Pressure from Height (using the ICAO atmosphere)¶

Converts heights to pressures using the ICAO atmosphere. The newly calculated variable is included in the same obs space.

Transform: PressureFromHeightForICAO

obs filters:
- filter: Variable Transforms
  Transform: PressureFromHeightForICAO
  height coordinate: geopotentialHeight
  pressure coordinate: pressure
  pressure group: MetaData

Observation parameters needed (JEDI name)

geopotentialHeight (\(Z\)), specified with the height coordinate parameter.

Parameters

height coordinate [Required] Height coordinate variable name in group ObsValue (if a DerivedObsValue exists, it will be used instead).
pressure coordinate [Required] Pressure coordinate variable name.
pressure group [Optional | default = ``ObsValue``] Pressure coordinate group name, default is ObsValue (if a DerivedObsValue exists, it will be used instead).

Method(s) available

Only one method is available. (Any setting of METHOD will result in using this unique method.) Setting METHOD can be omitted.

Pressure from Height over a vertical profile¶

Derive pressure from height for vertical profile (e.g. sonde report). This is especially needed for radiosonde using a 3 09 055 BUFR template.

Transform: PressureFromHeightForProfile

obs filters:
- filter: Variable Transforms
  Transform: PressureFromHeightForProfile
  Method: UKMO
  observation relative humidity units: percentage
  height coordinate: geopotentialHeight
  pressure coordinate: pressure
  pressure group: MetaData

Observation parameters needed (JEDI name)

geopotentialHeight (\(Z\)), specified with the height coordinate parameter.
airTemperature (\(T\))
dewPointTemperature (\(T_{d}\)) or relativeHumidity (\(RH\))

Parameters

observation relative humidity units [Required] The units of relative humidity, in case it is used by the transform. Valid values are percentage or fraction.
height coordinate [Required] Height coordinate variable name in group ObsValue (if a DerivedObsValue exists, it will be used instead).
pressure coordinate [Required] Pressure coordinate variable name.
pressure group [Optional | default = ``ObsValue``] Pressure coordinate group name, default is ObsValue (if a DerivedObsValue exists, it will be used instead).

Method(s) available

Only one method is available. (Any setting of METHOD will result in using this unique method.) Setting METHOD can be omitted.

Nash et al (2011) showed that with GPS heights and accurate temperatures measured pressures are almost redundant and it seems likely that the use of pressure sensors will decrease over time. The pressure can be calculated hydrostatically starting from the station pressure. For two adjacent levels i and i+1 (eg eqn 2.2 of Chouinard and Staniforth, 1995):

\[\frac{Z_{i+1}-Z_{i}}{ln(\frac{P_{i-1}}{P_{i}})} = \frac{-R_{d}(T_{i+1}-T_{i})}{2g}\]

which gives

\[P_{i+1} = P_{i} \times e^{ \frac{2g(Z_{i}-Z_{i+1})}{R_{d}(T_{i+1}-T_{i})}}\]

Where \(R_{d}\) is the specific gas constant for dry air.

For better accuracy one can replace the temperature with the virtual temperature \(T_{v}\):

\[Tv = T \frac{P+\frac{e'_\text{sat w}}{\epsilon}}{P+e'_\text{sat w}}\]

where \(e'_\text{sat w}\) is the saturated vapour pressure which can be calculated from \(T_{d}\) or \(RH\) using saturation vapor pressure from temperature, and \(\epsilon\) is ratio of the gas constant for dry air (\(R_{d}\)) over the gas constant for water vapor (\(R_{v}\)).

The Sonntag formulation for calculating the saturated or actual vapour pressure of pure water vapor (\(e_\text{sat w} = h(T)\) or \(e = h(T_d)\)) is used (see the description of the Sonntag equation here). An enhancement factor is used to correct this for moist air

\[e'_\text{sat w} = f_\text{w}(P, T)) e_\text{sat w}\]

or

\[e' = f_\text{w}(P, T_d)) e\]

where the enhancement factor \(f_\text{w}\) is taken from Eq. A4.6 of Gill (1982) “Atmosphere-Ocean Dynamics”, Academic Press. This approximates table 89 of the Smithsonian Meteorological Tables correct to 2 parts in \(10^4\).

In this equation we use the pressure \(P\) from the previous level as we don’t yet have \(P\) for the current level (this should be a good approximation for the high-resolution reports). Note that if the pressures have been calculated hydrostatically (or from the model height/pressure profile) there is no point in applying the hydrostatic check below.