atmos_thermo package¶

Submodules¶

atmos_thermo.atmoslib module¶

atmos_thermo.atmoslib.Lv_from_T(T)¶

Calculate latent heat of vaporization for water, Lv.

Args:: T: temperature (Kelvin)
Returns:: Latent heat of vaporization [J / kg K]

atmos_thermo.atmoslib.T_from_p_theta(p, theta, p0=100000.0)¶

Calculate the temperature of air.

Calculate the temperature (T) given pressure (p) and potential temperature (theta).

Formula is : T = theta * (p / p0) ** (R_d / C_pd)

Args:: p: total pressure (Pascals) theta: potential temperature (Kelvin) p0: reference pressure used in calculating potential temperature
Returns:: temperature in Kelvin

atmos_thermo.atmoslib.Tv_from_r_T(r, T)¶

Calculate the virtual temperature.

Calculate the virtual temperature (T_v) given temperature (T) and mixing ratio (r).

Args:: r: mixing ratio (dimensionless) T: temperature (Kelvin)
Returns:: Virtual Temperature in Kelvin

atmos_thermo.atmoslib.e_from_r_p(r, p)¶

Calculate partial pressure of water vapor.

Calculate partial pressure of water vapor (e) from mixing ratio (r) and total pressure (p).

Args:: r: Mixing ratio in dimensionless ([kg H2O]/[kg Air]) units. p: Total pressure in Pascals.
Returns:: Vapor pressure (e) in Pascals.

atmos_thermo.atmoslib.esat_from_T(T)¶

Calculates saturation vapor pressure.

Using the reference Emanuel 1994 (Atmospheric Convection) p.116, equation 4.4.13 , this function calculates the saturation vapor pressure (esat) at the given temperature.

Args:: T: Air temperature in Kelvin. Can be numpy array.
Returns:: Saturation vapor pressure (esat) in units of Pa.

atmos_thermo.atmoslib.h_Em1994_from_r_T_z(r, T, z)¶

Calculate the moist static energy (h).

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.23

h = (C_pd + r_t C_pv) T + Lv r + g z

Args:: r: mixing ratio (dimensionless) T: temperature (Kelvin) z: height (meters)
Returns:: Moist static energy in J/kg (m^2 / s^2)

atmos_thermo.atmoslib.h_KF_from_r_T_z_rliq_rfroz(r, T, z, rliq, rfroz)¶

Calculate moist static energy according to the Kain-Fritsch definition.

The standard frozen MSE formulation is:

h = cp * T + Lv * r + g * z - Lf * r_froz

Kain-Fritsch uses:

cp_moist = cp_dry * (1 + 0.887 * r) # this is only the vapor r

Lv = XLV0 - T * XLV1 Lf = XLS0 - T * XLS1

XLV0 = 3.15E6 J/kg XLV1 = 2370 J/(kg K) XLS0 = 2.905E6 J/kg XLS1 = 259.532 J/(kg K)

atmos_thermo.atmoslib.h_from_r_T_z(r, T, z)¶

Calculate the moist static energy (h).

Using the classical definiton of moist static energy h = C_pd T + Lv r + g z

Args:: r: mixing ratio (dimensionless, or kg/kg) T: temperature (Kelvin) z: height (meters)
Returns:: Moist static energy in J/kg (m^2 / s^2)

atmos_thermo.atmoslib.hd_Em1994_from_r_T_z(r, T, z)¶

Calculate the dry static energy (hd).

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.23. Notice that the mixing ratio is required to calculate the heat capacity correctly.

hd = (C_pd + r_t C_pv) T + g z

Args:: r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin) z: height (meters).
Returns:: Dry static energy in J/kg (m^2 / s^2)

atmos_thermo.atmoslib.hd_from_r_T_z(r, T, z)¶

Calculate the classical dry static energy (hd).

Args:: p: total pressure (Pascals) T: temperature (Kelvin) z: height (meters).
Returns:: Dry static energy in J/kg (m^2 / s^2)

atmos_thermo.atmoslib.hstar_Em1994_from_p_T_z(p, T, z)¶

Calculate the saturation moist static energy (h).

