# Prediction of Vacant Parking Spaces in Multiple Parking Lots: A DWT-ConvGRU-BRC Model
## 3 Methodology  
### Data Description  
To evaluate the performance of the proposed prediction model, we conducted a case study in Santa Monica, CA, USA (longitude range: [\(-\)118.499378, \(-\)188.49361], latitude range: [34.019575, 34.010806]) [37], which has 11 parking lots scattered over the road network, as illustrated in Figure 1. The data were collected from 6 April 2021 to 13 May 2021. The number of VPSs was collected every 5 min, resulting in 10,944 pieces of historical data per parking lot. We use a 100 m \(\times\) 100 m grid to divide the target area into H \(\times\) W grids (Figure 1). Each parking lot in the region is distributed in a different grid, and a grid without a parking lot distribution is considered to have no VPSs in that grid. Then, the number of VPSs in the area at time t is denoted as:  
\[V_{t}= \begin{bmatrix}v_{t}{}^{(1,1)}&v_{t}{}^{(1,2)}&\cdots&v_{t}{}^{(1,W)}\\ v_{t}{}^{(2,1)}&v_{t}{}^{(2,2)}&\cdots&v_{t}{}^{(2,W)}\\ \vdots&\vdots&\ddots&\vdots\\ v_{t}{}^{(H,1)}&v_{t}{}^{(H,2)}&\cdots&v_{t}{}^{(H,W)}\end{bmatrix}  \tag{1}\]  
where each element in the matrix, denoted as \(v_{t}{}^{(h,w)}\), \(h\in[0,\text{H}]\), and \(w\in[0,\text{W}]\), is the number of VPSs in the grid \((h,w)\). This area is divided into a total of 60 grids, with H being 10 and W being 6. The 11 parking lots we selected in the grid area are the St1-St9 parking lots, Lot1 parking lot, and Library parking lot. These parking lots are mainly distributed in recreational, commercial, and residential areas. It is worth noting that there are similarities and differences in the evolution of the number of spaces in these parking lots. We can imagine that the closer the parking lot types and the closer the distance, the more they should have the characteristics of time-space correlation. We take the Lot1, St5, and St7 parking lots as examples to mine the characteristics of different parking lots from the perspective of spatiotemporal correlation, considering that the St5 and St7 parking lots represent commercial areas and are close to each other, and the Lot1 parking lot represents entertainment areas. Figures 2 and 3 show the spatiotemporal characteristics of these 3 parking lots. The x-axis represents the time interval. The y-axis represents the change in VPSs, where a positive number represents the outflow of vehicles. The larger the number is, the greater the number of VPSs. Figure 2 shows that the inflow on weekends is significantly higher than that on weekdays during the almost full day in the Lot1 parking lot. The Lot1 parking lot represents an entertainment area, which tends to be crowded on weekends. In contrast, between 7 a.m. and 9 a.m., the inflow of the St5 and St7 parking lots is higher on weekdays than on weekends, which may be influenced by the parking of small workers. In addition, we explore the impact of weather factors on the availability of VPSs. Figure 1: Distribution of parking lots in the region. The number of parking occupancies is different for hazardous weather and normal weather. It can be imagined that when encountering hazardous weather such as heavy rain, heavy snow, and smog, people may reduce travel in private cars, so the number of available parking spaces will increase. The results for the three representative parking lots are shown in Figure 3. For the entertainment area represented by Lot1 and the commercial areas represented by St5 and St7, a significant decrease in parking occupancy was observed for all hours of the day under hazardous weather conditions. To assess the impact of hazardous weather conditions on parking demand, we define weather to be considered hazardous if one or more of the following conditions are met: (1) fog or snow, (2) wind speed greater than 39 km/h, (3) precipitation intensity greater than 0.15 inches per hour. All other conditions are considered normal weather conditions. Similar to the research of [PERSON] et al. [38] and [PERSON] et al.