A Process-oriented Multi-representation of Gradual Changes

GIDA________________________Journal of Geographic Information and Decision Analysis2003, Vol. 7, No. 1, pp. 1-13A Process-oriented Multi-representation of Gradual ChangesYanwu YangInstitute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing 100101, Chinayangyw@andNaval Academy Research InstituteBP 600, 29240, Brest Naval, Franceyang@ecole-navale.frChristophe ClaramuntNaval Academy Research InstituteBP 600, 29240, Brest Naval, Franceclaramunt@ecole-navale.frABSTRACT Although GIS has been applied to many application areas, there is still a need for successful integration of the temporal dimension in current spatial data models in order to deal with the complexity of urban and environmental systems. In particular, there are a few spatio-temporal data models for representing gradual changes. The objective of this paper is to design, at the conceptual level, a spatio-temporal data model that represents and reasons over gradual changes. Our modeling approach considers entities, changes, evolution, events, and processes as modeling primitives in the spatial, temporal and thematic dimensions. Gradual changes are represented at different levels of abstraction while spatio-temporal predicates manipulate the modeling primitives identified. The potential of our modeling approach is illustrated by a case study oriented to the study of “dynamic field” changes in air temperatures in a region of North-East China.KEYWORDS: Process-oriented, Multi-represen- tation, Spatio-temporal model, Gradual changesA Process-oriented Multi-representation of Gradual Changes1. IntroductionThe integration of time in Geographical Information Systems (GIS) is an important objective to explore in order to make those systems successful for real-world applications from the social, environmental to the urban sciences. Over the past years, temporal GISs have been an important and active research area for many research communities. At the conceptual level, many spatio-temporal data models have been developed such as the snapshot model (Armstrong 1988), the space-time composite model (Langran and Chrisman 1988, Langran 1992), the triad model (Peuquet 1994, Peuquet and Qian 1996), the three-domain model (Yuan 1996a and 1996b), event-oriented models (Frank 1994, Peuquet and Duan 1995, Claramunt and Thériault 1995; 1996, Claramunt et al., 1999), and extensions to the object-oriented model (Worboys 1992; 1994).While most of these approaches represent discrete changes in the spatial domain, many spatio-temporal phenomena require a continuous treatment of changes. In order to take into account the complexity of continuous phenomena, there is a current trend in database research to represent and manipulate gradually moving objects (Wu et al. 1998, Roddick and Spiliopoulou 1999, Roddick et al. 2000). Those advances represent significant contributions to model and reason over continuous or gradual changes at the database modeling level. However, these advances should be completed by comparable facilities at the conceptual level in order to offer appropriate modeling primitives. This will provide a bridge between the conceptual and the logical database levels, that is, between the application and the database.The research described in this paper introduces a preliminary conceptual model oriented to the modeling of gradual changes in the spatial, temporal and thematic domains. This approach is based on an entity and process-based model that allows for the representation and propagation of continuous changes at different levels of abstraction. Entities model either moving regions or moving lines (e.g. region boundaries). The proposal integrates spatio-temporal operators that manipulate those modeling primitives. It is illustrated by a case study applied to the modeling of air temperature changes in a region of China. The remaining of the paper is organized as follows. Section 2 presents the modeling background and related work. Section 3 introduces a conceptual model and query operators for gradual changes. Section 4 applies those concepts to a case study. Finally section 5 draws some conclusions.2. Modeling background and related workEntities, processes and events are elementary primitives necessary to the modeling of change. Each entity forms a spatial or non-spatial lifeline that begins with its birth, and goes through its whole (or part of) life (similar to the term "geospatial lifeline" suggested by Hornsby and Egenhofer 2002). The life cycle of an entity along its spatial or non-spatial lifeline consists of a series of contiguous states (versions) separated by evolutions or mutations (Langran and Chrisman 1988). At the database modeling level, each