One additional wavelength has been introduced, namely 10.00 microns. Since all other wavelengths needed only 4 letters to describe, this one has been named '0001'. In this case, the backscattering values at least for the larger particles are not calculated with sufficient accuracy and therefore should not be used separately. The use in radiation transfer models should not be affected. Additionally, one should keep in mind, that the theory of geometrical optics, which has been used to calculate these data, probably is not valid for such small size parameters.
München, 08.11.93
Michael Hess
Since recent measurements found a considerable number of ice crystals smaller than 20 microns in cirrus clouds, COP has been extended by two columnar crystals in the size range between 2 and 20 microns. COP.FOR has been changed accordingly. Nevertheless, these smaller particles are not used for the size distributions after Heymsfield and Platt, which are based on measurements restricted to sizes greater than 20 microns.
12 new wavelengths between 1. and 4. microns have been added for columnar crystals. They allow a better representation of the ice absorption in radiation transfer calculations over the whole solar spectrum.
München, 09.12.93
Michael Hess
I received the following question and comment from Dave Winker:
31.03.95
Dr. Hess,
I have downloaded some of the files from your COP data library. Being a lidar researcher I am particularly interested in values of the extinction- to-backscatter ratio: specifically, the ratio of the volume extinction cross-section (/km) to volume backscatter cross-section (/km/sr). I believe this corresponds to the parameter you have defined as 'L' in the first equation on page 7742 of your recent paper in Applied Optics. However, the values of L given in the COP library generally lie between 1 and 2 for visible wavelengths, while experimental measurements of the extinction to backscatter ratio give values more in the range of 10 to 40. Does the 'L' contained in the tables have a different definition than given in the Applied Optics paper? Is there a conversion factor I have overlooked? Should the 'L' values be multiplied by 4 Pi to obtain the extinction to backscatter ratio? An explanation of this apparent discrepancy would be greatly appreciated.
One other question: calculations for plates seem to have only been performed at non-laser wavelengths. Do you have plans to do those calculations at 355, 532, and 1064 nm also?
Dave Winker
Here is my answer:
04.04.95
Dear Dr. Winker,
the very low values of 'L' result from the idealized shape of the hexagonal columns and plates. The 90 degree angles at bottom and top of the particles produce high backscattering at exactly 180 degree scattering angle. This means that the value of the phasefunction is strongly dependent on the size of the solid angle around 180 degree used to sample the rays leaving the crystal. I used a solid angle with an aperture of 0.5 degree in the backscatter direction. Using smaller solid angles, as would be appropriate for lidar receiver angles, would yield even lower 'L'-values. Takano and Liou (1989) used a larger solid angle in their Appl. Opt. paper which happened to yield a reasonably looking lidarratio. I was not aware of this effect when I wrote the COP paper. Otherwise I would have omitted the lidarratios.
Lidarratios below 5 have been measured by Ansmann et al.. They attributed these values to horizontally oriented crystals. Horizontally orientated plates yield L=0.2 in our calculations, i.e., considerably lower than those for random orientation. Since there are no in situ measurements for Ansmanns' lidarratios, it is not clear, whether they are due to a certain amount of oriented crystals or of nicely shaped hexagonal columns.
To get lidarratios which are closer to the usually expected values, it would be necessary to do calculations for crystals with irregular surfaces, with included air bubbles and/or with hollow ends. Unfortunately, we are not able to continue the research on ice crystal phasefunctions in the near future.
Nevertheless, it should be possible to use the results in a relative manner in order to examine the influence of particle size and shape and of wavelength on the backscatter properties.
The calculations for plates at lidar wavelengths are not complete. If you are interested in them yet, I could provide them as soon as I port the code to a Unix work station. The Cyber computer where the calculations had been done, is no longer available.
München, 13.07.95
Michael Hess
5 new wavelengths between 0.28 and 0.4 microns have been included for calculations in the UV.
Muenchen, 13.11.95
Michael Hess
As pointed out in the COP paper, all optical parameters in COP are corrected with respect to the "unscattered" energy, i.e., the energy leaving the crystal exactly with a scattering angle of 0 degree. This energy is considered to be not scattered at all and therefore the scattering and extinction coefficients are reduced and the phasefunction and the asymmetry parameter are also changed, all compared to the results of the raytracing model. The reason for this procedure is a numerical one. It makes shure, that the integral over the phasefunctions from 0 degree to 180 degree yields 1.
This correction might not be useful in all cases, especially if you use only the asymmetry parameters. So you should be aware of this correction when you are using COP data. The original values (without the correction) can be calculated with help of the value "R" in the last column of the "COPTAB" files and with the formula given below.
ATTENTION:
The correction formula used for the calculation of the asymmetry parameters
has been wrong in former versions! For this reason all asymmetry parameters
in the COP versions before March 1996 are too high. The other optical parameters,
including the phasefunctions, are NOT affected.
I am sorry for that!
The formula for recalculating the original, uncorrected asymmetry parameter "Gorg" from the corrected one "Gcorr" is:
Gorg = Gcorr * (1 - R) + R
Muenchen, 29.03.1996
Michael Hess
Ptotal = Ppar + Pperp.
In the results file, the degree of linear polarization is given, too:
lin. Pol. = (Pperp - Ppar) / (Pperp + Ppar)
Muenchen, 01.04.96
Michael Hess
- There had some data been missing in file COPTABR.
- Some minor errors in COP20.FOR have been fixed. It is now COP21.FOR.
Muenchen, 24.06.96
Michael Hess
There is now a version COPE available, which contains scattering matrices of randomly oriented columns.
04.12.97
Michael Hess