Efecto Del Tiempo y Las Condiciones Del Camino de Superficie en Velocidad TrÃ¡Fico de Carreteras...

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





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


Garrett Donaher

MASc student




Phone: (519) 888-4567 ext. 33984

Fax: (519) 725-5441


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

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


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


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


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


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

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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


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


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


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


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


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


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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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

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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


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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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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


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


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


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REFERENCES 1 2 1. Highway Capacity Manual. TRB, National Research Council, Washington, D.C., 2010. 3 4 2. Kyte, M., Z. Khatib, P. Shannon, and F. Kitchener. Effects of Environmental factors on Free- 5

Flow Speed. Transportation Research Circular presented at the Fourth National Symposium on 6 Highway Capacity, Maui, Hawaii, 2000, pp.108-119. 7

8 3. Maze, T., Agarwal, M. and Souleyrette, R. Impact of Weather on Urban Freeway Traffic Flow 9

Characteristics and Facility Capacity. Center for Transportation Research and Education, Iowa 10 State University, 2005. 11

12 4. Liang, W. L., Kyte, M., Kitchener, F. and Shannon, P. Effect of Environmental Factors on Driver 13

Speed - A Case Study. Transportation Research Record. No. 1397. TRB, National Research 14 Council, Washington, D.C., 1998, pp.155 -161. 15

16 5. Camacho, F. J., Garcia, A. and Belda, E. Analysis of Impact of Adverse Weather on Freeway 17

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34 10. Maki, P. J. (1999). Adverse Weather Traffic Signal Timing, ITE Annual Meeting, Institute of 35

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11. Perrin, J., P. T. Martin, and W. Cottrell (2000). Effects of Variable Speed Limit Signs on Driver 38 Behavior During Inclement Weather, Institute of Transportation Engineers, Washington, D.C. 39

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