# Working with Mesh Data#

Note

Several of the operations below rely on the optional dependencies mentioned in Iris’ Mesh Partner Packages.

## Operations Summary#

 Making a Mesh ✨ New Making a Cube ♻️ Unchanged Save ♻️ Unchanged Load ⚠️ Different - UGRID parsing is opt-in Plotting ⚠️ Different - plot with GeoVista Region Extraction ⚠️ Different - use GeoVista for mesh analysis Regridding ⚠️ Different - use iris-esmf-regrid for mesh regridders Equality ♻️ Unchanged Combining Cubes 🚧 Support Pending Arithmetic ♻️ Unchanged

## Making a Mesh#

✨ New

Creating Iris objects from scratch is a highly useful skill for testing code and improving understanding of how Iris works. This knowledge will likely prove particularly useful when converting data into the Iris mesh data model from structured formats and non-UGRID mesh formats.

The objects created in this example will be used where possible in the subsequent example operations on this page.

Code
```>>> import numpy as np

>>> from iris.coords import AuxCoord
>>> from iris.experimental.ugrid import Connectivity, Mesh

# Going to create the following mesh
#  (node indices are shown to aid understanding):
#
#  0----1
#  |    |\
#  | +  |+\
#  2----3--4

>>> node_x = AuxCoord(
...     points=[0.0, 5.0, 0.0, 5.0, 8.0],
...     standard_name="longitude",
...     units="degrees_east",
...     long_name="node_x_coordinates",
... )
>>> node_y = AuxCoord(points=[3.0, 3.0, 0.0, 0.0, 0.0], standard_name="latitude")

>>> face_x = AuxCoord([2.0, 6.0], "longitude")
>>> face_y = AuxCoord([1.0, 1.0], "latitude")

>>> edge_node_c = Connectivity(
...     indices=[[0, 1], [0, 2], [1, 3], [1, 4], [2, 3], [3, 4]],
...     cf_role="edge_node_connectivity",
...     attributes={"demo": "Supports every standard CF property"},
... )

# Create some dead-centre edge coordinates.
>>> edge_x, edge_y = [
...     AuxCoord(
...         node_coord.points[edge_node_c.indices_by_location()].mean(axis=1),
...         node_coord.standard_name,
...     )
...     for node_coord in (node_x, node_y)
... ]

>>> face_indices = np.ma.masked_equal([[0, 1, 3, 2], [1, 4, 3, 999]], 999)
>>> face_node_c = Connectivity(
...     indices=face_indices, cf_role="face_node_connectivity"
... )

>>> my_mesh = Mesh(
...     long_name="my_mesh",
...     topology_dimension=2,  # Supports 2D (face) elements.
...     node_coords_and_axes=[(node_x, "x"), (node_y, "y")],
...     connectivities=[edge_node_c, face_node_c],
...     edge_coords_and_axes=[(edge_x, "x"), (edge_y, "y")],
...     face_coords_and_axes=[(face_x, "x"), (face_y, "y")],
... )

>>> print(my_mesh)
Mesh : 'my_mesh'
topology_dimension: 2
node
node_dimension: 'Mesh2d_node'
node coordinates
<AuxCoord: longitude / (degrees_east)  [...]  shape(5,)>
<AuxCoord: latitude / (unknown)  [...]  shape(5,)>
edge
edge_dimension: 'Mesh2d_edge'
edge_node_connectivity: <Connectivity: unknown / (unknown)  [...]  shape(6, 2)>
edge coordinates
<AuxCoord: longitude / (unknown)  [...]  shape(6,)>
<AuxCoord: latitude / (unknown)  [...]  shape(6,)>
face
face_dimension: 'Mesh2d_face'
face_node_connectivity: <Connectivity: unknown / (unknown)  [...]  shape(2, 4)>
face coordinates
<AuxCoord: longitude / (unknown)  [...]  shape(2,)>
<AuxCoord: latitude / (unknown)  [...]  shape(2,)>
long_name: 'my_mesh'
```

## Making a Cube (with a Mesh)#

♻️ Unchanged

Creating a `Cube` is unchanged; the `Mesh` is linked via a `MeshCoord` (see MeshCoords):

