Literature Review f Spati-Tempral Database Mdels Niks Pelekis 1,2,, Babis Thedulidis 1, Iais Kpaakis 1, Yais Thedridis 2 1 Ceter f Research i Ifrmati Maagemet (CRIM) Departmet f Cmputati, UMIST URL: http://www.crim.rg.uk E-mail: pele@ath.frthet.gr, babis@c.umist.ac.uk, kpaak@csd.uc.gr Abstract 2 Departmet f Ifrmatics Uiversity f Piraeus Athes, Hellas URL: http://www.uipi.gr E-mail: {pelekis, ythed}@uipi.gr Recet effrts i spatial ad tempral data mdels ad database systems attempt t achieve a apprpriate kid f iteracti betwee the tw areas. This paper reviews the differet types f spati-tempral data mdels that have bee prpsed i the literature as well as ew theries ad ccepts that have emerged. It prvides a verview f previus achievemets withi the dmai ad critically evaluates the varius appraches thrugh the use f a case study ad the cstructi f a cmparis framewrk. This cmparative review is fllwed by a cmprehesive descripti f the ew lies f research that emaate frm the latest effrts iside the spati-tempral research cmmuity. 1 Itrducti Spati-tempral databases deal with applicatis where data types are characterized by bth spatial ad tempral sematics. Develpmet ad research i this area started decades ag, whe maagemet ad maipulati f data, relatig t bth spatial ad tempral chages, was recgized as a idispesable assigmet. Hwever, spati-tempral data hadlig was t a straightfrward task due t the cmplexity f the data structures requirig careful aalysis i structurig the dimesis, tgether with the represetati ad maipulati f the data ivlved. Therefre, the earlier wrk i this area bega frm separate research i bth tempral [TCG+93] ad spatial [Gut94] databases. This effrt later became the basis fr spati-tempral database mdels. Sice the itegrati f spatial ad tempral database mdels it spati-tempral database mdels, a umber f ew appraches have bee prpsed. At the same time, reviews f these wrks have classified ad cmpared the existig spati-tempral mdels. Curretly, dmai experts are tryig t achieve mre effective itegrati f the spatial ad tempral aspects prvidig practical, uified spati-tempral data mdelig, ad clarifyig the directi fr further research ad develpmet. Stadig at this pit the ctributi ad ctempraeusly the aim f this paper is t prvide a cmplete literature review f existig spati-tempral database mdels develped r suggested i recet decades ad fr the first time t critically cmpare ad evaluate them i terms f sme uiversal criteria, i rder t idetify the tred as well as the eeds fr further research i the area. The attempt t classify mst f the existig data mdels was facilitated by previus reviews i the field. Oe f the mst sigificat ctributrs f the dmai has bee Gail Lagra wh first lked at the aspects f time i Gegraphic Ifrmati Systems (GIS) [La92]. Althugh Lagra s wrk cvers may f the mst imprtat issues f spati-tempral systems, a umber f ew prpsals have emerged sice. I this survey, earlier review wrks are csidered ad icluded i rder t capture all the treds ad the ideas prpsed i the dmai f spati-tempral database mdelig. [Fra92] was e f the first attempts t preset the pr (till the) theries ad methds f reasig i the timevaryig spatial space, while a bibligraphy spati-tempral databases util 1994 was published i [ASS94], which ctais iterestig piters fr further referece. Mre fruitful reviews f the dmai were available the frthcmig years i [Yua96a], [Re97a], [AR99], [Sel99], [Peu01] ad especially i [Pav98] where is itrduced the classificati f spati-tempral database mdels used i the curret survey f the area. Ctact authr s address: 80 Karali-Dimitriu St., GR-18534 Piraeus, Greece. Tel: +30-2104142449, Fax: +30-2104142264.
2 Defiitis Spati-Tempral Data Mdelig As delieated i the papers just cited, evlvig research space-time represetati has fcused a umber f specific areas, icludig: (a) the tlgy f space ad time ad the develpmet f efficiet ad rbust space-time database mdels ad laguages; (b) iexactess ad scalig issues; (c) graphical user iterfaces ad query ptimisati; (d) idexig techiques fr space-time databases. Give the eed fr a mre cmplete theretical fudati ad the requiremet fr crrespdig implemetati slutis, this paper fcuses the area first listed, rather tha the ther three areas where secdary implemetati issues are utlied. Spati-Tempral data mdels are the cre f a Spati-Tempral Ifrmati System (STIS); they defie bject data types, relatiships, peratis ad rules t maitai database itegrity. A rigrus data mdel must aticipate spati-tempral queries ad aalytical methds t be perfrmed i the STIS. Spati-tempral database mdels are iteded t deal with real wrld applicatis, where spatial chages ccur ver the time lie. A serius weakess f existig mdels is that each f them deals with few cmm characteristics fud acrss a umber f specific applicatis. Thus the applicability f the mdel t differet cases, fails spati-tempral behaviurs t aticipated by the applicati used fr the iitial mdel develpmet. The study f the literature f the dmai highlighted a set f precise characteristics f existig mdels that stad fr the requiremets f spati-tempral database cmmuity. These requiremets implicitly frm a evaluati rm fr spati-tempral data mdelig. Frm this study cmm directis f mdelig i the area were idetified ad weak ad strg pits f differet research appraches were als detected. Csequetly, this allws us t recgise the achievemets f previus wrks, t idetify the issues where we shuld ccetrate t ad as such chse the rutes fr subsequet imprvemets. The abve-metied requiremets fall i fur categries. The first categry deals just with the ature f time icludig the basic features that are used t describe it. The secd categry hadles the pure spatial aspects f the existig appraches. The third deals with the uified spati-tempral sematics, while the last categry csiders the query capabilities f the mdels. As we believe, if these requiremets are fllwed carefully i the prcess f desigig a spati-tempral database mdel, a rbust ad expadable mdel ca be achieved, capable f dealig with mst f the real wrld spatitempral prcesses. 