Analytical Procedures for Determining the Impacts of Reliability Mitigation Strategies (2012)

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229 A p p e n d i x e Weather varies by time and locations for which there are no actual data sources. Consequently, the weather data used for these analyses were obtained from publicly available records collected from the National Oceanic and Atmospheric Administration (NOAA) weather station at SeaTac Interna­ tional Airport. Data are reported once per hour by NOAA, unless weather is severe or changes dramatically, in which case it may be reported more frequently. The analytic data­ base created for this study tracked the major statistics reported by NOAA, including the following: • Visibility 44 Up to 10 miles; • Temperature 44 Dry bulb; • Wind speed 44 Average speed, and 44 Gust speed (highest gust speed that hour); • Precipitation 44 Inches; and • Weather type 44 Rain, 44 Mist, 44 Thunderstorm, 44 Drizzle, 44 Haze, 44 Snow, 44 Freezing, 44 Small hail, 44 Hail, 44 Ice pellets, 44 Squall, and 44 Fog. The research team acknowledges that these data are limited because they are provided only once per hour and they do not cover microclimates over a large region. For example, it may be raining at SeaTac, south of Seattle, but not on the SR 520 bridge. However, the team chose the SeaTac station as the most reliable and consistent of regional weather data sources. In addition, the data were too detailed for the basic analy­ ses intended for this study. Consequently, the team performed extensive analyses to determine the types of summary weather statistics that would effectively indicate whether weather con­ ditions contributed to congestion. The outcome of those tests, which are summarized below, was to define bad weather most commonly as any period in which any measurable pre­ cipitation had fallen at some time in the previous hour. Importantly, the use of this indicator discounted several weather effects, including wind, fog, snow, and rainfall inten­ sity. The analysis of wind effects is given later in this appen­ dix. However, because the original weather data are retained within the Washington State Transportation Center’s L03 data sets, they were available for both the analyses described below and for future analyses, should other researchers desire to use them. Attempts to Compute a Summary Weather Variable The complexity of the various weather conditions led the pro­ ject team to test various approaches to dealing with weather in the cause of congestion analyses. One of the initial efforts involved attempting to convert the various weather statistics available into a single, categorical weather variable that could be used as an indicator of bad weather. Considerations When Developing a Composite Weather Variable One of the initial concerns with using the SeaTac weather records was that those records only provide a good measure of weather conditions at the airport. The weather experienced Summary of Weather Data Tests: Seattle Analysis

230 simultaneously in other areas of the Seattle metropolitan region can be different. For example, a storm moving north­ ward that affects SeaTac at 5:00 p.m. will have occurred in the southernmost roadway sections before 5:00 p.m. and in the northern part of the city some time after 5:00 p.m. These temporal and spatial shifts are particularly impor­ tant when trying to examine the effects of heavy, but short­ duration, rainfall events. Conventional regional weather station data simply do not provide the temporal and geo­ graphic resolution required to observe these effects, but because regional weather station data are routinely avail­ able around the country, using these data means the SHRP 2 analysis can be more readily replicated in other parts of the country. Another aspect of the differences between site­specific weather events and those recorded at a weather station is that the example storm above may have dropped exactly 0.25 inches of rain at the airport, but it may have deposited only 0.1 inch south of the airport, and 0.5 inches in areas north of the airport. Therefore, although the rain data are a reasonable estimate of weather conditions, they cannot be used as a pre­ cise, highly accurate measure of the actual weather occurring on any given segment of roadway during a specific 5­minute interval. In addition to the basic time and geographic problems noted above, the snow and rainfall intensity variables pre­ sented a second problem in that many of the effects of precipi­ tation occur after the precipitation has fallen. This is especially true for snowfall, as the effects of the snow falling are not nearly as significant as the effects from snow accumulations on the ground, depending on the amount remaining on the roadway. Snow flurries have little effect on driving, but 4 inches of snow on the ground 2 hours after the snow has stopped falling has a major impact on roadway performance. Another issue associated with snowfall in the Seattle area was caused by a combination of how rarely snow falls in the region and how travel times are computed. When snow falls (and sticks), Seattleites tend to avoid driving whenever pos­ sible. The region does not routinely use salt to deice road­ ways. As a result, most cities do not clear snow as effectively as those in regions of the country that routinely experience snowfall, and snow is frequently turned into sheet ice on the roadways by cars that do travel, making the area’s hilly terrain dangerous. The result is that a large percentage of travelers simply avoid going out. Therefore, after snow falls, volume and lane occupancy are frequently low on the freeways, despite the relatively slow speed of those cars that are present. How­ ever, the loop detector system only sees low volumes and low occupancy values and may thus overestimate the speeds at which the vehicles are moving. Finally, for this study, the number of days on which snow fell or heavy thundershowers occurred during the analysis year was small. Tests of a Single Composite Weather Variable The initial attempt to compute this variable tried to create a four­category variable with the following definitions: • 1 = good; • 2 = mediocre (minor weather conditions exist); • 3 = bad (moderate weather conditions exist); and • 4 = very bad. The detailed definitions of these conditions were as follows: • 1 = everything else (dry, clear); • 2 = at least one of these weather elements is present: rain, mist, thunderstorm, drizzle, or haze. This definition was meant to represent a situation in which the pavement is wet or may still be wet, meaning that spray may be an issue; • 3 = at least one of these weather elements is present: wind speed >20 mph or precipitation >0.125 in.; and • 4 = at least one of these weather elements is present: snow, freezing, small hail, hail, ice pellets, squall, visibility <0.25 mile, or minor weather conditions with a temper­ ature <33°F. For the initial test, the weather value was reset to one at mid­ night of each day, and remained at that value until weather conditions occurred that set the weather statistic to a higher value (i.e., weather became worse than previously indicated). The weather value would then be set to that higher number, and would remain there until weather conditions worsened, or the end of the day was reached. One major limitation with this approach was that it did not allow conditions to improve as the day progressed. For example, it is well known that wet roadways dry off as the day progresses if additional rain does not fall. Consequently, a second iteration in the testing of a categorical weather variable attempted to gradually reset the weather variable. A literature search identi­ fied various drying factors for roadways, but they required far more detailed geometric and temperature information than that which was available to the project team. A variety of time­ based drying adjustments were tested. The final version of this categorical variable based the value of that variable on the worst condition measured during the previous 2 hours. The project team also tested 1­, 4­, 6­, and 8­hour periods. In the end, this approach was abandoned. The primary issue was that a 4 rating frequently did not produce travel conditions that were worse than those produced by a 3 rating because a snowy hour as defined by NOAA did not affect travel time as much as a windy or heavy rain hour did. Simi­ larly, a windy or heavy rain hour was often not worse than a rainy hour. For example, the mean travel time for p.m. peak travel times on the SR 520 Seattle westbound analysis

