use of nautical radar as a wave monitoring...

Ž .Coastal Engineering 37 1999 331–342www.elsevier.comrlocatercoastaleng

Use of nautical radar as a wave monitoringinstrument

Jose Carlos Nieto Borge a,) ,1, Konstanze Reichert b,2,´Jurgen Dittmer b,3¨

a Clima Marıtimo, Puertos del Estado, Antonio Lopez 81, ES-28026 Madrid, Spain´ ´b Ocean SensWare, GKSS Technologiezentrum, D-21502 Geesthacht, Germany

Abstract

Common marine X-Band radars can be used as a sensor to survey ocean wave fields. The wavefield images provided by the radars are sampled and analysed by a wave monitoring systemŽ .called WaMoS II developed by the German research institute GKSS. This measuring system canbe mounted on a ship, on offshore stations or at coastal locations. The measurement is based onthe backscatter of microwaves from the ocean surface, which is visible as ‘sea clutter’ on the radarscreen. From this observable sea clutter, a numerical analysis is carried out. The unambiguousdirectional wave spectrum, the surface currents and sea state parameters such as wave periods,wave lengths, and wave directions can be derived. To provide absolute wave heights, the responseof the nautical radar must be calibrated. Similar to the wave height estimations for SyntheticAperture Radars, the so-called ‘Signal to Noise Ratio’ leads to the determination of the significant

Ž .wave height H . In this paper, WaMoS II results are compared with directional buoy data toS

show the capabilities of nautical microwave radars for sea state measurements. q 1999 ElsevierScience B.V. All rights reserved.

Keywords: Sea clutter; Wave and current measurements; Remote sensing; Operational monitoring

1. Introduction

Within the last two decades, rough-surface microwave-scattering theories have beenŽexploited to determine sea state properties, such as the wave power spectra Valenzuela,

.1978; Plant, 1990; Wetzel, 1990 .

) Corresponding author. Fax: q34-91-335-7705; E-mail: [email protected] E-mail: [email protected] Tel.: q49-4152-87-1458; Fax: q49-4152-87-1459; E-mail: [email protected] Tel.: q49-4152-87-1458; Fax: q49-4152-87-1459.

0378-3839r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0378-3839 99 00032-0

( )J.C.N. Borge et al.rCoastal Engineering 37 1999 331–342332

In the near range of nautical radars, a noise signal is received. This so-called ‘seaclutter’, is normally suppressed for navigational purposes. However, an analysis leads to

Žthe three-dimensional spatial and temporal variability of the sea surface Young et al.,.1985 . For this objective, the operational microwave radar system WaMoS II has been

Ž .developed at the German GKSS research centre Ziemer, 1991; Dittmer, 1995 . Thesystem consists of a conventional navigational X-band radar, a high-speed videodigitising and storage device and a standard PC. The analogue radar video signal is readout and transferred to the PC for storage and further real-time processing.

Each WaMoS II measurement consists of a time series of consecutive radar images.The spatial and temporal sampling rates depend on the hardware of the individualmarine radar. The temporal resolution is the antenna revolution period. The spatialresolution is a function of the antenna length and the radar pulse length.

The minimum system requirements for wave-analysis purposes are:Antenna rotation speed: 32 r.p.m.Pulse length: 80 nsAntenna length: 2.5 mWith the above mentioned set-up, an azimuthal resolution of 0.98, a range resolution

of 8.5 m and a temporal resolution of 2.5 s can be obtained.In contrast to other space or air-borne remote-sensing instruments, the images

obtained from a marine radar cover a smaller area but contain, in addition to the spatialinformation, the temporal evolution of the sea surface. The grey-scale time series of

Ž .radar images include the sea state information in space x, y and time t coordinates.These are transformed into the spectral domain by a Discrete Fourier TransformationŽ . ŽDFT to determine the unambiguous three-dimensional wave spectrum Young et al.,

.1985 . In this paper, the measuring of sea states, the data sampling and processingprocedure is described. Special emphasis is put on the method to compute the significantwave height from navigational radar data. The radar data is compared with directionalbuoy measurements to prove the capabilities of microwave radars for wave measure-ments.

