### Science Facts - HITRAN Spectral Analysis Overview

HITRAN - high-resolution transmission molecular absorption database - a free database provided by the Harvard-Smithsonian Center for Astrophysics.

These pages discuss the HITRAN data and the equations used to determine how much energy is absorbed or emitted by the atmosphere. There is also a related program (Windows XP only) that lets you to see the effects of varying

• Temperature
• Pressure
• Mixing ratio
Unfortunately, the HITRAN database does not contain UV spectra. Therefore, this data (and my program) can not be used to evaluate the absorption of solar energy in the atmosphere.
• Water vapor up to 400 nm - no UV
• CO2 up to 1,036 nm

### Spectra

Light, radio waves, and infrared radiation are examples of electromagnetic radiation. Basically, they are the same .. except for the frequency. Atoms are able to absorb (and emit) energy at ultraviolet (UV) and visible light frequencies - the UV-Vis band. Molecules tend to absorb radiation in the UV, visible, and infrared bands.

By definition, the frequency (ν) is equal to the speed of light (c) divided by the wavelength (λ). (There are ways to measure the speed of light and the wavelength. While it is easy to measure the frequency of radio waves, for visible and UV frequencies, the frequency must be computed from quantities that can be measured.) Rearranging the equation, wavelength equals the speed of light divided by frequency .. and wavenumber (number of waves per centimeter) equals one over the wavelength.

 ``` ν = c / λ cycles/sec = meters/sec / meters/cycle c = λ ν meters/sec = meters/cycle * cycles/sec λ = c/ν wavenumber = 1/λ = ν/c ```
The funny looking "v" symbol used for frequency is actually the lower case Greek letter nu (ν).

Notice that wavenumber is equal to the frequency divided by a constant (the speed of light). As a result, some sources label the x-axis Frequency (cm-1) and others use Wavenumber (cm-1) .. and that both mean the same thing.

A related relation is that the energy in a photon is equal to the frequency times Planck's constant (h).

 ```E = h ν = h * c * wavenumber ```

For IR radiation, the wavenumber is usually expressed in (scaled to) units of "per centimeter" (cm-1 or cm-1, but never 1/cm). The correct value is obtained by first converting a wavelength to centimeters before inverting the value. (Or convert to meters, invert, then divided by 100). This value should be interpreted as "the number of cycles in a centimeter", assuming (incorrectly) that light is a continuous sine wave. Green light (550nm) corresponds to 18,182 cm-1. The main CO2 absorption bands are near 2,358 cm-1 (4,241nm) and 666.67 cm-1 (15,000nm) .. inside the far IR region.

A spectra is a plot of the amount of energy absorbed (or emitted) verses frequency (or wavelength, or wavenumber). Because of the quantum nature of nature, a vacuum spectra consists of many zero width lines. For infrared frequencies, the frequency of each line is determined by quantum theory, bond strengths, and the mass of the atoms. For instance, the strength of an oxygen-hydrogen bond is different than the strength of an oxygen-carbon bond. In addition, the mass of hydrogen is different than the mass of carbon. As a result, the IR spectral lines of different gases do not overlap.

To be clear, there is little, or no, overlap of water vapor and CO2 spectra at zero degrees Kelvin and zero pressure.

However, in the atmosphere, the spectral "lines" do not have zero width (due to temperature and pressure). As a result, there is significant overlap in some bands, and no overlap in others.

The HITRAN data contains the vacuum spectra (zero width lines) and parameters used to determine approximate widths at normal temperatures and pressure.

Actually, for each gas, there are several different spectra - a different spectra for each unique combination of isotopes. When all the available spectra are displayed, it is difficult to determine exactly what is being displayed. Therefore, HITRAN_Data_Plot.exe only plots the data for the most common isotopologues of water vapor and CO2.

The discussion above applies to gases .. solids and liquids are similar, but individual spectra lines tend to disappear due to additional band broadening. In the extreme, most substances will absorb (or emit) electromagnetic energy in a continuous blackbody spectrum (i.e. there are no individual lines).

Note: Some solids are IR transparent. Some emit an almost continuous blackbody spectrum. And others emit spectra that are unique enough to identify the solid.

As a first order approximation, liquid water (including clouds), ice, rock, and sand emit electromagnetic energy in the IR bands with a spectrum very close to the blackbody ideal. (With an accuracy of better than 95%.) While most leaves have a non-blackbody IR spectra, it is convenient to assume that their spectra also follows the blackbody ideal.

### HITRAN_Data_Plot.exe

It is generally known that the energy absorbed by water vapor and CO2 in the atmosphere is not the sum of the energy absorbed by each as though it was the only gas in the atmosphere. This is because the broadened spectra overlap. My program - HITRAN_Data_Plot.exe - computes and plots the spectra for 2 of these - water vapor and CO2. I have written a program - HITRAN_Data_Plot.exe - to compute the temperature and pressure broadened spectra. This program displays (plots)

• The raw, unprocessed, HITRAN spectra data
• The individual spectra of water vapor and CO2
• The combined spectra of water vapor and CO2
• The blackbody spectra for 3 different temperatures
There are several ways to display the spectra
• The raw, unprocessed, HITRAN spectra data
• Temperature and pressure broadened spectra
• Doppler broadened spectra (slow - computation intensive)
• The blackbody spectra for 3 different temperatures
At this time, all date is plotted verses wave number. If you left click on the graph, the program displays both the wave number and the wavelength.

Author: Robert Clemenzi