- Email: [email protected]
Analysis of rainfall impacts on platooned vehicle spacing and speed
Transportation Research Part F 15 (2012) 395–403
Contents lists available at SciVerse ScienceDirect
Transportation Research Part F journal homepage: www.elsevier.com/locate/trf
Analysis of rainfall impacts on platooned vehicle spacing and speed Ashrafur Rahman ⇑, Nicholas E. Lownes Department of Civil and Environmental Engineering, University of Connecticut, 261 Glenbrook Road, Unit 2037, Storrs, CT 06268, USA
a r t i c l e
i n f o
Article history: Received 17 September 2010 Received in revised form 21 February 2012 Accepted 15 March 2012
Keywords: Driver behavior Car following Platoon Rainfall Speed Gap
a b s t r a c t This paper investigates the impact of rainfall on the behavior of drivers in a car-following state by analyzing the differences in time gap, speed, and following distance of platooned vehicles between no-rain and rainy weather conditions on a two-lane rural state highway. Time gap, following distance, and individual vehicle speed were observed. Platooned vehicles were identified by a maximum time gap threshold of 4 s, allowing for interactions between vehicles beyond perception–reaction time. Rainfall intensity was utilized as the measure of local precipitation conditions and was categorized according to American Meteorological Society standards. The analysis showed that rainy weather conditions were strongly correlated with greater spread in speed distributions when compared to dry conditions. Further, the shift from no-rain to rain showed an increase in time gap and a reduction in speed. No statistically significant differences were observed between following distances in any weather conditions – suggesting that drivers tend to maintain following distance irrespective of weather conditions and speed reduction causes the observed time gap increase. This is supported by the observed 5.6% decrease in mean time gap – from 1.97 s to 2.1 s and the 3.7% decrease in mean speed – from 47 mph (75.6 km/h) to 45.3 mph (72.9 km/h). Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Driver comfort and perception of safety are associated with weather and roadway conditions. These perceptions impact driver behavior and therefore the operation, safety, and capacity of a roadway. Precipitation (either rain or snow) can increase accidents risks to a significant extent (Andrey, Mills, Leahy, & Suggett, 2003; Keay & Simmonds, 2005; Kilpeläinen & Summala, 2007). However, the driver behavior mechanisms that drive these changes to safety and operations are not completely understood. In particular, the existing literature is inconclusive in addressing the tendency of drivers to increase following distance or slow down in adverse weather, or both. This distinction is important practically, as it will enable engineers to better design roadways and signal systems to accommodate safety in adverse weather. It is important theoretically because most of the existing microsimulation tools on the market model driver behavior as a function of following distance and speed – improvements in understanding should lead to improved performance of these tools in modeling transportation systems in adverse weather conditions. 2. Background Two primary aspects of the driving experience dominate driver perception and make driving more hazardous in adverse weather: visual acuity and pavement friction (Dewar & Olson, 2007; Jung, Qin, & Noyce, 2010). Reduced visibility due to the ⇑ Corresponding author. Tel.: +1 860 420 9483; fax: +1 860 486 3398. E-mail address: [email protected] (A. Rahman). 1369-8478/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trf.2012.03.004
396
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
presence of water, snow or fog the on windshield (Morris, Mounce, Button, & Walton, 1977) reduces the span of preview and thus increases uncertainty of the presence and behavior of other vehicles on the road (van der Hulst, Rothengatter, & Meijman, 1999). Increased slipperiness that comes with a reduction in pavement friction has also been shown to increase accident risks (Kokkalis & Panagouli, 1998). In most cases, the risk associated with weather is not estimated by drivers properly (Edwards, 1999; Kilpeläinen & Summala, 2007); they adjust their behavior to some extent by reducing speed, maintaining larger headway, and avoiding overtaking (Kilpeläinen & Summala, 2007; van der Hulst et al., 1999) but their responses are based more upon perceived than actual risk. During adverse weather, the response of drivers while they are in a car-following state (in a platoon) can be more complex than free-flowing vehicles. Platooned drivers have to react to not only the actions of surrounding vehicles but also to the uncertain conditions created by adverse weather. Vehicles in platoon have their operations restricted by other vehicle movements, the result being that models of traffic utilize the concept of car following to predict the behavior of a vehicle in the next time step. Studies have found that car-following behavior will vary, but that in general it is the result of a driver’s attempt to maintain a desired safety margin between them and the leading vehicle (Brackstone & McDonald, 1999; Brackstone, Waterson, & McDonald, 2009; Saad, 1996). At low traffic volumes, drivers are able to drive at their desired speeds until they encounter another vehicle. As traffic volume increases, the frequency of these encounters increases and the frequency of passing opportunities becomes less common, leading to the formation of platoons (Brackstone et al., 2009). Platoons also occur when queues discharge from a signalized intersection – with the lead vehicle in the platoon dictating the acceleration and speed of following vehicles in the queue. In this paper we take advantage of platoon formation downstream of signalized intersections to observe platoon driver response. We observe both choice of speed and the spacing maintained between vehicles and contrast observations in rainy and clear conditions. Characterizing driver response to weather is an important task, evidenced by the number of studies over the past four decades that have investigated this relationship. A significant amount of research has been dedicated exploring the impact of rainfall on traffic parameters. The Federal Highway Administration’s Road Weather Management Program (2009) compiled studies of the impact of adverse weather on traffic and mentions that rain can cause anywhere from a 3% to 17% decrease in average speed, a 5–14% decrease in volume, and a 4–30% decrease in capacity. Unrau and Andrey (2006) found increases in mean time gap due to rain of 0.4 s and 0.1 s during the nighttime and daytime, respectively. In each study cited here and in reports such as the FHWA’s, observed impacts can vary significantly depending on the intensity of rainfall and how that intensity is classified. Rainfall classification is a major issue, adopting a particular rainfall classification can produce different results than another classification system. There is also a tradeoff between using more detailed classification systems and the ability to observe a statistically significant number of drivers in those conditions. For example, Smith, Byrne, Copperman, Hennessy, and Goodall (2004), who categorized light rain as 0.01–0.25 in/h (0.25–6.35 mm/h) and heavy rain as 0.25 in/h (6.35 mm/h) or greater, found a 3 mph (4.8 km/h) and 4 mph (6.4 km/h) reduction of speed in light and heavy rain conditions respectively on a 3-lane freeway in Virginia. Saberi and Bertini (2010) adopted a completely different classification system, categorizing very light rain as 0.01 in/h (0.25 mm/h), light rain as 0.01–0.04 in/h (0.25–1 mm/h), moderate rain as 0.04–0.16 in/h (1–4.05 mm/ h), and heavy rain as greater than 0.16 in/h (4.05 mm/h). They found a maximum speed reduction of 2 mph (3.2 km/h), 4 mph (6.4 km/h), and 10 mph (16 km/h) in very light, light, and moderate rainfall conditions, respectively. We see a general agreement between the two studies, though the magnitude of the effects changes with the more detailed classification scheme. This increased detail comes at the cost of data availability – the latter study being unable to observe enough drivers in heavy rain to draw any conclusions. Among the many studies associated with rainfall’s impact on free-flow traffic, relatively few address driver behavior in a platoon during rainfall. In part this may be due to the lack of general consensus on an appropriate following threshold to identify a platooned vehicle. Vogel (2002) measured front axle to front axle time spacing of platooned vehicles and calculated the correlation of successive vehicle speeds and plotted these correlation values against time headways. He then constructed two best-fit regression lines: one for larger correlation values (vehicles with strong observed interaction) and smaller correlation values. He considered the intersection point of the two regression lines as the separation point between free cars and interacting cars. He found that a 6-s time headway is optimal for distinguishing free vehicles from following vehicles. Al-Kaisy and Durbin (2009) concluded similar results from a study in Montana, USA. They calculated the mean travel speed of vehicles with time headways equal to or greater than a specific threshold value. Then they plotted mean speeds against time headways and observed when the curve became horizontal. The curves started to flatten out asymptotically in the range of 5–7 s, indicating that after this time the interaction between successive vehicles is almost zero. Though he concluded this, they used a 3-s time headway for platoon identification. Values of 5–7 s represent the upper range of following vehicle threshold – there is a higher degree of uncertainty that vehicles are truly following for these values of time gap. This is the reason most researchers apply a lower threshold value (as do we) when identifying following vehicles. The Highway Capacity Manual 2000 (TRB, 2000) recommends using percent time spent following (the average percent of travel time that a vehicle must travel in platoon behind a slower vehicle due to the inability to pass) to identify platooned vehicles. However it admits that it is difficult to measure percent time spent following and provides a surrogate measure of a 3-s threshold. Gattis, Alguire, Townsend, and Rao (1997), used 5 s as a time headway criterion for identifying platoons, while Hoban (1983) of Australia recommended a 4 s time headway criterion. Another traffic parameter useful for platoon identification is the number of vehicles in the group (Gaur & Mirchandani, 2001). Billot, El Faouzi, and De Vuyst (2009) followed this method and used both time headways and number of vehicles
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
397
Traffic Recorder
Fig. 1. Site description: traffic data recorder location (above), platooned vehicles (below).