2.1 Tempral Sematics Graularity: Graularity is specified by a achred pit the time axis ad a partitiig legth [KT96b]. The achred pit detes where the partitiig begis while the partitiig legth detes the size f each graule. Differet applicatis require differet levels f graularity. Tempral peratis: I the literature a series f specific peratis describig tempral relatiships have bee prpsed ad prved ecessary i hadig ay time-refereced ifrmati. Alle [All83] was the first wh itrduced such kid f peratis (e.g. timepit T iside tempral perid A which meets perid B). Time desity: This issue arises whether time shuld be mdeled as discrete elemets (ismrphic t itegers) r as ctiuus elemets (ismrphic t real umbers). Mre specifically, time desity is clsely related t the types f chages/evets that ca ccur t the value f a thematic r spatial characteristic. Stable features that are expsed t sudde evets preset stepwise cstat values (e.g. psiti f tectic rcks). Ctiuusly chagig attributes ca be divided it tw sub-categries accrdig t their patter f chage. As such we tice either uifrm (e.g. ships, airplaes) r irregular (e.g. taxis mvig i a city cetre) types f ctiuus chages. A third type f etities exhibits discrete values (e.g. seismgrams that iterrelate measuremets f earthquakes at differet lcatis), which are cllected a peridical r irregular basis. Additially sme etities are static ad ever chage (e.g. histric battlefields) while ther etities may be measured r deped the time itself [Re96]. 2
a Stepwise cstatt a Discrete a Smth Irregular Figure 1 Types f chages accrdig t time desity Represetati f time: I a mdel time is represeted by timestamps, where represetati methds are differet fr each mdel. This criteri allws us t cmpare each mdelig techique, by whether maitaiig the durati f the status f a bject r recrdig evets that imply status chage. A practical questi that arises with the represetati f spati-tempral data is what t timestamp r which level t assciate the tempral refereces. I [Wr94b] Wrbys depicts tw appraches f amalgamatig spatial ad tempral refereces i a cmputer-based system: The first pti is t timestamp the etire gegraphical bject. This is likely t be the mst iexpesive f the ptis i terms f cmputer strage. Hwever, it allws ly a limited expressi f the tempral prperties f the bject thrughut its life. The secd pti is t fuse time ad space at the primitive spatial bject level (pit, plyg). Althugh this pti leads t a greater strage verhead, it allws a much fier graularity f expressi f tempral variability withi bjects. Trasacti / Valid time: There are tw differet clauses that a mdel utilizes t assciate time with spatial chages-prcesses. The trasacti time (r registrati time) idicates the time a evet is actually recrded i the database. The valid time (r real-wrld time) describes the time that a evet actually happeed i the real wrld. A spati-tempral mdel that supprts bth trasacti ad valid time is said t maitai bitempral time [KT96b]. Time rder: [Haz92] bserves tw majr metaphrs/criteria fr describig the perspective f time, that f time as a arrw, represetig prgress, ad as a cycle, represetig cstacy ad ctiuity. They are cmplemeted by tw ther (-liear) metaphrs, amely brachig ad multidimesial time [TL91]. Lifespa: This factr shws if a mdel supprts ad deals with the durati f a evet. This als ccers whether a mdel keeps track f the histry f the real wrld bjects, i terms f strig the lifespa f a discrete pheme r the tempral differeces fr a ctiuus e. 2.2 Spatial Sematics Structure f space: This criteri represets the tw basic appraches fr cmputer strage f gegraphic data, which are the raster ad vectr spatial data mdels [Wr94b]. Raster data are structured as a array f cells, pixels r vxels fr 2D r 3D represetatis respectively. Space is partitied it grids where each cell is addressed by its psiti i the raster array. O the ther had, vectr techiques describe each spatial bject i terms f start ad ed pits. Vectr represetatis make mre efficiet use f cmputer strage as they utilize ly useful data ad t the etire plae. Orietati/Directi: This stadard demstrates whether a mdel supprts the rietati ad the directi features that real wrld bjects shw i space (e.g. the left side f, t the right). Measuremet: This issue examies whether it is pssible t get a value f a spatial bject (e.g. legth, perimeter, distace etc) usig a particular mdel r if a mdel supprts cmparative peratis such as bigger, lger. Tplgy: With this criteri we distiguish existig spati-tempral mdelig techiques accrdig t whether they supprt differet tplgical relatiships fr the real wrld spatial bjects. [Haz92] 3
lists all pssible tplgical relatiships betwee bjects f varius dimesis i up t 4- dimesial space. Figure 2 visualizes cmm tplgical relatiships. Disjit Meet Overlap Equal Cvers CveredBy Iside Ctais 2.3 The Spati-Tempral Sematics Figure 2 Tplgical relatiships Data types: This issue refers t the basic spatial, tempral r spati-tempral data types adpted by each mdel. Examples f spatial data types are the pit, lie ad regi whereas tempral pit ad iterval are samples f tempral data types. Fially, mvig pit ad mvig regi are characteristic cases f uified spati-tempral data types. Primitive tis: This criteri specifies the abstracti f the real wrld used by each mdel. Each mdel ccetrates differet aspects f the real wrld t represet spati-temprality i the ifrmati system. The tis vary depedig t ly the methd used but the bservatis ad chices f the particular mdeller as well. Type f chage: This rm cmpares the mdels if they are able t deal with chages i shape ad size f the bjects. Mdels are als evaluated whether a chage i the descripti f a spati-tempral bject ca be cmbied with a sychrus represetati f the chage f a bject s psiti. Csequetly, the mrphlgy, tplgy ad attributes f a spati-tempral bject may r may t chage ver time, allwig fr eight differet scearis (figure 3). Chage i Gemetry Chage i Tplgy Chage i Attribute Chage i Gemetry, Tplgy & Attribute Spati Tempral Object N Chage Chage i Tplgy & Attribute Chage i Gemetry& Attribute Chage i Gemetry& Tplgy Figure 3 The eight pssible types f chage f a spati-tempral bject This rm further csiders whether a mdel supprts spati-tempral real wrld bjects that chage ctiuusly r just bjects that are subject t discrete chages. A additial emergig criteri that further categrizes existig appraches that fllw the ctiuus paradigm is whether the latter ca deal with the mvemet f the spatial bjects ver time. This is a extra decisive factr that differetiates mdels that supprt chages up the psiti ad/r the extet f bjects i the uified space-time ctiuum. Evluti i time & space: This factr shws if there are defied fuctis like evluti, creati, fusi etc. t bserve ad describe the mvemet r chage f bjects i space, idepedetly frm their bject idetificati. The rm is als applied t cmpare mdels the existece f peratis able t calculate the velcity ad/r the accelerati f the mvemet f spati-tempral bjects. There are specific difficulties preseted by the evluti f bjects at differet speeds. Nrmally, a physical bject is thught t ctiuusly mve/chage durig its lifespa. O the ther had, a reccurrig evet must be viewed discretely. Slw ctiuus evluti f a bject may als be disrupted by sudde drastic chages, sme f which may be permaet, thers temprary, r eve part f a cycle. T mdel such evluti, a mdeller may chse a discrete represetati r alteratively 4
