POSEIDON.emission

Radiative transfer calculations for generating emission spectra.

Attributes

cp

block

thread

Functions

find_nearest(array, value)

planck_lambda_arr(T, wl)

Compute the Planck function spectral radiance for a range of model

planck_lambda_arr_GPU(T, wl, B_lambda)

GPU variant of the 'planck_lambda_arr' function.

emission_single_stream(T, dz, wl, kappa[, Gauss_quad])

Compute the emergent top-of-atmosphere flux from a planet or brown dwarf.

emission_single_stream_w_albedo(T, dz, wl, kappa[, ...])

Compute the emergent top-of-atmosphere flux from a planet or brown dwarf.

emission_single_stream_GPU(T, dz, wl, kappa[, Gauss_quad])

GPU variant of the 'emission_rad_transfer' function.

determine_photosphere_radii(dtau, r_low, wl[, ...])

Interpolate optical depth to find the radius corresponding to the

determine_photosphere_radii_GPU(tau_lambda, r_low, wl, ...)

GPU variant of the 'determine_photosphere_radii' function.

slice_gt(array, lim)

Function to replace values with upper or lower limit

setup_tri_diag(N_layer, N_wl, c_plus_up, c_minus_up, ...)

Before we can solve the tridiagonal matrix (See Toon+1989) section

tri_diag_solve(l, a, b, c, d)

emission_Toon(P, T, wl, dtau_tot, kappa_Ray, ...[, ...])

This function uses the source function method, which is outlined here :

numba_cumsum(mat)

Function to compute cumsum along axis=0 to bypass numba not allowing kwargs in

reflection_Toon(P, wl, dtau_tot, kappa_Ray, ...[, ...])

Computes toon fluxes given tau and everything is 1 dimensional. This is the exact same function

emission_bare_surface(T_surf, wl, surf_reflect)

Compute the emergent top-of-atmosphere flux from a bare rock

reflection_bare_surface(wl, surf_reflect[, Gauss_quad])

Compute the emergent top-of-atmosphere flux from a bare rock

assign_assumptions_and_compute_single_stream_emission(P, ...)

Assigns assumptions (surfaces, clouds) and computes single-stream emission

assign_assumptions_and_compute_thermal_scattering_emission(P, ...)

Assigns assumptions (surfaces, clouds) and computes thermal scattering emission

assign_assumptions_and_compute_reflection(P, T, dz, ...)

Assigns assumptions (surfaces, clouds) and computes reflection

Module Contents

POSEIDON.emission.cp
POSEIDON.emission.block
POSEIDON.emission.thread
POSEIDON.emission.find_nearest(array, value)
POSEIDON.emission.planck_lambda_arr(T, wl)

Compute the Planck function spectral radiance for a range of model wavelengths and atmospheric temperatures.

Parameters:

  • T (np.array of float) – Array of temperatures in each atmospheric layer (K).

  • wl (np.array of float) – Wavelength grid (μm).

Returns:

Planck function spectral radiance as a function of layer temperature and wavelength in SI units (W/m^2/sr/m).

Return type:

B_lambda (2D np.array of float)

POSEIDON.emission.planck_lambda_arr_GPU(T, wl, B_lambda)

GPU variant of the ‘planck_lambda_arr’ function.

Compute the Planck function spectral radiance for a range of model wavelengths and atmospheric temperatures. :param T: Array of temperatures in each atmospheric layer (K). :type T: np.array of float :param wl: Wavelength grid (μm). :type wl: np.array of float

Returns:

Planck function spectral radiance as a function of layer temperature and wavelength in SI units (W/m^2/sr/m).

Return type:

B_lambda (2D np.array of float)

POSEIDON.emission.emission_single_stream(T, dz, wl, kappa, Gauss_quad=2)

Compute the emergent top-of-atmosphere flux from a planet or brown dwarf.

This function considers only pure thermal emission (i.e. no scattering).

Parameters:

  • T (np.array of float) – Temperatures in each atmospheric layer (K).

  • dz (np.array of float) – Vertical extent of each atmospheric layer (m).

  • wl (np.array of float) – Wavelength grid (μm).

  • kappa (2D np.array of float) – Extinction coefficient in each layer as a function of wavelength (m^-1).

  • Gauss_quad (int) – Gaussian quadrature order for integration over emitting surface (Options: 2 / 3).

