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Annually within the European Union, there are over 50,000 road accident fatalities and 2 million other casualties, of which the majority are either the occupants of cars or other road users in collision with a car. The European Commission now has competency for vehicle-based injury countermeasures through the Whole Vehicle Type Approval system. As a result, the Commission has recognised that casualty reduction strategies must be based on a full understanding of the real-world need under European conditions and that the effectiveness of vehicle countermeasures must be properly evaluated. The PENDANT study commenced in January 2003 in order to explore the possibility of developing a co-ordinated set of targeted, in-depth crash data resources to support European Union vehicle and road safety policy. Three main work activity areas (Work Packages) commenced to provide these resources. This paper describes some of the outcomes of Work Package 2 (WP2, In-depth Crash Investigations and Data Analysis). In WP2, some 1,100 investigations of crashes involving injured car occupants were conducted in eight EU countries to a common protocol based on that developed in the STAIRS programme. This paper describes the purposes, methodology and results of WP2. It is expected that the results will be used as a co-ordinated system to inform European vehicle safety policy in a systematic, integrated manner. Furthermore, the results of the data analyses will be exploited further to provide new directions to develop injury countermeasures and regulations.
The paper aims to study the injury risk and kinematics of pedestrians involved in different passenger vehicle collisions. Furthermore, the difference of pedestrian kinematics in the accidents involved minivan and sedan was analyzed. The 18 sample cases of passenger car to pedestrian collisions were selected from the database of In-depth Investigation of Vehicle Accident in Changsha of China (IVAC),of which the 12 pedestrian accidents involved in a minivan impact for each case, and the 6 accidents in a sedan impact for each. The selected cases were reconstructed by using mathematical models of pedestrians and accident vehicles in a multi-body dynamic code MADYMO environment. The logistic regression models of the risks for pedestrian AIS 3+ injuries and fatalities were developed in terms of vehicle impact speed by analyzing the minivan-pedestrian and sedan-pedestrian accidents. The difference of pedestrian kinematics was identified by comparing the results from reconstructed pedestrian accidents between the minivans and sedans collisions. The result shows that there is a significant correlation among the impact speed and the severity of pedestrian injuries. The minivan poses greater risk to pedestrian than sedan at the same impact speed. The kinematics of pedestrian was greatly influenced by vehicle front shape.
The declining trend since 1991 in the number of killed people was broken in 2011 when overall 4 009 people died in traffic accidents in Germany. The question arises if there is a stagnating trend of fatalities in Germany in future? By breaking down the accidents with casualties towards a monthly view one can see a decreasing trend of fatalities in the warmer months especially since 2009. When comparing against winter months higher deviations are observed. In December 2011 an increase of 191 traffic deaths were registered (181 in 2010 compared to 372 in 2011). Further analyses of different accident influences were evaluated and their possibility of drastic change from one year to the other was determined. As seen weather- and environmental conditions are one of the major contributing factors and are one of the causes for the increased number of fatalities. To support the underlying assumption a model had been created to calculate the number of traffic deaths on a daily basis approach. As an input, road conditions projected through weather parameters and also different driving behaviors on weekdays or holidays were used. As a result, estimates of daily fatality with up to 75% precision can be achieved out of the 2009, 2010 and 2011 data. Further on it shows that weather and street conditions have a high influence on the overall resulting number of traffic accidents with casualties, and especially to the number of fatalities. Hence it is estimated that approximately 3 300 people were killed in traffic accidents in Germany in 2013 which would be again a reduction of another 13% compared to 2012. Therefore an answer to the question will be that the decreasing trend in traffic fatalities in Germany somehow is not broken when environmental conditions are included in national statistics. Their effects will become more visible in future accident statistics and it is estimated variances of 5% to 8% of the annual number of traffic fatalities in Germany will be seen.
The paper presents a methodology for the benefit estimation of several secondary safety systems for pedestrians, using the exceptional data depth of GIDAS. A total of 667 frontal pedestrian accidents up to 40kph and more than 500 AIS2+ injuries have been considered. In addition to the severity, affected body region, exact impact point on the vehicle, and the causing part of every injury, the related Euro NCAP test zone was determined. One results of the study is a detailed impact distribution for AIS2+ injuries across the vehicle front. It can be stated, how often a test zone or vehicle part is hit by pedestrians in frontal accidents and which role the ground impact plays. Basing on that, different secondary safety measures can be evaluated by an injury shift method concerning their real world effectiveness. As an example, measures concerning the Euro NCAP pedestrian rating tests have been evaluated. It was analysed which Euro NCAP test zones are the most effective ones. In addition, real test results have been evaluated. Using the presented methodology, other secondary safety like the active bonnet (pop-up bonnet) or a pedestrian airbag measures can be evaluated.
