Cirrus Optical Properties, Enhanced version (COPE)

In addition to the single scattering properties in COP, this version contains:

1. The Scattering Matrix

The state of polarization of electromagnetic radiation can completely be described by the 4 elements of the Stokes vector. The Stokes vector of scattered radiation is related to that of the incoming radiation by a 4x4 scattering matrix:

For the present data base, only particles in random orientation are considered. In this case, the scattering matrix contains only six independent elements which are not dependent on the scattering azimuth angle:

These six elements are available in COPE.

2. Imperfect hexagonal ice crystals

Imperfect hexagons are modelled using statistical deviations of ray paths during the ray tracing (Figure 1) in hexagonal ice crystals. Each time a ray hits a crystal surface, the normal to this surface is tilted against its original direction by a certain angle, and it is also rotated around it (Figure 2). This tilt angle is chosen by use of random numbers, which are uniformly distributed between 0 and a given maximum value. The azimuth angle is randomly distributed between 0 and 2*Pi. The directions of the refracted and reflected ray are calculated according to this tilted surface element.

Figure 1: Ray tracing in a hexagonal column. Figure 2: Tilting of plane normals during the ray tracing.

A maximum tilt angle of 1° only affects the direct forward and backward scattering. This scattering matrix may better be suited for lidar applications than the original scattering matrix without any tilting because the extremely strong increase in the direct backscattering at 180° does not occur here. A maximum tilt angle of 30° removes all halo features in the scattering function and may therefore be a more realistic model of ice crystals in many cirrus clouds which don't show halos.

3. The data files

The scattering matrices of randomly oriented hexagonal columnar ice crystals are stored in the directory dat/corr. There is one file for each scattering matrix. The file names reflect size and shape of the crystal, the wavelength, and the maximum tilt angle. They consist of 9 letters (e.g. c40550r01.cs) with the following meaning:

These data files contain the following information:

There are two additional columns after the matrix elements, which are related to a scattering matrix test and correction algorithm after Hovenier and van der Mee (1996).

4. The program cope.f

This program uses results of the ray tracing program for particles of different sizes to calculate size distribution weighted averages of the single scattering properties. cope.f relies on certain conventions about the number of size intervals and the sizes of the particles (see table). For each calculation of size distribution weighted scattering properties, the scattering matrices of the 8 columns must exist for the desired wavelength. There is also a convention about the composition of the names of the files (see above).

The currently available contents of the data base is indicated in the file cope.cfg. This file is read by cope.f to fill in its selection menus.

Once started, the program asks several questions. This dialog is shown here.

5. How to get and install COPE ?

You can download COPE from our anonymous ftp server ftp.lrz-muenchen.de in the directory "pub/science/meteorology/cirrus".

Copy the file cope.tar.gz in a new directory, unzip and untar it:

> gzip -d cope.tar.gz
> tar -xvf cope.tar
Now, you will see two new subdirectories: cope and dat. cope contains the program cope.f and all other files necessary for running it. dat contains the two subdirectories dat/corr and dat/sums, where dat/corr contains the scattering matrices of 8 columnar ice crystals for 5 wavelengths and 3 maximum tilt angles. In dat/sums, the output of the program cope.f will be stored.

page created by Michael Hess
update: 15. Jan. 1999