Units of measurement

Quantitative data is always expressed using a scale, commonly referred to as the unit of measurement (UOM). The representation of any quantity can be conceived as a ‘tuple’ comprised of:

• a number

• the scale or UOM

• (optionally) a quantity-kind, which provides context and semantics for the quantity

The quantity-kind is sometimes required because the same unit of measure can be used for incompatible quantity-kinds (e.g., energy and torque can both be quantified as Newton-metres). When encoding quantities, there are three common patterns:

• Micro-format, using a standard uom notation, and separator between the number and UOM:

109.5 km/hr

• Tuple or data-structure:

	{
	"@value" : "109.5" ,
	"@type" : "https://si-digital-framework.org/SI/units/kilometre.hour-1"
	}

• Fix the UOM for an array or collection, where a header or metadata gives the uom for all values, and the datastream then provides an array of values only:

( "km/hr" , ( 60.4 , 75.1, 99.0, 109.5 ) )

For any of these approaches the code or symbol that denotes the uom must come from a well defined system with unambiguous semantics. Note that CDIF Data Description provides properties on variables for specifying both UOM and quantity-kind (see TBD), using the micro-format described in TBD).

UOM code systems¶

The following list is provided for reference, giving information about some of the common coding systems used for UOM.

SI Digital Framework - https://si-digital-framework.org/

• Scope: Semantic reference for SI base and derived units

• Maintained by BIPM https://www.bipm.org/en/ - the official custodian of the International System of Units (SI) International System of Units

• Symbols for units follow ISO/IEC 80000 (incl special characters, superscripts etc)

  • m, eV, h, km/h

• Each UOM is denoted by a URI e.g.

  • SI Units and Quantities

    • Unit https://si-digital-framework.org/SI/units/metre

• Quantity https://si-digital-framework.org/quantities/LENG

  • Unit https://si-digital-framework.org/SI/units/pascal

• Quantity https://si-digital-framework.org/quantities/PRES

  • Non-SI units accepted for use with the SI units

    • Unit https://si-digital-framework.org/SI/units/electronvolt

• Quantity https://si-digital-framework.org/quantities/ENGY

  • Unit https://si-digital-framework.org/SI/units/hour

• Quantity https://si-digital-framework.org/quantities/TIME

  • Prefixes

    • Prefix https://si-digital-framework.org/SI/prefixes/kilo

    • Prefix https://si-digital-framework.org/SI/prefixes/nano

  • URIs for compound units based on SI Units are formulated as follows:

    • Unit https://si-digital-framework.org/SI/units/kilometre.hour-1

QUDT (Quantities, Units, Dimensions and Types) - qudt.org

• Scope: semantic descriptions of UOM for science and engineering

• Enumeration of ca. 2500 UOM - qudt.org/doc/DOC_VOCAB-UNITS.html

• Each UOM is denoted by a URI - e.g.

  • http://qudt.org/vocab/unit/M

    • http://qudt.org/vocab/quantitykind/Distance

    • http://qudt.org/vocab/quantitykind/Length

  • http://qudt.org/vocab/unit/PA

    • http://qudt.org/vocab/quantitykind/Pressure

    • http://qudt.org/vocab/quantitykind/Stress

  • http://qudt.org/vocab/unit/EV

    • http://qudt.org/vocab/quantitykind/Energy

  • http://qudt.org/vocab/unit/HR

    • http://qudt.org/vocab/quantitykind/Time

    • http://qudt.org/vocab/prefix/Kilo

  • http://qudt.org/vocab/prefix/Nano

  • http://qudt.org/vocab/unit/KiloM-PER-HR

• Local-name defined by a rule (non-opaque, almost computable)

• Dereferencing URI gets a definition of the UOM, with link to dimensionality

  • Enough information to support unit conversion

  • Codes and symbols from various systems, including UCUM, SI, and UN/ECE Recommendation 20

• System also has an enumeration of ‘quantity-kinds’ - i.e. semantics

  • E.g., energy and torque have the same scale and dimensionality, but should not be transformed

• Maintained by volunteers

• Change requests processed ca. weekly - https://github.com/qudt/qudt-public-repo/issues.

UCUM (Unified Code for Units of Measure) - https://ucum.org/

• Scope: codes for UOM for science

• Terminal symbols plus a rule for constructing arbitrary units - extensible/scalable

• Codes match traditional scientific notation, with simplifications to match 7-bit ascii keyboard (no special characters, italics, superscripts) - e.g. km/hr, km.hr-1, N.m-2

• Maintained by LOINC - Biomedical/clinical standards authority

• Change requests processed slowly - https://github.com/ucum-org/ucum/issues

• Public specification document at https://ucum.org/ucum

• Validation and conversion

  • interactive https://ucum.nlm.nih.gov/ucum-lhc/demo.html

  • API https://ucum.nlm.nih.gov/ucum-service.html.