Master’s Thesis

Road Safety and Adverse Weather ConditionsAn empirical analysis of speeding behavior under wet pavement conditions

Submitted at theFaculty of Business, Economics and Social Sciences

University of Bern

Institute of Business Management and MarketingSection Consumer Behavior

SupervisorDr. Michael Schulte-Mecklenbeck

Submitted byAuthor: Ozan Harman

Student ID: 08-926-305Address: Muhlemattstrasse 59

3007 BernPlace of origin: Zurich, ZH

E-Mail: on.harman@gmail.comDate of Submission: September 13, 2016

Abstract

Precipitation is known to increase traffic accidents and fatalities.

However, it is not fully understood how precipitation impact driver

behavior. This study examined how drivers’ adapt speed to changes

from dry to wet pavement conditions. Speed and pavement condition

were evaluated using radar data and surveillance images in a speed

limit 50 km/h two way road section in Zurich, Switzerland. The total

sample consisted of 195’799 vehicles and 7’988 images for the entire

month of February, 2016. To balance our sample we matched pairs by

day, hour, congestion, and hour category (for weekdays). Using the

wilcoxon signed rank test and the fligner-killeen variance homogeneity

test we analyzed speed median and dispersion for differences between

dry and wet pavement conditions. We found that a change from dry

to wet pavement conditions induce drivers’ to reduce speed by 2.7-

5.4 percent. For speed dispersion the results are less consistent; for

weekends and weekday middays dispersion did not differ, whereas dis-

persion differed for weekday mornings and evenings between dry and

wet conditions. Finally, we found that drivers’ do not reduce speed

sufficiently to have equal braking distances in dry and wet conditions.

2

Acknowledgement

First and foremost, I would like to express my gratitude to my supervisor

Dr. Michael Schulte-Mecklenbeck, who competently guided me and granted

me the freedom to explore the topics I was interested in.

I am also grateful to my dear friend, David Wartmann and my father in

law, Olivier Peter for their insightful comments and encouragement on those

scientifically dark days.

My parents supported me wherever possible during my whole life and enabled

me to pursue my education. They deserve my sincere gratitude.

Last but not least, my sincere thanks also goes to Audrey Peter for her loving

support, attention and encouragements.

3

Contents

1 Introduction 6

1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . 7

2 Overview 8

2.1 Road Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Driver Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.3 Rain and Traffic . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Research Question and Hypothesis . . . . . . . . . . . . . . . 18

3 Methodology 19

3.1 Site Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2 Traffic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Weather Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Results 23

4.1 Data Preparation . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Subsetting Data . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.3 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.4 Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Conclusion and Discussion 33

5.1 Causal Chain Model and the Haddon Matrix . . . . . . . . . . 33

5.2 Strengths and weaknesses . . . . . . . . . . . . . . . . . . . . 39

5.3 Directions for Future Research . . . . . . . . . . . . . . . . . . 41

4

Appendix A 42

References 48

List of Tables 54

List of Figures 54

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1 Introduction

Along with driver attributes many factors impact the probability of traffic

accidents. Environmental factors such as visibility, road design, weather, and

vehicle attributes interact with driver behavior (Tiwari et al., 2005). It is

widely accepted that increased vehicle speed, speed dispersion, and adverse

weather conditions – such as road slipperiness – increase traffic accident prob-

abilities (Brodsky & Hakkert, 1988; Sabey & Staughton, 1975; Almqvist &

Heinig, 2013; Aarts & Van Schagen, 2006; Garber & Gadirau, 1988), therefore

it is important to understand how changes in weather and road conditions

influence driver behavior. Speed alone merely causes an accident; speeding,

speed dispersion, and adverse weather on the other hand are a deadly mix-

ture. Accordingly, pavement conditions are of special interest because they

have a direct measurable influence on vehicle performance. Hamilton (2012)

demonstrated the significance of pavement condition regarding road safety

and showed that the majority of weather induced accidents are related to

wet road surfaces.

Over the past two decades, researchers in this field were challenged regarding

validity, replicability, and accuracy. There is no best way to find an appro-

priate proxy for weather or a preferable measurement method. and (Brodsky

& Hakkert, 1988; Jagerbrand & Sjobergh, 2016; Edwards, 1999).

1) We address accuracy and replicability problems by using raw data from

automated measurements. 2) Previous findings show that adverse weather

conditions such as rainfall measured at nearby weather station lead to higher

accident rates and reduced speeding.

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We add to this by collecting our data – including our weather data – at

a single study site and by focusing on road surface wetness rather than on

precipitation. 3) Finally, to best of our knowledge there exists no similar

study in Switzerland. This location is of special interest because Switzerland

in line with Sweden is considered to be the safest driving environment world-

wide (BITRE, 2015). Nevertheless road safety needs to be improved since

wet road surface is the most frequent weather related cause of accidents in

Switzerland (ASTRA, 2016).

1.1 Problem Statement

It is commonly accepted that adverse weather conditions increase accident

risk. However, findings in road safety research show flaws regarding study

design, data quality, and methodology (Hauer, 2002). One issue is that

covariates indicating weather condition are based on measurements of nearby

weather stations. This leads to uncertainty about validity – ex post it can’t

be proven if the weather was identical at the different measurement locations.

Further it is loose to assume that a driver’s weather perception is identical

with measurements from a weather station. We solve this problem generating

our weather variable using images from a on site surveillance camera. The

image material is close to the driver’s visual perception of the road conditions.

Weather station measurements however are based on technical equipment

measuring physical conditions rather then human perception. An additional

issue using weather station measurements in the context of pavement state

is that the pavement stays wet after rain has stopped. This can lead to

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erroneous classification into dry when generating a factor variable for weather

based on meteorological data.

In our paper we chose the causal chain model presented by Elvik (2003) as our

base to interpret our findings. The model provides a framework to analyze

the impact of road safety measures through two pathways – the engineering

and behavior effect. Former, captures the impact of safety measures on

accident risk and severity. Latter analyzes the behavioral adaptation to the

road safety measure. However, using the causal chain model for our purpose

is rather unconventional since the model was initially intended to evaluate

road safety measures. We assume that the model has the capacity to provide

a deeper understanding of the effect wet pavement has on driver behavior.

2 Overview

2.1 Road Safety

There is no doubt about the importance of road safety in our mobile society.

However, there is no universal measure of road safety or singular solution

to improve road safety. Moreover, through the lack of generally valid rules,

like they exist in physics, most of the conducted research does not have an

axiomatic base (Elvik, 2004). For example, one would expect drivers’ to slow

down under adverse light conditions – empirical finding indicate otherwise

(de Bellis et al., 2015). Differing from scientific areas with well accepted

rules, road safety researchers cannot rely on such premises for further rea-

soning. Nevertheless, there are well established theoretical frameworks that

8

seem to be a good starting point to classify phenomena on common grounds.

