THE IMPACT OF WEATHER ON TRANSIT RIDERSHIP IN CHICAGO

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1 THE IMPACT OF WEATHER ON TRANSIT RIDERSHIP IN CHICAGO Zhan Guo, Massachuses Insiue of Technology, Room 9-524, 77 Massachuses Ave., Cambridge, MA, 02139, Nigel H.M. Wilson (Corresponding Auhor), Massachuses Insiue of Technology, Room 1-238, 77 Massachuses Ave., Cambridge, MA, 02139, (617) , Adam Rahbee, Chicago Transi Auhoriy (CTA), 567 W. Lake S, Chicago IL, 60661, U.S.A Absrac This paper explores he weaher-ridership relaionship and is poenial applicaions in ransi operaions and planning. Using he Chicago Transi Auhoriy (CTA) as a case, he paper invesigaes he impac of five weaher elemens (emperaure, rain, snow, wind, and fog) on daily bus and rail ridership, and is variaion across modes, day ypes, and seasons. The resuling relaionships are applied o he CTA ridership rend analysis, showing how preliminary findings may change afer conrolling for weaher. The paper emphasizes he imporance of having a heoreical framework encompassing weaher and ravel. Keywords: Weaher, Transi, Ridership, Chicago INTRODUCTION Weaher influences almos every aspec of ransi service. Bad weaher can reduce ransi ridership, lenghen vehicle running ime and dwell ime, reduce service reliabiliy, and increase he cos of operaion. Beer undersanding of he weaher impac on ransi performance can no only improve ransi service, bu also help o assess invesmens relaed o weaher proecion such as bus sheler consrucion, or air condiioning. Given is poenial imporance, i is surprising ha here has been lile research on he impac of weaher on ransi sysems. Prior sudies ha deal wih weaher and ravel have focused on driving, raffic volumes (1, 2, 3), vehicle speed (4, 5, 6, 7, 8), or accidens (9, 10, 11, 12, 13, 14). There are hree plausible reasons why he weaher-ransi relaionship has been rarely invesigaed. The firs one is lack of daa. Tradiionally, ransi auhoriies have used manual mehods, convenionally poin or ride checks, o collec informaion on vehicle 1

2 rip ime, passenger load, and boardings per rip (15, 16). Daa collecion is usually spread across differen ime periods and days o obain a represenaive sample in order o esimae ypical performance. Therefore, each ime period or day usually has only a few observaions. However, o invesigae he relaionship beween weaher and ransi performance, we need o conrol for he impac of ime of day or day of week on performance, and hus need large amouns of daa wihin each period of ineres. Tradiional manual daa collecion simply can no suppor such analysis. In conras, daa colleced on he weaher-auo relaionship is sraighforward: auomaic raffic couners insalled on highways can generae a large amoun of daa on raffic volumes and speeds wihin a shor period of ime. Similar ypes of auomaic daa collecion for ransi sysems have become available only recenly wih he insallaion of Auomaic Fare Collecion (AFC) sysems. For example, in New York Ciy, he Meropolian Transi Auhoriy (MTA) became he firs major muli-modal US ransi agency o insall an AFC sysem in January AFC was acceped sysem wide a he end of 1995 for bus, and in May 1997 for subway. In Chicago, an AFC sysem was insalled on he subway in 1998, and on bus in In Boson, an AFC sysem is now being commissioned. Secondly, he weaher impac on ransi performance is more complex han on driving. Drivers are affeced by weaher hrough is effec on he operaion of vehicles (17). For ransi riders, hey are ofen direcly subjec o weaher while waiing or walking o and from he sysem as well as indirecly affeced by he deerioraion in ransi service in he in-vehicle porion of he rip. Boh direc and indirec effecs influence he ravel demand for ransi as well as riders behavior for hose who sill ravel by ransi. 2

