def _level_coords(self):
        """Return a mapping of all MultiIndex levels and their corresponding
        coordinate name.
        """
        level_coords = OrderedDict()
        for name, index in self.indexes.items():
            if isinstance(index, pd.MultiIndex):
                level_names = index.names
                (dim,) = self.variables[name].dims
                level_coords.update({lname: dim for lname in level_names})
        return level_coords