Distortion Effects in Equal Area Unit Maps

Vol.:(0123456789) 1 3 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 h ps://doi.o g/10.1007/s42489-021-00072-5 Dis o ion E ec s inEqual A ea Uni Maps JochenSchiewe1 Recei ed: 5 Decembe 2020 / Accep ed: 7 Janua y 2021 / Published online: 1 Feb ua y 2021 © The Au ho (s) 2021 Abs ac Maps ha co ec ly ep esen he geog aphic size and shape o egions, aking in o accoun scaling and gene aliza ion, ha e he disad an age ha small egions can easily be o e looked o no seen a all. Hence, o some map use asks whe e small egions a e o impo ance, al e na i e map ypes a e needed. One op ion is he so-called equal a ea uni maps (EAUMs), whe e e e y enume a ion uni has he same a ea size, possibly also he same basic shape such as squa es o hexagons. The geome ical dis o ion o EAUMs, howe e , leads o a mo e di icul sea ch o egions as well as a alsi ica ion o opological ela ionships and spa ial pa e ns. To desc ibe hese dis o ions, a se o analy ical measu es is p oposed. Bu i u ns ou ha he exp essi eness o hese measu es is a he limi ed. To be e unde s and and o model he in luence o dis o ions, wo use s udies we e conduc ed. The s udy on he sea ch in EAUMs (also wi h he aim o econs uc he sea ch s a egies o he use s) e ealed how impo an i is o conside he local opology (e.g. co ne o bo de posi ions o egions) du ing he gene a ion p ocess. Wi h ega d o pa e n iden i ica ion, i could be shown ha EAUMs signi ican ly inc ease he de ec ion a e o local ex eme alues. On he o he hand, global la e al g adien s o geos a is ical ho spo s o en ge blu ed o e en los . As a consequence, a ask-o ien ed selec ion o map ypes and u he de elopmen s a e ecommended. Keywo ds Equal a ea uni maps· Cho ople h maps· Pa e n iden i ica ion· Usabili y Ku z assung Ka en, die un e Beach ung des Maßs abes und de Gene alisie ung die geog aphische G öße und Fo m on Regionen ko - ek wiede geben, haben den Nach eil, dass kleine Regionen leich übe sehen ode ga nich gesehen we den. Dahe we den ü einige Ka ennu zungsau gaben, bei denen kleine Regionen on Bedeu ung sind, al e na i e Ka en ypen benö ig . Eine Op ion sind sogenann e Equal A ea Uni Maps (EAUMs), bei denen jede Einhei dieselbe Flächeng öße und zumeis auch dieselbe G und o m wie Quad a e ode Hexagone besi z . Die geome ische Ve ze ung on EAUMs üh jedoch zu eine schwie ige en Suche nach Regionen sowie zu eine Ve älschung opologische Beziehungen und äumliche Mus e . Um diese Ve ze ungen zu besch eiben, wi d ein Sa z on analy ischen Maßzahlen o geschlagen. Es zeig sich jedoch, dass die Aussagek a diese Maßzahlen ehe beg enz is . Um den Ein luss on Ve ze ungen besse e s ehen und modellie en zu können, wu den zwei Anwende s udien du chge üh . Die S udie zu Suche in EAUMs (auch mi dem Ziel, die Such- s a egien de Benu ze nachzu ollziehen) e gab, wie wich ig es is , die lokale Topologie (z. B. Eck- ode Randposi ionen on Regionen) wäh end des Gene ie ungsp ozesses zu be ücksich igen. In Bezug au die Iden i ika ion äumliche Mus e konn e gezeig we den, dass EAUMs die E kennungs a e lokale Ex emwe e signi ikan e höhen. Ande e sei s e schwim- men globale la e ale G adien en ode geos a is ische Ho Spo s häu ig ode gehen soga e lo en. In olgedessen we den eine au gabeno ien ie e Auswahl on Ka en ypen sowie wei e e En wicklungen emp ohlen. Schlüsselwo e Equal A ea Uni Maps· Cho ople henka en · Mus e e kennung· Geb auchs auglichkei 1 In oduc ion Maps gene ally ollow he p inciple o co ec ly ep esen ing he geog aphic size and shape o egions, o cou se, unde