for platoon identification. They carried out an empirical study on the impact of rainfall on platoon formation on a two-line interurban freeway section located on 118 National Road near Paris, France. Platoons were identified on the basis of both critical time headway and the number of vehicles in the group. The median time headway of all vehicles traveling on the road was defined as the threshold time headway for identifying platooned vehicles – which relies on a restrictive assumption of half of all vehicles being in a platoon. Their reported median headway values were 3, 3.6 and 4.5 s for no-rain, light rain and medium rain condition respectively. These values, along with a designated minimum 4 vehicles in a group were used to define a platoon. They found a 7.5% increase in the number of platooned vehicles from dry to rainy conditions. In this paper, platooned vehicles are defined utilizing a 4-s time gap (the time between the rear axle of the leading vehicle and the front axle of the following vehicle) instead of time headway (front axle to front axle). The study seeks to quantify the effect of rainfall on following behavior, specifically the choice of time and/or space gap between vehicles. In this context, time gap corresponds as well or better to the spacing drivers will likely perceive in making car-following decisions (the distance from the back of the preceding vehicle to their front bumper). 3. Methods In developing the experimental design, care was taken to (1) isolate the effects of rainfall on behavior through careful site selection, (2) improve the spatial compatibility of weather and traffic datasets with careful instrumentation location, (3) identify platoons to capture vehicles in car following states, and (4) collect time gap data at a scale (milliseconds) that is appropriate for the comparisons being made. The following subsections describe each of these efforts briefly. 3.1. The site Traffic data collection took place on a section of Route 195 (Storrs Road) in Mansfield, Connecticut. It is a two-lane state highway with minimum access control. This section has a posted speed limit of 45 mph (72.5 km/h) and a wide shoulder. It is free from roadway condition defects, vertical curvature and any sharp horizontal curvature that may affect driver speed and gap choice. Two photographs of the site are shown in Fig. 1. There are few access points close to the data collection point, those that do exist have relatively low volumes compared to Route 195. A manual observation carried out on a weekday for 3 h (at 9:00–10:00 AM, 1:00–2:00 PM, and 4:30–5:30 PM) shows that the turning volume to these access points compared to the hourly highway volume are 6–8% of the highway volume.
398
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
Headway (sec)
6 5 4 3 2 1 0 Hoban (1983)
Gattis et al. (1997)
HCM 2000
Billot et al. (2009)
Sources Fig. 2. Headway threshold values for distinguishing free-flow/platooned vehicles.
It was assumed that this low turning volume would have minimal effect on the speed and gap distribution of platooned vehicles. To further reduce any impact, very slow-moving vehicles (speeds less than three standard deviations from mean highway speed) were removed from analysis – it was assumed these would represent turning or malfunctioning vehicles. There are two traffic signals along this stretch of Route 195 one on either side of the data collection point. They are both located far enough away – 0.4 miles (0.64 km) and 0.5 miles (0.8 km) from the traffic recorder to allow leading vehicles (even if leading vehicle is a truck) to reach their desired speed prior to reaching the data collection. This site was selected to isolate, to the greatest extent possible, the impact of weather events on driver behavior by removing the other geometric stimuli (narrow shoulders, grade changes, horizontal curvature, etc.) that impact driver behavior. 3.2. Traffic data collection An automatic traffic data recorder with pneumatic tubes was installed at the study site. The traffic data recorder was used to collect data 24 h a day for approximately 5 months, from May 2009 to October 2009. Speed data (in mph) was collected directly by the software supplied with the traffic counter. The software recorded the time gap between vehicles in whole seconds. To get a more accurate representation of drivers’ gap choices at realistic speeds, a computer programming code was developed to retrieve gap data in milliseconds. This code utilized the unedited data recorded by the traffic counter and the time gap data produced by the software. Later, following distance (in feet) was calculated by multiplying time gap by following vehicle speed. 3.3. Platoon vehicle identification Al-Kaisy and Durbin (2009) suggests that time headways less than 5 s should capture most following (and platooned) vehicles. This threshold should hold for time gap as well, since time gap and time headway only differ by the fraction of a second it takes for the front and rear axle of a vehicle to pass a specific point. As previously discussed and shown in Fig. 2, there is no single accepted value for this following threshold. Further, drivers’ perception–reaction time is typically
0.35
No-Rain
0.30
Light Moderate
Density
0.25 0.20 0.15 0.1 0.05 0 0
2
4
6
8
10
Time Gaps (sec) Fig. 3. Density plot of time gaps in different weather condition.
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
45
NoRain Light Medium
40
Relative Frequency
399
35 30 25 20 15 10 5 0 <25
25-30 30-35 35-40 40-45 45-50 50-55 55-60
>60
Speed (mph) Fig. 4. Driver speed distribution in different weather condition.
