Spatial pattern of the Walkability Index, Walk Score and Walk Score modification for elderly

Ci a ion: Ho ak, J.; Kukuliac, P.; Ma eso a, P.; O liko a, L.; Kolodziej, O. Spa ial Pa e n o he Walkabili y Index, Walk Sco e and Walk Sco e Modi ica ion o Elde ly. ISPRS In . J. Geo-In . 2022,11, 279. h ps:// doi.o g/10.3390/ijgi11050279 Academic Edi o : Wol gang Kainz Recei ed: 24 Feb ua y 2022 Accep ed: 26 Ap il 2022 Published: 27 Ap il 2022 Publishe ’s No e: MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional a il- ia ions. Copy igh : © 2022 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h ps:// c ea i ecommons.o g/licenses/by/ 4.0/). In e na ional Jou nal o Geo-In o ma ion A icle Spa ial Pa e n o he Walkabili y Index, Walk Sco e and Walk Sco e Modi ica ion o Elde ly Ji i Ho ak 1,* , Pa el Kukuliac 1, Pe a Ma eso a 2, Lucie O liko a 1and Ond ej Kolodziej 1 1Depa men o Geoin o ma ics, VSB—Technical Uni e si y o Os a a, FMG, 17. lis opadu 2172/15, Po uba, 70800 Os a a, Czech Republic; [email p o ec ed] (P.K.); [email p o ec ed] (L.O.); [email p o ec ed] (O.K.) 2Depa men o Economics, Uni e si y o H adec K álo é, FIM, Roki anského 62, 50003 H adec K alo e, Czech Republic; [email p o ec ed] *Co espondence: [email p o ec ed] Abs ac : Con empo a y ci ies equi e excellen walking condi ions o suppo human physical ac i i y, inc ease humans’ well-being, educe a ic, and c ea e a heal hy u ban en i onmen . Va ious indica o s and me ics exis o e alua e walking condi ions. To e alua e he spa ial pa e n o objec i e- based indica o s, wo popula indices we e selec ed— he Walkabili y Index (WAI), ep esen ing en i onmen al-based indica o s, and Walk Sco e (WS), which applies an accessibili y-based app oach. Bo h indica o s we e e alua ed using adequa e spa ial uni s (ci cle bu e s wi h adii om 400 m o 2414 m) in wo Czech ci ies. A new so wa e ool was de eloped o he calcula ion o WS using OSM da a and eely a ailable ne wo k se ices. The new a ian o WS was speci ically designed o he elde ly. Di e ing gai speeds, and a iable se ings o a ge s and hei weigh s enabled he adap a ion o WS o local condi ions and pe sonal needs. WAI and WS demons a ed di e en spa ial pa e n whe e WAI is be e used o smalle adii (up o app ox. 800 m) and WS o la ge adii (s a ing om 800 m). The assessmen o WS o bo h ci ies indica es ha app ox. 40% o inhabi an s li e in unsa is ac o y walking condi ions. A sensi i i y analysis disco e ed he majo in luences o gai speed and he βcoe icien on he walkabili y assessmen . Keywo ds: walkabili y; Walk Sco e; Walkabili y Index; elde ly; sensi i i y analysis; accessibili y; GIS 1. In oduc ion Walking con ibu es o a heal hy li es yle. U ban esiden s’ lack o su icien physical ac i i y con ibu es o he de elopmen o ch onic diseases. Physical inac i i y has been no ed as he second leading modi iable isk ac o o ch onic disease a e smoking and con ibu es signi ican ly o o al mo ali y in Wes e n coun ies [ 1 , 2 ]. Inc easing popula ion- le el physical ac i i y and educing physical ac i i y and heal h inequali ies is a g owing in e es o policy make s [3–6]. Mobili y is undamen al o ac i e aging [ 7 , 8 ] and is a necessa y p e equisi e o senio s o hei independen way o li e and sel - eliance, including he capaci y o go ou [ 9 , 10 ], and o ca y ou social and leisu e ac i i ies [ 10 , 11 ]. Wi h aging, declines in heal h o en limi easible ac i i ies [ 12 ] and pu cons ain s on one’s capaci y o pe o m daily li e ac i i ies [ 11 , 13 ]. “Denied accessibili y,” when he numbe o op ions sh inks, is a g ea e p oblem o he elde ly [ 8 ]. Howe e , senio s o m a qui e di e se social g oup [ 14 ] wi h he e ogeneous a el beha iou . Many la en psycho-social ac o s a ec hei a el beha iou , such as di e se li es yles and a i udes (e.g., [ 15 ]), as well as hei sel - epo ed physical and unc ional abili ies (e.g., [12,16]). Today’s ci ies ocus on hei inhabi an s and aim o imp o e he u ban en i onmen h ough a complex se o ac i i ies [ 3 , 10 , 17 , 18 ]. Building a pleasan en i onmen is essen ial o he well-being o esiden s and isi o s, bu also has a mul iplica i e syne gy e ec on business and en ep eneu ship. G owing accen s on g een policy, na u al p o ec ion, ISPRS In . J. Geo-In . 2022,11, 279. h ps://doi.o g/10.3390/ijgi11050279 h ps://www.mdpi.com/jou nal/ijgi ISPRS In . J. Geo-In . 2022,11, 279 2 o 29 and iendly, sa e, and heal hy u ban en i onmen s a e leading local go e nmen s o p o- g essi ely es ic indi idual and comme cial mo o ized anspo , namely in ci y cen es, enla ge pedes ian zones, and adop measu es aimed a p omo ing pedes ians. “Pedes ian i s ” is a key e m o many ci y ep esen a i es. “Ci ies o all” and a swi ch o pa adigm owa ds mo e iendly and inclusi e u ban en i onmen s [ 8 ] a e now in e na ionally ecog- nised policies (e.g., [ 1 , 8 , 19 ]). Such imp o emen s posi i ely a ec he majo i y o senio s whe he o no hey hemsel es eel physically handicapped. Due o he g adual decline o physical capabili ies and equen empo al es ic ions due o episodic heal h issues in senio s, any dec ease in mobili y ba ie s is welcome. Webbe e al. [ 7 ] es ablished 5 undamen al ca ego ies o mobili y de e minan s— cogni i e, psycho-social, physical, en i onmen al, and inancial. Those s udies add essing en i onmen al ac o s p e ail because hey a e modi iable and can be add essed by local s akeholde s. They exhibi o e s o he en i onmen o he inhabi an s which can be modi ied o imp o ed o be mo e com o able and a ac i e and, in u n, mo i a e people, including senio s, o walk mo e o en. Many s udies explo e he physical and en i onmen al cha ac e is ics o he buil en- i onmen o de ec which ac o s in luence he “walkabili y” o he elde ly [ 12 , 17 , 20 – 30 ] so as o p o ide use ul in o ma ion o imp o ing pedes ian accessibili y. Mainly, highe le els o esiden ial densi y, s ee connec i i y, and land use mix epo ed highe walking and cycling equency [ 31 – 34 ]. Addi ional ac o s may also play an impo an ole in local s udies, e.g., geomo phological ac o s such as he slope o he e i o y [ 26 , 35 – 37 ], he dis- ibu ion o landma ks [ 38 , 39 ], block pe meabili y [ 39 , 40 ], unc ional conno a ions [39,41] , and a ac i eness o he u ban buil en i onmen [39,42–44]. Fu he mo e, he u ban buil en i onmen is pe cei ed and e alua ed di e en ly by di e en social g oups. Di e ences in pe cep ion be ween adul and senio popula ions a e explica ed by [ 45 ] who documen ed ha mo e han 60% o “good” pedes ian ne wo k o “adul s” in wo obse ed dis ic s o Lisbon was ca ego ised as “ ai ” o “bad” o senio s. Schola s ha e de eloped mo e han 80 indica o s o assess he walkabili y o an u ban en i onmen [ 46 – 48 ]. They a e based p incipally on human pe cep ion (usually sel - epo ing, subjec i e measu es), on measu able cha ac e is ics o u ban en i onmen s (objec i e measu es), o a combina ion o he wo. They analyse u ban condi ions in di e en uni s o space wi h a a ie y o se ings. Howe e , hei usage esul s in a g ea a iabili y o ope a ionalisa ion o ele an ac o s because any gi en neighbou hood cha ac e is ic can be measu ed many di e en ways [ 49 ] and hei combina ion is highly a ec ed by inconsis encies [ 49 , 50 ]. Mo eo e , walkabili y can be assessed using di e en spa ial uni s [51] and di e en me hods o agg ega ion. Some o he indices enable he a ge and weigh se ings o adap he measu emen o local condi ions and/o o he equi emen s o special g oups o inhabi an s. The ques ion is how o se app op ia e weigh s, a ge s, and alues o dis ance-decay unc ions and wha he impac o he unce ain y linked o hese se ings migh be. The goal o his pape is o con ibu e o he discussion on walkabili y me ics; we enume a e wo mains eam indica o s, each based on di e en app oaches o iden ical spa ial uni s, compa e hei pa e n acco ding o scale, desc ibe di e ences be ween adul and elde ly popula ions, and assess he sensi i i y o he e alua ion based on pa ame e s such as gai speed, dis ance-decay unc ion and mobili y a ge weigh ing. The pape is o ganized as ollows: he backg ound p o ides a e iew o di e en app oaches and me ics used o walkabili y assessmen , and wo main g oups o indica- o s a e exempli ied. La e , he con igu a ion o indica o s is discussed wi h a ocus on des ina ions, dis ance-decay unc ions, weigh s, spa ial uni s, sea ch adii, and easonable walking dis ances. The hi d chap e sho ly in oduces wo pilo ci ies and explains he me hods o calcula ion o wo selec ed indica o s, WAI and WS. App op ia e modi ica ions and new so wa e ools a e documen ed. Resul s o WAI and WS in bo h ci ies o ou di e en sea ch adii a e p esen ed and discussed. A modi ica ion o WS o elde ly in ISPRS In . J. Geo-In . 2022,11, 279 3 o 29 Czech condi ions is in oduced and compa ed wi h s anda d WS. Finally, a sensi i i y analysis in es iga es he impac o di e en se ings on WS o elde ly assessmen . 