Missing time dimension

Dear CDS-Team,

some datasets do not contain a time coordinate, there is (beside "lat" and "lon") just the information: "Dimensions without coordinates: time" (see below)

<xarray.DataArray 'prw' (time: 96, lat: 360, lon: 720)>
dask.array<xarray-prw, shape=(96, 360, 720), dtype=float32, chunksize=(48, 360, 720), chunktype=numpy.ndarray>
Coordinates:
  * lon      (lon) float64 -180.0 -179.5 -179.0 -178.5 ... 179.0 179.5 180.0
  * lat      (lat) float64 -90.0 -89.5 -89.0 -88.5 ... 88.5 89.0 89.5 90.0
Dimensions without coordinates: time
Attributes:


Is there somehow a chance to add a dimension and fill it with a self-created vector? Or is there any other chance to plot e.g. a Hovmöller plot with time on the x-axis
and calculations with monthly anomalies?

Thanks in advance and cheers,
Tim