Becker et al.

European Transport
European Transport Research Review (2022) 14:37
https://doi.org/10.1186/s12544-022-00561-2 Research Review

ORIGINAL PAPER Open Access

Weather impacts on various types

of road crashes: a quantitative analysis using
generalized additive models
Nico Becker1,2* , Henning W. Rust1,2 and Uwe Ulbrich1

Abstract
Adverse weather conditions can have different effects on different types of road crashes. We quantify the combined
effects of traffic volume and meteorological parameters on hourly probabilities of 78 different crash types using
generalized additive models. Using tensor product bases, we model non-linear relationships and combined effects of
different meteorological parameters. We evaluate the increase in relative risk of different crash types in case of precipi-
tation, sun glare and high wind speeds. The largest effect of snow is found in case of single-truck crashes, while rain
has a larger effect on single-car crashes. Sun glare increases the probability of multi-car crashes, in particular at higher
speed limits and in case of rear-end crashes. High wind speeds increase the probability of single-truck crashes and, for
all vehicle types, the risk of crashes with objects blown on the road. A comparison of the predictive power of models
with and without meteorological variables shows an improvement of scores of up to 24%, which makes the models
suitable for applications in real-time traffic management or impact-based warning systems. These could be used by
authorities to issue weather-dependent driving restrictions or situation-specific on-board warnings to improve road
safety.
Keywords: Road crashes, Crash type, Traffic volume, Weather, Precipitation, Sun glare, Wind speed, Generalized
Additive Model, Relative risk, Impact model

1 Introduction variable risk factors like adverse weather conditions,

In almost all regions of the world, the road transport sys- temporary restrictions or warnings can be imposed.
tem is a key infrastructure most people have to use on a To support the identification of measures that help to
daily basis, in spite of knowing about the pending danger improve road safety, quantitative knowledge of the rela-
of severe crashes. [1]. In Germany, for example, 300,143 tionships between weather and crash probabilities should
road crashes with injuries and 3,046 fatalities were be provided at a sufficiently high spatial and temporal
recorded in 2019 [2]. Various factors can influence the resolution.
probability of road crashes, including technical or envi- Of course, weather is not only a direct factor for
ronmental conditions as well as driver behavior. Under- the risk of crashes. It also influences traffic volume,
standing these influencing factors can help authorities which in turn is one of the main factors related to
to establish precursory measures like permanent speed road crashes; generally, an increasing traffic volume is
limits or improvements of road design. With respect to related to increasing crash rates [3]. Studies addressing
crashes at the level of individual road segments gen-
erally take traffic volume into account [4]. However, if
*Correspondence: nico.becker@fu-berlin.de
crashes are analyzed in aggregated form at a regional
1
Institute of Meteorology, Freie Universität Berlin, Carl‑Heinrich‑Becker‑Weg scale, traffic volume is less frequently considered. The
6‑10, 12165 Berlin, Germany
Full list of author information is available at the end of the article
larger the spatial aggregation of crash information, the

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Becker et al. European Transport Research Review (2022) 14:37 Page 2 of 18

more difficult it is to relate it to measured traffic data, it would be useful to apply a single methodological
since traffic volume measurements are only available at approach to multiple crash types.
limited number of locations. A common approach to In a previous study, a logistic regression model for
bypass this problem is to use variables like the hour of hourly probabilities of weather-related road crashes was
the day [5] or the day of the week [6] as a substitute for developed at the level of administrative districts in Ger-
actual traffic measurements. Furthermore, characteris- many, taking into account the combined effect of precipi-
tics of the permanent road environment, such as speed tation and temperature [5]. Using weather forecast data it
limit, curvature or slope, are important aspects affect- was shown that skillful predictions of crash probabilities
ing the risk of road crashes. While the effect of speed are possible. However, the model did not explicitly con-
limits as a measure for risk reduction has often been sider traffic volume, but instead assumed a simple diurnal
confirmed [7], the effect of other road characteristics cycle. Furthermore, only weather-related crashes were
such as slope and curvature have been analyzed less considered that were classified by the police as being
frequently [4]. caused by road condition (e.g., slippery road due to water,
A large number of studies addresses the effects of dif- snow or ice).
ferent meteorological factors on road safety [3]. A meta The aim of the present study is to extend this model by
analysis of 34 studies addressing the effect precipitation including observed hourly traffic volume, as well as the
finds an average increase in crash rates of 71% and 84% effect of precipitation, temperature, sun glare and wind
in case of rain and snowfall, respectively [8]. In terms of gusts. While previous studies have commonly used tra-
crash severity, however, there is a significant reduction ditional weather station data, we derive meteorological
under rainy conditions compared to fine weather [9]. predictor variables from gridded radar and reanalysis
The effect of precipitation on crash risk can be different products. To allow for more flexible functional relation-
for different types of crashes. For example, the relative ships and combined effects of multiple variables, the
risk for single- and multiple-vehicle crashes on Finnish classical logistic regression model is replaced by a Gen-
motorways in case of snow is 3.37 and 1.98, respectively, eralized Additive Model (GAM) for dichotomous target
compared to the probability within a random sample [10]. variables. Models are developed for 78 different crash
This effect is partly related to single-vehicle run-off-road types in a consistent approach, to compare the weather
crashes, which appear to occur more frequently under effects and predictive power of the models for different
rain, sleet or snow and in curved road sections [11]. speeds limits, crash types, road environments and crash
The effect of wind on road safety has not been exten- severities.
sively explored in the literature [3]. In general, the num-
ber of road vehicle crashes caused by strong wind is small 2 Data
compared to the total number of crashes [9]. However, 2.1 Crash data
wind gusts are shown to increase run-off-road crashes A data set with anonymized information from police
by small but significant amounts of 0.3 to 0.5% [6]. reports of road crashes in Germany from 2006 to 2017 is
Among different vehicle types, high-sided trucks, vans or used (Source: Research Data Centre of the Federal Statis-
buses are most affected by wind [12]. In general, greater tical Office and Statistical Offices of the Länder, Statistik
recorded wind speeds increase the severity of injuries in der Straßenverkehrsunfälle, 2006-2017, own calculations).
single-truck crashes [13]. The data set includes severe road crashes, which refers to
The effect of sun glare on crashes is only addressed all crashes with vehicles left unroadworthy, with injuries
in a few studies. Crash data from signalized crossroads or fatalities. Crashes related to alcohol consumption of
in Tucson, Arizona, show that broad-side and rear-end the driver are not included. In total 4,695,687 complete
crashes occur more frequently during glare, but no effect crash reports are available for the period under investiga-
of sun glare on crash severity is found [14]. Injury crashes tion. The location of the individual crashes is available at
in Japan indicate that sun glare has an particularly strong the level of administrative districts (Landkreise). Because
impact on pedestrian crashes, bicycle crashes and crashes of several territorial reforms during the study period, all
at crossroads, while there is no indication that the effect crashes are assigned to boundaries of the 401 German
of sun glare increases with vehicle speed [15]. administrative districts as they existed in 2017.
Although different studies focus on the effects of spe- Based on the crash reports, we distinguish between dif-
cific meteorological parameters on specific crash types, ferent crash characteristics: the type of vehicles involved,
these studies usually differ with respect to region, time the speed limit at the location of the crash, the crash
period, and methodology, which makes it difficult to type, the characteristics of the road environment, and
compare the results. For a consistent comparison, the crash severity (see Table 1 for a detailed description
of crash characteristics used in this study). It should be
Becker et al. European Transport Research Review (2022) 14:37 Page 3 of 18