taken to be in the 2–3 s range (Dewar & Olson, 2007). So, a threshold value of 5 s might capture a portion of free flowing vehicles, if it is assumed that drivers maintain only enough distance to react properly to a travel or roadway condition. Considering these factors, a conservative maximum time gap of 4 s (similar to Hoban, 1983) between successive vehicles was chosen as a threshold in this study to capture a large percentage of following vehicles without diluting results with free-flow vehicles. 3.4. Weather data spatial compatibility Weather data were collected from the nearest weather station, approximately 2 miles away from the traffic recorder location. This distance should allow for a spatially compatible study of the relationship between traffic parameters and weather, meaning that weather happening at the station is very similar to that at the traffic data collection site. The station provided rainfall (in) and rainfall rate (in/h) in 5 min intervals. The American Meteorological Association’s (AMSs) rainfall classification system was used in this study (Glickman, 2000). Rainfall was classified as either (1) light rain, from trace to 0.1 in/h (2.5 mm/h); (2) moderate rain, from 0.11in/h to 0.3 in/h (2.6–7.6 mm/h); or (3) heavy rain, over 0.3 in/h (7.6 mm/h). Only a small amount of heavy rainfall data was gathered during the data collection period, so a decision was made to eliminate the higher level of rainfall intensity from the data. A second analysis aggregated light and moderate rainfall to compare with clear conditions. A note: this study was conducted with data up to moderate rainfall and is not verified with heavy rainfall when visual acuity and friction are expected to be reduced further. 3.5. Data reduction and integration Past literature shows that driving behavior and performance can differ from day to night (Ivey, Lehtipuu, & Button, 1975) and that when visibility drops, speed also drops (Liang, Kyte, Kitchener, & Shannon, 1998). Therefore, this study only considered daytime traffic. Additionally, only weekday data were taken in this study to reduce the likely impact of variation in trip purpose (commute vs. recreational trips) on the results. Platooned traffic data (i.e. time gaps, speeds, and following distances) gathered during rainy conditions were compared to data gathered during no-rain conditions from either 1 week before or after the rainfall at the same time of rainfall occurrence. In this way we attempted to control for seasonal variations in weather, visibility and the myriad other variables that influence the way people drive. If the week after the event or prior did not have clear weather conditions, data from the next closest week was utilized. Statistical methods and tests employed in the analysis of data are presented in the following section. Statistical tests were performed assuming the data are independent i.e. there is no cross-correlation among the datasets due to seasonality, time of day and day of week – satisfying the assumptions of the analytical methods employed. 4. Results 4.1. Analysis of means A density plot of time gaps for all vehicles in no-rain, light rain, and moderate rain conditions is shown in Fig. 3. Densities are increasingly skewed to the right from no-rain to moderate rain conditions, though no distinct difference can be observed above 4–5 s. Fig. 3 illustrates the shift of the time gap distribution to the right as rainfall intensity increases. The peaks of the distributions are in the vicinity of 1.5–2 s which is drivers preferred gap choice. This is similar to a finding by Vogel (2002) who found that drivers preferred time headway is 2 s using a similar plot. Fig. 4 shows the proportion of platooned passenger
400
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
Table 1 F-test results (a = 0.05). Parameter
Comparison
P-value
Significant difference (Y/N/Greater)
Time gaps
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.1299 0.6755
N N
Speeds
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.9374 0.0009
N Greater in rain
Table 2 Summary of data. Parameter
Weather
Mean
Min
Max
Time gap
No-rain Rain
1.971 2.083
0.113 0.119
3.993 3.997
Speed
No-rain Rain
47.0 45.3
21.0 8.0
69.0 70.0
cars driving within the specified speed ranges under the three rainfall conditions. It shows a clear trend of vehicles traveling at higher speeds in no-rain conditions. For example, the proportions of drivers in the 40–45 mph (64–72 km/h) and 50– 55 mph (80.5–88.5 km/h) speed ranges during clear conditions are approximately the same, while a distinctly greater proportion of drivers choose 40–45 mph (64–72 km/h) over 50–55 mph (80.5–88.5 km/h) in light rain and moderate rain conditions. To check for differences in variance (or the spread of the data), F-tests with 5% level of significance (a = 0.05) were conducted between the time gaps in light rainfall and moderate rainfall condition; the test results did not imply any statistically significant difference in variance, nor did a similar analysis show a difference between clear and rainy conditions (in which light and moderate rain data were combined). Similar to time gaps, no significant difference of speed variances between light rainfall and moderate rainfall conditions was found. Increased variance of speed from no-rain to rainy weather was found. Results are shown in Table 1. Table 2 summarizes the primary traffic data parameters used in analysis, including values for the mean, minimum, and maximum values for time gap and speeds. The table shows a 5.7% (0.11 s) increase in mean time gaps from clear to rainy conditions. The mean speed reduction is 3.7% – about 2 mph (3.2 km/h) from clear to rainy conditions. The gap increment agrees with the findings of Unrau and Andrey (2006) for uncongested flow during daytime from no-rain to light rain conditions. The mean speed reduction in this study is greater than that found for free-flow vehicles in uncongested conditions (Rahman & Lownes, 2010), where a statistically significant but very small speed reduction of 1.8% or 0.9 mph (1.5 km/h) was observed between no-rain and rain. The statistical significance of the observed differences between mean time gaps and speeds in clear and rainy conditions were analyzed using Z-tests performed with a = 0.05. For both mean time gap and speed, the null hypothesis was that there is no difference between means in clear and rainy conditions. The alternative hypothesis for the time gap Z-test was that the mean time gap is higher in rain than in no-rain conditions. The alternative hypothesis for mean speed analysis was that the mean speeds are lower in rain than in no-rain. The Z-test for time gap gave a Z-statistic of 5.598 (which is less than critical Z-value of 1.645) indicating that mean time gap is larger in rainy conditions. The Z-test for speed gave a Z-statistic of 13.947 (which is greater than the critical Z value 1.645) indicating that mean speed is greater in no-rain conditions. In summary, an anlaysis of the means of speed and time gap produced results that are intuitive and statistically significant. Our observations suggest that drivers (a) slow down in rainy conditions and that (b) an increase in vehicle spacing (measured in time units) is observed. What is not known at this point is whether the increase in vehicle spacing is a function of a driver decision to increase their following distance, or is simply a function of their observed speed reduction.
Table 3 K–S test results (a = 0.05). Parameter
Comparison
Dcritical
Dcalculated
Significant difference (Y/N)
Time gaps
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.0627 0.0328
0.0438 0.0781
N Y
Speeds
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.0627 0.0328
0.0571 0.1476
N Y
Following distance
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.0627 0.0328
0.0426 0.0327
N N
401
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
Following Dist. in Rain
70 60
Speed in Rain
Time Gap in Rain
4 3 2 1
50 40 30 20 10
0 0
1
2
3
Time Gaps in No-Rain
(a)
4
400 300 200 100 0
20
30
40
50
Speeds in No-Rain
(b)
60
0
100
200
300
Following Dist. in No-Rain
(c)
Fig. 5. Quantile–quantile plots between no-rain (clear) and rainy conditions (a) time gaps, (b) speeds, (c) following distances.
