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Cao et al.
Effect of Weather and Road Surface Conditions on Traffic Speed
of Rural Highways
Luchao Cao (Corresponding Author)
MASc student
Department of Civil & Environmental Engineering
University of Waterloo
Waterloo, ON, N2L 3G1
Phone: (519) 888-4567 ext. 33984
Fax: (519) 725-5441
Email: [email protected]
Lalita Thakali PhD Student
Department of Civil & Environmental Engineering
University of Waterloo
Waterloo, ON, N2L 3G1
Email: [email protected]
Liping Fu, Professor
Department of Civil & Environmental Engineering, University
of Waterloo
Waterloo, ON, N2L 3G1, Canada
School of Transportation and Logistics, Southwest Jiaotong
University
Chengdu, P. R. China
Phone: (519) 888-4567 ext 33984
Email: [email protected]
Garrett Donaher
MASc student
Department of Civil & Environmental Engineering
University of Waterloo
Waterloo, ON, N2L 3G1
Phone: (519) 888-4567 ext. 33984
Fax: (519) 725-5441
Email: [email protected]
A Paper Submitted for Presentation at the 2013 Annual Meeting of
the Transportation Research Board
and Publication in the Transportation Research Record
Submission Date: Aug 1st, 2012
Total words = 5230 + 250*8 (4 Figures + 4 Tables) = 7454
TRB 2013 Annual Meeting Paper revised from original
submittal.
UsuarioResaltar
UsuarioResaltar
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Cao et al. 1
ABSTRACT 1 2 This paper describes a study focusing on the impact
of winter weather and road surface conditions on 3 the average
vehicle speed of rural highways with the intention of examining the
feasibility of using 4 traffic speed from traffic sensors as an
indicator of the performance of winter road maintenance 5 (WRM).
Detailed data on weather, road surface conditions, and traffic over
three winter seasons from 6 two two-lane and two four-lane rural
highways in Iowa, US, are used for this investigation. Three 7
modeling techniques are applied and compared for modeling the
relationship between traffic speed 8 and various road weather and
surface condition factors, including multivariate linear
regression, 9 artificial neural network (ANN), and time series
analysis. The modeling results have confirmed the 10 statistically
strong relationship between traffic speed and road surface
conditions, suggesting that 11 speed could potentially be used as
an indicator of bare pavement conditions and thus the performance
12 of winter road maintenance operations. The analysis has also
confirmed the expected effects of 13 several weather variables
including precipitation, temperature and wind speed. Lastly, the
time series 14 model developed could be a valuable tool for
predicting real-time traffic conditions based weather 15 forecast
and planned maintenance operations. 16
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Cao et al. 2
INTRODUCTION 1 2 Many transportation authorities in US and
Canada are facing mounting challenges to keep their road 3 network
clear of snow and ice for safe and efficient travel throughout
winter seasons. Significant 4 amounts of resources are spent in
winter road maintenance every year, including over $1 billion 5
dollars of direct investment and use of an average of five million
tones of road salts. It therefore 6 becomes increasingly important
to develop a rigorous performance measurement system that shows 7
clear linkage between the inputs of winter road maintenance and its
outcomes such as safety and 8 mobility benefits. This paper focuses
particularly on the mobility impact of winter weather and road 9
maintenance, motivated by the premise that the traffic speeds on a
highway, which are available from 10 regular traffic sensors, could
be used as an indicator of the effectiveness of winter road
maintenance 11 services provided on that highway. Traffic speed is
not only easy to monitor, it is also linked to the 12 ultimate
outcome of a winter road maintenance program. 13 14
In order to examine the feasibility of using traffic speed as a
performance indicator of winter 15 road maintenance, it is
necessary to corroborate that traffic speed is related to the main
output of 16 winter road maintenance, i.e., road surface
conditions. This research is therefore to conduct an 17 empirical
investigation on the dependency of traffic speed on road surface
conditions while 18 controlling other road weather and traffic
factors. Three modeling approaches are attempted, 19 including
multivariate linear regression, artificial neural network (ANN),
and time series analysis. 20 This paper provides an overview of
these methods along with the calibration results and some main 21
findings of a comparative analysis. 22 23 LITERATURE REVIEW 24 25
Much research work has been carried out to address the impacts of
adverse weather on vehicle speed. 26 Highway Capacity Manual 2010
(1) provides information about the impact of weather condition on
27 vehicle speed for the freeways. Precipitation was categorized
into two categories: light and heavy 28 snow. Accordingly, there is
