1. 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 Paper #:

2. 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.

3. 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

4. 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.

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

6. 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

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

8. 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.

9. 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.

10. 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.

11. 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

12. 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%

13. 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 

14. 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).

15. 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

16. 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.