Returns:

Spectral surface flux in SI units (W/m^2/sr/m).

Return type:

F (np.array of float)

POSEIDON.emission.emission_single_stream_w_albedo(T, dz, wl, kappa, Gauss_quad=2, surf_reflect=[], index_below_P_surf=0)

Compute the emergent top-of-atmosphere flux from a planet or brown dwarf.

This function considers only pure thermal emission (i.e. no scattering).

Parameters:

  • T (np.array of float) – Temperatures in each atmospheric layer (K).

  • dz (np.array of float) – Vertical extent of each atmospheric layer (m).

  • wl (np.array of float) – Wavelength grid (μm).

  • kappa (2D np.array of float) – Extinction coefficient in each layer as a function of wavelength (m^-1).

  • Gauss_quad (int) – Gaussian quadrature order for integration over emitting surface (Options: 2 / 3).

  • surf_reflect – numpy.ndarray Surface reflectivity as a function of wavelength.

  • index_below_P_surf – int Index below P_surf, so that the blackbody can be computed. (Note that P_surf can be between two pressure levels, we take the lower one)

Returns:

Spectral surface flux in SI units (W/m^2/sr/m).

Return type:

F (np.array of float)

POSEIDON.emission.emission_single_stream_GPU(T, dz, wl, kappa, Gauss_quad=2)

GPU variant of the ‘emission_rad_transfer’ function.

Compute the emergent top-of-atmosphere flux from a planet or brown dwarf.

This function considers only pure thermal emission (i.e. no scattering).

Parameters:

  • T (np.array of float) – Temperatures in each atmospheric layer (K).

  • dz (np.array of float) – Vertical extent of each atmospheric layer (m).

  • wl (np.array of float) – Wavelength grid (μm).

  • kappa (2D np.array of float) – Extinction coefficient in each layer as a function of wavelength (m^-1).

  • Gauss_quad (int) – Gaussian quadrature order for integration over emitting surface (Options: 2 / 3).

Returns:

Spectral surface flux in SI units (W/m^2/sr/m).

Return type:

F (np.array of float)

POSEIDON.emission.determine_photosphere_radii(dtau, r_low, wl, photosphere_tau=2 / 3)

Interpolate optical depth to find the radius corresponding to the photosphere (by default at tau = 2/3).

Parameters:

  • dtau (2D np.array of float) – Vertical optical depth across each layer (starting from the top of the atmosphere) as a function of layer and wavelength.

  • r_low (np.array of float) – Radius at the lower boundary of each layer (m).

  • wl (np.array of float) – Wavelength grid (μm).

  • photosphere_tau (float) – Optical depth to determine photosphere radius.

Returns:

Photosphere radius as a function of wavelength (m).

Return type:

R_p_eff (np.array of float)

POSEIDON.emission.determine_photosphere_radii_GPU(tau_lambda, r_low, wl, R_p_eff, photosphere_tau=2 / 3)

GPU variant of the ‘determine_photosphere_radii’ function.

Interpolate optical depth to find the radius corresponding to the photosphere (by default at tau = 2/3).

Parameters:

  • dtau (2D np.array of float) – Vertical optical depth across each layer (starting from the top of the atmosphere) as a function of layer and wavelength.

  • r_low (np.array of float) – Radius at the lower boundary of each layer (m).

  • wl (np.array of float) – Wavelength grid (μm).

  • photosphere_tau (float) – Optical depth to determine photosphere radius.

Returns:

Photosphere radius as a function of wavelength (m).

Return type:

R_p_eff (np.array of float)

POSEIDON.emission.slice_gt(array, lim)

Function to replace values with upper or lower limit

POSEIDON.emission.setup_tri_diag(N_layer, N_wl, c_plus_up, c_minus_up, c_plus_down, c_minus_down, b_top, b_surface, surf_reflect, gamma, dtau, exptrm_positive, exptrm_minus)

