© ISO 2006 – All rights reserved
ISO TC 211/SC N
Date: 2006-01-12
ISO/WD xxxxx.3
ISO TC 211/SC /WG
Secretariat: SN
Geographic information — Spatial referencing by coordinates extension for parametric values
Information géographique — Élément complémentaire
Warning
This document is not an ISO International Standard. It is distributed for review and comment. It is subject to
change without notice and may not be referred to as an International Standard.
Recipients of this draft are invited to submit, with their comments, notification of any relevant patent rights of
which they are aware and to provide supporting documentation.
Document type: International Standard
Document subtype:
Document stage: (20) Preparatory
Document language: E
D:\81907475.doc STD Version 2.1c2
ISO/WD xxxxx.3
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Contents
Page
Foreword ............................................................................................................................................................. v
Introduction ......................................................................................................................................................... v
1
Scope ...................................................................................................................................................... 1
2
Conformance requirements.................................................................................................................. 1
3
Normative references ............................................................................................................................ 1
4
Terms and definitions ........................................................................................................................... 1
5
5.1
5.2
5.3
Conventions ........................................................................................................................................... 2
Abbreviated terms ................................................................................................................................. 2
UML notation .......................................................................................................................................... 2
Attribute status ...................................................................................................................................... 2
6
6.1
6.2
6.3
6.4
6.5
6.5.1
6.6
6.7
Spatio-parametric referencing ............................................................................................................. 3
Overview ................................................................................................................................................. 3
Parametric coordinate reference system ............................................................................................ 3
Parametric coordinate system ............................................................................................................. 3
Parametric datum .................................................................................................................................. 5
Spatio-parametric coordinate reference system ................................................................................ 6
Spatio-parametric coordinate reference system with time ............................................................... 7
Transformation and conversion of parametric coordinate reference systems .............................. 7
Geography Markup Language (GML) .................................................................................................. 7
Annex
A.1
A.1.1
A.1.2
A.1.3
A.2
A.2.1
A.2.2
A (normative) Conformance ................................................................................................................. 8
Conformance of a parametric coordinate reference system ............................................................ 8
Abstract test suite ................................................................................................................................. 8
Parametric coordinate reference system ............................................................................................ 8
Spatio-parametric or spatio-parametric-temporal coordinate reference system ........................... 8
Conformance of a coordinate operation ............................................................................................. 8
Abstract test suite ................................................................................................................................. 8
Coordinate operation on a parametric CRS........................................................................................ 8
Annex B (informative) Examples ..................................................................................................................... 10
B.1
Parameters and functions .................................................................................................................. 10
B.1.1 Pressure ............................................................................................................................................... 10
B.1.2 Density .................................................................................................................................................. 10
B.1.3 Log-pressure height ............................................................................................................................ 10
B.1.4 Potential temperature .......................................................................................................................... 10
B.1.5 Sigma .................................................................................................................................................... 11
B.1.6 Hybrid sigma-pressure ....................................................................................................................... 11
B.1.7 Hybrid height ....................................................................................................................................... 11
B.1.8 SLEVE ................................................................................................................................................... 11
B.1.9 Potential vorticity ................................................................................................................................ 11
B.1.10 More elaborate functional forms. ....................................................................................................... 11
B.1.11 Datums.................................................................................................................................................. 12
B.1.12 References ........................................................................................................................................... 12
B.2
Examples .............................................................................................................................................. 12
Annex C (normative) Geography Markup Language (GML) ......................................................................... 16
C.1
Introduction .......................................................................................................................................... 16
C.2
Parametric coordinate reference system .......................................................................................... 16
C.2.1 ParametricCRS .................................................................................................................................... 16
C.2.2 ParametricCRSPropertyType ............................................................................................................. 17
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C.3
C.3.1
C.3.2
C.4
C.4.1
C.4.2
iv
Parametric coordinate system .......................................................................................................... 17
ParametricCS ...................................................................................................................................... 17
ParametricCSPropertyType ............................................................................................................... 17
Parametric datum................................................................................................................................ 17
ParametricDatum ................................................................................................................................ 17
ParametricDatumPropertyType ......................................................................................................... 18
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Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO xxxxx was prepared by Technical Committee ISO/TC 211, Geographic information / Geomatics,
Subcommittee SC , .
This second/third/... edition cancels and replaces the first/second/... edition (), [clause(s) / subclause(s) /
table(s) / figure(s) / annex(es)] of which [has / have] been technically revised.
