Title: A Seasonal Autoregressive Model of Vancouver Bicycle Traffic Using Weather Variables
Number of Words:
Number of Figures:
Number of Tables:
4044
5
7
Authors:
Christopher Gallop
School of Community and Regional Planning
University of British Columbia,
#433-6333 Memorial Road, Vancouver, BC V6T 1Z2, CANADA
Tel: 778-689-2737
Email: [email protected]
Cindy Tse
Department of Civil Engineering
University of British Columbia
#10-8000 Heather Street, Richmond, BC V6Y 2R1, CANADA
Tel: 604-617-7736
Email: [email protected]
Jinhua Zhao (Corresponding author)
Department of Civil Engineering / School of Community and Regional Planning
University of British Columbia
#2007-6250 Applied Science Lane, Vancouver, BC V6T 1Z4, CANADA
Tel: 604-822-2196
Email: [email protected]
KEY WORDS
Weather, cycling, seasonal autoregressive model, time series analysis, Vancouver, transit
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
2
ABSTRACT
This paper uses hourly bicycle counts and weather data that are continuous and year-round to model
bicycle traffic in Vancouver, Canada. The study uses seasonal autoregressive integrated moving average
(ARIMA) analysis to account for complex serial correlation patterns in the error terms and tests the model
against actual bicycle traffic counts. Temperature, rain, rain in the previous 3 hours and humidity are all
found to be significant, with clearness found to be marginally significant at the 10% level. The combined
effect of rain and its lags is close to 24% of the average hourly bicycle traffic counts, which is larger than
the impact of it being a holiday or a Saturday, although the impact of it being a Sunday is still larger. An
increase of one degree Celsius from the mean is generally found to increase bicycle traffic counts by
1.65%, so an increase of 10 degrees would increase bicycle traffic by 16.5%. The coefficients on
humidity and clearness are small. A decrease in bicycle traffic of only 0.08% is observed per unit change
in relative humidity and 0.62% at each of the four transitions between categories of cloudy to perfectly
clear skies.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
3
INTRODUCTION
Since 1994, the number of bike trips per day in Vancouver tripled, increasing from 20,000 to 60,000 (1).
Even so, only 1.7% of trips to work in Metro Vancouver, and 3.7% within the City of Vancouver proper,
were made by bike in 2006 (2). Although cycling in Vancouver has seen a dramatic increase, mode share
is still very small and has room to grow.
In Vancouver, bicycle traffic is expected to continue growing quickly over the coming decades as
both the City of Vancouver and Translink, Metro Vancouver’s regional transportation authority, are
aiming to grow the share of sustainable modes of transportation (cycling, walking and transit) to 50% (3,
4) by 2040 from the current share of 25% (5). The target mode share for cycling specifically in European
cities, under the Charter of Brussels, is 15%. Translink and the City have developed strategies for
achieving a complete, safe and attractive cycling network that provides an abundant supply of bicycle
parking and end of trip facilities, improved integration of cycling with transit and the implementation of a
bike-sharing program in the downtown and other high cycling-potential areas (2, 3). The increases in
cycling in Vancouver are apparent and will likely continue into the future.
!
FIGURE 1 Bicycle trips per day in Vancouver, Canada (1, 6).
As shown in Figure 1, while cycling is on the rise, day-to-day bicycle traffic fluctuates
considerably. For example, one report from the City points out that bike counts for the Ontario Bikeway
at 10th Avenue for September 2009 were as low as 400 on a rainy weekend and as high as 1600 on a nonrainy weekday. Even same days of the week can vary widely. For example, the count on Wednesday
September 10 was 1600 whereas, on Wednesday September 24, a rainy day, it was only 700 (6). More
than 3,500 cyclists commute to work downtown every morning, which is the equivalent of 65-75 full
transit buses (1). Citywide, daily bicycle trips are the equivalent of up to 1276 full transit buses.