Analysis of the accident scenario of powered two-wheelers on the basis of real-world accidents
(2013)
For the first time since 20 years the German national statistics of traffic accidents revealed an increasing number of fatalities and seriously injured persons in 2011. This negative development was especially caused by increasing numbers in all groups of vulnerable road users (VRU). Furthermore, the comparison of fatality reduction rates between several categories of road users shows that persons on motorcycles show the worst performance over years. Although every second fatality in German traffic accidents is still a car occupant, users of PTW make up more than 20% in the meantime. Assuming further improvements in the field of occupant protection this trend will continue. For that reason, a study on the basis of real-world accidents was conducted to describe the accident scenario involving motorcycles and to identify the reasons of the above-described fact. Approximately 1.800 motorcycle accidents out of GIDAS database were used for the analyses. The first part of the study deals with the question how representative the GIDAS database is for the German motorcycle accident scenario. Afterwards, detailed descriptive statistics on motorcycle accidents were presented considering numerous parameters about the accident scene, environmental influences, vehicle information, individual characteristics, interview data, injury severity and injury causation. One important point is the identification of the most frequent critical situations that are typical for motorcycle accidents. Furthermore, a special focus was on accident causation. Finally, conspicuous facts out of the analysis are emphasized. All in all, the study gives a comprehensive overview about the German motorcycle accident scenario. One the one hand, the use of weighted GIDAS data allows representative and robust statements on the basis of large case numbers; on the other hand highly detailed conclusions can be drawn. The results of the study help to understand the particularities of motorcycle accidents and provide approaches for further improvements in the field of PTW safety.
The grip between the road surface and vehicle tires is the physical basis for the moving of all vehicles in road traffic. In case of an accident the available grip level is one of the most relevant influence factors, influencing the causation and the procedure of the accident. However, the estimation of the grip level is not easy and therefore, is commonly not done on the accident scene. This is especially true for the measurement of the water depth. Until now, real accident databases provide no measurement data about the grip level and the water film depth and thus, the estimation of its influence is not possible yet. From the tyre manufacturers point of view, it is important to know about the road conditions (namely grip level, macro-texture, water depth, temperature) at the accident scene, as well as the operating conditions of the vehicles (braking, loss of control, speed, etc). These data is necessary to define relevant tyre traction tests for the end-user and for regulations. For this reason VUFO and Michelin developed a consistent method for the measurements of grip level and water depth for the accidents of the GIDAS database. The accident research team of Dresden, which documents about 1000 accidents with at least one injured person every year, is measuring the micro-roughness and the macro-roughness directly on the spot. For the measurement of the micro-roughness a Skid Resistance Tester (British Pendulum) is used. The Mean Texture Depth (describing the macro-roughness) is measured by the Sand Depth Method. Since June 2009, measurements for more than 700 accidents including 1200 participants have been carried out. In case of wet or damp road conditions during the accident, the water depth is measured additionally. Therefore VUFO and Michelin developed a special measurement device, which allows measurements with an accuracy of 1/10 millimetre. The measurement point at the accident scene is clearly defined and thus, the results are comparable for all different accidents and participants. The use of the GIDAS database and the accident sampling plan allows representative statements for the German accident scenario. With this data it is possible for the first time to have an accurate view of the road conditions at the accident scene. One possibility is a more detailed estimation of hydroplaning accidents using the actually measured water depths. The development of new testing methods and new tires can be based on the real situation of the road infrastructure. Furthermore, the combination of the technical GIDAS data and the measured road surface properties can also be used for the estimation of effectiveness of several safety systems like the brake assist and/or emergency braking systems. The calculation of a reduced collision speed due to the use of a brake assist is only one example for the application of real measured grip level data.
