Chinese Journal of Oceanology and Limnology

Vol. 27 No. 1, P. 112-116, 2009

DOI: 10.1007/s00343-009-0112-1

A new model to estimate significant wave heights with

ERS-1/2 scatterometer data*

GUO Jie, HE Yijun, William Perrie, SHEN Hui,

CHU Xiaoqing,

Institute of Oceanology, Chinese Academy of Sciences, Key Laboratory of Ocean Circulation and Wave, CAS,

Qingdao 266071, China

Graduate School of the Chinese Academy of Sciences, Beijing 100039, China

Bedford Institute of Oceanography, Dartmouth, NS, Canada

Received Oct. 10, 2008; revision accepted Nov. 17, 2008

Abstract A new model is proposed to estimate the significant wave heights with ERS-1/2

scatterometer data. The results show that the relationship between wave parameters and radar

backscattering cross section is similar to that between wind and the radar backscattering cross section.

Therefore, the relationship between significant wave height and the radar backscattering cross section is

established with a neural network algorithm, which is, if the average wave period is 7s, the root mean

square of significant wave height retrieved from ERS-1/2 data is 0.51 m, or 0.72 m if it is >7s otherwise.

Keyword: scatterometer; significant wave height; neural networks; wind waves; swell

1 INTRODUCTION and H1/3 with the buoys in the Gulf of Mexico,

estimating the wave periods from wind speeds and

A good description of ocean wave conditions is altimeter-measured H1/3. These wave parameters can

crucial to the safety of voyage as well as of marine be measured at 7 km resolution along the track.

constructions. Ocean waves can be described with However, the two-dimensional spatial resolution

the parameters such as significant wave height, wave quite low; therefore, its applications have been

period, and wave direction etc. In the past, ocean limited.

wave parameters are measured with wave gauges and A scatterometer is a specialized sensor for

buoys; however, it is almost not possible for the measuring sea surface wind vector in spatial

detail and constant measurement operations at sea in resolution of 50 km or less, and the precision of wind

a large marine area or global oceans. This situation speed is about 2 m/s. As QuikSCAT can cover 90%

remains unchanged until oceanic satellites were of the global oceans every day, the data have been

launched. applied widely. The wind vector can be measured by

At present, synthetic aperture radar (SAR) a scatterometer because the NRCS is wind-vector

mounted in a satellite is the only sensor used to dependent. In fact, the NRCS represents the radar

remotely measure ocean wave spectra. However, return intensity at sea surface forced by wind. Ocean

because of the azimuthal wave cutoff and the lack of waves almost always include wind waves and swell.

power, it is unable to measure the high-frequency Therefore, the NRCS depends not only on wind

part of a wave spectrum. The application is therefore vectors, but also on ocean waves. For TRMM

limited. On the other hand, significant wave height (tropical rainfall mapping mission), the NRCS

(H1/3) can be measured globally with such a satellite depends on the waves and wind speed, having one

radar altimeter by inferring directly from the shape of precipitation radar (PR) and two satellite altimeters

radar pulse returning to the nadir-looking altimeter (Jason-1 and ENVISAT) installed (Tran et al., 2007).

with the assumption of the Gaussian surface The spectrum model by Stephen et al. (1985) is used

elevations. Moreover, wind speed can also be

retrieved from the altimeter-measured normalized * Supported by the National High Technology Research and Development

radar cross section (NRCS). Hwang et al. (1998) Program of China (863 Program) (No.2008AA09Z102), and by the

Canadian Space Agency (CSA) GRIP Program.

established the relation among wind speed, period

** Corresponding author: abpnxs@r.postjobfree.com

No.1 GUO et al.: A new model to estimate significant wave heights with ERS-1/2 scatterometer data 113

data of only 12 NDBC buoys can be used (Fig.1).

at ocean surface, in which two-scale scattering theory

They covered the North Pacific Ocean and the North

is applied, and can well predict the observed

Atlantic Ocean. The distances of buoys to coastal

dependence of NRCS on radar frequency,

regions are over 50 km. Table 1 lists the property of

polarization, incidence angle, and wind velocity in an

the data set, including the buoy station number,

wide incidence angle range of 0 70 . The spectrum

coordinates, water depth, and the number of data

model is integrated with swell effect examination on

point in each data set. In total, 10 485 data from

a radar cross section. The effect is significant in low

radar frequency (L band) at normal incidence, and ERS-1/2 scatterometer are collocated with the

can be nearly eliminated in high frequency (Ku band) NDBC buoy data in this study, of which 5 300 are

at a large angle of incidence (about 50 ). With neural used to built the model and 5 185 data are used for

networks and large high-quality collocated datasets, validation.