state corresponds to an entity version valid for a specific instant or a given period of time. A process is a concept developed by scientists to understand and relate changes in space and time (Claramunt et al. 1997). Processes record spatio-temporal relationships, that is, dependence links, among entity statesYang and Claramunt(Claramunt and Thériault 1996). The notion of process establishes a form of relationship between space and time (Langran 1992). (Claramunt and Li 1999) defined “a process” as “an action that modifies a set or real world entities” (the action is of interest), and “composite process” as an “expression formed through processes and logical operators”. Events are things that happen; they are conditions, processes, or entities that exist and can be observed (Abler et al. 1971).Several conceptual and logical models have been proposed to represent changes, processes and events in GIS. (Claramunt and Thériault 1995 and 1996) proposed a model to describe primitive and composite spatio-temporal processes using an event-oriented approach, where changes and events are represented as explicit events. An event is modeled as a set of processes that transform entities (the result of the action is of interest). A taxonomy of spatio-temporal processes and changes is identified, it retains the semantics of processes and events. This model makes the difference between events that happen either at a given instant or over a period of time. Events are formalized by expressions of basic and composite processes using logical operators that explicitly define a temporal ordering on those processes. In a related effort (Hornsby and Egenhofer 1997, 2000) introduced another taxonomy of changes and processes, with an explicit description of changes based on the notion of identity. Renolen (1999) proposed a general framework in which temporal relationships between states and events are preserved explicitly and linked together in a directed a-cyclic graph, called a “history graph”, schematized using a graphical notation.3. Towards a representation of gradually changing phenomenaA “field” can be roughly defined as a region of space characterized by a physical property continuously distributed. This definition is similar to the definition of “continuous phenomena” given in (Yuan 2001), which stands for a distribution of single-value variables that model a geographical phenomena, such as air temperature, fluid pressure, and gravitational or electromagnetic force. The values of an attribute distributed in a field may also change along the time line giving thus a form of “gradually changing phenomena”. The distribution of air temperatures can be represented as a “field” or by a spatio-temporal index as temperature values are continuously distributed in those two dimensions.The proposed conceptual framework builds on a clear demarcation between the spatial, temporal, and thematic domains as in (Claramunt and Thériault 1995, Yuan 1996a). This fulfills an “orthogonal principle” where the spatial, temporal, and thematic domains are independently modeled but interconnected by “domain links” (Claramunt and Thériault 1995). In this paper, we consider life and motion processes, and make a separation between thematic and spatial processes: life and stability, motion and more generally geometrical processes, and thematic processes. Our modeling approach is based on an object-oriented spatio-temporal model that favors integration of complex data types and operations (Worboys 1992 and 1994, Egenhofer and Frank 1992). It has been elsewhere shown that temporal and spatio-temporal applications require complex types to support and advanced modeling concepts (Fegaras and Elmasri 1998). An entity is defined as “a real-world abstraction of an existing feature”, object means its representation in the database. ST acts as the root class of all the spatio-temporalA Process-oriented Multi-representation of Gradual Changestypes (elements), as well as an abstract class (an abstract class is a class which is not directly instantiable). The class ST has two subclasses, STEntity and STChange (Table 1). The former is the root class of all spatio-temporal entity types, also an abstract class; the latter is the root class of all spatio-temporal change types, also an abstract class. Spatio-temporal entity types are defined according to application and user needs. To reflect the fact that one might wish to model a given phenomena at different levels of abstraction, spatio-temporal entities and their states, processes, and events are defined at one to many specific levels of representation in the spatial, temporal, and thematic domains. The ST class is basically specified as follows (where we make the