The climate_statistics preprocessor sometimes changes the dtype
**Describe the bug**
It has been reported that the multi-model statistics can have a problem with inconsistent dtypes (see https://github.com/ESMValGroup/ESMValTool/discussions/2218#discussioncomment-992288 and https://github.com/ESMValGroup/ESMValTool/issues/2198#issuecomment-863908898).

This seems, however, to originate a bit higher up in the processing chain. In this case, the climate_statistics preprocessor sometimes changes the dtype of the incoming cube, leading to inconsistent dtypes in the input to the multi-model statistics.

Probably the best way to address this is to fix the climate_statistics preprocessor to produce output with a consistent dtype.
diff --git a/esmvalcore/preprocessor/_time.py b/esmvalcore/preprocessor/_time.py
index 55a95eda5..ddf5aa255 100644
--- a/esmvalcore/preprocessor/_time.py
+++ b/esmvalcore/preprocessor/_time.py
@@ -544,6 +544,7 @@ def climate_statistics(cube,
     iris.cube.Cube
         Monthly statistics cube
     """
+    original_dtype = cube.dtype
     period = period.lower()
 
     if period in ('full', ):
@@ -552,25 +553,32 @@ def climate_statistics(cube,
             time_weights = get_time_weights(cube)
             if time_weights.min() == time_weights.max():
                 # No weighting needed.
-                cube = cube.collapsed('time', operator_method)
+                clim_cube = cube.collapsed('time', operator_method)
             else:
-                cube = cube.collapsed('time',
-                                      operator_method,
-                                      weights=time_weights)
+                clim_cube = cube.collapsed('time',
+                                           operator_method,
+                                           weights=time_weights)
         else:
-            cube = cube.collapsed('time', operator_method)
-        return cube
-
-    clim_coord = _get_period_coord(cube, period, seasons)
-    operator = get_iris_analysis_operation(operator)
-    clim_cube = cube.aggregated_by(clim_coord, operator)
-    clim_cube.remove_coord('time')
-    if clim_cube.coord(clim_coord.name()).is_monotonic():
-        iris.util.promote_aux_coord_to_dim_coord(clim_cube, clim_coord.name())
+            clim_cube = cube.collapsed('time', operator_method)
     else:
-        clim_cube = iris.cube.CubeList(clim_cube.slices_over(
-            clim_coord.name())).merge_cube()
-    cube.remove_coord(clim_coord)
+        clim_coord = _get_period_coord(cube, period, seasons)
+        operator = get_iris_analysis_operation(operator)
+        clim_cube = cube.aggregated_by(clim_coord, operator)
+        clim_cube.remove_coord('time')
+        if clim_cube.coord(clim_coord.name()).is_monotonic():
+            iris.util.promote_aux_coord_to_dim_coord(clim_cube,
+                                                     clim_coord.name())
+        else:
+            clim_cube = iris.cube.CubeList(
+                clim_cube.slices_over(clim_coord.name())).merge_cube()
+        cube.remove_coord(clim_coord)
+
+    new_dtype = clim_cube.dtype
+    if original_dtype != new_dtype:
+        logger.warning(
+            "climate_statistics changed dtype from "
+            "%s to %s, changing back", original_dtype, new_dtype)
+        clim_cube.data = clim_cube.core_data().astype(original_dtype)
     return clim_cube
 
 
diff --git a/tests/unit/preprocessor/_time/test_time.py b/tests/unit/preprocessor/_time/test_time.py
index 860fc62c3..5c7ee555d 100644
--- a/tests/unit/preprocessor/_time/test_time.py
+++ b/tests/unit/preprocessor/_time/test_time.py
@@ -312,71 +312,69 @@ class TestClimatology(tests.Test):
 