2. Backg ound In one o he mos acknowledged analyses, Ewing and Ce e o [ 30 ] ou lined i e dimensions o he walking en i onmen in luencing a el beha iou and walking. The basic h ee dimensions [ 52 ], i.e., densi y, des ina ions and design we e la e ex ended by adding—des ina ion accessibili y, and dis ance o ansi . These 5 dimensions (5Ds) a e o en used o p opose sui able one-dimensional indica o s and allow a complex e alua ion o walkabili y co e ing he majo i y o hese dimensions. Densi y is usually measu ed by indica o s such as Household/popula ion densi y, Job densi y o Comme cial loo a ea a io. Di e si y can be exp essed as Land use mix (en opy index), e en ually as Jobs- housing and simila a ios. Design measu es include a e age block size, p opo ion o ou - way in e sec ions, and numbe o in e sec ions pe squa e mile. Des ina ion accessibili y measu es ease o access o ip a ac ions. Dis ance o ansi is usually measu ed as an a e age o he sho es ou es om he o igin o he nea es Public T anspo (PT) s op. Coincidence o some o hese dimensions equen ly causes issues in s ong collinea i y be ween he 5Ds [ 48 , 53 ]. Zhang e al. [ 54 ] c i isize he missing ela ionship be ween he dimensions and scale and he lacking guidance o implemen a ion. Howe e , his concep s ill ep esen s a solid base o unde s and he main ac o s a ec ing walkabili y. O cou se, no all walkabili y indices add ess all 5 dimensions. Au ho s can emphasize speci ic ea u es wi h s onge in luence in a gi en en i onmen (e.g., shade o noise [ 55 , 56 ]) o o a speci ic g oup o people (e.g., s ee cleanliness o women’s walkabili y [ 57 ]; o ehicula a ic exposu e o school walkabili y [58]). No mally, basic en i onmen al cha ac e is ics ela ed o p opensi y o walk a e mod- i ied o special in e es g oups such as you h o senio s. In he case o senio s, hey a e usually elabo a ed mo e owa ds de ail u ban cha ac e is ics (e.g., [ 19 ]), emphasizing he essen ial ole o a ious obs acles and ba ie s o people wi h cons ained mobili y, as well as unde lining psychological ba ie s such as ea o alling, and ea o c ime. Basically, we can classi y indices based on measu able objec i e ac o s, pe cep ion (audi -based, su eys) ac o s, o a hyb id o he wo. Acco ding o se e al au ho s, objec- i e measu es ha e s onge associa ions wi h walking han subjec i e measu es [59–61] . In his s udy, we ocus on objec i e measu es which can be well ope a ionalised in Geog aphic In o ma ion Sys em (GIS). Wi hin he objec i e measu es o walkabili y, wo main app oaches a e popula : 1. En i onmen al (s a is ical) based indica o s—calcula e local u ban cha ac e is ics ela ed o walking po en ial. No dis ances a e aken in o accoun and ce ain ela i e measu es o neighbou hood condi ions such as a ios a e applied. 2. Accessibili y based indica o s—e alua e a el pa ame e s in a oad ne wo k o se- lec ed des ina ions. F om he poin o iew o a h ee-accessible amewo k [ 54 , 62 ], walking measu es a e use ul o assess local access o acili ies (local accessibili y) and ansi access. Zhang e al. [63] emphasize non-linea and h eshold e ec s o p oximi y o accessibili y, and speci ica ion o e ec i e anges o speci ic land use a iables. One o he mos equen ly used en i onmen al-based walkabili y indices is he Walkabili y Index (WAI) de eloped by F ank e al. [ 64 ], used in a mul i ude o a ailable s udies [ 19 , 28 , 48 , 65 , 66 ]. WAI e alua es connec i i y, he e ogenei y o land use, shopping a ea, and household densi y. The Pedes ian Po en ial Index, based on WAI, e alua es esiden ial densi y, in e - sec ion densi y, land use mix, and des ina ion densi y. Due o clea simila i y wi h WAI, esul s a e qui e simila o he ou pu s o WAI [48]. Imp o ed compa abili y o communi ies is a ge ed in he Na ional Walkabili y Index de eloped by he En i onmen al P o ec ion Agency [ 67 ]. The index elemen s include design, dis ance o ansi , and di e si y o land use. ISPRS In . J. Geo-In . 2022,11, 279 4 o 29 Usually, only a ew u ban ex u al p ope ies a e e alua ed in each s a is ical index. This me hod is expanded in a new syn he ic walkabili y index [ 42 ] whe e many ypes o ameni ies a e explo ed o calcula ion o ameni y densi y combined wi h a Shannon di e - si y index, in e sec ion densi y, and a e age ele a ion and slope as opog aphical a iables. The dominan ep esen a i e o accessibili y-based walkabili y indices is Walk Sco e (WS) [ 65 , 68 ]. WS equi es sea ching o he sho es pa hs o ameni ies in 9 ca ego ies, e alua ing hei dis ance using a speci ic dis ance decay unc ion (DDF), applying weigh s o each ca ego y, and educing he esul ing WS in cases o poo pedes ian condi ions. Ad an ages o WS a e he e alua ion o eal ne wo k accessibili y o he mos impo an des ina ions, and he sys em o weigh ing based on a dis ance-decay app oach [ 61 ]. WS is also b oadly used by e.g., [19,28,42,66,69], bu no wo ldwide due o da a sho ages. WS also ep esen s a s a line o a ious modi ica ions, pa ly d i en by simpli ica ion e o s such as eplacing ne wo k dis ances wi h Euclidean ones [ 42 ], o mo i a ion o de elop a be e adap ed o mula o speci ic en i onmen s such as apidly u banizing ci ies [25]. The e a e many o he walkabili y indices in ol ing ne wo k accessible, objec i e, measu able componen s such as he Pedes ian Index o he En i onmen [ 48 , 65 , 70 ], he Neighbou hood Des ina ion Accessibili y Index [ 48 , 65 , 71 ], Pedshed [ 66 , 69 ], Mo abili y index [66], and he Pedes ian Po en ial Index [48]. A mixed e alua ion con aining bo h ne wo k accessibili y measu es and s a is ical p ope ies o he neighbou hood is exempli ied by A ea Walking Po en ial [ 4 ], assessing accessibili y o 9 weigh ed des ina ion ca ego ies (heal h, public ansi , educa ion, open space, social & cul u al, non- ood e ail, inancial, ood e ail and employmen ), as well as esiden ial densi y and in e sec ion densi y as s a is ical pa ame e s o he neighbou hood. Ano he mixed index, Peel Walkabili y Composi e Index, [ 72 ] consis s o 3 equally weigh ed componen s whe e he i s componen is dedica ed o esiden ial densi y and di e si y while he o he s e alua e ne wo k accessibili y using access o e ail and se ice ou le s, schools and g een spaces. 3. Con igu a ion o Indica o s To measu e walkabili y, one mus i s choose a basic uni o space. Spa ial uni s used o walkabili y assessmen a e o en adminis a i e uni s o u ban planning uni s. While u ban planning uni s a e he subjec o na u al de elopmen o u ban en i onmen s, delimi a ion o adminis a i e uni s is in luenced by policy egula ions which do no always con o m o eal u ban ca chmen s; ab up empo al changes, a iabili y in size, Modi iable A ea Uni P oblem (MAUP), and s ong bo de e ec s a e some o he ypical issues ha a ise. Walkabili y can be assessed o all o selec ed poin s (e.g., add esses o esidences), bu usually a egula g id is applied o p o ide con inuous e alua ion o he e i o y and o elimina e bo de e ec s [ 48 ] and undesi ed in luences o di e en size and shape o spa ial uni s. While some au ho s p e e g ids a ound 100 m (e.g., 80 × 80 m [ 73 ], 100 × 100 m [ 66 ], 150 m [ 25 ], a highly dense g id o 25 m × 25 m is p oposed in [ 12 ]), and a b oade g id o 500 m was employed in assessmen s o Ge man ci ies based on he OS-WALK-EU ool [ 74 ]. Schola s aim o p o ide de ailed e alua ions o add ess he e ogeneous walking condi ions, bu he se ings a e seldom jus i ied o explained [48]. Conce ning sea ch adius , Le eb e-Ropa s and Mo ency [ 48 ] commen “no consen- sus has been eached on he size o he ca chmen a ea ha should be used o measu e walkabili y”. O iginally, Pe y [ 75 ] p oposed a 5-min walking dis ance which is usually ansla ed in o a 400 m adius, e.g., [ 66 , 76 – 78 ]. Re . [ 12 ] used he 500 m bu e , [ 4 ] used 1000 m ne wo k bu e zones in Sco land, [ 28 ] a 1.6 km ne wo k bu e and [ 58 ] a 2 km ne - wo k bu e a ound each school. WS ex ends each ne wo k bu e up o 1.5 miles (app ox. 2.4 km). Na u ally, he sea ch adius should co espond o accep able walking dis ance . Maxi- mal walking dis ance o people wi hou limi a ions is usually se a 1–2 km [ 28 , 58 , 61 ], how- ISPRS In . J. Geo-In . 2022,11, 279 5 o 29 e e some indices use a sho e app op ia e walking dis ance such as 400 m [ 61 , 66 , 79 , 80 ]. Recommenda ions a e mo e a iable o senio s, pa ly due o hei di e si y o needs and le els o mobili y. A common opinion is ha senio s ul il he majo i y o hei needs wi hin 15 min walking om hei esidence [ 10 ]. Some au ho s dis inguish p ima y and seconda y se ices o he elde ly; basic se ices should be loca ed wi hin 400 m o elde ly peoples’ esidences, which co esponds o a 5-min walking dis ance [ 18 ], and seconda y se ices should be loca ed wi hin 800 m, o wice he walking dis ance. Bu on and Mi chell [ 81 ] a gue o longe dis ances, ecommending 500 m o he 1s g oup and subs an ially enla g- ing he second pe ime e o no limi elde ly people o eaching seconda y se ices du ing hei daily ou ines. Also, esul s o he local su ey using he day ecogni ion me hod in Os a a and Olomouc, 2014 [ 82 ], con i med longe walking dis ances. Based on he shape o he cumula i e ela i e equency g aph (Figu e 1), common senio s’ walking dis ances each up o 700 m, while maximal dis ances each up o 1200 m. