1 Introduction
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Traffic and meteorological data need to be matched accurately in time and space to study their relationships. This can be difficult, if traditional weather station data is used, because stations might be located far away from the location of the traffic measurement. This is particularly relevant in case of precipitation, which can vary strongly in time and space and might not be captured well by station data. Therefore, we use reanalysis and radar-based precipitation products to derive meteorological parameters from high-resolution gridded data sets.
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Existing studies make use of a wide variety of multivariate modeling techniques. However, in many studies linear relationships are assumed between weather and different types of travel behavior, although not all effects seem to be linear in all situations [1]. By applying a stepwise predictor selection procedure, we explore non-linear relationships in a controlled setting.
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While most studies focus on weather impacts on bicycles, cars, or trucks, little is known about weather impacts on motorbike usage. By analyzing a comprehensive database of long-term traffic measurements in Germany that includes motorbike counts, we can fill this gap.
2 Data
2.1 Traffic data
2.2 Reanalysis data
2.3 Radar data
2.4 Population data
Class | Inhabitants (class range) | Inhabitants (as used for aggregation) | Frequency |
---|---|---|---|
1 | 0–3 | 1.5 | 146,845 |
2 | 3–250 | 126.5 | 158,317 |
3 | 250–500 | 375 | 20,342 |
4 | 500–2000 | 1250 | 26,183 |
5 | 2000–4000 | 3000 | 6741 |
6 | 4000–8000 | 6000 | 2543 |
7 | 8000–\(\infty\) | 8000 | 507 |
Variable name | Variable type | Variable description |
---|---|---|
Potential predictor variables for NO_MET | ||
hour | Categorical (24) | Hour of the day |
dow | Categorical (7) | Day of the week (public holidays are treated as Sundays) |
mon | Categorical (12) | Month of the year |
holiday | Categorical (2) | School holiday in the federal state of the traffic station |
trend | Continuous | Linear trend in time |
hour:dow | Interaction | Different diurnal cycles on different days of the week |
break | Categorical (n) | \(n={2,3,4}\) segments determined by breakpoint detection (if \(n=1\) this term and its interactions are excluded) |
break:trend | Interaction | Different trends in different segments |
break:hour | Interaction | Different diurnal cycle in different segments |
Potential predictor variables for MET | ||
temp\(^k\) | Continuous | Daily maximum temperature at 2 m height at the ERA5 grid cell closest to the traffic station |
cloud\(^k\) | Continuous | Daily mean total cloud cover at the ERA5 grid cell closest to the traffic station |
wind\(^k\) | Continuous | Daily maximum wind gust at 10 m height at the ERA5 grid cell closest to the traffic station |
precip\(^{1/k}\) | Continuous | Average hourly precipitation sum of all RADOLAN grid cells within a radius of 10 km around traffic station |
weekend | Categorical (3) | Distinguish between working day, Saturday, and Sunday (only included in interaction terms below, but not as single variable) |
weekend:temp\(^k\) | Interaction | Different relationships between temperature and traffic |
weekend:precip\(^{1/k}\) | Interaction | Different relationships between precipitation and traffic |
weekend:clt\(^k\) | Interaction | Different relationships between cloud cover and traffic |
weekend:wind\(^k\) | Interaction | Different relationships between wind speed and traffic |
3 Methods
3.1 Linear regression and breakpoint detection
