THE CHARACTER OF SHORT-PERIOD INTERNAL WAVE ERS SAR SIGNATURES AT VERY LOW WIND SPEEDS.

Abstract

Results of an analysis of a set of ERS-1 SAR images are presented, demonstrating the existence of three different types of IW signatures and their characteristics. Short-period oceanic Internal Waves are commonly observed in Synthetic Aperture Radar (SAR) images as systems of quasi-periodic parallel bands, typically bright and dark bands on a grey background, and sometimes simply as dark bands. Another type of signature, which has received very little attention in the literature, will be discussed in this paper. This is when internal waves appear as bright bands in a very low (dark) SAR background level. The circumstances under which the mentioned three character types of radar signatures are observed is analysed. A mechanism is proposed to explain the occurrence of single positive sign IW signatures at very low wind speeds (V < 2 m/s).

Keywords: internal waves, SAR, internal wave / surface wave interaction

1. Introduction

Oceanic internal waves (IW) are commonly observed in Synthetic Aperture Radar (SAR) images as systems of quasi-periodic parallel bands [Ref. 1-4]. These are frequently discussed in the literature as bright and dark bands on a grey background [Ref. 2, 4]. On some occasions, however, they are seen as dark bands, the expected bright bands being either absent or strongly attenuated. Additionally, there is another type of signature which has received very little attention in the literature. This is when internal waves appear as bright bands in a very low (dark) SAR background level.

Radar signatures of IWs result from the modulation of wind generated surface waves by the surface currents associated with the IWs, which produce horizontal convergence and divergence. The change in roughness can be caused by straining of the surface waves in the gradients of the surface velocity field and/or by wave damping due to films when periodically compacted and expanded in the internal wave field. The imaging of IWs by L-band SAR in the form of bright/dark bands was discussed by Alpers (1985), who suggested that the signatures could be satisfactorily explained by the hydrodynamic modulation theory. It was also assumed that the dark SAR signatures of IWs are observed primarily in coastal waters and related to surfactant films on the sea surface. The role of a contaminating surface film of organic composition in the action of oceanic internal waves on surface waves has been discussed since the 1950s (see e.g. [Ref 5]). Under light winds, such surface active materials (surfactants) can inhibit the formation of ripples and damp those already formed, causing visible differences in the short scale roughness of the water. Quantitatively the film effect on modulation of short surface waves by IWs was analysed by Ermakov and Pelinovsky (1984), and Ermakov et al., (1992), who also presented experimental evidence of the film mechanism.

Here we present an analysis of a set of ERS-1 SAR images (C-band radar), demonstrating the existence of three different types of IW signatures and their characteristics. In particular, we discuss the circumstances under which single positive IW radar signatures are observed. The analysis is applied to SAR images of IWs occurring in the North East Atlantic on the Portuguese continental shelf (fig.1). The Iberian margin is a good example of an area where short-scale nonlinear internal waves, commonly termed solitons in the literature [Ref. 8], propagate in groups or packets. A packet of solitons appears to originate from near the shelf-break almost every tidal cycle during the summer.

The analysis of satellite data is supported by the results of a detailed programme of in situ measurements on the Iberian shelf near 41° N in August 1994. These measurements provided valuable information about the internal waves in the region and their surface manifestations, including the distribution of surface films within the internal wave field [Ref. 8].

2. The Character of Internal Wave signatures on ERS-1 SAR images.

Since ERS-1 was launched in 1991, we have studied over 60 images from its C-band SAR, which confirm the ubiquity of internal waves propagating towards the Portuguese coast across the continental shelf. They are imaged in a wide variety of wind conditions from April to September over several years, but no internal wave signatures have been found during the winter months. This is presumably because only the development of thermal stratification during spring and summer creates suitable conditions for the propagation of internal waves.

Figure 1: Example of Internal Wave signatures at very low wind speeds. Note the vast region of very low (dark) backscatter. This image was acquired by ERS-1 on 19 August 1994 (Orbit 16185, Frame 819).

Typically IWs show up as bright and dark bands as compared to the unmodulated background clutter and we refer to this signature as being of double sign (+/-). On some occasions the dark bands are wider and much more intense then the accompanying bright bands, which may even be absent from the imagery. We refer to such signatures as a single negative sign (-). Another type of signature, although more rare, is when the SAR backscatter is very low and the IWs appear as bright bands in a homogeneously dark background (see figure 1). This signature we describe as a single positive sign (+) and is the focus in this work.

We define IW signature, d I/I₀, as:

where I is the intensity of the IW profile taken in the direction of the IW propagation and I₀ is the intensity of the image background. The background is taken from a homogeneous area in the image away from the IW field, and is a square of side 2.5 km (200x200 original pixels of size 12.5x12.5 m). To obtain a meaningful measure of the intensity and to reduce speckle to a negligible magnitude, it is necessary to average over at least 500 pixels [Ref. 9]. This condition was satisfied for I by averaging the profiles over a line of 60 pixels perpendicular to the IW propagation direction and at least 8 pixels in the IW propagation direction. Note that for the case of very low wind conditions, as in figure 1, I₀ tends to zero and we observe very high contrasts compared to the other two types of signatures.

