example of how to make a netCDF file with CF conventions of a
variable that is defined on a grid that is curvi-linear
in a lat-lon coordinate system. In this case
the dimensions (m,n) do not coincide with the coordinate axes.

This case is described in:
http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#id2984605
as "Two-Dimensional Latitude, Longitude, Coordinate Variables".

An example of a curvi-linear lat,lon grid is for instance a satellite
image: a digital image with a constant width in terms of number of
pixels ncols (swath), and a length nrows determined by how long a ground
station can recieve the satellite above the (electro-magnetic) horizon.

  ^ latitude (degrees_north)
|         x
| ncols /   \
|     /  /\   \
|   /   /15\    \
|  x  /10   \     \
|    <5     14\     \
|     \   9    \      \
|      \4       \      |
|       \        \     |
|        )3  8  xx)    | nrows
|       /        /     |
|      /2       /      |
|     /   7    /      /
|    <1     12/     /
|     \6    /     /
|       \11/    /
|        \/   x
|
+----------------------> longitude
(degrees_east)

Note that ncBrowse does not contain plot support for curvi-linear grids, so ncBrowse will display the same rectangular plot as for the netCDF file created by NC_CF_GRID_WRITE_LAT_LON_ORTHOGONAL_TUTORIAL, albeit with different axes annotations (col/row instead of lat/lon).

%See also: SNCTOOLS, NC_CF_GRID, NC_CF_GRID_WRITE,
%          NC_CF_GRID_WRITE_LAT_LON_ORTHOGONAL_TUTORIAL,
%          NC_CF_GRID_WRITE_X_Y_ORTHOGONAL_TUTORIAL,
%          NC_CF_GRID_WRITE_X_Y_CURVILINEAR_TUTORIAL,
%          NC_CF_STATIONTIMESERIES

% This tool is part of <a href="http://www.OpenEarth.eu">OpenEarthTools</a> under the <a href="http://www.gnu.org/licenses/gpl.html">GPL</a> license.

   OPT.title                  = '';
OPT.institution            = '';
OPT.source                 = '';
OPT.history                = ['tranformation to netCDF: $HeadURL: https://repos.deltares.nl/repos/OpenEarthTools/trunk/matlab/io/netcdf/nctools/nc_cf_grid_write_lat_lon_curvilinear_tutorial.m $'];
OPT.references             = '';
OPT.email                  = '';
OPT.comment                = '';
OPT.version                = '';
OPT.acknowledge            =['These data can be used freely for research purposes provided that the following source is acknowledged: ',OPT.institution];
OPT.disclaimer             = 'This data is made available in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.';

   lon1                       = [2 4 6];
lat1                       = [50 51 52 53 54];
[lon2,lat2]                 = ndgrid(lon1,lat1);
ang                        = [-15 0 15 30 45;-15 0 15 30 45;-15 0 15 30 45];
OPT.lat                    = lat2 + sind(ang).*lon2./2;
OPT.lon                    = lon2 + cosd(ang).*lon2./2; clear lon1 lon2 lat1 lat2

OPT.ncols                  = size(OPT.lon,1);
OPT.nrows                  = size(OPT.lat,2);
OPT.lat_type               = 'single'; % 'single', 'double' for high-resolution data (eps 1m)
OPT.lon_type               = 'single'; % 'single', 'double' for high-resolution data (eps 1m)

OPT.wgs84.code             = 4326; % % epsg code of global grid: http://www.epsg-registry.org/
OPT.wgs84.name             = 'WGS 84';
OPT.wgs84.semi_major_axis  = 6378137.0;
OPT.wgs84.semi_minor_axis  = 6356752.314247833;
OPT.wgs84.inv_flattening   = 298.2572236;

   OPT.val                    = [1 2 3 4 5;6 7 8 9 10;11 12 nan 14 15]; % use ncols as 1st array dimension to get correct plot in ncBrowse (snctools swaps for us)
OPT.varname                = 'depth';       % free to choose: will appear in netCDF tree
OPT.units                  = 'm';           % from UDunits package: http://www.unidata.ucar.edu/software/udunits/
OPT.long_name              = 'bottom depth';% free to choose: will appear in plots
OPT.standard_name          = 'sea_floor_depth_below_geoid'; % or 'altitude'
OPT.val_type               = 'single';      % 'single' or 'double'
OPT.fillvalue              = nan;

   ncfile = fullfile(fileparts(mfilename('fullpath')),[mfilename,'.nc']);

nc_create_empty (ncfile)

http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#description-of-file-contents

   nc_attput(ncfile, nc_global, 'title'         , OPT.title);
nc_attput(ncfile, nc_global, 'institution'   , OPT.institution);
nc_attput(ncfile, nc_global, 'source'        , OPT.source);
nc_attput(ncfile, nc_global, 'history'       , OPT.history);
nc_attput(ncfile, nc_global, 'references'    , OPT.references);
nc_attput(ncfile, nc_global, 'email'         , OPT.email);

nc_attput(ncfile, nc_global, 'comment'       , OPT.comment);
nc_attput(ncfile, nc_global, 'version'       , OPT.version);