he may use step sematics r sme kid f iterplati t represet the urecrded states. Similarly, extraplati ca be utilized t predict the shrt-term future. Space-time Tplgy: This criteri sets a stadard whether mdels ca estimate metrics like values f distace, directi ad chage i size f a particular bject. It further evaluates the ability f the mdels t represet tplgical relatiships (figure 2) betwee (i particular ctiuusly) evlvig spatial bjects fr a certai perid f time. I ther wrds, it csiders relatiships that are defied as the cmbiati f the spatial tplgical relatiships with Alle s [All83] tempral relatiships. Object idetities: Ather issue that ca be emplyed t evaluate the mdelig ability f existig spati-tempral data mdels is the maipulati f the idetity f a bject. I particular, the lifespa f a bject is a imprtat applicati depedat variable. The questi is whe des chage affect a bject s as t t be called the same bject ay mre? Sme times it may be mre apprpriate t destry the rigial istace f a bject ad re-create a ew e, due t a extesive chage. Ather critical issue is that f splittig r uifyig bjects. Dimesiality: With this criteri mdels are examied whether they supprt 2 dimesis t mdel the spati-tempral bjects, as traditial GIS d. Althugh 2.5 dimesial slutis exist (perspectives, stere views etc.), vlumetric 3 dimesial GIS prvide advatages i displayig spati-tempral data. I mre recet appraches, relegatig the attribute value assciated with grid lcatis t a furth dimesi, time ca be itrduced as a fifth. 2.4 Query Capabilities This secti classifies existig spati-tempral database mdels i terms f their query capabilities. The prpsed categrizati is a superset f a similar bechmarkig framewrk preseted i [The03]. Queries abut lcatis, spatial prperties, ad spatial relatiships: Queries f this categry ivlve statiary referece bjects. Examples iclude attribute f etities idepedet f space ad time (e.g. wh is the wer f this parcel?), as well as pit (e.g. where is this buildig?), rage / distace-based (e.g. fid gas statis i this rectagular area / i this circle), earest-eighbr (e.g. fid the clsest gas stati) ad tplgical queries (e.g. fid streets crssig a particular area). Queries abut time, tempral prperties, ad tempral relatiships: These queries ca be simple tempral queries (e.g. what is the state f a spatial feature at time t?), tempral rage queries (e.g. what happes t that feature ver a give perid?) ad tempral relatiship queries (e.g. fid stadiums that were built i Athes ccurretly ad their cstructi tk less tha six mths). Queries abut spati-tempral behavirs ad relatiships: This set f queries is further classified it three sub-categries: (a) Simple spati-tempral queries discretely chagig (e.g. what is the state f a parcel at time t?) r mvig referece bjects; examples iclude distace-based (e.g. fid humas passed clse t me yesterday) ad similarity-based queries (e.g. fid a similar trajectry t the e I fllwed tday). (b) Spati-tempral rage queries (e.g. what happes t a regi ver a give perid?) ad/r ji queries; examples iclude distace-ji (fid the three clsest restaurats t my fleet) ad similarity-ji queries (fid the tw mst similar pairs f trajectries i mth Jauary). (c) Spati-tempral behavir queries ivlvig uary peratrs, such as traveled distace r speed (e.g. fid the average speed Saturday ights, whe/where did the fire reach its maximal rate f spread?). Based related research wrk [KS+03], the abve queries cstitute a miimum fuctiality a spati-tempral system shuld prvide ad we expect that s cmig releases f cmmercial DBMSs will partially supprt them. 2.5 Case study: Lad Ifrmati System (LIS) The dyamic evirmet f the real wrld ca be represeted by spati-tempral databases icrpratig the behaviur f bjects i space ad time. Gegraphical ifrmati systems, autmated mappig facilities, lad use ifrmati, rad r city plaig, migrati f ppulati ad frest fires are sme applicatis where a spati-tempral data mdel ca be used. Figure 4 illustrates such a spati-tempral applicati. The case study deals with bjects that chage their shape ad/r their psiti discretely r gradually ver time. Ccurretly it eables the descripti f the chages that take place up the thematic prperties f the ivlved bjects. 5
P1 P2 B1 T1 T2 T3 P3 P4 B2 R T4 T5 T6 P1 P2 B1 T1 T2 T3 P3 P4 R T4 T5 T6 P1 P2 B1 T1 T2 T3 P4 R T4 T5 T6 P3 Jauary 2002 April 2002 July 2002 P1 P2 B1 B3 T1 T2 T3 T7 T8 R T4 T5 T6 T9 T10 P3 P1 P2 B1 B3 T1 T2 T3 T7 T8 R T4 T5 T6 T9 T10 P3 B1 P1 T11 B3 P2 T1 T2 T3 T7 T8 P3 T4 T5 T6 T9 T10 Octber 2002 Jauary 2003 April 2003 Figure 4 The Lad Ifrmati System Jauary 2002: A lad parcel wed by Bb (P1), a lad parcel wed by Jh (P2), a lad parcel wed by cucil (P3), a parcel wed by Bill (P4), buildigs B1 ad B2, river R ad trees T1-T6. February 2002: Cucil prpses Bill t buy his lad t build a park i the future. April 2002: Cucil decided t remve buildig B2 frm its parcel ad expads the parcel icrpratig part f the parcel P4. May 2002: Bb decides t sell a part f his lad t cucil. Cucil develps a prject t build a park. July 2002: Cucil expads its parcel by icrpratig part f the P1 with trees T1-T3 wed by Bb ad part f the parcel P4 wed by Bill. It further chages the rt f the river R ad starts t create a lake L. T d s it chages the psiti f tree T6. Jh starts the cstructi f B3. Octber 2002: Cucil gets parcel P4 ad plats trees T7-T10. Lake L becmes larger while by this time Jh cmpletes buildig B3 his parcel P2. Jauary 2003: Lake ctiues t grw. April 2003: Cucil stps the flw f river R. Parcel P3 becmes a park with several trees T1-T10 ad lake L amg them. P2 is elarged ad T11 is plated