conside a ion o scale and gene aliza ion. Howe e , due o * Jochen Schiewe jochen.schiew[email p o ec ed] 1 Lab o Geoin o ma ics andGeo isualiza ion (g2lab), Ha enCi y Uni e si y Hambu g, Henning-Vosche au-Pla z 1, 20457Hambu g, Ge many 72 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 he he e ogeneous di e ences in he size o he enume a ion a eas, his o en leads o a e y small egions appea ing so small ha hey can be o e looked o no seen a all (e.g. Singapo e is shown in a wo ld map a a scale o 1: 90 million as an a ea o 0.3mm by 0.5mm). In cho ople h maps, he e a e also he cogni i ely caused e ec ha la ge egions a e pe cei ed as mo e dominan , al hough hey ha e he same colo alue compa ed o he small egions, which leads o misin e p e a ions and w ong decisions (Slocum e al. 2009). Empi ical s udies ha e con i med ha he de ec ion a es in he o de o 60% o global ex eme alues in small a eas wi hin cho ople h maps a e signi ican ly wo se han hose o la ge a eas, which a e in he o de o 90% (Schiewe 2019). As an al e na i e o he ue-scale ep esen a ion, Equal A ea Uni Maps (EAUMs) ha e gained an inc easing pop- ula i y in he ecen pas , especially in he news media.1 EAUMs ep esen each enume a ion a ea in he same size and possibly use uni o m basic shapes (e.g. squa es, ec an- gles, hexagons, o mul i-hexagons—see Fig.1). Chap e 2 gi es a deepe insigh in o e minology ela ed o EAUMs and me hods o gene a ing hem. The ad an age o EAUMs is ha o a a ie y o map use asks all enume a ion a eas a e shown wi h equal p omi- nence. This makes i easy o look-up and compa e alues and o a oid he a ea size-bias. Assuming a ce ain size o he basic uni s, EAUMs can accommoda e no only one colo o hachu e o e e y egion, bu also ex , symbols o small diag ams, which enables he display o mul i a ia e da a. EAUMs a e also mo i a ing o use because hey ep- esen an unusual depic ion o egions and p oduce a ce ain su p ise e ec due o he alse-scale ep esen a ion. I can also be a gued ha he consis en use o clea shapes such as squa es o hexagons is aes he ically pleasing. Looking a he disad an ages, he gene a ion o EAUMs leads o dis o ions conce ning he dis ances be ween egional uni s, a ea sizes, shapes and opological ela ion- ships (such as loss and addi ion o neighbo hoods and mem- be ships) compa ed o he o iginal geog aphical da a. As a esul , he sea ch o speci ic egions and he in e p e a- ion o spa ial dis ibu ions o pa e ns in he o iginal da a becomes mo e di icul and mo e e o -p one. To desc ibe he dis o ions in a mo e objec i e and quan i a i e man- ne , Chap e 3 p esen s selec ed geome ical and opological measu es. F om his, i can be concluded ha hese meas- u es show a la ge a ia ion wi hin a map and do no p o- duce a clea o e all imp ession o dis o ions. Fu he mo e, he qui e la ge se o analy ical measu es is no sui able o pu poses such as compa ing map designs o con olling an EAUM gene a ion algo i hm. To be e unde s and he ele ance o dis o ions, his con ibu ion also ollows an empi ical app oach. While o some map ypes, such as alue-by-a ea maps (Sun and Li 2010), s udies on he e ec s o he dis o ions on he in e - p e abili y exis , he e is s ill no empi ical e idence o he cogni i e e ec o EAUMs. A i s use s udy (Chap e 4) deals wi h he e ec i eness o he sea ch in EAUMs bu also wi h he de i a ion o ypi- cal sea ch s a egies ha can be o in e es o con olling he EAUM gene a ion p ocess. The second s udy (Chap e 5) ocuses on he iden i ica ion o pa e ns in EAUMs: i s ly, he hypo hesis is examined ha pa e ns ela ed o indi idual