A Survey of Modelling Trends in Temporal GIS

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A Survey of Modelling Trends in Temporal GISWillington Siabato, Christophe Claramunt, Sergio Ilarri

To cite this version:Willington Siabato, Christophe Claramunt, Sergio Ilarri. A Survey of Modelling Trends in TemporalGIS. ACM Computing Surveys, Association for Computing Machinery, 2018, 51 (2), pp.30:1-30:41.�hal-01900660�

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ACM Computing Surveys, Vol. xx, No. x, Article xx, Publication date: Month YYYY

39

A Survey of Modelling Trends in Temporal GIS1

WILLINGTON SIABATO, Universidad Nacional de Colombia, Department of Geography; Universidad Politécnica de Madrid CHRISTOPHE CLARAMUNT, Naval Academy Research Institute SERGIO ILARRI, University of Zaragoza, I3A, Department of Computer Science and Systems Engineering

The main achievements of spatio-temporal modelling in the field of Geographic Information Science that spans over the past three decades are surveyed. This article offers an overview of: (i) the origins and history of Temporal Geographic Information Systems (T-GIS); (ii) relevant spatio-temporal data models proposed; (iii) the evolution of spatio-temporal modelling trends; and (iv) an analysis of the future trends and developments in T-GIS. It also presents some current theories and concepts that have emerged from the research performed, as well as a summary of the current progress and the upcoming challenges and potential research directions for T-GIS. One relevant result of this survey is the proposed taxonomy of spatio-temporal modelling trends, which classifies 186 modelling proposals surveyed from more than 1450 articles.

CCS Concepts: • Information systems~Geographic information systems • Information systems~Temporal data • Computing methodologies~Spatial and physical reasoning • Computing methodologies~Temporal reasoning

Additional Key Words and Phrases: spatio-temporal models; survey; literature review; temporal GIS; time geography; spatio-temporal databases; temporal models.

1. INTRODUCTION

While research on conventional databases started over 50 years ago (Charles Babbage Institute 1959, Codd 1970, Olle 1978), the focus on spatial databases as a specialized domain began with the groundwork of Berman and Stonebraker (1977) and Chang and Fu (1980), who defined the main principles of a spatial database architecture, suggesting for instance the Layered Architecture approach. During this process, the evaluation and adaptation of query languages for retrieving geometries (Frank 1982) and several proposals for indexing spatial data structures (e.g., Stonebraker et al. 1983, Guttman 1984) were also significant milestones. These works evolved into the Dual (Schilcher 1985, Ooi et al. 1989, Aref and Samet 1991) and Integrated architectures (Dayal et al. 1987). The latter represented a crucial instant in the development of spatial database architectures and resulted in several Spatial Database Management Systems (SDMS) such as PROBE (Orenstein 1986,

This work was supported by the Technical University of Madrid (Universidad Politécnica de Madrid), under grant ref.CH/056/2008, and partially supported by the UPM Training and Mobility of Researchers Programme (Resolutions 23/02/2011 – 28/06/2012). The authors wish to thank the Mercator Research Group for its dedicated support as well as the support of the projects TIN2016-78011-C4-3-R (AEI/FEDER, UE), TIN2013-46238-C4-4-R, and DGA-FSE. Willington Siabato was a research visitor at the Naval Academy Research Institute (IRENav), where he developed a large part of this survey. The authors thank all the anonymous reviewers and the editor for their valuable, detailed comments on the initial manuscript. We apologize to authors not included in this survey. Author’s addresses: W. Siabato, Universidad Nacional de Colombia, Sede Bogotá, Department of Geography, Carrera 30 No. 45-03 Edificio 212 Ofc. 323, Bogotá D.C., P.C. 111321 – Colombia; Universidad Politécnica de Madrid, School of Topography, Geodesy and Cartography, [email protected]; C. Claramunt, Naval Academy Research Institute, Lanveóc-Poulmic, France, [email protected]; S. Ilarri, University of Zaragoza, I3A, Department of Computer Science and Systems Engineering, [email protected]. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. To copy otherwise, distribute, republish, or post, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2017 ACM. 123-4567-24-567/08/06.$15.00

DOI: 10.1145/**********

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Orenstein and Manola 1988) and POSTGRES (Stonebraker and Rowe 1986). A comprehensive introduction and review of the state of the art of the evolution of spatial databases is available in Güting (1994); a previous overview of research issues in spatial databases was performed by Günther and Buchmann (1990).

Formal studies of the temporal aspects of both non-spatial and spatial systems can be found since the early 1980s (Allen 1983, Clifford and Warren 1983, Ariav 1986, Rolland et al. 1987, Snodgrass 1987, Armstrong 1988) (see Figure 1). Nonetheless, time as a research subject has been specifically studied long before in other fields, such as natural language processing (Bull 1960), information systems (Langefors 1966), logic (Prior 1967, McArthur 1976), artificial intelligence (AI) (Allen 1983, Allen 1984), and Temporal Information Retrieval (Campos et al. 2015). Worboys (2005) indicates the existence of formal studies of time even since Hamilton (1837) concerning the algebraic theory conjugate functions. Despite initial academic attempts to include time in database systems (Brooks 1956), the earliest studies in which the time variable was considered for information processing, although not formally defined, were the ones proposed by Langefors and Sundgren (1975) and Wiederhold et al. (1975). An early review of the use of time in information processing systems is available in Bolour et al. (1982).

Figure 1. Milestones in the development of T-GIS

On the other hand, it is widely recognized that the first landmark project related to geographic information systems (GIS) is the early Canada Geographic Information System (Tomlinson 1967). Meanwhile, another important milestone in the development of GIS is a series of developments made at the Harvard Laboratory still

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in the 1960s. This lab has been pioneer in the implementation of several GIS software packages such as SYMAP (Robertson 1967) and POLYVRT (see Peucker and Chrisman 1975) and in the design of geographical data structures and formats such as TIGER and DIME (Chrisman 1988). These spatial data structures played a significant role that enforced layered architectures in GIS databases and extended their impacts on temporal GIS development. A description of initial cartographic data structures is available in Peucker and Chrisman (1975).

The integration of time in GIS has been an important research subject since the late 1980s and still continues to be developed. In an early work, Donna J. Peuquet (1984) presented a taxonomy and an in-depth study of spatial data models and also mentioned the importance of time in spatial and geographic information systems. Regarding the integration of the time dimension, she concluded that “it is the one area currently identified in spatial data models and computer spatial data handling where we have barely scratched the surface.” (Peuquet 1984, p. 110). However, it was Langran and Chrisman (1988) who introduced, for the first time, some initial concepts for the temporal GIS (T-GIS) research field. If one considers that several proposals have been published during approximately the last 30 years (Langran 1988, Peuquet 1988, Delafontaine et al. 2011, Del Mondo et al. 2013, Ferreira et al. 2014, Zhu et al. 2017), this means that the GIS research field has considered the modelling and integration of temporal aspects about half the time of its lifespan and development. Figure 1 represents this fact.

How to represent time is a fundamental complex problem in temporal GIS. Three distinct types of time described originally by Snodgrass and Ahn (1985) became the de facto standard for defining time in temporal databases and information systems: valid-time (representing the time when an event occurs in the real world), transaction-time (representing the time when such event is recorded in a database), and user-time (for additional events registered by users). Most of the models described in this survey follow a linear, discrete, absolute temporal model, which must be assumed unless a different temporal model is explicitly stated.

Historically, the snapshot approach has often been the most common solution to manipulating and analysing spatio-temporal data in GIS, where temporal layers and spatio-temporal series are the data structures considered. Practically, the way geographic features change in space over time is not taken into account at the local level, and neither is the nature of the geographical processes that generate these changes; rather, changes are depicted at a global level not considering either related local factors or change of scale. This leads to several scientific questions such as those relating to the theoretical and modelling foundations upon which these components must be based. How can those modelling principles support successful implementations and convincing applications?

The goal of this article is to provide a broad historical overview of T-GIS, analysing the state of the art and identifying contributions from relevant related topics. Although it is grounded on the T-GIS research field, the intrinsic nature of data and processes in that field is complexity, a characteristic that has an impact on diverse disciplines. Therefore, this survey shows how other fields have contributed in various ways, addressed such characteristic from different perspectives, and are currently defining a new path determining the latest trends in temporal and spatio-temporal aspects in GIScience (geographic information science); among those influencing fields, the areas of artificial intelligence and temporal logic can be particularly highlighted. We identify the actual and respective achievements of those different disciplines in the field of T-GIS, and how together they have made a coherent contribution. We also describe significant milestones and landmarks that have made T-GIS an independent research subject. Chiefly, we present a description of relevant spatio-temporal models proposed over the past three decades. The article is also intended to identify the dominant modelling trends and discuss the next research challenges in T-GIS.

1.1 Literature Covered in this Survey

This survey mainly covers research on T-GIS performed during the last three decades. The surveyed literature is classified considering the scientific disciplines described in Appendix A.1 (see Figure A) and the following criteria: The different areas that have made some valuable contributions to T-GIS and including them in the four

main disciplines identified.

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Considering the theoretical models on which each proposal is based, i.e., location-based, semantic-based, feature-based, event-based, process-based, identity-based, object-oriented, ontology-driven, graph-based, lifespan-based, agent-based and based on moving objects.

The selected approaches discussed in this article are amongst the most representative because they show key

developments for spatio-temporal modelling, and temporal modelling and reasoning. In addition, the approaches described reflect in a way the evolution of this research subject starting from its early-1960s foundations to today's conceptual modelling formalisms across the multidisciplinary areas that have made relevant contributions.

To make this survey reasonably self-contained and comprehensive, we have included early and modern perspectives to illustrate the evolution of T-GIS. This article and the online appendix offer an extended description of the topics surveyed and a large number of references. As a result, one could read this review from three different perspectives: (i) origins and historical evolution of T-GIS; (ii) development of the spatio-temporal models; and (iii) future trends and developments in T-GIS. Although these views are well-aligned and complement each other, making a single body article, they also provide a detailed description of each topic by themselves. Figure 2 represents a conceptual map that serves as the thread of the survey. Appendix F.5 describes the bibliographic sources on which this survey is based.

Figure 2. Conceptual map of the survey. Connection of the concepts described in the article and the online appendix

In the remainder of this article, Section 2 provides a detailed analysis of the different spatio-temporal models. Section 3 compares the surveyed modelling approaches and provides a classification for the identified spatio-temporal modelling trends. Finally, Section 4 collects conclusions and future research trends. Besides, several



electronic appendices, that provide relevant complementary information and detailed descriptions of other modelling approaches, complete the survey.

2. SPATIO-TEMPORAL MODELS

This section outlines the fundamental aspects of several spatio-temporal data models proposed during the late 1980s, the 1990s, and the 2000s, as well as some of the latest approaches that have arisen during the current decade. Some of them are theoretical models; others are grounded upon specific case studies that have dealt with the evolution of spatial objects over time applied to specific scenarios, such as land use evolution, wildfire growth, or road network reconfiguration. First, a classification of spatio-temporal modelling trends is presented in Section 2.1, and then a set of representative spatio-temporal modelling proposals are described in the subsequent subsections. This section is complemented by Appendix D and Appendix E, which include a description of other relevant spatio-temporal proposals and provide additional details of the ones discussed.

In addition, Appendix A and Appendix B describe in detail the context and characteristics of this survey. They present (i) a review of the scientific disciplines related to T-GIS; (ii) a complementary overview of the literature covered herein; (iii) fundamental ideas that support the concept of T-GIS; and (iv) related works.

2.1 Categorization of Spatio-temporal Modelling Trends

Over the past years several spatio-temporal models have been proposed (see Peuquet 2001, Pelekis et al. 2004). They can be classified by considering their theoretical approach; Table 1 presents different modelling methodologies that have arisen in the last three decades. These approaches are intended to describe the dynamic nature of geographic phenomena through five dimensions: events, processes, movement, actions, and dynamic objects. According to Yuan (1994), the snapshot method, time-stamping, the approach by using base state amendment vectors, the space-time composite model, and the domain-based models could be generalized and classified as location-based models, also called by other authors version-based approaches (e.g., Halls et al. 1999) or changed-based approaches (e.g., Yuan and Stewart Hornsby 2008). Table E, in Appendix D.1, lists most of the spatio-temporal models developed for each modelling approach.