3 The hird and maybe he mos imporan reason is ha he imporance of he weaherransi relaionship has no been well recognized. A common misundersanding is ha since we can no conrol weaher, such an invesigaion would no be beneficial. However, his paper argues ha a beer undersanding of he impac of weaher on ransi performance could provide benefi in a leas wo areas. Firs, i can help improve ransi service qualiy. For example, knowing how weaher affecs service reliabiliy, we may redesign saions or vehicles accordingly. Knowing how good or bad weaher may increase or decrease ridership on paricular roues, we may change schedules beforehand if large ridership changes are expeced based on forecas weaher. Second, such research can help in projec appraisal relaed o weaher proecion. For example, bus shelers improve cusomer proecion from bad weaher, and likely arac new riders. A weaherridership model may be able o quanify he benefi of such projecs in erms of ridership gain. Given he poenial benefis, we expec more weaher-ransi sudies will follow his, given he grea availabiliy of AFC daa. This paper sars his exploraion. Clearly, ransi is more complicaed han driving in erms of he weaher impac. Accordingly, here is lile heory on he relaionship beween weaher and ransi use. The few prior sudies in he area are sricly empirical following ad hoc research designs and mehodologies and producing inconsisen resuls. For example, one sudy found higher ransi ridership during adverse weaher because of he diversion from oher modes including auo, walk and bike (18), while ohers found no appreciable change or a sligh decrease in ransi ridership in bad weaher (19, 20). However, he real reason behind he difference in hese observed impacs is ha he firs sudy only looked a a blizzard in Chicago ha affeced he afernoon commue, when road service was disruped, and rail 3

4 remained one of he few operaional urban ranspor modes, while he oher sudy argeed more moderae adverse weaher. This research invesigaes he weaher impac on ransi ridership a he sysem level. We focus on ransi ridership because i is perhaps he single mos imporan dimension of sysem performance, and on he sysem level impac because he relaionship is likely o be more eviden a his level han a he roue level. Individual roue level analysis is a logical follow-on opic. We arge boh bad and good weaher condiions in order o have a more complee picure of he weaher impac on ransi ridership. We also analyze he variaion of he impacs across mode and day ype. Secion 2 caegorizes he sources of weaher impac on ransi ridership. Secion 3 defines he research design o link weaher changes o ridership changes. Secion 4 inroduces he Chicago case sudy, and defines he weaher variables. Secion 5 develops a group of models, and presens and inerpres esimaion resuls. Secion 6 applies he findings o a form of performance racking used by mos ransi agencies. Secion 7 concludes he analysis and proposes furher research in his area. POTENTIAL IMPACTS OF WEATHER Weaher can influence ravel behavior in wo ways. Firs, i affecs he aciviies ha drive ravel demand. For example, ho dry weaher may increase recreaion aciviies a beaches and parks, while cold we weaher may depress oudoor spors, recreaion, and even social evens. Secondly, weaher affecs ravel experience. Transi users are subjec o direc physical impacs from weaher when hey wai or walk in exposed areas. When hey are in a vehicle, hey are affeced indirecly by bad weaher hrough deerioraion in 4

5 ransi service qualiy. In his paper he poenial sources of weaher impac are caegorized ino four ypes: infrasrucure, service, rip, and passenger characerisics. However, he purpose of his invesigaion is o explore he impac of weaher on ridership, no o model hese poenial sources of weaher impac individually. Infrasrucure refers o he physical roues, buildings, and vehicles ha involve long erm capial invesmen by ransi agencies. The echnology used for he physical roues, e.g. pavemen vs. rack or shared vs. full separaion, affecs he movemen of vehicles under various weaher condiions. The differen ypes of saion/sop faciliy (all-weaher proecion, simple sheler, or jus a sop) affec ravelers waiing and ransfer experience. The disance beween saions (sops) influences he access and egress walking disance, and hus he ime exposed o weaher. Vehicle aribues such as air condiioning direcly affec he comfor of ravel. Therefore, differen ransi modes (bus, subway, ligh rail, or commuer rail) may be impaced differenly by weaher. Subway is leas affeced by weaher due o is full separaion from oher raffic and full proecion from weaher. Bus is likely o be mos affeced because i shares roads wih local raffic and offers less proecion from weaher a sops, compared o rail sysems. Service characerisics primarily refer o frequency and ravel ime. Service frequency deermines passenger waiing imes, and hus he ime exposed o weaher if he waiing environmen is no proeced. Toal ravel ime in adverse weaher migh be lenghened due o slower speed and longer dwell ime a saions. For example, rainy weaher may cause longer dwell ime because passengers need o open or close umbrellas when hey ge on and off he vehicle. Service reliabiliy may deeriorae due o longer and more variable run imes and dwell imes, hus increasing passenger waiing imes. In 5

