DETERMINING ROAD SURFACE AND WEATHER CONDITIONS WHICH HAVE A SIGNIFICANT IMPACT ON TRAFFIC STREAM CHARACTERISTICS   Reza Golshan Khavas1 and Bruce Hellinga2 1,2 Department of Civil & Environmental Engineering, University of Waterloo Transportation research Board (TRB) Annual Conference January 2016 Paper #: 16-5819

INTRODUCTION Traffic micro-simulation models are widely used to evaluate the expected impacts of transportation network improvements, new traffic management policies, and use of new technologies. There is increasing interest in being able to use micro-simulation models to estimate the impact of the proposed improvement/policy/technology on travel time reliability and therefore there is a need to evaluate over the range of conditions expected throughout the year. In many areas, weather and road surface conditions are important source of the variation in traffic stream behavior, and therefore, should be captured within the modelling framework. This research develops a method to identify a set of weather categories and road surface conditions that best describes the different weather regimes that have a statistically significant influence on the traffic stream characteristics.  

PROBLEM FORMULATION Schemes of Categorization Consider a set of environmental factors (F1,…, Fn) such as type of precipitation, wind speed, road surface condition, air temperature, etc. Each factor Fi is quantified in terms of mi discrete levels (Lij, j=1,..,mi).Total number of unique categories is computed based on the following formula:   n: number of parameters mi: number of levels of parameter i Total Number of Categories

PROBLEM FORMULATION Schemes of Categorization We define a categorization scheme as the ordered sequence of the environmental factors in vector C. The number of schemes for n parameters is n!. To illustrate, consider three factors, F1, F2, and F3. There are six categorization schemes, as follows:   The category aggregation starts within initial category sets which are those categories in each scheme for which the parameter levels are equal except for the very last (most right) parameter.

PROBLEM FORMULATION Aggregate Categories Figure 1 - Category aggregation process in each scheme r

PROBLEM FORMULATION Measure of Effectiveness After finalizing the categories in the scheme r , RMSE as the measure of effectiveness is computed. The scheme with the smallest RMSE is determined to be the best categorization scheme.   RMSEr: root mean square error of scheme r u, q , k: speed (km/h), flow (vphpl), and density (veh/ln-km) respectively Xobs: observed value of traffic variable X Xest: estimated value of traffic variable X (the closest point on Van Aerde’s macroscopic speed-flow-density relationship) Xmax: maximum observed value of traffic variable X mr: number of categories in scheme r nj: number of observations in category j

APPLICATION TO FIELD DATA Study Area Figure 3 - Five-minute-aggregated station speed data for two randomly selected weekdays

APPLICATION TO FIELD DATA Considered Environmental Factors As a starting point to illustrate the methodology three environmental factors were considered in the analysis. 1. Road surface condition (RSC) (5 levels: dry, wet, chemically wet (CHW), ice watch(IWH), ice warning (IWN)); 2. Type of precipitation (3 levels: no precipitation, rain, snow); and 3. Diurnality (2 levels: day (sunrise to sunset), night (after sunset and before sunrise; excluding 11 pm to 5 am)). The proposed method can be applied with a larger number of factors and larger number of levels for each factor.  

APPLICATION TO FIELD DATA Possible Schemes Diurnality Road Surface Precipitation Day Dry Rain Wet Night Snow CHW IWH IWN Table 1 - All possible categorization schemes * * In Table 1, “No Precipitation” level is shown by the term “DRY” in precipitation parameter columns.

APPLICATION TO FIELD DATA Possible Schemes The number of categories resulting from the interaction of all parameters in each scheme is 30 (5×3×2).  Data set was parsed into 30 sub-sets – one for each categorization. The number of observations in each of the 30 categories is shown in Table 2. We can observe that for some of the categories there are no observations (e.g. Chemical Wet-Rain-Night) Also, we decided, somewhat arbitrarily, to require a minimum of 10 observations to calibrate Van Aerde’s model. This results in 21 categories for which Van Aerde’s model can be calibrated.  

APPLICATION TO FIELD DATA Field Observations RSC Precipitation Diurnality Number of Observations Dry No Precip. Day 34341 CHW Rain Night 9718 Snow 6 165 35 IWH 3952 95 3524 58 Wet 1396 592 410 314 254 37 IWN 161 57 138 23 487 255 11 Table 2 - Number of observations in categories

APPLICATION TO FIELD DATA Category Aggregation-First Iteration Figure 4 - Category aggregation for scheme 1 (first iteration) The first iteration of the category aggregation process is illustrated in Figure 4 for scheme 1. ANOVA has been conducted for each parameter (i.e. uf, uc, kj, and qc) in each category. Grey cells: categories that were excluded from the analysis because of insufficient observations Null hypothesis: all categories have the same population (are similar) Alternative hypothesis: at least one category is different. Significance level: 5%

APPLICATION TO FIELD DATA Category Aggregation-Next Iteration Compared Categories Traffic Flow Parameter Values   uf (kph) uc(kph) kj(vpkpl) qc(vph) Day Dry No Snow 112.4 93.8 61.6 1927.8 Snow 106.8 98.5 108.0 1753.2 ANOVA P-value 0.95 0.91 0.01* 0.65 Night Wet 110.3 100.7 76.6 1851.2 93.0 80.7 77.4 1369.6 0.00* 0.69 0.19 Table 3 - Examining the Differences between Newly Formed Categories 

APPLICATION TO FIELD DATA Final Scheme Categories Schemes 1 & 2 Schemes 3 & 4 Schemes 5 & 6 RSC Precipitation Diurnality CHW No precip Whole Day No Precip Day Dry No Snow Snow Rain Night All precip IWN No Rain IWH Wet Whole RSC10* RSC11*   Table 4 - Final categories in each categorization scheme As shown in Table 4 the schemes with the same highest-level factor (i.e. Fm in the vector of C= {Fm, Fn, Fk}), have the same set of final categories (i.e. schemes 1 and 2, 3 and 4, 5 and 6).

APPLICATION TO FIELD DATA Compare Schemes RMSE values were computed for all schemes (Table 5) It is observed that schemes 5 and 6 have the lowest RMSE values and are preferred over other categorization schemes.  Table 5 - Specifications and RMSE of the Categorization Schemes   Schemes Factor Order Number of final categories RMSE Scheme 1 Diurnality--->Road Surface---> Precipitation 13 191.91 Scheme 2 Road Surface--->Diurnality---> Precipitation Scheme 3 Precipitation--->Diurnality---> Road Surface 11 189.01 Scheme 4 Diurnality--->Precipitation---> Road Surface Scheme 5 Road Surface--->Precipitation---->Diurnality 16 186.95 Scheme 6 Precipitation---->Road Surface---> Diurnality

CONCLUSIONS The proposed method can be practically applied using field data to determine the optimal categorization of weather, road surface, and environmental conditions and the associated traffic stream characteristics. It is not necessary to represent all possible combinations of the weather, road surface condition, or environmental factors in the categorization because some of these combinations are associated with traffic stream characteristics that are not statistically different from the characteristics associated with one or more other categories. The aggregation of categories is a function of the order in which the weather, road surface condition, and environmental factors are considered within the categorization scheme. Consequently, it is necessary to consider all possible schemes and to have an objective means of selecting the optimal scheme. In the example application, the number of categories is reduced from 21 to 16 as a result of aggregation of categories which are not statistically different. It is recommended that the proposed method be applied to a larger set of data capturing conditions from multiple sites.