Support description

(Temporal) relationships between variables may be obscured or distorted when viewed with different connections between the spatial units. The change of support (COS) problem is concerned with inference about the values of the variables at supports different from at which it has been observed. The term “support” has come to mean simply the size or volume associated with each data value, but the complete specification of this term also includes the geometrical size, shape, and spatial orientation of the regions associated with the measurements.

Question to be answered: What was the change of support A (t) -> A (t + dt) for all t

Input:

Data

Set of polygons having the attributes
[mandatory]: ID
[mandatory]: geometry
[mandatory]: time stamp
[optional]: predecessors
[optional]: data value
[optional]: thematic attribute

Parameters

[optional]: Function which determines the predecessor

Reference time stamp is always the first layer, change is determined according to the sorting of the polygons, default sorting is time stamp ascending.

If predecessors are not defined, generate them, else use the values provided in the input. Default method to determine predecessor is spatial overlap.

If data values or thematic attributes are set, they will be considered in the step for creating links (e.g. use only polygons with class "water" to generate links).

Example structure

ID	Geometry	Time Stamp	Predecessors (optional)	Data Value (optional)	Thematic Attribute (optional)
1	geom	t_1	-	3.14	"Water"
2	geom	t_2	1	1337	"Water"
3	geom	t_2	1	666	"Forest"
4	geom	t_3	2,3	1234	"Water"

Output:

Encoding of Change of Support

Possibilities of qualitative COS:

Describing the process, which generates the polygon.

- Split
- Merge
- Dissolve/Annihilation
- Stable

Possibilities of quantitative COS:

Geometric:
	- area
	- compactness
	- circumference
Topologic:
	- orientation

Example output

If column predecessors are not populated in the input, it will be added.

ID	Geometry	Time Stamp	Predecessors	Data Value (optional)	Thematic Attribute (optional)	Qualitative Change of Support	Quantitative Change of Support
1	geom	t_1	-	3.14	"Water"	-	{overall_variability: 0.3}
2	geom	t_2	1	1337	"Water"	Split	{"area":{"increase", "5%", 235},"compactness":{"decrease", "3%", 0.1}, ...}
3	geom	t_2	1	666	"Forest"	Split
4	geom	t_3	2,3	1234	"Water"	Merge

Visualisation

Example visualisation (from Guttler, Fabio; Ienco, Dino; Nin, Jordi; Teisseire, Maguelonne; Poncelet, Pascal (2017): A graph-based approach to detect spatiotemporal dynamics in satellite image time series. In ISPRS Journal of Photogrammetry and Remote Sensing 130, pp. 92–107. DOI: 10.1016/j.isprsjprs.2017.05.013).