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Grid Topologies

Introduction

This page tries to inspect many of the different types of N-dimensional (spatiotemporal) gridded coverage topologies that could be stored in rasdaman, accompanying every case with GML Web Coverage Service (WCS) responses upon both trimming and slicing.

Despite some cases might rarely have a practical real-world example, here we want to give examples for as many allowed geometries as possible.

Slicing on a certain CRS axis means that its knowledge is removed in the output result, so that the dimensionality of the CRS gets decreased for each slicing appearing in the WCS request. However, this does not mean that the grid dimensionality gets decreasead as well: N-D grids can span an (N+M)-D CRS space, having (M≥0), so as long as the grids can exist in the sliced space, their dimensions will not be reduced.

When a CRS is sliced on each of its defined axes, then it can be safely removed from the output description. However, a CRS might be partially sliced on a subsets of the axes it defines, hence this prompts the issue of defining a CRS URI nomencalture to specify that only certain axes are considered within that CRS definition. Still the issue is open, so by now we will propose an interim solution: e.g. if slicing on longitude is applied on a WGS84 geographic 3D CRS (e.g. EPSG:4327, axes Lat, Long and h), then we will identify the sliced CRS as http://kahlua.eecs.jacobs-university.de:8080/def/crs/EPSG/0/4326?axes='Lat,h'.

All responses will highlight the domainSet of each coverage, which will all translate to some gml:Grid rectified or referenceable subtype. We will assume that warped grid will be described via ReferenceableGridByArray, although an alternative description via origin, offset vectors and matrices of coefficients is also possible. In case of mixed rectilinear/curvilinear geometries, a non-standard so-called ReferenceableGridByArrayAndVectors type [1] will be used, for a more compact and convenient GML description. Coefficients in a ReferenceableGridByVector are also kept optional, to allow mixing of regularly and irregularly spaced axis in a same geometry (see again [1]).

It should be noted that in some examples the type of the geometry gets simplified from a referenceable to a rectified grid (e.g. see case 2a-ITS). This might happen that trimming or slicing would extract a part of the whole grid with simpler geometry indeed (think of a time slice in an irregular time series of regularly gridded images). Geometry simplification is not mandatory however, nor it is prescribed by WCS standard. A regular grid can always we described via a ReferenceableGridBy* GML type.

When determining which CRS type should be bound to a certain coverage, the term SpatialCRS will mean any Earth or Planetary (or Image) related CRS, like VerticalCRS, GeographicCRS, ProjectedCRS, etc. See GML 3.2.1 (OGC 07-036) for more info on the available CRS types.

Finally, we will assume that all the time series will be referenced by the daily-resolution (UoM=days [d]) ANSI-Date CRS along the temporal dimension, which (by default) has a t positive-onwards axis. By default the composition order of spatiotemporal CRSs here is first space, then time; this however is not required at all.

NB. The axes labels expressed in the geometric domain of a coverage are the labels of the coverage axes, which here will be labelled as increasing numbers (0, 1, 2, ...), by default. Indeed, they are independent from the axes labels of its CRS, which are instead used in the WCS GetCoverage requests.

grid topology issues list

Abbreviations:

GML : Geographic Markup Language
CRS : Coordinate Reference System
SO : Single object
RTS : Regular Time Series
ITS : Irregular Time Series
MRTS : Moving Regular Time Series
MITS : Moving Irregular Time Series

[1] P. Campalani, A. Beccati, and P. Baumann. Improving Efficiency of Grid Representation in GML, 2013. EnviroInfo'13.

Topologies Index

Due to the high number of possible cases, hereinafter we propose a first main table for global view which puts purely-spatial types of topology per row, which can then be repeated, or evolve, in time with or without regular time steps (columns).
Each cell then links to a dedicated subsection with the GML descriptions (assume default namespace is "gml").

In the 1D case, it is also clear how the gridded coverages can cover datasets which are not usually associated with the concept of grids (e.g. trajectories)