Table 1. Classification of spatio-temporal modelling trends by the key conceptual element

Modelling approach Modelling approach Modelling approach

Snapshot method * Semantic–based Moving Objects Time-stamping * Event–based Graphs–based Base state amendment vectors * Process–based Lifespan–based Space–time composite model * Ontology-based Agents–based Domain–based modelling * Feature–based (Entity-based) Kinematics Object–Oriented Identity–based Ontological foundations Conceptual modelling extensions

* location-based models / changed-based approaches A full version of this table is available in Appendix D.1, Table E

Different classifications have been proposed for spatio-temporal models. Yuan and Stewart Hornsby (2008)

advocate distinguishing approaches based on the origin of change and propose six classes: time-stamped; event-based; changed-based; process-based; movement-based; and activity-based. Another alternative differentiates between the object–based and the field–based modelling approaches, classifying the proposals according to their underlying (i) raster (e.g., Peuquet and Duan 1995, Sengupta and Yan 2004) and (ii) vector (e.g., Claramunt and Thériault 1996, Choi et al. 2008) data structures; considering (iii) hybrid approaches (e.g., Tryfona and Jensen 1999, Galton 2004, McIntosh and Yuan 2005b, Liu et al. 2008); or being (iv) generic enough to support both

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raster and vector data structures (e.g., Armstrong 1988). The SNAP/SPAN ontology introduced by Grenon and Smith (2004) offers a solid conceptual foundation that emphasizes the existing dichotomy between objects and fields, as well as the concepts of snapshot, change, and process. Worboys (2005) presented a “brief history of time”, which represents a summary of the evolution of time in GIS. He describes four main phases in the development of spatio-temporal information systems: “static GIS, temporal snapshots, object change, and events and actions”. Nowadays, it would be necessary to add a fifth stage: intelligent agent systems (see Appendix D.3.1 for further description). El-Geresy et al. (2002) propose five categories by considering conceptual modelling aspects: (i) location-based, (ii) object or feature-based, (iii) event-based, (iv) functional or behavioural, and (v) causal approaches. Bothwell and Yuan (2011, p. 153) claim that “six descriptors are needed to adequately describe object spatio-temporal dynamics”: location, extent, attribute, movement, mutation, and evolution. Nonetheless, for the purposes of this survey the classification proposed in Table 1 is followed; highlighting the most relevant contributions and presenting a chronological evolution of both the modelling approaches and trends. Since some proposals are related to different modelling approaches, they have been classified in the dominant approach; Table 8 in Section 3, however, shows the various approaches to which each model is related.

2.2 T-GIS Early Models and Proposals

During the 1980s, in a domain closely related to T-GIS, several early proposals were made in order to incorporate temporal data in relational databases, e.g., time-stamping tables (Gadia and Vaishnav 1985, Gadia 1988), time-stamping tuples (Snodgrass and Ahn 1985, Snodgrass and Ahn 1986), and time-stamping cells (Gadia and Yeung 1988). These database models clearly influenced the development of early T-GIS proposals. Tables were replicated as time-stamped layers, e.g., the snapshot model (Armstrong 1988); tuples (rows) as time-stamped attributes (columns), e.g., the space-time composite model (Langran and Chrisman 1988); and cells as spatio-temporal objects, e.g., the spatio-temporal object model (Worboys 1994a).

A complete description of these early models, as well as other foundational proposals, is available in Appendix D. The snapshot method, the base state amendment vectors approach, the space-time composite model, the time-stamping ST method, the triad framework, as well as other trends regarding the snapshot approach are described in Appendices D.1 and D.2.

2.3 Domain-Based Models

Yuan’s Three-Domain Model (TDM) (Yuan 1994, 1997, 1999) represents spatial, temporal, and semantic objects, and provides references amongst them to describe geographic processes and phenomena. This three-domain representation, developed in the context of wildfire studies, is defined as a normalization of three previous modelling proposals: the space-time composite model; the snapshot model; and the initial stages of the spatio-temporal object model (time-stamped ST Objects, Worboys 1992a,b). In this sense, this proposal inherits part of the characteristics and strengths of the location-based models (see Section 2.2). As the author states, “the three-domain representation is a normalization” of the location-based models because it “eliminates repetitive data records in spatial attribute tables … by only using a single attribute record for separated locations with common properties.” (Yuan 1999, p. 148). Nevertheless, it goes one step further regarding the utility that spatio-temporal systems can bring to users through GIS in considering queries about attributes, locations, spatial features and relationships, as well as time and temporal features and relationships.

Yuan identifies a set of the minimum spatio-temporal queries that any spatio-temporal system should answer: simple and range queries. While simple queries consider instants, range queries consider periods. The three-domain model is proposed as a modelling approach to answering such queries; it focuses on the functionality of the model in actual systems through the implementation of the three-domain framework.

The improvement of this model is its capacity to manage change in the three modelling components. This characteristic represents a significant enhancement over existing models that manage either the time or the location. It considers the time as a temporal object rather than an attribute. Semantic changes “include variations



in attributes over time and the static spatial distribution of a geographic phenomenon.” (Pelekis et al. 2004, p. 246). Spatial variations may be static (looking at changes in a snapshot) or transitional (comparing “states of an event or a process at different [locations] through entity snapshots.” (Yuan 1996, p. 27). Changes are either the movement of an entity or mutations of an entity that is spatially fixed. Time is modelled as an independent domain instead of being a location’s attribute, unlike the snapshot model (see Appendix D.2.1), or a part of spatial entities, like in the case of the space-time composites and spatio-temporal objects (Yuan 1996). The model supports valid–time and transaction–time, and time can be represented in both absolute and relative terms. Besides, it is able to represent the six types of spatio-temporal changes and analysis defined by Yuan (1997); for further details see Table D in Appendix B.3. The dynamic nature of the three-domain framework is a remarkable difference of this proposal and its supporting models.

2.4 Event-Based Modelling

While time-stamping approaches focus on the idea of change to enhance spatial data with temporal components, event-oriented approaches “focus on the dynamic happening as a whole, and not just the time of the event.” (Yuan and Stewart Hornsby 2008, p. 38). When there is a change, a time-stamp marks the time of the change; the event-based approach, however, allows the distinction of event attributes and relations besides object attributes and relations (Yuan and Stewart Hornsby 2008). This section presents some of the most representative event–based modelling approaches.

Several academic discussions exist about the definitions of processes and events and their differences. It is not clear where the former finish and the latter begin. There is no single or exclusive relationship between them; depending on the phenomena modelled their nature changes. Galton and Worboys (2005), Yuan and Stewart Hornsby (2008), Yuan (2001), Claramunt and Thériault (1995) and Yuan (2008) have provided valuable discussion as to these conceptual elements. Some definitions seem to be contradictory. According to Galton and Worboys (2005, p. 48), there is a general consensus that the “key concepts required for the modelling of dynamic phenomena include object, state, process and event”, but how these should be defined is not so clear: Galton and Worboys (2005) state that while objects and processes can experience change and such changes

can be described as multiple states, an event does not experience change. An event is by definition an episode of history finished, that does not experience changes after being; the event appears in time and can subsequently appear in another point in time as a subsequent event, but different from the previous one.

Yuan and Stewart Hornsby (2008) offer a conceptualization quite aligned with Galton’s (see Table A in Appendix A.2). In contrast, Yuan (2001) asserts that an event is a spatio-temporal aggregate of its corresponding processes, and a process is a sequential change of states in space and time. While events operate at the coarsest spatial and temporal resolution, states have the finest resolutions.

Despite the differences in meaning, both Yuan and Galton agree that a process involves different states. Claramunt and Thériault (1995) also consider a process as the aggregation of changes that are related or produced simultaneously; they state that processes can be defined naturally through changes and events. An event can be represented as a set of processes that modify entities. In addition, they consider as a key element the definition of the temporal scale; the chronon is the minimum unit for establishing such scale. Since an event can be seen as a process depending on the granularity of modelling, it is not possible to define a hard boundary between such concepts. As Worboys (2005, p. 3) states, “one person’s process is another’s event, and vice versa”. This discussion can be even deeper when considering more general concepts such as continuants and occurrents. Ultimately, as Yuan (2008, p. 178) asserts, “events and processes are central to the understanding of geographic worlds. They constitute information of interest to many, and perhaps, the majority of applications and scientific inquiries”. Despite the blurred definitions, a large number of spatio-temporal models considering events and processes have been proposed.

Time-based analysis of spatio-temporal data. Peuquet and Wentz (1994) proposed an initial approach for a time-based analysis of spatio-temporal data. The model was defined as a complement to the object-based and location-based analysis approaches because of their natural restrictions to temporal representations and temporal

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querying capabilities. Starting from an initial state, called the base map, events are recorded in increasing order of their occurrence, with each event linked to a list of changes experienced since the event vector was last updated. To avoid data redundancy, the changes can be recorded based on the differences from previous versions. If changes are extensive to the whole mapped area, “the full map may be registered.” (Pelekis et al. 2004, p. 244). This proposal was validated by a prototype, TEMPEST (Edsall and Peuquet 1997), that incorporated the time-based data model and the corresponding relational operators.

TEMPEST implemented the triad conceptualization (see Appendix D.2.1): where (location-based), when (time-based), and what (object-based), and provided the first temporal analytical capabilities in a GIS software. This prototype also demonstrated the feasibility of the triad framework. In contrast to the amendment vector approach (see Appendix D.2.1), which also stores a base map and considers incremental object changes but restricts searching to location, TEMPEST was defined around a timeline instead of a location, which increased the performance of temporal data queries, considering not only where but also when change occurs.

Event Oriented Spatio-Temporal Data Model (ESTDM). In a follow-up work, Peuquet and Duan (1995) introduced the ESTDM, a raster-based event-oriented proposal that has shown its efficiency in supporting spatial and temporal queries. It represents information about changes at pre-defined cells. It stores changes regarding an initial state (represented by a base map) rather than a snapshot of an instance. Basically, (i) a base map represents the initial condition; (ii) “it groups time-stamped layers to show observations of a single event in a temporal sequence” (Pelekis et al. 2004, p. 244); (iii) a header file stores the temporal sequence of events when there are changes; and (iv) a set of components encodes the locations where changes occur and the attribute values at the time of the event. The authors define an ESTseries (i.e., an Event-based SpatioTemporal series) as a “single ESTDM-formatted file that represents the spatio-temporal dynamics of a single thematic domain for a specific geographic area, equivalent to a single thematic map layer.” (Peuquet and Duan 1995, p. 15).

According to the authors, the most significant capabilities of ESTDM in GIS are the possibility to perform temporal data manipulations (e.g., temporal scale change) and sequential time-based comparisons. However, the ESTDM does not maintain the object’s identity beyond the initial location, and therefore it cannot “represent its discrete object properties, such as moving, splitting, merging, and incarnation.” (Yuan 2001, p. 85). This results in an obvious behaviour, since the model is focused on fields rather than objects: the evolution is focused on continuous, extended, general areas rather than specific objects and their properties.

Hybrid Spatio-Temporal Data Model and Structure (HST-DMS). The HST-DMS (Sengupta and Yan 2004) presented a significant improvement on the ESTDM regarding searching efficiency and data storage in very large databases. Querying improvements are based on the storage of based maps, change maps and complement maps at the time of each event. The base map “only stores those elements that never change through the entire time period represented by the event list.” (Sengupta and Yan 2004, p. 357). The “change map for an event” only stores changes since the previous event, which is similar to the sequence of events managed in ESTDM. On the other hand, the complement map stores additional changes from the change map instant to a “past time step”. The base, change, and the complement maps are associated with equal starting instants.

HST-DMS solves the problem of object identity (a single identity disappears across changes avoiding change tracking), and it can build a snapshot for a given time period ti without the need to visit all the time nodes starting from the base map. The authors report that the “data model requires significant processing when a new time step is added to existing information. To creating a new change map and complement map for the added time step, a new base map and starting complement map will also have to be created.” (p. 357). This limitation can be omitted if one considers the processing capabilities available nowadays. Both ESTDM and HST-DMS manage implicit spatial and explicit temporal topology. The models have proved to be efficient in raster data scenarios; however, they are limited to valid–time.

Event-oriented approach based on extended-versioning. Claramunt and Thériault (1995) proposed an event-oriented approach for the management of time in GIS which relies on two complementary phases: (i) defining a suitable conceptual model by identifying the spatio-temporal processes and the related spatio-temporal operators; and (ii) designing the corresponding logical architecture. The proposed model is based on an extension of the versioning concept, the extended-versioning, defined as “a mechanism for recording the history



of the database and for describing successive events in the real world.” (Claramunt and Thériault 1995, p. 24). Considering that processes can be naturally defined through changes and events, the authors based their approach on the modelling of processes and the changes involved. According to their nature, processes are divided into three categories: basic (appearance, disappearance, spatial stability), transformation (expansion, contraction, deformation), and movement (displacement, rotation). As usual, geographic phenomena are represented by the three main domains (thematic, spatial, and temporal), each of them recorded in an independent table (the attribute, the version, and the spatial tables, respectively) every time a change occurs. Changes are recorded in three versioning tables, i.e., past, present, and future. Each table is related to both the attributes and the spatial component. When there is a spatial or thematic change, a new version is added to the versioning tables; thus, the evolution of entities is recorded for attributes and geometries at any time.

