exojax.atm package

Submodules

exojax.atm.amclouds module

Ackerman and Marley 2001 cloud model.

  • based on Ackerman and Marley (2001) ApJ 556, 872, hereafter AM01

exojax.atm.amclouds.compute_cloud_base_pressure(pressures, saturation_pressure, vmr_vapor)

compute cloud base pressure from a T-P profile and Psat(T) curves

Parameters:

  • pressures – pressure array

  • saturation_presure – saturation pressure arrau

  • vmr_vapor – volume mixing ratio (VMR) for vapor

Returns:

cloud base pressure

Return type:

float

exojax.atm.amclouds.effective_radius(rg, sigmag)

computes the paritculate effective radius from lognormal parameters, rg and sigmag

Parameters:

  • rg (float) – rg parameter in lognormal distribution in cgs

  • sigmag (float) – sigma_g parameter in lognormal distribution

Note

The cross section is given by $S = Q_e pi r_eff^2$

Returns:

effective radius in cgs

Return type:

_type_

exojax.atm.amclouds.find_rw(rarr, terminal_velocity, Kzz_over_L)

finding rw from rarr and terminal velocity array.

Parameters:

  • rarr – particle radius array (cm)

  • terminal_velocity – terminal velocity (cm/s)

  • Kzz_over_L – Kzz/L in Ackerman and Marley 2001

Returns:

rw in Ackerman and Marley 2001

exojax.atm.amclouds.geometric_radius(rg, sigmag)

computes the paritculate geometric radius

Parameters:

  • rg (float) – rg parameter in lognormal distribution in cgs

  • sigmag (float) – sigma_g parameter in lognormal distribution

Note

The cross section is given by $S = Q_e pi r_geo^2$

Returns:

geometric radius in cgs

Return type:

_type_

exojax.atm.amclouds.get_pressure_at_cloud_base(pressures, smooth_index)

get pressure at cloud base from pressures

Parameters:

  • pressures – pressure array

  • smooth_index – smooth index

Returns:

pressure at cloud base

Return type:

float

exojax.atm.amclouds.get_rg(rw, fsed, alpha, sigmag)

compute rg of the lognormal size distribution defined by (9) in AM01. The computation is based on (13) in AM01.

Parameters:

  • rw – rw (cm)

  • fsed – fsed

  • alpha – power of the condensate size distribution

  • sigmag – sigmag parameter (geometric standard deviation) in the lognormal distribution of condensate size, defined by (9) in AM01, must be sigmag > 1

Returns
rg: rg parameter in the lognormal distribution of condensate size,

defined by (9) in AM01

exojax.atm.amclouds.get_rw(terminal_velocity, Kzz, L, rarr)

compute rw in AM01 implicitly defined by (11)

Parameters:

  • vfs – terminal velocity (cm/s)

  • Kzz – diffusion coefficient (cm2/s)

  • L – typical convection scale (cm)

  • rarr – condensate scale array

Returns:

rw (cm) in AM01. i.e. condensate size that balances an upward transport and sedimentation

Return type:

rw

exojax.atm.amclouds.mixing_ratio_cloud_pressure(pressure, cloud_base_pressure, fsed, mr_cloud_base, kc)

mol mixing ratio of clouds based on AM01 a given single pressure.

Parameters:

  • pressure (float) – pressure (bar) where we want to compute VMR of clouds

  • cloud_base_pressure – cloud base pressure (bar)

  • fsed – fsed

  • mr_cloud_base – mass mixing ratio (MMR) or mol mixing ratio of condensate at cloud base

  • kc – constant ratio of condenstates to total mixing ratio

Returns:

mol mixing ratio of condensates

exojax.atm.amclouds.mixing_ratio_cloud_profile(pressures, cloud_base_pressure, fsed, mr_cloud_base, kc=1)

volume mixing ratio of clouds based on AM01 given pressure.

