diff --git a/compliance_checker/cf/cf_1_9.py b/compliance_checker/cf/cf_1_9.py
index 5e085bd7..73211e44 100644
--- a/compliance_checker/cf/cf_1_9.py
+++ b/compliance_checker/cf/cf_1_9.py
@@ -113,8 +113,9 @@ def check_domain_variables(self, ds: Dataset):
             for var in ds.get_variables_by_attributes(
                 coordinates=lambda c: c is not None,
             )
-            # IMPLICIT
-            if not var.dimensions
+            # IMPLICIT CONFORMANCE REQUIRED 1/4
+            # all variables have dimensions attribute, but should be scalar
+            if var.dimensions == ()
         ):
             domain_valid = TestCtx(BaseCheck.MEDIUM, self.section_titles["5.8"])
             domain_valid.out_of += 1
@@ -149,7 +150,7 @@ def check_domain_variables(self, ds: Dataset):
                     continue
                 appendix_a_not_recommended_attrs = []
                 for attr_name in domain_var.ncattrs():
-                    if "D" not in self.appendix_a[attr_name]["attr_loc"]:
+                    if attr_name in self.appendix_a and "D" not in self.appendix_a[attr_name]["attr_loc"]:
                         appendix_a_not_recommended_attrs.append(attr_name)
 
                 if appendix_a_not_recommended_attrs:
@@ -162,6 +163,22 @@ def check_domain_variables(self, ds: Dataset):
                 # no errors occurred
                 domain_valid.score += 1
 
+
+            # IMPLEMENTATION CONFORMANCE 5.8 REQUIRED 4/4
+            if hasattr(domain_var, "cell_measures"):
+                cell_measures_var_names = regex.findall(r"\b(?:area|volume):\s+(\w+)", domain_var.cell_measures)
+                # check exist
+                for var_name in cell_measures_var_names:
+                    try:
+                        cell_measures_variable = ds.variables[var_name]
+                    except ValueError:
+                        # TODO: what to do here?
+                        continue
+                    domain_coord_var_names = {var_like.name for var_like in domain_coord_vars}
+                    domain_valid.assert_true(set(cell_measures_variable.dimensions).issubset(domain_coord_var_names),
+                                             "Variables named in the cell_measures attributes must have a dimensions attribute with "
+                                             "values that are a subset of the referring domain variable's dimension attribute")
+
             results.append(domain_valid.to_result())
 
         return results
diff --git a/compliance_checker/tests/test_cf.py b/compliance_checker/tests/test_cf.py
index 04ca15b2..f053f837 100644
--- a/compliance_checker/tests/test_cf.py
+++ b/compliance_checker/tests/test_cf.py
@@ -3240,7 +3240,28 @@ def test_domain(self):
             "coordinates attribute from domain variable domain: "
             "xyxz, abc",
         )
-
+        # TEST CONFORMANCE 5.8 REQUIRED 4/4
+        # check reference cell measures
+        domain_var.cell_measures = "volume: cube"
+        domain_var.coordinates = "lon lat depth"
+        # reset to good domain var coordinates
+        dataset.createDimension("lon", 20)
+        dataset.createDimension("lat", 20)
+        dataset.createDimension("depth", 20)
+        domain_var.setncattr("dimensions", "lon lat depth")
+        cube = dataset.createVariable("cube", "f8", ("lon", "lat", "depth"))
+        # OK, coordinates in cell_measures are subset of coordinates of
+        # referring domain variable's coordinates attribute
+        results = self.cf.check_domain_variables(dataset)
+        assert not results[0].msgs
+        # failing example, coordinates for cell_measures variable are no longer subset
+        domain_var.cell_measures = "volume: cube_bad"
+        dataset.createVariable("cube_bad", "f8", ("lon", "lat", "depth", "time"))
+        results = self.cf.check_domain_variables(dataset)
+        self.assertTrue("Variables named in the cell_measures attributes must "
+                        "have a dimensions attribute with values that are a "
+                        "subset of the referring domain variable's dimension "
+                        "attribute" in results[0].msgs)
         del dataset
         dataset = MockTimeSeries()
         # domain should be dimensionless -- currently not an error in