Collapsing Entire Data Dimensions¶
In the Subsetting a Cube section we saw how to extract a subset of a cube in order to reduce either its dimensionality or its resolution. Instead of simply extracting a sub-region of the data, we can produce statistical functions of the data values across a particular dimension, such as a ‘mean over time’ or ‘minimum over latitude’.
For instance, suppose we have a cube:
>>> import iris >>> filename = iris.sample_data_path('uk_hires.pp') >>> cube = iris.load_cube(filename, 'air_potential_temperature') >>> print(cube) air_potential_temperature / (K) (time: 3; model_level_number: 7; grid_latitude: 204; grid_longitude: 187) Dimension coordinates: time x - - - model_level_number - x - - grid_latitude - - x - grid_longitude - - - x Auxiliary coordinates: forecast_period x - - - level_height - x - - sigma - x - - surface_altitude - - x x Derived coordinates: altitude - x x x Scalar coordinates: forecast_reference_time 2009-11-19 04:00:00 Attributes: STASH m01s00i004 source Data from Met Office Unified Model um_version 7.3
In this case we have a 4 dimensional cube;
to mean the vertical (z) dimension down to a single valued extent
we can pass the coordinate name and the aggregation definition to the
>>> import iris.analysis >>> vertical_mean = cube.collapsed('model_level_number', iris.analysis.MEAN) >>> print(vertical_mean) air_potential_temperature / (K) (time: 3; grid_latitude: 204; grid_longitude: 187) Dimension coordinates: time x - - grid_latitude - x - grid_longitude - - x Auxiliary coordinates: forecast_period x - - surface_altitude - x x Derived coordinates: altitude - x x Scalar coordinates: forecast_reference_time 2009-11-19 04:00:00 level_height 696.6666 m, bound=(0.0, 1393.3333) m model_level_number 10, bound=(1, 19) sigma 0.92292976, bound=(0.8458596, 1.0) Cell methods: mean model_level_number Attributes: STASH m01s00i004 source Data from Met Office Unified Model um_version 7.3
Similarly other analysis operators such as
can be used instead of
iris.analysis for a full list
of currently supported operators.
For an example of using this functionality, the
Hovmoller Diagram of Monthly Surface Temperature
in the gallery takes a zonal mean of an
XYT cube by using the
collapsed method with
iris.analysis.MEAN as arguments.
Some operators support additional keywords to the
a weights keyword which can be combined with
iris.analysis.cartography.area_weights() to calculate an area average.
Let’s use the same data as was loaded in the previous example.
grid_longitude were both point coordinates
we must guess bound positions for them
in order to calculate the area of the grid boxes:
import iris.analysis.cartography cube.coord('grid_latitude').guess_bounds() cube.coord('grid_longitude').guess_bounds() grid_areas = iris.analysis.cartography.area_weights(cube)
These areas can now be passed to the
collapsed method as weights:
>>> new_cube = cube.collapsed(['grid_longitude', 'grid_latitude'], iris.analysis.MEAN, weights=grid_areas) >>> print(new_cube) air_potential_temperature / (K) (time: 3; model_level_number: 7) Dimension coordinates: time x - model_level_number - x Auxiliary coordinates: forecast_period x - level_height - x sigma - x Derived coordinates: altitude - x Scalar coordinates: forecast_reference_time 2009-11-19 04:00:00 grid_latitude 1.5145501 degrees, bound=(0.14430022, 2.8848) degrees grid_longitude 358.74948 degrees, bound=(357.494, 360.00497) degrees surface_altitude 399.625 m, bound=(-14.0, 813.25) m Cell methods: mean grid_longitude, grid_latitude Attributes: STASH m01s00i004 source Data from Met Office Unified Model um_version 7.3
Several examples of area averaging exist in the gallery which may be of interest, including an example on taking a global area-weighted mean.
Partially Reducing Data Dimensions¶
Instead of completely collapsing a dimension, other methods can be applied to reduce or filter the number of data points of a particular dimension.
