VARIABILITY OF THE CALIBRATION FACTORS OF THE HSM SAFETY

0 0 0 0 VARIABILITY OF THE CALIBRATION FACTORS OF THE HSM SAFETY PERFORMANCE FUNCTIONS WITH TRAFFIC, REGION AND TERRAIN The case of the Italian rural two-lane undivided road network Pasquale Colonna Technical University of Bari via Orabona, Bari, 000 (Italy) Tel: +00 Fax: +00; Email: pasquale.colonna@poliba.it Nicola Berloco Technical University of Bari via Orabona, Bari, 000 (Italy) Tel: +00 Fax: +00; Email: nicola.berloco@poliba.it Paolo Intini Technical University of Bari via Orabona, Bari, 000 (Italy) Tel: +00 Fax: +00; Email: paolo.intini@poliba.it Antonio Perruccio Technical University of Bari via Orabona, Bari, 000 (Italy) Tel: +00 Fax: +00; Email: antonio.perruccio@poliba.it Vittorio Ranieri Technical University of Bari via Orabona, Bari, 000 (Italy) Tel: +00 Fax: +00; Email: vittorio.ranieri@poliba.it Vincenzo Vitucci Technical Engineer via Orabona, Bari, 0 (Italy) Tel: +00 Fax: 0--00; Email: v.vitucci@hotmail.it Word count: 0 abstract,, words text + tables/figures x 0 words (each) =, words Submission Date: November, th 0

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 ABSTRACT Crash prediction is a crucial step for each part of the road safety management process. The HSM first edition provided safety performance functions (SPF) in order to predict crash frequencies on different types of road infrastructures. However, crash frequencies of similar roadway segments or intersections can vary widely from one jurisdiction to another. Hence, a calibration process to local conditions is necessary before the application of HSM SPFs. HSM (00) provides guidelines for the calibration process. However, the recent NCHRP 0-0() (0) emphazises the need of considering the variability of the local calibration factor with other specified variables (severity, traffic, segment lengths, regions, terrain). Also, in that report, the matter of the assessment of calibration results is addressed. However, there is still uncertainty on which and how many variables should be considered for the calibration with regards to their influence on the overall jurisdiction factor. In this paper, the influence of traffic volume ranges, terrain types and regions on the results of the calibration study is analyzed. The NCHRP 0-0 () recommendations about the calibration process and the assessments of its results were applied. For the purpose of the study, a sample of roads belonging to the Italian two-lane undivided highways network was employed, considering a five-years study period. Calibration factors at the nationwide scale and for different sub-groups of the sample based on traffic volumes, terrain types and regions (macro-regions and administrative regions) were computed. The influence of those variables was assessed through the analysis of the obtained results. Keywords: Safety Performance Functions, Highway Safety Manual, SPFs Calibration, Traffic Ranges, Terrain Type, Region.

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 0 VARIABILITY OF THE CALIBRATION FACTORS OF THE HSM SAFETY PERFORMANCE FUNCTIONS WITH TRAFFIC, REGION AND TERRAIN The case of the Italian rural two-lane undivided road network By Pasquale Colonna, Nicola Berloco, Paolo Intini, Antonio Perruccio, Vittorio Ranieri, Vincenzo Vitucci INTRODUCTION The reduction of injuries and deaths caused by road traffic crashes is one of the primary objectives of European Union () and countries all over the world (). For existing roads, this can be accomplished by complying with the steps of the following iterative process: ) screen the road network of a given area in order to individuate sites in which crashes cluster, ) select the appropriate countermeasures based on the diagnosis of crashes at those sites in order to achieve the reduction in crashes, ) conduct economic evaluations in order to implement countermeasures corresponding to the best benefit/cost ratio and prioritize more urgent interventions. This process is called Road Safety Management Process in the Highway Safety Manual () and it represents also the basis of the EU Directive on Road Infrastructure Safety Management (). However, the official European guidelines (and the Italian Guidelines (), based on them) related to road safety analyses do not provide analytical instruments able to quantify the effects on crashes of decisions made by practitioners in each feature concerning roadways. Instead, in order to get a more reliable outcome, the steps of the road safety management process require quantitative predictions of future crashes at a given site. Safety performance functions (SPFs) can be used in order to predict the average number of crashes per year at a site as a function of exposure and, in some cases, roadway or intersection characteristics. For highway segments, exposure is represented by the segment length and annual average daily traffic (AADT) associated with the study section. According to the HSM procedure, predicted crash frequencies can be calculated by using baseline safety performance functions (SPFs) for rural two-lane undivided highways, rural multilane highways and urban and suburban arterials. The obtained frequencies have to be multiplied by the crash modification factors (CMFs) listed in the HSM Part D to take into account of the differences in geometric charactestics and other features from the baseline conditions. The predicted crash frequency can be also adjusted by using the empirical Bayes method, when historical data of crashes are avalaible (). The calculation of the predicted crash frequency is summarized in the equation. N predicted = C x x N spf x CMF x CMF x CMF n () where Nspf is the number of crashes predicted by the SPF for base conditions, CMFs are the crash modification factors and Cx is the calibration factor which accounts for the application of a base SPF in different jurisdictions or in different time periods. The calibration factor is computed as the ratio of the total observed crash frequencies for a selected set of sites to the total predicted average crash frequency estimated for the same sites, during the same time period, using the appropriate predictive method provided by the HSM. The calibration factors will show values greater than.0 for roadways that, on average, experience more crashes than the roadways used for the SPFs development and vice versa. Generally, the calibration of the safety performance functions is necessary because crash frequencies of similar roadway segments or intersections can vary widely from one jurisdiction to another, whether between states, geographic regions belonging to the same state or different sub-

