On the estimation of oceanic wind speed and stress from ambient noise measurements

Deep-Sea Research. Vol ~5. pp ~225 to 1233 ( ( Pergamon Press Ltd lt)v~ Printed in Great Britain

0011-74Vl vS 1201-122"3':,(t~tt0 I)

INSTRUMENTS A N D METHODS On the estimation of oceanic wind speed and stress from ambient noise measurements* P. T.

SHAW,tD. RANDOLPH WATTS+ and H. THOMAS ROSSBY~

(Received 17 October 1 9 7 7 ; i n revised /brm 12 July 1978;accepted 15 July

1978)

A simple method of measuring wind speeds over the oceans by monitoring ambient acoustical noise in the water is demonstrated. Ambient noise in our measurement band (5 kHz) is predominantly wind-generated. The accuracy in this test is + 5 knots (+_2.5 m s 1) at wind speeds greater than 5 knots. A sample calculation of wind stress illustrates how this method can be used to improve greatly our knowledge of the wind stress distribution over the world oceans. Abstract

INTRODUCTION

KNOWLEDGE of wind stress is of central importance in studies of the response of the ocean to atmospheric forcing, such as the generation of surface waves and drift currents, deepening of the wind-mixed layer (POLLARD, RHINES and THOMPSON, 1973), eddy motion (PmLLIPS, 1966), and the wind-driven circulation. Estimation of wind stress over the ocean requires detailed measurement of the structure of the wind field close to the surface, Although several methods for this have been described by ROLL (1965), most estimates for wind-driven circulation models, for example, are made from climatological wind information. The wind stress is a quadratic function of the wind speed, and it is considerably underestimated by calculating the square of the mean wind speed. In a comprehensive study of the global distribution of wind stress, HELLERMAN (1967) compiled m o n t h l y and annual mean wind stress tables from the frequency distributions of wind speeds and directions instead of the average wind velocity. In a recent c o m p u t a t i o n of wind stress from weather reports of ships in the N o r t h Atlantic Ocean, BUNKER and WORTHINGTON (1976) got a higher average than that of Hellerman by c o m p u t i n g the vector average of wind stress from individual shipboard wind velocity records. Even so, these results m a y be 'fair weather biased' because ships avoid areas of high wind. In this note we investigate a novel method of monitoring the surface winds over the oceans. It has been k n o w n for some time that a high correlation exists between wind speed and the acoustic noise level in the ocean. The well-known Knudsen spectra of noise (KNUDSEN, ALFORD and EMLING, 1948) have sea state or wind force as a parameter, although later data indicate better correlation with the wind speed than with sea state (PERRONE, 1969). A n u m b e r of papers in the acoustic literature d o c u m e n t the dependence of ambient noise upon the wind speed [-see, for example, WENZ (1962), FRISCH (1966), and PERRONE (1976)], but there is little information on the physical processes of noise generation. * MODE contribution No. 97. t Present address: Department of Meteorology, Massachusetts Institute of Technology. ~3Graduate School of Oceanography, University of Rhode Island, Kingston, R102881. U.S.A. 1225

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P.T. SHAW,D. RANDOLPHWATTSand H. THOMASROSSBY

Empirically a simple linear relationship between the logarithm of the wind speed and the noise spectrum level (NSL)* was reported by PIGGOTT (1964) for shallow water ( ~ 4 0 m ) and extended to deep water (5000m) by CROUCH and BURT (1972). These studies have concentrated u p o n noise frequencies below 3 kHz. However, WENZ (1962) showed that the wind dependence of noise levels in the range 1 to 10 k H z is similar. SHAW, WATTS and ROSSBY (1977), reviewed this literature. Here we consider the hypothesis that ambient noise measurements can be used for making unbiased estimates of surface wind speed and stress in open ocean areas (ROSSBY, 1973). To do this, ambient noise data were obtained at a depth of 5000 m at a frequency of 5 kHz. Advantages for this choice of frequency are that the surface wind is the primary noise source with local and distant shipping noise virtually absent, and contributing sources should be localized within about 10 km of the measurement site.+ Furthermore, we suggest that the noise generation m a y be most directly related to the wind stress itself. However, the resolution of such a question demands a clear understanding of the physics of noise generation as well as further observational evidence than was available in the experiment reported here. Instead, we use the traditional quadratic drag law in a later section to illustrate the potential of this method. THE NO[SE AND WIND DATA ANALYSIS

