## 4 Discussion  
The Earth energy budget is determined by the radiant energy flow of the Earth. In general, the incoming solar radiation (about 341 W/m\({}^{2}\)) is partially reflected by the clouds and atmosphere (about 79 W/m\({}^{2}\)) and by the surface (about 23 W/m\({}^{2}\))); the remainder is absorbed by the atmosphere (about 78 W/m\({}^{2}\)) and the surface (161 W/m\({}^{2}\)). When the surface is heated, it will emit approximately 396 W/m\({}^{2}\) longwave radiation upward, of which just 40 W/m\({}^{2}\) could pass through the atmosphere to the outer space and the rest is absorbed by the atmosphere (356 W/m\({}^{2}\)). When the atmosphere is heated, it would emit about 199 W/m\({}^{2}\) upward to the outer space and about 333 W/m\({}^{2}\) downward back to the surface [22]. In this case, the energy budget at Earth TOA is balanced; the incoming solar energy (341 W/m\({}^{2}\)) is equal to the outgoing radiant energy (the OSR: about 102 W/m\({}^{2}\) and the OLR: nearly 239 W/m\({}^{2}\)). This balanced Earth radiation budget may be the actual case in a relatively long period (such as the magnitude of hundreds of years or larger). However, several studies reported that the Earth radiation energy is imbalanced in recent decades; the outgoing radiation is less than the incoming solar radiation by approximately 0.71 W/m\({}^{2}\)[23], possibly due to the anthropogenic emissions of greenhouse gases. Such an Earth radiation imbalance (ERI) is vital to the synoptic and climate change. Nevertheless, current space-based ERB missions quantify the absolute value of the ERI with large uncertainty, which cannot satisfy the required \"climate accuracy\" due to the limited temporal sampling coverage and the non-simultaneous sampling of the spatial-temporal variability. As a next-generation Earth radiation budget mission, a MERO could overcome these limitations through the long-term continuous measurement of OSR and OLR in the diurnal cycle and simultaneous half-globe OSR and OLR observations. Generally, a detector would output an averaging value to blur the actual variance of the OSR and OLR fluxes within the pixel GFOV (ground field of view, which is the actual Earth TOA area that a pixel covers), thus resulting in certain errors. This error would become larger when the size of the pixel GFOV increased. For a MERO system, the border detector unit therefore possesses larger measurement error than the middle one, due to the larger GFOV of the border pixel caused by the Earth surface curvature. Accordingly, controlling the measurement error of border pixels is crucial to reduce the spatial-resolution-induced error of the whole system. As indicated above, the sampling-scheme-induced error is comprised of two parts: the sampling-interval-induced error (Figure 7) and the sampling-sequence-induced error (Figure 10). For a MERO system with a 40 km spatial resolution, the sampling-interval-induced measurement error of the TOA OSR flux stays around 5% when the sampling interval is less than 90 min; such a threshold is 120 min for the TOA OLR flux (Figure 7). This indicates that reducing measurement error by reducing the sampling interval has a limitation under certain spatial resolutions. Since more temporal samples need better capability for data storage and transmission (higher manufacturing cost), setting the sampling interval as the measurement error threshold indicated above could guarantee the nearly smallest measurement error with the least manufacturing cost (for example, 90 min is the best sampling interval for MERO with a spatial resolution of 40 km). After the best sampling interval is set (90 min), it is necessary to ascertain the temporal sampling sequence that result in the least measurement error. It is indicated that the sampling sequence starting time of 63 min would result in a least measurement error of the TOA OSR flux, and a starting time of 64 min would result in the least measurement error of the TOA OLR flux (Figure 9b).