Fluctuations in these bicycle traffic counts will have service planning implications for transit, especially
with the number of cyclists expected to rise. Further dedicated studies could have a more systematic
approach, employ variables besides rain, account for cyclical fluctuations due to time/day of the week and
utilize a larger dataset over a longer period of time. This study seeks to better understand weather’s
effects on bicycle traffic as well as the planning implications.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
4
LITERATURE REVIEW
A number of factors, including the built environment, socio-economics, psychological (attitudes, norms,
habits) and cost, travel time, effort and safety, have been identified as influencing the demand for bicycle
travel (7, 8). Among these factors is the natural environment, including the effect of climate and weather
on cycling. This study focuses on the day-to-day and hour-to-hour effects of weather rather than the city’s
long-run climate.
Bicycle traffic is generally found to increase with temperature and decrease with precipitation (9,
10, 11, 12, 13, 14, 15, 16). Miranda-Moreno (2011) also finds humidity and additional precipitation
variables including the presence of rain in the morning and/or during the previous three hours to be
significant too. In both Thomas (2008) and Miranda-Moreno (2011), wind is tested but only found
significant in Thomas (2008). Niemier (1996), Lewin (2011) and Thomas (2008) all suggest that the
effects of precipitation and temperature are nonlinear. Richardson (2000) notes that bicycle traffic
decreases in both very cold and very hot weather and bicycle traffic is found to decrease slightly after 28
degrees in Montreal (14) and 32 degrees in Boulder (15). Although most cyclists value the weather in a
similar way, recreational demand is much more sensitive to weather than the utilitarian demand of, for
example, commuters (12, 13). Bicycle traffic is found to decrease on weekends in Boulder (15) and
Montreal (14), suggesting that there are more utilitarian cyclists on weekdays.
Studies generally use simple regression, setting bicycle counts as the dependent variable and
weather variables as the independent, or survey analysis to draw conclusions about the weather and
climate’s effects on bicycle traffic. Exceptions include Miranda-Moreno (2011) which develops a count
model and Thomas (2008) which develops a time-series model. Niemier (1996) also uses a Poisson model
to statistically confirm that many of the factors thought to influence cyclists, including both weather and
non-weather variables, and identifies that count volume may be biased +/-15% depending on the time of
year in which the count was taken. Richardson (2000), similarly, uses the results of the analysis to derive
seasonal adjustment factors that can be applied to the results of cycle surveys conducted under varying
weather conditions. The present study takes an approach similar to that of Thomas (2008) that attempted
to develop a time-series model for forecasting future bicycle traffic, although Thomas (2008) differed in
that it focused on the differences between recreational and utility cyclists.
The most recent studies use data collected from automatic counters (13, 14, 15), although past
studies have also drawn upon travel surveys (12, 16), time-lapse video recording (9, 10) and manual
counting methods (11, 17). With the exception of Thomas (2008) and Miranda-Moreno (2011), daily, as
opposed to hourly, bicycle counts and weather are employed. Miranda-Moreno (2011) uses hourly data
from April 2008 to July 2010, excluding winters because the bulk of the bicycle network is closed during
that time. In addition, other portions of data are missing due to construction, bike path closures and
maintenance. The Lewin (2011) study used data from between 2000 and 2004 but only subsets of those
days actually have counts due to issues such as formatting, duplicating and stamping. Thomas (2008)
drew upon a large and consistent dataset collected by Wageningen University on various bicycle paths
throughout the Netherlands. The present study takes an approach similar to Thomas 2008 as a uniform
and continuous dataset has been obtained.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
5
RESEARCH OBJECTIVES AND HYPOTHESIS
The objective of this study is to determine the significance and magnitude effect of temperature, relative
humidity, wind speed, clearness, fog and precipitation (including drizzle, showers, rain and snow) on
bicycle traffic in Vancouver and devise a time series model that can be used to forecast future bicycle
traffic.
It is expected that weather variables, especially temperature and precipitation, will continue to be
significant predictors of bicycle traffic, but that the coefficients and t-statistics will be lower in a model
that uses autoregressive integrated moving average (ARIMA) analysis.
DATA ANALYSIS
Hourly bicycle traffic counts were obtained for four sites at which the City of Vancouver has installed
permanent inductive loop counters. The data for each site was mostly intact and continuous, although
some exceptions, due to equipment malfunction and vandalism, are noted in Table 1. The total number
observations amount to 15,312 hours.