Code
```>>> import numpy as np

>>> from iris.coords import DimCoord
>>> from iris.cube import Cube, CubeList

>>> vertical_levels = DimCoord([0, 1, 2], "height")

>>> my_cubelist = CubeList()
>>> for conn in (edge_node_c, face_node_c):
...    location = conn.location
...    mesh_coord_x, mesh_coord_y = my_mesh.to_MeshCoords(location)
...    data_shape = (len(conn.indices_by_location()), len(vertical_levels.points))
...    data_array = np.arange(np.prod(data_shape)).reshape(data_shape)
...
...    my_cubelist.append(
...        Cube(
...            data=data_array,
...            long_name=f"{location}_data",
...            units="K",
...            dim_coords_and_dims=[(vertical_levels, 1)],
...            aux_coords_and_dims=[(mesh_coord_x, 0), (mesh_coord_y, 0)],
...        )
...    )

>>> print(my_cubelist)
0: edge_data / (K)                     (-- : 6; height: 3)
1: face_data / (K)                     (-- : 2; height: 3)

>>> for cube in my_cubelist:
...     print(f"{cube.name()}: {cube.mesh.name()}, {cube.location}")
edge_data: my_mesh, edge
face_data: my_mesh, face

>>> print(my_cubelist.extract_cube("edge_data"))
edge_data / (K)                     (-- : 6; height: 3)
Dimension coordinates:
height                          -          x
Mesh coordinates:
latitude                        x          -
longitude                       x          -
Mesh:
name                        my_mesh
location                    edge
```

## Save#

♻️ Unchanged

Note

UGRID saving support is limited to the NetCDF file format.

The Iris saving process automatically detects if the `Cube` has an associated `Mesh` and automatically saves the file in a UGRID-conformant format:

Code
```>>> from subprocess import run

>>> from iris import save

>>> cubelist_path = "my_cubelist.nc"
>>> save(my_cubelist, cubelist_path)

>>> ncdump_result = run(["ncdump", "-h", cubelist_path], capture_output=True)
>>> print(ncdump_result.stdout.decode().replace("\t", "    "))
netcdf my_cubelist {
dimensions:
Mesh2d_node = 5 ;
Mesh2d_edge = 6 ;
Mesh2d_face = 2 ;
height = 3 ;
my_mesh_face_N_nodes = 4 ;
my_mesh_edge_N_nodes = 2 ;
variables:
int my_mesh ;
my_mesh:cf_role = "mesh_topology" ;
my_mesh:topology_dimension = 2 ;
my_mesh:long_name = "my_mesh" ;
my_mesh:node_coordinates = "longitude latitude" ;
my_mesh:edge_coordinates = "longitude_0 latitude_0" ;
my_mesh:face_coordinates = "longitude_1 latitude_1" ;
my_mesh:face_node_connectivity = "mesh2d_face" ;
my_mesh:edge_node_connectivity = "mesh2d_edge" ;
double longitude(Mesh2d_node) ;
longitude:units = "degrees_east" ;
longitude:standard_name = "longitude" ;
longitude:long_name = "node_x_coordinates" ;
double latitude(Mesh2d_node) ;
latitude:standard_name = "latitude" ;
double longitude_0(Mesh2d_edge) ;
longitude_0:standard_name = "longitude" ;
double latitude_0(Mesh2d_edge) ;
latitude_0:standard_name = "latitude" ;
double longitude_1(Mesh2d_face) ;
longitude_1:standard_name = "longitude" ;
double latitude_1(Mesh2d_face) ;
latitude_1:standard_name = "latitude" ;
int64 mesh2d_face(Mesh2d_face, my_mesh_face_N_nodes) ;
mesh2d_face:_FillValue = -1LL ;
mesh2d_face:cf_role = "face_node_connectivity" ;
mesh2d_face:start_index = 0LL ;
int64 mesh2d_edge(Mesh2d_edge, my_mesh_edge_N_nodes) ;
mesh2d_edge:demo = "Supports every standard CF property" ;
mesh2d_edge:cf_role = "edge_node_connectivity" ;
mesh2d_edge:start_index = 0LL ;
int64 edge_data(Mesh2d_edge, height) ;
edge_data:long_name = "edge_data" ;
edge_data:units = "K" ;
edge_data:mesh = "my_mesh" ;
edge_data:location = "edge" ;
int64 height(height) ;
height:standard_name = "height" ;
int64 face_data(Mesh2d_face, height) ;
face_data:long_name = "face_data" ;
face_data:units = "K" ;
face_data:mesh = "my_mesh" ;
face_data:location = "face" ;

// global attributes:
:Conventions = "CF-1.7" ;
}
```

