The mie_derivs_ln.pro procedure performs Mie scattering calculations on aerosol with a log normal size distribution and provides analytically derived derivatives, with respect to the properties of the distribution, of all output parameters. The procedure provides the distribution of scattering radiation (in the form of the Mie intensity functions), the volume extinction and scattering coefficients and their derivatives.

A the derivation of expressions for the analytical derivatives of Mie scattering terms is covered by:
Grainger, R.G., J. Lucas, G.E. Thomas, G. Ewan, "The Calculation of Mie Derivatives", Appl. Opt., 43(28), 5286-5393, 2004.

Calling the procedure

mie_derivs_ln.pro is an IDL procedure and can be called with the following command line from the IDL prompt (as long as the source file lies within your IDL_PATH environment variable):

mie_derivs_ln, N, Rm, S, wavenumber, Cm[, Dqv=Dqv] [, Bext][, Bsca][, dBextdN][, dBextdRm][, dBextdS] [, dBscadN][, dBscadRm][, dBscadS][, i1][, i2] [, di1dN][, di1dRm][, di1dS][, di2dN][, di2dRm][, di2dS]

The input parameters in the above call are:

The output parameters are: Note: All of the above output variables are scalars of type double. Note: All of these output variables will be vectors of type double, with the same number of elements as Dqv and will only be calculated if Dqv is specified.

Limitations and dependences

It should be noted that is a very new routine and has yet to be extensively tested.

This procedure calls the mie_single.pro procedure.As a result of this, any distribution that contains particles with size parameters greater than 12000 will result in the programme exiting with the error message "Error: Size Parameter Overflow in Mie".

This procedure also calls the quadrature.pro and shift_quadrature.pro procedures (click to download). Quadrature is called with the command line:
quadrature, 'g', Npts, abs, wght
the string 'g' can be either 'g' for Gaussian quadrature, 'l' for Lobatto quadrature, 'r' for Radau quadrature, 's' for Simson's rule or 't' for the Trapezium rule. Npts specifies the number of quadrature points required and the routine returns the abscissa and weighting values in abs and wght respectively.

shift_quadrature.pro is called with the command line:
and simply transforms the abscissa and weights from the interval [-1,1] to [A,B], place the new values in new_abscissa and new_weights.

Download source code

The source code for this routine and supporting routines is part of the EODG Mie scattering distribution which may be downloaded as a gzipped tar file here.

Maintained by Greg McGarragh