Road crashes and field rainfall data: mathema cal modeling for the Brazilian mountainous highway BR-376/PR

Recebido: 21 de novembro de 2020 Aceito para publicação: 10 de maio de 2021 Publicado: 2 de dezembro de 2021 Editor de área: Sara Ferreira ABSTRACT Recent studies analyze the influence of rainfall on traffic crashes, indica0ng that precipita0on intensity is an important factor, for modeling crashes occurrence. This research presents a rela0onship between daily-basis traffic crashes and precipita0on, from 2014 to 2018, in a rural mountainous Brazilian Highway (BR-376/PR), where field rain gauges were used to obtain precipita0on data. Data modeling considered a Nega0ve Binomial regression for precipita0on influence in crash frequency. Separate regression models were es0mated to account for the rainfall effect in different seasons, and for different vehicle types. All models analyzed presented a posi0ve rela0onship between daily rainfall intensity and daily crashes number. This can indicate that generally rainfall presence is a hazardous factor. Different cri0cal seasons for rainfall influence were also highlighted, aler0ng for the possible necessity of dis0nct road safety policies concerning seasonality. Finally, for the vehicle type analysis, typically, rainfall seemed to have a greater effect in lighter vehicles. Moreover, results are useful for traffic control, in order to increase safety condi0ons.


INTRODUCTION
In road safety study, there is a common perception that adverse weather conditions, such as rain and snowfall, favors the occurrence of traf ic accidents. In fact, several studies performed in expressways and/or urban freeways have found that these conditions play an important role in higher crash counts (Levine et al., 1995;Eisenberg, 2004;Keay and Simmonds, 2006;Bergel-Hayt et al., 2013). Precipitation as a variable, included in mathematical models, works as a proxy of other aspects that might be hard to quantify, identify or collect (Winston et al., 2006), such as visibility and road slipperiness. Hence, it is important that precipitation data is correlated spatially to accident information (Mannering and Bhat, 2014).
The use of local precipitation data (instead of data from pluviometric stations) is, therefore, more likely to provide a better correspondence of the effect that is actually veri ied in a highway. In fact, in association with traf ic detection systems, in ield rain gauges can be used to provide adequate estimates of a crash risk in real time. Other than that, adverse weather conditions can also create a situation in which there is an increased effect in traf ic disturbance, which is extremely important for traf ic monitoring and predicting crash behavior (Ahmed and Abdel-Aty, 2012).
The present work sought to develop a statistical model using in situ rainfall data (from rain gauges) and traf ic/crash frequency for a segment of the BR-376/PR Highway, in order to correlate accident frequency and weather conditions in a key Brazilian highway segment. In addition, two other models were developed to address the seasonality effect of rainfall and vehicle type response in crash occurrence.

BACKGROUND
Adverse weather conditions have been suggested in literature to prompt traf ic crashes. This correlation has been analyzed considering various aspects, on different countries.
For the primary Dutch road system, a mathematical model reported that 5% of the variation in crashes resulting in injuries could be explained by weather conditions (Hermans et al., 2006). Similarly, a research on crash occurrence in Connecticut (USA), found that the relative risk of an accident was roughly 40% lower in dry conditions, when compared to wet situations (Zhang et al., 2005). Rainfall is consistently associated with crashes by an increase in the number of accident records (Theo ilatos and Yannis, 2014). The volume of vulnerable drivers in the road is also affected by the weather effect, due to the change in number of trips, as well as in means of transportation choices (Martensen et al., 2016). In this context, a model developed for the contiguous USA, based on monthly and daily analyses (Eisenberg, 2004), found a pronounced positive rainfall relationship in the proposed daily models, while also identifying a negative effect in the monthly analysis, which, according to the author, may have occurred due to a lagged rainfall effect in crash numbers. Also, a study on accident frequency on a major transportation Highway in Taiwan (Chang and Cheng, 2005), stressed that traf ic volume and rainfall were indispensable factors determining accident frequency.
The seasonality effect has also been examined in studies evaluating precipitation and risk of crashes. Crash behavior in a mountainous Freeway (Zhang et al., 2005) had distinct effects for the combination of weather and road geometrics on dry and wet seasons, and the risk of accident in the wet period was 82% higher when compared to the dry season. Moreover, different effects may be observed when modeling rainfall and traf ic crashes: the rain effect may be less pronounced in the wettest season of the year, as reported for an urban Freeway (Keay and Simmonds, 2006), and a different effect of rainfall intervals could also be found in the four seasons. In contrast, a study on single vehicle crashes in an US Highway (Dabbour and Haider, TRANSPORTES | ISSN: 2237-1346 3 2019) indicated that in the wettest season crash risk was at its highest, and weather effect may not be a signi icant factor depending on the year of analysis. Another factor considered by traf ic research is the vehicle type. According to police reported crashes, incidents with light trucks were found to be more severe, in comparison to passenger cars (Grabler and Hollowell, 1998). However, few researches, if any, have examined rainfall effect in crash frequency with respect to vehicle type. Furthermore, it is noticeable that traf ic crash-precipitation studies usually rely on crash data for large road segments, sometimes even an entire State area (see Eisenberg, 2004), and combine this to regional weather stations data. Even though the contributions from research using this methodology are important, they could possibly lack spatial correlation, since regional climate effects may be present and signi icant variation in some areas can be observed. In addition, the majority of studies that correlate crash frequency with rainfall target urban expressways or freeways, whereas rural areas have been sparsely examined (see Theo ilatos and Yannis, 2014 for a thorough review on the subject).