The ambient acoustic noise at 5 k H z was an auxiliary measurement made on Inverted Echo Sounders (IES) during the Mid-Ocean Dynamics Experiment ( M O D E - I ) in the western N o r t h Atlantic Ocean. The IES is a b o t t o m - m o u n t e d instrument primarily designed to measure the travel time of an acoustic signal from the ocean b o t t o m to the surface and back (WATTSand ROSSBY,1977). Each instrument was also equipped with a separate 5-kHz transducer to m o n i t o r the ambient noise to provide an indication of the sea state and thus check on the quality of the surface echo. Simultaneous records were obtained at three sites (A, B, C) in March and April, 1973, and at four sites (D, E, G, H) in M a y and June, 1973 (Fig. 1 ). Figure 2 shows a block diagram of the noise measurement circuitry, Noise signals received by the h y d r o p h o n e were amplified, filtered, passed through a logarithmic peak detector and digitally recorded every 4min. The frequency response of the system is a band centered at 5 k H z with a width of ~ 1.4 kHz. Measurement and instrumental details were documented by S H A W , WATTS and ROSSBY (1977). This paper deals with hourly noise spectrum levels c o m p u t e d from the hourly mean noise r.m.s, pressure. + The primary source of information regarding the wind in the M O D E area consists of meteorological observations a b o a r d the R.V. Reseclrcher.§ Although the wind records themselves are of g o o d quality, the m o v e m e n t of the ship about the entire M O D E area (a 200-km radius circle) allows the observed wind speeds to differ from that observed within 10 km of the IES sites. However, this is the best information available of the local weather conditions during M O D E . The records at the three sites. A, B, and C, 100 to 2 0 0 k m apart, all have a close * The noise spectrum level is defined as the amount of energy in dB units relative to 1 ~tPa within a pass band 1 Hz wide. t Sound absorption alone in 10 km at this frequency is about 4 dB. ~The r.m.s, noise pressure is related to the noise speclrum level by {p2)12 = 10NS~-', § Originally at the MODE central mooring a wind recorder was present on a surface mooring; however, thai surface buoy was unfortunately lost.

Estimation of oceanic wind speed and stress from ambient noise measurements

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Fig. 1. The position of ambient noise measurement sites A, B, and C are indicated on a surface pressure chart (pressures in millibars), at the time of the passage of a cold front.

DIGITAL

RECORDER Fig. 2. The ambient noise measurement system. The signal from a hydrophone in the frequency band 5_+0.TkHz is amplified, passed through a logarithmic converter (Sea Data Corp., Model DC-35), from which the voltage is digitized for recording on magnetic tape. resemblance to the pattern of the R.V. Researcher wind speeds (Fig. 3). For example, the buildup to high winds near March 26 has the corresponding shape in all records. During that time the weather log of R.V. Researcher and the surface pressure charts show the passage of squall lines with wind gusts from 30 to 40 knots. Figure 1 shows the cold front corresponding to the conspicuous peak on 27 March. It is possible that the peaks of high noise were partly caused by rain. In our data the contribution of rain to the total noise cannot be determined. However, as heavy precipitation occurs only in a small fraction of the weather records, its effect is insignificant to the long-term wind stress and speed estimates. In the second set of experiments (series D, E, G, and H; May and June, 1973), by contrast, virtually no fronts or storms moved through the area. The winds were generally lighter and less well organized and indeed the resemblance between records is not so striking as above. In the March and April set of measurements (A, B, C) the wind field was characterized by the repeated passage of weather fronts through the M O D E area, advancing toward the southeast. The surface winds and the associated ambient noise generated from them were organized along the fronts, but localized across the fronts. They arrive at different 1ES sites at a rather well-defined lag time (consistent with their position) relative to the propagation of the fronts. Our analysis procedures were chosen to deal with the inadequacies of the mobile wind observations, which ideally should be directly over each IES. The error caused by the separation of the sites of noise measurements and wind

1228

P.T. SHAW, D. RANDOLPH WATTS and H. THOMAS ROSSBY

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speed observations was partially eliminated by shifting the time axes by the time lag of m a x i m u m correlation to calculate the linear regression of wind and noise for each site that showed significant correlation. Time correlation functions among series A, B, and C are plotted in Fig. 4. For all three series a high correlation coefficient and a sharp peaked maximum exist because of the propagation of the weather fronts. The correlation decreases to zero at a lag of around 30 h. The mean velocity of the atmospheric disturbances can be estimated from the lag time to be 3 0 k m h 1 southeastward, in good agreement with surface weather maps for that period. The linear least squares fit between the noise level (NSL) in dB re 1 pPa, according to each IES, and wind speed (V) in knots (1 knot = 0 . 5 2 m s - ' ) , as observed by the R.V. Researcher, can be expressed as 20log V = 1.01NSL - 30.4.

