Internationa l Journal of Geosciences, 2014, 5, 85-92
Published Online January 2014 (http://www.scirp.org/journal/ijg)
http://dx.doi.org/10.4236/ijg.2014.51010
An Improved Met h od of Ret ri evi ng Sea Surface W ind
Speed Based on a Four-Layer Medium Model
at High Sea States
Jiasheng Tian*, Qiaoyun Liu, Wan Pan, Jian Shi
The Department of Electronics and Information Engineering,
Huazhong University of Science and Technology, Wuhan, China
Received June 23, 2013; revised July 28, 2013; accept ed August 22, 2013
Copyright © 2014 Jiasheng Tian et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accor-
dance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual
property Jiasheng Tian et a l. All Copyright © 2014 are guarded by law and by SCIRP as a guard ian.
ABSTRACT
Consideri ng about the effe ct of whitecaps and f oams on pulse-limited Radar Altimeters, an improved algorithm
of retrieving sea surface w ind speed is proposed in thi s paper. Firstly, a four-layer dielectric model is establ ished
in order to simulate an air-sea interface. Secondly, the microwave reflectivity of a sea surface covered by spray
droplets and foams at 13.5 GHz is computed based on the established model. These co mputed results show that
the eff ect of spray dro plets and fo a ms in high sea sta te c ondit ions s ha ll not be negligible on retrieving sea surface
wind speed. Finally, compared with the analytical algorithms proposed by Zhao and some calculated results
based on a thre e-layer dielectric model, an improved algorithm of retrieving sea surface w ind spee d is pre se nte d.
At a high wind speed, the improved algorithm is in a better accord with some empirical algorithms such as
Brown, Young ones and et al., and also in a good agreement with ZT and other algorithms at low wind speed.
This new improved alg orithm w ill be suitable not only fo r low wind spe ed retrie val, but also for hig h wind speed
retrieval. Better accuracy and effectiveness of wind speed retrieval can also be obtained.
KEYWORDS
Satellite Altimeter; Wind Speed Retrieving Algorithm; H igh Sea Sta tes; Stratified Media;
Whitecap Coverage Rate
1. Introduction
Satellite radar altimetry research project could date back
to the conference of solid earth and ocean physics held in
Williamstown in 1969. After the recent decades, the al-
timeter has evolved through Skylab [1], GEOS-3 [2],
Seasat and Geosat, Topex/Poseidon and ERS-1 missions.
However, the retrieval of the sea surface wind speed
from the radar altimeter data poses a great challenge due
to the accuracy requirement set forth by the oceano-
graphic research community and some applications, such
as wind speed measurement with an accuracy of 2 m/s,
especially in high sea state conditions.
Historically, almost all the altimeter wind speed re-
trieving algor ithms (or mode functions) were based on
the relationship between the backscattering coefficient
0
σ
and the neutral stable wind speed U10 at 10 meters
high above sea level. A large number of wind speed re-
trie ving al gorith ms ha s been p ubli shed from 1950s [3-7].
Almost all low speed mode functions tend to overlap
whe n the wind speed is about U10 = 10∼7 m/s. This rea-
son is that sea states are mainly related to the maximum
probability of 10∼7 m/s wind speed. The second pheno-
menon is that some high wind speed model functions
converge near 9.5 m/s, but spread quickly when the wi nd
speed is more than 9.5 m/s. The discrete situation is
mainly because most wind speed retrieving algorithms
only play an emphasis on the scattering coefficient
0
σ
and neglect wave states (significant wave height, the
wave age, etc.) [8-10]. Moreover, for those presented
functions, some other factors such as spray droplets,
*
Corresponding author.
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J. S. TIAN ET AL.
86
foams and whitecap coverage rate [11] caused by a cyc-
lone or hurricane were also not considered about.
In 1983, Q. A. Zheng [11] computed the reflectivity of
a sea surface covered by whitecaps and foams at 13.9
GHz based on electromagnetic field theory of stratified
media, and studied the effect of oceanic whitecaps and
foams on pulse-limited rad ar altimeters. In 19 86, Gairola
[12] also investigated the reflectivity of a sea surface
covered by whitecaps and foams at 13.9 GHz based on a
three-layer medium model, and applied the computed
result to the sea surface wind speed retrieval. In 2008,
Yang [13] also computed a three-layer model for cor-
recting backscattering coefficient. When these research
results were app lied in retrieving sea surface wind speed,
the accuracy would be improved to some extent. Howev-
er, in high sea state conditions, some differences from
Young algorithm or Brown’s would still exist.
In 2003, Zhao and Toba proposed an analysis algo-
rithm (referred to as ZT) [6,7] considering about the ef-
fect of wave states (or sea states). The algorithm was
derived from electromagnetic wave scattering theory and
wave spectral theory, and was independent of the spatial
and temporal registration data, the size of the measured
data and the spatial and temporal data registration stan-
dards and so on. The algorithm took the role of wave age
into account in retrieving wind speed, and thus its sym-