4.2. Analysis of distributions Moving beyond simple analysis of means, efforts were made to investigate the difference in distributions under different weather conditions. The Kolmogorov–Smirnov (K–S) test, which determines if two datasets differ significantly from each other, was employed. It does not require any knowledge of prior distribution and the data set sizes do not need to be equal. Two-sided K–S tests were performed with the null hypothesis that there is no significant difference in spacing and speed distributions between light rain and moderate rain conditions, and no-rain and rain (combined light and moderate) conditions. The critical value D of K–S test statistics was calculated using the following equation (Lamm, Choueiri, & Mailaender, 1990):
Dcritical ¼ c
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n1 þ n2 n1 n2
where n1 and n2 are the sample sizes of the datasets and c = 1.36 at a significance level of a = 0.05. If the calculated D-value is greater than the critical D-value, the data suggests evidence of a significant difference between the datasets. The results of the K–S test are shown in Table 3. The test found no significant differences between speed and time gap data in light rain and moderate rain conditions. However, significant differences were found between data in clear and rainy conditions (with combined light and moderate rain data). No significant differences in following distance were found in any weather conditions. The results in Table 3 suggest that drivers do not distinguish between light and moderate rain in their time gap and following distance choices, though there is evidence of a difference between clear and aggregated rainy conditions. 4.2.1. Graphical comparison of distributions As a final method of examining the relationship between rainy conditions and driver behavior and their distributions, quantile–quantile (Q–Q) plots of clear and rainy conditions (combined light and moderate rain) data were drawn, as shown in Fig. 5. A Q–Q plot is a graphical method for comparing two distributions by plotting their quantiles. If two variables are identically distributed, the plot of the quantiles of the variables set against each other will be a straight line with a slope of one (Wilk & Grandesikan, 1968). As seen in Fig. 5, the Q–Q plots of time gaps and speeds lie above and below the reference line, respectively, suggesting that time gaps values are higher in rainy conditions and speeds are smaller. The Q–Q plot of following distances almost perfectly coincides with the 45° line which agrees with the K–S test results of a statistically nonsignificant difference in following distance. Interestingly, following distance did not produce a statistically significant difference in any comparison (though the rain vs. clear comparison of distributions came quite close in a practical sense). This finding suggests that drivers tend to maintain the same spatial distance between vehicles and slow down slightly, producing the observed difference in time gap. 5. Discussion There are interesting insights, both qualitative and quantitative, to be gleaned from this study. Other questions are also raised. Both are addressed here. Our observations suggest that drivers slow down in rainy conditions. Some of these drivers, the platoon leaders, do so by choice. The followers in a platoon have their choice of speed dictated to a certain extent. This speed reduction did lead to an increase in the spacing of vehicles (as measured by time headway), though it appears that drivers do not choose to increase their following distance in rainy conditions. This observation raises an interesting question: Is the increase in time headway imparted by speed reduction a large enough increase to mitigate the effects of loss of pavement friction? In short, are drivers compensating enough for the conditions of the roadway? Although time gaps are observed growing larger from light to moderate rainy condition (cf. Fig. 3), distributional differences are not statistically significant. This is also true for speeds. The AMS rainfall classification did not provide the means to
402
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
distinguish between driver response at light and moderate rainfall intensity levels, indicating that (1) no such distinction exists, (2) a different rainfall classification system might be more appropriate for modeling driver behavior in rainy conditions, or (3) this study did not have enough data points within each level to distinguish smaller, marginal differences across the classification levels. It would be worthwhile in the future to investigate cut-off intensity levels that correlate with significant differences in these parameters using natural breaks. An important aspect of this kind of study is the selection of time window. In this study only the actual rainfall period was used. No consideration was given to effects observed in the post-rainfall time period in which effects on pavement friction and visibility may still play a role in driver behavior. The duration and extent of the loss of pavement friction will be a function of a great number of pavement, weather and traffic variables. The inclusion of the post-rainfall period is of great interest and would be a natural and important extension of this study. This study found a significant decrease in speed and an increase in time gap from clear to rainy conditions; however, following distance displayed no significant effects. The decrease of overall speed reduction of platoon was mainly due to the speed reduction of each platoon leader, which is most likely caused by a reduction in visibility and a perceived increased risk from reduced pavement friction. The following drivers reduced their speed to maintain their desired following distances as the same mechanism of platoon formation (Brackstone et al., 2009). This desired following distance did not change between in rainy conditions. The only change in following behavior observed was an increase in the time gap between vehicles, and this increase can be account for by the speed reduction. This would suggest that platooned drivers decrease may react to perceived weather risk not by increasing following distances but only reacting to the speed of their leading vehicle. This paper provides empirical insights that may be useful in accurately modeling the driver-environment relationship. Models of driver behavior and traffic flow form the backbone of a variety of important analytical tools, including traffic microsimulation, traffic assignment, and signal optimization packages. Nearly all of these tools assume the environment is static and has minimal or no effect on driver and/or vehicle behavior (Maze, Agarwal, & Burchett, 2006). As traffic simulation software and analytical tools increase in sophistication and precision, the modeling of driver-environment interactions, such as the relationship between driver and weather conditions, can be increasingly beneficial. Acknowledgements This study was funded in part by the University of Connecticut Research Foundation. Special thanks to Jon Sleezer for providing weather data, Kelly Bertolaccini for her editing efforts and Pujan Joshi for his coding assistance. References Al-Kaisy, A., & Durbin, C. (2009). Platooning on two-lane two-way highways: An empirical investigation. Journal of Advanced Transportation, 43, 71–88. Andrey, J., Mills, B., Leahy, M., & Suggett, J. (2003). Weather as a chronic hazard for road transportation in Canadian cities. Natural Hazards, 28, 319–343. Billot, R., El Faouzi, N., & De Vuyst, F. (2009). Multilevel assessment of the impact of rain on drivers’ behavior: Standardized methodology and empirical analysis. Transportation Research Record, 2107, 134–142. Brackstone, M., & McDonald, M. (1999). Car-following: A historical review. Transportation Research Part F: Traffic Psychology and Behaviour, 2, 181–196. Brackstone, M., Waterson, B., & McDonald, M. (2009). Determinants of following headway in congested traffic. Transportation Research Part F: Traffic Psychology and Behaviour, 12, 131–142. Dewar, R. E., & Olson, P. L. (2007). Human factors in traffic safety. Tucson, Arizona: Lawers & Judges Publishing Company, Inc.. Edwards, J. B. (1999). Speed adjustment of motorway commuter traffic to inclement weather. Transportation Research Part F: Traffic Psychology and Behaviour, 2, 1–14. FHWA Road Weather Management Program (2009). How do weather events impact roads? Last modified 11.05.09. Last accessed 14.07.10. Gattis, J. L., Alguire, M. S., Townsend, K., & Rao, S. (1997). Rural two-lane passing headways and platooning. Transportation Research Record, 1579, 27–34. Gaur, A., & Mirchandani, P. (2001). Method for real-time recognition of vehicle platoons. Transportation Research Record, 1748, 8–17. Glickman, T. S. (2000). Glossary of meteorology. Boston: American Meteorological Society. Hoban, C. J. (1983). Towards a review of the concept of level of service for two-lane roads. Australian Road Research, 13, 216–218. Ivey, D. L., Lehtipuu, E. K., & Button, J. W. (1975). Rainfall and visibility: The view from behind the wheel. Journal of Safety Research, 7, 156–169. Jung, S., Qin, X., & Noyce, D. A. (2010). Rainfall effect on single-vehicle crash severities using polychotomous response models. Accident Analysis and Prevention, 42, 213–224. Keay, K., & Simmonds, I. (2005). The association of rainfall and other weather variables with road traffic volume in Melbourne, Australia. Accident Analysis & Prevention, 37, 109–124. Kilpeläinen, M., & Summala, H. (2007). Effects of weather and weather forecasts on driver behaviour. Transportation Research Part F: Traffic Psychology and Behaviour, 10, 288–299. Kokkalis, A. G., & Panagouli, O. K. (1998). Factual evaluation of pavement skid resistance variation: Surface wetting from chaos. Chaos, Solitons and Fractals, 9(11), 1875–1890. Lamm, R., Choueiri, E. M., & Mailaender, T. (1990). Comparison of operating speeds on dry and wet pavements of two-lane rural highways. Transportation Research Record, 1280, 199–207. Liang, W. L., Kyte, M., Kitchener, F., & Shannon, P. (1998). Effect of environmental factors on driver speed: A case study. Transportation Research Record, 1635, 155–161. Maze, T. H., Agarwal, M., & Burchett, G. (2006). Whether weather matters to traffic demand, traffic safety, and traffic operations and flow. Transportation Research Record, 1948, 170–176. Morris, R. S., Mounce, J. M., Button, J. W., & Walton, N. E. (1977). Visual performance of drivers during rainfall. Transportation Research Record, 628, 19–25. Rahman, A., & Lownes, N. E. (2010). Spatially compatible rainfall-speed analysis. In Proceedings of the 89th annual meeting of the transportation research board, Washington, DC. Saad, F. (1996). Driver strategies in car following situations. In A. G. Gale (Ed.), Vision in vehicle – V (pp. 61–70). Oxford: Elsevier. Saberi, M., & Bertini, R. L. (2010). Empirical analysis of the effects of rain on measured freeway traffic parameters. In Proceedings of the 89th annual meeting of the transportation research board, Washington, DC.