The `iris.experimental.ugrid.save_mesh()` function allows `Mesh`es to be saved to file without associated `Cube`s:

Code
```>>> from subprocess import run

>>> from iris.experimental.ugrid import save_mesh

>>> mesh_path = "my_mesh.nc"
>>> save_mesh(my_mesh, mesh_path)

>>> ncdump_result = run(["ncdump", "-h", mesh_path], capture_output=True)
>>> print(ncdump_result.stdout.decode().replace("\t", "    "))
netcdf my_mesh {
dimensions:
Mesh2d_node = 5 ;
Mesh2d_edge = 6 ;
Mesh2d_face = 2 ;
my_mesh_face_N_nodes = 4 ;
my_mesh_edge_N_nodes = 2 ;
variables:
int my_mesh ;
my_mesh:cf_role = "mesh_topology" ;
my_mesh:topology_dimension = 2 ;
my_mesh:long_name = "my_mesh" ;
my_mesh:node_coordinates = "longitude latitude" ;
my_mesh:edge_coordinates = "longitude_0 latitude_0" ;
my_mesh:face_coordinates = "longitude_1 latitude_1" ;
my_mesh:face_node_connectivity = "mesh2d_face" ;
my_mesh:edge_node_connectivity = "mesh2d_edge" ;
double longitude(Mesh2d_node) ;
longitude:units = "degrees_east" ;
longitude:standard_name = "longitude" ;
longitude:long_name = "node_x_coordinates" ;
double latitude(Mesh2d_node) ;
latitude:standard_name = "latitude" ;
double longitude_0(Mesh2d_edge) ;
longitude_0:standard_name = "longitude" ;
double latitude_0(Mesh2d_edge) ;
latitude_0:standard_name = "latitude" ;
double longitude_1(Mesh2d_face) ;
longitude_1:standard_name = "longitude" ;
double latitude_1(Mesh2d_face) ;
latitude_1:standard_name = "latitude" ;
int64 mesh2d_face(Mesh2d_face, my_mesh_face_N_nodes) ;
mesh2d_face:_FillValue = -1LL ;
mesh2d_face:cf_role = "face_node_connectivity" ;
mesh2d_face:start_index = 0LL ;
int64 mesh2d_edge(Mesh2d_edge, my_mesh_edge_N_nodes) ;
mesh2d_edge:demo = "Supports every standard CF property" ;
mesh2d_edge:cf_role = "edge_node_connectivity" ;
mesh2d_edge:start_index = 0LL ;

// global attributes:
:Conventions = "CF-1.7" ;
}
```

⚠️ Different - UGRID parsing is opt-in

Note

While Iris’ UGRID support remains `experimental`, parsing UGRID when loading a file remains optional. To load UGRID data from a file into the Iris mesh data model, use the `iris.experimental.ugrid.PARSE_UGRID_ON_LOAD` context manager:

Code
```>>> from iris import load

# Sort CubeList to ensure consistent result.
0: edge_data / (K)                     (-- : 6; height: 3)
1: face_data / (K)                     (-- : 2; height: 3)
```

All the existing loading functionality still operates on UGRID-compliant data - `Constraint`s, callbacks, `load_cube()` etcetera:

Code
```>>> from iris import Constraint, load_cube

# Sort CubeList to ensure consistent result.
>>> ground_cubelist.sort(key=lambda cube: cube.name())
>>> print(ground_cubelist)
0: edge_data / (K)                     (-- : 6)
1: face_data / (K)                     (-- : 2)

>>> print(face_cube)
face_data / (K)                     (-- : 2; height: 3)
Dimension coordinates:
height                          -          x
Mesh coordinates:
latitude                        x          -
longitude                       x          -
Mesh:
name                        my_mesh
location                    face
Attributes:
Conventions                 'CF-1.7'
```

Note

We recommend caution if constraining on coordinates associated with a `Mesh`. An individual coordinate value might not be shared by any other data points, and using a coordinate range will demand notably higher performance given the size of the dimension versus structured grids (see the data model detail).