2. Measurement and data analysis

Sea states are described as wave fields with statistical properties invariant in spaceŽ .rs x, y and time t, i.e., the wave fields are regarded as homogeneous in their spatial

dependence and stationary in their temporal evolution. Under these assumptions, the freeŽ . Ž .surface elevation h r,t is described by Eq. 1 :

h r ,t s eiŽkPryv t .dZ k ,v 1Ž . Ž . Ž .HVk ,v

Ž .where ks k ,k is the two-dimensional wave number vector and v, the angularx y

frequency. The set V is the admissible integration domain of wave number andk ,v

frequencies for ocean waves.Ž .The spectral random measure dZ k,v is usually considered as a Gaussian random

Ž . Ž .variable. dZ k,v is statistically uncorrelated for different wave components k,v .

( )J.C.N. Borge et al.rCoastal Engineering 37 1999 331–342 333

Under these conditions, the sea surface elevation h can be regarded as a linear,homogeneous and stationary, zero-mean stochastic process. The stochastic process

Ž .defined by Eq. 1 can usually be described by its three-dimensional power spectraldensity

UŽ3. 2 2F k ,v d k dvsE dZ k ,v dZ k ,v 2Ž . Ž . Ž . Ž .

Here, E is the expectation operator, and the upper index U indicates the complexconjugate.

Ocean waves are dispersive showing a strong dependence between k and v

Ž .LeBlond and Mysak, 1978 . For linear wave theory, the dispersion relation is given by

(vss k s gk tanh kd qkPU 3Ž . Ž . Ž .

where d is the water depth, k is the modulus of the wave number vector andŽ .Us U ,U is the surface current.x y

Ž .By integrating the three-dimensional spectrum 3 over the domain of positiveŽ . Ž .frequencies and considering the dispersion relation vss k 3 , different spectral sea

Ž .state descriptions can be derived Young et al., 1985 :Unambiguous wave number spectrum:

F Ž2. k s2 F Ž3. k ,v dvŽ . Ž .Hv)0

Frequency-direction spectrum:

dkŽ2. Ž2.E v ,u sF k v ,u kŽ . Ž .Ž .

dv

One-dimensional frequency spectrum:

pŽ2.S v s E v ,u duŽ . Ž .H

yp

Ž .The directional sea state parameters e.g., mean direction, angular spreading, etc. areŽ2. Ž . Ž .computed from the spectra E v, u and S v .

The measurement of sea states using nautical radars is based on the backscatter of theelectromagnetic waves by the ripples and the roughness of the sea surface caused by thelocal wind. Hence, the presence of wind blowing over the sea is necessary to obtainwave information from radar images. This pattern of backscattered electromagnetic

Žwaves is modulated by the larger sea-surface structures, such as the ocean waves Young.et al., 1985 . Fig. 1 gives an example of one radar image out of a time series taken at the

north coast of Spain. This installation covers an angular sector of 1808 that correspondsto the sea surface. The rest of the image covers land side and therefore, is not stored. Forplatform and ship-borne installations, WaMoS II can store the full 3608 image to accessinformation on all possible wave field propagation directions.


ŽFig. 1. Picture of a WaMoS II measurement taken at a land based station in northern Spain the coastline is. ŽWest–East oriented . The data acquisition system only covers the area related to the ocean surface right part.of the radar image . The white part of the image belongs to land areas where the radar does not transmit. The

radar station is located in the middle of the inner circle.

The image in Fig. 1, shows a swell-dominated wave system approaching the coastfrom the Northwest. In addition, wave refraction due to the variable bottom topographycan be observed in the areas closer to the coast. The white shadow in the upper part ofthe raw-data image is caused by a large rock.

To obtain wave field information in space and time, a sequence of consecutive radarimages is stored. From this sampled raw-data set, a sub image is selected both to reducethe amount of data and to prepare the time series for the three-dimensional Fourier

Ž .transformation to the spectral domain k,v . Fig. 2 gives an example of these temporalsequences of radar raw-data sub images. In the figure, the spatial structure of the wavefield and its time dependence is already visible. Therefrom, the three-dimensional image

Ž3.Ž .power spectrum I k,v is computed. There are three main contributions to the totalŽ3.Ž .spectral energy in the function I k,v :

Ž .1. Wave energy due to the modulation of the backscatter Young et al., 1985Ž .2. Background noise due to the roughness of the sea surface Seemann, 1997

Ž3. Higher harmonics of the wave energy due to radar imaging effects Nieto, 1997;.Seemann, 1997 .