231 segment when the past 2 hours was set to 4 (severe = snowy) was 612 seconds, but the mean travel time for the same time period was 676 seconds when the variable was set to 3. Simi­ larly, on the SR 520 Redmond westbound test segment, the mean travel time for Condition 4 (snowy) was 350 seconds, but the mean travel time for Condition 3 was 408 seconds, and Condition 2 was 416 seconds. Further tests showed that determining which variables had the most impact on roadway performance and should be used to determine the various degrees of bad weather in a categori­ cal weather variable was a task beyond the ability of the research team, within the greater context of analyzing the causes of con­ gestion. It was consequently decided to concentrate on the major types of weather conditions independently. The main weather variables carried forward to the next set of analyses were • Rain = 1 if NOAA weather type of rain (RA), mist (BR), drizzle (DZ), thunderstorm (TS), or haze (HZ) was reported for the most recent time period (0 otherwise); • Heavy_Rain = 2 if rain as defined above with NOAA hourly precipitation was >0.125 inches (0 otherwise); • Wind = 3 if NOAA wind speed greater than 19 mph (0 otherwise); • Snow = 4 if NOAA weather type of snow (SN), freezing (FZ), small hail (GS), hail (GR), ice pellet (PL) or squall (SQ) was reported for the most recent time period (0 otherwise); • Fog = 5 if NOAA weather type of fog (FG) or NOAA visi­ bility <0.25 mile (0 otherwise); • Wind Speed = Wind speed (in knots) directly from NOAA data for the most recent time period reported; • Wind Gusts = Wind speed for gusting winds (in knots) directly from NOAA data for the most recent time period reported; • Precip_hour = Hourly precipitation (in inches and hun­ dredths) from the most recent reported hourly NOAA data; • Precip_2hours = Sum of past 2 hours of precipitation; • Precip_4hours = Sum of past 4 hours of precipitation; • Precip_8hours = Sum of past 8 hours of precipitation; and • Hours_since_rain = Number of hours since last reported precipitation of any amount. All of these variables are available in the final analysis data sets. Analysis of Different Rain Variables Because of the frequent rain in Seattle, the team hypothesized that rain was likely a significant contributing source of con­ gestion in the region. Consequently, considerable effort was placed on examining the effects of rain and determining which measure of rain worked most effectively. One of the most illustrative analyses examined the effects of rain on the formation of congestion as measured using different definitions of rain. The analysis computed the probability that a given test section of roadway was operat­ ing in each regime for each time slice of a day. (See Appendi­ ces C and D and the Chapter 5 section “Computed Variables Used for Tracking the Influence of Disruptions on Travel Times and Delays” for a definition of the regime variable.) These probabilities were computed for days when rain occurred within the past hour and were then compared with probabilities on days when the same roadway was dry at that same time of day. The mean, median, 80th percentile, and 95th percentile travel times and speeds for each corridor and time period also could be computed for wet and dry condi­ tions. The following analysis uses the SR 520 roadway sec­ tions as the illustrative example of these findings; summary results are included. As Tables E.1 and E.2 show, the percentage of travel time that occurs in Regimes 1 and 2 is not affected by rain. In cor­ ridors and times when the population would be traveling in ideal conditions (60 mph and Regime 1 or 2), rain does not appear to affect the speed of travel at all. For example, on SR 520 Seattle westbound between 5:00 and 6:00 a.m., with no rain the percentage of travel time in combined Regimes 1 and 2 is almost 100% regardless of the weather condition. This effect is seen across all four corridors of SR 520 for both Regimes 1 and 2. However, when conditions approach roadway capacity, the effects of rain become apparent. Rain causes a signifi­ cant decrease in the percentage of time a roadway spends in Regime 3 (near­capacity volumes with free­flowing speeds) and a commensurate increase in Regime 4 (congested) travel. For example, if no rain falls between 7:00 and 8:00 a.m., then 21% of the time westbound SR 520 operates in Regime 3; however, if it has rained in the past hour, only 5% of the time. Similarly, if there is no bad weather between 4:00 and 5:00 p.m. on Seat­ tle SR 520 eastbound, the probability of traveling in Regime 3 is 30.49%, and Regime 4 is 62.73%. Once it begins raining, the probability of traveling in Regime 4 jumps to 80.53%, and Regime 3 moves to around 13.94%. Because speeds vary slightly in Regime 3 (they can range between 42 and 58 mph), a drop in average speed is seen within this regime. Figure E.1, shows how mean speed is at its slowest in this regime when rain has fallen recently. Figure E.1 also shows how this change in speed is partly dependent on how long it has been since it rained. The variable used in this figure is an inclusive variable that is set to rain if any rain has fallen in the past 1, 2, 4, or 8 hours. As the time period during which rain has fallen is increased (i.e., moves further away from when it might have last rained), it can be seen that the speeds gradually increase and return to what they were before the rain began. This same time effect, which is illustrated in