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 5 o 32 Conce ning sea ch adius, Le eb e-Ropa s and Mo ency [48] commen “no consen- sus has been eached on he size o he ca chmen a ea ha should be used o measu e walkabili y”. O iginally, Pe y [75] p oposed a 5-min walking dis ance which is usually ansla ed in o a 400 m adius, e.g., [66,76–78]. Re . [12] used he 500 m bu e , [4] used 1000 m ne wo k bu e zones in Sco land, [28] a 1.6 km ne wo k bu e and [58] a 2 km ne wo k bu e a ound each school. WS ex ends each ne wo k bu e up o 1.5 miles (ap- p ox. 2.4 km). Na u ally, he sea ch adius should co espond o accep able walking dis ance. Max- imal walking dis ance o people wi hou limi a ions is usually se a 1–2 km [28,58,61], howe e some indices use a sho e app op ia e walking dis ance such as 400 m [61,66,79,80]. Recommenda ions a e mo e a iable o senio s, pa ly due o hei di e si y o needs and le els o mobili y. A common opinion is ha senio s ul il he majo i y o hei needs wi hin 15 min walking om hei esidence [10]. Some au ho s dis inguish p ima y and seconda y se ices o he elde ly; basic se ices should be loca ed wi hin 400 m o elde ly peoples’ esidences, which co esponds o a 5-min walking dis ance [18], and seconda y se ices should be loca ed wi hin 800 m, o wice he walking dis ance. Bu on and Mi chell [81] a gue o longe dis ances, ecommending 500 m o he 1s g oup and subs an ially enla ging he second pe ime e o no limi elde ly people o eaching seconda y se ices du ing hei daily ou ines. Also, esul s o he local su ey using he day ecogni ion me hod in Os a a and Olomouc, 2014 [82], con i med longe walking dis ances. Based on he shape o he cumu- la i e ela i e equency g aph (Figu e 1), common senio s’ walking dis ances each up o 700 m, while maximal dis ances each up o 1200 m. Figu e 1. Cumula i e ela i e equency o walking dis ances in Os a a and Olomouc, 2014. One o he mos impo an ac o s o accessibili y-based indices is he selec ion o des ina ions. WS in es iga es accessibili y o he ollowing ameni ies: g oce y, es au- an s, shopping, co ee, banks, pa ks, schools, books o es, and en e ainmen [83]. These a ge s should co espond well o gene al public in e es s, bu no o hose o speci ic g oups such as you h o he elde ly. Gene ally, he pu poses and des ina ions o mobili y depend on he ca ego y o people in ques ion and a e based on ac o s such as age, eco- nomic s a us, and cul u al/geog aphical di e ences (e.g., he mos isi ed des ina ions in Saudi A abia a e mosques [84]). Figu e 1. Cumula i e ela i e equency o walking dis ances in Os a a and Olomouc, 2014. One o he mos impo an ac o s o accessibili y-based indices is he selec ion o des ina ions . WS in es iga es accessibili y o he ollowing ameni ies: g oce y, es au an s, shopping, co ee, banks, pa ks, schools, books o es, and en e ainmen [ 83 ]. These a ge s should co espond well o gene al public in e es s, bu no o hose o speci ic g oups such as you h o he elde ly. Gene ally, he pu poses and des ina ions o mobili y depend on he ca ego y o people in ques ion and a e based on ac o s such as age, economic s a us, and cul u al/geog aphical di e ences (e.g., he mos isi ed des ina ions in Saudi A abia a e mosques [84]). Weigh ing o a ge s enables he dis inc ion o di e en a ge impo ance in mobili y pa e ns and ep esen s an essen ial equi emen in he applica ion o a g a i y-based app oach. WS de ines equal weigh s o mos ca ego ies, excep o g oce y s o es (sum o weigh s 3), es au an s/ba s (sum o weigh s 3), and shopping and co ee shops (sum o weigh s 2). The majo i y o ne wo k-based indica o s include a dis ance-decay e ec o emphasize he ole o close a ge s and exp ess he diminished p opensi y o walk wi h g owing dis ance. Va ious DDF a e p oposed o walking modelling. The o iginal WS uses a polynomial DDF ha gi es ull sco e o nea ull sco e o ameni ies ha a e wi hin 0.25 miles o he o igin. A e his, sco es dec ease smoo hly wi h dis ance. A a dis ance o 1 mile, ameni ies ecei e only abou 12% o he sco e hey would ha e had i hey we e igh nex o he o igin. A e 1 mile, sco es dec ease less quickly wi h g ea e dis ance, un il ISPRS In . J. Geo-In . 2022,11, 279 6 o 29 hey each 1.5 miles, a e which hey do no coun owa ds he inal sco e [ 83 ]. Va ious modi ica ions and simpli ica ions o DDFs o he WS calcula ion ha e been applied. e.g., Reye e al. [ 28 ] simpli ied he calcula ion o a se ies o dis ance bands. Simila ly [ 25 ], used a se o poin alues based on [85]. Some au ho s [ 61 , 86 ] conside a cumula i e Gaussian unc ion o ha e he bes i o walking: Wij =e− ij2/β, whe e ij s ands o a el ime and he coe icien β is he only adjus able pa ame e . The unc ion’s main cha ac e is ic is ha i quickly dec eases when ime a el is close o he maximum a ailabili y o minu es ha people equi e [87]. The Gaussian DDF was adap ed o he elde ly in [ 88 ]. The β coe icien was se o 180 o people aged be ween 65 and 69, 160 o hose be ween 70 and 74 and 140 o hose aged 75 and o e in o de o bes ep esen he mobili y a i udes o di e en elde ly age ca ego ies acco ding o ou comes in he scien i ic li e a u e [89]. 4. Ma e ials and Me hods Two indica o s we e selec ed o con as he wo main app oaches in objec i e mea- su emen o walkabili y—WAI and WS. WAI ep esen s a ypical s a is ical-based indica o while WS is a popula ep esen a i e o ne wo k-based accessibili y indica o s which is widely used in he USA, Canada, Aus alia and elsewhe e. Because each indica o de ines i s spa ial uni s a di e en way, we used a squa e g id o 500 m as an o igin wi h a ci cula bu e a ound each o igin. Using he mos simila spa ial uni s o assessmen and apply- ing he same se ings whe e applicable, we assu ed consis ency in he e alua ion o he wo indica o s. We also applied di e en bu e s modelling di e en maximal accep able walking dis ances. Using only g id o 500 m may be a subjec o discussion. Only one egula scheme o bu e s was explo ed due o limi a ions o his s udy. A walkabili y assessmen o o he g id dis ances would subs an ially ex end he s udy and ep esen s an oppo uni y o a u he c oss- alida ion s udy. Also, he in luence o he posi ion o he s a ing poin o assessmen o bo h indica o s should be analysed, bu he an icipa ed impac is no high. To e alua e he impac o walkabili y assessmen , he numbe o esiden s in each spa ial uni (ci cle bu e ) is agg ega ed using he numbe o esiden s om census 2011 e e enced wi h add ess poin s. Mo e de ailed demog aphic da a o each add ess poin is no a ailable in Czechia due o p i acy p o ec ion. The indica o s we e e alua ed in Os a a and H adec K alo e (Figu e 2), wo middle- sized ci ies and egional capi als in Czechia. H adec K alo e (popula ion 100,000) is a ypical old cen al Eu opean ci y wi h an old ci y co e, and which was de eloped mainly a e he decline o o i ica ion in he 19 h cen u y. Os a a (popula ion 290,000) consis s o an agglome a ion o ela i ely closed communi ies (u ban blocks) sepa a ed by c op ields, o es s, and indus ial pa ks as a esul o sho bu in ensi e indus ial de elopmen and adminis a i e union o o iginally independen municipali ies. 4.1. WAI WAI agg ega es ou indica o s: he connec i i y index (CONN), which measu es he densi y o in e sec ions o walkable oads, Shannon’s en opy index (ENT), which quan i ies he he e ogenei y o land uses wi hin an a ea, he loo a ea a io (FAR) index, which e alua es he in ensi y o shopping oppo uni ies as a a io o loo a ea and a ailable comme cial land use, and he household densi y index (HDENS), which is ela ed o esiden ial land use. The equi ed inpu da a is demons a ed in Figu e 3. WAI is ypically e alua ed using geog aphical zones such as adminis a i e uni s, equen ly due o he una ailabili y o any o he o m o app op ia e s a is ical da a. Fo his s udy, WAI was calcula ed inside a ci cula bu e a ound each g id poin (cen oid) o imp o e he compa ison wi h WS. This way, all spa ial uni s o WAI ha e he same size ISPRS In . J. Geo-In . 2022,11, 279 7 o 29 and shape. This solu ion also elimina es some o he disad an ages o he WAI calcula ion o adminis a i e uni s. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 7 o 32 ields, o es s, and indus ial pa ks as a esul o sho bu in ensi e indus ial de elop- men and adminis a i e union o o iginally independen municipali ies. Figu e 2. Loca ion o e alua ed ci ies. 4.1. WAI WAI agg ega es ou indica o s: he connec i i y index (CONN), which measu es he densi y o in e sec ions o walkable oads, Shannon’s en opy index (ENT), which quan- i ies he he e ogenei y o land uses wi hin an a ea, he loo a ea a io (FAR) index, which e alua es he in ensi y o shopping oppo uni ies as a a io o loo a ea and a ailable comme cial land use, and he household densi y index (HDENS), which is ela ed o es- iden ial land use. The equi ed inpu da a is demons a ed in Figu e 3. Figu e 3. Main inpu da a equi ed o calcula ion o WAI and WS. WAI is ypically e alua ed using geog aphical zones such as adminis a i e uni s, equen ly due o he una ailabili y o any o he o m o app op ia e s a is ical da a. Fo his s udy, WAI was calcula ed inside a ci cula bu e a ound each g id poin (cen oid) o imp o e he compa ison wi h WS. This way, all spa ial uni s o WAI ha e he same Figu e 2. Loca ion o e alua ed ci ies. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 7 o 32 ields, o es s, and indus ial pa ks as a esul o sho bu in ensi e indus ial de elop- men and adminis a i e union o o iginally independen municipali ies. Figu e 2. Loca ion o e alua ed ci ies. 4.1. WAI WAI agg ega es ou indica o s: he connec i i y index (CONN), which measu es he densi y o in e sec ions o walkable oads, Shannon’s en opy index (ENT), which quan- i ies he he e ogenei y o land uses wi hin an a ea, he loo a ea a io (FAR) index, which e alua es he in ensi y o shopping oppo uni ies as a a io o loo a ea and a ailable comme cial land use, and he household densi y index (HDENS), which is ela ed o es- iden ial land use. The equi ed inpu da a is demons a ed in Figu e 3. Figu e 3. Main inpu da a equi ed o calcula ion o WAI and WS. WAI is ypically e alua ed using geog aphical zones such as adminis a i e uni s, equen ly due o he una ailabili y o any o he o m o app op ia e s a is ical da a. Fo his s udy, WAI was calcula ed inside a ci cula bu e a ound each g id poin (cen oid) o imp o e he compa ison wi h WS. This way, all spa ial uni s o WAI ha e he same Figu e 3. Main inpu da a equi ed o calcula ion o WAI and WS. Acco ding o he e iew o ecommended sea ch adii and walkable dis ance, he ollowing adii we e selec ed: 400 m (app ox. 5 min walking dis ance and maximal dis ance o p ima y se ices o handicapped elde ly), 800 m (maximal dis ance o seconda y se ices o he elde ly), 1200 m (maximal dis ance o s anda d popula ion [ 48 ]) and 2414 m (equi alen o 1.5 miles, and s anda d sea ch adius o WS). Calcula ion o WAI was acili a ed by he A cGIS oolbox de eloped a Palacky Uni- e si y [ 90 ]. The oolbox consis s o 5 ools: Connec i i y index (connec .py), En opy (Shannon) index (en opy.py), FAR ( a .py), Household densi y index (hdens.py) and Walk- abili y index (wai.py). The ools we e c ea ed using py hon p og amming language e sion 2.5.1, and A cGIS Desk op so wa e e sion 9.3.1. Though he ools we e p og ammed in an olde e sion o A cGIS, hey can be un in A cGIS Desk op 10. When calcula ing he walkabili y index o usual adminis a i e uni s, no modi ica ion o he sc ip s is equi ed, howe e , in he p oposed o e lapping zones, some modi ica ions o he sc ip s and index calcula ions a e needed. We ha e de eloped a new e sion o his ool [ 91 ] which sol es he se e al issues desc ibed in he ollowing pa ag aph. ISPRS In . J. Geo-In . 