Versions Compared

Old Version 1

changes.mady.by.user Bert Jagers

Saved on

compared with

New Version Current

changes.mady.by.user Bert Jagers

Saved on

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.
Comment: Migration of unmigrated content due to installation of a new plugin
scrollbar
 Sep 25, 2013 - IMPORTANT NOTE: To make the proposal a more formal standard, the content of this page has been migrated to GitHub, please follow this link.
 The documentation below is no longer updated.
--------- snapshot Sep 25, 2013 ---------
 Latest update Feb 28, 2013: use topology_dimension attribute rather than dimension, as suggested by Jonathan Gregory here.
 Update Sep 12, 2012: closed clockwise discussion, explained meaning of Optionally required attributes.
 You can use the following shorthand http://bit.ly/ugrid_cf to refer to this page.
PLEASE NOTE: The title of this page suggests that this is only a proposal by Deltares. However, the support for this proposal is already much wider than that (see the UGRID Google Group) and is under active discussion with an important subset of the CF community. We keep the current title only such that it does not break any existing external links to this information.
The section of creating mosaics of meshes has been moved to this child page. Since experience with unstructured grid mosaics is still limited, and demand is low, the mosaics are not yet part of the current proposal.
Introduction.
This page describes a proposal for storing unstructured (or flexible mesh) model data in a netCDF file. Our focus is on data for environmental applications and hence we start from the CF-conventions which has been the standard in climate research for many years, and is increasingly adopted by others as the metadata standard for netCDF, see e.g. NASA Standards Process Group and OGC. The CF conventions allow you to define values at points, and the associated coordinates may have bounds attributes to indicate a spatial extent bigger than a single point. A two-dimensional array of points, encodes a structured topology but the CF conventions do not yet provide the means to define an unstructured topology. That's what this proposal adds.
In its most basic form unstructured data may be stored as data defined at a series of points, the CF-conventions are then sufficient. However, it is often useful or even necessary to also know the topology of the underlying unstructured mesh: is it a 1D network, a 2D triangular mesh or more flexible mixed triangle/quadrilateral mesh, a 2D mesh with vertical layers, or a fully unstructured 3D mesh. This document describes the attribute conventions for storing the mesh topology and for associating variables with (specific locations on) the mesh topology. The conventions have been designed to store the output data of a combined 1D-2D-3D flow model with staggered data, but the metadata for a simple 1D network or 2D triangular mesh doesn't suffer from the genericity needed for the most complex models.
Due to the wide variety in unstructured mesh models, some relevant concepts have not yet been worked out in detail. This includes the following concepts:
  • adaptive mesh topology (this could be supported by defining a time_concatenation attribute for a time-series of mesh topologies)
  • higher order element data; for an idea how such data could be stored see this other proposal.
  • subgrid data; the netCDF pages by the BAW contain some proposals on this topic (see their pages (in German)).
  • 3D fully unstructured meshes (included but still limited in scope).
     See also a related proposal for an unstructured mesh data model by Jeff Daily at PNNL.
More details can be found in the various sections below:
 Table of Content Zone
locationtop
typelist
Topology.
Naming conventions for geometrical elements.
Inspired by Wikipedia's definition of network topology, we define the mesh topology here as the interconnection of various geometrical elements of the mesh. The pure interconnectivity is independent of georeferencing the individual geometrical elements, but for the practical applications for which we are defining this CF extension, we'll always add coordinate data. Within a mesh, one can distinguish 0-, 1-, 2- and 3-dimensional elements. We need some names to identify these four types of elements; after discussion we propose the following names:
Dimensionality
Proposed Name
Comments
0
node
A point, a coordinate pair or triplet: the most basic element of the topology.
 The word node seems to be more commonly used than the alternative "vertex".
1
edge
A line or curve bounded by two nodes.
2
face
A plane or surface enclosed by a set of edges.
 In a 2D horizontal application one may consider the word "polygon", but in the hierarchy of elements the word face is most common.
3
volume
A volume enclosed by a set of faces.
(warning) In favor of simpler code for interpreting compliant files, we have dropped to use of the locations attribute which allowed the user to specify his/her own names for nodes, edges, faces and volumes.
1D network topology.
The topology information is stored as attributes to a dummy variable (in the example below called "Mesh1") with cf_role mesh_topology.
Required topology attributes
Value
cf_role
mesh_topology
topology_dimension
1
node_coordinates
edge_node_connectivity
Optional attributes
edge_coordinates
The attribute topology_dimension indicates the highest dimensionality of the geometric elements; for a 1D network this should be 1. The attribute node_coordinates points to the auxiliary coordinate variables representing the node locations (latitude, longitude, and optional elevation or other coordinates). These auxiliary coordinate variables will have length nNodes. The attribute edge_node_connectivity points to an index variable identifying for every edge to the indices of its begin and end nodes. The connectivity array will thus be a matrix of size nEdges x 2. For the indexing one may use either 0- or 1-based indexing; the convention used should be specified using a start_index attribute to the index variable (i.e. Mesh1_edge_nodes in the example below). Consistent with the CF-conventions compression option, the connectivity indices are 0-based by default.
(warning) The option to support both 0- and 1-based indexing was introduced to be able to support existing files with 1-based index tables using ncML. See this section on 0-/1-based indexing for more details.
The mesh_topology may optionally include an edge_coordinates attribute which points to the auxiliary coordinate variables associated with the characteristic location of the edge (commonly the midpoint). These auxiliary coordinate variables will have length nEdges, and may have in turn a bounds attribute that specifies the bounding coordinates of the edge (thereby duplicating the data in the node_coordinates variables).
(warning) This use of the bounds attribute is consistent with the CF-convention on the use of bounds for multi-dimensional coordinate variables with p-sided cells, but it may not strictly be supported by the CF-convention right now.
Image Added
Example:
 Code Block
dimensions:
        nMesh1_node = 5 ; // nNodes
        nMesh1_edge = 4 ; // nEdges

        Two = 2;

variables:
// Mesh topology
        integer Mesh1 ;
                Mesh1:cf_role = "mesh_topology" ;
                Mesh1:long_name = "Topology data of 1D network" ;
                Mesh1:topology_dimension = 1 ;
                Mesh1:node_coordinates = "Mesh1_node_x Mesh1_node_y" ;
                Mesh1:edge_node_connectivity = "Mesh1_edge_nodes" ;
                Mesh1:edge_coordinates = "Mesh1_edge_x Mesh1_edge_y" ; // optional attribute
        integer Mesh1_edge_nodes(nMesh1_edge, Two) ;
                Mesh1_edge_nodes:cf_role = "edge_node_connectivity" ;
                Mesh1_edge_nodes:long_name = "Maps every edge/link to the two nodes that it connects." ;
                Mesh1_edge_nodes:start_index = 1 ;

// Mesh node coordinates
        double Mesh1_node_x(nMesh1_node) ;
                Mesh1_node_x:standard_name = "longitude" ;
                Mesh1_node_x:long_name = "Longitude of 1D network nodes." ;
                Mesh1_node_x:units = "degrees_east" ;
        double Mesh1_node_y(nMesh1_node) ;
                Mesh1_node_y:standard_name = "latitude" ;
                Mesh1_node_y:long_name = "Latitude of 1D network nodes." ;
                Mesh1_node_y:units = "degrees_north" ;

// Optional mesh edge coordinate variables
        double Mesh1_edge_x(nMesh1_edge) ;
                Mesh1_edge_x:standard_name = "longitude" ;
                Mesh1_edge_x:long_name = "Characteristic longitude of 1D network edge (e.g. midpoint of the edge)." ;
                Mesh1_edge_x:units = "degrees_east" ;
                Mesh1_edge_x:bounds = "Mesh1_edge_xbnds" ;
        double Mesh1_edge_y(nMesh1_edge) ;
                Mesh1_edge_y:standard_name = "latitude" ;
                Mesh1_edge_y:long_name = "Characteristic latitude of 1D network edge (e.g. midpoint of the edge)." ;
                Mesh1_edge_y:units = "degrees_north" ;
                Mesh1_edge_y:bounds = "Mesh1_edge_ybnds" ;
        double Mesh1_edge_xbnds(nMesh1_edge,Two) ;
                Mesh1_edge_xbnds:standard_name = "longitude" ;
                Mesh1_edge_xbnds:long_name = "Longitude bounds of 1D network edge (i.e. begin and end longitude)." ;
                Mesh1_edge_xbnds:units = "degrees_east" ;
        double Mesh1_edge_ybnds(nMesh1_edge,Two) ;
                Mesh1_edge_ybnds:standard_name = "latitude" ;
                Mesh1_edge_ybnds:long_name = "Latitude bounds of 1D network edge (i.e. begin and end latitude)." ;
                Mesh1_edge_ybnds:units = "degrees_north" ;

2D triangular mesh topology.
The topology information is stored as attributes to a dummy variable (in the example below called "Mesh2") with cf_role mesh_topology.
Required topology attributes
Value
cf_role
mesh_topology
topology_dimension
2
node_coordinates
face_node_connectivity
Optionally required attributes*
edge_node_connectivity
Optional attributes
face_edge_connectivity
face_face_connectivity
face_coordinates
edge_coordinates
*The "Optionally required" attribute edge_node_connectivity is required only if you want to store data on the edges (i.e. if you mind the numbering order of the edges).
The attribute topology_dimension indicates the highest dimensionality of the geometric elements; for a 2-dimensional (triangular) mesh this should be 2. The attribute node_coordinates points to the auxiliary coordinate variables representing the node locations (latitude, longitude, and optional elevation or other coordinates). These auxiliary coordinate variables will have length nNodes. The attribute face_node_connectivity points to an index variable identifying for every face (here consistently triangle) the indices of its three corner nodes. The corner nodes should be specified in anticlockwise (also referred to as counterclockwise) direction as viewed from above (consistent with the CF-convention for bounds of p-sided cells. The connectivity array will thus be a matrix of size nFaces x 3. For the indexing one may use either 0- or 1-based indexing; the convention used should be specified using a start_index attribute to the index variable (i.e. Mesh2_face_nodes in the example below). Consistent with the CF-conventions compression option, the connectivity indices are 0-based by default. See this section on 0-/1-based indexing for more details.
In case you want to define variables on the edges of the triangular mesh topology you need to specify the edge_node_connectivity attribute to map edges to nodes. Although the face to node mapping implicitly also defines the location of the edges, it does not specify the global numbering of the edges. Again the indexing convention of edge_node_connectivity should be specified using the start_index attribute to the index variable (i.e. Mesh2_edge_nodes in the example below) and 0-based indexing is the default.
Optionally the topology may have the following attributes:
  • face_edge_connectivity pointing to an index variable identifying for every face (here consistently triangle) the indices of its three edges. The edges should be specified in anticlockwise direction as viewed from above. This connectivity array will thus be a matrix of size nFaces x 3. Again the indexing convention of face_edge_connectivity should be specified using the start_index attribute to the index variable (i.e. Mesh2_face_edges in the example below) and 0-based indexing is the default.
  • face_face_connectivity pointing to an index variable identifying pairs of faces (here consistently triangle) that share an edge, i.e. are neighbors. TODO: CHECK DEFINITION This connectivity array will thus be a matrix of size nFacePairs x 2. Again the indexing convention of face_face_connectivity should be specified using the start_index attribute to the index variable (i.e. Mesh2_face_links in the example below) and 0-based indexing is the default.
  • face_coordinates and/or edge_coordinates pointing to the auxiliary coordinate variables associated with the characteristic location of the faces and edges. These auxiliary coordinate variables will have length nFaces and nEdges respectively, and may have in turn a bounds attribute that specifies the bounding coordinates of the face or edge (thereby duplicating the data in the node_coordinates variables).
Image Added
Example:
 Code Block
dimensions:
        nMesh2_node = 4 ; // nNodes
        nMesh2_edge = 5 ; // nEdges
        nMesh2_face = 2 ; // nFaces
        nMesh2_face_links = 1 ; // nFacePairs

