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Document use of new_axis to control merge (#6180)
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* first draft

* address review comments

* Update docs/src/further_topics/controlling_merge.rst

Co-authored-by: Patrick Peglar <patrick.peglar@metoffice.gov.uk>

* change title

---------

Co-authored-by: Patrick Peglar <patrick.peglar@metoffice.gov.uk>
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204 changes: 204 additions & 0 deletions docs/src/further_topics/controlling_merge.rst
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.. _controlling_merge:

=================================
Controlling Merge and Concatenate
=================================


Sometimes it is not possible to appropriately combine a CubeList using merge and concatenate on their own. In such cases
it is possible to achieve much more control over cube combination by using the :func:`~iris.util.new_axis` utility.
Consider the following set of cubes:

>>> file_1 = iris.sample_data_path("time_varying_hybrid_height", "*_2160-12.pp")
>>> file_2 = iris.sample_data_path("time_varying_hybrid_height", "*_2161-01.pp")
>>> cubes = iris.load([file_1, file_2], "x_wind")
>>> print(cubes[0])
x_wind / (m s-1) (model_level_number: 5; latitude: 144; longitude: 192)
Dimension coordinates:
model_level_number x - -
latitude - x -
longitude - - x
Auxiliary coordinates:
level_height x - -
sigma x - -
surface_altitude - x x
Derived coordinates:
altitude x x x
Scalar coordinates:
forecast_period 1338840.0 hours, bound=(1338480.0, 1339200.0) hours
forecast_reference_time 2006-01-01 00:00:00
time 2160-12-16 00:00:00, bound=(2160-12-01 00:00:00, 2161-01-01 00:00:00)
Cell methods:
0 time: mean (interval: 1 hour)
Attributes:
STASH m01s00i002
source 'Data from Met Office Unified Model'
um_version '12.1'
>>> print(cubes[1])
x_wind / (m s-1) (model_level_number: 5; latitude: 144; longitude: 192)
Dimension coordinates:
model_level_number x - -
latitude - x -
longitude - - x
Auxiliary coordinates:
level_height x - -
sigma x - -
surface_altitude - x x
Derived coordinates:
altitude x x x
Scalar coordinates:
forecast_period 1339560.0 hours, bound=(1339200.0, 1339920.0) hours
forecast_reference_time 2006-01-01 00:00:00
time 2161-01-16 00:00:00, bound=(2161-01-01 00:00:00, 2161-02-01 00:00:00)
Cell methods:
0 time: mean (interval: 1 hour)
Attributes:
STASH m01s00i002
source 'Data from Met Office Unified Model'
um_version '12.1'

These two cubes have different time points (i.e. scalar time value). So we would normally be able to merge them,
creating a time dimension. However, in this case we can not combine them with :meth:`~iris.cube.Cube.merge`
due to the fact that their ``surface_altitude`` coordinate also varies over time:

>>> cubes.merge_cube()
Traceback (most recent call last):
...
iris.exceptions.MergeError: failed to merge into a single cube.
Coordinates in cube.aux_coords (non-scalar) differ: surface_altitude.

Since surface altitude is preventing merging, we want to find a way of combining these cubes while also *explicitly*
combining the ``surface_altitude`` coordinate so that it also varies along the time dimension. We can do this by first
adding a dimension to the cube *and* the ``surface_altitude`` coordinate using :func:`~iris.util.new_axis`, and then
concatenating those cubes together. We can attempt this as follows:

>>> from iris.util import new_axis
>>> from iris.cube import CubeList
>>> processed_cubes = CubeList([new_axis(cube, scalar_coord="time", expand_extras=["surface_altitude"]) for cube in cubes])
>>> processed_cubes.concatenate_cube()
Traceback (most recent call last):
...
iris.exceptions.ConcatenateError: failed to concatenate into a single cube.
Scalar coordinates values or metadata differ: forecast_period != forecast_period

This error alerts us to the fact that the ``forecast_period`` coordinate is also varying over time. To get concatenation
to work, we will have to expand the dimensions of this coordinate to include "time", by passing it also to the
``expand_extras`` keyword.

>>> processed_cubes = CubeList(
... [new_axis(cube, scalar_coord="time", expand_extras=["surface_altitude", "forecast_period"]) for cube in cubes]
... )
>>> result = processed_cubes.concatenate_cube()
>>> print(result)
x_wind / (m s-1) (time: 2; model_level_number: 5; latitude: 144; longitude: 192)
Dimension coordinates:
time x - - -
model_level_number - x - -
latitude - - x -
longitude - - - x
Auxiliary coordinates:
forecast_period x - - -
surface_altitude x - x x
level_height - x - -
sigma - x - -
Derived coordinates:
altitude x x x x
Scalar coordinates:
forecast_reference_time 2006-01-01 00:00:00
Cell methods:
0 time: mean (interval: 1 hour)
Attributes:
STASH m01s00i002
source 'Data from Met Office Unified Model'
um_version '12.1'

.. note::
Since the derived coordinate ``altitude`` derives from ``surface_altitude``, adding ``time`` to the dimensions of
``surface_altitude`` also means it is added to the dimensions of ``altitude``. So in the combined cube, both of
these coordinates vary along the ``time`` dimension.

