issues: 180676935

I often have to deal with datasets in this form (multiple variables of different sizes, each representing different categories, on the same physical dimension but using different names as they have different labels),

<xarray.Dataset> Dimensions: (wn_band1: 4, wn_band2: 6, wn_band3: 8) Coordinates: * wn_band1 (wn_band1) float64 200.0 266.7 333.3 400.0 * wn_band2 (wn_band2) float64 500.0 560.0 620.0 680.0 740.0 800.0 * wn_band3 (wn_band3) float64 1.5e+03 1.643e+03 1.786e+03 1.929e+03 ... Data variables: data_band3 (wn_band3) float64 0.7515 0.5302 0.6697 0.9621 0.01815 ... data_band1 (wn_band1) float64 0.3801 0.6649 0.01884 0.9407 data_band2 (wn_band2) float64 0.8813 0.4481 0.2353 0.9681 0.1085 0.0835

where it would be more convenient to have the data re-arranged into the following form (concatenate the variables into a single variable with a multi-index with the labels of both the categories and the physical coordinate):

<xarray.Dataset> Dimensions: (spectrum: 18) Coordinates: * spectrum (spectrum) MultiIndex - band (spectrum) int64 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 - wn (spectrum) float64 200.0 266.7 333.3 400.0 500.0 560.0 620.0 ... Data variables: data (spectrum) float64 0.3801 0.6649 0.01884 0.9407 0.8813 0.4481 ...

The latter would allow using xarray's nice features like ds.groupby('band').mean().

Currently, the best way that I've found to transform the data is something like:

``` python data = np.concatenate([ds.data_band1, ds.data_band2, ds.data_band3]) wn = np.concatenate([ds.wn_band1, ds.wn_band2, ds.wn_band3]) band = np.concatenate([np.repeat(1, 4), np.repeat(2, 6), np.repeat(3, 8)])

midx = pd.MultiIndex.from_arrays([band, wn], names=('band', 'wn')) ds2 = xr.Dataset({'data': ('spectrum', data)}, coords={'spectrum': midx}) ```

Maybe I miss a better way to do this? If I don't, it would be nice to have a convenience method for this, unless this use case is too rare to be worth it. Also not sure at all on what would be a good API such a method.