This model was “the first successful attempt to record the individual descriptive characteristics of dynamic objects.” (Pelekis et al. 2004, p. 248). The incorporation of indexes based on binary trees, such as the B+Tree value-oriented index (Comer 1979) for the current version table and a multi-dimensional R-Tree (Guttman 1984) for previous and future tables, improves the performance when querying and retrieving the different states of each element.

Temporal logic-based approach. From a temporal logic perspective, Eric Allen et al. (1995) presented a generic model to represent causal links related to events in a spatio-temporal GIS, a qualitative causal modelling in T-GIS. The causal theory compounds elements and relations that are presented via a conceptual data model using an extended entity-relation formalism based on MODUL-R (Caron et al. 1993). These elements include four entities (i.e., objects, events, agents, and conditions) and three relations (i.e., produces, is part of, and conditions). Both objects and events may have spatial representations, and all entities may have temporal representations. Based on Bunge’s (1966) theory of causality and Kowalski and Sergot's (1986) event calculus, the authors propose a model that explicitly deals with spatial and temporal phenomena; they state that “no existing temporal logic yet deals adequately with spatial relations.” (Allen et al. 1995, p. 410). In general, the authors adapted Bunge's theory to a theory of events. This model emphasizes that the data structure must be accessible for efficient analysis. As Peuquet (2002) suggests, the authors also consider that causal relations must be explicitly represented within the database if one needs to retrieve them for analysis. The explicit representation of events in the database is not difficult since they can be treated as any other object.

The resulting model provides tools for analysing historical scenarios and for understanding the current status of a region as a function of causal dependencies in the past. However, there is some ambiguity in the treatment of causality and dependence. In addition, the issue of obtaining or inferring causal connections between events is not addressed.

Pure event-oriented theory of space and time. Defined as a step forward from the object-oriented concepts developed in Worboys et al. (1990b) and Worboys (1994b), Worboys (2005) presents a new event-based model to describe geographic phenomena. He developed what he defines as a “pure event-oriented theory of space and time”. He asserts that it is necessary to model world observations not just as singular data collections but also as complex entities containing identity, internal structure and behaviour, and with capabilities to relate them to other entities and integrating in the environment in which they are included. He also states that a fully event-oriented framework should allow one “to move on from simple snapshot queries of the form ‘What happened at this location at this time?’ to a much richer language involving the interplay between object and events, and event–event relationships.” (Worboys 2005, p. 9). Thus, he argues that a breakthrough in the computer modelling of geographic phenomena will arise thanks to switching from an object-oriented view of the world to an event-oriented perspective. Defining a four-stage classification in the progression of spatio-temporal information systems (Static GIS, Temporal snapshots, and Events and actions) in which the author describes the basic elements, advantages, and problems of each approach, he concludes how “the final stage in this evolution is a full-blooded treatment of change, in terms of events and actions.” (p. 7). Worboys considers a division of world entities into continuants, “that endure through time” (e.g., houses and people), and occurrents, “that happen or occur and are then gone” (e.g., dinners and house repair jobs). His approach is, therefore, classified into the SPAN modelling ontology (see Grenon and Smith 2004).

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For the formalization of the model, Worboys considers temporal structures of precedent works (tense and temporal logics, situation calculus, event calculus, interval temporal logic) and shows why the use of algebraic theories produces better results than logic-based approaches to defining a formal model of concurrent occurrences. Concurrency and interaction are the basic operations with which this model describes dynamic complex processes. Several processes are concurrent if they occur in the same time period. Two processes interact if their input and output actions (complementary pair) can be matched. The tick atom describes the temporal component, defining time as a sequence of ticks. The location describes the spatial component as “a connected region, partitioned into a set of blocks.” (p. 18). The final component is a spatio-temporal entity (ST-entity) through which the dynamic nature of the world is represented by using structured collections of ST-entities.

The advantages of the model and its formalization are described in a case study representing the movement of a vehicle along a route that goes through a specific spatial region. Three temporal states (ticks) and five locations are considered, modelled as Clock3 and Region5, respectively. The movement system is defined as Motion = Vehicle|Clock3|Region5. The solution of the system demonstrates how the basic elements are applied and illustrates the spatio-temporal dynamics of the analysed phenomenon, e.g., the interactions of the vehicle at different instants (ticks) in some position in space (location).

This work is undoubtedly an evolution in the taxonomy of spatio-temporal models. The proposal shows how spatio-temporally extended process calculi is a powerful tool to represent the dynamics of geographic phenomena. The fact that the model is based on general mathematical theories and constructs guarantees the developed concepts as being general and computationally implementable. However, as the author asserts, this theory “needs to be scaled up to work with full-scale occurrents [processes] in the world.” (Worboys 2005, p. 26). The model considers a discrete viewpoint of reality, so continuous representations are beyond its scope. The proposal also lacks the possibility of multiple temporal granularities for describing phenomena. A significant advantage of this proposal is that geographic happenings (occurrents) and interactions are modelled considering their significance, i.e., by explicitly considering their semantics.

Geospatial Event Model (GEM). In a follow-up work, based on the conclusions of Worboys (2005), Worboys and Hornsby (2004) proposed the Geospatial Event Model (GEM). Since objects and events are “needed to model fully a dynamic system” (p. 328), the authors adopt a hybrid approach considering “three basic entity types: geospatial object, geospatial event, and geospatial setting (geo-settings).” (p. 339). A geo-setting is defined as “the distinguishing characteristic of a geospatial entity” (p. 328), and therefore one could have geo-settings for both objects and events. It could be purely spatial, purely temporal (instant, interval, or period —defined as a composition of intervals—), or mixed spatio-temporal (trajectories, histories, or geospatial lifelines). The mixed spatio-temporal setting is considered as a function from the temporal to spatial settings. A unique characteristic of the model is that it does not allow combinations of the three kinds of settings in relationships; for instance, a spatial setting cannot be mixed with a temporal setting.

In essence, the model is described as follows: (i) the events are modelled “as instances or classes”; (ii) events (like objects) can have “attributes describing their properties”; (iii) “classes of both objects and events may be arranged in a hierarchy” (p. 333); and (iv) objects and events can be “aggregated into composite entities, and decomposed into parts”, i.e., spatial parts in the case of objects, and temporal or spatio-temporal parts in the case of events. Regarding the existing relations, situation corresponds to the geographic location of events and objects. “The static geospatial object model is timeless and the settings in which geospatial events are situated are spatio-temporal.” (Worboys and Hornsby 2004, p. 333).

The model considers four event-event and five object-event relationships (see Table 2). The latter represent the mutual dependency of objects and events: objects need an event occurrence to exist, and objects provide meaning to events. The participation and involvement relationships represent that objects take part in events and events imply objects (Grenon and Smith 2004).

The authors also consider an extension of the Unified Modelling Language (UML) (Booch et al. 1999) class diagram to make a distinction amongst different types of classes, particularly between the object class and the event class. The GEM provides a general approach to modelling dynamic geospatial domains by considering



changes in objects, the events that produced such changes, and the definition of possible dependency relationships between them.

Table 2. Event-event and object-event relationships defined by Worboys and Hornsby (2004)

Relation Description Geospatial event-event relationships Initiation The occurrence of event A starts event B. Perpetuation/facilitation The occurrence of event A influences positively the beginning or

continuation of event B. Hindrance/blocking The occurrence of event A influences positively the weakening, pause, or

finalization of event B. Termination The occurrence of event A allows or causes event B to finish. Geospatial object-event relationships Creation An event that results in the creation of an object. Sustaining in being An event that results in the continuation in existence of an object. Reinforcement/degradation An event that influences positively/negatively the existence of an object. Destruction An event that results in the destruction of an object. Splitting/merging An event that creates/eliminates a boundary between objects.

Although an extension to UML (Booch et al. 1999) is proposed, it does not go far beyond a diagram

specification and it does not consider strong concepts such as the ones presented in the extensions of conceptual-modelling approaches (see Section 2.10). The proposal considers a basic, theoretical case study which shows how to apply the modelling concepts; however, it is not possible to evaluate its feasibility, since no implementations are reported. In spite of this, the example shows how the GEM adds, as a new characteristic, further clarification of the object-event relationships.

Event-based query framework. Supported upon the dynamic time warping (DTW) similarity method, McIntosh and Yuan (2005a,b) introduced an event-based query framework, along with a set of six indices (change indicators, such as elongation, growth, etc.) of static and dynamic measures that quantify the characterization and similarity of geographic events (see Table 3). As discussed above, the comparison of snapshot pairs considers only changes between two time instants rather than the life cycle of an event; this proposal applies a method to identify such a life cycle. Since the DTW method measures the similarity between sequences which could vary in time or speed, varying events of all natures can be analysed. This proposal presents a novel method that measures changes in fields using objects as an intermediary stage, i.e., areas of interest from fields (continuous areas) are converted into objects in order to apply the six proposed indices and show how events evolve and interact.

Table 3. Indices proposed by McIntosh and Yuan (2005a,b) to characterize objects and relationships

Static Indices For objects Elongation … of the best ellipsoidal approximation of the object. Orientation … of the major axis relative to the movement direction. For object relationships Distribution … of objects considering a measure of clustering. Dynamic Indices For objects Growth Percentage of growing. Granularity Scale of change in the conceptual object’s surface. For object relationships Relative

Movement A measure of speed variation amongst the conceptual objects over distance and time.



While some spatial models, namely the ESTDM, are able to track changes in individual cells, events

represented in raster data are usually related to more than one cell. The authors indicate that with GIS technology it is not possible to associate and summarize cells that jointly correspond to changes caused by a geographic event. They propose, as a possible solution, to identify interesting cells as features and to represent those features explicitly as data objects. In brief, the proposal comprises four steps: (i) to extract features as the footprints of a geographic event; (ii) to store the features as vector objects (each consisting of a field that encodes the spatial change captured by raster data); (iii) to link these vector objects temporally using a linear model; and (iv) to reference the vector objects back to the corresponding cells in the original images.

The same feature can be drawn on multiple and sequential snapshots resulting in a collection of objects that represents how the geographic entity evolves in space and time. Querying the resulting change patterns is achieved “by comparing the temporal sequence of features by characterizing vector objects and their embedded fields.” (McIntosh and Yuan 2005b, p. 226). The six indices quantify the characteristics of objects and fields. The measurement of similarity is based on three assumptions: (i) meaningful features identified from raster data in a temporal sequence (i.e., the identification of conceptual objects) represents the development of geographic entities; (ii) the behaviour of conceptual objects describes the progression of a geographic event; and (iii) temporal sequences of indices that measure the behaviour of conceptual objects can quantify the evolution of an event.

The static indices portray the current state of the object and its relationships, in addition to providing a baseline for the dynamic descriptions. In turn, a temporal sequence of static indices provides historic data representing the changes produced in space and time. In essence, according to the authors, “… the shorter the distance between two events in the measurement space of the indices, the higher the degree of similarity.” (p. 227).

Although the DTW algorithm is computationally intensive, the contemporary processing capabilities make it viable when computing large sequences to measure and identify changes. However, a significant limitation of this proposal is the indeterminacy of the delimitation of a phenomenon’s boundary when extracting the objects from the field; there is uncertainty in the real boundary of the phenomenon and slight changes in incompatibility for the attributes as for the pixels defining the borders of the fields (raster values intersected by an object). This uncertainty also impacts on the topological relationships amongst different delimited features; such relations will change according to the way in which the boundaries have been delimited. The Geo-atom model (Goodchild et al. 2007), further described in Section 2.7, could act as a complementary model to this proposal since the geo-objects (aggregations of geo-atoms according to rules defined in the values) could be an alternative to the aggregation concept. Moreover, the integration of the two models would support the management of both events and processes simultaneously.

Continuous spatial change in an event-oriented discrete spatio-temporal framework. Worboys and Duckham (2006) tackled the problem of modelling continuous spatial change in an event-oriented discrete spatio-temporal framework. The authors show how the proposed framework can be used to detect conventional spatial events (e.g., merging, splitting, stasis, movement, and hole formation and disappearance). The proposal is based on a triangulation of the analysed surface. Combinatorial maps and triangulations are the key elements for analysing spatial structures evolving in a two-dimensional Euclidean space. The evolution is based on the principle that triangulations can evolve through time, modelling space like a spatio-temporal scalar field function (f : T(SD)), i.e., for each time instant T, there is a spatial change S of values from D (the value domain). Continuity and incremental change determine the evolution of the triangulated network over which geographic phenomena changes are represented.

A couple of properties guarantee the continuity of the surface. Firstly, in strong connectedness, there is a path between two vertices in such a way that every point in the path, except maybe the beginning and end points, can be surrounded by or enclosed within an open set entirely contained within a defined region R. Secondly, with weak connectedness, on the other hand, this condition is not satisfied. Computationally, to determine whether or not a triangulated region R is connected, the underlying graphs contained in R must be considered; for instance, by applying a standard breadth-first search.



