## 4 Discussion
Therefore, a sampling temporal sequence with a starting time of 64 min with a sampling interval of 90 min ought to be the optimal sampling scheme for a MERO with a 40 km spatial resolution. Our results indicate that the temporal sampling error do not change when the sampling interval is less than or near 1 h for both the TOA OSR and OLR fluxes; however, this may not be the fact. We chose the 1 hourly CERES OSR/OLR data and interpolated it to 1 min temporal resolution, which is then be regarded as the \"true value\" in our study. Afterward, this true value is used to simulate the MERO-measured OSR/OLR flux. We choose theCERES measurements as \"true data\" since CERES is currently one of the most reliable ERB systems around the world and because the CERES data is consistent with the CERES ADMs we used in our study, which is the core function to generate the TOA OSR/OLR anisotropic factors. However, such a 1 min interpolated true value is smoothed between two 1-h samples (Figure 2), which neglects the actual less-than-1-h temporal variability of the TOA OSR and OLR fluxes. As such, the temporal sampling error would have little change when the sampling interval is less than 1 h, which can be interpreted as follows: 1. for the true data, the 1 min interpolation is based on the 1 hourly CERES data, and the information of less-than-1-h OSR/OLR variation is lost (see Figure 2); therefore, the shape of the true OSR/OLR diurnal curve is actually determined by the original 12/24 key temporal samples (the OSR curve only exist at daytime; OSR at nighttime stays at 0); the newly interpolated 1 min temporal points do not affect the curve shape (see Figure 2); 2. the simulated MERO measured OSR/OLR flux variation is calculated based on the true data curve; therefore, the less-1-h OSR/OLR variability of the simulated MERO-measured curve is also lost. When the sampling interval is less than or near 1 h, the newly calculated value would have less effect on the simulated MERO-measured OSR/OLR flux variation curve, leading to a relatively unchanged temporal sampling error. We think that a more realistic TOA OSR and OLR flux data with better temporal resolution (such as 10 min) could help to figure out the actual temporal sampling error when the sampling interval is less than 1 h. The CMIP 6 (Coupled Model Intercomparison Project Phase 6) generated data along with the GERB measurements may be a feasible way, which we would try in our future work. In the actual design of a MERO system, the spatial resolution could be ascertained by the balance between the spatial-resolution-induced error and the manufacturing cost using the spatial resolution assessment results derived in our study. Then the optimal sampling scheme could be determined through the method we proposed above for a MERO with a spatial resolution of 40 km. In this study, we evaluated the temporal sampling scheme induced error during March 2019, since both the Arctic and Antarctic has TOA OSR during this month. However, since the OSR and OLR for the summer and winter months have very different radiative flux distributions than those of the transitional months (spring and autumn), the full assessment of this sampling-scheme-induced error over four seasonal months could result in better results. We would conduct this study in the further work. We assessed the spatial resolution at an extensive range from 1000 km to 20 km to facilitate the scientific design of a MERO with consideration of the state of art and future advances in technology. For example, considering an assumed case that the MERO can only have a spatial resolution of 50 km and a temporal resolution of 1 h under the limitation of the state of the art and mission fund budget, this paper can help to give the corresponding measurement error caused by spatial-temporal resolution, which is part of the inherent error of a MERO system. Instead, if our assessment range is too small (for example, 1000 km-100 km), the spatial-temporal-resolution-induced error of the MERO system in the above case cannot be derived.