3. ‘In Situ’ Observations of Internal Wave Surface Signatures.

In the summer of 1994, as part of the EC MAST MORENA project, in situ measurements of the IWs were made from the R.V. Hakon Mosby on the Iberian shelf near 41° N. Isotherm displacements were measured by moored thermistor chains and CTD, while an ADCP measured the current profile. When possible a small boat was launched to sample surface films near the moored buoy.

On 11th August, the IW surface manifestations appeared from the ship as slick bands in a gentle ruffled sea, the wind speed average being <V>=1.9 m/s ± 0.5 from the South. On 12th August conditions were much calmer and the wind speed had dropped to <V>=1.2 ± 0.4 m/s from the West. The whole sea surface was extremely smooth, resembling a slick (glass mirror) with no discernible ripples. The only differentiating features were bands of very gently ruffled water, orientated in approximately the same direction as the slicks observed the previous day. These features which are refereed to as ‘anti-slicks’ proved to be the IW surface manifestations, because isotherm displacements were observed as they propagated past the observation point. The anti-slick bands were 100-200 meters wide and contained small wavelets, trochoidal in shape and quasiperiodic. The wavelength and amplitude of these wavelets was estimated to be between 20-30 cm and 2.5-5 cm, respectively. The wavelets had very long crests which were oriented approximately parallel to the anti-slick bands propagating in the same direction as the IWs.

Amplitudes of up to 40 meters were frequently observed and typical periods of IWs are about 20 minutes. Visual observations of the sea surface roughness concurrent with measurements of the isotherm depressions show that slicks are generally observed over the IW troughs, which is consistent with previous observations by Ermakov et al, (1992), and that can be explained by the film damping effect. Anti-slicks are observed over the IW crests, and are less wide than their slick companions.

Thermocline oscillations simultaneous with the ERS-1 overpass of 19 August were recorded by a moored buoy located at 40° 59.92¢ N and 9° 14.54¢ W where the water depth is 149 m. The SAR image (figure 1) was acquired at 22:50 UTC, the time delay between the SAR overpass and the IW train arrival time to the moored buoy being only 90 min. The sea state was very calm and the wind speed was lower than V=2m/s. We therefore assume that the SAR bright bands in figure 1 correspond to the surface manifestations of the internal waveforms recorded by the thermistor chain, demonstrating an example of a single positive sign feature, which is quite different from the other types of signature.

4. Theory of Internal Wave/Surface Wave Interaction in the presence of Surface Films.

In order to account for the interactions of IWs with centimeter-decimeter wind waves we must consider not only the straining effect of the associated surface currents, but also the effect of damping due to advected surfactants. To represent this, we examine the wind wave spectrum variations in the IW field, as described by the wave action balance equation (see e.g. [Ref. 10])

(2)

where N(k,x,t)=E(k,x,t)/w (k) is the spectral density of wave action, E is the spectral energy density, and w (k)=(gk+(s /r )k³)^1/2 is the eigenfrequency of gravity-capillary waves. The r.h.s of (2) in the form suggested by Hughes (1978) [Ref. 15] represents the wind input given by the wind wave growth rate b , wave dissipation due to films given by the damping coefficient g , and non-linear limitation of the spectrum given by a phenomenological coefficient a .

The damping coefficient g in (2) depends on the film elasticity parameter, which in turn depends on surfactant concentration G . The surfactant concentration variations in the IW field is described by the conservation equation [Ref. 16]

(3)

The solution of (3) for a plane IW profile propagating with phase velocity C was given by Ermakov et al., (1992) . The general first order solution of (2) is given by Ermakov et al. (1992), assuming variations d N of the spectral density to be small compared with the undisturbed spectrum N₀. The relative spectrum variations K=d N/N₀ can be represented as a sum of contrasts due to the kinematic (straining) effect and the film effect, which is related to variations of g due to redistribution of surfactant in the internal wave field

The kinematic contrast K_kin can be written in a simple form [Ref. 2],

assuming that the characteristic scale L of the IWs exceeds the characteristic relaxation scale of short surface waves, i.e.

L >> (c_g-C_i)/(b ₀-g ₀)

where c_g is the ripple group velocity (c_g=¶ w (k)/¶ k), b ₀ and g ₀ are the wind wave growth and wave damping respectively away from the IW field and C_i is the IW phase speed. The last condition is usually satisfied for typical oceanic IWs and for surface waves in the cm-dm wavelength range.

The film contrast can also be obtained from the kinetic equation for the spectral density of wave action, and is given by [Ref. 7],

where g [E(G )] is the ripple damping rate across the IW and E(G ) is the elasticity dependence on surfactant concentration. To scale the surfactant concentration into elasticity variations we have used a Virial equation of state with coefficients averaged from marine film samples [Ref. 11].