iside its extesi. Frm the chrlgy f the evets ad the actual chages shw i figure 5 it is bvius there are refereces t trasacti ad valid time. I May 2002 (trasacti time) Bb decides t sell part f his lad t cucil ad the actual fact happes i July 2002 (valid time). Frm the ifrmati prvided may f the valid times are t exact. Fr example, it is t clear which exact time pit the directi f the river was chaged. I figure 5 circles shw the evets measured r recrded. The dtted circles shw the chages made by mutual agreemet r ctract, which d t chage the psiti f the bjects. These chages ca be recrded i the database as plaed prject fr park. The actual park ca be t develped i a real wrld, but the plaed picture ca exist virtually i the database. The filled dtted circles shw chages, which take place i the real wrld but are t recrded r captured by ay meas. The idexes used i the evet diagram are explaied i table 1. Chage f spati-tempral bjects idetity is described by peratis like create, destry, susped ad resume, i case f a crrespdig creati, deleti, tempral freezig ad restrati f a bject. Fissi shws the emergig f ew successr bjects the psiti f a destryed bject. Csequetly, fusi shws the creati f a sigle bject the psiti f several bjects destryed. 6
Jauary, 2002 February,2002 P1 B1 T1 T2 T3 P3 B2 2 R T4 T5 T6 P2 P4 1 April,2002 M ay,2002 6 3 4 5 July,2002 7 8 L R T6 9 10 L 11 Octber,2002 T10 L B3 T9 T7 T8 L Jauary,2003 L L April,2003 L 12 T11 Figure 5 Evet diagram fr the Lad Ifrmati System Idex Evet Operati Time 1 Cucil prpses t buy a lad frm Bill Susped TT 2 Demlishig f the buildig B2 Susped TT 3 B2 is demlished ad the lad where the buildig std Destry VT is a part f P3 4 Cucil gets a part f the P4 Create VT 5 A part f P4 still belgs t Bill Create VT 6 As a result f Bb s decisi t sell a part f his lad t Susped TT cucil, the prject the ew park is develped 7 P1 is decreased i size, prperty f Bb Create (fissi) VT 8 Cucil gets a part f P1 Create (fissi) VT 9 Cucil gets a part f P4 Create (fissi) VT 10 P4 is decreased i size, prperty f Bill Create (fissi) VT 11 Last part f P4 becmes a cucil s estate Susped TT 12 The river is stpped, ad its bak becmes a part f P3 Destry, resume VT P1-P4 Parcel 1-Parcel 4 Create VT T1-T11 Tree1 Tree 11 Create VT B1-B3 Buildig1-Buildig3 Create VT R River Create VT L Lake Create VT T6 Tree T6 mved t a ew psiti Resume (fissi) VT R River R chaged its rute Resume (fissi) VT L -L Recrded chage f lake L. Resume (fissi) TT 3 Spati-Tempral Data Mdels Table 1 Evet idexes fr LIS Thrughut the relatively yug histry f research spati-tempral mdelig, a substatial umber f mdels have bee preseted. This secti examies mst f the spati-tempral mdels prpsed i the literature the last tw decades. Each mdel is applied t the case study ad evaluated with respect t the cmparis framewrk frmed by the requiremets preseted i secti 2. 3.1 The Sapsht Mdel Oe f the simplest spati-tempral data mdels is the sapsht mdel [La88]. Tempral ifrmati has bee icrprated it this spatial data mdel by time-stampig layers. I this mdel, every layer is a cllecti f temprally hmgeeus uits f e theme. It shws the states f a gegraphic distributi at differet times withut explicit tempral relatis amg layers. 7
The time dimesi f the sapsht mdel is based the liear, discrete, abslute time mdel. Oly valid time is supprted. Time is csidered as a attribute f the lcati. The mdel is the simplest way t represet spati-tempral ifrmati, but its capability t supprt cmplex queries is the mst limited. It is therefre capable t aswer simple spatial, tempral ad spati-tempral queries but it is difficult fr the mdel t reslve all the ther types f queries. The sapsht sequece f time slices fr the LIS is give by figure 4 that describes ur case study. The sapsht mdel depicts three majr disadvatages [La92]: The mdel is t apprpriate t describe chages i space thrugh time. Each sapsht describes what exists at T i. But t detect hw T i differs frm T j, the tw sapshts must be cmpared exhaustively. Regardless the magitude f chages, a cmplete sapsht is prduced at each time slice, which duplicates all the uchaged data. It is very difficult t devise r efrce rules fr iteral lgic r itegrity because the mdel des t prvide uderstadig f the cstraits up tempral structure. Ather clsely related apprach was preseted i [Arm92], where spati-tempral data are lked at with respect t strage, retrieval ad update efficiecy. He cmpares three appraches, which he calls estimati methds t describe time-varyig spatial ifrmati. The aim f his ivestigati is t see if these methds have the ability t stre/recstruct cmplete gegraphical states, ffer fuctiality fr cmpariss betwee states, ad describe the evets that lead t chages betwee states. I static mde, sapshts f full states are kept which leads t the strage f redudat ifrmati. T detect chages betwee sapshts, relatively expesive cmputatial algrithms must be used, althugh this wuld still t explai the prcesses leadig t the chage. I differetial mde, ly the iitial state is fully recrded. Chages are stred i e f tw pssible kids f delta files, which recrd the differeces frm either the previus state r the iitial e. This reduces strage requiremets substatially, ad makes the cmputati f chages betwee states less cstly. Hwever, t reistate previus states r the curret e, a series f delta files must be applied t the iitial state, which makes this perati iefficiet. Alteratively, the curret state ca be chse t be stred i full, keepig delta files t trace back t previus states, which is the preferable sluti if the curret state is mre frequetly accessed tha histric es. This is smewhat similar t the fial, sequetial updatig mde that als keeps the curret state f the map recrd. Hwever, this apprach recrds chages as they happe ad t i a sapsht-like fashi, ad uses idexes t access previus ifrmati, elimiatig data redudacy. Ather alterative, still fllwig the idea f sequetial updatig, is t drp the use f delta files ad retai uchaged cmpets istead. I this sceari, whe a bject chages, its previus versi is superseded but fully retaied accessible by tempral liks ad idexes, while a ew bject is created t describe the curret state f the cmpet. 3.2 The Space-Time Cmpsite (STC) Data Mdel This mdel has bee suggested by Lagra i [La88]. It is based the priciple that every lie i space ad time is prjected dw t the spatial plae ad itersected with each ther creatig a plyg mesh. Each plyg i this mesh has its w attribute histry assciated with it. Each ew amedmet is itersected with the already existig lies, ad ew plygs are frmed with idividual histries. The mdel has bee tested with a umber f existig methds [La92]. The results that were btaied lked prmisig, but ly small data sets were tested. The space-time cmpsite fr LIS is shw i figure 6. We tice that each chage causes the chaged prti f the cverage t break frm its paret bject t becme a discrete bject with its w distict histry. 8
