# CSN Quantity Templates

## Contents

- 1
**CSDMS Standard Names — Quantity Templates**- 1.1 Absorptance
- 1.2 Affinity
- 1.3 Age
- 1.4 Albedo
- 1.5 Altitude
- 1.6 Amplitude
- 1.7 Angle
- 1.8 Anomaly
- 1.9 Area
- 1.10 Aspect
- 1.11 Capacity
- 1.12 Charge
- 1.13 Circulation
- 1.14 Code
- 1.15 Coefficient
- 1.16 Component
- 1.17 Compressibility
- 1.18 Concentration
- 1.19 Conductance
- 1.20 Conductivity
- 1.21 Constants in Math
- 1.22 Constants in Physics
- 1.23 Content
- 1.24 Coordinate
- 1.25 Correlation
- 1.26 Count
- 1.27 Current
- 1.28 Curvature
- 1.29 Density
- 1.30 Depth
- 1.31 Diameter
- 1.32 Diffusivity
- 1.33 Dimension
- 1.34 Dimensionless Numbers
- 1.35 Discharge or Volume Flow Rate
- 1.36 Distance
- 1.37 Duration
- 1.38 Efficiency
- 1.39 Elevation
- 1.40 Emissivity
- 1.41 Emittance
- 1.42 Energy
- 1.43 Enthalpy
- 1.44 Exponent
- 1.45 Factor
- 1.46 Flag
- 1.47 Flow Rate
- 1.48 Flux
- 1.49 Force
- 1.50 Fraction
- 1.51 Frequency
- 1.52 Friction
- 1.53 Fuel Efficiency
- 1.54 Hardness
- 1.55 Head
- 1.56 Heat
- 1.57 Height
- 1.58 Humidity and Relative Saturation
- 1.59 Impedance
- 1.60 Impulse
- 1.61 Increment
- 1.62 Index
- 1.63 Inertia
- 1.64 Intensity
- 1.65 Latitude
- 1.66 Limit
- 1.67 Longitude
- 1.68 Magnitude
- 1.69 Mask
- 1.70 Mass
- 1.71 Maximum
- 1.72 Miles per Gallon
- 1.73 Minimum
- 1.74 Modulus
- 1.75 Number
- 1.76 Parameter
- 1.77 Partial Pressure
- 1.78 Perimeter
- 1.79 Period
- 1.80 Permeability
- 1.81 pH
- 1.82 Point
- 1.83 Porosity
- 1.84 Power
- 1.85 Precipitation
- 1.86 Pressure
- 1.87 Process Attributes
- 1.88 Radiation
- 1.89 Radius
- 1.90 Rate
- 1.91 Ratio
- 1.92 Reference Quantities
- 1.93 Reflectance
- 1.94 Resistance
- 1.95 Resistivity
- 1.96 Scale
- 1.97 Sinuosity
- 1.98 Slope
- 1.99 Solubility
- 1.100 Span
- 1.101 Speed
- 1.102 Step
- 1.103 Strain
- 1.104 Strength
- 1.105 Stress
- 1.106 Temperature
- 1.107 Tension
- 1.108 Term
- 1.109 Thickness
- 1.110 Threshold
- 1.111 Time
- 1.112 Time Step
- 1.113 Transmittance
- 1.114 Unit-width (and similar) Quantities
- 1.115 Velocity
- 1.116 Viscosity
- 1.117 Voltage
- 1.118 Vorticity
- 1.119 Wavelength
- 1.120 Wavenumber
- 1.121 Weight
- 1.122 Work
- 1.123 Yield

# ** CSDMS Standard Names — Quantity Templates **

- A CSDMS Standard Name must have an
and a**object part**, with adjectives and modifiers (as prefixes) being used to help avoid ambiguity and identify a specific object and a specific, associated quantity. This document contains "quantity templates". For "object templates", see:**quantity part****CSDMS Object Templates**.

- The "templates" listed below are not exhaustive, but they do address many commonly needed cases where the pattern may not be obvious. Additional templates will continue to be added over time.

- This page used to contain sections with titles like "Attributes of Channels". All of these sections have been moved to a separate page:
**CSDMS Standard Name Examples**.

- Each template includes examples and explanatory notes, and many of them make reference to the CF Standard Names, sometimes using the abbreviation "CF".

seems to be the best word choice here, see Quantity and Physical quantities. The word "attribute" is more general and may also be a good choice, but many attributes cannot be measured or quantified with a numerical value that has units. Here we define a**Quantity**as an attribute of an object that has units. (But including dimensionless units like [m/m].)**quantity**

A "quantity suffix" is a word like "anomaly", "component", "correction", "fraction", "increment", "limit", "magnitude", "offset", "scale", "step" or "threshold" (and in some cases "ratio") that produces a new quantity name from an existing quantity name (e.g. "elevation_increment", "time_step" and "length_scale"). The units are usually unchanged, but "fraction" and "ratio" are exceptions. While quantity suffixes are a common pattern in describing quantities, CSDMS is moving away from using them in standard names because they can also be expressed (with more flexibility) using an**Quantity Suffix Pattern.**. ( See the**operation prefix****CSDMS Operation Templates**.) For example, "east_velocity_component" can be expressed as "east_component_of_velocity". As an operation prefix, additional adjectives can be applied for clarity (when necessary) without losing parsability, as in "east_down_component_of_shear_stress". In addition, operations can be composed, as in "x_component_of_gradient_of_elevation", again without losing parsability.

. An optional operation name can be added in front of a quantity name to create a new quantity name that often has different units. See:**Operation_name + Quantity Pattern****CSDMS Operation Templates**.

. Many quantity names contain a**Process_name + Quantity Pattern**modifier from the standardized list of**process name****CSDMS Process Names**. Process names are nouns, not adjectives, so we would use "refraction_index" instead of "refractive_index". (Or "diffusion_coefficient" vs. "diffusive_coefficient", etc.) The templates for Process Attributes and Rates of Processes below provide many more examples.

. Some quantities require 2 objects/substances to be specified where one is contained within the other. Examples include: "concentration", "diffusion_coefficient", "partial_pressure", "relative_saturation" (see Humidity), "solubility" and "volume_fraction". CSDMS has experimented with using the reserved word "_in_" and the pattern: object = (object + "_in_" + object) for such cases as in:**Object-in-Object Quantity Pattern**

carbon_dioxide_in_air + partial_pressure carbon_dioxide_in_air + relative_saturation carbon_dioxide_in_water + solubility clay_in_soil + volume_fraction helium_plume_in_air + richardson_number sand_in_soil + volume_fraction silt_in_soil + volume_fraction visible_light_in_air + speed ## (possibly; See the Constants in Physics template.) water_vapor_in_air + dew_point_temperature water_in_atmosphere + precipitation_leq-volume_flux

- However, using this pattern causes related quantities to become alphabetically separated, like "clay_in_soil" + "volume_fraction" and "sand_in_soil" + "volume_fraction". For this reason, CSDMS is moving toward expressing the "in" relationship through object nesting (as used in the Part of Another Object Pattern). The examples listed above then become:

air_helium-plume__richardson_number air_radiation~visible__speed atmosphere_air_carbon-dioxide__partial_pressure atmosphere_air_carbon-dioxide__relative_saturation atmosphere_air_water~vapor__dew_point_temperature atmosphere_water__precipitation_leq-volume_flux soil_clay__volume_fraction soil_sand__volume_fraction soil_silt__volume_fraction water_carbon-dioxide__solubility

- As of 7/23/14, hyphens are used in certain contexts to bundle multiple words that are part of a single concept or object, such as "carbon-dioxide". This allows the object part of a name to be parsed (on underscores) into its component parts. For example, "atmosphere_carbon-dioxide" can be parsed into "atmosphere" and "carbon-dioxide". Without the hyphen, "carbon" and "dioxide" would be identified as two separate objects, with "dioxide' contained in (or a part of) "carbon".
- Note that bubble_point_temperature, dew_point_temperature and frost_point_temperature also require one substance within another, as in: air_water~vapor__dew_point_temperature. See the Temperature template.

. When using the**Saturated Quantity Rule****Object-in-object Quantity Pattern**there are several quantities that refer to a system that is saturated or "at saturation". In these cases the word "saturated" is inserted in front of the quantity name to define a new quantity. Examples include:

air_water~vapor__saturated_partial_pressure soil_water__saturated_hydraulic_conductivity soil_water__saturated_volume_fraction (i.e. water content)

- While it is true that the soil is saturated in the first two examples, we use this rule instead of inserting "saturated" as an adjective in front of soil and instead of appending a suffix like "at_saturation", which doesn't fit our (object + quantity) pattern. This rule is natural in the sense that each of the "saturated quantities" listed above would be represented by a separate variable in a model, often denoted with a subscript such as "s".

. Some quantities require 2 objects/substances to be specified where one is "on" or in contact with the other. Examples often involve friction. In such cases we use the reserved word "_on_" and the pattern: object = (object + "_on_" + object), as in:**Object-on-Object Quantity Pattern**

concrete_rubber__kinetic_friction_coefficient pavement_rubber__static_friction_coefficientNote:Maybe "-and-"or "-to-" would be better than "_on_" here. We should also list the two object names in alphabetical order to avoid two names for the same thing.

. When the quantity refers to a relationship between two objects, we use the reserved word "-to-" and the pattern: (object + "-to-" + object + quantity). The reserved word "-to-" can also be used for ratios. See the Ratio template. Examples include:**Object-to-Object Quantity Pattern**

bear_brain-to-body__mass_ratio earth-to-mars__travel_time earth-to-sun__mean_distance

- When two objects are required to define a quantity, the last 2 objects in the object part of the name are often used, as in:

carbon_hydrogen__bond_length hydrogen_oxygen__bond_energy (See: Table of bond energies.)

- In the last two examples, we put the two object names in alphabetical order to avoid two standard names for the same thing.
- We may also be able to use this pattern in constructions like: "land_subsurface-to-surface_water + seepage_rate", or "land_subsurface_water-to-surface + seepage_rate" or "ground_water-to-surface_water + seepage_rate" or "land_subsurface-to-land_surface_water + seepage_rate".

. In some cases, a quantity may apply to either of two alternate objects, as in:**Object-or-Object Quantity Pattern**

land-or-sea_surface_radiation~incoming~shortwave__energy_flux

. Although similar to the Object-to-object Quantity Pattern, this pattern is used when two quantities (measured on the same object) are needed to define a new quantity as in:**Quantity-to-Quantity Pattern**

channel_x-section__width-to-depth_ratio electron__charge-to-mass_ratio charge to mass ratio electron__mass-to-charge_ratio

- Note that "hydraulic radius" is a valid quantity name, but could also be expressed as "channel_x-section" + "wetted-area-to-perimeter_ratio".

. There are several terms that may provide a "short name" or synonym for another quantity, such as:**Short Quantity Name Synonyms**

aspect = azimuth_angle_of_antigradient_of_elevation (relative to a fixed axis) density = mass-to-volume_ratio (but density sometimes has other meanings; use "mass_density" ??) discharge = water~outgoing + volume_flow_rate slope = magnitude_of_gradient_of_elevation speed = magnitude_of_velocity (or even "motion_rate"; process_name + quantity)

. Fluxes, flows and vector quantities may either enter or exit a given object (viewed as a control volume). In these cases, it is therefore necessary to distinguish between "incoming" or "outgoing". As of 7/23/14, "incoming" and "outgoing" are used as standard adjectives in such cases, even though it is also possible to use the Process Name + Quantity Pattern and then choose a process name that indicates whether the quantity is "incoming" or "outgoing". As of 8/16/14, the adjectives "incoming" and "outgoing" (with hyphens) may be applied to the transported substance in the object part of the name. Examples include:**Incoming and Outgoing Quantity Rule**

atmosphere_top_surface_radiation~incoming~longwave__energy_flux atmosphere_top_surface_radiation~incoming~shortwave__energy_flux lake_water~incoming__volume_flow_rate lake_water~outgoing__volume_flow_rate model_grid_cell_water~incoming__volume_flow_rate model_grid_cell_water~outgoing__volume_flow_rate

- Recall that "discharge" is a short synonym for "outgoing_volume_flow_rate". (The word "discharge" connotes an "outflow".) Note that "inflow" and "outflow" are valid process names. See the Discharge template.
- Note: In the CF Standard Names, "incoming" is only used in one name (namely, "toa_incoming_shortwave_flux") while "outgoing" is used in only 6 names (always containing "toa_outgoing_longwave_flux" or "toa_outgoing_shortwave_flux"). Recall that "toa" = "top_of_atmosphere".

## Absorptance

base_quantity = "absorptance"

*Examples of Specific Quantities:*

"spectral_absorptance"

*Examples*

atmosphere_air_radiation~incoming~longwave__absorptance

- Absorptance (also called "absorptivity" and "absorption factor") is the dimensionless ratio of the radiation intensity absorbed by something to the original, incident radiation intensity. It is a number between 0 and 1.

- Absorptance + Reflectance + Transmittance = 1. See Reflectance and Transmittance below.

- Various authors recommend using the terms: Absorptivity, Emissivity, Reflectivity and Transmissivity as properties of a pure material and Absorptance, Emittance, Reflectance and Transmittance as the analogous terms for the characteristics of a specimen or sample. See: Palmer, J.M. (1994) Chapter 25: The measurement of transmission, absorption, emission and reflection, Handbook of Optics, 2nd ed., Part II, M. Bass, editor, McGraw-Hill, NY. (A PDF file is available
**here**.)

- At a given wavelength, absorptance = emittance.

- The quantity "spectral absorptance" is the absorptance associated with a specific wavelength.

- The term
**absorbance**, although similar, is a different quantity that involves a log function.

- See: Absorbance, Attenuation coefficient, Beer-Lambert law, Mass attenuation coefficient, Opacity (optics), Reflectance and Transmittance.

## Affinity

base_quantity = "affinity"

*Examples of Specific Quantities:*

"chemical_affinity"

"electron_affinity" (of an atom or molecule)

*Examples*

chlorine_electron__affinity magnesium-chloride_water__chemical_affinity sulphuric-acid_water__chemical_affinity water_electron__affinity

- Chemical affinity is defined in terms of Gibbs free energy. It is a quantity associated with two chemical species (atoms, molecules, ions, etc.) and therefore uses the
**Object-to-object Quantity Pattern**.

- See Chemical affinity, Electron affinity and Desiccant.

## Age

base_quantity = "age"

*Examples of Specific Quantities:*

"deposition_age"

*Examples*

sea_bottom_sediment__deposition_age

- The quantity
**age**indicates the elapsed time since something was first formed or created, whether it be sea ice, a person or a sediment deposit. It has units of time.

- Note that "deposition_age" follows the Process Name + Base Quantity Name Pattern.

- See Duration and Time.

## Albedo

base_quantity = "albedo"

*Examples of Specific Quantities:*

"black-sky_albedo"

"blue-sky_albedo"

"bond_albedo"

"geometric_albedo"

"visual_geometric_albedo"

"white-sky_albedo"

*Examples*

earth__bond_albedo land_surface__albedo

- Albedo (also called "reflection coefficient") is the ratio of the power per unit area [W m-2] of electromagnetic radiation
by a surface to the original,**reflected**power per unit area (or irradiance). It is a dimensionless number between 0 (for a perfectly black surface) and 1 (for a perfectly white surface). The word albedo comes from the Latin word for "whiteness".**incident**

**Reflectance**is a very closely related concept but there does not appear to be a universally accepted distinction between albedo and reflectance. Some authors take them to be equivalent, others use albedo for an average over shortwave radiation and reflectance as a function of wavelength, others describe albedo as either "diffuse reflectance" or "broadband reflectance" etc.. Dingman (2002) in his book Physical Hydrology defines albedo as the average of reflectance over visible wavelengths. This ambiguity was already recognized in a 1917 paper by Louis Bell. There have been recent efforts by Schaepman-Strub (2006) and others to standardize the terminology in descriptions of satellite surface albedo products. See Reflectance below.

- There is an important distinction between
**Bond albedo**and**Geometric albedo**, and a formula relating the two. Bond albedos are strictly between 0 and 1 while geometric albedos can be greater than 1. (Enceladus, a large moon of Saturn, reportedly has a bond albedo of 0.99 and a visual geometric albedo of 1.4.) Bond albedo takes all wavelengths and phase angles of electromagnetic radiation into account.

- To more accurately characterize the scattering properties of a surface, a Bidirectional Reflectance Distribution Function (BRDF) is often used. The integral of the BRDF over all viewing angles is called the Directional-hemispherical reflectance (DHR) or "black-sky albedo". There are two types of Bi-hemispherical reflectance (BHR). The first is often called "blue-sky albedo" (or "actual albedo"). The second -- often called "white-sky albedo" -- is the BHR under isotropic diffuse irradiance conditions (i.e. reflectance when there is only diffuse and no direct illumination, denoted as BHRiso). For many applications it is possible to approximate the albedo at a particular solar zenith angle as a linear combination of DHR (or black-sky albedo) and BHRiso (or white-sky albedo). The contribution from each is determined by D, the proportion of diffuse illumination. See: White-sky and black-sky albedo.

- A
**Lambertian surface**is an idealized model. In this sense it is similar to "black body", "channel centerline", "earth ellipsoid" or "mean-sea-level datum".

- See: Albedo, Albedo discussion, Bidirectional Reflectance Distribution Function (BRDF), Bond albedo, Geometric albedo, Irradiance, Lambert's cosine law, Lambertian reflectance and Reflectance.

## Altitude

base_quantity = "altitude"

*Examples*

airplane__altitude balloon__altitude projectile__altitude skydiver__altitude submarine_above-seafloor__altitude (need "seafloor" vs. "bottom" for clarity here)

- There is a subtle but important difference between the quantities "altitude" and "elevation". The word
**altitude**refers to the distance of an object (e.g. aircraft, air parcel or balloon) above the ground, regardless of the local elevation of the land surface. The word**elevation**refers to the distance of an object (typically a land surface) above a datum, such as the mean sea level datum. Elevation is one of the three Geographic coordinates used to specify a 3D location (i.e. elevation, latitude and longitude).

- A skydiver or aircraft pilot is interested in knowing their height above the ground, locally, especially with regard to landing. Barometric altimeters (or pressure altimeters) measure the distance above mean sea level (so elevation), but may then be corrected using a QFE setting so that they display an altitude of zero for a given airfield (regardless of its elevation above sea level). Radar and laser altimeters measure the height above the ground directly by measuring the time it takes for a signal to reflect from the land surface and return to the aircraft.

- The standard sport skydiving altitude is 12,500 feet AGL (Above Ground Level); sometimes up to 18,000 feet AGL.

- Can we also use "altitude" for the height of an object (e.g. particle, submarine) above the sea floor (i.e. height above seafloor)? Do we need an extra adjective, like "bathymetric_altitude" or "above-bottom_altitude" ? We could also use something like "particle-to-bottom" + "distance" or just "particle_bottom_distance". The current approach is to use "above-bottom" as a "place" or "part", in the
**object part**of the name.

- The standard term "equilibrium line altitude" (ELA) is discussed in the Attributes of Glaciers template.

- Note that in the CF Standard Names, "altitude" is used as a synonym for "elevation".

- See: Altitude above ground level, Elevation, Height above average terrain (HAAT), Lowest safe altitude and Mean sea level.