Fig. 2. Time series of radar raw data.

It is necessary to filter out all the effects that do not belong directly to the wave field,Ž .such as the background noise and the higher harmonics. Taking into account Eq. 4 , the

Ž3.Ž .wave energy in the three-dimensional image spectrum I k,v must be located in thevicinity of the dispersion shell and can be separated from the other spectral contributionsŽ . Ž .Nieto, 1997; Seemann, 1997 . The wave energy distribution in the k,v space isstrongly dependent on the current U. Fig. 3 illustrates the effect of an existing surfacecurrent on the wave energy distribution. The example is a projection of a three-dimen-

Ž3.Ž . Ž .sional spectrum F k,v to the two-dimensional plane. The black line a indicates theŽ .dispersion relation without current, the grey line b shows how this curve is distorted

and the wave energy is shifted due to an existing surface current U.


Fig. 3. Two-dimensional example of the wave number-frequency dependence on the dispersion relation. TheŽ . Ž .black line a represents the dispersion relation without current, the grey line b shows the shift due to an

™existing surface current U. The current direction is aligned with the positive wave number.

The surface-current information is extracted via analysis of the wave energy distribu-tion in the three-dimensional image spectrum. This estimated current is needed for the

Ž .further computation of the wave spectrum Young et al., 1985 . Once the current isknown, a filter can be defined to separate the wave energy from the other contributions.

Ž .3I k ,v ; if vss kŽ . Ž .Ž3.F k ,v s 4Ž . Ž .½0 ; otherwise

Ž3.Ž .Knowing the three dimensional wave spectrum F k,v , the different spectral seastate descriptions can be derived by integrating over the spectral variables of expressionŽ . Ž .2 and considering the dispersion relation 3 . WaMoS II provides the two-dimensional

Ž2.Ž . Ž2.Ž .directional spectra F k and E v,u , and the corresponding frequency-dependentŽ . Ž . Ž . Ž . Ž . Žquantities S v frequency spectrum , u v mean direction and s v angular

.spreading . The quantities are shown in Table 1.Once the raw data are stored, the wave and current analysis is carried out in real-time.

Ž2.Ž .Fig. 4 gives as an example, a two-dimensional directional wave spectrum F k ascomputed by WaMoS II from the raw data shown in Fig. 1. The spectrum is slightlybi-modal and indicates Northwest as dominant incoming wave direction.

Ž . Ž .Fig. 5 gives the one-dimensional frequency spectrum S v , the mean direction u v

Ž .and the angular spreading s v as provided by the WaMoS II software from the samedata set as shown above.


Table 1Spectral sea state presentations of WaMoS II

In addition to the spectral estimations, the sea state parameters given in Table 2 areŽ3.Ž .derived directly from the three-dimensional wave spectrum F k,v . In order to

estimate the significant wave height H , a short calibration phase with an additionalSŽ .wave elevation sensor is needed Ziemer and Gunther, 1994 . The method is described¨

in the next section.As an example, Fig. 6 illustrates the temporal evolution of the spectral peak period

T , and the corresponding in-situ results derived from a moored buoy close-by. It can beP

seen that both T estimations show a similar behaviour in their temporal evolution.P

3. Estimation of significant wave height and comparisons with buoy data

The WaMoS II calculation of the significant wave height H for nautical radar dataSŽis based on similar methods as used in H estimation from SAR Alpers and Hassel-S

. Ž .mann, 1982 . After separating the wave signal from the background noise BGN , theŽ .so-called ‘Signal to Noise Ratio’ SNR can be used to determine the absolute wave

heights by a linear regression:

'H sAqB SNR 5Ž .S


™Ž2.Ž .Fig. 4. Two-dimensional wave spectrum F k measured with WaMoS II.