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Introduction
ISO 19111 describes the elements necessary to fully define various types of reference systems used for
spatial referencing by coordinates. In ISO 19111 a coordinate is one of n scalar values that define the position
of a point. ISO 19111 allows for coordinates which are angular such as latitude and longitude or linear such as
easting and northing. ISO 19111 also describes the concept of a compound coordinate reference system. A
compound coordinate reference system uses at least two independent coordinate reference systems to
describe a 3-dimensional spatial position.
Scientific communities, especially those concerned with the environmental sciences, frequently express
spatial position in terms of a parameter or function. Examples are widespread, but latitude, longitude and
pressure is a commonly encountered example. Within these communites this parameter or function is treated
as a coordinate. This International Standard defines a parametric coordinate reference system using the
concepts from ISO 19111. The provisions of ISO 19111 are then used to include a parametric coordinate
reference system as part of a compound coordinate reference system. Optionally time may also be included
as additional axis or axes.
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WORKING DRAFT
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Geographic information — Spatial referencing by coordinates extension for parametric values
1
Scope
This International Standard describes the conceptual schema for the description of spatial referencing using
parametric values or functions. It uses the schema of ISO 19111 to combine a position referenced by
coordinates with a parametric value to form a spatio-parametric coordinate reference system. The spatioparametric coordinate reference system may optionally be extended to include time.
This International Standard is applicable to producers and users of environmental information.
2
Conformance requirements
Any coordinate reference system claiming conformance to this International Standard shall satisfy the
requirements of Annex A.
3
Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the cited edition applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO/TS 19103, Geographic information - Conceptual schema language
ISO 19108, Geographic information - Temporal schema
ISO/DIS 19111 (2005), Geographic information - Spatial referencing by coordinates, edition 2
ISO 19136, Geographic information - Geography Markup Language (GML)
4
Terms and definitions
For the purposes of this document the terms and definitions of ISO 19111 and the following terms and
definitions apply.
4.1
parametric coordinate system
one-dimensional coordinate system where the axis units are parameter values
4.2
parametric coordinate reference system
coordinate reference system based on a parametric datum
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4.3
parametric datum
datum describing the relationship of a parametric coordinate system to an object
NOTE
The object is normally the Earth.
4.4
spatio-parametric coordinate reference system
compound coordinate reference system in which one component is spatial and another component is a
parametric coordinate reference system
NOTE
Normally the spatial component is "horizontal" and the parametric component is "vertical".
4.5
spatio-parametric-temporal coordinate reference system
compound coordinate reference system comprised of spatial, parametric and temporal coordinate reference
systems
5
Conventions
5.1
Abbreviated terms
CCRS
compound coordinate reference system
CRS
coordinate reference system
GML
Geography Markup Language
UML
Unified Modelling Language
5.2
UML notation
In this International Standard, the conceptual schema for describing spatio-parametric referencing is modelled
with the Unified Modelling Language (UML). The basic data types and UML diagram notations are defined in
ISO/TS 19103 and ISO/IEC 19501.
5.3
Attribute status
In this International Standard, attributes are given an obligation status:
Obligation
Definition
Meaning
M
mandatory
This attribute shall be supplied.
C
conditional
This attribute shall be supplied if the condition (given in the attribute
description) is true. It may be supplied if the condition is false.
O
optional
This attribute may be supplied.
In this International Standard the Maximum Occurrence column indicates the maximum number of
occurrences of attribute values that are permissible, with N indicating no upper limit.
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6
6.1
Spatio-parametric referencing
Overview
ISO 19111, Geographic information - Spatial referencing by coordinates, defines a coordinate reference
system as coordinate system which is related to an object (such as the Earth) by a datum. A coordinate
system is a set of mathematical rules for specifying how coordinates are to be assigned to points. A
coordinate system will have one or more axes. A datum defines the position of the origin, the scale, and the
orientation of a coordinate system. ISO 19111 describes several subtypes of coordinate reference system,
coordinate system and datum. This International Standard defines a further subtype of each to accommodate
parametric referencing.
6.2
Parametric coordinate reference system
A parametric coordinate reference system shall be a subtype of a single CRS. It shall consist of one
parametric coordinate system and one parametric datum; these elements are described in 6.3 and 6.4. Table
1 describes the attributes of a parametric coordinate reference system inherited from SC_SingleCRS.
Table 1 — Defining elements of SC_ParametricCRS class
Description:
One-dimensional coordinate reference system which uses parameter values or functions.