The evaluation of the expected benefit of active safety systems or even ideas of future systems is challenging because this has to be done prospectively. Beside acceptance, the predicted real-world benefit of active safety systems is one of the most important and interesting measures. Therefore, appropriate methods should be used that meet the requirements concerning representativeness, robustness and accuracy. The paper presents the development of a methodology for the assessment of current and future vehicle safety systems. The variety of systems requires several tools and methods and thus, a common tool box was created. This toolbox consists of different levels, regarding different aspects like data sources, scenarios, representativeness, measures like pre-crash-simulations, automated crash computation, single-case-analyses or driving simulator studies. Finally, the benefit of the system(s) is calculated, e.g. by using injury risk functions; giving the number of avoided/mitigated accidents, the reduction of injured or killed persons or the decrease of economic costs.
Injury probability functions for pedestrians and bicyclists based on real-world accident data
(2017)
The paper is focusing on the modelling of injury severity probabilities, often called as Injury Risk Functions (IRF). These are mathematical functions describing the probability for a defined population and for possible explanatory factors (variables) to sustain a certain injury severity. Injury risk functions are becoming more and more important as basis for the assessment of automotive safety systems. They contribute to the understanding of injury mechanisms, (prospective) evaluation of safety systems and definition of protection criteria or are used within regulation and/or consumer ratings. In all cases, knowledge about the correlation between mechanical behavior and injury severity is needed. IRFs are often based on biomechanical data. This paper is focusing on the derivation of injury probability models from real world accident data of the GIDAS database (German In-depth Accident Study). In contrast to most academic terms there is no explicit term definition or definition of creation processes existing for injury probability models based on empirical data. Different approaches are existing for such kind of models in the field of accident research. There is a need for harmonization in terms of the used methods and data as well as the handling with the existing challenges. These are preparation of the dataset, model assumptions, censored/unknown data, evaluation of model accuracy, definition of dependent and independent variable, and others. In the presented study, several empirical, statistical and phenomenological approaches were analyzed regarding their advantages and disadvantages and also their applicability. Furthermore, the identification of appropriate prediction parameters for the injury severity of pedestrians has been considered. Due to its main effect on injuries of pedestrians and bicyclists, the importance of the secondary impact has also been analyzed. Finally, the model accuracy, evaluated by several criteria, is the rating factor that gives the quality and reliability for application of the resulting models. After the investigation and evaluation of statistical approaches one method was chosen and appropriate prediction variables were examined. Finally, all findings were summarized and injury risk functions for pedestrians in real world accidents were created. Additionally, the paper gives instructions for the interpretation and usage of such functions. The presented results include IRFs for several injury severity levels and age groups. The presented models are based on a high amount of real world accidents and describe very well the injury severity probability of pedestrians and bicyclists in frontal collisions with current vehicles. The functions can serve as basis for the evaluation of effectiveness of systems like Pedestrian-AEB or Bicycle-AEB.
Accident data shows that the vast majority of pedestrian accidents involve a passenger car. A refined method for estimating the potential effectiveness of a technology designed to support the car driver in mitigating or avoiding pedestrian accidents is presented. The basis of the benefit prediction method consists of accident scenario information for pedestrian-passenger car accidents from GIDAS, including vehicle and pedestrian velocities. These real world pedestrian accidents were first reconstructed and the system effectiveness was determined by comparing injury outcome with and without the functionality enabled for each accident. The predictions from Volvo Cars" general Benefit Estimation Model are refined by including the actual system algorithm and sensing models for a relevant car in the simulation environment. The feasibility of the method is proven by a case study on a authentic technology; the Auto Brake functionality in Collision Warning with Full Auto Brake and Pedestrian Detection (CWAB-PD). Assuming the system is adopted by all vehicles, the Case Study indicates a 24% reduction in pedestrian fatalities for crashes where the pedestrians were struck by the front of a passenger car.