Ž . Ž . Ž .Fig. 5. The frequency spectrum S v a non-normalized representation , the mean direction u v and theŽ .angular spreading s v , provided as standard output of WaMoS II software.


Table 2Sea state parameters provided by WaMoS II

H Significant wave heightS

T Peak periodP

Tm Spectral mean period2

T 1st peak period of multi-modal spectrumP1

T 2nd peak period of multi-modal spectrumP2

l Peak wave lengthP

l 1st peak wave length of multi-modal spectrumP1

l 2nd peak wave length of multi-modal spectrumP2

MDIR Integrated mean directionSpr Integrated wave spreadingu Peak directionP

u 1st peak direction of multi-modal spectrumP1

u 2nd peak direction of multi-modal spectrumP2

u Surface current speedu Surface current directionu

where A and B are calibration constants depending on the spatial resolution of the usedŽ .radar Alpers and Hasselmann, 1982 . The SNR is determined by separating the

Ž Ž ..different spectral components using the dispersion relation Eq. 3 .

F Ž3. k ,v d2 kdvŽ .HVk ,vSNRs . 6Ž .

Ž3. 2F k ,v d kdvŽ .H bgnVk ,v

Ž3.Ž . Ž .where the function F k,v is the wave spectral estimation given by Eq. 4 and theŽ3. Ž . Ž .function F k,v expresses the power spectral density of the components k,vbgn

Ž . Ž .located outside the dispersion relation 3 Nieto, 1998 .

ŽFig. 6. Comparison of a time series of buoy and WaMoS II estimated peak periods T . Data: Statoil FPSO:P.Norne .


Fig. 7. Comparison of the significant wave height H between a directional wave rider and WaMoS II duringSŽ .the calibration phase. Data: Statoil FPSO: Norne .

Fig. 7 shows a comparison of buoy and WaMoS II estimated H time series. TheS

data were taken during the calibration phase at an offshore installation in the northernŽ .North Sea FPSO: Norne, STATOIL . The measuring interval for both devices was set

to 3 h, with a data storage time of a half an hour. The radar data sets were sampledevery 2 min, whereas the buoy delivered the data every 10 min. Both data sets were

ŽFig. 8. Scatter plot of the buoy and WaMoS II estimated H using a linear regression. Data: Statoil FPSO:S. Ž .Norne . The first fit fit 1 corresponds to the least square solution with minimization in the vertical axis

Ž . Ž . Žlower slope line , the second fit fit 2 is the result after minimization in the horizontal axis higher slope. Ž .line . The third fit fit 3, line between first and second fits results after averaging the coefficients A and B

Ž Ž ..see Eq. 5 obtained by the two previous fits.


brought to the same temporal scale by computation of 30 min average values. The buoydeployment was only temporary and the amount of corresponding data sets limited.Therefore, the comparison of the significant wave height and the computation of theregression coefficients A and B was done with the same measurements. The scatter plotin Fig. 8 indicates a good agreement between the two measuring techniques. Thecorresponding correlation coefficient is rs0.89.

4. Future activities

Up to the present, the data processing algorithms are well-approved for ‘deep waterconditions’, which are characterised by spatial homogeneity of the wave field. Inshallow water, wave refraction and varying bottom topography cause inhomogeneitieswhich appear in the analysed radar sub image.

In cooperation with the GKSS research centre, the inhomogeneities in wave fieldswill be investigated at a coastal installation on the German island of Heligoland. Firstapproaches to estimate the actual water depth and the local wind field are made.

A WaMoS II system which is currently mounted on a German coast guard vessel willbe used for ship borne calibration purposes.

5. Conclusions

The spatial sea state information is required to measure the directional surfacemotions of ocean waves. It is especially important to obtain information on multi-modalsea states which can be caused by complex meteorological situations. WaMoS II as amicrowave remote sensing instrument measures time series of sea surface images. It thusdelivers time series of the evolution of an oceanic area. The results describe the sea statein space and time.

The wave parameters determined by the navigation radar system are in goodagreement with the available ground truth data.

Acknowledgements

Ž .The authors thank STATOIL and RC Symek Norway for the provision of the data.

References

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