2022,11, 279 8 o 29 The ools c ea e empo a y iles (in e media e esul s) ha a e sa ed in he ESRI shape ile o ma . This o ma , howe e , is inapp op ia e o complex o e lay ope a ions, he e o e i is necessa y o edi ec he s o age o empo a y iles o he ile geoda abase. Fu he mo e, he Connec i i y index ool uses he Spa ialJoin me hod wi hin which a ca dinali y ype mus be changed om ONE TO ONE o JOIN ONE TO MANY. Fo FAR and Household densi y indices, i is necessa y o elimina e he p oblema ic a ios o he a eas o in e es o he size o he bu e a ea. I he a io is less han 1%, he index alues a e se o 0. Conce ning FAR, ins ead o using ac ual loo space, which is unknown (di icul o assess in a ield su ey wi h a limi ed o e o comme cial p oduc s), he size o he buildings is based on hei bluep in s and is used as he nea es app oxima ion a ailable. Such app oxima ion was accep ed in [ 28 , 90 ] and appea s o be app op ia e in Eu opean coun ies. All ou sub-indices need a land use laye con aining ypology such as Li ing (L), Comme cial (C) o Wa e (W) as an inpu . O he ca ego ies do no necessa ily ha e o coincide wi h he au ho s’ speci ica ions (eigh land use ca ego ies), bu he one-le e designa ion o single-use a eas and he n-le e designa ion o n land uses should be ollowed. The U ban A las 2018 da abase con aining a o al o 21 land use ypes was used. A eas de ined as “U ban Fab ic” we e classi ied as Li ing a eas, “Indus ial, comme cial, public, mili a y and p i a e uni s” as Comme cial, and “Wa e bodies” as Wa e . The U ban A las co e s he la ges u ban agglome a ions in he Czech Republic (including Os a a and H adec K alo e), he e o e i ep esen s a sui able uni ied da a sou ce o compa ison o locali ies. Agg ega ion o di e en non- esiden ial a eas oge he made i impossible o be e speci y comme cial a ea. Cu en ly, no a ailable da a sou ce (e.g., U ban a las, o Co ine Land Co e ) con ains speci ic comme cial polygons (a ea). This simpli ica ion has an impac on FAR assessmen whe e he a ea o comme cial land use is he denomina o . The o al e ec is small because he inal index FAR is s anda dised using he Z-sco e. 4.2. Walk Sco e WS is calcula ed by mapping ou he walking dis ance o ameni ies in he 9 impo an daily li e ameni y ca ego ies o each gi en o igin. In ameni y ca ego ies whe e dep h o choice is impo an , mul iple ameni ies in ha ca ego y a e coun ed. Ca ego ies a e also weigh ed acco ding o hei impo ance [ 83 ]. A e no maliza ion, he add ess may ecei e a penal y o ha ing poo pedes ian iendliness me ics, such as long blocks o low in e sec ion densi y. WS was calcula ed o he compa able spa ial uni s using he selec ed adii o ne wo k sea ching o eques ed des ina ions and a bu e o he assessmen o connec i i y. A new applica ion was de eloped o WS assessmen a ailable a [ 91 ]. The applica ion was c ea ed using py hon p og amming language e sion 3.9. I is based on open-sou ce py hon lib a ies such as Ne wo kX, Pandana, Geopandas, Shapely and momepy and is a ailable on gi hub as a jupy e no ebook ile. The ne wo k dis ance calcula ions a e based hea ily on he Pandana py hon package ha uses con ac ion hie a chies o calcula e supe - as a el accessibili y me ics and sho es pa hs [ 92 ]. OSM s ee ne wo k da a, cen oids and ameni ies’ loca ions a e equi ed as inpu s in o he applica ion in he o m o spa ial laye s ( o ma shape ile) (Figu e 3). OSM is p e e ed due o i s a ailabili y and equen usage bu i equi es ca e ul checking and p e-p ocessing. Checking and co ec ions o he class a ibu e assu e selec ion o app op ia e pa hs. The highway a ibu e was comple ed o adjus ed. Connec i i y es ing enabled he disco e y o isola ed pa s o ne wo ks (islands) which had o be p ope ly connec ed o o he pa s o he ne wo k. To suppo his ask we used a connec ed_componen s unc ion in he ne wo kx lib a y [ 93 ]. This is implemen ed in he sc ip o he WS calcula ion. I iden i ies he la ges componen o he connec ed ne wo k and hen uses i u he in he calcula ion. Thus, he use mus ensu e ha he ne wo k is as well connec ed bu no longe has o deal wi h islands o small unconnec ed sec ions o he ne wo k. Usually, some pa s o he ne wo k ha e o be addi ionally ec o ized. ISPRS In . J. Geo-In . 2022,11, 279 9 o 29 Values o mul iple pa ame e s can be adjus ed such as maximum walking dis ance, walking speed, Gaussian DDF βcoe icien and ameni y weigh s. The co e p ocesses o his applica ion include he c ea ion o a pedes ian ne wo k and calcula ion o walking dis ances (sho es ou es) o a ious nea es ameni ies om e e y cen oid loca ion wi hin a gi en locali y. The pedes ian ne wo k is a da a model esembling a ne wo k g aph (edges and nodes) weigh ed by linea dis ance. The sho es walking dis ances a e ansla ed in o walking imes, and ameni ies’ weigh s and he Gaussian DDF a e applied. A e wa ds, he base sco e o he cen oids is de e mined and no malized o a sco e om 0 o 100. This o iginal WS me hodology in oduces wo pedes ian iendliness me ics: in e - sec ion densi y and a e age block leng h. A e he base sco e is calcula ed, he pedes ian iendliness me ics penalize g id loca ions o ha ing long blocks o low in e sec ion densi y by lowe ing he base WS [83]. Sho e blocks mean mo e in e sec ions, and, he e- o e, sho e a el dis ances and a g ea e numbe o ou es be ween loca ions. Se e al communi ies ha e adop ed maximum block leng h s anda ds o new de elopmen s [ 94 ] usually anging om 300 o 600 ee . A e age block leng h alues abo e 120 m (400 ee ) ob ain a penal y due o low connec i i y. Unde Eu opean condi ions, whe e old ci y a eas a e equipped wi h in ica e ne wo ks o lanes and eleased (sub)u baniza ion wi h almos no closed ci y blocks, he e a e di icul ies in es ablishing building blocks and calcula ing his pa ame e . The e o e, in his s udy, we app oxima ed he a e age block leng h using he a e age leng h o s ee segmen s be ween c ossings. To imp o e he lis o des ina ions, Poin o In e es (POI) om Open S ee Map (OSM) is ex ended using selec ed coun ywide egis e s, such as he egis e o heal hca e acili ies, and des ina ions selec ed om he consolida ed da a base. WS was assessed o usual condi ions (“adul s”), e e ed o as S anda d WS, mainly o compa e esul s wi h WAI. The lexibili y o WS and a newly p epa ed so wa e applica ion also enabled he p epa a ion o a modi ica ion sui able o senio s, e e ed o as a Walk Sco e o elde ly. 4.3. Walk Sco e o Elde ly The assessmen o walkabili y o senio s should ake in o accoun he speci ic equi e- men s and abili ies o his g oup. I should comp ise mainly o a selec ion o app op ia e des ina ions and di e en weigh ing, dec easing maximal walkable dis ance, and dec eased walking speed. Fo his s udy, senio s’ des ina ions we e selec ed acco ding o an icipa ed p e e ences disco e ed in he e iew and local su ey. While p e ious s udies usually conside ed a wide ange o impo an se ices o he elde ly (e.g., ood s o e, pha macy, doc o , bank, pos o ice, bus o am s op, chu ch, ceme e y, hai d esse /ba be , lib a y, and g een a eas in [ 11 ]), Czech s udies show a di e en pa e n gi ing mo e p e e ence o shopping and less o chu ch and a ious o he ci izens’ se ices [ 95 ]. The mos impo an a ge s acco ding o a wide su ey conduc ed in egional capi als 10 yea s ago a e: small shopping, pa ks, la ge shopping, employmen , ela i es and iends, and gene al p ac icians [ 10 ]. The local su ey in Os a a and Olomouc in 2014 ound simila des ina ions, bu he equency o isi s was sligh ly di e en (Table 1). The weigh s we e de i ed om ques ionnai es asking o he des ina ions o senio s’ mobili y and hei equency o isi ing. Fo each des ina ion ype, he a e age numbe o isi s pe mon h was enume a ed and s anda dized. Due o local and empo al closeness, he esul ing weigh ing was applied o he assessmen o WS o elde ly, despi e he smalle scope o he su ey. The coun ywide weigh ings we e used in he sensi i i y analysis. No all des ina ions can be u ilized o ne wo k sea ching. Employmen (wo kplace), amily, ga dens, and co ages a e places o gene ally unknown loca ion. In he case o a chu ch o ceme e y, i is belie ed ha such ypes o des ina ions in ci ies a e subjec s o membe ship in a communi y, o hey a e s ic ly in luenced by people’s indi idual ISPRS In . J. Geo-In . 