metry was good and its root mean square error could also
be accepted. However, for this algorithm, the effect of
sea foams and spray droplets was not taken i nto acc ount.
The reflectivity
( )
2
0R
in the expression of the ZT
function should not be considered to be generated only
by the sea water, but a hybrid interface consisting of
multilayer media including sea water, foams, spray
drop le ts, the a ir .
The purpose of this study is to discuss the effect of
whitecaps, spray droplets and foams on meas ure ments o f
wind speed on pulse-limited rad ar altimeters by calcula t-
ing quantitatively the microwave reflectivity of a foam-
covered sea surface based on a four-la yer-medium model.
The calculated results will be applied into retrieving sea
surface wind speed at high sea states.
2. Electromagnetic Scattering from the Sea
Surface
2.1. Physical Model
The approach for measuring sea surface wind speed by
radar altimeter is based on the theory that the sea surface
backscattering coefficient
0
σ
is a function of the wind
speed. Namely, the usual wind speed retrieval algorithm
is based on the direct relationship between wind speed
and backscattering coefficient
0
σ
. Based on the specu-
lar point theory almost all algorithms (including empiri-
cal, semi-empirical or analytic algorithms) can be ex-
pressed as [14,15]
() ()
2
04
πsec ,
xy
Rp σθθ ζζ =
where
( )
,
xy
p ζζ
is the probability density function of
sea surface mean square slopes
2
S
relating to wind
speed.
()
2
R θ
is the reflectivity of the air-to-surface
interface at the incident angle
θ . The wind speed is re-
lated not only to mean square slopes
2
S
but also to the
air-sea interface reflectivity factor
( )
2
R θ
. Under the
classical assumption that the sea surface mean squre
slopes are near ly Gaussian and isotr opic in their distribu-
tion, the scatter ing coefficient is given b y
( )( )( )( )
( )
2
0 22
2secexp tan
RS
S
θ
σθθ θ = −
(1)
In fact the sea surface process is more complex. In
high sea states, sea wave is broken with the high wind
speed, an air-sea interface will become a multilayer
medium that is made of air, spray droplets(or droplets),
foams, and sea water. It is also known that the thickness
of the foam and the droplets layer and the coverage rate
will vary with the wind speed [16,17]. In 1982, Zheng
studied sea foams influence on electromagnetic wave
reflection
()
2
0 R
at a normal incident wave, and
pointed out that the effect of foams and whitecaps on
wave reflection should not be insignificant. However
zheng or Gairola only computed the microwave re-
flectivity based on a three-layer medium made of air,
foams and sea water, and the effect of the spray droplets
was neglected. In order to improve the accuracy of es-
timated wind speed, it is necessary to establish the
electromagnetic wave incidence-reflection physical model
in high sea state conditions. Based on the above analysis
and experience , in high sea state conditions the air-sea
surface should be made up of a four-layer media (Figure
1). The top layer is atmosphere (or air), followed by the
sea spray droplet layer. The third layer is foams and the
bottom is the seawater layer (Figure 1). The electro-
magnetic wave from an altimeter penetrates into the air,
and enters into the spray droplet layer and foams, finally
plun ges up o n the se a wat er . The e c ho from t he fo ur -layer
medium will be received by the altimeter.
θ stands for
the incident angle, d1 and d2 is the thickness of the
droplets and foam layer (Figure 1), respectively.
2.2. Electromagnetic Scattering Theory
2.2.1. TE Wave
Let’s suppose that the electric field intensity of an inci-
dent wave with the vertical po la r iz a tion is given as
00
sin cos
00
ee
jk xjk z j
yy yy
EE
θθ −− −⋅
= ==
kr
E aEaa
(2)
and p lunges into the four-laye r mediu m at incide nt angle
θ .
y
a
is the unit vector along y direction, k0 is t he wave
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J. S. TIAN ET AL.
87
(a)
(b)
Figure 1. A multilayer dielectric incident-reflected model. (a)
TE wave; (b) TM wave.
number in free space. According to electromagnetic
theory, electromagnetic waves in the four-layer media
can be expressed as the form of the sum of incident wave
and reflected wave, that is
()
sin
e ee
zmzmm m
jk zjk zjkx
y ymymm
EE E
θ −− +−
= =+Ea a
(3)
where m = 0, 1, 2, 3 represent the air layer, the droplets
layer, the foam layer and the sea water layer respectively.
When m = 3, the second term of Equation (3) is zero in
the sea water layer. There
m mm
k ω µε =
, µ
m and
ε
m are
the permeability and permittivity, respectively. Accord-
ing to the Maxwell equations, we can get the magnetic-
field co mponent s given as
()
sin
e ee
zmzmmm
jkzjkzjk x zm
xmm m
m
k
H EE
θ
ωµ
−−
+−
−
= −
(4)
( )
sin
sin e ee
zmzmm m
jk zjk zjkx mm
zmm m
m
k
H EE
θ
θ
ωµ
−− +−
= +
(5)
where θ
m is an angle of incidence or refraction. Ob-
viously
00
sinsin ,1,2,3
mm
k km θθ = =
(6)
( )
2
22
00
sin,1,2, 3
zm m
kkk m θ =−=
(7)
according to electromagnetic theory and the boundary
condition which the electromagnetic field tangential
components are continuous at the interface, we can get
( )
( )
( )()
()
()( )
11
11
1
1
1
e
e
ee
zm m
zm m
zm mzm m
jk d
jk dym
ym jkdm mjk d
ym ym
E
EN
E
E
++
++
−
+
− ++
+ −−
+