The way in which the network continuously evolves constrains the representation of the event at a specific instant, i.e., the representation of the evolving event depends on the incremental evolution of the triangulated network. To control the evolution of the network, a collection of transition rules and conceptual neighbourhood definitions are considered. The transition rules are combinations of (constraining or not) insertions and deletions to occur at the boundary (subject to preserving or not regularity). The neighbourhood definitions depend on the established rules; they determine the adjacency relations between the evolving triangles of the network. The application of the transition rules and the neighbourhood definitions determines the changes (e.g., movement, contraction, expansion, or splitting) of an event.

Worboys and Duckham (2006) offer a computational model of spatio-temporal data that supports the representation and querying of events in regions. The authors suggest that the model has particular relevance in scenarios in which data are derived from sensor networks, for instance in environmental monitoring. A significant advantage of this proposal is that it offers a comprehensive modelling option for analysing and modelling the continuous change of geographic phenomena. Since the delimitation of the boundary of the modelled phenomenon depends on the density of the triangulated network, it would be necessary to adopt a fine-grained network in order to reduce significantly the spatial imprecision and the corresponding edge effects. While the proposed model assumes a triangulation of the surface to control the evolution of the events, it could be generalized in order to support, as a spatial framework, any planar tessellation.

2.5 Graph-Based Modelling

While the graph-based modelling approach seems to have been put aside during the 2000s, the current decade shows an active interest in this approach. The simplicity of defining relationships amongst geographic entities and the representation of their evolution results in significant flexibility for the representation of changes, movement, and events, which in turn allows the integration of graphs with other modelling trends. For instance, it might be possible to complement the graph-based approach to model events and processes by following the principles that rule Petri nets (Murata 1989). Graph-based modelling approaches proposed during the last years are the following.

History Graph Model. Although Yuan’s three-domain model uses a graph to represent the transitions amongst spatial objects at different locations, the first graph-based modelling approach, called the History Graph Model, was actually proposed by Renolen (1996). Its main purpose is to identify the different sorts of temporal behaviours and to handle objects and events. The model is intended to visualize the temporal element in order to reproduce the evolution of geographic information. The basic idea is that an object may be in a changing state, static state, or dead state. Each version of an object is identified by two timestamps that describe the time interval during which the state of the object is valid (i.e., alive). A transition is an entity that links versions of objects with their successors and/or predecessors. Two additional timestamps describe the period when the transition has taken place. Events are transitions of no duration, that characterize objects that change suddenly, while snapshots are versions with no duration, that represent intermediate states of objects that change continuously. The objects of a dataset can be characterized by a sequence of states and changes (Pelekis et al. 2004).

For representing the evolution of the objects, the model’s notation is based on Petri nets (Murata 1989). The object versions (static states) are represented with square boxes, whereas the transitions between versions (changing states) are denoted by boxes with rounded ends. Sudden changes are represented as circles. Both states and changes are linked to a time interval; the boxes are extended to represent the corresponding time interval (Renolen 2000). A dead object is denoted by a dashed square box. The arrows between states show successor-predecessor relationships between the origin and target state. Seven types of changes are considered: creation; reincarnation; destruction; alteration; merging/annexation; splitting/deduction; and re-allocation. A typology of processes was introduced earlier by Claramunt and Thériault (1996).

According to Pelekis et al. (2004, p. 249), “the primary application of a history graph is to describe a limited extent in time and space”. The authors also state that its advantage is that “temporal relationships can be derived directly and that time can be modelled both as discrete or continuous as well as absolute or relative”



and that it captures “all the knowledge we need in order to further develop a spatio-temporal system”. Furthermore, it captures the concepts of both movement and change and supports most spatio-temporal query types. The model expresses events such as “splitting and merging”, and can be extended to better characterize the duration of events. A restriction is that history graphs poorly describe the interaction between objects, e.g., split/deduction processes usually imply the creation of an additional object and the modification of another. In addition, there is not a defined method to determining all the processes and/or mutations: events are referenced to a given timeline and can only be queried one at a time.

Spatio-temporal graph-based model for two-dimensional regions. The graph-modelling approach has been reconsidered recently, as Del Mondo et al. (2013) have presented a discrete, spatio-temporal graph-based model oriented to the modelling of evolving two-dimensional regions. The authors introduce a formal approach for analysing “the consistency of relationships of evolving entities” through a spatio-temporal graph. This proposal is an extension of previous research (Del Mondo et al. 2010) in which the authors modelled the spatio-temporal interaction networks derived from the evolution of entities considering spatial relations, spatio-temporal relations, and temporal filiations (temporal data related to the events), which in turn allow the representation of spatial and temporal connections. They propose a spatio-temporal graph along with several operators for graph manipulation (graph intersection, graph union, and graph join). An extended-relational data model is used to represent a spatio-temporal graph and the associated integrity constraints. Thus, the model provides elements for verifying the consistency of the graphs and, by extension, data consistency. The spatio-temporal graph is defined “without making distinction between graphs with entities at a single time instant or at different time instants.” (Del Mondo et al. 2013, p. 61). This characteristic offers “a more general and homogenous definition of graphs”, enabling the specification of “subgraphs based on temporal criteria.” (p. 61).

The model supports connecting “entities at non-consecutive time instants” (p. 61), which leads to a more generic definition of “operations over spatio-temporal graphs.” (p. 62). At the conceptual level, entities (vertices) are associated by “spatial and filiation binary relations (edges).” (p. 61). The authors define four core elements for the formalization of the graph: a temporal domain, a collection of topological relations, a collection of filiation relations (called continuation and derivation), and a domain of temporal labels.

The model is implemented in a spatial database (PostgreSQL + PostGIS) using an extended relational model through a schema in which the entities, the relations between entities, and the filiation relations are represented. The filiation relations need to be explicitly stated considering that one of such relations cannot be inferred from the geometries but only from thematic correlation. The authors also consider that continuation relations are an exception, as they depend on the identifiers of the entities and can be obtained from the entity tables.

The authors formalize “integrity constraints for spatio-temporal databases” (p. 67), classifying them in two categories: model constraints should be fulfilled in most spatio-temporal databases (primary key, foreign key, filiation constraint), and semantic constraints enforce conditions on the filiation relations (expansion, contraction, split, separation, merge, and annexation) and are application-dependent. Two spatio-temporal semantic constraints are defined: identity-existence dependency (IED) and topological-filiation dependency (TFD). The whole set of constraints guarantees a logical evolving of the processes and their feasible storage in the database system. Satisfiability of integrity for the constraints is supported, e.g., does the set of constraints have internal contradictions?

The performed experimental results proved the feasibility of the proposal and high performance at the database level. The consistency and integrity of the constraints (satisfiability) is well supported and validated: the IED and TFD constraints provide databases with a reliable model capable of verifying the consistency of data and the derived evolving relationships. The proposal’s results are useful for checking the consistency of queries and for defining strategies for data cleaning based on the integrity constraints. A significant advantage of this proposal is that several query languages and strategies for query processing on graphs could be applied, thanks to the flexibility offered in the modelling of the graph. This characteristic increases the potential of the model through the integration of other graph formalisms; e.g., the use of LOREL (Abiteboul et al. 1997) could be of interest. Finally, depending on the application, users can define their own semantic constraints and operators on the graph.



2.6 Feature-Based Modelling

SSD-based approach. An approach focused on the use of semi-structured data (SSD) models for modelling dynamic geographic data is presented by Stefanakis (2003). The author indicates that the object exchange model (OEM) (Papakonstantinou et al. 1995), which was proposed to exchange semi-structured data between object-oriented databases, can be used and extended to represent the history of semi-structured geographic entities. Although semi-structured geographic data have some structure, it could be irregular and incomplete and not necessarily conform to a predefined schema (e.g., data are usually collected at multiple resolutions, consider complex thematic information, and are continuously updated while representing different scenarios). In this sense, the author states that other database modelling approaches, such as the object-oriented or the relational approaches, are not appropriate for modelling SSD. Thus, relying on the assumption that geographic entities are naturally semi-structured, the author extended his previous work (Stefanakis 2002) from map objects to geographic entities and created a database model for this kind of semi-structured data.

For the temporal component, the author took into account instant changes (valid–time) avoiding duration changes (changes that happen during a certain period); although the author justifies that instant changes fit many application domains, this assumption is in fact a shortcoming of his proposal. The model describes spatio-temporal changes enriching the temporal constructs defined in the History Graph Model (see Section 2.5) and the event-oriented approach of Claramunt and Thériault (see Section 2.4 – extended-versioning). The representation of the time dimension is based on the life-motion-succession scheme (LMS-scheme), i.e., the three elements that are concerned with changes of historical-spatio-temporal entities (see Table 4).

Considering that geographic entities have at least four dimensions (identity, spatial, thematic, and temporal), the author defines what he calls a minimal structure to manage semi-structured geographic entities. An OEM (Object Exchange Model) graph-like representation of the four dimensions of an entity is the key component in the model. With the spatial, thematic, and temporal definitions, the “recording of history” is achieved thanks to “the relationships established between entities involved in a temporal construct of type succession.” (Stefanakis 2003, p. 523). Although the model does not allow tracking the evolution of attributes with extreme accuracy, the thematic dimension allows it to relate the attributes to spatial components considering their variation in time.

Table 4. Temporal constraints in the LMS-Scheme (based on Stefanakis 2003)

Life Motion Succession Created Updated Evolves into Disaggregates

Destroyed Identifies to Fissions into Killed Spawns Fuses into Reincarnated Aggregates to

In order to demonstrate how the model works, Stefanakis defines a case study based on a cadastral scenario

in which a set of application domain queries to manage spatio-temporal geographic data were solved successfully. The flexibility that this proposal shows in supporting spatio-temporal queries is due to the use of the LOREL query language (Abiteboul et al. 1997) for retrieving information. However, complex spatio-temporal queries are not supported; the way in which the “recording history” is tracked (linking records up and down) does not allow querying spatio-temporal changes to take into account more than one temporal stage. This shortcoming obviously affects the general performance. The major restriction that arises from this model is the impossibility of recording duration changes, since the behaviour of a wide number of geographic entities in several domains is described by durations (periods) rather than instants. In contrast to the potentialities offered in Del Mondo et al. (2013), this model is not able to take the most from LOREL because of the rigidity of the graph.

Feature-Based Temporal Model (FBTM). By extending the key concepts of the spatio-temporal object (ST-object) developed in the Object-Oriented Spatio-Temporal Model (OOST) (Worboys 1992b, Worboys



1994a,b) (see Section 2.8) and the Three-Domain Model (TDM) (see Section 2.3), Choi et al. (2008) proposed the Feature-Based Temporal Model (FBTM) to “represent changes of both space and theme independently.” (p. 1). The authors consider three types of changes: (i) geometry changes over time “along with theme changes”; (ii) geometry changes over time “without theme changes”; and (iii) theme changes over time “without geometry changes”. In contrast to the TDM and OOST, the FBTM uses single-feature identifiers to associate space, theme, and time as opposed to a domain link table (the links between semantic, spatial, and temporal objects applied to the TDM) and enhances the “OOST-model by adding an object identifier for thematic changes.” (p. 5).

The model allows one to track the change history by maintaining persistent object identifiers for changes in space. To track the feature history and enhance the performance by removing the need to execute topological comparisons during the query processing, the authors have modified the ISO’s temporal schema (ISO 2002) and incorporated an explicit temporal relationship structure. The ISO’s temporal primitives (nodes and edges) are used to construct an explicit temporal relationship that allows storing the “temporal topology and the types of changes for spatial and thematic queries over time.” (Choi et al. 2008, p. 5). Specifically, “seven types of temporal relationships” are defined (see Table 5). This model has limitations to capture continuous changes; discrete changes of features are modelled using linear time. The implemented prototype shows the feasibility of the proposal and the case study (land use) demonstrates the querying performance.

Table 5. Temporal relationships with time primitives (Choi et al. 2008)

Temporal relationship Case

Time primitives Relationship value (temporal edge value) From node Begin Newly created feature From node Begin_replaced Newly created but separated from existing

feature Edge Was a (Space) (Theme) No changes in both geometry and theme Edge Changed (Space only) Change only in geometry

Edge Changed (Theme1) (Theme2)... Change only in themes Edge Changed (Space) (Theme1) (Theme2)... Changes in both geometry and themes To node End Destroyed or ceased feature

This model shows clearly the advantages of representing temporal changes and theme changes independently,

mainly for querying processes and for tracking attribute modifications. It also provides evidence of several disadvantages of the ISO standard regarding changes of features over time. It must be noted that the ISO standard has been under revision status (90.92) since 2008. The FBTM could be catalogued as a complementary approach in the evolution of spatio-temporal modelling in GIS, since it proposes a new approach considering as its focus the third basic component of geographic information, i.e. theme, which has usually been treated as a secondary element in previous proposals (i.e., as an attribute of spatial objects).

In the same line of thought, and based on the previous relational/object-oriented and spatio-temporal data models, Wu et al. (2008) present a proposal to describe feature changes through the Change-of-Feature Based Spatio-Temporal Object-Relational Data Model. Although the authors argue for extending the FBTM by emphasizing the concepts of event and state, they do not provide enough information about how the model is extended.