nc_attput(ncfile, nc_global, 'Conventions'   , 'CF-1.4');
nc_attput(ncfile, nc_global, 'CF:featureType', 'Grid');  % https://cf-pcmdi.llnl.gov/trac/wiki/PointObservationConventions

nc_attput(ncfile, nc_global, 'terms_for_use' , OPT.acknowledge);
nc_attput(ncfile, nc_global, 'disclaimer'    , OPT.disclaimer);

  http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#dimensions

   nc_add_dimension(ncfile, 'col', OPT.ncols); % !!! use this as 1st array dimension to get correct plot in ncBrowse (snctools swaps for us)
nc_add_dimension(ncfile, 'row', OPT.nrows); % !!! use this as 2nd array dimension to get correct plot in ncBrowse (snctools swaps for us)

% You might insert a vector 'col' that runs [OPT.ncols:-1:1] to have
% the arcGIS ASCII file approach of having upper-left corner of
% the data matrix at index (1,1) rather than the default of having the
% lower-left corner of the data matrix  at index (1,1).

%  nc_add_dimension(ncfile, 'time', 1); % if you would like to include more instances of the same grid,
% you can optionally use 'time' as a 3rd dimension. see
% nc_cf_stationTimeSeries_write_tutorial for info on time.

    http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#longitude-coordinate

   clear nc;ifld = 1;
nc(ifld).Name             = 'lon';
nc(ifld).Nctype           = nc_type(OPT.lon_type);
nc(ifld).Dimension        = {'col','row'}; % !!!
nc(ifld).Attribute(    1) = struct('Name', 'long_name'      ,'Value', 'longitude');
nc(ifld).Attribute(end+1) = struct('Name', 'units'          ,'Value', 'degrees_east');
nc(ifld).Attribute(end+1) = struct('Name', 'standard_name'  ,'Value', 'longitude');
nc(ifld).Attribute(end+1) = struct('Name', 'actual_range'   ,'Value', [min(OPT.lon(:)) max(OPT.lon(:))]);
nc(ifld).Attribute(end+1) = struct('Name', 'coordinates'    ,'Value', 'lat lon'); % !!! lon matrix can be plotted as a function of lat and itself
nc(ifld).Attribute(end+1) = struct('Name', 'grid_mapping'   ,'Value', 'wgs84');

    http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#latitude-coordinate

   ifld = ifld + 1;
nc(ifld).Name             = 'lat';
nc(ifld).Nctype           = nc_type(OPT.lat_type);
nc(ifld).Dimension        = {'col','row'}; % !!!
nc(ifld).Attribute(    1) = struct('Name', 'long_name'      ,'Value', 'latitude');
nc(ifld).Attribute(end+1) = struct('Name', 'units'          ,'Value', 'degrees_north');
nc(ifld).Attribute(end+1) = struct('Name', 'standard_name'  ,'Value', 'latitude');
nc(ifld).Attribute(end+1) = struct('Name', 'actual_range'   ,'Value', [min(OPT.lat(:)) max(OPT.lat(:))]);
nc(ifld).Attribute(end+1) = struct('Name', 'coordinates'    ,'Value', 'lat lon'); % !!! lat matrix can be plotted as a function of lon and itself
nc(ifld).Attribute(end+1) = struct('Name', 'grid_mapping'   ,'Value', 'wgs84');

    global ellispes: WGS 84, ED 50, INT 1924, ETRS 89 and the upcoming ETRS update etc.
http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#grid-mappings-and-projections
http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#appendix-grid-mappings

   ifld = ifld + 1;
nc(ifld).Name         = 'wgs84'; % preferred
nc(ifld).Nctype       = nc_int;
nc(ifld).Dimension    = {};
nc(ifld).Attribute    = nc_cf_grid_mapping(OPT.wgs84.code); % is same as
nc(ifld).Attribute    = struct('Name', ...
{'name',...
'epsg',...
'grid_mapping_name',...
'semi_major_axis', ...
'semi_minor_axis', ...
'inverse_flattening', ...
'comment'}, ...
'Value', ...
{OPT.wgs84.name,...
OPT.wgs84.code,...
'latitude_longitude',...
OPT.wgs84.semi_major_axis, ...
OPT.wgs84.semi_minor_axis, ...
OPT.wgs84.inv_flattening,  ...
'value is equal to EPSG code'});

    http://cf-pcmdi.llnl.gov/documents/cf-conventions/1.4/cf-conventions.html#variables
Parameters with standard names:
http://cf-pcmdi.llnl.gov/documents/cf-standard-names/standard-name-table/current/