Parameters:

  • pressures – pressure array (Nlayer) (bar) where we want to compute VMR of clouds

  • cloud_base_pressure – cloud base pressure (bar)

  • fsed – fsed

  • mr_cloud_base – mass mixing ratio (MMR) or mol mixing ratio of condensate at cloud base

  • kc – constant ratio of condenstates to total mixing ratio

Returns:

VMR of condensates

exojax.atm.amclouds.sigmag_from_effective_radius(reff, fsed, rw, alpha)

computes sigmag from reff

Parameters:

  • reff – effective radius (cm) defined by E_3/E_2

  • fsed – fsed

  • rw – rw (cm)

  • alpha – alpha

Returns:

sigmag

Return type:

sigmag

exojax.atm.amclouds.smooth_index_base_pressure(pressures, saturation_pressure, vmr_vapor)

computes smooth_index for cloud base pressure from an intersection of a T-P profile and Psat(T) curves :param pressures: pressure array :param saturation_presure: saturation pressure arrau :param vmr_vapor: volume mixing ratio (VMR) for vapor

Returns:

smooth_index

Return type:

float

exojax.atm.atmconvert module

converts quantities in the atmosphere, between mass mixing ratio, volume mixing ratio, and density

exojax.atm.atmconvert.mmr_to_density(mmr, molmass, Parr, Tarr, unit='g/L')

converts MMR to density

Parameters:

  • mmr (float or array) – mass mixing ratio

  • molmass (float) – molecular mass

  • Parr (float or array) – pressure array (bar)

  • Tarr (float or array) – temperature array (K)

  • unit (str) – unit of the density (β€œg/L” or β€œg/cm3”)

Note

mass density (g/L) = fac * MMR

Returns:

density in the specified unit

Return type:

float or array

exojax.atm.atmconvert.mmr_to_vmr(mmr, molecular_mass, mean_molecular_weight)

converts mass mixing ratio (mmr) to volume mixing ratio (vmr)

Parameters:

  • mmr (float or array) – mass mixing ratio(s)

  • molecular_mass (float or array) – molecular mass(es)

  • mean_molecular_weight (float) – mean molecular weight

Returns:

volume mixing ratio(s)

Return type:

float

exojax.atm.atmconvert.vmr_to_mmr(vmr, molecular_mass, mean_molecular_weight)

converts volume mixing ratio (vmr) to mass mixing ratio (mmr)

Parameters:

  • vmr (float or array) – volume mixing ratio(s)

  • molecular_mass (float or array) – molecular mass(es)

  • mean_molecular_weight (float) – mean molecular weight

Returns:

mass mixing ratio(s)

Return type:

float

exojax.atm.atmphys module

Atmospheric MicroPhysics (amp) class

class exojax.atm.atmphys.AmpAmcloud(pdb, bkgatm, size_min=1e-05, size_max=0.001, nsize=1000)

Bases: AmpCloud

calc_ammodel(pressures, temperatures, mean_molecular_weight, molecular_mass_condensate, gravity, fsed, sigmag, Kzz, MMR_base, alphav=2.0)

computes rg and VMR of condensates based on AM01

Parameters:

  • pressures (array) – Pressure profile of the atmosphere (bar)

  • temperatures (array) – Temperature profile of the atmosphere (K)

  • mean_molecular_weight (float) – Mean molecular weight of the atmosphere

  • molecular_mass_condensate (float) – Molecular mass of the condensate

  • gravity (float) – Gravitational acceleration (cm/s^2)

  • fsed (float) – Sedimentation efficiency factor

  • sigmag (float) – Width of the lognormal size distribution

  • Kzz (array) – Eddy diffusion coefficient profile (cm^2/s)

  • MMR_base (float) – Mass Mixing Ratio of condensate at the cloud base

  • alphav (float, optional) – Shape parameter for the lognormal distribution. Defaults to 2.0.