232 Table E.1. Percentage of Travel Time Occurring in Specific Regimes Given Different Weather Conditions (A.M. Peak) SR 520 Seattle WB 5:00 to 6:00 a.m. SR 520 Seattle WB 7:00 to 8:00 a.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,656.000 409.00 528.000 N 2,724.00 339.00 477.00 Regime 1 63.10% 61.12% 62.69% Regime 1 0.29% 0.00% 0.00% Regime 2 36.71% 37.90% 36.55% Regime 2 1.06% 0.00% 0.00% Regime 3 0.00% 0.00% 0.00% Regime 3 20.96% 4.72% 7.34% Regime 4 0.15% 0.98% 0.76% Regime 4 73.64% 93.81% 91.61% Regime 5 0.04% 0.00% 0.00% Regime 5 4.04% 1.47% 1.05% SR 520 Seattle EB 5:00 to 6:00 a.m. SR 520 Seattle EB 7:00 to 8:00 a.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,536.00 409.00 528.000 N 2,556.00 318.00 459.00 Regime 1 77.21% 82.40% 81.82% Regime 1 0.04% 0.00% 0.00% Regime 2 22.67% 17.60% 18.18% Regime 2 0.82% 0.00% 0.00% Regime 3 0.00% 0.00% 0.00% Regime 3 8.49% 1.89% 3.49% Regime 4 0.08% 0.00% 0.00% Regime 4 89.63% 98.11% 96.51% Regime 5 0.04% 0.00% 0.00% Regime 5 1.02% 0.00% 0.00% SR 520 Redmond WB 5:00 to 6:00 a.m. SR 520 Redmond WB 7:00 to 8:00 a.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,643.00 409.00 538.000 N 2,711.00 339.00 487.00 Regime 1 68.63% 67.48% 68.96% Regime 1 0.44% 0.00% 0.00% Regime 2 31.37% 32.52% 31.04% Regime 2 2.73% 0.59% 0.62% Regime 3 0.00% 0.00% 0.00% Regime 3 92.48% 72.27% 78.64% Regime 4 0.00% 0.00% 0.00% Regime 4 4.02% 27.14% 20.74% Regime 5 0.00% 0.00% 0.00% Regime 5 0.33% 0.00% 0.00% SR 520 Redmond EB 5:00 to 6:00 a.m. SR 520 Redmond EB 7:00 to 8:00 a.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,643.00 409.00 528.000 N 2,643.00 409.00 528.00 Regime 1 51.46% 52.32% 52.27% Regime 1 60.00% 60.00% 60.00% Regime 2 48.35% 46.45% 46.78% Regime 2 60.00% 60.00% 60.00% Regime 3 0.00% 0.00% 0.00% Regime 3 0.00% 0.00% 0.00% Regime 4 0.00% 0.00% 0.00% Regime 4 0.00% 0.00% 0.00% Regime 5 0.19% 1.22% 0.95% Regime 5 53.00% 49.00% 49.00% Note: N = number of 5-minute periods included in each 1-hour period for each analysis; WB = westbound; EB = eastbound. Precip 1 Hour and Precip 2 Hour = sum of past 1 and 2 hours of precipitation, respectively.

