exo_k.atm_evolution.convection

@author: jeremy leconte

Module Contents

exo_k.atm_evolution.convection.dry_convective_adjustment_numba(timestep, Nlay, t_lay, exner, dmass, tracer_array, Mgas, verbose=False)

Computes the heating rates needed to adjust unstable regions of a given atmosphere to a convectively neutral T profile on a given timestep.

Parameters:

• timestep (float) – Duration of the adjustment. If given in seconds, H=dT/timestep is in K/s. In the current model, timestep is in second over cp. This ensures that H=dT/timestep is in W/kg.

• Nlay (int) – Number of atmospheric layers

• t_lay (array, np.ndarray) – Temperatures of the atmospheric layers (K)

• exner (array, np.ndarray) –

  Exner function computed at the layer centers ((p/psurf)**rcp)

  \[\Pi=(p / p_{s})^{R/c_p}\]

• dmass (array, np.ndarray) – Mass of gas in each layer (kg/m^2)

Returns:

array

Heating rate in each atmospheric layer (W/kg).

exo_k.atm_evolution.convection.convective_acceleration_numba(timestep, Nlay, H_rad, rad_layers, tau_rad, tau_rads, dmass, convective_acceleration_mode=0, convective_acceleration_factor=1.0, verbose=False)

Computes a heating rate for the whole convective region to accelerate convergence

Parameters:

• timestep (float) – Duration of the adjustment. If given in seconds, H=dT/timestep is in K/s. In the current model, timestep is in second over cp. This ensures that H=dT/timestep is in W/kg.

• Nlay (int) – Number of atmospheric layers

• H_rad (array, np.ndarray) – Radiative heating rate

• rad_layers (array, np.ndarray of bool) – Elements in the array are true if layer is purely radiative

• tau_rad (array, np.ndarray) – Baseline radiative timescale for the atmosphere. (e.g. the min of tau_rads) Should use the same units as timestep.

• tau_rads (array, np.ndarray) – Radiative timescale for each layer. Should use the same units as timestep.

• dmass (array, np.ndarray) – Mass of gas in each layer (kg/m^2)

• convective_acceleration_mode (int) – convective_acceleration_mode=0 is the default mode =1 emulates an old (and bad) behavior.

• convective_acceleration_factor (int) – Multiplying factor for convection acceleration

Returns:

array

Heating rate in each atmospheric layer (W/kg).

exo_k.atm_evolution.convection.turbulent_diffusion_numba(timestep, Nlay, p_lay, p_lev, dmass, t_lay, exner, t_lay_ov_mu, g, Kzz, tracer_array, cp, mix_potential_temp=False, verbose=False)

Solves turbulent diffusion equation:

\[\rho frac{\partial q}{\partial t} = \frac{\partial F_{diff}}{\partial z}\]

with a diffusive flux given by

\[F_{diff} = - \rho K_{zz} \frac{\partial q}{\partial z}\]

The equation is solved with an implicit scheme assuming that there is no flux at the top and bottom boundaries (evaporation must be treated separately for now).

For the potential temperature mixing, the equation in not completely nrj conserving. One should mix enthalpy as in GCM.

Parameters:

• timestep (float) – Time step in seconds.

• Nlay (int) – Number of atmospheric layers

• t_lay_ov_mu (array, np.ndarray) – Temperatures of the atmospheric layers divided by the molar_mass in kg/mol

• p_lay (array, np.ndarray) – Pressure at the layer centers (Pa)

• p_lev (array, np.ndarray) – Presure at the Nlay+1 level boundaries (Pa)

• dmass (array, np.ndarray) – Mass of gas in each layer (kg/m^2)

• g (float) – Gravity (m/s^2)

• Kzz (float) – Eddy mixing coefficient (m^2/s)

• tracer_array (array, np.ndarray (Ntrac, Nlay)) – Array containing the mass mixing ratio of all tracers at each layer before the mixing

Returns:

new_tracers: array, np.ndarray (Ntrac, Nlay)

Array containing the mass mixing ratio of all tracers at each layer after the mixing

exo_k.atm_evolution.convection.compute_condensation_numba(timestep, Nlay, tlay, play, cp, Mgas, qarray, idx_vap, idx_cond, thermo_parameters, latent_heating=True, condensation_timestep_reducer=None, verbose=False)

Computes the heating rates needed to bring sursaturated regions back to saturation

Parameters:

• timestep

• Nlay (float) – Number of layers

• tlay (array, np.ndarray) – Layer temperatures

• cp (float) – Specific heat capacity

• Mgas (array, np.ndarray) – Layer molar mass

• qarray (array, np.ndarray) – Array of tracer specific concentrations

• idx_vap (int) – Indices for condensing species in tracer array

• idx_cond (int) – Indices for condensing species in tracer array

• thermo_parameters (array, np.ndarray) – Array of thermodynamical paramaters for condensing species. See :class:`~exo_k.atm_evolution.condensation.Condensation_Thermodynamical_Parameters

• latent_heating (bool) – Whether latent heating should be taken into account

Returns:

H_cond: array, np.ndarray

Heating rate in W/kg

exo_k.atm_evolution.convection.moist_convective_adjustment_numba(timestep, Nlay, tlay, play, dmass, cp, Mgas, q_array, i_vap, i_cond, thermo_parameters, moist_inhibition=True, verbose=False)

Computes the heating rates needed to adjust unstable regions of a given atmosphere to a moist adiabat.