Stereotype:
Type
Class attribute:
Concrete
Inheritance from:
SC_SingleCRS
Association roles:
(aggregation) datum to CD_ParametricDatum [1], association named DefiningDatum
(aggregation) coordinateSystem to CS_ParametricCS [1], association named CoordinateSystem
(associations inherited from SC_SingleCRS)
Public Attributes:
6 attributes inherited from SC_SingleCRS:
Attribute name
6.3
UML identifier
Data type
Obliga
tion
Maximum
Occurrence
Attribute description
This is the primary name for the CRS. Aliases and other
identifiers may be given through the attributes alias and
identifier.
CRS name
name
RS_Identifier
M
1
CRS alias
alias
GenericName
O
N
An alias by which this CRS is known.
CRS identifier
identifier
RS_Identifier
O
N
An identifier which references elsewhere the CRS's
defining information; alternatively an identifier by
which this CRS can be referenced.
CRS scope
scope
CharacterString
M
N
CRS validity
domainOfValidity
EX_Extent
O
N
Area or region or timeframe in which this CRS is
valid.
CRS remarks
remarks
CharacterString
O
1
Comments on or information about this CRS,
including data source information.
Description of usage, or limitations of usage, for which
this CRS is valid. If unknown, enter "not known".
Parametric coordinate system
A coordinate system shall be of type "parametric" if a physical or material property or function is used as a
dimension. The parameter may be measured or function defined in other contexts, but in reference systems
provides the coordinate system axis.
EXAMPLES
Pressure in meteorological applications; density (isopycnals) in oceanographic applications.
A parametric coordinate system shall be a subtype of a coordinate system and shall be used as a part of a
parametric coordinate reference system. Figure 1 shows the UML schema.
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<<Type>>
SC_SingleCRS
(from Coordinate Reference Systems)
0..*
CoordinateSystem
+referenceSystem
1
+coordinateSystem
<<Type>>
CS_CoordinateSystem
(from Coordinate Systems)
0..*
+coordinateSystem
1..*
(ordered)
+axis
<<Type>>
CS_CoordinateSystemAxis
(from Coordinate Systems)
+axis
<<Type>>
SC_ParametricCRS
0..*
CoordinateSystem
+referenceSystem
1
<<Type>>
CS_ParametricCS
1
0..*
+coordinateSystem
+coordinateSystem
Figure 1 — UML schema for a parametric coordinate system
Table 2 describes the attributes, inherited from CS_CoordinateSystem as defined in ISO 19111.
Table 2 — Defining elements of CS_ParametricCoordinateSystem class
Description:
One-dimensional coordinate reference system which uses parameter values or functions. The values or functions may vary
monotonically with height. A ParametricCS shall have one axis association.
Stereotype:
Type
Class attribute:
Concrete
Inheritance from:
CS_CoordinateSystem
Association roles:
(aggregation) coordinateSystem from SC_ParametricCRS [1], association named CoordinateSystem
(reverse: referenceSystem to SC_ParametricCRS [0..*] navigable only from SC_ParametriclCRS – see table 1)
(associations inherited from CS_CoordinateSystem, including (aggregation) axis to CS_CoordinateSystemAxis [1])
Public attributes:
4 attributes inherited from CS_CoordinateSystem:
Attribute name
UML identifier
Data type
Obliga
tion
Maximum
Occurrence
Attribute description
This is the primary name for the CS. Aliases and other
identifiers may be given through the attributes alias and
identifier.
CS name
name
RS_Identifier
M
1
CS alias
alias
GenericName
O
N
An alias by which this CS is known.
CS identifier
identifier
RS_Identifier
O
N
An identifier which references elsewhere the CS's
defining information; alternatively an identifier by
which this CS can be referenced.
CS remarks
remarks
CharacterString
O
1
Comments on or information about this CS, including
data source information.
A parametric coordinate reference system shall be one-dimensional and shall have one axis. The defining
elements are described in ISO 19111 tables 27 and 28.
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6.4
Parametric datum
A parametric datum shall be a subtype of a datum and shall be used as a part of a parametric coordinate
reference system. Figure 2 shows the UML schema.
<<Type>>
SC_SingleCRS
(from Coordinate Reference Systems)
<<Type>>
SC_ParametricCRS
0..*
DefiningDatum
+referenceSystem
0..*
+datum
DefiningDatum
+referenceSystem
<<Type>>
CD_Datum
(from Datums)
0..*
<<Type>>
CD_ParametricDatum
1
+datum
Figure 2 — UML schema for a parametric datum
Table 3 describes the attributes, inherited from CD_Datum as defined in ISO 19111.
