dparcel.thermo module

Thermodynamic calculations for parcel theory.

This module implements various atmospheric thermodynamics calculations, both original and from literature.

dparcel.thermo.descend(pressure, temperature, specific_humidity, liquid_ratio, reference_pressure, improve=2, improve_reversible=2, kind='pseudo')

Calculate the temperature of a descending parcel.

Uses conservation of equivalent potential temperature to determine the final temperature if the parcel switches from a moist to a dry adiabat.

Parameters

  • pressure – Final pressure.

  • temperature – Initial temperature.

  • specific_humidity – Initial specific humidity.

  • liquid_ratio – Initial liquid ratio.

  • reference_pressure – Initial pressure.

  • improve – Number of iterations to use if the parcel must switch from moist to dry adiabat (default: 1). Alternatively, specify False to skip iteration and take the moist adiabatic value, or ‘exact’ to iterate until convergence.

  • improve_reversible – Number of iterations to use for reversible adiabat calculation.

  • kind – ‘pseudo’ for pseudoadiabats, ‘reversible’ for reversible adiabats.

Returns

Final temperature, specific humidity and liquid ratio.

dparcel.thermo.equilibrate(pressure, t_initial, q_initial, l_initial)

Find parcel properties after phase equilibration.

Parameters

  • pressure – Pressure during the change (constant).

  • t_initial – Initial temperature of the parcel.

  • q_initial – Initial specific humidity of the parcel.

  • l_initial – Initial ratio of liquid mass to parcel mass.

Returns

A tuple containing the final parcel temperature, specific

humidity and liquid ratio.

dparcel.thermo.equivalent_potential_temperature(p, Tk, q, prime=False)

Calculate equivalent potential temperature.

Uses the approximation of theta-e given in eq. 39 of Bolton (1980). Variable names follow the notation of Bolton.

Parameters

  • p – Pressure.

  • Tk – Temperature.

  • q – Specific humidity.

  • prime – Whether or not to also return the derivative of theta-e with respect to temperature at the given temperature and pressure (optional, defaults to False).

Returns

The equivalent potential temperature (and its derivative w.r.t. temperature if prime=True).

References

Bolton, D 1980, ‘The Computation of Equivalent Potential Temperature’, Monthly weather review, vol. 108, no. 7, pp. 1046–1053.

dparcel.thermo.lcl_romps(p, T, q)

Analytic solution for the LCL (adapted from Romps 2017).

This code is adapted from Romps (2017): https://romps.berkeley.edu/papers/pubdata/2016/lcl/lcl.py

Parameters

  • p – Pressure.

  • T – Temperature.

  • q – Specific humidity.

Returns

(pressure, temperature) at the LCL.

References

Romps, DM 2017, ‘Exact Expression for the Lifting Condensation Level’, Journal of the atmospheric sciences, vol. 74, no. 12, pp. 3891–3900.

dparcel.thermo.mix(parcel, environment, rate, dz)

Mix parcel and environment variables (for entrainment).

Parameters

  • parcel – Parcel value.

  • environment – Environment value.

  • rate – Entrainment rate.

  • dz – Distance descended.

Returns

Mixed value of the variable.

dparcel.thermo.moist_lapse_dj(pressure, initial_temperature, reference_pressure=None, improve=True)

Compute temperature from pressure along pseudoadiabats.

Follows the method of Davies-Jones (2008).

Parameters

  • pressure – Array of pressures for which the temperature is to be found.

  • initial_temperature – Initial parcel temperature.

  • reference_pressure – The pressure corresponding to initial_temperature. Optional, defaults to pressure[0].

  • improve – Whether or not to apply an iteration of Newton’s method (only relevant for method == ‘fast’).

Returns

Array of final temperatures.

References

DAVIES-JONES, R 2008, ‘An Efficient and Accurate Method for Computing the Wet-Bulb Temperature along Pseudoadiabats’, Monthly weather review, vol. 136, no. 7, pp. 2764–2785.

dparcel.thermo.reversible_lapse_daviesjones(pressure, initial_temperature, initial_liquid_ratio, reference_pressure=None, improve=2)

Compute temperature along reversible adiabats.

Uses the method of Davies-Jones (2008). Variable names follow the notation of Davies-Jones.