=

 



(8)
whe re
( )
( )
( )
( )( )
( )
( )
( )( )
( )
( )
( )( )
( )
( )( )
( )
11 11
11 11
1
11
,1
,1
11
2
ee
ee
mm zm mzm m
mm zm mzm m
mzm
mm zm
m
jkd djkd d
TE m m
jkd djkd d
TE m m
k
Nk
R
R
µ
µ
++ ++
++ ++
+
+
+
− −−
+
− −−
+


= +




⋅


(9)
and
( )
( )
( )
( )
( )
1
1
,1 1
1
1
,0,1, 2
1
mzm
zm m
TE m mmzm
zm
m
k
k
Rm
k
k
µ
µ
µ
µ
+
+
++
+
−
= =
+
(10)
Thus for the four-layer model (Figure 1), we have
00 33
00 33
03
01 1223
03
ee
ee
zz
zz
jk djk d
yy
jk djk d
yy
EE
NNN
EE
−− ++
−−
 
=
 
 
 
(11)
Because the thickness of the sea water layer is infinite
and there may be considered no reflection wave, we can
let d3 = 0 and
3y
E
−
= 0, and obtain the ratio RTE of the
reflecte d wave t o the incident wave at z = 0 (Figure 1(a)).
1
0
1
0
up
TE low
R
E
RR
E
−
+
= =
(12)
whe re
22
11112 2
2
1,01,01 ,12,23
2 22
,12 ,23
e
ee
z
z zz
jk d
upTETETE TE
jkdjkdjk d
TE TE
R RRRR
RR
−
− −−
= +
++
and
2 211
112 2
22
1,12,23,01 ,12
22
,01 ,23
1e e
e
zz
zz
jk djkd
lowTE TETE TE
jkdjk d
TE TE
R RRRR
RR
−−
−−
=++
+
d1, d2 is the thickness of the dro plets layer, the foam layer
at high wind speed, respectively. d1 and d2 has the rela-
tions hi p wit h the wi nd sp ee d U10 at 10 meters height over
the sea surface. They can be given as (Andreas E. L.,
1995; Wu Jin, 1979) [16,17].
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J. S. TIAN ET AL.
88
2
1 10
0.0075dU=
(13)
( )
10
210 10
0.004 7m/s
0.00470.0012 7m/s
U
dUU
≤


