a framework for temporal geographic information - gail langran and nicholas r. chrisman

8/10/2019 A Framework for Temporal Geographic Information - Gail Langran and Nicholas R. Chrisman

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A FRAMEWORK FOR TEM PORAL GEOG RAPHIC INFOR M ATION

GAIL LANGRAN AND NICHOLAS R CHRISMAN

University of Washington I Washington USA

AB STR AC T This pa pe r def ines the c r it ica l co mp on en t s o f car tog raph ic t ime and comp ares t empo

ral and spat ial topologies . Because t ime is topological ly s imilar to space, spat ial data s t ructur ing

pr inc ip les can be adap ted to t empora l da ta . We presen t th ree concep tua l i za t ions o f t empora l geo

graphic informat ion and select one as the most promis ing bas is for a temporal geographic informat ion

sys tem. This conceptual izat ion creates a spat ial composi te of al l geometr ic informat ion (at al l t imes) ,

wh ere each object has an at t r ibu te his tory dis t inct f rom that of it s nei ghb ors .

I N T R O D U C T I O N

Parkes and Thr i f t (1980) d i s t i ngui sh geography f rom geomet ry because i n

geography , space i s i nd iv i s ib ly coupled wi th t ime . Whi l e pe rhaps an unde rs t a t e

ment , th i s observa t ion highl ights the importance of t ime to geographic ana lys i s .

Despi te thi s fac t , car tographers have not achieved notable success in represent ing

the t empora l i n forma t ion so v i t a l t o unde rs t anding geographic p rocesses .

A l imi ted se t of s ta t ic and dynamic mapping methods a re ava i lable to repre

sent geographic change or mot ion graphica l ly ( for a di scuss ion, see Muehrcke

1978, p .

138141;

and M oe l l e r ing 1980) . T o ana lyze spa t io t em pora l i n form a t ion

dig i t a l l y , however , cur ren t ca r tographic t heory and me thods a re i nadequa te . One

reason i s the s t rong a l legiance of digi ta l maps to the i r ana log roots . For example ,

S in ton (1978) desc r ibes geographic da t a a s hav ing th ree component s - t heme ,

loca tion , and t ime . T o me asu re on e co m po ne nt requ i re s t ha t a second co m po ne nt

be cont rol led an d the thi rd c om po n en t be f ixed (Ta ble 1). No t surp r i s ingly, on

maps i t i s the tempora l component tha t i s usua l ly f ixed. Muehrcke 's (1978)

explana t ion i s t ha t ca r tographe rs ma in t a in t he i r composure i n t he face of a

cont inual ly changing world by making s ta t ic maps of re la t ive ly s ta t ic phenomena,

the reby sh i ft ing the bu rd en of dea l in g wi th t em po ra l ph en om en a to t he m ap use r .

Because thi s prac t ice has been t ransferred f rom the ana log to the digi ta l world,

the da ta s t ruc tures in use today are des igned for , and l imi ted to , the representa

t ion of s ta t ic phenomena.

How to express change and mot ion graphica l ly i s a problem we leave to

future d iscuss ions . Th is wo rk 's focus is on digi ta l m eth od s of s tor in g an d m an ipu

la t ing sequent s ta tes of geographic informat ion. Our intent i s to se lec t a concep

tual model of geographic temporal i ty that can serve as a basis for effect ive digi tal

representa t ion. The f i rs t sec t ions of thi s paper def ine the components of car to

graphic t ime and compare t he i r r e l a t i onsh ips wi th t hose occur r ing in space . The

pape r t hen pre sen t s t h ree conceptua l i za t i ons of t ime and of fe r s rea sons why one

is m o r e p r om i s i ng fo r f u t u r e de v e l opm e n t s .

BACKGROUND

Tim e , a ph en o m en on tha t can be pe rce ived on ly by it s e f fec ts , ha s i n t r i gu ed and

preoccupied p h i loso phe rs t h ro ug h th e ages . T i m e is com mo nly v i ewed a s a l ine

wi thout endpoints tha t s t re tches inf ini te ly into the pas t and the future , a l though

NICHOLAS R CHRISMAN is an Ass is tant Professo r in the De pa r tm en t of Ge og rap hy , Univers i ty of

Washing ton . GAIL LANGRAN i s a PhD candida te in the Depar tment o f Geography , Univer s i ty o f

Washing ton . T h e thoug hts p rese n ted he re were in f luenced by the percep t ive com me nts o f R ic Vrana ,

Morgan Thomas and T im Nyerges . Par t i a l fund ing was p rov ided by the Univer s i ty o f Washing ton

Graduate School Research Fund . MSsubmitted May 1988; acceptedAugust 1988

C A R T O G R A P H I C A V o l 2 5 N o 3 19 8 8 p p 1 - 1 4


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2 GAIL LANGRAN AND NICOLAS R CHRISM AN

ble 1 . TH E REPRESENTATION O F GEOGRAPHIC DATA IN VARIOUS

F O R M A T S

( E X T E N D E D F R O M S I N T O N

I 9 7 8 ) .

Soils data

T o p o g r a p h i c m a p

U.S.

