The thermodynamics module.¶

This module implements thermodynamics functions for monc_utils.

Note: Functions can be used to provide derived variables where Derived variable name: is defined.

Detailed Module Contents¶

The entire module is documented below.

General Thermodynamics functions.

Peter Clark

monc_utils.thermodynamics.thermodynamics.esat(T)¶

Saturation Vapour Pressure over Water.

Derived variable name: esat

Parameters:: T (numpy array or xarray DataArray) – Temperature (K)
Returns:: res – Vapour pressure over water (Pa)
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.esat_ice(T)¶

Saturation Vapour Pressure over Ice.

Derived variable name: esat_ice

Magnus Teten, Murray (1967)

Parameters:: T (numpy array or xarray DataArray.) – Temperature (K)
Returns:: res – Vapour pressure over ice(Pa)
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.inv_esat(es)¶

Temperature for given Saturation Vapour Pressure over Water.

Parameters:: es (numpy array or xarray DataArray) – Vapour pressure over water (Pa)
Returns:: T – Temperature (K)
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.inv_esat_ice(es)¶

Temperature for given Saturation Vapour Pressure over Water.

Magnus Teten, Murray (1967)

Parameters:: es (numpy array or xarray DataArray) – Vapour pressure over water (Pa)
Returns:: T – Temperature (K)
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.esat_over_Tkappa(T)¶

Computes $e_s/T^{(1/kappa)}$ (es in Pa).

From Bolton 1980.

Parameters:: T (numpy array or xarray DataArray) – Temperature (K)
Returns:: res
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.exner(p)¶

Compute Exner Pressure.

Derived variable name: exner

Parameters:: p (numpy array or xarray DataArray) – Pressure (Pa).
Returns:: p_exner
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.inv_exner(p)¶

Compute 1/(Exner Pressure).

Parameters:: p (numpy array or xarray DataArray) – Pressure (Pa).
Returns:: inv_p_exner
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.temperature(theta, p)¶

Compute Potential Temperature.

Derived variable name: T

Parameters:

theta (numpy array or xarray DataArray) – Potential temperature of dry air (K),
p (numpy array or xarray DataArray) – Pressure (Pa).

Returns:

T – Temperature (K).

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.potential_temperature(T, p)¶

Compute Potential Temperature.

Derived variable name: th

Parameters:

T (numpy array or xarray DataArray) – Temperature (K).
p (numpy array or xarray DataArray) – Pressure (Pa).

Returns:

theta – Potential temperature of dry air (K),

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.moist_potential_temperature(T, p, m)¶

Compute Moist Potential Temperature.

Parameters:

T (numpy array or xarray DataArray) – Temperature (K).
p (numpy array or xarray DataArray) – Pressure (Pa).
m (numpy array or xarray DataArray) – Mixing ratio(kg/kg).

Returns:

theta – Potential temperature of moist air (K) .

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.q_to_mix(q)¶

Convert specific humidity to mixing ratio.

Derived variable name: m_x where input is q_x

Parameters:: q (numpy array or xarray DataArray) – Specific humidity (kg/kg).
Returns:: m – Mixing Ratio(kg/kg)
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.mix_to_q(m)¶

Convert mixing ratio to specific humidity.

Derived variable name: q_x where input is m_x

Parameters:: m (numpy array or xarray DataArray) – Mixing Ratio(kg/kg)
Returns:: q – Specific humidity (kg/kg).
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.q_p_to_e(q, p)¶

Convert specific humidity and pressure to vapour pressure.

Parameters:

q (numpy array or xarray DataArray) – Specific humidity (kg/kg)
p (numpy array or xarray DataArray) – Total Pressure (Pa)

Returns:

e – Vapour pressure (Pa)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.e_p_to_q(e, p)¶

Convert vapour pressure and total pressure to specific humidity.

Parameters:

e (numpy array or xarray DataArray) – Vapour pressure (Pa)
p (numpy array or xarray DataArray) – Pressure (Pa)

Returns:

q – Specific humidity (kg/kg)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.t_lcl_td(T, TD)¶

T at lifting condensation level from Dewpoint.