difference between spatial, temporal, thematic properties and relationships, and spatio-temporal operations):ST {… //spatial properties and relationships… //temporal properties and relationships… //thematic properties and relationships… //spatio-temporal operations}Spatio-temporal entities and changes are modeled as either instances of classes (i.e. objects), properties of those objects in the spatial, temporal (either instant or period stamped), and thematic domains, or spatio-temporal operations defined within those objects. In the example below the attributes Position and SpatialExtent denote the center or gravity and the extent of a ST entity, respectively, while TracePosition and TraceExtent denote the center or gravity and the extent of a ST change, if any (e.g. modeling of a displacement). Let us consider the example illustrated in Figure 1(1) where the 10 °C isotherm moves towards Northwest from 1980s(“a”) to 1990s(“A”). The position of the isotherm “a” is denoted by its center or gravity, its extent is the spatial extent occupied. The TracePosition of the process “displacement” is a polyline which starts from position of “a” to that of “A” (i.e. that denotes the displacement of the center of gravity), TraceExtent, the spatial extent (i.e. polygon) bounded by the respective boundaries of the two versions of the 10 °C isotherm. This displacement is modeled as an event expression that gives the Traceposition and the Traceextent of the origin and destination of a moving entity.a:: DisplacementIso (traceposition (position1, position2), traceextent; 1980s’,1990s’; entilist (a, A))The links between the classes STEntity and STChange (Table 1) denote some semantic dependencies, for instance, C_attrlist in STChange corresponds to a series of thematic data on the property involved, and Entilist, a list of versions of one to several entities involved in the process.The spatial properties of the class STEntity denote the spatial position and extent occupied by this entity including some additional spatial properties such as the main direction of a displacement (e.g. in the example above this is the case of the attribute DisplacementIso). Note that the properties of the ST entities are either valued or undetermined (such as the position andYang and Claramuntspatial extent of a moving region or moving line). For instance, in the case of a displacement of a moving line, the values of the attributes TracePosition and TraceExtent may be not known at the end time of that process. In this case the attribute Direction can be used to give alternative data on this spatial displacement.Table 1. STEntity and STChangeSTIsotherm a{Position;Extent;Start time;End time;Type;… //spatio-temporal relationships … //spatio-temporal queries}DisplacementIso { Traceposition; Traceextent;Direction;C_attrlist (position1, position2); Start time;End time;Entilist;…//spatio-temporal relationships … //spatio-temporal queries}This spatio-temporal object-oriented model supports entity-based and change-based queries due to the fact it treats spatio-temporal entities and changes as different classes. A second class of operations is inspired by Active Databases advances in the manipulation of complex patterns of composite temporal events. Several active database languages such as ODE, Snoop, SAMOS and EPL were developed to support the specification of rules that are fired when complex patterns of events are detected (Gehani et al. 1992, Giuffrida and Zaniolo 1994). We integrate EPL event-pattern operators and apply them to represent and reason over spatio-temporal processes as in (Claramunt and Thériault 1996). EPL provides some basic constructs whose main logical operators are briefly introduced. Let E1, E2,..., En denote a event or a process, an EPL expression includes the immediate sequence (E1, E2, …, En), the immediate sequence of n instances of E *:E, the negation !E, the conjunction (E1&E2&...&En), the disjunction {E1, E2, ..., En}, and the relaxed sequence [E1, E2,..., En].4. Application to a case study4.1. Modeling elements – isotherms and homogeneous regionsA dynamic field models a phenomenon which is spatially distributed, and continuously changes over time. Let us consider the example of an air temperature phenomena represented by isotherms (cf. Figure 1). In order to represent the spatial distribution of air temperature, we derive homogeneous regions from those isotherms (e.g. above 0°C and below0°C). We model isotherm changes over time using the concepts of either “moving lines” or “moving regions”. This section introduces the principles behind this approach and illustrates its potential by entity- and process-based queries.A Process-oriented Multi-representation of Gradual Changes4.2. Air