        Two = 2 ;
        Three = 3 ;

variables:
// Mesh topology
        integer Mesh2 ;
                Mesh2:cf_role = "mesh_topology" ;
                Mesh2:long_name = "Topology data of 2D unstructured mesh" ;
                Mesh2:topology_dimension = 2 ;
                Mesh2:node_coordinates = "Mesh2_node_x Mesh2_node_y" ;
                Mesh2:face_node_connectivity = "Mesh2_face_nodes" ;
                Mesh2:edge_node_connectivity = "Mesh2_edge_nodes" ; // attribute required if variables will be defined on edges
                Mesh2:edge_coordinates = "Mesh2_edge_x Mesh2_edge_y" ; // optional attribute (requires edge_node_connectivity)
                Mesh2:face_coordinates = "Mesh2_face_x Mesh2_face_y" ; // optional attribute
                Mesh2:face_edge_connectivity = "Mesh2_face_edges" ; // optional attribute (requires edge_node_connectivity)
                Mesh2:face_face_connectivity = "Mesh2_face_links" ; // optional attribute
        integer Mesh2_face_nodes(nMesh2_face, Three) ;
                Mesh2_face_nodes:cf_role = "face_node_connectivity" ;
                Mesh2_face_nodes:long_name = "Maps every triangular face to its three corner nodes." ;
                Mesh2_face_nodes:start_index = 1 ;
        integer Mesh2_edge_nodes(nMesh2_edge, Two) ;
                Mesh2_edge_nodes:cf_role = "edge_node_connectivity" ;
                Mesh2_edge_nodes:long_name = "Maps every edge to the two nodes that it connects." ;
                Mesh2_edge_nodes:start_index = 1 ;

// Optional mesh topology variables
        integer Mesh2_face_edges(nMesh2_face, Three) ;
                Mesh2_face_edges:cf_role = "face_edge_connectivity" ;
                Mesh2_face_edges:long_name = "Maps every triangular face to its three edges." ;
                Mesh2_face_edges:start_index = 1 ;
        integer Mesh2_face_links(nMesh2_face_links, Two) ;
                Mesh2_face_links:cf_role = "face_face_connectivity" ;
                Mesh2_face_links:long_name = "Indicates pairs of (triangular) faces that share an edge." ;
                Mesh2_face_nodes:start_index = 1 ;

// Mesh node coordinates
        double Mesh2_node_x(nMesh2_node) ;
                Mesh2_node_x:standard_name = "longitude" ;
                Mesh2_node_x:long_name = "Longitude of 2D mesh nodes." ;
                Mesh2_node_x:units = "degrees_east" ;
        double Mesh2_node_y(nMesh2_node) ;
                Mesh2_node_y:standard_name = "latitude" ;
                Mesh2_node_y:long_name = "Latitude of 2D mesh nodes." ;
                Mesh2_node_y:units = "degrees_north" ;

// Optional mesh face and edge coordinate variables
        double Mesh2_face_x(nMesh2_face) ;
                Mesh2_face_x:standard_name = "longitude" ;
                Mesh2_face_x:long_name = "Characteristics longitude of 2D mesh triangle (e.g. circumcenter coordinate)." ;
                Mesh2_face_x:units = "degrees_east" ;
        double Mesh2_face_y(nMesh2_face) ;
                Mesh2_face_y:standard_name = "latitude" ;
                Mesh2_face_y:long_name = "Characteristics latitude of 2D mesh triangle (e.g. circumcenter coordinate)." ;
                Mesh2_face_y:units = "degrees_north" ;
        double Mesh2_edge_x(nMesh2_edge) ;
                Mesh2_edge_x:standard_name = "longitude" ;
                Mesh2_edge_x:long_name = "Characteristic longitude of 2D mesh edge (e.g. midpoint of the edge)." ;
                Mesh2_edge_x:units = "degrees_east" ;
        double Mesh2_edge_y(nMesh2_edge) ;
                Mesh2_edge_y:standard_name = "latitude" ;
                Mesh2_edge_y:long_name = "Characteristic latitude of 2D mesh edge (e.g. midpoint of the edge)." ;
                Mesh2_edge_y:units = "degrees_north" ;

2D flexible mesh (mixed triangles, quadrilaterals, etc.) topology.
The case of a 2D mesh with mixed face sizes is identical to the 2D triangular mesh discussed above with the exception that not all faces have the same number of nodes. To support this variability we may use in the future a ragged array, but here we propose to use _FillValue to indicate faces with smaller number of nodes than the arrays allow.
The topology information is stored as attributes to a dummy variable (in the example below called "Mesh2") with cf_role mesh_topology.
Required topology attributes
Value
cf_role
mesh_topology
topology_dimension
2
node_coordinates
face_node_connectivity
Optionally required attributes*
edge_node_connectivity
Optional attributes
face_edge_connectivity
face_face_connectivity
face_coordinates
edge_coordinates
*The "Optionally required" attribute edge_node_connectivity is required only if you want to store data on the edges (i.e. if you mind the numbering order of the edges).
The attribute topology_dimension indicates the highest dimensionality of the geometric elements; for a 2-dimensional mesh this should be 2. The attribute node_coordinates points to the auxiliary coordinate variables representing the node locations (latitude, longitude, and optional elevation or other coordinates). These auxiliary coordinate variables will have length nNodes. The attribute face_node_connectivity points to an index variable identifying for every face the indices of its corner nodes. The corner nodes should be specified in anticlockwise direction as viewed from above (consistent with the CF-convention for bounds of p-sided cells. The connectivity array will be a matrix of size nFaces x MaxNumNodesPerFace; if a face has less corner nodes than MaxNumNodesPerFace then the last node indices shall be equal to _FillValue (which should obviously be larger than the number of nodes in the mesh). For the indexing one may use either 0- or 1-based indexing; the convention used should be specified using a start_index attribute to the index variable (i.e. Mesh2_face_nodes in the example below). Consistent with the CF-conventions compression option, the connectivity indices are 0-based by default. See this section on 0-/1-based indexing for more details.
In case you want to define variables on the edges of the 2D mesh topology you need to specify the edge_node_connectivity attribute to map edges to nodes. Although the face to node mapping implicitly also defines the location of the edges, it does not specify the global numbering of the edges. Again the indexing convention of edge_node_connectivity should be specified using the start_index attribute to the index variable (i.e. Mesh2_edge_nodes in the example below) and 0-based indexing is the default.
Optionally the topology may have the following attributes:
  • face_edge_connectivity pointing to an index variable identifying for every face the indices of its edges. The edges should be specified in anticlockwise direction as viewed from above. This connectivity array will be a matrix of size nFaces x MaxNumNodesPerFace. Again, if a face has less corners/edges than MaxNumNodesPerFace then the last edge indices shall be equal to _FillValue, and the indexing convention of face_edge_connectivity should be specified using the start_index attribute to the index variable (i.e. Mesh2_face_edges in the example below) and 0-based indexing is the default.
  • face_face_connectivity pointing to an index variable identifying pairs of faces that share an edge, i.e. are neighbors. TODO: CHECK DEFINITION This connectivity array will thus be a matrix of size nFacePairs x 2. Again the indexing convention of face_face_connectivity should be specified using the start_index attribute to the index variable (i.e. Mesh2_face_links in the example below) and 0-based indexing is the default.
  • face_coordinates and/or edge_coordinates pointing to the auxiliary coordinate variables associated with the characteristic location of the faces and edges. These auxiliary coordinate variables will have length nFaces and nEdges respectively, and may have in turn a bounds attribute that specifies the bounding coordinates of the face or edge (thereby duplicating the data in the node_coordinates variables).
(warning) The use of _FillValue to indicate faces with less nodes than MaxNumNodesPerFace extends to the coordinate bounds variables; this is an extension of the current convention.
Image Added
Example:
 Code Block
dimensions:
        nMesh2_node = 5 ; // nNodes
        nMesh2_edge = 6 ; // nEdges
        nMesh2_face = 2 ; // nFaces
        nMesh2_face_links = 1 ; // nFacePairs
        nMaxMesh2_face_nodes = 4 ; // MaxNumNodesPerFace

        Two = 2 ;

variables:
// Mesh topology
        integer Mesh2 ;
                Mesh2:cf_role = "mesh_topology" ;
                Mesh2:long_name = "Topology data of 2D unstructured mesh" ;
                Mesh2:topology_dimension = 2 ;
                Mesh2:node_coordinates = "Mesh2_node_x Mesh2_node_y" ;
                Mesh2:face_node_connectivity = "Mesh2_face_nodes" ;
                Mesh2:edge_node_connectivity = "Mesh2_edge_nodes" ; // attribute required if variables will be defined on edges
                Mesh2:edge_coordinates = "Mesh2_edge_x Mesh2_edge_y" ; // optional attribute (requires edge_node_connectivity)
                Mesh2:face_coordinates = "Mesh2_face_x Mesh2_face_y" ; // optional attribute
                Mesh2:face_edge_connectivity = "Mesh2_face_edges" ; // optional attribute (requires edge_node_connectivity)
                Mesh2:face_face_connectivity = "Mesh2_face_links" ; // optional attribute
        integer Mesh2_face_nodes(nMesh2_face, nMaxMesh2_face_nodes) ;
                Mesh2_face_nodes:cf_role = "face_node_connectivity" ;
                Mesh2_face_nodes:long_name = "Maps every face to its corner nodes." ;
                Mesh2_face_nodes:_FillValue = 999999 ;
                Mesh2_face_nodes:start_index = 1 ;
        integer Mesh2_edge_nodes(nMesh2_edge, Two) ;
                Mesh2_edge_nodes:cf_role = "edge_node_connectivity" ;
                Mesh2_edge_nodes:long_name = "Maps every edge to the two nodes that it connects." ;
                Mesh2_edge_nodes:start_index = 1 ;

