# Colouring anomaly data with logarithmic scaling¶

In this example, we need to plot anomaly data where the values have a “logarithmic” significance – i.e. we want to give approximately equal ranges of colour between data values of, say, 1 and 10 as between 10 and 100.

As the data range also contains zero, that obviously does not suit a simple logarithmic interpretation. However, values of less than a certain absolute magnitude may be considered “not significant”, so we put these into a separate “zero band” which is plotted in white.

To do this, we create a custom value mapping function (normalization) using the matplotlib Norm class matplotlib.colours.SymLogNorm. We use this to make a cell-filled pseudocolour plot with a colorbar.

NOTE: By “pseudocolour”, we mean that each data point is drawn as a “cell”
region on the plot, coloured according to its data value.
This is provided in Iris by the functions `iris.plot.pcolor()`

and
`iris.plot.pcolormesh()`

, which call the underlying matplotlib
functions of the same names (i.e. matplotlib.pyplot.pcolor
and matplotlib.pyplot.pcolormesh).
See also: http://en.wikipedia.org/wiki/False_color#Pseudocolor.

```
"""
Colouring anomaly data with logarithmic scaling
===============================================
In this example, we need to plot anomaly data where the values have a
"logarithmic" significance -- i.e. we want to give approximately equal ranges
of colour between data values of, say, 1 and 10 as between 10 and 100.
As the data range also contains zero, that obviously does not suit a simple
logarithmic interpretation. However, values of less than a certain absolute
magnitude may be considered "not significant", so we put these into a separate
"zero band" which is plotted in white.
To do this, we create a custom value mapping function (normalization) using
the matplotlib Norm class `matplotlib.colours.SymLogNorm
<http://matplotlib.org/api/colors_api.html#matplotlib.colors.SymLogNorm>`_.
We use this to make a cell-filled pseudocolour plot with a colorbar.
NOTE: By "pseudocolour", we mean that each data point is drawn as a "cell"
region on the plot, coloured according to its data value.
This is provided in Iris by the functions :meth:`iris.plot.pcolor` and
:meth:`iris.plot.pcolormesh`, which call the underlying matplotlib
functions of the same names (i.e. `matplotlib.pyplot.pcolor
<http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.pcolor>`_
and `matplotlib.pyplot.pcolormesh
<http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.pcolormesh>`_).
See also: http://en.wikipedia.org/wiki/False_color#Pseudocolor.
"""
import cartopy.crs as ccrs
import iris
import iris.coord_categorisation
import iris.plot as iplt
import matplotlib.pyplot as plt
import matplotlib.colors as mcols
def main():
# Load a sample air temperatures sequence.
file_path = iris.sample_data_path('E1_north_america.nc')
temperatures = iris.load_cube(file_path)
# Create a year-number coordinate from the time information.
iris.coord_categorisation.add_year(temperatures, 'time')
# Create a sample anomaly field for one chosen year, by extracting that
# year and subtracting the time mean.
sample_year = 1982
year_temperature = temperatures.extract(iris.Constraint(year=sample_year))
time_mean = temperatures.collapsed('time', iris.analysis.MEAN)
anomaly = year_temperature - time_mean
# Construct a plot title string explaining which years are involved.
years = temperatures.coord('year').points
plot_title = 'Temperature anomaly'
plot_title += '\n{} differences from {}-{} average.'.format(
sample_year, years[0], years[-1])
# Define scaling levels for the logarithmic colouring.
minimum_log_level = 0.1
maximum_scale_level = 3.0
# Use a standard colour map which varies blue-white-red.
# For suitable options, see the 'Diverging colormaps' section in:
# http://matplotlib.org/examples/color/colormaps_reference.html
anom_cmap = 'bwr'
# Create a 'logarithmic' data normalization.
anom_norm = mcols.SymLogNorm(linthresh=minimum_log_level,
linscale=0,
vmin=-maximum_scale_level,
vmax=maximum_scale_level)
# Setting "linthresh=minimum_log_level" makes its non-logarithmic
# data range equal to our 'zero band'.
# Setting "linscale=0" maps the whole zero band to the middle colour value
# (i.e. 0.5), which is the neutral point of a "diverging" style colormap.
# Create an Axes, specifying the map projection.
plt.axes(projection=ccrs.LambertConformal())
# Make a pseudocolour plot using this colour scheme.
mesh = iplt.pcolormesh(anomaly, cmap=anom_cmap, norm=anom_norm)
# Add a colourbar, with extensions to show handling of out-of-range values.
bar = plt.colorbar(mesh, orientation='horizontal', extend='both')
# Set some suitable fixed "logarithmic" colourbar tick positions.
tick_levels = [-3, -1, -0.3, 0.0, 0.3, 1, 3]
bar.set_ticks(tick_levels)
# Modify the tick labels so that the centre one shows "+/-<minumum-level>".
tick_levels[3] = r'$\pm${:g}'.format(minimum_log_level)
bar.set_ticklabels(tick_levels)
# Label the colourbar to show the units.
bar.set_label('[{}, log scale]'.format(anomaly.units))
# Add coastlines and a title.
plt.gca().coastlines()
plt.title(plot_title)
# Display the result.
iplt.show()
if __name__ == '__main__':
main()
```

(Source code, png)