WIND-WAVE RELATIONSHIP FROM SEASAT RADAR

ALTIMETER DATA

P. C. PANDEY, R. M. GAIROLA, and B. S. GOHIL

Space Applications Centre, Ahmedabad-3800S3. India

(Received in final form 13 June, 1986)

Abstract. We present a nonlinear relationship between ocean surface wind at 10 m height (U,,) and significant wave height of wind-generated gravity waves, (H,,,)gw, over the open oceans using SEASAT radar altimeter data. The data represent a variety of fetches, durations and strength of winds. Concurrent measurement of significant wave height, (H,,& which may contain a measure of swell and U,, obtained from the processed geophysical data record (GDR) of the SEASAT radar altimeter were used in the analysis. The total wave energy, &, characterised by altimeter H,,3 measurements was compared with the energy of a fully developed sea, E’,, derived from U,, measurements using the Pierson-Moskowitz model. The criteria ,!&, I E,,, was used in data selection to minimise the influence of swell. (H,,,)gw thus obtained was used in a regression in terms of U,, in a second-degree polynomial. Verification with independent radar altimeter data confirmed the validity of the proposed wind-wave model, which could be used for operational wave forecasting.

1. Introduction

The SEASAT satellite, launched on June 28, 1978, carried onboard, among other active and passive microwave sensors, a radar altimeter at 13.5 GHz. The instrument operated successfully and returned excellent quality of data for about three months, after which the satellite failed on October 10, 1978 due to the power problem in the spacecraft. The radar altimeter was intended to provide global monitoring of wind speed, significant wave height and ocean geoid along the sub-satellite track from which other oceano- graphic parameters like swell height etc., could be extracted. Hljs was retrieved from the analysis of the shape of the return pulse while wind speed was obtained from the normalized back-scattering coefficient; measurements were made over a resolution cell of 12 km. The first global fields of wind and significant wave height were reported by Chelton et al. (1981), which revealed previously unknown features of a narrow jet of winds in the eastern tropical pacific. Pandey (1983) compared the global wind fields obtained from altimeter, scatterometer and scanning multichannel microwave radiome- ter and observed the zonal banding of the wind fields. Mognard et al. (1984) extracted the significant swell height from simultaneous altimeter data of H,,, and U,, using the Pierson and Moskowitz (1964) spectrum for fully developed seas and obtained mean monthly maps of waves, wind and swells. Their study clearly demonstrated the

. . contnbutlon of swell to H,,, . We are not aware of any study seeking to 6nd a relationship between ocean surface wind speed and Hlls of wind-generated gravity waves, using satellite data, the subject of the present paper. However, Thiruvengadathan (1984) has obtained a nonlinear relation between significant wave height and wind speed based on in situ observations over the Arabian sea and Bay of Bengal. We have compared the

Boundary-Layer Meteorology 37 (1986) 263-269. 0 1986 by D. Reidel Publishing Company.

264 P. C. PANDEY ET AL.

results of our proposed wind-wave model with that of Thiruvengadathan (1984) and the Pierson-Moskowitz model.

2. Data Analysis

We have analysed SEASAT altimeter data for the period June 27-30, and July 1-3, 1978 over the latitude region of 35” S and 20” N and longitude region 55” to 95” E excluding the data over the land areas. This is a region of minimum swell height (Mognard et al., 1984).

Concurrent measurements of H1,3 and U,, were obtained from Geophysical Data Record tapes created by the Jet Propulsion Laboratory. These geophysical variables were validated during the Gulf of Alaska Experiment (GOASEX, Tapley et al., 1979) and during the Joint Air-Sea Interaction experiment (JASIN, Webb, 1978). An r.m.s. deviation of 0.29 m over a range of 0.5 to 5 m H,,3 were obtained and an r.m.s. deviation of1.6ms-‘inwindspeedovertherangeof1tolOms~’.

The total amount of energy contained in the wave field can be estimated from the significant wave height Hli3 using the Longuet-Higgins (1952) relation

E = O.O625(H,,,)‘. (1)

Thus the Ealt contained in the wave field characterised by the (H,,&, altimetric measurements can be compared with the energy of the fully developed sea Efd. If the Ealt is higher than Efd, we assume the residual energy comes from the presence of swell. Neglecting the nonlinear interaction between wind waves and swell, the following relation can be written:

Ea,t = Ef, + Es . (2)

The energy of a fully developed sea is obtained using the Pierson and Moskowitz (1984) relation

S(o) = [crg*/o’] exp-(B’“‘““)“),

where S = frequency spectrum,

; = 8.1 x 10-3, = 0.73,

(3)

(a and b are empirically adjusted constants) w = frequency 00 = dU19.5 g = acceleration due to gravity u 19.5 = wind speed (m SK’) at 19.5 m height.

A fully developed sea characterised by (H,,,)f,, and a relation between (HI,,), and U,, can be deduced from Equation (3) (Mognard, 1984).

