## 3 Collocation and Evaluation Methodology  
### Collocation and Evaluation Methodology  
The focus of this paper was to quantify the performance of the cloud products over the TP from the recently launched AGRI onboard FY-4A by a comparison with the coincident MODIS cloud retrievals. However, there are not only significant differences in the temporal sampling between AGRI and MODIS, but also spatial sampling differences between these two instruments. First, in order to avoid uncertainties in their comparison caused by the changes of cloud properties due to different observation time, only cloud retrievals of the exactly the same start scan time of these two systems were selected for comparison. Then, the spatial collocation rule was formulated as follows. For AGRI, the cloud mask and cloud top height are generated at a 4-km resolution. For MODIS, CM, and CTH products are retrieved at 1-km resolution. Therefore, multiple MODIS ground-projected instantaneous field-of-view (GIFOV) pixels will be collocated for a single AGRI retrieval, that is, the \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Cloud Mask Channels (\(\upmu\)m)** & **Cloud Top Height Channels (\(\upmu\)m)** \\ \hline MODIS & 0.659, 0.865, 0.47, 0.555, 1.24, 1.64, 2.13, & \\ MODIS & 0.415, 0.443, 0.905, 0.936, 3.75, 3.959, 1.375, & 11.03, 13.335, 13.635, 13.935, 14.235 \\  & 6.175, 7.235, 8.55, 11.03, 12.02, 13.335, 13.935 & \\ \hline AGRI & 0.65, 1.60, 3.8, 7.12, 11.0, 12.09 & 11.0, 12.09, 13.55 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Moderate Resolution Imaging (MODIS)/Advanced Geosynchronous Radiation Imager (AGRI) bands used in the MODIS/AGRI cloud mask algorithm and cloud top height algorithm. AGRI 4-km GIFOV is the \"reference\" with multiple MODIS measurements within the AGRI GIFOV. To find the MODIS pixels within the AGRI GIFOV means that the distance between AGRI pixel and MODIS pixel is required \(\leq\)2 km (i.e., half of AGRI resolution). If it is based on a conventional method, the distance between pixels of these two sensors has to be calculated individually. The total computation time complexity will be O(N\({}^{2}\)), which requires a huge computational resource. Assuming that AGRI and MODIS each have N pixels at a certain observation time over a certain area, for any single AGRI pixel, to find those points within 2 km from it among the N MODIS pixels, N distance calculations must be carried out. As AGRI has N pixels, the total number of computation is N \(\times\) N. In computer science, the time complexity of this calculation is defined as O(N\({}^{2}\)). In order to solve this massive computation problem as well as minimize the uncertainties resulting from the spatial sampling differences, a collocation algorithm--\"multiple grid matching algorithm\"--was developed in this paper to facilitate comparisons of the MODIS and AGRI cloud retrievals. This multiple grid matching algorithm was designed to be computationally efficient and accurate, allowing for rapid identification of the coincident MODIS and AGRI observations. The grid can be implemented by hash table keywords in computer science. The procedure is described in detail as follows. First, pixels of AGRI and MODIS are subsampled and placed onto an equal-angle grid over the TP. The distance between AGRI pixel and MODIS pixel in the same grid cell should be within 2 km as much as possible. Then, AGRI and MODIS pixels are scanned separately and all pixels fall into each grid cell. Those pixels within the same grid box are exactly the required matches. However, it is possible that the nearest pixel is in the adjacent grid box. The next step is adjusting the size of the grid or shifting the coordinates of the entire grid appropriately, and scanning the AGRI and MODIS samples respectively in another iteration. The target pixels (distance within 2 km) and the nearest pixel can easily fall into a new grid cell. Figure 1 outlines this process. There is no doubt that multiple grid matching can significantly improve the matching accuracy.