exojax.atm package

Submodules

exojax.atm.amclouds module

Ackerman and Marley 2001 cloud model.

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

exojax.atm.amclouds.VMRcloud(P, Pbase, fsed, VMRbase, kc=1)

VMR of clouds based on AM01.

Parameters:

  • P – Pressure (bar)

  • Pbase – base pressure (bar)

  • fsed – fsed

  • VMRbase – VMR of condensate at cloud base

  • kc – constant ratio of condenstates to total mixing ratio

Returns:

VMR of condensates

exojax.atm.amclouds.dtau_cloudgeo(Parr, muc, rhoc, mu, VMRc, rg, sigmag, g)

the optical depth using a geometric cross-section approximation, based on (16) in AM01.

Parameters:

  • Parr – pressure array (bar)

  • muc – mass weight of condensate

  • rhoc – condensate density (g/cm3)

  • mu – mean molecular weight of atmosphere

  • VMRc – VMR array of condensate [Nlayer]

  • rg – rg parameter in the lognormal distribution of condensate size, defined by (9) in AM01

  • sigmag – sigmag parameter in the lognormal distribution of condensate size, defined by (9) in AM01

exojax.atm.amclouds.find_rw(rarr, vf, KzzpL)

finding rw from rarr and terminal velocity array.

Parameters:

  • rarr – particle radius array (cm)

  • vf – terminal velocity (cm/s)

  • KzzpL – Kzz/L in Ackerman and Marley 2001

Returns:

rw in Ackerman and Marley 2001

exojax.atm.amclouds.get_Pbase(Parr, Psat, VMR)

get Pbase from an intersection of a T-P profile and Psat(T) curves :param Parr: pressure array :param Psat: saturation pressure arrau :param VMR: VMR for vapor

Returns:

base pressure

Return type:

Pbase

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 in the lognormal size distribution

Returns

exojax.atm.amclouds.get_rw(vfs, 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.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(pressure, gravity, kappa, gamma, Tint, Tirr, f=0.25)

Notes

Guillot (2010) Equation (29)

Parameters:

  • pressure – 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(pressure, gravity, kappa, Tint)
Parameters:

  • pressure (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(pressure, T0, alpha)

powerlaw temperature profile

Parameters:

  • pressure – 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)

prodict 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.

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_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:

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

Return type:

pressure

Note

d logP is constant using this function. d log_e P = dParr[i]/pressure[i] = constant = 1 - pressure_decrease_rate, dParr[0] = (1- pressure_decrease_rate) Parr[0] for ascending mode

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.condinfo module

condensate information.

  • LF98 Lodders and Fegley (1998)

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.psat module

Saturation Vapor Pressure.

exojax.atm.psat.Psat_Fe_liquid(T)

Saturation Vapor Pressure for liquid Fe (Fe)

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_Fe_solid(T)

Saturation Vapor Pressure for Solid Fe (Fe)

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.

Parameters:

T – temperature (K)

Returns:

saturation vapor pressure (bar)

exojax.atm.simple_clouds module

cloud opacity.

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, “H2”, “O2”, and “N2”

  • 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.vf(r, g, eta, rhoc, rho, Nkn=0.0)

terminal velocity.

Parameters:

  • r – particle size (cm)

  • g – gravity (cm/s2)

  • eta – dynamic viscosity (g/s/cm)

  • rhoc – condensate density (g/cm3)

  • rho – 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)
>>> vf(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