// Optional mesh topology variables
        integer Mesh2_face_edges(nMesh2_face, nMaxMesh2_face_nodes) ;
                Mesh2_face_edges:cf_role = "face_edge_connectivity" ;
                Mesh2_face_edges:long_name = "Maps every face to its edges." ;
                Mesh2_face_edges:_FillValue = 999999 ;
                Mesh2_face_edges:start_index = 1 ;
        integer Mesh2_face_links(nMesh2_face_links, Two) ;
                Mesh2_face_links:cf_role = "face_face_connectivity" ;
                Mesh2_face_links:long_name = "Indicates which faces are neighbors." ;
                Mesh2_face_links:start_index = 1 ;

// Mesh node coordinates
        double Mesh2_node_x(nMesh2_node) ;
                Mesh2_node_x:standard_name = "longitude" ;
                Mesh2_node_x:long_name = "Longitude of 2D mesh nodes." ;
                Mesh2_node_x:units = "degrees_east" ;
        double Mesh2_node_y(nMesh2_node) ;
                Mesh2_node_y:standard_name = "latitude" ;
                Mesh2_node_y:long_name = "Latitude of 2D mesh nodes." ;
                Mesh2_node_y:units = "degrees_north" ;

// Optional mesh face and edge coordinate variables
        double Mesh2_face_x(nMesh2_face) ;
                Mesh2_face_x:standard_name = "longitude" ;
                Mesh2_face_x:long_name = "Characteristics longitude of 2D mesh face." ;
                Mesh2_face_x:units = "degrees_east" ;
                Mesh2_face_x:bounds = "Mesh2_face_xbnds" ;
        double Mesh2_face_y(nMesh2_face) ;
                Mesh2_face_y:standard_name = "latitude" ;
                Mesh2_face_y:long_name = "Characteristics latitude of 2D mesh face." ;
                Mesh2_face_y:units = "degrees_north" ;
                Mesh2_face_y:bounds = "Mesh2_face_ybnds" ;
        double Mesh2_face_xbnds(nMesh2_face,nMaxMesh2_face_nodes) ;
                Mesh2_face_xbnds:standard_name = "longitude" ;
                Mesh2_face_xbnds:long_name = "Longitude bounds of 2D mesh face (i.e. corner coordinates)." ;
                Mesh2_face_xbnds:units = "degrees_east" ;
                Mesh2_face_xbnds:_FillValue = 9.9692099683868690E36;
        double Mesh2_face_ybnds(nMesh2_face,nMaxMesh2_face_nodes) ;
                Mesh2_face_ybnds:standard_name = "latitude" ;
                Mesh2_face_ybnds:long_name = "Latitude bounds of 2D mesh face (i.e. corner coordinates)." ;
                Mesh2_face_ybnds:units = "degrees_north" ;
                Mesh2_face_ybnds:_FillValue = 9.9692099683868690E36;
        double Mesh2_edge_x(nMesh2_edge) ;
                Mesh2_edge_x:standard_name = "longitude" ;
                Mesh2_edge_x:long_name = "Characteristic longitude of 2D mesh edge (e.g. midpoint of the edge)." ;
                Mesh2_edge_x:units = "degrees_east" ;
        double Mesh2_edge_y(nMesh2_edge) ;
                Mesh2_edge_y:standard_name = "latitude" ;
                Mesh2_edge_y:long_name = "Characteristic latitude of 2D mesh edge (e.g. midpoint of the edge)." ;
                Mesh2_edge_y:units = "degrees_north" ;
        // bounds variables for edges skipped

3D layered mesh topology.
For a 3D layered unstructured mesh topology this proposal follows the approach of the existing CF-conventions for structured meshes: horizontal and vertical dimensions are treated separately. For the horizontal plane a 2D unstructured mesh topology is defined, which is extruded in the vertical direction by means of a vertical coordinate. The example below matches the example in the previous section combined with a vertical coordinate according CF-conventions. This example introduces also the attributes mesh and location on the 2D variables "Mesh2_surface" and "Mesh2_depth". For more information about these attributes see the data definition section below.
Image Added
Example:
 Code Block
dimensions:
        nMesh2_node = 6 ; // nNodes
        nMesh2_edge = 7 ; // nEdges
        nMesh2_face = 2 ; // nFaces
        nMesh2_face_links = 1 ; // nFacePairs
        nMaxMesh2_face_nodes = 4 ; // MaxNumNodesPerFace
        Mesh2_layers = 10 ;

        Two = 2 ;

variables:
// Mesh topology
        integer Mesh2 ;
                Mesh2:cf_role = "mesh_topology" ;
                Mesh2:long_name = "Topology data of 2D unstructured mesh" ;
                Mesh2:topology_dimension = 2 ;
                Mesh2:node_coordinates = "Mesh2_node_x Mesh2_node_y" ;
                Mesh2:face_node_connectivity = "Mesh2_face_nodes" ;
                Mesh2:edge_node_connectivity = "Mesh2_edge_nodes" ; // attribute required if variables will be defined on edges
                Mesh2:edge_coordinates = "Mesh2_edge_x Mesh2_edge_y" ; // optional attribute (requires edge_node_connectivity)
                Mesh2:face_coordinates = "Mesh2_face_x Mesh2_face_y" ; // optional attribute
                Mesh2:face_edge_connectivity = "Mesh2_face_edges" ; // optional attribute (requires edge_node_connectivity)
                Mesh2:face_face_connectivity = "Mesh2_face_links" ; // optional attribute
        integer Mesh2_face_nodes(nMesh2_face, nMaxMesh2_face_nodes) ;
                Mesh2_face_nodes:cf_role = "face_node_connectivity" ;
                Mesh2_face_nodes:long_name = "Maps every face to its corner nodes." ;
                Mesh2_face_nodes:_FillValue = 999999 ;
                Mesh2_face_nodes:start_index = 1 ;
        integer Mesh2_edge_nodes(nMesh2_edge, Two) ;
                Mesh2_edge_nodes:cf_role = "edge_node_connectivity" ;
                Mesh2_edge_nodes:long_name = "Maps every edge to the two nodes that it connects." ;
                Mesh2_edge_nodes:start_index = 1 ;

// Optional mesh topology variables
        integer Mesh2_face_edges(nMesh2_face, nMaxMesh2_face_nodes) ;
                Mesh2_face_edges:cf_role = "face_edge_connectivity" ;
                Mesh2_face_edges:long_name = "Maps every face to its edges." ;
                Mesh2_face_edges:_FillValue = 999999 ;
                Mesh2_face_edges:start_index = 1 ;
        integer Mesh2_face_links(nMesh2_face_links, Two) ;
                Mesh2_face_links:cf_role = "face_face_connectivity" ;
                Mesh2_face_links:long_name = "Indicates which faces are neighbors." ;
                Mesh2_face_links:start_index = 1 ;

// Mesh node coordinates
        double Mesh2_node_x(nMesh2_node) ;
                Mesh2_node_x:standard_name = "longitude" ;
                Mesh2_node_x:long_name = "Longitude of 2D mesh nodes." ;
                Mesh2_node_x:units = "degrees_east" ;
        double Mesh2_node_y(nMesh2_node) ;
                Mesh2_node_y:standard_name = "latitude" ;
                Mesh2_node_y:long_name = "Latitude of 2D mesh nodes." ;
                Mesh2_node_y:units = "degrees_north" ;

// Optional mesh face and edge coordinate variables
        double Mesh2_face_x(nMesh2_face) ;
                Mesh2_face_x:standard_name = "longitude" ;
                Mesh2_face_x:long_name = "Characteristics longitude of 2D mesh face." ;
                Mesh2_face_x:units = "degrees_east" ;
                Mesh2_face_x:bounds = "Mesh2_face_xbnds" ;
        double Mesh2_face_y(nMesh2_face) ;
                Mesh2_face_y:standard_name = "latitude" ;
                Mesh2_face_y:long_name = "Characteristics latitude of 2D mesh face." ;
                Mesh2_face_y:units = "degrees_north" ;
                Mesh2_face_y:bounds = "Mesh2_face_ybnds" ;
        double Mesh2_face_xbnds(nMesh2_face,nMaxMesh2_face_nodes) ;
                Mesh2_face_xbnds:standard_name = "longitude" ;
                Mesh2_face_xbnds:long_name = "Longitude bounds of 2D mesh face (i.e. corner coordinates)." ;
                Mesh2_face_xbnds:units = "degrees_east" ;
                Mesh2_face_xbnds:_FillValue = 9.9692099683868690E36;
        double Mesh2_face_ybnds(nMesh2_face,nMaxMesh2_face_nodes) ;
                Mesh2_face_ybnds:standard_name = "latitude" ;
                Mesh2_face_ybnds:long_name = "Latitude bounds of 2D mesh face (i.e. corner coordinates)." ;
                Mesh2_face_ybnds:units = "degrees_north" ;
                Mesh2_face_ybnds:_FillValue = 9.9692099683868690E36;
        double Mesh2_edge_x(nMesh2_edge) ;
                Mesh2_edge_x:standard_name = "longitude" ;
                Mesh2_edge_x:long_name = "Characteristic longitude of 2D mesh edge (e.g. midpoint of the edge)." ;
                Mesh2_edge_x:units = "degrees_east" ;
        double Mesh2_edge_y(nMesh2_edge) ;
                Mesh2_edge_y:standard_name = "latitude" ;
                Mesh2_edge_y:long_name = "Characteristic latitude of 2D mesh edge (e.g. midpoint of the edge)." ;
                Mesh2_edge_y:units = "degrees_north" ;
        // bounds variables for edges skipped