- See the Elevation template.

## Amplitude

base_quantity = "amplitude"

*Examples*

sea_surface_water_wave__amplitude # wave~gravity wave~airy__amplitude wave~cnoidal__amplitude wave~electromagnetic__amplitude wave~seismic__amplitude wave~stokes__amplitude

- "Amplitude" is a basic property of a periodic function or waveform, along with wavelength and wavenumber.

## Angle

base_quantity = "angle"

*Examples*

azimuth_angle, bank_angle, bond_angle, camber_angle, caster_angle, declination_angle, depression_angle, dihedral_angle, elevation_angle, exterior_angle, flare_angle, friction_angle, incidence_angle, inclination_angle, look_angle, nadir_angle, phase_angle, pitch_angle, polarization_angle, rake_angle, repose_angle, roll_angle, rotation_angle, scattering_angle, shock_angle, slope_angle, solid_angle, spreading_angle, tilt_angle, torsion_angle, vertex_angle, yaw_angle, zenith_angle

- The local
**azimuth angle**,**zenith angle**, and**elevation angle**(the complement of the zenith angle, less often called "altitude angle") that can be associated with a 2D or 3D vector field are treated as operations in the CSDMS Standard Names. See the**CSDMS Operation Templates**for more information.

- There are two major conventions used for measuring angles. For
**bearings**, the angle is usually measured, and this typically includes wind data. (We also need to clarify whether the wind is blowing "to" or "from" that direction.) Most other angles are measured the way you learned in high school,**clockwise from north**(or from the east). It is therefore important to specify the convention that is used. This can be done by including the appropriate <assume> tag in a model's Model Metadata File, chosen from the standardized assumption names on the**counterclockwise from the x-axis****CSDMS Assumption Names**page. A smart framework would be able to convert between these two conventions, when necessary, after examining these <assume> tags.**Note:**We could also introduce "bearing" as another base quantity so that the metadata wouldn't be necessary.

- A
**bearing**(to an observed object) can also be specified relative to the direction of travel of a vehicle (e.g. truck, ship or airplane) instead of relative to north. See: Bearing (navigation).

- A
**heading**is the direction (usually given as a bearing) in which an object, such as a ship or airplane, is traveling. It is related to the**course**and**track angle**; see: Course (navigation).

- Note that "earth_axis" + "tilt_angle" uses the object name "earth_axis" to refer to a "part" of the Earth (
**Part of Another Object Pattern**) and the quantity name "tilt_angle" follows the**Process_name + Quantity Pattern**. We use "tilt" vs. "tilting" as allowed by one of the Basic Rules. We use "earth_axis__tilt_angle" vs. "earth" + "axial_tilt_angle" in accordance with the**Object vs. Adjective Rule**.

- In the context of a satellite or airplane viewing the Earth's surface, the terms
**look angle**and**nadir angle**are used to indicate the angle between straight down from the satellite (i.e. the nadir direction) and the ray that points from the satellite to a location on the Earth's surface. The complement of the "look angle" is often called the**depression angle**. The term "off-nadir angle" would be more descriptive but is not as widely used. "Zenith angle" and "elevation angle" are also complementary angles, typically used for a viewer on Earth's surface looking up at an object in the sky (e.g. the sun or a planet).**Note**: The terms "view angle" or "viewing angle" should not be used in this context because they have other, more common meanings related to a camera's "angle of view" or the angles from which a TV or monitor are being viewed.

- In the CSDMS Standard Names, the quantities "azimuth_angle_of_position_vector", "elevation_angle_of_position_vector" and "zenith_angle_of_position_vector" are used for an object viewed from the Earth's surface (e.g. satellite), while "azimuth_angle_of_look_vector", "depression_angle_of_look_vector", "nadir_angle_of_look_vector" are used for objects on the Earth's surface viewed from above (e.g. a satellite).

- The quantity
**angle_of_repose**is called "repose_angle" in the CSDMS Standard Names. This may sound a bit strange when spoken, but this is outweighed by the benefits of following a standardized pattern.

- Many of these follow the
**Process_name + Quantity Pattern**.

- CSDMS standard names use "aspect_angle" vs. "aspect" for clarity since we distinguish between "slope" and "slope_angle".

- bank_angle is related to banking (e.g. aircraft) in turns but may also be used in the context of channel banks. The object part of the name allows the same quantity name to be used in different contexts.

- In the context of wheeled vehicles, several angles are used such as: Camber angle and Caster angle (or Rake angle).

- Three Euler angles can be used to describe the orientation of a rigid body, but different conventions are used. These would have some adjective(s) inserted before "euler_angle".

- The term
**flare angle**refers to an angle measured from the vertical or main axis. The verb "flare" means to gradually become wider. (e.g. bell-bottom pants) The term "spreading_angle" is very similar.

## Anomaly

operation_prefix = "anomaly_of"

*Examples*

atmosphere_air__anomaly_of_pressure (i.e. difference from climatology) atmosphere_air__anomaly_of_temperature sea_surface_water__anomaly_of_geopotential_height sea_surface_water__anomaly_of_temperature

- Before 3/19/13 this was treated as a
**quantity suffix**, but now it is treated as an "operation prefix". It does not change the units. See Component, Increment and Magnitude.

- Means the "difference from climatology" in CF Standard Names. The "mean climatology" used as a reference should be specified in the Model Metadata File with an <assume> tag. See Reference Quantities.

- The word "anomaly" is used in 4 CF Standard Names, namely:

air_pressure_anomaly air_temperature_anomaly geopotential_height_anomaly surface_temperature_anomaly

## Area

base_quantity = "area"

*Examples of Specific Quantities:*

"surface_area"

*Examples*

basin_outlet__total_contributing_area channel_x-section__area glacier_surface__area lake_surface__area sphere_surface__area

- This quantity can be defined for any polygon and has units of length squared.

- The quantity "surface_area" can be defined for a surface that lies above some planar domain. However, this is usually not what is meant by the term "area". For CSDMS Standard Names, use "surface_area" for this situation and "area" otherwise.

- Several different terms are used for the area of a drainage basin, such as "drainage area", "contributing area", "upstream contributing area", "total contributing area (TCA)" and "specific contributing area (SCA)". A drainage basin can be viewed as a polygon with a well-defined area. The terms "total contributing area" (TCA) and "specific contributing area" (SCA) are used in reference to the region that contributes flow to an arbitrary line segment placed perpendicular to the flow direction at some point in a landscape. SCA is then defined as TCA divided by the length of this segment.

- When "surface" is used in connection with a body of water or ice, it indicates the top of that body and the area is the map view area.

## Aspect

base_quantity = "angle"

*Examples of Specific Quantities:*

"aspect_angle"

*Examples*

land_surface__aspect_angle

- "Aspect angle" is the azimuth angle of the
**opposite**of the gradient vector of elevation. Recall that the gradient is a 2D vector that points in the direction ofand which has a magnitude equal to the slope. (See slope). The opposite of the gradient vector is a vector that points in the opposite direction, or the the direction of**steepest downhill**. It is sometimes referred to as the**steepest uphill****antigradient**. Aspect angle could therefore also be expressed as: "azimuth_angle_of_antigradient_of_elevation".

## Capacity

base_quantity = "capacity"

*Examples of Specific Quantities:*

"anion_exchange_capacity" (used in soil physics)

"cargo_capacity" (e.g. of an automobile)

"cation_exchange_capacity" (used in soil physics)

"carrying_capacity" (of an ecosystem)

"infiltration_capacity" ####### (in hydrology; also called "infiltrability")

"interception_capacity" (in hydrology)

"isobaric_heat_capacity" (constant pressure) (of an entire object, extensive)

"isochoric_heat_capacity" (constant volume) (of an entire object, extensive)

"mass-specific_isobaric_heat_capacity" (constant pressure)

"mass-specific_isochoric_heat_capacity" (constant volume)

"volume-specific_isobaric_heat_capacity" (constant pressure)

"volume-specific_isochoric_heat_capacity" (constant volume)

*Examples*

air__volume-specific_isochoric_heat_capacity anvil__isobaric_heat_capacity aluminum__mass-specific_isobaric_heat_capacity earth_human__carrying_capacity (need to specify two objects) space-shuttle_tile__isochoric_heat_capacity

- The word "capacity" indicates the maximum "amount" of something that an object can hold. When applied to an empty container, like a fuel tank, it has units of volume. However, it may also be a nonnegative integer, as in "carrying capacity" or have other units, as in various types of heat capacity.

**Heat capacity**is an extensive property of an object (or matter); it is proportional to the amount of matter and can be used for discrete objects (like an anvil). There are two types of heat capacity, one computed with the pressure held constant, called "isobaric" and another with the volume held constant, called "isochoric". "Specific heat capacity" (often called "specific heat capacity") is an intensive property, that is, an amount per unit mass or volume. In the CSDMS Standard Names, the adjectives "mass-specific", "volume-specific" and "mole-specific" are used to remove ambiguity.

- "Thermal capacity" is another, but less commonly used term for "heat capacity".

- Aluminum, copper, cast iron and stainless steel cookware are often compared in terms of their thermal conductivity (how well they conduct heat) and heat capacity (how well they retain heat). See: Cookware and bakeware.

- The term
**carrying capacity**follows the**Process_name + Quantity Pattern**and is the maximum population size for a given ecosystem.

- There are 4 CF Standard Names that contain "capacity", namely "soil_thermal_capacity" and 3 others that contain the phrase "at_field_capacity" and refer to soil moisture. The coresponding CSDMS standard name is: "soil_field_capacity_water_content". See the Soil template on the
**CSDMS Object Templates**page for more information.

- See: Battery capacity, Cation-exchange capacity, Channel capacity, Combining capacity, Heat capacity and Tonnage.

## Charge

base_quantity = "charge" [C = Coulombs, SI unit]

*Examples*

electron__electric_charge

- The total electric charge is a fundamental conserved quantity of an isolated system.

- Electric charge is
*quantized*, that is, it comes in multiples of the the charge of an electron, called the*elementary charge*, denoted as "e". The charge of a quark is 1/3 of this value. Electric charge also carries a sign; protons and electrons have charges of e and -e.

- See: Electric charge and Elementary charge.

## Circulation

base_quantity = "circulation"

*Examples*
airfoil_curve~enclosing__circulation

- In fluid dynamics, circulation is the line integral of a velocity field around a closed curve. If not otherwise specified, that closed curve is taken to enclose the object in the object part of the name (i.e. in a CSDMS Standard Name). The closed curve is also assumed to lie wholly within the "potential flow" region and not in the boundary layer close to the boundary of the airfoil/object.

- We could also use something like: "airfoil" + "closed_line_integral_of_velocity"

- See: Circulation.

## Code

base_quantity = "code"

*Examples*

basin__pfafstetter_code basin__usgs_hydrologic_unit_code location__postal_code (See: Postal code.)

- For hydrologic features such as rivers, unique identification numbers such as the USGS Hydrologic Unit Code (or "HUC number") and Pfafstetter Code are used.

- Codes sometimes include both numbers and letters.

- See Number.

## Coefficient

base_quantity = "coefficient"

*Examples of Specific Quantities:*

"absorption_coefficient"

"attenuation_coefficient"

"diffusion_coefficient"

"drag_coefficient"

"eddy_diffusion_coefficient"

"exchange_coefficient"

"expansion_coefficient"

"extinction_coefficient"

"friction_coefficient"

"lift_coefficient"

"partition_coefficient"

"reaeration_coefficient"

"reflection_coefficient"

"scattering_coefficient"

"sieving_coefficient"

"transfer_coefficient"

"transmission_coefficient"

*Examples*

airfoil__drag_coefficient airfoil__lift_coefficient concrete_rubber__kinetic_friction_coefficient atmosphere_air_radiation__beer_lambert_law_attenuation_coefficient iron__thermal_volume_expansion_coefficient glacier__glen_law_coefficient math__binomial_coefficient (See Constants in Math) pavement_rubber__static_friction_coefficient polynomial__leading_coefficient spring~steel__hooke_law_coefficient [kg s-2] (the "spring constant" in Hooke's law) water_salt__diffusion_coefficient

- Coefficients are
**multiplicative factors**that often occur in empirical laws, and other mathematical expressions. In the CSDMS Standard Names, other "control variables" that do not appear as multiplicative factors are referred to as**parameters**. (However, sometimes people refer to these other parameters as coefficients.) Coefficients and exponents can be viewed as special types of parameters.**Parameters**are typically not model state variables, but instead are "tunable" "control parameters" that define the model itself.

- Many quantity names (see above) are built from the base quantity "coefficient" and a process name, which conforms to the
**Process_name + Quantity Pattern**.

**Diffusion**is the process by which a substance moves (down gradient) from regions of high concentration to regions of low concentration. In**molecular diffusion**this process is driven by thermal energy. In**turbulent diffusion**it is driven by random fluctuations and swirling structures in the flow, such as eddies. When unqualified, a diffusion coefficient refers to the parameter, D, in the diffusion equation that has units of [m2 s-1], regardless of what substance is diffusing. The term**eddy diffusion coefficient**(also called "eddy diffusivity") is used for turbulent diffusion and also has units of [m2 s-1]. See the section for Diffusivity (which needs to be reconciled with this one).

- The concept of
**bulk parameterization**is used in atmosphere and ocean science in order to estimate the rates (as fluxes) at which mass, momentum and heat are transferred between the atmosphere and the surface of either the land or sea. This approach uses the logarithmic law of the wall to relate the fluxes to values of heat, momentum, humidity (water vapor) or other gases that are measured at some fixed height above the interface (e.g. 10 meters). The use of the adjective "bulk" seems to stem partly from the idea of "bulk flow" (also called "free stream flow"), or flow that is far enough away from the interface boundary that it moves relatively unimpeded, as opposed to near-boundary flow. It also indicates that fluxes obtained by this method should be applicable over larger areas.**Bulk transfer coefficients**(also called "bulk exchange coefficients") are quantities associated with this approach, and can be defined somewhat differently by different authors, for example as dimensionless quantities or including shear velocity as a factor (with velocity units). There are separate bulk transfer coefficients for mass (water vapor or another gas, which may condense at the interface), momentum and heat. These bulk transfer coefficients are initially computed for a "neutral" state (e.g. when the surface temperature is equal to the air temperature), and then typically adjusted (e.g. by a function of bulk Richardson number) depending on whether the (stratified) atmosphere is in a "stable" (e.g. T_surf > T_air) or "unstable" (T_surf < T_air) state. These considerations lead to standard names such as "bulk_mass_transfer_coefficient" and "bulk_sensible_heat_transfer_coefficient" which are taken to be dimensionless. Note that the adjectives "stable" and "unstable" are not included because they are attributes of the atmosphere that are used to compute the bulk transfer coefficient but can change during a model run. The adjective "neutral" can be included, however, since this allows access to the "base value" that is modified for the stable and unstable cases.**Note**: The product of the wind speed at the reference height and a bulk transfer coefficient is sometimes called the "bulk aerodynamic conductance" (of mass, momentum or heat). The reciprocal is then the "bulk aerodynamic resistance".

- In the book, "Hydrology: An Introduction" by Brutsaert (2005, p. 41), the transfer coefficients for mass, momentum and heat are defined as dimensionless numbers and denoted as: Ce, Cd and Ch. Ce is also called the Dalton number (for water vapor). Cd is also called the
**drag coefficient**. Ch is also called the**Stanton number**. However, this differs from other definitions; see: Heat transfer coefficient (SI units of [W m-2 K-1]) and Mass transfer coefficient (SI units of [m s-1]).

- The "Manning n parameter" is sometimes called "Manning's roughness coefficient" or "Manning's coefficient" or something similar. (But the word "roughness" is not needed to remove ambiguity.) Since Manning's n appears in the denominator of Manning's formula, it technically isn't a coefficient (i.e. its inverse is the multiplicative factor, or coefficient). Note that Manning's formula also contains another parameter, usually denoted by "k" that serves as a unit conversion factor. In the CSDMS Standard Names these are both referred to as "parameters" and use that pattern.

- The terms "attenuation_coefficient" and "attenuation_factor" are both used but they refer to different quantities associated with the
**Beer-Lambert Law**. The "attenuation coefficient" is a parameter in the Beer-Lambert law with units of inverse length. When applied to gases in the atmosphere, dimensionless quantities called "optical air mass" and "optical depth" are instead used in the exponential. "Attenuation factor " is apparently a synonym for "transmittance", which is the ratio of transmitted to incident radiation, I(x)/I(0), a positive number less than 1. See: Absorbance, Air mass, Attenuation coefficient, Beer-Lambert Law, Optical depth and Transmittance.

- See: Attenuation coefficient, Ballistic coefficient, Binomial coefficient, Coefficient, Drag coefficient, Extinction coefficient, Friction, Heat transfer coefficient, Lift coefficient, Manning formula, Mass diffusivity, Mass transfer coefficient, Partition coefficient, Pressure coefficient, Reflection coefficient, Sieving coefficient, Skin friction coefficient, Thermal expansion and Transmission coefficient.

- See Constant, Exponent, Factor, Index, Number and Parameter.

- See Friction.

## Component

[ direction adjective(s) ] + "_component_of_" + [ vector quantity ]

*Examples*

atmosphere_air_flow__east_component_of_velocity atmosphere_air_flow__north_component_of_vorticity channel_water_flow__x_component_of_velocity sea_water_flow__down_east_component_of_stress

- Components of vectors and tensors are constructed using coordinate-direction adjectives and the "component_of" operation, as shown in the examples above.

- The coordinate-direction adjectives are: east, west, north, south, x, y, z, up, down, offshore, longshore, cross_stream and downstream. Two coordinate-direction adjectives are needed for a component of "flow_shear_stress". As of 7/28/14, eastward, westward, northward and southward have been shortened to east, west, north and south.

- Note that the word "flow" is used in the object part of the name as a shorthand for "flow_field". It is another example of the Object Name + Model Name Pattern.

- See Stress, Velocity and Vorticity.

- This was changed from a "quantity suffix" to a vector operation on 2/7/13. See
**CSDMS Operation Templates**.

## Compressibility

base_quantity = "compressibility"

*Examples of Specific Quantities:*

"isentropic_compressibility"

"isothermal_compressibility"

*Examples*

atmosphere_air__isothermal_compressibility

- Compressibility is a measure of the relative change in volume in response to a pressure.

- See: Compressibility and Compressibility equation.

## Concentration

base_quantity = "concentration"

*Examples of Specific Quantities:*

"mass_concentration" [kg m-3]

"molar_concentration" [mol m-3] (molarity)

"number_concentration" [m-3]

"volume_concentration" [1] = [m3 / m3]

*Examples*

channel_water_sediment~suspended__mass_concentration sea_water_magnesium-chloride__molar_concentration sea_water_sediment~suspended__mass_concentration

- There are four main types of concentration, shown above, and they all have different units.

- The quantity "concentration" is always associated with two substances (objects) so we use the
**Object-in-object Quantity Pattern**.

is a related concept with SI units of [mol kg-1].**Molality**

and**Mass fraction**are both dimensionless ratios.**mole fraction**

and**Mass ratio**are also dimensionless ratios and are considered "mixing ratios". See: Mixing ratio.**mole ratio**

- "Molar concentration" is also called "molarity". See: Molarity.

