saturation_equivalent_potential_temperature#

metpy.calc.saturation_equivalent_potential_temperature(pressure, temperature)#

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
Returns

pint.Quantity – Saturation equivalent potential temperature of the parcel

Examples

>>> from metpy.calc import saturation_equivalent_potential_temperature
>>> from metpy.units import units
>>> saturation_equivalent_potential_temperature(500 * units.hPa, -20 * units.degC)
<Quantity(313.804174, 'kelvin')>

Notes

[Bolton1980] formula for Theta-e is used (for saturated case), since according to [DaviesJones2009] it is the most accurate non-iterative formulation available.

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