// Vertical coordinate
        double Mesh2_layers(Mesh2_layers) ;
                Mesh2_layers:standard_name = "ocean_sigma_coordinate" ;
                Mesh2_layers:long_name = "sigma at layer midpoints" ;
                Mesh2_layers:positive = "up" ;
                Mesh2_layers:formula_terms = "sigma: Mesh2_layers eta: Mesh2_surface depth: Mesh2_depth" ;
        double Mesh2_depth(nMesh2_node) ;
                Mesh2_depth:standard_name = "sea_floor_depth_below_geoid" ;
                Mesh2_depth:units = "m" ;
                Mesh2_depth:positive = "down" ;
                Mesh2_depth:mesh = "Mesh2"
                Mesh2_depth:location = "node" ;
                Mesh2_depth:coordinates = "Mesh2_node_x Mesh2_node_y" ;
        double Mesh2_surface(nMesh2_node) ;
                Mesh2_surface:standard_name = "sea_surface_height_above_geoid" ;
                Mesh2_surface:units = "m" ;
                Mesh2_surface:mesh = "Mesh2"
                Mesh2_surface:location = "face" ;
                Mesh2_surface:coordinates = "Mesh2_face_x Mesh2_face_y" ;

fully 3D unstructured (i.e. non-layered) mesh topology.
For a fully 3D unstructured mesh topology we extend the hierarchy of nodes, edges and faces to volumes. Contrary to layered case this type of mesh requires a fully 3D specification of the mesh; hence we not only need latitude and longitude coordinates but also some kind of elevation coordinate (this probably requires a new standard name).
The topology information is stored as attributes to a dummy variable (in the example below called "Mesh3D") with cf_role mesh_topology.
Required topology attributes
Value
cf_role
mesh_topology
topology_dimension
3
node_coordinates
volume_node_connectivity
volume_shape_type
Optionally required attributes*
face_node_connectivity
edge_node_connectivity
Optional attributes
volume_edge_connectivity
volume_face_connectivity
volume_volume_connectivity
face_edge_connectivity
volume_coordinates
face_coordinates
edge_coordinates
*The "Optionally required" attributes edge_node_connectivity and face_node_connectivity are required only if you want to store data on the edges or faces respectively (i.e. if you mind the numbering order of the edges/faces).
The attribute topology_dimension indicates the highest dimensionality of the geometric elements; for a fully 3-dimensional unstructured mesh this should be 3. The attribute node_coordinates points to the auxiliary coordinate variables representing the node locations (latitude, longitude, elevation and optional other coordinates). These auxiliary coordinate variables will have length nNodes. The attribute volume_node_connectivity points to an index variable identifying for every volume the indices of its corner nodes. For faces in the horizontal plane, it was possible to prescribe the order of the nodes, but this is not possible for the nodes of generic 3D volumes. For this reason we introduce an additional attribute volume_shape_type which points to a flag variable that specifies for every volume its shape:
flag_meaning name
description
tetrahedron
pyramid with triangular base, 4 nodes
pyramid
pyramid with square base, a pentahedron, 5 nodes
wedge
prism with triangular base, a pentahedron, 6 nodes
hexahedron
distorted cube, 8 nodes
These four volume shapes are the ones most commonly used. More shapes can be added; and if necessary, it's possible to add a generic shape type which allows for specification of the volume shape indirectly via volume_face_connectivity and face_node_connectivity variables. Such a generic shape is not included in this proposal since there is no practical need for such feature at this time.
(warning) If all volumes have the same shape type, then the shape typed could be determined based on the number of nodes per volume. Another option could be to allow the volume_shape_type to specify the shape type directly rather than pointing to a variable. However, for the time being we assume that the currently proposed volume shape type variable doesn't have too much impact on the performance.
The order in which the corner nodes of a volume are specified is fixed given its shape; this approach is common in 3D modeling, see e.g. this graph in the OpenFOAM documentation and PARAVIEW or VTK documentation. The volume_node_connectivity array will be a matrix of size nVolumes x MaxNumNodesPerVolume; if a volume has less corner nodes than MaxNumNodesPerVolume then the last node indices shall be equal to _FillValue (which should obviously be larger than the number of nodes in the mesh). For the indexing one may use either 0- or 1-based indexing; the convention used should be specified using a start_index attribute to the index variable (i.e. Mesh3D_vol_nodes in the example below). Consistent with the CF-conventions compression option, the connectivity indices are 0-based by default. See this section on 0-/1-based indexing for more details.
In case you want to define variables on the faces or edges of the 3D mesh topology you need to specify the face_node_connectivity or edge_node_connectivity attribute, respectively, to map faces or edges to nodes. Although the volume to node mapping implicitly also defines the location of the faces and edges, it does not specify their global numbering. Again the indexing convention of face_node_connectivity and edge_node_connectivity should be specified using the start_index attribute to the index variable and 0-based indexing is the default.
Optionally the topology may have the following attributes:
  • volume_face_connectivity pointing to an index variable identifying for every volume the indices of its faces. The order in which the face indices should be specified is determined by the volume geometry type. This connectivity array will be a matrix of size nVolumes x MaxNumFacesPerVolume. If a volume has less faces than MaxNumFacesPerVolume then the last face indices shall be equal to _FillValue, and the indexing convention of volume_edge_connectivity should be specified using the start_index attribute to the index variable and 0-based indexing is the default.
  • volume_edge_connectivity pointing to an index variable identifying for every volume the indices of its edges. The order in which the edge indices should be specified is determined by the volume geometry type. This connectivity array will be a matrix of size nVolumes x MaxNumEdgesPerVolume. Again, if a volume has less edges than MaxNumEdgesPerVolume then the last edge indices shall be equal to _FillValue, and the indexing convention of volume_edge_connectivity should be specified using the start_index attribute to the index variable and 0-based indexing is the default.
  • volume_volume_connectivity pointing to an index variable identifying pairs of volumes that share a face, i.e. are neighbors. This connectivity array will thus be a matrix of size nVolumePairs x 2. As usual the indexing convention of volume_volume_connectivity should be specified using the start_index attribute to the index variable (i.e. Mesh3D_vol_links in the example below) and 0-based indexing is the default.
  • face_edge_connectivity pointing to an index variable identifying for every face the indices of its edges. The edges should be specified in anticlockwise direction as viewed from above. This connectivity array will be a matrix of size nFaces x MaxNumNodesPerFace. As always, if a face has less corners/edges than MaxNumNodesPerFace then the last edge indices shall be equal to _FillValue, and the indexing convention of face_edge_connectivity should be specified using the start_index attribute to the index variable and 0-based indexing is the default.
  • face_node_connectivity pointing to an index variable identifying for every face the indices of its nodes. The nodes should be specified in either clockwise or anticlockwise order. This connectivity array will be a matrix of size nFaces x MaxNumNodesPerFace. Again, if a face has less corners/edges than MaxNumNodesPerFace then the last node indices shall be equal to _FillValue, and the indexing convention of face_node_connectivity should be specified using the start_index attribute to the index variable and 0-based indexing is the default.
  • volume_coordinates, face_coordinates and/or edge_coordinates pointing to the auxiliary coordinate variables associated with the characteristic location of the volumes, faces and edges. These auxiliary coordinate variables will have length nVolumes, nFaces and nEdges respectively, and may have in turn a bounds attribute that specifies the corner coordinates of the volume, face or edge (thereby duplicating the data in the node_coordinates variables). The order in which the corner coordinates of the volumes is given by the volume geometry type.
Image Added
Example:
 Code Block
dimensions:
        nMesh3D_node = 12 ; // nNodes
        nMesh3D_edge = 23 ; // nEdges
        nMesh3D_face = 16 ; // nFaces
        nMesh3D_vol  = 4 ; // nVolumes
        nMesh3D_vol_links = 4 ; // nVolumePairs
        nMaxMesh3D_face_nodes = 4 ; // MaxNumNodesPerFace
        nMaxMesh3D_vol_nodes  = 8 ; // MaxNumNodesPerVolume
        nMaxMesh3D_vol_edges  = 12 ; // MaxNumEdgesPerVolume
        nMaxMesh3D_vol_faces  = 6 ; // MaxNumFacesPerVolume

        Two = 2 ;

variables:
// Mesh topology
        integer Mesh3D ;
                Mesh3D:cf_role = "mesh_topology" ;
                Mesh3D:long_name = "Topology data of 3D unstructured mesh" ;
                Mesh3D:topology_dimension = 3 ;
                Mesh3D:node_coordinates = "Mesh3D_node_x Mesh3D_node_y Mesh3D_node_z" ;
                Mesh3D:volume_shape_type = "Mesh3D_vol_types" ;
                Mesh3D:volume_node_connectivity = "Mesh3D_vol_nodes" ;
                Mesh3D:face_node_connectivity = "Mesh3D_face_nodes" ; // attribute required if variables will be defined on faces
                Mesh3D:edge_node_connectivity = "Mesh3D_edge_nodes" ; // attribute required if variables will be defined on edges
                Mesh3D:edge_coordinates = "Mesh3D_edge_x Mesh3D_edge_y Mesh3D_edge_z" ; // optional attribute (requires edge_node_connectivity)
                Mesh3D:face_coordinates = "Mesh3D_face_x Mesh3D_face_y Mesh3D_face_z" ; // optional attribute (requires face_node_connectivity)
                Mesh3D:volume_coordinates = "Mesh3D_vol_x Mesh3D_vol_y Mesh3D_vol_z" ; // optional attribute
                Mesh3D:volume_face_connectivity = "Mesh3D_vol_faces" ; // optional attribute (requires face_node_connectivity)
                Mesh3D:volume_edge_connectivity = "Mesh3D_vol_edges" ; // optional attribute (requires edge_node_connectivity)
                Mesh3D:face_edge_connectivity = "Mesh3D_face_edges" ; // optional attribute (requires face_node_connectivity and edge_node_connectivity)
                Mesh3D:volume_volume_connectivity = "Mesh3D_vol_links" ; // optional attribute
        integer Mesh3D_vol_types(nMesh3D_vol) ;
                Mesh3D_vol_types:cf_role = "volume_shape_type" ;
                Mesh3D_vol_types:long_name = "Specifies the shape of the individual volumes." ;
                Mesh3D_vol_types:flag_range = 0b, 2b ;
                Mesh3D_vol_types:flag_values = 0b, 1b, 2b ;
                Mesh3D_vol_types:flag_meanings = "tetrahedron wedge hexahedron" ;
        integer Mesh3D_vol_nodes(nMesh3D_vol, nMaxMesh3D_vol_nodes) ;
                Mesh3D_vol_nodes:cf_role = "volume_node_connectivity" ;
                Mesh3D_vol_nodes:long_name = "Maps every volume to its corner nodes." ;
                Mesh3D_vol_nodes:_FillValue = 999999 ;
                Mesh3D_vol_nodes:start_index = 1 ;