Before we can solve the tridiagonal matrix (See Toon+1989) section “SOLUTION OF THE TwO-STREAM EQUATIONS FOR MULTIPLE LAYERS”, we need to set up the coefficients. :param N_layer: number of layers in the model :type N_layer: int :param N_wl: number of wavelength points :type N_wl: int :param c_plus_up: c-plus evaluated at the top of the atmosphere :type c_plus_up: array :param c_minus_up: c_minus evaluated at the top of the atmosphere :type c_minus_up: array :param c_plus_down: c_plus evaluated at the bottom of the atmosphere :type c_plus_down: array :param c_minus_down: c_minus evaluated at the bottom of the atmosphere :type c_minus_down: array :param b_top: The diffuse radiation into the model at the top of the atmosphere :type b_top: array :param b_surface: The diffuse radiation into the model at the bottom. Includes emission, reflection

of the unattenuated portion of the direct beam

Parameters:

  • surf_reflect (array) – Surface reflectivity

  • g1 (array) – table 1 toon et al 1989

  • g2 (array) – table 1 toon et al 1989

  • g3 (array) – table 1 toon et al 1989

  • lamba (array) – Eqn 21 toon et al 1989

  • gamma (array) – Eqn 22 toon et al 1989

  • dtau (array) – Opacity per layer

  • exptrm_positive (array) – Eqn 44, exponential terms needed for tridiagonal rotated layered, clipped at 35

  • exptrm_minus (array) – Eqn 44, exponential terms needed for tridiagonal rotated layered, clipped at 35

Returns:

coefficient of the positive exponential term

Return type:

array

POSEIDON.emission.tri_diag_solve(l, a, b, c, d)

‘ Tridiagonal Matrix Algorithm solver, a b c d can be NumPy array type or Python list type. refer to this wiki and to this explanation.

A, B, C and D refer to: .. math:: A(I)*X(I-1) + B(I)*X(I) + C(I)*X(I+1) = D(I) This solver returns X. :param A: :type A: array or list :param B: :type B: array or list :param C: :type C: array or list :param C: :type C: array or list

Returns:

Solution, x

Return type:

array

POSEIDON.emission.emission_Toon(P, T, wl, dtau_tot, kappa_Ray, kappa_cloud, kappa_tot, w_cloud, g_cloud, zone_idx, surf_reflect, kappa_cloud_seperate, hard_surface=0, tridiagonal=0, Gauss_quad=5, numt=1, T_surf=0)

This function uses the source function method, which is outlined here : https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/JD094iD13p16287

The result of this routine is the top of the atmosphere thermal flux as a function of gauss and chebychev points across the disk. Everything here is in CGS units: Fluxes - erg/s/cm^3 Temperature - K Wave grid - cm-1 Pressure ; dyne/cm2 Reminder: Flux = pi * Intensity, so if you are trying to compare the result of this with a black body you will need to compare with pi * BB !

Adapted from get_thermal_1d

Parameters:

  • nlevel (int) – Number of levels which occur at the grid points (not to be confused with layers which are mid points)

  • wno (numpy.ndarray) – Wavenumber grid in inverse cm

  • N_wl (int) – Number of wavenumber points

  • numg (int) – Number of gauss points (think longitude points)

  • numt (int) – Number of chebychev points (think latitude points)

  • tlevel (numpy.ndarray) – Temperature as a function of level (not layer)

  • dtau (numpy.ndarray) – This is a matrix of nlayer by nwave. This describes the per layer optical depth.

  • w0 (numpy.ndarray) – This is a matrix of nlayer by nwave. This describes the single scattering albedo of the atmosphere. Note this is free of any Raman scattering or any d-eddington correction that is sometimes included in reflected light calculations.

  • cosb (numpy.ndarray) – This is a matrix of nlayer by nwave. This describes the asymmetry of the atmosphere. Note this is free of any Raman scattering or any d-eddington correction that is sometimes included in reflected light calculations.

  • plevel (numpy.ndarray) – Pressure for each level (not layer, which is midpoints). CGS units (dyne/cm2)

  • ubar1 (numpy.ndarray) – This is a matrix of ng by nt. This describes the outgoing incident angles and is generally computed in picaso.disco

  • surf_reflect (numpy.ndarray) – Surface reflectivity as a function of wavenumber.