Table 3 — Defining elements of CD_ParametricDatum class
Description:
A textual description and/or a set of parameters identifying a particular reference surface used as the origin of a
parametric coordinate system, including its position with respect to the Earth.
Stereotype:
Type
Class attribute:
Concrete
Inheritance from:
CD_Datum
Association roles:
(aggregation) datum to CD_ParametricDatum [1], association named DefiningDatum
(reverse: referenceSystem to SC_ParametricCRS [0..*] navigable only from SC_ParametricCRS – see table 1)
Public attributes:
8 attributes inherited from CD_Datum:
Attribute name
UML identifier
Data type
Obliga
tion
Maximum
Occurrence
Attribute description
This is the primary name for the datum. Aliases
and other identifiers may be given through the
attributes alias and identifier.
Datum name
name
RS_Identifier
M
1
Datum alias
alias
GenericName
O
N
An alias by which this datum is known.
Datum identifier
identifier
RS_Identifier
O
N
An identifier which references elsewhere the
datum's defining information; alternatively
an identifier by which this datum can be
referenced.
Datum anchor
anchorDefinition
CharacterString
O
1
The datum definition – a description,
possibly including coordinates of an
identified point or points, of the relationship
used to anchor the coordinate system to the
Earth or alternate object.
- For a parametric datum, the anchor may
be an identified physical surface with the
orientation defined relative to the surface.
Datum realization epoch
realizationEpoch
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Date
O
1
The time after which this datum definition is
valid. This time may be given to any
precision.
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Datum scope
scope
CharacterString
M
N
Description of usage, or limitations of usage,
for which this datum is valid. If unknown,
enter "not known".
Datum validity
domainOfValidity
EX_Extent
O
1
Area or region or timeframe in which this
datum is valid.
Datum remarks
remarks
CharacterString
O
1
Comments on or information about this
datum, including data source information.
Editors note for working draft: May be a need for additional attributes to allow more detailed definitions of parametric datum
6.5
Spatio-parametric coordinate reference system
ISO 19111 descibes the concept of and UML schema for a compound coordinate reference system (CCRS).
A spatio-parametric coordinate reference system shall be a compound CRS in which the horizontal
component is a geodetic 2D, projected or engineering 2D CRS and this is supplemented by a parametric CRS
to describe position in three dimensions. This is illustrated in figure 3. An example is included in Annex B.
Spatio-Parametric CRS
is composed of
Geodetic 2D CRS
or
Projected CRS
or
Engineering 2D CRS
and
Parametric CRS
Figure 3 — Conceptual model of a spatio-parametric coordinate reference system
The geodetic 2D CRS may be the horizontal component of a geodetic 3D CRS.
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6.5.1
Spatio-parametric coordinate reference system with time
Using the provisions of ISO 19111, any of the above listed combinations forming a spatio-parametric
coordinate reference systems may be associated with a temporal coordinate reference system to form a
spatio-parametric-temporal compound coordinate reference system. More than one temporal coordinate
reference system may be included if these axes represent different time quantities. Nesting of CCRSs shall
not be permitted – the individual single systems shall be aggregated together. Figure 4 shows the possible
composition of a spatial, a parametric and a temporal coordinate reference systems in a spatio-parametrictemporal compound coordinate reference system. Temporal coordinate reference systems are described in
ISO 19108.
Compound CRS
is composed of
Geodetic 2D CRS
or
Projected CRS
or
Engineering 2D CRS
and
Parametric CRS
and
Temporal CRS
Figure 4 — Conceptual model of a compound CRS including spatial, parametric and temporal CRSs
6.6
Transformation and conversion of parametric coordinate reference systems
ISO 19111 describes the schema for changing coordinates from one coordinate reference system to another.
This schema may be applied to parametric, spatio-parametric and spatio-parametric-temporal coordinate
reference systems.
6.7
Geography Markup Language (GML)
ISO 19136, Geographic information - Geography Markup Language (GML), specifies XML encodings of the
coordinate reference system schema described in ISO 19111. For parametric coordinate reference systems,
coordinate systems and datums as described in 6.2 through 6.4 of this International Standard, GML schema
which are consistent with those of ISO 19136 are given in annex C.
GML schema for spatio-parametric and spatio-parametric-temporal coordinate reference systems follow the
provisions of compound coordinate reference systems given in ISO 19136.