// Optional mesh topology variables
        integer Mesh3D_edge_nodes(nMesh3D_edge, Two) ;
                Mesh3D_edge_nodes:cf_role = "edge_node_connectivity" ;
                Mesh3D_edge_nodes:long_name = "Maps every edge to the two nodes that it connects." ;
                Mesh3D_edge_nodes:start_index = 1 ;
        integer Mesh3D_face_nodes(nMesh3D_face, nMaxMesh3D_face_nodes) ;
                Mesh3D_face_nodes:cf_role = "face_node_connectivity" ;
                Mesh3D_face_nodes:long_name = "Maps every face to its corner nodes." ;
                Mesh3D_face_nodes:_FillValue = 999999 ;
                Mesh3D_face_nodes:start_index = 1 ;
        integer Mesh3D_vol_faces(nMesh3D_vol, nMaxMesh3D_vol_faces) ;
                Mesh3D_vol_faces:cf_role = "volume_face_connectivity" ;
                Mesh3D_vol_faces:long_name = "Maps every volume to its faces." ;
                Mesh3D_vol_faces:_FillValue = 999999 ;
                Mesh3D_vol_faces:start_index = 1 ;
        integer Mesh3D_vol_edges(nMesh3D_vol, nMaxMesh3D_vol_edges) ;
                Mesh3D_vol_edges:cf_role = "volume_edge_connectivity"
...
Example of a combination of connected 1D network, 2D mesh and 3D mesh.
The variable and dimension names used in this example differ slightly from those used in the examples on Unstructured grids. Please find a translation table below:
Unstructured grids 
This example 
 NetNode 
 node 
 NetLink 
 edge/edge_nodes 
 NetElem/NetCell 
 face 
 NetElemNode/NetCellNode 
 face_nodes 
 NetElemLink/NetCellLink/FlowLink 
 face_links 
 Code Block

netcdf test_map {  

dimensions:  
        // dimensions for mesh 1
        nMesh1_node = 3 ;
        nMesh1_edge = 2
 ;
        
nMaxMesh1_contour_pts = 99
        Mesh3D_vol_edges:long_name = "Maps every volume to its edges." ;
        
// dimensions for mesh 2

        Mesh3D_vol_edges:_FillValue = 999999 ;
          
nMesh2_node
      Mesh3D_vol_edges:start_index = 
6
1 ;
        integer 
 nMesh2_edge = 7 
Mesh3D_face_edges(nMesh3D_face, nMaxMesh3D_face_nodes) ;
        
nMesh2_face
 
=
 
2
 
;

     Mesh3D_face_edges:cf_role = 
 nMesh2
"face_edge_
nodes
connectivity" 
= 7
;
        
nMesh2_face_nodes
 
= 4;

       
 nMesh2
Mesh3D_face_
links
edges:long_name = 
1;

"Maps every face to its edges." ;
  
nMaxMesh2_contour_pts
 
=
 
99
 
;

        
//
 
dimensions
 
for mesh 3
   
 Mesh3D_face_edges:_FillValue = 999999 ;
     
nMesh3_node
 
=
 
6
 
;

        
nMesh3_edge
Mesh3D_face_edges:start_index = 
7
1 ;
        
 nMesh3_face = 2 
integer Mesh3D_vol_links(nMesh3D_vol_links, Two) ;
        
nMesh3_edge_nodes
 
=
 
7;

      Mesh3D_vol_links:cf_role = 
nMesh3
"volume_
face_nodes = 4
volume_connectivity" ;
        
nMesh3_face_links
 
=
 
1;

      
  nMaxMesh3_contour_pts = 99 ;
   
Mesh3D_vol_links:long_name = "Indicates which volumes are neighbors." ;
     
Mesh3_layers
 
=
 
3
 
;

        
Mesh3_interfaces
Mesh3D_vol_links:start_index = 1 
4
;

// Mesh node coordinates
      
//
 
common
 
dimensions
  
double Mesh3D_node_x(nMesh3D_node) ;
      
Two
 
=
 
2;

        
time
Mesh3D_node_x:standard_name = 
UNLIMITED
"longitude" ;
 
//
 
(1
 
currently)
  


variables:
  



        
double
 
Mesh1
Mesh3D_node_x
(nMesh1_node) ;  
:long_name = "Longitude of 3D mesh nodes." ;
                
Mesh1
Mesh3D_node_x:
standard_name
units = "
projection
degrees_
x_coordinate
east" ;
        double Mesh3D_node_y(nMesh3D_node) ;
                
Mesh1
Mesh3D_node_
x
y:
long
standard_name = "
netnodal x-coordinate
latitude" ;
  

                
Mesh1
Mesh3D_node_
x
y:
units
long_name = "
m
Latitude of 3D mesh nodes." ;
  

                
Mesh1
Mesh3D_node_
x
y:
bounds
units = "
Mesh1_node_contour_x
degrees_north" ;
  

        double 
Mesh1
Mesh3D_node_
y
z(
nMesh1
nMesh3D_node) ;
  

                
Mesh1
Mesh3D_node_
y
z:standard_name = "
projection_y_coordinate
elevation" ;
  

                
Mesh1
Mesh3D_node_
y
z:long_name = "
netnodal y-coordinate
Elevation of 3D mesh nodes." ;
                
Mesh1
Mesh3D_node_
y
z:units = "m" ;
  


// Optional mesh volume, face and edge coordinate variables
        
Mesh1_node_y:bounds = "Mesh1_node_contour_y" ;  

double Mesh3D_vol_x(nMesh3D_vol) ;
               
double
 
Mesh1
Mesh3D_
edge
vol_x
(nMesh1_edge) ;  
:standard_name = "longitude" ;
                
Mesh1
Mesh3D_
edge
vol_x:
standard
long_name = "
projection_x_coordinate" ;  
      
Characteristics longitude of mesh volumes." ;
          
Mesh1_edge_x:long_name
 
=
 
"Center
 
coordinate
 
of
 
net link (velocity point).
 Mesh3D_vol_x:units = "degrees_east" ;
  

                
Mesh1
Mesh3D_
edge
vol_x:
units
bounds = "
m
Mesh3D_vol_xbnds" ;
  

        double 
Mesh1
Mesh3D_
edge
vol_y(
nMesh1
nMesh3D_
edge
vol) ;
  

                
Mesh1
Mesh3D_
edge
vol_y:standard_name = "
projection_y_coordinate
latitude" ;
  

                
Mesh1
Mesh3D_
edge
vol_y:long_name = "
Center
Characteristics 
coordinate
latitude of 
net link (velocity point)
mesh volumes." ;
  

                
Mesh1
Mesh3D_
edge
vol_y:units = "
m
degrees_north" ;
       


        
double
 
Mesh1_node_contour_x(nMesh1_node, nMaxMesh1_contour_pts) ;  
Mesh3D_vol_y:bounds = "Mesh3D_vol_ybnds" ;
        double Mesh3D_vol_z(nMesh3D_vol) ;
                
Mesh1
Mesh3D_
node
vol_
contour_x
z:standard_name = "
projection_x_coordinate
elevation" ;
  

                
Mesh1
Mesh3D_
node
vol_
contour_x
z:long_name = "
List of x-points that form outline of flow volume
Characteristics elevation of mesh volumes." ;
  

                
Mesh1
Mesh3D_
node
vol_
contour_x
z:units = "m" ;
  

        
double
 
Mesh1_node_contour_y(nMesh1_node,
 
nMaxMesh1_contour_pts)
 
;
  


   Mesh3D_vol_z:bounds = "Mesh3D_vol_zbnds" ;
        double 
 Mesh1
Mesh3D_
node
vol_
contour_y:standard_name = "projection_y_coordinate" ;  
xbnds(nMesh3D_vol,nMaxMesh3D_vol_nodes) ;
                
Mesh1
Mesh3D_
node
vol_
contour_y:units
xbnds:standard_name = "
m
longitude" ;
  

                
Mesh1
Mesh3D_
node
vol_
contour_y
xbnds:long_name = "
List
Longitude bounds of 
y-points that form outline of flow volume" ;  

mesh volumes (i.e. corner coordinates)." ;
               
integer
 
Mesh1
Mesh3D_
edge_nodes(nMesh1_edge, Two) ;  

vol_xbnds:units = "degrees_east" ;
                Mesh3D_vol_xbnds:_FillValue = 9.9692099683868690E36;
        
 Mesh1_edge_nodes:long_name = "links between two nodes" ;  

double Mesh3D_vol_ybnds(nMesh3D_vol,nMaxMesh3D_vol_nodes) ;
                
integer Mesh1
Mesh3D_vol_ybnds:standard_name = "latitude" ;
 

                
Mesh1
Mesh3D_vol_ybnds:long_name = "
Topology
Latitude 
data
bounds of
 Mesh1
 mesh volumes (i.e. corner coordinates)." ;
                
Mesh1:dimensionality
Mesh3D_vol_ybnds:units = 
1
"degrees_north" ;
                
Mesh1:locations
Mesh3D_vol_ybnds:_FillValue = 
"link node"
9.9692099683868690E36;
        double Mesh3D_vol_zbnds(nMesh3D_vol,nMaxMesh3D_vol_nodes) ;
                
Mesh1:node_coordinates = "Mesh1_node_x Mesh1_node_y
Mesh3D_vol_zbnds:standard_name = "elevation" ;
                
Mesh1:edge_coordinates
Mesh3D_vol_zbnds:long_name = "
Mesh1_edge_x Mesh1_edge_y
Elevation bounds of mesh volumes (i.e. corner coordinates)." ;
                
Mesh1:edge_nodes
Mesh3D_vol_zbnds:units = "
Mesh1_edge_nodes
m" ;
                
Mesh1
Mesh3D_vol_zbnds:
parent
_
mesh
FillValue = 
"CombinedMesh" ;

9.9692099683868690E36;
        double 
Mesh2
Mesh3D_
node
face_x(
nMesh2
nMesh3D_
node
face) ;
  

                
Mesh2
Mesh3D_
node
face_x:standard_name = "
projection_x_coordinate
longitude" ;
  

                
Mesh2
Mesh3D_
node
face_x:long_name = "
netnodal x-coordinate
Characteristics longitude of mesh faces." ;
  

                
Mesh2
Mesh3D_
node
face_x:units = "
m
degrees_east" ;
  

        double 
Mesh2
Mesh3D_
node
face_y(
nMesh2
nMesh3D_
node
face) ;
  

                
Mesh2
Mesh3D_
node
face_y:standard_name = "
projection_y_coordinate
latitude" ;
  

                
Mesh2
Mesh3D_
node
face_y:long_name = "
netnodal y-coordinate
Characteristics latitude of mesh faces." ;
                
Mesh2
Mesh3D_
node
face_y:units = "
m
degrees_north" ;
  

        double 
Mesh2
Mesh3D_face_
x
z(
nMesh2
nMesh3D_face) ;
  

                
Mesh2
Mesh3D_face_
x
z:standard_name = "
projection_x_coordinate
elevation" ;
  

                
Mesh2
Mesh3D_face_
x
z:long_name = "
Flow
Characteristics elevation 
element
of 
circumcenter
mesh 
x
faces." ;
  

                
Mesh2
Mesh3D_face_
x
z:units = "m" ;
  

        
        Mesh2_face_x:bounds = "Mesh2_face_contour_x" ;  
// bounds variables for faces skipped
        double 
Mesh2
Mesh3D_
face
edge_
y
x(
nMesh2
nMesh3D_
face
edge)
 ; 
 ;
                
Mesh2
Mesh3D_
face
edge_
y
x:standard_name = "
projection_y_coordinate
longitude" ;
  