TABLE 1 Daily Bicycle Counts by Lane
Bike Lane
Mean
Standard
Deviation
Coefficient
of
Variation
Min
Max
Central
Valley
Greenway at
Rupert
Street
460
261
0.57
0
1167
Ontario
Street at
11th Avenue
663
385
0.58
0
1582
Burrard
Street
Bridge
2521
1414
0.56
110
6808
Cambie
Street
Bridge
852
488
0.57
0
2211
TRB 2012 Annual Meeting
Date and time of
Data Availability
12am Sep 1 2009 –
11pm May 31 2011
Missing Data: 11am
Apr 20 – 12pm Apr
27 2011
12pm Sep 1 2009 –
11pm May 31 2011
Missing Data: 9am
Feb 3 – 10am Mar 7
2011; 7am Mar 14 –
6am Mar 18 2011;
1pm Apr 20 – 1pm
Apr 27 2011
12pm Sep 1 2009 –
1pm May 31 2011
Missing Data: 2pm
Nov 24 – 11pm Nov
30 2010
12am Sep 1 2009 –
11pm May 31 2011
Missing Data: 11am
Feb 11 – 12pm Feb
14 2011; 12pm May
20 – 9am May 27
2010 (in hourly data
only)
Percent
of Data
Missing
1.10%
6.74%
0.94%
1.60%
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
6
The counts for each lane were also graphed and visually assessed. Because the coefficient of
variation and cyclical patterns in bicycle counts are similar for each lane, it is reasonable to combine the
lane totals for analysis. Burrard has the highest count, so will hold the most weight. The total bicycle
count across all lanes was adjusted where data for an individual lane was missing by using mean counts to
determine each lane’s average contribution to total count, and multiplying that factor by the total where
individual lane data is missing. The amount of missing data was quite small.
As will be discussed in the next section, cyclists frequently base their decision to bike on current
rather than forecasted weather. Therefore, our analysis is based on actual rather than forecasted weather.
The Canada National Climate Data and Information Archive maintain a historical record of hourly
weather information the Vancouver International Airport station. A description of the weather variables
used is included in the table below.
Fog
TABLE 2 Weather Variables Used in the Model
Description
Continuous, measured in °C to the tenth of a degree
Continuous, measured in % to the whole percent
Continuous, measured in km/h to the whole kilometre
Qualitatively observed, ordered categorical variable assigned 1 for mostly
cloudy, 2 for partly cloudy, 3 for mainly clear, 4 for clear. 0 is assigned
for other observations, including fog and precipitation.
Qualitatively observed, presence assigned a dummy variable of 1
Precipitation
- Drizzle
- Rain
- Snow
Qualitatively observed, presence assigned a dummy variable of 1
Qualitatively observed, presence assigned a dummy variable of 1
Qualitatively observed, presence assigned a dummy variable of 1
Weather Variable
Temperature
Relative Humidity
Wind Speed
Clearness
Figure 2 plots daily bicycle traffic counts, seven-day average, daily mean temperature and days where
more than 50% of the hours between 6am and 9pm had precipitation. At the annual scale, bike counts
generally cycle with temperature, peaking in July and hitting a low in December. Counts also tend to be
higher during periods without precipitation. Weekend and holiday counts tend to fall beneath the moving
average. February counts in 2010 are higher than usual because of the Winter Olympics. Table 3
summarizes the statistics for weekday, weekend, holiday and Olympic counts. Weekdays had higher
bicycle counts and lower variation than weekends and holidays.
Figure 3 shows that bicycle traffic follows annual, weekly and daily cycles. As counts closely
follow temperature at the annual scale, temperature can be used to account for the annual fluctuations.