- "Volume concentration" is also called "volume fraction". See Fraction.

- The term "osmotic concentration" is also used.

- See: Concentration, Seawater and Sediment transport.

## Conductance

base_quantity = "conductance"

*Examples of Specific Quantities:*

"atmospheric_conductance" [m s-1]

"bulk_atmospheric_conductance" [m s-1]

"electrical_conductance" [A V-1]

"fluid_conductance" [m2 s-1]

"thermal_conductance"

*Examples*

snow__thermal_conductance

- Conductance is the reciprocal of resistance.

- Conductance is different from conductivity. See Conductivity.

- The product of wind speed at a reference height and a bulk transfer coefficient is called the "bulk aerodynamic conductance" (of mass, momentum or heat). The reciprocal, "bulk aerodynamic resistance", is also used. See Coefficient.

- Units cannot be determined from the "base quantity" name as shown above.

## Conductivity

base_quantity = "conductivity"

*Examples of Specific Quantities:*

"electrical_conductivity" [siemens m-1] or [ohm-1 m-1]

"hydraulic_conductivity" [m s-1]

"ionic_conductivity"

"molar_conductivity"

"thermal_conductivity" [W m-1 K-1] (this is an intensive property; don't need to add "specific")

*Examples*

sea_water__electrical_conductivity snow__thermal_conductivity soil__saturated_hydraulic_conductivity

- Units cannot be determined from the "base quantity" name as shown above.

- Hydraulic conductivity can depend on coordinate direction unless the soil is assumed to be isotropic. When applicable, include an <assume> tag in the Model Metadata File with the standard assumption name: "isotropic_medium". See CSDMS Assumption Names for more information.

- "Relative hydraulic conductivity" is the ratio of (K / K_sat). See Smith (2002).

- See: Electrical conductivity, Hydraulic conductivity, Ionic conductivity, Molar conductivity and Thermal conductivity.

## Constants in Math

base_quantity = "constant"

"math_" + constant_name + "_constant"

*Examples*

math__catalan_constant math__chaitin_constant math__conway_constant math__e_constant (or math_euler_e_constant ??) math__euler_gamma_constant math__feigenbaum_alpha_constant math__feigenbaum_delta_constant math__golden_ratio_constant math__googol_constant math__khinchin_constant math__pythagoras_constant (= square root of 2) math__sierpinski_constant math__twin_prime_constant math__pi_constant

- This includes numbers like "pi", "phi" and "e". See Wikipedia: Mathematical constant for a table with numerous examples.

- These numbers are not a quantity associated with an object like our others so we have used "math" as a placeholder object. Note that one model may want to check the number of significant digits of a math constant (like pi) that are used in another model, for example.

- phi = 1.61803... is known as the golden ratio.

- See the Dimensionless Number template.

## Constants in Physics

base_quantity = "constant"

*Examples*

air__dielectric_constant [1] (can be complex) earth__solar_constant [W m-2] (solar_irradiation_constant may be better) earth__standard_gravity_constant [m s-2] ("little g", see Attributes of Planets template) physics__atomic_mass_constant [kg] (about 1.660538921e-27) physics__avogadro_constant [unit mol-1] (see Note below) physics__bohr_radius_constant [m] (about 5.2917721092e-11) physics__boltzmann_constant (See ideal_gas_constant) physics__cosmological_constant [m-2] (about 10^{-52}; object = universe) physics__coulomb_constant [N m2 C-2] (C = Coulomb SI unit) physics__elementary_charge_constant [C] (charge of a proton and > 0; -1 times charge of an electron) physics__fine_structure_constant [1] (about 1/137.035999074) physics__first_radiation_constant [W m2] (for a black body) physics__gravitational_coupling_constant [1] (about 1.7518e-45) physics__hartree_energy_constant [J] physics__ideal_gas_constant [J mol-1 K-1] (R = 8.3144621) physics__planck_constant [J s] (h = 6.62606957e-34) physics__planck_charge_constant [C] (about 1.875545956e-18) physics__planck_length_constant [m] (about 1.616199e-35) physics__planck_mass_constant [kg] (about 2.17651e-8) physics__planck_temperature_constant [K] (about 1.416833e+32) physics__planck_time_constant [s] (about 5.39106e-44) physics__reduced_planck_constant physics__rydberg_constant [m-1] physics__second_radiation_constant [m K] (for a black body) physics__stefan_boltzmann_constant [W m-2 K-4] physics__universal_gravitation_constant [m3 kg-1 s-2] ("big G", from Newton's law; or just "gravitational_constant") physics__vacuum_electric_permittivity_constant [F/m] (also called "electric constant") physics__vacuum_impedance_constant [ohms] (about 376.73031) physics__vacuum_light_speed_constant [m s-1] (put "vacuum" in the object part ??) ########## physics__vacuum_magnetic_permeability_constant [N A-2] or [H m-1] (also called "magnetic constant") physics__von_karman_constant [1]

- If there is no naturally-associated object, the object name "physics" can be used as a placeholder object name. In some cases we could use "universe" or "vacuum" as the object name.

- Although "latent heat of fusion" and "latent heat of vaporization" are constants for a given substance (e.g. water), they have the following CSDMS standard names:

water__mass-specific_latent_fusion_heat (334 [kJ kg-1]) water__mass-specific_latent_vaporization_heat (2500 [kJ kg-1])

- Note that "specific_latent_heat" is a quantity name so the quantity name part of these examples conforms to the
**Process_name + Quantity Pattern**. See the template for Heat and Latent heat.

- The modern name for "Avogadro's number" is the "avogadro_constant". (See Avogadro constant.) It has units and is equal to: 6.02214129(27)x10^{23} [mol-1] or [unit mol-1]

- The speed of light depends on the medium it is traveling through. In a vacuum, v = c = 299,792,458 [m s-1]. In other materials, v = (c / n), where n > 1 is the
*refraction index*. For visible light in air, n is about 1.0003. So an unambiguous standard name should indicate the medium and the wavelength range in the object name. Since the medium that the light is traveling through matters, we use the**Object-in-object Quantity Pattern**to create standard names such as: "visible_light_in_air_speed".

- The speed of light in a vacuum is a constant that is independent of wavelength. Perhaps we should give it the standard name "light_in_vacuum_speed_constant" which follows the
**Object-in-object Quantity Pattern**.

- The "universal gravitational constant' appears in Newton's Law of Gravitation and is denoted as G (big G). It has units of [m3 kg-1 s-2]. The "Earth gravitational constant" is more correctly called the "Earth standard gravity constant". It is the average free-fall acceleration of Earth's gravitational field near the surface of the Earth and is denoted as g (little g). Even though it varies with position on Earth, it is defined to be precisely 9.80665 [m s-2] (an average value). See: Standard gravity and Gravity of Earth.

- While the coefficient in Hooke's law is often called the
, we instead use '**spring constant****spring~steel__hooke_law_coefficient***for consistency with coefficients in other empirical laws.*

- In meteorology, the ratio of the ideal gas constant, R, and the isobaric mass-specific heat capacity, cp, is called the
**Poisson constant**. It is used in the definition of potential temperature.

- See: Boltzmann constant, Coulomb constant, Elementary charge, Fine-structure constant, Gravitational coupling constant, Ideal gas constant,Planck constant, Psychrometric constant,Rydberg constant, Stefan-Boltzmann constant, Universal gravitational constant, Vacuum electric permittivity, Vacuum magnetic permeability and von Karman constant.

- See: Physical constant.

## Content

base_quantity = "content"

*Examples of Specific Quantities:*

"energy-per-area_cold_content"

"energy_content"

"mass_content"

"volume_content"

*Examples*

coal__thermal_energy_content gasoline__thermal_energy_content snowpack__energy-per-area_cold_content ? (See Note below.) wood~dry__thermal_energy_content

- The word "content" refers to the "amount contained within". It is therefore naturally associated with two objects and the
**Object-in-object Quantity Pattern**.

- In the CF Standard Names, the term "content" is taken to mean an "amount per unit area", usually determined as a z-integral from the bottom to the top of the atmosphere of a mass or volume fraction. (e.g. CF has "soil_moisture_content", "soil_moisture_content_at_field_capacity" and "soil_carbon_content".) However, in other contexts it means an amount per unit volume, as in the term "water_content" from infiltration theory, which is a volume fraction. See Water Content.

- While soil "water content" is a fairly standard term in hydrology (infiltration theory), the CSDMS Standard Names use "volume_fraction" instead since it is less ambiguous, provides the definition, applies equally well to other objects like clay and sand, and keeps the word "water" in the object part of the name. See Attributes of Soil at CSDMS Standard Name Examples. However, it might be better to retain the word "content" for easy recognition (since "water content" is so widely used, and then use "volume_content" and "mass_content" instead of "volume_fraction" and "mass_fraction". Sometimes the terms
*gravimetric water content*and*volumetric water content*are also used.

- The quantity "thermal_energy_content" is used in the context of fuels like coal, gas and wood, to indicate the amount of useful energy that can be extracted.

- The quantity "cold_content" is used in snow hydrology to describe the "energy deficit" that must be overcome before melting starts to occur. It is expressed as energy per unit area [J m-2]. This deficit results in an observed time lag between when the temperature is raised above the melting point to when snow actually begins to melt. It involves the concept of "latent heat of fusion" -- the (originally mysterious) amount of heat energy that must be added to a solid material before there is any change in its temperature. (See: Latent heat. In the CF Standard Names, the term "thermal_energy_content_of_surface_snow" is used, apparently to mean "cold_content". However, a Google search on "thermal energy content of snow" only returns 2 hits, and these are from the CF names. Note that "cold_content" is negative and "thermal_energy_content" is typically positive.

- Many CF Standard Names contain the base quantity "content". The following list shows the number, in parentheses, or each use pattern:

carbon_content [kg m-2] (14) energy_content [J m-2] (25) e.g. "thermal_energy_content_of_surface_snow" enthalpy_content [**********] (4) heat_content [J m-2] (2) ice_content [kg m-2] (2) mass_content [kg m-2] (235) moisture_content [kg m-2] or [m] (6) number_content [m-2] (7) ozone_content [Pa] or [m] (2) soot_content [kg m-2] (1) sulfate_content [kg m-2] (1) vapor_content [kg m-2] (14) (most are "tendencies") water_content [kg m-2] (16)

- We may therefore have a conflict with "water_content" unless it is resolved by the object part.

## Coordinate

base_quantity = "coordinate"

*Examples*

alongshore_coordinate (oriented along and based on a shoreline; similar to sigma coordinates) cross-shore_coordinate (off-shore and on-shore directions) cross-stream_coordinate (oriented along and based on a stream centerline) streamwise_coordinate (upstream and downstream directions) east_coordinate (for a model; if not same as longitude) west_coordinate north_coordinate (for a model; if not same as latitude) south_coordinate r_coordinate (Cylindrical and Spherical coordinates, with azimuth_angle and elevation_angle) u_coordinate (e.g. orthogonal curvilinear coordinate systems) v_coordinate (e.g. orthogonal curvilinear coordinate systems) x_coordinate (Cartesian coordinates) y_coordinate (Cartesian coordinates) z_coordinate (Cartesian coordinates)

- Note that Geographic coordinates use
**latitude**(north-south coordinate),**longitude**(east-west coordinate) and**elevation**(vertical coordinate). These are treated as standard base quantity names in the CSDMS Standard Names. See: Geographic coordinates.

- For spherical coordinates, we would usually use "azimuth_angle" and "elevation_angle" instead of "theta_coordinate" and "phi_coordinate". But perhaps the latter should also be allowed.

- The terms "normal_coordinate" and "tangential_coordinate" are also used in some contexts.

- See: Barycentric coordinates (astronomy), Barycentric coordinates (for a triangle or other simplex), Canonical coordinates, Coordinate system, Fermi coordinates, Fractional coordinates (crystallography), Galilean transformation, Generalized coordinates, Isothermal coordinates, Normal coordinates (from differential geometry) and Sigma coordinate system (also called terrain-following).

- See the section for Components above, where the same prefixes are used. In fact, instead of using "coordinate" as a base quantity, it would be possible to use "position", which is a vector quantity, similar to velocity. Then we could use "x_component_of_position" instead of "x_coordinate", etc. just as we use "x_component_of_velocity". Note that while the components of a position vector are called "coordinates", there is no similar, short term for the components of a velocity vector.

## Correlation

base_quantity = "correlation"

*Examples*

(None yet)

- Note that correlations require two quantities to be specified, which is similar to certain other quantities such as Partial Pressure and Solubility.

- Although the Guidelines for Constructing CF Standard Names includes a provision for correlations as the transformation pattern: "correlation_of_X-and-Y_over_Z", there are currently no examples of CF Standard Names that contain "correlation". The same is true for "covariance" and "convergence". There are only three names with "divergence".

## Count

base_quantity = "count"

*Examples of Related Quantities:*

"number_concentration" (count per volume)

*Examples*

basin_rain-gauge__count human_blood_cell~platelet__number_concentration [count / microliter] human_blood_cell~red__number_concentration human_blood_cell~white__number_concentration lake_water_fish_sample__count mars_moon__count model_grid_column__count

- This quantity name is sometimes used when the attribute being quantified can only take non-negative integer values, as in the examples above. The word "count" is preferable to "number", since a "number" doesn't need to be an integer and is used as a root quantity for dimensionless numbers (e.g. Reynold's number). However, "count concentration" is not typically used, so we use "number concentration" in that case.

- In the case of blood cell counts, the units are usually a number per volume (e.g. number per microliter). See: Blood cell count. Once units are specified (e.g. in a Model Coupling Metadata (MCM) file), then "number_concentration" is unambiguous. Is a platelet technically considered to be a type of blood cell?

- The "Wolman pebble count" due to M. Gordon "Reds" Wolman is sometimes used in river hydraulics and sediment transport. However, the goal of this procedure is to estimate the mean diameter of the pebbles on the stream bed, so the actual "count" (usually 100) is not of primary interest.

- The "diatom count" of a sample may be another example; are the units then the same as "abundance"? (e.g. "sediment_core_diatom_relative_abundance" ?)

- The number of occurrences of a given event may also be called a "count". (e.g. Geiger counters)

- See Count data and the Number template.

## Current

base_quantity = "current"

*Examples of Specific Quantities:*

"electrical_current"

*Examples*

None yet.

- An electric current is a flow of charge, with an SI unit of "amperes" (i.e. "coulombs per second").

- See: Electric current.

## Curvature

base_quantity = "curvature"

*Examples of Specific Quantities:*

"gaussian_curvature"

"mean_curvature"

"max_normal_curvature" (a principle curvature)

"min_normal_curvature" (a principle curvature)

"plan_curvature"

"profile_curvature"

"streamline_curvature"

"tangential_curvature"

*Examples*

land_surface__plan_curvature land_surface__profile_curvature

- Curvatures can be defined for surfaces that are twice-differentiable. In reality, natural surfaces are rough but they can be approximated as twice-differentiable surfaces.

- Plan curvature (or "contour curvature"), profile curvature and streamline curvature are used in geomorphometry, the analysis of land surfaces or topography.

- See Attributes of Topography and Attributes of Oceans on the Examples page.

- Curvature can also be defined for curves, such as coastline curves and space curves (or trajectories).

- See: Curvature, Geomorphometry and Radius of curvature.

## Density

base_quantity = "density"

*Examples of Specific Quantities:*

"bits-per-area_density"

"bulk_mass-per-volume_density"

"charge-per-area_density"

"current-per-area_density" [A m-2] (known as "current density")

"energy-per-area_density" [J m-2]

"energy-per-volume_density" [J m-3]

"length-per-area_density" [m-1]

"mass-per-area_density" [kg m-2]

"mass-per-volume_density" [kg m-3]

"number-per-area_density" [m-2]

"number-per-volume_density" [m-3]

"particle_mass-per-volume_density"

"power-per-length_density" [W m-1] (used for ocean wave crests)

"power-per-area_density" [W m-2] (known as "surface power density")

"power-per-volume_density" [W m-3]

"torque-per-volume_density" [N m / m-3] = [N m-2]

*Examples*

atmosphere_air__mass-per-volume_density atmosphere_air__mass-per-volume_density (stp = standard temperature and pressure) basin_channels__total-length-per-area_density (known as "drainage_density") universe~friedmann__critical_h-atom-per_volume_density sea_water__mass-per-volume_density

- The word
**density**usually refers to the amount of something within a fixed amount of space. The "amount of space" could be 1D (line), 2D (area) or 3D (volume). For greater clarity (and to avoid ambiguity), standard quantity names like*mass-per-volume_density*and the others listed above are used in the CSDMS Standard Names. Similar issues occur for Concentration (see section by that name). Also see the section for Flux.

- The quantity name
**Bulk density**refers to the mass of many particles (e.g. sediment grains) divided by the volume that they occupy. For clarity, here we use "bulk_mass-per-volume_density".

- Column density is a type of area density defined as the z integral of a volume fraction from the bottom to the top of a column of water or air, as in the ocean or atmosphere. In the CF names, the quantity name "content" is used for this concept. In the context of sediment plumes, the quantity name "sediment inventory" is used for this concept (a z-integral over the depth of a freshwater plume entering the sea).

- Physicists sometimes use the term "flux_density".

- Hydrologists use the term "drainage_density", which is defined as the total length of channels in a drainage basin divided by the drainage area. Generic units are therefore inverse length. Similarly, "source_density" can refer to the total number of sources (i.e. channel heads) in a basin divided by the drainage area.

- Other valid quantities include "current_density", "electron_density" (in plasma physics), "thermal_energy_density" and "magnetic_energy_density".

- See: Area density, Column density, Bulk density, Critical density,Current density, Density, Drainage density, Electron density, Energy density, Knot density, Linear density, Memory storage density, Number density, Orthobaric density, Particle density, Population density, Potential density, Power density, Probability density function, Relative density, Surface power density, Torque density and Vapour density.

## Depth

base_quantity = "depth"

*Examples of Specific Quantities:*

"secchi_depth"

*Examples*

channel_water__mean_depth sea_water__secchi_depth sea_water_below-surface__depth sea_water_bottom__depth soil_sat-zone_top__depth ##### (or if not soil, land_subsurface_sat-zone_top__depth).

- Measured as a positive downward distance below a reference surface. In this sense, it is the opposite of "height" which is measured positive upward from a reference surface.

- CF Standard Names often use "thickness" instead of "depth". See the template for Thickness.

- The words "depth" and "thickness" are sometimes used interchangeably. In the context of "layers", "thickness" is usually used (e.g. in meteorology, geology and hydrogeology). In the context of surface water or snow, "depth" is usually used. (As in: "How deep is the lake?" or "The lake depth is 5 meters.") The word "depth" indicates a value that is positive downward from some reference datum, and which may take values less than some maximum possible value.

- Note that "secchi_depth" is a standard term that measures turbidity using a "visible depth". See: Secchi disk.

- While the term "precipitable_water_content" is commonly used, its units of length are not really consistent with the base quantity "content". The terms "precipitable water depth" and "precipitable depth of water vapor" are also used and imply units of length, but not all of the water can actually "precipitate". An unambiguous and currently-used standard name for this quantity is: "atmosphere_water~vapor" + "z_integral_from_bottom-to-top_of_volume_fraction".