Table 1 Description of crash characteristics used to create the dependent variables of the generalized additive models
Name Description
Vehicle type

any All single- and multi-vehicle crashes and all vehicle types are considered (including bicycles, motorbikes, buses and tractors).
multi-car Only crashes with two or more passenger cars are considered.
single-car Only crashes of single passenger cars are considered.
single-truck Only crashes of single trucks are considered.
Speed limit
[0, 50) Only crashes at speed limits below 50 km/h are considered
[50, 70) Only crashes at speed limits between 50 and 70 km/h are considered
70, 100) Only crashes at speed limits between 70 and 100 km/h are considered
100, 130) Only crashes at speed limits between 100 and 130 km/h are considered
[130, Inf) Only crashes at speed limits of 130 km/h and above are considered
Crash type
run-off-road A vehicle run off the road.
hit-object A vehicle collided with an obstacle on the road (e.g. trees, debris, wildlife).
broad-side Crash with cross traffic or vehicles that turn onto the road from a side road.
head-on Crash with oncoming traffic, without one of the crash partners intending to turn across the opposite lane.
side-swipe Crash with another vehicle travelling sideways in the same direction, when driving side by side or when changing lanes.
rear-end Crash with another vehicle driving ahead or waiting for traffic reasons.
parking Crash with vehicles stopping or parking at the edge of the carriageway, in the marked parking spaces immediately adjacent
to the edge of the carriageway, on footpaths or in parking spaces.
Road environment
curve Crash occurred on a curved road section.
descent Crash occurred on a descending road section.
ascent Crash occurred on an ascending road section.
t-junction Crash occurred at a t-junction.
crossroads Crash occurred at a crossroads.
Crash severity
no injuries No injuries or fatalities.
minor injuries At least one road user with minor injuries, but no serious injuries or fatalities.
serious injuries At least one road user with serious injuries, but no fatalities.
fatalities At least one road user died.

noted that the actual driving speed of vehicles may dif- 2.2 Traffic data
fer from the speed limit used to categorize the crashes. The German Federal Highway Research Institute (Bun-
The speed limit should therefore only be interpreted as desanstalt für Straßenwesen, BASt) operates a traffic
a rough indicator of the traffic conditions at the location measurement network on federal highways (Autobahn)
of the crash. In total 78 different crash types with spe- and federal roads (Bundesstraßen). Federal highways
cific characteristics are considered by always combining usually have two or three lanes per direction, partly
one of the four vehicle types with one of the other crash without speed limits, while federal roads usually have
characteristics (e. g. single-truck crashes at speed limits one lane per direction and general speed limits of up to
between 70 and 100 km/h, or multi-car crashes at cross- 100 km/h. At about 2,000 traffic counting stations the
roads). For each of the resulting 78 crash types an hourly hourly number of vehicles is registered. The data set
time series of a dichotomous variable is created for all provides separate counts for different vehicle types. In
administrative districts, being zero if no crash happened this study the total vehicle counts are used, as well as
within the hour considered and one otherwise. These the counts of passenger cars and trucks.
hourly time series are used as target variables (dependent Hourly count data of 1,400 traffic measurement sta-
variables) in generalized additive models. tions, which contain at least five years of data between
2006 and 2017, are used in this study. Missing data in
the traffic count time series are filled using Poisson
Becker et al. European Transport Research Review (2022) 14:37 Page 4 of 18

regression models for weather-related variations of noted that local station measurements can deviate from
hourly traffic counts developed in a previous study [16]. the gridded ERA5 values.
The hourly traffic counts of each station are rescaled so For each administrative district all ERA5 grid points
that 0 and 1 correspond to the average daily minimum within the district boundaries are identified and for each
and maximum hourly traffic count, respectively. This hourly time step the district average surface temperature,
makes the data at different traffic stations comparable total cloud cover and maximum hourly wind gust is com-
and suitable for an application as a predictor variable in puted and subsequently used as a predictor variable.
our modeling approach. Note, that values below 0 and
above 1 can occur at individual hours as the reference for
rescaling is an average minimun/maximun. 3 Methods
Because a single traffic measurement station might not 3.1 Generalized additive models
be representative for a whole administrative district, for The probability p for a certain event to occur can be
each district the five traffic stations closest to the district described with a logistic linear model
center are identified and for each hourly time step the
mean of the rescaled traffic volume of these five stations p
log = α + Xi β� (1)
is computed. This is done separately for federal road and 1−p
highway stations.
with l predictor variables (or independent variables)
Xi = (Xi1 , ...Xil ), where β� = (β1 , ..., βl ) are the corre-
2.3 Radar‑based precipitation data sponding model parameters, α is the intercept and n is
Precipitation values are derived from the RADOLAN the number of available observations. The logistic regres-
data set [17], provided by the German Meteorological sion model is a powerful tool for modeling the effects of
Service, which contains hourly precipitation sums on a predictor variables on event probabilities. However, if
spatial grid with a spatial resolution of 1 km for the area the functional relationship between predictor variables
of Germany. RADOLAN combines radar reflectivity, and probability is complex, or if non-linear interactions
measured by the 16 C-band Doppler radars of the Ger- between different continuous predictor variables have to
man weather radar network, and ground-based precipi- be taken into account, finding an appropriate transfor-
tation gauge measurements. As from radar reflectivity mation of the predictor variables can be cumbersome.
we cannot directly infer the precipitation amount at the In generalized additive models [19] the concept of gen-
ground, observations from rain gauges are used to cali- eralized linear models is extended by adding smooth
brate the precipitation amounts estimated from the radar functions of predictor variables to the linear term of the
reflectivity in an online-procedure. Thus, RADOLAN equation, so that
combines the benefits of high spatial resolution of the
radar network with the accuracy of gauge-based precipi-
 