Census da ta

Raster data

Weather r epor t s

Flood tables

Tide tables

Air l ine schedules

Fixed

T i m e

T i m e

T i m e

T i m e

Locat ion

Locat ion

T h e m e

Locat ion

Cont ro l l ed

T h e m e

T h e m e

Locat ion

Locat ion

T i m e

T i m e

Locat ion

T h e m e

M e a s u r e d

Locat ion

Locat ion

T h e m e

T h e m e

T h e m e

T h e m e

T i m e

T i m e

coherent a rguments exis t for such a l te rna te topologies as mul t iple para l le l l ines ,

t r ee s t ruc ture s , c i rcu la r i ty , d i sc re t eness , an d non exi s t ence (Resche r and U rq uh a r t

1971 an d N ew ton- Sm i th 1980 pro vid e exce l lent di scuss ions of thi s topic) . Ca r tog

rap he rs , how ever , can s ides tep deb ates on wh at t ime is , an d ins tead focus on how

best to represent i ts effects .

TemporalData Processing in Cartography

The ca r tographic l i t e ra ture i nc ludes one prev ious a t t empt t o s t ruc ture spa t io t em

pora l da t a . In 197 8 , Basoglu an d M orr i son d es ign ed a da t a s t ruc tu re t o re t ri eve

the county boundar ies of a given s ta te for any da te s ince tha t s ta te achieved

sta tehood. The s t ruc ture i s over t ly hie rarchica l , as shown in Figure 1 . Sta tes own

count i e s , and count i e s own bounda ry records . Each bounda ry record ho lds a l i ne

segment , and the t ime in t e rva l dur ing which tha t segment fo rmed pa r t o f t ha t

county ' s bounda ry . Thi s h i e ra rch i ca l s t ruc ture cannot recognize t ha t one l i ne

segment might no longe r bound a pa r t i cu l a r county , bu t r ema in i n use a s t he

bounda ry of a d i f fe ren t county t h rough h i s to r i ca l subdiv i s ion . In add i t i on , t he

s t r uc tu r e c a nno t p r o du c e a n a ns w e r to t he que r y W ha t bou nda r i e s c ha ng e d

be tween two g iven da t e s? T h e s t ruc ture ' s fund am enta l weakness , howev er , is

tha t i t cannot ensure tha t a l l mapped space be longs to some county a t a l l poss ible

t imes . Th i s pap e r p rov ides some so lu t ions to t hese p rob le ms .

Aspatial Temporal Data Processing

The da tabase sys tems l i t e ra ture has wi tnessed an explos ion of publ ica t ions con

ce rn ing t empora l and h i s to r i ca l da t abases . Wi th few except ions , however , r e

search has focused on aspa t ia l appl ica t io ns . N on ethe less , a review of thi s l i t e ra tu re

is instructive.

The goal of a tempora l da tabase i s to make the t ime dimension access ible to

users . Cl i fford an d W ar re n (1983 ) desc r ibe such a da tab ase as a m od el of the

dynamical ly cha ng ing wor ld , i n which da t a a re neve r 'fo rgo t t en . ' T o des ign such

a da t abase , on e m us t deve lop pro ce du res by which da t a a re sup e rsed ed bu t nev e r

de l e t ed , t he reby avoid ing wha t Co pe la nd 1982) has te r m ed the agon y of de le te .

Vi r tua l ly a l l t empora l da tabase research bui lds on the re la t iona l da tabase

model . The re la t iona l model s tores informat ion in mat r ices ca l led tables . Each

ent i t y i s r epre sen ted by a ma t r ix row, ca l l ed a t up l e ; ma t r ix co lumns repre sen t

en ti ty a t t r ibu t e s . W he n t e m po ra l i n fo rm a t ion is m od e led in th i s way , t he des ign-


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A FRAMEWORK FOR TEMPO RAL GEO GRA PHIC INFORMA TION 3

tates

FIGURE1. Morrison an d Basoglu s (1978) hierarchical representation of U.S. c ounty boundary changes.


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4 GAIL LANGRAN AND NICOLAS R CHRISMA N

e r 's d i l emm a is w he the r t o p ro pa ga te new da t ab ase ve rs ions a t t he t ab l e , t up l e , o r

a t t r ibute leve l. T h e ear l ies t wo rk g en er a te d a new vers ion of a table each t ime on e

of its cells cha ng ed; how ever , r e sea rche rs qu i ck ly prog resse d to t he mo re space -

eff ic ient approaches of tuple- and a t t r ibute- leve l vers ioning.

The re l a t i ve mer i t s o f t up l e - and a t t r i bu t e - l eve l ve rs ion ing a re bes t summa

r ized a s a t r adeof f be tween process ing spe ed an d s to rag e . T o gen e ra t e a com ple t e

new tup le ve rs ion each t ime an a t t r i bu t e change s m eans t ha t r e du n da n t i n forma

t ion i s s tored. Converse ly, to s tore mul t iple a t t r ibute vers ions wi thin a tuple

violates the relat ional model 's s t r icture against variable-length fields. Present ly,

seve ra l d i f fe ren t t up l e - and a t t r i bu t e - l eve l ve rs ion ing me thods have been pro

posed bu t on ly one me thod has been implemented expe r imenta l l y (Ahn and

Snodgrass 1986) ; none i s used opera t iona l ly .

T h er e is l it tl e d o ub t tha t aspa t ia l t em po ra l da tab ase m eth od s will p lay a role in

s pa t i o t e m por a l

G I S

how ever , t he t r e a tm en t o f spa ti a l da t a is a p rob lem tha t

rema ins t o be addressed by ca r tographe rs . A fundamenta l p rob lem i s how to

conceptua l ize t he geog raph ic sequ ences we will r ep re s en t .