   ifld = ifld + 1;
nc(ifld).Name             = OPT.varname;
nc(ifld).Nctype           = nc_type(OPT.val_type);
nc(ifld).Dimension        = {'col','row'}; % {'time','col','row'}
nc(ifld).Attribute(    1) = struct('Name', 'long_name'      ,'Value', OPT.long_name    );
nc(ifld).Attribute(end+1) = struct('Name', 'units'          ,'Value', OPT.units        );
nc(ifld).Attribute(end+1) = struct('Name', '_FillValue'     ,'Value', OPT.fillvalue    );
nc(ifld).Attribute(end+1) = struct('Name', 'actual_range'   ,'Value', [min(OPT.val(:)) max(OPT.val(:))]);
nc(ifld).Attribute(end+1) = struct('Name', 'coordinates'    ,'Value', 'lat lon');
nc(ifld).Attribute(end+1) = struct('Name', 'grid_mapping'   ,'Value', 'epsg');
if ~isempty(OPT.standard_name)
nc(ifld).Attribute(end+1) = struct('Name', 'standard_name'  ,'Value', OPT.standard_name);
end

   for ifld=1:length(nc)
nc_addvar(ncfile, nc(ifld));
end

   nc_varput(ncfile, 'lon'          , OPT.lon       );
nc_varput(ncfile, 'lat'          , OPT.lat       );
nc_varput(ncfile, 'wgs84'        , OPT.wgs84.code);
nc_varput(ncfile, OPT.varname    , OPT.val       );

   nc_dump(ncfile);
fid = fopen(fullfile(fileparts(mfilename('fullpath')),[mfilename,'.cdl']),'w');
nc_dump(ncfile,fid);
fclose(fid)

netCDF F:\checkouts\OpenEarthTools\matlab\io\netcdf\nctools\nc_cf_grid_write_lat_lon_curvilinear_tutorial.nc { 

dimensions:
col = 3 ;
row = 5 ;


variables:
// Preference 'PRESERVE_FVD':  false,
// dimensions consistent with ncBrowse, not with native MATLAB netcdf package.
single lon(col,row), shape = [3 5]
lon:long_name = "longitude" 
lon:units = "degrees_east" 
lon:standard_name = "longitude" 
lon:actual_range = 2.70711 9 
lon:coordinates = "lat lon" 
lon:grid_mapping = "wgs84" 
single lat(col,row), shape = [3 5]
lat:long_name = "latitude" 
lat:units = "degrees_north" 
lat:standard_name = "latitude" 
lat:actual_range = 49.2235 56.1213 
lat:coordinates = "lat lon" 
lat:grid_mapping = "wgs84" 
int32 wgs84([]), shape = [1]
wgs84:name = "WGS 84" 
wgs84:epsg = 4326 
wgs84:grid_mapping_name = "latitude_longitude" 
wgs84:semi_major_axis = 6.37814e+006 
wgs84:semi_minor_axis = 6.35675e+006 
wgs84:inverse_flattening = 298.257 
wgs84:comment = "value is equal to EPSG code" 
single depth(col,row), shape = [3 5]
depth:long_name = "bottom depth" 
depth:units = "m" 
depth:_FillValue = NaN 
depth:actual_range = 1 15 
depth:coordinates = "lat lon" 
depth:grid_mapping = "epsg" 
depth:standard_name = "sea_floor_depth_below_geoid" 


//global attributes:
:title = "" 
:institution = "" 
:source = "" 
:history = "tranformation to netCDF: $HeadURL: https://repos.deltares.nl/repos/OpenEarthTools/trunk/matlab/io/netcdf/nctools/nc_cf_grid_write_lat_lon_curvilinear_tutorial.m $" 
:references = "" 
:email = "" 
:comment = "" 
:version = "" 
:Conventions = "CF-1.4" 
:CF:featureType = "Grid" 
:terms_for_use = "These data can be used freely for research purposes provided that the following source is acknowledged: " 
:disclaimer = "This data is made available in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE." 
}

ans =

0

   Da.dep   = nc_varget(ncfile,'depth');
Da.lat   = nc_varget(ncfile,'lon');
Da.lon   = nc_varget(ncfile,'lat')

Da = 

dep: [3x5 double]
lat: [3x5 single]
lon: [3x5 single]
datenum: [6x1 double]
var: [1 2 3 NaN 5 6]

   depname  = nc_varfind(ncfile,'attributename', 'standard_name', 'attributevalue', 'sea_floor_depth_below_geoid')
Db.z     = nc_varget(ncfile,depname);

coords   = nc_attget(ncfile,depname,'coordinates');
[ax1,coords] = strtok(coords); ax2 = strtok(coords);
if strcmpi(nc_attget(ncfile,ax1,'standard_name'),'latitude')
Db.lat   = nc_varget(ncfile,ax1);
Db.lon   = nc_varget(ncfile,ax2)
else
Db.lat   = nc_varget(ncfile,ax2);
Db.lon   = nc_varget(ncfile,ax1)
end

depname =

depth


Db = 

z: [3x5 double]
lat: [3x5 single]
lon: [3x5 single]
datenum: [6x1 double]
var: [1 2 3 NaN 5 6]

   [Dc,Mc] = nc_cf_grid(ncfile,OPT.varname)

Dc = 

lon: [3x5 single]
lat: [3x5 single]
depth: [3x5 double]


Mc = 

lon: [1x1 struct]
lat: [1x1 struct]
depth: [1x1 struct]