p
log = α + Xi β� + f1 (x1i ) + f2 (x2i ) + f3 (x3i , x4i ) + ... ,
tation measurements. 1−p
For each administrative district, all RADOLAN grid (2)
points within the district boundaries are identified and where the fj are smooth functions of the predictor vari-
for each hourly time step the average precipitation of all ables xk . Specifying relationship between predictor and
identified grid points is computed. These hourly precipi- target variable (dependent variable) in terms of smooth
tation estimates at district level are subsequently used as functions makes generalized additive models more flex-
a predictor variable. ible than generalized linear models.
The predictor variables can contribute to the model as
2.4 Reanalysis data additive effects, like f1 (xx1 ) and f2 (xx2 ) in Eq. 2, for exam-
The fifth generation European Centre for Medium- ple. In this case, the effect of x1 on the target variable is
Range Weather Forecasts (ECMWF) global atmospheric independent from the value of x2. The smooth function f
reanalysis (ERA5) is a synthesis of various heterogene- can be written as
ous meteorological observational data and atmospheric J
model simulations, which is produced using a fixed ver-

f (x) = bj (x)βj , (3)
sion of the numerical weather forecasting model and data j=1
assimilation scheme [18]. ERA5 contains different atmos-
pheric and surface variables on a global grid with a spatial where bj (x) is the j th of some basis functions and βj are
resolution of 30 km at an hourly temporal resolution. The some unknown parameters, which must be estimated.
advantage of ERA5 over station-based observations is the The basis functions are usually based in some way on
spatial and temporal homogeneity. However, it should be splines. Commonly used smoothers in generalized
Becker et al. European Transport Research Review (2022) 14:37 Page 5 of 18

additive models are cubic regression splines which are is difficult for sparsely populated districts or rare crash
also used in the present study. types, because there are not enough crashes in the time
The assumption of additive effects is a quite restric- series to establish robust relationships between crash
tive case of the more general function of two variables probability and the different meteorological parameters.
f (x1 , x2 ) [19]. Eq. 3 can be generalized to allow smooth Instead, a single model including all districts is built for
functions of any number of predictor variables using ten- each of the 78 crash types. We distinguish between the
sor product bases. For a smooth function of two predic- districts by using the time averaged crash probability of
tor variables, for example, we can write each district p̄a,d as a predictor variable.
The rescaled hourly traffic volume Trf is based on
I 
L
 hourly counts of all vehicles, cars or trucks, according to
f (x1 , x2 ) = δil ai (x1 )cl (x2 ) (4)
the crash type considered in the model. When consider-
i=1 l=1
ing speed limits above 100 km/h, only traffic counts at
where δil are the parameters, and the ai (x1 ) and cl (x2 ) are highway stations are used, since on federal roads speed
the basis functions. limits larger than 100 km/h are rare.
The interaction term for temperature and precipita-
3.2 Model setup tion in Eq. 5 allows for a different effect of precipitation
For each of the 78 crash types introduced above two dif- on crash probability for different temperatures. This is
ferent models are developed: First, model Mmet important, since we cannot directly distinguish between
  rain and snow using the radar-based precipitation
pa
log =α + Yr + f1 (p̄a,d ) + f2 (Trf) + f2 (Wnd) estimates.
1 − pa Furthermore, cloud cover and sun elevation is included
+ f4 (Tmp, Prc) + f5 (Cld, Elv) as an interaction term to allow for different effects of
(5) cloud cover at different elevation angles. This is impor-
to describe the effects of meteorological and non-mete- tant to capture potential effects of sun glare.
orological variables on crash probability pa (see Tab 2 for For each of the the 78 crash types, we use a bootstrap
a description of the variables in the predictor). Second, approach and estimate the model parameters of Mmet
model Mnomet 100 times, each time drawing randomly 10,000,000 of
  the 42,153,120 available observations (with replacement).
pa
log = α + Yr + f1 (p̄a,d ) + f2 (Trf) , (6) This allows us to estimate confidence intervals for the
1 − pa analysis of the functional relationships and to estimate, if
values of relative risk increase can be regarded as statisti-
with only non-meteorological terms in the predictor as a
cally significant, as described below.
reference model.
There are different possible approaches to distinguish
3.3 Relative risk
between administrative districts. For example, a sepa-
The crash probability under adverse meteorological condi-
rate model could be built for each district. However, this
tions pa,adv can be compared to the crash probability under

Table 2 Independent variables used in generalized additive models

Variable Description

Yr Categorical variable with a category for each year from 2006 to 2017 to capture long term temporal changes in crash probability due to
external factors like improved safety features of vehicles.
pa Probability of at least one occurrence of a specific crash type within a one hour time interval in a certain district with an average crash prob-
ability p̄a,d.
p̄a,d Average hourly crash probability in an administrative district.
Trf Average hourly traffic volume of the five traffic measurement stations closest to the district centre. Traffic volume is rescaled, so that 0 and 1
correspond to the average daily minimum and maximum traffic volume at a traffic station, respectively.
Wnd Hourly maximum wind gusts, averaged over all ERA5 grid cells within disctrict boundaries.
Tmp Hourly surface temperatures, averaged over all ERA5 grid cells within disctrict boundaries.
Prc Hourly precipitation sum, averaged over all RADOLAN grid cells within disctrict boundaries.
Cld Hourly total cloud cover, averaged over all ERA5 grid cells within disctrict boundaries.
Elv Angle of sun elevation above the horizon, where positive and negative values correspond to the sun beeing located above and below the
horizon, respectively.
Becker et al. European Transport Research Review (2022) 14:37 Page 6 of 18