233 Table E.2. Percentage of Travel Time Occurring in Specific Regimes Given Different Weather Conditions (P.M. Peak) SR 520 Seattle WB 4:00 to 5:00 p.m. SR 520 Seattle WB 7:00 to 8:00 p.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,675.000 429.00 514.000 N 2,636.00 393.00 521.00 Regime 1 0.00% 0.00% 0.00% Regime 1 0.95% 0.00% 1.54% Regime 2 0.11% 0.00% 0.00% Regime 2 21.85% 13.49% 13.82% Regime 3 1.79% 0.70% 0.58% Regime 3 7.66% 1.53% 3.65% Regime 4 97.72% 99.07% 99.22% Regime 4 58.19% 73.79% 66.22% Regime 5 0.37% 0.23% 0.19% Regime 5 11.34% 11.20% 14.78% SR 520 Seattle EB 4:00 to 5:00 p.m. SR 520 Seattle EB 7:00 to 8:00 p.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,624.00 416.00 502.000 N 2,599.00 381.00 517.00 Regime 1 0.00% 0.00% 0.00% Regime 1 1.23% 4.20% 4.45% Regime 2 0.50% 0.00% 0.00% Regime 2 76.49% 70.87% 69.63% Regime 3 30.49% 13.94% 14.34% Regime 3 1.19% 0.00% 0.19% Regime 4 62.73% 80.53% 80.82% Regime 4 9.08% 12.07% 0.00% Regime 5 6.29% 5.53% 5.38% Regime 5 12.00% 12.86% 0.58% SR 520 Redmond WB 4:00 to 5:00 p.m. SR 520 Redmond WB 7:00 to 8:00 p.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,690.00 429.00 525.000 N 2,645.00 393.00 537.00 Regime 1 0.19% 0.23% 0.19% Regime 1 2.38% 3.31% 4.42% Regime 2 61.12% 31.70% 35.81% Regime 2 89.91% 84.48% 85.29% Regime 3 6.88% 1.63% 2.10% Regime 3 0.08% 0.00% 0.00% Regime 4 31.60% 66.20% 61.71% Regime 4 7.60% 11.45% 11.73% Regime 5 0.22% 0.23% 0.19% Regime 5 0.04% 0.76% 0.56% SR 520 Redmond EB 4:00 to 5:00 p.m. SR 520 Redmond EB 7:00 to 8:00 p.m. No Bad Weather Precip 1 Hour Precip 2 Hour No Bad Weather Precip 1 Hour Precip 2 Hour N 2,689.00 428.00 513.000 N 2,642.00 393.00 521.00 Regime 1 0.04% 0.00% 0.00% Regime 1 1.51% 1.02% 0.19% Regime 2 2.31% 1.40% 1.17% Regime 2 78.73% 68.96% 73.13% Regime 3 2.86% 1.64% 2.34% Regime 3 0.00% 0.00% 0.00% Regime 4 90.03% 90.65% 91.91% Regime 4 14.72% 22.14% 18.81% Regime 5 4.76% 6.31% 4.68% Regime 5 5.03% 7.89% 7.87% Note: N = number of 5-minute periods included in each 1-hour period for each analysis; WB = westbound; EB = eastbound. Precip 1 Hour and Precip 2 Hour = sum of past 1 and 2 hours of precipitation, respectively.

234 Figure E.2, can be seen in the percentage shift from Regime 3 travel to Regime 4 travel. Regime 4 sees a much sharper change in speed than Regime 3. In a normal Regime 4 condition, without rainfall, SR 520 Redmond eastbound between 4:00 and 5:00 p.m. has a mean speed of 38.82 mph. When precipitation has fallen in the past hour, however, the mean speed for Regime 4 drops to 35.60 mph. One limitation with the above analyses is best explained with an example. Rain falls between 3:00 and 4:00 p.m. The time periods between 3:00 and 5:00 p.m. are assumed to be rain affected (within 1 hour of when measurable rain has fallen). Travel times occurring at 4:55 p.m. that day are rain affected, but travel times at 5:05 p.m. are considered dry trips. The limitation with this analysis is that the rain may have cre­ ated a queue that affects the 5:05 dry trip. This possibility was Figure E.1. Percentage of time spent in Regimes 3 and 4 (eastbound on SR 520, Seattle section). Figure E.2. Percentage of time spent in Regimes 3 and 4 (eastbound on SR 520, Seattle section).

