ABSTRACT

Travel speed is an essential criterion for evaluating motorists’ driving experiences and the traffic conditions they encounter when they travel. However, travel speed can be affected by many factors, such as the geometric design of roadways. Travel speed also varies according to different operational conditions, such as whether the roads are congested or uncongested.

In this study, the impacts of weather—specifically, precipitation and visibility—on travel speed were studied during uncongested and congested travel conditions. To do so, probe speed data were obtained from the Regional Integrated Transportation Information System website and combined with weather data from the Pennsylvania State Climatologist website. In the uncongested condition, travel speed is specified as free flow travel speed. In the congested condition analysis, the travel speed takes into account the impacts of ambient traffic on vehicle speed. Generally, past studies on travel speed develop simple regression models to quantify the impact of weather on speed. However, beyond these approaches, this paper proposes an advanced model, random forest, to further explore possible factors that will impact travel speed.

This study found that hourly precipitation, which is measured by precipitation intensity, had a negative impact on travel speeds in both uncongested and congested conditions. Visibility, which is measured by distance, has slightly positive impact on free flow travel speed in uncongested conditions. If hourly precipitation increases by 0.01 inch/hr, the free flow travel speed will decrease by 1.711 mph. In congested regions, the only continuous variable is hourly precipitation, because visibility is not considered. The results showed that for each increase in increments of 0.01 inch/hr of precipitation, the free flow travel speed on the congested corridor decreases about 8.86 mph.

Instead of utilizing linear models, this study also implemented non-linear transformations for hourly precipitation and visibility. Both the uncongested and congested analyses conducted a non-linear transformation for both hourly precipitation and visibility. The study found that, in the uncongested analysis, the square root form of hourly precipitation and linear form of visibility has the highest model performance which is measured using R² value. In the congested analysis, the cubic form of hourly precipitation and exponential form of visibility has the highest model performance.

Given that linear models assume that the relationship between independent and dependent variables is linear, a non-linear model, random forest, is proposed to further explore the relationship between travel speeds and hourly precipitation and visibility. In the analysis, the importance of each independent variable is calculated and ranked. The random forest model indicates that in uncongested condition, 45 mph speed limit has the largest impact on free flow travel speed; in congested condition, hourly precipitation and visibility have comparatively larger impact on travel speed. Moreover, the impact of weather on travel speed will be visualized using Partial Dependence Plot (PDP). An interesting finding is, no matter in which condition, travel speed drops dramatically if hourly precipitation is light. But, when hourly precipitation is greater than a certain value, travel speed will not decrease.

TABLE OF CONTENTS

LIST OF TABLES…………………………………………………………………………………………………………… viii

LIST OF FIGURES…………………………………………………………………………………………………………. xiv

ACKNOWLEDGEMENTS……………………………………………………………………………………………… xxiii

1. INTRODUCTION AND LITERATURE REVIEW………………………………………………………………… 1

1.1 Motivation………………………………………………………………………………………………………………… 1

1.2 Literature Review………………………………………………………………………………………………………. 1

1.3 Research Objectives……………………………………………………………………………………………………. 3

2. METHODOLOGY………………………………………………………………………………………………………….. 4

2.1 Linear Regression………………………………………………………………………………………………………. 4

2.2 Random Forest Regression…………………………………………………………………………………………… 5

2.2.1 Decision Tree………………………………………………………………………………………………………. 5

2.2.2 Bootstrap Aggregation Trees…………………………………………………………………………………… 6

2.2.3 Random Forest…………………………………………………………………………………………………….. 6

2.3 Model Evaluation………………………………………………………………………………………………………. 6

2.3.1 Linear Regression Evaluation………………………………………………………………………………….. 6

2.3.2 Random Forest Evaluation……………………………………………………………………………………… 7

2.3.3 Partial Dependence Plots……………………………………………………………………………………….. 8

3. DATA AND ANALYSIS……………………………………………………………………………………………….. 10

3.1 Studied Data……………………………………………………………………………………………………………. 10

3.3.1 Traffic Data………………………………………………………………………………………………………. 10

3.1.2 Climate Data……………………………………………………………………………………………………… 11

3.2 Study Area……………………………………………………………………………………………………………… 12

3.3 Uncongested Locations:…………………………………………………………………………………………….. 14

3.3.1 Data Description………………………………………………………………………………………………… 14

3.3.2 Data Preprocessing……………………………………………………………………………………………… 19

3.3.3 Data Visualization………………………………………………………………………………………………. 20

3.3.4 Linear Regression Analysis…………………………………………………………………………………… 25

3.3.5 Regression Counting with Hour-of-day, Month-of-year, Sub-corridor and Speed limit, Hourly precipitation and Visibility……………………………………………………………………………………………………………. 31

