From ad90a12fd56dc426b06441591f4f4dabaa14a7cf Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Fri, 18 Nov 2022 18:52:58 +0100
Subject: [PATCH 1/8] Improved equalizing coords for mmm preproc

---
 esmvalcore/preprocessor/_multimodel.py        | 106 ++++++++++++++++--
 .../_multimodel/test_multimodel.py            |  30 ++++-
 2 files changed, 119 insertions(+), 17 deletions(-)

diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index 1b994ecbad..9cc0f3f6b0 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -17,6 +17,8 @@
 import iris
 import iris.coord_categorisation
 import numpy as np
+from iris.common.metadata import CoordMetadata
+from iris.coords import DimCoord
 from iris.util import equalise_attributes
 
 from esmvalcore.iris_helpers import date2num
@@ -230,13 +232,8 @@ def _equalise_cell_methods(cubes):
         cube.cell_methods = None
 
 
-def _equalise_coordinates(cubes):
-    """Equalise coordinates in cubes (in-place)."""
-    if not cubes:
-        return
-
-    # If metadata of a coordinate metadata is equal for all cubes, do not
-    # modify it; else remove long_name and attributes.
+def _get_equal_coords_metadata(cubes):
+    """Get metadata for exactly matching coordinates across cubes."""
     equal_coords_metadata = []
     for coord in cubes[0].coords():
         for other_cube in cubes[1:]:
@@ -248,13 +245,100 @@ def _equalise_coordinates(cubes):
                 break
         else:
             equal_coords_metadata.append(coord.metadata)
+    return equal_coords_metadata
+
+
+def _get_equal_coord_names_metadata(cubes, equal_coords_metadata):
+    """Get metadata for coords with matching names and units across cubes.
+
+    Note
+    ----
+    Ignore coordinates whose names are not unique.
+
+    """
+    equal_names_metadata = {}
+    for coord in cubes[0].coords():
+        coord_name = coord.name()
+
+        # Ignore exactly matching coordinates
+        if coord.metadata in equal_coords_metadata:
+            continue
+
+        # Ignore coordinates that are not unique in original cube
+        if len(cubes[0].coords(coord_name)) > 1:
+            continue
+
+        # Check if coordinate names and units match across all cubes
+        for other_cube in cubes[1:]:
+
+            # Ignore names that do not exist in other cube/are not unique
+            if len(other_cube.coords(coord_name)) != 1:
+                break
+
+            # Ignore names where units do not match across cubes
+            if coord.units != other_cube.coord(coord_name).units:
+                break
 
-    # Modify coordinates accordingly
+        # Coordinate name exists in all other cubes with identical units
+        # --> Filter out matching metadata
+        else:  # Coordinate name exists in all other cubes with identical units
+            std_names = list(
+                {c.coord(coord_name).standard_name for c in cubes}
+            )
+            long_names = list(
+                {c.coord(coord_name).long_name for c in cubes}
+            )
+            var_names = list(
+                {c.coord(coord_name).var_name for c in cubes}
+            )
+            equal_names_metadata[coord_name] = CoordMetadata(
+                standard_name=std_names[0] if len(std_names) == 1 else None,
+                long_name=long_names[0] if len(long_names) == 1 else None,
+                var_name=var_names[0] if len(var_names) == 1 else None,
+                units=coord.units,
+                attributes={},
+                coord_system=None,
+                climatological=None,
+            )
+
+        return equal_names_metadata
+
+
+def _equalise_coordinates(cubes):
+    """Equalise coordinates in cubes (in-place)."""
+    if not cubes:
+        return
+
+    # Filter out coordinates with exactly matching metadata across all cubes
+    # --> these will not be modified at all
+    equal_coords_metadata = _get_equal_coords_metadata(cubes)
+
+    # Filter out coordinates with matching names and units
+    # --> keep matching metadata of these coordinates
+    # Note: ignore duplicate coordinates
+    equal_names_metadata = _get_equal_coord_names_metadata(
+        cubes,
+        equal_coords_metadata
+    )
+
+    # Modify all coordinates of all cubes accordingly
     for cube in cubes:
         for coord in cube.coords():
-            if coord.metadata not in equal_coords_metadata:
-                coord.long_name = None
-                coord.attributes = None
+
+            # Exactly matching coordinates --> do not modify
+            if coord.metadata in equal_coords_metadata:
+                continue
+
+            # Matching names and units --> set common metadata
+            if coord.name() in equal_names_metadata:
+                coord.metadata = equal_names_metadata[coord.name()]
+                continue
+
+            # Remaining coordinates --> remove coordinate metadata
+            coord.long_name = None
+            coord.attributes = {}
+            if isinstance(coord, DimCoord):
+                coord.circular = None
 