temperature changes as moving linesMoving lines (e.g. isotherms) can appear, disappear, reappear, and the whole or even some parts of moving lines may move towards one to several different directions according to the modeling needs and the level of granularity chosen. One can remark that a moving line does not hold – at the database modeling level - a valued position along the timeline of a supposed displacement between two known positions (i.e. between 1980 and 1990 in Figure 1(1)). However a displacement can be modeled using an event-based expression. As an example, let us consider the case given in Figure 1(1) and the evolution of the 10°C from 1980 to 1990. The spatial scale is 1:60,000,000, and temporal granularity, 10 years (note that this process is spatial only). There are three 10°C isotherms in 1980s (a, b, and c) and five ones in 1990 (A, B, C, D, and E). These processes, at the level described in Figure 1(1), are modelled as follows where displacement, fissiparism, contraction and appearance are elementary processes (the complete semantics of these logical expressions is given in Yang 2003).a:: (displacement (northwest; 1980s’,1990s’; a, A) & fissiparism (position-E, spatial extent-E; 1980s’,1990s’; aà A, E)) & b:: contraction (position-b, traceExtent (union(extent-b, extent-B)); 1980s’,1990s’; b, B) & c:: contraction (position-c, traceExtent (union(extent-c, extent-C)); 1980s’,1990s’; c, C) & D:: appearance(position-D, spatial extent-D; 1980s’,1990s’; D)Figure 1(2) shows the same phenomena but at a lower level of abstraction with a temporal granularity of 5 years. Compared to Figure 1(1), more detailed information on spatio-temporal entities and changes appeared. For instance, a new entity F’ appeared, the 10°C isotherms “A”, “D” and E take on different patterns, etc. Changes on the isotherm “a” are modeled as follows (Figure 1(2))a:: displacement (northwest; 1981~1985, 1986~1990; air temperature isotherm), a’:: displacement (northwest; 1986~1990, 1991~1995; air temperature isotherm), A’:: displacement (northwest; 1991~1995, 1996~2000; air temperature isotherm).Figure 1. Moving isolines: (1) 10°C isotherm in 1980s’and in 1990s’,and (2) 10°C isotherms in 1981~1985, 1986~1990, 1991~1995, 1996~200.Yang and Claramunt4.3. Moving regionsA moving region is modelled as a whole entity, which can appear, disappear, reappear, contract, extend, deform, and move from one position to another. Using the concept of moving region, changes on air temperatures regions can also be modelled. Let us consider a representation of gradual changes in air temperature over the period from 1980s to 1990s in the region of interest (note that those regions are computed using homogeneous areas of air temperatures). Those regions are represented at different levels of abstraction (i.e. so-called multi-representation changes as denoted in Figure 2(a) to (f)). At levelA (Figure 2(a) and (b)), let us consider the case of the regions “a” and “d”. The entity “a” contracts while “d” expands. During the same period of time, both “a” and “d” experience a displacement process – not completely determined – together with a “deformation”. LevelB (Figure 2(c),(d),(e) and (f)) gives a more precise representation of the phenomenon with a lower level of spatial resolution (i.e. 1/10 of levelA), a temporal granularity of 5-years, and additional classes of air temperatures. Let us model changes on the entity “a” according to those two levels of abstraction:LevelAa:: (deformation (position-a, traceExtent (spatial extent-a, spatial extent-A); 1980s’, 1990s’; a, a’) & displacement (position(position-a, position-A), traceExtent (union(spatial extent-a, spatial extent-A)); 1980s’, 1990s’; a, a’)LevelBa:: (contraction (position-a, traceExtent (spatial extent-a, spatial extent-a’); 1981~1985, 1986~1990; a, a’) & displacement (position(position-a, position-a’), traceExtent (union(spatial extent-a, spatial extent-a’)); 1981~1985, 1986~1990; a, a’)& deformation() & fissiparism (position-a, position-a’, position-b’, traceExtent (union (spatial extent-a, spatial extent-a’, spatial extent-b’); 1981~1985, 1986~1990; a à a’ + b’)),a’:: (contraction (position-a’, traceExtent (spatial extent-a’, spatial extent-A’);1986~1990, 1991~1995; a’, A’) & displacement (position(position-a’, position-A’), traceExtent (union(spatial extent-a’, spatial extent-A’)); 1986~1990, 1991~1995; a’, A’) & deformation()) & b’:: contraction (position-b’, traceExtent (spatial extent-b’, spatial extent-B’); 1986~1990, 1991~1995; b’, B’),A’:: (contraction (position-A’, traceExtent (spatial extent-A’, spatial extent-A);1991~1995, 1996~2000; A’, A) & displacement (position(position-A’, position-A), traceExtent (union(spatial extent-A’, spatial