meteorological reference conditions pa,ref using the meas- meteorological predictor variables to the AUC of
ure of Relative Risk model Mnomet (Eq. 6) without meteorological predictor
pa,adv variables.
RR = (7) We compute the AUCSS in a two-fold cross valida-
pa,ref
tion approach. The available data is split randomly into
and Relative Risk Increase a training and a testing data set. The training data is used
for estimating the model parameters, while testing data
pa,adv is used for computing the AUCSS. This is repeated after
RRI = 1 − . (8)
pa,ref switching the testing and training data and the resulting
AUCSS values are averaged.
The RRI is computed for winter precipitation, summer
precipitation, sun glare and extreme wind speeds using
4 Results
Eq. 5 (see Table 3 for parameter settings).
4.1 Average crash probability
As described above, for each of the 78 crash types the
Prior to the analysis of the statistical models, the average
model Mmet is fitted 100 times in a bootstrap approach.
probability that at least one road crash occurs within one
For each of the 100 model versions RRI values are com-
hour in a German administrative district is computed
puted and the averages of these RRI values are presented in
for each of the 78 crash types considered (Fig. 1). If all
the results section. If more than 95 of the 100 models show
crashes are considered without distinguishing between
a positive or negative RRI, we conclude that the RRI is sig-
specific crash characteristics, the hourly probability is
nificantly positive or negative, respectively.
9.487%. Probabilities are lower if computed for more
specific vehicle types. For example, the probability for
3.4 Model performance
single-car or a single-truck crashes is 1.441% and 0.111%,
The area under the receiver operating characteristic curve
respectively. The lower crash probability for trucks can
(AUC) is a measure of the ability of a model to discrimi-
at least partly be attributed to a lower number of trucks
nate between events and non-events (see Additional file 1
on the roads and to a lower vulnerability of trucks due to
for details and additional metrics for testing the validity of
their structural characteristics.
the models). The AUC ranges between 0.5 and 1, which
Crashes are further classified in terms of the speed
compares to random guessing and perfect discrimination,
limit at the crash location, crash type, road environment
respectively.
and crash severity. For certain crash types probabilities
A skill score SS is a relative measure of how much a pre-
are relatively low, in particular in case of some sub-types
diction S outperforms a reference prediction Sr , defined as
of single-truck crashes (hit-object crashes, crashes at
SS = (S − Sr )(Sp − Sr )−1 , (9) crossroads and with fatalities), where the probability is
0.002. This should be kept in mind when interpreting the
where Sp is the score of a perfect prediction. In this RRI values for these crash types.
study we compute the AUC Skill Score (AUCSS),
which compares the AUC of model Mmet (Eq. 5) with

Table 3 Setup of meteorological parameters for calculation of relative risk increase for different meteorological conditions. pa,adv and
pa,ref is the crash probability under adverse and reference conditions, respectively. In all cases, Yr = 2017, Trf = 1 and p̄a,d is set to the
median value of all districts
Weather condition Probability Tmp Prc Cld Elv Wnd

Winter precipitation pa,adv −3◦C 1 mm/h 100% 30 ◦ 10 m/s

pa,ref +3◦C 0 mm/h 100% 30 ◦ 10 m/s
Summer precipitation pa,adv 15◦C 1 mm/h 100% 30 ◦ 10 m/s
pa,ref 15◦C 0 mm/h 100% 30◦ 10 m/s
Low sun, no clouds pa,adv 15◦C 0 mm/h 0% 20◦ 10 m/s
pa,ref 15◦C 0 mm/h 100% 20 ◦ 10 m/s
Extreme wind pa,adv 15◦C 0 mm/h 100% 30 ◦ 25 m/s
pa,ref 15◦C 0 mm/h 100% 30◦ 5 m/s
Becker et al. European Transport Research Review (2022) 14:37 Page 7 of 18

Fig. 1 Average hourly probabilities for 78 different crash types in German administrative districts
Becker et al. European Transport Research Review (2022) 14:37 Page 8 of 18