Vf,/,)fd = o.o22u:9.~.

WIND-WAVE RELATIONSHIP FROM SEASAT RADAR ALTIMETER DATA 265

The wind speed U19.5 measured by ship can be related to the altimeter wind speed U,, using a logarithmic model to describe the boundary layer and is given by

u ,9.5 = 1.08U,0. (5)

Equation (4) can be written in terms of the satellite altimeter-derived wind speed U,, as

W,3)fd = 0.WW2~ (6)

With the same concept as that of Ealt, the wave energy for a fully developed sea in terms of (HI,& is given by

E,, = O.O625(H,,&.

We thus have the criterion E,,, I Efd, to mmimise the effect of swell, in modeling wind-wave relationships. Parson (1979) has developed a technique which utilises only significant wave height (SWH) and wind speed measurements available from radar altimeter data to locate the swell dominated regions of the Earth’s oceans. The parameter defined by (Parson, 1979)

l- = 13844(SW~/U$,), (8)

decides the boundary of swell no-swell regions and although non-unique, it does depict the region of swell domination, for values of F > 50, which has been verified using GEOS data. We have used the above parameter to ensure minimum swell contribution in our data. The following nonlinear relation between wind and wind-generated gravity- waves was obtained:

(HI,& = 0.051-O.O15U,, + O.O23Uf,,

r.m.s. error = 0.28 m.

(9)

The constant term in Equation (9) is possibly due to errors in Ealt, inadequacies in the Pierson-Moskowitz (PM) spectrum for fully developed seas and/or errors in the determination of wind speed from backscatter, and the residual swell present in the data used for analysis. This wind-wave model differs from the relationship obtained using the assumption of the PM spectrum for a fully developed sea (Equation (7)), suggesting an unbiased relation.

3. Results and Verification of the Wind-Wave Relation

Equation (9) shows that the contribution to (Hl,s)p is dominated by the UT, term in the above relation; a small residual bias is due to the combined effect of any residual swell and bias in H,,3 and U,,, derived from the radar altimeter. Figure 1 gives a plot of U,, versus (H,,&,+, which shows a nonlinear behaviour. A careful examination of Figure 1 reveals a threshold value of wind speed 7 m s - ’ below which the relationship is nonlinear and above which there is an approximate linear relationship. This has been drawn separately in Figures 2 and 3, respectively, together with the regression equations

266 P. C. PANDEY ET AL.

7.10

3 0

g 5.60 - DATA POINTS = 1295

I (H 1/3)gw=~051--015U,o+~023U,02 r ms error = 0.28

5 4.20 -

iii I

2.80

0.00 3.60 7.20 10.80 14.40 1840

Fig. 1.

WIND SPEED, IlID (m I Set )

Relationship between ocean surface wind (U,,) and significant wave height of wind generated gravity waves (H,,S)g*I.

1.5 1.5 - - NO. OF DATA POINTS= 76 NO. OF DATA POINTS= 76

( ( H H 1/3)gw 1/3)gw = = 0.2 0.2 28 28 - - 0.073 0.073 u u 1.2 1.2

10 10 l l O-0 O-0 26U,02 26U,02 - -

RM S ERROR= 0.12m RM S ERROR= 0.12m . .

-I

s oo~“l’““‘“‘““‘“’

0.0 l-4 2.8 b-2 5.6 7.0 WIND SPEED,Ulo (m/Set)

Fig. 2. Wind-wave relationship for wind speeds less than 7 m s - ‘.

WIND-WAVE RELATIONSHIP FROM SEASAT RADAR ALTIMETER DATA 261

7.5 NO OF DATA POINTS = 1219

( 6-O -

Hi/3 )gw =- 2.125 + O-43 UlD

RIdSERROR= 0.30 m

6.4 6'4 104 13-2 156 18.0 WIND SPEED UlD (m/Set)

Fig. 3. Wind-wave relationship for wind speeds greater than 7 m s - I.

between (II!& and wind speed. The linear behaviour of Ur, versus (Hr,&, is supported by the observations of Mukherjee and Sivaramakrishnan (198 1) for a tropical cyclone and depression field in the Arabian Sea, suggesting a mechanism of linear transfer of kinetic energy into wave energy. This implies that after initial disturbance of the sea, the wave and wind fields are quickly in resonance. However, it appears that at lower wind speeds (U,, < 7 m s- ‘), other factors such as weak wave-wave interactions, viscous dissipation and thermal stratification changing the surface drag coefficient, are contri- buting to the process of energy transfer from wind to waves, making the system nonlinear.

An independent experimental verification of Equation (9) was undertaken using altimeter data other than those used in deriving Equation (9). The plot between predicted (fi1,3)W and observed (Hr,&,, is depicted in Figure 4 for a limited data set (35 points) confirming the validity of our results. An r.m.s. difference of 0.5 m was obtained.