Study Area
The study area ( Figure 1a) is located in the BR-376 Highway, Paraná State (PR), Brazil. It covers km 644+000 m to 680+000 m. This speci ic segment is at the "Serra do Mar", which is a mountain range with strongly undulated relief. The "Serra do Mar" is exposed to high annual average rainfall with prolonged periods of rain, with one of the largest volumes of rainfall in the country (Hasui et al., 2012;Vieira and Gramani, 2015;de Almeida and Carneiro, 2017). BR-376 Highway is one of the most important traf ic routes for Brazilian products and passenger transports. The area has strategic economic importance, since it connects the exporting and importing port area and the most industrialized and populated regions of the country (Hasui and Carneiro, 2012). Between 2009 and 2012 the BR-376 presented the highest numbers of accidents from all the Paraná highways (Sehaber, 2013). In its total extension, 17,429 accidents were registered involving 31,677 vehicles. In spite of this scenario, only one study (Sehaber, 2013) has described and analyzed accident behavior along the BR-376.
During the years of analysis used in the present study (i.e., 2014 to 2018), in the entire extension of the BR-376, 15,314 total crashes have been registered (PRF, 2018).

Precipita on Input Data
This study considered rain data from six rain gauges (RG1 to RG6) distributed along the roadway in two hydrographic basins, North and South (Figure 1b), from March, 2014 to September, 2018. These two areas are inserted in the "São João" River Basin. The precipitation data used herein is part of a research project related to monitoring of landslide risks in the area (Victorino, 2015;Ferreira et al., 2018;Trevizzoli et al., 2018, Silva et al., 2019. It would be possible to employ the rain data for each of the rain gauges in luence areas. However, this would result in too many regression models, thus making it very dif icult to analyze the outcomes. This issue was overcome by grouping areas of in luence that correspond to rain gauges that present similar recordings. An Analysis of Variance was performed comparing daily precipitation from each of the six rain gauges. The analysis indicated that data from RG1 and RG2 were similar in each other, while the same happened for RG3, RG4, RG5 and RG6 data. The formers' recordings also presented signi icant difference from the latter's; therefore, the two groups were determined: RG1 + RG2, (henceforth North Area); and RG3 + RG4 + RG5 + RG6 (South Area). Despite RG3 being located on the North hydrographic basin, the analysis indicated that data from this rain gauge is statistically more similar to the data from the South basin rain gauges (RG4, RG5 and RG6), thus the combination groups were not based on the hydrographic basins.
Daily rainfall data was categorized into six classes, according to the rain gauge register limit value and intervals based on quantiles (Xavier and Xavier, 1987;de Lima Leite et al., 2011;Souza et al., 2012;, Silva et al., 2020. In general, there were lesser days of moderate to extreme precipitation. The South Area registered more days, 98 and 23 days respectively, of these intense events. In the North Area, the days without registered rainfall (480 days) is also evidently greater than that registered in the South (344 days), while in the latter, in most of days (518 days) there was occurrence of drizzle (0.1 to 2.5 mm).