Weekly and daily cycles are more of the function of the temporal patterns of human activity. We will use
lagged variables, autoregressive and seasonal autoregressive terms to account for them. Additional
observations are worth noting: peak in bicycle traffic in July is 4.5 times higher than December’s low and
variation within each month hits a low in the summer months and peaks in the winter months. Also,
bicycle traffic is about 40% higher on weekdays than weekends and there is more count variation on
weekends. Finally, bicycle traffic generally peaks twice per day, between 8-9am and 5-6pm and variation
in bicycle traffic hits a low during the afternoon.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
7
Bike#Count#
Temp#
14000#
25.00#
12000#
20.00#
10000#
15.00#
8000#
6000#
10.00#
4000#
5.00#
2000#
0#
0.00#
Sep-09#
Dec-09#
Mainly#Rainy#Day*#
Mar-10#
Temperature#
Jun-10#
Weekday#
Sep-10#
Weekend#
Dec-10#
Holiday#Count#
Olympics#
Mar-11#
7#Day#Moving#Count#Average#
FIGURE 2 Daily bicycle counts, temperature and precipitation. (*mainly rainy day defined as >50% of hours between 6am and 9pm have precipitation)
TABLE 3 Statistics for Bicycle Counts by Weekday, Weekend, Holiday and Olympics
Weekday
Weekend
Holidays
Olympics
All Counts
TRB 2012 Annual Meeting
Mean
Standard
Deviation
Coefficient
of Variation
Min
Max
4873
3551
2499
4914
4496
2408
2273
2070
1402
2443
0.49
0.64
0.83
0.29
0.54
396
190
378
2132
190
11547
9315
6998
6595
11547
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
8
0.70!
600!
1.20!
0.50! Va
5000!
0.60!
500!
1.00!
400!
0.80!
300!
0.60!
200!
0.40!
r
i
a
0.40! t
i
o
n(
2000!
Jan!
Feb!
Mar!
Apr!
May!
Jun!
Jul!
Aug!
Sep!
Oct!
Nov!
Dec!
1000!
3000!
0.20!
2000!
0.10!
1000!
0.10!
100!
0.20!
0.00!
0!
0.00!
0!
0.00!
0.30!
0.20!
1am!
3am!
5am!
7am!
9am!
11am!
1pm!
3pm!
5pm!
7pm!
9pm!
11pm!
3000!
0.30!
Sun!
4000!
0.40!
Fri!
5000!
4000!
Sat!
6000!
0.50!
Thu!
7000!
0!
6000!
Tue!
8000!
0.60!
Wed!
9000!
Mon!
10000!
B
i
k
e(
C
o
u
n
t!
!
FIGURE 3 Mean and variation for bike count data by month, day of week and time of day.
!
TABLE 4 Summary Statistics for Weather Variables
Continuous Variables - Descriptive Statistics
Coefficient of
Mean
Minimum
Maximum
Variation
Temperature
9.5
0.58
-9.3
29.2
Relative
77.0
0.18
16
100
Humidity
Wind Speed
13.6
0.67
0
78
Dummy and Categorical Variables Counts and Percent of Total (Total Observations =
15,312 hours)
Total Count
Count Percent of Total
Precipitation*
3087
20.2%
Drizzle
89
0.6%
Rain
2939
19.2%
Snow
78
0.5%
Fog
Cloudy
Mostly Cloudy
Mainly Clear
Clear
517
4055
3448
3560
1031
*Precipitation is drizzle, rain, showers, snow or any combination
3.4%
26.5%
22.5%
23.2%
6.7%
The weather variables were each studied in turn. The proportion of hours with rain peaks in
November and hits a low in July, which is typical for Vancouver. The mean temperatures for all months
during the study period were typical for Vancouver, except for the January data, which was cooler than
usual.
ARIMA ANALYSIS
Only the first 75% of the data series was used to estimate the model and the last 25% was saved to verify
the model. A forecasting model capturing the data’s trend, seasonality and correlation among error terms
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
9
was developed using ARIMA analysis, also known as the Box-Jenkins analysis. The unit root test was
used to test for non-stationarity. ARIMA is an iterative model-building strategy consisting of three stages:
identification, estimation and diagnosis. The first, identification, involved estimating the autocorrelation
and partial autocorrelation functions from the raw data. The correlogram will help indicate whether a
stationary series is a white noise or has a moving average or autoregressive pattern. In the estimation
stage, the regression is run with ARIMA terms. In this paper, EViews version 7 is used for the model
estimation. Parameter estimates of the autoregressive or moving average terms must be statistically
significant and lie within the bounds of stationarity and invertibility. Finally, diagnosis examines whether
the residuals were not different from ‘white noise’ by checking that the autocorrelation function had no
statistically significant spikes, and using Ljung-Box Q-statistics and the Breusch-Godfrey Serial
Correlation Test to test high-order serial correlations.