In this paper we base the discussion of our assumptions and findings on two

models – the haddon matrix for our assumptions and the causal chain model

for our findings. 1) The haddon matrix is the most prominent framework

from a situational point of view. Haddon (1972) distinguishes three traffic

factors (human, vehicle, and environment) that influence the risk and sever-

ity of an accident within three phases (pre-crash, crash, and post-crash). The

Table 1: Haddon Matrix

Crash Phases Traffic Factors

Human Vehicle Environment

Pre-crash alcohol consumption tire blowout pavement condition

Crash bleeding disorder safety equipment safety barriers

Post-crash first-aid skills cost of vehicle repair rescue facilities

Note: Adapted from Haddon (1972).

combination of different traffic factors and crash phases is shown in Table

1. In addition, exemplary elements of the haddon matrix are presented in

italic letters. The haddon matrix allows a systematic classification of com-

mon accident causes and provides a conceptual framework. In case of an

accident the three factors can be described in three phases. For example, an

alcoholized individual had a tire blowout while driving on a wet road section

(Pre-crash). The driver lost control of his vehicle and crashed into the safety

barriers. Severe injuries were prevented by the airbag and the driver suffered

a minor laceration. However, the driver needed medical care due to bleeding

(Crash). On-site the driver treated the wound with a compression bandage

and received treatment at the hospital in walking distance. Since the vehicle

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was a limited edition the cost of repairs exceeded the value of the vehicle

(PostCrash).

Even though the haddon matrix has its strength in ad hoc and post hoc

descriptions of traffic situations it has its weakness from a procedural point

of view. It does not identify the driver’s behavioral adaptation to the situa-

tion nor how the accident and the human, vehicle, and environmental factors

affect each other. This is improved in the causal chain model (Elvik, 2004).

To understand this approach we take a step back. Our traffic infrastructure

Figure 1: Causal Chain Model

Note: Reprinted from Elvik (2004).

can be seen as a complex network of numerous road safety measures. To-

days roads are the result of incremental changes to our infrastructure aiming

to provide an efficient system. Traffic incidents are correlated in a way or

another to those road safety measures. As shown in Figure 1 a road safety

measure influences final outcomes through two pathways – target risk factors

and other risk factors. Target risk factors, also called ”engineering effect”,

identify nine factors similar to those classified by the haddon matrix. Their

main characteristic is a high level of physical measurability.

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According to the causal chain model target risk factors of a road safety

measure can be reduced to one or more of the following types:

1. Kinetic energy2. Friction3. Visibility4. Compatibility5. Complexity6. Predictability7. Road user rationality8. Road user vulnerability9. Forgiveness

Kinetic energy is measured by the mass and speed of a vehicle. Con-

trolled kinetic energy is not a risk as such. However, if the friction between

the tires and the surface is not high enough (skid resistance) the driver will

loose control over the vehicle. Visibility identifies the distance at which a

traffic participant can identify objects. Compatibility refers to differences in

kinetic energy of proximate traffic participants. For example, a tractor is not

allowed on highways due to incompatibility. Another type of risk is the traffic

complexity measured by the amount of information a driver has to process

per unit of time. Closely related to the previous type predictability stands for

the reliability of a driver’s predictions of the immediate traffic situation. For

instance, oncoming traffic on a highway has a high predictability. Individual

rationality denotes the driver’s individual utility maximization. Accordingly,

driver rationality is influenced by multiple aspects such as delay to an ap-

pointment and speeding, alcohol consumption and alertness. Drivers’ are

in this case not minimizing risk but maximizing individual utility. Another

type of risk is a road users vulnerability, e.g., a driver – ceteris paribus –

with a bleeding disorder will behave different, since he is facing higher levels

of injury risk in case of an accident. Finally, system forgiveness measures

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how forgiving the traffic infrastructure is in case of human and/or technical

failure. For example, safety barriers at steep curves possibly reduce the out-

come severity of an accident.

Up to this point many of the target risk factors can be classified in the haddon

matrix. However the main difference of the two approaches lie in the second

path over which road safety measures influence final outcomes, namely other

risk factors. These risk factors are also called ”behavioral effects” and will

be discussed in the next section.

2.2 Driver Behavior

Road safety measures influence traffic outcomes through behavioral effects.

These effects can be fragmented into the six factors below:

1. How easily a measure is noticed2. Antecedent behavioural adaptation to basic risk factors3. Size of the engineering effect on generic risk factors4. Whether or not a measure reduces injury severity and accident risk5. The likely size of the material damage incurred in an accident6. Whether or not additional utility can be gained

Road users evaluate their environment in order to adapt behavior to

sensory perception. Behavioral adaptation is a result of how a traffic

participant perceives a road safety measure. (1) Road safety measures that

are easily noticed by the driver are more likely to have a behavioral effect.

(2) If a target risk factor has provoked behavioral adaptation in a past

situation a road safety measure affecting this risk factor is more likely to

have a behavioral effect. For instance, the indication of aquaplaning risk

on a highway is more likely to have an effect on drivers’ that are conscious

about the risk of aquaplaning and have adapted their behavior in past

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situations. (3) Safety measures that have a large engineering effect are more

likely to have a behavioral effect. (4) Accidents are unwanted events and

traffic participants adapt their behavior to road safety measures that affect

the perceived probability and severity of an accident. (5) Drivers’ weight the

consequences of an accident in terms of material damage. Ceteris paribus

an individual will drive more carefully in a parking lot with an expensive

car. (6) Lastly, road users are more likely to change their behavior if this

increases their individual utility.

So far we described theoretical frameworks in which we will discuss our

empirical findings. A missing point is that each individual has different

risk tolerances. In our approach we assume road users to have a invariant

level of risk tolerance. Haight’s (1986) discussion about human risk taking

behavior and the measurement of risk as such seems to complement our

approach rather well. In the following we will present some of his statements

regarding risk. To begin with one has to acknowledge that there is no

universally valid measurement unit such as kilograms or meters to measure

risk. Nevertheless, risk seems to be used synonymous with probability. In

this perspective we have to follow certain rules of probability theory such as

non-additivity of correlated events. Further, risk in the sense of probability

theory requests the measure to be defined in the unit space and to be –

at least in the road safety research – path dependent. Probability theory

is ubiquitous in natural sciences and is helpful to road research from a

technical perspective however formal logic breaks down when individual

risk behavior is studied. Accordingly Shermer (2008) shows that humans

tend to misperceive and miscalculate probabilities. Even though a pure

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probabilistic approach seems fruitless, driver’s risk believe can be seen as

a mix of probability and outcome expectation. In other words, individuals

subjectively evaluate outcome severity and the probability of an event to

happen. Some attention is required distinguishing subjective and objective

risk. While the former is the risk experienced by the road user, the latter

refers to expert calculations. This distinction is of special interest for

our study analyzing differences in technically required and actual speed

reduction under reduced surface friction.

