High spectral resolution remote sensing has a wide range of applications in studying
the atmosphere and surface. Examples of satellite high spectral resolution IR sensors
include the Atmospheric Infrared Sounder (AIRS) and the Infrared Atmospheric Sounding
Interferometer (IASI). AIRS has 2378 spectral bands in the IR spectral range from
650 to 2700 cm^{1}. The IASI sensor covers the spectral range from 645
to 2760 cm^{1} at a constant spectral sampling interval of 0.25 cm^{1}.
An example of a high spectral resolution groundbased IR sensor is the Atmospheric
Emitted Radiance Interferometer (AERI) that covers the spectral range from 520 to
3300 cm^{1} with a spectral resolution of 1 cm^{1}. Retrievals
from this type of observations involve a modeling of radiances at very high spectral
resolution (called linebyline radiative transfer). This is necessary to correctly
account for absorption/emission by individual lines of atmospheric gases. The spectroscopic
information required for linebyline modeling is provided by the HITRAN database.
To gain a better understanding of the nature of absorption of atmospheric gases
and the spectral signature of the Earth's atmosphere, in this task you are asked
to work with a few lines of water vapor. Then in task 2 you will analyze the spectral
transmission of the atmosphere calculated with a linebyline numerical model developed
at
ATMOSPHERIC AND ENVIRONMENTAL RESEARCH INC.
Table 1 gives a very small subset of data from HITRAN database in the vicinity
of the 1.38 μm H_{2}O band.
 Calculate and plot the spectral absorption coefficient k_{ν} as a function
of wavenumber. Consider standard pressure, temperature, and the Lorentz profile.
 Pick any individual line from Table 1. Show how k_{ν} plot for this line
will change if atmospheric pressure P will decrease at constant temperature. What
spectral resolution will be required for a sensor to resolve this line at P = 200
mb? Consider the Lorentz line profile.
 Calculate the monochromatic transmittance T_{ν} at ν = 7281.72912
cm^{1} of a layer containing H_{2}O only. Take a path length of
u= 10 (atm cm).
Table 1. Subset of HITRAN line data for H2O (P =1013 mb; T=273 K)
Line center ν_{o}(1/cm)

Line intensity
S (cm^{1}/(atm cm))

Line halfwidth
α (1/cm)

7280.31512

4.194E03

0.0704

7280.47400

8.872E04

0.0846

7281.08200

3.764E02

0.0994

7281.72912

4.033E03

0.0602
