id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1706864252,I_kwDOAMm_X85lvK58,7838,Anomaly calculation with groupby leaves seasonal cycle,14111025,open,0,,,5,2023-05-12T03:34:07Z,2023-05-12T17:33:03Z,,NONE,,,,"### What happened?

When calculating EOFS with sea surface temperature (SST) anomaly, We see the seasonal cycle still in the data.
Tested with xarray v2023.03.0 and v202304.02, both have the same problem (seasonal cycle still in the data).
So the anomaly calculated with groupby is not correct.

Attached is the results of using xarray v2023.04.02
<img width=""1262"" alt=""Screenshot 2023-05-11 at 11 31 30 PM"" src=""https://github.com/pydata/xarray/assets/14111025/c0717e2d-0168-49fa-87b3-f1162cbc210c"">


### What did you expect to happen?

The EOFs will not have seasonal cycle. Attached is the results from xarray v0.20.2
<img width=""783"" alt=""Screenshot 2023-05-11 at 1 37 32 PM"" src=""https://github.com/pydata/xarray/assets/14111025/fcf8365b-a625-43fb-93dd-4e4874273d08"">


### Minimal Complete Verifiable Example

```Python
import xarray as xr
import numpy as np
import pandas as pd
from eofs.xarray import Eof

url = 'http://kage.ldeo.columbia.edu:81/SOURCES/.LOCAL/.sst.mon.mean.nc/.sst/dods'
ds = xr.open_dataset(url)

gb = ds.sst.groupby('time.month')
ds_anom = (gb - gb.mean(dim='time')).compute()
solver = Eof(ds_anom)
pcs = solver.pcs(npcs=4,pcscaling=1)
eofs = solver.eofsAsCorrelation(neofs=4)

eofs.plot(x='lon',y='lat',col='mode',col_wrap=4,add_colorbar=1)
pcs.plot(x='time',col='mode',col_wrap=4);
```


### MVCE confirmation

- [ ] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- [X] Complete example — the example is self-contained, including all data and the text of any traceback.
- [ ] Verifiable example — the example copy & pastes into an IPython prompt or [Binder notebook](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [ ] New issue — a search of GitHub Issues suggests this is not a duplicate.

### Relevant log output

_No response_

### Anything else we need to know?

_No response_

### Environment

<details>
INSTALLED VERSIONS
------------------
commit: None
python: 3.10.10 | packaged by conda-forge | (main, Mar 24 2023, 20:08:06) [GCC 11.3.0]
python-bits: 64
OS: Linux
OS-release: 4.13.16-100.fc25.x86_64
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: ('en_US', 'UTF-8')
libhdf5: 1.12.2
libnetcdf: 4.8.1

xarray: 2023.4.2
pandas: 1.5.3
numpy: 1.23.5
scipy: 1.10.1
netCDF4: 1.6.0
pydap: None
h5netcdf: None
h5py: None
Nio: None
zarr: None
cftime: 1.6.2
nc_time_axis: None
PseudoNetCDF: None
iris: None
bottleneck: None
dask: 2023.4.0
distributed: 2023.4.0
matplotlib: 3.7.1
cartopy: 0.21.1
seaborn: None
numbagg: None
fsspec: 2023.4.0
cupy: None
pint: None
sparse: 0.14.0
flox: None
numpy_groupies: None
setuptools: 66.0.0
pip: 23.0.1
conda: None
pytest: None
mypy: None
IPython: 8.12.0
sphinx: None


</details>
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