The `iris.experimental.ugrid.load_mesh()` and `load_meshes()` functions allow only `Mesh`es to be loaded from a file without creating any associated `Cube`s:

Code
```>>> from iris.experimental.ugrid import load_mesh

Mesh : 'my_mesh'
topology_dimension: 2
node
node_dimension: 'Mesh2d_node'
node coordinates
<AuxCoord: longitude / (degrees)  [...]  shape(5,)>
<AuxCoord: latitude / (unknown)  [...]  shape(5,)>
edge
edge_dimension: 'Mesh2d_edge'
edge_node_connectivity: <Connectivity: mesh2d_edge / (unknown)  [...]  shape(6, 2)>
edge coordinates
<AuxCoord: longitude / (unknown)  [...]  shape(6,)>
<AuxCoord: latitude / (unknown)  [...]  shape(6,)>
face
face_dimension: 'Mesh2d_face'
face_node_connectivity: <Connectivity: mesh2d_face / (unknown)  [...]  shape(2, 4)>
face coordinates
<AuxCoord: longitude / (unknown)  [...]  shape(2,)>
<AuxCoord: latitude / (unknown)  [...]  shape(2,)>
long_name: 'my_mesh'
var_name: 'my_mesh'
```

## Plotting#

⚠️ Different - plot with GeoVista

The Cartopy-Matplotlib combination is not optimised for displaying the high number of irregular shapes associated with meshes. Thankfully mesh visualisation is already popular in many other fields (e.g. CGI, gaming, SEM microscopy), so there is a wealth of tooling available, which GeoVista harnesses for cartographic plotting.

GeoVista’s default behaviour is to convert lat-lon information into full XYZ coordinates so the data is visualised on the surface of a 3D globe. The plots are interactive by default, so it’s easy to explore the data in detail.

2D projections have also been demonstrated in proofs of concept, and will be added to API in the near future.

This first example uses GeoVista to plot the `face_cube` that we created earlier:

Code
```>>> from geovista import GeoPlotter, Transform
>>> from geovista.common import to_xyz

# We'll re-use this to plot some real global data later.
>>> def cube_faces_to_polydata(cube):
...     lons, lats = cube.mesh.node_coords
...     face_node = cube.mesh.face_node_connectivity
...     indices = face_node.indices_by_location()
...
...     mesh = Transform.from_unstructured(
...         lons.points,
...         lats.points,
...         indices,
...         data=cube.data,
...         name=f"{cube.name()} / {cube.units}",
...         start_index=face_node.start_index,
...     )
...     return mesh

>>> print(face_cube)
face_data / (K)                     (-- : 2; height: 3)
Dimension coordinates:
height                          -          x
Mesh coordinates:
latitude                        x          -
longitude                       x          -
Attributes:
Conventions                 'CF-1.7'

# Convert our mesh+data to a PolyData object.
# Just plotting a single height level.
>>> face_polydata = cube_faces_to_polydata(face_cube[:, 0])
>>> print(face_polydata)
PolyData (0x7ff4861ff4c0)
N Cells:      2
N Points:     5
X Bounds:     9.903e-01, 1.000e+00
Y Bounds:     0.000e+00, 1.392e-01
Z Bounds:     6.123e-17, 5.234e-02
N Arrays:     2

# Create the GeoVista plotter and add our mesh+data to it.
>>> my_plotter = GeoPlotter()

# Centre the camera on the data.
>>> camera_region = to_xyz(
...     face_cube.coord("longitude").points,
...     face_cube.coord("latitude").points,
... )
>>> camera_pos = camera_region.mean(axis=0)
>>> my_plotter.camera.position = camera_pos

>>> my_plotter.show()
``` This artificial data makes West Africa rather chilly!

Here’s another example using a global cubed-sphere data set:

