fluxnet.org/))), SURFRAD: Surface Radiation Network ([[http://www.esf.noaa.gov/gmd/grad/surfrad/](http://www.esf.noaa.gov/gmd/grad/surfrad/)]([http://www.esf.noaa.gov/gmd/grad/surfrad/](http://www.esf.noaa.gov/gmd/grad/surfrad/))). & & \\ \end{tabular}
\end{table} 
Table 1: Information about the three measuring networks. Figure 1: (**a**) Spatial distribution of the 105 sites used in this study and their land cover types, and (**b**) the statistics of their ten main land cover types. These sites mainly distributed over (**c**) North America and (**d**) Europe. contained three variables \(R_{ni}\), \(R_{nt}\), and \(R_{mmx}\). Finally, all samples under clear sky, which were determined as long as their CI values (see Section 2.1.3) at both instantaneous and daily scales were both larger than 0.7, were screened for the following study. Finally, all clear-sky samples were randomly divided into training datasets and validation datasets in the ratio of 7:3. Specifically, the number of samples for model training and validation were 49,927 and 21,403 for New Model, 15,828 and 6788 in total for \(S\) model at three moments (12:00, 13:00, 14:00), and 7730 and 3314 for \(R\) model, respectively. Figure 2 presents the number of samples at each half-hour from 9:30 to 12:30 hours.