Derived variable name: t_lcl_td

From Bolton 1980

Parameters:

T (numpy array or xarray DataArray) – Temperature (K).
TD (numpy array or xarray DataArray) – Dew point Temperature (K).

Returns:

Tlcl – temperature at lifting condensation level (K)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.t_lcl_e(T, e)¶

T at lifting condensation level from vapour presssure.

Derived variable name: t_lcl_e

From Bolton 1980

Parameters:

T (numpy array or xarray DataArray) – Temperature (K).
e (numpy array or xarray DataArray) – Vapour pressure (Pa).

Returns:

Tlcl – temperature at lifting condensation level (K)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.t_lcl_rh(T, RH)¶

T at lifting condensation level from RH.

Derived variable name: t_lcl_rh

From Bolton 1980

Parameters:

T (numpy array or xarray DataArray) – Temperature (K).
RH (numpy array or xarray DataArray) – Relative humidity (%)

Returns:

Tlcl – temperature at lifting condensation level (K)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.p_lcl(Tp, pp, T_lcl)¶

Pressure at lifting condensation level.

Parameters:

Tp (numpy array or xarray DataArray) – Parcel Temperature (K).
pp (numpy array or xarray DataArray) – Parcel pressure (Pa).
T_lcl (numpy array or xarray DataArray) – Temperature at lifting condensation level.

Returns:

p_lcl – : Pressure at lifting condensation level.

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.latheat(T, sublim=0, model=0, focwil_T=None)¶

Latent heat of condensation or sublimation.

Parameters:

T (numpy array or xarray DataArray) – Temperature (K).
sublim (int (optional)) – = 1 return Latent heat of sublimation
Model (int (optional)) – = 1 use UM fixed values
focwil_T (float (optional)) – use linear ramp in ice fraction from focwil_T to freezing.

Returns:

latheat – Latent heat of condensation(K)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.dewpoint(T, p, q)¶

Dewpoint.

Derived variable name: T_dew

Parameters:

T (numpy array or xarray DataArray) – Temperature.
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)

Returns:

TD – Dew-point temperature (K).

Return type:

Nnmpy array

monc_utils.thermodynamics.thermodynamics.qsat(T, p)¶

Saturation vapour pressure.

Derived variable name: qsat

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).

Returns:

qs – Saturation specific humidity (kg/kg) over water.

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.dqsatbydT(T, p)¶

${alpha= dq_{s}}/{dT}$ .

Derived variable name: alpha

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).

Returns:

alpha

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.equiv_potential_temperature_approx(T, p, q)¶

Equivalent potential temperature.

From Bolton 1980

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)

Returns:

theta_e – Fast estimate of equivalent potential temperature (K).

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.equiv_potential_temperature(T, p, q)¶

Equivalent potential temperature.

Derived variable name: th_e

From Bolton 1980

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)

Returns:

theta_e – Accurate estimate of equivalent potential temperature (K).

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.wet_bulb_potential_temperature(T, p, q)¶

Wet-bulb potential temperature.

Derived variable name: th_w

From Davies-Jones 2007

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)

Returns:

theta_w – Wet-bulb potential temperature (K) numpy array or xarray DataArray

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.sat_wet_bulb_potential_temperature(T, p)¶

Saturated wet-bulb potential temperature.

Derived variable name: th_s

From Davies-Jones 2007

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).

Returns:

theta_w – Wet-bulb potential temperature (K) numpy array or xarray DataArray

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.sat_unsat_wet_bulb_potential_temperature(T, p, q, Tp=None, TDp=None, pp=None, sl=None)¶

Saturated/unsaturated wet-bulb potential temperature.

Derived variable name: th_sw

From Davies-Jones 2007

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)
Tp (numpy array or xarray DataArray) – Parcel Temperature. (K) Default=None
TDp (numpy array or xarray DataArray) – Parcel Dewppoint Temperature. (K) Default=None
pp (numpy array or xarray DataArray) – Parcel pressure. (Pa) Default=None
sl (slice object.) – Used to select levels for mean for parcel properties. default=None which gives sice(1,3,None)
None (If parcel properties are) –
averaged. (the sl levels are) –

Returns:

theta_sw – Wet-bulb potential temperature below LCL, saturated wet-bulb PT above (K) numpy array or xarray DataArray

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.wet_bulb_temperature(T, p, q)¶

Wet-bulb temperature.