egions (such as local ex eme alues) a e well ecognized wi hin EAUMs. The second hypo hesis is ela ed o he iden- i ica ion o o he pa e ns such as No h–Sou h g adien s o ho spo s, which is much mo e di icul due o he inhe en geome ical dis o ions. Chap e 6 summa izes he esul s o he wo s udies and gi es ecommenda ions o u u e de elopmen s in he EAUM en i onmen . Fig. 1 Example o equal a ea uni maps (EAUMs), composed o egula g id cells (middle) o hexagons ( igh ), in compa ison o o iginal geog aphical egions (le ) 1 Examples o EAUMs in news media [las access Dec 1, 2020]: NY Times: h ps ://a chi e.ny im es.com/www.ny im es.com/in e ac i e/2013/06/26/us/sco u s-gay-ma i age.h ml abc News: h ps :// i e hi y eigh .com/ ea u es/whe e -you -s a e -ge s- i s-money / Bloombe g: h ps ://www.bloom be g.com/g aph ics/2015-pace-o - socia l-chang e/ The Gua dian: h ps ://www. hegu a dia n.com/us-news/ng-in e ac i e/2014/oc /22/-sp- o in g- igh s-iden i ica ion-how- ien dly-is-you - s a e . 73KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 2 Equal A ea Uni Maps 2.1 Te minology In he ollowing I de ine an equal a ea uni map (EAUM) as a base map whe e e e y enume a ion uni (geog aphic en i y) is gi en he same size, possibly also he same shape (such as squa es, ec angles o hexagons). O e lapping uni s a e no allowed; howe e , gaps a e possible. The a ange- men o uni s is done acco ding o one o mo e op imiza ion c i e ia (e.g. minimizing he posi ional shi o cen oids be ween geog aphic o iginal and esul ing EAUM). I should o be no ed ha he e is no common e minology in li e a u e o his ype o ep esen a ion. One op ion is he e m “equal a ea ca og am” (B ai h 2015; O dnance Su ey 2020). S ic ly speaking, a ca og am is no app op ia e he e, since a modi ica ion o shapes and sizes o uni s is no based on da a alues as de ined by Slocum e al. (2009). On he o he hand, he e m “equal a ea ca og am” lea es ou he e m “map”—as Raisz (1934) does, who s a es ha he “ ec- angula s a is ical ca og ams” in his wo k a e no maps. I one akes he s ic de ini ion by Hake e al. (2002) in o accoun , an EAUM does no ul ill he condi ion o a co ec o hogonal p ojec ion; ins ead, i could be ca ego ized as a map-alike p oduc . On he o he hand, aking in o accoun he less s ic de ini ion o he In e na ional Ca og aphic Associa ion (ICA 2003), i is applicable o use he e m “map” since he p ima y ele ance o spa ial ela ionships is s ill gi en. Some imes, his map ype is associa ed o he e m “ ile map” (e.g. McNeill and Hale 2017). Howe e , he e is also ano he (and mo e dominan ) meaning ha ile maps cu geog aphical space—wi hou explici ly conside ing admin- is a i e egions—in o egula elemen s o allow as e and indi idualized access (Pe e son 2012). O he au ho s such as Epps ein e al. (2015) o Wongsuphasawa (2016) use he e m “g id map”. This sugges s a egula as e , neglec ing o he uni ep esen a ions such as hexagons. Finally, EAUMs should no be con used wi h alue-by- a ea maps (Den 1999) o a ea ca og ams (Slocum e al. 2009), in which he a eas o each enume a ion uni a e scaled o sized p opo ionally o an a ibu e alue (e.g. popula ion). 