extent-A)); 1991~1995, 1996~2000; A’,A)&deformation() & fissiparism (position-A’, position-A, position-G, traceExtent(union (spatial extent-A’, spatial extent-A, spatial extent-G); 1991~1995, 1996~2000;A’ à A + G)) &B’:: disappearance (position-B’, spatial extent-B’; 1991~1995, 1996~2000; B’, B)A Process-oriented Multi-representation of Gradual Changes(a)1980s (b)1990s(c)1981~1985 (d)1986~1990(e) 1991~1995 (f)1996~2000Figure 2. Multiple representation of air temperature distribution and changesEntity-based queriesEntity-based queries involve spatial and thematic properties, possibly over time. We identify three types of entity-based queries depending on the values returned:(1) return-spatial queries. Let us consider the following query example “Where are the air temperature areas up to 0°C(or above 10°C, below 10°C) in 1980s north of 36°N in the region of interest”. This query is expressed as follows (the following queries are expressed in a basic grammatical form illustrated with some values that correspond to the semantic of the examples given)SpatialE_QS(36°N~42’N: 111´E ~123’E, 1980s, air temperature, {value| value>0°C})Yang and ClaramuntAt levelA (Figure 2(a) and (b)), this query returns (i.e. the output of the query) some spatial values, that is, the homogenous region entities “a”, “b”, “d”, but not “e” as “e” is not in the given spatial extent, and not “c” as it’s below 0°C. At levelB (Figure 2(c),(d),(e),(f)), the query returns the regions “A”, “B”, “D”, “F”.(2) return-thematic queries. This is illustrated by the following example “What is the air temperature in Beijing (39°56'N: 116°17'E) in 1990s?”. This query is specified as followsThematicE_Q(39°56'N: 116°17'E, 1990s),where the query returns a thematic value{value| value>10°C} at levelA.(3) return-temporal query. This is illustrated at the levelB by the query “when is the air temperature in entity o(o’) {value| value>15°C}?”. The query is as followsTemporalE_Q(spatial extent of entity o(o’), air temperature, {value| value>15°C}), where the query returns two periods: 1991~1995 and 1995~2000.Let us finally introduce the example of a spatio-temporal “when and where air temperature is up to 10°C in the region of interest over the period from 1980s to 1990s?”. The query is as followsSpatio-temporalE_Q(28°N~42’N: 111°E ~123’E, 1980s, 1990s, air temperature, {value| value>10°C }),This query returns a list of moving regions together with their temporal values. At levelA, the result is, “d” in 1980s, “B” in 1990s, “D” in 1990s. At levelB, the result is, “d”, “l”, “k”, “m”, “o”, “i” from 1981 to 1985, “d’”, “i’”, “o’”, “p’” from 1986 to 1990, “D’”, “I’”, “K’”, “P’” from 1991 to 1995, and “D”, “H”, “I”, “J”, “N”, “Q”, “R” from 1996 to 2000.4.4. Change-based queriesChange-based queries model changes on either moving lines or moving regions. We illustrate this class of query using either increase or decrease on air temperature, where these changes happen, and when those changes happen (or the combination of those criteria). An example of change-based query is as follows: “where are the places where the air temperature increase from 1980s to 1990s?”. The signature of this query is as followsC_QSTA(28°N ~42’N: 111°E ~123’E, 1980s, 1990s, air temperature increase, 10°C, 11°C),where this query returns the intersection of the isotherms “a” and “a1” as illustrated in Figure 3. Another example is the retrieval of the places where air temperature increases from {value| value<10°C} to {value|value>10°C} from 1980s to 1990s at the levelA. The query is as followsC_QSTA(28°N~42’N: 111°E ~ 123’E, 1980s, 1990s, air temperature increase, {value|0°C < value<10°C}, {value| value>10°C}).A Process-oriented Multi-representation of Gradual Changeswhere this query returns the intersection of the entities “a” and “D”. Finally let us give the example of a spatio-temporal and thematic query related to the changes on some specified entities “when does the air temperature of the entity o’ increase from {value| 10°C<value<15°C} to {value| value>15°C}?”. This query is expressed asTemporalC_Q(points in o’:: increase({value| 10°C <value<15°C}, {value| value>15°C})), where this query returns “from 1986~1990 to 1991~1995”.Figure 3. 