Parameter settings

Load libraries

# Convenient jupyter setup
%load_ext autoreload
%autoreload 2
%config IPCompleter.greedy=True

from numpy import log, e
import pint
from scipy.constants import Stefan_Boltzmann # W m^-2 K^-4
ureg = pint.UnitRegistry()

Radiative Forcing calculations

#  ∆RF = 5.35ln(C/Co)
# 405
# 315
# https://journals.sagepub.com/doi/pdf/10.1260/0958-305X.25.8.1439#:~:text=On%20this%20basis%2C%20the%20IPCC,to%20the%20Beer%2DLambert%20law.
# IPCC relation
5.35*log(405/315) / log(e) * ureg.watt / ureg.meter ** 2

1.3445321913028478 watt/meter²

def ipcc_delta_co2(ratio: float):
    return 5.35*log(ratio) / log(e) * ureg.watt / ureg.meter ** 2

print(ipcc_delta_co2(2))
print(ipcc_delta_co2(400/300))

3.708337415995707 watt / meter ** 2
1.5390990876170274 watt / meter ** 2

log(1.33) * 3

0.8555368267009874

# Lightfoot and Mamer 2014 relation
def rf_quad_co2(conc: float):
    return (-0.00002480* conc**2 + 0.03231 * conc) * ureg.watt / ureg.meter ** 2

rf_quad_co2(405) - rf_quad_co2(315)

1.3008600000000001 watt/meter²

Redoing f1prime calculation in the paper

# c. 300 to c. 400 ppm
def f1_prime(
    delta_forcing=0.75 * ureg.watt / ureg.meter ** 2,  # W m -2
    temp_surface=301 * ureg.kelvin,  # K
    cloud_cover=0.6,  # dimensionless fraction
    cloud_constant_a=0.4,  # dimensionless fraction
    emissivity=0.97,  # dimensionless fraction
):
    stefan_boltzmann = (
        Stefan_Boltzmann * ureg.watt / ureg.meter ** 2 / ureg.kelvin ** 4
    )  # W m^-2 K^-4
    return -delta_forcing / (
        emissivity
        * stefan_boltzmann
        * (temp_surface ** 4)
        * (1 - cloud_constant_a * (cloud_cover ** 2))
    )

print(f1_prime())

-0.0019406090190503145 dimensionless

print(f1_prime(delta_forcing=rf_quad_co2(405) - rf_quad_co2(315)))

-0.00336594753136239 dimensionless

print(f1_prime(delta_forcing=ipcc_delta_co2(400/300)))

-0.003982386094188952 dimensionless

print(f1_prime(delta_forcing=ipcc_delta_co2(405/315), cloud_constant_a=0.6))

-0.0037984436566326457 dimensionless

temp_surface=301 * ureg.kelvin
temp_surface.to(ureg.celsius)
# almost 28 degrees

27.850000000000023 degree_Celsius

type(temp_surface)

pint.quantity.build_quantity_class.<locals>.Quantity