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 0 networks in the same region (see e.g. Tarko ()). In fact, geographic regions may differ in climate, driver populations, crash reporting thresholds, crash reporting practices, animal populations and other features. All these differences could be practically involved in road safety issues as long as they depend on the interactions of many elements related to human, road, environments, traffic and vehicle factors (,). The HSM provides the procedure to develop calibration factors (Appendix to Part C). Some studies document results of the calibration process in the United States (0 - ) and discuss about the transferability of the HSM SPFs in different parts of the world ( - ). These studies have shown a great variability in the calibration factor, also due to the different road networks on which the calibration process was applied. However, even if it is well known that calibration factors can vary according to different variables, no methodologies in the HSM are suggested to address this matter. Also, no guidance is provided about assessing the validity of the results obtained from the calibration study. These gaps have been covered by the recent publication made by the AASHTO (NCHRP 0-0 () (0)). This report emphazises the need of considering the variability of the calibration factor with other specified variables (severity, traffic, segment lengths, regions, terrain) and it recommends some techniques in order to evaluate results of the obtained calibration. Nevertheless, the authors of the report encourage research in this sense. In fact, there is still uncertainty on which and how many variables should be considered for the calibration with regards to their influence on the overall factor. So, in this paper, the NCHRP 0-0 () recommendations about the calibration process will be applied to a sample of roads belonging to the Italian two-lane rural road network for the study period 00-0. In particular, the main objective of this paper is to study the variability of the calibration factor with traffic, region and terrain for the considered sample of roads and to assess the importance of those variables through the validation of the results obtained. DATA COLLECTION For the purpose of the study, traffic, crashes and geometric data related to Italian two-way twolane undivided rural roads were employed. As suggested in the Highway Safety Manual (HSM) calibration procedure, the roads investigated were randomly selected among roads on which both traffic and crash data were available. In order to explore the geographic variability of the calibration factor, roads belonging to different areas were inquired. In fact, apart from the merely administrative divisions, the terrain type can vary greatly from flat to mountainous between different Italian regions and in the regions itself. Thus, in order to match the objectives of this study, roads from different Italian administrative regions: Puglia, Basilicata,Campania, Calabria, Molise (Southern Italy), Umbria (Central Italy), Emilia-Romagna, Veneto (Northeast Italy) and Lombardia (Northwest Italy) were included in the data set. The administrative regions were firstly grouped into macro-regions (Southern, Central, Northeast and Northwest), according to the official statistical regional division of Italy used by the National Institute of Statistics (ISTAT). All the road segments selected belong to the functional category C according to the Italian Road Design Standards (). These highways are mainly collectors used for medium-distance travels, from a functional point of view. The final data set is composed by homogeneous road segments, for a total length of 0 kilometers of roads. In particular, segments are distributed in the administrative regions as follows: Puglia (), Basilicata (), Calabria (), Campania (), Molise (), Umbria (), Emilia- Romagna (), Veneto (), Lombardia ().

