Hello @ChrisBarker-NOAA and all,

After some very illuminating discussion over at 
https://urldefense.us/v3/__https://github.com/ugrid-conventions/ugrid-conventions/issues/52__;!!G2kpM7uM-TzIFchu!gsrPpUHyBO1L3RCLlnbI4ykGpE8GyFUQGCnBa97TVwjO6tJnc_z4tfusXiad6JE3NXdsbwwppNw$
 , and some offline discussions, @JonathanGregory and I have come up with some 
suggested text to the data model in [Appendix 
I](https://urldefense.us/v3/__https://cfconventions.org/cf-conventions/cf-conventions.html*appendix-CF-data-model__;Iw!!G2kpM7uM-TzIFchu!gsrPpUHyBO1L3RCLlnbI4ykGpE8GyFUQGCnBa97TVwjO6tJnc_z4tfusXiad6JE3NXdsLhQqXgs$
 ) that we hope will update the CF data model for the mythical connectivity.

The new text is hopefully self-explanatory and edits the "Domain construct" 
section of Appendix I (edits in italics) and provides a new section describing 
a new construct type - the "network topology construct". Here we are using 
"network topology" in [this 
sense](https://urldefense.us/v3/__https://en.wikipedia.org/wiki/Network_topology__;!!G2kpM7uM-TzIFchu!gsrPpUHyBO1L3RCLlnbI4ykGpE8GyFUQGCnBa97TVwjO6tJnc_z4tfusXiad6JE3NXdsctCuFWE$
 ), but there may well be better names.

Remember that the CF data model is a logical data model that is independent of 
the encoding, so it not a problem that  the connectivity array  does not look 
like a UGRID netCDF connectivity variable. 
 
(I took the liberty of rearranging some the network topology text after 
Jonathan last saw this - I take full responsibility for any negative 
consequences.)

----

### Domain construct

The domain construct (figure 3) describes a domain comprising measurement 
locations and cell properties. The domain construct is the only metadata 
construct that may also exist independently of a field construct. The domain 
construct contains properties to describe the domain (in the same sense as for 
the field construct) and relates the following metadata constructs

  * Domain axis constructs.
  * Dimension coordinate and auxiliary coordinate constructs.
  * Coordinate reference constructs.
  * Domain ancillary constructs.
  * Cell measure constructs.
  * _Network topology constructs._

All of the constructs contained by the domain construct are optional (as 
indicated by "0.." in figure 3).

In CF-netCDF, domain information is stored either implicitly via data variable 
attributes (such as coordinates), or explicitly in a domain variable, _or a 
UGRID mesh topology variable. In the latter two cases_, the domain exists 
without reference to a data array.

### Network topology construct

A network topology describes the connectivity of cells of domain indexed by a 
subset of the domain axis constructs. When two cells are connected, operations 
on the data stored on them may be assumed to be continuous across their common 
boundary. A network topology construct describes logically and explicitly the 
network topology of cells indexed by a single domain axis construct. A network 
topology construct contains a connectivity array that spans a unique domain 
axis construct with the addition of an extra dimension of the same size, such 
that each dimension indexes the cells. The array is symmetrical, and each 
element indicates whether the pair cells to which its indices refer are 
connected.

A network topology that has no corresponding network topology construct, which 
includes those for multiple domain axis constructs, is nonetheless implicitly 
defined by a function of both the physical contiguousness of the cells, and the 
nature of the real world or simulated processes that produced the data. For 
example, in a field which contains both land and ocean cells, connections 
between land and ocean cells might be excluded for some physical processes.The 
description of such an implicit network topology may require metadata that is 
external to CF.

In CF-netCDF a network topology can only be provided for a domain defined by a 
UGRID mesh topology variable. In this case, the connectivity array is supplied 
by a UGRID connectivity variable (such as a "face_face_connectivity" variable).



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