# Computer Modeling Laboratory 2

Written report due: 16 September

## Spectral absorption by atmospheric gases and the transmission function.

REQUIRED MATERIALS:
Lecture 4

HITRAN database

http://www.hitran.com
MPI-Mainz-UV-VIS Spectral Atlas of Gaseous Molecules
www.atmosphere.mpg.de/spectral-atlas-mainz

You are asked to assist in the development of ATBD for a new satellite sensor. The sensor will provide high spectral resolution measurements to study the atmospheric composition of a hypothetical planet X.

1. It is expected that the atmosphere of this planet consists only of SO2. The absorption by SO2 in the UV-visible spectrum depends on temperature. Calculate a change in the transmission function at the 0.2 um wavelength if the temperature of the planet atmosphere drops from 400K to 200K. Instruction: SO2 absorption data are available from MPI-Mainz-UV-VIS Spectral Atlas of Gaseous Molecules, www.atmosphere.mpg.de/spectral-atlas-mainz. See under Catalogue/Sulfur compounds. Use data for SO2 reported by Wu et al.(2000).
2. The satellite will be orbiting at 800 km altitude, and the sensor will have the nadir-viewing geometry. The telescope optics will give a pixel size of 250 m on the planet X. There will be a 100 nm spectral filter at the 0.5 um wavelength channel before the detector. How many photons will be accumulated by the detector in 10ms exposure if measured radiance will be 50 W m-2 sr-1 m -1? Assume that the collecting area of the detector is 100 cm2.

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 ground-based 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 line-by-line radiative transfer). This is necessary to correctly account for absorption/emission by individual lines of atmospheric gases. The spectroscopic information required for line-by-line 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 3 you will analyze the spectral transmission of the atmosphere calculated with a line-by-line numerical model developed at ATMOSPHERIC AND ENVIRONMENTAL RESEARCH INC.

Table 1 below gives a very small subset of data from HITRAN database in the vicinity of the 1.38 μm H2O band.

1) Calculate and plot the spectral absorption coefficient kν as a function of wavenumber. Consider standard pressure and temperature.

2) Pick any individual line from Table 1. Show how kν 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.

3) Calculate the monochromatic transmittance Tν at ν = 7281.72912 cm-1 of a layer containing H2O 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 νo(1/cm) Line intensity S (cm-1/(atm cm)) Line half-width α (1/cm) 7280.31512 4.194E-03 0.0704 7280.47400 8.872E-04 0.0846 7281.08200 3.764E-02 0.0994 7281.72912 4.033E-03 0.0602