     def test_time_mean(self):
         """Test for time average of a 1D field."""
-        data = np.ones((3))
+        data = np.array([1., 1., 1.], dtype=np.float32)
         times = np.array([15., 45., 75.])
         bounds = np.array([[0., 30.], [30., 60.], [60., 90.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='mean')
-        expected = np.array([1.])
+        expected = np.array([1.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_mean_uneven(self):
         """Test for time average of a 1D field with uneven time boundaries."""
-        data = np.array([1., 5.])
+        data = np.array([1., 5.], dtype=np.float32)
         times = np.array([5., 25.])
         bounds = np.array([[0., 1.], [1., 4.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='mean')
-        expected = np.array([4.])
+        expected = np.array([4.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_mean_365_day(self):
         """Test for time avg of a realistic time axis and 365 day calendar."""
-        data = np.ones((6, ))
+        data = np.array([1., 1., 1., 1., 1., 1.], dtype=np.float32)
         times = np.array([15, 45, 74, 105, 135, 166])
         bounds = np.array([[0, 31], [31, 59], [59, 90], [90, 120], [120, 151],
                            [151, 181]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='mean')
-        expected = np.array([1.])
+        expected = np.array([1.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_sum(self):
         """Test for time sum of a 1D field."""
-        data = np.ones((3))
-        data[1] = 2.0
+        data = np.array([1., 2., 1.], dtype=np.float32)
         times = np.array([15., 45., 75.])
         bounds = np.array([[0., 30.], [30., 60.], [60., 90.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='sum')
-        expected = np.array([4.])
+        expected = np.array([4.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_sum_weighted(self):
         """Test for time sum of a 1D field."""
-        data = np.ones((3))
-        data[1] = 2.0
+        data = np.array([1., 2., 1.], dtype=np.float32)
         times = np.array([15., 45., 75.])
         bounds = np.array([[10., 20.], [30., 60.], [73., 77.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='sum')
-        expected = np.array([74.])
+        expected = np.array([74.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_sum_uneven(self):
         """Test for time sum of a 1D field with uneven time boundaries."""
-        data = np.array([1., 5.])
+        data = np.array([1., 5.], dtype=np.float32)
         times = np.array([5., 25.])
         bounds = np.array([[0., 1.], [1., 4.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='sum')
-        expected = np.array([16.0])
+        expected = np.array([16.0], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_sum_365_day(self):
@@ -389,24 +387,24 @@ class TestClimatology(tests.Test):
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='sum')
-        expected = np.array([211.])
+        expected = np.array([211.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_season_climatology(self):
         """Test for time avg of a realistic time axis and 365 day calendar."""
-        data = np.ones((6, ))
+        data = np.array([1., 1., 1., 1., 1., 1.], dtype=np.float32)
         times = np.array([15, 45, 74, 105, 135, 166])
         bounds = np.array([[0, 31], [31, 59], [59, 90], [90, 120], [120, 151],
                            [151, 181]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='mean', period='season')
-        expected = np.array([1., 1., 1.])
+        expected = np.array([1., 1., 1.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_custom_season_climatology(self):
         """Test for time avg of a realisitc time axis and 365 day calendar."""
-        data = np.ones((8, ))
+        data = np.array([1., 1., 1., 1., 1., 1., 1., 1.], dtype=np.float32)
         times = np.array([15, 45, 74, 105, 135, 166, 195, 225])
         bounds = np.array([[0, 31], [31, 59], [59, 90], [90, 120], [120, 151],
                            [151, 181], [181, 212], [212, 243]])
@@ -416,36 +414,36 @@ class TestClimatology(tests.Test):
                                     operator='mean',
                                     period='season',
                                     seasons=('jfmamj', 'jasond'))
-        expected = np.array([1., 1.])
+        expected = np.array([1., 1.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_monthly(self):
         """Test for time avg of a realistic time axis and 365 day calendar."""
-        data = np.ones((6, ))
+        data = np.array([1., 1., 1., 1., 1., 1.], dtype=np.float32)
         times = np.array([15, 45, 74, 105, 135, 166])
         bounds = np.array([[0, 31], [31, 59], [59, 90], [90, 120], [120, 151],
                            [151, 181]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='mean', period='mon')
-        expected = np.ones((6, ))
+        expected = np.ones((6, ), dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_day(self):
         """Test for time avg of a realistic time axis and 365 day calendar."""
-        data = np.ones((6, ))
+        data = np.array([1., 1., 1., 1., 1., 1.], dtype=np.float32)
         times = np.array([0.5, 1.5, 2.5, 365.5, 366.5, 367.5])
         bounds = np.array([[0, 1], [1, 2], [2, 3], [365, 366], [366, 367],
                            [367, 368]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='mean', period='day')
-        expected = np.array([1, 1, 1])
+        expected = np.array([1, 1, 1], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_period_not_supported(self):
         """Test for time avg of a realistic time axis and 365 day calendar."""
-        data = np.ones((6, ))
+        data = np.array([1., 1., 1., 1., 1., 1.], dtype=np.float32)
         times = np.array([15, 45, 74, 105, 135, 166])
         bounds = np.array([[0, 31], [31, 59], [59, 90], [90, 120], [120, 151],
                            [151, 181]])
@@ -456,46 +454,46 @@ class TestClimatology(tests.Test):
 
     def test_time_max(self):
         """Test for time max of a 1D field."""
-        data = np.arange((3))
+        data = np.array([0., 1., 2.], dtype=np.float32)
         times = np.array([15., 45., 75.])
         bounds = np.array([[0., 30.], [30., 60.], [60., 90.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='max')
-        expected = np.array([2.])
+        expected = np.array([2.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_min(self):
         """Test for time min of a 1D field."""
-        data = np.arange((3))
+        data = np.array([0., 1., 2.], dtype=np.float32)
         times = np.array([15., 45., 75.])
         bounds = np.array([[0., 30.], [30., 60.], [60., 90.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='min')
-        expected = np.array([0.])
+        expected = np.array([0.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_median(self):
         """Test for time meadian of a 1D field."""
-        data = np.arange((3))
+        data = np.array([0., 1., 2.], dtype=np.float32)
         times = np.array([15., 45., 75.])
         bounds = np.array([[0., 30.], [30., 60.], [60., 90.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='median')
-        expected = np.array([1.])
+        expected = np.array([1.], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
     def test_time_rms(self):
         """Test for time rms of a 1D field."""
-        data = np.arange((3))
+        data = np.array([0., 1., 2.], dtype=np.float32)
         times = np.array([15., 45., 75.])
         bounds = np.array([[0., 30.], [30., 60.], [60., 90.]])
         cube = self._create_cube(data, times, bounds)
 
         result = climate_statistics(cube, operator='rms')
-        expected = np.array([(5 / 3)**0.5])
+        expected = np.array([(5 / 3)**0.5], dtype=np.float32)
         assert_array_equal(result.data, expected)
 
 
['esmvalcore/preprocessor/_time.py', 'tests/unit/preprocessor/_time/test_time.py']