Alternative implementation of the scatter index

fmskill/metrics.py

@@ -42,7 +42,7 @@
 >>> mef(obs, mod)
 0.9231099877688299
 >>> si(obs, mod)
-0.7294663886165093
+0.8715019052958266
 >>> spearmanr(obs, mod)
 0.5
 >>> cc(obs, mod)
@@ -410,6 +410,26 @@ def si(obs: np.ndarray, model: np.ndarray) -> float:
 def scatter_index(obs: np.ndarray, model: np.ndarray) -> float:
     """Scatter index (SI)
 
+    Which is the same as the unbiased-RMSE normalized by the absolute mean of the observations.
+
+    .. math::
+        \\frac{ \\sqrt{ \\frac{1}{n} \\sum_{i=1}^n \\left( (model_i - \\overline {model}) - (obs_i - \\overline {obs}) \\right)^2} }
+        {\\frac{1}{n} \\sum_{i=1}^n | obs_i | }
+
+    Range: [0, \\infty); Best: 0
+    """
+    assert obs.size == model.size
+    if len(obs) == 0:
+        return np.nan
+
+    residual = obs.ravel() - model.ravel()
+    residual = residual - residual.mean()  # unbiased
+    return np.sqrt(np.mean(residual**2)) / np.mean(np.abs(obs.ravel()))
+
+
+def scatter_index2(obs: np.ndarray, model: np.ndarray) -> float:
+    """Alternative formulation of the scatter index (SI)
+
     .. math::
         \\sqrt {\\frac{\\sum_{i=1}^n \\left( (model_i - \\overline {model}) - (obs_i - \\overline {obs}) \\right)^2}
         {\\sum_{i=1}^n obs_i^2}}

tests/test_multimodelcompare.py

@@ -118,7 +118,7 @@ def test_mm_skill_obs(cc):
     assert s.loc["SW_2"].bias == s2.loc["SW_2"].bias
 
     df = cc.mean_skill(model=0, observation=[0, "c2"]).df
-    assert pytest.approx(df.si[0]) == 0.10358979
+    assert pytest.approx(df.si[0]) == 0.11113215
 
 
 def test_mm_skill_missing_obs(cc, o1):