## 3 Results  
### Spatial Resolution Induced Errors (Spatial Sampling Error)  
The major source of this spatial resolution induced error is the pixel mixing of TOA OSR and OLR. A pixel viewed area on Earth would usually be comprised of several endmembers. The OSR/OLR value between these endmembers are usually different due to the fact that the TOA OSR/OLR varies markedly with time and space [2]. Therefore, there will be bias between the pixel TOA OSR/OLR measurement, which is the spatial average value (see Equation (1)), and the actual TOA OSR/OLR values of the endmembers. This bias is set as the spatial sampling error of the pixel. Note that the TOA OSR/OLR of these endmembers are derived from the true 0.1-degree spatial resolution OSR and OLR in this study. To further investigate the general relationship between the spatial resolution and its induced errors for the whole focal plane array, we averaged the spatial sampling errors of all the pixels. The pixel-averaged spatial sampling error as a function of the spatial resolution of a MERO system is exhibited in Figure 5. The measurement error of Earth TOA OSR/OLR flux stays lower than 25%/17% when the spatial resolution of a MERO is finer than 1000 km. This error in the unit of percentage reduces linearly as the spatial resolution varies from 1000 km to 100 km; the rate is 2.5%/100 km for the TOA OSR flux, which is higher than that (1%/100 km) for TOA OLR flux. This is due to the larger variance of the actual Earth TOA OSR flux within the MERO pixel than that of the TOA OLR flux (this variance of OSR flux is larger than 200 W/m\({}^{2}\), while that of OLR flux is less than 50 W/m\({}^{2}\)). The same enhancement of spatial resolution would therefore recover more actual variation details for the OSR flux than the OLR flux, resulting in more increase in the OSR flux measurement precision than the OLR flux. It is also found that the error of the OSR flux is larger than that of the OLR flux at the same spatial resolution. This is due to the fact that the spatial-resolution induced error is computed as the average of the deviations of all pixels (deviation of one pixel is the difference between the whole pixelmeasurement and the individual endmember true values); accordingly, the true OSR fluxes of these endmembers have a larger variance than their true OLR fluxes (the variance of OSR flux is larger than 200 W/m\({}^{2}\), while that of OLR flux is less than 50 W/m\({}^{2}\)). It is noted that the decreasing rate of the measurement error become larger when the spatial resolution is finer than 40 km, which indicates that more precise measurement could be obtained when the MERO spatial resolution is finer than 40 km. However, as spatial resolution refines, more detector units will be required, which substantially heightens the manufacturing cost. Particularly, the increase in the manufacturing cost is almost the square of that in the spatial resolution under the assumption that the manufacturing cost is linearly correlated with the amount of detector units in the focal plane. For example, 2 times enlargement of spatial resolution would result in a 4 times increase of the manufacturing cost. These imply that the minimum manufacturing cost under a certain precision requirement could be estimated using our results shown in Figure 5. For example, a less-than-5% measurement error needs 40 km or finer spatial resolution, which means that at least 80,732 detector units are required. Conversely, if the budget of the MERO mission is ascertained, the corresponding spatial-resolution-induced error could be derived using the results shown in Figure 5.