Crash Input Data
The crash data applied in this study was obtained in the public database from the Federal Highway Police (PRF, 2018), which provided information related to a total of 2,314 crash occurrences in a period of 1,490 days from March, 2014 to September, 2018. The number of crashes analyzed were registered in the segment of interest, which covers km 644+000 m to 680+000 m. The database has a complete description of each accident including location, date and time, road direction, road and weather conditions, day of the week, and accident severity. The main input from this database was the daily frequency of crashes.
The location was used to correspond the accidents count to either North (33.72 km extension) or South Area (38.96 km). In addition, vehicle type and date information were accounted for the type and seasons modeling. Other qualitative variables were not included in the analysis as they did not necessarily relate to the research's purpose. However, some of the unused qualitative factors were analyzed in previous work (Silva et al., 2020). It was demonstrated that in this area, adverse precipitation tends not to shape crashes characteristics, TRANSPORTES | ISSN: 2237-1346 5 such as location and severity. The absence/presence of rain, though, was found to be de ining to the crashes peculiarities. A summary of the data used in the analysis is presented in Table 1, separated in (i) areas (North or South), (ii) seasons (December, January and February -DJF; March, April and May -MAM; June, July and August -JJA; September, October and November -SON) and (iii) vehicle type (Light or Heavy).  Data from traf ic volume ( Figure 2a) comes from toll stations registers of "São José dos Pinhais" and "Garuva" municipalities, for North and South Areas, respectively. The register ranges from 2014 to 2018. Throughout the ive years, both areas showed a similar distribution of traf ic volume, with peaks above the average mostly between the end of December and January, which is mostly associated with Christmas and Summer holidays, as the highway connects the state capital and other cities to the Santa Catarina state coast.
The daily accident count is illustrated in Figure 2b, for North and South Areas. The South Area presents a higher average daily accident count compared to the North Area, with values around 0.92 and 0.65, respectively. Traf ic volume data of the highway (Figure 2a) was used to normalize the road accident count (Figure 2b).
The normalization approach was used to account for traf ic volume exposure. The detailed procedure adopted to carry out the normalization is described in section 3.4. As shown in Figure  2b, it is evident that in both areas there are expressive luctuations in traf ic volume during the years, with much greater traf ic during Christmas season.

Nega ve Binomial Model
In order to account for traf ic exposure, the model considered the application of a volumenormalized traf ic crash count. This consisted of applying Equation 1 to the available data.

=
(1) And: Equation 1) is the normalized crash count, C stands for the daily traf ic crash count, and V (Equations 1 and 2) is the volume normalization factor, calculated by dividing the daily traf ic volume (Vd) by the Annual Average Daily Traf ic (AADT). This same approach has been used by Keay and Simmonds (2006) and, as stated by the authors, it allows variations in daily volume relative to days of the week, as well as holidays, to be incorporated to the model.
The model was developed in the R environment. Initial trials of modelling took into consideration the application of a Poisson distribution (Ma and Kockelman, 2006;Li et al., 2013;Ye et al., 2013). However, the data did not meet the assumptions required, being over-dispersed. Thus, a Negative Binomial (NB) model (Eisenberg, 2004;Keay and Simmonds, 2006;Poch and Mannering, 2013) was chosen, since it is able to account for data dispersion. Its application in the present study can be described as shown in Equation 3.

= +
(3) Where Xi consists of the vector representing the explanatory variables on the highway segment and time period, and ε is the model error. It should be noted that ε has a gamma distribution (Hauer et al., 1988), which the mean value is 1 and has a variance of θ = 1/α 2 , with θ being de ined as the dispersion parameter. If θ can be assumed as 1, it shows evidence that NB model is preferable than the Poisson model. That was the case for every model presented herein, justifying the choice for NB methodology.
Concerning the explanatory variables, the decision criteria of whether a subset of independent variables should or not be added to the crashes estimation model consisted of an application of the Akaike's Information Criterion (AIC). The procedure started considering the model dummy variables for days of the week (DOW), Christmas period, Brazilian Calendar Holidays and Rain classes. If the Holiday dummy is removed, there is an improvement in the model itting, however the same did not happen when Christmas variable was left out, thus Christmas was maintained in the model. That is the same case for DOW when removed, hence they were also not removed. This procedure was not applied to the Rain classes' dummies, since these variables constitute the main interest of this work. Where αj is the model intercept, Mo (Monday) through Sa (Saturday) are dummy variables representing DOW (Mo equals 1 if it is a Monday, and 0 if another day), Tu through Sa follow the same de inition. The model does not include "Sunday" variable due to the linear restriction imposed on the fact that there are 7 days of the week, thus if there was a Su variable, it would always equal zero. Thus, the model coef icients β1 through β6 represent the day effect in the accident occurrence in comparison to Sunday. The same applies to the other variables representing Christmas, "X", and "Drizzle" through "Extreme", which are dummies that insert weather variables into the model, i.e., rainfall classes. In this case the coef icients β8 through β12 will dictate the difference in means from a rainy day (e.g., if it rained 5 mm, it will it in the Light dummy).
Finally, for overall goodness-of-it assessment, the approach selected was the evaluation of the deviance value, 2(LL(β)−LL (0)), which follows a squared-chi distribution (Agresti, 2003). The criteria consists of determining the model deviance, and compare that to the chi-square value corresponding to the degree of freedom of the model. A deviance value greater than the chi-square value should indicate that the evaluated model presents an overall adequate goodness-of-it in representing the data.