235 ignored in the analysis results (discussed below), thus slightly underestimating the potential impacts of rain on travel time. Analysis of Rain effects on Accident Rates on SR 520 Comparing Accident Rates Under Rain and No-Rain Conditions Although the above analysis shows that rain helps cause con­ gestion under the correct volume conditions, the research team was also interested in whether rain increases the likeli­ hood of crashes. A statistically rigorous analysis of this ques­ tion was undertaken using the data for all four SR 520 test segments. The results of that analysis are as follows. For the year 2006 there were 105,120 (365 × 24 × 12) con­ secutive 5­minute measurement intervals with a wide variety of recorded or deduced variables, including indicators for the presence of rain and the occurrence of accidents during each interval. Such data were available for four freeway segments of the Seattle–Redmond SR 520 corridor, designated here as Sea520WB, Sea520EB, Red520WB, and Red520EB. For the following analysis the intervals were divided into those with rain (15,703) and those without rain (89,417). These counts were the same for all four segments, since the weather indicator came from a single location (SeaTac Inter­ national Airport). Given the distance between SeaTac and the 520 corridor, the rain indicator may sometimes be in error (see discussion above concerning the team’s decision to use NOAA weather observations from SeaTac); nevertheless, it was used to determine differences in accident occurrence rates during intervals with rain and intervals without rain. These measurement intervals were also classified by their accident indicator, which should be accurate for each of the four segments. The resulting cross­classifications are shown in Tables E.3 through E.6. Since accidents are rare events, it is reasonable to treat their occurrence from time interval to time interval as indepen­ dent events, with probability p1 when there is no rain and probability p2 when there is rain. The number X1 of acci­ dents observed over the n1 = 89,417 no­rain intervals can be treated as having a binomial distribution with parameters n1 and p1. This distribution is well approximated by a Poisson distribution with mean l1 = n1p1. This distributional relation is expressed as X1 < Pois(l1 = n1p1). Similarly, X2 < Pois(l2 = n2p2), where X2 is the accident count over the n2 = 15,703 intervals with rain. Estimates of p1 and p2 are easily obtained as i = Xi/ni for i =1, 2, respectively, with a resulting estimate of 1/2 for p1/p2. 100g% confidence intervals for p1/p2 are obtained by the exact method (Clopper–Pearson): xL qbeta gam X X n nl= +( ) +[ ]−( ) <1 1 2 2 1 1 1 2, , where xL is the lower limit; and xU qbeta gam X X n nl= −( ) +[ ]−( ) <1 1 2 2 1 1 1 2, , where xU is the upper limit, gam = g = 0.95, X1 = X1, X2 = X2, n1 = n1, n2 = n2, and qbeta denotes the beta distribution quantile function that is intrinsic to R. Table E.3. Accident–Rain Cross-Classification for Sea520WB Accident Rain TotalNo Yes No 89,239 15,644 104,883 Yes 178 59 237 Total 89,417 15,703 105,120 Table E.4. Accident–Rain Cross-Classification for Sea520EB Accident Rain TotalNo Yes No 89,196 15,633 104,829 Yes 221 70 291 Total 89,417 15,703 105,120 Table E.5. Accident–Rain Cross-Classification for Red520WB Accident Rain TotalNo Yes No 89,358 15,686 105,044 Yes 59 17 76 Total 89,417 15,703 105,120 Table E.6. Accident–Rain Cross-Classification for Red520EB Accident Rain TotalNo Yes No 89,365 15,687 105,052 Yes 52 16 68 Total 89,417 15,703 105,120

236 The resulting estimates and 95% confidence bounds for p1/ p2 are shown in Table E.7 and graphically illustrated in Fig­ ure E.3. The estimates for p1/p2 are consistently around 0.53 to 0.61. The confidence intervals for the Sea520WB and Sea520EB segments do not contain the value 1, and the hypothesis p1 = p2 can be rejected in those situations at significance level a = 0.05. For segments Red520WB and Red520EB these intervals do con­ tain 1, and the same hypothesis cannot be rejected at that sig­ nificance level. However, this weaker form of evidence in those two cases probably results from there being fewer accidents on those segments. The combined analysis rejects the hypothesis p1 = p2 quite strongly. Based on that analysis, it can be stated with 95% confidence that the true ratio p1/p2 is in the interval [0.462, 0.664]. This interval is the tightest of all intervals because of the combined number of involved accidents. This result indi­ cates that the accident rate during rain is almost twice as high as during periods without rain. In both the table and figure, an aggregated analysis was performed for all four segments com­ bined; analysis results for that case are labeled “520 Corridor.” Figures E.4 through E.7 show the derived travel times for each workday, averaged over each respective commute period, in relation to the highest accident severity recorded for that commute period. Accident severity = 0 means that there was no accident, 1 indicates a minor accident, and 2 indicates a major accident. The results are shown as box plots for morn­ ing and afternoon commute periods. Some of the box plots in these figures suggest that accident severity may not affect the average travel time over the com­ mute period very much; see, for example, the box plot for Sea520WB during the afternoon commute. To examine this issue the team performed the Anderson–Darling k­sample test, which tests whether k independent samples could arise from sampling the same population. Here the k = 3 popula­ tions concern average commute travel times when no acci­ dent occurs, when the most severe accident during that period has a severity level of either 1 or 2. The Anderson–Darling k­sample test can be performed in R by installing the package adk (this needs to be done just once for each installation of R), then executing library (adk) for each new R session during which adk.test is needed, and then executing the command: adk.test x x x1 2 3, ,( ) where x1, x2, and x3 are the k = 3 samples to be compared. Table E.7. Estimates and 95% Confidence Intervals for p1/p2 Segment Estimate Lower Bound Upper Bound Sea520WB 0.530 0.393 0.724 Sea520EB 0.554 0.422 0.736 Red520WB 0.609 0.350 1.115 Red520EB 0.571 0.321 1.071 520 Corridor 0.553 0.462 0.664 Figure E.3. Estimates and 95% confidence intervals for p1/p2.

237 Figure E.4. Sea520WB travel times in relation to accident severity or no accident. Figure E.5. Sea520EB travel times in relation to accident severity or no accident.

