The purpose of this appendix is to present some general information about the procedures used to determining the particle size distribution and mass of the volcanic cloud. There are two main IDL procedures that were developed to find the particle distribution and mass; "mie" and "ssmi_widget". These two programs are described in the following two sections.
To calculate the transmittance in equation 3, the scattering efficiency factor needs to be evaluated. The scattering efficiency factor is calculated using Mie theory. The Mie theory calculations are based on a FORTRAN computer code written by W. J. Lentz which calculates the efficiency factor for spherical particles. Several IDL codes where written to interface with the FORTRAN code and to produce output plots. By choosing a wavelength and index of refraction, the IDL Mie code can produce plots of the absorption, scattering and extinction efficiency factor or cross section.
The IDL Mie code also produces plots of the modified gamma and lognormal distributions. The main purpose served by the IDL Mie code is to find the mean value of the lognormal distribution using SSM/I data. By using the surface and cloud top temperatures for two of the channels of the SSM/I and assuming a standard deviation, the mean value of the distribution can be determined from equation 7 . Note that it is important to use channels where scattering is dominant. Equation 7 can be rearranged so that the left side equals zero. The resulting function is plotted as a function of the mean value. The mean value of the particles in the observed cloud is where the function intersects the x-axis.
The IDL program "ssmi_widget" is used to calculate the mass of the volcanic cloud. The program calculates the mass based on both the theoretical and empirical methods. The input data file can be created using the Terascan "xvu" interface with the "Utils/Misc Reports" utility, along with the "Varvalues" and "File" options. An IDL widget interface is used to enter the parameters necessary to preform the mass calculations. The input mean value for the lognormal distribution is determined from the Mie program outline in the above section. The minimum and maximum radius should be chosen to ensure that the majority of the particles in the size distribution are covered. A scattering index threshold is used to define which volcanic cloud pixels are used from the input file. For more information about these programs, see the IDL online help function.