String handling when using .sel (method='nearest') to find a location

Is your feature request related to a problem?

Hi!

Below I have provided a scenario that may not be code that minimally reproduces the problem, but had to be done to more clearly describe the meaning of the behaviour.

import xarray as xr
import numpy as np
import pandas as pd
 
# example data
time = pd.date_range("2000-01-01", "2001-12-31", freq="D")
time = time[~((time.month == 2) & (time.day == 29))] 

lon = np.linspace(100, 110, 5)
lat = np.linspace(30, 35, 4)
data = np.random.rand(len(time), len(lon), len(lat))

da = xr.DataArray(
    data,
    coords={"time": time, "lon": lon, "lat": lat},
    dims=["time", "lon", "lat"],
    name="pr"
)

# Split based on year and month-days
da1 = da.assign_coords(year = da.time.dt.year, monthday = da.time.dt.strftime("%m-%d")).groupby(['year', 'monthday']).first()

# Make a selection on the data of da1:
da1.sel(year = 2000, monthday = '03-24', lon = 105, lat = 30) # It's ok

# Problems arose once the method was used for the most recently search:
da1.sel(year = 2000, monthday = '03-24', lon = 105, lat = 30, method='nearest') 

Describe the solution you'd like

I'm guessing the problem is related to its type: monthday (monthday) object

# I know there are many solutions. For example:
da1.sel(year = 2000, monthday = '03-24').sel(lon = 105, lat = 30, method='nearest')

For greater clarity and simplicity in the use of indexes, is it possible to add judgement to the function?

• Firstly make a judgement on the type of the sel, it is this type that can't be used with method = “nearest”, such as strings, etc., and if it doesn't match exactly break the operation and point it out in the error message.
• After the types that can't be “nearest” have been processed, then the subsequent selections are used.

Describe alternatives you've considered

No response

Additional context

No response

Start with the provided DataArray.sel reproduction, especially the combined selection using method='nearest' on the string monthday coordinate. Trace the selection and index handling from the .sel entry point. Done means unsupported nearest selection on string-like coordinates is handled with the intended validation or error behavior while valid selections continue to work.