a drop of 8-10 percent in free flow speed due to light snow while
heavy 29 snow can reduce the free flow speed between 3040
percentage compared with clear and dry 30 conditions. 31 32
Kyte et al. (2) conducted a study on the effect of adverse
weather conditions on freeway free 33 flow speed. This study
considered the effect of road surface conditions, but was limited
to two types, 34 namely, wet or snow covered. It was found that wet
or snow covered pavement reduced speeds by 35 10-16 km/h. A
combination of heavy snow, low visibility and high wind speed
resulted in a speed 36 reduction of about 50 km/h. 37
38 Maze et al. (3) also investigated the impact of weather on
urban freeway traffic flow 39
characteristics. rain, snow, temperature, wind speed and
visibility were considered in the study. Each 40 of these variables
was classified into 3 to 5 categories, and the impact on traffic of
each category was 41 estimated by using the previously mentioned
methods. The research finally compared the capacity and 42 speed
reduction results with the recommended values in HCM 2000, and
suggested that light and 43 moderate snow show similar capacity and
speed reductions with the HCM 2000 while heavy snow has 44
significantly lower impact on speed reduction than those
recommended by the manual. In addition, 45 temperature and wind
speed had almost no impact on the speed. Lower visibility caused
10% to 12% 46 reductions in capacity and 6% to 12% reductions in
speed. 47
48 Liang et al (4) conducted a case study on the effects of
visibility and other environmental 49
factors on traffic speed. The study site was located on an
interstate freeway in rural Idaho, US. A 50 regression analysis was
carried out to evaluate the feasibility of providing local drivers
with driving 51 speed advisories based on the information collected
by weather and visibility sensors. The effect of 52 wind speed was
found to be significant over 40 km/hr where it reduced vehicle
speed approximately 53 by 1.1 km/h for every kilometer per hour
that the wind speed exceeded 40 km/h. 54
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Cao et al. 3
1 Similarly, Camacho et al. (5) conducted research on impact of
weather on freeway free flow 2
speed in Spain. The authors reported that snow layer depth could
cause reduction in speed, ranging 3 from 9.0 to 13.7 km/h. The
effect of visibility loss had a logarithmical form while wind speed
with 4 lower than 28.8km/hr didnt have obvious effect. It was also
found that the effect of weather variables 5 (i.e. visibility, wind
speed and precipitation intensity) on vehicle speed was higher in
snow conditions 6 than in the other three conditions. 7
8 Qiu and Nixon (6) developed a model to quantify the average
free flow traffic drop caused by 9
winter storm events. Greenfield et al. (7) proposed a revised
model and applied it for real-time winter 10 road performance
analysis. The new model takes into account uncertainty in the
sensor-based inputs is 11 capable of estimate post-storm effect on
traffic. 12
13 Huang and Ran (8) developed a neural network model to predict
traffic speed as a function of 14
adverse weather conditions for a highway located in Chicago
metropolitan area. Multi-perceptron 15 neural networks were used
were developed for each hour of day, day of week to represent
time-16 varying traffic patterns. 17
18 Ibrahim and Halls (9) conducted a study to quantify the
effect of adverse weather on freeway 19
speed using the data collected on Queen Elizabeth Way (QEW),
Mississauga, Ontario. It was found 20 that light snow resulted in a
significantly significant drop of 0.96 km/hr in free-flow speeds,
while 21 heavy snow resulted in a 37.0 to 41.8 km/hr (35 to 40
percent) free-flow speed reduction. Similarly, 22 Maki (10)
reported that speed reduction caused by heavy snow is about 40% in
Minneapolis, 23 Minnesota and Perrin et al. (11) found that speed
reduction caused by light snow and heavy snow are 24 13% and
25%-30% in Salt Lake City and Utah, respectively,. 25
26 Another research conducted by the Federal Highway
Administration (FHWA) in 1977 (12) 27
reported that the freeway speed reduction caused by adverse road
conditions are 13% for wet and 28 snowing, 22% for wet and slushy,
30% for slushy in wheel paths, 35% for snowy and sticking and 42%
29 for snowing and packed. 30
31 While differing in research objectives, circumstances and
data used, past studies have all 32
confirmed that adverse winter weather has a negative effect on
traffic speed. However, there were 33 inconsistency in findings in
terms of weather factors being significant and the size of the
effects for 34 these variables that were found significant. This is
partially due to the different traffic and 35 environmental
characteristics of the study sites. It can also be caused by the
sources and quality of the 36 data used in these studies. Past
studies also have limitations in terms of modeling methodology.
