4. Methodology
This section presents the overall conceptual framework for capturing weather effects in a DTA model, representation of weather data, and the principal supply-side elements that would affect the representation of adverse weather effects on traffic flow propagation and system performance. The demand-side elements that determine user responses to weather and related information and control measures are also presented.
4.1 Conceptual Framework
Capturing the effect of adverse weather on traffic patterns entails both supply side and demand side modifications to existing dynamic traffic assignment (DTA) tools. These weather-related elements and their interaction with current DYNASMART functionalities are shown in Figure 4 1 (Dong et al., 2010a). In this study, we mainly focus on two elements, namely, weather impacts on supply-side relations and parameters and user response to weather information and control actions.
Figure 4-1. Demand- and Supply- Side Impacts of Adverse Weather
4.2 Weather Data Representation
Several TMC's across the nation, especially in flood-prone areas (e.g. Houston/Harris County's TranStar TMC) are now connected to weather information and forecasting systems. A suitable interface system could help a TMC obtain weather data automatically and simultaneously in real-time from weather stations. The required weather-related inputs for traffic estimation and prediction purposes will be the type, severity and duration of a particular weather condition, and the geographic area influenced by the reported/predicted adverse weather. The specific configuration of the communication architecture and media from weather stations to the TMC is not especially problematic, from the standpoint of real-time performance, because weather data is usually updated only every hour or so, and does not generally fluctuate every minute.
The weather data can be queried from well-established organizations measuring, recording and storing temperature, dew point, wind, altimeter setting, visibility, sky condition, precipitation, and so on. In particular, precipitation type, precipitation intensities (inch/h) and visibility readings (mile) were used in previous studies, including the FHWA Report (Hranac et al., 2006). Therefore, three link-specific weather parameters can be specified through the GUI (Graphical User Interface) or input file, that is, visibility, rain intensity and snow intensity. The default values of these parameters correspond to clear weather conditions. Based on the regional weather conditions, the user could modify all or some of the weather parameters of the links within the impacted area. This will then allow incorporating the effect of the specified inclement weather condition on the estimated/predicted traffic patterns. The procedures devised to capture this impact are discussed next.
4.3 Modeling Weather Impacts on Supply Side Relations and Operational Parameters
The principal elements in the simulation that would be affected by adverse weather, and hence may provide a mechanism for capturing weather effects on traffic patterns, include the following:
- Speed-density model for freeway sections (and ramps) Both the functional form and the parameter values (free mean speed, jam density, breakpoints for multiple regime models) may be affected by weather, and may be affected differently by the characteristics of different weather instances. The above-mentioned FHWA report (Hranac et al., 2006) summarizes changes in the so-called fundamental diagram observed at a limited number of locations (e.g. Twin Cities, Minnesota).
- Speed-density model for signalized arterials and unsignalized approaches Empirical evidence collected through the calibration experience with DYNASMART in various cities strongly suggests different functional forms for the speed-density relations for arterials than for freeways. For instance, the latter exhibit distinct multi-regime features that are not present in arterial data. In addition, there is considerably more variation in both functional form and parameter values for arterials than for freeways.
- Service rates and section capacities for freeways and ramps It is not well understood in the traffic simulation community that service rates and capacities play at least as important a role as the speed-density relation parameters in governing traffic flow under highly congested conditions, when queueing phenomena become critical in determining traffic propagation. Hence specifying these parameters correctly is an essential aspect of calibrating these models. Such parameters will naturally be affected by weather of varying characteristics. Reductions ranging from 5% to 35% have been reported in the literature, and provide a starting point for the modifications addressed in this study.
- Saturation flow rates, section capacities and turning service rates at signalized junctions Under normal weather condition, the default values of saturation flow rates are consistent with accepted highway capacity manual practices. Yet, these values will be dramatically affected by inclement weather conditions.
- Saturation flow rates and operational parameters at unsignalized junctions Controls at unsignalized junctions include yield signs, stop signs and roundabouts. Weather effects on these facilities are likely to be of greater magnitude than at signalized intersections given the reliance of unsignalized junctions on human interaction in sharing the right of way, which becomes more difficult under adverse weather.
- Operational characteristics associated with incidents and their impact Adverse weather magnifies the impact of traffic incidents, increasing their severity and possibly their duration as well. It is suggested that higher severity, longer duration, and possibly greater frequency of occurrence, be used in devising incident scenarios under adverse weather.
- Operational characteristics of work zones and other special events Work zones typically affect the maximum speed as well as the capacity of the directly affected sections, as well as those that carry traffic in the opposite direction for certain work zone geometries (see DYNASMART-P User's Manual, Mahmassani et al., 2006). Given the significance of weather events that occur in conjunction with work zones in most parts of the country, it would be important to revisit the entire approach to modeling work zones in order to enable better representation of traffic flow in and around work zones under adverse weather conditions.