238 The p­values for all eight comparisons (four segments, two commute periods each) are given in Table E.8. As suspected, there seems to be no significant difference in average travel time under the three accident scenarios during the afternoon commute for Sea520WB. There also seems to be no significant difference for the morning commute of Red520EB. However, that lack of significance is easily explained by the small num­ ber of accidents, three of Severity 1 and none of Severity 2. Accidents After Significant Dry Periods Another rain analysis explored the link between long dry periods and the accident rates during subsequent periods of rain. The idea was to determine where long periods of dry weather allow sufficient oil to soak into pavements, so that oil comes to the surface when it rains, making roadways unusu­ ally slick and increasing accident rates. Figure E.6. Red520WB travel times in relation to accident severity or no accident. Figure E.7. Red520EB travel times in relation to accident severity or no accident.

239 The analysis examined whether accident rates are higher during the 6 hours after rainfall after it has been dry for 504 hours (3 weeks) or 336 hours (2 weeks). Summary There were five occurrences in 2006 when it was dry for >336 hours and then rained 0.01 inch or more and two occurrences in 2006 when it was dry for >504 hours and then rained 0.01 inch or more. They are as follows: • Wednesday, August 9, 7:55–13:50: 639 hours rain free, then rain; • Saturday, September 9, 1:50–7:45: 633 hours rain free, then rain; • Tuesday, July 4, 4:55–10:50: 424 hours rain free, then rain; • Tuesday and Wednesday, August 29–30, 18:15–00:40: 490 hours rain free, then rain; and • Friday, October 6, 5:50–16:45: 349 hours rain free, then two independent rains. Accident numbers were aggregated and nonparametric inde­ pendent sample tests were run to compare accidents during these days and times with the numbers of accidents during these cases. A basic accident per hour number was developed to determine if the accident rate during these cases was higher than the yearly average. For example, all Wednesdays from 7:55 to 13:50 were compared with the August 9 case. This analysis was limited because it used 0 and 1, which excluded multiple accidents; thus, the findings were not relevant. To deal with the multiaccident problem, a basic cross­tabs analysis was done to account for times with multiple accidents. This technique allowed a basic probability of an accident at the given times to be determined overall compared with the probability of an accident when it rained after an extended dry period. The results of the cross­tabs analysis suggested that accident rates were not significantly higher when it was dry and then rained compared with accident rates at similar times. The probability of accidents during all days and all hours compared with the +336 hours of dry weather followed by rain cases was • Probability of an accident anywhere: 0.082235; and • Probability of an accident during the dry, then wet cases: 0.121429. The probability of accidents during all days in the p.m. peak period (2:00 to 7:30 p.m.) only compared with the +336 hours of dry weather followed by rain cases was • Probability of an accident anywhere: 0.1502; and • Probability of an accident during the dry, then wet cases: 0.095238. The probability of accidents during the weekday p.m. peak period compared with the +336 hours of dry weather followed by rain cases was • Probability of an accident anywhere: 0.170639; and • Probability of an accident during the dry, then wet cases: 0.095238. The probability of accidents during all days and all hours compared with the +504 hours of dry weather followed by rain cases was • Probability of an accident anywhere: 0.082235; and • Probability of an accident during the dry, then wet cases: 0.090278. Results and Recommended Further Analysis The results above show that the probability of accidents dur­ ing the 6 hours after rainfall subsequent to 336 hours or more of dry weather was slightly higher than the probability of acci­ dents any day or time on major roadways in greater Seattle. However, the probability of accidents during these times was lower than the probability of accidents anywhere when look­ ing only at p.m. peak times and p.m. peak weekdays. Without a clear result that states that accident rates are significantly higher during these times, the claim cannot be made that there is a higher likelihood of getting into accidents when it has been dry for a significant period of time and then rains. Other analyses may include • Adjusting the threshold for rain to include, for example, >0.02 inch instead of >0.01 inch; Table E.8. p-Values for Anderson–Darling k-sample Test When Comparing Travel Times with No Accident with Accident Severity 1 and with Accident Severity 2 (1; 2, pp. 918–924) Commute Morning Afternoon Segment p-Value Sea520WB 4e-05 0.17753 Sea520EB 0.00053 0.00242 Red520WB 0.00959 0 Red520EB 0.56444 0.00555