Individuals somehow balance different risk factors to maximize their indi-

vidual utility with subjective risk as a side condition. Closely linked, the

risk compensation theory assumes that individuals adapt their behavior to

changes in risk factors. For example, improved vehicle safety will lead to

less attentive driving in order to compensate the lower risk level (Wilde,

1976). A rather radical version of risk compensation is represented by the

risk homeostasis theory. It states that no road safety measure will have

any longterm safety improvement effect if the individual risk tolerance

remains unchanged (Wilde, 1988). The risk compensation theory is relevant

to our study in numerous ways. In line with the theory speed (kinetic

energy) should be reduced to compensate for the increased breaking distance

(friction) due to wet pavement.

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2.3 Rain and Traffic

It is well accepted that precipitation has two main effects. First, crash prob-

ability is higher and second, drivers’ slow down. In the following we will

distinguish between traffic-accident and /-operation research. Prior studies,

analyzing traffic accidents and precipitation, are focusing on crash severity,

crash probabilities, seasonality, amount of rainfall per unit of time, and wet

pavement. There are three prominent methods of analysis dealing with traf-

fic research. 1) The matched pair approach where two measurement periods,

for example a Monday morning, under dry and wet conditions are compared.

2) The difference-in-differences approach where the accident ratios are based

on predicted expectations versus actual accidents in the wet pavement con-

dition rather than a direct comparison of dry and wet conditions. 3) Crash

frequency analysis using count data models.

Closely related to our study, Brodsky & Hakkert (1988) found by using a

difference-in-differences approach that the mean risk of fatal accident was

five (U.S.) to six (Israel) times higher on wet than on a dry pavement. Fur-

ther, in Israel the probability of accidents increases in the period between

November and March, where rain is sporadic. This is in line with our be-

havioral approach suggesting drivers’ risk adaptation to be more prominent

if the individual was previously exposed to the risk factor.

Based on data from a nearby weather station Eisenberg (2004) found a pos-

itive relationship between precipitation and crash rates using a negative bi-

nomial regression. Without exception, literature in which the matched-pair

approach is used present accident risk to be at least 50 % higher under rainy

15

weather compared to dry (Andrey & Olley, 1990; Andrey & Yagar, 1993;

Bertness, 1980; Sherretz & Farhar, 1978). However, there is no general re-

sult regarding accident severity (Andrey & Olley, 1990). Results differ on

country basis as well as urban / rural area. Fridstrøm et al. (1995) found in-

creased accident fatalities under rainy conditions in Denmark while no such

effect was found in Norway and Sweden. Bertness (1980) measured crash

severity as the average number of injuries per accident and found a positive

relationship in rural areas but not in urban areas.

In what follows we will survey past empirical findings on the effects of rainy

conditions on traffic operations. Even though accident and operation re-

search are closely related, operation research requires a broader perspective.

Researchers need to build their arguments in a procedural manner rather

than event based. In most cases accidents are well documented incidents in

the past as a result of traffic operations (Evans, 1991). Traffic operations

on the other hand are the interrelated movement of individuals through a

complex system connected by routes (Chowdhury et al., 2000). Therefore

traffic operations include the micro (car following), meso (link level), and

macro-level (network level) (Daganzo & Daganzo, 1997). In the scope of this

paper we will focus on the impact of rainy conditions on the micro-level vari-

ables, such as individual speeds and speed dispersion. Studying traffic on the

micro-level goes in line with driver behavior research. Summarizing previ-

ous findings, precipitation leads to reduction in speed, and increases in time

and headway spacing (El Faouzi et al., 2010). Findings are contradicting

regarding speed dispersion, while Unrau & Andrey (2006) found a decrease

in dispersion, Padget et al. (2001); Liang et al. (1998) found an increase.

16

Edwards (1999), studying commuter traffic on a speed limit 113 km/h high-

way section in south Wales, has found a speed reduction of 5 km/h in rainy

opposed to dry conditions concluding the speed reduction to be insufficient

for the increased risk related to adverse weather conditions. The measure-

ments were taken by onsite individuals using handheld speed cameras, and

manual notation of perceived weather conditions. In agreement, Unrau &

Andrey (2006) found a speed reduction of 10%, reduced speed dispersion,

and increase in time spacing under rainy conditions based on data from the

speed limit 90 km/h Gardiner Expressway, Canada. The results were more

pronounced in daytime compared to nighttime. The the findings are based

on weather data from nearby weather stations.

Based on a multilevel approach Billot et al. (2009) found reduced speed

and increased time/space headways under rainy conditions measured at a

nearby weather station. The study site was a speed limit 110 km/h national

road near Paris, France. The dependent variables were generated by catego-

rizing measurements into different ranges, for example 70 ≤ speed (km/h) <

90, 2 ≤ time headway (s) < 4, or 15 ≤ space headway (m) < 30. The in-

dependent variable was based on counts of observations in these categories

conditional on weather status. The categorical dependent variables provide

a novel perspective. However, no information about statistical significance is

provided.

Research in this domain found coherent results. However, the research

is to best of our knowledge solely carried out on expressways and highways,

where speed limits are higher then at our study site and weather measure-

ments where mostly taken at nearby weather stations.

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2.4 Research Question and Hypothesis

The research question addressed in this paper is whether rainy conditions

impact traffic on the micro-level. Using cross selectional traffic data from

our study site in Zurich, Switzerland we answer this question by testing the

following hypotheses.

Uniform speed reduction hypothesis:

H0 : Wet pavement has no effect on vehicle speed

compared to dry conditions.

HA : Vehicle speed under wet pavement conditions are

slower than under dry conditions.

(1)

Homogenous speed dispersion hypothesis:

H0 : Wet pavement has no effect on vehicle speed dispersion

compared to dry conditions.

HA : Vehicle speed dispersion under wet pavement conditions differ

from those under dry conditions.

(2)

Friction risk compensation hypothesis:

H0 : The speed reduction is sufficient to compensate

for the increase in braking distance under wet,

compared to dry conditions.

HA : The speed reduction is lower than it would be required

to stop within the same distance under wet, compared to dry conditions.

(3)

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To test our hypotheses (1, 2) we use speed as our numerical dependent vari-

able and pavement condition as our binary treatment variable with two states

wet and dry. In line with previous literature on this subject we subset, limit,

and match our data to reduce biases from confounding. Accordingly, vari-

ables considered are vehicle length, headway time, time of the day, day of

the week, weekdays and weekends, and direction.

To test our hypothesis (3) we use the results from our hypothesis (1) regard-

ing speed reduction to calculate which speed reduction is required if drivers’

aim to stop their vehicle within the same braking distance under dry and

wet conditions.