A L J R B M S K N Y Y Z X X X X I O T T D P U C Q E F G V Figure 6 Space-Time Cmpsite Mdel fr the LIS The time dimesi f the space-time cmpsite data mdel is based the liear, discrete, relative time mdel. Bth valid ad trasacti time are supprted while the mdel supprts multiple graularities ad time is represeted as a itegral part f spatial etities. The mdel assumes vectr structure f space ad the basic data type is the plyg. A space-time cmpsite cceptually describes the chage f a spatial bject thrugh a perid f time. Attribute chages are recrded at discrete times, althugh its tempral resluti is t ecessarily accurate. The STC mdel is able t recrd temprality withi the largest cmm uits f attribute, space ad time but it fails t capture temprality amg attributes acrss space (i.e. mvemet). I additi, updatig a STC database requires recstructi f STC uits. The mdel has shw sufficiet supprt fr mst types f spati-tempral queries. Hwever, it has difficulty i facilitatig queries abut spati-tempral behaviurs ad relatiships. A serius prblem with the STC mdel ccers retractive chages t idetifiers. Each time the space-time cmpsite splits a bject it tw, the ld bject is effectively replaced by tw ew bjects with ew idetifiers. This meas that thrughut the database, each ccurrece f the ld bject idetifier must be replaced with e r bth f the ew es. 3.3 Data Mdels based Simple Time-Stampig Ather simple apprach is t tag every bject with a pair f timestamps, e fr the time f creati ad e fr the time f cessati. Curret bjects have their cessati time give by a special value NOW, CURRENT, r NULL [Re96]. I [HW90] the authrs have implemeted such a apprach ad shw that time slices ca easily be retrieved by simple queries. They argue that i digital cadastral databases, strig full layers f graphical ifrmati fr differet time perids is impractical, ad describe a system that keeps a graphics file f curret parcels fr day t day use while archivig histrical spatial data it a separate file. Referece t this ifrmati is still kept i the files that stre aspatial ifrmati via multiple versied cpies f the same parcel recrd. The mdel is based the liear, discrete, abslute time mdel. Oly valid time is supprted while the mdel supprts multiple graularities. Time is represeted as a attribute f the bject ad vectr structure f space is assumed. Hwever, such a mdel spreads the differet versis f the same bject ver several -related tuples arud the same table. This makes it hard t trace the histry f e sigle bject. This deficiecy ca be reslved by addig explicit refereces t precedig ad succeedig versis f the bjects. The idea cmes frm a bject-rieted mdel [RMD94] where is itrduced the Tempral Chage Object, which is a bject csistig f a set f refereces t past (histric), future (scheduled) ad the curret versi. The time crss-secti f this mdel fr the LIS is described i figure 7. The stregth f simple time-stampig apprach is that it is relatively easy t btai states f bjects at certai times. The mai disadvatage is that it is t pssible t btai direct ifrmati f what happeed r why it happeed. I ther wrds, the chages ca be btaied i terms f their effects rather tha as explicit ifrmati. This meas that the mdel is strg queries like What was the state f ad weak queries like What happeed. 9
L P3 Apr, 03 P2 P2 P1 L Ja, 03 B3 P3 L T7 T8 T9 T10 P3 Oct, 02 T1 T2 T3 P3 L T6 R P3 P4 Jul, 02 P2 P1 P3 P3 P4 Apr, 02 T1 T2 T3 P3 T4 T5 T6 R P4 3.4 Evet-Orieted Mdels Figure 7 Simple Time-Stampig apprach fr the LIS The previus mdels cat idetify idividual chages r evets t the data set. Oe way t vercme this is t represet the evets explicitly. Imagie a traditial GIS, if all chages that were made t each data set were lgged it a trasacti lg, that lg itself wuld prvide all the ifrmati eeded i a spati-tempral system. The actual database wuld the act as a curret state database, ad i rder t btai histrical states f the map, a rewid ca be btaied by tracig the trasacti lg backwards. Thus, the trasacti lg itself truly is a tempral database. Data mdels that have bee implemeted r eve discussed at ay level f detail fr hadlig spatitempral data are extesis f traditial r vectr mdels. These traditial mdels ca be see as lcati-based r bject-based. It is w well kw that bth f these mdels are required i a GIS if bth lcati-based ad bject-based queries are t be hadled effectively. It fllws that either f these tw frms, eve whe exteded t iclude time wuld be as effective as a tempral-based represetati fr hadlig time-based queries. I [PW94] is prpsed such a apprach fr the time-based aalysis f spati-tempral data, as a adjuct t lcati-based ad bject-based aalysis. The desig f TEMPEST, a prttype Tempral Gegraphic Ifrmati System (TGIS) that implemets this apprach, icrprates this time-based data mdel ad assciated relatial peratrs. Startig with a iitial state (base map), evets are recrded i a chai-like fashi i icreasig tempral rder, with each evet assciated with a list f all chages that ccurred sice the last update f the evet vectr. A evet may represet abrupt chage r ca be triggered whe gradual evluti is csidered t be sigificat eugh (ver sme predefied threshld), t register chage. Chages ca be stred as differeces frm the previus versi, which avids data redudacy, r if they are csidered t be extesive, the full map may be registered. Additially, Peuquet ad Dua have implemeted a raster-based evet-rieted apprach, called the Evet Orieted Spati-Tempral Data Mdel (ESTDM) [PD95]. ESTDM grups time-stamped layers t shw bservatis f a sigle evet i a tempral sequece. The ESTDM stres chages i relati t a previus state rather tha a sapsht f a istace. A header file ctais ifrmati abut its thematic dmai, piter t a base map, ad piters t the first ad last evet lists. The base map shws a iitial sapsht f a sigle theme f iterest i a gegraphic area. Every evet is timestamped ad assciated with a list f evet cmpets t idicate where chages have ccurred (figure 8). A evet cmpet shws chages t a predefied lcati (a raster cell) at a particular pit i time. The ESTDM has shw its capabilities ad efficiecy t supprt bth spatial ad 10
