[Python] Splitting the time dimension of nc data using xarray

Now I have a timelonlat 3D data where time is recorded as year, month and day. I need to split time in the form of year*month+day. So that the data becomes 4 dimensional. How should I do this?

I have given a simple data below:

import xarray as xr
import numpy as np
import pandas as pd

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"
)


except dim:

year: 2000, 2001

monthly: 01-01, 01-02,...12-31

lon: ...

lat: ...


One additional question: Why is .first and .last reporting errors? How should I use them?

da.assign_coords(year = da.time.dt.year, monthday = da.time.dt.strftime("%m-%d")).groupby(['year', 'monthday']).first()
da.assign_coords(year = da.time.dt.year, monthday = da.time.dt.strftime("%m-%d")).groupby(['year', 'monthday']).last()

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