         # Additionally remove specific scalar coordinates which are not
         # expected to be equal in the input cubes
diff --git a/tests/unit/preprocessor/_multimodel/test_multimodel.py b/tests/unit/preprocessor/_multimodel/test_multimodel.py
index 00ced5a348..0b08cdddf8 100644
--- a/tests/unit/preprocessor/_multimodel/test_multimodel.py
+++ b/tests/unit/preprocessor/_multimodel/test_multimodel.py
@@ -134,19 +134,27 @@ def get_cube_for_equal_coords_test(num_cubes):
         cube = generate_cube_from_dates('monthly')
         cubes.append(cube)
 
-    # Create cubes that have one equal coordinate ('year') and one non-equal
-    # coordinate ('x')
+    # Create cubes that have one exactly equal coordinate ('year'), one
+    # coordinate with matching names ('m') and one coordinate with non-matching
+    # names
     year_coord = AuxCoord([1, 2, 3], var_name='year', long_name='year',
                           units='1', attributes={'test': 1})
+    m_coord = AuxCoord([1, 2, 3], var_name='m', long_name='m', units='s',
+                       attributes={'test': 0})
     x_coord = AuxCoord([1, 2, 3], var_name='x', long_name='x', units='s',
                        attributes={'test': 2})
     for (idx, cube) in enumerate(cubes):
+        new_m_coord = m_coord.copy()
+        new_m_coord.var_name = f'm_{idx}'
         new_x_coord = x_coord.copy()
         new_x_coord.long_name = f'x_{idx}'
         cube.add_aux_coord(year_coord.copy(), 0)
+        cube.add_aux_coord(new_m_coord, 0)
         cube.add_aux_coord(new_x_coord, 0)
         assert cube.coord('year').metadata is not year_coord.metadata
         assert cube.coord('year').metadata == year_coord.metadata
+        assert cube.coord('m').metadata is not m_coord.metadata
+        assert cube.coord('m').metadata != m_coord.metadata
         assert cube.coord(f'x_{idx}').metadata is not x_coord.metadata
         assert cube.coord(f'x_{idx}').metadata != x_coord.metadata
 
@@ -482,11 +490,16 @@ def test_combine_preserve_equal_coordinates():
     cubes = get_cube_for_equal_coords_test(5)
     merged_cube = mm._combine(cubes)
 
-    # The equal coordinate ('year') was not changed; the non-equal one ('x')
-    # does not have a long_name and attributes anymore
+    # The equal coordinate ('year') was not changed; the var_name of the
+    # matchine name coordinate ('m') has been removed, and the non-equal one
+    # ('x') does not have a long_name and attributes anymore
     assert merged_cube.coord('year').var_name == 'year'
     assert merged_cube.coord('year').standard_name is None
     assert merged_cube.coord('year').long_name == 'year'
+    assert merged_cube.coord('m').var_name is None
+    assert merged_cube.coord('m').standard_name is None
+    assert merged_cube.coord('m').long_name == 'm'
+    assert merged_cube.coord('m').attributes == {}
     assert merged_cube.coord('year').attributes == {'test': 1}
     assert merged_cube.coord('x').var_name == 'x'
     assert merged_cube.coord('x').standard_name is None
@@ -911,12 +924,17 @@ def test_preserve_equal_coordinates():
     stat_cube = stat_cubes['sum']
     assert_array_allclose(stat_cube.data, np.ma.array([5.0, 5.0, 5.0]))
 
-    # The equal coordinate ('year') was not changed; the non-equal one ('x')
-    # does not have a long_name and attributes anymore
+    # The equal coordinate ('year') was not changed; the var_name of the
+    # matchine name coordinate ('m') has been removed, and the non-equal one
+    # ('x') does not have a long_name and attributes anymore
     assert stat_cube.coord('year').var_name == 'year'
     assert stat_cube.coord('year').standard_name is None
     assert stat_cube.coord('year').long_name == 'year'
     assert stat_cube.coord('year').attributes == {'test': 1}
+    assert stat_cube.coord('m').var_name is None
+    assert stat_cube.coord('m').standard_name is None
+    assert stat_cube.coord('m').long_name == 'm'
+    assert stat_cube.coord('m').attributes == {}
     assert stat_cube.coord('x').var_name == 'x'
     assert stat_cube.coord('x').standard_name is None
     assert stat_cube.coord('x').long_name is None

From c5e53967df9e04086de4ae7a644a7bd61baf1065 Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Mon, 21 Nov 2022 12:43:30 +0100
Subject: [PATCH 2/8] Added tests

