Physical/Geometrical Optics results were computed by J. T. Johnson
using a code based on:
Tsang, L. and Kong, J. A., ``Energy conservation for reflectivity
and transmissivity at a very rough surface," J. Appl. Phys,
vol. 51, pp. 673-680, 1980.
and
Yueh, S. H., ``Modeling of wind direction signals in polarimetric sea
surface brightness temperatures," IEEE Transactions on Geoscience and
Remote Sensing, vol. 35, pp. 1400-1418 Nov 1997.
Note all authors (Stogryn, Fuks, Gasiewski and Kunkee, etc.) agree on the
basic form for ``single scattering" optical limit results, with
results which can be expressed in terms of an integral over the surface
slope PDF. Differences between authors lie in the method used to
address shadowing effects. In terms of the Yueh paper, optical results
are obtained simply by setting the small scale spectrum of the sea surface
to zero. No atmospheric or foam contributions are included in these
calculations. Results were tilted over the Cox-Munk sea surface PDF
as reviewed in
Kunkee, D. B. and A. J. Gasiewski, ``Simulation of
passive microwave wind direction signatures over the ocean using an
asymmetric-wave geometrical optics model,'' Radio Science,
Vol. 32, pp. 59, 1997.
Shadowing effects include the following: (below the z direction
is defined as pointing upward from the mean surface plane into
free space)
1) Local incident angle from radiometer to surface facet is greater
than 90 degrees (incidence shadowing)
2) Specular reflection of ray from radiometer to facet has local
scattering angle > 90 degrees (scattering shadowing)
3) Specular reflection of ray from radiometer to facet has a
negative z component ("Stogryn shadowing")
4) Using a scaled surface slope PDF to account for shadowing
effects ("scaled PDF's")
When calculating emissivity as one minus reflectivity, statements
2 and 3 above are equivalent. Similar statements to these can
be made for transmitted powers; then statements 2 and 3 above
are not equivalent. When any of these effects are included,
power is not conserved and differing brightness temperature are
obtained when computing emissivity as one minus the reflectivity
or as the transmissivity.
To avoid power conservation issues between transmitted and
reflected power calculations (as discused in the Tsang and Kong
paper above), no shadowing is included in the calculation, and
the integrations are performed over all possible surface slopes.
Tests eliminating contributions from surface facets not directly
observed by the radiometer (Case 1 above, and as described in the
Yueh paper) showed negligible differences.
Input parameters to the code at 19.35 GHz were as follows:
Frequency 19.35 GHz
Sea Water Dielectric Constant 29.04+i35.55
Surface temperature 285 K
U for Cox-Munk PDF 9 m/s
Incidence angle Theta 55 degrees
Azimuth angle Phi 0 to 180 degrees in 15 degree steps
(0 degrees indicates upwind observation)
Long wave upwind rms slope 0.1686
(from Cox-Munk PDF)
Long wave crosswind rms slope 0.1424
(from Cox-Munk PDF)
At 37 GHz parameters were the same as above, except
Frequency 37 GHz
Sea Water Dielectric Constant 14.34+i24.17
Integrations over the slope PDF were performed using
Gauss-Hermite quadrature, with the number of points increased
until convergence to within 0.01 K was observed.
The files contain data in 6 columns. The data are:
Theta (deg) | Phi (deg) | Th-Th0 (K) | Tv-Tv0 (K) | U (K) | V (K) |
where Th0=75.279K , Tv0=172.932K for 19.35 GHz,
Th0=89.329K , Tv0=194.083K for 37 GHz
Please contact me to discuss how our codes compare.
I expect there may be some internal parameters not listed
above that may cause some differences between codes.
We can develop more detailed comparisons of internal
code variables to assist in locating the sources of
any differences observed. Other cases can also be tried as
the study progresses.
--------------------------------------------------------------------------
Joel T. Johnson, Associate Prof. ------------- The Ohio State University
E-mail: johnson@ee.eng.ohio-state.edu -------- Dept. of Electrical Eng.
Voice: (614) 292-1593 or 1606 ------------- 205 Dreese Laboratories
FAX: (614) 292-7297 ------------- 2015 Neil Ave
URL:http://eewww.eng.ohio-state.edu/~johnson - Columbus, OH 43210