Spatio-temporal Data. Modeling Spatio-temporal Objects 80s and 90s research for spatial and temporal databases. 90s space and time objects are put together in one single data model => spatio-temporal data models. First attempts: adding time attributes in a spatial data model or adding spatial objects in a temporal data model. Then ST data models that treat space and time equally, as similar dimensions / domains (unified ST view).
Spatio-temporal Semantics Spatio-temporal attribute: an attribute that contains the evolution of a spatial object in time (spatial attribute + time attribute) Spatio-temporal object: an object that contains a ST attribute Spatio-temporal evolution: the spatial evolution of an object, in time. For example: land parcels are evaluated when a working day is finished this kind of evolution is a discrete point- based; the shape of a land parcel is modifying in time, but only in discrete steps; a car that is moving on a road has a continuous evolution of its spatial position.
Spatial attributes and changes of ST objects spatial attributes Spatial properties represent characteristics: metric (position and size), directional (orientation or direction), or topological (shape). These properties may suffer changes during following actions: translation: changing of position (in case of objects of type point, line, or region), rotation: changing of direction (in case of objects of type line or region), expansion or contraction: changing of direction size (in case of objects of type line or region), mutation: changing of shape (in case of objects region).
Spatial attributes and changes of ST objects spatial attributes Remark. Other types of transformations (as mutations) are aggregation (reunion or join) and fragmentation (division or detachment). These operations are affecting more than one object; usually some objects are destroyed or created during these actions. Figure 1.7. represents a spatial object (rectangle) in its initial state (a), its state after performing a 90 rotation (in trigonometric direction) (b), and its state after performing a mutation (other shape, but with the same area) (c). Usually for a spatial object we represent only its coordinates (the coordinates if it is a point, the coordinates of its end-points if it is a line segment, or the coordinates of the polygons vertexes if it is a region). The other properties can be evaluated using the coordinates.
Figure 1.7. (a), (b), (c)
Spatio-temporal applications 1.events in space and time: point spatial objects with discrete point- based evolution in time (e.g. world records); 2.objects (positions) valid on a time interval: point spatial objects X time intervals (e.g. trailers); 3.mobile objects: objects for which the shape is not important, are represented as point, and their position has a continuous evolution in time (e.g. transportation systems); 4.regions with instantaneous existence: the spatial properties include position and shape, and they have a discrete point-based evolution in time (e.g. region where Olympic Games take place in one year); 5.regions that are valid for a time interval: spatial objects with shape X time intervals (e.g. land parcels); 6.mobile regions: the shape of spatial objects is continuously changing in time (e.g. meteorological phenomenon).
The Properties of Spatio-temporal Objects Practically, the properties of a single ST object may include: non-spatial, non-temporal (thematic); without spatial or temporal meaning; spatial (geometric); usually objects with complex structure; temporal (non-spatial); thematic time-varying attributes + time attribute; spatio-temporal; spatial attribute + time attribute.
Spatio-temporal Databases Definition. Spatio-temporal databases (STDB) manage spatial objects and their evolution in time. A ST DBMS should include ST data types, ST query language, ST indexes etc. Example. Lets consider a relation that contains information about land parcels Land, having one spatial attribute (the rectangular shape of the parcel) and a time attribute that represents the VT interval for that spatial. The pair of attributes (shape, time) is a ST attribute, and Land objects are ST objects. Table 1.12. contains example of Land objects.
Identifying Spatio-temporal Objects Some ST data models consider that an object preserves its id after its spatial state is changing, but other models consider that such an object changes its id for every change. Exception in case of aggregation or fragmentation actions: Aggregation reunion: the affected objects are destroyed and we obtain a new object join: the objects that are attached to another object are destroyed, and the object to which we attached some objects preserves its id Fragmentation division: one object is destroyed and new objects are obtained after division detachment: we are detaching some parts from one object; this object preserves its id, and we also obtain some new objects. See Figure 1.9.
Figure 1.9. (a) Initial configuration of three objects; (b) Spatial configuration after the reunion of P1 and P3, or after attachment of P3 to P1; (c) Spatial configuration after the division of P2 in P5 and P6, or after detaching P6 from P2
Modeling Spatio-temporal Data: Spatio-temporal Data Models Snapshot data model [LC88] It is one of the simplest ST data models. It starts from a spatial data model (with any structure of space) and adds a time attribute. This model applies a timestamping at the level of a set of objects. The objects are represented as spatial layers, and each layer is timestamped. The spatial objects that can be represented are points, lines, regions, or partitions or networks. All the states that belong to one object are marked with the same id (id preservation in time). If at least one spatial object is changed (position and / or shape), one spatial object is created, or one spatial object disappears, a new layer is stored (of course with a new timestamp).
There is no direct relation between two successive layers. There is no information about the events that caused the changing in represented layers. The time is VT, and it is linear, discrete, absolute, represented as time instances (discrete point-based evolutions). Figure 1.10. represents a succession of spatial layers. Advantages. This model can be easily implemented. The current state of all objects is available in any moment. Disadvantages. If one object is changing more frequently than the others, than all the generated layers contain the same information about those objects. The list of layers does not contain explicit information about the changes in order to see the changing suffered by an object, we have to compare the successive layers.
Figure 1.10. Layers for Snapshot data model
Improvement for Snapshot model [Ar92]: in order to see easier the changes suffered by objects and to reduce the amount of redundant data, the usage of so-called delta- files is proposed. Only the initial and the current layers are stored. All the changes that took place are stored in delta-files. Therefore, if we want to see the evolution of one spatial object or its state in a specific moment, we read the delta-files beginning with the first layer, until we reach the moment in which we want to know the objects state.
Another ST data model that tries to add Time in GIS [La92] proposes to apply timestamps at attribute level (it is a model spatial-oriented). In this model, space is partitioned and for each partition the evolution of some attribute is stored. Figure 1.11.(a) represents a partition of space. Each of these regions can be in one of two states: flooded (1) and not-flooded (0). For each region we have its spatial characteristic (shape) and the evolution of its state in time. Each timestamp (when something changed for at least one region) is a new attribute in this ST table. The spatial objects are represented in a vectorial manner, and the temporal domain is linear, discrete, and both time types (VT and TT) are supported.
The model presented in [HW90] (Historical Cadastral Database) associates timestamps to spatial objects. One timestamp is represented as a time interval [tc, td], where tc and td represent the moments when the objects was created / destroyed, and are VT time instances. The temporal domain is linear, discrete, and absolute. The objects that exist in reality have td = Now. Spatial objects are modeled using vectorial representation, and they can be points, lines, or regions. This model is able to represent their interval-based discrete evolution. This model has the advantage that does not store redundant data (as Snapshot model). One object is loosing its id after one change. A solution [RM94] for this problem is to store references between the successive states of