C O M P O N E N T S O F C A R T O G R A P H I C T I M E

Car to grap hic t ime is pu nc tua t ed by ' even t s , ' o r chang es , which a re reco rde d a long

two axes . One axis marks when changes occur (or a re di scovered) in the rea l

world; we wi l l re fer to thi s type of tempora l i ty as 'world t ime. ' The second axis

t races when changes a re recorded in t he da t abase ; we have named th i s t ype of

tempora l i ty 'da tabase t ime. ' These essent ia l ly or thogonal t imes a re wide ly noted

in the tempora l da tabase l i t e ra ture , and are var ious ly re ferred to as 'va l id ' and

' t ransac t iona l ' (Snodgrass and Ahn 1985) , ' logica l ' and 'physica l ' (Lunn et al.

1984) , ' ext r ins ic ' and ' recording his tory ' (Ariav 1986) , and 'objec t l eve l ' and

'sys tem leve l' (Bo lour an d D ekey ser 1983) .

In prac t ice , world t ime would begin on the da te of the ear l ies t known in

forma t ion and end wi th t he mos t recen t i n forma t ion , a l t hough pred i c t i ve mode l s

might be employed to ex t end wor ld t ime beyond the pre sen t . Da tabase t ime

would begin when the f i rs t da ta entered the da tabase and end wi th the las t da ta

ent ry. To c la r i fy the dis t inc t ion be tween world t ime and da tabase t ime, consider

two quer ies :

- t o t he bes t o f our cur ren t knowledge , how d id t h i s reg ion ac tua l ly appea r on a

given da te?

-w h a t i n form a t ion on th i s reg io n ex i s t ed in t he da t abase on a g iven da t e?

M ainta inin g info rm at io n on bo th world a nd d a tab ase tim e is c r it ica l . W hi le

the intent ion of a tempora l informat ion sys tem might focus on the his tor ica l

sequence of events , there i s no guarantee tha t thi s informat ion wi l l a r r ive in the

da t abase in t he same or de r . I n add i t i o n , new inform a t ion m ight shed l igh t o r ca st

doubt on ex i s t i ng da t abase i n forma t ion , necess i t a t i ng re t roac t ive amendment s .

The most prac t ica l approach to a l l eventua l i t i es i s to adopt the ' supersede-but -

neve r -de l e t e ' p r inc ip l e s o f Account ing , which document bo th t he h i s to ry of an


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A FRAMEWORK FOR TEMPO RAL GEOG RAPH IC INFORMA TION 5

FIGURE 2.

T herel tionshipof mapst tesa ndobjectversions

enterprise s finances and the sequence of its recordk eepin g. A n errone ous entry is

not corrected by erasure , but by posting an adjustment at the later date.

THE NATU R E OF TEMPOR AL OB JEC TS

Time, like space, must be subdivided, ranked, or measured before it can be

analyzed. Drawing analogies between spatial and temporal entities is one useful

device for understanding their commonalities.

T he tempo ral parallel o f m ap is state. We borrow this term for aggregate

conditions from systems theory, which considers the history of a system to be a

series of states punctuated by events that transform one state into the next (see

Ferg 1985, and Bolour and Dekeyser 1983). A cartographic state consists of a

spatial configuration of objects, each of which can change somew hat ind ep ende nt-

ly

of the othe rs. Jus t as a ma p

is

trans form ed from state to state

by

events, an ob ject

is transforme d from o ne version to the next by m utations. Th us, each m ap state

freezes geographic evolution in to a configuration of object versions.

Of course, each object m utation is an event that causes a new map state. This

interrelationship results in a world-time topology comprised of many parallel

lines (Figure 2)a view of time that coincides with that of o the r time specialists.

For example:

Given that temporal information is expressed in space, and that intervals between events

are subjecttovariability in the recording...we can begintoenvisage topology of temporal

informationin which we h verubber strings ornetsor sheets on which eventsare recorded

as knots or other singularities, expressing certain necessary relations between events,

rel tions whichhold good even though the rhythms of allthe clocksconcerned are variable

(Meredith

1972, p.

260).


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GAIL LANGRAN AN D NICOLAS R CHRIS MAN

982

984

987

FIGURE

3 .

Spatialandtemporal neighbors.

Aside f rom theobvious i n t e r re l a t i onsh ips be tween ob jec t ve rs ionsand map

states,

the

succession

of

each object 's versions

and

m u t a ti o n s

or one

map's s tates

and events)

has an

i n t e r na l s t r uc t u r e .

A

vers ion

or

state

can be

seen

as a

line

segment t ha t r epre sen t sthedu ra t i on of a cond i t i on , whi leam u t a t i onoreven t isa

poin t t ha t t e rmina t e s t ha t condi t i on and begins the next , fo rming a ze ro-

d i m e ns i ona l bounda r y be t w e e n twoone - d i m e n s i ona l ' r e g i ons . ' T h us , t e m po r a l

uni t s tha t share a b o u n d a r y can be c ons i de r e d c on t i guous ne i ghbo r s in t ime

(Figure 3). Final ly, convention al lowsus todraw spa ti a l bo un da r i e s f irmly , r eg a rd

less of wh e the r t hey rep re s en t g r ad ua l t r ans i t ion zones or formal l ines of de

m a r c a t i on . W hi l e t e m por a l bounda r i e s are, in real i ty,no more d i sc re t e t han are

spa t ia l boundar ies , sharp l ines a l so prove useful

in

r e p r e s e n t i n g te m p o r a l b o u n d

aries.