The unit root test rejects the null hypothesis that the data series is non-stationary. The
correlograms of residuals, shown in Figure 4, suggests that autoregressive terms AR1, seasonal
autoregressive terms SAR24 (24 hour cycle in a day) and SAR168 (168 hour cycle in a week) should be
used in the ARIMA model. Then dozens of different combination of additional AR terms and lagged
variables were tried. Two criteria are used to identify the final model: first the estimated residuals should
not have significant serial dependence; and given the first condition being met, minimize the Akaike Info
Criterion value. The final model includes additional autoregressive terms (AR2, AR6, AR9, AR10, AR72,
AR192) and lagged variables for bike counts from previous hours counts (hours 1-27, 30, 31, 33, 37-39,
41, 48, 72, 96, 120, 144, 168, 192 and 216). The Durbin-Watson Statistic was not a sufficient test for this
model because it contains lagged dependent variables. The Ljung-Box Q-Statistics shown in Table 6 are
insignificant and the final correlograms in Figure 4 show that the autocorrelations and partial
autocorrelations are nearly zero. The Breusch-Godfrey test also confirms that serial correlation has been
accounted for in the ARIMA model.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
10
Table 5 Estimation Results of the Base and ARIMA Models
Variable
Temperature
Relative Humidity
Rain
Rain(-1)
Rain(-2)
Rain(-3)
Drizzle
Snow
Fog
Wind Speed
Clearness
Holiday
Olympics
Saturday
Sunday
Constant
R-Squared
Adjusted R-Squared
S.E. of Regression
Log Likelihood
F-Statistic
Mean Dependent Var
S.D. Dependent Var
Akaike Info Criterion
Schwarz Criterion
Durbin-Watson Stat
Base Model
Coefficient T-Statistic
15.12
45.56
-3.98
-26.96
0.02
0.00
-10.49
-1.44
-14.69
-2.02
-18.24
-2.88
7.25
0.31
71.16
2.65
45.94
4.47
-0.51
-2.71
8.42
4.43
-29.38
-3.96
99.22
11.05
-49.54
-10.40
-69.04
-14.50
361.19
25.05
0.35
0.35
175.12
-75573.60
365.21
200.78
217.28
13.17
13.18
0.46
ARIMA Model
Coefficient T-Statistic
3.32
8.21
-0.17
-2.06
-7.39
-4.54
-17.81
-12.28
-15.61
-10.36
-6.50
-4.64
-5.04
-0.98
-2.05
-0.27
-2.18
-0.84
-0.07
-1.05
1.25
1.73
-27.83
-5.40
31.57
2.83
-36.52
-2.97
-69.09
-5.60
142.68
5.19
0.95
0.95
47.73
-57597.08
3071.23
196.82
214.21
10.58
10.62
2.00
Table 5 reports the estimated coefficients for both the ARIMA model and the base model (a
simple linear regression model without ARIMA or lagged variables). The signs of the coefficients are
generally the same in both models. But the significance and magnitude of the coefficients are
systematically larger in the base model, indicating that the effects of weather variables are exaggerated
when complex serial correlation patterns in the error terms are not accounted for. Rain and the one hour
lag of rain were rejected in the base model but accepted in the ARIMA model, which makes more sense.
Snow and fog are accepted in the base model with the wrong signs but rejected in the ARIMA model.
Drizzle remains rejected in both models.