---
 esmvalcore/preprocessor/_multimodel.py        |   8 +-
 .../_multimodel/test_multimodel.py            | 168 ++++++++++++++++--
 2 files changed, 158 insertions(+), 18 deletions(-)

diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index 9cc0f3f6b0..aeb6859721 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -280,8 +280,8 @@ def _get_equal_coord_names_metadata(cubes, equal_coords_metadata):
                 break
 
         # Coordinate name exists in all other cubes with identical units
-        # --> Filter out matching metadata
-        else:  # Coordinate name exists in all other cubes with identical units
+        # --> Get metadata that is identical across all cubes
+        else:
             std_names = list(
                 {c.coord(coord_name).standard_name for c in cubes}
             )
@@ -298,10 +298,10 @@ def _get_equal_coord_names_metadata(cubes, equal_coords_metadata):
                 units=coord.units,
                 attributes={},
                 coord_system=None,
-                climatological=None,
+                climatological=False,
             )
 
-        return equal_names_metadata
+    return equal_names_metadata
 
 
 def _equalise_coordinates(cubes):
diff --git a/tests/unit/preprocessor/_multimodel/test_multimodel.py b/tests/unit/preprocessor/_multimodel/test_multimodel.py
index 0b08cdddf8..d3eb40d374 100644
--- a/tests/unit/preprocessor/_multimodel/test_multimodel.py
+++ b/tests/unit/preprocessor/_multimodel/test_multimodel.py
@@ -11,7 +11,7 @@
 import pytest
 from cf_units import Unit
 from iris.coords import AuxCoord
-from iris.cube import Cube
+from iris.cube import Cube, CubeList
 
 import esmvalcore.preprocessor._multimodel as mm
 from esmvalcore.iris_helpers import date2num
@@ -485,22 +485,29 @@ def test_combine_with_scalar_coords_to_remove(scalar_coord):
     assert merged_cube.shape == (5, 3)
 
 
-def test_combine_preserve_equal_coordinates():
+def test_combine_equal_coordinates():
     """Test ``_combine`` with equal input coordinates."""
     cubes = get_cube_for_equal_coords_test(5)
     merged_cube = mm._combine(cubes)
 
-    # The equal coordinate ('year') was not changed; the var_name of the
-    # matchine name coordinate ('m') has been removed, and the non-equal one
-    # ('x') does not have a long_name and attributes anymore
+    # The equal coordinate ('year') was not changed
     assert merged_cube.coord('year').var_name == 'year'
     assert merged_cube.coord('year').standard_name is None
     assert merged_cube.coord('year').long_name == 'year'
+    assert merged_cube.coord('year').attributes == {'test': 1}
+
+
+def test_combine_non_equal_coordinates():
+    """Test ``_combine`` with non-equal input coordinates."""
+    cubes = get_cube_for_equal_coords_test(5)
+    merged_cube = mm._combine(cubes)
+
+    # The var_name of the matchine name coordinate ('m') has been removed, and
+    # the non-equal one ('x') does not have a long_name and attributes anymore
     assert merged_cube.coord('m').var_name is None
     assert merged_cube.coord('m').standard_name is None
     assert merged_cube.coord('m').long_name == 'm'
     assert merged_cube.coord('m').attributes == {}
-    assert merged_cube.coord('year').attributes == {'test': 1}
     assert merged_cube.coord('x').var_name == 'x'
     assert merged_cube.coord('x').standard_name is None
     assert merged_cube.coord('x').long_name is None
@@ -920,22 +927,155 @@ def test_preserve_equal_coordinates():
                                         statistics=['sum'])
 
     assert len(stat_cubes) == 1
-    assert 'sum' in stat_cubes
     stat_cube = stat_cubes['sum']
     assert_array_allclose(stat_cube.data, np.ma.array([5.0, 5.0, 5.0]))
 