T a b l e

2

sum ma r i zes som e ana log ie s be tween space

and

t ime , bu i ld ing

on

those offered byP a r ke sandTh r i f t (1980) .

Table 2.

PARALLELS

IN

S P A T IA L A N D T E MP O R A L S T R U C T U R E

C a r t o g r a p h i c

Space

C a r t o g r a p h i c

T i m e

Overal l conf igurat ion map

Conf igu r a t ions sepa r a t ed

by ...

shee t l ines

Regu lar sam pl ing uni ts ce l ls

Mea ningful uni ts objects

Subdivis ions separated

by ...

b o u n d a r i e s

S ize measu r ed

by ...

l eng th , a r ea

Posi tion descr ib edby ... c o o r d i n a t e s

C o n t i g u o u s n e i g h b o r s

are ...

adjacen t objects

M a x i m u m n u m b e r

of

con t igu ous ne igh bor s i n fin it e

state

events

hour s , days , decades ,

etc.

versions

muta t ions

d u r a t i o n

date

p r ev iousandnex t m anifesta t ions

two


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A F R A M E W O R K F O R T E M P O R A L G E O G R A P H I C I N F O R M A T I O N 7

SPATI AL VS . TEM PORA L STRU CTU RE

Because many geographic ques t ions conce rn spa t i a l s t ruc ture ,

GIS

a lgor i t hms

draw on basic search p ro ce du re s tha t ident i fy for a given objec t :

- w h a t a r e itsn e i ghbo r s ?

-wha t a re i t s bounda r i e s?

what enclo ses it?

what

doe s i t enclose?

When geographic da ta s t ruc tures t rea ted objec ts in i sola t ion, searches for

ne igh bors we re exceed ingly long an d ineff ic ient (Ch rism an 197 4) . As geog rap hic

i n f o r m a t i on p r oc e s s i ng a pp l i c a t i ons be c a m e m or e de m a nd i ng a nd ge og r a phe r s

grew more ski l led in working wi th spa t ia l da ta , new s t ruc tures were developed to

enco de the topologica l as well as the geo m etr ic char ac te r of the m ap pe d area . T h e

effec t iveness of the ear ly implementa t ions of topologica l cons t ruc ts demonst ra ted

in t he U.S . Censu s Bu reau ' s D I M Efiles (Coo ke an d M axfield 1967 ; see also Co rb et t

1979) l ed t o t he i r widespread adopt ion . Now mos t geographic da t abases p ro

duced by government ins t i tut ions for ana lyt ica l purposes employ some var iant of

the topologica l s t ruc ture , inc luding the U.S. Geologica l Survey 's Digi ta l Line

Graphs , t he Defense Mapping Agency ' s S t anda rd L inea r Forma t , and the Census

Bureau ' s

T I G E R

sys tem. Ad di t i ona l ly , mos t m od er n co mm erc i a l sof tware syst ems

use topologica l da ta s t ruc tures .

Topologica l s t ruc ture s can improve spa t i a l i n forma t ion process ing capabi l i

t i es in three ways . Fi rs t , spa t ia l s t ruc ture i s evident , which means tha t many

algor i thm s are s imp ler and sp ee die r because spa t ia l sear chin g is re du ce d (as

dem ons t ra t ed i n Whi t e 197 8) . Secon d , da t a e r ro rs can be t rap pe d , which pro t ec t s

da ta qual i ty . To t rap e rrors , sof tware checks whether the da ta ' s spa t ia l s t ruc ture

adheres to the model ' s rules for topologica l integr i ty , thus ident i fying the gaps ,

s livers , an d over sho ots tha t plag ue less descr ipt ive m ode ls (Chrism an 1983 ; W hi te

1983) . F ina l ly , min ima l da t a redundancy reduces s to rage requi rement s .

S imi l a r ly , a t empora l i n forma t ion process ing scheme should explo i t t empora l

s t ruc ture to fac i l i t a te qua l i ty cont rol and tempora l ana lys i s . By consider ing con

t iguous tempora l ne ighbors to be topologica l ly connected, a temporal topological

da ta s t ruc ture can be devised to l ink one to the next , thereby avoiding exhaust ive

searches th ro ug h layers of t ime and space . Th u s , ju s t as the spa t ia l topologica l

da ta s t ruc ture provides a means of naviga t ing f rom an objec t to i t s ne ighbors in

space , t he cor re sponding t empora l da t a s t ruc ture would prov ide a means of

naviga t ing f rom a s ta te or a vers ion to i ts ne igh bo rs in t ime. Th is capabil i ty wo uld

facili tate such queries as:

-what was the previous s ta te or vers ion?

-w ha t has cha ng ed (du r ing a pe r iod , o r a t a p lace)?

-what i s the per iodic i ty of change?

what t rends are evident?

In sum, a higher leve l of informat ion would be encoded in the da ta , s ince the


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8 GAIL LANGRAN AND NICOLAS R CHRISMAN

connectivity of time is as important to temporal analysis as is the connectivity of

space to spatial analysis.

The next three sections describe three methods of conceptualizing

geographic tem porality. Each is ju dg ed by how well it repre sents tem pora l

topology, since this criterion is indicative of data com pactness, com pleteness, an d

descriptiveness.

