Toon solver

Modules contains all functions required to run the Toon (1989) radiative transfer solver.

toon_solver

Makes function calls relating to radiative transfer solver in sequence and returns outputs.

Args

• tau: optical thickness
• ssa: single scattering albedo
• g: asymmetry parameter
• L_snw: mass of ice in each layer
• ice: instance of Ice class
• illumination: instance of Illumination class
• model_config: instance of ModelConfig class
• rt_config: instance of RTConfig class

Returns

• outputs: instance of Outputs class

validate_inputs_toon

Checks for known invalid data configurations that break the Toon solver. If invalid config is detected a ValueError is raised, halting execution.

Args:

• ice: class representing the ice column and containing related physical constants
• illumination: class representing incoming irradiance containing related physical constants

Returns:

• None

Raises:

• ValueError: raised with descriptive error message if invalid input detected

delta_transformation

Applies Delta transformation.

Args:

• rt_config: instance of RTConfig class
• g: asymmetry parameter
• ssa: single scatterign albedo
• tau: optical thickness

Returns:

• g_star: delta scaled asymmetry parameter
• ssa_star: delta scaled singloe scattering albedo
• tau_star: delta scaled optical thickness

calculate_optical_depth_of_column

Calculates column optical thickness.

Args:

• ice: instance of Ice class
• model_config: instance of ModelConfig class
• tau_star: delta scaled optical thickness

Returns:

• tau_clm: optical thickness of column

boundary_condition

Calculates reflectance from underlying surface.

Args:

• ice: instance of Ice class
• illumination: instance of Illumination class
• tau_clm: optical thickness of column
• tau_star: delta_scaled optical thickness

Returns:

• S_sfc: reflectance from underlying surface

two_stream_approximation

Applies two-stream approximation.

Three 2-stream approximations are available: Eddington, Quadrature and hemispheric mean. The equations for each approximation are provided in Toon et al. (1989) Table 1.

The hemispheric mean scheme is derived by assuming that the phase function is equal to 1 + g in the forward scattering hemisphere and to 1 - g in the backward scattering hemisphere. The asymmetry parameter is g. The hemispheric mean is only useful for infrared wavelengths.

Args:

• rt_config: instance of RTConfig class
• ssa_star: delta scaled signle scattering albedo
• g_star: delta scaled asymmetry parameter

Returns:

• gamma1: coefficient for matrix solution
• gamma2: coefficient for matrix solution
• gamma3: coefficient for matrix solution
• gamma4: coefficient for matrix solution
• mu_one: adjusted incidence angle

calculate_matrix_coefficients

Calculates coefficients required for matrix calculation.

Args

• gamma1: coefficient for matrix solution
• gamma2: coefficient for matrix solution
• tau_star: delta scaled optical thickness

Returns

• lam: coefficient for matrix solution
• GAMMA: coefficient for matrix solution
• e1: coefficient for matrix solution
• e2: coefficient for matrix solution
• e3: coefficient for matrix solution
• e4: coefficient for matrix solution

c_functions

Calculate fluxes through column.

Args

• ice: instance of Ice class
• model_config: instance of ModelConfig class
• illumination: instance of Illumination class
• ssa_star: delta scaled single scatterign albedo
• tau_star: delta scaled optical thickness
• tau_clm: column optical thickness
• lam: coefficient for matrix solution
• gamma1: coefficient for matrix solution
• gamma2: coefficient for matrix solution
• gamma3: coefficient for matrix solution
• gamma4: coefficient for matrix solution

Returns

• C_pls_btm: upwards flux from bottom of layer
• C_mns_btm: downwards flux from bottom of layer
• C_pls_top: upwards flux from top of layer
• C_mns_top: downwards flux from top of layer

matrix_solver

Execute matrix calculation.

Args

• ice: instance of Ice class
• illumination: instance of Illumination class
• model_config: instance of ModelConfig class
• s_sfc: reflectance of underlying surface
• C_pls_btm: upwards flux from bottom of layer
• C_mns_btm: downwards flux from bottom of layer
• C_pls_top: upwards flux from top of layer
• C_mns_top: downwards flux from top of layer
• e1: coefficient for matrix solution
• e2: coefficient for matrix solution
• e3: coefficient for matrix solution
• e4: coefficient for matrix solution

Returns

• Y: intermediate representing t-0 boundary fluxes

layer_fluxes

Calculates total fluxes

Args

• ice: instance of Ice class
• illumination: instance of Illumination class
• model_config: instance of ModelConfig class
• tau_clm: optical thickness of column
• lam: intermediate coefficient
• GAMMA: intermediate coefficient
• tau_star: delta scaled optical thickness
• C_pls_btm: upwards flux from bottom of layer
• C_mns_btm: downwards flux from bottom of layer
• C_pls_top: upwards flux from top of layer
• C_mns_top: downwards flux from top of layer
• e1: coefficient for matrix solution
• e2: coefficient for matrix solution
• e3: coefficient for matrix solution
• e4: coefficient for matrix solution
• mu_one: adjusted indicence angle

Returns

• F_net: net flux in each layer
• F_top_pls: net upwards flux from upper surface of each layer
• F_btm_net: net flux at bottom surface
• F_top_net: net fluxes at upper surface
• intensity: mean intensity at base of each layer

absorbed_fluxes

Calculates energy absorbed in each layer.

Args

• ice: instance of Ice class
• model_config: instance of ModelConfig class
• F_net: net flux in each layer
• F_top_net: net flux at upper model boundary

Returns:

• F_abs: absorbed flux in each layer

conservation_of_energy_check

Checks there is no conservation of energy violation.

Args

• illumination: instance of Illumination class
• F_abs: absorbed flux in each layer
• F_btm_net: net flux at bottom surface
• F_top_pls: upwards flux from upper boundary

Returns

• None

Raises

• ValueError is conservation of energy error is detected

get_outputs

Assimilates useful data into instance of Outputs class.

Args

• illumination: instance of Illumination class
• albedo: ratio of upwwards fluxes and irradiance
• model_config: instance of ModelConfig class
• L_snw: mass of ice in each layer
• F_abs: absorbed flux in each layer
• F_btm_net: net flux at bottom surface

Returns

• outputs: instance of Outputs class

apply_smoothing_function

Optionally applies a Savitsky-Golay smoothing filter to the returned albedo

Args

• model_config: instance of ModelConfig class
• albedo: the model-predicted spectral albedo

Returns

• albedo: smoothed spectral albedo