Temperature, as with past studies, is positive and significant in both models but the base model
wildly overestimates its magnitude. In the ARIMA model, an increase of one degree Celsius from the
mean is expected to increase ridership by 1.65%, so an increase of 10 degrees would increase ridership by
16.5%. It should be noted that this study could not verify the negative effect of extremely hot
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
11
temperatures (i.e. temperatures >28 degrees Celsius) found in past studies because Vancouver summers
are too mild. The coefficient on humidity is small, decreasing bicycle traffic only 0.08% per unit change
in relative humidity from the mean, but significant. Clearness is only marginally significant at the 10%
level and would increase bicycle traffic by 0.62% at each of the four transitions between cloudy and clear
skies. As with past studies, rain is found to be negative and significant and, as in the Miranda-Moreno
(14) study, the coefficients on the lags of rain are significant too, up to the previous three hours. The
combined effect of rain and its lags is close to 50 trips per hour, 23.54% of the average hourly bike trips,
which is larger than that of holidays, the Olympics or Saturday, although Sunday’s impact is still larger.
It should be noted that the effect of rain in the previous hour (8.86%) is larger than rain in the current hour
(3.68%). Snow is not significant, but conclusions cannot be drawn from these findings since Vancouver’s
sample size (i.e. hours with snow) is small.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
12
Base)Model)(Autocorrela7on)))
1!
0.5!
0!
I0.5!
1!
13!
25!
37!
49!
61!
73!
85!
97! 109! 121! 133! 145! 157! 169! 181! 193!
Base)Model)(Par7al)correla7on)))
1!
0.5!
0!
I0.5!
I1!
1!
13!
25!
37!
49!
61!
73!
85!
97! 109! 121! 133! 145! 157! 169! 181! 193!
!
ARIMA)Model)(Autocorrela7on)))
0.6!
Correlogram)of)Residuals:)Base)Model)
(Autocorrela7on)))
0.1!
I0.4!
1! 1!
13!
25!
37!
49!
61!
73!
85!
97! 109! 121! 133! 145! 157! 169! 181! 193!
! 0.5!
0!
ARIMA)Model)(Par7al)correla7on)))
I0.5!
0!
0.9!
12!
24!
36!
48!
60!
72!
84!
96!
108! 120! 132! 144! 156! 168! 180! 192!
73!
85!
97! 109! 121! 133! 145! 157! 169! 181! 193!
0.4!
I0.1!
I0.6!
1!
13!
25!
37!
49!
61!
!
FIGURE 4 Correlograms for base and ARIMA Models
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
13
TABLE 6 Ljung-Box Q-Statistics
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
PAC
0.772
-0.472
0.133
-0.105
-0.073
-0.026
0.055
0.144
-0.029
-0.334
0.011
0.032
0.115
0.087
-0.192
-0.264
0.025
-0.019
0.257
0.202
Base Model
AC
Q-Stat
0.772
6837.8
0.404
8716
0.137
8931.2
-0.018
8934.8
-0.114
9085
-0.168
9410.5
-0.155
9684.8
-0.049
9712.8
0.066
9763
0.022
9768.3
-0.117
9924.8
-0.195
10360
-0.152
10624
-0.041
10643
0.004
10644
-0.076
10709
-0.148
10960
-0.147
11209
-0.098
11320
-0.02
11325
Prob
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
PAC
0
-0.001
-0.001
0.01
-0.004
0.003
-0.003
-0.002
0.003
0.007
-0.005
0.003
-0.006
0.001
0.003
-0.004
0.005
-0.008
-0.008
0.002
ARIMA Model
AC
Q-Stat
0
0.0023
-0.001
0.015
-0.001
0.0246
0.01
1.1198
-0.004
1.2671
0.003
1.3971
-0.003
1.5267
-0.002
1.5607
0.003
1.6365
0.007
2.2439
-0.006
2.5754
0.003
2.6556
-0.006
2.9879
0.001
2.9926
0.003
3.0755
-0.004
3.2683
0.005
3.5332
-0.007
4.1344
-0.008
4.8199
0.002
4.8817
Prob
n.a.
n.a.
n.a.
n.a.
n.a.
n.a.
n.a.
n.a.
n.a.