-    # The equal coordinate ('year') was not changed; the var_name of the
-    # matchine name coordinate ('m') has been removed, and the non-equal one
-    # ('x') does not have a long_name and attributes anymore
+    # The equal coordinate ('year') was not changed
     assert stat_cube.coord('year').var_name == 'year'
     assert stat_cube.coord('year').standard_name is None
     assert stat_cube.coord('year').long_name == 'year'
     assert stat_cube.coord('year').attributes == {'test': 1}
-    assert stat_cube.coord('m').var_name is None
-    assert stat_cube.coord('m').standard_name is None
-    assert stat_cube.coord('m').long_name == 'm'
-    assert stat_cube.coord('m').attributes == {}
+
+
+def test_preserve_non_equal_coordinates():
+    """Test ``multi_model_statistics`` with non_equal input coordinates."""
+    cubes = get_cube_for_equal_coords_test(5)
+    stat_cubes = multi_model_statistics(cubes, span='overlap',
+                                        statistics=['sum'])
+
+    assert len(stat_cubes) == 1
+    stat_cube = stat_cubes['sum']
+    assert_array_allclose(stat_cube.data, np.ma.array([5.0, 5.0, 5.0]))
+
+    # The long_name and attributes of the non-equal coordinate ('x') have been
+    # removed
     assert stat_cube.coord('x').var_name == 'x'
     assert stat_cube.coord('x').standard_name is None
     assert stat_cube.coord('x').long_name is None
     assert stat_cube.coord('x').attributes == {}
+
+
+@pytest.mark.parametrize(
+    'equal_names',
+    [
+        ['var_name'],
+        ['standard_name'],
+        ['long_name'],
+        ['var_name', 'standard_name'],
+        ['var_name', 'long_name'],
+        ['standard_name', 'long_name'],
+        ['var_name', 'standard_name', 'long_name'],
+    ]
+)
+def test_preserve_equal_name_coordinates(equal_names):
+    """Test ``multi_model_statistics`` with equal-name coordinates."""
+    all_names = ['var_name', 'standard_name', 'long_name']
+    cubes = CubeList(generate_cube_from_dates('monthly') for _ in range(5))
+
+    # Prepare names of coordinates of input cubes accordingly
+    for (idx, cube) in enumerate(cubes):
+        time_coord = cube.coord('time')
+        for name in all_names:
+            if name in equal_names or idx != 0:
+                setattr(time_coord, name, 'time')
+            else:  # Different value for first cube if non-equal name
+                setattr(time_coord, name, None)
+
+        # Use different coordinate attributes for each cube so the different
+        # coordinates are not exactly identical
+        time_coord.attributes = {'test': idx}
+
+    stat_cubes = multi_model_statistics(cubes, span='overlap',
+                                        statistics=['sum'])
+
+    assert len(stat_cubes) == 1
+    stat_cube = stat_cubes['sum']
+    assert_array_allclose(stat_cube.data, np.ma.array([5.0, 5.0, 5.0]))
+
+    assert len(stat_cube.coords()) == 1
+    time_coord = stat_cube.coords()[0]
+
+    for name in all_names:
+        if name in equal_names:
+            assert getattr(time_coord, name) == 'time'
+        else:
+            assert getattr(time_coord, name) is None
+    assert time_coord.units == 'days since 1850-01-01'
+    assert time_coord.attributes == {}
+    assert time_coord.coord_system is None
+    assert time_coord.climatological is False
+
+
+def test_ignore_equal_coordinates():
+    """Test ``_get_equal_coord_names_metadata``."""
+    cubes = CubeList(generate_cube_from_dates('monthly') for _ in range(5))
+
+    equal_coords_metadata = [cubes[0].coord('time').metadata]
+    equal_names_metadata = mm._get_equal_coord_names_metadata(
+        cubes,
+        equal_coords_metadata,
+    )
+
+    # The equal_names_metadata dict should be empty since the exactly identical
+    # coordinate should be ignored
+    assert not equal_names_metadata
+
+
+@pytest.mark.parametrize('cube_idx', [0, 1, 2, 3, 4])
+def test_ignore_duplicate_equal_name_coordinates(cube_idx):
+    """Test ``_get_equal_coord_names_metadata``."""
+    cubes = CubeList(generate_cube_from_dates('monthly') for _ in range(5))
+
+    # Add duplicate scalar coordinate
+    d_coord_0 = AuxCoord(
+        0.0,
+        var_name='d',
+        long_name='d',
+        units='m',
+        attributes={'test': 1}
+    )
+    d_coord_1 = AuxCoord(
+        1.0,
+        var_name='d',
+        long_name='d',
+        units='m',
+    )
+    for cube in cubes:
+        cube.add_aux_coord(d_coord_1, ())
+    cubes[cube_idx].add_aux_coord(d_coord_0, ())
+
+    equal_names_metadata = mm._get_equal_coord_names_metadata(cubes, [])
+
+    # The equal_names_metadata dict should only contain the equal 'time'
+    # dimension, not the duplicate dimension
+    assert len(equal_names_metadata) == 1
+    assert 'time' in equal_names_metadata
+
+
+def test_ignore_non_existing_coordinates():
+    """Test ``_get_equal_coord_names_metadata``."""
+    cubes = CubeList(generate_cube_from_dates('monthly') for _ in range(5))
+
+    # Add coordinate only for first cube
+    cubes[0].add_aux_coord(AuxCoord(0.0, long_name='x'), ())
+
+    equal_names_metadata = mm._get_equal_coord_names_metadata(cubes, [])
+
+    # The equal_names_metadata dict should only contain the equal 'time'
+    # dimension, not the duplicate dimension
+    assert len(equal_names_metadata) == 1
+    assert 'time' in equal_names_metadata
+
+
+def test_ignore_coordinates_different_units():
+    """Test ``_get_equal_coord_names_metadata``."""
+    cubes = CubeList(generate_cube_from_dates('monthly') for _ in range(5))
+
+    # Adapt time units of one cube
+    cubes[3].coord('time').units = 'days since 1900-01-01'
+
+    equal_names_metadata = mm._get_equal_coord_names_metadata(cubes, [])
+
+    # The equal_names_metadata dict should be empty since the time units do not
+    # match
+    assert not equal_names_metadata

