## 5 Discussion
### Comprehensive Discussion of Model Performance  
Our study used LightGBM, Prophet and SARIMA models to predict the PM\({}_{2.5}\) concentration in Nanning urban area in 2023, and compared and analyzed the performance of each model from many aspects:  
Spatial dimension: In terms of the spatial distribution prediction of PM\({}_{2.5}\) concentration, our study used ArcMap software (version 10.8) and ArcGIS Pro software (version 3.1) to conduct geographic visualization analysis of the raster data prediction results of the three models. Among them, the LightGBM model showed certain advantages. It has a relatively strong ability to capture spatial distribution and can roughly delineate the scope of high-concentration areas. However, there are deficiencies in the internal details of high-concentration areas, and the predicted values are sometimes too high, which cannot accurately reflect the actual concentration changes in high-pollution areas. The Prophet model has obvious shortcomings in spatial prediction. There is a deviation between its predicted spatial position distribution and the actual situation. The predicted values in some areas are too low, and its ability to deal with concentration gradient changes is limited, making it difficult to accurately present the concentration change trend in space. Although the SARIMA model can outline the general outline of the concentration distribution and show the overall trend, it does not accurately grasp the spatial change characteristics of some areas, and the prediction accuracy in these areas needs to be improved. Time dimension and stability in different months: From the perspective of time series trend prediction, the performance of each model is also different. With its strong learning ability, the LightGBM model can better capture the complex change trends in historical data, such as being able to identify the pattern of PM\({}_{2.5}\) concentration being high at the beginning of the year, then decreasing, and rising at the end of the year. However, in actual predictions, its overall prediction results deviate greatly from the true value, and there is a general \"overestimation\" phenomenon, especially in winter months with poor atmospheric diffusion conditions, where the prediction error is more obvious. The Prophet model has a certain processing ability for seasonality and trend in time series, but it over-relies on seasonal patterns in historical data during the prediction process. In the face of more complex concentration changes in May-July, the model is not adaptable enough and the prediction effect is not ideal, especially in the concentration decline stage, the predicted value deviates significantly from the original data, showing an \"underestimation\" trend. As a classic time series model, the SARIMA model can reflect the trend of PM\({}_{2.5}\) concentration in some months. However, due to its high requirements for data stability, it has poor adaptability when facing non-stationary data caused by various factors in 2023, and its forecast performance in January, May, September and November is poor. However, in comparison with the other two models, the overall deviation of the SARIMA model is relatively low. Accuracy and reliability: Through in-depth analysis of model performance indicators, it can be found that there are differences in the accuracy and reliability of each model. The performance of the LightGBM model fluctuates greatly in different months. In some months (such as May), its error indicators (MSE, RMSE, MAE) are low, the prediction effect is good, and it can more accurately reflect the actual concentration situation. But in January, October and December, the error indicators are high and the prediction error is large. During the period from May to July, the MSE, RMSE and MAE values of the Prophet model were significantly larger, indicating that the prediction effect of the model during this period was poor. While in other months, its performance was relatively stable.