                
Mesh2
Mesh3D_
face
edge_
y
x:long_name = "
Flow
Characteristic 
element
longitude 
circumcenter
of 
y"
2D 
;
mesh edge 


(e.g. midpoint of 
             Mesh2_face_y:units = "m" ;  
the edge)." ;
                
Mesh2
Mesh3D_
face
edge_
y
x:
bounds
units = "
Mesh2_face_contour_y
degrees_east" ;
  

        double 
Mesh2
Mesh3D_
face
edge_
contour_x
y(
nMesh2_face, nMaxMesh2_contour_pts
nMesh3D_edge) ;
  

                
Mesh2
Mesh3D_
face
edge_
contour_x
y:standard_name = "
projection_x_coordinate
latitude" ;
  

                
Mesh2
Mesh3D_
face_contour
edge_
x
y:long_name = "
List
Characteristic latitude of 2D 
x-points
mesh 
that form outline
edge (e.g. midpoint of 
flow
the 
volume
edge)." ;
  

                
Mesh2
Mesh3D_
face
edge_
contour_x
y:units = "
m
degrees_north" ;
  

        double 
Mesh2
Mesh3D_
face
edge_
contour_y
z(
nMesh2_face, nMaxMesh2_contour_pts) ;  
nMesh3D_edge) ;
                Mesh3D_edge_z:standard_name = "latitude" ;
                
Mesh2
Mesh3D_
face
edge_
contour_y
z:
standard
long_name = "
projection_y_coordinate
Characteristic latitude of 2D mesh edge (e.g. midpoint of the edge)." ;
  

                
Mesh2
Mesh3D_
face
edge_
contour_y
z:units = "
m
degrees_north" ;
   


     // bounds variables for edges skipped

Data defined on unstructured meshes.
According to CF-conventions a variable defined on a structured mesh is specified as
 Code Block
      
Mesh2_face_contour_y:long_name
 
=
 
"List of y-points that form outline of flow volume" ;  

double waterlevel(time,nmax,mmax) ;
                waterlevel:standard_name 
double Mesh2_edge_x(nMesh2_edge) ;  
= "sea_surface_height_above_geoid" ;
                
Mesh2_edge_x:standard_name
waterlevel:units = "
projection_x_coordinate
m" ;
  

                
Mesh2_edge_x:long_name
waterlevel:coordinates =
 "Center coordinate of net link (velocity point)." ;  
                Mesh2_edge_x:units = "m" ;  
        double Mesh2_edge_y(nMesh2_edge) ;  
                Mesh2_edge_y:standard_name = "projection_y_coordinate" ;  
                Mesh2_edge_y:long_name = "Center coordinate of net link (velocity point)." ;  
                Mesh2_edge_y:units = "m" ;  
        integer Mesh2_edge_nodes(nMesh2_edge, Two) ;  
 "lat lon" ;

The coordinates attribute refers to the variables that contain the latitude and longitude coordinates. For a curvilinear grid these variables will share two spatial dimensions, here nmax and mmax: lat(nmax,mmax) and lon(nmax,mmax). In numerical models the various quantities are often computed at different locations of the mesh: staggered data. The standard CF-conventions don't offer specific support for this functionality and thus for every stagger location coordinates need to be provided separately: cell center coordinates, corner point coordinates, u-flux point coordinates, and v-flux point coordinates. The underlying topology of the mesh, i.e. how these coordinates (variable definition locations) relate to each other isn't stored in the file. This shortcoming is to some degree solved by the gridspec proposal by Balaji. We introduce here attributes that link to the topological data defined above.
Data variables.
The use of the coordinates attribute is copied from the CF-conventions. It is used to map the values of variables defined on the unstructured meshes directly to their location: latitude, longitude and optional elevation. To map the variable onto the topology of the underlying mesh, two new attributes have been introduced. First, the attribute mesh points to the mesh_topology variable containing the meta-data attributes of the mesh on which the variable has been defined. Second, the attribute location points to the (stagger) location within the mesh at which the variable is defined. Note that in this example the coordinates attribute is redundant since the coordinates could also be obtained by using the face_coordinates attribute of the "Mesh2" variable.
 Code Block
        double Mesh2_waterlevel(time,nMesh2_face) ;
                Mesh2_
edge_nodes
waterlevel:
long
standard_name = "
link between two nodes" ;  

sea_surface_height_above_geoid" ;
               
integer
 Mesh2_
face_nodes(nMesh2_face_nodes, nfaceMaxNode) ;  
waterlevel:units = "m" ;
                Mesh2_
face_nodes:long_name
waterlevel:mesh = "
Mapping
Mesh2"
 
from
 
net
 
face
 
to
 
net
 
nodes."
 
;
  


       Mesh2_waterlevel:location 
integer
= 
Mesh2_face_links(nMesh2_face_links, Two) ;  
 
"face" ;
             
  FlowLink:long_name = "link/interface between two flow elements (faces)"
 
;
  


Mesh2_waterlevel:coordinates = "Mesh2_face_x 
     integer Mesh2 ; 
                Mesh2:long_name = "Topology data of Mesh2" ;
                Mesh2:dimensionality = 2 ;
                Mesh2:locations = "face edge node" ;
                Mesh2:node_coordinates = "Mesh2_node_x Mesh2_node_y" ;
                Mesh2:edge_coordinates = "Mesh2_edge_x Mesh2_edge_y" ;
Mesh2_face_y" ;

Volume and flux variables.
The same mesh geometry can be used in different ways to schematize the hydrodynamic volumes and fluxes. Let's take a simple triangular mesh. From a finite volume point of view this mesh will generally be interpreted as consisting of two volumes with triangular base. However, others may use a continuous Galerkin finite element method that can be shown to be equivalent to a subdivision into four volumes. In the former case the two faces correspond to volumes and the fluxes cross the edges. In the latter case the volumes are defined surrounding the four nodes and the fluxes are directed along the edges. The two abbreviated ncdumps below show how the basic 2D triangular mesh definition can be extended to include this data. The coordinate variables for the volume data now include bounds attributes to define the surface area of the volumes. Note the subtle difference in the long names between the flux variables in the two cases; the standard_name attribute has to make a more formal distinction between the two cases.
Image Added Image Added
Variant 1: Volume at faces:
 Code Block
dimensions:
        
        Mesh2:edge_nodes
nMesh2_node = 
"Mesh2_edge_nodes"
4 ;


 // nNodes
        
      Mesh2:face_coordinates
nMesh2_edge = 
"Mesh2_face_x Mesh2_face_y"
5 ;


 // nEdges
        
      Mesh2:face_nodes
nMesh2_face = 
"Mesh2_face_nodes"
2 ;


 // nFaces
        
      Mesh2:
nMesh2_face_
connectivity
links = 
"Mesh2_face_links"
1 ;


 // nFacePairs

        
      Mesh2:parent_mesh
Two = 
"CombinedMesh"
2 ;



        Three 
double Mesh3_node_x(nMesh3_node) ;  

= 3 ;

variables:
// Mesh topology
        integer Mesh2 ;
         
Mesh3_node_x:standard_name = "projection_x_coordinate" ;  
       
       // as in 2D triangular mesh example
        integer 
Mesh3
Mesh2_
node_x:long_name = "netnodal x-coordinate" ;  

face_nodes(nMesh2_face, Three) ;
                // 
 Mesh3_node_x:units = "m" ;  
as in 2D triangular mesh example
        
double
integer 
Mesh3
Mesh2_
node
edge_
y
nodes(
nMesh3_node) ;  
nMesh2_edge, Two) ;
                
Mesh3_node_y:standard_name = "projection_y_coordinate" ;  
    
// as in 2D triangular mesh example

// Optional mesh topology variables
        integer 
   Mesh3_node_y:long_name = "netnodal y-coordinate"
Mesh2_face_edges(nMesh2_face, Three) ;
                
 Mesh3_node_y:units = "m" ;  
// as in 2D triangular mesh example
        
double
integer 
Mesh3
Mesh2_face_
x
links(
nMesh3
nMesh2_face_links, Two) ;
   

       
             // as in 2D triangular mesh example

// Mesh node coordinates
        double 
Mesh3
Mesh2_
face
node_x
:standard_name = "projection_x_coordinate" ;  
(nMesh2_node) ;
                
Mesh3_face_x:long_name = "Flow element circumcenter x" ;  
// as in 2D triangular mesh example
        double 
   
Mesh2_node_y(nMesh2_node) ;
    
Mesh3_face_x:units
 
=
 
"m"
 
;
  


       // as in 2D triangular mesh example

// Optional mesh 
Mesh3_
face
_x:bounds
 
= "Mesh3_face_contour_x" ;  
and edge coordinate variables
        double 
Mesh3
Mesh2_face_
y
x(
nMesh3
nMesh2_face) ;
  

                
Mesh3
Mesh2_face_
y
x:standard_name = "
projection_y_coordinate
longitude" ;
  

                
Mesh3
Mesh2_face_
y
x:long_name = "
Flow element
Characteristics longitude of 2D mesh triangle (e.g. circumcenter 
y
coordinate)." ;
  

                
Mesh3
Mesh2_face_
y
x:units = "
m
degrees_east" ;
  

                
Mesh3
Mesh2_face_
y
x:bounds = "
Mesh3
Mesh2_face_
contour_y
xbnds" ;
  

        double 
Mesh3
Mesh2_face_
contour_x
y(
nMesh3
nMesh2_face
, nMaxMesh3_contour_pts) ;  
) ;
                Mesh2_face_y:standard_name = "latitude" ;
                
Mesh3
Mesh2_face_
contour_x
y:
standard
long_name = "
projection_x_coordinate
Characteristics latitude of 2D mesh triangle (e.g. circumcenter coordinate)." ;
  

                
Mesh3
Mesh2_face_
contour_x:long_name
y:units = "
List of x-points that form outline of flow volume
degrees_north" ;
  

                
Mesh3
Mesh2_face_
contour_x
y:
units
bounds = "
m
Mesh2_face_ybnds" ;
  

        double 
Mesh3
Mesh2_face_
contour_y
xbnds(
nMesh3
nMesh2_face,
 nMaxMesh3_contour_pts) ;  
Three) ;
                Mesh2_face_xbnds:standard_name = "longitude" ;
                
Mesh3
Mesh2_face_
contour_y
xbnds:
standard
long_name = "
projection_y_coordinate
Longitude bounds of 2D mesh triangle (i.e. corner coordinates)." ;
  

                
Mesh3
Mesh2_face_
contour_y
xbnds:units = "
m
degrees_east" ;
        double Mesh2_face_ybnds(nMesh2_face,Three) ;
                
