saturation_equivalent_potential_temperature¶
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metpy.calc.saturation_equivalent_potential_temperature(pressure, temperature)[source]¶ Calculate saturation equivalent potential temperature.
This calculation must be given an air parcel’s pressure and temperature. The implementation uses the formula outlined in [Bolton1980] for the equivalent potential temperature, and assumes a saturated process.
First, because we assume a saturated process, the temperature at the LCL is equivalent to the current temperature. Therefore the following equation
\[T_{L}=\frac{1}{\frac{1}{T_{D}-56}+\frac{ln(T_{K}/T_{D})}{800}}+56\]reduces to
\[T_{L} = T_{K}\]Then the potential temperature at the temperature/LCL is calculated:
\[\theta_{DL}=T_{K}\left(\frac{1000}{p-e}\right)^k \left(\frac{T_{K}}{T_{L}}\right)^{.28r}\]However, because
\[T_{L} = T_{K}\]it follows that
\[\theta_{DL}=T_{K}\left(\frac{1000}{p-e}\right)^k\]Both of these are used to calculate the final equivalent potential temperature:
\[\theta_{E}=\theta_{DL}\exp\left[\left(\frac{3036.}{T_{K}} -1.78\right)*r(1+.448r)\right]\]Parameters: - pressure (pint.Quantity) – Total atmospheric pressure
- temperature (pint.Quantity) – Temperature of parcel
Returns: pint.Quantity – The saturation equivalent potential temperature of the parcel
Notes
[Bolton1980] formula for Theta-e is used (for saturated case), since according to [DaviesJones2009] it is the most accurate non-iterative formulation available.