Derived variable name: T_w

From Davies-Jones 2007

Parameters:

T (numpy array or xarray DataArray) – Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)

Returns:

theta_w – Wet-bulb temperature (K) numpy array or xarray DataArray

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.liquid_water_potential_temperature(theta, q_cl, pi)¶

Liquid water potential temperature.

Derived variable name: th_L

Approximate form as in MONC

Parameters:

theta (numpy array or xarray DataArray) – Potential Temperature. (K)
q_cl (numpy array or xarray DataArray) – q_cloud_liquid_mass.
pi (numpy array or xarray DataArray) – Exner pressure.

Returns:

theta_w – Wet-bulb potential temperature (K) numpy array or xarray DataArray

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.virtual_potential_temperature(theta, q_v, q_cl)¶

Virtual potential temperature.

Derived variable name: th_v

Parameters:

theta (numpy array or xarray DataArray) – Potential Temperature. (K)
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.

Returns:

theta_v – Virtual potential temperature (K)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.virtual_potential_temperature_monc(theta, thref, q_v, q_cl)¶

Virtual potential temperature.

Derived variable name: th_v_monc

Approximate form as in MONC

Parameters:

theta (numpy array or xarray DataArray) – Potential Temperature. (K)
thref (numpy array or xarray DataArray) – Reference Potential Temperature (usually 1D). (K)
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.

Returns:

theta_v – Virtual potential temperature (K)

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.q_total(*args)¶

Specfic Total Water Content.

Derived variable name: q_total

Parameters:: args (list of numpy array or xarray DataArrays) – specific water variables (e.g.[ q_v, q_cl]).
Returns:: q_total – sum of args
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.buoyancy(th_v)¶

Buoyancy from theta_v.

Derived variable name: buoyancy

Parameters:: th_v (numpy array or xarray DataArray) – Virtual potential temperature.
Returns:: buoyancy
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.buoyancy_monc(th_v, thref)¶

Buoyancy from theta_v.

Derived variable name: buoyancy_monc

MONC approximation.

Parameters:: th_v (numpy array or xarray DataArray) – Virtual potential temperature.
Returns:: buoyancy
Return type:: numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.dbdz(th, p, q_v, q_cl, z, zn)¶

Vertical Gradient of Buoyancy from theta_v.

Derived variable name: dbdz

Parameters:

theta (numpy array or xarray DataArray) – Potential Temperature. (K)
thref (numpy array or xarray DataArray) – Reference Potential Temperature (usually 1D). (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.
th_v (numpy array or xarray DataArray) – Virtual potential temperature.

Returns:

dbuoyancy/dz

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.dbdz_monc(th, thref, p, q_v, q_cl, z, zn)¶

Vertical Gradient of Buoyancy from theta_v.

Derived variable name: db_moncdz

MONC approximation

Parameters:

theta (numpy array or xarray DataArray) – Potential Temperature. (K)
thref (numpy array or xarray DataArray) – Reference Potential Temperature (usually 1D). (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.
th_v (numpy array or xarray DataArray) – Virtual potential temperature.

Returns:

buoyancy

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.rh(T, p, q)¶

Relative Humidity.

Derived variable name: rh

Parameters:

T (numpy array or xarray DataArray) – Temperature (K).
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)

Returns:

rh – Relative Humidity.

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.rh_ice(T, p, q)¶

Relative Humidity wrt Ice.

Derived variable name: rh_ice

Parameters:

T (numpy array or xarray DataArray) – Temperature.
p (numpy array or xarray DataArray) – Pressure (Pa).
q (numpy array or xarray DataArray) – specific humidity (kg/kg)

Returns:

rh – Relative Humidity.

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.a_L_monc(T, p)¶

Cloud Factor.

