Add functionality to convert a forecast to a climatological anomaly

[brhooper]

As an IMPROVER scientist wishing to develop SAMOS functionality in IMPROVER, I need a utility function to allow me to convert an input cube of data to a cube containing anomaly data.

This function should take as inputs:

• a cube containing diagnostic data to be converted to anomalies (e.g screen temperature data)
• a cube containing a mean average of that diagnostic (e.g mean screen temperature over a period)
• (optional) a cube containing a variance of that diagnostic (e.g screen temperature variance over a period)

the following calculation should then be performed:

if variance input present:
standardised_anomaly = (data - mean) / sqrt(variance)

else:
anomaly = data - mean

Acceptance criteria

• Plugin added to IMPROVER for creating a cube of climatological anomalies.
• Unit tests demonstrating the proper functioning of the new plugin

[brhooper]

This functionality might neatly fit in improver/utilities/mathematical_operations.py.

[gavinevans]

An example of such a function serving a similar purpose can be seen in the standardise_forecast_and_truths function in these branches:

• mobt_428_samos_plus
• mobt_535_samos

[brhooper]

@maxwhitemet and I discussed this ticket this morning to come up with an implementation plan. We expect that the new functionality will look something like as follows:

class calculate_climate_anomalies
  def init
  	# initialisation
  def verify_inputs
  	# confirm that input data makes sense
        # this could involve checking that the input data shapes are compatible,
        # and that the time bounds of the mean and variance cubes contain the time of the data cube
  def create_output_cube
  	# setup correct metadata
  def calculate_anomalies
  	# do the calculation here
  def process
        # call the previously defined functions
  output

[maxwhitemet]

Why a reference_epoch coordinate was added to the output cube
The reference_epoch coordinate records the time-bounds of the mean cube (i.e. 'climatology') with respect to which the anomaly was calculated. Bruce identified the need to implement this coordinate to align with the conventions for anomalies discussed in this CF-convention issue.