3.3.6 Tree-Based Regression Counting with Hour-of-day, Month-of-year, Sub-corridor, Speed limit, Hourly precipitation and Visibility…………………………………………………………………………………………… 38

3.3.7 Model Comparison……………………………………………………………………………………………… 41

3.3.8 Partial Dependence Plots……………………………………………………………………………………… 41

3.4 Congested Locations:………………………………………………………………………………………………… 43

3.4.1 Data Description………………………………………………………………………………………………… 44

3.4.2 Data Visualization………………………………………………………………………………………………. 48

3.4.3 Linear regression Analysis……………………………………………………………………………………. 51

3.4.4 Linear Regression Counting with Hour-of-day, Month-of-year, Sub-corridor, Speed limit, AM/PM, Hourly precipitation and Visibility…………………………………………………………………………………………… 56

3.4.5 Tree-Based Regression Counting with sub-corridor, hour-of-day, month-of-year, speed limit, morning/evening, hourly precipitation and visibility………………………………………………………….. 64

3.4.6 Model Comparison……………………………………………………………………………………………… 65

3.4.7 Partial Dependence Plots……………………………………………………………………………………… 66

4. DISCUSSION………………………………………………………………………………………………………………. 69

4.1 Uncongested Condition Analysis Discussion:………………………………………………………………. 69

4.2 Congested Condition Analysis Discussion:…………………………………………………………………. 70

5. CONCLUSION…………………………………………………………………………………………………………….. 73
6. FUTURE WORK………………………………………………………………………………………………………….. 77

APPENDIX A…………………………………………………………………………………………………………………. 80

Uncongested Corridors’ Information………………………………………………………………………………. 80

APPENDIX B…………………………………………………………………………………………………………………. 85

Uncongested Corridors’ Cutoff Tables……………………………………………………………………………. 85

APPENDIX C…………………………………………………………………………………………………………………. 87

Uncongested Corridors’ Information after cutting off…………………………………………………………. 87

APPENDIX D…………………………………………………………………………………………………………………. 89

Three-Group Precipitation CDF Graphs of Uncongested Corridors……………………………………….. 89

APPENDIX E………………………………………………………………………………………………………………….. 98

Two-Group Precipitation CDF Graphs of Uncongested Corridors…………………………………………. 98

APPENDIX F………………………………………………………………………………………………………………… 108

Four-Group Visibility CDF Graphs of Uncongested Corridors……………………………………………. 108

APPENDIX G……………………………………………………………………………………………………………….. 117

Linear regression Graphs and Tables of Uncongested Corridors………………………………………….. 117

APPENDIX HInformation and Congestion Ratio Tables of Congested Corridors in Philadelphia and Pittsburgh    153

Regions………………………………………………………………………………………………………………….. 153

APPENDIX I…………………………………………………………………………………………………………………. 162

Linear regression Graphs and Tables of Congested Corridors…………………………………………….. 162

APPENDIX J………………………………………………………………………………………………………………… 218

Two-Group Precipitation CDF Graphs of Congested Corridors…………………………………………………. 218

1. INTRODUCTION AND LITERATURE REVIEW

1.1 MOTIVATION

Travel speed is often used to evaluate a corridor’s performance. It is an important factor for traffic engineers and roadway designers to consider while performing traffic analyses. Travel speed can be impacted by many factors–such as weather, seasons, corridor location–and can affect the motorists’ driving experiences. It is especially important that, for their own safety, drivers consider the weather. In adverse weather and reduced visibility conditions, such as snow, rain, fog, and haze, drivers should drive much slower than on clear days. In light of these hazards, this study focused on how adverse weather influence travel speed.

1.2 LITERATURE REVIEW

Previous research on travel speed has investigated the following questions: What is the speed reduction in adverse weather compared with clear days? How do fog and haze affect driving visibility? Will strong winds cause a reduction of average free flow travel speed? Will adverse weather increase the possibility of traffic crashes? Will snow or rain cause new bottlenecks? How does adverse weather affect traffic delay, travel time, traffic flow, and traffic volume?