2022,11, 279 16 o 29 Table 3. Dis ibu ion o WS o di e en sea ch adii in Os a a. Range Sha e o Uni s (%) Sha e o Popula ion (%) 400 m 800 m 1200 m 2414 m 400 m 800 m 1200 m 2414 m Non-walkable (0) 61.8 37.1 25.8 7.5 22.6 6.1 3.8 1.1 Ve y ca dependen (1–24) 26.7 35.5 37.1 52.5 39.8 22.9 13.6 14.4 Ca dependen (25–49) 8.2 16.8 22.4 23.4 25.5 33.3 31.4 28.1 Somewha walkable (50–69) 1.9 5.9 9.0 10.6 7.1 19.6 29.0 34.0 Ve y walkable (70–89) 1.1 3.2 4.2 4.5 3.9 13.7 16.9 17.2 Walke ’s pa adise (90–100) 0.3 1.4 1.6 1.6 1.2 4.4 5.3 5.3 Table 4. Dis ibu ion o WS o di e en sea ch adii in H adec K alo e. Range Sha e o Uni s (%) Sha e o Popula ion (%) 400 m 800 m 1200 m 2414 m 400 m 800 m 1200 m 2414 m Non-walkable (0) 61.5 42.1 28.2 11.9 17.4 6.7 4.6 1.9 Ve y ca dependen (1–24) 31.0 38.5 46.0 57.9 50.4 26.9 20.2 20.2 Ca dependen (25–49) 4.8 9.1 11.1 14.3 18.4 26.0 19.3 19.9 Somewha walkable (50–69) 0.8 6.7 8.7 9.9 1.7 25.2 31.8 33.8 Ve y walkable (70–89) 1.2 2.0 4.0 4.0 7.7 5.9 12.1 12.1 Walke ’s pa adise (90–100) 0.8 1.6 2.0 2.0 4.4 9.3 12.1 12.1 Uni s wi h ich walking condi ions in close adii a ely occu . Only 12.2% and 13.8% o people wi h a walking adius o 400 m in Os a a and H adec K alo e, esp., can be sa is ied wi h walking condi ions in hei su oundings (WS abo e 50); all o he s a e ca dependen (Figu e 10). This sha e jumps wi h a sea ch adius o 800 m eaching 38% and 40%, esp., hen shows a lesse inc ease o 51% and 56%, esp., o 1200 m, and inally 56.5% and 58%, esp., o 2414 m. This means ha e en o people wi h no mal walking capaci y, mo e han 40% o inhabi an s li e in loca ions which a e classi ied by Walk Sco e as loca ions whe e esiden s a e ca o PT dependen . ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 18 o 32 (a) (b) Figu e 10. Dis ibu ion o popula ion acco ding o WS o di e en sea ch adii in H adec K alo e (a) and Os a a (b). Table 4. Dis ibu ion o WS o di e en sea ch adii in H adec K alo e. Range Sha e o Uni s (%) Sha e o Popula ion (%) 400 m 800 m 1200 m 2414 m 400 m 800 m 1200 m 2414 m Non-walkable (0) 61.5 42.1 28.2 11.9 17.4 6.7 4.6 1.9 Ve y ca dependen (1–24) 31.0 38.5 46.0 57.9 50.4 26.9 20.2 20.2 Ca dependen (25–49) 4.8 9.1 11.1 14.3 18.4 26.0 19.3 19.9 Somewha walkable (50–69) 0.8 6.7 8.7 9.9 1.7 25.2 31.8 33.8 Ve y walkable (70–89) 1.2 2.0 4.0 4.0 7.7 5.9 12.1 12.1 Walke ’s pa adise (90–100) 0.8 1.6 2.0 2.0 4.4 9.3 12.1 12.1 A co ela ion be ween WAI and WS show a sa is ac o y le el o co espondence wi h a good index o de e mina ion anging be ween 0.4 and 0.7 (Figu e 11), eaching he high- es alues o 800–1200 m. Figu e 10. Dis ibu ion o popula ion acco ding o WS o di e en sea ch adii in H adec K alo e ( a ) and Os a a (b). A co ela ion be ween WAI and WS show a sa is ac o y le el o co espondence wi h a good index o de e mina ion anging be ween 0.4 and 0.7 (Figu e 11), eaching he highes alues o 800–1200 m. ISPRS In . J. Geo-In . 2022,11, 279 17 o 29 ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 19 o 32 (a) (b) Figu e 11. Co ela ion be ween WAI and s anda d WS (H adec K alo e (a) and Os a a (b)). Howe e , he dis ibu ion shows a di e se e alua ion o WAI and WS. A close ela- ionship be ween hese indica o s is eached only wi h highe alues o WAI, especially in he case o H adec K alo e. Os a a is mo e he e ogeneous which is e lec ed in lowe R 2 and highe di e si y o si ua ions. Ex emely he e ogeneous condi ions can be seen o he la ges adius whe e i e pa ly sepa a ed clus e s can be dis inguished (Figu e 12). cl.3—high WAI and high WS. The bes walkabili y condi ions a e con i med by bo h indica o s. This occu s only in wo main dense se lemen s. cl.4—high WAI and lowe WS. He e high alues o WAI o igina e om high CONN and FAR pa ame e s. While he en i onmen in Os a a-sou h is walkable, accessibili y o des ina ions is no sa is ac o y showing lowe WS compa ed o o he u ban nuclei. Figu e 11. Co ela ion be ween WAI and s anda d WS (H adec K alo e (a) and Os a a (b)). Howe e , he dis ibu ion shows a di e se e alua ion o WAI and WS. A close ela- ionship be ween hese indica o s is eached only wi h highe alues o WAI, especially in he case o H adec K alo e. Os a a is mo e he e ogeneous which is e lec ed in lowe R 2 and highe di e si y o si ua ions. Ex emely he e ogeneous condi ions can be seen o he la ges adius whe e i e pa ly sepa a ed clus e s can be dis inguished (Figu e 12). cl.3—high WAI and high WS. The bes walkabili y condi ions a e con i med by bo h indica o s. This occu s only in wo main dense se lemen s. cl.4—high WAI and lowe WS. He e high alues o WAI o igina e om high CONN and FAR pa ame e s. While he en i onmen in Os a a-sou h is walkable, accessibili y o des ina ions is no sa is ac o y showing lowe WS compa ed o o he u ban nuclei. cl.1— e y low WAI wi h inc eased WS. Small and almos u al illages whe e WAI is dec eased by la ge su ounding c op ields while accessibili y o basic local a ge s is sa is ac o y. ISPRS In . J. Geo-In . 2022,11, 279 18 o 29 cl.2—middle WAI wi h high WS. Mino se lemen nuclei wi h ci y-like u banisa ion wi h some su ounding es ic ions (in ou case o es s and an indus ial zone). WAI is inc eased due o HDENS, bu o he pa ame e s (namely CONN) emain in he backg ound. High WS shows ull a ailabili y o local a ge s. cl.5—high WAI and low WS. A eas ypically si ua ed in a gap o dense u banisa ion o on he bo de o i . While he en i onmen encou ages walking, he eal accessibili y o eques ed des ina ions is e y low. These a eas su e om an unsa is ac o y supply o ci il ameni ies. Meanwhile, condi ions in H adec K alo e a e much simple , wi h only wo basic si ua ions a ising: di e gen WAI wi h low WS, and p opo ionally g owing WAI and WS. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 20 o 32 cl.1— e y low WAI wi h inc eased WS. Small and almos u al illages whe e WAI is dec eased by la ge su ounding c op ields while accessibili y o basic local a ge s is sa is ac o y. cl.2—middle WAI wi h high WS. Mino se lemen nuclei wi h ci y-like u banisa ion wi h some su ounding es ic ions (in ou case o es s and an indus ial zone). WAI is inc eased due o HDENS, bu o he pa ame e s (namely CONN) emain in he back- g ound. High WS shows ull a ailabili y o local a ge s. cl.5—high WAI and low WS. A eas ypically si ua ed in a gap o dense u banisa ion o on he bo de o i . While he en i onmen encou ages walking, he eal accessibili y o eques ed des ina ions is e y low. These a eas su e om an unsa is ac o y supply o ci il ameni ies. Figu e 12. Ou lie s in WAI—WS ela ionship and hei loca ion in Os a a. Meanwhile, condi ions in H adec K alo e a e much simple , wi h only wo basic si - ua ions a ising: di e gen WAI wi h low WS, and p opo ionally g owing WAI and WS. 5.2. Compa ison be ween S anda d WS and WS o he Elde ly WS o elde ly was e alua ed using he baseline se ings om es ing. The example he e shows he e alua ion o an 800 m adius (Figu e 13). I we compa e he esul s wi h Figu e 7, he pa e n e lec ing he main u banised se lemen s emains, bu hese a eas a e subs an ially e oded; he o al a ea wi h high WS is smalle and in e nally much mo e di e se. Changes be ween s anda d WS and WS o elde ly measu ed wi h he s anda dised WS alues we e e alua ed. P opo ional changes a e no app op ia e in his case due o hei exagge a ed % o small WS alues. The adius acco ding o s anda d WS is 2414 m whe eas he adius o senio s is se sho e a 800 m. As expec ed, he o e all change o WS om adul o elde ly is nega i e due o he educ ion in walking dis ance, s eepe DDF, and di e en se o a ge s. 50% o uni s e- po a decline o WS be ween 1 and 21 pe cen age poin s. Medians in bo h ci ies a e simi- la : −9.85 and −8.21 in Os a a and H adec K alo e, esp., showing less change in H adec K alo e. One hi d o spa ial uni s (Figu e 14) do no change signi ican ly in WS classi ica ion: 31% in Os a a and 35% in H adec K alo e, bu his ep esen s only 10% and 15%, esp., o he popula ion. 31% and 33% o uni s show mode a e dec ease, and s ong dec eases can be ound namely in highly popula ed a eas. A la ge d op o WS (abo e 15) was ec- o ded in 20% and 17% o uni s, esp. (33% and 25% o he popula ion), bu he dis ibu ion o such places is di e en . In Os a a, he la ges WS dec eases a e o en ound on bo de s Figu e 12. Ou lie s in WAI—WS ela ionship and hei loca ion in Os a a. 5.2. Compa ison be ween S anda d WS and WS o he Elde ly WS o elde ly was e alua ed using he baseline se ings om es ing. The example he e shows he e alua ion o an 800 m adius (Figu e 13). I we compa e he esul s wi h Figu e 7, he pa e n e lec ing he main u banised se lemen s emains, bu hese a eas a e subs an ially e oded; he o al a ea wi h high WS is smalle and in e nally much mo e di e se. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 21 o 32 o dense se lemen whe e sho e walking dis ance o elde ly signi ican ly limi s he ac- cessibili y o des ina ions. Di e en case is uni s whe e in e nal ba ie s ( i e s, ailway s a ions e c.) limi sho accessibili y and cause a signi ican d op in walkabili y. In such loca ions, any imp o emen o close walkabili y is di icul . Howe e , in H adec K alo e, signi ican d ops in WS do no accompany he bo de o dense se lemen s, likely due o mo e con inuous u ban de elopmen . The majo g oups o cells wi h d ama ic dec ease in WS o elde ly a e si ua ed in he ci y cen e. These cells ypically con ain la ge ins i u- ional complexes such as a hospi al o uni e si y. ( a ) ( b ) Figu e 13. WS o elde ly (800 m adius, H adec K alo e (a), Os a a (b)). ( a ) ( b ) Figu e 14. Di e ences be ween WS o he elde ly and s anda d WS (HK (a), Os a a (b)). Imp o emen o walkabili y o he elde ly seldom occu s, as expec ed, hough in Os a a, spa se isola ed loca ions ypically ep esen coun yside-like se lemen wi h in- di idual housing and good local shopping oppo uni ies. Figu e 13. WS o elde ly (800 m adius, H adec K alo e (a), Os a a (b)). ISPRS In . J. Geo-In . 