From 1598db2c0acb1b0e0104853c8dd2f441f600c729 Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Mon, 21 Nov 2022 13:07:07 +0100
Subject: [PATCH 3/8] Only adapt names for equal-name coordinates

---
 esmvalcore/preprocessor/_multimodel.py        | 30 ++++++++++---------
 .../_multimodel/test_multimodel.py            | 20 ++++++-------
 2 files changed, 25 insertions(+), 25 deletions(-)

diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index aeb6859721..024ac76f12 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -17,7 +17,6 @@
 import iris
 import iris.coord_categorisation
 import numpy as np
-from iris.common.metadata import CoordMetadata
 from iris.coords import DimCoord
 from iris.util import equalise_attributes
 
@@ -291,20 +290,16 @@ def _get_equal_coord_names_metadata(cubes, equal_coords_metadata):
             var_names = list(
                 {c.coord(coord_name).var_name for c in cubes}
             )
-            equal_names_metadata[coord_name] = CoordMetadata(
+            equal_names_metadata[coord_name] = dict(
                 standard_name=std_names[0] if len(std_names) == 1 else None,
                 long_name=long_names[0] if len(long_names) == 1 else None,
                 var_name=var_names[0] if len(var_names) == 1 else None,
-                units=coord.units,
-                attributes={},
-                coord_system=None,
-                climatological=False,
             )
 
     return equal_names_metadata
 
 
-def _equalise_coordinates(cubes):
+def _equalise_coordinate_metadata(cubes):
     """Equalise coordinates in cubes (in-place)."""
     if not cubes:
         return
@@ -329,16 +324,23 @@ def _equalise_coordinates(cubes):
             if coord.metadata in equal_coords_metadata:
                 continue
 
-            # Matching names and units --> set common metadata
+            # Non-exactly matching coordinates --> first, delete attributes and
+            # circular property
+            coord.attributes = {}
+            if isinstance(coord, DimCoord):
+                coord.circular = False
+
+            # Matching names and units --> set common names
             if coord.name() in equal_names_metadata:
-                coord.metadata = equal_names_metadata[coord.name()]
+                equal_names = equal_names_metadata[coord.name()]
+                coord.standard_name = equal_names['standard_name']
+                coord.long_name = equal_names['long_name']
+                coord.var_name = equal_names['var_name']
                 continue
 
-            # Remaining coordinates --> remove coordinate metadata
+            # Remaining coordinates --> remove long_name
+            # Note: remaining differences will raise an error at a later stage
             coord.long_name = None
-            coord.attributes = {}
-            if isinstance(coord, DimCoord):
-                coord.circular = None
 
         # Additionally remove specific scalar coordinates which are not
         # expected to be equal in the input cubes
@@ -365,7 +367,7 @@ def _combine(cubes):
     #    merge_and_concat.html#common-issues-with-merge-and-concatenate
     equalise_attributes(cubes)
     _equalise_cell_methods(cubes)
-    _equalise_coordinates(cubes)
+    _equalise_coordinate_metadata(cubes)
     _equalise_fx_variables(cubes)
 
     for i, cube in enumerate(cubes):
diff --git a/tests/unit/preprocessor/_multimodel/test_multimodel.py b/tests/unit/preprocessor/_multimodel/test_multimodel.py
index d3eb40d374..cf96c1ca0a 100644
--- a/tests/unit/preprocessor/_multimodel/test_multimodel.py
+++ b/tests/unit/preprocessor/_multimodel/test_multimodel.py
@@ -514,16 +514,16 @@ def test_combine_non_equal_coordinates():
     assert merged_cube.coord('x').attributes == {}
 
 
-def test_equalise_coordinates_no_cubes():
-    """Test that _equalise_coordinates doesn't fail with empty cubes."""
-    mm._equalise_coordinates([])
+def test_equalise_coordinate_metadata_no_cubes():
+    """Test _equalise_coordinate_metadata doesn't fail with empty cubes."""
+    mm._equalise_coordinate_metadata([])
 
