Diffusion equation derived from the space-time transport equation and light pulse propagation through thick clouds


  • K. Furutsu,

  • S. Ito


The diffusion equation is derived from the ordinary space-time transport equation and is shown to be given necessarily in the first order in time, as in cases of the diffusion equations derived from the Fokker-Planck and Boltzmann equations. The systematic way of obtaining the higher-order diffusion equations also has been shown elsewhere. The boundary equations on the boundary of free space are obtained and applied to the light pulse propagation through thick clouds. The explicit expression is obtained for the pulse broadening and is found to be considerably affected by a slight absorption of the medium, especially when the diffusion distances are large. With the experimental value of absorption for stratocumulus clouds, as suggested by Danielson et al., the theoretical values of pulse broadening are compared to those of experiments observed by Bucher and Lerner to show a good agreement.