Causation patterns and data collection blind spots for fatal intersection accidents in Norway
(2010)
Norwegian fatal intersection accidents from the years 2005-2007 were analysed to identify any causation patterns among their underlying contributing factors, and also to evaluate whether the data collection and documentation procedures used by the Norwegian in-depth investigation teams produces the information necessary to perform causation pattern analysis. A total of 28 fatal accidents were analysed. Details on crash contributing factors for each driver in each crash were first coded using the Driving Reliability and Error Analysis Method (DREAM), and then aggregated based on whether the driver was going straight or turning. Analysis results indicate that turning drivers to a large extent are faced with perception difficulties and unexpected behaviour from the primary conflict vehicle, while at the same time trying to negotiate a demanding traffic situation. Drivers going straight on the other hand have less perception difficulties. Instead, their main problem is that they largely expect turning drivers to yield. When this assumption is violated, they are either slow to react or do not react at all. Contributing factors often pointed to in literature, e.g. high speed, drugs and/or alcohol and inadequate driver training, played a role in 12 of 28 accidents. While this confirms their prevalence, it also indicates that most drivers end up in these situations due to combinations of less auspicious contributing factors. In terms of data collection and documentation, information on blunt end factors (those more distant in time/space, yet important for the development of events) was more limited than information on sharp end factors (those close in time/space to the crash). A possible explanation is that analysts may view some blunt end factors as event circumstances rather than contributing factors in themselves, and therefore do not report them. There was also an asymmetry in terms of reported obstructions to view due to signposts and vegetation. While frequently reported as contributing for turning drivers, they were rarely reported as contributing for their counterparts in the same accidents. This probably reflects an involuntary focus of the analyst on identifying contributing factors for the driver legally held liable, while less attention is paid to the driver judged not at fault. Since who to blame often is irrelevant from a countermeasure development point of view, this underlying investigator mindset needs addressing to avoid future bias in crash investigation reports.
The main objective of EC CASPER research project is to reduce fatalities and injuries of children travelling in cars. Accidents involving children were investigated, modelling of human being and tools for dummies were advanced, a survey for the diagnosis of child safety was carried out and demands and applications were analysed. From the many research tasks of the CASPER project, the intention of this paper is to address the following: • In-depth investigation of accidents and accident reconstruction. These will provide important points for the injury risk curve, in order to improve it. Different accident investigation teams collected data from real road accidents, involving child car passengers, in five different European countries. Then, a selection of the most appropriate cases for the injury risk curve and the purposes of the project was made for an in-depth analysis. The final stage of this analysis was to conduct an accident reconstruction to validate the results obtained. The in-depth analysis included on-scene accident investigation, creating virtual simulations of the accident/possible reconstruction, and conducting the reconstruction. In the cases of successful reconstructions, new points were introduced to the injury risk curves. Accident reconstructions of selected cases were carried out in test laboratories as the next step following in-depth road accident investigation. These cases were reconstructed using similar child restraint systems (CRS) and the same type make and model as in the real accidents. Reconstructing real cases has several limitations, such as crash angle, cars" approximation paths and crash speed. However, a few changes and applications on the testing conditions were applied to reduce the limitations and improved the representations of the real accidents. After conducting the reconstructions, a comparison between the deformations of the cars on the real accident and the vehicles from the reconstructions was made. Additionally, a correlation between the data captured from the dummies and the injury data from the real accident was sought. This finalises an in-depth analysis of the accident, which will provide new relevant points to the injury risk curve. The CASPER project conducted a large research programme on child safety. On technical points, a promising research area is the developing injury risk curves as a result of in-depth accident investigations and reconstructions. This abstract was written whilst the project was not yet finished and final results are not yet known, but they will be available by the time of the conference. All the works and findings will not necessarily be integrated in the industrial versions of evaluation tools as the CASPER project is a research program.
This study aimed at developing an injury estimation algorithm for AACN technologies for Germany and compared them to findings based on Japanese data. The data to build and to verify the algorithm was obtained from the German in-depth Accident Database (GIDAS) and split into a training and a validation dataset. Significant input variables and the generalized linear regression model to predict severe injuries (ISS>15) were selected to maximize area under the receiver operating characteristic curve (AUC). Probit regression with the input parameter multiple impact, delta v, seatbelt use and impact direction gave the largest AUC of 0.91. Sensitivity of the algorithm was validated at 90% and specificity at 76% for an injury risk threshold of 2%. It appears that no major differences between Japan and Germany exist for injury estimation based on delta v and impact direction. However, far side impact and multiple crash events appear to be associated with a larger risk increase in the German data.