tempral queries. Hwever, the trasfrmati f the ESTDM t a vectr-based system requires a substatial redesig f evet cmpets. Mechaisms are eeded t allw evet cmpets t keep track f their predefied etities ad lcatis. Header T0 Evet 1 T1 Evet 2 T2... Evet Q Tq Base map C m p e t 1 C m p e t 2 C m p e t k... C m p e t 1 C m p e t 2... C m p e t k C m p e t 1 C m p e t 2... C m p e t k Figure 8 Primary Elemet f a Evet-Oriet Mdel Lagra describes ather evet-rieted apprach, called the amedmet vectr apprach where a base state (r a fial state) is verlaid with amedmet maps, represetig the evets i the database [La92]. Figure 9 shws this evet-based mdel fr the LIS. The advatage f this represetati is that ifrmati abut what happeed t the bjects is stred i the database. The time dmai csiders discrete, relative, liear mdelig. Jauary, 2002 April, 2002 July, 2002 Octber, 2002 Jauary, 2003 April, 2003 3.5 The Three-Dmai Mdel Figure 9 Amedmet Vectr Mdel fr LIS Yua i [Yua94] ad [Yua96b] describes a three-dmai mdel fr spati-tempral mdelig. Her mdel (figure 10) represets sematics, space ad time separately ad prvides liks betwee them t describe gegraphic prcesses ad phemea. The sematic dmai hlds uiquely idetifiable bjects that crrespd t huma ccepts idepedet f their spatial ad tempral lcati. This is i ctrast t ther mdels where, fr example, a ladwer is represeted as a attribute f a lad parcel. I the three-dmai mdel, the ladwer is a sematic etity that is liked t a lad parcel (spatial bject), with chages t the parcel assciated with dates (tempral bjects), ad pssible ther lad parcels ivlved i the trasfrmati. Lss f wership is implemeted by likig ather sematic etity t the lad parcel tgether with the tempral bject represetig the date f sale. Sematic Dmai Tempral Dmai Spatial Dmai Figure 10 A Cceptual Framewrk fr the Three-Dmai Mdel 11
The advatage f this vectr mdel is the ability t hadle mvemet as well as chage, which is a imprvemet ver may existig mdels that hadle either the frmer r as i mst cases, the latter. A classificati f chage (as a geeral term icludig bth chage ad mvemet ) fr this purpse is give, with tw grups idetified i each f the three dmais. Sematic chages iclude variatis i attributes ver time ad the static spatial distributi f a gegraphic pheme. Spatial chages may be static, lkig at variatis f a gegraphic pheme at a sapsht, r trasitial, cmparig states f a evet at differet sites. Tempral chages are either spatially fixed mutatis f a evet r the actual mvemet f it frm e place t ather. The mdel is very applicable i reality because f its highly abstract structure. Mrever it supprts bth valid ad trasacti time ad time ca be mdelled either as abslute r relative. Furthermre, the three-dmai framewrk ca supprt a wide rage f spati-tempral queries because f its flexibility i ifrmati prducti by hadlig sematic, spatial ad tempral ifrmati separately. Yua i [Yua97] shws, that her mdel ca supprt simple ad rage tempral ad spati-tempral queries. I a alterative Three-Dmai methd preseted i [CT95], i additi t spatial ad tempral dmais a thematic dmai is added t represet the cmplete descriptive state f a spati-tempral bject. Recrdig f descriptive characteristics separately frm spatial ad tempral attributes allwed the capturig f chages f the aspatial attributes f a bject. The tempral dmai refers by idexes t spatial ad thematic dmais, thus makig it pssible t retai differet spatial ad thematic characteristics f spati-tempral bjects the same timestamp. Similarly the relatiship betwee dmais (figure 11), allws differet versis t refer t similar thematic ad spatial descriptis, which reduces data hadlig sigificatly. V ERSIO N IN G Tplgical avigati at the etity level B IN A R Y T R EES Idices fr tim e stam p selectis T hem e T H EM A T IC D A TA PA ST V ERSIO N S Tim e PR ESEN T V ER SIO N S Space SPA T IA L D A T A T H EM A T IC IN D IC E S SN A PSH O TS D irectry fr selectig all bject versis fr a tim e perid SPA T IA L IN D IC ES Figure 11 A Alterative Three-Dmai Mdel This mdel fcuses spati-tempral evets. Characteristics are categrized as thematic, spatial ad tempral ad are recrded i crrespdig tables every time a chage ccurs. The tempral dmai csists f three versi tables, where past, preset ad future versis are recrded. These tables carry the recrds relatig t attribute ad graphics, which csequetly derive their recrds frm thematic ad spatial dmais. Orderig i tempral tables is bi-directial ad valid time ad trasacti time are supprted. Cmplex prcesses ca be described by the exteded-versiig diagram, which refereces multiple etities ad liks. A frm f a spatial tree eables tracig the gemetry ad the tplgical relatiships f spatial bjects the time lie. The spatial chages ca be recrded i the spatial dmai as shw i table 2. Versiig table csists f tuples ctaiig refereces t attribute table, spatial table, valid ad trasacti time. I additi there are clums shwig ext recrd umber ad last recrd umber t perfrm ctiuus rll ver evets ad prcedures. Fr simplicity reass, we mit the attribute ad spatial tables ad we preset a illustrati f the trasiti f the spatial bjects (figure 12), the spatial tree idicatig the spatitempral chages (figure 13) ad the prduced versiig table fr the LIS. 12
1 3 6 8 9 2 7 4 10 11 5 12 1 3 6 8 9 2 7 4 10 5 11 12 14 16 3 6 8 9 2 17 22 7 4 10 5 18 19 12 20 13 16 3 6 8 9 2 17 4 7 22 5 23 18 19 12 20 26 25 21 15 24 28 27 15 16 3 6 8 9 17 2 4 7 22 10 5 29 23 18 19 12 20 26 25 21 15 24 28 27 Figure 12 Three-Dmai Spatial Trasitis fr LIS 0 21 15 16 3 6 8 9 17 2 4 7 22 10 5 29 23 18 19 12 31 20 30 26 25 21 15 24 28 27 Jauary 2002 1 2 3 4 5 6 7 8 9 10 11 12 13 April 2002 15 14 July 2002 16 17 18 19 22 20 21 Octber 2002 26 23 24 28 25 27 Jauary 2003 29 April 2003 t 30 31 Figure 13 Three-Dmai Spati-Tempral Tree fr LIS ID Attribute WD_Time VL_Time Graph Prev Next Last 1 1 Jauary 2002 1, 2, 3, 4, 5 0 2 2 2 Jauary 2002 12 1 3 3 3 Jauary 2002 6,7,8,9,10,11 2 4 4 4 Jauary 2002 13 3 5 5 3 Febr. 2002 15 4 6 6 3 April 2002 7,15 5 7 7 4 April 2002 14 6 8 8 1 May 2002 17 7 9 9 3 July 2002 17, 18,19,21, 22 8 10 10 4 July 2002 20 9 11 11 2 July 2002 24 10 12 12 3 Octber 2002 20,25,26,27, 28, 23 11 13 13 2 Octber 2002 24 12 14 14 3 Jauary 2003 29 13 15 15 3 April 2003 22, 30 14 16 16 2 April 2003 31 15 17 17 Table 2 Versiig table cmig frm applyig Three-Dmai Mdel it LIS. 13