4.2 Functional relationships surface temperature (Fig. 2e). For example, if precipi-

Within the frame of this paper a detailed discussion of tation changes from 0 mm/h to 1 mm/h at -3◦ C, crash
models for all 78 crash types is infeasible. Instead, as an probability increases by 80.1%. The varying effect of pre-
example, we discuss the functional relationships between cipitation depending on temperature can be described by
the occurrence probability of multi-car rear-end crashes including the two variables as an interaction term in the
and the different predictor variables. For this discussion, generalized additive model. One could expect a sharper
we focus on one predictor term in Eq. 5 at a time. Mod- increase in crash probability around 0 ◦ C, however, the
eled crash probability is then plotted against this term, functional relationship shows a rather smooth transition
while keeping the predictor variables of the other terms between positive and negative temperatures. This can be
constant at selected values. attributed to different sources of uncertainty, which are
An increase in traffic volume leads to a non-linear but represented by the smoothing term. For example, the
monotonous increase in rear-end crash probability, if all actual road surface temperatures at specific locations
other parameters are held constant (Fig. 2a). This is a rea- within a district can differ from the aggregated surface
sonable behavior, which indicates that the spatially aggre- temperatures based on the gridded ERA5 data used in
gated traffic data can adequately represent the effects of the model.
traffic volume on crash probability at district level. Finally, the visualization of the combined effect of
To account for different basic properties in differ- cloud cover and sun elevation angle shows that there are
ent administrative districts, such as the total number of two areas with increased probabilities of rear-end crashes
vehicles per district, we have included the average hourly (Fig. 2f ). First, increased probabilities occur at positive
crash probability p̄a,d in the model. In districts with sun elevation angles combined with low cloud cover. This
larger p̄a,d the model shows that also the crash probabil- could be attributed to a distraction of drivers due to sun
ity pa under specific meteorological conditions is larger glare, leading to a larger number of rear-end crashes.
(see Fig. 2b). The relationship between p̄a,d and pa is Second, an increasing probability is also observed with
approximately piecewise linear with a change in slope at increasingly negative elevation angles, indicating that the
around p̄a,d = 0.1. Note that values of p̄a,d > 0.1 are only sun is below the horizon. This increase could be attrib-
reached in a few highly populated districts. uted to reduced visibility under low-light conditions
Rear-end crash probability shows a small variability in during night time. Note that probabilities are computed
time after controlling for traffic volume and meteorologi- assuming a constant traffic volume. At night times one
cal factors (Fig. 2c). A systematic trend in rear-end crash can expect traffic volume (and thus also crash probabil-
probability is not evident. However, it should be noted ity) to decrease, which counteracts the increase in prob-
that other crash types show a decreasing trend, which ability due to low light conditions.
could be attributed to advanced safety features of cars,
for example (not shown). 4.3 Increase in crash probability due to weather
An increase in wind speed leads only to a small conditions
increase in probability of rear-end crashes (Fig. 2d). If the 4.3.1 Winter precipitation
confidence intervals are taken into account, this increase For the 78 crash types, we compute the Relative Risk
is not significant. This is not surprising, since one would Increase (RRI) for hours with winter precipitation
not expect a large impact of wind speed on this crash with respect to hours without winter precipitation as
type, but the following section will reveal wind speed described in the methods section. Under the selected
impacts on other crash types. conditions (Table 3), precipitation is most likely snow-
There is a clear impact of summer precipitation fall or freezing rain. In general, single-vehicle crashes (i.e.
(Tmp = 15◦C) on rear-end crash probability (indicated single-car and single-truck crashes) show a larger RRI
by color and line type in Fig. 2a and b). If the district compared to multi-vehicle crashes (i.e. multi-car crashes
average hourly precipitation changes from 0 to 1 mm/h, and crashes including all vehicle types; Fig. 3). Single-
crash probability increases by a factor of 1.548, which truck crashes show the largest RRI of 872.9%.
corresponds to an RRI of 54.8%. A further increase in A higher (or even no) speed limit at the location of the
precipitation to 2 and 3 mm/h leads to smaller increases crash leads to a larger RRI under conditions with win-
in crash probability, but it is still significant with respect ter precipitation. In case of single-truck crashes the RRI
to the confidence intervals. increases to 1521.7% at speed limits of 130 km/h. How-
At negative temperatures the increase in rear-end ever, it should be noted that generally the maximum
crash probability is even stronger in case of increas- speed of trucks above 3.5 t is limited to 80 km/h.
ing precipitation, which is shown in a visualization of Run-off-road and head-on crashes also show a
the combined effect (interaction) of precipitation and relatively large RRI under conditions with winter
Becker et al. European Transport Research Review (2022) 14:37 Page 9 of 18

Fig. 2 Functional relationships between predictor variables and the hourly probability of muli-car rear-end crashes estimated by a generalied linear
model. 95% confidence intervals (shaded areas) are estimated from 100 models fitted with randomly drawn training data
Becker et al. European Transport Research Review (2022) 14:37 Page 10 of 18

Fig. 3 Relative risk increase (RRI) of crash probabilities in situations with precipitation and negative temperature ( Tmp = −3 ◦ C and Prc = 1mm/h)
compared to situations without precipitation and positive temperatures ( Tmp = +3 ◦ C and Prc = 0 mm/h). Significant changes (i. e. more than 95
of 100 models fitted with randomly drawn training data show the same direction of change) are indicated with an asterisk
Becker et al. European Transport Research Review (2022) 14:37 Page 11 of 18

precipitation, indicating that vehicles tend to leave their within the hour of the crash there was no rain, the road
lane due to slippery road conditions. The RRI for other surface is more likely to be dry under cloud-free condi-
crash types are smaller, but in most cases positive and tions (e.g. due to evaporation effects due to sunshine) and
significant. When comparing different road environ- more likely to be wet under cloudy conditions (e.g. due
ments, RRI values are largest in curves and descending to possible precipitation at previous time steps). A higher
road segments. Single-truck crashes also show a strong likelihood for a dry road (with higher surface friction)
increase on ascending roads segments. If the RRI under consequently leads to the observed reductions of single-
winter precipitation conditions is computed separately car crash probabilities, which is particularly large in case
for crashes with different severities, it is evident that less of curves (-35.3%).
severe crashes show larger RRI values compared to more
severe crashes. 4.3.4 Extreme wind speeds
To evaluate the effect of extreme wind speeds on crash
4.3.2 Summer precipitation probability, the RRI at hours with high wind speeds is
Analogously to winter precipitation, we investigate the computed with respect to hours with low wind speeds
effect of summer precipitation (most likely rainfall). The (Fig. 6). In general, the RRI values in case of extreme wind
RRI is computed for hours with summer precipitation speeds are relatively small, compared to the effects of the
with respect to hours without summer precipitation. In other meteorological parameters analyzed above, and
case of summer precipitation, crash probability increases mostly not significant, except for single-truck crashes.
for all crash types (Fig. 4). However, the increase is gen- Those show a significant RRI of 104.9%, which is in line
erally smaller than in case of winter precipitation. Simi- with other studies showing that trucks are particularly
lar to winter precipitation, summer precipitation leads vulnerable to high wind speeds [12]. RRI values of single-
to larger RRI values in case of single-vehicle crashes, at truck crashes are largest at high speed limits between
higher driving speeds, as well as in case of run-off-road 100 and 130 km/h. Since the maximum speed of trucks is
crashes and in curves, descents and ascents. Probabilities limited to 80 km/h, this effect could be explained by the
of less severe crashes increase more than those of severer assumption that highways with such high speed limits
crashes. While in case of winter precipitation RRI values often run through open rural terrain and are particularly
for single-truck crashes were generally larger than single- exposed to high wind speeds.
car crashes, in case of summer precipitation the opposite What stands out are the hit-object crashes, which
is true. The largest RRI of 536.2% is found in case of sin- increase in probability by 413.6% for single-car crashes
gle-car crashes at speed limits of 130 km/h and above. and by 789.8% for single-truck crashes. These crashes
can be attributed to crashes with broken tree branches,
4.3.3 Low sun elevation at cloud‑free conditions debris, or other objects, which are blown onto the road
To evaluate the effect of sun glare on crash probability, by strong winds.
we compute the RRI for hours with low sun elevation
angle and cloud-free conditions with respect to hours 4.4 Cross‑validation results
with low sun elevation angle and full cloud cover. The The predictive power of the model Mmet and whether
RRI of different crash types under low sun and cloud-free meteorological terms in the predictor improve the pre-
conditions range from -35% to +52% (Fig. 5). In case of dictions compared to a model without these (Mnomet )
multi-vehicle crashes, probabilities increase for most is analyzed in a two-fold cross-validation experiment
crash types. The largest RRI values of multi-car crashes using the AUC and AUCSS. The AUC values for the 78
crashes occur at speed limits of 130 km/h and more different crash types mainly range between 0.7 and 0.85.
(+52.5%) and in case of rear-end crashes (+43.2%). These Values between 0.7 and 0.8 correspond to an acceptable
increases could be attributable to sun glare, which could discrimitation, values above 0.8 correspond to an excel-
lead to reduced visibility and increased reaction times of lent discrimination [20].
drivers, which is particularly dangerous at high driving For all crash types (except for single-truck crashes
speeds and in dense traffic. with fatalities), the AUCSS values are positive, indicat-
In case of single-car and single-truck crashes, RRI ing an improvement of the models ability to discriminate
values are negative in most cases. However, in case of between time steps with and without crashes due to the
single-trucks these decreases are mostly not significant. meteorological predictor variables (Fig. 7). The AUCSS
These decreases of crash probability of single-vehicle ranges between relatively low values of 0.44% in case of
crashes under low sun and cloud-free conditions could single-car crashes with fatalities to high values of 24.21%
be due to the fact that we have not taken time lagged in case of single-car crashes at locations with high speed
effects of precipitation into the design of our models. If limits of 130 km/h and above. In general, AUCSS values
Becker et al. European Transport Research Review (2022) 14:37 Page 12 of 18