- See Altitude, Elevation, Height and Thickness.

## Diameter

base_quantity = "diameter"

*Examples*

basin_channel-network_graph__diameter graph~tree~rooted__diameter tree~oak~bluejack_trunk__diameter impact-crater_circle__diameter (seeObject_name + model_name Pattern) square__diameter

- This quantity usually has units of length (except for rooted tree graphs).

- Although often associated with a circle, the general definition of diameter is the maximum distance (for some metric) between any two points in a set. So any bounded geometric shape (e.g. a square or any polygon) has a well-defined diameter, as does any bounded set of points. Note that the diameter of a bounded set is the same as the diameter of its convex hull. In graph theory, the diameter of a rooted tree graph is the maximum number of edges between the root and any leaf. River networks have a well-defined diameter (though topological vs. geometrical) since they can be viewed as rooted tree graphs (rooted at the outlet).

- See Perimeter.

## Diffusivity

base_quantity = "diffusivity"

*Examples of Specific Quantities:*

"magnetic_diffusivity" [m2 s-1]

"mass_diffusivity" [m2 s-1]

"momentum_diffusivity" [m2 s-1] (nickname for kinematic_viscosity)

"thermal_diffusivity" [m2 s-1]

- It appears that the units are always [m2 s-1].

- "thermal_diffusivity" seems preferable to "heat_diffusivity"

- Common adjectives are: biharmonic, laplacian, epineutral, etc.

- The term "eddy diffusivity" is sometimes used as a synonym for the "eddy diffusion coefficient", usually denoted as "K". See: Eddy diffusion.

- See: Magnetic diffusivity, Mass diffusivity, Kinematic viscosity, Momentum diffusion, Thermal diffusivity and Thermal conduction.

## Dimension

base_quantity = "dimension"

*Examples of Specific Quantities:*

"box_counting_dimension"

"hausdorff_dimension"

*Examples*

cantor-set__hausdorff_dimension peano-curve__hausdorff_dimension sierpinski-gasket__hausdorff_dimension

- This quantity is usually used in connection with fractals and it can be measured (usually using the box-counting dimension) for many objects in nature.

- See: Box-counting dimension, Dimension, Fractal dimension, Hausdorff dimension and Packing dimension.

## Dimensionless Numbers

[ famous person's name ] + "_number"

*Examples*

air_helium-plume__richardson_number airplane__mach_number channel_water_flow__froude_number channel_water_flow__reynolds_number equation~heat__courant_number #### (insert "model" ??) ship__froude_number

- Dimensionless numbers are widely used in physics and typically obtained as the ratio of two quantities that have the same units. For example, Reynolds number gives the ratio of inertial and viscous forces in a flow problem, and flows transition from laminar to turbulent as the Reynolds number increases.

- Wikipedia has a nice table of
**dimensionless numbers**which provides numerous examples.

- Some names, like "Reynolds", end in "s", but a possessive "s" is not added at the end. See the CSDMS Standard Name
**Basic Rules**.

- The modern name for "Avogadro's number" is the "Avogadro constant" and it is not dimensionless.

- See the Attributes of Atoms and Number templates for terms like "proton_number".

- See the Number template for more information.

## Discharge or Volume Flow Rate

"volume_flow_rate"

*Examples of Specific Quantities:*

*Examples*

channel_water_x-section__volume_flow_rate [m3 s-1] lake_water~incoming__volume_flow_rate [m3 s-1] lake_water~outgoing__volume_flow_rate [m3 s-1]

- The term "discharge" is used primarily by hydrologists and is commonly denoted as "Q". The term "volume_flow_rate" is more broadly understood.

- The term "discharge" has the connotation of something leaving a domain, so additional clarification is generally needed to indicate whether the volume flow rate is into or out of a given domain (e.g. with "incoming" or "outgoing"). This is now done in the object part of the name, by using either "water~incoming" or "water~outgoing".

- Hydrologists also use "unit_width_discharge" (discharge per unit contour width) in the context of surface flows. It is usually denoted by lower-case "q" and has SI units of [m2 s-1]. Note that "depth-integrated velocity" is a synonym for unit-width discharge, and in CSN this 2D vector field is called "z_integral_of_velocity". Note that the "lateral inflow rate" to the sides of a channel is given by: "channel_bank_water" + "volume-per-length_flow_rate".

- See: Discharge, Volumetric flow rate, Volumetric flux and Mass flow rate.

- A "volume_flux" has units of [m3 m-2 s-1] = [m s-1], as in Darcy's Law. Discharge is then the integral of a volume flux over the cross-sectional area of a channel or pipe. See the Flux template.

- Avoid "streamflow" and "outflow" as synonyms for "discharge" or else define them to be aliases.

- If a "sediment discharge" quantity has units of [mass / time], then it should be called something like "channel_water_sediment~suspended" + "mass_flow_rate" instead of "channel_water_sediment~suspended" + "volume_flow_rate", since discharge has units of [volume / time].

- See the
**Flow Rate**template.

## Distance

base_quantity = "distance"

*Examples of Specific Quantities:*

"average_distance"

"separation_distance"

*Examples*

channel_centerline_endpoints__separation_distance earth-to-sun__average_distance

- This quantity seems to require specifying two objects, just as solubility, partial_pressure and volume_fraction do. In the latter cases the special keyword "_in_" was introduced. Here the reserved word "-to-" and the pattern: (object + "-to-" + object + distance) is used in a similar way. The keyword "-to-" can also be used for ratios. See "Ratios".

- We could introduce "straight_distance" as a synonym for
**euclidean_distance**or just use the latter term. Or perhaps use "euclidean_length" instead?

- The word "distance" is sometimes used in a more abstract sense, as a measure of dissimilarity between two objects. For example, the Hamming distance measures the dissimilarity of two text strings. See: Metric, Distance, Euclidean distance, Uniform norm and Taxicab geometry (or "Manhattan distance").

## Duration

base_quantity = "duration"

*Examples of Specific Quantities:*

[process name] + "_duration" (e.g. exposure_duration, precipitation_duration)

*Examples*

aircraft__flight_duration atmosphere_water__precipitation_duration (vs. "rainfall duration") earth_day~sidereal__duration earth_day~solar-mean__duration earth_day~stellar__duration land_surface__sunshine_duration (or "daylight_duration") water_scuba-diver__dive_duration

- Used to indicate a time period.

- See the Precipitation section.

- Typically preceded by a process name modifier. See CSDMS Process Names for a list of process names.

## Efficiency

base_quantity = "efficiency"

*Examples of Specific Quantities:*

"electrical_efficiency"

"luminous_efficiency"

"mechanical_efficiency"

"thermal_efficiency"

*Examples*

engine__thermal_efficiency

- Efficiency is usually expressed as a ratio of what is achieved to the max possible (or ideal) value and is therefore a dimensionless number.

- See: Carnot heat engine, Electrical efficiency, Energy conversion efficiency, Fuel efficiency, Luminous efficiency, Mechanical advantage, Mechanical efficiency and Thermal efficiency.

## Elevation

base_quantity = "elevation"

*Examples*

bedrock_surface__elevation land_subsurface_sat-zone_top__elevation (vs. ground_water-table_surface) #### land_surface__elevation sea_water_surface__elevation

- There is a subtle but important difference between the quantities "altitude" and "elevation". The word
**altitude**refers to the distance of an object (e.g. aircraft, air parcel or balloon) above the ground, regardless of the local elevation of the land surface. The word**elevation**refers to the distance of an object (typically a land surface) above a datum, such as the mean sea level datum. Elevation is one of the three Geographic coordinates used to specify a 3D location (i.e. elevation, latitude and longitude).

- See the quantity templates for Altitude, Depth, Height, Thickness.

- See the object template for Surface. Elevation is one of many attributes that can be associated with a surface.

- See Reference Quantities.

## Emissivity

base_quantity = "emissivity"

*Examples*

land_surface__emissivity

- Emissivity is a measure of the effectiveness of a surface in emitting energy as
**thermal radiation**(also called "longwave radiation"). It is defined as the (dimensionless) ratio of the thermal radiation emitted by a surface/object and the thermal radiation that would be emitted by an ideal**black body**surface at the same temperature.

- Emissivity values are dimensionless and range between 0 and 1.

- See: Black body, Black-body radiation, Earth's energy budget, Emissivity, Outgoing longwave radiation and Shortwave radiation.

## Emittance

base_quantity = "emittance"

*Examples*

land_surface_radiation~incoming~longwave__emittance

- Emittance is the
**energy flux**emitted by a source, and has SI units of [W m-2] or [J m-2 s-1].

- See: Irradiance.

- See: Absorbance, Attenuation coefficient, Beer-Lambert law, Mass attenuation coefficient, Opacity (optics), Reflectance and Transmittance.

## Energy

base_quantity = "energy"

*Examples of Specific Quantities:*

"electric_energy"

"free_energy"

"internal_energy"

"kinetic_energy"

"potential_energy"

"thermal_energy"

*Examples*

projectile__potential_energy water__gibbs_free_energy

- The SI unit for energy is Joules.

- Specific energy is energy per unit volume or mass. Add the prefix mass-specific, mole-specific or volume-specific for clarity.

- Some possible forms of energy are thermal, chemical, radiant, nuclear, magnetic, elastic sound, mechanical, luminous and mass. See Energy.

- See Chemical energy, Chemical potential, Elastic energy, Electrical energy, Extent of reaction, Fermi energy, Food energy, Gibbs free energy, Helmholtz free energy, Internal energy and Magnetic energy, Magnetic moment, Thermodynamic free energy.

## Enthalpy

base_quantity = "enthalpy"

*Examples of Specific Quantities:*

"atomization_enthalpy"

"combustion_enthalpy"

"denaturation_enthalpy"

"dissolution_enthalpy" (also called "enthalpy of solution")

"formation_enthalpy"

"fusion_enthalpy"

"hydration_enthalpy"

"hydrogenation_enthalpy"

"mass-specific_enthalpy"

"mixing_enthalpy"

"reaction_enthalpy"

"sublimation_enthalpy"

"vaporization_enthalpy"

*Examples*

- Enthalpy is defined as the "thermodynamic potential", computed as H = U + pV, where U = internal energy, p = pressure and V = volume. It has SI units of Joules.

- Add the prefix "mole-specific" to a quantity like "combustion_enthalpy" when the units are Joules per mole.

- See: Enthalpy.

## Exponent

base_quantity = "exponent"

*Examples*

basin__flint_law_exponent basin_channel~longest__hack_law_exponent channel_water_sediment~suspended__volume_flow_rate_law_area_exponent glacier__glen_law_exponent

- Exponents often occur in empirical laws.

- Systems that can undergo phase transitions are often characterized by a critical exponent.

- See Coefficient, Constant, Factor, Index, Number and Parameter.

## Factor

base_quantity = "factor"

*Examples*

oscillator__q_factor pipe_water_flow__darcy_friction_factor (same as moody_friction_factor) pipe_water_flow__fanning_friction_factor sun-lotion_skin__protection_factor (known as SPF) wave~sine__crest_factor

- Use "manning_n_parameter" instead of "manning_friction_factor".

- Many different types of Shape factor are used in image analysis, such as the "circularity_shape_factor", "elongation_shape_factor", "compactness_shape_factor" and "waviness_shape_factor".

- Another type of shape factor is given by the square root of area divided by the shape's diameter (max distance between any 2 boundary points.).

- A model may use an "adjustment_factor", "correction_factor" or "compensation_factor".

- See: Atomic form factor (or atomic scattering factor), Crest factor, Cunningham correction factor (for small particles in a fluid), Q factor, Sun Protection Factor (SPF) and View factor.

- See Coefficient, Constant, Exponent, Index, Number and Parameter.

## Flag

base_quantity = "flag"

*Examples*

model__**_option_flag

- We may want to allow "flag" as a quantity since many models provide options as boolean values known as "flags". It isn't clear yet, however, how these would be shared between models or what the object_name would be.

- See Flag (computing).

## Flow Rate

base_quantity = "flow_rate"

*Examples of Specific Quantities:*

"mass_flow_rate"

"momentum_flow_rate"

"energy_flow_rate"

"volume_flow_rate"

"mole_flow_rate"

*Examples*

channel_entrance_water_x-section__volume_flow_rate channel_exit_water_x-section_sediment~suspended__mass_flow_rate lake_water~incoming__volume_flow_rate

- The quantity name "flow_rate" can be ambiguous in the context of a fluid that can either flow into or out of the object in the object part of the name. In such cases, the process names "inflow" and "outflow" can be used instead of "flow" and are viewed relative to the object. While "discharge" is commonly used as a quantity name in hydrology, it connotes a volume outflow rate and sounds strange when used to refer to a volume
*inflow*.

- The base quantity "rate" implies that units of inverse time are added to the units of the quantity that is being transported. For example, in SI units we have:

mass_flow_rate [ kg s-1 ] momentum_flow_rate [ kg m s-2 ] energy_flow_rate [ J s-1 ] = [ W ] volume_flow_rate [ m3 s-1 ] mole_flow_rate [ mol s-1 ]

- "Energy flow rate" is also known as "power". See: Power.

- See: Discharge, Volumetric flow rate and Mass flow rate.

- See the templates for Discharge, Flux and Rate of a Process.

## Flux

base_quantity = "flux"

*Examples of Specific Quantities:*

"mass_flux"

"momentum_flux"

"energy_flux"

"volume_flux"

"mole_flux" (perhaps this should be "number_flux" to be independent of units.)

process_name + "_flux" (e.g. "radiation_flux")

*Examples*

land_surface_radiation~outgoing~longwave__energy_flux (emitted and upward) land_surface_radiation~incoming~longwave__energy_flux (incident and downward)

- See the section on Radiation on the CSDMS Quantity Templates page for many examples of radiation fluxes.

- In the context of "transport phenomena", the definition of "flux" is
. In addition to the phrase "per unit area", this definition includes the word**flow rate per unit area**which implies per unit time. So the base quantity "flux" implies that units of [m-2 s-1] are added to the units of the quantity that is being transported. For example, in SI units we have:**rate**

mass_flux [ kg m-2 s-1 ] momentum_flux [ kg m s-1 m-2 s-1 ] = [ kg m-1 s-2 ] = [ Pa ] (force per unit area, same units as "pressure") energy_flux [ W m-2 ] = [ J m-2 s-1 ] volume_flux [ m s-1] = [ m3 m-2 s-1 ] mole_flux [ mol m-2 s-1 ]

- "Flux" can also be understood as "surface bombardment rate".

- "Flow rate" is the total amount of the transported quantity per unit time, or the product of an area and a flux. Replacing "flux" with "flow_rate" in a quantity name results in a different, but also valid quantity.

- The examples above show how the object name can be either a
or a**surface**. Either type of object can potentially "absorb", "emit", "reflect" or "transmit" a flux.**medium**

- An energy flux
*emitted by*an object is a quantity called(positive if outgoing). An energy flux that is**outgoing_radiation_flux***received by*or*incident on*an object is a quantity called(positive if incoming). That is, the sun "radiates" energy and the earth is "irradiated" by this energy. This distinction means that "incident_radiation" serves as a synonym for "irradiation" and "emitted_radiation" as a synonym for "radiation". Some objects, like a land surface, can radiate longwave energy or be irradiated by longwave energy. In such cases, the term "outgoing_radiation_flux" establishes a sign convention that "outgoing is positive". Similarly, "incoming_radiation_flux" implies "incoming is positive". Process names often occur in pairs that indicate "incoming" or "outgoing", such as "emigration" and "immigration" or "exporting" and "importing". Note that a process name, like "radiation" represents an action that applies to the object in the object name part.**incoming_radiation_flux**

- The shortwave radiation incident on the land surface is typically modeled as the sum of three components, called
,**direct**and**diffuse**. Only the "direct" component (radiation from the sun, transmitted directly through the atmosphere to the surface) is dependent on topographic slope and aspect. The other two are emitted (via reflections from aerosols) isotropically by the atmosphere so they appear to be arriving from a direction that is parallel to the local surface normal. For the "direct" component, an extra adjective like "slope_corrected" may be needed. See: Earth's radiation balance.**backscattered**

- A process name frequently precedes the base quantity "flux" in accordance with the
**Process_name + Quantity Pattern**. Examples include "evaporation_volume_flux", "precipitation_mass_flux".

- It turns out that
and**stress**both have the same units of Pascals (or N m-2, or kg m-1 s-2). When a fluid exerts a shear stress on a boundary, this results in a momentum flux into the boundary and this loss of momentum slows the flow.**momentum flux**

- What about "luminous flux" (for visible light)? See: Luminous flux.

- See: Flux, Transport phenomena.

- "Discharge" is a volume flow rate and not a flux. See Discharge.

- "momentum_diffusivity" [m2 s-1] is a nickname for kinematic_viscosity

- In the CF Standard Names, "flux" may be preceded by the words:

mass, momentum,

energy, heat, longwave, shortwave, radiative,

water, vapor, evaporation,

palm, photon, mole, salt

Units are [W m-2] for the "energy fluxes" such as: "heat", "longwave", "shortwave" and "radiative". In addition, "shortwave_radiation" is abbreviated to "shortwave".

- See the templates for Concentration, Discharge and Flow Rate.

## Force

base_quantity = "force"

quantity = "braking_force"

quantity = "drag_force"

quantity = "impact_force"

quantity = "lift_force"

*Examples*

automobile__braking_force

- A force may be thought of as a push or a pull exerted on an object and has SI units of Newtons. Note that "weight" is also a force.

- See Force.

## Fraction

quantity_suffix = "fraction"

*Examples of Specific Quantities:*

"area_fraction"

"mass_fraction"

"mole_fraction"

"time_fraction"

"volume_fraction"

*Examples*

basin_land~forested__area_fraction basin_land~grassland__area_fraction earth_surface_land__area_fraction earth_surface_water__area_fraction # surface of a 3D region vs. mathematical surface region_state_land~agricultural__area_fraction region_state_land~arable__area_fraction region_state_land~burned__area_fraction region_state_land~cloud-covered__area_fraction region_state_land~commercial__area_fraction region_state_land~dry__area_fraction region_state_land~farmed__area_fraction region_state_land~flooded__area_fraction region_state_land~flooded__max_of_depth #### region_state_land~forested__area_fraction region_state_land~grassland__area_fraction region_state_land~grazing__area_fraction region_state_land~ice-covered__area_fraction region_state_land~irrigated__area_fraction region_state_land~lake-covered__area_fraction region_state_land~water-covered__area_fraction region_state_land~parkland__area_fraction region_state_land~private__area_fraction region_state_land~public__area_fraction region_state_land~residential__area_fraction region_state_land~snow-covered__area_fraction region_state_land~urban__area_fraction region_state_land~vegetated__area_fraction region_state_land~wetland_fraction rocket_payload__mass_fraction rocket_propellant__mass_fraction (See: Propellant mass fraction.) sea_water_oxygen__volume_fraction soil_air__volume_fraction (Object-in-Object Pattern) soil_clay__volume_fraction soil_ice__volume_fraction soil_loam__volume_fraction soil_sand__volume_fraction soil_silt__volume_fraction soil_water__volume_fraction (instead of "soil" + "water_content") #####

- The word "fraction" can be viewed as a "quantity suffix" (as defined at the top) that can be applied to any base quantity (e.g. area, mass, mole, time, volume) to create a new quantity. In most (if not all) cases it is dimensionless.