Derived variable name: a_L

Parameters:

T (numpy array or xarray DataArray) – Temperature.
p (numpy array or xarray DataArray) – Pressure (Pa).

Returns:

a_L – Factor used in calculating liqid water content.

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.cloud_params_monc(th_ref, p_ref)¶

Cloud Parameters.

MONC Approximation

Parameters:

th_ref (numpy array or xarray DataArray) – Reference Potential Temperature.
p_ref (numpy array or xarray DataArray) – Reference Pressure (Pa).

Returns:

Factors used in calculating liqid water content. “T_ref”,”pi_ref”, “qs_ref”, “a_L”, “alpha_L”.

Return type:

dict

monc_utils.thermodynamics.thermodynamics.betas_monc(th, p)¶

Beta factors in cloudy buoyancy calculation.

Parameters:

th (numpy array or xarray DataArray) – Potential Temperature. (K)
p (numpy array or xarray DataArray) – Pressure (Pa).

Returns:

(bt, bq, bc, alpha_L, a_L).

Return type:

tuple of numpy array or xarray DataArrays

monc_utils.thermodynamics.thermodynamics.buoyancy_moist(th, th_ref, p, q_v, q_cl, thresh=1e-05)¶

Buoyancy including cloud condensation.

Derived variable name: buoyancy_moist

MONC approximation

Parameters:

th (numpy array or xarray DataArray) – Potential Temperature. (K)
thref (numpy array or xarray DataArray) – Reference Potential Temperature (usually 1D). (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.

Returns:

buoyancy

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.dmoist_bdz(th, th_ref, p, q_v, q_cl, z, zn, thresh=1e-05)¶

Vertical Gradient of (buoyancy including cloud condensation).

Derived variable name: dmoist_bdz

MONC approximation. This is db/dz with b = beta_t theta_l + beta_q q_t. Note - not to be used for vertical buoyancy flux.

Parameters:

th (numpy array or xarray DataArray) – Potential Temperature. (K)
th_ref (numpy array or xarray DataArray) – Reference Potential Temperature (usually 1D). (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.
z (xarray coord.) –
zn (xarray coord.) –
thresh ((Optional) float. Default is 1E-5.) – Threshold for cloud water.

Returns:

buoyancy

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.moist_dbdz(th, th_ref, p_ref, q_v, q_cl, z, zn, thresh=1e-05)¶

Vertical Gradient of buoyancy (including cloud condensation).

Derived variable name: moist_dbdz

MONC approximation This is db/dz = beta_t dtheta_l/dz + beta_q dq_t/dz. Note - to be used for vertical buoyancy flux.

Parameters:

theta (numpy array or xarray DataArray) – Potential Temperature. (K)
thref (numpy array or xarray DataArray) – Reference Potential Temperature (usually 1D). (K)
p (numpy array or xarray DataArray) – Pressure (Pa).
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.
z (xarray coord.) –
zn (xarray coord.) –
thresh ((Optional) float. Default is 1E-5.) – Threshold for cloud water.

Returns:

buoyancy

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.saturation(th, th_ref, p_ref, q_v, q_cl)¶

Effective saturation.

Derived variable name: saturation

MONC approximation

Parameters:

th (numpy array or xarray DataArray) – Potential Temperature. (K)
th_ref (numpy array or xarray DataArray) – Reference Potential Temperature (usually 1D). (K)
p_ref (numpy array or xarray DataArray) – Reference Pressure (Pa).
q_v (numpy array or xarray DataArray) – specific humidity
q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.

Returns:

saturation

Return type:

numpy array or xarray DataArray

monc_utils.thermodynamics.thermodynamics.cloud_fraction(q_cl, thresh=1e-05)¶

Compute indicator function on cloud.

Derived variable name: cloud_fraction

Parameters:

q_cl (numpy array or xarray DataArray) – specific cloud liquid water content.
thresh ((Optional) float. Default is 1E-5.) – Threshold for cloud water.

Return type:

numpy array or xarray DataArray

The thermodynamics module.¶

Detailed Module Contents¶

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