## 4 Discussion and Suggestions  
One of the well-known features of the machine learning method is that the model itself is a \"black-box\" to the user. The models trained here can identify the noise signals very well and performs better than the conventional CNR filtering method. However, how did the models achieve that? Did the models apply a similar CNR filtering but with a more precise threshold than the conventional CNR filtering? Table 3 shows the statistics of the data points that are classified as noise by the models from different data sets. If there is a CNR threshold, that would be the maximum value. As we can see, the maximum value varied between data sets. An exception is for the cases of 15 June and 31 July, where they have the same maximum value because they were used for model training together. Besides, these maximums are around \(-13\) to \(-10\) dB, which are much higher than the thresholds normally used (i.e., \(-32\) dB or \(-28\) dB) in previous studies [4,7]. To further explain this, a good example is during the morning of 10 July, which results can be found in Figure 9. There are some horizontal stripes caused by instrumental factors with higher CNR values that should be classified as noise. With a conventional CNR threshold approach, these signals may exceed the threshold and thus be kept after filtering. The trained models classify them as noise signals successfully. Figure 11 presents the model classified data points distribution over different CNR values. Figure 11a shows all data points on that day, classified by the model as noise and non-noise data. There is a boundary between noise and non-noise  
Figure 10: The case with the data collected by the Keflavik lidar: the lidar measurement on 31 July 2019 (**a**) CNR, (**b**) backscatter coefficient, (**c**) depolarization ratio and the machine learning classification result (**d**) predicted classes. data at \(-28\) dB due to the noise labeling method we use (first filter the data with \(-28\) dB then apply DBSCAN method). However, unlike the conventional threshold-based LUT method, there is some overlap around \(-28\) dB. Some classified noise data have CNR values larger than \(-28\) dB, and some non-noise data have CNR values lower than that. Figure 11b presents these data points, which are different from the conventional CNR filtering results. These data have a \"long tail\", which means the models do not simply filter the data with a CNR threshold, either the same or different from the value we used to apply, but use a more complicated method. As a supervised machine learning, the performance of RF is directly related to the labeled data set used for training. The accuracy of the noise discrimination model is higher than the classification model, partly because the noise of lidar measurements is better studied and easier to label compared to other classes. For non-noise classes, the rain classification has the worst performance; one reason is that this lidar is not sensitive to rain, and the way we label the rain data is mainly by descending movements, which could be hard to distinguish if the \(\beta\) or \(\delta\) values are similar to that of the background. Moreover, the rain data are relatively rare in the training data set we use. For rain classification, training on extended data sets with more rain events is needed. Including data from other instruments, such as the ceilometer and rain gauge next to the lidar, might also  
Figure 11: Model classified data points distribution as a function of CNR. Data collected on 10 July 2019 at Reykjavik. (**a**) All data are classified by the model as noise (blue) and non-noise (orange). (**b**) specifically, only the data points classified differently by the model than by the conventional CNR threshold method: the data points classified as noise but with CNR greater or equal to \(-28\) dB (purple) and the data points classified as non-noise but with CNR lower or equal to \(-28\) dB (yellow).