# Gridded Visibility Products over Marine Environments Based on Artificial Neural Network Analysis
## 2 Data and ANN Model
### Data  
In the analysis, AOD, SLP (sea level pressure), Ta at the 10 m, RH, Ts, TDsa, and Uh are considered important parameters affecting Vis. These parameters affecting Vis as a physical/optical process are shown as follows:  
AOD: AOD is defined as the integration of extinction coefficients in the vertical direction, which describes the reduction effect of aerosols for light. SLP: SLP has an important effect on precipitation, and precipitation has a great effect on Vis. Ta: Ta has an important influence on the particle size distribution and gas-solid distribution of air pollutants. The higher the temperature near the surface, the stronger the convection, the lower the concentration of pollutants, and the better the Vis  
RH: RH is not only closely related to precipitation, but also affects the concentration of aerosol chemical components, which is closely related to the scattering coefficient of particulate matter. Ts and TDsa: On the one hand, the higher Ts could cause the stronger convection near the surface, which lead the lower concentration of pollutants and the better Vis. On the other hand, Ts and TDsa are closely related to the occurrence of sea fog [18]. Uh: Uh cannot only dilute atmospheric pollutants, but also change atmospheric stability and has a greater impact on Vis. Usually, a greater Uh could cause better Vis. The data of meteorological parameters used to train ANN are taken from the International Comprehensive Ocean-Atmosphere Data Set (ICOADS), which is the largest collection of ocean surface observational data sets covering the period from 1784 to the present, including the data of the ships, buoys, and coastal sites from all parts of the world. Data of AOD are taken from MODIS Level 3 gridded atmosphere daily global joint product at a spatial resolution of \(1^{\circ}\times 1^{\circ}\), and that includes all aerosol types [9]. The data of gridded meteorological parameters are used to infer the historical gridded Vis data obtained from ECMWF model runs, and tropical cyclone data that were used to further test the accuracy of inferred Vis were obtained from the Joint Typhoon Warning Centre (JTWC). Figure 1: The technical flowchart to infer visibility (Vis) based on artificial neural network (ANN). Due to the inconsistent position of AOD data and ICOADS data in the areas studied, it was necessary to interpolate ICOADS and AOD data to the same position using a statistical method. Then, we were able to get the complete sample data set to train the ANN model. The statistical method used to govern this extrapolation in the study is the Inverse Distance Weighting Method [19], which assumed that AOD at the position of ICOADS data could be influenced by the AODs within a radius of R km. If there are Q numbers of locations in which AOD data are located within an R-km radius near the position of ICOADS data, then the AOD at the position of ICOADS data can be defined as:  
\[\text{AOD}=\sum_{k=1}^{k=Q}{aod_{k}*\lambda_{k}} \tag{1}\]  
where \(aod_{k}\) is the AOD value at the Kth location, \(\lambda_{k}\) is the weight of the AOD value at the Kth location influencing the AOD at the position of the ICOADS data. \(\lambda_{k}\) can be defined as:  
\[\lambda_{k}=\frac{1/D_{k}}{\sum_{k=1}^{k=Q}[1/D_{k}]} \tag{2}\]  
where \(D_{k}\) is the distance between the location \(k\) and the position of the ICOADS data located. Since the radius R is closely related to the AOD at the position of ICOADS data located, it is necessary to find the R values making the generated AOD have an optimum value relative to the measured AOD. To do this, we first randomly selected 10% of the data set to test the accuracy of the generated AOD, and the remaining 90% were used to generate the AOD in the location of the randomly selected data. The initial radius was set to 20 km, the radius difference between two iterations was set to 10 km, and then, the mean relative errors of the generated AOD with different R values were calculated.