## 1 Introduction  
Surface all-wave net radiation (\(R_{n}\)) is the difference between the incoming and outgoing shortwave and longwave radiation at surface, which represents the balance state of energy absorption, reflection, and emission on the Earth's surface. \(R_{n}\) can be mathematically expressed as follows:  
\[R_{n}=R_{ns}+R_{nl} \tag{1}\]  
\[R_{ns}=R_{s}^{\downarrow}-R_{s}^{\uparrow}=(1-\alpha)R_{s}^{\downarrow} \tag{1a}\]  
\[R_{nl}=R_{l}^{\downarrow}-R_{l}^{\uparrow} \tag{1b}\]  
where \(R_{ns}\) is the net shortwave radiation (Wm\({}^{-2}\)), \(R_{nl}\) is the net longwave radiation (Wm\({}^{-2}\)), \(R_{s}^{\downarrow}\) and \(R_{s}^{\uparrow}\) are the incoming and outgoing shortwave radiations (Wm\({}^{-2}\)), \(R_{l}^{\downarrow}\) and \(R_{l}^{\uparrow}\) are the incoming and outgoing longwave radiations (Wm\({}^{-2}\)), and \(\alpha\) is the broadband albedo. The downward direction is defined as positive in this study. \(R_{n}\) is one of the most essential parameters in Earth's energy radiative balance [1,2]. It drives various natural phenomena and processes on Earth and determines its energy redistribution, so it is of great significance in the surface-atmospheric energy exchange [1, 2, 3]. Hence, \(R_{n}\) has been widely used in various applications, such as agriculture, climate, hydrology, and so on. In practical use, due to the different limitations in ground measurements, the alternative way to obtain \(R_{n}\) is from model reanalysis or remotely sensed products. Relatively, the satellite-based radiative products are becoming more and more popular because of their superior performance, as pointed out by several studies [4, 5, 6, 7, 8]. Additionally, with the development of society, \(R_{n}\) at high spatial resolution is highly required nowadays. Hence, satellite observations, particularly those from polar-orbiting satellites with finer spatial size across kilometer-to-meter scales, have become one of the most popular data sources for \(R_{n}\) estimation [6], such as data from Moderate Resolution Imaging Spectroradiometer (MODIS) [9, 10, 11], Advanced Very High Resolution Radiometer (AVHRR) [12], and Landsat sensors [13], have been successfully applied in estimating \(R_{n}\). However, the number of available polar-orbiting satellite observations in one day varies around the globe, with the value gradually decreasing when the satellite approaches the equator. In addition, for those polar-orbiting satellites with the finer spatial resolution (e.g., Landsat, Sentinel), the available observations in one day are much less because of their longer revisit period (>1 day). Thus, the accuracy of the estimated \(R_{n}\) for a time period in some regions (i.e., low latitudes), such as the daily mean \(R_{n}\) (\(R_{nl}\)) at finer resolution, which is required more often in practical use, would be heavily influenced by the very limited availability of satellite observations. To address this issue by expanding the instantaneous satellite observations into \(R_{nl}\) reasonably, several methods have been proposed. Sinusoidal model, which was first proposed by [PERSON] et al. [14] for estimating daily mean shortwave radiation, was also commonly used to retrieve an accurate \(R_{nl}\) from the instantaneous values [2,14]. The assumption of sinusoidal model is that the instantaneous \(R_{n}\) (\(R_{nl}\)) varies, conforming to a theoretical sinusoidal curve during daytime without clouds, so the daytime average \(R_{n}\) (\(R_{nD}\)) could be estimated through at least one \(R_{nl}\) in daytime that could be derived from the corresponding instantaneous satellite observations, after which \(R_{nl}\) could be obtained from the \(R_{nD}\) based on their statistical relationship [2,14]. Sinusoidal model is popular because it is simple to understand and be conducted with its clear physical mechanisms. But the model performance is significantly influenced by the number of available \(R_{nl}\); the more \(R_{nl}\) used, the more accurate the estimated \(R_{nD}\).