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A comparison between wind speeds observed by R.V. Researcher and those computed from the noise measurements at site A illustrates that this method can be used to estimate wind speeds within -t-5 knots for wind speeds greater than 5 knots (Fig. 5). Converting the seven noise time series into wind records via equation (1). we find that

1230

P.T. SHAW.D. RANDOLPHWATTSand H. THOMASROSSBY

the power spectra show a smooth decrease in energy density with increasing frequency, falling off roughly as f-1.,~ t o f 1.6 for periods between 2 and 100h. BYSHEV and ]VANOV (1969) inferred a similar wind speed spectrum in this frequency range from ship observations. We remark that several factors may influence slightly the ambient noise level at different locations for a given wind speed: sound refraction and ray paths, which are governed by the thermal structure, determine the size of the surface area contributing : the bottom depth determines the amount of attenuation; also, bottom reflectivity and roughness can affect the overall gain, but not necessarily the proportionality factor.

W I N D STRESS E S T I M A T I O N FROM A M B I E N T N O IS E M E A S U R E M E N T S

Surface wind speeds derived from the noise spectrum levels can be used to calculate the wind stress using a quadratic resistance law [see, for example, ROLL (1965)]: = pCDIVIV, relating the stress vector z (dyne cm 2) to the wind velocity* V (cm s 1) and the density of air p (gm cm 3) via a drag coefficient C D. The drag coefficient is subject to the same uncertainties here as elsewhere (~50°;;), with dependence upon the surface roughness and the air stability [see, for example, KRAUS (1972), SETHURAMAN and RAYNOR (1975), DUNCKEL, HASSE, KRUGERMEYER, SCHRIEVER and WUCKNITZ (1974) and Hsu (1974)]. We have used a constant value of C o = 1.5 x 10 3 with p - 1.2 x 10 3 g m c m 3. In this study the wind direction information was obtained from the records of the R.V. Researcher; in general, ship's data would not be available. Fortunately, wind direction has a larger time constant than speed and can be obtained either from surface pressure charts, with a small ageostrophic correction (WILLETT and SANDERS, 1959), or it can be estimated from satellite photographs by tracking cumulus cloud movements and adding a correction angle to estimate the surface wind direction (HASLER, SCHENK and SKII,LMAN. 1976). The April and June mean wind stress vectors [east, north) have been calculated from the vector average of hourly wind stress values to be ( - 0 . 6 9 , -0.491 and ( - 0 . 6 5 , 0.041 dyne cm-2, respectively. It may be misleading to compare these values with HELLERMAN'S (1967), which are reported seasonally on 5 ~ squares from probability distributions of wind speed for many years' data. Our wdues are over twice as large as his, however. This section is intended only to be illustrative of the method, not to be conclusive regarding wind stress magnitudes. Because of inadequacies in the present data base the uncertainty in the wind stress is a factor of two. Future experiments will refine this. The point is that distinct advantages can be realized from the continuous recording capability: if the relationship between IV[ or especially It[ and the noise level is accurately specified, then unbiased statistics of the wind field can be found. A P P L I C A T I O N REMARKS

Our knowledge of the wind stress distribution in space and time over the world oceans needs to be improved greatly. This includes remote areas where coverage is poor, high latitude regions where observations are likely to be fair-weather biased, and regions where temporal variability is of interest such as in monsoonal regions or in eddy-generation *At the 10-m or deck level.

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Estimation of oceanic wind speed and stress from ambient noise measurements

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studies. Historically, meteorological coverage has been difficult to obtain because of the high cost of surface platforms. The inherently low cost of this acoustic technique would allow one to obtain accurate synoptic windstress coverage. Arrays of acoustical windstress measurements together with ocean current observations could be used to develop a better understanding of the ocean response to wind forcing. Throughout this note we have used the empirical relationship that the noise is a measure of wind speed. However, intuitively it seems likely that the noise generation is more directly related to the wind stress being applied to the sea surface. It is worth noting that the acoustics literature remains vague regarding the physical processes of ambient noise generation. Experimentally, the noise level correlates with wind speed better than with wave height (PERRONE, 1969). The reviews by W•yz (1962, 1971) mention such sources as turbulent pressure fluctuations in the air and excitement of near-surface bubble oscillations by ~surface agitation' by the wind. K u o (1968) showed that capillary patches on the surface could generate the ambient noise. In all cases we suggest that the wind stress is the best measure of the interaction between wind and sea. Unfortunately, we know of no way to test this hypothesis without simultaneously measuring separately and independently the wind speed and the wind stress during different sea states and varying air stratification, when the drag coefficient should vary. Precipitation is known to generate high levels of noise in the ocean (HEINDSMAN, SMITH and ARNESON, 1955). Although little is known about the quantitative relationship between noise and either rate of precipitation or drop size and impact velocity, it is known that in the 1- to 10-kHz range the spectrum is nearly 'white' (FRANZ, 1959) and distinguishable