Controlling over multiple dimensions
------------------------------------

We now consider a more complex case. Instead of loading 2 files across different time steps we now load 15 such files.
Each of these files covers a month's time step, however, the ``surface_altitude`` coordinate changes only once per year.
The files span 3 years so there are 3 different ``surface_altitude`` coordinates.

>>> filename = iris.sample_data_path('time_varying_hybrid_height', '*.pp')
>>> cubes = iris.load(filename, constraints="x_wind")
>>> print(cubes)
0: x_wind / (m s-1) (time: 2; model_level_number: 5; latitude: 144; longitude: 192)
1: x_wind / (m s-1) (time: 12; model_level_number: 5; latitude: 144; longitude: 192)
2: x_wind / (m s-1) (model_level_number: 5; latitude: 144; longitude: 192)

When :func:`iris.load` attempts to merge these cubes, it creates a cube for every unique ``surface_altitude`` coordinate.
Note that since there is only one time point associated with the last cube, the "time" coordinate has not been promoted
to a dimension. The ``surface_altitude`` in each of the above cubes is 2D, however, since some of these coordinates
already have a time dimension, it is not possible to use :func:`~iris.util.new_axis` as above to promote
``surface_altitude`` as we have done above.

In order to fully control the merge process we instead use :func:`iris.load_raw`:

>>> raw_cubes = iris.load_raw(filename, constraints="x_wind")
>>> print(raw_cubes)
0: x_wind / (m s-1) (latitude: 144; longitude: 192)
1: x_wind / (m s-1) (latitude: 144; longitude: 192)
...
73: x_wind / (m s-1) (latitude: 144; longitude: 192)
74: x_wind / (m s-1) (latitude: 144; longitude: 192)

The raw cubes also separate cubes along the ``model_level_number`` dimension. In this instance, we will need to
merge/concatenate along two different dimensions. Specifically, we can merge by promoting the ``model_level_number`` to
a dimension, since ``surface_altitude`` does not vary along this dimension, and we can concatenate along the ``time``
dimension as before. We expand the ``time`` dimension first, as before:

>>> processed_raw_cubes = CubeList(
... [new_axis(cube, scalar_coord="time", expand_extras=["surface_altitude", "forecast_period"]) for cube in raw_cubes]
... )
>>> print(processed_raw_cubes)
0: x_wind / (m s-1) (time: 1; latitude: 144; longitude: 192)
1: x_wind / (m s-1) (time: 1; latitude: 144; longitude: 192)
...
73: x_wind / (m s-1) (time: 1; latitude: 144; longitude: 192)
74: x_wind / (m s-1) (time: 1; latitude: 144; longitude: 192)

Then we merge, promoting the different ``model_level_number`` scalar coordinates to a dimension coordinate.
Note, however, that merging these cubes does *not* affect the ``time`` dimension, since merging only
applies to scalar coordinates, not dimension coordinates of length 1.

>>> merged_cubes = processed_raw_cubes.merge()
>>> print(merged_cubes)
0: x_wind / (m s-1) (model_level_number: 5; time: 1; latitude: 144; longitude: 192)
1: x_wind / (m s-1) (model_level_number: 5; time: 1; latitude: 144; longitude: 192)
...
13: x_wind / (m s-1) (model_level_number: 5; time: 1; latitude: 144; longitude: 192)
14: x_wind / (m s-1) (model_level_number: 5; time: 1; latitude: 144; longitude: 192)

Once merged, we can now concatenate all these cubes into a single result cube, which is what we wanted:

>>> result = merged_cubes.concatenate_cube()
>>> print(result)
x_wind / (m s-1) (model_level_number: 5; time: 15; latitude: 144; longitude: 192)
Dimension coordinates:
model_level_number x - - -
time - x - -
latitude - - x -
longitude - - - x
Auxiliary coordinates:
level_height x - - -
sigma x - - -
forecast_period - x - -
surface_altitude - x x x
Derived coordinates:
altitude x x x x
Scalar coordinates:
forecast_reference_time 2006-01-01 00:00:00
Cell methods:
0 time: mean (interval: 1 hour)
Attributes:
STASH m01s00i002
source 'Data from Met Office Unified Model'
um_version '12.1'

.. todo::
Mention the work done in #6168
3 changes: 2 additions & 1 deletion docs/src/further_topics/index.rst
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netcdf_io
dask_best_practices/index
ugrid/index
which_regridder_to_use
which_regridder_to_use
controlling_merge

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