## 4 Measurement Setup and Dataset
### Data Acquisition
#### 4.1.1 Weather Sensor Unit  
Primarily, the WSU is equipped with measurement tools from the manufacturer, _Thies Clima_. These devices are used to quantify wind, temperature, air humidity, sunshine expo  
Figure 3: Outdoor measurement setup consisting of a perception sensor unit with the devices under test and a weather sensor unit for continuous acquisition of comprehensive weather data. Both systems are connected to a cloud-computing platform in order to exchange, store, and visualize the respective data online. Adapted with permission from Ref. [13], 2024, IEEE.  
sure, and rain conditions. Out of these, the primary focus of this study is on precipitation, which is gauged via a laser dichrometer [34]. The dichrometer can accurately capture existing precipitation by registering particles based on their specific velocity \(v\) and diameter \(D\). The data on these particles are preserved in a discrete 2D histogram, denoted as \(n(1\times J)\), which comes with velocity bins \(j\) and diameter bins \(i\), each with a width \(\Delta v_{j}\), \(\Delta D_{i}\) and a nominal value \(v_{j}\), \(D_{i}\). The particle counting is performed over an integration time \(t_{\text{int}}\), which is typically around 60 s, as in our case, and within a certain detector cross-section \(A_{\text{det}}\) (in our setup, 0.00456 m\({}^{2}\)).  
An exemplary PSVD for a precipitation rate of \(R=21\,\text{mm}/\text{h}\) is shown in Figure 4. The patterns of these distributions may vary greatly based on location and type of rainfall [35; 36]. In addition to identifying the type of precipitation from the PSVD, it is also possible to calculate characteristic parameters like the wavelength-dependent signal attenuation \(\alpha\), the backscattering coefficient \(\beta\), and the rainfall rate \(R\)[32; 37]. For events of solely liquid rain, \(R\) can be calculated as shown below:  
\[R=\frac{6\pi}{10^{4}}\int_{D=0}^{\infty}D^{3}v(D)N(D)dD \tag{4}\]  
By incorporating the density of the corresponding particles, this relation can also be applied to solid precipitation like snow, expressing the liquid water equivalent precipitation rate [38]. Therefore, the measured \(n\) has to be normalized to the average number of particles per unit volume \(N(D_{i})\) by conducting the following transformation [34; 39]:  
\[N(D_{i})=\frac{n_{i}^{\Sigma j}}{v_{i}^{\overline{j}}\cdot t_{\text{int}}\cdot A _{\text{det}}\cdot\Delta D_{i}} \tag{5}\]  
with \(n_{i}^{\Sigma j}\) being the sum of all particles in diameter bin \(i\) and \(v_{i}^{\overline{j}}\) being the average particle velocity in diameter bin \(i\).  
Figure 4: Exemplary PSVD for a measured precipitation rate of \(R=21\,\frac{\text{mm}}{\text{h}}\), as reprinted with permission from Ref. [18], 2024, IEEE, describing the number of particles \(n\) with a diameter \(D\) and a velocity \(v\) as a 2D histogram. In addition to the precipitation rate, calculated with (6), the precipitation class can be identified by the particle characteristics, as indicated.  
By that, the corresponding key parameters, including the attenuation and backscattering coefficient, can be calculated by discrete integration over the particle size bins:  
\[R\approx\widehat{R}=\frac{6\pi}{10^{4}}\cdot\frac{1}{t_{\mathrm{int}}\cdot A_{ \mathrm{det}}}\cdot\sum_{i=1}^{I}D_{i}^{3}n_{i}^{\Sigma_{j}} \tag{6}\]  
and  
\[\alpha\approx\widehat{\alpha}=\frac{\pi}{4\cdot t_{\mathrm{int}}\cdot A_{ \mathrm{det}}}\sum_{i=1}^{I}D_{i}^{2}Q_{\mathrm{ext}}(D_{i})\frac{n_{i}^{ \Sigma_{j}}}{v_{i}^{j}} \tag{7}\]  
with \(\beta\) accordingly by replacing \(Q_{\mathrm{ext}}(D_{i})\) with \(Q_{\mathrm{b}}(D_{i})\).  
Opposed to the wavelength-dependent backscattering and extinction coefficient, the dishorrometer is able to derive precipitation rate and sum directly with an error of less than 15% in case of rain. The WSU dataset relevant for this work, however, consists of 15 recorded weather classes with the corresponding precipitation rate, as further elaborated in Section 4.2.