IMAGES OF CARTOGRAPHIC TIME: TIME SLICE

SNAPSHOTS

A comm on sp atiotemp oral mo del is a sequent set of data-state snapshots (Figure

4). Wood and Fels (1986) supply a useful description of such snapshots in their

description of maps as time-exposed photographs that record only fixed

phenomena because moving phenomena become transparent blurs on the film.

Attempts to create dynamic maps often turn into the creation of a sequence of

snapshots to be displayed using motion picture technology or video display.

Snapshot sequences are an intuitive spatiotemporal model but they have their

limitations. While finding what exists at T is easy, finding how has T, chan ged

from 7V, or what is the frequency of change is not, because the pertinent

snapshots must be com pare d exhaustively to detect differences.

The root of the problem is that snapshots represent states, but do not

represent the events that change one state to the next. Even worse, snapshots

provide no explicit represe ntatio n of object versions or their mu tations. While it

may be possible to detect d ifferen t versions of an object visually as snapshots flash

by, the model provides no means of recording their temporal structure or

assistance in locating tem po ral neig hbo rs (i.e., an object s p revious and nex t

manifestations). In many respects, time-slice snapshots are the temporal

equivalent of the formless spaghetti data structure; in both cases, the database

objects reflect the graphic, not its underlying meaning. Interestingly enough,

time-slice snapshots sha re the th ree major shortcom ings of spaghetti data.

FIGURE4 . Time dice

sn pshots representing

urban

exp nsion

into a rural

area.

Intervals

between time slices re not

necess rily

equal.


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A F R A M E W O R K F O R T E M P O R A L G E O G R A P H I C I N F O R M A T I O N 9

Hidden structure. We have def ined tempora l ne ighbors to be an objec t ' s

p rev ious and nex t ve rs ions , which a re bounded by the muta t ions t ha t caused the

me tamorphos i s . Because snapshot s cap ture s t a t e s , no t ve rs ions , t he bounda r i e s

between versions are difficul t to locate .

No error trapping. W i t h no unde r s t a nd i ng o f t e m por a l s t r uc t u r e , r u l e s t o

enforce logica l integr i ty a re di f f icul t to devise . Change for each par t icular map

mus t be i n t e rpre t ed t h rough the ru l e s o f t he t heme por t rayed . For i ns t ance , a

land use change f rom pas ture to res ident ia l may be more l ike ly than the reverse .

Redundant storage.Rega rd l e s s o f t he ex t en t o f cha ng e , a com ple t e snap sho t is

produced a t each t ime s l ice , which dupl ica tes a l l the unchanged da ta .

I M A G ES OF C A R T O G R A P H I C T I M E .

B A S E M A P W I T H O V E R L A Y S

Stand ing back f rom the t ime l ine an d ex am ini ng t ime-s lice snap sho ts is no t the

only way to view geographic tempora l i ty . Al te rna te ly , we can s tand di rec t ly upon

the t ime l ine an d look u p or do w n it in to the pas t or futu re . Fr om this persp ec t ive ,

a more versa t i le means of represent ing the t ime s l ices i s poss ible . We place an

opaq ue base m ap a t T

o

to def ine the da ta ' s or igina l s ta te . At appropr ia te (and not

necessar i ly even) inte rva ls , we inte r jec t a c lear over lay and record changes tha t

have occurred s ince the previous update . When used thi s way, the over lays a re

events tha t bound the map's s ta tes , whi le the marks on the over lays a re muta t ions

tha t bound objec t vers ions .

Now from a point on th e t ime l ine look ing back wa rd into the pas t , we see one

or more t ran spa ren t ove r lays t ha t am en d the base m ap , which s t ands a t t he far en d

of the t ime l ine. By back ing aw ay from this ov erlaid t im e series, as we did to view

the snaps hot t ime ser ies , we wou ld see prof i les of the base m ap a t on e end , a f ina l

over lay a t the other end, and inte rmedia te over lays inte rspersed a long the l ine

(Figure 5) . Eventua l ly , spa t ia l change i s comprehensive and the muta t ions

recorded on the ove r l ays supe rsede the en t i re base map.

This image of t ime is not unl ike a Minkowski diagram in i ts spat ial izat ion of

t ime. I t is a lso rem inis cen t of Ru ck er 's

1984) vision of real i ty as a t ime- spac e c ub e,

a nd H a ge r s t r a nd ' s ( 197 4 ) t i m e - s pa c e ' a qua r i um s , ' t h r ough w h i c h pe op l e a nd

objects t race paths of a given l i fe span. Rucker argues that the passage of t ime is an

i llusion; a ll of space / t ime i s pr ese nt a t any given m om en t . T his con ceptua l iza t ion is

a rea sonable mode l fo r a t empora l geographic i n forma t ion sys t em, i n which a l l

s tates of the study a re a ar e equal ly accessible to th e analyst . Recent ly, Szeg (1987 )

has deve lop ed H ag e rs t ran d ' s t ime geo gra ph y d i agra ms in to a m ode l o f

spa t iotemp ora l i ty . W hi le phi losophica l ly in te res t in g, this mod el offers l i tt le to the

prac t ica l mat te r of digi ta l representa t ion.

