diff --git a/CHANGELOG.md b/CHANGELOG.md
index abc131be9..401372d81 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -7,6 +7,12 @@ This project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.html
 
 ## [Unreleased]
 
+## [0.31.1] - 2022-11-11
+### Fixed
+- Fix bug introduced in StructuredMeshGenerator global numbering with release 0.31.0 in commit a63fc62a2
+- Fix healpix global numbering for pentagon pole elements in parallel
+- Fix validity check of atlas::HealpixGrid
+
 ## [0.31.0] - 2022-11-10
 ### Added
 - Extend PointCloud functionspace to do halo exchanges, including Fortran API
@@ -405,6 +411,7 @@ This project adheres to [Semantic Versioning](http://semver.org/spec/v2.0.0.html
 ## 0.13.0 - 2018-02-16
 
 [Unreleased]: https://github.com/ecmwf/atlas/compare/master...develop
+[0.31.1]: https://github.com/ecmwf/atlas/compare/0.31.0...0.31.1
 [0.31.0]: https://github.com/ecmwf/atlas/compare/0.30.0...0.31.0
 [0.30.0]: https://github.com/ecmwf/atlas/compare/0.29.0...0.30.0
 [0.29.0]: https://github.com/ecmwf/atlas/compare/0.28.1...0.29.0
diff --git a/VERSION b/VERSION
index 26bea73e8..f176c9441 100644
--- a/VERSION
+++ b/VERSION
@@ -1 +1 @@
-0.31.0
+0.31.1
diff --git a/src/atlas/grid/StructuredGrid.h b/src/atlas/grid/StructuredGrid.h
index ab7749ffb..a78feeabb 100644
--- a/src/atlas/grid/StructuredGrid.h
+++ b/src/atlas/grid/StructuredGrid.h
@@ -18,7 +18,6 @@
 #include "atlas/grid/detail/grid/Healpix.h"
 #include "atlas/grid/detail/grid/Structured.h"
 
-
 namespace atlas {
 
 //---------------------------------------------------------------------------------------------------------------------
@@ -275,7 +274,11 @@ class HealpixGrid : public StructuredGrid {
     HealpixGrid(const Grid&);
     HealpixGrid(int N);
 
-    bool valid() { return grid_; }
+    operator bool() const { return valid(); }
+
+    bool valid() const { return grid_; }
+
+    long N() const { return grid_->nxmax() / 4; }
 
 private:
     const grid_t* grid_;
diff --git a/src/atlas/meshgenerator/detail/HealpixMeshGenerator.cc b/src/atlas/meshgenerator/detail/HealpixMeshGenerator.cc
index 1cbe8bda7..189787e96 100644
--- a/src/atlas/meshgenerator/detail/HealpixMeshGenerator.cc
+++ b/src/atlas/meshgenerator/detail/HealpixMeshGenerator.cc
@@ -64,7 +64,7 @@ HealpixMeshGenerator::HealpixMeshGenerator(const eckit::Parametrisation& p) {
         options.set("3d", three_dimensional);
     }
 
-    std::string pole_elements{"quqds"};
+    std::string pole_elements{"quads"};
     if (p.get("pole_elements", pole_elements)) {
         if (pole_elements != "pentagons" and pole_elements != "quads") {
             Log::warning() << "Atlas::HealpixMeshGenerator accepts \"pentagons\" or \"quads\" for \"pole_elements\"."
@@ -931,8 +931,10 @@ void HealpixMeshGenerator::generate_mesh(const StructuredGrid& grid, const grid:
     ii               = 0;  // index inside SB (surrounding belt)
     int jcell_offset = 0;  // global index offset due to extra points at the north pole
     gidx_t jcell     = 0;  // global cell counter
+    gidx_t points_in_partition = 0;
     for (iy = iy_min; iy <= iy_max; iy++) {
         int nx = nb_lat_nodes(iy) + 1;
+        points_in_partition += (nx - 1);
         for (ix = 0; ix < nx; ix++) {
             const bool at_pole     = (iy == 0 or iy == ny - 1);
             int not_duplicate_cell = (at_pole ? ix % 2 : 1);
@@ -963,7 +965,7 @@ void HealpixMeshGenerator::generate_mesh(const StructuredGrid& grid, const grid:
 
                 // match global cell indexing for the three healpix versions
                 if (nb_pole_nodes == 1) {
-                    cells_glb_idx(jquadcell) = jquadcell + 1;
+                    cells_glb_idx(jquadcell) = parts_sidx + points_in_partition - nx + ix + 1;
                 }
                 else if (nb_pole_nodes == 8) {
                     if (iy == 0) {
@@ -979,11 +981,15 @@ void HealpixMeshGenerator::generate_mesh(const StructuredGrid& grid, const grid:
                     }
                 }
                 else if (nb_pole_nodes == 4) {
+                    if (iy == 0 or iy == ny - 1) {
+                        continue;
+                    }
                     if (pentagon) {
-                        cells_glb_idx(jpentcell) = jcell;
+                        cells_glb_idx(jpentcell) = (mypart != 0 ? 12 * ns * ns - 3 + ix : jcell);
+                        jcell_offset++;
                     }
                     else {
-                        cells_glb_idx(jquadcell) = jcell;
+                        cells_glb_idx(jquadcell) = parts_sidx + points_in_partition - nx - 6 + ix + (mypart != 0 ? 4 : jcell_offset);
                     }
                 }
 #if DEBUG_OUTPUT_DETAIL
diff --git a/src/atlas/meshgenerator/detail/StructuredMeshGenerator.cc b/src/atlas/meshgenerator/detail/StructuredMeshGenerator.cc
index c0fe3d4bf..4a4b773fe 100644
--- a/src/atlas/meshgenerator/detail/StructuredMeshGenerator.cc
+++ b/src/atlas/meshgenerator/detail/StructuredMeshGenerator.cc
@@ -1264,7 +1264,7 @@ void StructuredMeshGenerator::generate_mesh(const StructuredGrid& rg, const grid
     };
 
     bool regular_cells_glb_idx = atlas::RegularLonLatGrid(rg);
-    if( options.getBool("triangulate") ) {
+    if( options.getBool("triangulate") || y_numbering > 0) {
         regular_cells_glb_idx = false;
     }
 
@@ -1306,7 +1306,7 @@ void StructuredMeshGenerator::generate_mesh(const StructuredGrid& rg, const grid
                     if (periodic_east_west) {
                         ++nx;
                     }
-                    cells_glb_idx(jcell) = jlatN * nx + region.lat_begin[jlat] + jelem;
+                    cells_glb_idx(jcell) = glb_idx( quad_nodes[0] );
                 }
             }
             else  // This is a triag