First, 37 most past studies focused on the differences in speed or
other traffic variables between adverse and 38 normal weather
conditions using data under all weather conditions. Second, few of
the past studies 39 have taken a full account of the variation in
winter road surface conditions and the results are 40 therefore not
immediately useful for showing the feasibility of using speed as a
performance indicator 41 of winter road maintenance. Thirdly, most
of the past studies utilized linear regression models to 42
quantify the effect of weather and surface condition variables on
traffic speed, which cannot capture 43 the possible non-linear
effects of some factors. Lastly, most studies focused on freeways
only, in 44 which the effect of weather on traffic speed could be
easily confounded by traffic congestion, making 45 the model less
reliable. 46 47 DATA SOURCES AND PROCESSING 48 49 The analysis was
performed using three types of data, weather, road surface
condition and traffic, 50 from four highway sites located in the
rural area of Iowa, US, and those are Algona US 80 (denoted as 51
H2-1), Denison (denoted as H2-2), Adair I-80 (denoted as H4-1) and
Waterloo US-20 (denoted as H4-52 2), as shown in Figure 1. Among
all these four sites, H2-1 and H2-2 are 2-lane highways, and H4-1
53 and H4-2 are 4-lane highways. The road weather and surface as
well as traffic conditions at each of 54
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Cao et al. 4
these sites are monitored by a road weather information system
(RWIS) equipped with radar traffic 1 sensors. The RWIS weather
sensors provide observations on atmospheric and road surface 2
conditions while the automatic traffic recorder data provides speed
and volume data. The traffic 3 sensors are all radar detectors and
installed on the RWIS towers. The pavement sensors are embedded 4
in the pavement and connected to the main tower by cables. 5 6
7 8
FIGURE 1 Location of the Study Sites in Iowa, US 9 10
The atmospheric data set includes precipitation, visibility, air
temperature, and wind speed. 11 Precipitation data is given in two
forms, including precipitation intensity in centimeters per hour
and 12 categorical description of intensity (light snow (< 0.25
cm/15 min); moderate snow (0.25-0.755 cm/15 13 min); and, heavy
snow (>0.755 cm/15 min). Road surface condition data includes
surface 14 temperature and road surface states with the following
six types in order of severity from lowest to 15 highest: 16
17 Dry (moisture free surface) 18 Trace Moisture (thin or spotty
film of moisture above freezing and detected in absence of 19
precipitation) 20 Wet (continuous film of moisture on the
pavement sensor with a surface temperature above 21
freezing as reported when precipitation has occurred) 22
Chemically Wet (continuous film of water and ice mixture at or
below freezing with enough 23
chemical to keep the mixture from freezing, it is also reported
when precipitation has 24 occurred) 25
Ice Watch (thin or spotty film of moisture at or below freezing
and reported when 26 precipitation is not occurring) 27
Ice Warning (continuous film of ice and water mixture at or
below freezing with insufficient 28 chemical to keep the mixture
from freezing again, reported when precipitation occurs) 29
30 Traffic data contains normal traffic volume, percentage of
long traffic volume (i.e. truck and 31 recreational vehicles), and
average vehicle speed. 32 33
As the three types of data were collected separately by
different sensors, it was necessary to 34 aggregate them based on a
consistent time interval. Most of the traffic records have a time
interval of 35 2 minutes while the time interval of the atmospheric
and surface data ranges from 9 minutes to over 36 30 minutes with a
majority of 10 minutes. Based on this information, a 15 minutes
time interval was 37 selected to aggregate the three datasets. Note
that the 15 minutes time interval is also commonly used 38 in
various traffic studies. 39
H2-1
H2-2
H4-1
H4-2
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Cao et al. 5
1 After the three data sources were aggregated, each sample was
averaged over the lane based on 2
the directional flow of traffic. Corresponding directional
surface sensors were used for each direction. 3 As the objective of
this study is to investigate the variation of traffic speed during
snow storms, 4 snowstorm events (i.e., continuous snow
precipitation or the road surface condition is ice/snow 5 covered
during or after a snow storm) were extracted for the rest of the
analysis. The data was also 6 preprocessed to remove the obvious
outliers such as those with zero speed and volume. 7 8
An exploratory data analysis was subsequently carried out to
numerically summarize the data 9 and visually examine the
relationship between speed and the potential predictors. 10
11 Table 1 shows the summary statistics of all variables for the