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
403
Smith, B. L., Byrne, K. G., Copperman, R. B., Hennessy, S. M., & Goodall, N. J. (2004). An investigation into the impact of rainfall on freeway traffic flow. In Proceedings of the 83rd annual meeting of the transportation research board, Washington, DC. TRB (2000). Highway capacity manual 2000. Washington, DC: National Research Council. Unrau, D., & Andrey, J. (2006). Driver response to rainfall on urban expressways. Transportation Research Record, 1980, 24–30. van der Hulst, M., Rothengatter, T., & Meijman, T. (1999). The effect of reduced visibility and time pressure on drivers’ distance-keeping behaviour. In A. G. Gale (Ed.), Vision in vehicle – VII (pp. 311–318). Oxford: Elsevier. Vogel, K. (2002). What characterizes a ‘‘free vehicle’’ in an urban area? Transportation Research Part F: Traffic Psychology and Behaviour, 5, 15–29. Wilk, M. B., & Grandesikan, R. (1968). Probability plotting methods for the analysis of data. Biometrika, 55(1), 1–17.
Contents lists available at SciVerse ScienceDirect
Transportation Research Part F journal homepage: www.elsevier.com/locate/trf
Analysis of rainfall impacts on platooned vehicle spacing and speed Ashrafur Rahman ⇑, Nicholas E. Lownes Department of Civil and Environmental Engineering, University of Connecticut, 261 Glenbrook Road, Unit 2037, Storrs, CT 06268, USA
a r t i c l e
i n f o
Article history: Received 17 September 2010 Received in revised form 21 February 2012 Accepted 15 March 2012
Keywords: Driver behavior Car following Platoon Rainfall Speed Gap
a b s t r a c t This paper investigates the impact of rainfall on the behavior of drivers in a car-following state by analyzing the differences in time gap, speed, and following distance of platooned vehicles between no-rain and rainy weather conditions on a two-lane rural state highway. Time gap, following distance, and individual vehicle speed were observed. Platooned vehicles were identified by a maximum time gap threshold of 4 s, allowing for interactions between vehicles beyond perception–reaction time. Rainfall intensity was utilized as the measure of local precipitation conditions and was categorized according to American Meteorological Society standards. The analysis showed that rainy weather conditions were strongly correlated with greater spread in speed distributions when compared to dry conditions. Further, the shift from no-rain to rain showed an increase in time gap and a reduction in speed. No statistically significant differences were observed between following distances in any weather conditions – suggesting that drivers tend to maintain following distance irrespective of weather conditions and speed reduction causes the observed time gap increase. This is supported by the observed 5.6% decrease in mean time gap – from 1.97 s to 2.1 s and the 3.7% decrease in mean speed – from 47 mph (75.6 km/h) to 45.3 mph (72.9 km/h). Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Driver comfort and perception of safety are associated with weather and roadway conditions. These perceptions impact driver behavior and therefore the operation, safety, and capacity of a roadway. Precipitation (either rain or snow) can increase accidents risks to a significant extent (Andrey, Mills, Leahy, & Suggett, 2003; Keay & Simmonds, 2005; Kilpeläinen & Summala, 2007). However, the driver behavior mechanisms that drive these changes to safety and operations are not completely understood. In particular, the existing literature is inconclusive in addressing the tendency of drivers to increase following distance or slow down in adverse weather, or both. This distinction is important practically, as it will enable engineers to better design roadways and signal systems to accommodate safety in adverse weather. It is important theoretically because most of the existing microsimulation tools on the market model driver behavior as a function of following distance and speed – improvements in understanding should lead to improved performance of these tools in modeling transportation systems in adverse weather conditions. 2. Background Two primary aspects of the driving experience dominate driver perception and make driving more hazardous in adverse weather: visual acuity and pavement friction (Dewar & Olson, 2007; Jung, Qin, & Noyce, 2010). Reduced visibility due to the ⇑ Corresponding author. Tel.: +1 860 420 9483; fax: +1 860 486 3398. E-mail address: [email protected] (A. Rahman). 1369-8478/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trf.2012.03.004
396
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
presence of water, snow or fog the on windshield (Morris, Mounce, Button, & Walton, 1977) reduces the span of preview and thus increases uncertainty of the presence and behavior of other vehicles on the road (van der Hulst, Rothengatter, & Meijman, 1999). Increased slipperiness that comes with a reduction in pavement friction has also been shown to increase accident risks (Kokkalis & Panagouli, 1998). In most cases, the risk associated with weather is not estimated by drivers properly (Edwards, 1999; Kilpeläinen & Summala, 2007); they adjust their behavior to some extent by reducing speed, maintaining larger headway, and avoiding overtaking (Kilpeläinen & Summala, 2007; van der Hulst et al., 1999) but their responses are based more upon perceived than actual risk. During adverse weather, the response of drivers while they are in a car-following state (in a platoon) can be more complex than free-flowing vehicles. Platooned drivers have to react to not only the actions of surrounding vehicles but also to the uncertain conditions created by adverse weather. Vehicles in platoon have their operations restricted by other vehicle movements, the result being that models of traffic utilize the concept of car following to predict the behavior of a vehicle in the next time step. Studies have found that car-following behavior will vary, but that in general it is the result of a driver’s attempt to maintain a desired safety margin between them and the leading vehicle (Brackstone & McDonald, 1999; Brackstone, Waterson, & McDonald, 2009; Saad, 1996). At low traffic volumes, drivers are able to drive at their desired speeds until they encounter another vehicle. As traffic volume increases, the frequency of these encounters increases and the frequency of passing opportunities becomes less common, leading to the formation of platoons (Brackstone et al., 2009). Platoons also occur when queues discharge from a signalized intersection – with the lead vehicle in the platoon dictating the acceleration and speed of following vehicles in the queue. In this paper we take advantage of platoon formation downstream of signalized intersections to observe platoon driver response. We observe both choice of speed and the spacing maintained between vehicles and contrast observations in rainy and clear conditions. Characterizing driver response to weather is an important task, evidenced by the number of studies over the past four decades that have investigated this relationship. A significant amount of research has been dedicated exploring the impact of rainfall on traffic parameters. The Federal Highway Administration’s Road Weather Management Program (2009) compiled studies of the impact of adverse weather on traffic and mentions that rain can cause anywhere from a 3% to 17% decrease in average speed, a 5–14% decrease in volume, and a 4–30% decrease in capacity. Unrau and Andrey (2006) found increases in mean time gap due to rain of 0.4 s and 0.1 s during the nighttime and daytime, respectively. In each study cited here and in reports such as the FHWA’s, observed impacts can vary significantly depending on the intensity of rainfall and how that intensity is classified. Rainfall classification is a major issue, adopting a particular rainfall classification can produce different results than another classification system. There is also a tradeoff between using more detailed classification systems and the ability to observe a statistically significant number of drivers in those conditions. For example, Smith, Byrne, Copperman, Hennessy, and Goodall (2004), who categorized light rain as 0.01–0.25 in/h (0.25–6.35 mm/h) and heavy rain as 0.25 in/h (6.35 mm/h) or greater, found a 3 mph (4.8 km/h) and 4 mph (6.4 km/h) reduction of speed in light and heavy rain conditions respectively on a 3-lane freeway in Virginia. Saberi and Bertini (2010) adopted a completely different classification system, categorizing very light rain as 0.01 in/h (0.25 mm/h), light rain as 0.01–0.04 in/h (0.25–1 