240 • Adjusting the 6 hours of rain threshold to capture 8 or 10 hours after the rain begins to see if there are more accidents; and • Developing a statistical test to determine whether the above findings are statistically relevant. Analysis of Snowfall effects An analysis comparing roadway performance when snow was falling versus when snow was not falling and when no pre­ cipitation was falling resulted in counterintuitive findings that snow was not a significant contributing factor to road­ way performance. Because this result was counterintuitive, a series of case studies was undertaken to examine traffic per­ formance on those days that snow fell in the city. The case study of delays on I­90 when snow fell illustrates the difficulties in determining the effects of weather on road­ way performance. It also indicates why the selection of the vari­ able snow falling in the initial analysis of the effects of snow on travel time produced poor results. In the case study, the largest roadway performance effects caused by snowfall did not occur while the snow was falling at the SeaTac weather station. Instead, they occurred as a result of the accumulation of snow on the roadway and the conversion of that snow into sheet ice on some roadway sections. The latter event occurred well after the snow had stopped falling at the weather station. In addition, the analysis of that case study revealed that delays did not happen similarly on all roadway sections that evening (although the newspaper reported long delays on several corridors). In fact, the eastbound and westbound sec­ tions of I­90 (presumed to experience the same level of snow­ fall) experienced very different roadway performance (delay) conditions during and after the snow storm. While the west­ bound direction showed modest delays in the evening, with moderate delays occurring between 6:00 and 9:00 p.m., the eastbound section experienced an unusually heavy day of congestion before the snowfall, and then a major additional pulse of congestion starting at 8:00 p.m. that lasted well into the morning hours. Exacerbating the eastbound congestion was the traffic volume added because of a professional foot­ ball game that occurred that night in downtown Seattle. The Seahawks played the Packers on Monday Night football, add­ ing 65,000 fans, divided across multiple freeways, to the out­ bound traffic beginning at about 8:30 p.m. The snowfall case study revealed many of the analytic prob­ lems associated with an analysis of the effects of bad weather. The most significant problem was finding a good definition, in analytic terms, of bad weather. The key regionwide weather variable used to indicate bad weather, the presence of mea­ surable rainfall during the previous hour, was a poor choice for analyzing the effects of snowfall. The proper variable for analysis of the effects of snow on tra vel time performance would have been snowfall accu­ mulation on the roadway, but unfortunately the data neces­ sary to estimate or compute this variable were not available for this project. Analysis of Wind effects An analysis of the effects of wind on roadway performance indicated that on the two roadways (I­90 and SR 520) that cross Lake Washington on floating bridges, high winds (wind gusts above 19 mph) had an observable effect in moderate volume conditions. This effect was especially noticeable east­ bound when the winds, generally from the south, caused waves to crash against the bridge, creating significant spray. How­ ever, wind appeared to have inconsistent effects on all other freeway corridors in the region. Some roadway sections were adversely affected by strong winds, while the performances of other segments were not. The effects of wind on roadway performance were ana­ lyzed differently from the effects of rain. This is partly because other than the prolonged effect of any queues being formed, wind does not have a lasting effect similar to that of rain. Once wind stops, its direct effects stop. That is, wind does not have a lasting effect equivalent to spray from wet roadways caused by rain. The lack of this effect limited the project team’s confidence in the use of the available NOAA wind data for specific roadway sections. As a consequence, the team did not use the wind gust variable produced by NOAA because there was little confi­ dence that this variable was effectively applicable to geo­ graphically removed locations. Similarly, the wind speed variable that was used was assumed to be only a reasonable surrogate for windy conditions, rather than a definitive sta­ tistic indicating the precise wind speed at which travel might be affected. To test the effects of wind on travel times, the data set was divided into wind­affected and not­wind­affected groups on the basis of the wind speed variable present in each 5­minute time slice. The travel times for these two groups were compared within specific time intervals with both traditional t­tests, which assumed normally distributed travel times within those time periods, and nonparametric tests of the sample means. Tests were performed only for nonholiday Tuesdays, Wednesdays, and Thursdays (combined). Sensitivity tests were performed with different values of the wind speed variable to determine the sensitivity of the analysis results to the breakpoint selected for identifying windy versus not­windy conditions. Figures E.8 through E.11 illustrate how travel times by direction across the two floating bridges were affected by various wind speeds. The graphs show mean travel times by time of day by wind speed for nonholiday Tuesdays through Thursdays.

241 The analytic tests performed on the Seattle test corridors showed that travel times in all test corridors were not equally affected by wind. In fact, in many corridors, wind did not have any statistically significant effect on travel times. In other corridors, wind had a high impact on roadway performance. The authors believe that this is due in part to differences between actual wind speeds within the study corridor and those measured at the airport, and in part to the way that site­specific roadway geometry affects how drivers respond to wind. That is, travel times over the SR 520 floating bridge, which has nar­ row lanes, no shoulders, and physically moves when struck by wind­blown waves, are affected at much lower wind speeds than travel times on I­5 in the northern reaches of the metro­ politan region, where lanes are wider, full­width shoulders Figure E.8. SR 520 Seattle eastbound. Figure E.9. SR 520 Seattle westbound.

242 exist, and wind does not cause the roadway to move. Table E.9 gives examples of how wind affects various corridors dif­ ferently, even though the corridors are directly connected. Table E.9 also gives examples of the results of the sensitivity tests performed with different wind speeds to separate windy from not­windy conditions. As Table E.9 shows, the SR 520 bridge is affected by rela­ tively moderate winds (10 mph sustained wind speeds), mainly because the bridge is a 2­mile­long floating span. The roadway is two lanes in each direction with no shoulders. In even moderate wind, a driver crossing the bridge can feel the bridge sway. The wind also can create some spray, as wind­ driven waves break against the bridge, causing drivers to slow down. Because the bridge operates near capacity 12 to 14 hours each weekday, these wind effects are sufficient to cause congestion. The I­90 bridge, located nearby to the south, also is affected by wind, but to a lesser degree than the SR 520 bridge. This Figure E.10. I-90 Bridge eastbound. Figure E.11. I-90 Bridge westbound.