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.23

h = (C_pd + r_sat C_pv) T + Lv (r_sat) + g z

Args:: p: total pressure (Pascals) T: temperature (Kelvin) z: height (meters)
Returns:: Saturation moist static energy in J/kg (m^2 / s^2)

atmos_thermo.atmoslib.hstar_classical_from_p_T_z(p, T, z)¶

Calculate the saturation moist static energy (h).

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.23

h = (C_pd + r_sat C_pv) T + Lv (r_sat) + g z

Args:: p: total pressure (Pascals) T: temperature (Kelvin) z: height (meters)
Returns:: Saturation moist static energy in J/kg (m^2 / s^2)

atmos_thermo.atmoslib.moist_specific_entropy_Emanuel_from_r_p_T(r, p, T, r_rain=0, r_cloud=0, r_ice=0)¶

Calculate the moist specific entropy.

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.9

s = (C_pd + C_pv * r_t) * ln(T)

R_d ln (pd)

Lv r / T

r R_v ln (H)

Args:

r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin)

Returns:

Equivalent potential temperature in Kelvin

atmos_thermo.atmoslib.moist_specific_entropy_Emanuel_sat_from_p_T(p, T, r_rain=0, r_cloud=0, r_ice=0)¶

Calculate the moist specific entropy.

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.9

s = (C_pd + C_pv * r_t) * ln(T)

R_d ln (pd)

Lv r / T

r R_v ln (H)

Args:

p: total pressure (Pascals) T: temperature (Kelvin)

Returns:

Equivalent potential temperature in Kelvin

atmos_thermo.atmoslib.moist_specific_entropy_from_r_p_T(r, p, T)¶

Calculate the moist specific entropy.

Calculate moist specific entropy for the mixing ratio (r), total pressure (p), and temperature (T).

Uses the definition given in Benedict et. al 2014 - Gross Moist Stability and MJO Simulation Skill ... Equation 1

Args:: r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin)
Returns:: Moist specific entropy in J / (kg K)

atmos_thermo.atmoslib.pd_from_r_p(r, p)¶

Calculate dry pressure without water vapor.

Calculate dry pressure (pd) from mixing ratio (r) and total pressure (p)

Args:: r: Mixing ratio in dimensionless ([kg H2O]/[kg Air]) units. p: Total pressure in Pascals.
Returns:: Dry pressure (pd) in Pascals.

atmos_thermo.atmoslib.q_from_e_p(e, p)¶

Calculates specific humidity.

Calculates specific humidity given vapor pressure (e) and total pressure (p). Typically vapor pressure is e and specific humidity is q in the literature.

q = [mass of H20 vapor] / [mass of total air]

relationship is : q = epsilon * e / (p - e*(1-epsilon))

Args:: e: Vapor pressure in Pascals p: Total pressure in Pascals
Returns:: Specific humidity in dimensionless ([kg H2O]/[kg Air]) units.

atmos_thermo.atmoslib.q_from_r(r)¶

Calculates specific humidity.

Calculates specific humidity given mixing ratio. Typically mixing ratio is r and specific humidity is q in the literature.

r = [mass of H20 vapor] / [mass of dry air] q = [mass of H20 vapor] / [mass of total air]

relationship is : q = r / (1+r)

Args:: r: Mixing ratio in dimensionless ([kg H2O]/[kg Air]) units.
Returns:: Specific humidity in dimensionless ([kg H2O]/[kg Air]) units.

atmos_thermo.atmoslib.r_from_e_p(e, p)¶

Calculate mixing ratio of water vapor.

Calculate mixing ratio of water vapor(r) from vapor pressure (e) and total pressure (p).

Args:: r: Mixing ratio in dimensionless ([kg H2O]/[kg Air]) units. p: Total pressure in Pascals.
Returns:: Vapor pressure (e) in Pascals.

atmos_thermo.atmoslib.relhum_from_e_esat(e, esat)¶

Calculate the relative humidity of air.

Calculate the relative humidity of air (H) given the vapor pressure (e) and saturation vapor pressure (esat).

Args:: e: Vapor pressure in Pascals. esat: Saturation vapor pressure in Pascals.
Returns:: relative humidity in dimensionless units.

atmos_thermo.atmoslib.relhum_from_r_p_T(r, p, T)¶

Calculate the relative humidity of air.

