code: def monthly_mean_at_each_ind(monthly_means, sub_monthly_timeseries):
      
      time = monthly_means[TIME_STR]
      start = time.indexes[TIME_STR][0].replace(day=1, hour=0)
      end = time.indexes[TIME_STR][-1]
      new_indices = pd.DatetimeIndex(start=start, end=end, freq='MS')
      arr_new = monthly_means.reindex(time=new_indices, method='backfill')
      return arr_new.reindex_like(sub_monthly_timeseries, method='pad')
docs: Copy monthly mean over each time index in that month.
  
      Parameters
      ----------
      monthly_means : xarray.DataArray
          array of monthly means
      sub_monthly_timeseries : xarray.DataArray
          array of a timeseries at sub-monthly time resolution
  
      Returns
      -------
      xarray.DataArray with eath monthly mean value from `monthly_means` repeated
      at each time within that month from `sub_monthly_timeseries`
  
      See Also
      --------
      monthly_mean_ts : Create timeseries of monthly mean values