The DLSM 4.2 outputs the grid volume average of atmospheric temperature, the molecular Gaussian broadening function and the Lorentzian aerosol broadening function (Skinner and Hays, 1994) to the DLSM’s  PHT output file. The Lorentzian aerosol broadening functions are provided for very small, small , and large size aerosol sizes including Doppler shift information from the LOS wind, LOS wind and Earth motion and LOS wind plus Earth motion plus satellite motion.

Molecular Gaussian Broadening Function

The Molecules have a Gaussian broadening function is defined as

Dn_G = 4.3X10^-7 * n * (T/M)^1/2                                    equation 8 of Skinner and Hayes

where

        Dn_G = Rayleigh broadening

        n = wavenumber (cm^-1)

        T = average temperature (K)

        M = mean molecular weight (28.964)

For example, a typical Rayleigh width at a temperature, 250 K, and a wavelength, 0.355 mm is 3.56X10^-2 cm^-1.

Lorentzian aerosol broadening function

The aerosol broadening function is a Lorentzian form defined as

L_a (Dn,a_a) = 1/p * a_a/(a_a² + Dn²)                        equation 9 of Skinner and Hayes

   a_a = (2p * n² * D)/(c* mcm)                               equation 10 of Skinner and Hayes

Dn = n * (2 * U * sin(f)/c)                                    equation 4 of Skinner and Hayes

where

          L_a (Dn,a_a) = aerosol broadening function

        a_a = half width 

        n = wavenumber (cm^-1)

           D = diffusion coefficient (cm²/s)

           c = speed of light (m/s)

           mcm = meters to centimeters conversion factor

         Dn = Doppler shift due to mean wind motions (cm^-1)

           U = the horizontal wind speed in the direction of the viewing (m/s)

         f = angle from nadir the beam makes as it passes through the atmospheric layer (rad)

The DLSM 4.2 outputs to the PHT file the Lorentzian aerosol broadening for the following three aerosol radius sizes and diffusion coefficients.

Doppler Shift Due to Earth Motion and the Satellite Motion

In addition, the DLSM 4.2 outputs to the PHT file the Lorentzian broadening for Doppler shift due to earth's motion and the  Lorentzian broadening for Doppler shift due to earth's motion plus Doppler shift due to satellite motion .

The Doppler shift due to Earth's motion is defined as

 V_e= (UX * cos(b) + VX * sin(b)) * cos(f)

where

        V_e - Doppler Shift Due to Earth's Motion (m/s)

        UX - cross track component of the Earth's rotation speed (m/s) assuming an Earth's rotation 727.7 m/s at the equator

        VX - along track component of the Earth's rotation speed (m/s) assuming an Earth's rotation 0.0 m/s at the equator

      b - DWL azimuth scan angle (rad)

      f - DWL nadir scan angle (rad)

The Doppler shift due to Satellite's motion is defined as

 V_s= sin(b) * sin(f) * V_sat

where

        V_s - Doppler Shift Due to Satellite's Motion (m/s)

        V_sat - satellite velocity (m/s)

      b - DWL azimuth scan angle (rad)

      f - DWL nadir scan angle (rad)

Last Updated: 02/07/2007