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In example 7.3 ("Cell areas for a spherical geodesic grid") the standard_name for the area of the grid cell is given as "area", which is not in the current standard_name table. The correct standard_name for this variable is "cell_area", so a correction of this defect should be made.

1. Title

Add absolute value statistics to cell methods

2. Moderator

David Hassell

3. Requirement

The statistics mabs/mibs/mebs stand for "Maximum absolute value", "Minimum absolute value", and "Mean absolute value", respectively. They are similar to max/min/mean statistics, and they can be useful in characterizing data when one wants positive-definite metrics. mebs (unlike mean) does not allow positive and negative values to compensate eachother. Unlike rms, mebs not does weight outliers quadratically. NCO implements mabs/mibs/mebs as fundamental statistics (like max/min/mean), and annotates the cell_methods attribute of variables reduced by these statistics with the strings "maximum_absolute_value", "minimum_absolute_value", "mean_absolute_value".

4. Initial Statement of Technical Proposal

This recommendation could be implemented in CF by inserting the following lines into Table E.1. Cell Methods

​http://cfconventions.org/Data/cf-conventions/cf-conventions-1.7/build/cf-conventions.html#appendix-cell-methods

cell_methods:		Units:	Description:
maximum_absolute_value	u	Maximum absolute value
minimum_absolute_value	u	Minimum absolute value
mean_absolute_value	u	Mean absolute value

5. Benefits

This would improve the CF-compliance of fields processed by absolute-value statistics.

6. Status Quo

There is no standard CF terminology to describe absolute-value statistics so fields analyzed with these methods may have missing, erroneous, or non-standard cell_methods for this stage of processing. Unless the statistics were computed with NCO which has implemented the proposed cell_methods since February, 2015.

Based on a statement appearing in the conformance document, the CF checker raises an error when the formula_terms attribute is attached to a variable other than a coordinate variable. It turns out that formula_terms are essential for interpreting the bounds on dimensionless vertical coordinates, so formula_terms should be provided whenever a variable with one of the standard_names listed in Appendix C appears in a file. The formula terms associated with bounds are needed, for example, to compute the pressure-thickness of model atmospheric layers (needed to compute the grid cell mass).

To correct this defect (and remove any impression that the formula_terms can *only* be attached to coordinate variables (as formally defined by the NUG), I propose:

1. In section 1.3 Overview, the standard states: "The definitions are associated with a coordinate variable via the standard_name and formula_terms attributes." I would revise the sentence to read: "The definitions are associated with variables containing dimensionless coordinate values via the standard_name and formula_terms attributes."

2. Similarly in section 1.4 Relationship to the COARDS Conventions, the standard states: "But we recommend that the standard_name and formula_terms attributes be used to identify the appropriate definition of the dimensionless vertical coordinate ...". I would revise the sentence to read: "But we recommend that the standard_name and formula_terms attributes be used to identify the appropriate definition of a variable storing dimensionless vertical coordinate values ...".

3. In Chapter 4 Coordinate Variables. The standard states "The definitions are associated with a coordinate variable via the standard_name and formula_terms attributes." I would revise the sentence to read: "The definitions are associated with variables containing dimensionless vertical coordinate values via the standard_name and formula_terms attributes."

4. In section 4.3.2. Dimensionless Vertical Coordinates, the standard states: "A new attribute, formula_terms, is used to associate terms in the definitions with variables in a netCDF file." I would add to this sentence the phrase ", as described in Appendix D".

5. In Appendix D. Dimensionless Vertical Coordinates, the standard states: "A coordinate variable is associated with its definition by the value of the standard_name attribute. The terms in the definition are associated with file variables by the formula_terms attribute. The formula_terms attribute takes a string value, the string being comprised of blank-separated elements of the form "term: variable", where term is a keyword that represents one of the terms in the definition, and variable is the name of the variable in a netCDF file that contains the values for that term. The order of elements is not significant." I would add to this paragraph the sentence: "Use of the standard_names and formula_terms defined in this Appendix is not limited to coordinate variables (as defined in section 2.3.1 of the NUG); it is recommended that they be included for any variable storing dimensionless vertical coordinate values."

6. The CF Conformance Requirements and Recommendations document currently states: "The formula_terms attribute is only allowed on a coordinate variable which has a standard_name listed in Appendix C." In addition to correcting "Appendix C" to read "Appendix D", I suggest modifying the sentence as follows: "The formula_terms attribute is only allowed on a variable that has a standard_name listed in Appendix D or contains coordinates bounds for a coordinate variable defined in Appendix D." [Note that this means we can have formula_terms associated with *any* variable that has a standard_name listed in the Appendix.]

7. The current CF checker(s) should be revised to be consistent with the above change in the conformance document.

A final note: In CMIP5 (and as planned for CMIP6), formula_terms are defined for vertical dimensionless coordinates and also for the bounds on those coordinates. If the CF checker is modified as suggested above, it will no longer raise an error in checking CMIP output files.