Mesh3
Mesh2_face_
contour_y
ybnds:
long
standard_name = 
"List of y-points that form outline of flow volume" ;  
        double Mesh3_edge_x(nMesh3_edge) ;  
"latitude" ;
                Mesh2_face_ybnds:long_name = "Latitude bounds of 2D mesh triangle (i.e. corner coordinates)." ;
                
Mesh3
Mesh2_
edge
face_
x
ybnds:
standard_name
units = "
projection
degrees_
x_coordinate" ;  
       
north" ;
        double 
Mesh3
Mesh2_edge_x
:long_name = "Center coordinate of edges (velocity point)." ;  

(nMesh2_edge) ;
                // 
 Mesh3_edge_x:units = "m" ;  
as in 2D triangular mesh example
        double 
Mesh3
Mesh2_edge_y(
nMesh3
nMesh2_edge) ;
           


     // as in 2D triangular mesh example

// Volume and flux 
 Mesh3_edge_y:standard_name = "projection_y_coordinate" ;  
data
        double Mesh2_volumes(nMesh2_face) ;
                
Mesh3
Mesh2_
edge_y
volumes:long_name
 = "Center coordinate of edges (velocity point).
 = "volumes" ;
  

                
Mesh3
Mesh2_
edge_y
volumes:units = "
m
m3" ;
       


        
integer
 
Mesh3_edge_nodes(nMesh3_edge, Two) ;  
Mesh2_volumes:mesh = "Mesh2" ;
                
Mesh3
Mesh2_
edge_nodes:long_name
volumes:location = 
"link between two nodes" ;  

"face" ;
                Mesh2_volumes:coordinates 
integer
= 
Mesh3
"Mesh2_face_
nodes(nMesh3
x Mesh2_face_
nodes, nfaceMaxNode)
y" ;
  

        
        Mesh3_face_nodes:long_name = "Mapping from faces to nodes." ;  

double Mesh2_fluxes(nMesh2_edge) ;
               
integer
 
Mesh3
Mesh2_
face_links(nMesh3_face_links, Two) ;  
fluxes:long_name = "flux across edge" ;
                
FlowLink:long_name
Mesh2_fluxes:units = "
link/interface between two flow elements (faces)" ;  

m3 s-1" ;
               
double
 
Mesh3_layers(Mesh3_layers) ;
Mesh2_fluxes:mesh = "Mesh2"
                
Mesh3
Mesh2_
layers
fluxes:
standard_name
location = "
ocean_sigma_coordinate
edge" ;
                
Mesh3
Mesh2_
layers
fluxes:
long_name
coordinates = "
sigma at layer midpoints
Mesh2_edge_x Mesh2_edge_y" ;

       
Variant 2: Volume at nodes:
 Code Block
dimensions:
        
 Mesh3_layers:positive
nMesh2_node = 
"up"
4 ; // nNodes
        nMesh2_edge = 5 ; // nEdges
   
Mesh3_layers:formula_terms
 
=
 
"sigma:
 
Mesh3_layers
 
eta:
 
Mesh3
nMesh2_
zwl
face 
depth: Mesh3_depth"
= 2 ; // nFaces
        
double Mesh3_interfaces(Mesh3_interfaces) ;
    
nMesh2_face_links = 1 ; // nFacePairs
        
    Mesh3_interfaces:standard_name
nMaxMesh2_bnds = 
"ocean_sigma_coordinate"
6 ;

        
        Mesh3_interfaces:long_name = "sigma at layer interfaces"
Two = 2 ;

     
        Three = 
 Mesh3_interfaces:positive = "up" ;
3 ;

variables:
// Mesh topology
        integer Mesh2 ;
      
Mesh3_interfaces:formula_terms
 
=
 
"sigma:
 
Mesh3_interfaces
 
eta:
 
Mesh3_zwl
 
depth:
 
Mesh3_depth"
 
;

  // as in 2D triangular mesh 
integer
example
 
Mesh3
 
;
 


     integer Mesh2_face_nodes(nMesh2_face, Three) ;
        
Mesh3:long_name
 
=
 
"Topology
 
data
 
of
 
Mesh3"
 
;

  // as in 2D triangular mesh example
        
Mesh3:dimensionality = 2
integer Mesh2_edge_nodes(nMesh2_edge, Two) ;
                
Mesh3:locations = "face edge node" ;
       
// as in 2D triangular mesh example

// Optional mesh topology variables
        integer 
Mesh3:node_coordinates = "Mesh3_node_x Mesh3_node_y"
Mesh2_face_edges(nMesh2_face, Three) ;
                
Mesh3:edge_coordinates = "Mesh3_edge_x Mesh3_edge_y" ;
  
// as in 2D triangular mesh example
        
      Mesh3:edge_nodes = "Mesh3_edge_nodes"
integer Mesh2_face_links(nMesh2_face_links, Two) ;
                
Mesh3:face_coordinates = "Mesh3_face_x Mesh3_face_y" ;
         
// as in 2D triangular mesh example

// Mesh node coordinates
       
Mesh3:face_nodes
 
= "Mesh3_face_nodes"
double Mesh2_node_x(nMesh2_node) ;
                
Mesh3:face_connectivity
Mesh2_node_x:standard_name = "
Mesh3_face_links
longitude" ;
                
Mesh3:parent_mesh
Mesh2_node_x:long_name = "
CombinedMesh
Longitude of 2D mesh nodes." ;



               
integer
 
CombiMesh
Mesh2_
edge_mesh(nCombiMesh_contacts, Two) ; 
node_x:units = "degrees_east" ;
                
CombiMesh
Mesh2_
edge
node_
mesh
x:
long_name
bounds = "
Mesh number of contact
Mesh2_node_xbnds" ;
 


      
        double 
 CombiMesh
Mesh2_
edge_mesh:valid_range = 0, 2
node_y(nMesh2_node) ;
                
CombiMesh
Mesh2_
edge
node_
mesh
y:
valid
standard_
values
name = 
0, 1, 2
"latitude" ;
                
CombiMesh
Mesh2_
edge
node_
mesh
y:
flag
long_
meanings
name = "
Mesh1
Latitude 
Mesh2
of 
Mesh3"
2D 
;
        integer CombiMesh_edge(nCombiMesh_contacts, Two) ; 
mesh nodes." ;
                
CombiMesh
Mesh2_node_
edge
y:
long_name
units = "
Edge number of contact
degrees_north" ;
 

        
integer
 
CombinedMesh(nCombinedMesh_contacts,
 
Four)
 
;
 


    Mesh2_node_y:bounds = "Mesh2_node_ybnds" ;
        
 CombinedMesh:long_name = "Topology data of CombinedMesh"
double Mesh2_node_xbnds(nMesh2_node, nMaxMesh2_bnds) ;
                
CombinedMesh:sub_meshes
Mesh2_node_xbnds:standard_name = "
Mesh1 Mesh2 Mesh3
longitude" ;
                
CombinedMesh:contact
Mesh2_node_xbnds:long_name = "
CombiMesh_edge_mesh CombiMesh_edge" ;

        double time(time) ;  
List of x-points that form outline of flow volume" ;
                
time:standard_name
Mesh2_node_xbnds:units = "
time
degrees_east" ;
                
time:units = "seconds since 1992-08-31 00:00:00" ;  

Mesh2_node_xbnds:_FillValue = 9.9692099683868690E36;
        double 
Mesh1
Mesh2_node_
zwl
ybnds(
time
nMesh2_node, 
nMesh1
nMaxMesh2_
node
bnds) ;
  

                
Mesh1
Mesh2_node_
zwl
ybnds:standard_name = "
sea_surface_height_above_geoid
latitude" ;
                
Mesh1
Mesh2_node_
zwl
ybnds:units = "
m
degrees_north" ;
                
Mesh1
Mesh2_node_
zwl
ybnds:
grid
long_name = "
Mesh1"
List of y-points that form outline of flow volume" ;
                
Mesh1
Mesh2_node_
zwl
xbnds:
location
_FillValue = 
"face" ;
       
9.9692099683868690E36;

// Optional mesh face and edge coordinate variables
        double 
Mesh1_zwl:coordinates = "Mesh1_node_x Mesh1_node_y"
Mesh2_face_x(nMesh2_face) ;
        
double
 
Mesh1_u(time,
 
nMesh1_edge)
 
;
  


   // as in 2D triangular mesh example
       
Mesh1_zwl:standard_name = "sea_water_speed"
 double Mesh2_face_y(nMesh2_face) ;
                
Mesh1_u:long_name = "Velocity (along the edge)" ; 
// as in 2D triangular mesh example
        
        Mesh1_u:units = "m s-1" ;  
double Mesh2_edge_x(nMesh2_edge) ;
                
Mesh1_u:grid = "Mesh1"
    
// as in 2D triangular mesh example
        
    Mesh1_u:location = "edge" ;  

double Mesh2_edge_y(nMesh2_edge) ;
                // 
 Mesh1_u:coordinates = "Mesh1_edge_x Mesh1_edge_y" ;  


as in 2D triangular mesh example

// Volume and flux data
        double Mesh2_
depth
volumes(nMesh2_node) ;
  

                Mesh2_
depth
volumes:
standard
long_name = "
sea_floor_depth_below_geoid
volumes" ;
                Mesh2_
depth
volumes:units = "
m
m3" ;
                Mesh2_
depth
volumes:
positive
mesh = "
down
Mesh2" ;
                Mesh2_
depth
volumes:
grid
location = "
Mesh2
node" ;
                Mesh2_
depth
volumes:
location
coordinates = "Mesh2_node_x Mesh2_node_y" ;
        double 
  
Mesh2_fluxes(nMesh2_edge) ;
     
Mesh2_depth:coordinates = "Mesh2_node_x Mesh2_node_y" ;

          
double
 Mesh2_
zwl(time, nMesh2_face) ;  
fluxes:long_name = "flux along edge" ;
                Mesh2_
zwl
fluxes:
standard_name
units = "
sea_surface_height_above_geoid
m3 s-1" ;
                Mesh2_
zwl
fluxes:
units
mesh = "
m
Mesh2"
 ;

                Mesh2_
zwl
fluxes:
grid
location = "
Mesh2
edge" ;
                Mesh2_fluxes:coordinates = 
Mesh2_zwl:location = "face" ;
                Mesh2_zwl:coordinates = "Mesh2_face_x Mesh2_face_y" ;
        double Mesh2_ucx(time, nMesh2_face) ;  
                Mesh2_ucx:standard_name = "eastward_sea_water_velocity" ;
                Mesh2_ucx:units = "m s-1" ;
                Mesh2_ucx:grid = "Mesh2"
                Mesh2_ucx:location = "face" ;
                Mesh2_ucx:coordinates = "Mesh2_face_x Mesh2_face_y" ;  
        double Mesh2_ucy(time, nMesh2_face) ;  
                Mesh2_ucy:standard_name = "northward_sea_water_velocity" ;
"Mesh2_edge_x Mesh2_edge_y" ;