3 Methodology

3.1 Site Characteristics

Data was collected on a two-lane main road section in a suburban area in

Zurich, Switzerland. As illustrated in Figure 2 and 3, the study site lies in a

speed limit 50 km/h zone connecting to a speed limit 80 km/h zone.

3.2 Traffic Data

The traffic measurements contain information about speed, vehicle length,

and road light switching times. Our entire sample contains speed measure-

ments for 195’799 vehicles for the entire month of February, 2016. The speed

cameras were provided by the traffic service department of Zurich.

On average there is a daily volume of 3’292 vehicles driving out of the 50

19

Figure 2: Study Site Map

Note: Reprinted from Google (2016).

km/h zone and 3’460 in the other direction. As illustrated in Figure 4 we

see morning and afternoon (local maxima) peak periods at 7:00 and 17:00 in

both directions. As weekends are inspected a less pronounced peak is around

15:00 for vehicles out while vehicle counts in are scattered equally between

9:00 and 17:00.

In a next step we inspect if there are speed differences for direction and

weekday. A visual inspection of Figure 5 allows to conclude higher speeds

when vehicles are heading out.

In Table 2 we can see basic statistics of our complete sample.

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Figure 3: Study Site Streetview

Table 2: Speed Statistics – Entire Sample

direction weekend N speed.mean speed.sdout weekday 75452 46.51 6.68out weekend 20014 46.94 6.93in weekday 81922 36.59 5.51in weekend 18423 37.28 5.41

3.3 Weather Data

There is no general agreement how precipitation impact on traffic should be

measured. Acknowledging this uncertainty, we argue that pavement wetness

is advantageous first because it is the predominant cause of weather related

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Figure 4: Traffic Counts

weekday weekend

0

2500

5000

7500

10000

0

2500

5000

7500

10000

out

in

0 5 10 15 20 0 5 10 15 20

time of day

veh

icle

co

un

t

Figure 5: Speed Counts

weekday weekend

0

2000

4000

6000

0

2000

4000

6000

out

in

30 60 90 120 30 60 90 120

speed

ve

hic

le c

ou

nt

accidents and second because it is well known to traffic participants that the

stopping distances are increased under wet pavement conditions. Wet pave-

ment is caused by various atmospheric phenomena such as drizzle, rain, sleet,

22

snow, hail, mist, and fog. As a result researchers miss numerous causes of

wet pavement when they merely base their road surface variable on rainfall.

We generate data from digital surveillance camera images. The onsite camera

automatically records images every 5 minutes the entire month of February,

2016. In order to generate our pavement variable we classified the raw im-

ages into three categories ( dry, wet, and snow) by visual inspection. The

classification procedure is stated below.

(1) Order images according to date stamp and generate three subfolders dry,wet, and snow.

(2) Half of the road surface which has contact with vehicle tires is dry. Moveimage to subfolder dry. Repeat until rejected.

(3) There is snow on the road surface. Move image to subfolder snow. Repeatuntil rejected.

(4) Move images to subfolder wet.

As the date stamp was encoded in the filename, we then used the image

file names as well as the folder structure from the classification procedure to

generate a categorical variable indicating pavement status.

4 Results

4.1 Data Preparation

In the following section we will describe how the data was merged which ob-

servations were excluded and which primary subsetting steps were conducted.

To merge our traffic data and our weather data into one we generated a frame-

work consisting of a timestamp with one second precision. In a second step

the traffic data was calibrated to an atomic clock by adding 72 seconds to

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each measurement timestamp. The calculation of the delay is based on cross

calibrating using a mobile phone video record of the study site.

• The mobile phone starts recording at 15:46 (seconds unclear) and switchesto 15:47 after 33 seconds. Therefore, the recording begins at 15:47:27

• A speed measurement recorded by the radar has the time stamp 15:45:07,the same vehicle appears on the video after 31 seconds.

• videot-39s+31s = videoT = video timestamp adjusted for atomic watch.

• videoT -radart = 72s

• radart+72s = radarT = radar timestamp adjusted for atomic watch.

Finally both samples were merged by filling the measurements into the

time framework. Since there are missing observations between the 5 minute

spot measurements of our weather measure gaps were continuously filled with

the preceding pavement category.

In order to ensure that our sample contains vehicles of the same type –

excluding motorcycles and trucks – we limit our vehicle length to lie between

2.5 m and 5.5 m (Schuster et al., 2011).

Further, we generated a variable indicating congestion if the time headway

was less then two seconds. The time headway of two seconds at 50 km/h

corresponds to approximately 27 meters (50×23.6

) which in turn is close to the

advised safety distance of 25 meters (half the value of the indicator in meters,

Treiber & Kesting (2010)).

4.2 Subsetting Data

Before we can begin with our main analysis subsetting of the data is required.

Following findings presented by Billot et al. (2009) we assume that time im-

pacts driver behavior and travel purpose, e.g., commuter traffic on weekdays

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and transport for leisure purposes on weekends. Therefore, we distinguish

four subsets separated by direction (in/out) and day (weekday/weekend). As

we are interested in daytime behavior and our sample size is rather small for

nighttime observations we limit all our subsamples to the time between 6:00-

19:00. For weekdays a categorical variable is generated as follows: morning

6:00-9:00, midday 9:00-16:00, and evening 16:00-19:00. These time brackets

were selected based on Gao & Niemeier’s (2007) work where they identified

weekday differences in the three time categories regarding volume, vehicle

miles traveled, and fleet composition. In line with their results we can see in

Figure 4 that a time categorization is not needed for weekends if temporal

vehicle density is used as a proxy for intra day pattern identification – other

than weekdays, weekends have a single density peak.

4.3 Matching

To balance our samples we follow the paired match approach. Matching

is the preferred technique to study driver behavior in observational traffic

research. Since we wish to have an identical size of treatment and control

groups we have to find measurement pairs with similar characteristics. Iden-

tifying pairs enables us to obtain balanced samples. In a first step we balance

our sample by finding 1:1 exact matches for the variables presented in Table

3. We consider only pairs of observations that were subject to the treatment

on the same day. This step is considered to successfully capture any day re-

lated bias. An additional exact match variable (hour category) is introduced

for weekdays, since we expect different driving patterns on mornings, mid-

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Table 3: Variables of Interest

Name Type Matching DescriptionDependent

speed discrete Measured speed in km/h.Treatment

category binary exact Indicator variable where zerostands for dry and one for wetpavement.

Covariateswday factor exact Indicator variable ranging from

Saturday to Sunday and Mondayto Friday.

hour category factor exact Indicator variable for {morning},{midday}, and {evening}.

hour discrete logistic Hour of the day rounded to fullhours.

congestion binary exact Indicator variable for congestionwhen time headway <2 seconds.

days, and evenings. Further, we identify commuter traffic by this indicator.

Congestion is also an exact match variable. In this regard we assume that a

binary indicator is sufficient to capture headway time related speed behavior.

