A quantitative model is presented which describes the ocean surface as an ensemble of flat facets with slopes distributed partially covered with an absorbing nonpolarized foam layer. Experimental evidence is presented for this model

Wilheit, T. T.

English

NASA Technical Reports Server

Paper No. 38
A MODEL FOR THE MICROWAVE EMISSIVITY OF THE OCEAN'S
SURFACE AS A FUNCTION OF WIND SPEED
Thomas T. Wilheit, Greenbelt, Maryland
ABSTRACT
A quantitative model is presented which describes the ocean
surface as an ensemble of fiat facets with slopes distributed as per
Cox and Munk (1955)partially covered with an absorbing nonpolar-
ized foam layer. Experimental evidence is presented for this model.
INTRODUCTION
The launch in 1978 of the Scanning Multichannel Microwave Radiometer
(SMMR) on both the Nimbus-7 and Seasat satellites has opened new possibilities
for measurement of many geophysical observables, primarily the wind speed and
water temperature at the ocean surface. Since the microwave brightness tempera-
ture observed in each of the SMMR channels is significantly affected by at least
four variables, the liquid and vapor components of atmospheric water, sea surface
temperature and surface wind, retrieval of the surface parameters is a non-trivial
problem. The weak point in the physical understanding of these effects is in the
effect of wind on the sea surface. Hopefully, the model presented here improves
the situation somewhat. The model is clearly imperfect, but hopefully, will pro-
vide a framework and reference point for future refinements.
There have been two closely related programs supported by the Global Weather
and GARP programs. The improved modeling of the microwave emissivity of the
ocean surface, here reported, has been supported by Global Weather and is the key
physical input to the algorithm for the retrieval of wind speed and sea surface tem-
perature developed under the GARP Program. The approach taken here will be to
present the model then to discuss several supporting observations.
THE MODEL
It is a straightforward problem to calculate the emissivity of a smooth water
surface. The dielectric properties of sea water and saline solutions have been dis-
cussed by many authors. (Lane and Saxton (1952), Klein and Swift (1977), and
Stogryn (1971)). We will use values derived from the Lane and Saxton (1952)
measurements and expressed in an analytic form by Chang and Wilheit (1978). The
formalism for calculating the emissivity for a given view angle and polarization is
the so called Fresnel relations (Jackson 1962). The resulting emissivity as a func-
tion of view angle is shown in Figure 1 for a frequency of 10.7 GHz and a tem-
perature of 285°K. Unfortunately, the ocean's surface is not a smooth surface;
the wind roughens the surface, and, if it is blowing hard enough, partially covers
the surface with foam. Cox and Munk (1955) have quantitatively described the
distribution of surface slopes as a function of wind speed. They found that the
227
https://ntrs.nasa.gov/search.jsp?R=19790012500 2020-03-20T18:24:58+00:00Z
)-
b-
W
0.65
0.60 SMOOTH WATER SURFACE
----- 7 m/s
0.55 ......... 14 m/s
F = 10.69 GHz
0.50 T = 285 ° K
0.45 VERTICAL
POLARIZATION
......... ....'"'""
0.40
0.35
HORIZONTAL
0.30 POLARIZATION
0.25
0 10 20 30 40 50
VIEW ANGLE (DEGREES)
Fig. l-Emissivity as a function of view angle for a
smooth water surface and for the ocean surface
with 7 and 14m/s wind speed.
6O
surface slopes were normally distributed with a variance, 02 given by 02 = .003cm,
+ .0048W where W is the wind speed in meters/second at 20m height. The factor
multiplying W in the above equation is slightly different from that in the Cox and
Munk (1955) paper because the winds were measured at 12.5M in their work; the
conversion to 20m was done using the Cardone (1969) model for the atmospheric
boundary layer assuming neutral stability.
The Cox and Munk (1955) measurements were made at visible wavelengths.
Much of the roughness they observe is at scales very small compared to microwave
wavelengths. This model requires only a fraction of the Cox and Munk roughness
at the longer microwave wavelengths. Specifically, the slope variance observed at