The inclement weather impact on each of the above-mentioned parameters can be represented by a corresponding weather adjustment factor (WAF), as follows:
where
F1 weather adjustment factor for parameter i
v = visibility
r = precipitation intensity of rain
s = precipitation intensity of snow
β0, β1, β2, β3, β4, β5, β6 = coefficients
The parameters are adjusted accordingly if a link is specified as an impacted link. Namely, if link a is impacted by inclement weather that is characterized by (v, r, s), a set of WAFs can be calculated for link a based on Equations (4 1) and (4 2). Therefore, all the parameters can be adjusted by the corresponding WAFs. For example, the saturation flow rate under inclement weather is represented as follows:
where
fi' = saturation flow rate under inclement weather
Ff1 = weather adjustment factor for parameter
fi = saturation flow rate under clear weather
Therefore, this representation offers a flexible approach to capturing weather effects on traffic flow propagation, allowing sensitivity to a wide range of conditions, and capability to characterize varying types of traffic behaviors under adverse weather conditions.
4.4 Modeling Demand Side Behaviors and Parameters
The demand side dimensions and parameters that determine how traffic patterns may be affected by adverse weather consist of two principal categories: (1) those that affect the dynamic OD pattern in the network, and (2) those that affect the distribution of flows in the network, especially in response to information and/or various traffic controls. Hence, changes in destination, departure time or trip cancellation (and, if dealing with a vehicle rather than person OD pattern, changes in mode choice as well) would be reflected in the dynamic OD pattern. On the other hand, route diversions in response to information, route choice decisions based on pre-trip or en-route information, response to various advisory messages and the like would be in the second category. While, of course, we can view the first category as resulting from individual decisions as well, modeling such mechanisms directly would be considerably more complicated (and require a much richer, and unfortunately lacking, empirical survey basis) than trying to capture their net result by inferring the dynamic OD pattern.
(1) Changes in dynamic OD pattern
One of the advantages of an on-line system is its ability to adaptively estimate and predict OD and associated flow patterns as the latter are unfolding. The hybrid Kalman Filter approach with structural temporal effects developed for DYNASMART-X (Mahmassani and Zhou, 2005), along with the consistency checking and updating modules, are intended to capture changes in dynamic OD patterns resulting from weather-related adjustments in tripmaking. As such, both the overall levels of demand, their distribution across OD pairs as well as over time should be captured by the existing system. The main limitation today is that the traffic models may not capture traffic propagation correctly under adverse weather, hence introducing a potentially important source of error in the overall estimation and prediction process (which will affect the OD predictions as well since the latter are linked to the observed measurements through the DTA model and resulting link proportion matrix).
In addition, user response to pre-trip or en route information would also affect dynamic OD pattern, including: (1) Leaving earlier or later; travelers might adjust their departure times due to inclement weather, that is, the decision to leave earlier (e.g. returning home on a day when bad weather is forecast) or later (e.g. waiting out a bad storm). (2) Real-time mode choice; like departure time choice, real-time mode choice is a pre-trip decision that considers weather-related measures in the context of Integrated Corridor Management (ICM) strategies. (3) Trip chaining and tour alteration; adverse weather may lead to changes in the sequence of stops along a tour, or may lead to adding or deleting stops, e.g. when stopping unexpectedly to pick up a child at school early in anticipation of a bad storm.
(2) User responses to information and control measures
This category of demand side phenomena is of critical importance to the ability of DYNASMART-X to serve as an effective decision support tool for traffic management under adverse weather conditions. The principal types of decision situations include the following:
- Response to variable message signs
New message types and their attributes are introduced in DYNASMART, as well as the behavioral rules that govern the responses to these messages, taking into consideration the attributes of the driver. Note in this regard that the mesoscopic modeling approach adopted in DYNASMART is especially well suited to this type of representation. The fact that individual decision entities are retained in the simulation effectively gives the model the same capabilities as a microsimulation tool from a travel behavior decision standpoint.
- Route choice under adverse weather and related information
A new attribute associated with weather-related risk is included in the generalized cost. Users with varying degrees of risk aversion would choose their routes accordingly. Therefore, the criteria for the driver's route choice include monetary cost, travel time and travel penalty (due to low visibility, or precipitation). Accordingly a generalized cost is specified in Equation (4 3) to reflect these attributes:
where
GC = generalized cost [$]
c = monetary cost [$]
t = travel time [min]
p = travel penalty due to adverse weather [min]
β0, β1, β2 = coefficients [-, $/min, $/min]
The coefficients indicate the relative importance of travel time, cost and weather condition. The value of time is expressed as
.
Similarly, travelers' valuation of weather impact is defined as 
,
that is, the traveler's risk taking regarding the adverse weather conditions;
by default, 
.
Therefore, the generalized travel time can be expressed as follows: 
where
GT = generalized travel time [min]
αVOT = value of time [$/min]
αp = risk taking preference [-]
4.5 Traffic Advisory and Control Strategies
When the estimation and prediction for a given horizon is completed under inclement weather, the predicted information provided by DYNASMART-X can form the basis for intervention by operators at a TMC, in the form of traffic control actions or advisory/mandatory guidance for drivers. If necessary, such actions or strategies can be disseminated to drivers through VMS or other media to alleviate road weather impacts. This section discusses the traffic advisory and control strategy features in the DYNASMART program.