Mathematical feature-based modelling. A mathematical feature-based modelling proposal, formalized trough spatio-temporal functions, was described by Maldonado Ibañez and Vázquez Hoehne (2010). The authors proposed a set of spatio-temporal geometrical primitives for the representation of dynamic features considering the topological relationships derived from them. The model considers not only spatial topological relations, but also temporal relations as for the occurrence of the phenomena, e.g., after, before, and during. The spatio-temporal context follows the relationships proposed by Claramunt and Jiang (2000). The primitives consist of a set of three-dimensional structures which are the result of three basic spatial primitives (arc, surface, and node)



extruded along the temporal dimension while considering two basic temporal primitives (instant and interval). The formalization of the spatio-temporal primitives allows one to infer the relationships existing in the features modelled through the primitives.

The authors demonstrate the methodology for creating six spatio-temporal primitives based on the temporal and spatial primitives. They also demonstrate their application inferring some dynamic relationships in two different case studies: the variation of the flooding level in a lake, and the representation of trajectories of moving objects (pedestrians). An advantage is the capability to infer relationships amongst dynamic phenomena through flexible mathematical definitions: it is possible to represent various scenarios based on the definition of geometric solids, areas, and lines. Although this characteristic gives a wide range of analytical possibilities and makes it easily computable, it is also a disadvantage mainly because real geographic phenomena are not usually described by geometric boundaries. Thus, areas not described by feasible geometric representations (e.g., square, circle, triangle) are out of the scope of this model when the geographic phenomenon requires to be represented continuously. Nonetheless, boundaries could be divided into feasible representations, but this would add a new level of complexity; for instance, topological integration of the components would be required so that the represented area acts as a single unit. On the other hand, phenomena represented by geographic points could always be considered without restrictions.

2.7 Process-Based Modelling

STPs-based approach. Claramunt and Thériault (1996) and Claramunt et al. (1997, 1998) introduced a model oriented towards the representation of processes. The authors state that although previous proposals were oriented towards the evolution of spatial entities, they did not provide methods for considering processes. Following a previous work (Claramunt and Thériault 1995), this new “framework provides a temporal topology for representing joint evolution of geographical entities associated through processes.” (Claramunt et al. 1999, p. 186).

The modelling approach is based on the concept of spatio-temporal processes (STPs). According to the authors, events are defined through processes that transform entities. They propose a typology of three main classes of basic STPs: (i) evolution of a single entity (basic changes, transformations, and movements), (ii) functional relationships between entities (replacement and diffusion processes), and (iii) evolution of spatial structures affecting several entities. The authors propose a classification of basic processes that include spatial evolutions (i.e., movement, life, re-allocation) and functional relationships between spatial entities (i.e., permutation, replacement, diffusion). In addition, they present a logical database structure that describes the evolution of spatial entities and the processes that generate those changes, which “gives supports toward the design of database modelling methods suited for the development of T-GIS and that fulfils the requirement of environmental applications because they explicitly convey linkages between events through entity-process networks.” (p. 186).

STPs distinguish between endogenous, exogenous, and spatial restructuring processes (see Table 6). Basic STP types are pre-defined at the system level. STPs are defined as object types in a database. Thus, actual processes are materialized “as object instances of the appropriate type.” (p. 191). STPs can be specialized as needed for the users’ needs: the database designer can define a special object type to represent a class comprising similar processes that are relevant to the application. The authors also propose extending the description of the attributes with an STP clause; thus, the attribute component is also modified through STPs. This facilitates the recording of the different STPs which act on the object’s geometry, as well as the enumeration of the STPs that can act on objects of that type. This allows, in turn, the description of integrity constraints. This work offers a clear enumeration and definition of the processes involved in the dynamics of geographic phenomena.

Table 6. Spatio-temporal process primitives (based on Claramunt et al. 1999)



Category Processes Endogenous processes Describing transformation and movement of a specific entity.

Stability, deformation, expansion, contraction, translation, and rotation

Exogenous functional processes Linking entities and leading to (i) replacement and (ii) diffusion.

Homogeneous/heterogeneous succession and permutation Production, reproduction and transmission

Spatial restructuring processes Defined between adjacent or connected spatial entities. Split, union, and re-allocation

Process-based spatio-temporal model. Yang and Claramunt (2003) introduced this model in order to

represent gradual changes and provide them with reasoning elements. Considering entities, processes, and changes as modelling primitives, and describing entities and processes in spatial, temporal, and thematic domains, the model allows describing geographic phenomena in a given spatial region at different abstraction levels as continuous changes. This proposal also considers spatial, temporal, and thematic operators that can be used to interact with entities and changes in those domains. Following the background concepts previously defined in Claramunt and Thériault (1995) and Yuan (1997), the domains are modelled independently although interconnected by domain links (orthogonal independence).

Based on the object-oriented approach, the authors define two ST superclasses (STEntity and STChange), that support the modelling of spatio-temporal entity types and spatio-temporal change types, respectively. Spatio-temporal entities and changes can be represented as (i) instances of classes, (ii) properties of those instances in the spatial, temporal (using time instants or time periods), and thematic domains, or (iii) spatio-temporal operations defined within those objects. The authors demonstrate the feasibility of the proposal through a case study modelling air temperature phenomena as moving regions and moving lines.

The main advantage of the model is that it allows identifying changes at different levels of abstraction and granularity, both in the spatial and the thematic dimensions. The model allows one to identify what, how, where, and when a phenomenon happens in a geographic space considering either a period or an instant. The fact that the model handles spatio-temporal entities and changes in a different way provides great flexibility for querying the modelled phenomena. This provides the capability of exploring geographic modifications at the entity level and also, to a certain extent, spatio-temporal patterns. This proposal clearly shows the benefits of modelling GI (geographic information) dimensions as orthogonal components. Although the model claims to be object-oriented at the database level, the authors do not provide either a method or a model for the implementation of the abstract classes. The queries are described well, but it is not possible to know how the classes must be queried.

Geo-atom Model. Goodchild et al. (2007) proposed a general theory providing simple building blocks appropriate for geographic representation, description, analysis, visualization, and simulation. The authors argue that although the geographic world is complex, the rules that need to be defined and integrated into systems to represent it do not necessarily need to be complex. Considering Galton’s (2003) ontology desiderata (described in Appendix C.4), the authors extend the field-based and object-based views into the temporal domain. To do so, they propose the Geo-atom Model.

A geo-atom is an abstract concept, thus not necessarily associated to a specific measurement system, human cognition model, or computer representation. It is an association between a property and a four-dimensional point location in space–time. Such an association is described by the “tuple <x, Z, z(x)>, where x defines a point in space–time, Z identifies a property, and z(x) defines the particular value of the property at that [four-dimensional] point.” (Goodchild et al. 2007, p. 243).

Fundamentally, the geo-atom is the foundation for discrete/object as well as continuous/field abstractions. Aggregation is the key concept considered in the unification of the field-based and object-based modelling approaches. “Geo-fields are formed by aggregating the geo-atoms for a single property Z” (p. 255), while “geo-



objects are formed by aggregating geo-atoms according to rules defined” on the z(x) values. Eight cases of dynamic geo-objects are identified, depending on three conditions: (i) movement: the geo-object may be static or it may move; (ii) geometry: it may change shape along time; and (iii) internal structure: the object maintains an internal uniformity or has an internal structure that is heterogeneous and evolving. Although higher-dimensional objects can be considered in the model, in practice every representation of a phenomenon (pixels, lines, areas, volumes) is reduced to aggregations of claims about geo-atoms (points); for instance, contours are aggregates of points with identical elevation. This consideration is true at the physical level in database modelling, but probably not at the logical level. As for the geo-field element, a temporal lineal model describes the evolution of continuous elements in a similar way to the snapshot model (see Appendix D.2.1); the discretization of the snapshots could be identical or irregular.

A second core element called a geo-dipole is introduced; it provides the essence for interactions. Interactions are the processes that modify the geo-fields and geo-objects. The geo-dipole is defined as a tuple that links a property with a value, but (as opposed to the case of the geo-atom) not only to one location in space–time but two: (x1, x2, Z, z(x1, x2)). This results in a logical description since there must be at least two elements for stabilizing an interaction. In this case, Z can represent a set of concepts related to measurable properties such as the direction, the distance, the interaction, and the flow. These are key elements for the description of the evolution of phenomena.

The significant contributions of this theoretical framework are the integration of the continuous/field and discrete/object conceptualizations through two basic elements (geo-atom and geo-dipole), and the clear identification of the evolving scenarios that they can face. Although the fundamentals do not apply for complex scenarios in which, for instance, scale and indeterminacy play a relevant role, the integration of the object/field dichotomy in a single model allows the modelling of spatio-temporal phenomena to be more flexible and general. Nonetheless, the temporal behaviour is restricted by the geo-atom properties, i.e., temporal attributes are always related to point geometries.

G-Field model. Later on, Liu et al. (2008) continued to develop the integration of the continuous/field/raster and discrete/object/vector abstractions. They consider a set of objects as an object-field single unit and unify it with standard field models, resulting in the General Field (G-Field) model. According to the authors, both the conventional field and the object-field representing geospatial data are particular cases of G-Fields. The G-Field is defined to integrate “continuous-field and discrete-object conceptualizations” and “geographic analysis can be viewed as a sequence of operations on General Fields.” (Liu et al. 2008, p. 640). Once defined, the G-Field can be used “to unify common geospatial data models” as well as “most geospatial data can be seen as the specialized instances of G-Fields.” (p. 634). Information extraction operations are used to extract significant information (reclassification, focal operations, zonal operations, global operations, subset, object identification, generalization, overlay), whereas other operations simply provide a new view of a data set (geometrical transformation, exact interpolation, Fourier transformation). As stated above, the continuous/field and discrete/object abstractions are the basis of geospatial conceptual data modelling (Couclelis 1992); nonetheless, the boundary between such concepts is being blurred nowadays.

EDGIS model. Based upon the space time points (STPs)2, a more general concept derived from the Geo-atom Model, Pultar et al. (2010) proposed EDGIS (an Extended Dynamic GIS). The authors state that, since the STP approach supports the modelling of discrete and continuous phenomena, as well as their dynamic evolution, such an approach results in a more basic concept than objects/fields and a fundamental element to model them along time. The STP is defined by a tuple <x, Z, z(x)>, exactly like the one defining a geo-atom, but considering that Z and z(x) are not defined for a single element but for a set of attributes.

The EDGIS model comprises three classes: theme, feature, and spaceTimePoint. The many-to-many relationships between the classes show the aggregative characteristic of the model: a feature is a set of STPs and a theme is a set of features. Similarly to STPs, both theme and feature are formalized through the tuples “<s, Z, z(s)>“ and “<f, Z, z(f)>“, respectively, where s is a collection of STPs linked to a feature and f is a collection of features associated with a theme. The aggregation of the tuples as subsets (s f x, where x represents a

2 This concept is different from the notion of spatio-temporal processes (STPs) discussed above in this section.



location) makes it possible to represent any dynamic geographic phenomena by the integration of STPs and their attributes.

A relevant characteristic of this proposal is the management of granularity. Since multiple sets of STPs can represent a single phenomenon and such STPs can be grouped into features, several groups of features can be defined while considering various temporal resolutions, which will lead to different visualizations and possibilities for querying. Since each STP comprises space, time, and attributes, any of these can be queried to obtain results for the other two. In this sense, the measurement framework presented by Sinton (1978) can be applied here. For example, a query about time t will obtain the STPs existing at that time and considering any feature for any theme. In addition, it is possible to formulate queries by setting two dimensions and querying a third one; for instance, when (t) was a specific location (x, y) classified as rural? Different scenarios such as cross-paths in geospatial lifelines are also possible; the identification of STPs that meet in time and space will produce as evidence the intersection of lines at the same time. This shows the advantages of this proposal in modelling dynamic scenarios considering moving objects.

Although it is possible to consider basic topological relationships by using STPs as a fundamental building block, more complex relationships such as covers, inside, or contains are not considered. EDGIS is the result of the implementation of the STP framework in a raster GIS context. Thus, although it does not overcome all the geographic representation challenges, it is an extendable solution that supports the representation and visualization of dynamic geographic phenomena based on the use of STPs, features, and themes.

2.8 Object-oriented Modelling

Object-orientation (OO) has been widely recognized in spatio-temporal data modelling as a powerful tool that captures far more of the meaning of concepts within a problem domain (Wachowicz 1999). Since OO supports an intuitive representation of the behaviour of dynamic entities moving in the space along time (e.g., moving objects, Bian 2000), several authors have proposed a significant number of models considering different perspectives and based on such an approach. OO has been the most prolific approach regarding spatio-temporal modelling trends because of its flexibility in handling independent objects and their properties. The idea of object identity, which implies that objects can be identified unambiguously, is a key element of the object-modelling approach. As such, it has been recognized as a reliable element in tracking changes and the evolution of independent objects and it is, therefore, applied in most of the spatio-temporal models. 31% out of the whole spatio-temporal models reported in the ST bibliography are object-oriented proposals (see Appendix F.5), which means that this trend is the most prolific and analysed for ST modelling.