2.2 Gene a ion o EAUMs The gene a ion o EAUMs can be iewed as a so-called assignmen p oblem, which is known om g aph heo y: gi en is a bipa i e g aph, which consis s o wo subse s wi h he same numbe o nodes, one pa i ion o he o iginal geo- g aphic inpu si ua ion and he o he o he ou pu EAUM. While he nodes ep esen egion cen oids, he edges model he ac ual neighbo hood o egions. The g aph ma ching is now a combina o ial op imiza ion p oblem ha looks o a unique assignmen be ween nodes o he wo pa i ions, in which he o e all cos s o edge weigh s (e.g. he dis ances o cen oids) mus be minimized. The con en ional algo i hm o weigh ed ma chings in bipa i e g aphs is he Hunga ian me hod, also called he Kuhn-Munk es algo i hm (Kuhn 1955; Munk es 1957). I sol es he assignmen p oblem in O(n3) ime (whe e n is he numbe o nodes). This algo i hm was also used o gene a - ing map examples o he ollowing s udy.2 The e a e se e al specialized o ex ended o ms o his algo i hm as well as o he app oaches such as he simplex me hod (Ba e al. 1977). Howe e , i is beyond he scope o his pape o gi e a comp ehensi e o e iew o he a ie y o hese me hods. 3 Dis o ions inEAUMs To enable an objec i e and nume ical desc ip ion o dis- o ions in EAUMs o absolu e o ela i e compa ison pu poses, a ious measu es a e p esen ed in he ollowing (Sec .3.1). These measu es a e hen applied o h ee exam- ple maps in o de o assess hei exp essi eness (Sec .3.2). 3.1 Measu es The dis o ion e ec be ween wo maps can be desc ibed by se e al measu es. Fo example, Nus a and Kobou o (2016) use he ca ego ies s a is ical accu acy (p ese a- ion o hema ic alues), con igui y (p esence o o e laps o gaps), geog aphy (p ese a ion o shape and size), and opology (especially p ese a ion o neighbo hoods). Alam e al. (2016) e e o dis o ions o geome y, opology and complexi y. EAUMs a e no deal wi h in hese publica ions. Fo ou pu poses, he ollowing geome ical and opological measu es ha e been de ined: Geome ical dis o ions: • Dis ance dis o ion (G_DD): mean alue o all dis ances be ween egion cen oids in geog aphical and EAUM map ha co espond o each o he ’s (no malized by dis ance o longes ex ension o o al map, i.e. ei he in No h–Sou h o Eas –Wes di ec ion). • Single enume a ion a ea size a iance (G_SA): s anda d de ia ion o a ea sizes o geog aphical egions (no mal- ized by di ision by mean alue o a ea sizes). The la ge he s anda d de ia ion is, he la ge he dis o ion wi hin an EAUM (wi h a ea s anda d de ia ion o Ze o) will be. 2 PyEAC so wa e: h ps ://gi la b.com/g2lab /pyeac . 74 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 • To al enume a ion a ea size a iance (G_TA): di e ence o o al a eas be ween geog aphical and EAUM ep esen- a ion (no malized by o al a ea o geog aphical a ea). • Di e ence A ea o pe ime e (G_DP): sum o p o uding and clipped a eas o EAUM in compa ison o geog aphi- cal a ea (no malized by o al geog aphical a ea). Topog aphical dis o ions: • Omission o neighbo s (T_ON): numbe o neighbo - hood ela ionships ha a e missing a e ans o ma ion o EAUM (no malized by o al numbe o neighbo hoods in map) • Commission o neighbo s (T_CN): numbe o neigh- bo hood ela ions ha a e added a e ans o ma ion o EAUM (no malized by o al numbe o neighbo hoods in map). • To al numbe o neighbo hood e o s (T_TN): sum o T_ON and T_CN. • P opo ion o islands (T_PI): numbe o islands (which by de ini ion canno be p ese ed in EAUMs) in ela ion o o al numbe o egions. In all cases he measu es a e designed in such a way ha he alue ange is limi ed o [0; 1] and he ideal case (i.e., no dis o ion) is e lec ed by he alue 0. 