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Annex A
(normative)
Conformance
A.1 Conformance of a parametric coordinate reference system
A.1.1 Abstract test suite
To check that a coordinate reference system including parametric values is in conformance with this
International Standard, check that it satisfies the requirements given in A.1.2 and A.1.3
A.1.2 Parametric coordinate reference system
a)
Test purpose: To determine whether all of the relevant entities and elements which are specified to be
mandatory or mandatory under the conditions specified have been provided in the description.
b)
Test method: Check the parametric coordinate reference system description to ensure that it includes as
a minimum all of the elements indicated as mandatory in Tables 1 to 3.
c)
Reference: 6.2 to 6.4.
d)
Test type: Basic.
A.1.3 Spatio-parametric or spatio-parametric-temporal coordinate reference system
a)
Test purpose: To determine whether all of the relevant entities and elements which are specified to be
mandatory or mandatory under the conditions specified have been provided in the description.
b)
Test method: Check the spatio-parametric coordinate reference system description to ensure that it
includes as a minimum all of the elements indicated.
c)
Reference: 6.5 and ISO 19111 clause 8.
d)
Test type: Basic.
A.2 Conformance of a coordinate operation
A.2.1 Abstract test suite
To check that a coordinate transformation or coordinate conversion operating on a parametric coordinate
reference system is in conformance with this International Standard, check that it satisfies the requirements
given in A.2.2.
A.2.2 Coordinate operation on a parametric CRS
a)
Test purpose: To determine whether all of the relevant entities and elements which are specified to be
mandatory or mandatory under the conditions specified have been provided in the description.
b)
Test method: Check the coordinate operation description to ensure that it includes as a minimum all of
the all of the elements indicated as mandatory.
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c)
Reference: 6.6 and ISO 19111 clause 11.
d)
Test type: Basic.
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Annex B
(informative)
Examples
B.1 Parameters and functions
Editorial comment for working draft. The text in B.1 outlines parameters and functions used as a coordinate in
meteorological applications. It is given as background information. It is anticipated clause B.1 might be omitted
from further drafts and the final document.
B.1.1 Pressure
This is the basic height unit in meteorology.
increasing height.
It is monotonic in height, but note that it decreases with
It has the useful simplifying property that in pressure coordinates, the continuity equation takes a simpler form
because the mass of a volume element dx.dy.dp is constant (assuming hydrostatic balance).
When using pressure as vertical coordinate, horizontal gradients of pressure on geometric height levels
translate into horizontal gradients of geopotential height on pressure levels -- hence fields of 500mb height etc.
Note that the unit commonly used is non-SI: millibars (mb) -- or equivalently, hectopascals (hPa)
(To geolocate pressure-level data in geometric height coordinates, you would need the geopotential field, but
there isn't normally a strong reason to do this.)
B.1.2 Density
Measured density of sea-water
B.1.3 Log-pressure height
As pressure, but use of logarithm allows for a coordinate that varies closer to linearly with geometric height.
Defined as z = -H ln (p/p0) where p0 = standard pressure, H is scale height (a constant).
Note the minus (-) sign, so increases with geometric height.
Useful in stratospheric studies, particularly for plots where the lower atmosphere isn't to dominate the plot.
Units = metres.
B.1.4 Potential temperature
Potential temperature (theta) is defined as the temperature an air parcel would have if taken adiabatically to
standard atmospheric pressure. The useful property is that it remains roughly constant in fluid flow over a few
days, so that in theta coordinates, vertical motions are small. Theta increases with height where air is stably
stratified, so theta coordinates (also known as isentropic coordinates) tend to be more useful in the
stratosphere than in the troposphere. Example application: stratospheric chemistry and transport models.
Units: kelvin.
To geolocate data in pressure-coordinates, need temperature field.
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B.1.5 Sigma
Surface-following coordinate: defined as pressure / surface pressure. Has the advantage in models that the
levels do not intersect the topography. Disadvantages are that the equations are more complex in sigma
coordinates, and that the levels continue to reflect the surface topography all the way to the top of the model.
Dimensionless.
To geolocate sigma-level data in pressure-coordinates, need the surface pressure field
B.1.6 Hybrid sigma-pressure
A useful compromise between sigma coordinates and pressure coordinates in models. Levels are pure
pressure above a certain height, and pure sigma near the surface, and there is some smooth transition
between the two.
This is common in models, e.g. the Met Office Unified Model (UM).
Levels commonly defined as:
p = A p0 + B ps
where p = level pressure, p0 = standard pressure, ps = surface pressure, A and B are dimensionless leveldependent constants.