Location index set.
Some variables may only be defined at specific locations within the mesh, e.g. only at boundary points or at special locations like weirs and gates. To save space and to improve readability, the concept of a location_index_set is introduced. It is basically identical to the compression option in the the CF-conventions except for the fact that the compression works on a (set of) orthogonal coordinate dimension(s) and the location_index_set works on a topology location.
The location index set is an integer variable that contains the indices of the locations at which a specific quantity is defined. The example below defines a location index set "Mesh1_set" as a subset of the "node"s of Mesh1 (red points). The attribute location_index_set of the variable "Mesh_waterlevel" points to this index set and the coordinates attribute points to the corresponding (subset) of latitude and longitude coordinates. The mesh and location attributes of the location_index_set variable are required; the coordinates attribute is optional. Note that the coordinates attributes on both "Mesh1_cell" and "Mesh1_waterlevel" are again redundant since the coordinates could also be obtained by using the index set "Mesh1_set" and the node_coordinates attribute of the "Mesh1" variable. Consistent with all other index variables defined here, the indexing convention of the location index set should be specified using the start_index attribute to the index variable and 0-based indexing is the default. See this section on 0-/1-based indexing for more details.
Contrary to a coordinate variable, the index set doesn't have to be monotonic. So, it can be used for creating subsets of the original locations as well as for renumbering the locations. If the location_index_set attribute is used on a variable, then the mesh and location attributes should not also be used on that variable.
Image Added
 Code Block
dimensions:
        
        Mesh2_ucy:units
nMesh1_set = 
"m s-1"
4 ;

                Mesh2_ucy:grid = "Mesh2"
       

variables:
        integer 
Mesh2_ucy:location = "face" 
Mesh1_set(nMesh1_set) ;
                
Mesh2
Mesh1_
ucy
set:
coordinates
cf_role = "
Mesh2
location_
face_x Mesh2_face_y
index_set" ; 
 

        
double
 
Mesh2_unorm(time,
 
nMesh2_edge) ; 
 


     
           Mesh2_unorm
Mesh1_set:long_name = "
Normal component
Defines Mesh1_set as subset of 
velocity
the 
at
nodes 
the
of 
interface
Mesh1." ;
 

                
Mesh2
Mesh1_
unorm
set:
units
mesh = "
m s-1
Mesh1" ;
  

                
Mesh2
Mesh1_
unorm
set:
grid
location = "
Mesh2
node" ;
                
Mesh2
Mesh1_
unorm
set:
location
start_index = 
"edge"
1 ;
  

                
Mesh2
Mesh1_
unorm
set:coordinates = "
Mesh2
Mesh1_
edge
set_x 
Mesh2
Mesh1_
edge
set_y" ;
  

        
integer
double 
Mesh2
Mesh1_set_
edgetype
x(
nMesh2
nMesh1_
edge
set) ;
  

                
Mesh2
Mesh1_set_
edgetype
x:
long
standard_name = "
Type of edge
longitude" ;
 

                
Mesh2
Mesh1_set_
edgetype
x:
valid
long_
range
name = 
0, 2;
                Mesh2_edgetype:valid_values = 0, 1, 2
"Characteristic longitude of set (e.g. longitude of node)." ;
                
Mesh2
Mesh1_set_
edgetype
x:
flag_meanings
units = "
closed_edge open_internal_edge open_boundary_edge" ;
     
degrees_east" ;
        
   Mesh2_edgetype:grid = "Mesh2"
double Mesh1_set_y(nMesh1_set) ;
                
Mesh2
Mesh1_set_
edgetype
y:
location
standard_name = "
edge
latitude" ;
  

                
Mesh2
Mesh1_set_
edgetype
y:
coordinates
long_name = "
Mesh2_edge_x Mesh2_edge_y" ;  

        double Mesh3_depth(nMesh3_node) ;  
Characteristic latitude of set (e.g. latitude of node)" ;
                
Mesh3
Mesh1_set_
depth
y:
standard_name
units = "
sea_floor_depth_below_geoid"
degrees_north" ;

        double Mesh1_waterlevel(time, nMesh1_set) ;
                
Mesh3
Mesh1_
depth
waterlevel:
units
standard_name = "
m
sea_surface_height_above_geoid" ;
                
Mesh3
Mesh1_
depth
waterlevel:
positive
units = "
down
m" ;
                
Mesh3
Mesh1_
depth:grid
waterlevel:location_index_set = "
Mesh3
Mesh1_set" ;
                
Mesh3
Mesh1_
depth
waterlevel:
location
coordinates = "
node" ;
                Mesh3_depth:coordinates = "Mesh3_node_x Mesh3_node_y" ;
        double Mesh3_zwl(time, nMesh3_face) ;  
                Mesh3_zwl:standard_name = "sea_surface_height_above_geoid" ;
                Mesh3_zwl:units = "m" ;
                Mesh3_zwl:grid = "Mesh3"
Mesh1_set_x Mesh1_set_y" ;

0-/1-based indexing
The indexing using by the CF compression option is 0-based. Therefore, it is most consistent for this CF extension for unstructured data to also use 0-based indexing, which means that points, edges, faces and volumes will be numbered starting with 0. This convention is consistent with languages like C and Java, but unlike FORTRAN and MATLAB. Since many of the unstructured models have been programed in FORTRAN and legacy netCDF files exist that use 1-based indexing (which could be upgraded to be consistent with this new proposal using ncML if 1-based indexing were allowed), we propose to support both 0- and 1-based indexing by means of the start_index attribute. You will find below two examples of the same network geometry using either 0- or 1-based indexing. Switching between 0- and 1-based indexing is as easy as adding 1 to or subtracting 1 from the indices upon reading or writing depending on the setting of start_index; allowing both options should only have a minor impact on the reading routines and no effect at all on the rest of your code.
Example of 0-based indexing:
Image Added
 Code Block
dimensions:
        
        Mesh3_zwl:location
nMesh1_node = 
"face"
5 ;


 // nNodes
        
      Mesh3_zwl:coordinates
nMesh1_edge = 
"Mesh3_face_x Mesh3_face_y"
4 ;


 
       double Mesh3_ucx(time, nMesh3_face, Mesh3_layers) ;  

// nEdges

        Two = 2;

variables:
// Mesh topology
       
Mesh3_ucx:standard_name = "eastward_sea_water_velocity"
 integer Mesh1 ;
                
Mesh3_ucx:units
Mesh1:cf_role = "
m s-1
mesh_topology" ;
                
Mesh3_ucx:grid
Mesh1:long_name = "
Mesh3"
Topology data of 1D network" ;
                
Mesh3_ucx:location
Mesh1:topology_dimension = 
"face"
1 ;
                
Mesh3
Mesh1:node_
ucx:
coordinates = "
Mesh3
Mesh1_
face
node_x 
Mesh3
Mesh1_
face
node_y
 Mesh3_layers
" ;
  


             
double
 
Mesh3_ucy(time, nMesh3_face, Mesh3_layers) ;  
Mesh1:edge_node_connectivity = "Mesh1_edge_nodes" ;
                
Mesh3_ucy
Mesh1:
standard
edge_
name
coordinates = "
northward_sea_water_velocity
Mesh1_edge_x Mesh1_edge_y" ;


 // optional attribute
        
     Mesh3_ucy:units = "m s-1"
integer Mesh1_edge_nodes(nMesh1_edge, Two) ;
                
Mesh3
Mesh1_edge_
ucy
nodes:
grid
cf_role = "
Mesh3"
edge_node_connectivity" ;
                
Mesh3
Mesh1_edge_
ucy
nodes:
location
long_name = "
face
Maps every edge/link to the two nodes that it connects." ;
                
Mesh3
Mesh1_edge_
ucy
nodes:
coordinates
start_index = 
"Mesh3_face_x Mesh3_face_y Mesh3_layers" ;  
        double Mesh3_unorm(time, nMesh3_edge, Mesh3_layers) ;  
0 ; // default setting, attribute could have been skipped.

// Coordinate variables skipped
        
data:

    Mesh1 = 0 ; // dummy
    
    
Mesh3
Mesh1_
unorm:long
edge_
name
nodes =
  
"Normal
  
component
 
of
 
velocity
 
at
 
the
 
interface"
0, 
;
 2,
         1,  2,
     
Mesh3_unorm:units
 
=
 
"m
 
s-1" ;
 2,  3,
         3,  
  
4 ;

Example of 1-based indexing:
Image Added
 Code Block
dimensions:
   
Mesh3_unorm:grid
 
=
 
"Mesh3"

   nMesh1_node = 5 ; // nNodes
        
Mesh3
nMesh1_
unorm:location
edge = 
"edge"
4 ; // nEdges

        Two = 2;

variables:
// Mesh topology
     
Mesh3_unorm:coordinates
 
=
 
"Mesh3_edge_x Mesh3_edge_y Mesh3_layers" ;  

 integer Mesh1 ;
               
integer
 
Mesh3_edgetype(nMesh3_edge) ;  
Mesh1:cf_role = "mesh_topology" ;
                
Mesh3_edgetype
Mesh1:long_name = "
Type
Topology data of 
edge
1D network" ;
 

                
Mesh3_edgetype
Mesh1:
valid
topology_
range
dimension = 
0,
1 
2
;
                
Mesh3_edgetype
Mesh1:
valid
node_
values
coordinates =
 0, 1, 2
 "Mesh1_node_x Mesh1_node_y" ;
                
Mesh3_edgetype:flag_meanings
Mesh1:edge_node_connectivity = "
closed
Mesh1_edge
 open_internal_edge open_boundary_edge
_nodes" ;
                
Mesh3_edgetype:grid
Mesh1:edge_coordinates = "
Mesh3"
    
Mesh1_edge_x Mesh1_edge_y" ; // optional attribute
        
    Mesh3_edgetype:location = "edge" ;  
integer Mesh1_edge_nodes(nMesh1_edge, Two) ;
                
Mesh3
Mesh1_edge_
edgetype
nodes:
coordinates
cf_role = "
Mesh3_
edge_
x Mesh3_edge_y
node_connectivity" ;
      


//
  
global
 
attributes:
  


     Mesh1_edge_nodes:long_name = "Maps every edge/link to the two nodes that 
 :institution = "Deltares
it connects." ;
  

                
:references
Mesh1_edge_nodes:start_index = 
"http:
1 ;

//
www.deltares.nl" ;  
 Coordinate variables skipped
        
data:

    Mesh1 = 0 ; 
:source = "UNSTRUC" ;
// dummy
    
    Mesh1_edge_nodes =
         1,  
:history = "Created on 2010-04-12, Bert Jagers" ;  
3,
         2,  3,
         3,  4,
       
:Conventions
 
=
 
"CF-1.4:Deltares-0.1" ;  
4,  5 ;