=+ −×>


(14)
Fro m Equation (12), reflection characteristics of the
air-sea interface can be calculated.
2.2.2. TM Wave
Let’s suppose that the magnetic field intensity of an in-
cident wave with the parallel polarization is given as
00
sin cos
0
e
jkx jkz
yy yy
HH
θθ −−
= =Ha a
(15)
Similarl y, the magnetic field i ntensity in the four-layer
media can be expressed as the form of the sum of inci-
dent wave and reflected wave
( )
0
sin
e ee
zm zm
my ym
jk zjk zjkx
y ymym
H
HH
θ −− +−
=
= +
Ha
a
(16)
In the sea water layer (m = 3), the second term of Equ-
ation (16) is zero. From Maxwell’s equation, we can get
the electric field intensity. In term of electromagnetic
field boundary conditions，we can have
( )
( )
() ()
()
( )()
11
11
1
1
1
e
e
ee
zm m
zm m
zm mzm m
jk d
jk dym
ym jkdmmjk d
ym ym
H
HM
HH
++
++
−
+
−
++
+ −−
+



=

 



(17)
whe re
( )
( )
( )
( )()
( )
( )
( )()
( )
( )
( )()
( )
( )()
( )
11 11
11 11
1
11
1
1
11
2
ee
ee
mm
zm mzm m
mm zm mzmm
mzm
mm zm
m
jkd djkd d
mm
jkd djkd d
mm
k
Mk
R
R
ε
ε
++ ++
++ ++
+
+
+
− −−
+
−− −
+


= +




⋅


(18)
and
()
( )
( )
()
( )
1
1
,1 1
1
1
1
mzm
zm m
TMm mmzm
zm
m
k
k
Rk
k
ε
ε
ε
ε
+
+
++
+
−
=
+
(19)
Thus for the fo ur -layer-model (Figure 1), we have
00 33
00 33
03
01 1223
03
ee
ee
zz
zz
jk djk d
yy
jk djk d
yy
HH
MMM
HH
−− ++
−−
 
=
 
 
 
