An Ocean Wave Spectrum Derived from Polarimetric Microwave Radiometer Data

Abstract

This paper presents a detailed analysis of a simplified Two-Scale Model for ocean surface polarimetric microwave emission, and investigates the extent to which varying ocean surface length scales contribute to brightness temperature zeroth and second azimuth harmonics. The Two-Scale Model can be expressed as a weighting function M^0,2 multiply ocean surface curvature spectrum C^0,2. This implies a simple way to investigate the effect of curvature spectrum on ocean emission. It is found that ocean waves with wavelengths both comparable to and much greater than the electromagnetic wavelength can contribute to these harmonics, depending on the value of the ocean surface spectrum in these length scales. An ocean wave spectrum was derived from polarimetric microwave radiometer data according to constrained linear least-squares method.

Full text

Page 1

AN OCEAN WAVE SPECTRUM DERIVED FROM POLARIMETRIC
MICROWAVE RADIOMETER DATA
Xiaobin Yin1, Zhenzhan Wang1, Lei Han2, Qing Xu3
Center for Space Science and Applied Reserch, Chinese Academy of Sciences, Beijing, 100080
First Institute of Oceanography, State Oceanic Administration, Qingdao, 266061
Institute of Space and Earth Information Science, The Chinese University of Hong Kong, Hong Kong
Email: yinxb@yahoo.com.cn
1.
2.
3.
Abstract:
Oceanic emission and scattering model is critical in remote sensing wind vector using passive polarimetric
microwave radiometer [1, 2]. This paper presents a detailed analysis of a simplified Two-Scale Model for ocean surface
polarimetric microwave emission and derives an ocean wave spectrum from polarimetric microwave radiometer data.
The two-scale model states that brightness temperatures observed by a radiometer at observation angle ? can be
written as [3]:
cot
3
4
(1tan )(,)
v
h
Sxy ss
BSyxx
T
T
TT dSdSSP SSRE
T
T
?
?
?
?? ??
???
? ?
? ?
? ?
? ?
? ?
? ?
? ??
??
, (1)
Based on an efficient two-scale model [4] [5], we derive an even simpler express of (1) as:
ll
ll
??
'
?
'
?0022
(k )(k )
BS
ee
bb
TdlCMdlCM
????
, (2)
Where, M0 and M2 are weighting functions. C0 and C2 are zeroth and second cosine harmonics of the curvature
spectrum, which relate to the spectrum of the small-scale ocean wave W as:
4
02
( , )C k( , )( ) cos(2 )C k
?
( )k W kC k
?????
, (3)
Fig. 1 shows M0 and M2 for all four Stokes parameters versus log10(k) at 18.7GHz.
2 2.533.5
2
4
6
Th
M0
22.533.5
-2
0
2
4
6
Tv
2 2.533.5
-1
-0.5
0
0.5
T3
2 2.5
log10(k)
33.5
-1
0
1
T4
22.53 3.5
-2
0
2
M2
22.533.5
-2
0
2
22.533.5
-0.2
0
0.2
2 2.5
log10(k)
33.5
-0.06
-0.04
-0.02
0
? =0
? =90
? =180
kd
kd
kd
kd
kd
kd
kd
kmax
kmax
kmax
kmax
kmax
kmax
kmax

Fig. 1 Weighting functions of 0°, 90° and 180° azimuth angle at 18.7GHz and 55.3° incidence angle.

Page 2

Several resonance type behaviors of the weighting functions are observed for wavelength scales comparable to half
and twice the electromagnetic wavelength at 18.7GHz, as indicated by Fig. 1. It is found that ocean waves with
wavelengths both comparable to and much greater than the electromagnetic wavelength can contribute to these
harmonics, depending on the shape of the ocean wave spectrum in these length scales [6~8].
As indicated by (2), obtaining a final prediction of emission requires inclusion of the product of the weighting
function M0 and M2 and ocean curvature spectrum harmonics C0 and C2. This implies a simple way to investigate the
effect of ocean surface parameters and curvature spectrum on ocean emission separately. Base on (2), an ocean wave
spectrum was derived using all four Stokes emission data of WindSat and WindRad at 10.7GHz, 18.7GHz and 37GHz
[9~11]. This spectrum is thought to be more accurate in a wide range of wave numbers.

REFERENCES:
F. J. Wentz, “A model function for ocean microwave brightness temperatures”, J. Geophys. Res., vol. 88, no. c3, pp.
1892-1908, 1983.
J.T. Johnson and M. Zhang, “Theoretical study of the small slope approximation for ocean polarimetric thermal
emission”, IEEE Trans. Geosci. Remote Sensing, vol. 37, no.5, pp. 2305- 2316, Sep. 1999.
S.H. Yueh, “Modeling of wind direction signals in polarimetric sea surface brightness temperatures”, IEEE Trans.
Geosci. Remote Sensing, vol. 35, no.6, pp. 1400-1418, Nov. 1997.
D. R. Lyzenga and J. F. Vesecky, “Two-scale polarimetric emissivity model: Efficiency improvements and comparisons
with data”, Progress in electromagnetics research, pier 37: 205–219, 2002.
J.T. Johnson, “An efficient Two-Scale model for the computation of thermal emission and atmospheric reflection from
the sea surface”, IEEE Trans. Geosci. Remote Sensing, vo. 44, no.3, pp. 560-568, Mar. 2006.
S. P. Durden and J. F. Vesecky, “A physical radar cross-section model for a wind-driven sea with swell”, IEEE J.
Oceanic Eng., vol. 10, no. 4, pp. 445-451, Oct. 1985.
Y. Liu, X. Yan, and M. Su, “Direction spectrum of wind waves: Part II - comparision and confirmation”, Journal of
Ocean University of Qingdao, vol. 2, no.1, pp. 1-12, Jan. 2003.
T. Elfouhaily, B. Chapron, and K. Katsaros, “A unified directional spectrum for long and short wind-driven waves”,
Journal of Geophysical Research, vol. 102, no. C7, pp. 15781-15796, 1997.
P.W. Gaiser, K. St. Germain, et al. “The WindSat spaceborne polarimetric microwave radiometer: Sensor description and
early orbit performance,” IEEE Transactions on Geoscience and Remote Sernsing, vol. 42, no.11, pp. 2347-2361, Nov.
2004.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10] S. H. Yueh, W. J. Wilson, S. J. Dinardo, and S. V. Hsiao, “Polarimetric microwave wind radiometer model function and
retrieval testing for WindSat”, IEEE Trans. Geosci. Remote Sensing, vol. 44, no.3, pp. 684-596, Mar. 2006.
[11] Wentz F. J., T. Meissner, and D. K. Smith, Assessment of the Initial Release of WindSat Wind Retrievals, RSS Technical
Report, Jan, 2005.