diff --git a/pyicon/pyicon_calc_xr.py b/pyicon/pyicon_calc_xr.py
index afd12af67396a98fb2ea9e4b6e4d996eccce77df..26bb740a2d838d84e3d0adcb95a27f3557b65071 100644
--- a/pyicon/pyicon_calc_xr.py
+++ b/pyicon/pyicon_calc_xr.py
@@ -471,28 +471,22 @@ def xr_calc_curl(ds_IcD, vector, rot_coeff=None):
         Dataarray containing vector variable on cell edges.
 
     rot_coeff : xr.DataArray or None
-        Array with dims ("vertex", "ne")
+        Array containing dims ("vertex", "ne")
 
     Returns
     -------
     curl_vec : xr.DataArray
-        vertical component of the curl of the vector
+        vertical component of the curl of the vector defined on vertex points
 
     Notes
     -----
-    We calculate the curl through the use of Stokes' theorem (technically
-    Green's theorem as we're working with 2D velocity!), however, only the
-    vertical component is calculated. A similar procedure can be used to
-    calculate the horizontal components of the curl (oriented along cell edges
-    and defined at intermediate Z levels.) This will be implemented in a future
-    release.
+    We calculate the curl through the use of Stokes'/Green's theorem
+    Green's theorem as we're working with 2D velocity!), A similar procedure can be used to calculate the horizontal components of the curl (oriented
+    along cell edges and defined at intermediate Z levels.) This will be implemented in a future release.
 
     If you're using this function on large datasets, performance gains may be
     made if you play around with the dimension order.
 
-    When applying to a gradient we get identically zero. Should add this as a
-    test to the testing suite
-
     """
     assert "edge" in vector.dims
 
diff --git a/pyicon/tests/test_pyicon_calc_xr.py b/pyicon/tests/test_pyicon_calc_xr.py
index c8eb7be64e2b8e9499dfeeb1d8eb9e4e18d9f065..0121600c8bcc0a4a882e1155d58f047ff41c4f10 100644
--- a/pyicon/tests/test_pyicon_calc_xr.py
+++ b/pyicon/tests/test_pyicon_calc_xr.py
@@ -86,3 +86,12 @@ def test_xr_crop_tgrid(tgrid, request):
 
     assert cropped_tgrid["ireg_v"].sum() == 135385
     assert cropped_tgrid["ireg_v"].prod() == -1427286351937536000
+
+
+def test_nabla_funcs(processed_tgrid):
+    # Want to check curl of a gradient
+    gradient = pyic.xr_calc_grad(processed_tgrid, processed_tgrid["clon"])
+    curl_of_grad = pyic.xr_calc_curl(processed_tgrid, gradient)
+    assert np.allclose(curl_of_grad, 0)
+
+    # Should include other tests in the future if any refactoring is done