Quilfen and Chapron (2003) studied the relation The NRCS, azimuth angles, and incidence

between the C-band scatterometer NRCS angles are measured by the ERS-1/2

measurement by ERS (European Remote Sensing scatterometer. The wind directions, wind speed

Satellite) and integrated sea state parameters (i.e., the (V), average wave periods (T), and significant wave

mean wave period and significant wave height) heights (H1/3) are measured in NDBC buoy stations.

measured by buoys, and found that the NRCS is The comparison period spans from January 1991 to

affected by wave parameters. In the following December 2000. For comparisons between

sections, our methodology, results, and conclusions scatterometer and buoy data, the maximum

to retrieve wave parameters from ERS-1/2 differences in longitude is 0.15, 0.15 in latitude,

scatterometer data are presented. and 0.5 h in time.

2 METHODS AND RESULTS

2.1 Data

The ERS missions consist of two remote sensing

satellites launched in the 1990s by the European

Space Agency. The first series, ERS-1, was launched

in July 1991, and ERS-2 in April 1995 in order to

ensure long term continuity of data, which is

essential for researches and applications. ERS-1/2

(ERS-1 and ERS-2 in short) scatterometer data are Fig.1 Locations (triangles) of 12 buoys in the North Pacific

used in this paper Ocean and the North Atlantic Ocean

Because National Data Buoy Center (NDBC)

2.2 The effect of ocean wave on the radar

buoy collects wave data hourly, for each ERS-1/2

scattering cross section

scatterometer data point, any two buoy data points

For the TRMM PR (active), Tran et al. (2007)

before and after the ERS-1/2 scatterometer time are

discussed the effect of H1/3 on NRCS. Their results

selected for comparison. The wave data from NDBC

are consistent with a previous analysis at higher

buoys are acquired and reported hourly. H1/3, the

incidence angles (20, 30, 40 and 60 ) (Nghiem et

significant wave height (in meter) is the 1/3 of the

al., 1995). Here, ERS-1/2 scatterometer data are used

highest waves during the 20 min sampling period,

with NDBC buoy data to determine the relation

and the average wave period (T, in second) is the H1/3

between wave parameters and the NRCS. Fig.2

that observed during the same period. The wind

shows the relationship between the NRCS and

direction is the degrees clockwise off the true

relative azimuth angle at an incidence angle of 30

geographical North. The significant wave height and

when H1/3/(gT2) is 0.005. Fig.3 shows the NRCS

average wave period are derived from the buoy heave

versus relative azimuth angle curve with an incidence

motion spectrum measured over a 20-min acquisition

angle of 45 when H1/3 is 2 m. The relationship is

period starting at 30 min after the hour. The wind and

close to that between NRCS and wind. The blue

wind direction data are collected with a wind sensor

asterisks are the results from our model and the red

located on the buoy s mast. The elevation of the wind

dots represent the buoy and scatterometer

sensor is 5 m or 10 m above sea level. In this research,

observations (Figs.2 and 3).

data from 34 NDBC buoys are collected; however,

CHIN. J. OCEANOL. LIMNOL., 27(1), 2009 Vol.27

114

Table 1 Buoys data and the data collocated with ERS-1/2 scatterometer data in

the Pacific and Atlantic Oceans (1991 2000)

Station Location Water depth (m) Number of data points

The Pacific

460**-**-**-** N, 130 16 19 W 3 374 67

46005 46 03 N,131 01 12 W 2 779.8 642

460**-**-**-** N, 177 34 35 W 3 662.3 140

510**-**-**-** N, 162 12 28 W 3 252 866

510**-**-**-** N, 152 28 51 W 5 303.5 340

460**-**-**-** N, 120 26 54 W 447.1 12

460**-**-**-** N,123 19 00 W 126.5 6

The Atlantic

410**-**-**-** N, 75 21 36 W 3 316.2 843

440**-**-**-** N, 66 34 47 W 88.4 143

440**-**-**-** N, 69 09 48 W 195.7 642

42002 25 10 N, 94 25 00 W 3566.16 46

420**-**-**-** N, 88 12 48 W 443.6 123

Fig.2 Relationship between relative azimuth angle and NRCS for incidence angle 30 when H1/3/(gT2) is 0.005

Fig.3 Relationship between relative azimuth angle and NRCS for incidence angle 45 when the H1/3 is 2 m

of modeling a large variety of physical phenomena.