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci The spatial distribution of the road segments included in the data set is shown in Fig.. 0 0 FIGURE Spatial distribution of the road segments included in the data set. Geometric and traffic data Geometric characteristics and annual average daily traffic (AADT) are the main input data requested for the application of the HSM procedure. All traffic data used for the calibration were obtained from the ANAS Database (Road Italian Agency). Traffic data of the available most recent year of the study period (00-0) were used. According to the HSM recommendations, road segments with AADT greater than,00 vehicles were discharged from the database due to the lack of consistency of the two-lane rural highways SPF for those values. The road geometric characteristics required for the calibration study were measured with different tecnhniques. More in detail, according to the HSM, data about road segment length, annual average daily traffic, lane width, shoulder width, shoulder type, radius of curvature of horizontal curves, presence of two-way left turn lane (TWLTL) were strictly required. Instead, data about superelevation variance, vertical grades, driveways density, presence of centerline rumble strips, roadside hazard rating (RHR), presence of road lighting, presence of passing lanes/four lanes sections and the presence of automated speed enforcement were considered as desirable. Since a roadway geometric inventory database was not available for each region, some measures (i.e. lane width, shoulder width and type) were obtained by using different softwares, coherently with previous similar applications (, ).

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 Once all the road geometric characteristics were measured, road segments, homogeneous from the point of view of geometry (both horizontal and vertical alignments) and traffic (constant AADT values) were defined. A summary of the geometric characteristics of the studied road segments, and the method selected for measuring them, are reported in Table. Required 0 00 Google Earth Pro TABLE Summary of the geometric characteristics of the road segments belonging to the database employed. Measure Rule by Descriptive statistics (employed Measurement HSM database) method Min Max Mean Dev.. St. Segment length [m] Required 000 Google Earth/ Street View AADT Required 0 Provided by ANAS Lane width [m] Required.00..0 0.0 Google Earth Right shoulder width [m] Required 0.0.0.0 0. Google Earth Left shoulder width [m] Required 0...0.0 0. Google Earth 0 Shoulder type Required - - - - Google Street View Radius of curvature of horizontal curves [m] Superelevation variance for Desirable - - - - Not measured horizontal curves Vertical Grade [%] Desirable 0.... Google Earth Driveways density [number of Desirable 0..0 Google Street driveways/km] View Centerline rumble strips Desirable - - - - Not present TWLTLs Required - - - - Google Street View RHR Desirable.0. Google Street View Road lighting Desirable - - - - Google Street View Passing lanes or short fourlanes Desirable - - - - Google Earth section Automated speed Desirable - - - - Not present enforcement Superelevation variance was the only measure discharged by the database because it was considered unreliable. So, HSM default assumptions about curve superelevation were used. Road sections with centerline rumble strips and automated speed enforcement were not present in the employed database. So, HSM default assumptions were used for these two variables. Crash data Crash data on the selected roads were obtained by the annual reports made by the National Institute of Statistics (ISTAT) jointly with the Italian Automobile Club (ACI) (). These reports give crashes statistics related only to personal injuries (fatal and injury crashes) in which at least a motorvehicle was involved. These statistics are provided in a kilometric-scale.

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 0 Based on a similar study () and on the ISTAT reports, the fatal and injury crashes reported in the ISTAT+ACI database can be reconducted to KAB crashes according to the KABCO severity scale (where: K = killed, A = incapacitating injury, B = non incapacitating injury, C = possible injury, O = property damage only). Therefore, crashes responsible for possible injuries were not considered as part of the injury crash database due to their high probability of under-reporting. The crash database was composed by crashes (showing KAB severity) over the -years period: 00-0 (namely: 00 (), 00 (), 00 (), 0 (), 0 ()). However, since the percentage of KAB crashes is about the % of the total, as reported in the HSM for the United States, the total number of total crashes is for sure much greater than the available KAB crashes. Since the calibration study is focused on roadway segments, all intersections-related crashes were discharged from the dataset. METHODS In this section, details about the methods adopted for the study of the Italian regional/terrain calibration of the safety performance functions provided by HSM are given. In general, the HSM calibration procedure will be applied for each sub-group of the total database according to the indications given in the NCHRP guide. General calibration procedure In this paper, the SPF calibration was performed according to the HSM Calibration procedure for the transferability of SPFs in different jurisdictions. The case of rural two-lane undivided highways is considered. According to that procedure, a minimum number of road segments varying from 0 to 0 was selected for each study sub-group (traffic, region and terrain). Each segment is characterized by an adequate length in order to correctly represent its road category and in order to be homogeneous from the point of view of road geometry. Furthermore, on the selected road segments, a total of almost 00 crashes/year was recorded by considering only KAB crashes. However, since fatal and injury crashes data are more reliable than those referred to all crashes, a sample of KAB crashes slightly less than 00 crashes/year could be sufficient (). The adopted study period is the most recent possible. It consists of five years (00 0), a period which can allow to take into account the temporal variability of crashes. It is recommended values of the calibration factors be derived at least every two to three years (), However, in this case, the calibration coefficients cannot be updated since the latest available data are related to the above reported past period. This case study is thought to be a pilot project aimed at understanding the influence of traffic, region and terrain on the calibration factor. Therefore, a longer time period was chosen, according also to (), (). Traffic and crash data for the inquired study period were paired for the selected homogeneous road segments. After, the observed crashes at all selected road segments over the chosen study period were summed. The predicted number of crashes was computed separately for each road segment (since AADT and segment length can vary) by using the equation () considering Cx =.00. Finally, the calibration factor was computed as: C x = Observed number of crashes all segments all segments Predicted number of crashes (uncalibrated spf) ()

