## 2 Methodology
### Simulation of MERO-Measured TOA OSR and OLR Fluxes  
The measurement error could be derived through the difference between the simulated MERO-measured value and the true value, where the simulated MERO-measured OSR flux (\(M^{\text{OSR}}\)) and OLR flux (\(M^{\text{OLR}}\)) of a certain pixel could be derived through Equation (1):  
\[M^{k}=\frac{\sum\limits_{i=1}^{N}F_{i}^{k}D_{i}{}^{-2}P_{i}{}^{k}A_{i}\cos v_{ i}\cos\omega_{i}}{P^{k}\cos(v)\cos(\omega)D^{-2}A}\qquad k=\text{OSR or OLR} \tag{1}\]  
where the subscript \(i\) denote a sub grid point (0.1\({}^{\circ}\) longitude \(\times\) 0.1\({}^{\circ}\) latitude) within the pixel. The relationship between the MERO detector array and the pixel array on Earth TOA is shown in Figure 3. The pixel is the area on Earth TOA, which is viewed by the corresponding detector of a MERO instrument; for example, detector 1 views pixel 1\({}^{\prime}\). Every pixel is discretized into uniformed sub grid points, every sub grid point represents a 0.1\({}^{\circ}\) latitude \(\times\) 0.1\({}^{\circ}\) longitude area, e.g., the pixel 8\({}^{\prime}\) in Figure 3. \(F_{i}^{\text{OSR}}\) and \(F_{i}^{\text{OLR}}\) are the true  
Figure 2: The selected true hourly TOA Earth TOA (**a**) OSR flux and (**b**) OLR flux data and the temporal interpolations to derive the 1-min true OSR and OLR fluxes of a location on Earth (20\({}^{\circ}\) E, 30\({}^{\circ}\) S). The true hourly data comes from the CERES SYN dataset of March 2019. OSR and OLR fluxes of the internal point \(i\) respectively, which could be derived from the true OSR and OLR fluxes constructed above by cubic spline interpolation. \(v_{i}\) is the viewing zenith angle of sub grid point \(i\). \(\omega_{i}\) denotes the angle between the viewing vector and the Earth's center viewing vector. \(D_{i}\) is the distance between the MERO and the internal grid point \(i\). \(v\) is the viewing zenith angle of the whole pixel, which is set as the viewing zenith angle of the centre internal point of the pixel; \(\omega\) and \(D\) are defined in the same way. \(A\) and \(A_{i}\) are the area that the whole pixel and the internal point represent, respectively. \(v_{i}\), \(v\), \(\omega_{i}\), \(\omega\), \(D_{i}\), \(D\), \(A\) and \(A_{i}\) could be derived through the MERO pixel positioning method we proposed based on our previous work [18]; geometries of these parameters are shown in Figure 4. \(P_{i}\textsuperscript{OSR}/P_{i}\textsuperscript{OLR}\) in Equation (1) is the TOA OSR/OLR anisotropic factor of the sub grid point \(i\), which is the ratio of the actual OSR/OLR radiance to the Earth TOA OSR/OLR flux and could be derived by Equation (2):  
\[P_{i}^{k}=\frac{\pi I_{i}^{k}}{F_{i}^{k}}\qquad k=\text{OSR or OLR} \tag{2}\]  
where \(I_{i}\textsuperscript{OSR}\) and \(I_{i}\textsuperscript{OLR}\) are the actual OSR and OLR radiances from the sub grid point \(i\) of the pixel to the MERO detector, respectively. \(P_{i}\textsuperscript{OSR}\) could be derived through the CERES angular distribution models (ADMs) [19; 20]. The ADMs generate the TOA OSR anisotropic factors according to the OSR scene type. Every OSR scene type corresponds to a certain TOA OSR anisotropic factor by considering the dependence of the TOA OSR anisotropic factor on related parameters. These parameters are shown in Table 1, which includes: (1) the type of the surface beneath the TOA area based on the International Geosphere and Biosphere Program (IGBP) type classification; (2) the cloud conditions: clear (\(f\leq 0.1\%\), \(f\) is the cloud fraction) or cloudy(\(f>0.1\%\)); (3) other cloud and meteorological parameters, such as the optical depth, cloud fraction, wind speed and cloud type; and (4) the viewing geometry parameters, such as the solar zenith angle (\(s\)), the relative azimuth angle (\(r\)) and the viewing zenith angle (\(v\)) [19]. Once the OSR scene type is determined, the corresponding \(P_{i}\textsuperscript{OSR}\) can be derived.