CSN Operation Templates

  CSDMS Standard Names — Operation Templates

• Operations can optionally be given as a prefix to the quantity part of an existing standard name. The prefix always ends in the word "_of", which is a reserved word. It can therefore be used as a delimiter to separate the operation from the quantity name it acts on.
  
  

• Applying an operation to a quantity results in a new quantity that frequently has different units than the original quantity.
  
  

• In CF Standard Names, the word "transformation" is used in the same sense as we use "operation".
  
  

• These templates attempt to avoid operations that require two standard names, say X and Y, like these from the CF Standard Names:

change_in_X_due_to_change_in_Y
correlation_of_X_with_Y
derivative_of_X_wrt_Y
integral_of_X_wrt_Y
  
and instead express operations as a prefix whenever possible.

• Some of the "transformations" in the CF Standard Names are:

change_in_X_due_to_change_in_Y
curl_of_X
derivative_of_X_wrt_Y
direction_of_X
divergence_of_X
gradient_of_X
integral_of_X_wrt_Y
magnitude_of_X
tendency_of_X  (time_derivative)

Time Derivatives

  operation = "derivative_wrt_time_of_" (maybe we should allow "d_dt_of" ??)

Examples

bedrock_surface__derivative_wrt_time_of_elevation
sea_water__derivative_wrt_time_of_northward_velocity_component
soil__derivative_wrt_time_of_saturated_hydraulic_conductivity

• This pattern is extended to higher-order derivatives by adding a prefix like "second_", as in: "second_derivative_wrt_time_of_".
  
  

• "wrt" = "with respect to"
  
  

• Many quantity names built from process names have a sign connotation, such as "erosion_rate", "deposition_rate" and "accumulation_rate". If either sign is possible, the "derivative_wrt_time_of_X" pattern is generally less ambiguous and therefore preferable.
  
  

• We could possibly use a base quantity like "_change_rate" for time derivatives, but this seems limited and ambiguous and it isn't used much in practice.
  
  

• In CF Standard Names, a "transformation" called "tendency_of" is used to indicate a time derivative. There are 435 names that use this pattern. But it is not standard across the sciences and is not allowed in CSDMS Standard Names.
  
  

• In CF Standard Names, there is also the transformation pattern: "derivative_of_X_wrt_Y" and "time" is a CF Standard Name.
  
  

• In CF Standard Names, the transformation pattern for the derivative of a vector component is: "[component]_derivative_of_X". In the CSDMS Standard Names, "_component" is used as a "quantity suffix" (like "increment") and the name would start with an operation prefix like "derivative_wrt_time_of".
  
  

• CF Standard Names also has the transformation pattern: "change_over_time_in_X", with bounds given in metadata.

Spatial Derivatives

  operation = "derivative_wrt_east_of_"
  operation = "derivative_wrt_x_of_"
  operation = "derivative_wrt_north_of_"
  operation = "derivative_wrt_y_of_"

• There are only 10 CF Standard Names that contain "derivative" and they do not follow a consistent pattern. Note, however, that in CF Standard Names, time derivatives start with "tendency_of" and don't contain the word "derivative".
  
  

• There are 4 CF Standard Names that use the "x_derivative_of_" or "y_derivative_of_" pattern.

General Derivatives

  operation_pattern = "derivative_wrt_X_of_Y"

• In this case, it may not be possible to express the operation using an "operator prefix". This pattern is permitted in CF Standard Names, where both X and Y can also be standard names.
  
  

• In most cases, it appears that we can accommodate this pattern by replacing X by a single-word, base quantity name like "temperature" and replacing Y by a fully-qualified standard name.
  
  

Time Integrals

  operation = "integral_wrt_time_of_"

• "wrt" = "with respect to"

• In CF Standard Names, there is also the transformation pattern: "integral_of_X_wrt_Y" and "time" is a CF Standard Name. Bounds for the integral are given in metadata. There are currently 18 CF Standard Names that contain "integral" and 12 of these end with "_wrt_time".
  
  

• Perhaps we should allow the time interval to be given in the operation name, at least for intervals like "day" and "year". e.g.

air__integral_over_one_day_of_upward_longwave_radiation_flux OR 
air__one_day_integral_of_upward_longwave_radiation_flux
  
Note that "air" is used as a synonym for "earth_atmosphere".  See the template for Air in the  CSDMS Object Templates.

Applied Functions

  operation = [ function_name ] + "_of_"

Examples

log_of_X       (instead of "ln_X" in CF)
log10_of_X     (instead of "log10_X" in CF)
sin_of_X       (not in CF)
sqrt_of_X      (not in CF)
square_of_X    (also a CF Standard Names transformation)

Statistical Operators

  operation = [ operator_name ] + "_of_"

Examples

max_of_X
mean_of_X
min_of_X
variance_of_X

• Many quantities vary in both space and time, so an operation like "max_of" could be ambiguous. In order to address such cases, the following operation names can be used:

max_over_space_of
max_over_time_of     (e.g. for a "peak discharge")
min_over_space_of
min_over_time_of
   
And perhaps also:
max_over_day_of
min_over_day_of
max_over_period_of
min_over_period_of

• When there is interest in a "peak" value (i.e. a maximum with respect to time), there is generally also interest in the time at which that peak value occurs. We could use "time" as a quantity suffix in such cases, but it might be better to introduce an operation like:

time_of_max_over_time_of_discharge  OR
peak_time_of_discharge
 
and maybe:
peak_value_of_discharge    (or just "peak_of_discharge")

• Similarly, it may not always be clear how "mean_of_" should be interpreted unless extra adjectives/modifiers are used. For example, does "mean_of_channel_water_depth" mean the mean over a cross section or over an entire channel reach or over a grid of such values? This case also needs a more prescriptive rule and/or the details of the operation could be provided in metadata along with units, etc.
  
  

• Note that min, max or "peak" could also be used as adjectives/modifiers in the construction of a full quantity name if the meaning is clear.

Mathematical Operators that Return Scalars

  operation = [ operator_name ] + "_of_"

Examples

direction_of_X     (X must be a 2D vector field;  returns an angle)
magnitude_of_X     (X must be a vector or tensor)

• In our "Quantity" templates, "magnitude" is a "quantity suffix" and turns a vector or tensor quantity into a scalar quantity. We may want to restrict "mathematical operators" to those that don't return a scalar value and require all "base quantities" to be scalars.

Mathematical Operators that Return Vectors

  operation = [ operator_name ] + "_of_"

Examples

curl_of_X          (X must be a vector field;  returns a vector.)
divergence_of_X    (X must be a vector field;  returns a vector.)
gradient_of_X      (X must be a scalar field;  returns a vector.)
 
air__divergence_of_pressure_gradient
air__divergence_of_temperature_gradient      
bedrock_surface__divergence_of_elevation_gradient

• These all return vectors, so if we require base quantities to be scalars they would not qualify unless combined with a scalar-producing operator like "magnitude_of_". So we could have derived quantities like: "magnitude_of_gradient_of_X".

Change Increments

• Instead of a "change_in_X" operator (as in CF), the CSDMS Standard Names have a "quantity suffix" called "increment" that can be applied to any base quantity to create a new base quantity. See the discussion at the top of CSDMS Quantity Templates.