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 0 Thus, a global Italian calibration factor for two-lane rural highways was obtained in this study by following the above reported procedure. After, the same process was repeated for each combination of traffic and geomorphological conditions, as summarized in the next section. Research investigation about the influence of traffic, region and terrain According to the HSM recommendations, for entire states, with a variety of topographical and climate conditions, it may be desirable to develop separate calibration factors for each specific terrain type or geographical region. This need is related to practical matters involved in the road safety management process. In fact, e.g., applying the nationwide calibration factor (Cnationwide) to a site located in a mountainous terrain could lead to significant biases in the estimated number of crashes if the Cnationwide and the Cmountainous are very different. So, different calibration factors for different boundary conditions should be developed. However, even if there are a lot of variables influencing Cx values, they should be limited by considering: The bias in the estimated Cx values; The differences between the Cx values in different conditions. In this study, these two matters are addressed by considering the recommendations given by the NCHRP 0-0 (). For what about the biases in the Cx values, more accurate estimates of the Cx values than what can be done for CMFs and for the predicted base value from the SPF itself is useless. In fact, based on the functional form of the HSM SPF, the coefficient of variation of the Npredicted is related to the coefficients of variation of the different involved variables as in the following equation: (cv{n predicted }) = (cv{n predicted from base SPF}) + (cv{product of CMFs}) + (cv{c x }) () So, the accuracy of the Cx values contributes to the accuracy of Npredicted in the same way as does the accuracy of the Preditcted base value and the Product of all the applicable CMFs. Hence, the magnitude of the bias in the Npredicted is dominated by the largest bias among the three variables of the model. Considering that it could be assumed that the coefficient of variation of the product of the CMFs is larger than that of the predicted base value from the SPF and that the HSM CMFs have standard errors of less than 0. to 0.; a coefficient of variation related to the Cx estimations less than 0. is considered as a good target in this study, according to the NCHRP 0-0 () recommendations. Instead, for what about the differences in Cx values in different conditions, the Cx factor can depend on crash severity, AADT, segment length, terrain, region and other variables. The wellknown high dependence on crash severity and AADT, and to a lesser extent on segment length, is remarked by the authors of the NCHRP 0-0 () after an exploratory study on a dataset belonging to the Ohio State. Instead, no guidance on the influence of region, terrain and other variables is given because of lack of data. Also, the choice of which influential variables should be primary studied is still an open question, encouraging research in this sense. Based on the NCHRP report, an attempt to assess wether also region and terrain should be prioritized as influential variable on the Cx values was made. AADT ranges were considered as well due to the highlighted influence of traffic values on Cx. Instead, since the database is composed only of fatal and injury crashes, differences in crash severity were not considered. Therefore, after a nationwide calibration coefficient was obtained, the calibration process was repeated by dividing the samples in sub-groups according to traffic values, terrain types and region. Data were grouped considering the following assumptions for the three inquired