To use the base map/over lay const ruc t , a new over lay would be c rea ted for

each da tabase update sess ion to represent t ransac t ions in da tabase t ime. World

t ime would be expressed us ing da tes or color codes on the over lay 's change

nota t ions . Thus , ne ighbors in da tabase t ime are loca ted on adjacent over lays whi le

ne ighb ors in wo rld t ime are not , unless bo th t imes a re e ffec tively syn chro nized .

The base map/ove r l ay cons t ruc t can answer que r i e s on bo th s t a t e s and

versions:


10/14

10 GAIL LANGRAN AND NICOLA S R CHRISM AN

FIGURE

5 .Abase map overlay representationof urbanencroachmentinto a rural area.

-

To find what was the data state at

T

it

merge the base map at

T

o

with the

overlays at T, toT

t

.

T o find what has chan ged between \and

7},

create

com posite overlay T;... 7}

by mergin g the overlays from

T

t+ 1

to2}.


11/14

A F R A M E W O R K F O R T E M P O R A L G E O G R A P H I C I N F O R M A T I O N 1 1

- T o find wh at vers ions has thi s objec t ha d and wh en did it m uta te? check each

over lay for amendments in tha t objec t ' s loca t ion.

- To compute t he f requency of change , accumula t e t he number o f muta t ions a t

each locat ion.

Because i t represents the boundar ies of both s ta tes and vers ions , the base

m ap/ov er lap co nst ru c t is su pe r io r to sna psh ots . Ju s t as the as t ruc tura l s tyle of

snapshot s sha re s t he spaghe t t i s t ruc ture ' s p rob lems , t he t empora l s t ruc ture o f t he

over lays mimics the top ologica l s t r uc ture 's asse t s .

Tem poral structure is evident. Tempora l ne ighbors ( i . e . , a ve rs ion ' s p rev ious or

next forms) a re loca ted by f inding the muta t ion tha t separa tes them.

Errors canbetrapped

because im pro bab le event s can be proh ib i t ed .

Minimal redundancy. Use of s torage i s spar tan; each objec t vers ion i s s tored

only once.

I M AG E S O F C A R T O G R A P H I C T I M E : S P A C E - T I M E C O M P O S I T E

Th e f inal image of t ime is a var ia t ion o n the base m ap/ov er lay th em e. Rat he r t ha n

re t a in ing change no ta t i ons on sepa ra t e ove r l ays , t he base map becomes a

t empora l compos i t e bu i l t f rom accumula t ed geomet r i c changes . Each change

causes the changed por t ion of the coverage to break f rom i t s parent objec t to

become a discre te objec t wi th i t s own dis t inc t hi s tory. In other words , the

represen ta t i on decomposes ove r t ime in to i nc reas ing ly sma l l e r f ragment s

the

cove rage ' s g rea t e s t common spa t io t empora l un i t s each of which re ferences a

d i st inc t t em po ra l a t t r i bu t e se t (F igu re 6) . Th i s me t ho d of t emp ora l decom pos i t i on

was or ig inal ly sug ges t ed by Ch r i sm an (1983) . T h e sp a t io t em por a l un i t s c rea ted by

this inte rsec t ion should be ca l led grea tes t common uni t s to correc t the mis leading

te rminology pro m ulg a t ed by Peu cke r an d C hr i sm an (197 5) fo r a re l a t ed case .

The mechanic s o f space - t ime compos i t i ng beg in wi th a base map tha t r epre

sents a region 's geo m etry an d spa t ia l topolo gy a t som e s ta r t ing t ime . A n over lay is

gene ra t ed dur ing each da t abase upda te se s s ion , a s desc r ibed prev ious ly for t he

base map/over lay model . Once accepted for permanent inc lus ion, the over lay i s

incorpora t ed in to t he sys t em us ing the same in t e r sec t ion procedure cur ren t ly

used for polygon over lay (Dougenik 1980) . New nodes and cha ins a re added to

the his tor ica l accumula t ion, forming new polygons tha t have a t t r ibute hi s tor ies

dis t inc t f rom those of the i r ne ighbors . Each uni t ' s a t t r ibute hi s tory i s represented

by an or de re d l is t of rec or ds . A re co rd co nta in s an a t t r ib ute se t an d the da tab ase

and world- t ime inte rva ls dur ing which tha t a t t r ibute se t was va l id . Whi le thi s

tempora l a t t r ibute concept seems logica l , i t i s di f f icul t to implement in current

re la t iona l da tabase sof tware , because the tempora l ranges c rea te a hos t of var iable

l ength anomal i e s f rom the ' norma l fo rm ' .

Access ing tempora l informat ion s tored in the space- t ime composi te i s con

ceptua l ly s t ra ight forward. To compi le a s ingle t ime s l ice f rom the composi te , one

has only to 'walk' the at t r ibute history l is t of each polygon to locate the at t r ibute

tha t was current a t the des i red t ime s l ice . I f polygon ne ighbors in the t ime s l ice

sha re a s ing l e a t t r i bu t e , t he cha in t ha t sepa ra t e s t h em is d r op pe d .


12/14

1 2 GAIL LANGRAN AND NICOLAS R CHRISM AN

FIGURE

6 .

Aspace time compositeof urban encroachment Eachpolygonhas an attributehistorydistinct from that

of

itsneighbors

DISCU SSION

Both the base map/overlay and space-time intersection are reasonable models

upon which to base a spatiotemporal data-structuring methodology. However,

because the base m ap/overlay m odel is not space filling, it is m ore pron e to err or

unless an alternate way of checking for internal consistency can be devised.