The mdel was a revluti i spati-tempral database develpmet, because it was the first successful attempt t recrd idividual descriptive characteristics f dyamic bjects. At every ccurrece f a thematic ad/r a spatial chage a ew versi f time is beig added t the versis table. The spatial tree allws tracig f the chages i the spatial dmai i accrdace t the time lie. At the same time it captures the evets ad prcedures f the spati-tempral database tgether with the spatial crdiates, gemetrical ad tplgical prperties. Hwever, there are t defied peratrs fr dealig with the relatiships amg spatial bjects ad it eeds mechaisms t calculate the chage. 3.6 The Histry Graph Mdel Uderstadig tempral behaviur is e f the mst fudametal issues i spati-tempral systems. A simplistic view that may researchers seem t adpt, is t represet bjects ly i terms f static represetatis, viewig chages as sudde evets. Hwever, we kw that may chages i the real wrld have durati. Actually, features i the real wrld exhibit a wide rage f tempral behaviur. As such, we classify real wrld bjects it three categries: (a) ctiuusly chagig bjects, (b) bjects that are basically static, but they are chaged by evets that have durati ad (c) bjects that are always static ad chage ly by sudde evets. The mai purpse f the histry graph mdel [Re96] is t idetify all types f tempral behaviur ad t maage bth bjects ad evets. The iteti f the histry graph tati is t visualize the tempral elemet f gegraphical ad ther ifrmati. It is based the simple idea that a bject may either be i a static, a chagig r a ceased state. I the histry graph tati, the static states called bject versis are shw with rectagular bxes, while the chagig states called trasitis betwee versis are shw with rud eded bxes (r circles i case f sudde chages). Each bject versi is idetified by tw timestamps describig the iterval f time i which the state f the bject is valid. Each trasiti is a etity that relates bject versis with its successrs r predecessrs. It is als characterized by tw time stamps describig the perid f time i which the trasiti tk place. Liks r arrws betwee states display successr-predecessr relatiships betwee them. A bject s histry may be described thrugh a series f csecutive versis ad trasitis. Objects that chage suddely are described by trasitis with zer durati (i.e. evets), while bjects that chage ctiuusly are described by versis with zer durati (i.e. sapshts) describig itermediate states. I geeral, at least six types f trasitis represetig differet cardiality cstraits the precedig ad succeedig bject versis may be idetified. Figure 14 exhibits the sematics f the histry graph tati, while figure 15 illustrates the six differet types f chage. Creati: A bject is created. Alterati: A bject is chaged r mdified either by chage i attribute r i gemetry. Cessati: A bject is destryed r remved ad des lger exist i the real wrld. Reicarati: A bject that previusly has bee destryed r remved is reitrduced, pssibly with a ew state ad lcati. Split/Deducti: A bject is subdivided i tw r mre ew bjects r e r mre bjects are deducted frm a existig bject. Merge/Aexati: Tw r mre bjects are jied tgether t frm a ew bject r e r mre bjects are swallwed it ather bject. Ctiusly chagig Evets with durati Sudde evets Trasitis Versis Figure 14 The behaviur types f Tempral Objects 14
Creati Alterati Cessati Reicarati Merge / Aexati Splittig / Deducti Figure 15 Six Basic Types f Chages i Histry Graph Mdel Althugh the evet-based mdels ad the data mdels simple time-stampig have their advatages ad their disadvatages, they cmplemet each ther. Hece, it is atural t suggest that spatitempral databases shuld maage bth evets ad bjects i their data sets. Histry graphs are the utcme f this prcedure. The primary applicati f a histry graph is t describe a limited extet i time ad space, called a stry. Actually this mdel des t ecessarily have t describe a spatial system, althugh the ccept f splittig ad mergig is mtivated frm spatial prcesses. The bvius way t mdel LIS with histry graphs, is t csider that evets are istataeus ad therefre have durati (figure 16). Hwever, geerally speakig this is t the situati. Fr example the buildig f a rad may take several years, but the rad may exist i a database frm the day it was peed. The peig f the rad may be mdelled as a sudde evet, while the buildig ad plaig f it may take several years. If we assume that evets have durati the the peig date f a rad will be its creati date. M1 B1 M2 P1 P1 M5 P1 M3 T1,T2,T3,T4,T5,T6 M4 T1,T2,T3,T4,T5,T6 M6 P2 M7 P2 M8 B3 R R M9 R R R M10 M11 B2 M12 M13 L L L L M14 P3 M15 P3 M16 P3 M21 T11 M17 P3 M18 P4 M19 P4 M20 P4 M18 T7,T8,T9,T10 Jauary, 2002 April, 2002 July, 2002 Octber,2002 Jauary, 2003 April, 2003 Figure 16 The Histry Graph fr the LIS As a whle, histry graphs ca be thught as a extesi t the evet-rieted way f thikig. Their advatage is that tempral relatiships ca be derived directly ad that time ca be mdelled bth as discrete r ctiuus as well as abslute r relative. The time axis is liear ad bth valid ad trasacti time are supprted. The majr advatage f this vectr mdel is that histry graphs capture all the kwledge we eed i rder t further develp a spati-tempral system. Mrever, they capture bth the tis f chage ad mvemet ad they ca easily supprt mst types f spatitempral queries. Fially, Rele has shw [Re96] that it is pssible t take advatage f iheritace whe implemetig the mdel usig bject-rieted methdlgy. The basic idea is t implemet the six differet types f prcesses as sub-classes f the prcess bject. He further believes that the prgrammer s jb is simplified if the data structures ca be visualized i a cceptual mdel. Mrever, a implemetati based bth prcesses ad states shuld be well suited fr mst types f queries, t havig the deficiecies f the evet-rieted r data-rieted mdels. 15