10°C isotherm in 1980s and 11°C isotherm in 1990s4.5. DiscussionThis case study provides an illustration of the potential of our modeling approach. Moving regions and moving lines give alternative representation of geographical changes. They help in the inductive observation of the distribution of air temperature changes and the classes of process that generate those changes. Changes can be observed at different levels of abstraction, resolution and granularity in the spatial and thematic dimensions. that is, when and where air temperature increased, qualitatively (e.g. where a given change appeared) and quantitatively (e.g. total area of the regions transformed by an air temperature increase). At a high level, it can reflect long-term (even globally) climatic or environmental changes. At a low level, it can help to explore microclimate or short-term environmental changes. This gives a large range of applications from the observation of environmental to the understanding of the physical mechanism behind the phenomena observed.The modeling approach is entity- and change-based at the conceptual level, object-oriented at the database level. Entities are derived from continuous representations of space at different time steps, processes from a modeling analysis of entity changes. This allows for a form of multi-representation as the temporal granularity and the spatial resolution are redefined during those derivation. Three-domain queries support then an observation of changes, queries manipulate moving regions, moving isotherms or even the processes that trigger those changes. Such a query language provides a new way of exploring geographical changes at the entity level and a support for preliminary exploration of spatio-temporal patterns. These facilities might complement spatial data analysis (e.g. map algebra and overlay operations), this enlarging the range of operations available to scientists and decision-makers. As illustrated in this case study the proposed approach is particularly adapted to the modeling of gradual changes. Overall the model helps to describe and reason over what and how (e.g.Yang and Claramuntappearance vs. disappearance of an entity, displacement of a region or an isotherm), when (e.g. at an instant or over a period of time), where (e.g. at a given location, along a line, over a region) a phenomenon happens in a geographical space. These information are particularly useful for environmental scientists that wish to represent and analyze geographical changes and discover the physical rules behind them.5.ConclusionThis paper introduces a process-based approach oriented to the modeling of gradual changes, The model considers entities and changes as modeling primitives. Entities and processes together with their properties are described in the spatial, temporal and thematic dimensions. Processes are classified using a taxonomy of elementary processes, and composite processes using logical expressions. Those logical expressions allow for a description of geographical phenomena in a given region of interest, at different levels of abstraction. The model is completed by spatial, temporal and thematic operators that allows users to interact with entities and changes and explore patterns in all those dimensions.The model is illustrated by a case study oriented to the observation of air temperature changes in North and partly East China. This work constitutes a preliminary step of our research. We plan to enrich the semantics of our model by exploiting the capabilities of object-oriented modeling at both the geographical data description and manipulation levels. This should facilitate further implementation developments such as the design of an entity-based and change-based query interface that manipulates gradually changing phenomena in the spatial, temporal and thematic dimensions.ReferencesAbler, R., Adams, J. S., and Gould, P. (1971) Spatial Organization: The Geographer’s View of the World. London, Englewood Cliffs: Prentice Hall.Armstrong, M.P. (1988) Temporality in spatial databases. In GIS/LIS ‘88 Proceedings: Accessing the World, Volume II. Falls Church, VA: American Society for Photogrammetry and Remote Sensing, pp. 880-889.Claramunt, C. and Thériault, M. (1995) Managing Time in GIS: An event-oriented approach, Clifford, J. and Tuzhilin, A. (eds.), Recent Advances on Temporal Databases, Zurich, Switzerland: Springer-Verlag, pp. 23-42.Claramunt, C. and Thériault, M. (1996) Toward semantics for modelling spatio-temporal processes within GIS, Kraak, M. J. and Molenaar, M. (eds.), Advances in GIS II, Delft, the Netherlands: Taylor and Francis, pp. 47-64.Claramunt, C., Parent, C. and Thériault, M. (1997) Design patterns for spatio-temporal processes, Spaccapietra S. and Maryanski F. (eds.), in Searching for Semantics: Data Mining, Reverse Engineering, Chapman & Hall, pp. 415-428.Claramunt, C., Parent, C., Spaccapietra, S. and Thériault, M. (1999) Database modelling for environmental and land use changes, Geertman, S., Openshaw S. and Stillwell J. (eds.), Chapter 10 in Geographical Information and Planning: European Perspectives, Springer-Verlag, pp. 181-202.Claramunt, C. and Li, B. (1999) A multi-scale approach to the propagation of temporal。