6 general, high frequency service should be less affeced by weaher han low frequency service. Accordingly, bus is likely o be more sensiive o weaher han rail because he laer normally has higher service frequencies. A ransi sysem using effecive real ime operaion conrol should be less affeced by weaher han a sysem based only on a saic operaions plan. Trip characerisics which may affec he weaher impac include rip lengh, ime flexibiliy, and rip purpose. A longer rip migh be more sensiive o weaher because he period of exposure is higher. If a rip has ime consrains such as laes arrival ime or earlies deparure ime, i migh be less sensiive o weaher because i is less flexible. If he rip purpose is discreionary such as personal business raher han mandaory such as work, i migh be more sensiive o he weaher. If he rip purpose is suscepible o weaher, i will be more sensiive. In summary, long, ime-flexible, and non-commuing rips are likely o be affeced more by weaher han shor, ime-consrained commuing rips. Personal characerisics can influence he weaher-ransi relaionship in wo ways. Firs, differen people may respond differenly o idenical weaher. A eenager may view a snowfall differenly from an elderly person. A professional in a sui may respond differenly o rain han a runner in shors. Second, people may have differen ravel opions, and heir response o weaher may vary accordingly. The ransi ravel of people who don own a car may be less affeced by weaher compared o people who can easily swich o auo. 6

7 The above discussion suggess ha he weaher impac may vary across ransi modes, roues, rips, and passengers. Bus may be more sensiive o weaher han rail. Roues serving shopping ceners may be more sensiive o weaher han roues serving employmen ceners. A passenger who jus akes ransi occasionally migh be more sensiive o weaher han a rider who akes ransi every day. The same passenger migh be more sensiive o weaher in off-peak hours han peak hours, and on weekends han weekdays, because off-peak and weekend service frequencies are ypically lower. RESEARCH DESIGN: LINKING WEATHER TO RIDERSHIP Boh weaher and ransi ridership are changeable from hour o hour and from day o day, so a criical issue in invesigaing he weaher-ridership relaionship is how o conrol for hese inheren flucuaions when examining heir inerrelaionship. Three aspecs of he research design are discussed below: absolue level vs. relaive change, uni of analysis, and mehod of comparison. Absolue Level or Relaive Change The weaher-ridership relaionship can be srucured in wo ways. Firs, we can compare he absolue levels of weaher and ridership, wih he underlying raionale ha he curren weaher condiions affec he curren level of ransi ridership. For example, cold weaher may lead o low ransi ridership. Secondly, we can relae he changes in weaher condiions and ridership. The underlying raionale is ha changes in weaher can lead o changes in ravel. The absolue-level mehod capures he rue impac of weaher (cold, hea, rain, ec.), while he relaive-change mehod ignores he absolue weaher 7

8 condiions. For example, a 5 degree emperaure rise in a cold winer sill represens cold weaher, bu he relaive-change mehod will rea i as relaively warm weaher and ignore he fac ha i is sill cold in an absolue sense. However, he disadvanage of he absolue-level mehod is ha i brings in sysemaic seasonal impacs, which are no based solely on weaher. For example, he lowes ridership monhs (ypically January and December) are due o he holiday season, while low Augus ridership is due o vacaions, In conras, he highes ridership monhs (ypically Sepember and Ocober) are due o he sar of school and college years. These flucuaions are no due o seasonal changes in weaher. The relaive-comparison mehod can avoid his problem by focusing on he pure impac of shor-erm weaher variaion. This research uses he relaive-comparison mehod because i is less problemaic in saisical esimaion and more likely o reflec he shor-erm impac of weaher on ravel. Uni of Analysis Because weaher and ridership can change all he ime, hey should be compared based on he same uni of analysis, for example, ridership and weaher in he same hour, or on he same day. The uni of analysis is seleced based on four crieria. Firs, i should allow sufficien variaion beween unis in boh weaher and ridership o make for a saisically meaningful analysis, e.g. daily ridership should be differen. Secondly, here should be lile inrinsic flucuaion beween unis in erms of boh weaher and ridership. A monh is a bad uni of analysis because here is sysemaic change in monhly ridership from January o December. Third, he weaher condiion(s) should be easy o represen by a specific variable. Fourh, he uni of analysis should reflec he real decision-making 8

