Raise NotImplementedError when attempting to save a MultiIndex to disk.

doc/whats-new.rst

@@ -62,6 +62,10 @@ Bug fixes
   DataArray constructor (:issue:`1709`).
   By `Stephan Hoyer <https://github.com/shoyer>`_.
 
+- Raise ``NotImplementedError`` when attempting to save a MultiIndex to a
+  netCDF file (:issue:`1547`).
+  By `Stephan Hoyer <https://github.com/shoyer>`_.
+
 Testing
 ~~~~~~~
 

xarray/conventions.py

@@ -17,7 +17,7 @@
 
 from .core import duck_array_ops, indexing, ops, utils
 from .core.formatting import format_timestamp, first_n_items, last_item
-from .core.variable import as_variable, Variable
+from .core.variable import as_variable, IndexVariable, Variable
 from .core.pycompat import iteritems, OrderedDict, PY3, basestring
 
 
@@ -832,6 +832,15 @@ def _infer_dtype(array, name=None):
 def ensure_dtype_not_object(var, name=None):
     # TODO: move this from conventions to backends? (it's not CF related)
     if var.dtype.kind == 'O':
+        if (isinstance(var, IndexVariable) and
+                isinstance(var.to_index(), pd.MultiIndex)):
+            raise NotImplementedError(
+                'variable {!r} is a MultiIndex, which cannot yet be '
+                'serialized to netCDF files '
+                '(https://github.com/pydata/xarray/issues/1077). Use '
+                'reset_index() to convert MultiIndex levels into coordinate '
+                'variables instead.'.format(name))
+
         dims, data, attrs, encoding = _var_as_tuple(var)
         missing = pd.isnull(data)
         if missing.any():

xarray/tests/test_backends.py

@@ -719,6 +719,13 @@ def test_append_overwrite_values(self):
     def test_vectorized_indexing(self):
         self._test_vectorized_indexing(vindex_support=False)
 
+    def test_multiindex_not_implemented(self):
+        ds = (Dataset(coords={'y': ('x', [1, 2]), 'z': ('x', ['a', 'b'])})
+              .set_index(x=['y', 'z']))
+        with raises_regex(NotImplementedError, 'MultiIndex'):
+            with self.roundtrip(ds):
+                pass
+
 
 _counter = itertools.count()