(20)
Letting d3 = 0 and
3y
H
−
= 0, we can obtain the ratio
RTM of the reflected wave to the incident wave at z = 0
(Figure 1 (b)).
2
0
2
0
up
TM low
R
H
RR
H
−
+
= =
(21)
whe re
22
11112 2
2
2,01,01 ,12 ,23
2 22
,12 ,23
e
ee
z
z zz
jk d
upTMTM TM TM
jkdjkdjk d
TM TM
R RRRR
RR
−
− −−
= +
++
and
2 211
112 2
22
2,12,23,01 ,12
22
,01 ,23
1e e
e
zz
zz
jk djkd
lowTM TMTM TM
jkdjk d
TM TM
R RRRR
RR
−−
−−
=++
+
From Equation (21), we can discuss the reflection
characteristics of the four-layer-medium for TM wave.
2.3. Some Discussions about the Reflected Wave
from the Sea Surface
In terms of Equations (12) and (21), four curves ( θ = 0˚,
5˚, 10˚, 15˚) of the reflectivity
2
TE
R
,
2
TM
R
versu s t he
wind speed were plotted (Figure 2). The computed re-
sults show that the power reflectivity oscillates when the
wind speed is less than 5 m/s or the thickness of spray
droplets and foams is less than 0.2 m with the thickness
of foams being 0.004 m. Those minmax points (Figure 2)
are caused by the resonant absorption of the spray drop-
lets layer and the foams layer. When the wind speed is
more than 5 m/s, The reflectivity is 0.236 or so. Although
the curves (Figure 2) are obtained under some assumed
conditio ns (e.g., the incident angle is assumed to be 0˚, 5˚,
the temperature is 20˚C.), the curves may represent typi-
cal ocean conditions. For a radar altimeter, the incident
angle is often less than 5˚, so we can draw a conclusion:
( )()
( )
22
2
0.2347
0.23720 0.2360
TM TE
RR
R
θθ = ≈
=≈=
when
θ is less than 5˚, the difference will cause an err
±0.02 dB and is insignificant. However,
( )
2
0 0.6066R=
without whitecaps, the difference will cause an erro of
about 4.1 dB in reflected power at normal incident, and
will be important for measuring the wind speed on a
pulse-limited radar altimeter. So the effect of whitecaps
on wind speed retrieval should be considered at a normal
incident.
3. The Improved Wind Speed Model
Function at High Sea State Conditions
3.1. The Improved Wind Speed Algorithm
In term of Equation (12) or (21), the wave reflectivity
( )
2
0R
is a nonlinear function of wind speed. The for-
mation of sea spray droplets and foams is related to the
wind speed, which can be represented by the whitecap
coverage rate wf. The greater the wind speed is, the
thicker the droplets layer is, and also the whitecap cov-
erage rate wf becomes biger and biger with increasing the
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J. S. TIAN ET AL.
89
(a) (b)
Figure 2. The reflectivities of TE wave (a) and TM wave (b) ve rsus the wind speed.
wind speed. In 1993, Yeli Yuan et al. carried out a de-
tailed analysis on sea surface broken process, and ob-
tained the analytical expression of whitecap coverage
rate wf given as [18].
4 1.41
10
2.56 10
fs
w HU
−
= ×
(22)
where Hs is the significant wave height, which can be
retrieved from the leading curve of the sea surface echo
and can also be given as
2
10
0.015
s
HU=
(23)
suppose that
( )
2
0R
is the total sea surface reflectivity
factor,
2
R
is the reflectivity factor at the interface be-
tween the air, droplets and foams layer,
2
w
R
is the
reflectivity factor at the interface between the air and sea
layer. And thus
() ( )
22
2
01
fw f
RRw Rw=+−
(24)
The analytical expressions of ZT wind speed retrieving algorithm [6,7] is
( ) ()
( )
1
24
22 22
10
0 12
2
10
81 033
2 lnln
22
9
d
Dd
aag U Ra ak
Ck
gU
β
σβ
αβ
−
−

++ ++

=+−




(25)
in which
1
0.08, 314m
d
ak
−
= =
for K u wave b and ,
()
( )
0.6 12
2
10
3.31 ,
ss
gH Uag βγ = =
, and γ
s is related to sea water
density and tension. When the wind speed is more than 2.4 m/s we can take [6]
( )
3
10
0.8 0.06510
D
CU
−
=+×
. Substi-
tuti ng Eq uation (24) into Equation (25) we can get
( )
( )
( )
2 2
0
4
22 22
10
12
2
10
1
81
33
2 lnln
22
9
fw f
d
Dd
Rw Rw
aag Ua ak
Ck
gU
β
σ
β
αβ