9 conex. Based on hese crieria, a year or monh is no an appropriae uni of analysis because people don make ravel decisions on an annual,or monhly basis. An hour is also inappropriae because hourly ridership will have remendous inrinsic variabiliy, no relaed o weaher. The day is chosen as he uni of analysis because i mees he four crieria. Daily weaher condiions are quie variable. Ridership for he same ype of day (weekday, Saurday, or Sunday) has small inrinsic variabiliy. Alhough, ridership can also change from Monday o Friday in a sysemaic way, such differences are relaively small. I is easy o define variables o represen daily weaher condiions, and people do make ravel decisions on a daily basis. Mehods of Comparison Applying he relaive-comparison mehod, we need o compare he daily weaher and ridership o some benchmark weaher and ridership o assess he changes. Two mehods can be used o define he benchmark: adjacen-day comparison, and normalexreme comparison. In he firs approach, he benchmark is he weaher and ridership on he immediaely preceding day of he same ype (e.g. weekday, Saurday, Sunday). The raionale for his is ha people may adjus heir ravel behavior by comparing oday s weaher wih he forecas for omorrow: for similar weaher, ravel should also be similar. This is a reasonable argumen especially for non-work rips, which is likely o be he major par of weekday ridership variaion. In he second approach, he benchmark is defined as normal weaher and ridership for ha ime of year, recognizing he seasonal flucuaions in boh weaher and ridership. The underlying assumpion is ha a deviaion 9

10 from normal weaher will resul in a corresponding deviaion from normal ridership. In his paper, normal weaher is defined as having a emperaure wihin a 6 degree range around he 30 year hisorical average (1971 o 2000) for ha paricular day, and no precipiaion. Correspondingly, normal ridership is he average ridership on all normal weaher days. Each mehod has advanages and disadvanages. The advanage of he adjacen-day mehod is ha i has boh heoreical and empirical supporing evidence, and beer conrols for exogenous variables by narrowing he comparison o oday and he previous day. The disadvanage is ha i assumes a consan impac of a uni change of weaher variable. In realiy, an 0.1 inch rainfall increase from zero o 0.1 inch probably has a differen impac from he same increase bu from 1 inch o 1.1 inches. However, his mehod reas expeced impac as being equal, and averages hem o ge he final resul. The normal-exreme mehod parially resolves he problem by seing up a benchmark based on a hreshold of weaher impac. Changes in weaher condiions wihin he normal range will have lile impac on ransi ridership. Bu he disadvanage of his mehod is he loss of informaion. By seing up a normal weaher range and averaging ridership wihin ha range, some informaion is los, and here is less variaion in boh weaher and ridership variables. This may reduce he explanaory power of he esimaed models. Because of hese advanages and disadvanages, his research explores boh mehods o invesigae he weaher-ridership relaionship. If he wo mehods lead o consisen resuls, he weaher impac on ridership will be more srongly suppored and beer undersood. 10

11 CHICAGO TRANSIT AUTHORITY CASE STUDY Chicago Transi Auhoriy (CTA) is he naion's second larges public ransporaion sysem serving he Ciy of Chicago and 40 surrounding suburbs. The CTA bus sysem has abou 2,000 buses operaing on 152 roues serving more han 12,000 bus sops, while he rail sysem has 7 lines and 145 saions. On an average weekday, nearly 1 million rides are aken on he bus sysem, and a half million rides on he rail sysem. Ridership has been recorded by an AFC sysem since March 1998 for he rail sysem, and January 2001 for he bus sysem. The large resuling AFC daabase is well suied o suppor his ype of research and is used in his sudy. Chicago has dense lakefron developmen wih beaches and recreaional areas and a large lower densiy area away from he lakefron and he Loop. Lake Michigan has a moderaing influence on he local weaher, bu also frequenly causes overcas skies. Chicago averages 126 days annually wih precipiaion and 176 wih clouds. The weaher can also change rapidly as successions of air masses pass generally from wes o eas. Winers are no always consisenly cold while summers are no always consisenly ho, making Chicago paricularly aracive for his research. Meeorological daa for O Hare Airpor was chosen o represen he weaher condiions hroughou he region (hp:// Five weaher elemens are examined in his research: emperaure, wind, rain, snow, and fog. The highes daily emperaure is used o represen emperaure because i ypically occurs during dayligh hours, and so probably bes represens people s percepions of 11