id	description	dim	SO	RTS	ITS	MRTS	MITS
1	Temporal series of data with no spatial reference	1D	—-	link 	link 	—-	—-
2	*Point measurements (with* spatial reference) on a straight line …**	1D
2a	… parallel to a CRS axis (2D space)	"	link 	link 	link 	link 	link 
2b	… diagonal wrt CRS axes (in 2D space)	"	link 	link 	link 	link 	link 
2c	… diagonal wrt CRS axes (in 3D space)	"	link 	link 	link 	link 	link 
2d	… diagonal in 3D space with irregular spacing	"	link 	link 	link 	link 	link 
3	*Point measurements (with* spatial reference) on a curvilinear line …**	1D
3a	… in the 2D space	"	link 	link 	link 	link 	link 
3b	… in the 3D space	"	link 	link 	link 	link 	link 
4	Gridded geo-image in the 2D space …	2D
4a	… with regular spacing, aligned with CRS axes	"	link 	link 	link 	link 	link 
4b	… with regular spacing, and rotation	"	link 	link 	link 	link 	link 
4c	… with irregular spacing, and rotation	"	link 	link 	link 	link 	link 
4d	… with curvilinear axes (warped grid)	"	link 	link 	link 	link 	link 
4e	… warped grid, and 2 (real+simulation) time axes	"	—-	link 	link 	link 	link 
5	Gridded geo-image in the 3D space (oblique plane) …	2D
5a	… with regular spacing	"	link 	link 	link 	link 	link 
5b	… with irregular spacing	"	link 	link 	link 	link 	link 
5c	… with curvilinear axes (warped grid)	"	link 	link 	link 	link 	link 
6	Gridded 3D geo-cubes …	3D
6a	… with regular spacing	"	link 	link 	link 	link 	link 
6b	… with regular XY spacing, but irregular heights	"	link 	link 	link 	link 	link 
6c	… with irregular XYH spacing	"	link 	link 	link 	link 	link 
6d	… with curvilinear axes (warped cube)	"	link 	link 	link 	link 	link 
6e	… warped cube, and 2 (real+simulation) time axes	"	—-	link 	link 	link 	link 

Examples

Case 1

1D TEMPORAL SERIES OF ASPATIAL DATA.

This section covers time series of point observations with no spatial reference (or where the spatial reference was not considered relevant): in this case the only distinction is whether there is a regular time step between observations, or not. In its degenerate case, the series turns to a single point.

(Attach a scan of the sketches here with all types in this subcategory?)

1-RTS

GML coverage type	GML domainSet	native CRS	CRS dim
RectifiedGridCoverage	RectifiedGrid	TemporalCRS	1D

WCS trimming: ...subset=t("2013-01-21","2013-04-25")...

<domainSet>
  <RectifiedGrid id="1-RTS_t" dimension="1" uomLabels="d" srsDimension="1" 
   srsName="http://kahlua.eecs.jacobs-university.de:8080/def/crs/OGC/0/AnsiDate">
    <limits>
      <GridEnvelope>
        <low>0</low>
        <high>4</high>
      </GridEnvelope>
    </limits>
    <axisLabels>0</axisLabels>
    <origin>
      <Point id="O">
        <pos>150501</pos><!-- ANSI date for 2013-01-21 -->
      </Point>
    </origin>
    <offsetVector>1</offsetVector><!-- daily data -->
  </RectifiedGrid>
</domainSet>

WCS slicing: ...subset=t("2013-01-21")...

<domainSet>
  <!-- 0D geometry: slicing removes one dimension -->
  <RectifiedGrid id="1-RTS_s" dimension="0">
    <limits>
      <GridEnvelope>
        <low></low>
        <high></high>
      </GridEnvelope>
    </limits>
    <axisLabels></axisLabels>
    <origin>
      <Point id="O">
        <pos></pos>
      </Point>
    </origin>
    <offsetVector></offsetVector>
  </RectifiedGrid>
</domainSet>

Context Navigation

Grid Topologies

Introduction

Topologies Index

Examples

Case 1

1-RTS

1-ITS

Case 2

Case 2a

2a-SO

2a-RTS

2a-ITS

2a-MRTS

2a-MITS

Case 2b

2b-SO

2b-RTS

2b-ITS

2b-MRTS

2b-MITS

Case 2c

2c-SO

2c-RTS

2c-ITS

2c-MRTS

2c-MITS

Case 2d

2d-SO

2d-RTS

2d-ITS

2d-MRTS

2d-MITS

Case 3

Case 3a

3a-SO

3a-RTS

3a-ITS

3a-MRTS

3a-MITS

Case 3b

3b-SO

3b-RTS

3b-ITS

3b-MRTS

3b-MITS

Case 4

Case 4a

4a-SO

4a-RTS

4a-ITS

4a-MRTS

4a-MITS

Case 4b

4b-SO

4b-RTS

4b-ITS

4b-MRTS

4b-MITS

Case 4c

4c-SO

4c-RTS

4c-ITS

4c-MRTS

4c-MITS

Case 4d

4d-SO

4d-RTS

4d-ITS

4d-MRTS

4d-MITS

Case 4e

4e-RTS

4e-ITS

4e-MRTS

4e-MITS

Case 5

Case 5a

5a-SO

5a-RTS