Appendix E.1 complements this section by discussing other approaches based on the object-oriented modelling trend. Two relevant models are discussed here.

ST-objects. The application of object orientation methodologies for spatio-temporal modelling was pioneered by Worboys et al. (1990a,b), whose approach allows the modelling of geographic entities as independent units. According to Worboys (1992b, 1994a,b), a spatio-temporal object (ST-object) is a unified object comprising spatial and bi-temporal extents. By definition, a primary spatial object (i.e., a point, a finite straight-line segment, or a triangular area), called a simplex, can be linked to a bi-temporal element to compose an ordered pair resulting in a ST-simplex. Then, a ST-complex is defined as a finite set of such ST-simplexes. Based on ST-Complex, a kind of query algebra is defined. A range of operations on the ST-complex (e.g., union, intersection, subset, difference, boundary, equality, and spatial and temporal projection) offer the tools for spatial and temporal queries to be applied to single units. In particular, the spatio-temporal object model determines the spatio-temporal atom, defined as the smallest invariant geographic unit of change to which temporal attributes are assigned. Thus, geographic phenomena are represented as a set of independent objects formed by atoms, and the evolution of geographic entities is represented through the atoms. Time-stamping is used to mark the creation and end of a spatial extent and to show the evolution of objects over time.

This approach supports temporal queries in order to identify the state of an object at a specific time instant. As opposed to the space-time composite model (see Appendix D.2.1), this proposal allows spatial object



identifiers to be maintained. This characteristic solved one of the main shortcomings in the pioneering proposals. However, the model does not support spatio-temporal queries, which is a significant drawback.

Integrated temporal GIS system. Khaddaj et al. (2005) implemented this system based on the use of the OO approach and a full OO platform (programming environment and database management system). It can monitor the evolution of geographic objects based on their temporal relationships amongst the versions of each object. Besides, it can determine the events and processes affecting each object and analyse them. It offers object versioning as well as attribute versioning, which allows handling the changes of geographic phenomena. Similar to other OO models, this approach also provides spatial, temporal, and thematic classes. However, in this case the authors make a distinction between aggregated composite classes and associated composite classes. The former deal with changes in the three components, while the latter, defined through the events class and processes class, focus on the cause of the changes (events) and their effect on the geographic object (processes). The versions class controls a sequence of different states (changes) of a single object.

The feasibility of the proposed system is demonstrated through a case study involving a dataset that tracked the modification of attributes of geographic objects in the Canbury Ward (United Kingdom) in the years 1913, 1933, 1959, and 1998. Three versioning approaches are considered: linear, splitting, and merging. Linear changes are modelled by using a linear versioning method, with the setVersStatus(oocLinearVers) function, and a branching versioning technique is used for splitting changes, thanks to the setVersStatus(oocBranchingVers) function. Geographic phenomena involving merging changes are represented by the add_derivative function. Versioning is achieved through the version(copy) and version(move) functions, which copy and move the properties of the previous version to a new version, respectively.

Although versioning representation and spatio-temporal querying capabilities have been considered in the prototype, the system only answers basic temporal queries for single objects. Even though the authors state that the system “eliminates the need for large data storage capacities by recording only the changes in the spatial, temporal, thematic, event and process classes” (Khaddaj et al. 2005, p. 1594), no method is provided for the incremental storage of the spatial component. The modelling of every aspect in the independent classes provides the model with flexibility for analysing and querying each component. The main advantage of this proposal is that it offers a unified framework to track the evolution of geographic objects, considering causes (e.g., fire, earthquake, and flood) and effects (e.g., merge, split, expand, and move). The implemented system offers an optimal querying approach, thanks to a continuous tracking of movements forward and backward. Nonetheless, what the authors claim to be a continuous model is, in fact, a discrete representation of the phenomena within intervals and at instants.

2.9 Identity-Based Change

Hornsby and Egenhofer (1997, 2000) presented what they call the identity-based change model. It is based on the description of change regarding the states of existence and non-existence of objects. A key element in the model is the concept of object identity (“that unique characteristic that distinguishes one object from another” (Hornsby and Egenhofer 2000, p. 207)), as it allows tracking and querying objects and object types of interest independently of specific attribute values, properties, or structures (common elements).

A set of primitives and operations are defined. The primitives are identity states of objects and transitions, and are founded on the concept of existence. There are three identity states: (i) object existence; (ii) non-existing object with history (previous existence); and (iii) non-existing object without history. Identity states are associated with an object’s unique identifier; thus, when the identity state changes (e.g., from existing to non-existing) the object’s identity endures. Transitions represent evolving from an identity state to another. The explicit description of identity change is performed through a visual language, called Change Description Language (CDL). The model considers valid–time. The combination of the three main primitives through transitions defines a total of nine (3x3) change operations for an individual object (A): “continue non-existence without history, create, recall, destroy, continue existence, eliminate, forget, reincarnate, and continue non-existence with history.” (p. 213). The combination of operations involving two objects results in 18 plausible



operations (18 out of 81 possible combinations, i.e., 18 out of 9 x 9 combinations, nine for each object). Combinations such as non-existing object without history between two objects are invalid.

According to the authors, the identity-based change model (i) facilitates understanding of the possible alterations that an object can experience as it evolves over space and time; (ii) makes the extension of spatial data models possible; and (iii) pursues the development of appropriate GIS query languages incorporating semantics of change. Although the model is highly abstract, this characteristic allows it to be extended by adding new properties to objects and their relationships.

The spatio-temporal graph-based model for two-dimensional regions proposed by Del Mondo et al. (2013), discussed in Section 2.5, also considers the identity-based approach as a key element in the modelling of evolving entities when defining a graph-based structure. Other relevant proposals are the fuzzy identity-based temporal GIS proposed by Sriti et al. (2005), and the proposal for multi-scale spatio-temporal analysis of territorial changes by Plumejeaud et al. (2011).

2.10 Conceptual-Modelling Approaches

The database community has developed several novel conceptual models to integrate time and space in representational modelling approaches. Early proposals were based on extensions of the standard logical models: (i) the entity-relationship (ER) model (Chen 1976), (ii) the Object Modelling Technique (OMT) (Rumbaugh et al. 1991), and (iii) the Unified Modelling Language (UML) (Booch et al. 1999). Three proposals based on these logical models are described.

Spatio-Temporal Entity-Relationship (STER) Model. Since standard data models, namely the ER model, lack important capabilities to suitably manage geographic information evolving along time, Tryfona et al. proposed the Spatio-Temporal Entity-Relationship (STER) Model (Tryfona 1998, Tryfona and Hadzilacos 1998, Tryfona and Jensen 1999, Tryfona and Jensen 2000). Built on top of the Geo-ER Model described by (Hadzilacos and Tryfona 1997), which extended the ER model, the authors proposed a set of elements (i.e., ontological foundations, entity sets, constructs, and a textual notation) dealing with the spatio-temporal environment and considering the concepts of geographic objects, attributes and relationships, independent spatial and temporal aspects, and a set of operations to model spatio-temporal phenomena. Properties and interrelationships of objects and attributes can be defined on the basis of either discrete or continuous change, and for either of the basic types of spatial changes, i.e., motion, change of size/shape, and change of non-spatial properties (Peuquet 2001).

The goal is to capture the location of an object in space and time as well as its attributes, relationships, and existence features. The main advantage of the model is its universality, which makes it reusable thanks to its straightforward and powerful notation, as well as the facility of implementation inherited from the ER model. In general, it can represent complex spatial objects by defining higher levels of abstraction, using appropriate entity sets and grouping entities as needed to form reusable groups. This characteristic simplifies the ER schemas needed to represent complex spatio-temporal data. According to Pelekis et al. (2004), this model does not accurately indicate if an object is static or dynamic. Considering the same foundations, the authors also proposed the Geographic Object Model (Tryfona et al. 1997), an extension of OMT. This proposal, however, does not consider the temporal dimension and is specifically oriented to spatial databases.

Model for Application Data with Spatio-temporal features (MADS). Parent et al. (1997, 1999) introduced the MADS model, which incorporates thematic, spatial, and temporal constructs into an object-relationship conceptual model to facilitate the design of complex applications. It supports the modelling of data structures with spatial features using objects, an explicit description of topological relationships, and temporal specifications. Defining an extensible hierarchy of 12 spatial constructs (one general –Geo–, two principals –Simple Geo, Complex Geo–, and four types for each principal class –Point, Line, Oriented Line, Area–), six topological relationships (equality, overlapping, crossing, inclusion, adjacency, and disjunction), and a set of temporal attributes for different granularities (rate-of-flow, max, min, and average), MADS establishes a theoretical basis for building manipulation operations. It represents spatial elements at different levels: object, attribute, and relationship types. It supports the definition of integrity constraints based on spatial relationships



amongst spatial objects or other conditions on the geometry of objects. A CASE tool for modelling with MADS, which included translators for MADS schemata into GIS schemata (e.g., ArcInfo), is proposed.

The key benefit of this proposal is that it obeys the orthogonality principle when enhancing data structures with space and time features; this leads to the capability of modelling general applications dealing with the thematic, spatial and temporal dimensions independently and considering a discrete as well as a continuous view of the space. After MODUL-R (Caron et al. 1993, Bédard et al. 1996), which extends the ER model with “pictograms representing the geometry and temporality of spatio-temporal objects” (Parent et al. 1997, p. 174), MADS is considered as the first general modelling approach for spatio-temporal applications.

Claramunt et al. (1999) presented a case study in which the MADS model was extended. The authors model an application that captures changes in the environment and land use covering the description of the processes involved. They acknowledge progress performed in the representation of environmental changes, but at the same time they state that “GIS did not represent any explicit information about local changes involving spatial entities and their causing processes”. Thus, the authors extend MADS in order to integrate the representation of processes within spatial and temporal database schemata by adding the spatio-temporal process (STP) concept (described in Section 2.7, Table 6). The proposal builds “on an extensible classification and description of real-world processes” (p. 199) (as explained in Claramunt and Thériault 1995, a process can be a Basic Process or a Composite Process) and using a hierarchy of spatio-temporal types of process to characterise their properties (ST-Process Basic, Composite Stability, Translation, ... , Reallocation). Representation and modelling is basically based on three constructs: STP relationship type; STP object type; and temporal attributes. The main advantages of this proposal are: (i) it supports User Defined Processes, (ii) it enables the definition of a framework that includes processes at the conceptual and logical levels, and (iii) users can extend the model by adding new STPs.

Extended Spatiotemporal UML (XSTUML). Based on the Object Management Group (OMG) standard for OO modelling, Price et al. (2000, 2002) proposed an extension of UML (Booch et al. 1999) to model space–dependent and time–dependent applications: the Extended Spatiotemporal UML (XSTUML). The authors state that a conceptual data-modelling language for spatio-temporal applications “should provide a clear, simple, and consistent notation to capture alternative semantics for time, space, and change processes.” (Price et al. 2000, p. 14). Neither MADS nor STER (presented above in this section) provides explicit support for modelling thematic properties observed at the same locations and time instants, considers interpolation, or supports other temporal models. However, UML has strong tools and potential to overcome these shortcomings.

XSTUML provides spatio-temporal support for UML by adding five new modelling constructs, which can be applied to a UML class diagram to model different elements: (i) spatial extents; (ii) object existence and transactional time; and (iii) three different types of spatio-temporal data (temporal changes in spatial extents, thematic changes in space or time, and composite spatial data changing with time and/or location). They can be used at the attribute, object, and association levels. This modelling approach supports valid–time, transaction–time, and existence–time dimensions. Valid–time and existence–time refer to the existence of objects at different times under different conditions; for instance, a bed in a hospital can be defined as existing during a period but it can be busy or available depending on the number of patients in the hospital.

The main advantage of this proposal is that XSTUML inherits the potential modelling background of UML and increases its flexibility for modelling spatio-temporal scenarios by introducing appropriate constructs that can be combined and applied at different levels of the UML model and considering several kinds of times (valid–time, transaction–time, and existence–time, as explained above) for a single object and its properties. The modelling language remains clear and simple. These constructs, however, do not strictly follow the definition rules of UML, which leads into modelling restrictions for general-purpose models and the development of applications with CASE (Computer-Aided Software Engineering) tools.