- In order for "area_fraction" and "volume_fraction" to be well-defined, the object part of the name should ideally refer to a 2D or 3D shape (e.g. polygon or polytope) for which the area or volume can be computed. (e.g. for 2D, a state or a drainage basin)

- If an "area fraction" variable name is used with gridded data, then the "area_fraction" applies to the area of the grid cell. If the area fraction applies to some specific domain or object, such as a U.S. state or a drainage basin, then constructions like: "basin_land~forested + area_fraction" can be used and conform to the
**Part of Another Object Pattern**.

- The quantity
is often used in connection with the fraction of land (in map or plan view) that meets some criteria. Adjectives like "burned", "forested", "public" and "urban" can be used to define the criteria as shown in the examples. As of 7/23/14, hyphenated adjectives like "snow-covered" are allowed.**area_fraction**

- If an "area fraction" variable name is meant to distinguish between two possible states, such as land and water, then a reserved word like "vs" (or "to") could be used in a construction like: "land-vs-water + area_fraction".

- Variable names with "volume fraction" usually use the
**Object-in-object Quantity Pattern**as in the examples.

- In the CF Standard Names, "fraction" is used in 306 names to form the following 5 quantities where the number of occurrences is indicated in parentheses:

area_fraction (19) mass_fraction (179) mole_fraction (95) time_fraction (2) volume_fraction (11)

- The ones for "volume_fraction" fall into 5 groups:

ocean_volume_fraction volume_fraction_of_oxygen_in_sea_water volume_fraction_of_[clay, silt or sand]_in_soil volume_fraction_of_condensed_water_in_soil + [assumptions] volume_fraction_of_frozen_water_in_soil

- Hydrologists typically use the shorter term "soil_water_content" instead of "volume_fraction_of_condensed_water_in_soil". However, using "soil_water~condensed + volume_fraction" instead is consistent with the
**Object-in-object Quantity Pattern**.

## Frequency

base_quantity = "frequency" [1/second] (but the meaning is "cycles per second")

*Examples of Specific Quantities:*

"angular_frequency" [radians/second]

"nyquist_frequency" [1/second]

*Examples*

cesium_atom__characteristic_emission_frequency sea_water__brunt_vaisala_frequency (also called "buoyancy_frequency") sea_surface_water_wave__frequency

- Units of frequency are usually hertz = [1/second].

- Note that the word "frequency" alone means
and "wavenumber" means**temporal frequency**. Note that "angular_frequency" is distinct from "frequency" and "angular_wavenumber" is distinct from "wavenumber", but they are closely related quantities.**spatial frequency**

- For periodic waves, the frequency is equal to the phase velocity divided by the wavelength. See the Period and Wavelength templates.

- See Angular frequency, Brunt–Väisälä frequency, Frequency, Normalized frequency and Nyquist frequency.

## Friction

- Friction is not a quantity and is really a
**force**as opposed to a process. It is not included in this list of CSDMS Process Names because it doesn't fit the general verb-to-noun process name pattern explained on that page. The word "traction" has similar issues.

- The adjective "frictional" is used in terms like "frictional_momentum_loss_rate". But the net loss of momentum (per unit time and per unit area) due to friction in a fluid is equivalent to the
**shear stress**. Note that both have units [M L T-2]. See the template for Stress.

- Some quantities associated with friction are:

kinetic_friction_coefficient (See the Coefficient template.) log_law_roughness_length ("z0" for law of the wall) manning_n_parameter

shear_stress (See the Stress template.) static_friction_coefficient

- A Google search indicates that "friction_rate" is sometimes used in connection with air ducts.

## Fuel Efficiency

*Examples of Specific Quantities:*

"consumption_rate" ["gallons per mile" or "liters per km"] (of fuel)

"fuel-economy" ["miles per gallon" or "km per liter"]

"mass-specific_energy_content" [Joules / kg]

*Examples*

automobile_fuel__consumption_rate automobile__fuel-economy automobile_fuel__mass-specific_energy_content

- In everyday language, the term "miles_per_gallon" is often used as if it were a quantity name but it is really a units name. "mileage" has various meanings and is not a well-defined quantity name.

- energy_efficiency and energy_intensity are related quantities.

- Efficiency of electric vehicles is often given as "cents_per_mile" which allows comparison to gas-powered vehicles.

## Hardness

base_quantity = "hardness"

*Examples of Specific Quantities:*

"indentation_hardness"

"rebound_hardness"

"scratch_hardness"

*Examples*

snowpack_surface__indentation_hardness

- Hardness is a function of many things and there are 3 main types of hardness measurements called indentation hardness, rebound hardness and scratch hardness.

- See Hardness and Scratch hardness.

- The word hardness is also used in chemistry, in the context of "hard water". See: Carbonate hardness and Hard water.
*Permanent hardness*is defined as Calcium hardness + Magnesium hardness, while*temporary hardness*is a synonym for Carbonate hardness. Water hardness can be measured as a**molar concentration**of calcium and magnesium ions, but several alternate units are used around the world and there are conversion factors between them.

## Head

base_quantity = "head"

*Examples of Specific Quantities:*

"friction_head"

"hydraulic_head"

"pressure_head"

"velocity_head"

*Examples*

pump__hydraulic_head soil_water__pressure_head

- Head is a quantity used in fluid dynamics (hydraulics) that relates the energy in an incompressible fluid to the an equivalent height in a column of fluid. It has units of length.

- "Total hydraulic head" is the sum of the elevation head and pressure head.

- The "hydraulic_gradient" is computed by taking differences or derivatives of head values and determines the direction of fluid flow.

- See: Hydraulic head, Pressure head and Total hydraulic head.

## Heat

base_quantity = "heat"

*Examples of Specific Quantities:*

"mass-specific_fusion_latent_heat"

"sensible_heat"

*Examples*

water__mass-specific_latent_fusion_heat (334 [kJ kg-1]) water__mass-specific_latent_sublimation_heat water__mass-specific_latent_vaporization_heat (2500 [kJ kg-1])

- The quantity "heat" refers to "thermal energy" that is being transferred from one system to another by thermal interaction. It has SI units of Joules.

- The word "specific" is often inserted as in "specific_latent_heat" and "specific_sensible_heat" to indicate thermal energy per unit mass [J kg-1].

- While the "latent heat of fusion" and "latent heat of vaporization" are constants for a given substance (e.g. water), they don't use the Constant template but are treated as in the two examples above in accordance with the
**Process_name + Quantity Pattern**. Note that "latent_heat" is a quantity name and "fusion" and "vaporization" are process names.

- The quantities "advection_heat_flux", "conduction_heat_flux", "latent_heat_flux" and "sensible_heat_flux" are also used.

- See Energy and Flux of Heat or Energy.

## Height

base_quantity = "height"

*Examples of Specific Quantities:*

"geopotential_height"

"reference_height"

*Examples*

building~empire-state__height human__mean_height tree~oak~bluejack__mean_height

- See Reference Quantities.

## Humidity and Relative Saturation

base_quantity = "humidity"

*Examples of Specific Quantities:*

"absolute_humidity" (is "volumetric_humidity" a synonym ?)

"relative_humidity"

"relative_saturation"

"specific_humidity"

*Examples*

atmosphere_air_carbon-dioxide__relative_saturation ## CHECK atmosphere_air_water~vapor__relative_saturation (instead of air_relative_humidity)

- Relative humidity is a dimensionless ratio of partial pressures. It is defined as the ratio of the partial pressure of water vapor in the air-water mixture (often called the "vapor pressure") to the saturated vapor (partial) pressure of the water at a prescribed temperature.

- The relative humidity is often known (measured) and empirical equations for computing saturated vapor pressure as a function of temperature have been given by both Brutsaert and Satterlund. From these, vapor pressure can be computed from the definition.

- Relative humidity of air depends on both temperature and pressure.

- The more general term for relative humidity (when not talking about water vapor in air) is
**relative_saturation**. It is the ratio of the partial pressure to the saturated partial pressure of one (condensable phase) gas in another (non-condensable phase) gas mixture.

## Impedance

base_quantity = "impedance"

*Examples of Specific Quantities:*

"acoustic_impedance"

"characteristic_acoustic_impedance"

"characteristic_electrical_impedance"

"electrical_impedance"

"mechanical_impedance"

"nominal_electrical_impedance"

"specific_acoustic_impedance"

"wave_impedance"

*Examples*

None yet

- Electrical impedance is a complex-valued quantity, where the real part is the familiar
**resistance**(with SI unit "ohm") and the imaginary part is the less-familiar**reactance**.

**Admittance**is defined as the inverse of impedance, and is therefore also complex-valued. Its real part is called**conductance**(with SI unit "siemens") and its complex part is called:**susceptance**.

- See: Acoustic impedance, Electrical impedance, Impedance (Accelerator Physics), Mechanical impedance and Wave impedance.

- Also see: Capacitance, Electrical reactance, Electrical resistance and Inductance.

## Impulse

base_quantity = "impulse"

*Examples of Specific Quantities:*

"impact_impulse"

*Examples*

baseball-bat_baseball__impact_impulse

- An "impulse" quantifies the change in linear momentum that results from a force applied over a time interval. It has units of (force x time), and SI units of [N s].

- See: Impulse (physics).

## Increment

operation_prefix = "increment_of"

*Examples*

atmosphere_air__increment_of_pressure bedrock_surface__increment_of_elevation land_surface__increment_of_elevation

- This can be used for the change in a quantity that occurs over some time period, such as a model time step. Models often update state variables with each time step by an incremental amount and this amount may be the quantity of interest. Note that an increment can be positive or negative.

- Before 3/19/13 this was treated as a
**quantity suffix**but now it is treated as an "operation prefix". See Anomaly, Component, Limit, Magnitude, Ratio and Scale.

- For an "increment_of_time", the quantity suffix "step" is usually used instead of "increment". See the Step and Time Step templates.

## Index

base_quantity = "index"

*Examples*

atmosphere_air_radiation__standard_refraction_index consumer__price_index ecosystem__diversity_index land_surface__topographic_wetness_index model_grid_cell__column_index model_grid_cell__row_index __normalized_difference_vegetation_index ################ __palmer_drought_index

- The word "index" serves as a
in the CSDMS Standard Names. It has two distinct meanings. One meaning of index is a subscript to an array, as used in "model_grid_cell__column_index" and "model_grid_cell__row_index" above. In this case, the index is a nonnegative integer. A second, and widely-used meaning for index is a**base quantity****composite statistic**or**measure**. See the Wikipedia article: Index (statistics). Examples of this type include: Consumer Price Index, Normalized Difference Vegetation Index, Palmer Drought Index, Topographic Wetness Index and Urban Accessibility Index and others listed below.

- Perhaps we should use the word
*subscript*instead of index for the first meaning of index above.

- In order to distinguish between many different indices of a certain type, such as a
*diversity index*, the last name of the author who introduced a particular index (and also the publication year, if necessary) can be used as a prefix to disambiguate, as in*shannon_diversity_index*.

- We use "refraction_index" instead of "refractive_index" in accordance with the
**Process_name + Quantity Pattern**. See Attributes of Radiation for information on the "standard_refraction_index".

- See Coefficient, Constant, Exponent, Factor, Number and Parameter.

- See: Diversity index, Forest fire weather index, Haines index, Heat index, Index (economics), Index (statistics), Jaccard index, Lifted index, Normalized Difference Vegetation Index, Palmer drought index, Price index, Producer Price Index, Refraction index and S & P Dow Jones Indices, Stock market index, Topographic Wetness Index.

## Inertia

base_quantity = "inertia"

*Examples of Specific Quantities:*

"rotational_inertia" [kg m2]

"thermal_inertia" [J m-2 K-1 s-0.5]

"translational_inertia" [kg] (sometimes used as a synonym for "mass")

*Examples*

projectile__rotational_inertia sea_water__thermal_inertia

- The term
**inertia**by itself refers to the degree to which an object resists changes to its translational motion, which depends only on its mass. The term "translational inertia" (a synonym for mass?) is sometimes used for clarity, especially since the concept of inertia lends its name to the quantity names "rotational inertia" (also called moment of inertia) and "thermal inertia".

- The concept of inertia comes from Newton's first law of motion and can be stated as: "When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted on by an external force." It is often summarized with the adage: "Objects in motion tend to stay in motion. Objects at rest tend to stay at rest."

**Rotational inertia**is also called "moment of inertia" and is a measure of the resistance to an object to changes in its angular momentum.

- The
**thermal inertia**of a material is a measure of its resistance to changes in temperature. It is defined as the square root of the product of thermal conductivity, mass density and mass specific thermal capacity.

- Thermal inertia is an "intensive property" since it involves mass specific thermal capacity.

- See Inertia, Moment of inertia (rotational inertia), Thermal effusivity and Thermal inertia.

## Intensity

base_quantity = "intensity"

*Examples of Specific Quantities:*

"luminous_intensity" (optics)

"radiant_intensity" (optics)

"sound_intensity" (or "acoustic_intensity")

*Examples*

atmosphere_air_radiation~incoming~shortwave__energy_intensity [ W m-2] ############# energy_flux ??

- Intensity is an overloaded term, but often means "power per unit area" and is therefore equivalent to an "energy flux".

- It is not yet clear when (or if) the CSDMS Standard Names should use "intensity" instead of "energy_flux", which is more descriptive. See Flux.

- See: Intensity (physics), Radiant intensity and Sound intensity.

## Latitude

base_quantity = "latitude"

*Examples of Specific Quantities:*

"authalic_latitude"

"conformal_latitude"

"geocentric_latitude"

"geodetic_latitude"

"isometric_latitude"

"rectifying_latitude"

"reduced_latitude"

*Examples*

model_grid_cell_center__geodetic_latitude model_grid_cell_edge~north__geodetic_latitude model_grid_cell_edge~south__geodetic_latitude model_grid_edge~north__geodetic_latitude model_grid_edge~south__geodetic_latitude

- For an ellipsoid (of the type used to model the shapes of planets), there are many different ways to define latitude, but really just one way to define longitude. This is because the longitude lines (meridians) trace out ellipses (of the same size and shape) while the latitude lines are circles (of different sizes). When unqualified, the word "latitude" usually refers to
**geodetic latitude**. The other six types of latitude are called "auxiliary latitudes" and are used for special problems in geodesy. Full explanations of these different types of latitude are provided at the links below.

- For a spheroid, the various definitions of latitude become the same. This is because the equatorial and polar radius are then the same, so the flattening, f, and eccentricity, e, are both zero. This can be checked by inserting e=0 into formulas for
**auxiliary latitudes**.

- Typical units for latitude are "decimal degrees".

- This quantity is always relative to a particular (reference) ellipsoid model which should be specified using an <ellipsoid> tag in the Model Coupling Metadata (MCM) file. Similarly, <datum> and <projection> tags can be used. An <assume> tag should also be used to specify "geographic_coordinate_system".

- Note: Should we use "geographic_grid" instead of just "grid" for the object name in the examples above?

- See the sections for Coordinates and Longitude.

- See: Colatitude, Geodetic datum, Geographic coordinate system, Geographical distance, Latitude, Longitude, Meridian arc and Reference ellipsoid.

## Limit

operation_prefix = "limit_of"

*Examples*

human__lower_limit_of_hearing_frequency (Note: hearing is a process name) human__upper_limit_of_hearing_frequency human_eye_photon__lower_limit_of_detection_number (process_name + quantity) star~neutron__tolman_oppenheimer_volkoff_limit_mass star~white-dwarf__chandrasekhar_limit_mass

- Before 3/19/13 this was treated as a
**quantity suffix**, but now it is treated as an "operation prefix". See Anomaly, Component, Increment and Magnitude. A "limit" is not a quantity by itself, but is an operation that can be applied to virtually any quantity.

- For clarity, it is often necessary to insert an adjective like "lower" or "upper" before the word "limit", as in the examples above.

- Note that the two limits above named after people include the quantity name "limit_mass" instead of "limit_of_mass". There is also a related "Schwarzchild radius"; see the quantity template for Radius. It is not clear that "_limit" would ever be used by itself. See Point.

- "cutoff" or "threshold" may sometimes be used similarly.

## Longitude

base_quantity = "longitude"

*Examples*

model_grid_cell_center__longitude model_grid_cell_edge~east__longitude model_grid_cell_edge~west__longitude model_grid_edge~east__longitude model_grid_edge~west__longitude

- While there are several different ways to define
**latitude**for an ellipsoid, there is really just one way to define longitude, as explained in the Latitude section.

- Since "center", "edge~east", "edge~west", etc. refer to parts of a cell, it is consistent with the use of similar words like "bottom" and "top" to include these in the object name part of the name (as of 7/23/14). Hyphens are used as shown here to clarify that "edge~east" is a single object or sub-object.

- Typical units are "decimal degrees".

- Typical units for longitude are "decimal degrees".

- This quantity is always relative to a particular (reference) ellipsoid model which should be specified using an <ellipsoid> tag in the Model Coupling Metadata (MCM) file. Similarly, <datum> and <projection> tags can be used. An <assume> tag should also be used to specify "geographic_coordinate_system".

- Note: Should we use "geographic_grid" instead of just "grid" for the object name in the examples above?

- See the sections for Coordinates and Latitude.

- See: Colatitude, Geodetic datum, Geographic coordinate system, Geographical distance, Latitude, Longitude, Meridian arc and Reference ellipsoid.

## Magnitude

"magnitude_of_" + [vector quantity]

*Examples*

sea_bottom_water__magnitude_of_shear_stress sea_water__magnitude_of_vorticity

- Magnitude is a general term in mathematics, used to indicate a scalar-valued "size" of something like a vector or complex number.

- The quantity name "speed" should be used instead of "magnitude_of_velocity".

- This was changed from a "quantity suffix" to a vector operation on 2/7/13. See CSDMS Operation Templates.

- In the CF Standard Names, "magnitude_of_" is a transformation (used as a prefix to an entire name) that is used in about 5 names.

## Mask

base_quantity = "mask"

*Examples*

land_mask ocean_mask

- In computer graphics and geographic information systems (GIS), the word "mask" is used to indicate a gridded (usually 2D or 3D) binary mask where two values (e.g. 0 and 1) are used to indicate whether or not a given feature or property is present in that grid cell. The term "data mask" is sometimes used to indicate that grid cells contain a data value if they are in the mask and a nodata value otherwise.

- A mask is often associated with a threshold value of some other grid of data. For example, a "land mask" may be set to 1 for every grid cell with an elevation value greater than 0 and set to 0 otherwise. We could use a standard name like "elevation_threshold_mask" or "temperature_threshold_mask" and then define the threshold value and how the masked values are related to the threshold value (>, >=, <, <= or =) with an <assume> tag in a Model Coupling Metadata (MCM) file.

- Masks provide a mechanism to identify a subset of a larger set, so they are a way to refer to a part of a larger object. Because of this, it is reasonable to use "land-mask" as an object in the object part of a CSDMS Standard Name. However, it is also reasonable to use "binary_mask" as a quantity name since it indicates the possible values (0 and 1) and the absence of units. A "data mask", on the other hand, inherits the quantity name and units of the data. So it would be reasonable to use "data_mask_of" as an operation, as in "positive_data_mask_of_elevation".

