Units of Measure

Definitions of Units of Measure used in MMS data product files:

• Densities: [cm^-3]
• Speed, Velocities : [km/s]
• Angles, Phase shifts : [deg]
• Pressures (plasma - dynamic, thermal, magnetic): [nPa]
• Temperatures: [eV]
• HeatFlux: [mW/m^2]
• Entropy: [J/K]
• Electric Field: [mV/m]
• Probe to Spacecraft Potential: [V]
• Electric Field Power Spectral Density : [(V/m)^2/Hz]
• ExB velocity: [km/s]
• Poynting Flux : [mW/m^2]
• Magnetic Field: [nT]
• Magnetic field power spectral density: [nT^2/Hz]
• Current density: [nA/m^2]
• Differential Number Flux: [cm^-2 s^-1 sr^-1 eV^-1]
• Differential Energy Flux: eV [cm^-2 s^-1 sr^-1 eV^-1]
• Earth radius: 6371.2 km
• Distance: [km]
• Date/Time (PROPOSED): ISO8601 standard (e.g. YYYY-MM-DDTHH:MM:SS.SSS or YYYY-DDDTHH:MM:SS.SSS)

MMS Team members are welcome to ADD ADDITIONAL QUANTITIES as they are defined.

The CDF Format Guide requires that UNITS and SI_CONVERSION must be specified for each parameter.

• It is proposed that conventions should be defined, so that a standard nomenclature is used for these metadata. 
• UNITS attribute
  • units in Level 2 CDF files shall be taken from the list above
  • The units shall be specified as a human-readable ASCII string, using the abbreviations listed above. 
  • guidelines for unit nomenclature are proposed, below.
• SI_CONVERSION attribute
  • Gives the conversion from the MMS unit of measure to SI units
  • This attribute allows for plotting/analysis tools to combine MMS data with data from other missions which use different units. 
  • Guidelines for SI unit nomenclature are proposed, below.
  • Requires guidelines for syntax, which are also included below.

Proposed convention for unit nomenclature and SI conversion attribute:

• SI unit symbols to be used for SI conversion (rather than SI unit names) without SI prefixes: e.g. T, rather than nT or Tesla; sr, rather than steradians.
  The SI_CONVERSION from nT would then be "1.0e-9>T".
• SI prefixes are allowed in variable units, but not in the converted SI unit (units of [km] are required for distances, but the SI conversion must be to [m]).
• Note that the SI unit for angles is radians [rad]. 
  The SI_CONVERSION for angles (in degrees as defined above) would be "pi/180>rad" (Alternative 1: uses division in unit conversion but preserves precision.)
  The SI_CONVERSION for angles (in degrees as defined above) would be "0.0174532925>rad" (Alternative 2: gives number in unit conversion but loses precision.)
• Dimensionless variables are required (by ISTP standard) to be a blank character. For consistency the conversion should also be a blank character.
  The SI_CONVERSION for a dimensionless variable would be " > ".
• Units that are already SI (e.g. Hz, V) will have a multiplicative factor of 1, so the SI_CONVERSION for spacecraft potential would be "1.0>V".

Proposed convention for compound units:  [Note: this is proposed for the sake of consistency to facilitate future automation using this metadata]

• Compound units should be denoted by exponents only, with unit symbols separated by white space, as illustrated by the following examples:
  Area  - [m^2], not [m m]
  Acceleration - [m s^-2] (or with LaTeX markup - see note - [m s^{-2}]), not [m/s/s] or [m/s^2]
• Only dimensional units should be used. For example, a number density would have units of [cm^{-3}] not [#/cm^{3}]. Similarly an electron number flux would have units of [cm^-2 s^-1 sr^-1 eV^-1], not [#/(cm^-2 s^-1 sr^-1 eV^-1)] or [e/(cm^-2 s^-1 sr^-1 eV^-1)].

Additional note: Unless there's a reason not to, I suggest LaTeX math notation for the exponents, so the units for acceleration would be [m s^{-1}]

• • This is usable through IDL with the graphics routines from "Coyote's guide" (David Fanning) or the TexToIDL package.
  • This is usable through MATLAB, which directly supports TeX markup in graphics by specifying an interpreter to the text object.
  • This is usable in Python through the graphics package matplotlib, which can use LaTeX to render the text in graphics output for several plotting backends.
  • LaTeX is directly supported by GNUplot, in case anyone still uses that!
  • Where this isn't currently supported is Autoplot, though it may not be difficult for Jeremy to support basic TeX-style markup for units.
  • If LaTeX markup is allowed here then there is no reason people can't use it to give equations in other attributes, which could be handy when defining calculated quantities.