four highway locations. The 12
maximum traffic volume for four sites is 920, 584, 424 and 100
veh/ln/hr, respectively, which 13 indicates that the traffic at
these four highway locations was far below their capacity and
therefore can 14 be considered as free flow condition. 15
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53
54
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Cao et al. 6
TABLE 1 Summary Statistics 1
H4-1 (sample size 4376)
Average
Speed
(km/hr)
Total
Volume
(veh/ln/hr)
% Long
Vehicles
(%)
Surface
Temperature
(C )
Wind
Speed
(km/hr)
Visibility
(km)
Precipitation
Rate
(mm/hr)
Mean 99.14 193.70 45.00 -7.62 20.02 5.65 6.31
Std. Deviation 14.20 142.78 9.00 4.53 14.23 4.18 26.08
Minimum 28.89 4.00 0.00 -23.00 0.00 0.22 0.00
Maximum 123.35 920.00 75.00 5.20 255.00 11.00 324.00
H4-2 (sample size 6500)
Mean 89.90 145.65 25.00 -4.94 13.12 9.45 2.90
Std. Deviation 12.53 108.98 11.00 3.82 7.84 2.29 19.36
Minimum 19.68 4.00 0.00 -21.70 0.00 0.64 0.00
Maximum 112.53 584.00 75.00 11.50 47.00 11.00 484.00
H2-1 (sample size 2344)
Mean 83.68 69.07 19.00 -2.97 13.95 9.70 4.20
Std. Deviation 11.82 53.81 14.00 4.66 13.61 2.70 20.41
Minimum 24.135 4.00 0.00 -17.40 0.00 0.82 0.00
Maximum 128.72 424.00 50.00 10.90 67.00 11.00 191.50
H2-2 (sample size 1968)
Mean 87.20 17.31 20.00 -5.90 20.45 9.40 1.83
Std. Deviation 14.11 13.74 20.00 5.13 10.40 2.80 8.38
Minimum 13.50 4.00 0.00 -17.70 0.00 1.33 0.00
Maximum 148.97 100.00 50.00 11.00 63.00 11.00 158.40
Combined H2-1& H2-2
Mean 85.04 49.92 19.00 -4.16 16.01 9.63 3.12
Std. Deviation 12.57 50.45 16.00 5.08 12.73 2.71 16.48
Minimum 23.99 4.00 0.00 -17.70 0.00 0.82 0.00
Maximum 148.97 424.00 50.00 10.90 67.00 11.00 191.50
Combined H4-1& H4-2
Mean 93.62 164.98 33.20 -6.02 15.89 7.92 3.90
Std. Deviation 13.98 125.91 14.10 4.33 11.39 3.69 22.24
Minimum 19.70 4.00 0.00 -23.00 0.00 0.22 0.00
Maximum 123.35 920.00 75.00 11.50 255.00 11.00 485.20
2 MULTIVARIATE LINEAR REGRESSION ANALYSIS 3 4 In order to
quantify the impact of adverse weather and road surface conditions
on speed, a 5 multivariate linear regression analysis is carried
out. Before proceeding with the regression, a 6 correlation
analysis was performed to identify the potential issue of
multi-collinearity among the 7 independent variables. However, no
significant correlation was found and hence all the variables were
8 considered in the subsequent regression analysis. 9 10
The effect of precipitation on speed was tested in two
representation forms, namely, categorical 11 and continuous. It was
found that the categorical form resulted in a higher explanation
power, i.e., 12
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Cao et al. 7
higher R2 value and thus was used in the model. Separated models
were developed for each of these 1
four sites, and two combined models were also developed for two
types of highways. Therefore, the 2 analysis resulted in six models
in total. The reason for developing combined models is that the
effect 3 of most external factors on speed is expected to be
similar for a given type of highways. In addition, a 4 combined
model is expected to be more generalizable or transferable than a
highway specific model. 5
6 The data set from each site was divided into two parts
randomly: one included 90% of the data 7 to be used for model
calibration and the remaining 10% of data was held out for
subsequent model 8 validation. The statistical significance of each
variable was based on the 95% confidence interval at a 9
significance level of 5%. Any variables with p-value of greater
than 5% were eliminated sequentially 10 from the model. The overall
performance of the regression model was assessed using adjusted
R
2 and 11
Root Mean Square Error (RMSE). 12 13 The coefficients of the
regression model are shown in Table 2. Note that for the
categorical variables 14 such as precipitation and road surface
conditions, a base category is defined in advance. For 15
precipitation, no snow is considered as the base condition. For
road surface conditions, different 16 base conditions are used for
different sites. For example, as the effect of dry, trace moisture,
wet and 17 chemically wet are almost zero at H2-1, the base
condition, therefore, is the combination of all these 18 four
conditions. In addition, because it turns out that some categories,
for example ice watch and ice 19 warning have similar effect on
speed at H2-2 so that they are considered as a single category in
the 20 regression analysis, and the calibrated coefficients of
these two categories are the same. The rest is 21 analyzed in the
same manner. 22 23
The calibrated models are validated using the 10% holdout data.
Figure 2 shows the scatterplots 24 of the speeds predicted by the
models versus the observed speeds. The adjusted R square value is
0.2 25 and 0.48 for the 2-lane combined case and 4-lane combined
case, respectively. The RMSE is 10.11 26 and 10.44, respectively.
