From 1d55986c74ab38251c89f8a124102747946561aa Mon Sep 17 00:00:00 2001
From: Jesper Sandvig Mariegaard
 <34088801+jsmariegaard@users.noreply.github.com>
Date: Fri, 7 Oct 2022 15:14:32 +0200
Subject: [PATCH 1/4] Alternative implementation of the scatter index

---
 fmskill/metrics.py | 20 ++++++++++++++++++++
 1 file changed, 20 insertions(+)

diff --git a/fmskill/metrics.py b/fmskill/metrics.py
index 71ed8268b..f8c0e57e8 100644
--- a/fmskill/metrics.py
+++ b/fmskill/metrics.py
@@ -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 mean of the observations. 
+
+    .. math::
+        \\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^2}}
+
+    Range: [0, 100]; 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(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}}

From 7a472f8243d7abc0230abe8ac50910907b7421b8 Mon Sep 17 00:00:00 2001
From: Jesper Sandvig Mariegaard
 <34088801+jsmariegaard@users.noreply.github.com>
Date: Wed, 12 Oct 2022 10:30:41 +0200
Subject: [PATCH 2/4] normalize with abs mean

---
 fmskill/metrics.py | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/fmskill/metrics.py b/fmskill/metrics.py
index f8c0e57e8..58ebf2bf2 100644
--- a/fmskill/metrics.py
+++ b/fmskill/metrics.py
@@ -410,13 +410,13 @@ 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 mean of the observations. 
+    Which is the same as the unbiased-RMSE normalized by the absolute mean of the observations.
 
     .. math::
-        \\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^2}}
+        \\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, 100]; Best: 0
+    Range: [0, \\infty); Best: 0
     """
     assert obs.size == model.size
     if len(obs) == 0:
@@ -424,7 +424,7 @@ def scatter_index(obs: np.ndarray, model: np.ndarray) -> float:
 
     residual = obs.ravel() - model.ravel()
     residual = residual - residual.mean()  # unbiased
-    return np.sqrt(np.mean(residual**2)) / np.mean(obs.ravel())
+    return np.sqrt(np.mean(residual**2)) / np.mean(np.abs(obs.ravel()))
 
 
 def scatter_index2(obs: np.ndarray, model: np.ndarray) -> float:

From caa1acf1f3df8e87098edc51260d3b33265f1423 Mon Sep 17 00:00:00 2001
From: caichac-dhi <97288080+caichac-dhi@users.noreply.github.com>
Date: Wed, 12 Oct 2022 15:05:45 +0200
Subject: [PATCH 3/4] changed_SI_test

---
 tests/test_multimodelcompare.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/test_multimodelcompare.py b/tests/test_multimodelcompare.py
index efed980c4..cb5193459 100644
--- a/tests/test_multimodelcompare.py
+++ b/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):

From 5aa326a64b7a14981db88d90af7fed4d25d57088 Mon Sep 17 00:00:00 2001
From: caichac-dhi <97288080+caichac-dhi@users.noreply.github.com>
Date: Wed, 12 Oct 2022 15:14:48 +0200
Subject: [PATCH 4/4] fixed docstring

---
 fmskill/metrics.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/fmskill/metrics.py b/fmskill/metrics.py
index 58ebf2bf2..33386b91d 100644
--- a/fmskill/metrics.py
+++ b/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)