Unexpected behaviour of `climpred.utils.add_time_from_init_lead()`

Describe the bug The function climpred.utils.add_time_from_init_lead (which adds the “valid_time” coordinate) seems to return unusual values when the lead frequency is “yearly” and the init frequency is higher than annual (e.g. 6 monthly). The “valid_time” coordinate is used heavily by climpred internals so this causes strange behaviour/bugs further downstream.

Code Sample

# Hindcasts initialised every 6 months with yearly lead
init = xr.cftime_range(start="2000-01-01", end="2002-01-01", freq="6MS")
lead = range(0, 5)
data = np.random.random((len(init), len(lead)))
hind = xr.DataArray(data, coords=[init, lead], dims=["init", "lead"], name="var")
hind["lead"].attrs["units"] = "years"

# Add "valid_time" coordinate using `climpred.utils.add_time_from_init_lead()`
hind = climpred.utils.add_time_from_init_lead(hind)
print(hind["valid_time"])

Returns

<xarray.DataArray 'valid_time' (lead: 4, init: 5)>
array([[cftime.DatetimeGregorian(2000, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2000, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2001, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2001, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2002, 10, 1, 0, 0, 0, 0, has_year_zero=False)],
       [cftime.DatetimeGregorian(2000, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2000, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2001, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2001, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2002, 10, 1, 0, 0, 0, 0, has_year_zero=False)],
       [cftime.DatetimeGregorian(2001, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2001, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2002, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2002, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2003, 10, 1, 0, 0, 0, 0, has_year_zero=False)],
       [cftime.DatetimeGregorian(2002, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2002, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2003, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2003, 10, 1, 0, 0, 0, 0, has_year_zero=False),
        cftime.DatetimeGregorian(2004, 10, 1, 0, 0, 0, 0, has_year_zero=False)]],
      dtype=object)
Coordinates:
  * init        (init) object 2000-01-01 00:00:00 ... 2002-01-01 00:00:00
  * lead        (lead) int64 0 1 2 3
    valid_time  (lead, init) object 2000-10-01 00:00:00 ... 2004-10-01 00:00:00
Attributes:
    long_name:      validity time
    standard_name:  time
    description:    time for which the forecast is valid
    calculate:      init + lead

You can see that the "valid_time"s at the first two leads are identical and that all “valid_times” are at month 10, regardless of initialisation month (which alternates between 1 and 7).

Expected behavior "valid_time"s should correspond to L years after the initialisation date, where L is the lead.

Output of climpred.show_versions()

# Paste the output here climpred.show_versions() here INSTALLED VERSIONS ------------------ commit: None python: 3.9.4 | packaged by conda-forge | (default, May 10 2021, 22:13:33) [GCC 9.3.0] python-bits: 64 OS: Linux OS-release: 4.18.0-305.19.1.el8.nci.x86_64 machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: None LOCALE: en_US.UTF-8

climpred: 2.1.7.dev10+gb8bf61b xarray: 0.20.1 pandas: 1.3.4 numpy: 1.21.4 scipy: 1.6.3 cftime: 1.5.0 netcdf4: None nc_time_axis: 1.4.0 matplotlib: 3.4.2 cf_xarray: 0.6.1 xclim: 0.31.0 dask: 2021.11.2 distributed: 2021.11.2 setuptools: 49.6.0.post20210108 pip: 21.1.2 conda: 4.11.0 IPython: 7.24.0 sphinx: None

[dougiesquire]

I started digging into xarray, must be somewhere here: https://github.com/pydata/xarray/blob/eea76733770be03e78a0834803291659136bca31/xarray/coding/frequencies.py#L149

do you mind if I post the issue?

Please go ahead

[aaronspring]

ok. the above should be an xarray issue, but there is still an unrelated issue in climpred. .utils.my_shift just needs the quartely_rule and nquarters or monthly_rule and nmonths and so far doesnt use nquarters afaik: https://github.com/pangeo-data/climpred/blob/7440d7ca1d75618f6e6582b9dded942038031731/climpred/utils.py#L546