Alternatively levels can be defined using: p = A_p + B ps (in which case A_p has dimensions of pressure).
Following these definitions, the hybrid sigma-pressure coordinate itself is given as A + B (or A_p / p0 + B in
the second formulation), and is given the symbol eta. NB eta is dimensionless.
Note that the quantity (eta x p0) is the pressure that a point on the level would have if the surface pressure at
that location were p0. This will closely approximate the true pressure over sea and over low ground.
NB: to "geo-locate" hybrid level data in pressure-coordinates, need not only the surface pressure field but also
the A and B (or A_p and B) coefficients.
B.1.7 Hybrid height
Levels are surface following near the surface and constant height near the top, so similar to hybrid sigma-p,
but this measure is based on geometric height rather than pressure.
B.1.8 SLEVE
Like hybrid height, but allow for the influence of the small-scale topography to fall off at a different rate with
height above the surface (presumably more quickly) than that of the large-scale topography. I guess you'd
need a lot of extra information to geolocate SLEVE-level data.
B.1.9 Potential vorticity
PV varies rather strongly with height. One common application of PV levels is to show values of fields on a
single level of +/-2PVU, as this is a PV value often taken to denote the mid-latitude tropopause.
B.1.10 More elaborate functional forms.
While a field of temperatures varying across a horizontal domain but referenced to a fixed (geopotential)
height is obvious, information can also be referenced to a fixed temperature, (the zero degree isotherm, and
the -20 isotherm are two common reference values) and the information defined at the coordinated of latitude,
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longitude and temperature is the varying (geopotential) height, usually specified as the lowest value should it
exist at the point.
I should mention that the non-horizontal dimension is often used to specify a projection of the atmosphere or
ocean within the 3 spatial dimensions, the temporal dimension and the space of (many) physical, chemical or
biological parameters.
So the horizontal spatial variation of the cloud amount at a height is obvious, but the horizontal spatial
variation of the lowest height at which n (e.g. 3) oktas of cloud is found is often used to help determine where
Visual Flying Regulations (VFR) apply for non instrument rated pilots.
B.1.11 Datums
B.1.11.1 Common single levels
1. Top of atmosphere
2. Tropopause (also see PV above)
3. Surface
4. Mean sea level
5. near-surface, e.g. 1.5m above mean sea level
B.1.11.2 Model-specific levels
Sometimes you get a level with no particular meaning outside a particular model, e.g. I think soil levels in the
UM are hard to "geo-locate".
(And this may not be relevant, but the UM also sometimes goes in for "pseudo-levels", which really just refers
to treating a set of 2D fields as a single 3D field for computational expediency.)
B.1.12 References
http://www.cgd.ucar.edu/cms/eaton/cf-metadata/CF-1.0.html#vert
http://www.cgd.ucar.edu/cms/eaton/cf-metadata/CF-1.0.html#vrt_app
B.2 Examples
Several examples are given below to illustrate how this International Standard can be applied when defining a
parametric coordinate reference system or coordinate transformation. The examples give both UML identifier
and attribute name. For digital data processing purposes the UML identifier should be used. When presenting
coordinate reference system metadata to human beings the attribute name should be given.
The following examples are given:
i)
Parametric coordinate reference system using a parameter (pressure).
ii)
Parametric coordinate reference system using a function (potential vorticity).
iii)
Spatio-parametric coordinate reference system.
iv) Parametric coordinate transformation.
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Example B.1: Parametric coordinate reference system using a parameter.
Pressure is the basic height unit in meteorology. It is monotonic in height, but note that it decreases with
increasing height. It has the useful simplifying property that in pressure coordinates, the continuity equation
takes a simpler form because the mass of a volume element dx.dy.dp is constant (assuming hydrostatic
balance). Note that the unit commonly used is non-SI: millibars (mb) -- or equivalently, hectopascals (hPa).
When using pressure as vertical coordinate, horizontal gradients of pressure on geometric height levels
translate into horizontal gradients of geopotential height on pressure levels -- hence fields of 500mb height etc.
(To geolocate pressure-level data in geometric height coordinates, you would need the geopotential field, but
there isn't normally a strong reason to do this.)
UML identifier
Attribute
Entry
name
Parametric CRS name
UK Met Office atmospheric
pressure 2006-01-10 1200Z
Comment
SC_ParametricCRS
alias:
Datum alias
scope
CRS scope
Meteorology
This is an optional attribute.
domainOfValidity
CRS validity
UK for 6 hours from 2006-0110 0900Z
remarks
CRS remarks
This is an optional attribute.