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P.T. SHAW,D. RANDOLPH WATTS and H. THOMAS ROSSBY

from the 'red' spectral component due to the wind by monitoring the ambient noise level at two or more frequencies. SUMMARY

We have inverted a much-studied acoustical problem in the ocean, that of estimating ambient noise levels from wind measurements, to demonstrate the feasibility of calculating wind speed records from time series of ambient noise measurements. This deep water study in the western North Atlantic was conducted at a higher frequency (5 kHz) than past acoustic studies, with the advantage that the noise generation is almost entirely attributable to the wind (in the absence of precipitation) with no evidence of contamination by shipping, either local or distant. We determined empirically a linear relationship between the log of the wind speed and the noise spectrum level [equation (1)], with errors less than 5 knots in the range 5 to 25 knots, in agreement with PIGGOTT (1964). This relationship should extend to higher noise levels and wind speeds. By comparing and cross-correlating the derived wind records at three different measurement sites we have demonstrated that the method can be used to track the movement of weather fronts through the area. Vector-averaged wind stress estimates, determined using wind direction observations from R.V. Researcher, were generally higher than those in the literature for this location and time period. In future experiments, the wind directions would have to be estimated from either surface pressure charts or satellite photographs of cloud motion. We foresee the following advantages to this method of recording wind stress: (1) the average wind stress can be calculated in the proper way from the squared wind speed instead of approximating it from the squared mean wind speed : and (2) it is not fair-weather biased. The relationship between ambient noise and wind stress may even be more direct, as discussed above, but that remains for further experimental investigation. Acknowledgements The authors would like to acknowledge the engineering development of the ambient noise electronics by Mr. WINFIELD HILL (Sea Data Corporation). This research was supported by NSF grant GX 30416 to Yale University and by O N R contract N00014-76-C-0226 to the University of Rhode Island.

REFERENCES

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Hsu S. A. (1974) On the log-linear wind profile and the relationship between shear stress and stability characteristics over the sea (research notes). Boundary-Layer Meteorolo~ty, 6, 509 514. KNUDSEN V. 0., R. S. ALFORD and J. W. EMLING (1948) Underwater ambient noise. Journal q/Marine Research. 7, 410-429. KRAUS E. B. (1972) A tmosphere ocean interaction. Clarendon Press, p. 153. K u o E. (1968) Deep-sea noise due to surface motion. Journal o/ the Acoustical Society ~!t 4merica, 43. 1017 1024. P~RrONE A. J. (19691 Deep-ocean ambient noise spectra in the northwest Atlantic..l¢mrJlal ~>/the Ae~mstical Society of America, 46, 762 770. PERRONI¢ A. J. (1976) Summary of a one-year ambient noise measurement program off Bermuda. Nawll Underwater Systems Center, New London, Laboratory Technical Report 4979, 46 pp. (Unpublished document.) PIIILLIPS N. (1966) Large-scale eddy motion in the western Atlantic. ,lour,al ~)1 Geophysical Research, 71. 3883 3891. PI(;CIOTT C. L. 11964) Ambient sea noise at low frequencies in shallow water of the Seotian Shell. J~mrtlal o/the Acoustical Society ol America, 36, 2152 2163. l:'ol LARD R. T., P. B. RHI~qES and R. O. R. Y. TllOMPSON (1973) The deepening of the wind-mixed layer. Geophysical Fluid Dymmffes, 4, 381 404. Rol 1, H. U. (1965) Physics ql'the marine atmo,~phere. Academic Press, pp. 8 41. RossRY H. T. (1973) Inverted echo sounder: a description and some results from MODE-1..~,IODE ttot I,me News, 41, October 12, 1973. (Unpublished document.) SEI HURAMAN S. and G. S. RAYNOR (1975) Surface drag coefficient dependence on the aerodynamic roughness of the sea. Journal ~>lGeophysical Research, 80, 4983 4988. SHAW P. T,, D. R. WATTS and H. T. ROSSBY (1977) Oceanic wind speed and wind stress estimation from ambient noise measurements. Technical Report No. 77-2, Graduate School of Oceanography. University of Rhode Island, 69 pp. (Unpublished document.) WA rIs D. R. and H. T. ROSSBY (1977) Measuring dynamic heights with ln,,erted Echo Sounders: resuhs from MODE. Journal o/Physical Oceanography, 7, 345 358. WtNZ G. M. (1962) Acoustic ambient noise in the ocean: spectra and sources. Journal ~!1the Acoustical Society ~?lAmerica, 34, 1936 1956. WINZ G. M. (1971) Review of underwater acoustics research: noise. ,lom'~al ~![the Acoustical Society q! America, 51.1010 1(/24. WIH;ETT H. C. and F. SANI)ERS (1959) Descriptil,e meteorolo{ty. Academic Press, p. 118fl'.