strucchange
[40, 41], which implements the algorithm described in Bai and Perron [42] for simultaneous estimation of multiple breakpoints. Eq. 1 is extended tostrucchange
applies an efficient algorithm to find the breakpoints \(\hat{\imath }_1, \ldots ,\hat{\imath }_m\) that minimize the objective function3.2 Poisson regression
3.3 Assessing model performance
3.4 Model selection procedure
3.4.1 Step 1: Breakpoint detection
3.4.2 Step 2: Model without meteorological variables
3.4.3 Step 3: Model with meteorological variables
4 Results
4.1 Statistics of meteorological variables
Temp | Precip | Cloud | Wind | |
---|---|---|---|---|
Temp | 1.00 | |||
Precip | − 0.03 | 1.00 | ||
Cloud | − 0.37 | 0.22 | 1.00 | |
Wind | − 0.07 | 0.21 | 0.19 | 1.00 |
Highway | Federal road | |||||||
---|---|---|---|---|---|---|---|---|
Predictor variable | Mot | Car | Van | Trk | Mot | Car | Van | Trk |
hour | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
dow | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
mon | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
hour:dow | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
holiday | 6 | 54 | 74 | 99 | 1 | 78 | 79 | 91 |
trend | 13 | 38 | 12 | 58 | 19 | 23 | 9 | 27 |
break | 2 | 4 | 11 | 11 | 1 | 6 | 8 | 4 |
break:trend | 36 | 32 | 79 | 27 | 10 | 44 | 70 | 38 |
break:hour | 52 | 33 | 70 | 23 | 14 | 46 | 74 | 48 |
temp | 95 | 89 | 76 | 8 | 93 | 86 | 38 | 16 |
temp | 33 | 0 | 0 | 0 | 55 | 0 | 0 | 1 |
temp\(^2\) | 3 | 4 | 1 | 0 | 7 | 0 | 0 | 0 |
temp\(^3\) | 7 | 0 | 0 | 0 | 17 | 0 | 0 | 0 |
temp\(^4\) | 15 | 0 | 0 | 0 | 14 | 1 | 0 | 0 |
weekend:temp | 59 | 82 | 54 | 5 | 39 | 82 | 29 | 13 |
weekend:temp\(^2\) | 10 | 18 | 30 | 2 | 18 | 11 | 9 | 3 |
weekend:temp\(^3\) | 7 | 3 | 1 | 1 | 23 | 8 | 1 | 0 |
weekend:temp\(^4\) | 23 | 4 | 1 | 0 | 17 | 18 | 1 | 0 |
cloud | 68 | 10 | 1 | 0 | 99 | 45 | 4 | 0 |
cloud | 3 | 0 | 0 | 0 | 3 | 0 | 0 | 0 |
cloud\(^2\) | 9 | 1 | 0 | 0 | 25 | 0 | 0 | 0 |
cloud\(^3\) | 1 | 0 | 0 | 0 | 3 | 0 | 0 | 0 |
cloud\(^4\) | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
weekend:cloud | 18 | 5 | 1 | 0 | 9 | 13 | 2 | 0 |
weekend:cloud\(^2\) | 31 | 3 | 0 | 0 | 50 | 15 | 1 | 0 |
weekend:cloud\(^3\) | 5 | 1 | 0 | 0 | 10 | 10 | 1 | 0 |
weekend:cloud\(^4\) | 1 | 0 | 0 | 0 | 2 | 7 | 0 | 0 |
wind | 52 | 7 | 4 | 4 | 89 | 15 | 3 | 1 |
wind | 1 | 0 | 0 | 0 | 2 | 0 | 0 | 0 |
wind\(^2\) | 3 | 0 | 0 | 0 | 10 | 0 | 0 | 0 |
wind\(^3\) | 1 | 0 | 0 | 0 | 6 | 0 | 0 | 0 |
wind\(^4\) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
weekend:wind | 24 | 6 | 4 | 4 | 7 | 9 | 3 | 0 |
weekend:wind\(^2\) | 14 | 1 | 1 | 0 | 27 | 4 | 0 | 0 |
weekend:wind\(^3\) | 9 | 0 | 0 | 0 | 30 | 2 | 0 | 0 |
weekend:wind\(^4\) | 1 | 0 | 0 | 0 | 7 | 0 | 0 | 0 |
precip | 40 | 5 | 25 | 0 | 90 | 1 | 2 | 0 |
precip | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
precip\(^{(1/2)}\) | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
precip\(^{(1/3)}\) | 5 | 0 | 1 | 0 | 3 | 0 | 0 | 0 |
precip\(^{(1/4)}\) | 3 | 0 | 0 | 0 | 9 | 0 | 0 | 0 |
weekend:precip | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
weekend:precip\(^{(1/2)}\) | 8 | 0 | 8 | 0 | 11 | 0 | 1 | 0 |
weekend:precip\(^{(1/3)}\) | 11 | 1 | 14 | 0 | 23 | 0 | 1 | 0 |
weekend:precip\(^{(1/4)}\) | 9 | 3 | 1 | 0 | 43 | 1 | 0 | 0 |
4.2 Selection of predictor variables
Vehicle type | Highways | Federal roads |
---|---|---|
Mot | 0.53 | 0.37 |
Pkw | − 0.12 | − 0.17 |
Lfw | − 0.05 | − 0.16 |
Lkw | − 0.10 | 0.02 |
Variable | Value |
---|---|
Hour | 12 PM |
Month | June |
Holiday | no |
Trend | First day of time series |
Breakpoint | First segment |
Precip | 0 mm/h |
Temp | 25°C |
Cloud | 50% |
Wind | 10 m/s |