Code
```>>> from iris import load_cube

# Demonstrating with a global data set.
>>> from iris.tests import get_data_path
>>> file_path = get_data_path(
...     [
...         "NetCDF",
...         "unstructured_grid",
...         "lfric_surface_mean.nc",
...     ]
... )
>>> print(global_cube)
sea_surface_temperature / (K)       (-- : 1; -- : 13824)
Mesh coordinates:
latitude                        -       x
longitude                       -       x
Auxiliary coordinates:
time                            x       -
Cell methods:
0                           time: mean (interval: 300 s)
1                           time_counter: mean
Attributes:
Conventions                 UGRID
description                 Created by xios
interval_operation          300 s
interval_write              1 d
name                        lfric_surface
online_operation            average
timeStamp                   2020-Feb-07 16:23:14 GMT
title                       Created by xios
uuid                        489bcef5-3d1c-4529-be42-4ab5f8c8497b

>>> global_polydata = cube_faces_to_polydata(global_cube)
>>> print(global_polydata)
PolyData (0x7f761b536160)
N Cells:      13824
N Points:     13826
X Bounds:     -1.000e+00, 1.000e+00
Y Bounds:     -1.000e+00, 1.000e+00
Z Bounds:     -1.000e+00, 1.000e+00
N Arrays:     2

>>> my_plotter = GeoPlotter()

>>> my_plotter.show()
``` ## Region Extraction#

⚠️ Different - use GeoVista for mesh analysis

As described in The Mesh Data Model, indexing for a range along a `Cube`'s `mesh_dim()` will not provide a contiguous region, since position on the unstructured dimension is unrelated to spatial position. This means that subsetted `MeshCoord`s cannot be reliably interpreted as intended, and subsetting a `MeshCoord` is therefore set to return an `AuxCoord` instead - breaking the link between `Cube` and `Mesh`:

Code
```>>> edge_cube = my_cubelist.extract_cube("edge_data")
>>> print(edge_cube)
edge_data / (K)                     (-- : 6; height: 3)
Dimension coordinates:
height                          -          x
Mesh coordinates:
latitude                        x          -
longitude                       x          -
Mesh:
name                        my_mesh
location                    edge

# Sub-setted MeshCoords have become AuxCoords.
>>> print(edge_cube[:-1])
edge_data / (K)                     (-- : 5; height: 3)
Dimension coordinates:
height                          -          x
Auxiliary coordinates:
latitude                        x          -
longitude                       x          -
```

Extracting a region therefore requires extra steps - to determine the spatial position of the data points before they can be analysed as inside/outside the selected region. The recommended way to do this is using tools provided by GeoVista, which is optimised for performant mesh analysis.

This approach centres around using `geovista.geodesic.BBox.enclosed()` to get the subset of the original mesh that is inside the `BBox`. This subset `pyvista.PolyData` object includes the original indices of each datapoint - the `vtkOriginalCellIds` array, which can be used to index the original `Cube`. Since we know that this subset `Cube` represents a regional mesh, we then reconstruct a `Mesh` from the `Cube`'s `aux_coords` using `iris.experimental.ugrid.Mesh.from_coords()`:

Code
```>>> from geovista import Transform
>>> from geovista.geodesic import BBox
>>> from iris.experimental.ugrid import Mesh, PARSE_UGRID_ON_LOAD

# Need a larger dataset to demonstrate this operation.
>>> from iris.tests import get_data_path
>>> file_path = get_data_path(
...     [
...         "NetCDF",
...         "unstructured_grid",
...         "lfric_ngvat_2D_72t_face_half_levels_main_conv_rain.nc",
...     ]
... )

>>> print(global_cube)
surface_convective_rainfall_rate / (kg m-2 s-1) (-- : 72; -- : 864)
Mesh coordinates:
latitude                                    -        x
longitude                                   -        x
Auxiliary coordinates:
time                                        x        -
Cell methods:
0                                       time: point
Attributes:
Conventions                             UGRID
description                             Created by xios
interval_operation                      300 s
interval_write                          300 s
name                                    lfric_ngvat_2D_72t_face_half_levels_main_conv_rain
online_operation                        instant
timeStamp                               2020-Oct-18 21:18:35 GMT
title                                   Created by xios
uuid                                    b3dc0fb4-9828-4663-a5ac-2a5763280159

# Convert the Mesh to a GeoVista PolyData object.
>>> lons, lats = global_cube.mesh.node_coords
>>> face_node = global_cube.mesh.face_node_connectivity
>>> indices = face_node.indices_by_location()
>>> global_polydata = Transform.from_unstructured(
...     lons.points, lats.points, indices, start_index=face_node.start_index
... )

# Define a region of 4 corners connected by great circles.
#  Specialised sub-classes of BBox are also available e.g. panel/wedge.
>>> region = BBox(lons=[0, 70, 70, 0], lats=[-25, -25, 45, 45])
# 'Apply' the region to the PolyData object.
>>> region_polydata = region.enclosed(global_polydata, preference="center")
# Get the remaining face indices, to use for indexing the Cube.
>>> indices = region_polydata["vtkOriginalCellIds"]

>>> print(type(indices))
<class 'numpy.ndarray'>
# 101 is smaller than the original 864.
>>> print(len(indices))
101
>>> print(indices[:10])
[ 6  7  8  9 10 11 18 19 20 21]

# Use the face indices to subset the global cube.
>>> region_cube = global_cube[:, indices]

# In this case we **know** the indices correspond to a contiguous
#  region, so we will convert the sub-setted Cube back into a
#  Cube-with-Mesh.
>>> new_mesh = Mesh.from_coords(*region_cube.coords(dimensions=1))
>>> new_mesh_coords = new_mesh.to_MeshCoords(global_cube.location)
>>> for coord in new_mesh_coords:
...     region_cube.remove_coord(coord.name())

# A Mesh-Cube with a subset (101) of the original 864 faces.
>>> print(region_cube)
surface_convective_rainfall_rate / (kg m-2 s-1) (-- : 72; -- : 101)
Mesh coordinates:
latitude                                    -        x
longitude                                   -        x
Auxiliary coordinates:
time                                        x        -
Cell methods:
0                                       time: point
Attributes:
Conventions                             UGRID
description                             Created by xios
interval_operation                      300 s
interval_write                          300 s
name                                    lfric_ngvat_2D_72t_face_half_levels_main_conv_rain
online_operation                        instant
timeStamp                               2020-Oct-18 21:18:35 GMT
title                                   Created by xios
uuid                                    b3dc0fb4-9828-4663-a5ac-2a5763280159
```