2.11 Moving Objects

The field of moving objects has been a highly-prolific research area in which a large number of modelling proposals have appeared. The results are manifest when considering the exponential evolution of mobile



technology. Currently, moving objects is a very active research area in dynamic geographic domains. The huge spread of mobile and sensoring technologies has allowed significant and rich spatio-temporal datasets to be obtained and, due to this, moving objects have become a hot research topic (Wolfson and Mena 2005) and it is considered one of the building blocks of spatio-temporal analysis in movement analysis (see Demšar et al. 2015). Many research efforts have been addressed in data modelling (Xu and Güting 2013), querying methods (Ilarri et al. 2010, Kuijpers et al. 2011, Elmongui et al. 2013), identification and representation of mobility patterns (Orellana and Wachowicz 2011, Wachowicz et al. 2011, Orellana et al. 2012), computing with spatial trajectories (Zheng and Zhou 2011) and pedestrian networks (Fang et al. 2012), and space–time interpolation and locational inference (Wentz et al. 2010, Pragera and Barber 2012), amongst others. Specific spatio-temporal modelling approaches have been proposed for moving objects (Noyon et al. 2005, Noyon et al. 2007, Stewart Hornsby and Cole 2007), especially for phenomena represented by point geometries. Furthermore, methodologies for the representation of changing areas as moving regions have also been studied (Güting et al. 2000, Yang and Claramunt 2003, Huere Peña and Santos 2011). A recent review of existing quantitative methods to analyse mobility data was presented by Long and Nelson (2013).

However, research topics have mostly been oriented to databases and spatio-temporal databases. Today more than ever, people-based representations and analytical methods focused on location events are required. A person (an object) usually has multiple pocket-sized sensors (e.g., a smartphone, tablet, or GPS) capturing location-based data that describe their behaviour. Such behaviours clearly require spatio-temporal analytical methods that show the evolution of the activities performed across space over time. Unfortunately, this has resulted in most of the proposals considering only moving-point objects in a 4D (3D + t) space in searching for the trajectories of moving objects or the identification of patterns of movement. Only a few studies have been carried out considering two-dimensional spatial objects, such as moving regions or changes in 2D spaces over time, e.g., (Güting et al. 2000, Yang and Claramunt 2003, Huere Peña and Santos 2011).

The evolution of the moving objects approach has been exponential; the impact of this trend is so evident that even a specialized kind of database emerged: moving object databases (Wolfson et al. 1998, Forlizzi et al. 2000, Güting and Schneider 2005, Hajari and Hakimpour 2014). This may be due to the demanding necessity of modelling real-time moving data and the development of location-based services (that answer questions such as “what restaurants are near my current position?”). Moving object databases provide efficient methods for storing, indexing, and querying movement data.

Laube (2014) presents a discussion regarding the characteristics of spatio-temporal movement data, including uncertainty and scale issues. The author focuses his discussion on three aspects of Computational Movement Analysis: (i) conceptual modelling of movement, (ii) spatio-temporal analysis methods emphasizing movement processes, (iii) and spatial computing methods. A complementary study is the survey published by Demšar et al. (2015). This survey presents an analysis from the movement ecology viewpoint through an interdisciplinary discussion about movement analysis and visualisation methodologies. In addition, Dodge et al. (2016) present an editorial discussing about future directions in moving objects and the analysis of movement data.

Appendix D.3.2 presents a description of relevant spatio-temporal modelling proposals based on moving objects’ concepts and notions published during the last years.

3. COMPARISON, ANALYSIS, AND GENERAL OVERVIEW

In this section, we compare the described spatio-temporal models considering a set of characteristics that generate a common evaluation framework. In doing so, we have established as elements of comparison the following ones: (i) independent management of the evolution of each GI component (i.e., space, theme, and time); (ii) availability of temporal querying capabilities; (iii) incorporation and/or consideration of topological elements in space and/or time; (iv) consideration of the semantics of GI and temporal semantics; (v) the conceptualization for modelling space (i.e., object, field, or hybrid); (vi) the temporal model (i.e., linear or cyclic, discrete or continuous); (vii) the temporal attributes considered in modelling and implementation (i.e., valid-time, transactional-time, bi-temporal, user-time); and finally, (viii) the modelling approach (or approaches) on which



the model is defined. Afterwards, an overview and discussion on the evolution of T-GIS modelling trends are further developed in Section 4. Other relevant insights derived from this survey are discussed in Appendices F.1 - F.4.

Table 7. Abbreviations used for the comparison in Table 8

Modelling approach (MA)

OO: Object-Oriented FB: Feature-based EB: Event-based SM: Semantic-based SS: Snapshot AM: Amendment AB: Agent-based IB: Identity-based TS: Time-stamping PB: Process-based GB: Graph-based DM: Domain-based MO: Moving-Objects LS: Lifespan-based K: Kinematics CM: Conceptual Modelling Headers

ST: Spatio-temporal BT: Bitemporal time VT: Valid time TM: Temporal modelling

ET: Existence time UT: User time

Table 8 presents a comparison of the analysed models, while Table 7 collects the abbreviations used in Table

8. The first seven columns answer the following yes/no questions (a ✓ symbol is used to indicate the presence of a feature, and a -- symbol is used to indicate its absence): Space/Theme/Time: has the model considered independent structures for distinct evolution in each integrant

(thematic components)? Space-time: does the model consider a unified spatio-temporal structure showing object/feature evolution as

a whole? Semantics: does the model include elements for considering and representing geosemantics and/or the

semantic descriptors of the modelled phenomena? Topology and querying: does the model consider specific structures regarding spatio-temporal or temporal

topology; has it defined a query language or minimum elements for considering the potential spatio-temporal queries?

Table 8. Comparison of spatio-temporal models

Model

Sp

ace

Th

eme

Tim

e

Sp

ace

-tim

e

Sem

an

tics

To

po

logy

Qu

ery

ing

TM

att

rib

ute

s

Sp

ati

al

Mo

del

Tem

po

ral

Mo

del

ST

Mo

del

lin

g

Ap

pro

ach

Snapshot Model (Armstrong 1988)

✓ -- ✓ -- -- -- -- VT Field / Hybrid

Linear SS

Base state amendment vectors (Hazelton 1991, Hazelton et al. 1992, Langran 1992)

✓ -- ✓ -- -- -- -- VT Object Linear AM

Space-Time Composite (Langran and Chrisman 1988, Langran 1992)

✓ ✓ ✓ ✓ -- -- -- BT Object Linear AM

Simple time-stamping (Hunter and Williamson 1990) ✓ -- ✓ -- -- -- -- VT Object

Linear Periods

TS

Triad framework (Peuquet 1994)

✓ ✓ ✓ ✓ -- ✓ -- VT Object Linear DM

Scientific knowledge framework (Claramunt et al. 1997)

✓ ✓ ✓ ✓ -- -- -- VT Object Linear EB / PB

TEMPEST (Peuquet and Wentz ✓ ✓ ✓ ✓ -- -- ✓ VT Object Linear EB



Model

Sp

ace

Th

eme

Tim

e

Sp

ace

-tim

e

Sem

an

tics

To

po

logy

Qu

ery

ing

TM

att

rib

ute

s

Sp

ati

al

Mo

del

Tem

po

ral

Mo

del

ST

Mo

del

lin

g

Ap

pro

ach

1994, Edsall and Peuquet 1997) ESTDM (Peuquet and Duan 1995) ✓ ✓ ✓ ✓ -- ✓ ✓ VT Field Linear EB

HST-DMS (Sengupta and Yan 2004)

✓ ✓ ✓ ✓ -- ✓ ✓ VT Field Linear EB

Event-based (Versioning) (Claramunt and Thériault 1995) ✓ ✓ ✓ ✓ -- -- ✓ BT Object Linear EB

Causal links (Allen et al. 1995)

✓ -- ✓ ✓ -- ✓ -- VT Object Linear Periods

EB / OO

Pure event-oriented theory (Worboys 2005) ✓ -- ✓ ✓ ✓ -- -- VT Object Linear EB

GEM (Worboys and Hornsby 2004)

✓ ✓ ✓ ✓ -- -- ✓ VT Object Linear Periods

EB / OO

Similarity of geographic events (McIntosh and Yuan 2005a,b) ✓ ✓ ✓ ✓ ✓ -- ✓ VT Hybrid Linear EB

Continuous spatial change (Worboys and Duckham 2006)

✓ ✓ ✓ ✓ -- -- -- VT Hybrid Linear Continuous

EB / PB

Three-Domain Model (Yuan 1997, Yuan 1999) ✓ ✓ ✓ ✓ ✓ ✓ ✓ BT Object Linear

DM / SM

History Graph Model (Renolen 1996)

✓ -- ✓ ✓ -- -- -- BT Object Linear Continuous, discrete

GB / EB

Spatio-temporal graphs (Del Mondo et al. 2013)

✓ -- ✓ ✓ ✓ ✓ ✓ BT Object Linear GB / IB

Life-motion-succession (Stefanakis 2003) ✓ ✓ ✓ ✓ -- -- ✓ VT Object Linear

FB / GB

Feature-Based Temporal Model FBTM (Choi et al. 2008)

✓ ✓ ✓ ✓ -- ✓ ✓ VT Object Linear FB

S-T Geometrical primitives (Maldonado Ibañez and Vázquez Hoehne 2010)

✓ -- ✓ ✓ -- ✓ -- VT Object Linear FB

Spatio-Temporal processes (Claramunt and Thériault 1996, Claramunt et al. 1997, 1998)

✓ -- ✓ ✓ -- ✓ -- VT Object Linear Periods, Instants

PB

ST super-class (Yang and Claramunt 2003)

✓ ✓ ✓ ✓ -- -- ✓ VT Object Linear Continuous

PB / FB

Geo-atom model (Goodchild et al. 2007) ✓ ✓ ✓ ✓ -- -- -- VT Hybrid

Linear Continuous, discrete

PB

EDGIS (Pultar et al. 2010) ✓ ✓ ✓ ✓ -- ✓’ ✓ VT Hybrid

Linear Periods, Instants

PB

ST-object (Worboys 1994a)

✓ -- ✓ ✓ -- -- ✓ BT Object Linear OO

Object-oriented spatio-temporal data model (Wachowicz and Healey 1994, Wachowicz 1999)

✓ ✓ ✓ ✓ -- ✓ -- VT Object Linear OO

Spatio-temporal data sets (Hamre 1994).

✓ ✓ -- ✓ -- ✓ -- VT Hybrid Linear OO

Structure and Interface Definition ✓ ✓ ✓ ✓ ✓ -- -- BT Object Linear OO



Model

Sp

ace

Th

eme

Tim

e

Sp

ace

-tim

e

Sem

an

tics

To

po

logy

Qu

ery

ing

TM

att

rib

ute

s

Sp

ati

al

Mo

del

Tem

po

ral

Mo

del

ST

Mo

del

lin

g

Ap

pro

ach

Language (Rojas Vega and Kemp 1995) T/OOGDM (Becker et al. 1996, Voigtmann et al. 1996)

✓ -- ✓ ✓ -- ✓ ✓ BT/ UT

Hybrid


OO

STOM (Renolen 1997)

✓ ✓ ✓ ✓ -- ✓ -- VT Object Linear Periods, Instants

OO

Space and time primitives (Faria et al. 1998) ✓ ✓ ✓ ✓ -- ✓ ✓ VT Object


OO

Integrated temporal GIS (Khaddaj et al. 2005)

✓ ✓ ✓ ✓ -- -- ✓ VT Object Linear Periods, Instants

OO

Feature Evolution Model (FEM) (Lohfink et al. 2010)

✓ -- ✓ -- -- -- -- VT Object Linear OO / FB

Knowledge Discovery System (Venkateswara Rao et al. 2011) ✓ ✓ ✓ ✓ -- ✓ -- VT Object

Linear Multigranularity

OO

Identity-based change model (Hornsby and Egenhofer 1997, 2000)

✓ -- ✓ ✓ -- -- ✓ VT Object Linear IB

Moving Objects (Erwig et al. 1999, Güting et al. 2000, Cotelo Lema et al. 2003)

✓ ✓ ✓ ✓ -- ✓ ✓ BT Object Linear Continuous

MO

Space-Time Intelligence System (STIS) (Jacquez et al. 2005) ✓ ✓ ✓ ✓ -- -- ✓ VT Object Linear MO

Spatio-temporal trajectory (STT) (Zheni et al. 2009)

✓ ✓ ✓ ✓ ✓ -- ✓ VT Object

Trajectory Linear

MO / SM

Generic data model for managing moving objects (Xu and Güting 2013)

✓ ✓ ✓ ✓ -- -- ✓ VT Object

Linear Continuous. Periods, Instants

MO

Spatio-Temporal Entity-Relationship model (STER) (Tryfona 1998, Tryfona and Hadzilacos 1998, Tryfona and Jensen 1999, 2000)

✓ ✓ ✓ ✓ -- ✓ -- BT Object

Linear Continuous, discrete. Periods, Instants

CM

Model for Application Data with Spatio-temporal features (MADS) (Parent et al. 1997, 1999)

✓ ✓ ✓ ✓ -- ✓ -- VT Object Linear CM

MADS+ (Claramunt et al. 1999) ✓ ✓ ✓ ✓ -- ✓ -- VT Object Linear

CM / PB

eXtended SpatioTemporal UML (XSTUML) (Price et al. 2000, 2002)

✓ ✓ ✓ ✓ -- -- -- BT/ ET

Object Linear CM

Multigranular object-oriented framework (Camossi et al. 2003, 2006)

✓ ✓ ✓ ✓ ✓ ✓ ✓ VT Object Linear Multigranularity

CM

Fluid kinematics (Bothwell and Yuan 2010, 2011)

✓ ✓ ✓ ✓ ✓ -- ✓ VT/ BT

Field Linear Continuous

K / PB

Lifespan modelling based ✓ -- ✓ ✓ -- -- -- VT Object Linear LS /



Model

Sp

ace

Th

eme

Tim

e

Sp

ace

-tim

e

Sem

an

tics

To

po

logy

Qu

ery

ing

TM

att

rib

ute

s

Sp

ati

al

Mo

del

Tem

po

ral

Mo

del

ST

Mo

del

lin

g

Ap

pro

ach

(Nixon and Stewart Hornsby 2010) Periods IB FOTAR (Yu and Peuquet 2009) ✓ -- ✓ ✓ ✓ -- ✓ BT

Object / Hybrid

Linear AB

From Table 8, the following conclusions are extracted:

Regarding the dominant spatial model, most of the described models are oriented to the object-based representation (38), and just a few have been developed for the field–based (4) and the hybrid (8) approaches. This shows the clear dominance of the representation of dynamic geographic phenomena as objects.