3.2 Example The a o emen ioned measu es ha e been applied o h ee EAUMs ha ha e been de i ed om gi en base maps wi h co ec geog aphical appea ance—showing he s a es o Aus alia, Ge many, and he Uni ed S a es. Using he PyEAC so wa e men ioned in chap e 2.2, wo ypes o uni shapes ha e been c ea ed, namely egula squa es (REG) and hexagons (HEX). Table1 summa izes he esul s o all gi en measu es. Compa ing he indi idual measu es be ween he wo basic EAUM shapes (REG and HEX) o one and he same a ea, no signi ican di e ences wi h ega d o geome ical dis o ions can be obse ed (e.g. in he case o Aus alia: G_DD = 0.19 o HEX and G_DD = 0.20 o REG). On he o he hand, he e a e clea di e ences be ween REG and HEX in opological measu es, howe e , wi h no clea ends. The di e en maxi- mum numbe o neighbo s (REG: eigh , HEX: six) oge he wi h he ac ual dis ibu ion o egions is p obably esponsible o hese di e ences. When looking a he di e ences be ween a eas (wi h he same basic EAUM shape), Aus alia shows la ges dis o ions, which is due o he small numbe o egions and he speci ic loca ion o Tasmania. Compa ed o he Ge man map, he US example shows (wi h one excep ion) sligh ly smalle geome i- cal dis o ions. Rega ding opological changes, again no clea ends can be de i ed. Figu e2 shows o an exempla y measu e (D_GG) and a selec ed basic shape (REG) ha he e a e la ge spa ial a i- ances wi hin he measu es lis ed in Table1. The speci ied mean alues, he e o e, show a s ong smoo hing e ec and do no c ea e a clea o e all imp ession o dis o ions o a speci ic da a se . All in all, due o he in many cases unclea ends, he egional a ia ion o he measu es and he a he la ge se o analy ical measu es, his analy ical app oach is no easible o pu poses such as compa ing maps o e en con olling an EAUM gene a ion algo i hm. As a consequence, his con i- bu ion will ollow an empi ical app oach in he nex chap e s o be e unde s and he impo ance and ele ance o hese measu es. Table 1 Geome ical and opological dis o ions o EAUMs o h ee example a eas A ea Aus alia Ge many USA No. o egions 7 16 49 EAUM basic shape HEX REG HEX REG HEX REG Geome ical dis o ions G_DD 0.19 0.20 0.01 0.01 0.15 0.16 G_SA 0.91 0.91 0.81 0.81 0.77 0.77 G_TA 0.11 0.08 0.05 0.08 0.04 0.02 G_DP 0.37 0.43 0.27 0.25 0.18 0.18 Topological dis o ions T_ON 0.00 0.10 0.34 0.16 0.50 0.45 T_CN 0.19 0.48 0.48 0.60 0.54 0.81 T_TN 0.19 0.57 0.83 0.76 1.04 1.27 T_PI 0.00 0.00 0.13 0.13 0.00 0.00 75KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 4 Empi ical S udy: Sea ch o Regions inEAUMs 4.1 Resea ch Ques ion Fo many map usage asks ha a e o be sol ed wi h he help o hema ic maps wi h a ea e e ence (e.g. mosaic o cho o- ple h maps), he sea ch o egions is an essen ial ope a ion. In his case ei he he name o he egion o he loca ion on ano he map o compa ison pu poses is gi en. Since geo- me ical dis o ions a e ine i able wi h EAUMs, he ques ion a ises how e ec i e he sea ch can be. Fo u he de elop- men s o EAUMs and o he map ypes, i is also in e es ing o know which sea ch s a egies he use s a e using. 4.2 Hypo heses Based on he knowledge o cogni i e psychology and isual pe cep ion (e.g. op-down objec ecogni ion; Biede man 1981), i is assumed ha opological ela ionships a e key c i e ia o sea ching o speci ic egions in maps. This leads o he ollowing hypo heses: • [H1.1] Use s apply di e en sea ch s a egies o egions depending on hei opological si ua ion (e.g. co ne , bo - de , cen e , and island). • [H1.2] Algo i hms o gene a ing EAUMs can p ese e he espec i e opological ela ionships only o a ce ain deg ee and hus in luence he sea ch e ec i eness. 