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 0 variables. AADT ranges: Low traffic volume (< 0,000); High traffic volume (0,000,00). Terrain types: Flat terrain (< 00 m above mean sea level); Rolling terrain ( 00 m above mean sea level). Regions: Northern Italy (including regions belonging to Northeast and Northwest Italy, namely Veneto, Emilia Romagna, and Lombardia); Central/Southern Italy (including regions belonging to Central and Southern Italy, namely Puglia, Basilicata, Molise, Calabria, Campania, Umbria). Traffic volumes were split into the two chosen categories because previous studies (, ) highlighted that the model tends to underestimate crash frequencies for sections with more collisions, roughly for traffic values greater than 0,000. Further sub-grouping based on more disaggregated traffic ranges were avoided in order not to excessively reduce the size of the subgroups. For the same reason, for the other two variables, only two ranges were considered. The terrain types considered are flat and rolling. In fact, winding roads in impervious Alps and Appennines mountainous terrains were discharged from the final database due to their scarcity in the initial data set. However, differences between roads in flat and rolling terrains were searched, because rolling terrains are the most widespread in Italy (hills represent almost the percent of the total Italian territory). The limit value between flat and rolling terrains was set to 00 m after a preliminary analysis. In this analysis, a terrain elevation limit beyond which the road horizontal and vertical alignments start to be highly influenced by the surrounding greater elevations was searched for. Results from the analysis conducted to the limit value of 00 m. The two macro-regions in which the Italian territory was split in this study are the Northern Italy and the Central/Southern Italy. The two macro-regions selected correspond roughly to the continental and the mainland Italy. This macro-regional differentatiation is commonly used in Italy () because of the differences in climate, environment, population behavior. Specifically for this study, the differences regard also driving population, animal population, crash reporting procedures which can significantly affect the number of crashes. After this first macro-regional differentiation, also the calibration for each region, intended as administrative unit (Puglia, Veneto, Calabria, etc.) was performed. Validation of the calibration results Finally, the validation of the results obtained from the calibration study (the Cx values for different conditions) was made by using two different approaches. For the first validation approach, the indicators provided in the NCHRP guide were adopted. In particular, the variance of Cx (V{C }) x was computed. The variance can be easily related to both the standard deviation and the coefficient of variation. The following equation was used in order to estimate V{C }. x n ) V{C } x = j= (N a,j+ k j N a,j ( n () j= N u,j ) where: Nu,j is the uncalibrated predicted number of crashes for the segment j, Na is the calibrated

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 0 predicted number of crashes for the segment j (N a = C x N u ), k j is the overdispersion parameter of the base HSM SPF. Equation can be used when information about segment length, AADT and observed crashes at the inquired sites are known. In this case, calibrated predicted number of crashes could be replaced by observed crashes. In this study, all the required variables for its application were available. After V{C } x was obtained for each combination of the three variables considered, standard deviations and coefficient of variations were computed as follows: σ{c } x = V{C } x () cv{c } x = σ{c } x () C x For the second validation approach, the Mean Absolute Deviation (MAD) index was used. This goodness-of-fit measure was selected since it gave good results in similar applications (), (), (). The following equation explains the MAD index calculation procedure: The MAD index is the average of the absolute values of the difference between the observed (Nobserved) and the predicted (Npredicted) crash frequencies. MAD = n N observed,j N predicted,j J= () n where Nobserved and Npredicted are the observed and the predicted crash frequencies, respectively. The more the MAD index is close to zero, the better the model can predict values able to fit well the observed data. However, since it is an evaluation of absolute deviations, the MAD index cannot identify systematic over or under predictions. RESULTS AND DISCUSSION The calibration factors obtained for each combination of the variables inquired, together with the related values of standard deviation, coefficient of variation and MAD index are summarized in Table. TABLE Summary of the results of the calibration study. Number Variable Sub-Group AADT Ranges C of Segments x σ[c x] cv[c x] MAD overall. 0.0 0.0. Overall - < 0,000. 0.0 0.0 0. (Nationwide) 0,000-,00. 0. 0.0. Terrain Rolling Flat overall. 0. 0..0 < 0,000 00. 0. 0. 0. 0,000-,00. 0. 0.. overall. 0. 0.0. < 0,000. 0. 0.. 0,000-,00. 0.0 0..