Returns:

Parameter in the lognormal distribution of condensate size, defined by (9) in AM01 MMR_condensate (array): Mass Mixing Ratio (MMR) of condensates

Return type:

rg (array)

calc_ammodel_rw(pressures, temperatures, mean_molecular_weight, molecular_mass_condensate, gravity, fsed, Kzz, MMR_base)

computes rw and VMR of condensates based on AM01 without sigmag

Parameters:

  • pressures (array) – Pressure profile of the atmosphere (bar)

  • temperatures (array) – Temperature profile of the atmosphere (K)

  • mean_molecular_weight (float) – Mean molecular weight of the atmosphere

  • molecular_mass_condensate (float) – Molecular mass of the condensate

  • gravity (float) – Gravitational acceleration (cm/s^2)

  • fsed (float) – Sedimentation efficiency factor

  • Kzz (array) – Eddy diffusion coefficient profile (cm^2/s)

  • MMR_base (float) – Mass Mixing Ratio of condensate at the cloud base

Returns:

Parameter in the lognormal distribution of condensate size, defined by (9) in AM01 MMR_condensate (array): Mass Mixing Ratio (MMR) of condensates

Return type:

rw (array)

exojax.atm.atmprof module

Atmospheric profile function.

exojax.atm.atmprof.Teff2Tirr(Teff, Tint)

Tirr from effective temperature and intrinsic temperature.

Parameters:

  • Teff – effective temperature

  • Tint – intrinsic temperature

Returns:

iradiation temperature

Return type:

Tirr

Note

Here we assume A=0 (albedo) and beta=1 (fully-energy distributed)

exojax.atm.atmprof.Teq2Tirr(Teq)

Tirr from equilibrium temperature and intrinsic temperature.

Parameters:

Teq – equilibrium temperature

Returns:

iradiation temperature

Return type:

Tirr

Note

Here we assume A=0 (albedo) and beta=1 (fully-energy distributed)

exojax.atm.atmprof.atmprof_Guillot(pressures, gravity, kappa, gamma, Tint, Tirr, f=0.25)

Notes

Guillot (2010) Equation (29)

Parameters:

  • pressures – pressure array (bar)

  • gravity – gravity (cm/s2)

  • kappa – thermal/IR opacity (kappa_th in Guillot 2010)

  • gamma – ratio of optical and IR opacity (kappa_v/kappa_th), gamma > 1 means thermal inversion

  • Tint – temperature equivalence of the intrinsic energy flow

  • Tirr – temperature equivalence of the irradiation

  • point (f = 1 at the substellar) – and f = 1/4 for an averaging over the whole planetary surface

  • average (f = 1/2 for a day-side) – and f = 1/4 for an averaging over the whole planetary surface

Returns:

temperature profile

Return type:

array

exojax.atm.atmprof.atmprof_gray(pressures, gravity, kappa, Tint)
Parameters:

  • pressures (1D array) – pressure array (bar)

  • gravity (float) – gravity (cm/s2)

  • kappa – infrared opacity

  • Tint – temperature equivalence of the intrinsic energy flow

Returns:

temperature profile

Return type:

array

exojax.atm.atmprof.atmprof_powerlow(pressures, T0, alpha)

powerlaw temperature profile

Parameters:

  • pressures – pressure array (bar)

  • T0 (float) – T at P=1 bar in K

  • alpha (float) – powerlaw index

Returns:

temperature profile

Return type:

array

exojax.atm.atmprof.gh_product(temperature, mean_molecular_weight)

product of gravity and pressure scale height

Parameters:

  • temperature – isothermal temperature (K)

  • mean_molecular_weight – mean molecular weight

Returns:

gravity x pressure scale height cm2/s2

exojax.atm.atmprof.normalized_layer_height(temperature, pressure_decrease_rate, mean_molecular_weight, radius_btm, gravity_btm)

compute normalized height/radius at the upper boundary of the atmospheric layer, neglecting atmospheric mass, examining non-constant gravity.

Note

This method computes the height of the atmospheric layers taking the effect of the decrease of gravity (i.e. $ propto 1/r^2 $) into account.