To balance our samples we can now execute the exact matching. Based on

our variable specifications we first match a control (dry pavement) to each

treated unit (wet pavement) based on covariates defined for the exact match.

Further, we base our propensity score matching on a 1-nearest-neighbor al-

gorithm where the distance measure (propensity score) is calculated using a

logistic regression model. For the logistic regression we chose our dependent

variable to be pavement condition and our independent variable to be hour.

In a second step we discard observations – using the 1-nearest-neighbor algo-

rithm – that have the highest distance in propensity scores for the variable

hour until our sample is balanced. In the following we present the results of

the matching procedure. The matching procedure reduced our samples size

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Table 4: Sample Size Matching

WeekdaysIn Out

Dry Wet Dry WetAll 24895 23626 16979 18552Matched 13278 13278 11839 11839Unmatched 11617 8887 5140 6108Discarded 0 1461 0 605

WeekendsIn Out

Dry Wet Dry WetAll 7765 3394 5416 4848Matched 3394 3394 4776 4776Unmatched 4371 0 640 72Discarded 0 0 0 0

by a remarkable amount. However, even our smallest sample, Weekends In,

still contains 3’394 observations for both treatment and control group (see

Table 4). The matching procedure allowed to improve balance on all our

samples (for further details see Appendix A).

The balanced samples were then used to plot mean, median, and 95% con-

fidence interval for our dependent variable speed. Since we did not inspect

our samples for normality the confidence intervals were generated using boot-

strapped samples. As shown in Figure 6 our sample confirms that drivers’

slow down under wet pavement conditions. However, there was no signifi-

cant speed difference for weekday evening in and morning out for dry and

wet conditions (see Table 5)1.

1We accept this preliminary parametric testing result without distribution analysis,since we are not interested in the amplitude or position of difference and our samples arelarge.

27

Hence, we assume that there is a non identified covariate inducing this

discrepancy and exclude these observations from our samples.

Table 5: Weekday Morning and Evening Differences

Morning Out Evening In

dry wet dry wet

M ± SD 46.50 ± 6.55 46.33 ± 6.70 35.91 ± 5.33 35.86 ± 4.17t(df) -.0.59 (1204) -0.46 (4009)p-value 0.55 0.65

Figure 6: Balanced Sample Speed Plot

morning midday evening

36.0

36.5

37.0

37.5

38.0

38.5

dry wet dry wet dry wet

speed

Weekday In

morning midday evening

44

45

46

47

48

dry wet dry wet dry wet

pavement condition

speed

Weekday Out

So Sa

36.0

36.5

37.0

37.5

38.0

38.5

dry wet dry wet

Weekend In

So Sa

44

45

46

47

48

dry wet dry wet

pavement condition

Weekend Out

Note: mean(red), median(blue), confidence interval 95%.

28

4.4 Hypothesis Testing

Up to this point we were primarily concerned with data processing. In what

follows we will inspect our data for normality. First we plot distributions of

our speed variable along with the normal distribution adjusted for mean and

standard deviation of the concerning subset. Visual inspection of Figures 9

and 10 (Appendix A) indicate speed to be normally distributed with some

degree of skewness and kurtosis. Accordingly, the Jarque-Bera test rejects

normality (∀ S : p < 2.2 × 10−16). However, since we know that our

speed variable has a lower/upper limit we suspect short tails. Therefore the

jarque-bera test is potentially biased (Thadewald & Buning, 2007), so we also

inspect the quantile to quantile plots in Figure 7 and 8 to control for short

tails (Appendix A). All subsamples appear to be light tailed indicating lower

observation densities in the upper/lower quantiles. This is is reasonable since

speed measures concentrate around the posted speed limit. As we cannot

assume the samples to be normally distributed on both the jarque-bera test

and the quantile to quantile plots we use a non-parametric method to test the

uniform speed reduction hypothesis (1). We assume the wilcoxon signed-rank

test to be appropriate (Siegel, 1956).In the Table 6 we present the results for

29

each subsample. The median of the differences (pseudomedian) between an

observation from Dry and an observation from Wet ranges from -1.00 to -

2.50 km/h. The one sided 95% CI upper limit ranges from -0.50 to -2.00

km/h. Therefore, we reject our null hypothesis in favor of the alternative

hypothesis (α = 0.05). Based on our samples we conclude that drivers’

reduce their speed under wet compared to dry conditions.

Table 6: Summary and Results Wilcoxon Signed Rank Test with ContinuityCorrection

Weekday In Weekend In Weekday Out Weekend Out

Dry Wet Dry Wet Dry Wet Dry Wet

N 9268 9268 3394 3394 10634 10634 4776 4776

M 37.40 36.70 38.25 36.98 46.03 44.55 46.95 44.73

Mdn 37 36 38 37 46 44 46 44

SD 4.87 4.78 4.93 4.89 6.46 5.97 6.52 6.27

Range 12...62 14...69 18...63 10...68 14...84 14...94 10...109 11...79

Rank sums 16433000 2002500 19843000 3617900

Pseudomedian -1.00 -1.50 -1.50 -2.50

�

as percent

– of MdnDry -2.7 -3.9 -3.3 -5.4

CI (95%) -∞...-0.50 -∞...-1.00 -∞...-1.50 -∞...-2.00

p-value 2.2× 10−16 2.2× 10−16 2.2× 10−16 2.2× 10−16

Note: Observations from Weekday In Morning and Weekday Out Evening wereexcluded (see end of Section 4.3 and Figure 6).

30

In a next step we test our homogenous speed dispersion hypothesis (2) –

using the non-parametric fligner-killeen homogeneity of variances test. Based

on our weekend samples we have found that wet pavement has no effect on

speed dispersion. For weekdays wet pavement reduces dispersion for evenings

in both directions and mornings in. Dispersion increases for mornings out.

As shown in Table 7 the null (2) is partially rejected (α = 0.05).

Table 7: Fligner-Killeen Test of Homogeneity of Variances

Weekday In Weekend In

Morning Midday Evening

N 4361 4907 4010 3394

SD 4.67;4.45 5.03;5.03 5.33;4.17 4.93;4.89

χ2 8.45 0.05 105.30 0.51

p-value 3.65× 10−3 0.82 1.2×10−16 0.48

Weekday Out Weekend Out

Morning Midday Evening Mo.-Ev.

N 1205 4717 5917 4776

SD 6.55;7.00 6.23;6.25 6.62;5.72 6.52;6.27

χ2 6.57 0.31 36.67 1.00

p-value 0.01 0.58 4.95× 10−10 0.32

Note: SD (dry;wet); N (dry=wet); Results in italic letters were excluded fromanalysis regarding speed reduction (see end of Section 4.3 and Figure 6).

