# Aggregation rules¶

David Hassell and Jonathan Gregory

Version 3.0.3 for version 1.7 of the CF conventions.

These rules are be used for deciding whether or not two arbitrary field constructs may be aggregated into one, larger field construct. These rules are based solely on the field constructs’ metadata as recognised by the CF data model.

Aggregation is the combination of one field construct into another to create a new field construct that occupies a “larger” domain. In practice, this means combining two field constructs so that their data concatenated along exactly one domain axis, as are the data of their metadata constructs which span that domain axis.

More than two field constructs are be aggregated by repeated applications of the aggregation algorithm, and aggregations over multiple domain axes are similarly possible.

If all of the following statements are true for two arbitrary field constructs then the two field constructs may be aggregated to a new field construct.

• Both field constructs have identical standard name properties.
• The treatment of other properties, in terms of how they should match between the field constructs and whether or not they should be included in the aggregated field, is beyond the scope of these rules and is at the user’s discretion. This is also the case for all other construct properties unnamed by these rules.

Coordinate construct

A coordinate construct is either a dimension coordinate construct or an auxiliary coordinate construct.

Pair of matching coordinate constructs

A pair of matching coordinate constructs is a coordinate construct from each field construct of the same type (dimension or auxiliary), with equivalent calendar properties (if present) and identical standard names.

• Both field constructs have the same number of coordinate constructs, all of which have a standard name property, and each coordinate construct’s standard name is unique within its field construct. Each coordinate construct in one field construct forms a pair of matching coordinate constructs with a unique coordinate construct in the other field construct.

Domain axis’s associated coordinate constructs

A domain axis’s associated coordinate constructs are those coordinate constructs which span the domain axis.

• Each domain axis in both field constructs has at least one associated 1-d coordinate construct.

Pair of matching axes

A pair of matching axes is a domain axis from each field construct chosen such that the two domain axes have associated coordinate constructs that are all matching pairs.

• Each domain axis in one field construct forms a pair of matching axes with a unique domain axis in the other field construct.
• A consequence of this rule is that within each pair of matching coordinate constructs, the corresponding domain axes are matching pairs.

Pair of aggregating axes

The pair of matching axes for which one or more of the 1D matching coordinate constructs have different values for their coordinate arrays and, if present, their boundary coordinate arrays is called the pair of aggregating axes.

• There is exactly one pair of matching axes for which one or more of the 1D matching coordinate constructs have different values for their coordinate arrays and, if present, their boundary coordinate arrays.
• A pair of matching non-aggregating axes must have identical sizes.
• The aggregating axis may have either the same size or a different size in the two field constructs.
• If the domain axes of the arrays of matching associated constructs are ordered differently or run in different senses then one of the arrays must be rearranged prior to comparison. This is true for all array comparisons in these rules.
• If neither field construct has an aggregating axis then the field constructs are not aggregatable because their domains are identical.
• If either field construct has two or more domain axes which could qualify as an aggregating axis then the field constructs are not aggregatable because it is not possible to choose the single domain axis for array concatenation.

Pair of matching cell measure constructs

A pair of matching cell measure constructs is a cell measure construct from each field construct with equivalent units and corresponding domain axes that are matching pairs.

• Both field constructs have the same number of cell measure constructs, all of which have a units property. Each cell measure construct in either field construct forms a pair of matching cell measure constructs with a unique cell measure construct in the other field construct.
• Each pair of matching coordinate constructs and matching cell measure constructs that do not span their aggregating axes have identical values for their coordinate arrays and, if present, their boundary coordinate arrays.
• If the pair of matching aggregating axes has a pair of associated dimension coordinate constructs, then there are no common values in their coordinate arrays. If the matching dimension coordinate constructs have boundary coordinate arrays then no cells from one dimension coordinate construct lie entirely within any cell of the other dimension coordinate construct.
• This does not preclude the coordinate arrays’ ranges from overlapping.
• The condition on the boundary coordinate arrays prevents, for example, a monthly mean being aggregated with a daily mean from the same month.
• The condition on the boundary coordinate arrays allows, for example, the aggregation of overlapping running means; or the aggregation of a monthly mean and a daily mean from a different month.
• If one field construct has a cell methods construct then so does the other field, with the equivalent methods in the same order. Corresponding domain axes in each cell methods are matching pairs.

Pair of matching domain ancillary constructs

A pair of matching domain ancillary constructs is a domain ancillary construct from each field construct for identical standard coordinate conversion terms and corresponding domain axes that are matching pairs.

• Both field constructs have the same number of domain ancillary constructs. Each domain ancillary construct in either field construct forms a pair of matching domain ancillary constructs with a unique domain ancillary construct in the other field construct.

Pair of matching field ancillary constructs

A pair of matching field ancillary constructs is a field ancillary construct from each field construct with identical standard names and corresponding domain axes that are matching pairs.

• Both field constructs have the same number of field ancillary constructs. Each field ancillary construct in either field construct forms a pair of matching field ancillary constructs with a unique field ancillary construct in the other field construct.
• Both field constructs have the same number of coordinate reference constructs. For each coordinate reference construct in one field construct there is a coordinate reference construct in the other field construct with identical name and the same set of terms, taking optional terms into account. Corresponding terms which are scalar or vector parameters are identical, taking into account equivalent units. Corresponding terms which are domain ancillary constructs form a pair of matching domain ancillary constructs.