Calculate the relative humidity of air (H) given the mixing ratio (r), pressure (p) and temperature (T).

Args:: r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin)
Returns:: relative humidity in dimensionless units.

atmos_thermo.atmoslib.streamfunction_from_v_p(v, p)¶: Calculate streamfunction from v, p

atmos_thermo.atmoslib.theta_from_p_T(p, T, p0=100000.0)¶

Calculate the potential temperature of air.

Calculate the potential temperature (theta) given pressure (p) and temperature (T).

Formula is : theta = T * (p0 / p) ** (R_d / C_pd)

Args:: p: total pressure (Pascals) T: temperature (Kelvin) p0: reference pressure used in calculating potential temperature
Returns:: potential temperature in Kelvin

atmos_thermo.atmoslib.thetae_Bolton_from_r_p_T(r, p, T, p0=100000, r_rain=0.0, r_cloud=0.0)¶

Calculate the pseudoadiabatic equivalent potential temperature.

Using the Bolton 1980 definition.

Args:: r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin)
Returns:: Pseudoadibatic equivalent potential temperature in Kelvin

atmos_thermo.atmoslib.thetae_from_r_p_T(r, p, T, p0=100000, r_cloud=0.0)¶

Calculate the reversible equivalent potential temperature.

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.11

theta_e = T * [(p0 / pd) ** (R_d / (C_pd + C_pv * r_t))]

[H ** (-r R_v / (C_pd + C_pv * r_t)) ]
exp[L_v * r / ((C_pd + C_pv * r_t) * T)]

Args:

r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin)

Returns:

Reversible equivalent potential temperature in Kelvin

atmos_thermo.atmoslib.thetae_star_from_p_T(p, T)¶

Calculate the saturation equivalent potential temperature.

Using the definition of Emanuel 1994 (Atmospheric Convection). Equation 4.5.11

thetaesat = T * [(p0 / pd) ** (R_d / (C_pd + C_pv * r_t))]

exp[L_v * r / ((C_pd + C_pv * r_t) * T)]

Args:

r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin)

Returns:

Saturation equivalent potential temperature in Kelvin

atmos_thermo.atmoslib.thetav_from_r_p_T(r, p, T)¶

Calculate the virtual potential temperature.

Calculate the virtual potential temperature (thetav) given temperature (T) and mixing ratio (r).

Args:: r: mixing ratio (dimensionless) p: total pressure (Pascals) T: temperature (Kelvin)
Returns:: Virtual Temperature in Kelvin

atmos_thermo.constant module¶

The following constants are accessible as atmos_thermo.catmos. For example, atmos_thermo.catmos.R_d will return the gas constant for dry air. All quantities are in SI units.

@readonly
def R_d():
    'gas constant of dry air'
    return 287.04  # , ureg['J / (kg * degK)']

@readonly
def R_v():
    'gas constant of water vapor'
    return 461.50  # , ureg['J / (kg * degK)']

@readonly
def epsilon():
    'ratio of R_d / R_v'
    return 0.6220  # , ureg['dimensionless']

@readonly
def C_vd():
    'heat capacity of dry air at constant volume'
    return 719.0  # , ureg['J / (kg * degK)']

@readonly
def C_pd():
    'heat capacity of dry air at constant pressure'
    return 1005.7  # , ureg['J / (kg * degK)']

@readonly
def C_vv():
    'heat capacity of water vapor at constant volume'
    return 1410.0  # , ureg['J / (kg * degK)']

@readonly
def C_pv():
    'heat capacity of water vapor at constant pressure'
    return 1870.0  # , ureg['J / (kg * degK)']

@readonly
def C_l():
    'heat capacity of liquid water'
    return 4190.0  # , ureg['J / (kg * degK)']

@readonly
def Lv0():
    'Latent heat of vaporization for water at 0 degrees C'
    return 2.501E6  # , ureg['J / (kg * degK)']

@readonly
def L_v():
    'Latent heat of vaporization for water at 100 degrees C'
    return 2.26E6

Similarly, these two are earth constants. For example atmos_thermo.cearth.g.

@readonly
def R_Earth():
    return 6.371E6  # , ureg['m']

@readonly
def g():
    return 9.81  # , ureg['m/s/s']