flux_up

class lowEBMs.Packages.Functions.flux_up[source]

Bases: object

Class defining radiative fluxes directed upwards.

The equations used here are, expect from flux_up.planck, are estimated empirically and the standard parameters are mostly tailored to specific applications where they are used by the authors.

budyko_noclouds An empirically determined upward radiative energy flux which approximates the top of the atmosphere radiation emitted to space to be dependant linear on temperature.
budyko_clouds An empirically determined upward radiative energy flux which approximates the top of the atmosphere radiation emitted to space to be dependant linear on temperature.
planck The stefan-boltzmann radiation for a grey body as radiative energy flux directed upward.
sellers An empirically, by William Sellers adjusted stefan-boltzmann radiation as radiative energy flux directed upward.
lowEBMs.Packages.Functions.flux_up.budyko_noclouds(self, funcparam)

An empirically determined upward radiative energy flux which approximates the top of the atmosphere radiation emitted to space to be dependant linear on temperature. The presence of clouds is not specifically taken into account.

The upward radiative energy flux \(R_{up}\) of latitude \(\phi\) is given by:

\[R_{up}(\phi) = - (A + B \cdot T(\phi))\]

with the temperature \(T(\phi)\) and empirical constants \(A\) and \(B\). The Temperature is hereby converted to Celcius because the constants are optimized for Celcius not Kelvin.

Function-call arguments

Parameters:funcparams (dict) –

a dictionary of the function’s parameters directly parsed from lowEBMs.Packages.ModelEquation.model_equation

  • A: Empirical offset parameter
    • type: float
    • unit: \(Watt\cdot meter^{-2}\)
    • value: any (standard 222.74)
  • B: Empirical gradient parameter
    • type: float
    • unit: \(Watt\cdot meter^{-2}\cdot °Celcius^{-1}\)
    • value: any (standard 2.23)
Returns:The upward radiative energy flux \(R_{up}\)
Return type:float / array(floats) (0D / 1D)
lowEBMs.Packages.Functions.flux_up.budyko_clouds(self, funcparam)

An empirically determined upward radiative energy flux which approximates the top of the atmosphere radiation emitted to space to be dependant linear on temperature. The presence of clouds is specifically taken into account with a second temperature dependant term.

The upward radiative energy flux \(R_{up}\) of latitude \(\phi\) is given by:

\[R_{up}(\phi) = - ((A + B \cdot T(\phi)) - f_c\cdot (A_1+B_1\cdot T(\phi)))\]

with the temperature \(T(\phi)\) and empirical constants \(A\), \(B\), \(A_1\) and \(B_1\). The Temperature is hereby converted to Celcius because the constants are optimized for Celcius not Kelvin

Function-call arguments

Parameters:funcparams (dict) –

a dictionary of the function’s parameters directly parsed from lowEBMs.Packages.ModelEquation.model_equation

  • A: Empirical offset parameter
    • type: float
    • unit: \(Watt\cdot meter^{-2}\)
    • value: any (standard 222.74)
  • B: Empirical gradient parameter
    • type: float
    • unit: \(Watt\cdot meter^{-2}\cdot °Celcius^{-1}\)
    • value: any (standard 2.23)
  • A1: Empirical offset parameter cloud term
    • type: float
    • unit: \(Watt\cdot meter^{-2}\)
    • value: any (standard 47.73)
  • B1: Empirical gradient parameter cloud term
    • type: float
    • unit: \(Watt\cdot meter^{-2}\cdot °Celcius^{-1}\)
    • value: any (standard 1.59)
  • f_c: Cloud fraction
    • type: float
    • unit: -
    • value: 0 \(\leq\) f_c \(\leq\) 1 (standard 0.5)
Returns:The upward radiative energy flux \(R_{up}\)
Return type:float / array(floats) (0D / 1D)
lowEBMs.Packages.Functions.flux_up.planck(self, funcparam)

The stefan-boltzmann radiation for a grey body as radiative energy flux directed upward. The ideal stefan-boltzmann radiation with a temperature to the power of 4 scaled with an emissivity factor \(\epsilon\).

The upward radiative energy flux \(R_{up}\) of latitude \(\phi\) is given by:

\[R_{up}(\phi) = - \epsilon \cdot \sigma \cdot T(\phi)^4\]

with the temperature \(T(\phi)\), the emissivity \(\epsilon\) and stefan-boltzmann constant \(\sigma\).

Function-call arguments

Parameters:funcparams (dict) –

a dictionary of the function’s parameters directly parsed from lowEBMs.Packages.ModelEquation.model_equation

  • grey: The emissivity (greyness)
    • type: float
    • unit: -
    • value: 0 \(\leq\) grey \(\leq\) 1 (standard 0.612)
  • sigma: Stefan-boltzmann constant
    • type: float
    • unit: \(Watt\cdot meter^{-2}\cdot Kelvin^{-4}\)
    • value: \(5,67\cdot 10^{-8}\) (use const.sigma to load it from climlab.constants)
Returns:The upward radiative energy flux \(R_{up}\)
Return type:float / array(floats) (0D / 1D)
lowEBMs.Packages.Functions.flux_up.sellers(self, funcparam)

An empirically, by William Sellers adjusted stefan-boltzmann radiation as radiative energy flux directed upward. The ideal stefan-boltzmann radiation with a temperature to the power of 4 and an additional tangens hyperbolicus term with the temperature to the power of 6 to take into account that cloud formation is temperature dependant.

The upward radiative energy flux \(R_{up}\) of latitude \(\phi\) is given by:

\[R_{up}(\phi) = - \sigma \cdot T(\phi)^4 \cdot (1-m\cdot tanh(\gamma \cdot T(\phi)^6)\]

with the temperature \(T(\phi)\), the stefan-boltzmann constant \(\sigma\), the atmospheric attenuation \(m\) and an empirical constant \(\gamma\).

To make this function more adjustable there is an additional emissivity introduced (similar to flux_up.planck).

Function-call arguments

Parameters:funcparams (dict) –

a dictionary of the function’s parameters directly parsed from lowEBMs.Packages.ModelEquation.model_equation

  • m: The atmospheric attenuation
    • type: float
    • unit: -
    • value: 0 \(\leq\) m \(\leq\) 1 (standard 0.5)
  • sigma: Stefan-boltzmann constant
    • type: float
    • unit: \(Watt\cdot meter^{-2}\cdot Kelvin^{-4}\)
    • value: \(5,67\cdot 10^{-8}\) (use const.sigma to load it from climlab.constants)
  • gamma: Empirical constant in the cloud term
    • type: float
    • unit: \(Kelvin^{-6}\)
    • value: \(1.9\cdot 10^{-15}\)
  • grey: The emissivity (greyness)
    • type: float
    • unit: -
    • value: 0 \(\leq\) grey \(\leq\) 1 (standard 1)
Returns:The upward radiative energy flux \(R_{up}\)
Return type:float / array(floats) (0D / 1D)