Most of the models considering the field-based representation have been developed in the context of environmental applications. In contrast, object-based models consider urban scenarios such as cadastre and land information systems (LIS).

On the other hand, the dominant temporal model is the linear model: 100% of the analysed models consider such approach. Amongst them, eight consider in addition the continuous approach and three the discrete approach. Eight are able to model periods and instants and four only periods. Most of the modelling proposals consider a linear/discrete model for the representation of time. Finally, just two proposals are modelled following the multigranular temporal approach.

Regarding the temporal attributes, it is noteworthy that even though Snodgrass had already identified and defined the relevance of the bi-temporal model as early as 1986, and then Worboys showed its feasibility in GIS, only 13 of the analysed models have taken into account both valid–time and transaction–time. Moreover, only two models, T/OOGDM (Becker et al. 1996, Voigtmann et al. 1996) and XSTUML (Price et al. 2000, Price et al. 2002), went one step further in considering a third temporal type for the modelling of additional temporal attributes, such as user-time or existence-time, to represent the availability of elements or the validity of a phenomenon (e.g., expiry date). However, these models do not consider this additional time variable far beyond its being a new attribute. In this sense, the temporal requirements for T-GIS described by Donna Peuquet (2001) have not yet been fulfilled. A more complex representation considering transaction–time, valid–time, and observational–time as orthogonal elements does not exist. An analytical temporal framework considering this trilogy is far from being achieved. This lack clearly opens new alternatives for the analysis of geographic phenomena. One option, for instance, is the development of an analytical framework in a Euclidean space in ℝ3, in which the identification of patterns and temporal relationships could become evident.

The consideration of semantic elements (geosemantic and temporal) is not a commonality either. Conversely, topological elements, either spatial or temporal, are considered in a significant number of

models; this shows how modelling proposals are considering the strong background already developed in the spatial and temporal research fields independently.

Finally, half of the analysed models have considered either temporal attributes or enriched query language capabilities for supporting temporal or spatio-temporal queries. However, as discussed in Section 4, these capabilities do not cover the querying capabilities demanded by GIScientists in a general-purpose T-GIS.

Of the spatio-temporal models published during the last decade, some of them rely on other solid models and are based on strong proven concepts broadly accepted by the research community. Of the proposals analysed in this survey, we highlight four: (i) the geospatial event model defined by Worboys and Hornsby (2004) (Section 2.4); (ii) the pure event-oriented theory (Worboys 2005) (Section 2.4) based on the event-driven paradigm; (iii) the general theory of geographic representation in GIS introduced by Goodchild et al. (2007) (Section 2.7); and (iv) the modelling of dynamic geographic domains through geolifespans proposed by Nixon and Stewart



Hornsby, (2010) (Appendix E.3). These modelling proposals have shown innovative elements and have pursued the state of the art in the spatio-temporal modelling field. The integration of the hybrid approach and the modelling of dynamic phenomena considering lifespans involves novel core concepts on which, presumably, new proposals will be developed. In addition, proposals based on the principles of kinematics have shown a clear pathway to introducing robust mathematical and physical theories in spatio-temporal modelling; this trend could significantly enrich the modelling of dynamic phenomena, for instance, second-order tensors (two-dimensional array) could be applied to the evaluation of trajectories, especially when applying the Ricci calculus, i.e., the rules of index notation and manipulation for tensor fields and tensors.

The graph-based modelling approach would include a new level of intelligence in the modelling of events with which it might be easier to identify the set of events that comprise a process. This characteristic is precisely what the agent-based modelling approach (described in Appendix D.3.1) adds to spatio-temporal modelling: intelligence. The fact that objects have the ability to control themselves and interact in a common environment provides modellers with the ability to consider new behaviours defined by rules; a new behaviour would just require the integration of a new rule and a set of methods. Although fewer proposals have been published considering intelligent approaches, the integration of agents and graphs seems to be a promising research line: graphs focused on events and processes, agents representing intelligent objects, and a common environment in which all components interact. The agent-based modelling approach (Brown and Xie 2006, Yu and Peuquet 2009) (see Appendix D.3.1) is indeed a research line that has recently opened in spatio-temporal modelling with vast untapped potential. Agents have properties that objects do not, and perhaps the evolution from the object-oriented and event-driven paradigms to the agent-oriented paradigm (Shoham 1993) could be a promising pathway for the advantages that the simulation of interaction amongst geographic entities can offer.

Figure 3. Identified spatio-temporal modelling trends and number of proposals per trend.

Moving objects alongside the agent-based approach also offer potential scenarios for exploring new trends in modelling. Considering a network of moving objects in which each object is represented by an agent can establish the foundations for spatial intelligent systems that model reality in a much more natural way:



autonomous objects interacting in a common scenario which is defined and constrained by rules. The current state of the art in spatio-temporal databases, specifically moving object databases, already provides the technological background that would be required to propose this kind of cutting-edge modelling approach. In a way, the agent-based approach could be considered as a specific modelling approach for moving objects but considering a high level of intelligence and strong interaction amongst the objects in a controlled scenario.

One relevant result of this survey is the proposed taxonomy of spatio-temporal modelling trends. After having completed a review of over 186 modelling proposals (see the category Spatio-temporal Modelling in the TimeBliography (Siabato et al. 2014)) and analysed 50 of them in depth, we have identified 14 general spatio-temporal modelling trends in which most of the modelling efforts published during the last three decades have been compiled. Figure 3 schematizes the spatio-temporal modelling trends and proposals defined during the last years.

Several proposals have defined, together with the conceptual spatio-temporal model, a physical or logical data model for the management and storage of data on which the implementations and proofs-of-concept have been based. Most of them are defined for spatio–temporal management systems and structures, which are not designed for handling and managing movement and evolving data. Although moving object databases are making progress in this regard (moving points, moving regions), as for GIS data formats there is a clear lack of appropriate structures to manage movement data. The development of geospatial data formats exclusively for representing dynamic geographic phenomena is an imperative requirement. Nonetheless, current developments and advances in T-GIS already offer solid alternatives that could serve to modelling natural phenomena in more appropriate ways (e.g., Molina and Albarran 2013, Enriquez et al. 2014).

4. CONCLUSIONS AND FINAL REMARKS

In this survey, we have offered a thorough and systematic overview of the origins and historical evolution of T-GIS and the development of spatio-temporal data models and modelling trends. By considering the five modelling dimensions (processes, events, actions, movement, and dynamic objects) and the fundamentals upon which each proposal relies, we have identified 18 trends in the modelling of dynamic geographic phenomena (see Table 1 and a full description in Table E, Appendix D.1). Such classification can reduce this number to 14 if one considers the pioneering proposals as a single approach, i.e., location-based (see Figure 3). This taxonomy is a significant outcome of this survey. As discussed, several authors have attempted different classifications; however, this proposal presents a general picture of the last three decades in the spatio-temporal modelling field. A large number of modelling proposals have been discussed, highlighting some of the most representative in each modelling approach. As several surveys and review articles have been presented during the period discussed, this survey has mainly focused on the proposals developed during the 2000s but has also considered a historical overview. The latest review articles about temporal aspects in GIS, specifically on spatio-temporal data models and modelling trends, were published by Pelekis et al. (2004) and Yuan (2008), respectively. More recently, An et al. (2015) presented a review of quantitative methods for space–time analysis by describing concepts and future directions. Despite these previous studies and reviews, this article and the appendix together offer unprecedented detailed accounts of T-GIS development.

Temporal GIS remains a very active research area. Although the UCGIS Research Agenda was updated in 2002 and 2004 (University Consortium for Geographic Information Science -UCGIS- 2004), the long-term research challenge for spatio-temporal issues (Space and Space/Time Analysis and Modeling) remained an open-ended task which continues today. Current agendas still define spatio-temporal issues as long-term research topics; there is a consensus that much work must still be done before achieving a general spatio-temporal model and the basic functionalities for a real T-GIS. Nevertheless, Goodchild (2013) states that the great disparity in different types of space–time data and the diverse nature of questions that should be answered by a T-GIS argue against the emergence of a single T-GIS and model, in contrast to the emergence of the unified concept of GIS in the 1970s and 1980s (see a broader discussion in Appendix C).

There has been considerable progress in temporal GIS since the 1980s. Nevertheless, an approach sufficiently robust to support spatio-temporal information management, querying, analysis, and modelling is still



missing, as stated in Yuan (2008, p. 169). Regarding the state of the art in T-GIS, it is interesting to emphasize the following aspects: A metric for measuring and evaluating how much T-GIS has evolved in the last decade can be extracted

from the typology of 11 spatio-temporal information queries defined by Yuan and McIntosh (2002) more than ten years ago: attribute queries, spatial queries (three types), temporal queries (three types), and spatio-temporal queries (four types).

GIS technologies can still only answer queries related to attributes and space. Queries involving also the temporal dimension are still under active research. Moreover, there is no standard query language in temporal GIS on which the development of spatio-temporal queries can be supported. Such a language should provide the minimum elements in order to support the Peuquet/Claramunt framework when answering questions about attributes (what), time (when), location (where), process (why), and change (how).

There is consensus in the research community on the necessity of creating a general framework in which the dynamics of GI could be stored, retrieved, queried, analysed, and represented.

At the same time, there is consensus that neither a universal standard spatio-temporal data model nor a comprehensive solution has been proposed so far. In fact, several researchers have asserted that trying to find a unique model that applies to every single spatio-temporal scenario is somehow utopian and even wrong (e.g., see Goodchild 2013). Different disciplines have different understandings of change, and, therefore, different requirements. For instance, while planners and cartographers are concerned with the maintenance of up-to-date and accurate information, others, like archaeologists and geologists, are more often concerned with seeking to understand past, present, and future processes. It is somewhat surprising that in every single article in which a modelling approach is proposed, the authors always start by stating in one way or another that no general consensus for the modelling of dynamic geographic phenomena in the temporal dimension has been achieved but remains a challenge. The identification of minimal structures and ontological foundations is crucial for the implementation of spatio-temporal functionalities in T-GIS software. A general spatio-temporal information system has not yet been developed.

In addition to the current achievements and remaining issues of T-GIS herein discussed, Claramunt and Stewart (2015) outlined the following directions for further research. First the genericity of current T-GIS models is a theoretical important question: to which degree “Are the spatiotemporal concepts, models, and reasoning frameworks developed so far, generalizable across all fields? Is a unified theory of spatiotemporal information feasible and a worthwhile goal across all disciplines?” (p. 61). The authors also mentioned that environmental and urban sciences should also be key players in precisely defining their needs, as well as highlight the fact that interdisciplinary approaches will be mandatory if the objective is to develop sound and generic T-GIS models. As mentioned above, additional insights derived from this study are discussed in Appendices F.1 to F.4.

For this survey, the bibliographic sources described in Appendix F.5 have been considered. This survey covers a time span of about three decades of research, materialized in a high number of references (over 1450, categorized in 36 topics) that have been registered in the online bibliography (TimeBliography) that supports (and is at the same time a sub-product of) the in-depth study presented in this article. TimeBliography is described by Siabato et al. (2013, 2014). For more details, please visit http://spaceandtime.wsiabato.info.

This survey has offered a structured, comprehensive, and detailed view of the state of the art in T-GIS, which we expect to encourage further efforts. For additional details, the reader can look up a comprehensive set of online appendices that accompany this paper and present related and highly-relevant and complementary information.

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