Fig. 4 Relative risk increase (RRI) of crash probabilities in situations with precipitation and positive temperature ( Tmp = 15 ◦ C and Prc = 1mm/h)
compared to situations without precipitation and positive temperatures ( Tmp = 15 ◦ C and Prc = 0 mm/h). Significant changes (i. e. more than 95
of 100 models fitted with randomly drawn training data show the same direction of change) are indicated with an asterisk
Becker et al. European Transport Research Review (2022) 14:37 Page 13 of 18

Fig. 5 Relative risk increase (RRI) of crash probabilities in situations with low sun elevation angle and cloud free conditions (Elv = 20◦ and
Cld = 0%) compared to situations with low sun elevation angle and clouded conditions (Elv = 20◦ and Cld = 100%). Significant changes (i. e. more
than 95 of 100 models fitted with randomly drawn training data show the same direction of change) are indicated with an asterisk
Becker et al. European Transport Research Review (2022) 14:37 Page 14 of 18

Fig. 6 Relative risk increase (RRI) of crash probabilities in situations with high wind speeds (Wnd = 25 m/s) compared to situations with low wind
speeds (Wnd = 5 m/s) . Significant changes (i. e. more than 95 of 100 models fitted with randomly drawn training data show the same direction of
change) are indicated with an asterisk
Becker et al. European Transport Research Review (2022) 14:37 Page 15 of 18

Fig. 7 Area Under Reviever Operating Characteristics Curve Skill Score (AUCSS), with positive values indicating an improvement of the predictive
power if meteorological predictor variables are included in models for hourly probabilities of different crash types. The Area Under Reviever
Operating Characteristics (AUC) of the models with meteorological predictor variables is given in brackets
Becker et al. European Transport Research Review (2022) 14:37 Page 16 of 18

are higher in case of those crash types, which also showed Also the analysis of the combined effects of cloud
a strong relationship to one or more of the meteorologi- cover and sun elevation revealed missing meteorologi-
cal variables. Highest AUCSS values occur in case of sin- cal factors in the model, which are related to time-lagged
gle-vehicle crashes, at higher speed limits, at locations effects of precipitation and evaporation processes. Future
with curves, descents or ascents and in case of crashes research could focus on including such effects, for exam-
without or with minor injuries. Lower AUCSS values ple by using information from physical road surface
occur in case of multi-car crashes at lower speed limits, energy balance models taking into account evaporation
in case of crashes with other vehicles (except head-on processes [21].
crashes), at crossroads and in case of crashes with severe We have shown that sun glare particularly increases
injuries and fatalities. probabilities of rear-end crashes, which is in line with
findings for Tucson, Arizona [14]. However, we have also
5 Discussion identified a stronger effect of sun glare on crash probabil-
In general, the results of our analysis are in line with ities at higher speed limits and in case of increasing crash
previous studies. For example, an increase in crash severity, which has not been found in previous studies
probabilities due to precipitation has been found quite [15].
consistently in the literature [3]. However, the compre- In previous research weather station data is frequently
hensive crash data set in combination with the chosen used to study the impact of weather on crashes, while
modeling approach allows more precise and quantitative we have used post-processed gridded meteorological
statements about the functional relationships between data sets. Using weather station data assumes that the
the meteorological parameters and probabilities of differ- point measurement is representative for the location of
ent crash types. the crash, which might be a certain distance away. Using
We have compared results for a large number of dif- gridded data, which is spatially aggregated, assumes that
ferent crash types, which comes at the expense of detail the spatially aggregated weather information is repre-
regarding evaluation of the individual models. An in sentative for a certain location within the aggregation
depth diagnostic of the fitting procedure of each general- area and that the variability within the area is sufficiently
ized additive model was not possible within the frame of small so that this assumption is valid. We think that using
this article. For example, we have found that cubic regres- gridded data is most appropriate for our study design.
sion splines generally lead to reasonable functional rela- One might consider to compare both approaches in
tionships in the generalizes additive models, but a more future analyses.
detailed analysis could reveal that for specific parameters While for Germany count data of motorized road traf-
or crash types other smoothing functions might be more fic is available for a large number of stations on federal
appropriate. Furthermore, we have assumed that the roads and highways, there is no comprehensive data set
standard setting for the number of basis dimensions of for smaller roads. Here, we assumed that federal road
the splines is appropriate. stations are representative for smaller roads as well. The
The radar data used in this study provides highly validity of this assumption could be tested in districts,
resolved precipitation estimates. However, it does not where additional traffic data is available. Furthermore,
distinguish between rain and snowfall. Instead we ana- there is little measurement data of bicycle and pedestri-
lyzed the combined effect of precipitation and surface ans volume. The numbers of such non-motorized road
temperature. In future research, novel data products users themselves depend on the weather conditions.
could be used, which combine radar-data and atmos- This is problematic when analyzing crashes involving
pheric models, to provide additional information about such road users without an estimate of their actual share
the precipitation type. in the total traffic volume. For example, an increase in
Furthermore, it should be noted that only the weather crash probabilities during hours with sun glare could be
conditions within a specific hourly time interval are con- due to the effects of reduced visibility, but also due to an
sidered for predicting the hourly crash probability; pos- increased number of bicycles or pedestrians during fair
sible time-lagged effects are neglected. For example, if weather conditions. This should be kept in mind, when
precipitation occurred before the hour of a crash, but interpreting the corresponding numbers.
the road surface could still wet. Also the accumulation
of snow cover on roads over several hours is not consid- 6 Conclusions
ered. Both effects could lead to an underestimation of While previous studies on weather effects on road
crash probabilities during hours without precipitation. crash have often focused on specific weather conditions
A potential effect of winter road maintenance is also not or certain crash types, we have applied a modeling
included, because appropriate data is missing. approach that is able to capture the combined effects
Becker et al. European Transport Research Review (2022) 14:37 Page 17 of 18