With respect to these questions, many researchers have done a lot of work during last few decades. In 2000, Al-kaisy tried to discover the impact of darkness on the capacity of a freeway and found that darkness had a negative impact on traffic capacity in work zones. To be more specific, this negative impact was quantified as an approximate 7.5 and 3.25 percent reduction in capacity for two studied sites [1] . In the same year, Kyte et al. performed research on the relationship between general environmental factors and free-flow speed. Those factors included precipitation, roadway surface condition, visibility, and wind speed. Instead of focusing on each single factor’s impact, the aggregated impact of those factors was investigated. The authors concluded that rainfall had a free-flow reduction effect of about 31.6 km/h [2] . Some researchers have analyzed the effect of different weather conditions on average free flow travel speeds [3] [4] . Specifically, Oh, Shim, and Cho believe that adverse weather conditions reduce free flow speed. The ratio of free flow speed reduction was found to be 7 percent and 2 percent on snowy and rainy days, respectively. Meanwhile, this effect became 5 percent and 6 percent for rainy and snowy nights, respectively. In addition to studying average speed, researchers have also focused on describing traffic conditions using traffic volumes [5] . Moreover, due to advances in our understanding of the shape of the speed-flow curve, some researchers have viewed travel time as the dependent variable, applying statistical analysis like regression model and ANOVA to evaluate the relationship between travel time and weather [6] [7] . Other researchers have taken a different approach, analyzing free flow travel speed, short-term lane speed [7] , speed at capacity, free flow speed [8] , traffic intensity [9] , traffic activity [10] , traffic flow as the dependent variable [11] [12] . In recent years, some researchers started to identify and model inclement weather impacts on traffic stream behavior [13] . They concluded that rain will cause a 5 percent reduction in lightduty vehicle speed and 3 percent in heavy-duty truck speed. In snow, this reduction is more significant (in the range of 55 percent). Outside the United States, Hooper, Chapman, and Quinn investigated the impact of precipitation on vehicle speeds in the United Kingdom [14] . A400-km corridor from London to Carlisle was used for that study. The polynomial regression and linear regression analyses that the researchers used found that precipitation caused a significant reduction in speed and maximum flow on many links of the corridor, as well as a downward reduction in the overall speed-flow relationship. In Canada, Roh, Sharma, et al. observed that severe weather conditions will trigger variations in highway traffic; however, truck volume is not significantly affected by the snowfall or the cold category variables [15] . In an Arctic region study, Bardal concluded that temperature, wind speed, and precipitation have a negative impact on transport [16] . In Istanbul, Turkey, Akin, et al. investigated the impacts of weather on traffic speeds on urban freeways using regression analysis. Their findings showed that rain will reduce the average vehicular speeds by 8 to 12 percent, and a wet roadway surface will reduce the average speed by over 6 percent. Light snow will result in 4 to 5 percent reduction of average speed [17] . Similarly, Enbery and Mannan studied a highway segment and found that the effects of rain or slippery conditions were small; however, during snowfalls, the speeds were much lower than on clear days in winter [18] .

Generally speaking, these previous studies and papers only focused on two to three variables and seldom explored the relationship between hourly precipitation, visibility, corridor location, speed limit, hour-of-day, month-of-year, corridor direction, or travel speed. To overcome those limitations, this study used Cumulative Distribution Function (CDF) plots to visualize the impact of precipitation and visibility on free flow travel speed. Also, linear regression models and a random forest model were proposed to measure each categorical and continuous variable’s impact on free flow travel speed. To make the study more practical and consider that different traffic conditions can have different free flow travel speeds, this paper selected and studied traffic speed data in both non-peak and peak hours from May 1, 2015 to Oct 31, 2015 corresponding to uncongested and congested traffic speed data.

1.3 RESEARCH OBJECTIVES

In summary, the objectives of this research are to:

1. Visualize the difference of free flow travel speeds in adverse and clear weather by hour in both congested and uncongested traffic conditions;
2. Quantify the impact of adverse weather on free flow travel speed in both congested and uncongested traffic conditions; and
3. Determine the other potential factors that might have impact on free flow travel speed and quantify their impacts for both uncongested and congested traffic conditions.

USING REAL-TIME SPEED DATA TO QUANTIFY IMPACTS OF WEATHER ON TRAVEL SPEEDS

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