  • hard_surface (int) – 0 for no hard surface (e.g. Jupiter/Neptune), 1 for hard surface (terrestrial)

  • tridiagonal (int) – 0 for tridiagonal, 1 for pentadiagonal

Returns:

Thermal flux in CGS units (erg/cm3/s) in a matrix that is numg x numt x nwno

Return type:

numpy.ndarray

POSEIDON.emission.numba_cumsum(mat)

Function to compute cumsum along axis=0 to bypass numba not allowing kwargs in cumsum

POSEIDON.emission.reflection_Toon(P, wl, dtau_tot, kappa_Ray, kappa_cloud, kappa_tot, w_cloud, g_cloud, zone_idx, surf_reflect, kappa_cloud_seperate, single_phase=3, multi_phase=0, frac_a=1, frac_b=-1, frac_c=2, constant_back=-0.5, constant_forward=1, Gauss_quad=5, numt=1, toon_coefficients=0, tridiagonal=0, b_top=0)

Computes toon fluxes given tau and everything is 1 dimensional. This is the exact same function as get_flux_geom_3d but is kept separately so we don’t have to do unecessary indexing for fast retrievals. :param nlevel: Number of levels in the model :type nlevel: int :param wno: Wave number grid in cm -1 :type wno: array of float :param nwno: Number of wave points :type nwno: int :param numg: Number of Gauss angles :type numg: int :param numt: Number of Chebyshev angles :type numt: int :param DTAU: This is the opacity contained within each individual layer (defined at midpoints of “levels”)

WITHOUT D-Eddington Correction Dimensions=# layer by # wave

Parameters:

  • TAU (ndarray of float) – This is the cumulative summed opacity WITHOUT D-Eddington Correction Dimensions=# level by # wave

  • W0 (ndarray of float) – This is the single scattering albedo, from scattering, clouds, raman, etc WITHOUT D-Eddington Correction Dimensions=# layer by # wave

  • COSB (ndarray of float) – This is the asymmetry factor WITHOUT D-Eddington Correction Dimensions=# layer by # wave

  • GCOS2 (ndarray of float) – Parameter that allows us to directly include Rayleigh scattering = 0.5*tau_rayleigh/(tau_rayleigh + tau_cloud)

  • ftau_cld (ndarray of float) – Fraction of cloud extinction to total = tau_cloud/(tau_rayleigh + tau_cloud)

  • ftau_ray (ndarray of float) – Fraction of rayleigh extinction to total = tau_rayleigh/(tau_rayleigh + tau_cloud)

  • dtau_og (ndarray of float) – This is the opacity contained within each individual layer (defined at midpoints of “levels”) WITHOUT the delta eddington correction, if it was specified by user Dimensions=# layer by # wave

  • tau_og (ndarray of float) – This is the cumulative summed opacity WITHOUT the delta eddington correction, if it was specified by user Dimensions=# level by # wave

  • w0_og (ndarray of float) – Same as w0 but WITHOUT the delta eddington correction, if it was specified by user

  • cosb_og (ndarray of float) – Same as cosbar buth WITHOUT the delta eddington correction, if it was specified by user

  • surf_reflect (float) – Surface reflectivity

  • ubar0 (ndarray of float) – matrix of cosine of the incident angle from geometric.json

  • ubar1 (ndarray of float) – matrix of cosine of the observer angles

  • cos_theta (float) – Cosine of the phase angle of the planet

  • F0PI (array) – Downward incident solar radiation

  • single_phase (str) – Single scattering phase function, default is the two-term henyey-greenstein phase function

  • multi_phase (str) – Multiple scattering phase function, defulat is N=2 Legendre polynomial

  • frac_a (float) – (Optional), If using the TTHG phase function. Must specify the functional form for fraction of forward to back scattering (A + B * gcosb^C)

  • frac_b (float) – (Optional), If using the TTHG phase function. Must specify the functional form for fraction of forward to back scattering (A + B * gcosb^C)

  • frac_c (float) – (Optional), If using the TTHG phase function. Must specify the functional form for fraction of forward to back scattering (A + B * gcosb^C), Default is : 1 - gcosb^2

  • constant_back (float) – (Optional), If using the TTHG phase function. Must specify the assymetry of back scatterer. Remember, the output of A & M code does not separate back and forward scattering.

  • constant_forward (float) – (Optional), If using the TTHG phase function. Must specify the assymetry of forward scatterer. Remember, the output of A & M code does not separate back and forward scattering.