 
-def test_equalise_coordinates_one_cube():
-    """Test that _equalise_coordinates doesn't fail with a single cubes."""
+def test_equalise_coordinate_metadata_one_cube():
+    """Test _equalise_coordinate_metadata doesn't fail with a single cubes."""
     cube = generate_cube_from_dates('monthly')
     new_cube = cube.copy()
-    mm._equalise_coordinates([new_cube])
+    mm._equalise_coordinate_metadata([new_cube])
     assert new_cube is not cube
     assert new_cube == cube
 
@@ -1002,8 +1002,6 @@ def test_preserve_equal_name_coordinates(equal_names):
             assert getattr(time_coord, name) is None
     assert time_coord.units == 'days since 1850-01-01'
     assert time_coord.attributes == {}
-    assert time_coord.coord_system is None
-    assert time_coord.climatological is False
 
 
 def test_ignore_equal_coordinates():
@@ -1041,8 +1039,8 @@ def test_ignore_duplicate_equal_name_coordinates(cube_idx):
         units='m',
     )
     for cube in cubes:
-        cube.add_aux_coord(d_coord_1, ())
-    cubes[cube_idx].add_aux_coord(d_coord_0, ())
+        cube.add_aux_coord(d_coord_0, ())
+    cubes[cube_idx].add_aux_coord(d_coord_1, ())
 
     equal_names_metadata = mm._get_equal_coord_names_metadata(cubes, [])
 
@@ -1062,7 +1060,7 @@ def test_ignore_non_existing_coordinates():
     equal_names_metadata = mm._get_equal_coord_names_metadata(cubes, [])
 
     # The equal_names_metadata dict should only contain the equal 'time'
-    # dimension, not the duplicate dimension
+    # dimension, not the coordinate that only exists for the first cube
     assert len(equal_names_metadata) == 1
     assert 'time' in equal_names_metadata
 

From 057b2068ce5aeb4a1aefae7a7062180f120ef989 Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Mon, 21 Nov 2022 13:27:33 +0100
Subject: [PATCH 4/8] Fixed typos

---
 esmvalcore/preprocessor/_multimodel.py                 | 4 ++--
 tests/unit/preprocessor/_multimodel/test_multimodel.py | 5 +++--
 2 files changed, 5 insertions(+), 4 deletions(-)

diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index 024ac76f12..206c22e9c0 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -309,8 +309,8 @@ def _equalise_coordinate_metadata(cubes):
     equal_coords_metadata = _get_equal_coords_metadata(cubes)
 
     # Filter out coordinates with matching names and units
-    # --> keep matching metadata of these coordinates
-    # Note: ignore duplicate coordinates
+    # --> keep matching names of these coordinates
+    # Note: ignores duplicate coordinates
     equal_names_metadata = _get_equal_coord_names_metadata(
         cubes,
         equal_coords_metadata
diff --git a/tests/unit/preprocessor/_multimodel/test_multimodel.py b/tests/unit/preprocessor/_multimodel/test_multimodel.py
index cf96c1ca0a..325b02e9b0 100644
--- a/tests/unit/preprocessor/_multimodel/test_multimodel.py
+++ b/tests/unit/preprocessor/_multimodel/test_multimodel.py
@@ -502,8 +502,9 @@ def test_combine_non_equal_coordinates():
     cubes = get_cube_for_equal_coords_test(5)
     merged_cube = mm._combine(cubes)
 
-    # The var_name of the matchine name coordinate ('m') has been removed, and
-    # the non-equal one ('x') does not have a long_name and attributes anymore
+    # The var_name of the matching name coordinate ('m') has been removed, and
+    # the non-equal one ('x') does not have a long_name anymore
+    # Both coordinates lost their attributes
     assert merged_cube.coord('m').var_name is None
     assert merged_cube.coord('m').standard_name is None
     assert merged_cube.coord('m').long_name == 'm'

From 32a511b874806e5b13f54f6cd3ea0c7a45d347e3 Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Tue, 29 Nov 2022 18:07:28 +0100
Subject: [PATCH 5/8] Fixed tests

---
 .../_multimodel/test_multimodel.py            | 19 +++++++++++++++----
 1 file changed, 15 insertions(+), 4 deletions(-)

diff --git a/tests/unit/preprocessor/_multimodel/test_multimodel.py b/tests/unit/preprocessor/_multimodel/test_multimodel.py
index 69e6990608..840670be54 100644
--- a/tests/unit/preprocessor/_multimodel/test_multimodel.py
+++ b/tests/unit/preprocessor/_multimodel/test_multimodel.py
@@ -966,9 +966,10 @@ def test_map_to_new_time_int_coords():
     assert out_cube.coord('year').bounds is None
     assert out_cube.coord('decade').bounds is None
     assert np.issubdtype(out_cube.coord('year').dtype, np.integer)
+    assert np.issubdtype(out_cube.coord('decade').dtype, np.integer)
 