2022,11, 279 19 o 29 Changes be ween s anda d WS and WS o elde ly measu ed wi h he s anda dised WS alues we e e alua ed. P opo ional changes a e no app op ia e in his case due o hei exagge a ed % o small WS alues. The adius acco ding o s anda d WS is 2414 m whe eas he adius o senio s is se sho e a 800 m. As expec ed, he o e all change o WS om adul o elde ly is nega i e due o he educ ion in walking dis ance, s eepe DDF, and di e en se o a ge s. 50% o uni s epo a decline o WS be ween 1 and 21 pe cen age poin s. Medians in bo h ci ies a e simila : − 9.85 and − 8.21 in Os a a and H adec K alo e, esp., showing less change in H adec K alo e. One hi d o spa ial uni s (Figu e 14) do no change signi ican ly in WS classi ica ion: 31% in Os a a and 35% in H adec K alo e, bu his ep esen s only 10% and 15%, esp., o he popula ion. 31% and 33% o uni s show mode a e dec ease, and s ong dec eases can be ound namely in highly popula ed a eas. A la ge d op o WS (abo e 15) was eco ded in 20% and 17% o uni s, esp. (33% and 25% o he popula ion), bu he dis ibu ion o such places is di e en . In Os a a, he la ges WS dec eases a e o en ound on bo de s o dense se lemen whe e sho e walking dis ance o elde ly signi ican ly limi s he accessibili y o des ina ions. Di e en case is uni s whe e in e nal ba ie s ( i e s, ailway s a ions e c.) limi sho accessibili y and cause a signi ican d op in walkabili y. In such loca ions, any imp o emen o close walkabili y is di icul . Howe e , in H adec K alo e, signi ican d ops in WS do no accompany he bo de o dense se lemen s, likely due o mo e con inuous u ban de elopmen . The majo g oups o cells wi h d ama ic dec ease in WS o elde ly a e si ua ed in he ci y cen e. These cells ypically con ain la ge ins i u ional complexes such as a hospi al o uni e si y. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 21 o 32 o dense se lemen whe e sho e walking dis ance o elde ly signi ican ly limi s he ac- cessibili y o des ina ions. Di e en case is uni s whe e in e nal ba ie s ( i e s, ailway s a ions e c.) limi sho accessibili y and cause a signi ican d op in walkabili y. In such loca ions, any imp o emen o close walkabili y is di icul . Howe e , in H adec K alo e, signi ican d ops in WS do no accompany he bo de o dense se lemen s, likely due o mo e con inuous u ban de elopmen . The majo g oups o cells wi h d ama ic dec ease in WS o elde ly a e si ua ed in he ci y cen e. These cells ypically con ain la ge ins i u- ional complexes such as a hospi al o uni e si y. ( a ) ( b ) Figu e 13. WS o elde ly (800 m adius, H adec K alo e (a), Os a a (b)). ( a ) ( b ) Figu e 14. Di e ences be ween WS o he elde ly and s anda d WS (HK (a), Os a a (b)). Imp o emen o walkabili y o he elde ly seldom occu s, as expec ed, hough in Os a a, spa se isola ed loca ions ypically ep esen coun yside-like se lemen wi h in- di idual housing and good local shopping oppo uni ies. Figu e 14. Di e ences be ween WS o he elde ly and s anda d WS (HK (a), Os a a (b)). Imp o emen o walkabili y o he elde ly seldom occu s, as expec ed, hough in Os a a, spa se isola ed loca ions ypically ep esen coun yside-like se lemen wi h indi idual housing and good local shopping oppo uni ies. The co ela ion be ween he wo ypes o WS (Figu e 15) is ela i ely high—R 2 0.669 (H adec K alo e) and 0.691 (Os a a). As expec ed, mo e “non-walkable” spa ial uni s a e indica ed o elde ly WS and ha e ewe occu ences in Os a a han in H adec K alo e (15.5% and 24.2%, esp.). Thei elimina ion will inc ease R 2 and he slope o he eg es- sion lines. ISPRS In . J. Geo-In . 2022,11, 279 20 o 29 ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 22 o 32 The co ela ion be ween he wo ypes o WS (Figu e 15) is ela i ely high—R 2 0.669 (H adec K alo e) and 0.691 (Os a a). As expec ed, mo e “non-walkable” spa ial uni s a e indica ed o elde ly WS and ha e ewe occu ences in Os a a han in H adec K alo e (15.5% and 24.2%, esp.). Thei elimina ion will inc ease R 2 and he slope o he eg ession lines. ( a ) ( b ) Figu e 15. Rela ionship be ween s anda d WS and WS o elde ly (HK (a), Os a a (b)). 5.3. Sensi i i y Analysis o WS o Elde ly As men ioned abo e, di e en indings and opinions can be ound o which pa am- e e s a e impo an o walkabili y assessmen . Local condi ions and cul u al and anspo habi s a e di e en in di e en loca ions, and indi idual physical and men al capabili ies, heal h, a i udes, and beha iou a e e en mo e di e se. Unde such unce ain condi ions, i is a good idea o p o ide a sensi i i y analysis o unco e he eal impac s o di e en se ings and which pa ame e s ha e majo impac s on he inal WS. The sensi i i y analysis was based on one-a -a- ime app oach (OAP) [96] whe e one pa ame e is mo ed sequen ially, keeping o he s a hei baseline alues, hen he pa am- e e is e u ned o i s baseline alue and he nex pa ame e is hen mo ed. The ollowing modi ica ions we e es ed: 1. Changing DDF shape and walking speed. The DDF is modelled by he cumula i e Gaussian unc ion modi ied by he β pa am- e e . This pa ame e in luences he s eepness o he cu e as well as he an icipa ed walk- ing dis ance. e.g., β = 140 p o ides almos ze o Gaussian alue in 17 min, which can be ans o med o a walkable dis ance o 408 m using he slow gai speed o 0.4 m/s. The opposi e end o he es ing spec um uses β = 180 ex ending he walking ime up o 30 min and, co espondingly, he walking dis ance o 2400 m using a maximal expec ed gai speed o 1.3 m/s. We decided o join ly modi y bo h pa ame e s, because bo h a e bound by he phys- ical capabili ies o he elde ly; lowe gai speed usually di ec ly co esponds o smalle walkable dis ance. Gai speed was modi ied in he ange o 0.4 o 1.3 m/s based on he e iew. The β pa ame e was se in he ange o 140 o 180 acco ding o [88]. I co esponds well o he model o expec ed maximal walking dis ances in he ange o 400 o 1600 m (Figu e 16). Bo h anges we e di ided in o 10 s eps o es ing. 2. Changing weigh s o each ype o des ina ion. Figu e 15. Rela ionship be ween s anda d WS and WS o elde ly (HK (a), Os a a (b)). 5.3. Sensi i i y Analysis o WS o Elde ly As men ioned abo e, di e en indings and opinions can be ound o which pa ame- e s a e impo an o walkabili y assessmen . Local condi ions and cul u al and anspo habi s a e di e en in di e en loca ions, and indi idual physical and men al capabili ies, heal h, a i udes, and beha iou a e e en mo e di e se. Unde such unce ain condi ions, i is a good idea o p o ide a sensi i i y analysis o unco e he eal impac s o di e en se ings and which pa ame e s ha e majo impac s on he inal WS. The sensi i i y analysis was based on one-a -a- ime app oach (OAP) [ 96 ] whe e one pa ame e is mo ed sequen ially, keeping o he s a hei baseline alues, hen he pa ame e is e u ned o i s baseline alue and he nex pa ame e is hen mo ed. The ollowing modi ica ions we e es ed: 1. Changing DDF shape and walking speed. The DDF is modelled by he cumula i e Gaussian unc ion modi ied by he β pa- ame e . This pa ame e in luences he s eepness o he cu e as well as he an icipa ed walking dis ance. e.g., β = 140 p o ides almos ze o Gaussian alue in 17 min, which can be ans o med o a walkable dis ance o 408 m using he slow gai speed o 0.4 m/s. The opposi e end o he es ing spec um uses β = 180 ex ending he walking ime up o 30 min and, co espondingly, he walking dis ance o 2400 m using a maximal expec ed gai speed o 1.3 m/s. We decided o join ly modi y bo h pa ame e s, because bo h a e bound by he physical capabili ies o he elde ly; lowe gai speed usually di ec ly co esponds o smalle walkable dis ance. Gai speed was modi ied in he ange o 0.4 o 1.3 m/s based on he e iew. The β pa ame e was se in he ange o 140 o 180 acco ding o [ 88 ]. I co esponds well o he model o expec ed maximal walking dis ances in he ange o 400 o 1600 m (Figu e 16). Bo h anges we e di ided in o 10 s eps o es ing. 2. Changing weigh s o each ype o des ina ion. As discussed, we used i e ca ego ies o des ina ion o he elde ly. Fo each ype o des ina ion, en di e en weigh s we e se be ween wo op ions based on epo ed isi equencies in he wo su eys. These 50 weigh ing a ian s and 10 β and gai speed a ian s we e used o calcula e WS o he maximal bu e o 2414 m. To e alua e he impac s o modi ica ions, he change o elde ly WS o each s ep and each spa ial uni was calcula ed. Due o he high numbe o inhabi ed cells in Os a a (621) and H adec K alo e (252), i is di icul o show all esul s. The e olu ion o WS alues o ISPRS In . J. Geo-In . 2022,11, 279 21 o 29 all cells o modi ica ion o gai speed and β coe icien is demons a ed in Figu e 17. All weigh s and hei in luence on WS o senio s can be ound a [97]. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 23 o 32 As discussed, we used i e ca ego ies o des ina ion o he elde ly. Fo each ype o des ina ion, en di e en weigh s we e se be ween wo op ions based on epo ed isi equencies in he wo su eys. These 50 weigh ing a ian s and 10 β and gai speed a - ian s we e used o calcula e WS o he maximal bu e o 2414 m. Figu e 16. Dis ance-decay unc ions o 10 es ed combina ions o β and walking speed. To e alua e he impac s o modi ica ions, he change o elde ly WS o each s ep and each spa ial uni was calcula ed. Due o he high numbe o inhabi ed cells in Os a a (621) and H adec K alo e (252), i is di icul o show all esul s. The e olu ion o WS alues o all cells o modi ica ion o gai speed and β coe icien is demons a ed in Fig- u e 17. All weigh s and hei in luence on WS o senio s can be ound a [97]. ( a ) ( b ) Figu e 17. E olu ion o WS o he elde ly wi h gai speed and β modi ica ions (Os a a (a) and H adec K alo e (b)). Nei he es ing o di e en dis ances be ween e alua ed poin s (g id size) o elde ly WS no di e en placemen o hese poin s we e p o ided due o he high numbe o es ed pa ame e combina ions. Such a si ua ion could be sol ed using andom simula- ions, howe e his is beyond he cu en calcula ion capabili y. I is expec ed ha changes in oked by small di e ences in placemen would ha e a mino e ec on he o e all el- de ly WS assessmen . Changes a e summa ised in Table 5 whe e mean, 3 d qua ile and 95-pe cen ile a e lis ed. This simple o m o sensi i i y analysis shows ha he impac s o weigh modi ica- ions wi hin he expec ed ange is qui e small. Based on he compa ison o di e en ypes o des ina ions, a majo impac is ound o changes in he speed-β componen whe e he Figu e 16. Dis ance-decay unc ions o 10 es ed combina ions o βand walking speed. ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 21 o 32 As discussed, we used i e ca ego ies o des ina ion o he elde ly. Fo each ype o 653 des ina ion, en di e en weigh s we e se be ween wo op ions based on epo ed isi 654 equencies in he wo su eys. These 50 weigh ing a ian s and 10 𝛽 and gai speed 655 a ian s we e used o calcula e WS o he maximal bu e o 2414 m. 656 657 658 Figu e 13. Dis ance-decay unc ions o 10 es ed combina ions o 𝛽 and walking speed. 659 To e alua e he impac s o modi ica ions, he change o elde ly WS o each s ep and 660 each spa ial uni was calcula ed. Due o he high numbe o inhabi ed cells in Os a a 661 (621) and H adec K alo e (252), i is di icul o show all esul s. The e olu ion o WS 662 alues o all cells o modi ica ion o gai speed and 𝛽 coe icien is demons a ed in 663 Figu e 14. All weigh s and hei in luence on WS o senio s can be ound a : 664 h ps://public. ableau.com/app/p o ile/gis. sb/ iz/g a y_zp aco ani_walksco e/WALKS 665 CORE. 666 . 667 (a) (b) Figu e 14. E olu ion o WS o he elde ly wi h gai speed and 𝛽 modi ica ions (Os a a (a) and 668 H adec K alo e (b)). 669 Changes a e summa ised in able 5 whe e mean, 3 d qua ile and 95-pe cen ile a e 670 lis ed. This simple o m o sensi i i y analysis shows ha he impac s o weigh 671 modi ica ions wi hin he expec ed ange is qui e small. Based on he compa ison o 672 di e en ypes o des ina ions, a majo impac is ound o changes in he speed-𝛽 673 componen whe e he a e age change o WS o one s ep is app ox. 2 and 95-pe cen ile 674 eaches 7.7. A signi ican ly smalle impac is ound o pa k (0.5 mean and 2.5 o 95- 675 Figu e 17. E olu ion o WS o he elde ly wi h gai speed and β modi ica ions (Os a a ( a ) and H adec K alo e (b)). Nei he es ing o di e en dis ances be ween e alua ed poin s (g id size) o elde ly WS no di e en placemen o hese poin s we e p o ided due o he high numbe o es ed pa ame e combina ions. Such a si ua ion could be sol ed using andom simula ions, howe e his is beyond he cu en calcula ion capabili y. I is expec ed ha changes in oked by small di e ences in placemen would ha e a mino e ec on he o e all elde ly WS assessmen . Changes a e summa ised in Table 5whe e mean, 3 d qua ile and 95-pe cen ile a e lis ed. This simple o m o sensi i i y analysis shows ha he impac s o weigh modi ica- ions wi hin he expec ed ange is qui e small. Based on he compa ison o di e en ypes o des ina ions, a majo impac is ound o changes in he speed- β componen whe e he a e age change o WS o one s ep is app ox. 2 and 95-pe cen ile eaches 7.7. A signi i- can ly smalle impac is ound o pa k (0.5 mean and 2.5 o 95-pe cen ile), ollowed by e ail (0.4 and 2.1, esp.). Weigh s o hype ma ke , doc o and en e ainmen des ina ions in luence he WS on a small scale. e.g., each s ep in hype ma ke weigh s indica es only a 0.02 alue change o WS and 0.09 o 95-pe cen ile. The esul s a e in line wi h p e ious indings ha dis ance o en o e shadows o he ac o s [58]. ISPRS In . J. Geo-In . 2022,11, 279 22 o 29 Table 5. Impac o one s ep modi ica ion o weigh s o changes in WS o elde ly. Fac o Values S ep Ci y Walk Sco e Change o 1 S ep Mean 3 d Qua ile 95-Pe cen ile speed 0.5–1.3 0.1 HK 1.863 3.263 7.291 β144–180 4.5 speed 0.5–1.3 0.1 OV 2.436 4.258 7.742 β144–180 4.5 e ail 7–12 0.55 HK 0.253 0.111 1.509 OV 0.402 0.431 2.102 hype ma ke 1–5 0.44 HK 0.019 0.000 0.090 OV 0.017 0.000 0.068 en e ainmen 0.8–1.4 0.07 HK 0.008 0.000 0.043 OV 0.010 0.000 0.058 doc o 1–2 0.11 HK 0.033 0.012 0.208 OV 0.039 0.034 0.216 pa k 0.1–6 0.66 HK 0.467 0.575 2.468 OV 0.263 0.121 1.555 Ze o alues in 3 d qua ile indica e he lack o a ailable des ina ions o walking. The di e en in luences on one ca ego y o des ina ions poin s ou he di e ences be ween ci ies due o sho ages o equi ed a ge s and hei une en spa ial dis ibu ion. The changes in WS o each es ing s ep show ha no all s eps ha e he same impac . Usually, he i s 2–3 s eps de ia e om o he s p o iding smalle o la ge impac . As you can see, o he dominan speed- β ac o , he i s h ee s eps indica e he highes a iabili y, bu changes a e signi ican ly lowe o la e s eps whe e he change in WS is s abilized a ound 3 (Os a a) and 4 (H adec K alo e) (Figu e 18). ISPRS In . J. Geo-In . 2022, 11, x FOR PEER REVIEW 24 o 32 a e age change o WS o one s ep is app ox. 2 and 95-pe cen ile eaches 7.7. A signi i- can ly smalle impac is ound o pa k (0.5 mean and 2.5 o 95-pe cen ile), ollowed by e ail (0.4 and 2.1, esp.). Weigh s o hype ma ke , doc o and en e ainmen des ina ions in luence he WS on a small scale. e.g., each s ep in hype ma ke weigh s indica es only a 0.02 alue change o WS and 0.09 o 95-pe cen ile. The esul s a e in line wi h p e ious indings ha dis ance o en o e shadows o he ac o s [58]. Ze o alues in 3 d qua ile indica e he lack o a ailable des ina ions o walking. The di e en in luences on one ca ego y o des ina ions poin s ou he di e ences be ween ci ies due o sho ages o equi ed a ge s and hei une en spa ial dis ibu ion. Table 5. Impac o one s ep modi ica ion o weigh s o changes in WS o elde ly. Fac o Values S ep Ci y Walk Sco e Change o 1 S ep Mean 3 d Qua ile 95-Pe cen ile speed 0.5–1.3 0.1 HK 1.863 3.263 7.291 β 144–180 4.5 speed 0.5–1.3 0.1 OV 2.436 4.258 7.742 β 144–180 4.5 e ail 7–12 0.55 HK 0.253 0.111 1.509 OV 0.402 0.431 2.102 hype ma ke 1–5 0.44 HK 0.019 0.000 0.090 OV 0.017 0.000 0.068 en e ainmen 0.8–1.4 0.07 HK 0.008 0.000 0.043 OV 0.010 0.000 0.058 doc o 1–2 0.11 HK 0.033 0.012 0.208 OV 0.039 0.034 0.216 pa k 0.1–6 0.66 HK 0.467 0.575 2.468 OV 0.263 0.121 1.555 The changes in WS o each es ing s ep show ha no all s eps ha e he same impac . Usually, he i s 2–3 s eps de ia e om o he s p o iding smalle o la ge impac . As you can see, o he dominan speed-β ac o , he i s h ee s eps indica e he highes a iabil- i y, bu changes a e signi ican ly lowe o la e s eps whe e he change in WS is s abilized a ound 3 (Os a a) and 4 (H adec K alo e) (Figu e 18). Al hough sensi i i y analysis shows he dominan in luences o gai speed and be a coe - icien a e e lec ed in sui able walkable dis ance, and a mino e ec o weigh se ings o des ina ions, use s ha e o conside he eal condi ions, needs and beha io o speci ic g oups o pe sons o such se ings. Sys ems wi h an open se ing o weigh s a e ecom- mended. ( a ) ( b ) Figu e 18. Ranges o WS change o 9 s eps in speed- β modi ica ions (H adec K alo e ( a ) and Os a a (b)). Al hough sensi i i y analysis shows he dominan in luences o gai speed and be a coe icien a e e lec ed in sui able walkable dis ance, and a mino e ec o weigh se - ings o des ina ions, use s ha e o conside he eal condi ions, needs and beha io o speci ic g oups o pe sons o such se ings. Sys ems wi h an open se ing o weigh s a e ecommended. 6. Discussion Based on compa ison o he main indices, se e al au ho s ha e e alua ed WAI as he bes pe o ming measu e o u ban walking condi ions which success ully cap u es he a i- ISPRS In . J. Geo-In . 2022,11, 279 23 o 29 a ions o u ban o m [ 28 , 48 ]. Some weaknesses o his index can be seen in i s gene alisa ion o land-use classes o he land-use mix, as measu ed by Shannon’s en opy index [ 28 ], di icul ies wi h calcula ion [ 19 ], selec ion o only objec i e a iables [ 65 ], impossibili y o esul compa ison o di e en ci ies (no s anda dised o o e all assessmen ), and he MAUP p oblem [ 98 ]. We applied he calcula ion o uni o m spa ial uni s o elimina e he p oblem o he e ogenei y in size and shape o he spa ial uni s. A ci cle bu e was applied o es ablish equi alen uni s o bo h WAI and WS assessmen . App op ia e implemen a ion o WAI equi es some adap a ion and app oxima ion. I is highly ecommended o exclude spa ial uni s whe e he a ea o in e es is less han 1% han he size o he uni . We also applied he app oxima ion ecommended by Reye e al. [28] o subs i u e FAR wi h he a eal size o comme cial buildings. WS is c i icised o i s applicabili y when da a sou ces a e spa se and highly gene - alised [ 28 ]. Addi ionally, i does no ake in o accoun di e ences in ip pu pose [ 61 ], whe e only one DDF is applied. To comba hese issues, a new applica ion was de eloped using OSM, Pandada lib a y o sea ching sho es ips, and he cumula i e Gaussian unc ion ins ead o he polynomial DDF. Due o di icul ies in assessing block leng h in Czech u ban condi ions, we app oxima ed using he a e age s ee segmen leng h. The applica ion enables he adjus men o maximum walking dis ance, walking speed, Gaussian DDF β coe icien and ameni y weigh s. Some au ho s c i icize he unclea weigh ing sys em o WS [ 42 ]. Zhang e al. [ 25 ] modi ied weigh s o adap hem o apidly u banizing Chinese ci y condi ions. They added comme cial complexes wi h a weigh o 3 since hey a e he main enue o shopping and ec ea ion. The weigh s o school and pa k en ances we e bo h inc eased om 1 o 1.5, e lec ing hei highe impo ance o he public in Shenzhen and China as a whole. Engels and Liu [ 99 ] es ed h ee a ian s o weigh se ings o bus s ops, pa ks, ec ea ion acili ies, g oce y shops and EMS s a ions, bu he selec ion o weigh s was a bi a y. Resul s o ou OAP sensi i i y analysis indica e ha e ail and pa ks ep esen he la ges in luence on WS o elde ly, howe e , he weigh se ings a e less impo an han o he pa ame e s such as walkable dis ance. In ou assessmen , we used cumula i e Gaussian unc ion o dis ance-decay e ec modelling. Some schola s ecommend o he unc ions, e.g., Ti an e al. [ 61 ] es ed a no - malised powe -exponen ial unc ion, Box-Cox’s unc ion, Tanne ’s unc ion, and Richa ds’ unc ion. They ound he la e o be he bes o modelling pu poses, bu his unc ion u ilises six pa ame e s, which complica es he se