2.3 The algorithm of deriving ocean wave

Here, adaptive means the method is able to process a

parameters

large number of data or deal with new relevant

The significant wave height (H1/3) and H1/3/(gT2) variables. Second, even if the learning phase of the

are retrieved by ERS-1/2 scatterometer data using a network takes a long times, the operational phase is

neural network (NN) algorithm. very efficient. This phase requires few calculations

NN offer interesting possibilities for solving and can be performed with personal computers.

problems involved in transfer functions. First, the Moreover, NN architecture can be easily

NN are adaptive, providing a flexible and easy way implemented on dedicated hardware using parallel

No.1 GUO et al.: A new model to estimate significant wave heights with ERS-1/2 scatterometer data 115

algorithms, and further saving the processing time. 2.4 Comparison between derived and buoy wave

In this paper, H1/3 is retrieved from scatterometer data

data using neural networks technology.

If a wave period of buoy is less than 7 s (T 7s),

The learning data include incidence angles,

the case is defined as wind-wave domination. The

cos, NRCS, wind speed (V) and H1/3 from

learning data include 4 100 collocated pairs by

buoys. The module structure consists of a multi-layer

random choice. An additional 4 048 ones are

perception (MLP) that includes one hidden layers.

randomly taken as test data and not used in the

The transfer function of the input hidden layer is a

learning phase. Fig.4 shows H1/3 for buoy data in

sigmoid function f(x) =2/[1+exp(-2x)], and that of the

comparison with the retrieved H1/3 from ERS-1/2

output layer assumes the linear function f(x)=x. The

scatterometer. Fig.5 compares the H1/3/(gT2) from

input data are the incidence angles and cos,

buoy data with the retrieved ones from ERS-1/2

and NRCS, and wind speed (V) while the output

scatterometer. Table 1 displays the detail.

data are H1/3 or H1/3/(gT2). In the following equation,

d

Aj == f ( ij xi ) j=1,, n.

i =1

Aj is the output of the jth neuron, d is the amount

of input, and n is the neuron amount of the hidden

layer. The connection weights are determined during

the learning phase using the back-propagation

network (Lin et al., 2006).

The retrieved H1/3 and H1/3/(gT2) from

scatterometer data are compared with the H1/3 and

H1/3/(gT2) values from buoy data in Figs.4 7 and

Table 1.

Table 1 H1/3 (m) and H1/3/(gT2) RMS for NN inversion

Fig.4 Comparison in H1/3 (m) between buoy data and those

retrieved ones from ERS-1/2 scatterometer data

2

Item H1/3 H1/3/(gT )

Wind-wave Domination

Corr1 0.75 0.83

RMS1 0.51 m 0.000 97

Error1 0.41 m 0.000 74

Bias1 -0.002 8 m 1.29e-006

Swell domination

Corr2 0.84 0.92

RMS2 0.72 m 0.000 77

Error2 0.55 m 0.000 6

Bias2 0.002 m 6.06e-006

In Table 1, Corr is correlation coefficient, RMS

for root mean square, and

1 N

( k2 )2

1

RMS= (1) Fig.5 Comparison in H1/3/(gT2) between buoy data and

k

N k =1

retrieved ones from ERS-1/2 scatterometer data

1 N

k2

1

Error = (2) In total, 10 485 the ERS-1/2 scatterometer-yielded

k

N data that collocated with NDBC buoy readings are

k =1

used in this study, of which 8 148 are 7 s and 2 337

1 N

( k2 )

1

are >7 s in wave period. If a wave period of buoy is

Bias= (3)

k

N >7 s, swell domination is assumed; otherwise,

k =1

wind-wave domination. The learning data include

where N is the number of test data. 1 200 collocated pairs by random choice. Additional

CHIN. J. OCEANOL. LIMNOL., 27(1), 2009 Vol.27

116

1 137 collocated pairs are randomly taken as test data In wind-wave domination, the RMS of H1/3 is 0.51 m,

and not used in the learning phase. Fig.6 shows the while that in swell domination case, 0.72 m. The H1/3

comparison in H1/3 between buoy data and RMS values of the wind-wave domination in this

scatterometer data, and Fig.7 is for H1/3/(gT2) ones in study are consistent with those of Ebuchi and

the same manner. Kawamura s paper (1994), while in the swell

The bias, average absolute error and root mean domination, the RMS results are on the high end of

square (RMS) of the H1/3 and H1/3/(gT2) retrievals the Ebuchi and Kawamura (1994) results. It shows

with the buoy-measured values are given in Table 1. that the effect of swell on the radar cross section is

significant. It is practical to retrieve H1/3 and

H1/3/(gT2) values from the ERS-1/2 scatterometer

with neural networks methods. In the future, the

results from H1/3/(gT2) retrievals shall be used to

calculate T and wave lengths.

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3 CONCLUSIONS

Low Incidence Angles Using TRMM and Altimeter

A neural networks algorithm is developed by the Data. IEEE Geosci. & Remote Sensing Lett. 4(4):

authors for retrieving H1/3 and H1/3/(gT2) (as 542-546.

described in 2.3) from ERS-1/2 scatterometer data.

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