A means of assessing the passive safety of automobiles is a desirable instrument for legislative bodies, the automobile industry, and the consumer. As opposed to the dominating motor vehicle assessment criteria, such as engine power, spaciousness, aerodynamics and consumption, there are no clear and generally accepted criteria for assessing the passive safety of cars. The proposed method of assessment combines the results of experimental safety tests, carried out according to existing legally prescribed or currently discussed testing conditions, and a biomechanical validation of the loading values determined in the test. This evaluation is carried out with the aid of risk functions which are specified for individual parts of the body by correlating the results of accident analysis with those obtained by computer simulation. The degree of conformance to the respective protection criterion thus deduced is then weighted with factors which take into account the frequency of occurrence and the severity of the accident on the basis of resulting costs. Each of the test series includes at least two frontal and one lateral crash test against a deformable barrier. The computer-aided analysis and evaluation of the simulation results enables a vehicle-specific overall safety index as well as partial and individual safety values to be determined and plotted graphically. The passive safety provided by the respective vehicle under test can be defined for specific seating positions, special types of accident, or for individual endangered parts of the body.
This paper reviews briefly the evolution of the investigation of transport accidents from the early beginnings when individual events were studied but systematic data was not collected. In the transport modes other than on the roads, accident investigation early on, even of single events, was important in introducing safety improvements. Road accidents, however, evolved enormously with the growth of car ownership without any comparable political response to the consequent deaths and injuries, equivalent to what happened with the other modes. From the 1950s data bases started to contribute to our knowledge of the epidemiology of road traffic injuries, and in-depth sample studies have contributed much to the body of knowledge in the last 30 years. However, even the basic input and output variables of a crash, its severity and the seriousness of the outcomes in terms of injuries and their consequences are not complete or agreed upon. Issues of experimental design and sampling are discussed. It is proposed that the most important area for current research to address is the effect of population variations on injury outcomes. The need for the establishment of good data bases for active safety issues is emphasised with the consequent need for better links between the research community and the police.
Pelvic fracture, cracking or breaking of a portion of the pelvis are extremely common injuries in the side impact collisions of motor vehicles. Due to both its shape and structural architecture, mechanics of the pelvic bone is complicated. There is a lack of knowledge regarding the dynamic behavior of the pelvis and its biomechanical tolerance under impact environment. Hence this study is aimed at the understanding of the mechanical response of the human pelvis with three-dimensional finite element (FE) models, under side impact load, applied through a structure, equivalent to a car door. The door structure was modeled, considering few layers, consisting of foam (Styrodur®, 3035 CS), plastic (UHMWPE), steel, glass and steel, putting them in series. A soft tissue layer (equivalent to fat) was also considered on the greater trochanter location. These FE models (with and without the car door structure) were analyzed with ANSYS-LS-DYNA-® dynamic finite element software to compare the effect of the car door padding system for shock absorption. It was observed that with proper combination of shock absorbing material (foam, etc.) and its thickness, the transmission of impact load to the body part (pelvis, etc.) from the outer surface of the car door could be reduced.
A total survey of road traffic accidents involving most severely injured, defined as sustaining a polytrauma or severe monotrauma (ISS > 15) or being killed, was conducted over 14 months in a large study region in Germany. Data on injuries, pre-clinical and clinical care, crash circumstances and vehicle damage were obtained both prospectively and retrospectively from trauma centers, dispatch centers, police and fire departments. 149 patients with a polytrauma and eight with a severe monotrauma were recorded altogether. 22 patients died in hospital. Another 76 victims had deceased at the accident scene. In 2008, 49 % of patients treated with life-threatening injuries were car or van occupants, 21 % motorcyclists, 18 % cyclists and 10 % pedestrians. Among fatalities at the scene, vehicle occupants constituted an even larger portion. The number of road users with life-threatening trauma in the region was extrapolated to the German situation. It suggests that 10 % among the "seriously injured" as defined in national accident statistics are surviving accident victims with a polytrauma or severe monotrauma.
While many medical studies have dealt with the incidence, nature and treatment of polytrauma the injury-causing accident mechanisms are rarely discussed in detail, mostly due to the lack of documentation of the technical aspects. The present prospective study was started in late 2007 and collects data from traffic accidents with most severely injured in six south- German counties and two larger cities for the duration of one year. It is aimed at identifying and documenting all polytrauma cases (ISS ≥ 16) caused by traffic accidents and their crash circumstances. The data collection is based on an interdisciplinary concept to include both the police, emergency dispatch centers, hospitals and fire departments in the region and is completely anonymous. Potentially relevant cases where an emergency physician was called to the scene of a traffic accident are provided by the dispatch center. All three hospitals in the region suited for the treatment of polytraumatised patients record injuries, major diagnostic and surgery data. Data and images from the accident scene are provided by the police and by fire departments. The latter provide information which is usually not available from the police, like deployed airbags, vehicle extrication measures and detailed views of car interiors. The main objective of the study is to determine the structure of road users who sustain a polytrauma, their crash opponents and the injury patterns found in relation to the collision configuration and the protection by seat belts, air bags and other devices. With detailed documentation of vehicle damage and extrication measures the study is also intended to support the development of injury predictors for pre-hospital treatment and provide field data regarding further improvement of technical rescue.
