# Gridded Visibility Products over Marine Environments Based on Artificial Neural Network Analysis
## 3 Results
### Fitting Effect of ANN  
Since too much data needs to be shown in Figure 5 and one figure could not well show the result, we decided to use two figures to show the average relative error of each observation point between the inferred Vis and the measured Vis. The root mean square error (RMSE) of the inferred Vis is 0.9323 when considering AOD, and 0.9578 when neglecting AOD. Since the Vis data in this study is given at different levels, the RMSEs that are less than 1 should be regarded as small. Therefore, the ANN model constructed in this paper can highlight the relationship among Vis, AOD, and meteorological factors, whether or not AOD was taken into consideration, which also demonstrates the assumption above that it's reasonable to ignore the effect of aerosols on Vis when inferring Vis. At the same time, the error based on NWP and PCR can reach up to 29% and 21.4%, respectively [10; 13; 24], so the result based on ANN has a higher accuracy than the two common methods. However, there are a few inferred Vis with large relative error. Three reasons may cause this result. One of the reasons is the inadequate training of ANN due to the incomplete data set; the second reason is the deficiency of the model, such as the selected factors influencing Vis not being complete. The last reason is the inaccuracy of the data set used to test the accuracy of the trained model. All these three reasons combined likely played an important role for the accuracy of ANN analysis, which is discussed below. Note that the inferred Vis with a large relative error has a large relative error whether taking AOD into consideration or not, which indicates that the main reason for this is the first or the third reasons mentioned above. Data used to further test the effect of ANN is from the Chinese Ninth Arctic Science Examination (CNASE), which began on 20 July and ended on 26 September, in 2018. The scientific expedition covered more than 12.5 million nautical miles, including 3815 nautical miles in the ice area. The northernmost \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Visibility Level** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline Visibility value (km) & \(<\)0.05 & 0.05–0.2 & 0.2–0.5 & 0.5–1 & 1–2 & 2–4 & 4–10 & 10–20 & 20–50 & \(>\)50 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The rule classifying the Vis level. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Sample Sequence** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ \hline Year, month and day & & & & & & & & & & \\ (UTC) & 20100101 & 20100101 & 20100101 & 20100101 & 20100101 & 201010101 & 20100101 & 20100101 & 20100101 & 20100101 & 20100101 \\ Hour (UTC) & 3:00 & 5:00 & 6:00 & 6:00 & 6:00 & 6:00 & 9:00 & 10:55 & 11:00 \\ Lon (\({}^{\circ}\)E) & 101.6 & 83.2 & 102.6 & 126.5 & 119.1 & 124.5 & 74 & 47.4 & 41 \\ Lat (\({}^{\circ}\)N) & \(-\)24.8 & 5.8 & \(-\)25.8 & 22 & 14.5 & \(-\)7.8 & 10.7 & 12.8 & 16.6 \\ Vis level & 8 & 8 & 8 & 9 & 9 & 9 & 8 & 1 & 9 \\ RH & 62 & 82.3 & 65.7 & 68.9 & 76.9 & 75.2 & 79.8 & 64.3 & 66.6 \\ Ts & 22.4 & 27 & 22.3 & 24 & 28 & 30 & 30.2 & 25.6 & 28 \\ Ta & 21.9 & 28 & 21.9 & 23 & 27.5 & 31 & 31 & 26.7 & 30 \\ Uh & 12.3 & 9.3 & 13.4 & 9.8 & 13.4 & 5.1 & 2.1 & 0.6 & 10.3 \\ SLP & 1018.6 & 1012 & 1017.1 & 1019 & 1007.4 & 1005.1 & 1011.1 & 1020.3 & 1012.2 \\ TDsa & 0.5 & \(-\)1 & 0.4 & 1 & 0.5 & \(-\)1 & \(-\)0.8 & \(-\)1.1 & \(-\)2 \\ AOD & 0.16 & 0.34 & 0.15 & 0.32 & 0.2 & 0.22 & 0.46 & 0.21 & 0.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The sample data set to train the model for both fog and precipitation. location of the expedition is 84.8\({}^{\circ}\) N. The data recorded in this expedition include meteorological and marine data. The meteorological data include air temperature, relative humidity, dew point temperature, sea-level pressure, wind speed, horizontal Vis, etc., which are recorded once a minute.