# A Novel Interpretable Deep Learning Model for Ozone Prediction
## 4 Discussion  
### Interpretability Discussion  
Another important issue in O\({}_{3}\) prediction is how to interpret the results. For this purpose, we took the nine monitoring stations in Nanjing city as our analysis target. July 2019 was chosen for the interpretability discussion because of the generally consistent wind direction of the selected monitoring stations during this period. We collated the hourly data into a supervised dataset and 697 samples were obtained. The geographical distribution of the nine monitoring stations is shown in Figure 5a. The wind speed (classified based on the Beaufort wind scale) and wind direction distribution of all stations during this period are shown in Figure 5b. From Figure 5b, it can be seen that the dominant wind direction in July 2019 was ESE and the wind speed was between 1.3 m s\({}^{-1}\) and 3.1 m s\({}^{-1}\). For the interpretability discussion of temporality, we reviewed how the temporal attention layer assigns weights to each past moment; some statistical procedures were then conducted. The statistical process was conducted in two steps as follows: (1) We computed the summation of the temporal attention weight using all samples in July 2019. A \(24\times 24\) matrix representing the sum of the attention weight for each forecast time and past moment was constructed. (2) The min-max normalization was applied to the matrix to highlight the relative importance of each past moment to the prediction of the target station at each forecast time (the closer the value is to 1, the more important the past moment is to the corresponding prediction step and vice versa). As shown in Figure 6, the temporal attention layer tends to learn the short-term dependency in the prediction of the first several hours. Specifically, in the prediction of the 1 st to 4 th hour, the temporal attention layer assigns the largest weight to the \(-4\)th to \(-1\)st past moments and the Pearson correlation coefficient between the prediction steps and the most important moments was 0.94 (Figure 6). As the forecast lead time increases, the short-term dependency gradually shifts to periodical dependency. According to Figure 6, the periodical dependency dominates from the 8 th to the last prediction step and the corresponding most important past moment is from the \(-18\)th to the \(-4\)th. The Pearson correlation coefficient was 0.99, which means a highly positive correlation (Figure 6). In  
Figure 5: (**a**) The geographical locations of the nine monitoring stations in Nanjing. (**b**) The wind map of the monitoring stations in July 2019 (unit: frequency). Note, the hourly data contain wind direction and speed at the nine stations. summary, the temporal information was learned in short-term and periodical dependency and the temporal attention finely captured the trade-off of these two kinds of dependency. For the interpretability discussion of how the predictions of the target station are affected by stations nearby in the STAGRU, the same statistical procedures were conducted. We computed the summation of the attention weight for each prediction step of each surrounding monitoring station in July 2019. A \(24\times 8\) matrix representing the relation between each forecast lead time and surrounding stations was created. The statistical results of the station CCM (located in the middle of the study area) are depicted in Figure 7. According to the heat map, it is obvious that the RJL is the most important surrounding monitoring station to the CCM for the whole prediction, which is consistent with their relative geolocation and the dominant wind direction. XWH, SXL, ZHM and ATZX are also important; a certain number of NE, ENE, ESE and SW winds were present according to Figure 5b. According to Figure 5a, it can be seen that a mountain stands upwind of the station MGQ, which weakens the airflow and reduces the wind. Further, the relative humidity of the Xuanwu Lake is significant, which negatively influences ozone formation [10]. Meanwhile, MGQ is located downwind.