4.3 S udy Design Conside ing he a ious opological cases wi h dis inc solu ions ha allow single o mul iple choice ques ions, a quan i a i e, web-based s udy has been gene a ed. Because no use g oup-speci ic cha ac e is ics a e assumed, socio-demog aphic we e no ga he ed. In o de no o le he s udy p ocessing ime become oo long, only map examples o Ge many and he USA we e shown. The s udy used he wo mos common basic geome ical shapes o EAUMs, namely egula squa es (REG) and hexa- gons (HEX). The egion o be sea ched o was ma ked on a map wi h he “co ec ” geog aphical shape (GEO). Righ o i an EAUM—ei he in REG o HEX layou —was p e- sen ed and a single choice selec ion om ou sugges ed a ge egions was eques ed; in all cases he ques ion was: “Please loca e he ma ked egion in he igh map. Choose he bes solu ion o you” (Fig.3). “Please loca e he ma ked egion in he igh map. Choose he bes solu ion o you” (Fig.3). Wi h ha app oach, a pos- sible lack o knowledge abou he names o he egions was bypassed. A o al o 11 cases we e gi en—conside ing com- bina ions o possible opologies (co ne , bo de , cen e , and island) and di e en base maps ( ede al s a es o Ge many and USA). When applying hese cases o he wo EAUM shapes (REG, HEX), a o al o 22 asks had o be sol ed. Fig. 2 Spa ial dis ibu ion o measu e D_GG o h ee EAUM da a se s wi h basic REG shape (no e: maps use di e en da a classi ica ion schemes because absolu e alue anges di e oo much be ween examples) Fig. 3 Exempla y ask o sea ching gi en egion in map wi h geo- g aphical shape (GEO; le ) in he EAUM map (he e: REG; igh ) 76 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 The map examples we e no p esen ed in a sys ema ic o de in o de o a oid lea ning e ec s. As e iciency is no in he ocus o his su ey, ime measu emen s we e no conduc ed. 4.4 Resul s A o al o 222 pa icipan s ook pa in he su ey. While Fig.4 shows he espec i e loca ions o he cases men- ioned, Table2 gi es an o e iew o he esul s. The col- umn “use p e e ence” shows he pe cen age o use s who selec ed he mos common solu ion, ega dless o whe he his solu ion was iden ical wi h he algo i hmic assignmen o he espec i e s a e. This measu e e alua es he pu e sea ch s a egy. The column “calcula ed s a e de ec ed” shows he pe cen age a which use s selec ed he egion wi h a name ma ch be ween geog aphical and EAUM ep- esen a ion. Only in 9 o 22 cases (ma ked wi h “Y” in he column “compa ison”) did use p e e ence ac ually e e ed o he egion wi h he calcula ed s a e. No consis en s a egies and esul s could be obse ed o he sea ch o co ne egions. In case 1.1 ( egion in an uppe igh co ne ; Fig.5), 91% o he egions we e assigned in he REG ep esen a ion and 87% in he HEX ep esen a ion. In con as , he localiza ion in case 1.2 (lowe igh co ne ; Fig.6) shows signi ican ly poo e al- ues. The lowe igh co ne was selec ed in REG only by 48% ( hough he majo i y) and in HEX by 41% o he pa - icipan s. The sea ch c i e ion o a co ne (in his example he lowes and igh mos ) was ob iously no p edominan , bu he pe iphe al loca ion in combina ion wi h he imagi- na y o e lap o he EAUM egion wi h he o iginal egion. Case 1.2 is also an example o a misma ch be ween solu- ions ha we e p e e ed by use s and he one ha was gene a ed by he algo i hm. I is he e o e no su p ising ha only 4% ( o REG and HEX) o he pa icipan s iden i- ied ha algo i hmic solu ion as Ba a ia. Also o bo de egions, de ec ion esul s di e ed s ongly be ween examples. No h Rhine-Wes phalia (case 1.3) shows e y good de ec ion a es o 98% (REG) and Fig. 4 Localiza ion o cases 1 o 11 in s udy 1 Table 2 Resul s o s udy 1 conce ning egion sea ch in EAUMs Topological si ua ion Case S a e EAUM Use p e e ence Calcula ed s a e de ec ed Compa ison Co ne 1.1 Mecklenbu g-Wes e n Pome ania REG 91% 91% Y HEX 87% 87% Y 1.2 Ba a ia REG 48% 48% Y HEX 49% 4% N Bo de 2.3 No h Rhine-Wes