Normalized taylordiagram (#1764)

### What kind of change does this PR introduce?

* Add a `bool` option `normalize` and divide `ref_std, sim_std` by
`ref_std` if True

### Does this PR introduce a breaking change?

No.

### Other information:

I was planning a new plot option in `figanos`, but I was told we don't
want to do any computation in `figanos`, it would be handy that `sdba`
can manage this by itself.

CHANGES.rst

@@ -9,6 +9,7 @@ Contributors to this version: Trevor James Smith (:user:`Zeitsperre`), Éric Dup
 New features and enhancements
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 * New properties: Bivariate Spell Length (``xclim.sdba.properties.bivariate_spell_length``), generalized spell lengths with an argument for `window`, and specific spell lengths with `window` fixed to 1  (``xclim.sdba.propertiies.threshold_count``, ``xclim.sdba.propertiies.bivariate_threshold_count``). (:pull:`1758`).
+* New option `normalize` in ``sdba.measures.taylordiagram`` to obtain normalized Taylor diagrams (divide standard deviations by standard deviation of the reference). (:pull:`1764`).
 
 Breaking changes
 ^^^^^^^^^^^^^^^^

tests/test_sdba/test_measures.py

@@ -92,3 +92,11 @@ def test_taylordiagram(open_dataset):
     )
     test = sdba.measures.taylordiagram(sim, ref).values
     np.testing.assert_array_almost_equal(test, [13.12244701, 6.76166582, 0.73230199], 4)
+
+    # test normalization option
+    test_normalize = sdba.measures.taylordiagram(sim, ref, normalize=True).values
+    np.testing.assert_array_almost_equal(
+        test_normalize,
+        [13.12244701 / 13.12244701, 6.76166582 / 13.12244701, 0.73230199],
+        4,
+    )

xclim/sdba/measures.py

@@ -451,6 +451,7 @@ def _taylordiagram(
     ref: xr.DataArray,
     dim: str = "time",
     group: str | Grouper = "time",
+    normalize: bool = False,
 ) -> xr.DataArray:
     """Taylor diagram.
 
@@ -468,6 +469,9 @@ def _taylordiagram(
     group : str
         Compute the property and measure for each temporal groups individually.
         Currently not implemented.
+    normalize : bool
+        If `True`, divide the standard deviations by the standard deviation of the reference.
+        Default is `False`.
 
 
     Returns
@@ -496,6 +500,19 @@ def _taylordiagram(
         }
     )
 
+    # Normalize the standard deviations byt the standard deviation of the reference.
+    if normalize:
+        if (out[{"taylor_param": 0}] == 0).any():
+            raise ValueError(
+                "`ref_std =0` (homogeneous field) obtained, normalization is not possible."
+            )
+        with xr.set_options(keep_attrs=True):
+            out[{"taylor_param": [0, 1]}] = (
+                out[{"taylor_param": [0, 1]}] / out[{"taylor_param": 0}]
+            )
+        out.attrs["normalized"] = True
+        out.attrs["units"] = ""
+
     return out