31

Finally we test the friction risk compensation hypothesis (3). A change

from dry to wet pavement has a predominant effect on surface friction and

vehicle deceleration. Under dry conditions the average deceleration of vehi-

cles equipped with ABS is -8.31m/s2 and -4.86 m/s2 under wet conditions

(Wu et al., 1998). By the formulae below we evaluate the braking distances

and required speed reduction.

braking distance =speed2

2× deceleration

required speed reduction =√

stopping distancedry(2× decelerationwet)− speeddry

Table 8: Braking Distances

Weekday In Weekend In Weekday Out Weekend Out

Mdndry 10.28 10.56 12.78 12.78

Pseudomedian -0.28 -0.42 -0.42 -0.69

braking distance dry 6.35 6.70 9.82 9.82

braking distance wet 10.28 10.58 15.72 15.02

required speed reduction -2.42 -2.48 -3.01 -3.01

Note: All measures converted to m/s and m/s2; The speed measure to evaluate the brakingdistance under wet conditions was calculated by subtracting the Pseudomedian from theMdn in the dry state.

As shown in Table 8, the median speed reductions from our results (Pseu-

domedian) are not sufficient if the drivers’ aims to break – ceteris paribus –

within the same distance as in the dry pavement conditions. Based on our

samples we reject our null in favor of the alternative hypothesis (3).

32

5 Conclusion and Discussion

In this study, we have found that a change from dry to wet pavement

conditions lead to a reduction of speed. Across all samples we have found

that speed was reduced by 2.7 to 5.4 percent. For each direction the speed

reduction was higher when average speed was higher. However, the results

are unclear regarding speed dispersion. The dispersion in both directions

for weekends and weekday-middays are homogenous. For weekdays a

change from dry to wet decreases speed dispersion for all subsamples except

weekday mornings in the out direction. Therefore, we cannot make a

general statement regarding speed dispersion. Further, we have found that

drivers’ speed reduction is insufficient to compensate for the risk of lower

pavement friction. In the following we will discuss our assumptions and

findings using Haddon’s matrix (1972) and Elvik’s causal chain model (2003).

5.1 Causal Chain Model and the Haddon Matrix

The haddon matrix helped us to identify variables for our analysis and the

causal chain model to discuss our findings. Beginning with the haddon

matrix, for pre-crash phase human factors we based our analysis assum-

ing drivers’ to differ in their behavior regarding travel purpose (commuting,

leisure and others). We argue that the travel purpose has an impact on the

state of mind of an individual. E.g., commuters might be less attentive be-

cause they are – busy thinking about the oncoming workday (mornings) or

33

tired of the passed workday (evening). We identified travel purpose by dis-

tinguishing between weekends – assuming mostly leisure traffic – and week-

days. Further, we separated mornings, middays, and evenings to identify

commuters in the mornings and evenings. For the crash phase vehicle fac-

tors we assumed that most vehicles are equipped with ABS. This allowed

us to calculate average braking distances under dry and wet conditions to

test our friction risk compensation hypothesis (3). For the pre-crash phase

environmental factors we define two pavement conditions (dry, wet). For

the crash phase environmental factors we consider the route section to be

safe since there is no curvature or crossing traffic. Finally, for the post-crash

phase environmental factors we assume a favorable rescue situation since the

next hospital (Stadtspital Waid) is within 4.5km driving distance. The had-

don matrix is only partially identified since we have no individual level data

about drivers’ or their vehicles’.

Although the haddon matrix is useful to identify variables that potentially

impact traffic, it is inapplicable if we want to explore the relation of cause and

effect between our variables and speed. Therefore, we will asses if our em-

pirical findings make sense from a theoretical point of view using the causal

chain model.

As shown in Table 9 the causal chain model can be used as a checklist for en-

gineering and behavioral effects. The predominant engineering effects regard-

ing wet pavement are friction and visibility. Visibility is impaired through

reflections on the road surface – depending on the characteristics of light

(e.g., sunlight direction, other vehicles’ headlights, and illuminance) and at-

mospheric factors (e.g., fog and rain). Friction is reduced due to lower friction

34

of the pavement surface. Since friction and visibility are reduced by wet pave-

ment, drivers’ should adjust their speed to compensate for the higher risk due

to increased braking distances and impaired visibility. In line with Unrau &

Andrey (2006); Billot et al. (2009) we confirm that drivers’ reduce speed un-

der wet pavement conditions. However, in agreement with Edwards’s (1999)

findings the speed reduction is insufficient for each of our samples regarding

braking distance. Two possible explanations are: 1) Drivers’ misjudge their

driving abilities and the level of risk regarding speed. 2) The total stopping

distance – the sum of the braking distance and the reaction distance – re-

mains unchanged since drivers are more alert under wet pavement conditions

and reduce the reaction distance to compensate the risk from reduced fric-

tion. Road user rationality is adversely affected since the driving situation is

more challenging and the individual utility maximization is prone to human

error. The vehicle is harder to control and the driver depends stronger on

assumptions of the driving situation, his abilities, and the safety equipage of

his vehicle, e.g., rubber composition of the tires, ABS, and other technical

safety measures. Finally, the traffic infrastructure is less forgiving to human

and/or technical failure and the outcome of a collision is likely to be more

severe. Engineering effects by their own do not necessarily induce a change in

driver behavior. To explore how wet pavement affects driver’s behavior a set

of factors need to be assessed. To begin with, drivers’ continuously evaluate

their environment and determine how the level of risk changes. Measures

have to be noticed by the driver to affect their behavior – as wet pavement

can be noticed audibly and visually and drivers’ are sensibilised by their

driving education to the hazards of wet pavement drivers’ are likely to notice

35

surface wetness. Further, drivers’ seem to have a learning curve regarding

risk factors – if an individual faces a risk factor for the first time he is likely

to overlook it. However, if a risk factor such as wet pavement is regularly

noticed the driver learns how to react based on antecedent behavioral adap-

tation. As rain is a frequent event – wet pavement represented 48 percent of

our observations – drivers’ regularly adjust their behavior to wet pavement

conditions. Closely connected to the noticeability the size of an engineering

effect is positively correlated to the change in behavior. Drivers’ adapt their

behavior stronger for great changes in the engineering effect. Two of our

results seem to be affected by the size differences. 1) We found that speed

did not differ for a change from dry to wet pavement for weekday evening

in and morning out observations and assumed that there is some uniden-

tified covariate. We presume that the covariate leading to this bias is the

driver’s domicile. Commuting drivers’ living nearby leave for work in the

morning and come home in the evening. This subpopulation of drivers’ is

overrepresented in our sample predominantly in mornings and evenings lead-

ing to misbalances in our samples. The road section where the study site

is located leads out of the quarter Affoltern (population 25’000). Drivers’

living in Affoltern and frequently using this road section are familiar with the

surroundings and therefore behave differently then other traffic participants.

