`<Visual and Mathematical Demonstration>`

`<HITRAN spectral data for CO`_{2}>

`<Excel Method Explained>`

`<Earth Temperature by Excel>`

`<HITRAN data>`

for Visualization`<Igor Method Explained>`

`<Earth Temperature by Igor>`

`<Calculate_Temperature()>`

`<Calculate_Tau()>`

`<Calculate_Transmittance()>`

`<HITRAN Website>`

`<Download HITRAN Gaussian conversion code>`

`<CO2_na_hitran.csv>`

`<Excel: Spectrum of CO`_{2} (wait for Excel to downloand and open)>

`<IgorPro Pdf: Spectrum of CO`_{2} converted to pdf>

The constants P_{atm}/M_{CO2}g at 1 atm of pressure are multiplied by CO_{2} mole fraction in columnd D.

The mole fraction of x_{CO2}. 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, u_{TOA}=P_{atm}/M_{CO2}g.

F is the effective absorbance of CO_{2} 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:

`< CO`_{2}_Transmittance>

`<IgorPro Pdf: Transmittance of CO`_{2} 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.

`<Planck_Distribution>`

Column L is the Planck distribution times the transmittance in column I.

Both K and L are plotted for comparison in

`<Planck_Distribution and CO`_{2} Transmittance>

`<IgorPro Pdf: Integrated Transmittance of CO`_{2} converted to pdf>

We can visualize the steps of integration of the Planck distribution with and without CO_{2} transmission.

The global transmittance, tau_atm is the ratio of the integral (shown here as the sum) at each value of CO_{2} to I_{0} the intensity of radiation emitted by the bare earth.

Each of these curves is the summation of Planck radiation with no CO_{2} or varying ppm.

The M column contains a global average transmittance of CO_{2} and the temperature at the Earth's surface.

By calculating a number of different temperatures, transmittances, and CO_{2} ppm

we can visualize the temperature effect at the Earth's surface as CO_{2} increases.

`<hitran_to_gaussian.py >`

`<hitran_to_lorentzian.py >`

Column B: The HITRAN spectrum of CO_{2} calculated using line broadening.

`<transmittance_co2_ppm.py >`

Column I: The transmittance of CO_{2}

`<transmittance_co2_ppm.py >`

Columns K and L: Planck distribution (K) and product with The transmittance of CO_{2} (L)

`< planck_transmittance_compare.py >`

Integrated Planck curve and Planck times CO_{2} curve.

`< planck_transmittance_int_compare.py >`

The transmission and temperature as a function of CO_{2} ppm are given by:

`< plot_co2_ppm_vs_temp.py>`

The script will read the ppm values in co2_ppm_full.txt and use the transmittance at a given value of CO_{2} ppm to calculate the temperature.

Single point calculation of temperature as a function of CO_{2} ppm is given in:

`< plot_co2_ppm_vs_temp.py>`

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`<plot_co2_ppm_vs_temp.py>`

`<co2_ppm.csv>`

: two ppm values 410 and 1000 needed for`<planck_transmittance_compare.py>`

and`<planck_transmittance_int_compare.py>`

`<co2_bending.csv>`

: HITRAN data for CO_{2}bending needed for all scripts`<co2_bending_stretch.csv>`

: HITRAN data for CO_{2}bending and stretching needed for all scripts using the complete set of vibrationsl for CO_{2}`<hitran.csv>`

: HITRAN data for CO_{2}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 CO^{2 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.}