27
TRB 2013 Annual Meeting Paper revised from original
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Cao et al. 8
TABLE 2 Multivariate Linear Regression Model Results 1
2 Note: Values in the parenthesis are p-value, standard error,
t-value, respectively. 3 4 Based on the modeling results, the
following observations can be made on the effect of the significant
5 factors. 6
Effects of traffic volume and % long vehicles: It can be found
from Table 2 that traffic 7 volume has a positive effect on average
traffic speed in all the six models. This relationship is 8 somehow
counterintuitive as the opposite is commonly observed, at least,
under normal 9 weather conditions. This positive effect of traffic
may be attributed to its positive effect on 10 improving road
surface conditions through tire compaction, which might not have
been fully 11 captured by the road surface condition variable.
Another possible reason could be that on 12 rural highways where
traffic is generally low presence of other vehicles in visual range
may 13 have a positive effect on how fast a driver would be
comfortable to drive under adverse 14 weather conditions. The
modeling results show that for each 100 increase in traffic volume,
15 speed will increase by 3 km/hr. The proportion of truck and
recreational vehicles was found to 16 have a negative effect on the
average traffic speed at H4-1 and H4-2 while it is not 17
statistically significant for H2-1, H2-2 and the 2-lane combined
case. For the 4-lane combined 18 case, every 10% increase in long
volume is expected to decrease average traffic speed by 1.9 19
km/hr. 20 21
Effect of surface temperature: Surface temperature was found to
have a positive effect on 22 average traffic speed. One possible
explanation is that lower road surface temperature had 23
Constant89.66
( 0.00, 0.74,121.24)
101.58
( 0.00, 1.18, 86.09)
113.43
(0.00, 1.11, 102.47)
116.09
(0.00, 0.64,178.26 )
90.79
(0.00, 0.66, 138.33)
120.90
( 0.00, 0.73, 166.39)
Total Volume(veh/ln/hr)0.03
(0.00, 0.001, 7.79)
0.07
(0.00, 0.02, 3.05)
0.04
(0.00, 0.001, 37.31)
0.01
(0.00, 0.001, 10.76)
0.03
(0.00, 0.001, 7.77)
0.03
(0.00, 0.001, 35.38)
% Long Volume-0.19
(0.00, 0.02, -10.86)
-0.24
(0.00,, 1.087, -22.24)
-0.19
( 0.00, 1.09, -17.51)
Surface Temperature(C)0.14
(0.03, 0.07, 2.18)
0.24
(0.00, 0.04, 6.13)
0.44
(0.00, 0.034, 12.96)
0.05
(0.35, 0.05, 0.94)
0.10
(0.00, 0.03, 3.65)
Wind Speed(km/hr)-0.06
(0.00, 0.02, -3.39)
-0.05
(0.00, 0.03, -4.94)
-0.15
(0.00, 0.01, -12.76)
-0.23
(0.00, 0.0154,-14.93)
-0.07
(0.00, 0.02, -3.96)
-0.17
(0.00, 0.01, -17.33)
Slight Snow-4.16
(0.00, 0.49, -8.52)
-4.23
(0.00, 0.65, -6.51)
-7.95
(0.00, 0.34, -23.24)
-7.26
(0.00, 0.246, -29.44) -3.68
(0.00, 0.43, -8.64)
-7.61
(0.00, 0.23, -33.19)
Moderate Snow-5.50
(0.00, 1.22, -4.51)
-13.73
(0.00, 2.48, -5.53)
-13.35
(0.00, 0.70, -18.94)
-18.52
(0.00, 0.666, -27.77)
-5.35
(0.00, 1.21, -4.42)
-15.26
(0.00, 0.55, -27.58)
Heavy Snow-21.40
(0.00, 1.53, -13.99)
-19.60
(0.00, 2.58, -7.59)
-20.86
(0.00, 0.83, -25.02)
-22.44
(0.00, 1.160,-19.34)
-20.47
(0.00, 1.57, -13.0)
-22.19
(0.00, 0.72, -31.01)
Dry0.00 0.00 0.00 0.00 0.00 0.00
Trace Moisture0.00 0.00 0.00
-4.31
(0.00, 0.899,-4.79) 0.00 0.00
Wet0.00 0.00 0.00
-4.31
(0.00, 0.899,-4.79) 0.00
-1.50
(0.05, 0.91,-1.65)
Chemically Wet0.00 -5.33
(0.02, 2.28, -2.33)
-5.64
(0.00, 1.09, -5.19)
-11.73
(0.00, 0.971, -12.09)
-4.38
(0.01, 1.72, -2.54)
-8.53
(0.00, 0.81, -10.57)
Ice Watch-8.56
(0.00, 1.53, -13.99)
-9.58
(0.00, 0.82, -11.75)
-9.08
(0.00, 0.62, -14.62)
-13.47
(0.00.0.458, -29.38)
-8.5
(0.00, 0.53, -15.91)
-11.42
(0.00, 0.41, -28.19)
Ice Warning-8.56
(0.00, 1.53, -13.99)
-9.58
(0.00, 0.82, -11.75)
-9.08
(0.00, 0.62, -14.62)
-18.93
(0.00,1.248,-15.16)
-8.5
(0.00, 0.53, -15.91)
-11.42
(0.00, 0.41, -28.19)
H2-10.00
H2-26.65
(0.00, 0.53, 12.65)
H4-10.00
H4-2-13.18
(0.00, 0.32, -13.81)
Adjusted R square 0.232 0.137 0.487 0.445 0.2 0.48
Standard Error of Estimate 10.36 13.09 10.17 9.33 10.7 10
RMSE 10.11 10.44
H4-24-Lane
Combined
Regression for Individual Sites Regression for Combined
Sites
VariablesH2-1 H2-2
2-Lane
CombinedH4-1
TRB 2013 Annual Meeting Paper revised from original
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Cao et al. 9
contributed to worsening of road surface conditions and
decreasing in road surface friction (7). 1 However, the effect of
this factor is relatively small, as for each degree of drop in road
surface 2 temperature, there was only an average reduction of less
than 0.1 km/hr in traffic speed. 3 4
Effect of wind speed: As expected, wind speed was found to have
a statistically significant 5 effect on average traffic speed.