Accident Frequency Modeling
The relative coef icients for North and South Areas presented in Table 2 can be interpreted as changes in incidence rates for unit change in crash occurrence (Eisenberg, 2004). Hence, a coef icient of 0.01, for example, shows a 1% increase in accidents. Similarly, negative coef icients would mean a reduction in the crash count. The comparison for DOW dummies should be made with respect to Sunday, while for Precipitation, with respect to no precipitation occurrence (0.0 to 0.1 mm of daily rainfall). As mentioned, the deviance values were used in the determination of the model overall goodness-of-it. For both models, the chi-squared test of deviance values, North (deviance of 198) and South (deviance of 125), rejects the null hypothesis, thus con irming the data distribution has an adequate itting with respect to NB regression.
For the North Area model, all but Drizzle (0.1-2.5 mm) rain classes are signi icant to the model. Additionally, North and South Area coef icients show that with the increase of daily precipitation, a greater number of accidents followed, hence con irming this positive relationship on a daily analysis. For this area, rainfall dummies coef icients are positive, showing that in any precipitation condition (rainfall greater than 0.1 mm) accident frequency is increased. For daily rainfall greater than 50 mm, an increase of 6% would be expected, when compared to a dry day. Very similar result checks for the South Area model, where all precipitation coef icients were signi icant. Moreover, all rainfall coef icients present a consistent growth with the increase in the rain intensity. As in the North Area model, no negative (4) rainfall-crash frequency relationship was found. In general, the rain effect observed in the South Area is smaller than that observed for the North Area. Despite the lack of signi icance of some DOW dummies for the model, an important insight is that in all days that were presented in Table 2 (i.e., from Monday to Saturday), there is a tendency of greater crashes number than that would be veri ied in a Sunday. Friday and Saturday would be the most critical days in terms of increased accident risk. As abovementioned, the positive association between precipitation and crash frequency is consistent with previous reports. A model developed for crashes occurrence in a mountainous freeway in the Colorado state of the USA (Yu and Abdel-Aty, 2013) found that risk of crash is greater on weekends (Saturday and Sunday), and weekend crashes are more likely to happen under conditions of smooth traf ic low, with no speed variations.

