## 3 Results
### Temporal Sampling Scheme Induced Errors (Temporal Sampling Error)  
#### 3.2.1 Errors Induced by Sampling Interval  
As indicated by previous studies [17; 21], the continuous diurnal TOA OSR flux could be derived by the half-sine fitting of daytime samples, due to the nearly half-sine shape of the diurnal cycle solar insolation, whereas the continuous diurnal TOA OLR flux could be derived by the half-sine fit of the daytime samples and linear interpolation of the night-time samples. Therefore, the measurement error is substantially affected by the amounts of samples in the general case; more samples will result in better constraints for the interpolation of the measurement value (Figure 6), making the fitted measurement curve closer to the true value curve. For example, the sampling interval of 3.5 h make just 4 daytime OSR measurement samples (Figure 6a); the top and left slope of the half-sine measurement fit curve are poorly constrained, hence resulting in a relatively high OSR  
Figure 5: Pixel-averaged spatial sampling error as a function of spatial resolution of a MERO system (range of spatial resolution is 1000 km–20 km, step at the range of 1000 km–100 km is 100 km, step at the range of 100 km–10 km is 10 km). temporal sampling error (17.4%), whereas the sampling interval of 1 h could produce 12 daytime OSR measurement samples (Figure 6d), which covers almost the bottom, the left and right slope, and the peak of the half-sine measurement fit curve, therefore resulting in a smaller error (4.6%). Although the increase of the temporal samples leads to a better accuracy, such promotion would vanish when the sampling interval reach a threshold (Figure 7). For the OSR flux, this threshold is 1.5 h, sampling intervals of 1.5 h would make 16 temporal samples in a diurnal cycle, where nearly 8 to 9 is at daytime to cover the important positions (peak, two bottoms and the left and right slopes) of the half-sine fitting curve, making a good constraint on the fitting curve. Interpolation with sampling intervals bigger than 1.5 h would misfit some of these important positions; therefore, the change of the sampling interval within the range of \(>\)1.5 h would result in an evidence variance in the OSR measurement error. On the contrary, interpolation with sampling intervals of less than 1.5 h would just make a slight improvement to the constraint of the fitting curve compared to the 1.5-h-sampling-interval interpolation; hence, variation in the sampling interval within the range of \(<\)1.5 h would not make a significant change in the OSR measurement error. It is also indicated that the measurement error of the TOA OSR flux stays around 5% when the sampling interval is less than the threshold (1.5 h). This near constant 5% error results from the systematic error of a single sample, which would produce a certain offset between the measurement fitting curve and the true value interpolating curve no matter what the sampling intervals is. In our sampling interval assessment, the main source of this systematic error is the utilized fixed spatial resolution (40 km), which would result in an around 5% measurement error (Figure 5). For the OLR flux, this sampling measurement  
Figure 6: Comparisons of the true and the simulated MERO-measured TOA OSR fluxes of an Earth’s location (0\({}^{\circ}\) E, 40\({}^{\circ}\) S) in March 2019 under sampling intervals of (**a**) 3.5 h, (**b**) 2.5 h, (**c**) 2 h and (**d**) 1 h, respectively. error threshold is 2 h, and a less-than-2 h sampling interval would result in a near constant 5% measurement error. Note that the measurement error threshold of TOA OSR flux (1.5 h) is less than that of the TOA OLR flux (2 h). This is because the amplitude of TOA OSR flux curve is much larger than the TOA OLR flux in a diurnal cycle (OSR flux is larger than 300 W/m\({}^{2}\); OLR flux is less than 50 W/m\({}^{2}\)), and the OSR half-sine lateral slope is much steeper than the OLR, hence more sampling points are needed to constrain the OSR fitting curve than the OLR.