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci Region (Macro) Macro- Region/ Terrain Region (Admin.) Northern Italy Central-Southern Italy Northern Italy/ Rolling Terrain Northern Italy/Flat Terrain Cent.-South. Italy/Rolling Terrain Cent.-South. Italy/Flat Terrain Basilicata Calabria overall. 0. 0.0. < 0,000. 0. 0..0 0,000-,00. 0. 0.. overall. 0. 0.0. < 0,000. 0. 0.0 0. 0,000-,00. 0. 0.0. overall 0. 0. 0.. < 0,000. 0. 0.. 0,000-,00. 0. 0.. overall. 0. 0..0 < 0,000. 0. 0.. 0,000-,00. 0. 0.. overall. 0. 0. 0. < 0,000. 0. 0. 0. 0,000-,00 0.0 0. 0.. overall. 0. 0.0. < 0,000. 0. 0.. 0,000-,00. 0. 0.0. overall 0. 0. 0. 0. < 0,000 0. 0. 0. 0. 0,000-,00 0. 0..0.0 overall. 0. 0.. < 0,000 0. 0. 0..0 0,000-,00. 0. 0.. Campania < 0,000.0 0. 0..0 Emilia Romagna Lombardia overall. 0. 0.. < 0,000.0..0.0 0,000-,00.0 0. 0.. overall. 0. 0.. < 0,000 0. 0. 0. 0. 0,000-,00. 0. 0.. Molise < 0,000 0.0 0. 0. 0. Puglia overall. 0. 0. 0. < 0,000 0. 0. 0. 0. 0,000-,00. 0. 0.0. Umbria < 0,000.0 0. 0.. overall.0 0. 0.. Veneto < 0,000. 0. 0.. 0,000-,00. 0. 0.0. Boldface Cx values showed a coefficient of variation minor than 0.0 and they were computed on at least 0 road segments.

Calibration Factor Cx Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci Furthermore, a graphical representation of the variations in the Cx values due to traffic, terrain and macro-region is given in Fig.. All the Cx values which are computed on at least 0 homogeneous road segments showing an estimated coefficient of variation minor than 0.0 are highlighted in boldface in Figure, as well as in Table. The NCHRP guide suggests that the optimum value for the cv[cx] will be included in a range between 0. and 0. in the future. However, since no precise guidance on these values is given, the acceptable value for cv[cx] was set to 0.0 in this study... 0........................ 0.... 0 0 FIGURE Changes in the Cx values due to the combination of terrain, region (x-axis) and traffic (y-axis). As a result of this analysis, an overall nationwide calibration factor for the two-way two-lane Italian highways (collectors) network is.. This coefficient was obtained by considering: All the homogeneous road segments; -years study period: 00-0;. predicted fatal and injury crashes (KAB); observed fatal and injury crashes (KAB). A similar Italian calibration study conducted on a comparable highways network by using the methodology of the HSM (first edition) is due to Sacchi et al. (). In that study, the computed calibration factor referred to the rural two-way two-lane network in the Turin province (Northwest Italy) was 0.. This high difference in the two values may be mainly due to: ) the difference in road databases as long as that database included also local roads and, ) in this study the fatal and

