# Gridded Visibility Products over Marine Environments Based on Artificial Neural Network Analysis
## 3 Results
### Result of Gridded Vis  
In this section, results related to gridded Vis values obtained using the ANN analysis described in the previous section are provided. To test the accuracy of the inferred gridded Vis, gridded Vis data for the Indian Ocean at 00:00 UTC from the 1 January 2010 case is obtained. The parameters of the constructed ANN model utilizing measurements from the January 2010-2017 time period to train the model are first obtained. Then, the gridded data of child nodes are moved to the trained ANN model, and then, Vis at the grid points is inferred. The gridded data of child nodes include the ERA-Interim gridded data and AOD gridded data representing the resolution of \(0.125^{\circ}\times 0.125^{\circ}\). The ERA-Interim gridded data set included SLP, Ta, RH, Ts, TDsa, and Uh parameters, as described before. The statistical result showed that there are 63,206 groups of measured data from 1 January 2010 in the Indian Ocean, but only 52 groups of measured data contained a Vis value at 00:00 UTC. A comparison of ICOADS Vis data to that of the nearest gridded location of the ICOADS data found that the referred Vis is very close to the measured Vis with a relative error of 12% (Figure 7). Since the reanalysis data used to infer gridded Vis have unavoidable errors relative to measured Vis and the parameters of the trained ANN model have unavoidable errors relative to the real condition, it is necessary to correct the inferred Vis using the measured Vis. The inferred Vis are corrected based on the following three steps:  
Step 1: Calculate the weight value at the gridded data point representing a \(0.125^{\circ}\times 0.125^{\circ}\) area. It is assumed that the gridded Vis could be influenced by the measurements within the radius of 14 km around the grid point (because the longest distance between two adjacent grid points over a \(0.125^{\circ}\times 0.125^{\circ}\) area is less than 14 km). Then, the weight value can be defined as:  
\[\lambda_{k}=\frac{1/D_{k}(x_{i},y_{i})}{\sum_{k=0}^{k=Q}[1/D_{k}(x_{i},y_{i})]} \tag{5}\]  
where \(Q\) is the number of measured data points that fall into a circle with a 14-km radius around the grid point \((x_{i},y_{i})\). \(D_{k}(x_{i},y_{i})\) is the distance between the kth measured data point at the grid point \((x_{i},y_{i})\). Step 2: Calculate the difference between the measured Vis and the referred Vis on the nearest grid point to the measured Vis. It can be defined as:  
\[E_{k}=S_{k}-P_{k} \tag{6}\]  
Figure 7: Comparison of referred Vis, corrected Vis, and measured Vis. where \(E_{k}\) is the difference between the measured Vis and referred Vis on the nearest grid point. \(S_{k}\) is the measured Vis of the kth location, and \(P_{k}\) is the referred Vis on the nearest grid point to \(S_{k}\). Step 3: The corrected Vis after the above steps is defined as:  
\[\mathrm{e}(x_{i},y_{i})=\sum_{k=0}^{k=Q}\lambda_{k}E_{k} \tag{7}\]  
and:  
\[\mathrm{C}(x_{i},y_{i})=\mathrm{e}(x_{i},y_{i})+\mathrm{P}(x_{i},y_{i}), \tag{8}\]  
where \(\mathrm{e}(x_{i},y_{i})\) is the calculated difference between the referred Vis and measured Vis at the grid point \((x_{i},y_{i})\). The \(\mathrm{P}(x_{i},y_{i})\) and \(\mathrm{C}(x_{i},y_{i})\) are the referred and corrected Vis values at the grid point \((x_{i},y_{i})\). It is found out that the corrected Vis is closer to the measured Vis after numerical correction is applied, which greatly improves the accuracy of the inferred Vis (Figure 7). To further test the accuracy of the referred Vis, the referred Vis for the Indian Ocean case from the 6 to 7 November 2010 case using a spatial resolution of \(0.125^{\circ}\times 0.125^{\circ}\) is shown in Figure 8 when a tropical storm was crossing the region. The time resolution of the referred Vis is set up as 6 h. The locations marked by green ovals in Figure 8 represent the low Vis centers. The results suggested that the referred Vis accurately reflected the trajectory of tropical storms, which indicated that the inferred Vis is highly reliable compared to the observations.