a given microwave frequency is:
o2(f) = (0.3 + 0.02 f(GHz))Oc2m f < 35GHz
o2(f) = O2m f >/35GHz
To calculate a rough surface emissivity from this slope distribution, one simply
averages the Fresnel relations (Jackson 1962) over the distribution of surface slopes.
In doing so, one implicitly ignores surface curvature and all structure comparable
to a wavelength and thereby reduces the problem to geometric optics. The
228
comparison with observations which follow will demonstrate that this is a surpris-
ingly good approximation.
Wind also creates foam on the ocean's surface. Nordberg et al (1971) found
a linear increase in brightness temperature with wind speed whenever the wind
speed exceeded 7m/s. They were viewing directly at the nadir which essentially
eliminates the roughness effect leaving foam as the most reasonable explanation.
In our model, we will treat foam as partially obscuring the surface in a manner in-
dependent of polarization. A non-reflecting material partially covering the surface
would have this property as would an absorbing but partially transparent medium
with the same temperature as the water. Either description alone would be inade-
quate, but a combination of the two descriptions would be closer to reality. The
degree to which foam obscures the surface is frequency dependent and propor-
tional to the amount by which the wind speed exceeds 7m/s. A reasonable ap-
proximation to the available observations of the fraction, K, by which the surface
reflectivity is reduced by foam is
K _ a(1 - e-f/f°)(W - 7m/s)
where f is the frequency
and a = .006s/m
f0 = 7.5GHz
The primary available observations relevant to this are from the Bering Sea Expedi-
tion (BESEX) (Webster et al 1976) and from Cosmos 243 (Shutko 1978). These
results, along with a plot of aK/aw is given in Figure 2. The observations are dif-
ficult but nevertheless show reasonable self-consistency except possibly for the one
BESEX point at 37GHz.
.006
.005
.004
_ .003
.002
.001
0
X
5 10
@
a Foam =- a( I- _f/fo) x
a WS
a = .006 s/m
fo = 7.5 GHz
Cosmos - 243@
Besex x
I I I I
15 20 25 30 35
Frequency (GHz)
Fig. 2-Frequency dependence of reduction of reflectivity by foam.
229
Emissivities calculated according to this model for 7 and 14m/s are shown in
Figure 1 for comparison with the emissivity of a smooth surface.
SUPPORTING OBSERVATIONS
Because the assumed foam model has no polarization character, dual polarized
observations of the surface provide a test of the rough surface portion of the model.
If one makes the approximation that the atmosphere and the surface have the same
thermodynamic temperature T l, then it is straightforward to show that for any
given view angle
TH(0 ) - T] Rn(0)
FTI(0 ) - Tv(0 ) - T 1 - Rv(0 )
Here Tn(0) is the horizontal brightness temperature at an angle 0 and R.(0) is the
horizontally polarized reflectivity. Tv(0) and Rv(0) refer similarly to vertical po-
larization. Note that because FT1 (0) isthe ratio of two reflectivities, it is independ-
ent of foam cover and thus provides a measurement of surface roughening. The
data from the Electrically Scanned Microwave Radiometer (ESMR) on Nimbus-6
(37GHz, 50 ° view angle) have been so analyzed and compared with wind speeds
derived from the operational data buoys (Wilheit, 1978). A summary of this com-
parison is given in Figure 3. The plotted data are for the most part, averages of
F_IS
Fig.
1.85
1.80
1.75
1.711
I._
I._
I.GG
I._
1.45
1.40
1.35
1.30
1_5_) Ii 1'2 18 24 _ 36 M/S
WIND SPEED
3-Comparison between observed values of F285 and wind
speed averaged over 1.5 m/s intervals.
230
many observations; a total of 264 observations are represented. In analyzing the
data, it was found that a value of 285°K for T t worked best but that the impro_/e-
ment over any value in the range 280°K to 290°K was only marginal. Using the
model described in the previous section the expected value of F285 has been calcu-
lated; the agreement with the observations is striking. A geometric optics model
using the Cox and Munk sea surface slope distribution works extremely well at a
wavelength of 0.8cm and a view angle of 50 °. Hollinger (1971) has made obser-