of meteorological parameters on a large number of dif- available at the Climate Data Store [27]. The R [28] package “mgcv” [19] was
used for the development of the generalized additive models.
ferent crash types. By using additive logistic regression
models, we could capture and analyze non-linear func-
tional relationships between meteorological parameters Declarations
and crash probability, which would have been difficult Ethics approval and consent to participate
using other methods like traditional logistic regression. Not applicable
We have shown that including meteorological vari- Consent for publication
ables can substantially improve predictions of crash Not applicable
probabilities. This is particularly true for single-vehicle
Competing interests
crashes on road sections with high speed limits, where The authors declare that they have no competing interests.
the largest improvement of verification scores was
observed. Our findings can help authorities to identify Author details
1
Institute of Meteorology, Freie Universität Berlin, Carl‑Heinrich‑Becker‑Weg
crash types and road characteristics, where weather- 6‑10, 12165 Berlin, Germany. 2 Hans-Ertel-Centre for Weather Research, Berlin,
dependent driving restrictions like variable speed lim- Germany.
its or situation-specific warnings could be beneficial for
Received: 11 January 2022 Accepted: 21 July 2022
road safety. Such warnings could be communicated via
on-board computers and navigation systems depend-
ing on vehicle type, speed limit and characteristics of
the road characteristics. This would be an important
References
step towards moving from traditional weather forecasts 1. Peden, M., & Sminkey, L. (2004). World health organization dedicates
towards impact-based warnings, which is heavily pro- world health day to road safety. Injury Prevention, 10(2), 67–67. https://​doi.​
moted by the World Meteorological Organization and org/​10.​1136/​ip.​2004.​005405.
2. BASt: Verkehrs- und unfalldaten - kurzzusammenstellung der entwick-
national weather services [22, 23]. lung in deutschland. Technical report, Bundesanstalt für Straßenwesen,
Bergisch Gladbach, Germany (2020). https://​www.​bast.​de/​DE/​Publi​katio​
nen/​Medien/​VU-​Daten/​VU-​Daten.​pdf. Accessed 7 Jan 2022.
Abbreviations 3. Theofilatos, A., & Yannis, G. (2014). A review of the effect of traffic and
AUC​: Area under receiver operating characteristic curve; AUCSS: Area under weather characteristics on road safety. Accident Analysis and Prevention,
receiver operating characteristic curve skill score; ERA5: European centre 72, 244–256. https://​doi.​org/​10.​1016/j.​aap.​2014.​06.​017.
for medium-range weather forecasts reanalysis v5; RADOLAN: Radar-based 4. Ziakopoulos, A., & Yannis, G. (2020). A review of spatial approaches in road
precipitation data (RAdar-ONLine-ANeichung, radar online adjustment); RR: safety. Accident Analysis and Prevention, 135, 105323. https://​doi.​org/​10.​
Relative risk; RRI: Relative risk increase. 1016/j.​aap.​2019.​105323.
5. Becker, N., Rust, H. W., & Ulbrich, U. (2020). Predictive modeling of hourly
probabilities for weather-related road accidents. Natural Hazards and
Supplementary Information Earth System Sciences, 20(10), 2857–2871. https://​doi.​org/​10.​5194/​
The online version contains supplementary material available at https://​doi.​ nhess-​20-​2857-​2020.
org/​10.​1186/​s12544-​022-​00561-2. 6. El-Basyouny, K., Barua, S., & Islam, M. T. (2014). Investigation of time and
weather effects on crash types using full Bayesian multivariate Poisson
Additional file 1. Additional model verification results. lognormal models. Accident Analysis and Prevention, 73, 91–99. https://​doi.​
org/​10.​1016/j.​aap.​2014.​08.​014.
7. Wang, J., & Huang, H. (2016). Road network safety evaluation using Bayes-
Acknowledgements ian hierarchical joint model. Accident Analysis and Prevention, 90, 152–158.
This research was carried out within the framework of the Hans-Ertel-Centre https://​doi.​org/​10.​1016/j.​aap.​2016.​02.​018.
for Weather Research. This research network of universities, research institutes 8. Qiu, L., & Nixon, W. A. (2008). Effects of adverse weather on traffic crashes:
and the Deutscher Wetterdienst is funded by the Bundesministerium für Systematic review and meta-analysis. Transportation Research Record,
Verkehr und Digitale Infrastruktur. 2055(1), 139–146. https://​doi.​org/​10.​3141/​2055-​16.
We would like to thank the HPC service of ZEDAT at Freie Universität Berlin for 9. Edwards, J. B. (1998). The relationship between road accident severity and
the computing resources and assistance provided. recorded weather. Journal of Safety Research, 29(4), 249–262. https://​doi.​
org/​10.​1016/​S0022-​4375(98)​00051-6.
Author contributions 10. Malin, F., Norros, I., & Innamaa, S. (2019). Accident risk of road and weather
Data analysis and visualization was carried out by NB; all authors contributed conditions on different road types. Accident Analysis and Prevention, 122,
to writing the manuscript. All authors read and approved the final manuscript. 181–188. https://​doi.​org/​10.​1016/j.​aap.​2018.​10.​014.
11. Liu, C., & Subramanian, R.(2009). Factors related to fatal single-vehicle run-
Funding off-road crashes. Technical report, NHTSA’s National Center for Statistics
Open Access funding enabled and organized by Projekt DEAL. This research and Analysis, Washington, DC. https://​crash​stats.​nhtsa.​dot.​gov/​Api/​
has been supported by the Bundesministerium für Verkehr und Digitale Public/​ViewP​ublic​ation/​811232. Accessed 7 Jan 2022.
Infrastruktur (grant no. 4818DWDP3A). 12. Baker, C., & Reynolds, S. (1992). Wind-induced accidents of road vehicles.
Accident Analysis and Prevention, 24(6), 559–575. https://​doi.​org/​10.​1016/​
Availability of data and materials 0001-​4575(92)​90009-8.
The crash data for Germany was obtained from the Research Data Centre 13. Naik, B., Tung, L.-W., Zhao, S., & Khattak, A. J. (2016). Weather impacts on
of the Federal Statistical Office and Statistical Offices of the Länder [24]. The single-vehicle truck crash injury severity. Journal of Safety Research, 58,
hourly traffic count data for highways and federal roads in Germany is avail- 57–65. https://​doi.​org/​10.​1016/j.​jsr.​2016.​06.​005.
able via the Bundesanstalt für Straßenwesen [25]. The RADOLAN data set is
available via the German Weather Service [26]. The ERA5 reanalysis data is
Becker et al. European Transport Research Review (2022) 14:37 Page 18 of 18