- The CF Standard Names currently have two names that contain the word "mask", namely: "land_binary_mask" and "sunlit_binary_mask". The guidelines mention both "binary_mask" and "data_mask".

- Terms like "presence_mask", '"inclusion_mask" and "exclusion_mask" would fit the
**Process_name + Quantity Pattern**.

- Note that painters use Masking tape to "mask off" areas that should not be painted.

- See: Binary image and Mask (computing).

## Mass

base_quantity = "mass"

*Examples of Specific Quantities:*

"molar_mass"

"relativistic_mass"

"rest_mass"

*Examples*

### cesium_atomic_mass (also relative_atomic_mass = atomic_weight) electron__relativistic_mass electron__rest_mass (also invariant mass, intrinsic_mass, proper mass) star~neutron__tolman_oppenheimer_volkoff_limit_mass star~white-dwarf__chandrasekhar_limit_mass (object = star~white-dwarf)

- The SI units for mass are kilograms.

- What about "biomass"?

- See Attributes of Atoms, Concentration, Flux.

- See: Added mass, Biomass, Invariant mass, Mass-energy equivalence, Mass in special relativity, Molar mass, Planck mass and Transverse mass.

## Maximum

*Examples*

basin_outlet_water_x-section__time_max_of_volume_flow_rate (for "peak discharge')

- While we could use "max" as a quantity suffix, this is not unambiguous for quantities that can vary in both space and time, such as drainage basin discharge. It seems best to introduce "time_max_of_" and "domain_max_of_" as operations instead. See:
**CSDMS Operation Templates**.

## Miles per Gallon

- This is not allowed because it is not a good quantity name; it is really a units name. The associated concepts are "fuel consumption rate" and "fuel economy". The word "mileage" is sometimes used but is also a poor term.

- See the Fuel Efficiency template.

## Minimum

*Examples*

basin_outlet_water_x-section__time_min_of_volume_flow_rate

- While we could use "min" as a quantity suffix, this is not unambiguous for quantities that can vary in both space and time, such as drainage basin discharge. It seems best to introduce "time_min_of_" and "domain_min_of_" as operations instead. See:
**CSDMS Operation Templates**.

## Modulus

base_quantity = "modulus"

*Examples of Specific Quantities:*

"bulk_modulus"

"shear_modulus"

"young_modulus"

*Examples*

lithosphere__bulk_modulus lithosphere__young_modulus

- This quantity is used in continuum mechanics and materials science to measure a material's resistance to different types of deformation, sometimes called rigidity or stiffness. It has units of pressure.

- Bulk, shear and Young's are different types of "elastic modulus".

- There are several different models for how the shear modulus of metals varies with pressure and/or temperature, such as the MTS, SCG and NP models. See: Shear modulus.

- See: Bulk modulus, Dynamic modulus, Elastic modulus, Lamé parameters, P-wave modulus, Poisson's ratio, Shear modulus and Young's modulus.

## Number

base_quantity = "number"

*Examples of Specific Quantities:*

"julian_day_number"

"neutron_number"

"proton_number"

"quantum_number"

"wavenumber"

"winding_number"

*Examples*

automobile__vehicle_identification_number (i.e. VIN number) carbon_isotope__neutron_number iron_atom__neutron_number iron_atom__proton_number sea_surface_water_wave__wavenumber

- This quantity name is often used when the attribute being quantified can only take integer values, as in the examples above and detectors that count particles. The word "count" is used similarly.

- Many important
**dimensionless numbers**also end with the word "number" and are often named after a person (e.g. Reynolds number). These are discussed in the Dimensionless Number template and they are typically not integers. Also the wave number need not be an integer.

- Sometimes, there are multiple definitions for a dimensionless number, so they aren't always interchangeable. For example, there are at least 4 types of Richardson number. One is the reciprocal of the square of the Froude number. Three others are used in atmospheric science and are preceded by the adjective "flux", "gradient" or "bulk" (an approximation to the gradient version). For some definitions, the Richardson number can only take positive values, while for others it can also take negative values, which indicates an unstable atmosphere. The AMS provides several definitions of the Richardson number.

- Atomic number is a synonym for "proton_number" but the latter is used for clarity and consistency in the CSDMS standard names. The "mass_number" is defined as the sum of the "proton_number" and "neutron_number".

- Atomic physics uses several quantum_numbers, including the: principal quantum number, azimuthal quantum number, magnetic quantum number, spin quantum number and topological quantum number.

- Several other "numbers" are defined in particle physics, such as the "electronic_number", "muonic_number" and "tauonic_number".

- The winding number is used in mathematics as an attribute of closed, planar curves.

- See: Atomic number, Lepton number and Neutron number.

- Unique identification numbers are often assigned to people and other objects. See Credit card number,Employer Identification Number (EIN), Enzyme Commission Number, National Identification Number, Numbering scheme, Social Security Number, Transporter Classification Number and Vehicle Identification Number (VIN).

- In the branch of mathematics called
*number theory*there are many special numbers, often named after a famous person. The Online Encyclopedia of Integer Sequences (OEIS) maintains an extensive database of information on integer sequences. See: Bell number, Catalan number, Euler number, Fibonacci number, Hardy-Ramanujan number, Kaprekar number, Lucas number, Prime number and Smith number. Also see the template for Constants in Math.

- For hydrologic features such as rivers, unique identification numbers such as the USGS Hydrologic Unit Code (or "HUC number") and Pfafstetter Code are used. See Code.

- See the Count template and Julian day.

## Parameter

base_quantity = "parameter"

*Examples*

channel_bottom_water_flow_sediment__shields_parameter channel_water_flow__manning_n_parameter soil_water__van_genuchten_alpha_parameter

- Parameters often occur in empirical laws.

- The CSDMS Standard Names use "manning_n_parameter vs. "manning_coefficient".

- The CSDMS standard names use "coriolis_frequency" vs. "coriolis_parameter".

- Shields (1935) worked with a nondimensional shear stress that is now known as the Shields parameter.

- See templates for Coefficient, Constant, Exponent, Factor, Index and Number.

## Partial Pressure

base_quantity = "partial_pressure"

*Examples of Specific Quantities:*

name = [substance 1] + "_" + [substance 2] + "_partial_pressure"

*Examples*

atmosphere_carbon-dioxide__partial_pressure # (carbon dioxide in air) atmosphere_water~vapor__partial_pressure # (water vapor in air) atmosphere_water~vapor__saturated_partial_pressure

- This is an example of a quantity that uses the
**Object-in-object Quantity Pattern**because two substances are involved. See Solubility and Volume Fraction.

- The term "water vapor pressure" refers to the partial pressure of water vapor in air, and the "saturated water vapor pressure" is the partial pressure of water vapor in air at saturation. The CSDMS standard names for these are given above. One of them uses the
**Saturated Quantity Rule**.

- Partial pressure for a gas dissolved in a liquid is the partial pressure of that gas which would be generated in a gas phase in
with the liquid at the same temperature. See: Partial pressure.**equilibrium**

- CF Standard Names currently has only 6 names with "partial_pressure". They all have units of [Pa] and are:

surface_carbon_dioxide_partial_pressure_difference_between_air_and_sea_water surface_carbon_dioxide_partial_pressure_difference_between_sea_water_and_air surface_molecular_oxygen_partial_pressure_difference_between_sea_water_and_air surface_partial_pressure_of_carbon_dioxide_in_air surface_partial_pressure_of_carbon_dioxide_in_sea_water water_vapor_partial_pressure_in_air (alias: water_vapor_pressure)

- We could use the following CSDMS standard name for the first quantity listed above:

"sea_surface_air-vs-water_carbon-dioxide" + "difference_of_partial_pressure" (with "difference" as a quantity suffix). Or with a new rule for "-and-in_", we could use: surface_carbon_dioxide_in_air-and-in_sea_water_partial_pressure_difference.

- See the quantity template for Pressure.

## Perimeter

base_quantity = "perimeter"

*Examples*

basin_boundary__perimeter channel_x-section__perimeter

- This quantity has units of length and is well-defined for virtually any (nonfractal) planar shape. It can be infinite, however, for a fractal shape such as the Koch snowflake.

- See Diameter.

## Period

base_quantity = "period"

*Examples of Specific Quantities:*

"sidereal_period"

"synodic_period"

*Examples*

earth__rotation_period flood__expected_return_period ######### Need a flood size adjective. mars_orbit__sidereal_period mars_orbit__synodic_period sea_surface_water_wave__period virus_chicken-pox__incubation_period

- This quantity has units of time and is typically used to describe the time required for some time of
*periodic*motion to return to its starting point. Examples include the rotation of a planet on its axis, the orbit of a planet around the sun or the period of a wave.

- In hydrology the terms: Return period, "return time", "recurrence interval" and "flood frequency" are used to quantify the expected time between floods of a given size.

- See: Orbital period for definitions of "sidereal period", "synodic period", "draconic period", "anomalistic period" and "tropical period".

- The
**Process_name + Quantity Pattern**is often used, as in: "digestion period", "dormant period", gestation period, Hibernation period, incubation period, rotation period, "sleeping period"], waiting period and wave period.

- See Duration and Time.

## Permeability

base_quantity = "permeability"

*Examples*

sea_bottom_sediment__permeability

- Permeability is a property of a geologic material (and not the fluid) that indicates the ability of a fluid to move through it. It is related to
**hydraulic conductivity**.

- See Hydraulic conductivity and Permeability (earth sciences).

## pH

base_quantity = "ph"

*Examples*

channel_water__ph sulfuric-acid_solution__ph

- This quantity measures the activity of the (solvated) hydrogen ion in a solution. It is close to 7 for pure water, less than 7 for acidic solutions and greater than 7 for basic (i.e. alkaline) solutions.

- Should "pH" be viewed as a measurement unit instead of a quantity?

- See: Wikipedia: pH.

## Point

*Examples*

boiling_point breaking_point ?? bubble_point critical_point (See: Critical point.) curie_point (See: Curie point.) dew_point flash_point freezing_point frost_point melting_point wilting_point (used in infiltration theory) yield_point (See: Yield strength.) atmosphere_water~vapor__dew_point_temperature atmosphere_water~vapor__frost_point_temperature ice__melting_point_temperature water__boiling_point_temperature water__freezing_point_temperature

- This is not viewed as a quantity or quantity suffix within the CSDMS Standard Names. It is generally inserted just before a base quantity name and refers to a
**threshold**that occurs for that quantity. See the template for Temperature for many examples.

- Each of the examples above puts a "process name" prefix, from the list of process names in
**CSDMS Process Names**in front of "_point".

## Porosity

base_quantity = "porosity"

*Examples*

soil__porosity

- Could also be called "soil_air__volume_fraction".

## Power

base_quantity = "power"

*Examples*

channel_water__power

- "Power" has SI units of [J s-1] = [ W ]. In the context of a fluid in motion, it is an "energy flow rate" associated with the kinetic energy of the fluid. It is proportional to the cube of the fluid velocity. For a non-accelerating flow, the gravitational acceleration of the flow is exactly balanced by the loss of momentum due to friction. See the template for Flow Rate.

- In hydrology, the terms "stream_power" and "unit_width_stream_power" are used. See: Stream power.

## Precipitation

"precipitation_" + base_quantity

"precipitation_leq-volume_flux

"precipitation_mass_flux

"precipitation_volume_flux

*Examples*

atmosphere_water__precipitation_duration atmosphere_water__precipitation_leq-volume_flux (in liquid or solid form) atmosphere_ice__precipitation_volume_flux atmosphere_snow__precipitation_volume_flux titan_atmosphere_methane__precipitation_leq-volume_flux (on Titan)

- Precipitation is not a quantity, but rather a process as defined at the top of the
**CSDMS Process Names**page. However, there are several quantities associated with precipitation, as seen in the examples above. A "precipitation_volume_flux" is a volume per unit area and unit time, and therefore has units of [length / time] (e.g. mm per hour). A "precipitation_mass_flux" is a mass per unit area and unit time, and therefore has units of [mass / (area * time)] (e.g. kg per square meter per hour).

- "Rainfall" is a somewhat unusual example of a process name in that the relevant object (rain) and the associated process (falling) have been fused to create the process name. Adding the object part in front would mean repeating the word rain. But "rain" is also a verb and "raining" is therefore a valid process name, but only for liquids. In the CSDMS Standard Names, the object that is precipitating is specified in the object part of the name, such as "water", or perhaps "methane" for Titan.

- Since water can precipitate in liquid or solid form, each with a different density, precipitation rates are often quantified as
**liquid-water equivalent**. The corresponding CSDMS standard name is: "atmosphere_water" + "precipitation_leq-volume_flux", where "leq-volume" is an abbreviation for "liquid-equivalent volume". This quantity name generalizes to other substances (like methane on Titan). See: Precipitation (chemistry) and Precipitation (meteorology).

- Note that in the CSDMS Standard Names, it is considered unnecessary and redundant to insert "liqui-equivalent" into the names "ice" + "melt_volume_flux" and "snowpack" + "melt_volume_flux", since the process of melting converts ice and snow to liquid water.

- The name "snowpack" + "liquid-equivalent_depth" is also used and is computed by multiplying the snowpack depth by the "liquid-water-to-snow_density_ratio".

- The word "water" by itself does not indicate whether the state is gas, liquid or solid.

- See the templates for Process Attributes and Rates of Processes for more information.

## Pressure

base_quantity = "pressure"

*Examples of Specific Quantities:*

"dynamic_pressure"

"osmotic_pressure"

"radiation_pressure"

"partial_pressure" (See Partial Pressure above)

"stagnation_pressure"

"static_pressure"

"total_pressure"

"vapor_pressure"

*Examples*

atmosphere_bottom_air__pressure channel_bottom_water__static_pressure channel_bottom_water_flow__dynamic_pressure channel_bottom_water_flow__total_pressure channel_water__static_pressure channel_water_flow__dynamic_pressure (anywhere in the channel) channel_water_flow__total_pressure

- Pressure may be thought of as "force per unit area".

- There is a distinction between
**static pressure**and**dynamic pressure**. The first results from the weight of fluid above a location (called "hydrostatic" when the fluid is water) while the second is the kinetic energy per unit volume of a fluid flow. The "total pressure" is the sum of these two contributions. Also see: Bernoulli's principle, Pressure and Stagnation pressure.

- Pressure requires specifying a single object (e.g. air) but "partial pressure" requires two different objects to be specified using the "object-in-object" pattern. See the quantity template for Partial Pressure.

- In chemistry, the term
**vapor pressure**(also called "equilibrium vapor pressure") has a specific meaning, and is a property of a single compound or substance.

- In meteorology, the term "vapor pressure" is used to mean the
**partial pressure**of water vapor in the atmosphere, even if it is not in equilibrium, and the adjective equilibrium is inserted otherwise. In the CSDMS Standard Names, the term "vapor pressure" is only used as it is defined in chemistry, and for meteorology, names use "partial_pressure" or "saturated_partial_pressure" as in: "atmosphere_air_water~vapor" + "partial_pressure".

- Electromagnetic radiation exerts
**radiation pressure**on an illuminated surface. A Crookes radiometer is often used to illustrate this effect, but it is now known that a combination of Einstein and Reynolds forces (thermal transpiration) is actually responsible for making them turn.

- The quantity
**pressure head**is used in hydraulics and in ground water modeling but it has units of length. It is often negative, and negative pressure is sometimes called*suction*. See Head.

- In geology, the term
**overburden pressure**or*confining_pressure*, is used.

- Although the pressure generated by a sound wave is sometimes called
**sound pressure**, the standard name would then be something like: "air_sound-wave" + "pressure".

- In cosmology, there is also a concept of "negative pressure".

- Note that "atmosphere_bottom_air" + "pressure" and "land_surface_air" + "pressure" would mean the same thing, but the former is preferred.

- See: Atmospheric pressure, Dynamic pressure, Osmotic pressure, Overburden pressure, Partial pressure, Pressure, Pressure head, Radiation pressure, Stagnation pressure, Static pressure, Surface tension and Vapor Pressure.

## Process Attributes

[ process name ] + [ base_quantity ]

*Examples*

digestion_period, gestation_period, hibernation_period, incubation_period, sleeping_period ------------------------------------------------------------------- lapse_rate, ------------------------------------------------------------------- evaporation_mass_flux, infiltration_mass_flux, melt_mass_flux, precipitation_mass_flux evaporation_volume_flux, infiltration_volume_flux, melt_volume_flux, precipitation_volume_flux ------------------------------------------------------------------- conception_date delivery_date (vs. "expected_delivery_date" or "due_date") launch_date ovulation_date starting_date (or "start_date" ??) ---------------------- precipitation_duration sunshine_duration ---------------------- failure_frequency oscillation_frequency vibration_frequency wave_frequency (vs. "waving") ---------------------- recovery_time starting_time stopping_time ---------------------- flow_speed running_speed wind_speed (Note: "wind" = "air_flow".) ---------------------- birth_weight dissociation_energy penetration_depth striking_distance turning_radius

- Many quantity names are created by pairing a process name with a base quantity name. See the Process Name + Base Quantity Name Pattern are given on the
**CSDMS Process Name + Quantity Name Pattern**page for a long list of examples.

- Process names are almost always generated by converting a verb to a noun with a standard ending like "tion". See
**CSDMS Process Names**for details and a long list of examples.

- Pairing a process name with the base quantity name "rate" makes sense for most processes, but a given process if often naturally associated with other base quantities (e.g. gestation_period). See the Rate template for examples where the base quantity is "rate".

- In the example of "birth_weight", "birth" is a process that is happening to the baby, while "delivery" or "giving birth" is the process happening to the mother. (i.e. "infant_birth_weight" and perhaps "pregnant_female_delivery_date")

## Radiation

"radiation_" + quantity

*Examples*

light-bulb~incandescent__radiant_intensity ? ##### CHECK universe__cosmic_background_radiation_frequency

- See the
**CSDMS Standard Names Examples**page for many examples where "radiation" is viewed as an object and appears in the object part of the name and the quantity is an energy_flux. These examples include the atmosphere, glacier, land_surface, sea_water and snowpack. Together they cover most of the Earth's basic radiation budget.

- Note that "radiation" (the process where an object generates and sends out energy) and "irradiation" (the process where an object receives energy from a source) are really distinct processes, and neither is a quantity by itself. The object in the object part of the name is either radiating energy or being irradiated by some external source of energy. However, as of 7/23/14, the adjectives "incoming" and "outgoing" are used instead of distinguishing between these two process names. (Similarly, "inflow" and "outflow" will not be used for fluid flow quantities.) This provides additional flexibility with semantic matching and provides a single, general and more easily understood rule. Quantity names can be constructed using the
. See the Process Attributes template.**Process_name + Quantity Pattern**

- Incoming fluxes generated externally (from the point of view of the object name) and outgoing fluxes generated internally both have positive signs, by convention.

- The adjectives "upwelling" and "downwelling" are frequently used to mean "from the ground" and "from the sky". Note that "upwelling" longwave radiation would include longwave radiation emitted by the land surface as well as longwave radiation reflected from the land surface, but originally emitted from clouds or aerosols. So far, these adjectives are not used in the CSDMS Standard Names.

- Adjectives like longwave, shortwave, microwave, visible, infrared, thermal-infrared, ultraviolet and so on are typically inserted just before the word radiation.