vations from a fixed platform at frequencies of 1.4, 8.36, and 19.34GHz. He has
filtered the data to remove most of the foam effect but application .of an analysis
techniqpe similar to that applied to the Nimbus-6 ESMR data certainly removes
the remainder. These data all can be interpreted in terms of the geometric optics
model but with much less slope variance than the Cox and Munk values.
The fractions of the Cox and Munk slope variance required to account for
the Hollinger data are plotted in Figure 4 along with the Nimbus-6 ESMR obser-
vation. These data form a picture consistent with the roughness required in our
model (shown as a solid line).
CONCLUSION
A model has been presented for the microwave emissivity of a wind roughened,
foam covered ocean. The roughness portion of the description is remarkably con-
sistent with observations; the foam effects show somewhat more scatter. The
strength of the foam cover effect at 6.6 and 10.7GHz are important parameters in
the interpretation of Nimbus-7 and Seasat SMMR data; the strength at higher fre-
quencies, less so. In comparing the space observations with surface measurements
of temperature and wind speed, it should be possible to adjust the foam effect at
these two frequencies in order to fine-tune the retrieval algorithm.
tw
% OF COX 75
b. MUNK
SLOPE
VARIANCE 50
25
I I I
0 10 20 30
FREOUENCY
(GHz)
Fig. 4-Percentage of Cox and Munk (1955) slope variance required for a geometric
optics model to explain the Nimbus-6 observations (X) and HoUinger (1971) (o)
as a function of frequency.
231
REFERENCES
Cardone, V. J., "Specification of the Wind Distribution in the Marine Boundary
Layer for Wave Forecasting," Ph.D Thesis, New York University, Department
of Meteorology and Oceanography, 1969 (Available from NTIS Order No.
AD702490).
Chang, A. T. C., and T. T. Wilheit, "Remote Sensing of Atmospheric Water Vapor,
Liquid Water, and Wind Speed at the Ocean Surface by Passive Microwave
Techniques From the Nimbus-5 Satellite," NASA TM-79568, June 1978 sub-
mitted to Radio Science.
Cox, C. and Munk, W., "Some Problems in Optical Oceanography," J. Marine Res.
1___44,63-78 (1955).
Hollinger, J. P., "Passive Microwave Measurements of Sea Surface Roughness,"
Trans. IEEE Geoscience Electronics, GE-9, pp 165-169 (1971).
Jackson, J. D., "Classical Electrodynamics," John Wiley & Sons, Inc., New York
(1962), p 216ff.
Kline, L. A., and C. T. Swift, "An Improved Model for the Dielectric Constant of
Sea Water at Microwave Frequencies," Trans. IEEE AP-25 104-11 ! (1977).
Lane, J. A. and J. A. Saxton, "Dielectric Dispersion in Pure Polar Liquids at Very
High Radio Frequencies," Proc. Roy. Soc., London A, 214, pp 531-545,
(1952).
Nordberg, W., J. Conaway, D. B. Ross, and T. Wilheit, "Measurements of Micro-
wave Emission from a Foam-Covered Wind Driven Sea," J. Atmos. Sci., 38,
429-435 (1971).
Shutko, A., "Report on Soviet Progress in Microwave Radiometry of the Ocean's
Surface," presented at IUCRM Colloquium on Passive Radiometry of the
Ocean's Surface, Patricia Bay, B.C., Canada, June 1978.
Stogryn, A., "Equations for Calculating the Dielectric Constant of Saline Water,"
Trans. IEEE, MTT-19 733-736 (1971).
Webster, W. J., Jr., T. T. Wilheit, D. B. Ross, and P. Gloersen, "Spectral Charac-
teristics of the Microwave Emission from a Wind Driven Foam--Covered Sea,"
J. Geophys. Res. 8.__11,3095-3099 (1976).
Wilheit, T. T., "The Effect of Wind on the Microwave Emission From the Ocean's
Surface at 37GHz," NASA TM-79588, July 1978 submitted to J. Geophys.
Res.
232


A model for the microwave emissivity of the ocean's surface as a function of wind speed

A quanitative model is presented which describes the ocean surface as a ensemble of flat facets with a normal distribution of slopes. The variance of the slope distribution is linearly related to frequency up to 35 GHz and constant at higher frequencies. These facets are partially covered with an absorbing nonpolarized foam layer. Experimental evidence is presented for this model

A model for the microwave emissivity of the ocean's surface as a function of wind speed

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