0.134
0.276
0.448
0.56
0.701
0.799
0.859
0.897
0.902
0.903
0.937
FORECASTING
The model was used to generate predicted values for the 25% test data. The results for May 2011, the last
month in the data series, are displayed in Figure 5, overlaid with the two most important weather
variables, temperature and rain. The actual and forecasted values are close and the weekly and daily
cycles, generally match. Table 7 reports the statistics on the forecast precision based on the bike counts
between 7am and 7pm.
TABLE 7 Summary Statistics for Forecast
Included Observations
Root Mean Squared Error
Mean Absolute Error
Mean Abs. Percent Error*
Bias Proportion
Variance Proportion
Covariance Proportion
TRB 2012 Annual Meeting
744
62.1
43.5
24.7
0.002
0.068
0.930
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
14
Bike Count
1150
Temp
25
950
20
750
15
550
10
350
5
%50
0
0:00
5:00
10:00
15:00
20:00
1:00
6:00
11:00
16:00
21:00
2:00
7:00
12:00
17:00
22:00
3:00
8:00
13:00
18:00
23:00
4:00
9:00
14:00
19:00
0:00
5:00
10:00
15:00
20:00
1:00
6:00
11:00
16:00
21:00
150
Monday,4May402, Tuesday,4May403, Wednesday,4May Thursday,4May
2011
2011
04,42011
05,42011
Friday,4May406,
2011
Saturday,4May Sunday,4May408,
07,42011
2011
1350
25
1150
20
950
750
15
550
10
350
5
150
0
0:00
5:00
10:00
15:00
20:00
1:00
6:00
11:00
16:00
21:00
2:00
7:00
12:00
17:00
22:00
3:00
8:00
13:00
18:00
23:00
4:00
9:00
14:00
19:00
0:00
5:00
10:00
15:00
20:00
1:00
6:00
11:00
16:00
21:00
%50
Monday,4May409, Tuesday,4May410, Wednesday,4May Thursday,4May
2011
2011
11,42011
12,42011
Friday,4May413,
2011
Saturday,4May Sunday,4May415,
14,42011
2011
1350
25
1150
20
950
750
15
550
10
350
5
%50
1150
950
0:00
5:00
10:00
15:00
20:00
1:00
6:00
11:00
16:00
21:00
2:00
7:00
12:00
17:00
22:00
3:00
8:00
13:00
18:00
23:00
4:00
9:00
14:00
19:00
0:00
5:00
10:00
15:00
20:00
1:00
6:00
11:00
16:00
21:00
150
Monday,4May416, Tuesday,4May417, Wednesday,4May Thursday,4May
2011
2011
18,42011
19,42011
Friday,4May420,
2011
1200
0
1000
Saturday,4May Sunday,4May422,
21,42011
2011
800
750
1350
25
600
1150
550
950
20
400
15
200
10
350750
550
150350
150
!50%50
0:00
0:00
5:00
5:00
10:00
10:00
15:00
15:00
20:00
20:00
1:00
1:00
6:00
6:00
11:00
11:00
16:00
16:00
21:00
21:00
2:00
2:00
7:00
7:00
12:00
12:00
17:00
17:00
22:00
22:00
3:00
3:00
8:00
8:00
13:00
13:00
18:00
18:00
23:00
23:00
4:00
4:00
9:00
9:00
14:00
14:00
19:00
19:00
0:00
0:00
5:00
5:00
10:00
10:00
15:00
15:00
20:00
20:00
1:00
1:00
6:00
6:00
11:00
11:00
16:00
16:00
21:00
21:00
05
0
!200
Monday,4May423,
Tuesday,4May424,
Wednesday,4MayThursday,4May
Thursday,4May Friday,4May406,
Friday,4May427, Saturday,4May
Saturday,4May Sunday,4May408,
Sunday,4May429,
Monday,4May
Tuesday,4May403,
Wednesday,4May
2011
2011
25,42011
26,42011
2011
28,42011
2011
02,42011
2011
04,42011
05,42011
2011
07,42011
2011
Rain
!