phalia REG 98% 98% Y HEX 90% 90% Y 1.4 B andenbu g REG 59% 59% Y HEX 60% 38% N 1.5 Texas REG 45% – – HEX 65% 1% N Cen e 1.6 Hesse REG 63% 36% N HEX 78% 78% Y 1.7 Saxony-Anhal REG 40% 32% N HEX 55% – – 1.8 U ah REG 41% 41% Y HEX 95% – – 1.9 Neb aska REG 70% 1% N HEX 79% 6% N Island 1.10 B emen REG 52% 46% N REG 50% 50% Y 1.11 Be lin REG 62% 34% N REG 79% 18% N 77KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 90% (HEX). The s a egy he e was ob iously o ei he coun along he edge om op o bo om, o o selec he egion a abou he same heigh as in he o iginal. In case 1.4 (B andenbu g), he esul is signi ican wo se (59%/38%), which is appa en ly due o he unclea posi ion o he s a e B andenbu g ela i e o he island Be lin in he EAUMs. In he case o Texas (case 1.5; Fig.7) i was no he bulge a he lowe edge, bu he i s a eal o e lap wi h he o iginal egion ha was selec ed mos equen ly (65%)—using he eading o de om he le o igh . The HEX-algo i hm has Texas placed o a a he dis an loca- ion, which, unsu p isingly, was only ecognized by 1% o use s. Also o cen e egions, a s ong de ia ion be ween exam- ples can be obse ed— he use p e e ence alues ange be ween 40 and 70% (REG) and 55% and 95% (HEX). Ob i- ously, mos use s sol ed hese asks by coun ing enume a- ion uni s. Howe e , he coun ing as such was no always Fig. 5 Case 1.1: Sea ch o Mecklenbu g-Wes e n Pome a- nia (le , geog aphical shape)— use alloca ions (in pe cen ) in REG (middle) and HEX ( igh ) ep esen a ions; g een column indica es alloca ion o ha egion by algo i hm Fig. 6 Case 1.2: Sea ch o Ba a ia (le , geog aphical shape)—use alloca ions (in pe cen ) in REG (middle) and HEX ( igh ) ep esen a ions; g een column indica es alloca- ion o ha egion by algo i hm Fig. 7 Case 1.5: Sea ch o Texas (le , geog aphi- cal shape)—use alloca ions (in pe cen ) in HEX ( igh ) ep esen a ion; g een column indica es alloca ion o ha egion by algo i hm 78 KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 co ec —in pa icula , i mo e han h ee egions had o be conside ed like in he USA example. Fu he mo e, he mis- alignmen o spa ial uni s in he geog aphical and ( o some ex en ) in he HEX- ype hampe s he coun ing. In gene al, HEX has highe ecogni ion a es han REG in he gi en examples. Island egions ep esen a p oblem wi h he ep esen a ion in EAUMs as he e is pe se no pe ec solu ion. Acco d- ingly, he de ec ion a es a e also no sa is ying. In 50–79% o he cases, he island and he su ounding polygon we e a anged in he o de in which hey we e ead (usually om le o igh ; e.g. Be lin is assumed o be o he igh o B andenbu g, Fig.8). No HEX solu ion was o e ed o he sea ch o island egions bu one and he same REG a ian had o be p ocessed wice by he pa icipan s in he s udy wi h a ce ain ime lag. While he de ec ion a e emained he same in he case o B emen, he a e o Be lin luc- ua ed e y s ongly (62% s. 79%), which sugges s low in ui i eness. 4.5 In e p e a ion Hypo hesis [H1.1]—assuming di e en sea ch s a egies o di e en opological si ua ions—could be pa ially con- i med. In pa icula , co ne and bo de posi ions we e aken in o conside a ion du ing he sea ch. Essen ially, he ela i e loca ion was es ima ed o spa ial uni s we e coun ed— he le – igh o op-down sea ch sequences clea ly domina ed. In he case o la ge geog aphic egions, hose EAUM egions we e o en selec ed ha show an imagina y o e lap wi h he geog aphical egion (e.g. in case 1.2). Due o he sca e ed esul s and he unsa is ying mean o 66% o he use p e e ence nei he a clea no a success ul s a egy can be de i ed. Ne e heless, he iden