Higher wind speed was found to be associated with lower 6 average
vehicle speed. In average, every 10 km/hr increase in wind speed
would slow traffic 7 by approximately 0.7 and 1.7 km/hr for 2-lane
combined case and 4-lane combined case, 8 respectively. 9
10 Effect of precipitation: The modeling results suggest that
heavy precipitation could cause an 11
average reduction of over 20 km/hr in average traffic speed
while the speed reduction caused 12 by moderate snowfall was 5.35
and 15.26 km/hr and was 3.68 and 7.61 km/hr by slight 13 snowfall.
These results clearly indicate the significant effect of
precipitation on average traffic 14 speed. 15
16 Effect of road surface conditions: Road surface conditions
were found to have a significant 17
effect on average traffic speed. For the 2-lane combined case,
the average traffic speed 18 decreased by approximately 4.38 km/hr
when the pavement was chemically wet, and 8.5 19 km/hr when it was
in ice watch or ice warning. Similar findings were observed for the
4-lane 20 combined case with relatively higher reduction. These
results clearly show the high degree of 21 impact of the road
surface conditions on traffic pattern. 22
23 Note that visibility was not found to be significant in the
regression analysis, which was unexpected. 24 This result could be
caused by poor data quality or non-linear effect visibility on the
traffic speed. 25 The later cannot be fully captured by a linear
model. 26 27 28 29 30 31 32 33 34 35 36
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Cao et al. 10
1
2 FIGURE 2: Predicted Speed versus Observed Speed using
Regression Model 3
4 5 ARTIFICIAL NEURAL NETWORK 6 7 Artificial Neural Network
model (ANN) is a non-parametric method for modeling complex
non-linear 8 relationships. Unlike regression models that need an
explicitly defined function to relate the input and 9 the output,
the ANN can approximate a function and associate input with
specific output through the 10 process of training. Therefore, ANN
can be used to evaluate the robustness of regression models (13).
11 In this study, the most commonly used ANN - multi-layer
perceptron neural network (MLP-NN) was 12 selected for modeling the
relationship between traffic speed and various influencing factors.
MLP-13 NN consists of an input layer, one or more hidden layers,
and an output layer. The input layer includes 14
30
50
70
90
110
130
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Cao et al. 11
input nodes representing the weather, road and traffic factors
same as the independent variables used 1 in a regression model,
while the output layer includes the dependent variable to be
predicted, i.e., 2 traffic speed. The hidden layer provides a
mechanism to transfer inputs to output through activation 3
functions and weights (13). A detailed discussion on ANN is out of
the scope of this paper and can be 4 found in literature (e.g.,
13). In this research, the popular Sigmoid function is selected for
as 5 activation functions of the hidden layers and a linear
activation function for the output layer. The 6 weights of MLP-NN
are calibrated by back propagation algorithm with a learning rate
of 0.1, a 7 momentum of 0.8. The back propagation algorithm
minimizes the sum of squared deviation of the 8 output from the
target value at the nodes of the output layer by adjusting the
value of weight at nodes. 9 10
The significant independent variables found in our previous
regression analysis were included 11 as the input factors of the
MLP-NN. Table 3 shows the results of MLP-NN for the two types of 12
highways. Note that a single hidden layer with 7 nodes and two
hidden layers with 9 nodes in first 13 layer and two nodes in
second layer were found to be optimal for the 2-lane and 4-lane
highways, 14 respectively. The corresponding RMSE is 10.54 and
9.12, which are similar to the RMSE of the 15 regression models.
These results validate the robustness of linear regression models.