 
- def test_arbitrary_dims_5d(cubes_5d):
+def test_arbitrary_dims_5d(cubes_5d):
     """Test ``multi_model_statistics`` with 5D cubes."""
     stat_cubes = multi_model_statistics(
         cubes_5d,
@@ -1041,7 +1042,7 @@ def test_arbitrary_dims_0d(cubes_with_arbitrary_dimensions):
     assert 'sum' in stat_cubes
     stat_cube = stat_cubes['sum']
     assert stat_cube.shape == ()
-    assert_array_allclose(stat_cube.data, np.ma.array(0.0))   assert np.issubdtype(out_cube.coord('decade').dtype, np.integer)
+    assert_array_allclose(stat_cube.data, np.ma.array(0.0))
 
 
 def test_preserve_equal_coordinates():
@@ -1054,7 +1055,7 @@ def test_preserve_equal_coordinates():
     stat_cube = stat_cubes['sum']
     assert_array_allclose(stat_cube.data, np.ma.array([5.0, 5.0, 5.0]))
 
-    # The equal coordinate ('year') was not changed
+    # The equal coordinate 'year' was not changed
     assert stat_cube.coord('year').var_name == 'year'
     assert stat_cube.coord('year').standard_name is None
     assert stat_cube.coord('year').long_name == 'year'
@@ -1064,6 +1065,11 @@ def test_preserve_equal_coordinates():
 def test_preserve_non_equal_coordinates():
     """Test ``multi_model_statistics`` with non_equal input coordinates."""
     cubes = get_cube_for_equal_coords_test(5)
+
+    # Use "circular" attribute for one cube to check that it is set to "False"
+    # for each cube
+    cubes[2].coord('time').circular = False
+
     stat_cubes = multi_model_statistics(cubes, span='overlap',
                                         statistics=['sum'])
 
@@ -1071,7 +1077,12 @@ def test_preserve_non_equal_coordinates():
     stat_cube = stat_cubes['sum']
     assert_array_allclose(stat_cube.data, np.ma.array([5.0, 5.0, 5.0]))
 
-    # The long_name and attributes of the non-equal coordinate ('x') have been
+    # The attributes and circular property of the non-equal coordinate 'time'
+    # (due to differing circular) have been removed
+    assert stat_cube.coord('time').attributes == {}
+    assert stat_cube.coord('time').circular is False
+
+    # The long_name and attributes of the non-equal coordinate 'x' have been
     # removed
     assert stat_cube.coord('x').var_name == 'x'
     assert stat_cube.coord('x').standard_name is None

From c8dc2363c09f63895f25cb9b3d16794f5daa50cf Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Tue, 29 Nov 2022 18:33:01 +0100
Subject: [PATCH 6/8] Added doc

---
 esmvalcore/preprocessor/_multimodel.py | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)

diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index 80ce05e757..3a81a7fcc9 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -587,6 +587,31 @@ def multi_model_statistics(products,
     supported and can be specified like ``pXX.YY`` (for percentile ``XX.YY``;
     decimal part optional).
 
+    Metadata handling
+    -----------------
+    This function can handle cubes with differing metadata:
+
+    - **:attr:`~iris.cube.Cube.attributes`**: Differing attributes are deleted,
+      see :func:`iris.util.equalise_attributes`.
+    - **:meth:`~iris.cube.Cube.cell_methods`**: All cell methods are deleted
+      prior to combining cubes.
+    - **:meth:`~iris.cube.Cube.cell_measures`**: All cell measures are deleted
+      prior to combining cubes, see
+      :func:`esmvalcore.preprocessor.remove_fx_variables`.
+    - **:meth:`~iris.cube.Cube.ancillary_variables`**: All ancillary variables
+      are deleted prior to combining cubes, see
+      :func:`esmvalcore.preprocessor.remove_fx_variables`.
+    - **:meth:`~iris.cube.Cube.coords`**: Exactly identical coordinates are
+      preserved. For coordinates with equal :meth:`~iris.coords.Coord.name` and
+      :meth:`~iris.coords.Coord.units`, names are equalized,
+      :attr:`~iris.coords.Coord.attributes` deleted and
+      :attr:`iris.coords.Coord.circular` is set to ``False``. For all other
+      coordinates, :attr:`~iris.coords.Coord.long_name` is removed,
+      :attr:`~iris.coords.Coord.attributes` deleted and
+      :attr:`iris.coords.Coord.circular` is set to ``False``. Please note that
+      some special scalar coordinates (ancillary coordinates for derived
+      coordinates like `p0` and `ptop`) are removed as well.
+
     Notes
     -----
     Some of the operators in :py:mod:`iris.analysis` require additional