Additi Prcess Cessati Prcess Alterati Prcess Prcess Reicarati Prcess Split Prcess Merge Prcess Figure 17 Object-Orieted Desig f Histry Graphs Usig Iheritace 3.7 The Spati-Tempral Etity-Relatiship (STER) Mdel Etity-Relatiship is the earliest ad best kw amg cceptual database mdels ad it has recetly bee exteded t capture spati-tempral ifrmati. Fr sme years the ER mdel was used t represet temprally refereced busiess data [TL91] r exteded i rder t deal with slely spatially refereced data [HT97]. Hwever, e f the prpsed mdels satisfied the demadig requiremets f a spati-tempral ifrmati system. Later Tryfa i [Try97] prpsed a extesi f the etity relatiship mdel i rder t mdel the phemea f the real wrld ad t capture them it spati-tempral applicatis. She exteded the ER mdel with symbls t represet the gemetry ad temprality f spati-tempral etity sets. Despite the fact that the mdel was wrkig spatitempral applicatis, the tempral sematics f attributes were missig ad cardiality f time was t flexible eugh t satisfy the requiremets f spati-tempral databases. I additi, a frmal defiiti f the whle mdel was t demstrated. These attempts ad ivestigatis prvided the fudati fr develpig the Spati-Tempral Etity- Relatiship (STER) mdel [TJ99] & [TJ00]. The careful aalysis f spati-tempral applicatis ad behaviur f spatial ad tempral etities suggested that etity sets with their attributes ad relatiships culd capture the dyamic ature f spati-tempral databases. The, the extesive defiiti f spati-tempral bjects, attributes ad relatiships tgether with the requiremets fr the mdel were give. I additi, the applicatis fr spati-tempral databases are categrized by their data type, highlightig applicatis dealig with bjects with ctiuus mti, with discrete chages ad with bjects itegratig ctiuus mti as well as chages f shape. Further mre, the tlgical fudatis fr desigig spati-tempral databases are described ad the requiremets t capture t ly the psiti f a bject i space ad time, but als their descriptive attributes, relatiships ad existece aspects are preseted. What is mre, the STER mdel, which is able t deal with cmplex ge-etity sets ad iterrelatis f spatial ad tempral sematics, allws descripti f attributes such as wership ad f relatiships amg etity sets such as reicarati, splittig, ad existece time. The mdel is uiversal i terms f reusability due t its simple ad flexible tati; hece it ca be directly used as a framewrk fr ther cceptual mdels. Figure 18 demstrates the mdel applied t the LIS. Subsequetly we preset the traslati f just e f the etities f the graphical diagram fllwig the sytax f STER. It is csidered that the attempt t capture the spati-tempral aspects f ifrmati i the LIS usig the STER apprach was successful. The tempral ad spatial chages f the applicati are idetified, while the descriptive attributes are defied valid ad trasacti time lies. Hwever, it lacks the ability t capture the actual mti f the prcess f chage ad des t idicate if a spatial bject is dyamic r static. NAME OW NER vt vt BUILDING et vt Rvt bt belgs_t NAM E vt NAME NAME tt tt RIVER LAKE et et tt Lbt tt Rbt bt belgs_t bt belgs_t PARCEL OW NER et bt Rvt vt NUM BER vt TREE et vt Pvt bt belgs_t Etity set attribute relatiship Figure 18 A excerpt f the LIS desiged i STER 16
DEFINE ENTITY SET parcel ATTRIBUTES (Name VALID TIME valid time, Ower VALID TIME valid time) GEOMETRY REGION VALID TIME valid time EXISTENCE TIME existece time VALID TIME valid time TRANSACTION TIME trasacti time 3.8 Object-Relatiship (O-R) Mdel Previus cceptual level develpmet f spati-tempral database mdels may have ehaced the curret GISs prvidig a mre realistic wrld descripti f the chages ad prcesses i space ad time. Hwever, e f the abve cvered the descripti f chage prcesses. Csiderig this fact, researchers i [CPS+98] mdelled a applicati, which culd capture the atural phemea f evirmetal chages. They aalyzed already prpsed mdels ad came t the cclusi that existig mdels are mre ccered with desig rather tha the represetati f the atural evirmetal chages, prcesses ad evets. I their itrducti [CPS+98] review several wrks spati-tempral database mdelig. They highlighted bth the weak ad strg pits f earlier wrk i capturig the spatial chages, ctiuus visi, discrete ad liear database represetati. They als idetified the taxmy f spatial chages ad bject rieted database mdels, cectig spatial etities with tempral attributes. Three differet methdlgies fr spati-tempral database desig are described as the mai thrust f their research. These are Mdul-R, Mecsig ad Plle, which exted ER [HT97] ad Object-Orieted techiques. A furth apprach called MADS (Mdelig Applicati Data with Spati-tempral features) [PSZ99] is als preseted, which is implemeted fllwig bject relatiship (OR) apprach. The implemetati f bject-relatiship mdels describe prcesses, which act the gemetric attributes f a etity ad illustrate the imprtace f capturig the prcesses, which cause chage i cecti with space ad time. The MADS icrprates space ad time mdelig basics it the bject-relatiship mdel [PSZ99]. The authrs argue that spati-tempral database prcesses allw users t hadle the cmplex data mdels required by higher-level abstracted spati-tempral applicatis. Therefre, the types f prcesses were classified ad represeted as relatiships betwee ivlved spati-tempral bjects. At the same time, the bject prperties, which are required t be captured i the spati-tempral databases, are stated. These are imprtat t idicate the prcesses that cause a chage. Hece, the descripti f prcesses as a relatiship type betwee spati-tempral bjects describes best the spati-tempral phemea. The prcesses ifluecig a sigle bject s gemetry are described as the characteristic f the gemetry attribute. Fially, the spati-tempral prcesses are visualized thrugh ics i the schema. The prpsed desig usig the LIS case study is illustrated i figure 19 tgether with the descripti f e f the bjects i the sytax f the defiiti laguage f the OR Mdel. OBJECT Parcel TEMPORAL Day GEOMETRY AREA TEMPORAL DAY ATTRIBUTES Number: INTEGER Name: strig [1:N] TEMPORAL DAY Ower: [1:N] TEMPORAL DAY END Parcel The methd is a cceptual-level represetati f a spati-tempral database ad prvides the basis fr queries ivlvig actual prcesses f the applicati. Althugh it is bvius that there is eed t represet prcesses ad chages the cceptual level, there are extesive defiitis ad peratis give. The mdelig f the prcesses is a abstracti f the real wrld, ad a descripti suitable fr e applicati may be deficiet whe applied t ther real wrld scearis. 17