## 2 Methodology
### Machine Learning Algorithms  
Machine learning is a popular method used to achieve some tasks which are relatively easy to perform subjectively for a small data set but are difficult to achieve by conventional algorithms for large data sets, such as the classification of a large number of images. Several algorithms were developed based on Artificial Intelligence and Statistics [15]. In general, there are two approaches, supervised and unsupervised learning. The main difference is that for supervised learning, the data need to be labeled. The Random Forest (RF) classifier is a supervised ensemble classifier that uses a combination of decision trees to classify the target data set [22]. It is also called the bagged tree method since the data are split into the samples used for training the trees (in-bag samples) and the samples used for internal cross-validation (out-bag samples). The final prediction is made by a majority vote of the trees. [PERSON] and [PERSON] [23] reviewed the use of RF in remote sensing and revealed that the RF classifier could successfully handle high dimensional data, and at the same time, be fast and insensitive to over-fitting. RF was also used for lidar measurements specifically. [PERSON] et al. [17] used two algorithms, including RF, to discriminate aerosols from clouds in satellite-based lidar measurements, and they found the method had higher accuracy compared to probability distribution function-based algorithms. [PERSON] et al. [24] compared several machine learning algorithms on air pollution (SO\({}_{2}\) and NO\({}_{2}\)) classification and found that RF can give a good result. RF \begin{table}
\begin{tabular}{c c} \hline \hline
**Model** & **Windcube 200S** \\ \hline manufacturer & Leosphere Inc. \\ \hline wavelength (\(\mu\)m) & 1.54 \\ \hline detection range (m) & 50–14,000 \\ \hline range resolution (m) & 25, 50, 75, 100 \\ \hline elevation angle (\({}^{\circ}\)) & \(-\)10–90 \\ \hline azimuth angle (\({}^{\circ}\)) & 0–360 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The main specifications of the lidars in Iceland. is well-known for its competence in solving data imbalance problems and robustness to data noises [25]. In this study, we use an RF classifier to classify the lidar measurements. Unlike RF, DBSCAN clustering is an unsupervised algorithm used for unlabeled clustering. It is a popular density-based data clustering algorithm proposed by [PERSON] et al. [26]. The algorithm uses a simple minimum density level estimation, and the objects with a density exceeding a threshold for a number of neighbored data (minPts), within a radius \(\varepsilon\), will be considered as a core point of a group [27]. The algorithm can be used to separate data points with different densities. [PERSON] et al. [18] used the DBSCAN method and successfully identified the bio-mass burning aerosols from a lidar data set. We used the DBSCAN with a conventional CNR filter to identify and label the lidar noise data. Noise Discrimination Model  
The noise of the lidar data is normally identified by CNR thresholds [7; 8; 9]. In Iceland, the data quality within the boundary layer is mostly good, and the noise dominates the measurements above the boundary layer, except for the measurements of clouds and precipitation. However, in operation, we found the method of CNR filtering not optimal [4] as the data quality and CNR value are not strictly linearly correlated, i.e., low CNR value does not always represent noise signals. In some cases, the CNR value increases with height in the troposphere, which is unrealistic since fewer aerosols are expected at higher altitudes. Moreover, there are cases when the noise signals spike an unexpectedly high CNR value, which will be kept even after the CNR filtering. The CNR value of the cloud measurements, especially high clouds, are normally lower than the signal within the boundary layer, which makes it difficult to find the \"boundary\" between clouds and noises. Here, we introduce a new method to optimize noise identification.