From ca829451b995825d94791ce6517a5e4376386509 Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Tue, 29 Nov 2022 18:34:38 +0100
Subject: [PATCH 7/8] optimize doc

---
 esmvalcore/preprocessor/_multimodel.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index 3a81a7fcc9..2e781d84d3 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -605,10 +605,10 @@ def multi_model_statistics(products,
       preserved. For coordinates with equal :meth:`~iris.coords.Coord.name` and
       :meth:`~iris.coords.Coord.units`, names are equalized,
       :attr:`~iris.coords.Coord.attributes` deleted and
-      :attr:`iris.coords.Coord.circular` is set to ``False``. For all other
+      :attr:`~iris.coords.Coord.circular` is set to ``False``. For all other
       coordinates, :attr:`~iris.coords.Coord.long_name` is removed,
       :attr:`~iris.coords.Coord.attributes` deleted and
-      :attr:`iris.coords.Coord.circular` is set to ``False``. Please note that
+      :attr:`~iris.coords.Coord.circular` is set to ``False``. Please note that
       some special scalar coordinates (ancillary coordinates for derived
       coordinates like `p0` and `ptop`) are removed as well.
 

From 84b7df46685a3f93ddc589732cb4fd5afd50ad1d Mon Sep 17 00:00:00 2001
From: Manuel Schlund <manuel.schlund@dlr.de>
Date: Tue, 29 Nov 2022 19:16:57 +0100
Subject: [PATCH 8/8] Fixed doc

---
 esmvalcore/preprocessor/_multimodel.py | 23 +++++++++++------------
 1 file changed, 11 insertions(+), 12 deletions(-)

diff --git a/esmvalcore/preprocessor/_multimodel.py b/esmvalcore/preprocessor/_multimodel.py
index 2e781d84d3..948d1a694e 100644
--- a/esmvalcore/preprocessor/_multimodel.py
+++ b/esmvalcore/preprocessor/_multimodel.py
@@ -587,30 +587,29 @@ def multi_model_statistics(products,
     supported and can be specified like ``pXX.YY`` (for percentile ``XX.YY``;
     decimal part optional).
 
-    Metadata handling
-    -----------------
     This function can handle cubes with differing metadata:
 
-    - **:attr:`~iris.cube.Cube.attributes`**: Differing attributes are deleted,
+    - :attr:`~iris.cube.Cube.attributes`: Differing attributes are deleted,
       see :func:`iris.util.equalise_attributes`.
-    - **:meth:`~iris.cube.Cube.cell_methods`**: All cell methods are deleted
+    - :attr:`~iris.cube.Cube.cell_methods`: All cell methods are deleted
       prior to combining cubes.
-    - **:meth:`~iris.cube.Cube.cell_measures`**: All cell measures are deleted
+    - :meth:`~iris.cube.Cube.cell_measures`: All cell measures are deleted
       prior to combining cubes, see
       :func:`esmvalcore.preprocessor.remove_fx_variables`.
-    - **:meth:`~iris.cube.Cube.ancillary_variables`**: All ancillary variables
+    - :meth:`~iris.cube.Cube.ancillary_variables`: All ancillary variables
       are deleted prior to combining cubes, see
       :func:`esmvalcore.preprocessor.remove_fx_variables`.
-    - **:meth:`~iris.cube.Cube.coords`**: Exactly identical coordinates are
+    - :meth:`~iris.cube.Cube.coords`: Exactly identical coordinates are
       preserved. For coordinates with equal :meth:`~iris.coords.Coord.name` and
-      :meth:`~iris.coords.Coord.units`, names are equalized,
+      :attr:`~iris.coords.Coord.units`, names are equalized,
       :attr:`~iris.coords.Coord.attributes` deleted and
-      :attr:`~iris.coords.Coord.circular` is set to ``False``. For all other
+      :attr:`~iris.coords.DimCoord.circular` is set to ``False``. For all other
       coordinates, :attr:`~iris.coords.Coord.long_name` is removed,
       :attr:`~iris.coords.Coord.attributes` deleted and
-      :attr:`~iris.coords.Coord.circular` is set to ``False``. Please note that
-      some special scalar coordinates (ancillary coordinates for derived
-      coordinates like `p0` and `ptop`) are removed as well.
+      :attr:`~iris.coords.DimCoord.circular` is set to ``False``. Please note
+      that some special scalar coordinates which are expected to differe across
+      cubes(ancillary coordinates for derived coordinates like `p0` and `ptop`)
+      are removed as well.
 
     Notes
     -----