Temperature
Actual4Bicycle4Traffic4Count
Predicted4Bicycle4Traffic4Count
FIGURE 5 Plot of actual and predicted counts for May 2011 test data.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
15
DISCUSSION
This study confirms that weather has a significant and important impact on bicycle traffic, although it
suggests the effects are exaggerated in models that fail to account for complex serial correlation patterns
in the error terms. The findings of the ARIMA model show that temperature, humidity, rain and rain in
the previous three hours are significant, with clearness being marginally significant. Temperature and
rain stand out as having a particularly important effect on bicycle traffic counts.
Results of a preliminary survey, conducted in conjunction with the formulation of this study’s
model, confirm weather’s important influence on the decision of whether or not to bike, although many
will cycle regardless of the weather. 58% of cyclists responded that they do consider weather a factor
when deciding whether or not to bike. Of those who base their decision to bike on the weather, 77% base
their decision on current rather than forecasted or recent weather. Thus, in modeling each group, there is
some justification for using recent and forecasted weather variables, but current weather matters most.
Our model uses current weather variables and recent weather variables for rain.
Of respondents who base their decision on forecasted weather, 41% check just before they leave,
24% up to 2 hours before and 29% on the evening before. Inclement weather was also found to influence
mode choice. 44% of respondents claim to choose another mode in inclement weather. Transit is the
most popular alternative at 22% of respondents, half of those who do switch, meaning that weather could
have important service impacts on routes near heavily utilized bicycle paths. Finally, if the weather
changes after arriving at a destination, 94% of respondents claim to still return by bike, despite the
weather, and this was the same for males and females. This suggests that inclement weather may have a
greater influence on the outgoing trip than the returning trip. This would mean that certain times of day,
such as morning peak-hour, might be more prone to weather effects.
Responses to this preliminary survey were conducted through the Cycling Department of City of
Vancouver, Third Wave Cycling Group Inc. (a cycling consulting firm) and Velolove, a volunteerdirected, community-based, entity focused on promoting cycling culture and events and the official City
of Vancouver Cycling Facebook page. 143 cyclists (72% male) were surveyed in total. The number of
respondents who bike, despite the weather, is likely higher in Vancouver than other Canadian cities as the
climate is relatively mild year-round.
One potential use of the ARIMA model is to provide adjustment factors to scale manual bike
count data taken under different weather conditions. This method could be used to create a more accurate
historical series of counts to compare changes in bicycle traffic over time.
With respect to the fluctuations in bicycle traffic, one policy aim could be to accommodate the
choices cyclists make in cases of inclement weather. For example, a system would be created whereby a
decrease in bicycle traffic can be recognized when it is about to occur so that it can be absorbed by other
modes. Accommodating fluctuations in areas with high levels of bicycle traffic might involve putting
additional buses on the road during periods of inclement weather (i.e. not only planning for seasonal
norms, but also daily and weekly fluctuations).
Another aim of could be to reduce the fluctuations due to weather through affecting the comfort
level of cyclists in inclement weather. Examples might include increased sheltered areas along the route
(i.e. creative canopies), lane-side temporary or permanent businesses that provide hot drinks to
commuters, public education campaigns on the proper clothing for cycling in inclement weather, building
end-of-trip facilities such as showers in offices and other destinations and partnerships with major
employers to pilot employee incentive programs such as credits towards rain gear and gym passes.
TRB 2012 Annual Meeting
Paper revised from original submittal.
C. Gallop, C. Tse, J. Zhao
16
While this paper has solely focused on bicycle traffic, the scope of this analysis could be
expanded to consider the impact of weather on multiple travel modes in tandem with one another. In
effect, such an expanded analysis would amount to a study of weather-specific mode split in contrast to
annual average mode split for a particular region or city. In other words, an expanded analysis would look
at how walking, cycling, driving and transit mode share fluctuate relative to one another over time and
with respect to weather.
ACKNOWLEDGEMENT
We would like to recognize the City of Vancouver for providing us with the data for this study. We would
also like to acknowledge Lilian Yuen and Tim Magowan for assisting with surveying and research.
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TRB 2012 Annual Meeting
Paper revised from original submittal.
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17
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TRB 2012 Annual Meeting
Paper revised from original submittal.