Parameters:

  • temperature (1D array) – temperature profile (K) of the layer, (Nlayer, from atmospheric top to bottom)

  • pressure_decrease_rate – pressure decrease rate of the layer (k-factor; k < 1) pressure[i-1] = pressure_decrease_rate*pressure[i]

  • mean_molecular_weight (1D array) – mean molecular weight profile, (Nlayer, from atmospheric top to bottom)

  • radius_btm (float) – radius (cm) at the lower boundary of the bottom layer, R0 or r_N

  • gravity_btm (float) – gravity (cm/s2) at the lower boundary of the bottom layer, g_N

Returns:

layer height normalized by radius_btm starting from top atmosphere 1D array (Nlayer) : radius at lower bondary normalized by radius_btm starting from top atmosphere

Return type:

1D array (Nlayer)

exojax.atm.atmprof.pressure_boundary_logspace(pressures, pressure_decrease_rate, reference_point=0.5, numpy=False)

computes pressure at the boundary of the layers (Nlayer + 1)

Parameters:

  • pressures (_type_) – representative pressure (output of pressure_layer_logspace)

  • pressure_decrease_rate – pressure decrease rate of the layer (k-factor; k < 1) pressure[i-1] = pressure_decrease_rate*pressure[i]

  • reference_point (float) – reference point in a layer (0-1). Center:0.5, lower boundary:1.0, upper boundary:0

  • numpy – if True use numpy array instead of jnp array

Returns:

pressure at the boundary (Nlayer + 1)

Return type:

_type_

exojax.atm.atmprof.pressure_layer_logspace(log_pressure_top=- 8.0, log_pressure_btm=2.0, nlayer=20, mode='ascending', reference_point=0.5, numpy=False)

Pressure layer evenly spaced in logspace, i.e. logP interval is constant

Parameters:

  • log_pressure_top – log10(P[bar]) at the top layer

  • log_pressure_btm – log10(P[bar]) at the bottom layer

  • nlayer – the number of the layers

  • mode – ascending or descending

  • reference_point (float) – reference point in a layer (0-1). Center:0.5, lower boundary:1.0, upper boundary:0

  • numpy – if True use numpy array instead of jnp array

Returns:

representative pressures (array) of the layers delta_pressures: delta pressure layer, the old name is dParr pressure_decrease_rate: pressure decrease rate of the layer (k-factor; k < 1) pressure[i-1] = pressure_decrease_rate*pressure[i]

Return type:

pressures

Note

d logP is constant using this function.

exojax.atm.atmprof.pressure_lower_logspace(pressures, pressure_decrease_rate, reference_point=0.5)

computes pressure at the lower point of the layers

Parameters:

  • pressures (_type_) – representative pressure (output of pressure_layer_logspace)

  • pressure_decrease_rate – pressure decrease rate of the layer (k-factor; k < 1) pressure[i-1] = pressure_decrease_rate*pressure[i]

  • reference_point (float) – reference point in a layer (0-1). Center:0.5, lower boundary:1.0, upper boundary:0

Returns:

pressure at the lower point (underline{P}_i)

Return type:

_type_

exojax.atm.atmprof.pressure_scale_height(gravity, T, mean_molecular_weight)

pressure scale height assuming an isothermal atmosphere.

Parameters:

  • gravity – gravity acceleration (cm/s2)

  • T – isothermal temperature (K)

  • mean_molecular_weight – mean molecular weight

Returns:

pressure scale height (cm)

exojax.atm.atmprof.pressure_upper_logspace(pressures, pressure_decrease_rate, reference_point=0.5)

computes pressure at the upper point of the layers

Parameters:

  • pressures (_type_) – representative pressure (output of pressure_layer_logspace)

  • pressure_decrease_rate – pressure decrease rate of the layer (k-factor; k < 1) pressure[i-1] = pressure_decrease_rate*pressure[i]

  • reference_point (float) – reference point in a layer (0-1). Center:0.5, lower boundary:1.0, upper boundary:0

Returns:

pressure at the upper point (overline{P}_i)

Return type:

_type_

exojax.atm.condensate module

exojax.atm.condensate.condensate_density_liquid_ammonia(T)

condensate density of liquid ammonia as a function of T from Lange’s Handbook of Chemistry, 10th ed. page 1451 and 1468

Parameters:

T (_type_) – temperature in Kelvin

Returns:

liquid ammonia density in g/cm3

exojax.atm.condensate.read_liquid_ammonia_density()

read liquid ammonia density file

Returns:

temperature in K liquid ammonia density in g/cm3

exojax.atm.idealgas module

Functions about ideal gas.

exojax.atm.idealgas.number_density(Parr, Tarr)

number density of ideal gas in cgs.