This is an optional attribute.
CS_ParametricCS
name
Parametric coordinate system name
remarks
CS remarks
Pressure in mb
This is an optional attribute.
CS_CoordinateSystemAxis
name
Coordinate system axis name
Atmospheric pressure
axisAbbrev
Coordinate system axis abbreviation
P
axisDirection
Coordinate system axis direction
down
axisUnitID
Coordinate system axis unit identifier
mb
minimumValue
Coordinate system axis minimum
value
0
This is an optional attribute.
maximumValue
Coordinate system axis maximum
value
1050
This is an optional attribute.
rangeMeaning
Coordinate system axis range meaning exact
This is a conditional attribute.
See ISO 19111 tables 27 and
29.
remarks:
CS axis remarks
Decreases with height above
datum
This is an optional attribute.
name:
Parametric datum name
Standard pressure at 2006-0110 1200Z
alias:
Datum alias
scope
Datum scope
Meteorology
domainOfValidity
Datum validity
UK for 6 hours from 2006-0110 0900Z
This is an optional attribute.
realizationEpoch
Datum realization epoch
2006-01-10 1200Z
This is an optional attribute.
anchorDefinition:
Datum anchor
Mean sea level
This is an optional attribute.
remarks
Datum remarks
CD_ParametricDatum
This is an optional attribute.
This is an optional attribute.
Example B.2: Parametric coordinate reference system using a function.
(need an example!)
© ISO 2006 – All rights reserved
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UML identifier
Attribute
Entry
Comment
SC_ParametricCRS
name:
Parametric CRS name
domainOfValidity:
CRS validity
scope:
CRS scope
CS_ParametricCS
name:
Parametric coordinate system name
CS_CoordinateSystemAxis
name:
Coordinate system axis name
axisAbbrev:
Coordinate system axis abbreviation
axisDirection:
Coordinate system axis direction
axisUnitID:
Coordinate system axis unit identifier
CD_ParametricDatum
name:
Parametric datum name
Example B.3: Compound coordinate reference system formed from a geodetic 2D CRS with a parametric
CRS.
UML identifier
Attribute
Entry
Comment
name:
Compound CRS name
WGS 84 + UK Met Office
atmospheric pressure 200601-10 1200Z
domainOfValidity:
CRS validity
scope:
CRS scope
SC_CompoundCRS
Meteorlogy
The individual CRSs forming
the compound CRS are next
described. The sequence is
significant.
SC_GeodeticCRS
The geodetic CRS is then
described as in ISO 19111
example D.3. This is not
repeated in full here.
name:
Geodetic CRS name
WGS 84
remarks
CRS remarks
Horizontal component of 3D
system.
:
:
inverseFlattening:
:
:
:
Inverse flattening
:
:
The parametric CRS is then
described in a similar manner
to that in example B.1 above.
This is not repeated in full
here.
Parametric CRS name
:
anchorDefinition:
etc.
298.257223563
SC_ParametricCRS
name:
This is an optional attribute.
:
Datum anchor
:
UK Met Office atmospheric
pressure 2006-01-10 1200Z
:
:
etc.
Mean sea level
The order of coordinates in a
coordinate tuple referenced to
the compound CRS is then
implied as ,,P.
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Example B.4: Transformation of parametric coordinates.
(need an example)
UML identifier
Attribute
Entry
Comment
CC_Transformation
name:
Coordinate operation name
operationVersion:
Coordinate operation version
domainOfValidity:
Coordinate operation validity
scope:
Coordinate operation scope
remarks:
Coordinate operation remarks
coordinateOperationAccuracy:
Coordinate operation accuracy
SC_ParametricCRS
This is the source CRS for the
transformation, in this example
XXXX.
SC_ParametricCRS
This is the target CRS for the
transformation, in this example
YYYY.
CC_OperationMethod
name:
Coordinate operation method name
formula:
Coordinate operation method formula
sourceDimensions:
Dimension of source CRS
1
targetDimensions:
Dimension of target CRS
1
CC_OperationParameter
name:
Operation parameter name
CC_ParameterValue
value:
Operation parameter numeric value
CC_OperationParameter
name:
Operation parameter name
CC_ParameterValue
value:
Operation parameter numeric value
CC_OperationParameter
name:
Operation parameter name
CC_ParameterValue
value:
© ISO 2006 – All rights reserved
Operation parameter numeric value
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Annex C
(normative)
Geography Markup Language (GML)
C.1 Introduction
ISO 19136, Geographic information - Geography Markup Language (GML), describes a grammar and schema
for encoding geographic information in XML. ISO 19136 includes GML schema for spatial referencing by
coordinates that are in accordance with ISO 19111. This annex provides additions to the provisions of 19136
required for parametric coordinate reference systems.