4.5.1 Traffic Advisory-ATIS & Variable Message Signs
By use of the predictive travel time provision feature of DYNASMART, the weather/travel information dissemination interface allows selection of one or more paths for specified origin and destination pairs, and provision of predicted travel times for every prediction time interval under inclement weather. Travelers could therefore choose their departure time and/or route based on the predictive information.
In addition, roadside VMS plays an important role in en-route weather warning and route guidance. Field studies (Luoma et al., 2000; Rämä, 2001) have shown that weather advisory VMS can help decrease the average speed as well as the variance in speed so as to increase safety and reliability experienced by the traveling public. Weather VMS also proved most effective when adverse weather and road conditions were not easy to detect. Weather advisory VMS, in the form of slippery road condition signs and fog (low visibility) signs, are in use in various places around the world. For example, in Finland, slippery road condition, implemented in combination with the minimum headway sign, decreased the mean speed by 1.2 km/h with steady display and by 2.1 km/h when the sign was flashing (Rämä, 2001). Hogema and van der Horst (1997) showed that the Dutch fog warning signs, implemented in conjunction with variable speed limits, decreased the mean speed in fog by 8 to 10 km/h (i.e. 5 to 6 mph). Cooper and Sawyer (1993) found that the automatic fog-warning system on the A16 motorway in England reduced the mean vehicle speed by approximately 3 km/h (i.e. 2 mph).
In DYNASMART, two types of weather warning (advisory) VMS are implemented (Dong et al., 2010b): (1) Speed reduction: a VMS warning sign, indicating low visibility (e.g., fog) or slippery road (e.g. rain and snow), would generally reduce the speeds of the traveling public. Therefore a speed reduction value is specified, for this type of weather VMS, to capture travelers' response to the weather warning. The default values, for different types of adverse weather conditions, are set based on the field studies in the literature, discussed earlier. (2) Optional detour: a weather warning sign could also suggest that travelers reevaluate their current route if it passes through a certain area impacted by adverse weather events. Travel penalties, indicating the added delays caused by adverse weather, are specified for the impacted links. Travelers who respond to this type of VMS would take into account the adverse weather penalty in their route choice decision, that is, the penalty will be included in the generalized cost, discussed in the previous section.
4.5.2 Control Strategies
Control strategies include evacuation or diversion under extreme conditions (e.g. severe winter storms, hurricanes and floods), traffic signal control, and Variable Speed Limit displays.
1. Mandatory detour VMS
The mandatory detour VMS advises drivers of lane closures, and mandates all vehicles to follow some user-specified sub-path in the vicinity. This type of VMS is also used to inform drivers of extreme weather conditions and mandate all vehicles to detour, when a certain area or road is closed due to safety concerns. This can be achieved in the DYNASMART program by specifying an incident with 100% capacity reduction on the impacted links. A mandatory detour VMS could be specified upstream of the closed road to advise travelers of a detour path.
2. Weather-responsive signal timing plan
Martin et al. (2000) modified signal timing plans to improve traffic conditions under inclement weather. Several types of events may occur that require changes in prevailing signal times. Weather is such an event; signal timings maintained by traffic controllers in the field, say in a particular weather influence area, may be replaced with a priori prepared adverse weather signal timings. To this end, DYNASMART-X is able to read and implement signal timing plans that are available in real-time.
3. Variable speed limits
VSL utilizes traffic speed and volume detection, weather information, and road surface condition technology to determine appropriate speeds at which drivers should be traveling, given current roadway and traffic conditions. These advisory or regulatory speeds are usually displayed on overhead or roadside variable message signs (VMS). VSL systems are already being used as part of incident management, congestion management, weather advisory, or motorist warning systems to enhance the safety and reliability of roadways (Robinson, 2000). VSL messages are sometimes displayed alongside the weather advisory VMS to inform travelers as well as promote traffic safety, such as on the interurban Highway E18 in Finland (Rämä, 1999).
In DYNASMART, VSL is implemented to regulate the speed of the impacted links/areas under adverse weather conditions (Dong et al., 2010b). The speed limit posted may be adjusted based on prevailing weather conditions and a look-up table. In each look-up table, one or more weather conditions are specified, as well as the corresponding speed limit reductions. For instance, on E18 in Southern Finland between Kotka and Hamina speed limits are set as 120 km/h (74 mph) for good road conditions; 100 km/h (62 mph) for moderate road conditions; and 80 km/h (49 mph) for poor road conditions (Rämä, 1999). Similarly, on the Snoqualmie Pass section of I-90 in Washington State, the speed limit posted is reduced from 65 mph, in ten-mph increments, to 35 mph depending on visibility and weather severity, obtained from multiple weather stations, snow plow operators, and the state patrol (Robinson, 2000). The intent in DYNASMART is to be able to evaluate the response of users to such strategies, and incorporate their effect on predicted conditions.