Parameters:

  • Parr – pressure array (bar)

  • Tarr – temperature array (K)

Returns:

number density (1/cm3)

exojax.atm.lorentz_lorenz module

exojax.atm.lorentz_lorenz.refractive_index_Lorentz_Lorenz(polarizability, number_density)

Refractive index using Lorentz-Lorenz relataion

Notes

See D.25 in Liou 2002, for instance.

Parameters:

  • polarizability – polarizability (cm3)

  • number_density – number density of molecule (cm-3)

Returns:

refractive index

exojax.atm.polarizability module

Gas Polarizability

Notes

Originally taken from PICASO/GPLv3 picaso/rayleigh.py polarizabilities are mainly taken from CRC handbook of chemistry and physics vol. 95 unit=cm3 H3+ taken from Kawaoka & Borkman, 1971 Number density at reference conditions of refractive index measurements i.e. number density of the ideal gas at T=273.15K (=0 C) and P=1atm [cm-2], as Patm*bar_cgs / (kB * 273.15) http://refractiveindex.info n_ref_refractive = 2.6867810458916872e+19

exojax.atm.psat module

Saturation Vapor Pressure.

exojax.atm.psat.psat_Fe_AM01(T)

Saturation Vapor Pressure for iron

Note

Taken from Ackerman and Marley 2001 Appendix A (A3), originally from Barshay and Lewis (1976)

Parameters:

T – temperature (K)

Returns:

saturation vapor pressure (bar)

exojax.atm.psat.psat_ammonia_AM01(T)

Saturation Vapor Pressure for Ammonia

Note

Taken from Ackerman and Marley 2001 Appendix A (A4) see also their errata.

Parameters:

T – temperature (K)

Returns:

saturation vapor pressure (bar)

exojax.atm.psat.psat_enstatite_AM01(T)

Saturation Vapor Pressure for Enstatite (MgSiO3)

Note

Taken from Ackerman and Marley 2001 Appendix A (A4) see also their errata, originally from Barshay and Lewis (1976)

Parameters:

T – temperature (K)

Returns:

saturation vapor pressure (bar)

exojax.atm.psat.psat_water_AM01(T)

Saturation Vapor Pressure for water (but for T<1048K)

Note

Taken from Ackerman and Marley 2001 Appendix A (A4) see also their errata and updated Buck 1981, 1996

Parameters:

T – temperature (K)

Returns:

saturation vapor pressure (bar)

exojax.atm.psat.psat_water_Magnus(T)

Saturation Vapor Pressure for water (Magnus, or August-Roche-Magnus)

Note

See https://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation#August%E2%80%93Roche%E2%80%93Magnus_approximation

Parameters:

T – temperature (K)

Returns:

saturation vapor pressure (bar)

exojax.atm.simple_clouds module

simple cloud opacity model.

exojax.atm.simple_clouds.powerlaw_clouds(nus, kappac0=0.01, nuc0=28571.0, alphac=1.0)

power-law cloud model.

Parameters:

  • kappac0 – opacity (cm2/g) at nuc0

  • nuc0 – wavenumber for kappac0

  • alphac – power

Returns:

cross section (cm2)

Note

alphac = - gamma of the definition in petitRadtrans. Also, default nuc0 corresponds to lambda0=0.35 um.

exojax.atm.viscosity module

Viscosity of droplets.

exojax.atm.viscosity.calc_vfactor(atm='H2', LJPparam=None)
Parameters:

  • atm – molecule consisting of atmosphere, β€œH2”, β€œO2”, and β€œN2”

  • LJPparam – Custom Lennard-Jones Potential Parameters (d (cm) and epsilon/kB)

Returns:

dynamic viscosity factor for Rosner eta = viscosity*T**0.66 applicable tempature range (K,K)

Return type:

vfactor

Note

The dynamic viscosity is from the Rosner book (3-2-12) and caption in p106 Hirschfelder et al. (1954) within Trange.

exojax.atm.viscosity.eta_Rosner(T, vfactor)

dynamic viscocity by Rosner (2000)

Parameters:

  • T – temperature (K)

  • vfactor – vfactor

Returns:

dynamic viscosity (g/s/cm)

exojax.atm.viscosity.eta_Rosner_H2(T)

dynamic viscocity of the H2 atmosphere by Rosner (2000)

Parameters:

T – temperature (K) (applicable from 179 to 11940K)

Returns:

dynamic viscosity (g/s/cm)

exojax.atm.viscosity.get_LJPparam()

Lennard-Jones Potential Parameters.