## Regridding#

⚠️ Different - use iris-esmf-regrid for mesh regridders

Regridding to or from a mesh requires different logic than Iris’ existing regridders, which are designed for structured grids. For this we recommend ESMF’s powerful regridding tools, which integrate with Iris’ mesh data model via the iris-esmf-regrid package.

Regridding is achieved via the `esmf_regrid.experimental.unstructured_scheme.MeshToGridESMFRegridder` and `GridToMeshESMFRegridder` classes. Regridding from a source `Cube` to a target `Cube` involves initialising and then calling one of these classes. Initialising is done by passing in the source and target `Cube` as arguments. The regridder is then called by passing the source `Cube` as an argument. We can demonstrate this with the `MeshToGridESMFRegridder`:

Code
```>>> from esmf_regrid.experimental.unstructured_scheme import MeshToGridESMFRegridder

>>> from iris.tests import get_data_path
>>> mesh_file = get_data_path(
...     ["NetCDF", "unstructured_grid", "lfric_surface_mean.nc"]
... )
>>> grid_file = get_data_path(
...     ["NetCDF", "regrid", "regrid_template_global_latlon.nc"]
... )

# Load a list of cubes defined on the same Mesh.

# Extract a specific cube.
>>> mesh_cube1 = mesh_cubes.extract_cube("sea_surface_temperature")
>>> print(mesh_cube1)
sea_surface_temperature / (K)       (-- : 1; -- : 13824)
Mesh coordinates:
latitude                        -       x
longitude                       -       x
Auxiliary coordinates:
time                            x       -
Cell methods:
0                           time: mean (interval: 300 s)
1                           time_counter: mean
Attributes:
Conventions                 UGRID
description                 Created by xios
interval_operation          300 s
interval_write              1 d
name                        lfric_surface
online_operation            average
timeStamp                   2020-Feb-07 16:23:14 GMT
title                       Created by xios
uuid                        489bcef5-3d1c-4529-be42-4ab5f8c8497b

>>> print(sample_grid)
sample_grid / (unknown)             (latitude: 180; longitude: 360)
Dimension coordinates:
latitude                             x               -
longitude                            -               x
Attributes:
Conventions                 'CF-1.7'

# Initialise the regridder.
>>> rg = MeshToGridESMFRegridder(mesh_cube1, sample_grid)

# Regrid the mesh cube cube.
>>> result1 = rg(mesh_cube1)
>>> print(result1)
sea_surface_temperature / (K)       (-- : 1; latitude: 180; longitude: 360)
Dimension coordinates:
latitude                        -            x               -
longitude                       -            -               x
Auxiliary coordinates:
time                            x            -               -
Cell methods:
0                           time: mean (interval: 300 s)
1                           time_counter: mean
Attributes:
Conventions                 UGRID
description                 Created by xios
interval_operation          300 s
interval_write              1 d
name                        lfric_surface
online_operation            average
timeStamp                   2020-Feb-07 16:23:14 GMT
title                       Created by xios
uuid                        489bcef5-3d1c-4529-be42-4ab5f8c8497b
```

Note

All `Cube` `attributes` are retained when regridding, so watch out for any attributes that reference the format (there are several in these examples) - you may want to manually remove them to avoid later confusion.