Figure 3 show 16 the predicted speeds versus observed speeds for
the 10% holdout data. 17 18
TABLE 3 MLP-NN Results 19
Site # Variables
ANN architecture
(hidden layers & nodes) RMSE
First layer Second layer
H2-1 & H2-2
Site #, Total Volume, % Long Volume,
Road Surface Condition, Surface
Temperature, Wind Speed, Precipitation
Intensity
7 10.54
H4-1 & H4-2
Site #, Total Volume, % Long Volume,
Road Surface Condition, Surface
Temperature, Wind Speed, Precipitation
Intensity
9 2 9.12
20 21 22 23 24 25 26
TRB 2013 Annual Meeting Paper revised from original
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Cao et al. 12
1
2 FIGURE 3: Predicted Speed versus Observed Speed using MLP-NN
Models 3
4 5 TIME SERIES ANALYSIS 6 7 The data used in this research
consist of time series of observations over various snowstorm
events. 8 The observations within each event could therefore be
correlated to each other due to the similarity in 9 weather and
environmental conditions. This auto correlation violates the
assumption of randomness 10 and independency between observations
required by the multivariate regression method. An 11 alternative
approach would be time series analysis, which explicitly models the
correlation between 12 successive observations by considering the
effect on current behavior of variables in terms of linear 13
relationships with their past values (14). In this research, one of
the most popular time series models - 14
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Cao et al. 13
multivariate autoregressive integrated moving average (ARIMA),
was applied for predicting the 1 traffic speed based on traffic
volume, weather and surface data. Since the focus of our study is
to 2 investigate the speed variation during snowstorms, adjacent
events are stitched together in model 3 calibration. 4 5 The
general form of multivariate ARIMA(p, d, q) model used is given
below: 6 7
(B)(1-B)d(St-) = (B) at + (i)*Predictor (i)t (1) 8 9 Where
10
(B)= (1- 1B- 2B2-.. pBp) 11
(B) = (1- 1B- 2B2-.. qBq) 12
B = black slash operator 13 at = white noise N(0,
2) 14
(i) = coefficient of prediction variable 15 St = Speed at time t
16 = average speed 17 Predictor (i)t = cross sectional variables at
time t (14) 18
19 In a time series analysis, the stationarity of the data must
first be examined. If the time series is 20
non-stationary, it must be transformed into a stationary time
series by the method of differencing. This 21 can be determined
using autocorrelation factor (ACF) and partial autocorrelation
factor (PACF). It is 22 found that observed speeds did not show any
trend of being non-stationary; therefore, no 23 differentiation was
required for the data. Based on the pattern of ACF and PACF and the
investigation 24 of several combinations of ARIMA patterns, ARIMA
(1,0,1) for 2-lane highway and ARIMA (2,0,1) 25 for 4-lane highway
were calibrated. 26
27 The basic assumption in calibration of ARIMA model is that
the white noise (at) is uncorrelated 28
and random with zero mean and constant variance. The model
parameters shown in Equation 1 are 29 estimated using maximum
likelihood method with 95% confidence interval. Therefore, those 30
covariates and autocorrelation (AR) and moving average (MA) terms
of speeds of different time lags 31 with p-value greater than 0.05
were excluded. Table 4 shows the results of ARIMA model with cross
32 sectional predictors. Similar to multivariate regression
analysis, time series modeling is an iterative 33 process with the
modeling quality being diagnosed using residual ACF and PACF. 34
35
Based on the ARIMA model results in Table 4, it can be found
that similar with the multivariate 36 linear regression results,
precipitation and road surface conditions were found to have a
significant 37 effect on average traffic speed. The R-Square values
for the 2-lane and 4-lane highways are 0.45 and 38 0.85 which are
higher than the values in the regression analysis (i.e. 0.2 and
0.48). The RMSE values 39 are 9.73 and 5.36 which were also
improved significantly compared with the values in the regression
40 analysis (10.11 and 10.44) and MLP-NN (10.54 and 9.12). 41
42 To show the performance of the ARIMA model for estimating
traffic speed, the calibrated 43
ARIMA model is applied to estimate the traffic speed at a given
time over two selected events based 44 on past speed observations
and current weather conditions. The calibrated regression model and
ANN 45 were also used to estimate the traffic speed over the same
events. Figure 4 shows the results of speed 46 estimation from the
three alternatives. It can be observed that the regression model
and ANN model 47 had been outperformed by the ARIMA. This result is
somehow expected as the later used the past 48 speed observations