12 emperaure for ha day. Three ypes of emperaure variables are defined: emperaure change, and wo dummy variables: warm and cool. For he adjacen-day approach, emperaure change is he difference in he highes emperaure beween ha day and he previous day. Warm weaher is defined as an increase of a leas 12 degrees (Fahrenhei) from he previous day, while cool weaher is defined as a decrease of a leas 12 degrees. For he normal-exreme approach, emperaure change is he emperaure deparure from a 30-year average on ha paricular dae. Warm weaher is defined as a emperaure a leas 12 degrees above he average, while cool weaher is defined as a emperaure a leas 12 degrees below he average. Two ypes of wind variables are defined: he daily highes wind speed ha lass for a leas wo minues, and windy weaher defined as a speed exceeding 25 miles/hour. This hreshold is chosen because his ype of wind can blow dus and paper from he ground, and may indicae a hreshold a which wind begins negaively o affec walking. Srong wind may be especially unpleasan for pedesrians on chilly winer days in Chicago. For he adjacen-day approach, he wind speed variable is he difference beween ha day and he previous day. For he normal-exreme approach, i is defined as he highes wind speed. The dummy variable for windy weaher is he same for boh approaches. For variables such as rain and snow, he oal amoun of daily precipiaion is used as he variable. The wo precipiaion variables are defined as differences beween ha day and he previous day for he adjacen-day approach, and beween ha day and normal weaher (no precipiaion) for he normal-exreme approach. Dummy variables are also defined o capure he effec of significan precipiaion. For rain, i is defined as greaer han 0.6 inches (80 percenile for all rainy days), and for snow, i is greaer han

13 inches (50 percenile for all snowy days). Differen perceniles are chosen because here are fewer snow observaions, and snow is likely o have a larger impac han rain on vehicle movemen. Fog migh affec driving because of reduced road visibiliy, and i may also influence ransi use. The inensiy of fog probably makes a difference, bu he meeorological daa only records he occurrence of fog, and does no indicae inensiy. Therefore, fog is reaed as a single rinary variable in his analysis. For he adjacen-day approach, i is 0 if boh ha day and he previous day are idenical wih respec o fog, 1 if ha day has fog while he previous day did no, and -1 if he previous day had fog while ha day does no. For he normal-exreme approach, i is a wo-value dummy, 1 if here is fog, and 0 oherwise. MODEL ESTIMATION AND ANALYSIS Because he impac of weaher on ransi ridership is highly dependen on mode, ime, and rip purpose, i is unlikely ha a single model will apply in all siuaions. A balance beween in-deph analysis for a paricular siuaion and comparison among siuaions is required. We chose an Ordinary Leas Square (OLS) model srucure because i is simple, and can be easily applied o various siuaions. A oal of 12 OLS models are esimaed. These models are for mode and day ype wih seasons included as dummy variables. The goodness-of-fi saisics reflec he daily ridership variaions explained by weaher. Each model is esimaed based on boh he adjacen-day and he normalexreme specificaions. 13

14 The basic OLS equaion and he noaion for he wo specificaions are explained below. The models are calibraed using he backward-delee mehod. Esimaions wih he highes adjused R square are acceped. The resuls of he welve esimaions are summarized in Tables 1 and 2 for bus and rail respecively. ΔY = α + ( β ΔR + β Heavy * ΔR) + ( β ΔS + β Big * ΔS) + ( β ΔW β 7ΔF + ( β8δt + β 9Cool * ΔT + β10warm* ΔT ) + β j Season j β Windy * ΔW ) 6 (1) Adjacen-Day Specificaion ΔY : Ridership change from he previous day Δ R, ΔS, ΔW, ΔT : Changes in rain, snow, wind, and emperaure from he previous day. Δ F : 1 from no fog o fog, -1 from fog o no fog, 0 oherwise Heavy : rain dummy variables, 1 if change of rainfall >= 0.6 inch/day, 0 oherwise Big : snow dummy variables, 1 if change of snow fall >= 0.5 inch/day, 0 oherwise Windy : dummy variable, 1 if highes wind speed(2 minues) >= 25 miles/hour, 0 oherwise Warm: dummy variable, 1 if emperaure increases >= 12 degrees from he previous day, 0 oherwise Cool : dummy variable, 1 if emperaure decreases > -12 degrees from he previous day, 0 oherwise Season : dummy variables for seasons, j=1,2,3. Which season is he base varies by model j α, β1 β10, β j : parameers for esimaion, noe β 2,β 4 β 6, β 9, β capure exreme weaher 10 even(heavy rain or snow, srong wind, warm and cool emperaure) effecs addiional o rainfall, snowfall, wind speed, and emperaure impac on ridership. Normal-Exreme Specificaion Δ Y : Ridership change from he normal weaher ridership Δ R, ΔS, ΔW, ΔT : Deviaions of rain, snow, wind, and emperaure from normal. 14

