How to Specify Dimension Values when Creating NetCDF File in Python?

I am creating a NetCDF4 file which currently has four variables:

1) Land Surface Temperature (3D array - time, latitude, longitude)

2) Longitude (1D - coordinate of each pixel centre)

3) Latitude (1D - coordinate of each pixel centre)

4) Time (time of image acquisition in hours since 1900-01-01 00:00:00)

I am currently using the following code to do this:

    #==========================WRITE THE NETCDF FILE==========================#

    newfile = nc.Dataset(export_filename, 'w', format = 'NETCDF4_CLASSIC')


    #==========================SET FILE DIMENSIONS============================#

    newfile.createDimension('lat', ny)
    newfile.createDimension('lon', nx)
    newfile.createDimension('time', len(filenames))


    #==========================SET GLOBAL ATTRIBUTES==========================#

    newfile.title = ('Title')
    newfile.history = "File created on " + datetime.strftime(datetime.today(), "%c")
    newfile.Conventions = 'CF-1.6'



    #==========================CREATE DATA VARIABLES==========================#

    #--------------------------LST VARIABLE-----------------------------------#

    LSTs = newfile.createVariable('LST', np.int16, ('time', 'lat', 'lon'), fill_value = -8000)
    LSTs.units = 'Degrees C'
    LSTs.add_offset = 273.15
    LSTs.scale_factor = 0.01
    LSTs.standard_name = 'LST'
    LSTs.long_name = 'Land Surface Temperature'
    LSTs.grid_mapping = 'latitude_longitude'
    LSTs.coordinates = 'lon lat'

    LSTs[:] = LSTd[:]


    #--------------------------LON AND LAT AND TIME--------------------------#

    LONGITUDEs = newfile.createVariable('LONGITUDE', np.float64, ('lon',))
    LONGITUDEs.units = 'Decimal Degrees East'
    LONGITUDEs.standard_name = 'Longitude'
    LONGITUDEs.long_name = 'Longitude'
    LONGITUDEs[:] = LONd[:]

    LATITUDEs = newfile.createVariable('LATITUDE', np.float64, ('lat',))
    LATITUDEs.units = 'Decimal Degrees North'
    LATITUDEs.standard_name = 'Latitude'
    LATITUDEs.long_name = 'Latitude'
    LATITUDEs[:] = LATd[:]

    TIMEs = newfile.createVariable('TIME', np.int32, ('time',))
    TIMEs.units = 'hours since 1900-01-01 00:00:00'
    TIMEs.standard_name = 'Time'
    TIMEs.long_name = 'Time of Image Acquisition'
    TIMEs.axis = 'T'
    TIMEs.calendar = 'gregorian'
    TIMEs[:] = time[:]

    #--------------------------SAVE THE FILE---------------------------------#

    newfile.close();

This code produces a netCDF file with the land surface temperature variable having 24 bands (one for each hour of the day). This code works as I wanted it to albeit one small problem which I wish to address. When I run gdalinfo for the LST variable, I get (this is a reduced version):

Band 1.....
...
NETCDF_DIM_TIME = 1
...

I want this value of 1 to be set to the same as the 'time' variable (which is something like 1081451 hours since 1900-01-01 00:00:00) which I have included in my above code. I therefore want to understand how this can be changed for each band in the file?

UPDATE TO QUESTION: When I do gdalinfo on the file (again, a subset):

NETCDF_DIM_EXTRA={time}
NETCDF_DIM_time_DEF={24,3}

but there is an option missing 'NETCDF_DIM_time_VALUES' and I need to set this to the time variable and it should work. HOW DO I DO THIS?

At present it is just being set to the band number but I want it to contain information regarding its hour of acquisition.

UPDATE 1:

I have tried to specify

LSTs.NETCDF_DIM_Time = time

during the netCDF file formation and this has assigned all values from time to the NETCDF_DIM_TIME in gdal so that each band has 24 time values rather than just one.

UPDATE 2:

With some further digging I think it is the NETCDF_DIM_time_VALUES metadata which needs to be set to the 'time' variable. I have updated my question to ask how to do this.

Solution

The variables associated with the dimensions should have the same name as the dimensions. So in your code above replace the create variable line with:

TIMEs = newfile.createVariable('time', np.int32, ('time',))

now gdalinfo knows where to find the data. I ran your code using dummy times [1000000, 1000024] and gdal info returns:

Band1...
...
NETCDF_DIM_time=1000000    
...
Band2...
...
NETCDF_DIM_time=1000024
...

To answer your title question: You can't assign values to a Dimension but you can have a variable with the same name as the dimension that holds the data/values associated with the dimension. Readers of netcdf files, like gdal, look for conventions like this to interpret the data. See for example Unidata's 'Writing NetCDF Files: Best Practices' 'Coordinate Systems'