and thus had the advantage of making use of more information than
the other two 49 alternatives. 50
51 52 53
54
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Cao et al. 14
1 TABLE 4 ARIMA Model Results 2
Variables Lag position 2-Lane 4-Lane
Combined Combined
Constant 9.35 2.96
Average Speed (AR) Lag 1 0.89 1.02
(0.00, 0.01,87.8) (0.00, 0.03,39.87)
Average Speed (AR) Lag 2
-0.06
(0.01, 0.02, -2.2)
Average Speed (MA) Lag 1 0.55 0.45
(0.00,0.19,28.84) (0.00,0.02,19.43)
Total Volume Lag 0
0.01
(0.00, 0.001, 9.31)
% Long Volume Lag 0
-5.33
(0.00,0.72,-7.43)
Surface Temperature Lag 0 0.30 0.12
(0.00, 0.08, 3.8) (0.05, 0.05, 2.38)
Wind Speed Lag 0 -0.19
(0.05, 0.03, 7.29)
No Snow 0.00
Slight Snow Lag 0 -1.28 -0.58
(0.00, 0.43, -2.9) (0.00, 0.16, -3.64)
Moderate Snow Lag 0 -1.40 -1.82
(0.016, 1.4, -1.38) (0.00, 0.34, -5.38)
Heavy Snow Lag 0 -6.22 -5.14
(0.00, 1.43, -4.35) (0.00, 0.55, -9.35)
Dry Lag 0 0.00 0.00
Trace Moisture Lag 0 0.00 0.00
Wet Lag 0 0.00 0.00
Chemically Wet Lag 0 -4.64 -2.80
(0.00, 1.45, -3.19) (0.00, 0.48, -595)
Ice Watch Lag 0 -2.85 -2.85
(0.00, 0.32, -8.87) (0.00, 0.32, -8.87)
Ice Warning Lag 0 -3.58 -3.11
(0.00, 0.65, -5.9) (0.00, 0.48, -6.54)
H2-1 Lag 0 0.00
H2-2 Lag 0 5.73
(0.00, 1.17, -4.5)
H4-1 Lag 0
0.00
H4-2 Lag 0
-8.69
(0.00, 1.60, -5.44)
R-Square 0.45 0.85
RMSE 9.73 5.36
Note: Values in parenthesis are p-value, standard error,
t-value, respectively 3 4
5 6
TRB 2013 Annual Meeting Paper revised from original
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Cao et al. 15
1 2
3 4
FIGURE 4: Comparison of Model Performance for Traffic Speed
Estimation 5 6 7 CONCLUSION 8 9 This study investigates the impact
of adverse weather and road surface conditions on traffic speed 10
with the intention of exploring the feasibility of applying speed
as a performance indicator of winter 11 road maintenance. Four
locations in two types of highways in Iowa, US were chosen as the
case study 12 sites. Multivariate linear regression models, MLP-NN
and ARIMA models were developed for these 13 two highway types. 14
15
It was found that precipitation and road surface conditions have
a relatively higher effect on the 16 average traffic speed than
other factors such as temperature and wind speed. Different from
the linear 17 regression models, the MLP-NN could capture the
non-linear effect of independent variables on the 18 average
traffic speed. However, the modeling results did not confirm the
superiority of the MLP-NN 19 over the regression models. This
indifference, however, validates the robustness of the multivariate
20 linear regression models. By taking into account both the
autocorrelation nature of the data as well as 21 the effects of
cross-sectional variables, the ARIMA model provided much improved
explanatory and 22 prediction power as compared to regression
models and MLP-NN. It should be noted that the 23
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Cao et al. 16
ARIMA model makes use of recent past observations in estimating
the travel speed of the current 1 time period. In contrast, the
regression models and artificial neural network models estimate
speeds 2 based on external factors only. 3
4 The analysis results clearly indicated the dependency of
traffic speed on road surface conditions, 5
suggesting the feasibility of applying speed as a performance
monitoring tool. For example, for a 6 given weather and traffic
condition, the reduction in speed can be established from a
comparison to 7 baseline values and attributed to the change in
surface conditions. Based on the degree of speed 8 reduction, the
road surface condition can be predicted and their performance can
be gauged 9 accordingly and/or maintenance activities can be
mobilized. 10
11 It should be noted that this research has so far focused on
investigating the correlation between 12
traffic speed and road surface conditions. Further research is
needed to develop quantitative models 13 that can be used to infer
road surface conditions (e.g. bare pavement status) based on
observed traffic 14 speed and other known road weather parameters.
15
16 17 ACKNOWLEDGMENTS 18 19 The research reported in this paper
is funded jointly by AURORA - a pooled-fund program in US and 20
Ministry of Transportation Ontario (MTO). The authors also wish to
acknowledge several particular 21 individuals, including Tina
Greenfield Huitt of Iowa DOT and Max Perchanok from Ministry of 22
Transportation Ontario (MTO) for providing assistance, data and
thoughtful suggestions for this 23 project. 24 25
TRB 2013 Annual Meeting Paper revised from original
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Cao et al. 17
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