Errors were found in Equations (5.1) and (5.3). They have been corrected here after consultation with the author.

Parameters

  • pressure – Array of pressures for which the temperature is to be found.

  • initial_temperature – Initial parcel temperature.

  • q_initial – Initial specific humidity.

  • initial_liquid_ratio – Initial ratio of liquid mass to total.

  • reference_pressure – The pressure corresponding to initial_temperature. Optional, defaults to pressure[0].

  • improve – Number of iterations of Newton’s method to execute.

Returns

Array of final temperatures.

References

DAVIES-JONES, R 2008, ‘An Efficient and Accurate Method for Computing the Wet-Bulb Temperature along Pseudoadiabats’, Monthly weather review, vol. 136, no. 7, pp. 2764–2785.

dparcel.thermo.reversible_lapse_saunders(pressure, t_initial, l_initial, reference_pressure=None, improve=2)

Calculate temperature along reversible adiabats.

Uses Eq. 3 of Saunders (1957). Variable names follow the notation of Saunders.

Parameters

  • pressure – Pressure array.

  • t_initial – Initial temperature.

  • l_initial – Initial ratio of liquid mass to total

  • reference_pressure – Pressure corresponding to t_inital.

  • improve – Number of Newton’s method iterations to use.

Returns

Resultant temperature array.

References

Saunders, PM 1957, ‘The thermodynamics of saturated air: A contribution to the classical theory’, Quarterly journal of the Royal Meteorological Society, vol. 83, no. 357, pp. 342–350.

dparcel.thermo.saturation_equivalent_potential_temperature(p, Tk, prime=False)

Calculate saturation equivalent potential temperature.

Uses the approximation of theta-e given in eq. 39 of Bolton (1980). Variable names follow the notation of Bolton.

Parameters

  • p – Pressure.

  • Tk – Temperature.

  • prime – Whether or not to also return the derivative of theta-e with respect to temperature at the given temperature and pressure (optional, defaults to False).

Returns

The saturation equivalent potential temperature (and its derivative w.r.t. temperature if prime=True).

References

Bolton, D 1980, ‘The Computation of Equivalent Potential Temperature’, Monthly weather review, vol. 108, no. 7, pp. 1046–1053.

dparcel.thermo.saturation_specific_humidity(pressure, temperature)

Calculate saturation specific humidity.

dparcel.thermo.temperature_change(delta_q)

Calculate the temperature change due to evaporation of water.

Neglects the heat capacity of components other than dry air.

Parameters

delta_q – Specific humidity increase due to evaporation.

Returns

The resulting change in temperature.

dparcel.thermo.wetbulb(pressure, theta_e, improve=True)

Calculate wet bulb temperature using the method in Davies-Jones 2008.

Variable names follow the notation of Davies-Jones.

Parameters

  • pressure – Pressure.

  • theta_e – Equivalent potential temperature.

  • improve – Whether or not to perform a single iteration of Newton’s method to improve accuracy (defaults to False).

Returns

Wet bulb temperature.

References

DAVIES-JONES, R 2008, ‘An Efficient and Accurate Method for Computing the Wet-Bulb Temperature along Pseudoadiabats’, Monthly weather review, vol. 136, no. 7, pp. 2764–2785.

dparcel.thermo.wetbulb_potential_temperature(theta_e)

Calculate theta-w from theta-e using Eq. 3.8 of Davies-Jones 2008.

Variable names follow the notation of Davies-Jones.

Parameters

theta_e – Equivalent potential temperature.

Returns

Wet bulb potential temperature.

References

DAVIES-JONES, R 2008, ‘An Efficient and Accurate Method for Computing the Wet-Bulb Temperature along Pseudoadiabats’, Monthly weather review, vol. 136, no. 7, pp. 2764–2785.

dparcel.thermo.wetbulb_romps(pressure, temperature, specific_humidity)

Calculate wet bulb temperature using Normand’s rule and Romps (2017).

Parameters

  • p – Pressure.

  • T – Temperature.

  • q – Specific humidity.

Returns

Wet bulb temperature.

References

Romps, DM 2017, ‘Exact Expression for the Lifting Condensation Level’, Journal of the atmospheric sciences, vol. 74, no. 12, pp. 3891–3900.