(Editors notes for draft: (i) these provisions could be made as a technical amendment to 19136 and withdrawn
from
this
document.
(ii)
need
to
address
GML
schema
documents,
in
particular
coordinateReferenceSystems.xsd, coordinateSystems.xsd and datums.xsd).
C.2 Parametric coordinate reference system
C.2.1 ParametricCRS
<element name="ParametricCRS" type="gml:ParametricCRSType" substitutionGroup="gml:AbstractSingleCRS"/>
<complexType name="ParametricCRSType">
<complexContent>
<extension base="gml:AbstractCRSType">
<sequence>
<element ref="gml:parametricCS"/>
<element ref="gml:parametricDatum"/>
</sequence>
</extension>
</complexContent>
</complexType>
gml:ParametricCRS is a 1D coordinate reference system used for recording heights or depths. Parametric
CRSs make use of the direction of gravity to define the concept of height or depth, but the relationship with
gravity may not be straightforward. By implication, ellipsoidal heights (h) cannot be captured in a Parametric
coordinate reference system. Ellipsoidal heights cannot exist independently, but only as an inseparable part of
a 3D coordinate tuple defined in a geographic 3D coordinate reference system.
C.2.1.1
parametricCS
<element name="parametricCS" type="gml:ParametricCSPropertyType"/>
gml:parametricCS is an association role to the parametric coordinate system used by this CRS.
C.2.1.2
parametricDatum
<element name="parametricDatum" type="gml:ParametricDatumPropertyType"/>
gml:parametricDatum is an association role to the parametric datum used by this CRS.
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C.2.2 ParametricCRSPropertyType
<complexType name="ParametricCRSPropertyType">
<sequence minOccurs="0">
<element ref="gml:ParametricCRS"/>
</sequence>
<attributeGroup ref="gml:AssociationAttributeGroup"/>
</complexType>
gml:ParametricCRSPropertyType is a property type for association roles to a parametric coordinate
reference system, either referencing or containing the definition of that reference system.
C.3 Parametric coordinate system
C.3.1 ParametricCS
<element name="ParametricCS" type="gml:ParametricCSType"
substitutionGroup="gml:AbstractCoordinateSystem"/>
<complexType name="ParametricCSType">
<complexContent>
<extension base="gml:AbstractCoordinateSystemType"/>
</complexContent>
</complexType>
gml:ParametricCS is a one-dimensional coordinate system used to record the heights or depths of points.
Such a coordinate system is usually dependent on the Earth's gravity field, perhaps loosely as when
atmospheric pressure is the basis for the parametric coordinate system axis. A ParametricCS shall have one
gml:axis property element.
C.3.2 ParametricCSPropertyType
<complexType name="ParametricCSPropertyType">
<sequence minOccurs="0">
<element ref="gml:ParametricCS"/>
</sequence>
<attributeGroup ref="gml:AssociationAttributeGroup"/>
</complexType>
gml:ParametricCSPropertyType is a property type for association roles to a parametric coordinate
system, either referencing or containing the definition of that coordinate system.
C.4 Parametric datum
C.4.1 ParametricDatum
<element name="ParametricDatum" type="gml:ParametricDatumType" substitutionGroup="gml:AbstractDatum"/>
<complexType name="ParametricDatumType">
<complexContent>
<extension base="gml:AbstractDatumType">
<sequence/>
</extension>
</complexContent>
</complexType>
gml:ParametricDatum is a textual description and/or a set of parameters identifying a particular reference
level surface used as a zero-height surface, including its position with respect to the Earth for any of the height
types recognized by this International Standard.
© ISO 2006 – All rights reserved
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C.4.2 ParametricDatumPropertyType
<complexType name="ParametricDatumPropertyType">
<sequence minOccurs="0">
<element ref="gml:ParametricDatum"/>
</sequence>
<attributeGroup ref="gml:AssociationAttributeGroup"/>
</complexType>
gml:ParametricDatumPropertyType is property type for association roles to a parametric datum, either
referencing or containing the definition of that datum.
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© ISO 2006 – All rights reserved