Spatiotemporal Modelling
Reading : Temporal GIS, Chapter 2
Questions:
 What is a Spatiotemporal Continuum?
 What is a coordinate system?
 What is a space/time metric?
 What are examples of composite space/time metrics?
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Spatiotemporal Continuum
A spatiotemporal continuum (or domain) E is a set of points associated with a continuous spatial
arrangement of events combined with their temporal order.
A useful spatiotemporal continuum is equipped with a coordinate system and a measure of
space/time distance.
E: (coordinates p, metric
dp )
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The coordinate system
A coordinate system identifies a point in the spatiotemporal domain E can be identified by means of
n
the spatial coordinates s  ( s1 ,..., sn )  S  R and the temporal coordinate t along the temporal axis
T  R1 ,
p  (s, t )  E = S  T .
An interesting classification of the spatial coordinate systems ( s ) can be made in terms of the
Euclidean and the non-Euclidean group of coordinate systems
Example: Traditionally, geographic coordinates are expressed in terms of latitude and longitude:
N
Meridian
P
Meridians
Greenwich
meridian
P
P
70 0 N
Latitude
 P
0
60 N
Equator
0
100 E
S
0
110 E
Longitude
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The metric
The second feature of a spatiotemporal continuum E is its metric, that is, a mathematical expression
that defines distances in space/time. There is the separate metric, and the composite metric.

The separate metric includes a spatial distance ds and a time interval dt ,
dp : ( ds , dt )  R1 ,0  T
The composite metrical structure assumes that the space and time parameters are connected
by means of an analytical expression g , i.e.,
dp: dp  g (ds1 ,..., dsn , dt )
Examples of spatial metrics:
Spatial Euclidean metric
1-norm metric
ds e 
i 1 dsi2
n
ds a  i 1 dsi
(See and Reproduce Example 2.11 with BMElib)
n
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ds
Max permeability path
P1
pm
 max ds PM
P1
P2
P2
Examples of composite space/time metrics:
Some physical applications
dp  ds 2  v 2 dt 2
Space/time metric in BMElib
dp  ds  dmax(3) dt
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