- In a vacuum (e.g. space), the refraction index for all wavelengths of light is 1, so the speed of light is independent of wavelength. In other media, such as air and water, the refraction index (and therefore the speed) varies with wavelength. See the Index template.

- Radiation fluxes are
**energy fluxes**(see the Flux template) and have SI units of [W m-2] = [J m-2 s-1].

## Radius

base_quantity = "radius"

*Examples*

automobile__turning_radius black-hole__schwarzchild_radius earth_ellipsoid__equatorial_radius earth_ellipsoid__polar_radius railway_curve__minimum_radius (see link below)

- See the Wikipedia pages for: Bend radius, Bohr radius, Classical electron radius, Covalent radius, Earth radius (which gives several possible definitions), Filling radius, Ionic radius, Minimum Railway Curve Radius, Radius of curvature (mathematics), Schwarzschild Radius, Turning Radius, Van der Waals radius and Wigner-Seitz radius.

- What about Radius of Curvature? See the object template for Surface.

## Rate

base_quantity ="rate"

*Examples of Specific Quantities:*

[ process name ] + "_rate"

*Examples*

atmosphere_air__temperature_lapse_rate automobile_fuel__consumption_rate glacier_terminus__calving_rate human_alcohol__consumption_rate

- The word "rate" means
**per unit time**and is often paired with a process name to create a quantity name that quantifies how fast the process occurs, as in the examples above.

- Quantity names like: "evaporation rate", "infiltration rate", "melt rate" and "precipitation rate" are ambiguous because these rates can be quantified with either a mass flux [kg m-2 s-1] or a volume flux [m s-1]. (The latter is what is usually meant.) So, for example, we can have "glacier_ice" + "melt_mass_flux", "glacier_ice" + "melt_volume_flux", "evaporation_mass_flux", "evaporation_volume_flux", etc.

- Many examples of process names (and a definition) are given on the
**CSDMS Process Names**page.

- Many examples of the Process Name + Base Quantity Name Pattern are given on the
**CSDMS Process Name + Quantity Name Pattern**page.

- When necessary for clarification, the standard assumption name "liquid_equivalent" can be included with an <assume> tag in a Model Coupling Metadata (MCM) file. It seems that the quantity "ice_melt_rate", however, implies a rate at which water is being generated. In the CSDMS Standard Names, "leq-volume" is used as an abbreviation for "liquid-equivalent volume". In the CF Standard Names, "lwe" is used as a standard abbreviation for "liquid_water_equivalent" and this abbreviation is used as an adjective.

- Terms like "rainfall_rate" and "rain_rate", though commonly used, do not lend themselves to our general (object + quantity) pattern. Note that "rainfall" is a contraction of object (rain) and process (falling) names.

- See Precipitation.

## Ratio

base_quantity = "ratio"

*Examples of Specific Quantities:*

"aspect_ratio"

"bowen_ratio"

"dilution_ratio"

"mass_ratio"

*Examples*

bear_brain-to-body__mass_ratio earth_ellipsoid__inverse_of_flattening_ratio engine_air-to-fuel__mass_ratio (or "mixture_ratio") fuel-to-oxidizer__equivalence_ratio ### image__aspect_ratio lake__bowen_ratio lithosphere__poisson_ratio rocket_payload__mass_ratio rocket_propellant__mass_ratio channel_x-section__width-to-depth_ratio electron__charge-to-mass_ratio

- Some ratios are the ratio of the same quantity as measured for two different objects while others are ratios of two different quantities measured on a single object. The
**Object-to-object Quantity Pattern**is used for the first case and the**Quantity-to-Quantity Pattern**is used for the second case. Examples for both cases are given above.

- Ratios are often dimensionless. In fact, most dimensionless numbers are ratios of forces, etc. See the Dimensionless Number template.

- "ratio" serves as a quantity suffix in quantities like "mass_ratio", but is also allowed as a base quantity.

- Note that "relative_roughness" is a quantity that is defined as the ratio of the roughness length scale and the water depth in a channel. So
*channel_bed_relative_roughness*is a valid standard name but*channel_bed_roughness_length-to-water_depth_ratio*is also valid.

- "aspect_ratio" generally means the ratio of the lengths of the long and short sides of a rectangle; 1 for a square and > 1 otherwise.

- In chemistry, "dilution_ratio" and "dilution_factor" are used for a solute in a solvent.

- In meteorology and hydrology, the Bowen ratio is defined to be the ratio of sensible and latent heating of a water body.

- In geodesy, the "flattening ratio" and "inverse flattening ratio" are used to characterize a standard ellipsoid. See Flattening.

- There are many ratios in economics, including "debt-to-credit_ratio", Debt ratio, Debt-to-GDP ratio, Debt-to-income ratio and Loan-to-value_ratio.

- See Fineness ratio, Mass ratio, Poisson ratio, Power-to-weight ratio and Ratio.

## Reference Quantities

"reference_" + quantity1 + "_" + quantity2

quantity1 + "_reference_" + quantity2

*Examples*

atmosphere_air_radiation__standard_refraction_index land_surface_wind__reference_height_speed land_surface_wind__speed_reference_height ("reference" is between the quantities) sea_surface_air__reference_pressure ?? (insert "dry" before "reference"?) sea_surface_air__reference_temperature ?? soil__reference_depth_temperature soil__temperature_reference_depth

- Many quantities are defined with respect to a reference value of some quantity such as: height, pressure, temperature or wavelength. For example, wind speed is often reported for a reference height of 10 meters. Similarly, a model may require soil temperature at a reference depth of 1 meter.

- The "standard refraction index" for a given medium (e.g. air, water, vacuum) is given for a reference wavelength of 589 nm. For the latter, an <assume> tag should be included in the Model Metadata File that specifies: "at_reference_wavelength_of_589_nm" (and maybe also "yellow_doublet_sodium_d_line_reference".)

- Note that this typically requires that
**two**quantities be specified, e.g "reference_height" and "speed", that result in a matched pair of distinct quantity names. These two names follow the "quantity" patterns given above.

- These quantities typically contain a word like "reference" or "standard". These two words may be treated as reserved words in the CSDMS Standard Names.

- Many quantities are defined for "standard_temperature-and-pressure" or STP and this is one of the standardized
**CSDMS Assumption Names**that can be specified with an <assume> tag. However, there is not one standard definition of STP. The IUPAC (International Union of Pure and Applied Chemistry) defines STP as air at a temperature of 0 degrees C and a pressure of 10^5 Pa. In the US and elsewhere, STP is defined as air at a temperature of 60 degrees F and 14.696 psia (1 atm). An additional <assume> tag will therefore be required to avoid ambiguity.

- Many quantities, such as geopotential height are defined relative to Earth's mean sea level or MSL. An <assume> tag is needed to define the corresponding reference value.

- Georeferenced quantities, such as elevation, require specifying a reference ellipsoid. There is typically an associated datum and a projection may also be specified. Standard names for ellipsoids, datums and projections are provided on the
**CSDMS Metadata Names**page. They can be specified in a Model Metadata File using <ellipsoid>, <datum> and <projection> tags.

- In cumulative frequency analysis (e.g. flood frequencies), a reference value must be specified and this would also be done using an <assume> tag.

- One or more <assume> tags should be used in the Model Metadata File to define the reference quantity. For example, <assume> reference_height_is_10m </assume>. The value of the reference height ("10m" in this example) should not be given in the standard name itself.

- The quantity suffix "Anomaly" also requires providing <assume> tags in a Model Metadata File to specify how the "mean climatology" reference value is defined.

## Reflectance

base_quantity = "reflectance"

*Examples of Specific Quantities:*

"broadband_reflectance"

"spectral_reflectance"

*Examples*

atmosphere_air_radiation~incoming~longwave__reflectance

- Reflectance (also called "reflectivity") is the ratio of the power per unit area [W m-2] of electromagnetic radiation
by a surface to the original,**reflected**power per unit area (or irradiance). It is a dimensionless number between 0 (for a perfectly black surface) and 1 (for a perfectly white surface).**incident**

- Absorptance + Reflectance + Transmittance = 1. See Reflectance and Transmittance below.

- Various authors recommend using the terms: Absorptivity, Emissivity, Reflectivity and Transmissivity as properties of a pure material and Absorptance, Emittance, Reflectance and Transmittance as the analogous terms for the characteristics of a specimen or sample. See: Palmer, J.M. (1994) Chapter 25: The measurement of transmission, absorption, emission and reflection, Handbook of Optics, 2nd ed., Part II, M. Bass, editor, McGraw-Hill, NY. (A PDF file is available
**here**.)

**Reflectance**is the square of the magnitude of the "reflection coefficient" from**Fresnel's equation**. In general, the refraction index and reflection coefficient are complex numbers, as they are for materials that can absorb radiation.

- The quantity "spectral reflectance" is the reflectance associated with a specific wavelength, while "broadband reflectance" is an integral over a range of wavelengths. If a radiation band like "shortwave" or "longwave" is specified in the object part of the name, then it is unnecessary to specify broadband or spectral in the quantity part.

- Albedo is a very closely related concept. See Albedo above.

- See: Absorbance, Albedo, Attenuation coefficient, Beer-Lambert law, Fresnel equations, Mass attenuation coefficient, Opacity (optics), Reflectance and Transmittance.

## Resistance

base_quantity = "resistance"

*Examples of Specific Quantities:*

"electrical_resistance"

"stomatal_resistance"

"specific_thermal_resistance"

"thermal_resistance"

*Examples*

None yet.

- Electrical impedance is a complex-valued quantity, where the real part is the familiar
**resistance**(with SI unit "ohm") and the imaginary part is the less-familiar**reactance**. See Impedance above.

**Conductance**is the inverse of resistance, with SI unit "siemens".

- There is also: Antibiotic resistance.

## Resistivity

base_quantity = "resistivity"

*Examples of Specific Quantities:*

"electrical_resistivity" [siemens-1 m] or [ohm m]

"hydraulic_resistivity" [m-1 s]

"ionic_resistivity"

"thermal_resistivity" [W-1 m K] (this is an intensive property; don't need to add "specific")

*Examples*

snow__thermal_resistivity

**Resistivity**is the reciprocal of**conductivity**and both are "intensive" properties, so the prefix "specific" is not needed.

**Resistance**and**conductance**are also reciprocals, but are "extensive" properties.

- See: [http://en.wikipedia.org/wiki/Hydraulic_conductivity Hydraulic conductivity, Ionic conductivity, Thermal conductivity and Thermal resistance.

## Scale

quantity_suffix = "scale"

*Examples of Specific Quantities:*

"length_scale"

"time_scale"

"velocity_scale"

*Examples*

*_batchelor_scale *_kolmogorov_length_scale *_kolmogorov_time_scale *_kolmogorov_velocity_scale *_mesoscopic_length_scale *_obukhov_length_scale *_planck_length_scale *_planck_time_scale *_taylor_length_scale

- This is another quantity suffix, used to create new quantity names from existing quantity names. It often is used to indicate the value of a quantity that is as small as it can be for the given system and therefore able to serve as a natural unit of measure.

- The adjective "characteristic" is often inserted before the base quantity name, as in "characteristic_length_scale".

- See Natural units, Planck units, Planck length and Planck time.

- Other interesting length scales include the Obukhov length,Mesoscopic scale, Synoptic scale and Nanoscale.

## Sinuosity

base_quantity = "sinuosity"

*Examples of Specific Quantities:*

"downvalley_sinuosity"

*Examples*

channel_centerline__downvalley_sinuosity channel_centerline__sinuosity channel_valley_centerline__sinuosity

- Sinuosity is a dimensionless measure of the extent to which a river channel wiggles or deviates from a more direct path. Although it can be defined in different ways, the result is always a number that is greater than or equal to 1.

- In geomorphology, the standard type of sinuosity — which we here call "downvalley_sinuosity" — is the ratio of the centerline length of a channel to the centerline length of the valley that contains that channel. However, the centerline length of a valley can be difficult to measure with Geographic Information System (GIS) software. The word "sinuosity" (without qualification) is the ratio of the centerline length of a channel to the straight-line distance between the two endpoints of the channel (i.e. "as the crow flies"). Note that "sinuosity" will always be greater than or equal to "downvalley sinuosity".

- Note that the word "centerline" is inserted in accordance with the
**Object_name + model_name Pattern**(i.e. a model of the object in question for which "length" is well-defined) and seems preferable to "axis", "backbone" and "curve".

- Recall that a "geodesic" is the shortest path between two points in a space that may be curved. On the surface of a sphere, a geodesic is given by the "great circle" that passes through two given points on the sphere. In a plane, the geodesic is just the straight line segment or "chord" that connects the two points. Geometry in the plane is also called Euclidean geometry.

- Other types of sinuosity have also been defined in the literature, including: floodplain sinuosity, terrace sinuosity and meander belt sinuosity.

- Even in a channel with straight banks, one can define a "thalweg" sinuosity by using thalweg centerline length in the numerator.

- We could construct longer and more descriptive standard names for different types of sinuosities such as: <br\> "channel_centerline-to-valley_centerline" + "length_ratio" and <br\> "channel_centerline-to-straight_line" + "length_ratio".

This may help to avoid ambiguity for the less common types of sinuosity. We could even replace "length_ratio" in these names with "sinuosity".

- The standard definitions of sinuosity and tortuosity appear to be identical. The term "sinuosity_index" is sometimes used, here called "downvalley_sinuosity". See: Sinuosity and Tortuosity.

## Slope

base_quantity = "slope"

*Examples*

land_surface__slope

- Slope is a dimensionless measure of the local steepness of a surface. It is defined as the magnitude of the gradient of elevation. In 1D, it is computed as"rise over run".

- The term "slope_angle" is used for the angle, beta, such that: slope = tan( beta ), or beta = arctan( slope ).

## Solubility

base_quantity = "solubility"

*Examples*

water_carbon-dioxide__solubility water_diethyl-ether__solubility water_ethanol__solubility

- This quantity always involves two substances and therefore requires using the
**Object-in-object Quantity Pattern**. However, use of the reserved word "in" is now deprecated. (7/23/14). Instead, the containing object is listed first, followed by those contained and multi-word object names are hyphenated. See the templates for Partial Pressure and Fraction (volume fraction) which are similar in this regard.

- The solubility of a gas in a solvent is directly proportional to the partial pressure of that gas in the solvent. See: Solubility.

- Miscibility is the property of liquids to mix in all proportions to form a homogeneous solution and is a closely related concept. It is not a quantity, however.

## Span

base_quantity = "span"

*Examples*

airplane_wing__span beam__span bridge__span human_life__span #### (or human_life__max_of_duration ??)

- Span is an unusual quantity name that may have units of length or time depending on the context.

- "Wingspan" is a contraction of an object name (part of another object) and a quantity name. An underscore is inserted in a CSDMS standard name to indicate that "span" is the base quantity.

## Speed

base_quantity = "speed"

*Examples of Specific Quantities:*

"escape_speed"

"relative_speed"

"settling_speed"

"terminal_speed"

*Examples*

glacier_bottom__sliding_speed land_surface_air_flow__speed

- The quantity name "speed" is equivalent to "magnitude_of_velocity". Velocity components use the "component_of" operation prefix. See the Component template.

- When applied to fluids, the word "flow" is added to the end of the object part of the name, as an abbreviation for "flow field". It was formerly inserted before the word "speed".

- "Velocity" is a vector quantity while "speed" is a scalar quantity. The CSDMS Standard Names may allow vector quantities so that models can attempt to retrieve all velocity components in one data structure.

- The quantity
**relative_speed**is the speed of one object relative to another (which may also be moving, in an arbitrary direction). In general, the "relative speed" can be computed as the magnitude of the**vector difference**between the the velocity vectors of the two objects. Both objects must be named in the object part of the name as in: "aircraft_ground" + "relative_speed".

- See Velocity for "escape speed", "settling speed" and "terminal speed".

## Step

quantity_suffix = "step"

*Examples*

model__time_step

- This is another
**quantity suffix**(defined at the top) that is usually used when the base quantity is "time".

- While an increment can have either sign, a step is generally positive.

- See Increment and Time Step.

## Strain

base_quantity = "strain"

- Strain is a normalized measure of deformation in continuum mechanics and is therefore dimensionless.

- Different fluids and substances have different "stress-strain" relationships. For a Newtonian fluid, there is a linear relationship between the shear stress and the strain rate.

- See Deformation, Shear stress, Strain rate and Stress-strain curve.

## Strength

base_quantity = "strength"

*Examples*

None yet.

- In physics, the "strength" of a vector field is simply its
**magnitude**. See: Field strength and Signal strength. See Magnitude above.

- In materials science, the word "strength" often refers to a critical value of
**stress**. See: Compressive strength, Shear strength, Tensile strength and Yield strength.

- See: Physical strength.

## Stress

base_quantity = "stress"

*Examples of Specific Quantities:*

"deviatoric_stress"

"normal_stress"

"shear_stress" (vs. "shearing_stress"; see below)

*Examples*

channel_bottom_water_flow__magnitude_of_shear_stress channel_bottom_water_flow_sediment_grain__shields_critical_shear_stress sea_bottom_surface_water_flow__normal_component_of_stress sea_bottom_surface_water_flow__x_z_component_of_shear_stress sea_water_flow__down_east_component_of_stress sea_water_flow__down_east_component_of_reynolds_stress sea_water_flow__down_east_component_of_viscous_stress sea_water_flow__down_north_component_of_stress

- Components of stress are specified using the "component_of" operation prefix, as shown in the examples above. For models that use a geographic coordinate system, we would use "east", "north" and "up" to describe component directions. For models that use a Cartesian (or equal-area) coordinate system, we would use "x", "y" and "z".

- Standard adjectives for shear stress include: "skin_friction", "form_drag" and "total".

- Conventions like "right_hand_rule" and "positive_downward" can be indicated in a Model Metadata File with <assume> tags.

- Perhaps we should introduce a convention where "shear_stress" is taken to mean "magnitude_of_shear_stress" when there is no operation prefix.

- Stresses are more complex than vectors and are represented mathematically as tensors.

- There are two "kinds" of stress called "normal" and "shear" stress. While a normal stress is associated with a single vector, two vectors are required to describe a shear stress.

- Note that "shearing_stress" follows the
**Process_name + Quantity Pattern**, where the process name is "shearing". However, the "ing" ending is often dropped, as is often the case with process names; see the top of the**CSDMS Process Names**page. Many fluid dynamics textbooks use "shearing", e.g. Batchelor (1988), and "tangential stress" is a synonym.

- Reynolds stress is a contribution to the total stress tensor in a fluid due to momentum fluctuations that arise within turbulent flows. When "stress" appears by itself, it indicates the "total" stress tensor, which includes the so-called "viscous_stress" and the "Reynolds_stress" (or turbulent stress). (Is radiation stress also included in "total"? See below.)

- Shields (1935) introduced the concept of a "critical shear stress" that must be exceeded at the bed of a river channel in order to initiate sediment transport. The associated quantity name is "shields_critical_shear_stress", with the name "shields" being placed before "critical" to allow other definitions of "critical_shear_stress" by future researchers. We could use the Process Name + Base Quantity Name Pattern to construct a self-describing quantity name like: "transport_initiation_stress", "initial-transport_stress" or "initial-motion_stress".