Additionally, no simple means of structuring base map/overlay data is evident

which is not to say that a means does not exist). The arguments for retaining

separate overlays vs. storing a composite follow those of retaining categorical

coverages on sepa rate overlays vs. m ergin g them into one coverage integrated by

an overlay processor. A composite incurs preprocessing costs and offers direct

response to any qu ery, w hile separa te overlays mu st invoke an overlay processor

to respond to any query. In addition, a composite minimizes polygon-processing

error, while separate overlays permit greater flexibility in modeling the error

inhere nt in each overlay.

For both the base map/overlay and the space-time composite models, per-

formance efficiency might be improved by maintaining a current data state

separately from previous states, especially when queries on th e cu rre nt state are

more frequent than are forays into the past. Conversely, a temporal GISused by

historians or archeologists might maintain the oldest data separately on the

assumption that it will be accessed and altered most often. In either case, the

temp oral partitionin g would prev ent th e longitud inal data from adversely affect-


13/14

A FRAMEWORK

FOR

T E M P O R A L G E O G R A P H I C I N F O R M A T I O N 1

3

ingthemos t f requent o pe r a t i on s . Aspa t i a l m e th od soft e m p or a l p a r t i ti on i ngare

discussed

by Ahn and

S n o d g r a s s

(

1986) , Fer g

(

1985), Ariav

(

1986),

and Lum

et

al.

( 1984 ) . F u r t he r pe r f o r m a nc e i m pr ove m e n t s w i l l be poss ib l e t h r ou gh ind exin g

schemes . Insp i ra t i on for such schemescan bef o u n d inpe rs i s t en t da t a s t ruc ture s

(SarnakandTar j an 1986)andnon de s t r uc t i ve da t a s t r uc t u r e s de s i gne d forw ri te -

onc e - r e a d - m a ny- t i m e s

(WORM)

opt ica l s torage (e .g . , Rathmann 1984) .

In ope ra t i on , bo th da t abase t ime and world t ime wil l be i m p o r t a n t for

di f fe ren t pu rpo ses . Th e com pos i t e app ro ach can accom m od a te two t ime axes if its

a t t r ibu t e d a t abaseiss t ru c tu red app rop r i a t e ly . Even wi th ski ll ed des ign , how ever ,

da tabase records wi th a t e m por a l r a nge s t r a i n the capabi l i ty of m os t c u r r e n t

da tabase sys tems,andtwo su ch a xes willaddfur the r com pl i ca tions .

Y

CONCLUSION

Car tographic t ime inc ludes the s e p a r a b l e c o m p o n e n t s of wor ld and da t abase

t im e . T r e a t m e n t ofe i the r t e m po ra l ax is can bo r row f rom thet r e a t m e n tof spatial

da ta .

An

i m por t a n t c onc e p t

is

t ha t

of a

t em po ra l bo un da ry (cal led

a

muta t ion)

which separa tes objec t vers ions and p r ov i de s an effect ive means of desc r ib ing

tempora l s t ruc ture . Tempora l t opology should s impl i fy que r i e s

and

shou ld pe r

m it e n f o r c e m e n t of da ta integr i ty .

T w o r e a s ona b l e m e t hods

of

r e p r e s e n t i ng ge og r a p h i c c ha ng e w e r e p r e

sen t ed .Them or e p r o m i s i ng m e t ho d a llow sa s tudy a rea todeco m pos e ove r t ime

in to po lygons t ha t r epre sen t ' g rea t e s t common spa t io t empora l un i t s , ' e ach wi tha

dis tinc t a t t r ib ute h i s tory. Suchana p p r o a c h isa m e n a b l etoe n f o r c e m e n t oflogical

consistency because

of

its spac e-fil l ing

and

t ime-f i ll ing na tu re .

REFERENCES

AHN,

ILSOO

andSNODGRASS, RICHARD

1986 . Per formance eva lua t ion

of a

t e m p o r a l d a ta b a s e m a n a g e

ment sys tem.Proceedings of the SIGMO D 86Conference:96107.

ARIAV,

GA D

1986. A

tempora l ly o r i en ted da ta mo del .

ACM

Transactions

on

Database Systems

11/4:

4 9 9 - 5 2 7 .

BOLOUR, A.and DEKEYSER, L.J . 1983. Abstract ions in t e m p o r a l i n f o r m a t i o n .

Information Systems

8,1,

4 1 4 9 -

BASOGLU, UMIT and MORRISON, JOE L 1978. T he efficient hierarchical data Structure for the U.S.

Histor ical Boundary Fi le .Harvard Papers for GIS, v o l u m e 4 .

G.

D u t t o n ,

ed.

Reading , Massachuse t t s:

Addison-Wesley.

CHRISMAN, NICHOLAS 1974. T he

i m p a c t

of

d a t a s t r u c t u r e

of

geog raphic in format ion proces s ing .

Proceedings, Auto-Carlo

T. 165

176.

1975. Topolog ica l in format ion sys tems

for

g e o g r a p h i c a l r e p r e s e n t a t i o n .

Proceedings, Auto-Carto

2 : 3 4 6 3 5 1 .

1983. The

Role

of

Q u a l it y I n f o r m a t i o n

in the

long- te rm fun c t ion ing

ofa

G e o g r a p h i c I n f o r m a

tion System.Cartographica 21 / 2 & 3 7 9 8 7 .