14. Mitra, S. (2014). Sun glare and road safety: An empirical investigation of
intersection crashes. Safety Science, 70, 246–254. https://​doi.​org/​10.​1016/j.​
ssci.​2014.​06.​005.
15. Hagita, K., & Mori, K. (2014). The effect of sun glare on traffic accidents in
Chiba prefecture, Japan. Asian Transport Studies, 3(2), 205–219. https://​doi.​
org/​10.​11175/​easts​ats.3.​205.
16. Becker, N., Rust, H. W., & Ulbrich, U. (2022). Modeling hourly weather-
related road traffic variations for different vehicle types in Germany.
European Transport Research Review,14(16), https://​doi.​org/​10.​1186/​
s12544-​022-​00539-0.
17. Bartels, H., Weigl, E., Reich, T., Lang, P., Wagner, A., Kohler, O., & Gerlach, N.,
et al.:(2004) Projekt RADOLAN–Routineverfahren zur Online-Aneichung
der Radarniederschlagsdaten mit Hilfe von automatischen Bodennied-
erschlagsstationen (Ombrometer). Deutscher Wetterdienst, Germany.
https://​www.​dwd.​de/​DE/​leist​ungen/​radol​an/​radol​an_​info/​absch​lussb​
ericht_​pdf. Accessed 7 Jan 2022.
18. Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater,
J., et al. (2020). The era5 global reanalysis. Quarterly Journal of the Royal
Meteorological Society, 146(730), 1999–2049. https://​doi.​org/​10.​1002/​qj.​
3803.
19. Wood, S. N. (2017). Generalized additive models: an introduction with R.
Chapman and Hall/CRC.
20. Hosmer, D. W., Jr., Lemeshow, S., & Sturdivant, R. X. (2013). Applied logistic
regression (Vol. 398). John Wiley & Sons.
21. Jacobs, W., & Raatz, W. E. (1996). Forecasting road-surface temperatures
for different site characteristics. Meteorological Applications, 3(3), 243–256.
https://​doi.​org/​10.​1002/​met.​50600​30306.
22. WMO: WMO guidelines on multi-hazard impact-based forecast and
warning services - Part II: Putting Multi-hazard IBFWS into Practice. World
Meteorological Organization, Geneva, Switzerland (2021). https://​libra​r y.​
wmo.​int/​doc_​num.​php?​expln​um_​id=​10936. Accessed 7 Jan 2022.
23. RCC, IFRC, MetOffice, UKAid: The future of forecasts: impact-based
forecasting for early action. Climate Centre, International Federation
for Red Cross and Red Crescent Societies, UK Met Office, UK Aid (2020).
https://​www.​forec​ast-​based-​finan​cing.​org/​wp-​conte​nt/​uploa​ds/​2020/​
09/​Impact-​based-​forec​asting-​guide-​2020.​pdf. Accessed 7 Jan 2022.
24. Forschungsdatenzentren der Statistischen Ämter des Bundes und der
Länder: Statistik der Straßenverkehrsunfälle. https://​www.​forsc​hungs​
daten​zentr​um.​de/​de/​sonst​ige-​wirts​chaft​sstat​istik​en/​stras​senve​rkehr​
sunfa​elle. Accessed 7 Jan 2022.
25. Bundesanstalt für Straßenwesen: Automatische Zählstellen auf Autobah-
nen und Bundesstraßen. https://​www.​bast.​de/​BASt_​2017/​DE/​Verke​hrste​
chnik/​Facht​hemen/​v2-​verke​hrsza​ehlung/​Stund​enwer​te.​html. Accessed 7
Jan 2022.
26. Deutscher Wetterdienst: RADOLAN (Radar-Online-Aneichung): Analysen
der Niederschlagshöhen aus radar- und stationsbasierten Messungen im
Echtzeitbetrieb. https://​www.​dwd.​de/​DE/​leist​ungen/​radol​an/​radol​an.​
html. Accessed 7 Jan 2022.
27. Copernicus: Climate Data Store. https://​cds.​clima​te.​coper​nicus.​eu/.
Accessed 7 Jan 2022.
28. R Core Team: R: A Language and Environment for Statistical Computing.
R Foundation for Statistical Computing, Vienna, Austria (2022). R Founda-
tion for Statistical Computing. https://​www.R-​proje​ct.​org. Accessed 17
May 2022.

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