  • tridiagonal (int) – 0 for tridiagonal, 1 for pentadiagonal

  • toon_coefficients (int) – 0 for quadrature (default) 1 for eddington

Returns:

  • intensity at the top of the atmosphere for all the different ubar1 and ubar2

  • To Do

  • —–

  • - F0PI Solar flux shouldn’t always be 1.. Follow up to make sure that this isn’t a bad – hardwiring to solar, despite “relative albedo”

POSEIDON.emission.emission_bare_surface(T_surf, wl, surf_reflect)

Compute the emergent top-of-atmosphere flux from a bare rock

This function considers only pure thermal emission (i.e. no scattering). Uses gauss weights of 5 to stay consistent with emission_Toon

Parameters:

  • T (np.array of float) – Temperatures in each atmospheric layer (K).

  • wl (np.array of float) – Wavelength grid (μm).

  • surf_reflect – numpy.ndarray Surface reflectivity as a function of wavelength.

Returns:

Spectral surface flux in SI units (W/m^2/sr/m).

Return type:

F (np.array of float)

POSEIDON.emission.reflection_bare_surface(wl, surf_reflect, Gauss_quad=5)

Compute the emergent top-of-atmosphere flux from a bare rock

This function considers only pure thermal emission (i.e. no scattering). Uses gauss weights of 5 to stay consistent with emission_Toon

Parameters:

  • wl (np.array of float) – Wavelength grid (μm).

  • surf_reflect – numpy.ndarray Surface reflectivity as a function of wavelength.

  • Gauss_quad (int) – Gaussian quadrature order for integration over emitting surface (Options: 2 / 3).

Returns:

Spectral surface flux in SI units (W/m^2/sr/m).

Return type:

F (np.array of float)

POSEIDON.emission.assign_assumptions_and_compute_single_stream_emission(P, T, dz, wl, kappa_tot, dtau_tot, kappa_gas, kappa_Ray, kappa_cloud, kappa_cloud_seperate, zone_idx, Gauss_quad, device, P_cloud, cloud_dim, aerosol_species, f_cloud, albedo_deck, disable_atmosphere, surface, surface_model, P_surf, T_surf, surf_reflect, surf_reflect_array, surface_component_percentages, surface_percentage_apply_to)

Assigns assumptions (surfaces, clouds) and computes single-stream emission

Maximum complexity allowed: patchy 2D clouds (1 aerosol max), surfaces (and decks) with albedos

Parameters:

DO (TO)

Returns:

Spectral surface flux in SI units (W/m^2/sr/m).

Return type:

F (np.array of float)

POSEIDON.emission.assign_assumptions_and_compute_thermal_scattering_emission(P, T, dz, wl, kappa_tot, dtau_tot, kappa_gas, kappa_Ray, kappa_cloud, kappa_cloud_seperate, zone_idx, Gauss_quad, device, P_cloud, cloud_dim, aerosol_species, w_cloud, g_cloud, f_cloud, f_both, f_aerosol_1, f_aerosol_2, f_clear, albedo_deck, disable_atmosphere, surface, surface_model, P_surf, T_surf, surf_reflect, surf_reflect_array, surface_component_percentages, surface_percentage_apply_to)

Assigns assumptions (surfaces, clouds) and computes thermal scattering emission

Maximum complexity allowed: patchy 2D clouds (2 aerosols max), surfaces (and decks) with albedos

Parameters:

DO (TO)

Returns:

Spectral surface flux in SI units (W/m^2/sr/m).

Return type:

F (np.array of float)

POSEIDON.emission.assign_assumptions_and_compute_reflection(P, T, dz, wl, kappa_tot, dtau_tot, kappa_gas, kappa_Ray, kappa_cloud, kappa_cloud_seperate, zone_idx, reflection_up_to_5um, P_cloud, cloud_dim, aerosol_species, w_cloud, g_cloud, f_cloud, f_both, f_aerosol_1, f_aerosol_2, f_clear, albedo_deck, disable_atmosphere, surface, surface_model, P_surf, T_surf, surf_reflect, surf_reflect_array, surface_component_percentages, surface_percentage_apply_to)

Assigns assumptions (surfaces, clouds) and computes reflection

Maximum complexity allowed: patchy 2D clouds (2 aerosols max), surfaces (and decks) with albedos

2 aerosols max for patchy 2d clouds available for gas giants (no surface or shiny deck) 1 aerosol max for patchy 2d clouds available for all models

Parameters:

DO (TO)

Returns:

albedo (np.array of float)