The initialisation process is computationally expensive so we use caching to improve performance. Once a regridder has been initialised, it can be used on any `Cube` which has been defined on the same `Mesh` (or on the same grid in the case of `GridToMeshESMFRegridder`). Since calling a regridder is usually a lot faster than initialising, reusing regridders can save a lot of time. We can demonstrate the reuse of the previously initialised regridder:

Code
```# Extract a different cube defined on the same Mesh.
>>> mesh_cube2 = mesh_cubes.extract_cube("precipitation_flux")
>>> print(mesh_cube2)
precipitation_flux / (kg m-2 s-1)   (-- : 1; -- : 13824)
Mesh coordinates:
latitude                        -       x
longitude                       -       x
Auxiliary coordinates:
time                            x       -
Cell methods:
0                           time: mean (interval: 300 s)
1                           time_counter: mean
Attributes:
Conventions                 UGRID
description                 Created by xios
interval_operation          300 s
interval_write              1 d
name                        lfric_surface
online_operation            average
timeStamp                   2020-Feb-07 16:23:14 GMT
title                       Created by xios
uuid                        489bcef5-3d1c-4529-be42-4ab5f8c8497b

# Regrid the new mesh cube using the same regridder.
>>> result2 = rg(mesh_cube2)
>>> print(result2)
precipitation_flux / (kg m-2 s-1)   (-- : 1; latitude: 180; longitude: 360)
Dimension coordinates:
latitude                        -            x               -
longitude                       -            -               x
Auxiliary coordinates:
time                            x            -               -
Cell methods:
0                           time: mean (interval: 300 s)
1                           time_counter: mean
Attributes:
Conventions                 UGRID
description                 Created by xios
interval_operation          300 s
interval_write              1 d
name                        lfric_surface
online_operation            average
timeStamp                   2020-Feb-07 16:23:14 GMT
title                       Created by xios
uuid                        489bcef5-3d1c-4529-be42-4ab5f8c8497b
```

Support also exists for saving and loading previously initialised regridders - `esmf_regrid.experimental.io.save_regridder()` and `load_regridder()` - so that they can be re-used by future scripts.

## Equality#

♻️ Unchanged

`Mesh` comparison is supported, and comparing two ‘`Mesh`-`Cube`s’ will include a comparison of the respective `Mesh`es, with no extra action needed by the user.

Note

Keep an eye on memory demand when comparing large `Mesh`es, but note that `Mesh`equality is enabled for lazy processing (Real and Lazy Data), so if the `Mesh`es being compared are lazy the process will use less memory than their total size.

## Combining Cubes#

🚧 Support Pending

Merging or concatenating `Cube`s (described in Merge and Concatenate) with two different `Mesh`es is not possible - a `Cube` must be associated with just a single `Mesh`, and merge/concatenate are not yet capable of combining multiple `Mesh`es into one.

`Cube`s that include `MeshCoord`s can still be merged/concatenated on dimensions other than the `mesh_dim()`, since such `Cube`s will by definition share the same `Mesh`.

You may wish to investigate `iris.experimental.ugrid.recombine_submeshes()`, which can be used for a very specific type of `Mesh` combination not detailed here.

## Arithmetic#

♻️ Unchanged

Cube Arithmetic (described in Cube Maths) has been extended to handle `Cube`s that include `MeshCoord`s, and hence have a `cube.mesh`.

Cubes with meshes can be combined in arithmetic operations like “ordinary” cubes. They can combine with other cubes without that mesh (and its dimension); or with a matching mesh, which may be on a different dimension. Arithmetic can also be performed between a cube with a mesh and a mesh coordinate with a matching mesh.

In all cases, the result will have the same mesh as the input cubes.

Meshes only match if they are fully equal – i.e. they contain all the same coordinates and connectivities, with identical names, units, attributes and data content.