A comparison of Equation (9) has been made with the following relations in Equations (12) and (11) obtained by the Thiruvengadathan (1984) and Pierson- -Moskowitz (1964) models, respectively.

(HI,&,,, = 0.051-O.O15U,, + O.O23U:, , (10)

wl,dm = O.O25U:, , (11) (IT,&,+ = 0.17 + O.O087U,, + O.O14167U;, . (12)

268 P. ‘2. PANDEY ET AL.

5’4 0

4.32

3 cn

s 3.24

i-2 5 2.16

2 a a 1.08

o.ooL ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ ’ * ’ ’ 000 108 2.16 3.24 4.32 5.40

OBSERVED (H l/3) Fig. 4. Relationship between predicted significant wave height of wind generated gravity waves (fi,,,),,

obtained using the regression relation (9) and that observed using radar altimeter data.

- NO. OF DATA POINTS ~35 .

(h3)gw z-004+ 0.97 (H 1/3)gw

- RMS ERROR-0.5m

11. 00

10.00

T 8.00 Y

= 6.00 0 - w = 4.00

w > 2 2.00

0. 00

-.- PANDEV et. al. MOOEL

--- THIRUVENGADATHAN

0.00 4.00 8.00 12-00 16.00 2CMO 24JIO 2840

WIND SPEED (m I set 1

Fig. 5. Comparison between predictions obtained by the present wind-wave model and that obtained from the Pierson and Moskowitz (1964) and Thiruvegadathan (1984) models based on in situ observations.

WIND-WAVE RELATIONSHIP FROM SEASAT RADAR ALTIMETER DATA 269

The results are plotted in Figure 5. All three curves diverge at higher wind speeds, which is not surprising since the altimeter-derived relationship was spatially averaged over the altimeter footprint, whereas the latter was a point measurement. For lower wind speed, all three curves show reasonable agreement.

4. Conclusions and Future Research

A nonlinear relation between wind speed and wind generated waves has been establish- ed using SEASAT radar altimeter data. The model could be used operationally for wave forecasting, based on available wind speed data, from any other satellite. Due to sampling restrictions of altimeter data, the coupling of several satellites would be desirable. The proposed European Remote Sensing Satellite, ERS-1, scheduled for launch in 1989, will carry an active Microwave instrument package, including a 5.3 GHz sensor. This would provide a unique opportunity to verify/fine-tune the proposed wind-wave model. Theoretical models (e.g., Hassehnan, 1963) could be tested against the observational models.

Acknowledgements

We thank Dr T. A. Hariharan, Chief Scientist for his encouragement and support. Dr P. S. Desai and Dr M. S. Narayanan are gratefully acknowledged for reviewing the manuscript and providing valuable suggestions.

References

Chelton, R. E., Hussey K. J., and Parke M. E.: 1981, ‘Global Satellite Measurements ofWater Vapour, Wind Speed, and Wave Height’, Nature 294, 529-532.

Hasselmann, K.: 1963, ‘On the Nonlinear Energy Transfer in the Gravity Wave Spectrum; Part 3: Evaluation of Energy Flux ad Swell Sea Interaction for Neumann Spectrum’, J. Fluid Mech. 15, 385-398.

Longuet-Higgins, M.: 1952, ‘On the Statistical Distribution of the Heights of the Sea Waves’, J. Mar. Res. 11, 245-266.

Mognard, N. M., Campbell, W. J., and Bossiey, C.: 1984, ‘World Ocean Mean Monthly Waves, Swell and Surface Winds for July through October 1978 from Radar Altimeter Data’, Marine Geodesy 8, 159-181.

Mukherjee, A. K. and Shivaramakrishnan, T. R.: 1981, ‘A Relationship between Wind Speed and Wave Height in Cyclone and Depression Field in Arabian Sea’, Mawam 32, 371-374.

Pandey, P. C.: 1983, ‘Linear Retrieval and Global Measurements of Wind Speed from the Seasat SMMR’, Publ. No. 83-5, Jet Propulsion Laboratory, CA, pp. 26.

Parson, C. L.: 1979, ‘On the Remote Detection of Swell by Satellite Altimeter’, Mon. Weather Rev. 101, 1210-1218.

Pierson, W. J., and Moskowitz, L.: 1964, ‘A Proposed Spectral Form for Fully Developed Wind Sea Based on the Similarity Theory of A. Kitaigodskii’, J. Geophys. Res. 69, 5181-5190.

Tapley, B. D. and Barn, G. H. et al.: 1979, ‘Seasat Altimeter Calibration, Initial Results’, Science 2C4-1410-1412.

Thiruvengadathan, A.: 1984, ‘Waves in the Arabian Sea and Bay of Bengal During the Monsoon Season’, Mausam 35, 103-106.

Webb, D. J.: 1981, ‘A Comparison of Seasat-l Altimeter Measurements Made by a Pitch Roll Buoy’, J. Geophys. Res. 86, 6394-6398.