CLIFFORD, JAMES

and

WARREN,

D.S.

1983 . Form al s emant ics

for

t ime

in

da tabases .

ACM Transactionson

Database Systems 8/2,J u n e : 2 1 4 - 2 5 4 .

COOKE, D.F.

and

MAXFIELD, W.F. 1 9 6 7 .

The

d e v e l o p m e n t

of a

geographic base f i le

and its

uses

for

m a p p i n g . U r b a n

an d

Regiona l In forma t ion Sys tems

for

Social P rog ram s ,Papers rom

the

Fifth Annual

Conference of the Urban and Regional Inform ation System Association:207 218.

COPELAND, G. 1982 . Wh at

if

mass s to rage w ere free} IEEE Computer 15/7: 2 7 - 3 5 .

CORBETT, j . p .

1979.

Topo log ica l p r inc ip les

in

c a r t o g r a p h y .

Technical Paper

48,

U.S.

B u r e a u

of the

Census , Wash ing ton

DC.


14/14

1

4

GAIL LANGRAN AND NICOLAS

R

C H R I S M A N

DOUGENIK, JAMES

1980.

WHIRLPOOL:

A

g e o m e t r i c p r o c e s s o r

for

po lygon coverage da ta . Proceedings

Auto-Carlo

IV 2:

3 0 4 - 3 1 1 .

FERG, STEPHEN

1985. Model l ing

the

ti m e d i m e n s i o n

in an

en t i ty - r e la t ionsh ip d iagram .

Proceedings of the

Fourth International Conference on Entity-Relationship Approach :

2 8 0 - 2 8 6 .

HAGERSTRAND, T .

1 9 7 4 .

O n

socio- technical ecology

and the

s tudy

of

innovat ions . Elhnologia Europa

7:

2 5 3 7 .

LUM, v.et al.

1984 . Des ign ing da tabase suppor t

for the

t e m p o r a l d i m e n s i o n . Proceedings

ofthe

ACM

SIGMOD 84C onference: 1 1 5 1 2 6 .

MEREDITH, PATRICK 1 9 7 2 .

The

psychophys ica l s t ruc tu re

of

t e m p o r a l i n f o r m a t i o n

in

The Study of Time

I:

Proceed ings

of

the F i rs t Conferen ce

of

the In te rna t io na l Soc ie ty

for the

S tudy

of

T im e. New Yo rk :

S p r i n g e r - V e r l a g : 2 5 9 2 7 3 .

MOELLERING, HAROLD 1980. Strategies

of

r e a l -t i m e c a r t o g r a p h y . Cartographic Journal 1 7 / 1 : 1 2 - 1 5 .

MUEHRCKE, PHILLIP C.

1 9 7 8 .

Map

use.Madison , W iscons in :

JP

Publ icat ions .

NEWTON-SMITH, W.H.

1980 .The structure of time.B o s t o n : R o u t l e d g e

and

Kegan Paul .

PARKES, DON

and

THRIFT, NIGEL 1980.Times, spaces, and places.New York : Joh n Wi ley

and

Sons.

PEUCKER, THOMAS

K. and

CHRISMAN, NICHOLAS

1975. Cartographic data structures.

The American

Cartographer 1/2:5 5 6 9 .

RATHMANN, PETER 1984.

D y n a m i c d a t a s t r u c t u r e s

on

optical disks. Proceedings

of

the International

Conference on Data Engineering, IEEE 175 180.

RESCHER, NICHOLAS

and

URQUHART, ALASDAIR

1971.

Temporal logic.

New York: Springer-Verlag.

RUCKER, RUDY 1984.

The fourth dimension: Toward ageometry of higher reality.

New

Y o r k : H o u g h t o n

Mifflin.

SARNAK, NEIL

a n d

TARJAN, ROBERT

1986. Planar point locat ion us ing pers is tent search t rees .Communica

tions of

the

ACM 29 /7 : 6 6 9 - 6 7 9 .

SINTON, DAVID 1978. T he

i n h e r e n t s t r u c t u r e

of

i n f o r m a t i o n

as a

cons t r a in t

to

analys is : Ma pp ed

themat ic da ta

as a

case s tud y. Harvard Papers on GIS,vol.

7, G.

D u t t o n ,

ed.

Reading , Massachuse t t s :

Addison-Wesley.

SNODGRASS, RICHARD

and

AHN, ILSOO

1985 .

A

taxono my of t ime

in

da tabases .

Proceedings of

the

SIGMOD

'85 Conference:2 3 6 - 2 4 5 .

SZEG, JANOS

1 9 8 7 . Human cartography: Mapping

the

world

of

man. S tockholm: Swedish Counci l

for

Building Research.

WHITE, MARVIN 1 9 7 8 .T hecostof topological f i le access.

Harvard Papers

on GIS,vol.6, G.D u t t o n ,ed.

Reading , Massachuse t t s : Addison-W es ley .

1983. T r i b u l a t i o n s ofa u t o m a t e d c a r t o g r a p h y and howmathe mat ics he lps .

Proceedings, Auto-

Carto

6,

vol.

1 :

4 0 8 4 1 8 .

WOOD, DENIS

and

FELS, JOH N 1986. Des igns

on

s igns : Myth

and

m e a n i n g

in

m a p s . Cartographica25 /3 :

5 4 - 1 0 3 .

a framework for temporal geographic information - gail langran and nicholas r. chrisman

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