i ied basic opological sea ch p e e ences should be aken in o accoun when gene a ing he EAUM. I can be concluded ha he e- quen ly used pa ame e “minimizing dis ances o cen oids” (see Chap e 2.2) does no coincide wi h use ’s expec a ions. Hypo hesis [H1.2] could be con i med: dis o ions in EACMs lead o signi ican de ia ions ha use s canno eas- ily compensa e o . Compa ed o he a o emen ioned mean alue o 66% o he use p e e ence, he de ec ion a e o he egions wi h a name ma ch is only 43%. Fu he mo e, only in 9 ou o 22 asks did he use ’s majo choice ag ee wi h he algo i hmic solu ion. 5 Empi ical S udy: Pa e n Iden i ica ion inEAUMs 5.1 Resea ch Ques ion Cho ople h maps a e p ima ily used o iden i y spa ial pa - e ns. In he ollowing, egions wi h local ex eme alues (LE), global la e al g adien s (GLG; i.e. No h–Sou h o Eas –Wes g adien s) as well as ho spo s (HS) a e consid- e ed. The al e na i e use o EAUMs ha bo s he isk ha he inhe en spa ial dis o ion lead o he ac ha pa e ns a e no longe ecognized well o no a all. On he o he hand, EAUMs should ha e he po en ial o a be e ecogni ion o local ex emes o small enume a ion a eas, hus a oiding he a ea size-bias. 5.2 Hypo heses I is assumed ha due o geome ical dis o ions also he iden i ica ion o spa ial pa e ns in EAUMs is a ec ed in a nega i e manne wi h he excep ion o he iden i ica ion o local ex eme alue egions. This leads o he ollowing hypo heses: • [H2.1] The iden i ica ion o LE akes place in EAUMs wi h g ea e e ec i eness, because he a ea size bias is a oided. Since neighbo hoods a e i ele an in his con ex , no di e ence be ween REG and HEX is o be expec ed. • [H2.2] The iden i ica ion o GLG and HS is bes done in he o iginal geog aphical layou (GEO) due o po en ial neighbo hood dis o ions in REG and HEX. 5.3 S udy Design Conside ing he a ious pa e n cases wi h dis inc solu- ions ha allow single o mul iple choice ques ions, a Fig. 8 Case 1.11: sea ch o Be lin (le , geog aphical shape)—use alloca ions (in pe cen ) in REG ( igh ) ep esen a ion; g een column indica es alloca ion o ha egion by algo i hm 79KN - Jou nal o Ca og aphy and Geog aphic In o ma ion (2021) 71:71–82 1 3 quan i a i e, web-based s udy has been gene a ed. Because no use g oup-speci ic cha ac e is ics a e assumed, socio- demog aphic we e no ga he ed. In o de no o le he s udy p ocessing ime become oo long, only map exam- ples o Ge many and he USA we e shown. The ask was o iden i y pa e ns in di e en map ypes (GEO/REG/HEX). Fo each ask, one map wi h one o mo e pa e ns was p esen ed; in o al, eigh maps we e gi en (examples a e gi en in Figs.9, 10, 11). Pa icipan s we e asked o a mul iple choice-selec ion wi h he op ions o one locale ex eme alue egion (LE), wo LE, No h–Sou h and Eas –Wes g adien s, and HS (while he la e was desc ibed as, high alue su ound by o he qui e high alues “ o be - e unde s anding”). In all cases he ques ion was: “Please name he spa ial pa e n ha you iew in his map. Mul iple op ions a e possible. No e ha da ke colo s mean highe alues”. By pu pose, he espec i e loca ions (i.e., he s a es) should no be named in o de o a oid localiza ion e o s (see s udy 1). Fig. 9 Case 2.3: Rep esen a ion o he same single LE in small enume a ion a ea (he e: B emen in he No h–Wes ) in GEO, REG and HEX maps ( om le ; he da ke he colo he la ge he alue) Fig. 10 Rep esen a ion o he same Eas –Wes pa e ns in GEO, REG and HEX maps ( om le ; he da ke he colo he la ge he alue) Fig. 11 Rep esen a ion o he same ho spo in GEO, REG and HEX maps ( om le ; he da ke he colo he la ge he alue)