ings. Ho ak e al. [ 82 ] es ed a se o eg ession unc ions o di e en a el modes including walking: exponen ial, powe , Weibull, gamma, logno mal, and Box–Cox. Discussion on he beha iou and es ing o hese unc ions can be ound in, [ 100 – 102 ]. They ound he bes i was eached using he Weibull unc ion [ 103 ] in he majo i y o analysed cases. Ne e heless, due o he low in luence o weigh ing, he cumula i e Gaussian unc ion can be conside ed an app op ia e and simple solu ion. We es ed ou di e en adii—400, 800, 1200 and 2414 m, which co esponds o he p e e ed dis ances es ed by o he schola s. Mukh a e al. [ 72 ] calcula ed indica o s o 3 di e en ne wo k adii using 400 m, 800 m, o 1600 m ne wo k dis ances. Le eb e-Ropa s and Mo ency [ 48 ] es ed six di e en sea ch adii (200, 400, 800, 1200, 1600 and 2000 m) using s aigh -line dis ances. They concluded ha medium-sized sea ch adii (be ween 400 m and 1200 m) seem o o e a be e i , bu also commen ed ha changing sea ch adii has a ma ginal impac on he p ecision o mode choice p edic ion whe e he la ges imp o emen in model accu acy ba ely exceeds 2%. In ou s udy, we demons a ed ha adjus ing he walking dis ance has a majo impac on he ou pu s. Small bu e s o WAI enable he e alua ion o local condi ions, howe e , hey a e demanding on app op ia e da a sou ces. Ou esul s show ha he use ulness o WAI quickly deg ades wi h ex ension o he ci cle adius. Radii abo e 800 m co e la ge a eas and he e o e p o ide only gene al assessmen s; alues a e mo e s able, bu hey do no p o ide su icien spa ial de ail. ISPRS In . J. Geo-In . 2022,11, 279 24 o 29 Ci ies wi h highly di e se u banisa ion and une en dis ibu ion o ameni ies (e.g., Os a a) a e mo e sensi i e o spa ial uni se ings. Ex ension o he spa ial uni size causes WAI o d op in isola ed subu ban se lemen s ( illages) and on pe iphe ies o la ge dense u ban se lemen s. Con a ily, WS equi es la ge walking dis ances o be ans o med in o co esponding ne wo k sea ch adii. Sho e dis ances a e sensi i e o e o s in des ina ion loca ions and in oad o pedes ian ne wo k cons uc ion. One walking dis ance may no be su icien when s udying la ge a eas as schola s epo di e en easonable walking dis ances, mainly o elde ly o s uden s. Fu he mo e, s udies a e usually ocused on u ban condi ions, namely ci y cen es. This limi a ion should be aken in o accoun o analysis conduc ed ou side ci y cen es. In he coun yside, longe walking dis ances a e mo e ealis ic (e en o elde ly). Using he egula dis ibu ion o e alua ed poin s (bu e s) is no enough o ully explo e local condi ions. Resul s depend on selec ion o his poin and some small shi in i s loca ion will gene a e a sligh ly di e en assessmen . A Walk Sco e modi ica ion o elde ly was de eloped. The modi ica ion is based on selec ion o di e en des ina ions, adap a ion o gai speed, walkable dis ance and β coe icien . Senio s equi e a di e en se o des ina ions han employee and ha e di e en pu poses o walking ips. Based on he cu en local esea ch ou pu s, we selec ed e ail, hype ma ke , doc o , pa k, and en e ainmen as desi ed des ina ions because only hese ypes o a ge s can be localised and co espond o ci y condi ions. Fo u al condi ions, some des ina ions should be modi ied, e.g., he ole o pa k is minimised, howe e , he majo i y o des ina ions a e he same o s anda d WS and u al WS [104–106]. WS o elde ly shows a signi ican co ela ion (p= 0.01) wi h s anda d WS in he e alua ed ci ies (R 2 0.67 and 0.69) bu di e ences a e appa en and he assessmen o walking condi ions o elde ly could no be di ec ly de i ed om s anda d WS. As expec ed, he highly walkable a ea is smalle and much mo e di e se o elde ly han o adul s. App oxima ely 1/3 o spa ial uni s wi h 10–15% o he popula ion epo he same alues. S ong declines in WS o elde ly occu in some 20% o uni s, ep esen ing 25–33% o he popula ion. The emaining a ea shows only mode a e declines whe e di e ences in walking condi ions a e negligible. The sensi i i y analysis disco e s ha he changes o weigh s o des ina ions (in he expec ed ange o alues) ha e a low in luence on he inal WS; i is mo e impo an o se app op ia e gai speed and βcoe icien which in luence eal accessibili y o des ina ions. 7. Conclusions Imp o emen o u ban walking condi ions has nume ous posi i e e ec s including suppo ing a heal hy li es yle and pe sonal well-being, dec easing en i onmen al pollu- ion, and inc easing business bene i s. Walking as mode a e physical ac i i y, a means o sel - esilience, and a na u al media o o social con ac s is essen ial o many senio s. Modi ica ions and adap a ions o he u ban en i onmen o be mo e iendly owa ds he needs and wishes o senio pedes ians subs an ially imp o es he inclusi eness o ou ci ies. Objec i e indica o s o walkabili y con ibu e o analysis o he u ban en i onmen and help o unco e local walking issues and ake app op ia e measu es o imp o e li ing condi ions. Many indica o s ha e been de eloped and a e o en alida ed by esul s o local ques ionnai e su eys. Less is known, howe e , abou hei spa ial beha iou , how o se impo an pa ame e s and which impac s can be expec ed o a ious unce ain ies included in such models. To e alua e he spa ial pa e n o objec i e-based indica o s, wo popula indices we e selec ed—WAI [ 64 ] ep esen ing s a is ical-based indica o s, and WS which applies an accessibili y-based app oach. Bo h indica o s we e e alua ed in adequa e spa ial uni s (bu e s wi h adii om 400 m o 2414 m) in wo Czech ci ies. This enabled compa ison o he esul s and explo a ion o he pa e n o hese indices. The impac o di e en bu e s placemen was no examined. A new so wa e ool was de eloped o he calcula ion ISPRS In . J. Geo-In . 2022,11, 279 25 o 29 o Walk Sco e using OSM da a and eely a ailable ne wo k se ices. To be e add ess equi emen s o he elde ly, a new a ian o WS was designed and enume a ed. This ool is a ailable a [ 91 ]. The s anda d DDF o WS was subs i u ed by a cumula i e Gaussian unc ion wi h di e en se ings o β coe icien in luencing he s eepness and ange o he unc ion acco ding o ecommended walkable dis ances. Di e en gai speed and a iable se ings o a ge s and hei weigh s enabled he adap a ion o WS o local condi ions and pe sonal needs. A sensi i i y analysis disco e ed he majo in luences o gai speed and he βcoe icien on he walkabili y assessmen . The assessmen o WS o bo h ci ies indica es ha app ox. 40% o inhabi an s a e likely ca dependen due o unsa is ac o y walking condi ions. A join analysis o compa able WAI and WS assessmen s shows di e en spa ial pa e n o each index whe e WAI pe o ms be e wi h smalle adii (up o app ox. 800 m) while o WS a la ge adius is a ou able (>800 m). These indings a e pa ly in line wi h p e ious s udies whe e adii o 400–600 m [19,26,51,80] a e usually p e e ed. Fo people cons ained o sho walking dis ances, he esul s o adap ed WS o elde ly may be no ele an . A subs i u ion o una ailable usual a ge s by hose a ailable, e.g., pa ks o “no a ge ” walking such as a walking loop a ound one’s esidence can be expec ed. In such cases, en i onmen al-based indica o s such as WAI should pe o m be e o walkabili y assessmen . This limi a ion should also be aken in o accoun o mixed indica o s whe e he ne wo k-based componen s may be unde es ima ed as a esul o he combina ion o una ailable usual a ge s and sho walking dis ances. The compa ison o s anda d WS and WS o he elde ly con i ms an expec ed o e all dec ease in walkabili y, bu wi h unexpec ed in ensi y. App oxima ely 1/3 o loca ions, ep esen ing 10–15% o he popula ion, do no show a change in WS, he e o e he condi- ions o “s anda d walking” and “elde ly walking” a e assessed as he same. A la ge d op in WS o he elde ly is eco ded in app oxima ely 20% o he inhabi ed a ea in Os a a and 17% o he inhabi ed a ea o H adec K alo e, ep esen ing 33% o he popula ion in Os a a and 25% o he popula ion in H adec K alo e. A speci ic pa e n was ecognised in Os a a whe e hese loca ions su ound dense se lemen uni s o occu in places wi h in e nal geog aphical ba ie s. Conce ning limi a ions o he cu en s udy, only a egula g id o bu e s wi h 500 m dis ance was s udied and in luences o di e en placemen s we e no e alua ed. The in oduced WS o he elde ly ep esen s a simple adap a ion o WS and u he imp o e- men is en isaged. Ob iously, he e a e many simpli ica ion issues which occu om gene alisa ion o senio s’ capabili ies, in e es s and needs. Addi ionally, des ina ions and p opensi y o walk a e no s able o each pe son o g oup, bu change o e ime (e.g., due o seasonal changes o ends in luenced by aging). Fu he limi a ions can be seen in he OAP app oach and mesoscale ep esen a ion o u ban en i onmen s. An OAP app oach used o sensi i i y analysis p o ides a simple solu ion whe e, e.g., mul icollinea i y issues o weigh ing o des ina ions a e no conside ed. Mo e ad anced analysis wi h Mon e Ca lo simula ions and a iance-based me hods should b ing deepe unde s anding o ela ionships in he weigh ing sys em. The cu en assessmen is based on a simple g aph ep esen a ion o s ee s. Elde ly people equi e mo e de ailed e alua ion o pedes ian condi ions (mo ing om mezo- o mic o-scale). Ins ead o s ee ne , pedes ian ne usage on eal sidewalks should be cons uc ed u ilising pa ame e s in luencing p opensi y o walk such as wid h o he pa emen , he su ace, slope, a ic, obs acles, and es ing places. Inspi a ion may be ound in p oposals o new indices o elde ly dealing wi h such u ban issue de ails such as a mul i ac o Walkabili y Index o Elde ly Heal h (WIEH) [ 19 ]. Such app oaches a e qui e demanding on da a sou ces and equen ly equi e da a in eg a ion and supplemen a ion om di e en sou ces including ield su eys (see Supplemen a y Ma e ials).