Seasonal Effect in Accident Frequency Modeling
Eight models of daily accident frequency were estimated in order to quantify the effect of rain in each season, with four models for each segment. In these models, all variables from Equation 4 were included, with the exception of the Christmas variable, since it would appear only in the DJF period (Southern hemisphere summer). Although a few insights would follow from including the DOW dummies in the Seasonal model, only rainfall coef icients were added to this analysis, focusing on the effects of weather conditions throughout the year. The same procedure as for the DOW analysis was performed for goodness-of-it on Seasonal effect model. Since all models presented overall adequate goodness-of-it, this information was omitted from Table 3, to avoid data overcrowding. Similarly to what was found in the entire year analysis, there was a distinct seasonality effect in the North and South segments. First, for the North Area, Drizzle intensity was reported as non-signi icant, which is coherent with the entire period model. Hence, no matter the time of the year, this range seems not to be of considerable effect in the risk of crash for the North Area. In contrast, the other classes are signi icant. Coef icients show that DJF (i.e., summer) season is the most critical in terms of rainfall in luence in crashes, with an increased risk of up to 10% (for Extreme precipitation).
In fact, for all rainfall classes, summer is the season where rainfall substantially in luences crash frequency. This is generally the wettest season, and it could have been expected that drivers would be more careful at this time of the year (Keay and Simmonds, 2006;Mannering and Bhat, 2014). Nonetheless, that was not observed for this particular area. It is deduced that the reason for this is because the segment consists mostly of streamline extensions, or light curves, without accentuated curves or high road grade, which possibly gives the drivers a false impression of safety. However, for other seasons it seems that there is no clear tendency of a more critical period or intensity that outstands in affecting crash frequency.
In parallel, the South Area presented generally lighter rain effect than the North Area. The greatest contrast here is that JJA (i.e. winter) season was the most critical, with up to 7% more crashes at Extreme precipitation. Summer, however, was the season with less expressive effects. This highlights the importance on segmenting the region for the analysis. The South Area has greater grades and an increased incidence of curves with large degrees (Figure 1b), and the segment also contrasts with North in terms of radars and maximum speed, as it has a higher number of speed radars (three), and higher maximum speed allowed (80 km/h). These are some of the underlying factors that might be shaping the difference between the two study areas.
Another possible explanation for that is the evidence that the degree of curvature may have a negative relationship with accidents (Anastasopoulos et al., 2008). This is an indication that segments with sharper curves could be in safer conditions than those where curves are latter. In concern to the South Area seasonal model, the increased presence of sharp curves may have resulted in the reduced rainfall effect. It's likely that the sharper curves make drivers more aware and/or that they compensate for the increased risk by driving more slowly, resulting in lower accident rates (Anastasopoulos et al., 2008).
The effect of seasonality on crash risk under rainfall conditions for an urban freeway in Melbourne, Australia (Keay and Simmonds, 2006) indicated that for the wettest season, spring, the precipitation in luence on accident risk was reduced when compared to the other seasons. This observation is coherent to the results observed in the South Area of the present study, in which for the wettest season (Summer), rainfall effect on crash frequency was reduced in comparison with other seasons. A previous study model on a mountainous area (Ahmed et al., 2012) suggested that high precipitation and speed variation were factors that caused increased crash risk; and unexpectedly, in the dry season, low speeds together with low visibility increased the odds of accident occurrence. Hence, the interaction of weather and traf ic variables was different in the two seasons, indicating distinctive combined factors.

Vehicle category effect in accident frequency modeling
Four models of daily accident frequency were estimated in order to investigate the rain effect in two categories of vehicles: light and heavy vehicles. This division was based in the Brazilian traf ic code (Brasil, 2008). In summary, motorcycles, automobiles and others, such as carriages, are considered "light" vehicles. Trucks (articulated and non-articulated) and buses are categorized as "heavy".
As presented for the seasonal modeling, DOW coef icient and goodness-of-it results are also omitted from the table, since overall values were adequate. It is possible to identify that in the North Area rain is a more signi icant factor for light vehicles, but also has an expressive in luence in heavy vehicles (see Table 4). As for the other models, Drizzle was not signi icant for light vehicles, however the same does not happen for heavy vehicles, where there was a 2% increase in crashes. For the South Area, light vehicles consistently showed an increase in crashes followed by higher rainfall classes, with plus 7% accidents for Extreme precipitation. The results for heavy vehicles in this area, though, are remarkable. All precipitation classes' coef icients were encountered as non-signi icant. Hence, they seem to have minimal impact in explaining crash frequency, suggesting that factors other than rainfall are shaping accident frequency in the extension of South Area for this vehicle category.
In order to address the reason behind the non-signi icance of rain regarding the South Area, an accident type analysis with respect to heavy vehicles was key. We bring the analysis of the two accident categories, involving heavy vehicles, which are the most frequent in each of the two areas. The irst category is "runway exit", which in the North Area corresponds to 49% (104) of total heavy vehicles accidents. Meanwhile, in the South Area this category represents a lesser proportion, of 33% (192) of the total heavy vehicles' crashes.
The second category is overturning. While in the North Area, 25% (53 in absolute numbers) of total accidents involving this vehicle category is "overturning", in the South Area, 43% (212) accidents it into this crash type. In addition, the total crash number for heavy vehicles veri ied in the South Area are 171% greater than the North Area total numbers (576 for South Area, compared to 212 for North Area). This information can be analyzed in relative and absolute terms. Although the herein developed model did not included geometric characteristics, they can be qualitatively included in the discussion. The South Area has not only a greater number of horizontal curves, but also sharper ones. These are likely inducing the accidents in the overturning category (which, as mentioned, is the area's most common accident type for heavy vehicles), whether or not rain is present. In turn, in the North Area, there are fewer heavy vehicle accidents in absolute numbers, along with runway exits holding the greatest number by accident types. Since this kind of accident is directly related to road slick, and rain presence and/or intensity is crucial in determining slipperiness, the model is capturing rain as un underlying factor (a model signi icant factor), causing the runway exit accidents in the North Area, while in the South Area it could not be captured (i.e., not signi icant), likely due to overturning preponderancy in the crashes. Analysis of previous literature showed that vehicles most affected by rainfall are from nonwork-related travels (i.e. leisure) in automobiles (Bijleveld and Churchill, 2009). In addition, single vehicles accidents seem to be the ones most affected by weather (Satterthwaite, 1967). With respect to the behavior of accidents with heavy vehicles, a signi icant factor that can imply greater crash numbers is wind. A previous study indicated that in wind-induced accidents that resulted in injuries and/or fatalities, only 27% of vehicles involved were light vehicles, with the majority of accidents involving taller, heavier vehicles (Baker and Reynolds, 1992). Moreover, the most common accident for this type of vehicle is overturning, induced by their broader area of contact with the wind. Additionally, for a speci ic highway segment, other variables affecting heavy vehicles accidents frequency are the average daily traf ic, the percent of heavy vehicles in traf ic, and the difference in speed between heavy and light vehicles (Joshua and Garber, 1990).
Logistic regression models were previously used to explore the probability of involvement in a truck crash on road segments with negative grades, i.e., downgrade (Momen et al., 2019). In clear weather this probability was reduced when compared to the adverse condition, con irming the positive effect that unfavorable weather has in increasing crash occurrence.