Based on Description algorithmique d’un ensemble de paramétrisation physique - phylmd Zhaoxin Laurent LI

Parameters:

• timestep

• Nlay (float) – Number of layers

• tlay (array, np.ndarray) – Layer temperatures

• play (array) – Pressure at layer centers

• dmass (array, np.ndarray) – mass of layers in kg/m^2

• cp (float) – specific heat capacity at constant pressure

• q_array (array, np.ndarray) – mass mixing ratio of tracers

• i_vap (int) – index of vapor tracer in qarray

• i_cond (int) – index of condensate tracer in qarray

• qsat (array, np.ndarray) – Saturation mmr for each layer

• dqsat_dt (array, np.ndarray) – d qsat / dT in each layer

• Lvap (array, np.ndarray) – Latent heat of vaporization (can have different values in each layer if Lvap=f(T))

• dlnt_dlnp_moist (array, np.ndarray) – threshold thermal gradient (d ln T / d ln P) for a moist atmosphere computed at the layer centers.

• q_crit (array, np.ndarray) – Critical mass mixing ratio for the inhibition of moist convection (Eq. 17 of Leconte et al. 2017)

Returns:

H_madj: array, np.ndarray

Heating rate in each atmospheric layer (W/kg).

new_q: array, np.ndarray

tracer mmr array after adjustment.

new_t: array, np.ndarray

Temperature of layers after adjustment.

exo_k.atm_evolution.convection.moist_convective_adjustment_cloud_fraction_numba(timestep, Nlay, tlay, play, dmass, cp, Mgas, q_array, i_vap, i_cond, thermo_parameters, moist_inhibition=True, verbose=False, humidity_distribution_width=0.2)

Computes the heating rates needed to adjust unstable regions of a given atmosphere to a moist adiabat.

This approach with a cloud fraction is experimental and should be used with extreme caution. It does not seem to give good results when re-evaporation is very efficient because there is constant re-evaporation and condensation in the convective region.

Parameters:

• timestep

• Nlay (float) – Number of layers

• tlay (array) – Layer temperatures

• play (array) – Pressure at layer centers

• dmass (array) – mass of layers in kg/m^2

• cp (float) – specific heat capacity at constant pressure

• q_array (array) – mass mixing ratio of tracers

• i_vap (int) – index of vapor tracer in qarray

• i_cond (int) – index of condensate tracer in qarray

• qsat (array) – Saturation mmr for each layer

• dqsat_dt (array) – d qsat / dT in each layer

• Lvap (array) – Latent heat of vaporization (can have different values in each layer if Lvap=f(T))

• dlnt_dlnp_moist (array) – threshold thermal gradient (d ln T / d ln P) for a moist atmosphere computed at the layer centers.

• q_crit (array) – Critical mass mixing ratio for the inhibition of moist convection (Eq. 17 of Leconte et al. 2017)

Returns:

H_madj: array

Heating rate in each atmospheric layer (W/kg).

new_q: array

tracer mmr array after adjustment.

new_t: array

Temperature of layers after adjustment.

exo_k.atm_evolution.convection.compute_rainout_numba(timestep, Nlay, tlay, play, dmass, cp, Mgas, qarray, idx_vap, idx_cond, thermo_parameters, evap_coeff, qvap_deep, q_cloud=0.0, latent_heating=False, total_cloud_fraction=1.0, humidity_distribution_width=0.2, verbose=False)

Computes the heating rates needed to adjust unstable regions of a given atmosphere to a moist adiabat.

Parameters:

• timestep

• Nlay (float) – Number of layers

• tlay (array, np.ndarray) – Layer temperatures

exo_k.atm_evolution.convection.molecular_diffusion_numba(timestep, Nlay, p_lay, p_lev, dmass, tlay, mu, g, Dmol, verbose=False)

Solves turbulent diffusion equation:

\[\rho frac{\partialT}{\partial t} = \frac{\partial F_{diff}}{\partial z}\]

with a diffusive flux given by

\[F_{diff} = - \rho D_{mol} \frac{\partial T}{\partial z}\]

The equation is solved with an implicit scheme assuming that there is no flux at the top and bottom boundaries (evaporation must be treated separately for now).

Parameters:

• timestep (float) – Time step in seconds.

• Nlay (int) – Number of atmospheric layers

• t_lay_ov_mu (array, np.ndarray) – Temperatures of the atmospheric layers divided by the molar_mass in kg/mol

• p_lay (array, np.ndarray) – Pressure at the layer centers (Pa)

• p_lev (array, np.ndarray) – Presure at the Nlay+1 level boundaries (Pa)

• dmass (array, np.ndarray) – Mass of gas in each layer (kg/m^2)

• g (float) – Gravity (m/s^2)

• Dmol (float) – molecular diffusion coefficient (m^2/s)

Returns:

new_tlay: array, np.ndarray (Nlay)

Array containing the temperature at each layer after the mixing

exo_k.atm_evolution.convection.DTRIDGL(L, AF, BF, CF, DF)

! GCM2.0 Feb 2003

! DOUBLE PRECISION VERSION OF TRIDGL

DIMENSION AF(L),BF(L),CF(L),DF(L),XK(L) DIMENSION AS(2*L),DS(2*L)

!* THIS SUBROUTINE SOLVES A SYSTEM OF TRIDIAGIONAL MATRIX !* EQUATIONS. THE FORM OF THE EQUATIONS ARE: !* A(I)*X(I-1) + B(I)*X(I) + C(I)*X(I+1) = D(I)

!======================================================================!