Motorcycle riders are one of the most vulnerable road users. Annually, on estimate 6000 people are killed in motorcycle accidents in the former 15 EU countries. The objective of this research was to investigate and analyze the main aspects and causes of this vulnerability and the accidents in general. For this aim around 70 accidents in The Netherlands were investigated in the framework of an international research program (MAIDS). Also a control group of motorcycles with riders was investigated so that exposure could be taken into account. An important result is that human failure is in 82% of the cases the main cause of the accident, in 52% this is due the other vehicle driver. Perception and decision failures are the most common failures. The most injuries are caused by the environment but they are typically only less severe (AIS1). Injuries caused by the car (front and side) are typically severe injuries (AIS4+). Previous convictions of the MC rider seem to be related to the chance to get involved in an accident. It was shown that the Dutch and the total MAIDS accident sample are comparable.
The following paper presents the nature and mechanism of injuries sustained in frontal impacts, focusing on car to car impacts. It was found that the body regions most frequently sustaining severe to fatal injuries were the legs and the thorax. The nature and mechanism of the injury sustained was investigated only for the thorax injuries, due to their potentially life threatening nature. The analysis revealed that the most frequent cause of the injury recorded was the seatbelt for low severity injuries and the front structure of the vehicle for higher severity injuries. An analysis of the effect of load limiter technology in the restraint system showed that the proportion of occupants who sustained "no thorax injury" did not increase when a load limiter was fitted to the restraint system. However, a decrease in the "organ" and "organ and skeletal" injuries was observed in the load limiter sample. Sample size and variation mean that these findings are not conclusive.
Road authorities, freight, and logistic industries face a multitude of challenges in a world changing at an ever growing pace. While globalization, changes in technology, demography, and traffic, for instance, have received much attention over the bygone decades, climate change has not been treated with equal care until recently. However, since it has been recognized that climate change jeopardizes many business areas in transport, freight, and logistics, research programs investigating future threats have been initiated. One of these programs is the Conference of European Directors of Roads (CEDR) Transnational Research Programme (TRP), which emerged about a decade ago from a cooperation between European National Road Authorities and the EU. This paper presents findings of a CEDR project called CliPDaR, which has been designed to answer questions from road authorities concerning climate-driven future threats to transport infrastructure. Pertaining results are based on two potential future socio-economic pathways of mankind (one strongly economically oriented "A2" and one more balanced scenario "A1B"), which are used to drive global climate models (GCMs) producing global and continental scale climate change projections. In order to achieve climate change projections, which are valid on regional scales, GCM projections are downscaled by regional climate models. Results shown here originate from research questions raised by European Road Authorities. They refer to future occurrence frequencies of severely cold winter seasons in Fennoscandia, to particularly hot summer seasons in the Iberian Peninsula and to changes in extreme weather phenomena triggering landslides and rutting in Central Europe. Future occurrence frequencies of extreme winter and summer conditions are investigated by empirical orthogonal function analyses of GCM projections driven with by A2 and A1B pathways. The analysis of future weather phenomena triggering landslides and rutting events requires downscaled climate change projections. Hence, corresponding results are based on an ensemble of RCM projections, which was available for the A1B scenario. All analyzed risks to transport infrastructure are found to increase over the decades ahead with accelerating pace towards the end of this century. Mean Fennoscandian winter temperatures by the end of this century may match conditions of rather warm winter season experienced in the past and particularly warm future winter temperatures have not been observed so far. This applies in an even more pronounced manner to summer seasons in the Iberian Peninsula. Occurrence frequencies of extreme climate phenomena triggering landslides and rutting events in Central Europe are also projected to rise. Results show spatially differentiated patterns and indicate accelerated rates of increases.