mm/h), moderate rain as 0.04–0.16 in/h (1–4.05 mm/ h), and heavy rain as greater than 0.16 in/h (4.05 mm/h). They found a maximum speed reduction of 2 mph (3.2 km/h), 4 mph (6.4 km/h), and 10 mph (16 km/h) in very light, light, and moderate rainfall conditions, respectively. We see a general agreement between the two studies, though the magnitude of the effects changes with the more detailed classification scheme. This increased detail comes at the cost of data availability – the latter study being unable to observe enough drivers in heavy rain to draw any conclusions. Among the many studies associated with rainfall’s impact on free-flow traffic, relatively few address driver behavior in a platoon during rainfall. In part this may be due to the lack of general consensus on an appropriate following threshold to identify a platooned vehicle. Vogel (2002) measured front axle to front axle time spacing of platooned vehicles and calculated the correlation of successive vehicle speeds and plotted these correlation values against time headways. He then constructed two best-fit regression lines: one for larger correlation values (vehicles with strong observed interaction) and smaller correlation values. He considered the intersection point of the two regression lines as the separation point between free cars and interacting cars. He found that a 6-s time headway is optimal for distinguishing free vehicles from following vehicles. Al-Kaisy and Durbin (2009) concluded similar results from a study in Montana, USA. They calculated the mean travel speed of vehicles with time headways equal to or greater than a specific threshold value. Then they plotted mean speeds against time headways and observed when the curve became horizontal. The curves started to flatten out asymptotically in the range of 5–7 s, indicating that after this time the interaction between successive vehicles is almost zero. Though he concluded this, they used a 3-s time headway for platoon identification. Values of 5–7 s represent the upper range of following vehicle threshold – there is a higher degree of uncertainty that vehicles are truly following for these values of time gap. This is the reason most researchers apply a lower threshold value (as do we) when identifying following vehicles. The Highway Capacity Manual 2000 (TRB, 2000) recommends using percent time spent following (the average percent of travel time that a vehicle must travel in platoon behind a slower vehicle due to the inability to pass) to identify platooned vehicles. However it admits that it is difficult to measure percent time spent following and provides a surrogate measure of a 3-s threshold. Gattis, Alguire, Townsend, and Rao (1997), used 5 s as a time headway criterion for identifying platoons, while Hoban (1983) of Australia recommended a 4 s time headway criterion. Another traffic parameter useful for platoon identification is the number of vehicles in the group (Gaur & Mirchandani, 2001). Billot, El Faouzi, and De Vuyst (2009) followed this method and used both time headways and number of vehicles
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
397
Traffic Recorder
Fig. 1. Site description: traffic data recorder location (above), platooned vehicles (below).
for platoon identification. They carried out an empirical study on the impact of rainfall on platoon formation on a two-line interurban freeway section located on 118 National Road near Paris, France. Platoons were identified on the basis of both critical time headway and the number of vehicles in the group. The median time headway of all vehicles traveling on the road was defined as the threshold time headway for identifying platooned vehicles – which relies on a restrictive assumption of half of all vehicles being in a platoon. Their reported median headway values were 3, 3.6 and 4.5 s for no-rain, light rain and medium rain condition respectively. These values, along with a designated minimum 4 vehicles in a group were used to define a platoon. They found a 7.5% increase in the number of platooned vehicles from dry to rainy conditions. In this paper, platooned vehicles are defined utilizing a 4-s time gap (the time between the rear axle of the leading vehicle and the front axle of the following vehicle) instead of time headway (front axle to front axle). The study seeks to quantify the effect of rainfall on following behavior, specifically the choice of time and/or space gap between vehicles. In this context, time gap corresponds as well or better to the spacing drivers will likely perceive in making car-following decisions (the distance from the back of the preceding vehicle to their front bumper). 3. Methods In developing the experimental design, care was taken to (1) isolate the effects of rainfall on behavior through careful site selection, (2) improve the spatial compatibility of weather and traffic datasets with careful instrumentation location, (3) identify platoons to capture vehicles in car following states, and (4) collect time gap data at a scale (milliseconds) that is appropriate for the comparisons being made. The following subsections describe each of these efforts briefly. 3.1. The site Traffic data collection took place on a section of Route 195 (Storrs Road) in Mansfield, Connecticut. It is a two-lane state highway with minimum access control. This section has a posted speed limit of 45 mph (72.5 km/h) and a wide shoulder. It is free from roadway condition defects, vertical curvature and any sharp horizontal curvature that may affect driver speed and gap choice. Two photographs of the site are shown in Fig. 1. There are few access points close to the data collection point, those that do exist have relatively low volumes compared to Route 195. A manual observation carried out on a weekday for 3 h (at 9:00–10:00 AM, 1:00–2:00 PM, and 4:30–5:30 PM) shows that the turning volume to these access points compared to the hourly highway volume are 6–8% of the highway volume.
398
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
Headway (sec)
6 5 4 3 2 1 0 Hoban (1983)
Gattis et al. (1997)
HCM 2000
Billot et al. (2009)
Sources Fig. 2. Headway threshold values for distinguishing free-flow/platooned vehicles.
It was assumed that this low turning volume would have minimal effect on the speed and gap distribution of platooned vehicles. To further reduce any impact, very slow-moving vehicles (speeds less than three standard deviations from mean highway speed) were removed from analysis – it was assumed these would represent turning or malfunctioning vehicles. There are two traffic signals along this stretch of Route 195 one on either side of the data collection point. They are both located far enough away – 0.4 miles (0.64 km) and 0.5 miles (0.8 km) from the traffic recorder to allow leading vehicles (even if leading vehicle is a truck) to reach their desired speed prior to reaching the data collection. This site was selected to isolate, to the greatest extent possible, the impact of weather events on driver behavior by removing the other geometric stimuli (narrow shoulders, grade changes, horizontal curvature, etc.) that impact driver behavior. 3.2. Traffic data collection An automatic traffic data recorder with pneumatic tubes was installed at the study site. The traffic data recorder was used to collect data 24 h a day for approximately 5 months, from May 2009 to October 2009. Speed data (in mph) was collected directly by the software supplied with the traffic counter. The software recorded the time gap between vehicles in whole seconds. To get a more accurate representation of drivers’ gap choices at realistic speeds, a computer programming code was developed to retrieve gap data in milliseconds. This code utilized the unedited data recorded by the traffic counter and the time gap data produced by the software. Later, following distance (in feet) was calculated by multiplying time gap by following vehicle speed. 3.3. Platoon vehicle identification Al-Kaisy and Durbin (2009) suggests that time headways less than 5 s should capture most following (and platooned) vehicles. This threshold should hold for time gap as well, since time gap and time headway only differ by the fraction of a second it takes for the front and rear axle of a vehicle to pass a specific point. As previously discussed and shown in Fig. 2, there is no single accepted value for this following threshold. Further, drivers’ perception–reaction time is typically
0.35
No-Rain
0.30
Light Moderate
Density
0.25 0.20 0.15 0.1 0.05 0 0
2
4
6
8
10
Time Gaps (sec) Fig. 3. Density plot of time gaps in different weather condition.