The perceived complexity and predictability of the driving environment is

lower to those drivers’ living close to this road section and result in a smaller

sized engineering effect. However, the size difference of the engineering effect

is due to the drivers domicile and not the pavement condition. 2) Testing

the homogenous speed dispersion hypothesis (2) we found that dispersion

36

was only affected in weekday mornings and evenings. Therefore, there is no

generally valid answer how dispersion is impacted by wet pavement. This is

in line with previous findings since results are contradictory. While Unrau &

Andrey (2006) found an increase in dispersion, Padget et al. (2001); Liang

et al. (1998) stated dispersion to decrease. Nevertheless, weekday mornings

and evenings are the periods with the highest traffic density and drivers’

are most likely to be commuters. High traffic density and drivers being

commuters increase the complexity of the driving environment. High traffic

density is more demanding since drivers’ have to adjust their behavior to

nearby traffic participants such as oncoming traffic and overtaking vehicles.

Further, commuters are likely to think about their oncoming/passed work-

day making them less attentive. Middays and weekends are less prone to

these biases therefore the size of the engineering effect is smaller. Again, the

size difference of the engineering effect results from other measures than the

pavement condition. Our results are more clear regarding speed as a factor

affecting accident risk, severity, and the size of material damage. Drivers’

seem to acknowledge this relationship in the context of wet pavement. We

found that the relative speed adjustment is higher when the average speed is

higher. This indicates that drivers’ adjustment is overproportional – drivers’

overcompensate the risk of wet pavement and higher speeds. Finally, it seems

reasonable that drivers’ can increase their individual utility by reducing their

speed to compensate for the risk related to wet pavement.

37

Table 9: Causal Chain Model – Effects of Wet Pavement

Engineering effect of wet pavement

Generic risk factors Effect of measure on generic risk fac-tors.

1. Kinetic energy Not affected2. Friction Adversely affected; wet road surfaces

provide less friction.3. Visibility Adversely affected: Shorter visibility

and road surface glare depending onthe level of wetness and illuminance.

4. Compatibility Not affected5. Complexity Not affected6. Predictability Not affected7. Road user rationality Adversely affected: more challeng-

ing driving environment; subjectiveerrors are more likely.

8. Road user vulnerability Not affected9. Forgiveness Adversely affected: infrastructure is

less forgiving; outcomes of humanand technical failure are likely to bemore severe.

Behavioral effect of wet pavement

Factors eliciting behavioral adaptation Effect of measure on factors elicitingbehavioral adaptation.

1. How easily a measure is noticed Wet pavement is easily noticed.2. Antecedent behavioural adaptation

to basic risk factorsDrivers’ are regularly in wet pave-ment situations.

3. Size of the engineering effect ongeneric risk factors

Depends on the situation.

4. Whether or not a measure reducesinjury severity and accident risk

Both injury severity and accidentrisk are increased.

5. The likely size of the material dam-age incurred in an accident

Slight increase.

6. Whether or not additional utilitycan be gained

Utility can be increased by reducingspeed due to lower accident risk.

Note: Adapted from Elvik (2004)

38

5.2 Strengths and weaknesses

By using large samples and robust testing methods we provide rigorous re-

sults for the location Zurich, Switzerland. Further, we used a novel approach

to generate our weather data, which we assume to be both valid and reli-

able. Nevertheless, we based our results on strong assumptions regarding the

sample selection, subsetting, and variables of interest. Our analysis covers a

single study site only with daytime observations for the month of February

2016. Further we acknowledge one should proceed with great caution if con-

clusions about individual level behavior are based on non-individual data.

Nevertheless, by using a paired matching approach we reduce biases.

With respect to variable selection researchers analyzing the effect of adverse

weather use different proxies, measurement units and evaluation methods

when defining weather and speed (see Table 10). Regarding speed data we

assume stationary radar measurements to be superior to those generated

using a handheld radar camera. Accordingly, we expect the handheld mea-

surements to be biased due to the possibility of distance and angle variation.

We acknowledge the limitations of our study considering the myriad possibil-

ities choosing a weather proxy in terms of measurement location (on site or

nearby), evaluation method (sensory or by research personnel), and unit of

measure (precipitation or road surface). However, our approach is favorable

based on following points.

1) We assume on site measurement to be more reliable since the study site

weather conditions are not necessarily identical to those of nearby weather

stations. 2) We believe a driver’s behavior to be strongly influenced by his

39

visual perception.

The closest proxy to a driver’s visual perception is the evaluation of the

on site weather conditions by another individual. Research following this

approach has chosen to base their result on weather data noted on site by

research personnel. Nevertheless, the data generated in this manner is biased

by the personnels perception and is not replicable. We fill this gap by gener-

ating our raw weather data, on site, using surveillance images. The raw data

is then categorized by research personnel into dry, wet, and snow pavement

conditions. Finally, we argue that wet pavement condition is an appropriate

representation of weather because it is the main cause of accidents related to

adverse weather conditions.

Table 10: Research Design

Speed

Handheld radar Stationary radar

Edwards (1999); Padget et al. (2001) Unrau & Andrey (2006); Billot et al. (2009)

Liang et al. (1998)

Weather

On site Nearby weather station

sensory (technical) research personnel

Percipitation Liang et al. (1998) Edwards (1999) Unrau & Andrey (2006); Billot et al. (2009)

Road surface Padget et al. (2001)

40

5.3 Directions for Future Research

For future research, we advise to cover longer study periods at different loca-

tions and traffic speed limits. Second, in order to understand how different

weather factors are interrelated and how they impact traffic behavior we

encourage researchers to introduce further variables such as visibility, illu-

minance and precipitation. Finally, we recommend to collect data on the

individual level to gain a deeper understanding of traffic behavior.

41

Appendix A

Percent Balance Improvement Weekday In:

Mean Diff. eQQ Med eQQ Mean eQQ Max

distance 88.2061 89.5951 88.2069 77.6116

wdayMo 100.0000 0.0000 100.0000 100.0000

wdayTu 100.0000 0.0000 100.0000 100.0000

wdayWe 100.0000 0.0000 100.0000 100.0000

wdayTh 100.0000 0.0000 100.0000 100.0000

wdayFr 100.0000 0.0000 100.0000 100.0000

hour_categorymidday 100.0000 0.0000 100.0000 100.0000

hour_categoryevening 100.0000 0.0000 100.0000 100.0000

hour 85.5607 100.0000 85.5597 71.4286

congestion 100.0000 0.0000 100.0000 100.0000

wdayMo.1 100.0000 0.0000 100.0000 100.0000

wdayTu.1 100.0000 0.0000 100.0000 100.0000

wdayWe.1 100.0000 0.0000 100.0000 100.0000

wdayTh.1 100.0000 0.0000 100.0000 100.0000

wdayFr.1 100.0000 0.0000 100.0000 100.0000

hour_categorymorning 100.0000 0.0000 100.0000 100.0000

hour_categorymidday.1 100.0000 0.0000 100.0000 100.0000

hour_categoryevening.1 100.0000 0.0000 100.0000 100.0000

Percent Balance Improvement Weekday Out:

