<Visual and Mathematical Demonstration>
<HITRAN spectral data for CO2>
<Excel Method Explained>
<Earth Temperature by Excel>
<HITRAN data> for Visualization
<Igor Method Explained>
<Earth Temperature by Igor>
<Download HITRAN Gaussian conversion code>
<Excel: Spectrum of CO2 (wait for Excel to downloand and open)>
<IgorPro Pdf: Spectrum of CO2 converted to pdf>
The constants Patm/MCO2g at 1 atm of pressure are multiplied by CO2 mole fraction in columnd D.
The mole fraction of xCO2. Enter a new value here to calculate new transmittance.
The transmittance multiplied by the Planck emission is used to calculate the Earth's surface temperature.
This column is the cross-section number density in one square meter above the Earth's surface.
This is the product of the previous two columns C and D, uTOA=Patm/MCO2g.
F is the effective absorbance of CO2 per square meter.
F (= B * C * D) or F = B * E.
G is the simple transmittance G = 10-F. It is the fraction of radiation that passes through the atmosphere at a given wavenumber.
H is a correction to the transmittance based on numerical integration.
It converts the spectral point source into a radiation flux per square meter.
H = (10-1.245F + 10-0.13F)/2
I is the corrected transmittance converted from absorbance in column B and the cross-sectional number density in E.
It also converts the spectral point source into a flux.
I = (10-2.245BE + 10-1.13BE)/2
The output is plotted in column I of the Excel spreadsheet:
<IgorPro Pdf: Transmittance of CO2 converted to pdf>
J is the temperature in the calculated Planck distribution. The default used is 288 K.
K is the Planck distribution at temperature J. Visualize it in a plot of column K.
Column L is the Planck distribution times the transmittance in column I.
Both K and L are plotted for comparison in
<Planck_Distribution and CO2 Transmittance>
<IgorPro Pdf: Integrated Transmittance of CO2 converted to pdf>
We can visualize the steps of integration of the Planck distribution with and without CO2 transmission.
The global transmittance, tau_atm is the ratio of the integral (shown here as the sum) at each value of CO2 to I0 the intensity of radiation emitted by the bare earth.
Each of these curves is the summation of Planck radiation with no CO2 or varying ppm.
The M column contains a global average transmittance of CO2 and the temperature at the Earth's surface.
By calculating a number of different temperatures, transmittances, and CO2 ppm
we can visualize the temperature effect at the Earth's surface as CO2 increases.
Column B: The HITRAN spectrum of CO2 calculated using line broadening.
Column I: The transmittance of CO2
Columns K and L: Planck distribution (K) and product with The transmittance of CO2 (L)
< planck_transmittance_compare.py >
Integrated Planck curve and Planck times CO2 curve.
< planck_transmittance_int_compare.py >
The transmission and temperature as a function of CO2 ppm are given by:
The script will read the ppm values in co2_ppm_full.txt and use the transmittance at a given value of CO2 ppm to calculate the temperature.
Single point calculation of temperature as a function of CO2 ppm is given in:
Caveat: the Python code can process at least 24,000 data points. The result obtained is qualitatively similar, but slightly smaller. This is due to a resolution effect since the Python integration has steps of 0.1 cm-1, while Excell can handle 0.01 cm-1. We welcome any improvements.
<co2_ppm_full.csv>: column of ppm values from 300 to 1000 → needed for
<co2_ppm.csv>: two ppm values 410 and 1000 needed for
<co2_bending.csv>: HITRAN data for CO2 bending needed for all scripts
<co2_bending_stretch.csv>: HITRAN data for CO2 bending and stretching needed for all scripts using the complete set of vibrationsl for CO2
<hitran.csv>: HITRAN data for CO2 bending and stretching used in hitran_to_gaussian to convert to the peaks with a Gaussian width of 0.13 cm\-1\ with a spacting of the wavenumber of only 0.01 cm-1. This file contains the 67,000 lines of CO2 bending and stretching vibrations. The python script rewrites those peaks preserving their intensity but broadening them and plotting them on a uniform spectroscopy base of 0.01 cm-1 in Excel. At present the python scripts run at 0.1-1, which means that only 24,000 data points are used to integration. This apparently reduces the accuracy of the result, but the ease of use suggests that python may be developed to help design the educational message.