# Retrieval and Comparison of Multi-Satellite Polar Ozone Data from the EMI Series Instruments
## 4 Results and Discussions
### Weighted Fusion Correction  
The results indicated that certain differences existed between the different EMI instruments, which could be attributed to many factors, including algorithms, data sources, and environmental conditions. In addition, the EMI instruments also occasionally have missing tracks. Therefore, it was necessary to explore suitable data fusion methods to reduce the random and systematic errors in the EMI instruments, improve the spatial coverage, and provide higher-quality TOC products. The weighted fusion of the spatiotemporal data provided the prospect of improving the spatial and temporal resolutions of the EMI series instruments. By assigning weighting factors to each instrument, weighted fusion could achieve an optimal data fusion [51]. Thus, we assigned weighting factors according to the RMS values of the different EMI instruments. RMS values are obtained by QDOAS retrieval \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Stations**} & \multirow{2}{*}{
\begin{tabular}{c} **Latitude**, \\ **Longitude** \\ \end{tabular} } & \multirow{2}{*}{**Method**} & **EMI-GF5 (02)** & **EMI-GF5 (01A)** & **EMI-DQ01** \\  & & & **Averaged** & **Averaged** & **Averaged** \\  & & & **Difference** & **Difference** & **Difference** \\ \hline Reunion & \(20.9^{\circ}\)S, \(55.5^{\circ}\)E & SAOZ & \(-1.21\%\) & \(-1.05\%\) & \(-1.49\%\) \\ Rio Gallegos & \(51.6^{\circ}\)S, \(69.3^{\circ}\)W & Dobson & \(-1.53\%\) & \(-2.87\%\) & \(-1.98\%\) \\ Mini Saoz Paris & \(48.9^{\circ}\)N, \(2.3^{\circ}\)E & SAOZ & \(-4.12\%\) & \(-3.25\%\) & \(-3.39\%\) \\ Kerguelen & \(49.4^{\circ}\)S, \(70.3^{\circ}\)E & Dobson & \(2.39\%\) & \(-1.79\%\) & \(-1.68\%\) \\ Mini Saoz OHP & \(43.9^{\circ}\)N, \(5.7^{\circ}\)E & SAOZ & \(-1.87\%\) & \(-1.98\%\) & \(-1.26\%\) \\ TEH & \(51.32\)N, \(35.73^{\circ}\)E & Dobson & \(-5.41\%\) & \(-4.41\%\) & \(-5.27\%\) \\ Dumont & \(66.7^{\circ}\)S, \(140.0^{\circ}\)E & SAOZ & \(-3.16\%\) & \(2.71\%\) & \(2.75\%\) \\ Mini Saoz Seychelles & \(4.68^{\circ}\)S, \(55.53^{\circ}\)E & SAOZ & \(2.19\%\) & \(-2.99\%\) & \(-4.54\%\) \\ Marambio & \(64.23^{\circ}\)S, \(56.62^{\circ}\)W & Dobson & \(2.79\%\) & \(4.63\%\) & \(2.72\%\) \\ La Quiaca & \(22.11^{\circ}\)S, \(65.43^{\circ}\)W & Dobson & \(0.93\%\) & \(3.97\%\) & \(1.55\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Information on the stations and the mean relative differences between the EMI-GF5(01A), EMI-GF5(02), and EMI-DQ01 and ground-based TOCs. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Station**} & **Emi-GF5 (02)** & **EMI-GF5 (01A)** & **Emi-Dq01** \\  & **Averaged Std** & **Averaged Std** & **Averaged Std** \\ \hline Reunion & \(2.48\%\) & \(1.98\%\) & \(2.48\%\) \\ Rio Gallegos & \(3.52\%\) & \(5.27\%\) & \(3.71\%\) \\ Mini Saoz Paris & \(2.01\%\) & \(4.46\%\) & \(5.61\%\) \\ Kerguelen & \(5.86\%\) & \(2.91\%\) & \(3.15\%\) \\ Mini Saoz OHP & \(4.07\%\) & \(3.76\%\) & \(3.58\%\) \\ TEH & \(1.66\%\) & \(4.91\%\) & \(4.28\%\) \\ Dumont & \(5.96\%\) & \(7.45\%\) & \(6.32\%\) \\ Mini Saoz Seychelles & \(3.99\%\) & \(2.65\%\) & \(2.99\%\) \\ Marambio & \(7.34\%\) & \(5.04\%\) & \(5.13\%\) \\ La Quiaca & \(4.15\%\) & \(2.39\%\) & \(2.15\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Averaged standard deviation (std) between the EMI-GF5(01A), EMI-GF5(02), and EMI-DQ01 and ground-based TOCs. for different EMI instruments, and EMI values with lower RMS values are assigned higher weights. The basic equation describing weighted fusion is expressed as:  
\[\hat{y}=\frac{\sum_{i=1}^{N}w_{i}\hat{y}_{i}}{\sum_{i=1}^{N}w_{i}} \tag{2}\]  
where \(\hat{y}\) is the final fusion result, \(\hat{y}_{i}\) is the retrieval result for the \(i\)-th instrument, and \(w_{i}\) is the weight of the \(i\)-th instrument. This method determined the weight of a single sensor based on a variance matrix, which enabled the weight distribution of the EMI-DQ01, EMI-GF5(01A), and EMI-GF5(02) data to be obtained, thereby achieving weighted data fusion.