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 0 injury crashes were associated only to KAB crashes, which account for only about percent of the total crashes. Instead, KABC crashes account for aobut percent of the total crashes and consequently, including also possible injuries (C) while predicting fatal and injury crashes, can significantly reduce the obtained calibration factor (observed crashes being equal). The overall nationwide calibration factor varies according to the AADT ranges. For low traffic volumes (AADT < 0,000), Cx is equal to., while for higher traffic volumes (0,000,00) it is equal to.. Moreover, the remarkable difference between the two traffic ranges can be noticed in all combinations of region/terrain. In fact, on average, the Cx values obtained for higher traffic volumes are greater than the values for lower volumes. The high values computed for AADT greater than 0,000 are always related to high values of the MAD index, showing again that the baseline HSM SPF for two-lane undivided highways systematically underestimate crashes for higher traffic volumes. Actually, the MAD index can detect only systematic deviations in the prediction capability, but similar previous studies (, ) highlighted the underestimation tendency. Instead, the prediction capability of the calibrated nationwide model for lower traffic volumes can be considered as quite good considering the MAD index minor than. Furthermore, the estimated coefficient of variations of the nationwide calibration factors for both the traffic ranges are minor or equal to 0.0, even if the sample size of high traffic road segments is smaller. Those values can be used to predict crash frequencies with a reasonable margin of error of less than ± 0 %. Therefore, the calibration factors are:. ± 0.0 at the overall nationwide scale,. ± 0.0 at the nationwide scale for AADT <0,000 and. ± 0. at the nationwide scale for higher AADT. Anyway, based on these results, a different functional form of the SPF could be more reliable than the current one for traffic values greater than 0,000 (see Kononov et al. ()). The considered terrain types have an influence on the Cx value. However, this influence is smaller than the AADT ranges. At the nationwide scale, road segments in flat terrains show a Cx value (.) greater than road segments in rolling terrains (.). This effect is attributed only to the high AADT range, while for AADT < 0,000 no remarkable differences in the Cx values can be noticed. On considering the estimated standard deviations for the high AADT range, Cx can be reported as. ± 0. for rolling terrains and. ± 0.0 for road segments in flat terrains. Thus, estimated coefficient of variations are both minor than the 0.0 threshold suggested by the NCHRP guide. If the calibrated model is based on the HSM SPF for two-lane undivided highways, than the difference between flat and rolling terrain types should be considered for AADT values greater than 0,000. On dividing the road segments according to the different geographic macro-regions (Northern and Central/Southern Italy) is influential in the Cx values. A reliable comparison can be made for the low AADT range: the Cx factor for Northern Italy (.) is greater than the factor computed for Central/Southern Italy (.). The related estimated coefficient of variations are: 0.0 for Central/Southern Italy and 0. for Northern Italy (which is only slightly greater than the 0.0 threshold). Thus, Cx values for AADT < 0,000 can be reported as. ± 0. for Central/Southern Italy and. ± 0. for Northern Italy. This means that, on low-volume two-lane highways, macro-regional differences could have a measurable influence on crash frequencies. Anyway, since differences were noticed, calibration factors for AADT > 0,000 should be studied more in depth by increasing the number of the study sites, as long as the sub-group Central-Southern Italy High AADT is composed of a small number of road segments (). Generally, the further sub-grouping of data into more particular combinations of terrain and region led to small sample sizes of road segments. However, a reliable comparison (in terms of error and number of segments) can be made at the overall traffic scale between flat and rolling terrains in Northern and Central/Southern Italy. The difference between the two macro-regions

Colonna, Berloco, Intini, Perruccio, Ranieri, Vitucci 0 0 0 can be strongly attributed to the road segments belonging to rolling terrain types. Indeed, Cx values for rolling terrain types are:. ± 0. for Northern Italy and. ± 0. for Central/Southern Italy. Finally, some considerations can be made by looking at the results of the calibration study referred to the difference between administrative regions. The only Cx values considered as acceptable (for both estimated errors and number of road segments) belong to Puglia (only for the low AADT range), Calabria (only for the low AADT range) and Veneto. In particular, the calibration factor computed for the Puglia region, low AADT (. ± 0.) can be considered as the most reliable among the others, due to the large number of road segments (0) and the very low values of both the MAD index (0.) and the coefficient of variation (0.). As expected, its value is not so different from the Central/Southern Italy Cx (. ± 0.). This result shows that more precise estimates can be obtained by repeating the calibration process for each administrative region, if geometric, traffic and crash data are available for a large number of road segments. Where those results are not available, macro-regional calibration factor can be used. CONCLUSIONS A HSM SPF calibration study was performed by using a sample of Italian two-way undivided highways (collectors). The influence of traffic ranges, terrain types and regions on the calibration study was assessed. Main results are summarized as follows. Conducting SPF calibration studies without taking into account traffic variability could lead to significant errors in using the calibration factor. The computed calibration factors over the period: 00-0, for fatal and injury crashes only (KAB) for the nationwide Italian two-way undivided highways network are:. ± 0.0 for AADT < 0,0000 and. ± 0. for AADT included between 0,000 and,00. There are slight differences in the calibration factors computed for flat and rolling terrains. Calibration factors for road segments lying in flat terrains are greater than the factors computed for rolling terrains for the higher AADT range. There are noticeable differences in calibration factors computed for different Italian macro-regions. For the low AADT range, greater Cx values for road segments belonging to Northern Italy were found. Administrative region-based calibration factors could be meaningful if they are related to a significant sample of road segments for which traffic and crash data are available. This study applied recommendations about the HSM SPF calibration process and it assessed the influence of the considered variables. Independently from the area in which it was conducted, the study showed the importance of considering regional variability while carrying out the calibration process. In fact, some reliable factors were obtained at a more disaggregated level. They could be used by Italian practitioners in road safety-based decisions, at least until specific jurisdiction-based SPF have been developed, considering greater amount of data.

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