243 is most likely due to a combination of factors: the I­90 bridge is more modern, has full shoulders, and sits higher off the water (and therefore experiences less wind­driven spray). Interestingly, the evening commute across the I­90 bridge is affected by wind, but the morning commute is not, even though traffic volumes are similar in both periods. This dif­ ference is partly because the test section that included the I­90 bridge also included a large segment of nonbridge travel across Mercer Island. Back­ups on the bridge affecting east­ bound traffic actually create some free­flow conditions on the island itself, decreasing the travel time impact of the wind. However, wind­caused back­ups significantly affect the upstream section of eastbound I­90 (the Seattle section also shown in Table E.9). This explains why the I­90 Seattle sec­ tion is statistically affected by wind in the morning, even though it does not include the bridge itself. At more moderate wind speeds (e.g., 10 mph sustained winds), none of the I­90 segments showed a statistically significant change in expected travel time. The I­5 segments included in Table E.9 indicate that wind affects some corridors in some peak periods, but not all cor­ ridors or all peak periods within all corridors. In general, high peak period volumes relative to their capacity make roadway segments more likely to be affected by high winds. Other reasons that a roadway may be susceptible to winds are that the road segment is exposed to high levels of wind (e.g., the I­5 North Seattle segment crosses the Ship Canal Bridge, an exposed portion of road where wind is often felt) or that the segment is immediately upstream of another seg­ ment that is wind affected. For example, the I­5 North King segment is upstream of the I­5 North Seattle segment. The I­5 Everett segment is considerably farther north and does not experience spillback from North King or North Seattle seg­ ments, except in extreme cases. Figure E.12 illustrates how wind affects the SR 520 bridge westbound, and Figure E.13 illustrates the I­90 eastbound bridge section. In both figures it can be seen that the primary effects of wind are in the peak periods when traffic volumes are highest. If the same graphics were presented with a higher wind speed, more impacts would be seen in the middle of the day, especially on SR 520. In Figure E.13, wind appears to have a significant effect on expected travel times during the later portion of the a.m. peak period, but not on the earlier portion of the peak. This differ­ ence helps explain why the difference in mean travel times shown in Table E.9 is not statistically significant. In the end, sustained wind speeds of 16 mph were used as the primary split between windy and not­windy conditions. Adopting a different definition would marginally change the travel times associated with windy and not­windy conditions for some corridors, but would not change the ultimate conclusions of the study. Table E.9. Example Effects of Wind on Travel Times by Corridor Route Mean Travel Time A.M. Peak (s) Difference Statistically Significant? Mean Travel Time P.M. Peak (s) Difference Statistically Significant? With Winda Without Windb With Wind Without Wind I-5 Everett southbound 190 207 -17 No 191 209 -18 No I-5 North King southbound 759 690 68 Yes 400 422 -22 No I-5 North Seattle southbound 751 606 145 Yes 926 686 239 Yes I-5 South northbound 1,671 1,073 598 Yes 649 649 0 No SR 520 Seattle westbound 1,020 638 382 Yes 1,548 1,052 495 Yes I-90 Bridge eastbound 425 410 15 No 543 437 106 Yes I-90 Seattle eastbound 198 169 29 Yes 151 115 36 Yes SR 520 Seattle westbound, 10 mph wind speed 781 626 154 Yes 1,093 1,049 44 Yes I-90 Bridge eastbound, 10 mph wind speed 434 407 27 No 431 441 -10 No I-90 Seattle eastbound, 10 mph wind speed 174 169 5 No 107 118 -12 No a Sustained wind speed >16 mph. b Sustained wind speed ≤16 mph.

244 Analysis of Fog Effects The analysis of the effects of fog was problematic, as fog tends to be highly localized. Thus, while the airport may be very foggy (to the point that landings and take-offs are restricted for lack of visibility), at the same time I-5, pass- ing within 2 miles of SeaTac, may have clear visibility. As a result, the fog variable that described conditions only at SeaTac airport was not useful in identifying specific fog- related delays. References 1. Scholz, F. Confidence Bounds & Intervals for Parameters Relating to the Binomial, Negative Binomial, Poisson and Hypergeometric Distri- butions: With Applications to Rare Events. University of Washington, Seattle, 2008. www.stat.washington.edu/fritz/DATAFILES498B2008/ ConfidenceBounds.pdf. 2. Scholz, F. W., and M. A. Stephens. K-Sample Anderson–Darling Tests. Journal of the American Statistical Association, Vol. 82, No. 399, 1987, pp. 918–924. www.jstor.org/discover/10.2307/2288805?uid =3739960&uid=2&uid=4&uid=3739256&sid=21101238038017. Figure E.12. Mean travel times by time of day in wind and no-wind conditions on SR 520 westbound (Bellevue toward Seattle). Figure E.13. Mean travel times by time of day in wind and no-wind conditions on I-90 bridge section eastbound (Seattle toward Bellevue).