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
45
NoRain Light Medium
40
Relative Frequency
399
35 30 25 20 15 10 5 0 <25
25-30 30-35 35-40 40-45 45-50 50-55 55-60
>60
Speed (mph) Fig. 4. Driver speed distribution in different weather condition.
taken to be in the 2–3 s range (Dewar & Olson, 2007). So, a threshold value of 5 s might capture a portion of free flowing vehicles, if it is assumed that drivers maintain only enough distance to react properly to a travel or roadway condition. Considering these factors, a conservative maximum time gap of 4 s (similar to Hoban, 1983) between successive vehicles was chosen as a threshold in this study to capture a large percentage of following vehicles without diluting results with free-flow vehicles. 3.4. Weather data spatial compatibility Weather data were collected from the nearest weather station, approximately 2 miles away from the traffic recorder location. This distance should allow for a spatially compatible study of the relationship between traffic parameters and weather, meaning that weather happening at the station is very similar to that at the traffic data collection site. The station provided rainfall (in) and rainfall rate (in/h) in 5 min intervals. The American Meteorological Association’s (AMSs) rainfall classification system was used in this study (Glickman, 2000). Rainfall was classified as either (1) light rain, from trace to 0.1 in/h (2.5 mm/h); (2) moderate rain, from 0.11in/h to 0.3 in/h (2.6–7.6 mm/h); or (3) heavy rain, over 0.3 in/h (7.6 mm/h). Only a small amount of heavy rainfall data was gathered during the data collection period, so a decision was made to eliminate the higher level of rainfall intensity from the data. A second analysis aggregated light and moderate rainfall to compare with clear conditions. A note: this study was conducted with data up to moderate rainfall and is not verified with heavy rainfall when visual acuity and friction are expected to be reduced further. 3.5. Data reduction and integration Past literature shows that driving behavior and performance can differ from day to night (Ivey, Lehtipuu, & Button, 1975) and that when visibility drops, speed also drops (Liang, Kyte, Kitchener, & Shannon, 1998). Therefore, this study only considered daytime traffic. Additionally, only weekday data were taken in this study to reduce the likely impact of variation in trip purpose (commute vs. recreational trips) on the results. Platooned traffic data (i.e. time gaps, speeds, and following distances) gathered during rainy conditions were compared to data gathered during no-rain conditions from either 1 week before or after the rainfall at the same time of rainfall occurrence. In this way we attempted to control for seasonal variations in weather, visibility and the myriad other variables that influence the way people drive. If the week after the event or prior did not have clear weather conditions, data from the next closest week was utilized. Statistical methods and tests employed in the analysis of data are presented in the following section. Statistical tests were performed assuming the data are independent i.e. there is no cross-correlation among the datasets due to seasonality, time of day and day of week – satisfying the assumptions of the analytical methods employed. 4. Results 4.1. Analysis of means A density plot of time gaps for all vehicles in no-rain, light rain, and moderate rain conditions is shown in Fig. 3. Densities are increasingly skewed to the right from no-rain to moderate rain conditions, though no distinct difference can be observed above 4–5 s. Fig. 3 illustrates the shift of the time gap distribution to the right as rainfall intensity increases. The peaks of the distributions are in the vicinity of 1.5–2 s which is drivers preferred gap choice. This is similar to a finding by Vogel (2002) who found that drivers preferred time headway is 2 s using a similar plot. Fig. 4 shows the proportion of platooned passenger
400
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
Table 1 F-test results (a = 0.05). Parameter
Comparison
P-value
Significant difference (Y/N/Greater)
Time gaps
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.1299 0.6755
N N
Speeds
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.9374 0.0009
N Greater in rain
Table 2 Summary of data. Parameter
Weather
Mean
Min
Max
Time gap
No-rain Rain
1.971 2.083
0.113 0.119
3.993 3.997
Speed
No-rain Rain
47.0 45.3
21.0 8.0
69.0 70.0
cars driving within the specified speed ranges under the three rainfall conditions. It shows a clear trend of vehicles traveling at higher speeds in no-rain conditions. For example, the proportions of drivers in the 40–45 mph (64–72 km/h) and 50– 55 mph (80.5–88.5 km/h) speed ranges during clear conditions are approximately the same, while a distinctly greater proportion of drivers choose 40–45 mph (64–72 km/h) over 50–55 mph (80.5–88.5 km/h) in light rain and moderate rain conditions. To check for differences in variance (or the spread of the data), F-tests with 5% level of significance (a = 0.05) were conducted between the time gaps in light rainfall and moderate rainfall condition; the test results did not imply any statistically significant difference in variance, nor did a similar analysis show a difference between clear and rainy conditions (in which light and moderate rain data were combined). Similar to time gaps, no significant difference of speed variances between light rainfall and moderate rainfall conditions was found. Increased variance of speed from no-rain to rainy weather was found. Results are shown in Table 1. Table 2 summarizes the primary traffic data parameters used in analysis, including values for the mean, minimum, and maximum values for time gap and speeds. The table shows a 5.7% (0.11 s) increase in mean time gaps from clear to rainy conditions. The mean speed reduction is 3.7% – about 2 mph (3.2 km/h) from clear to rainy conditions. The gap increment agrees with the findings of Unrau and Andrey (2006) for uncongested flow during daytime from no-rain to light rain conditions. The mean speed reduction in this study is greater than that found for free-flow vehicles in uncongested conditions (Rahman & Lownes, 2010), where a statistically significant but very small speed reduction of 1.8% or 0.9 mph (1.5 km/h) was observed between no-rain and rain. The statistical significance of the observed differences between mean time gaps and speeds in clear and rainy conditions were analyzed using Z-tests performed with a = 0.05. For both mean time gap and speed, the null hypothesis was that there is no difference between means in clear and rainy conditions. The alternative hypothesis for the time gap Z-test was that the mean time gap is higher in rain than in no-rain conditions. The alternative hypothesis for mean speed analysis was that the mean speeds are lower in rain than in no-rain. The Z-test for time gap gave a Z-statistic of 5.598 (which is less than critical Z-value of 1.645) indicating that mean time gap is larger in rainy conditions. The Z-test for speed gave a Z-statistic of 13.947 (which is greater than the critical Z value 1.645) indicating that mean speed is greater in no-rain conditions. In summary, an anlaysis of the means of speed and time gap produced results that are intuitive and statistically significant. Our observations suggest that drivers (a) slow down in rainy conditions and that (b) an increase in vehicle spacing (measured in time units) is observed. What is not known at this point is whether the increase in vehicle spacing is a function of a driver decision to increase their following distance, or is simply a function of their observed speed reduction.
Table 3 K–S test results (a = 0.05). Parameter
Comparison
Dcritical
Dcalculated
Significant difference (Y/N)
Time gaps
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.0627 0.0328
0.0438 0.0781
N Y
Speeds
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.0627 0.0328
0.0571 0.1476
N Y
Following distance
Light rain vs. moderate rain No-rain vs. light and moderate rain combined
0.0627 0.0328
0.0426 0.0327
N N
401
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
Following Dist. in Rain
70 60
Speed in Rain
Time Gap in Rain
4 3 2 1
50 40 30 20 10
0 0
1
2
3
Time Gaps in No-Rain
(a)
4
400 300 200 100 0
20
30
40
50
Speeds in No-Rain
(b)
60
0
100
200
300
Following Dist. in No-Rain
(c)
Fig. 5. Quantile–quantile plots between no-rain (clear) and rainy conditions (a) time gaps, (b) speeds, (c) following distances.