Mean Diff. eQQ Med eQQ Mean eQQ Max

distance 90.2669 94.2448 90.0286 66.0881

wdayMo 100.0000 0.0000 100.0000 100.0000

wdayTu 100.0000 0.0000 100.0000 100.0000

wdayWe 100.0000 0.0000 100.0000 100.0000

wdayTh 100.0000 0.0000 100.0000 100.0000

wdayFr 100.0000 0.0000 100.0000 100.0000

hour_categorymidday 100.0000 0.0000 100.0000 100.0000

hour_categoryevening 100.0000 0.0000 100.0000 100.0000

hour 74.9204 100.0000 74.9256 50.0000

congestion 100.0000 0.0000 100.0000 100.0000

wdayMo.1 100.0000 0.0000 100.0000 100.0000

wdayTu.1 100.0000 0.0000 100.0000 100.0000

42

wdayWe.1 100.0000 0.0000 100.0000 100.0000

wdayTh.1 100.0000 0.0000 100.0000 100.0000

wdayFr.1 100.0000 0.0000 100.0000 100.0000

hour_categorymorning 100.0000 0.0000 100.0000 100.0000

hour_categorymidday.1 100.0000 0.0000 100.0000 100.0000

hour_categoryevening.1 100.0000 0.0000 100.0000 100.0000

Percent Balance Improvement Weekend In:

Mean Diff. eQQ Med eQQ Mean eQQ Max

distance 97.1691 100 97.1771 58.1291

wdaySo 100.0000 0 100.0000 100.0000

wdaySa 100.0000 0 100.0000 100.0000

hour 97.0831 100 97.5512 50.0000

congestion 100.0000 0 100.0000 100.0000

wdaySo.1 100.0000 0 100.0000 100.0000

wdaySa.1 100.0000 0 100.0000 100.0000

Percent Balance Improvement Weekend Out:

Mean Diff. eQQ Med eQQ Mean eQQ Max

distance 42.3380 66.8016 40.8860 49.9502

wdaySo 100.0000 0.0000 100.0000 100.0000

wdaySa 100.0000 0.0000 100.0000 100.0000

hour 16.1502 0.0000 15.5461 0.0000

congestion 100.0000 0.0000 100.0000 100.0000

wdaySo.1 100.0000 0.0000 100.0000 100.0000

wdaySa.1 100.0000 0.0000 100.0000 100.0000

43

Figure 7: Quanatile-Quantile Plot Weekday Matched Sample

−4 −2 0 2 4

20

40

60

Weekday In Wet

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

−4 −2 0 2 4

10

20

30

40

50

60

Weekday In Dry

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

−4 −2 0 2 4

20

40

60

80

Weekday Out Wet

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

−4 −2 0 2 4

20

40

60

80

Weekday Out Dry

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

44

Figure 8: Quanatile-Quantile Plot Weekend Matched Sample

−2 0 2

10

30

50

70

Weekend In Wet

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

−2 0 2

20

30

40

50

60

Weekend In Dry

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

−4 −2 0 2 4

20

40

60

80

Weekend Out Dry

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

−4 −2 0 2 4

10

30

50

70

Weekend Out Wet

Theoretical Quantiles

Sa

mp

le Q

ua

ntile

s

45

Figure 9: Density Plot Weekday Matched Sample

Weekday In Dry

m.final_wday_in_momi$speed[m.final_wday_in_momi$category_n

Density

10 20 30 40 50 60

0.0

00.0

20.0

40.0

60.0

80.1

0

Weekday In Wet

m.final_wday_in_momi$speed[m.final_wday_in_momi$category_n

Density

20 30 40 50 60 70

0.0

00.0

20.0

40.0

60.0

80.1

0

Weekday Out Dry

Density

20 30 40 50 60 70 80

0.0

00.0

20.0

40.0

60.0

8

Weekday Out Wet

Density

20 40 60 80

0.0

00.0

20.0

40.0

60.0

8

46

Figure 10: Density Plot Weekend Matched Sample

Weekend In Dry

m.final_wend_in$speed[m.final_wend_in$category_numer

Density

20 30 40 50 60

0.0

00.0

20.0

40.0

60.0

8

Weekend In Wet

m.final_wend_in$speed[m.final_wend_in$category_numer

Density

10 20 30 40 50 60 70

0.0

00.0

20.0

40.0

60.0

80.1

0

Weekend Out Dry

Density

20 40 60 80 100

0.0

00.0

20.0

40.0

6

Weekend Out Wet

Density

10 20 30 40 50 60 70 80

0.0

00.0

20.0

40.0

60.0

8

47

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List of Tables

1 Haddon Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Speed Statistics – Entire Sample . . . . . . . . . . . . . . . . . 21

3 Variables of Interest . . . . . . . . . . . . . . . . . . . . . . . 26

4 Sample Size Matching . . . . . . . . . . . . . . . . . . . . . . 27

5 Weekday Morning and Evening Differences . . . . . . . . . . . 28

6 Summary and Results Wilcoxon Signed Rank Test with Con-

tinuity Correction . . . . . . . . . . . . . . . . . . . . . . . . . 30

7 Fligner-Killeen Test of Homogeneity of Variances . . . . . . . 31

8 Braking Distances . . . . . . . . . . . . . . . . . . . . . . . . . 32

9 Causal Chain Model – Effects of Wet Pavement . . . . . . . . 38

10 Research Design . . . . . . . . . . . . . . . . . . . . . . . . . . 40

List of Figures

1 Causal Chain Model . . . . . . . . . . . . . . . . . . . . . . . 10

2 Study Site Map . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Study Site Streetview . . . . . . . . . . . . . . . . . . . . . . . 21

4 Traffic Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

5 Speed Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Balanced Sample Speed Plot . . . . . . . . . . . . . . . . . . . 28

7 Quanatile-Quantile Plot Weekday Matched Sample . . . . . . 44

8 Quanatile-Quantile Plot Weekend Matched Sample . . . . . . 45

9 Density Plot Weekday Matched Sample . . . . . . . . . . . . . 46

54

10 Density Plot Weekend Matched Sample . . . . . . . . . . . . . 47

55

Statement of Authorship

I hereby declare that I have written this thesis without any help from others

and without the use of documents and aids other than those stated above.

I have mentioned all used sources and cited them correctly according to

established academic citation rules. I am aware that otherwise the Senat is

entitled to revoke the degree awarded on the basis of this thesis, according

to article 36 paragraph 1 letter o of the University Act from 5 September

1996.

Berne, September 13, 2016

Ozan Harman

56