15 Δ F : 1 if here is fog, 0 oherwise Heavy : rain dummy variables, 1 if rainfall >= 0.6 inch/day for rain, 0 oherwise Big : snow dummy variables, 1 if snowfall >= 0.5 inch/day for snow, 0 oherwise Windy : dummy variable, 1 if highes wind speed (2 minues) >= 25 miles/hour, 0 oherwise Warm: dummy variable, 1 if emperaure >= 12 degrees above he hisorical average, 0 oherwise Cool : dummy variable, 1 if emperaure >= 12 degrees below he hisorical average, 0 oherwise Temperaure In mos cases, emperaure variables are significan and have a posiive sign, which means ha warmer weaher ends o lead o higher ransi ridership in all seasons. A one degree increase of emperaure resuls in a sysem-wide daily ridership increase of beween 652 and 1,087 for bus, and beween 240 and 663 for rail depending on day ype. The Cool and Warm weaher variables are no significan in mos cases, and when significan hey have inconsisen signs. One possible reason for his is he variable definiion: a sharp decrease (increase) in emperaure migh no be a good indicaor of cold (ho) weaher. Their impacs migh depend on he curren emperaure: a sharp emperaure decrease may be a pleasan relief in a ho summer, bu painful in a cold winer. A beer definiion which combines boh emperaure changes and human percepions is necessary o explore he possible effecs of exreme emperaure on ransi ridership. Precipiaion In mos cases, rainfall variables are significan, and have negaive coefficiens, which means ha rain ends o reduce ridership in all seasons for boh bus and rail. Such an 15

16 impac is sronger on weekends han on weekdays, and sronger for bus han for rail. One more inch of daily rainfall will reduce ypical sysem-wide daily ridership by beween 16,283 and 88,335 for bus, and beween 5,220 and 44,557 for rail depending on day ype. Snow, similarly o rain, ends o reduce bus ridership. One more inch of daily snowfall will reduce daily bus ridership by beween 9,650 and 188,080 depending on day ype. This effec is less eviden for rail. As wih emperaure, heavy rain or snow are eiher insignifican or have inconsisen signs. However, he explanaion migh be differen from ha for emperaure. Rain or snow may reduce rail ridership bu heavy rain or snow, paricularly blizzards, may shif ravelers from auo and bus o rail especially on weekdays, hus increasing rail ridership. Wind Wind speed is also significan in mos cases, and has a consisen negaive sign. One mile/hour increase of highes wind speed ypically reduces sysem-wide daily ridership by beween 723 and 2,747 for bus, and beween 506 and 996 for rail. Srong wind (>=25 miles/hour) has a negaive sign bu is no significan in mos cases, which means ha very windy weaher does no cause addiional loss of ransi ridership. As wih oher weaher elemens, wind affecs bus more han rail, and weekends more han weekdays. Fog Fog shows consisen posiive signs, and in several siuaions is significan a he 10 percen level. This migh sugges ha foggy weaher ends o increase ransi ridership and has a sronger effec on rail han bus. Fog is a conribuing variable in all rail models 16

17 (wo are significan), bu only in wo bus models (boh insignifican). A foggy day will ypically increase sysem-wide daily rail ridership beween 8,140 and 10,411. The explanaion is inuiive: fog increases he difficuly and risk of driving, and may shif ravelers o ransi, especially rail, which has is own righ-of-way. In mos cases, he adjacen-day mehod yields higher R squares han he normalexreme mehod, which is our expecaion. Therefore, he adjacen-day mehod is chosen for he planning implicaion in Secion 6. In general, coninuous variables such as rainfall, snowfall, emperaure, and wind speed are significan wih expeced signs. Exreme weaher variables such as warm, cool, windy, heavy rain or snow are eiher insignifican or have inconsisen signs. This indicaes ha he exreme weaher evens eiher do no have addiional impac on ridership, or he addiional impac is in he opposie direcion, which he OLS model is unable o deec. I is also likely ha he exreme weaher variables have small variaion compared o he coninuous variables in he daase, which causes inconsisen esimaion resuls. More observaions and oher saisical models such as nonparameric echniques are necessary o invesigae he impac of exreme weaher evens (21), The composie impac of weaher condiions may well be as imporan as he impac of individual weaher elemens in he weaher-ridership relaionship. The adjused R square is he goodness-of-fi of a model, indicaing how much of he variaion in he dependen variable daa is explained by he independen variables. I is a reasonable indicaor of he composie effec of weaher since all independen variables are weaher 17