+−

=
++ ++

+−


(26)
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J. S. TIAN ET AL.
90
It is obvious that the effect of spray droplets, foams on
electromagnetic wave reflection plays an important role
at wind speed retrieving in Equatio n (26). Ross had so me
observations of whitecaps in situ and found that when the
wind speed was 20 m/s, the whitecap coverage rate was
21.8% in the Atlantic Ocean. And when the wind speed
was 24.7 m/s, the whitecap coverage rate in the visible
band was 32% in the Nort h S ea [19]. Obvio usl y, so lar ge
a coverage by foam and whitecaps would not be negligi-
ble for active microwave remote sensing at high frequen-
cies. Therefore, it is necessary that the reflectivity factor
( )
2
0R
of the ZT algorithm s hould be improved to meet
with the needs of specific actual sea conditions. Equation
(26) is a new improved algorithm presented by the paper.
3.2. The Analysis of the Improved Wind Speed
Algorithm
For comparison, let us consider the general situation such
as wave age
β = 1. if the constant α = 0.08, the derived
NRCS from Equation (25) is closest to the satellite
NRCS on the condition that
( )
2
0
w
R
= 0.3.
( )
2
0
w
R
is thus taken as 0.3 [20,21]. Figure 3 is a comparison
chart of Young algorithm (YG), Brown algorithm (BR),
ZT algorithm and the proposed improvement algorithm.
In Figures 3 and 4, we can find some interesting conclu-
sions:
1) At low wind speed (<20 m/s), the proposed im-
provement algorithm can agree with ZT algorithm well.
This case is expected because whitecap coverage rate is
very small. And the change of
0
σ
is so small that it can
be ne gligible.
2) At high wind speeds (20 - 40 m/s), the proposed
improvement algorithm and ZT algorithm began to di-
verge. Thi s case can also be understood because the pro-
posed improvement algorithm fully considered about
some effects of the spray droplets, foams on electromag-
netic wave reflection while ZT algorithm did not.
3) At high wind speeds (20 - 40 m/s), the proposed
improvement algorithm is closer to some experienced
algorithms such as Brown-fitted curve and Young-fitted
curve in high wind-speed range. And in the 20 - 30 m/s
range, the proposed improvement algorithm is agreeable
well with Young algor ithm (F igure 3). These cases indi-
cate that spray droplets and foams make a contributio n to
the measurement of radar cross section o f the sea s urface,
and influence the retrieval results of wind speed. The
presented algorithms in the paper are valid.
4) Although the effect of foams was considered on
measurement results of wind speed [11-13], the plotted
curve based on a three-layer model diverged distinctly
from YG, BR and ZT especially in high wind speeds
(Figure 5) . Obvious ly, the four-la yer model in this paper
is closer to the practical sea conditions than the three-
layer one. It also indicates that the spray droplets layer
Figure 3. Several algorithms and the new improved algo-
rithm.
Figure 4. Differences among several functions at 10 - 40
m/ s .
Figure 5. Several algorithms and the new improved algo-
rithm.
010 203040 50 6070
-5
0
5
10
15
20
25
wind s peed U
10
(m/s)
Backscat teri ng coef fi cient
σ
0
(dB )
ZT A l gorithm
Improved Algorithm
The t hree-layer
YG A l gori t hm
BR A l gori thm
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J. S. TIAN ET AL.
91
makes a contribution to the measurement result of wind
speed. The proposed improvement algorithm based on
the fo ur -layer model is closer to actual sea surface prac-
tice than ZT.
5) We can draw a conclusion that the proposed im-
provement algorithm was applicable not only to the low
wind speed, but also to the high wind, and also it had a
good accuracy.
6) However, there is an inflection po int in the vicinity
of 40 m/s in the proposed improvement algorithm
(Figure 3), the phenomenon was because the whitecap
coverage rate was close to 1 or more than 1 at 40 m/s.
When the wind speed is more than 40 m/s, the whitecap
coverage rate is 1, and needed further research.
4. Summary
The process of an actual sea state is very complex. In
high sea states such as typhoon, the air-sea interaction is
very strong. When sea surface wind acts on the waves,
the sea waves are broken, and thus bubbles emerge on
the sea water surface and the foam layer comes into be-
ing, and also on the foam layer there is a spray droplet
layer. Foams and droplets have a greater influence on
electromagnetic wave reflection. In order to consider
about this effect, a four-layer media physical model was
established to calculate the microwave reflectivity at 13.5
GHz. Based on the model, an improvement algorithm
was presented. The proposed algorithm coincided well
with ZT algorithm at low speed wind, but began to di-
verge at high wind speed. However, the improved algo-
rithm was agreeable with some experienced algorithms
such as Young algorithm at the high wind speed (20 - 40
m/s). Compared with ZT algorithm and a three-layer
model algorithm, this improved algorithm fully consi-
dered the specific sea state, and had good precision in
high wind speed retrieving. T his algorithm is suitab le not
only for the low wind speed retrieving, but also for the
high wind speed retrieving.
Acknowledgements
Thi s re s ea rch wa s f i na nciall y s upp o r t ed b y t h e N a ti o nal Na-
tural Scie nce Fo undat ion o f China (Gr ant No. 41076113,
Grant NO. 41376181).
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