Remarks from Accident Frequency Modeling
The models developed in this work aimed at interpreting and correlating time-course of rainfall variations on BR-376, therefore the intrinsic characteristics of the highway (such as geometrics) were not considered for this speci ic analysis as it does not correspond to the research's aim. The literature indicates that conclusive research on rain effect on crashes can be built, in spite of the absence of space related characteristics, which include geometrics, pavement surface, and others (Eisenberg, 2004;Keay and Simmonds, 2006;Mannering, 2014). Also, the implementation of rainfall data obtained in situ for each of the regions of interest in this study is of great relevance to address particularities of the segments of the Highway.
In addition to the models presented, there was an attempt to develop a model to evaluate the effect of rainfall in crashes with distinct injury severity using separate samples, just like for vehicle classes. However, this analysis did not it in a NB regression model. Opportunities for further research include exploring the relationship of severity/injury with rainfall variables, while also considering new methodological approaches. Other factors could be investigated, such as driver's gender, age, type of accident and downgrade/upgrade distinction. Policy lessons can be drawn from the results here presented, which can be useful not only for governmental traf ic management agencies, but also to highway concessionaires.

CONCLUSIONS
This study presents a daily accident frequency modeling based on a NB regression, focusing on local rainfall effect, with precipitation data provided by in-ield rain gauges. In this speci ic area of the BR-376, no past research has explored the effects of precipitation in traf ic crashes numbers.
The method considered two separate geographical areas (North and South), where three models were built. Results from all models consistently showed that rain seems to be a signi icant factor in accident frequency, and that under rainfall conditions crash frequency tends to be higher. Moreover, when the road is subjected to greater rain intensity, there is a tendency of steady increase on the number of crashes. In the seasonal analysis, rain presence and intensity affected positively crash numbers for the two geographical areas modeled. Nevertheless, the two areas indicated different critical seasons, in terms of rain in luence. For the North Area, summer was the period in which rain mostly affected the crash frequency, whilst for the South, winter seemed to be the season in which that occurs. For vehicle type analysis, strong rainfall in luences in crashes numbers for both light and heavy vehicles in the North Area. For the South Area, the same effect was found only for light vehicles, whereas rain presence/intensity seemed to be a non-signi icant factor for heavy vehicles, which we suspect to be linked with the crash type (majority overturning in the South Area).
Rainfall should raise an alert to safety agencies, as well as to road management, since greater accident number is expected. Management should consider implementing traf ic signs indicating increased accident risk in a rainy situation, and speci ic actions can be taken for each of the regions analyzed when considering the most critical seasons. These actions could be applied for the entire year, but more locally speci ied, since in the South Area the biggest concern seems to be during winter, while for the North Area, summer appeared to be the most critical period of the year.