Returns:

Dict for Lennard-Jones Potential Parameters (d (cm)) LJPparam_epsilon_per_kB: Dict for Lennard-Jones Potential Parameters (epsilon/kB)

Return type:

LJPparam_d

Note

Lennard-Jones Potential Parameters (LJPparam) were taken from p107, Table 3.2.1 of Transport process in chemically reacting flow systems by Daniel E. Rosner, originally from Svehla (1962).

exojax.atm.vterm module

Terminal velocity of cloud particles.

Note

The code in this module is based on Hans R Pruppacher and James D Klett. Microstructure of atmospheric clouds and precipitation and Akerman and Marley 2001.

exojax.atm.vterm.Ndavies(r, g, eta, drho, rho)

Davies (Best) number.

Parameters:

  • r – particle size (cm)

  • g – gravity (cm/s2)

  • eta – dynamic viscosity (g/s/cm)

  • drho – density difference between condensates and atmosphere (g/cm3)

  • rho – atmosphere density (g/cm3)

Returns:

Davies number (Best Number)

exojax.atm.vterm.terminal_velocity(r, gravity, dynamic_viscosity, rho_cloud, rho_atm, Nkn=0.0)

computes terminal velocity in a wide particles size range.

Parameters:

  • r – particle size (cm)

  • g – gravity (cm/s2)

  • dynamic_viscosity – dynamic viscosity (g/s/cm)

  • rho_cloud – condensate density (g/cm3)

  • rho_atm – atmosphere density (g/cm3)

  • Nkn – Knudsen number

Returns:

terminal velocity (cm/s)

Example

>>> #terminal velocity at T=300K, for Earth atmosphere/gravity.
>>> g=980.
>>> drho=1.0
>>> rho=1.29*1.e-3 #g/cm3
>>> vfactor,Tr=vc.calc_vfactor(atm="Air")
>>> eta=vc.eta_Rosner(300.0,vfactor)
>>> r=jnp.logspace(-5,0,70)
>>> terminal_velocity(r,g,eta,drho,rho) #terminal velocity (cm/s)
exojax.atm.vterm.vf_largeNre(r, g, eta, drho, rho)

terminal velocity ( Reynolds number > 500, Davies number >10**5 )

Parameters:

  • r – particle size (cm)

  • g – gravity (cm/s2)

  • eta – dynamic viscosity (g/s/cm)

  • drho – density difference between condensates and atmosphere (g/cm3)

  • rho – atmosphere density (g/cm3)

Returns:

terminal velocity (cm/s)

exojax.atm.vterm.vf_midNre(r, g, eta, drho, rho)

terminal velocity (2 < Reynolds number < 500, 42 < Davies number < 10**5)

Parameters:

  • r – particle size (cm)

  • g – gravity (cm/s2)

  • eta – dynamic viscosity (g/s/cm)

  • drho – density difference between condensates and atmosphere (g/cm3)

  • rho – atmosphere density (g/cm3)

Returns:

terminal velocity (cm/s)

exojax.atm.vterm.vf_stokes(r, g, eta, drho, Nkn=0.0)

terminal velocity of Stokes flow (Reynolds number < 2, Davies number < 42)

Parameters:

  • r – particle size (cm)

  • g – gravity (cm/s2)

  • eta – dynamic viscosity (g/s/cm)

  • drho – density difference between condensates and atmosphere (g/cm3)

  • Nkn – Knudsen number

Returns:

terminal velocity (cm/s)

Note

(1.0+1.255*Nkn) is the Cunningham factor

Note

See also (10-138) p415 in Hans R Pruppacher and James D Klett. Microstructure of atmospheric clouds and precipitation. In Microphysics of clouds and precipitation, pages 10–73. Springer, 2010. Equation (B1) in Appendix B of Ackerman and Marley 2001.

Module contents