4.2. Analysis of distributions Moving beyond simple analysis of means, efforts were made to investigate the difference in distributions under different weather conditions. The Kolmogorov–Smirnov (K–S) test, which determines if two datasets differ significantly from each other, was employed. It does not require any knowledge of prior distribution and the data set sizes do not need to be equal. Two-sided K–S tests were performed with the null hypothesis that there is no significant difference in spacing and speed distributions between light rain and moderate rain conditions, and no-rain and rain (combined light and moderate) conditions. The critical value D of K–S test statistics was calculated using the following equation (Lamm, Choueiri, & Mailaender, 1990):
Dcritical ¼ c
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n1 þ n2 n1 n2
where n1 and n2 are the sample sizes of the datasets and c = 1.36 at a significance level of a = 0.05. If the calculated D-value is greater than the critical D-value, the data suggests evidence of a significant difference between the datasets. The results of the K–S test are shown in Table 3. The test found no significant differences between speed and time gap data in light rain and moderate rain conditions. However, significant differences were found between data in clear and rainy conditions (with combined light and moderate rain data). No significant differences in following distance were found in any weather conditions. The results in Table 3 suggest that drivers do not distinguish between light and moderate rain in their time gap and following distance choices, though there is evidence of a difference between clear and aggregated rainy conditions. 4.2.1. Graphical comparison of distributions As a final method of examining the relationship between rainy conditions and driver behavior and their distributions, quantile–quantile (Q–Q) plots of clear and rainy conditions (combined light and moderate rain) data were drawn, as shown in Fig. 5. A Q–Q plot is a graphical method for comparing two distributions by plotting their quantiles. If two variables are identically distributed, the plot of the quantiles of the variables set against each other will be a straight line with a slope of one (Wilk & Grandesikan, 1968). As seen in Fig. 5, the Q–Q plots of time gaps and speeds lie above and below the reference line, respectively, suggesting that time gaps values are higher in rainy conditions and speeds are smaller. The Q–Q plot of following distances almost perfectly coincides with the 45° line which agrees with the K–S test results of a statistically nonsignificant difference in following distance. Interestingly, following distance did not produce a statistically significant difference in any comparison (though the rain vs. clear comparison of distributions came quite close in a practical sense). This finding suggests that drivers tend to maintain the same spatial distance between vehicles and slow down slightly, producing the observed difference in time gap. 5. Discussion There are interesting insights, both qualitative and quantitative, to be gleaned from this study. Other questions are also raised. Both are addressed here. Our observations suggest that drivers slow down in rainy conditions. Some of these drivers, the platoon leaders, do so by choice. The followers in a platoon have their choice of speed dictated to a certain extent. This speed reduction did lead to an increase in the spacing of vehicles (as measured by time headway), though it appears that drivers do not choose to increase their following distance in rainy conditions. This observation raises an interesting question: Is the increase in time headway imparted by speed reduction a large enough increase to mitigate the effects of loss of pavement friction? In short, are drivers compensating enough for the conditions of the roadway? Although time gaps are observed growing larger from light to moderate rainy condition (cf. Fig. 3), distributional differences are not statistically significant. This is also true for speeds. The AMS rainfall classification did not provide the means to
402
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
distinguish between driver response at light and moderate rainfall intensity levels, indicating that (1) no such distinction exists, (2) a different rainfall classification system might be more appropriate for modeling driver behavior in rainy conditions, or (3) this study did not have enough data points within each level to distinguish smaller, marginal differences across the classification levels. It would be worthwhile in the future to investigate cut-off intensity levels that correlate with significant differences in these parameters using natural breaks. An important aspect of this kind of study is the selection of time window. In this study only the actual rainfall period was used. No consideration was given to effects observed in the post-rainfall time period in which effects on pavement friction and visibility may still play a role in driver behavior. The duration and extent of the loss of pavement friction will be a function of a great number of pavement, weather and traffic variables. The inclusion of the post-rainfall period is of great interest and would be a natural and important extension of this study. This study found a significant decrease in speed and an increase in time gap from clear to rainy conditions; however, following distance displayed no significant effects. The decrease of overall speed reduction of platoon was mainly due to the speed reduction of each platoon leader, which is most likely caused by a reduction in visibility and a perceived increased risk from reduced pavement friction. The following drivers reduced their speed to maintain their desired following distances as the same mechanism of platoon formation (Brackstone et al., 2009). This desired following distance did not change between in rainy conditions. The only change in following behavior observed was an increase in the time gap between vehicles, and this increase can be account for by the speed reduction. This would suggest that platooned drivers decrease may react to perceived weather risk not by increasing following distances but only reacting to the speed of their leading vehicle. This paper provides empirical insights that may be useful in accurately modeling the driver-environment relationship. Models of driver behavior and traffic flow form the backbone of a variety of important analytical tools, including traffic microsimulation, traffic assignment, and signal optimization packages. Nearly all of these tools assume the environment is static and has minimal or no effect on driver and/or vehicle behavior (Maze, Agarwal, & Burchett, 2006). As traffic simulation software and analytical tools increase in sophistication and precision, the modeling of driver-environment interactions, such as the relationship between driver and weather conditions, can be increasingly beneficial. Acknowledgements This study was funded in part by the University of Connecticut Research Foundation. Special thanks to Jon Sleezer for providing weather data, Kelly Bertolaccini for her editing efforts and Pujan Joshi for his coding assistance. References Al-Kaisy, A., & Durbin, C. (2009). Platooning on two-lane two-way highways: An empirical investigation. Journal of Advanced Transportation, 43, 71–88. Andrey, J., Mills, B., Leahy, M., & Suggett, J. (2003). Weather as a chronic hazard for road transportation in Canadian cities. Natural Hazards, 28, 319–343. Billot, R., El Faouzi, N., & De Vuyst, F. (2009). Multilevel assessment of the impact of rain on drivers’ behavior: Standardized methodology and empirical analysis. Transportation Research Record, 2107, 134–142. Brackstone, M., & McDonald, M. (1999). Car-following: A historical review. Transportation Research Part F: Traffic Psychology and Behaviour, 2, 181–196. Brackstone, M., Waterson, B., & McDonald, M. (2009). Determinants of following headway in congested traffic. Transportation Research Part F: Traffic Psychology and Behaviour, 12, 131–142. Dewar, R. E., & Olson, P. L. (2007). Human factors in traffic safety. Tucson, Arizona: Lawers & Judges Publishing Company, Inc.. Edwards, J. B. (1999). Speed adjustment of motorway commuter traffic to inclement weather. Transportation Research Part F: Traffic Psychology and Behaviour, 2, 1–14. FHWA Road Weather Management Program (2009). How do weather events impact roads?
A. Rahman, N.E. Lownes / Transportation Research Part F 15 (2012) 395–403
403
Smith, B. L., Byrne, K. G., Copperman, R. B., Hennessy, S. M., & Goodall, N. J. (2004). An investigation into the impact of rainfall on freeway traffic flow. In Proceedings of the 83rd annual meeting of the transportation research board, Washington, DC. TRB (2000). Highway capacity manual 2000. Washington, DC: National Research Council. Unrau, D., & Andrey, J. (2006). Driver response to rainfall on urban expressways. Transportation Research Record, 1980, 24–30. van der Hulst, M., Rothengatter, T., & Meijman, T. (1999). The effect of reduced visibility and time pressure on drivers’ distance-keeping behaviour. In A. G. Gale (Ed.), Vision in vehicle – VII (pp. 311–318). Oxford: Elsevier. Vogel, K. (2002). What characterizes a ‘‘free vehicle’’ in an urban area? Transportation Research Part F: Traffic Psychology and Behaviour, 5, 15–29. Wilk, M. B., & Grandesikan, R. (1968). Probability plotting methods for the analysis of data. Biometrika, 55(1), 1–17.