18 variables. The higher he adjused R square, he more variaion of ridership is explained by weaher. Models for bus have higher adjused R square values han models for rail across all day ypes. The average R squares from he wo specificaions are 0.32 and 0.24 for bus, bu only 0.09 and 0.04 for rail. Based on he discussion in Secion 2, possible explanaions include: (1) bus sops are ypically more exposed o weaher han rail saions, especially underground saions, (2) a much larger share of rail rips are work rips, and (3) rail usually has a higher service frequency han bus. Boh specificaions show he consisen resul ha weekend rips are more likely o be affeced by weaher han weekday rips. The average R squares for boh bus and rail from he wo specificaions are 0.29 and 0.19 for weekend, bu only 0.04 for weekdays. This is our expecaion since many more weekday riders are commuers, and weekdays have higher service frequencies han weekends. Work rips are less affeced by weaher because hey are inelasic and have inflexible schedules. Wihin weekends, Saurday rips seem more likely o be affeced by weaher han Sunday, bu he difference is less clear. The R squares from Saurday models are higher han hose from he Sunday models for rail (boh mehods) and bus (adjacen-day mehod), bu lower for bus using he normal-exreme mehod. One explanaion is he poenial ineracion beween he wo days. For example, if Saurday has bad weaher, ravelers may pospone heir rips o Sunday (22). 18

19 IMPLICATION OF THE WEATHER-RIDERSHIP RELATIONSHIP The weaher-ransi ridership relaionship revealed hrough his research has policy implicaions in ransi operaions and planning as we demonsrae here wih an applicaion o ridership rend analysis. In any ransi auhoriy, an imporan dimension of performance racking is o analyze sysem-level ridership rends. This is usually done a a monhly level by comparing he monhly ridership wih he same period of he previous year. Alhough ransi auhoriies acknowledge ha ridership flucuaes, misinerpreaion of underlying ridership rends can occur due o various exogenous facors such as major evens or unexpeced weaher condiions. Weaher can be viewed as a random elemen bu i can have a sysemaic impac on ransi ridership. Therefore, an imporan quesion in he monh-o-monh comparison is wha he rue ridership rend is afer conrolling for weaher impacs. The weaher models developed in his research can be used o correc for he weaher impac in ridership rend analysis. Suppose ha he acual monhly ridership in a year is R, which consiss of a weaher-affeced porion W, and a porion deermined by all oher facors E including economic cycle, populaion growh, service change, fare increase, ec. I is safe o assume ha W and E are no correlaed, so no including E in he weaher model does no affec he esimaion of he weaher impac. Therefore, he analysis is no o develop a general ridership model, bu raher look a he accumulaive effec of weaher on ridership. The following equaions illusrae he process, where he ridership prediced by he weaher model. Acual Ridership Change: P is ΔR = R R 1 = ( W + E ) ( W 1 + E 1) = ΔW + ΔE (2) 19

20 Prediced Ridership Change: ΔP = P P 1 = W W 1 = ΔW (3) Ridership Change Conrolling for Weaher Effec: Δ R ΔP = ΔE (4) Because he model is developed for daily ridership, we need o calculae he ridership for every day in a monh and sum hem for he monhly ridership comparison. There is a quesion on wheher he sum overlooks he poenial of ridership changes o cancel each oher ou because of he possible ineracion beween differen days. We believe i is no a concern because he model is buil based on he observed daily ridership ha already includes he canceling-ou effec. Anoher issue is ha he number of days in he compared monhs should be adjused because here migh be differen numbers of weekdays and weekends in he same monh in differen years. To accoun for his, he average weekday and weekend day ridership is esimaed and summed across he normal mix of weekdays and weekend days in ha monh (See Table 3). Anoher concern is wheher service changes during his period of analysis is conrolled for. We believe service change and fare increase may have influence, bu no significanly. Bus service changes infrequenly, maybe once or wice a year. This only affecs one observaion on he service-changing day in he adjacen-day mehod, or less han one percens of oal observaions used in model esimaion. This migh be a greaer concern for he normal-exreme mehod because i affecs all observaions in he servicechanging monh, which represen abou hree percen of oal observaions. We use he summer bus ridership based on he adjacen-day model for his applicaion wih he resuls summarized in Table 3. Clearly, he resul shows a noiceable difference 20