- In oceanography there is a concept of
**radiation stress**and for electromagnetic radiation there is**radiation pressure**. See Pressure.

- There are 19 CF Standard Names that contain the word "stress". Most contain only one "component adjective" like "eastward", but some have two, such as

surface_downward_eastward_stress surface_downward_northward_stress surface_downward_x_stress surface_downward_y_stress

## Temperature

base_quantity = "temperature"

*Examples of Specific Quantities:*

"convective_temperature"

"effective_temperature"

"equivalent_temperature"

"equivalent_potential_temperature"

"potential_temperature"

*Examples*

atmosphere_air_water~vapor__bubble_point_temperature atmosphere_air_water~vapor__dew_point_temperature atmosphere_air_water~vapor__frost_point_temperature iron__melting_point_temperature snow__temperature soil__temperature water__boiling_point_temperature water__freezing_point_temperature

- Use "dew_point_temperature" vs. "temperature_at_dew_point". Similarly for "boiling_point", "melting_point", "freezing_point", etc.

- Can include how measured with <assume> tags in a Model Metadata File.

- Note that "apparent_temperature" or "heat_index_temperature" (same as "felt_air_temperature") may be less ambiguous standard names than "heat_index", since it has units of temperature.

- Materials with impurities or in very small quantities may melt at a lower temperature than bulk amounts of pure material. This is quantified with Melting-point depressions. In the CSDMS Standard Names, these use the operation prefix "depression_of" + "melting_point_temperature".

- See the Wikipedia pages for: Critical point, Curie point, Dew point, Hydrocarbon dew point, Bubble point and Flash point.

- See the Wikipedia pages for: Temperature, Equivalent temperature, Potential temperature, Equivalent potential temperature, Effective temperature, Color temperature, Brightness temperature, Atmospheric temperature, Sea surface temperature, Convective temperature, Dry-bulb temperature and Wet-bulb temperature.

## Tension

base_quantity = "tension"

*Examples of Specific Quantities:*

"surface_tension"

*Examples*

- Tension is the opposite of compression. It is often used in connection with columns, ropes and strings.

- Tension is not a force, but has units of force (e.g. Newtons).

## Term

base_quantity = "term"

*Examples of Specific Quantities:*

"acceleration_term"

"convection_term"

"diffusion_term"

"forcing_term"

"friction_loss_term"

"sink_term"

"source_term"

"time_derivative_term" (or use "unsteady_term" instead?)

*Examples*

equation~convection-diffusion__convection_term" equation~convection-diffusion__diffusion_term" equation~navier-stokes__body_force_term equation~navier-stokes__convective_acceleration_term equation~navier-stokes__pressure_gradient_term equation~navier-stokes__unsteady_acceleration_term equation~navier-stokes__viscosity_term (or "viscous_diffusion_term" ?) equation~poisson__laplacian_term equation~poisson__source_term

- Many models allow various "terms" in an equation that the model solves numerically to be saved as output.

- In the Navier-Stokes equation, which is widely used for modeling fluid flow, each term has a standard name. The names are: "unsteady_acceleration_term", "convective_acceleration_term" (or "nonlinear_term"), "pressure_gradient_term" (or "pressure_term"), "viscosity_term" (or "diffusion_term" or "vector_laplacian_term") and "body_force_term".

- The convection-diffusion equation has a time derivative (or unsteady) term, a diffusion term, a convection term and source term.

- Many of the examples above follow the
**Process_name + Quantity Pattern**. See the top of the**CSDMS Quantity Templates**page and the list of**CSDMS Process Names**.

**This template is still under review**. The appropriate object_name (possibly an equation_name from the**CSDMS Assumption Names**page) and the associated units are not entirely clear. However, this type of quantity is commonly included among a model's output variables.

- We may also want to include "right_hand_side" and "left_hand_side", but this is dependent on how the equation is written.

- See: Field equation, Laplacian, Vector Laplacian, Poisson's equation, Pressure gradient and Shallow water equations.

## Thickness

base_quantity = "thickness"

*Examples*

shale~burgess_stratum__thickness ("stratum" or "layer" ?) human_hair__thickness mars_atmosphere__thickness model_soil_layer~0__thickness paper__thickness

- This quantity name refers to the
**full**, top-to-bottom vertical length dimension of something that tends to cover an area that is large relative to this length.

- The words "depth" and "thickness" are sometimes used interchangeably. In the context of "layers", "thickness" is usually used (e.g. in meteorology, geology and hydrogeology). In the context of surface water or snow, "depth" is usually used. (As in: "How deep is the lake?" or "The lake depth is 5 meters.") The word "depth" indicates a value that is positive downward from some reference datum. There is often the connotation that it may take values less than some maximum possible value, as in "sea_water_secchi_disk_depth".

- See Altitude, Depth, Elevation and Height.

## Threshold

operation_prefix = "threshold"

*Examples*

- Before 3/19/13, this was treated as a "quantity suffix" but now it is treated as an "operation prefix". In the example above, however, the word "threshold" is used as an adjective. Perhaps it should contain more information, something like "melting_point_temperature".

- It is more common for words like "critical" or "point" to be inserted as an adjective in front of a base quantity name to indicate a threshold value. See the template for Temperature.

- There is a standard name called: "snow + degree-day_threshold_temperature", but since there is no "degree-day_temperature", the name "snow + threshold_of_degree-day_temperature" doesn't make sense.

## Time

quantity_suffix = "time"

*Examples*

channel_water__peak_time_of_volume_flow_rate model__run_time model__start_time model__stop_time model__time

- The quantity "time" can refer to the specific time associated with an event, such as "mars__local_rise_time", or to a duration, as in "relaxation_time".

- We may allow "time" to be used as a "quantity suffix" associated with an event like reaching a peak value. But this use case may also be handled using an operation prefix.

- This is commonly used in the
**Process_name + Quantity Pattern**, as in "start_time" and "stop_time". Recall that the "ing" ending of many process names is dropped. See**CSDMS Process Names**.

- In the mathematics of stochastic processes, the quantities: Hitting time and Stopping time are used.

- In hydrology, the terms "return time", "return period", "recurrence interval" and "flood frequency" are used to quantify the expected time between floods of a given size. See Period.

- In astronomy, a "rise_time" and "set_time" can be defined for any celestial body and an observing location on Earth. See the US Navy's astronomical data services page. Note that these quantities require specifying two objects.

- See: Residence time, Relaxation time, Transition time, Arrival time (and ETA), Fall time, Lead time, Rise time and Holding time.

- See Duration and Period.

## Time Step

quantity_suffix = "step"

base_quantity = "time"

"time_step"

*Examples*

model__time_step

- Note that "increment" and "step" are both
**quantity suffixes**that do not change the units of the base quantity. "Step" is usually used when the base quantity is "time".

- See Increment and Step.

## Transmittance

base_quantity = "transmittance"

*Examples of Specific Quantities:*

"spectral_transmittance"

*Examples*

atmosphere_air_radiation~incoming~longwave__transmittance

- Transmittance is the ratio of the power per unit area [W m-2] of electromagnetic radiation
through something to the original,**transmitted**power per unit area (or irradiance). It is a dimensionless number between 0 and 1.**incident**

- Absorptance + Reflectance + Transmittance = 1. See Absorptance and Reflectance above.

- Various authors recommend using the terms: Absorptivity, Emissivity, Reflectivity and Transmissivity as properties of a pure material and Absorptance, Emittance, Reflectance and Transmittance as the analogous terms for the characteristics of a specimen or sample. See: Palmer, J.M. (1994) Chapter 25: The measurement of transmission, absorption, emission and reflection, Handbook of Optics, 2nd ed., Part II, M. Bass, editor, McGraw-Hill, NY. (A PDF file is available
**here**.)

- While "transmissivity" can mean the transmittance of a pure material (see above), it is also used for a concept in ground water hydrology.

- The quantity "spectral transmittance" is the transmittance associated with a specific wavelength.

- See: Absorbance, Attenuation coefficient, Beer-Lambert law, Mass attenuation coefficient, Opacity (optics), Reflectance and Transmittance.

## Unit-width (and similar) Quantities

base_quantity

*Examples*

human_blood_cell~red__count-per-volume sea_surface_water_wave_crestline__power-per-length

- CF Standard Names use "_across_unit_distance" and "_across_line" to handle this concept.

- "unit_stream_power" is somewhat similar.

- There are several other "per" concepts, such as:

- The "z_integral_of_velocity" in the CSDMS Standard Names is the same as "unit-width discharge".

per_capita per_unit_area per_unit_length per_unit_mass per_unit_time per_unit_width

- These could possibly be used as adjective or modifier prefixes for a base quantity.

## Velocity

base_quantity = "speed"

*Examples of Specific Quantities:*

"darcy_speed"

"drift_speed"

"escape_speed"

"fall_speed"

"flow_speed"

"group_speed"

"impact_speed"

"initial_speed"

"phase_speed" (also called "celerity")

"settling_speed"

"terminal_fall_speed"

base_quantity = "velocity"

*Examples of Specific Quantities:*

"darcy_velocity"

"drift_velocity"

"group_velocity"

"impact_velocity"

"initial_velocity"

"phase_velocity" (vector field of wave rays)

"shear_velocity" (also called "friction velocity")

"azimuth_angle_of_velocity"

"elevation_angle_of_velocity"

"x_component_of_velocity"

"y_component_of_velocity"

"z_component_of_velocity"

*Examples*

atmosphere_ball__fall_speed atmosphere_ball__terminal_fall_speed ### (air_ball__** sounds strange) earth__escape_speed (vs. escape_velocity) electron__drift_speed water_sand_grain__settling_speed # (sand grain in water) electron__x_component_of_drift_velocity electron__y_component_of_drift_velocity sea_water_flow__east_component_of_velocity sea_water_flow__north_component_of_velocity sea_water_flow__up_component_of_velocity sea_water_flow__speed sea_water_flow__x_component_of_velocity sea_water_flow__y_component_of_velocity sea_water_wave~internal~gravity__group_speed sea_water_wave~internal~gravity__phase_speed sea_surface_water_wave__group_speed ## wave~gravity ?? sea_surface_water_wave__phase_speed soil_water_flow__x_component_of_darcy_velocity soil_water_flow__y_component_of_darcy_velocity sea_surface_air_flow__magnitude_of_shear_velocity sea_surface_air_flow__x_component_of_shear_velocity sea_surface_air_flow__y_component_of_shear_velocity

- Velocity is a vector quantity with a magnitude and a direction. Most models store the components of a velocity field as separate variables, in which case the operation
**component_of**can be used as shown in the example above. (See the template for Component.) However, it is also possible that one model would request a complete vector field (i.e. all components) from another model as a single "quantity". Because of this, we need to allow "velocity" itself (a vector) as a base quantity name.

- In addition to the "component_of" operation, there are several other operations that can be used to identify an attribute of a vector, such as: "magnitude_of", "azimuth_angle_of" and "elevation_angle_of". For 2D vector fields, only the azimuth angle applies, but for 3D vector fields the elevation angle (from spherical coordinates) is also required. See the
**CSDMS Operation Templates**.

- The quantity name
**darcy_velocity**is used for 3D flow of water in soil to emphasize its macroscopic definition as a volume flux or "specific discharge". See the template for Attributes of Soil.

- The magnitude of the
**shear_velocity**is defined as the square root of the shear stress (at a boundary) divided by the mass density. It is also called the "friction velocity". Shear velocity is a vector quantity, and its direction is the same as the shear stress component used to define it.

- The shorter quantity name "speed" is used in CSDMS standard names instead of "magnitude_of_velocity" but they mean the same thing. See Speed.

- The terms shear velocity, terminal velocity and escape velocity are all used but they each refer to a speed, or velocity magnitude. The "escape_speed" for Earth is a scalar quantity, independent of direction.

- Note that terminal velocity (called "terminal_fall_speed" here) is a quantity that requires two objects to be specified, an object and the fluid through which it is falling. The
**Object-in-object Pattern**is therefore used. In the context of a particle falling through water, the term "settling velocity" (called settling_speed here) is commonly used.

- See: Angular velocity, Drift velocity, Flow velocity, Group velocity, Phase velocity, Proper velocity, Relative velocity, Soil mechanics (Darcy velocity) Stokes drift and Velocity.

- See the template for Speed.

## Viscosity

base_quantity = "viscosity"

*Examples of Specific Quantities:*

"apparent_viscosity"

"dynamic_shear_viscosity"

"dynamic_volume_viscosity"

"eddy_viscosity"

"extensional_viscosity"

"kinematic_shear_viscosity"

"kinematic_volume_viscosity"

*Examples*

air__dynamic_shear_viscosity air__dynamic_volume_viscosity air__kinematic_shear_viscosity air__kinematic_volume_viscosity polymer__extensional_viscosity sea_water__eddy_viscosity water__dynamic_shear_viscosity water__dynamic_volume_viscosity water__kinematic_shear_viscosity water__kinematic_volume_viscosity water__x_z_component_of_viscosity

- Viscosity is a tensor quantity and is decomposed into "shear" and "volume" components that are analogous to the "shear" and "normal" components used for stress, another tensor quantity. "bulk viscosity" is a synonym for volume viscosity which is important for compressible fluids but is less well-known than shear viscosity.

- Since viscosity is really a tensor, we can refer to each of its possible components using the "component_of" operation; e.g. "x_z_component_of_viscosity".

- Viscosity depends on temperature, so a reference temperature should be provided with an <assume> tag in a Model Metadata File. For an ideal gas, Sutherland's formula gives dynamic viscosity as a power-law function of temperature. For a dilute gas, the Chapman-Enskog equation can be used. For liquids, several different models are available; see: Temperature dependence of liquid viscosity.

- Kinematic viscosity is just the dynamic viscosity divided by the density of the fluid. It is used in the definition of the Reynolds number.

- "The "eddy viscosity" concept is used to parameterize small-scale details in models of turbulent flow. It is sometimes contrasted with "molecular viscosity". Also see the Diffusivity template.

- The reciprocal of viscosity is called
*fluidity*.

- See: Apparent viscosity, Viscosity, Inviscid flow, Large eddy simulation (LES), Newtonian fluid, Non-Newtonian fluid and Volume viscosity.

## Voltage

base_quantity = "voltage" [Volts = Joules per Coulomb]

*Examples*

battery__voltage appliance~electric__voltage fence~electric__voltage

- See: Voltage and Voltage drop.

## Vorticity

base_quantity = "vorticity"

*Examples of Specific Quantities:*

"absolute_vorticity"

"ertel_potential_vorticity" ### (a scalar quantity)

"planetary_vorticity"

"potential_vorticity"

"relative_vorticity"

*Examples*

sea_water_flow__down_component_of_vorticity sea_water_flow__east_component_of_vorticity sea_water_flow__magnitude_of_vorticity sea_water_flow__north_component_of_vorticity sea_water_flow__south_component_of_vorticity sea_water_flow__up_component_of_vorticity sea_water_flow__west_component_of_vorticity sea_water_flow__x_component_of_vorticity sea_water_flow__y_component_of_vorticity sea_water_flow__z_component_of_vorticity

- Vorticity is a vector quantity defined as the curl of a fluid velocity (vector) field. The quantity name for a component of the vorticity vector uses the "component_of" operation prefix as shown in the examples above. See the Component template.

is the vorticity of air velocity relative to the Earth. When "vorticity" appears without an adjective, relative vorticity with respect to a fixed coordinate system is assumed. See: Relative vorticity.**Relative vorticity**

is "relative vorticity" plus "planetary vorticity". See: Absolute vorticity.**Absolute vorticity**

is the vorticity associated with the rotation of the Earth.**Planetary vorticity**

is absolute vorticity divided by the vertical spacing between levels of constant entropy. It seems that there are two types of potential vorticity. Ertel's potential vorticity (ertel_potential_vorticity) is a scalar quantity, defined as a dot product of absolute vorticity and the gradient of potential temperature. See: Potential vorticity.**Potential vorticity**

- Here, "flow" is used as a shorthand for "flow_field" in the object part of the name. This is an example of the Object Name + Model Name Pattern.

- Since the curl of any gradient vector is zero, taking the curl of the Navier-Stokes equation eliminates the pressure gradient term.

- See Vorticity, Circulation and Vector calculus identities.

## Wavelength

base_quantity = "wavelength"

*Examples of Specific Quantities:*

"compton_wavelength"

"reduced_compton_wavelength"

*Examples*

electron__compton_wavelength sea_water_wave~internal~gravity__wavelength (### or sea_internal_water_wave ??) sea_surface_water_wave__wavelength wave~airy__wavelength wave~cnoidal__wavelength wave~sine__wavelength wave~stokes__wavelength

- The wavelength is the distance between successive crests or troughs in a periodic function.

- See the section called Attributes of Radiation above.

- See: Amplitude, Angular frequency, Compton wavelength, de Broglie wavelength, Frequency (and Period), Hertz, Thermal de Broglie wavelength, Wavelength, Wavenumber and Wave vector.

## Wavenumber

base_quantity = "wavenumber"

*Examples*

sea_surface_water_wave__wavenumber wave~airy__wavenumber wave~cnoidal__wavenumber wave~electromagnetic__wavenumber wave~seismic__wavenumber wave~stokes__wavenumber

- "Wavenumber" is a basic property of a periodic function or waveform, along with amplitude and wavelength. It can be understood as a
**spatial frequency**, in contrast to just*frequency*, which refers to a**temporal frequency**. Both wavenumber and frequency can be preceded with the word "angular" to define a different, but related quantity. See*Frequency*above.

- The phase speed of a wave is equal to ratio of the wavelength and period. It is also equal to the ratio of the angular frequency and angular wavenumber.

- A
*dispersion relation*is a relationship between the wavenumber and frequency that is determined by the specific physics of a wave propagation problem.

- See Dispersion relation, Wavenumber and Wave vector.

## Weight

base_quantity = "weight"

*Examples of Specific Quantities:*

"volume-specific_weight"

*Examples*

bear~alaskan~black__weight

- The weight of an object has units of force and is the product of its mass and the standard gravity constant for the planet on which the weight is being measured. (It actually even depends on distance above the planet's surface.) Because of this, perhaps we should use quantity names like "earth-weight" (or even "earth-surface-weight") and "mars-weight", etc.

- We could use "weight-per-volume" instead of "specific_weight".

- What about "submerged weight" ?

- See: Specific weight and Weight.

## Work

base_quantity = "work"

*Examples of Specific Quantities:*

""

*Examples*

- Work has units of energy and measures a change in energy due to a force being applied to an object over a distance.

- See: Work (physics).

## Yield

base_quantity = "yield"

*Examples of Specific Quantities:*

"specific_yield" (in groundwater modeling)

*Examples*

basin_outlet_sediment__yield

- In geology, "sediment yield" refers to the total mass of particulate matter (suspended or bedload) that reaches the outlet of a drainage basin over a fixed time interval. It has units of [mass / (area * time)] or [M L-2 T-1]. See: sediment yield.

- In agriculture, "crop yield" refers to the total amount produced (e.g. kilograms or bushels) per unit area. See: Crop yield and Yield (wine).

- What about "yield_strength" (plastic deformation) ? See: Yield (engineering).

- See also: Specific yield (groundwater), Yield (chemistry), Yield surface and Quantum yield.