Aggregation of Grouped Data¶
combines data for all points with the same value of a given coordinate.
To do this, you need a coordinate whose points take on only a limited set
of different values – the number of these then determines the size of the
iris.coord_categorisation module can be used to make such
‘categorical’ coordinates out of ordinary ones: The most common use is
to aggregate data over regular time intervals,
such as by calendar month or day of the week.
For example, let’s create two new coordinates on the cube to represent the climatological seasons and the season year respectively:
import iris import iris.coord_categorisation filename = iris.sample_data_path('ostia_monthly.nc') cube = iris.load_cube(filename, 'surface_temperature') iris.coord_categorisation.add_season(cube, 'time', name='clim_season') iris.coord_categorisation.add_season_year(cube, 'time', name='season_year')
The ‘season year’ is not the same as year number, because (e.g.) the months
Dec11, Jan12 + Feb12 all belong to ‘DJF-12’.
Printing this cube now shows that two extra coordinates exist on the cube:
>>> print(cube) surface_temperature / (K) (time: 54; latitude: 18; longitude: 432) Dimension coordinates: time x - - latitude - x - longitude - - x Auxiliary coordinates: clim_season x - - forecast_reference_time x - - season_year x - - Scalar coordinates: forecast_period 0 hours Cell methods: mean month, year Attributes: Conventions CF-1.5 STASH m01s00i024
These two coordinates can now be used to aggregate by season and climate-year:
>>> annual_seasonal_mean = cube.aggregated_by( ... ['clim_season', 'season_year'], ... iris.analysis.MEAN) >>> print(repr(annual_seasonal_mean)) <iris 'Cube' of surface_temperature / (K) (time: 19; latitude: 18; longitude: 432)>
The primary change in the cube is that the cube’s data has been reduced in the ‘time’ dimension by aggregation (taking means, in this case). This has collected together all data points with the same values of season and season-year. The results are now indexed by the 19 different possible values of season and season-year in a new, reduced ‘time’ dimension.
We can see this by printing the first 10 values of season+year from the original cube: These points are individual months, so adjacent ones are often in the same season:
>>> for season, year in zip(cube.coord('clim_season')[:10].points, ... cube.coord('season_year')[:10].points): ... print(season + ' ' + str(year)) mam 2006 mam 2006 jja 2006 jja 2006 jja 2006 son 2006 son 2006 son 2006 djf 2007 djf 2007
Compare this with the first 10 values of the new cube’s coordinates: All the points now have distinct season+year values:
>>> for season, year in zip( ... annual_seasonal_mean.coord('clim_season')[:10].points, ... annual_seasonal_mean.coord('season_year')[:10].points): ... print(season + ' ' + str(year)) mam 2006 jja 2006 son 2006 djf 2007 mam 2007 jja 2007 son 2007 djf 2008 mam 2008 jja 2008
Because the original data started in April 2006 we have some incomplete seasons (e.g. there were only two months worth of data for ‘mam-2006’). In this case we can fix this by removing all of the resultant ‘times’ which do not cover a three month period (note: judged here as > 3*28 days):
>>> tdelta_3mth = datetime.timedelta(hours=3*28*24.0) >>> spans_three_months = lambda t: (t.bound - t.bound) > tdelta_3mth >>> three_months_bound = iris.Constraint(time=spans_three_months) >>> full_season_means = annual_seasonal_mean.extract(three_months_bound) >>> full_season_means <iris 'Cube' of surface_temperature / (K) (time: 17; latitude: 18; longitude: 432)>
The final result now represents the seasonal mean temperature for 17 seasons from jja-2006 to jja-2010:
>>> for season, year in zip(full_season_means.coord('clim_season').points, ... full_season_means.coord('season_year').points): ... print(season + ' ' + str(year)) jja 2006 son 2006 djf 2007 mam 2007 jja 2007 son 2007 djf 2008 mam 2008 jja 2008 son 2008 djf 2009 mam 2009 jja 2009 son 2009 djf 2010 mam 2010 jja 2010