## 4 Measurement Setup and Dataset
### Dataset and Preprocessing  
#### 4.2.1 Dataset  
The recorded LiDAR data are stored in form of a serialized rosbag with an attached weather message, containing, among others, comprehensive precipitation data. The data were acquired in the field over a duration of one year, covering all seasons. This is illustrated by the precipitation class distribution (see Figure 5a), which shows quite a balanced data distribution for slight drizzle (1), rain (4-6), snow (9-10), or mixed precipitation, including small hail (13). All class IDs, including the respective SYNOP-standard ID and descriptions, are listed in Table 2.  
Some classes, like slight drizzle and rain (3), moderate drizzle (2), and slight snow pellets or small hail shower (12), were highly underrepresented due to their less-likely occurrence, which again results from them being either a transition class between two major categories (2), or containing some ambiguity like class 3 or 12. Consequently, the datasets from the corresponding classes are majorly augmented by oversampling, similarly to [PERSON] et al. [28]. The class-specific oversampling magnitude is illustrated in Figure 5a, in which the original data share of underrepresented classes is marked in black, whereas the final test/train split is visualized by the corresponding colors.  
For model training, the data are split into 80% training-, 15% validation-, and 5% test-data. Since the number of data samples after augmentation is still not fully uniformly distributed among SYNOP-classes, the training-validation-test split is applied class-specific in order to ensure a fair representation of generally underrepresented classes in the validation and test evaluations (see Figure 5a).  
Further, the dataset was found to cover a wide range of precipitation intensities, covering precipitation rates up to more than \(R=$50\,\mathrm{mm}\mathrm{/}\mathrm{h}$\)[13]. In order to illustrate this, Figure 5b shows the precipitation rate spread of the corresponding classes for all contained samples.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**ID** & **SYNOP** & **Description** \\ \hline
0 & 0 & No Precipitation \\
1 & 51 & Slight Drizzle \\
2 & 53 & Moderate Drizzle \\
3 & 58 & Slight Drizzle and Rain \\
4 & 61 & Slight Rain \\
5 & 63 & Moderate Rain \\
6 & 65 & Heavy Rain \\
7 & 68 & Slight Rain or Drizzle \\
8 & 69 & Moderate or heavy Rain or Drizzle \\
9 & 71 & Slight Snowfall \\
10 & 73 & Moderate Snowfall \\
11 & 77 & Snow Grains \\
12 & 87 & Slight Snow Pellet or Small Halli Shower \\
13 & 88 & Slight Snow Pellet or Small Halli Shower, mixed \\
14 & 90 & Hail Shower, mixed \\ \hline \hline \end{tabular}
\end{table}
Table 2: Precipitation class IDs and descriptions in accordance with the SYNOP standard [19], using the same indexing with permission from Ref. [18], 2024, IEEE.  
Figure 5: **(a)** Distribution of the training data with respect to the precipitation class (see Table 2). While the proportion of the originally recorded samples is highlighted by a black frame, the train, test, and validation split is highlighted by color. Highly underrepresented classes were augmented by oversampling. **(b)** Distribution of the measured precipitation rates \(R_{\text{meas}}\) with respect to the precipitation class, showing typically occurring Middle European \(R\) spans for the corresponding classes and precipitation rates of up to \(R\geq$90\,\mathrm{mm}\mathrm{/}\mathrm{h}$\).