## Verification of the New Approach
### Experiments for the Verification of Reliability
#### 3.4.2 Test Similarity Criteria Based on Snowfall Mode  
A reliable scale in experimental modeling depends on the right similarity criterion. In order to reproduce the non-uniform snowdrift phenomena caused by structures with scale models, the widely accepted fact is that it is necessary to meet geometric, kinematic, and dynamic similitude requirements. Since the beginning of snowdrift research,, many different similarity criteria have been proposed, validated, and applied by some famous scholars, such as [PERSON] [32], [PERSON] [33], [PERSON] [34], [PERSON] [19], [PERSON] [16], [PERSON] [35], [PERSON] [18], [PERSON] [36], [PERSON] [21], [PERSON] [2], and so on. However, just as it is not possible to satisfy the Froude numbers and Reynolds numbers simultaneously [37], it has been proved that some of the similarity criteria reveal incompatibility, therefore only the most important and widely accepted similarity parameters are selected and discussed. In the present study, considering the fact that the snow particles falling into the snow bed are provided by the sowing pattern, the experimental modeling is mainly focused on the reliable simulation of the Froude number and drifting volume. The original form of the Froude number is defined as  
\[\frac{U^{2}}{gL}, \tag{3}\]  
where \(U\) is the reference wind velocity, \(g\) is gravitational acceleration (m/s\({}^{2}\)), and \(L\) is the reference length (m). But considering the discrepancy of particle density between the prototype and the test, [PERSON] [33] and [PERSON] [34] proposed the densimetric Froude number:  
\[\frac{\rho}{\rho_{p}}\frac{U^{2}}{gL} \tag{4}\]  
where \(\rho\) is the air density, and \(\rho_{p}\) is the particle density. To confirm the reliable simulation of drifting volume, [PERSON] [35] suggested that the test should satisfy the following time scaling parameter:  
Figure 11: Photo of snow distribution for the field observation. Figure 10: Wind field during the observation. \[\frac{TQ\eta}{\rho_{P}L^{2}} \tag{5}\]  
where \(T\) is experiment time (s), \(Q\) is the transport rate of snow (kg/m\(\cdot\)s), and \(\eta\) is the snow collection efficiency. Except for the above similarity, a number of similarity requirements, like the flow field, ejection process, particle trajectory, and deposition pattern, must be satisfied in the experiments on snow drifting on roofs to ensure a reliable simulation. First, the near ground turbulent wind velocity profile for stable atmospheric conditions is  
\[U=\frac{u_{*}}{\kappa}\ln(\frac{z}{z_{0}}), \tag{6}\]  
where \(\kappa\) is the Von-Karman constant, \(u_{*}\) is the friction velocity, \(z\) is the height above the surface, and \(z_{0}\) is the roughness height parameter. Geometric similarity should be enforced through the relationship  
\[D_{P}/L. \tag{7}\]  
Except for the densimetric Froude number expressed as Equation (4), the following Froude number based on the threshold friction velocity should also be satisfied to simulate the shear stress of particles near the ground [16]:  
\[\frac{\rho}{\rho_{P}-\rho}\frac{u_{*t}^{2}}{gD_{P}} \tag{8}\]  
where \(D_{P}\) is the particle diameter, \(u_{*t}\) is the threshold friction velocity, and \(v\) is the kinematic viscosity. To ensure a similar movement trajectory of a particle, [PERSON] [24] indicated that the following equations must be satisfied:  
\[\frac{\rho}{\rho_{P}-\rho}\frac{u_{*t}^{2}}{gL}, \tag{9}\]  
\[w_{f}/U, \tag{10}\]  
where \(w_{f}\) is the settling velocity of snow particles (m/s). The deposition or erosion mechanisms could be modeled satisfactorily through the similarity of the particle ejection process [19; 38]:  
\[\frac{\rho}{\rho_{p}}\frac{U^{2}}{gL} \tag{4}\]0  
In the present study, because the simulation of the Froude number is considered to be more important, the limit of the Reynold number is released.