In general, the resulting contrast K can be represented simply as a sum of the kinematic and film contrasts K_kin and K_film, if both of these contrasts are small. This is valid if the following conditions are assumed [Ref. 7],

g (k,E) << b (k,v) and,

However, at very low wind speeds the terms in (7) can become of the same order of magnitude, so that our model, taking into account the kinematic and film effects as additive can be used only as a first approximation.

5. Discussion.

The SAR image of August 19, 1994 (see fig. 1) corresponds to the single positive IW SAR signature at very low wind conditions; at such low wind velocities the total growth rate is given by:

c = b -g if b >g

c =0 if b <g

The total growth rate is negative for some wavelengths so that corresponding waves cannot be generated by wind and the undisturbed spectrum should be assumed equal to zero. At wind speeds V<0.5 m/s there is no excitation of waves shorter than 50 cm. At increased wind speed, decimetre waves are excited. The threshold wind velocity for the wave excitation in the wavelength range 10<l <50 cm is about 1m/s. Note that for shorter waves the threshold wind velocity is higher, e.g., surface waves with a wavelength 7 cm (which is a Bragg wavelength for ERS-1 SAR) are excited only if V>1.5m/s.

Over IW troughs g -values increase due to the increase of film elasticity, and b -g can become negative, in which case the wave spectrum should be set equal to zero, and the wave spectrum contrast is equal to zero. The model results for variations of the dm-wave spectrum (l =28 cm) qualitatively agree with the visual observations of August 12, when intensified 20-30cm waves were observed in anti-slicks over IW crests. The ‘anti-slicks’ are located where the surface velocity increases over the leading slope of the IWs, preceding the region where films are compacted by the IW flow convergence.

The wave field within the anti-slick bands is characterised by the sharply-peaked, long-crested waves which were observed travelling with crests roughly parallel to the axis of the bands. This highly non-linear character of the wave field in the anti-slicks is consistent with the resonant interpretation of the interaction, with preferential growth of surface waves for which the energy propagation equals the IW phase speed [Ref. 12]. However such an interpretation is only valid when the r.h.s. of (2) vanishes, which is only true over the leading slope of the IW where surface films are still not very compact. The IW phase speed was estimated to be C_i=0.5 m/s, so that the resonant wavelength unperturbed by the IW flow is approximately 0.6 m, which is twice the wavelength of the highly non-linear wavelets observed. Although at present we can not explain this disagreement, we still feel that the sharply peaked surface waves are connected with the resonant effect. Gargett and Hughes (1972) observed the same phenomenon [Ref. 13], and explained it similarly.

To interpret SAR signatures of IWs we consider that radar backscattering at low to moderate incidence angles results from integration of discrete contributions from surface waves whose length ranges from the Bragg wavelength l _b to several l _b, and has to date been most successfully described by a Kirchoff model [Ref. 14]. In the case of ERS-1 SAR this range is from 7cm to about 20-30cm. We conclude that SAR backscatter contrasts result from the spectrum variations in the cm-dm-wavelength range, and interpret our results in this general sense.

At over-threshold winds (V>2m/s) cm- and dm-waves are excited in the background spectrum and give rise to the mean backscatter unperturbed by the short-period IWs. The resulting backscatter contrast is, in general, double sign (positive/negative). At very low wind velocities, only slightly exceeding the threshold wind speed for some dm-scale waves, there can be positive variations of the wind wave spectrum. The corresponding very high contrasts result from the very low level of the background spectrum N₀. Similarly, the positive backscatter SAR contrasts, defined in (1), obtained at near-threshold wind speeds are very strong when compared with the double sign contrasts in the over-threshold case. This is because the near-threshold background backscatter intensity I₀ tends to zero at such low wind speeds. For the near-threshold wind speeds negative spectrum variations are very small compared with the positive part, and the corresponding negative backscatter contrasts are negligible in this case.

The noise level of the SAR is the minimum cross section s ₀ that can be measured. For the ERS-1 SAR the quoted NEs ₀ (Noise Equivalent) is -25 dB, but in practice this value is slightly lower (-28 dB as measured for the case of the image background of August 19, 1994). Below this point any changes in backscatter are not detected by the radar. In the case of over-threshold wind speed images, the background backscatter level is well above the noise level and therefore we can observe both positive and negative variations from the mean background level. The background backscatter for the image of August 19 is at the noise level of the SAR and therefore negative variations of the IW contrast can not be observed. The single positive sign signature observed at such low wind speeds can be explained by the steep decrease of backscatter cross section as the wind speed falls below the near-threshold.

Given this explanation it is still necessary to account for why the SAR intensity I₀ falls so sharply at the near-threshold wind speed. According to the Kirchoff radar model [Ref. 14] a decrease of about 20 dB is expected to be observed when the contribution of cm-scale waves are removed from the integrated backscatter cross section (this computation is for wind speed 2.5 m/s and for a radar frequency of a X-band radar at the same nominal incidence angle as the ERS-1 SAR; Bragg wavelength l _B=3.3 cm). Similarly, for the C-band radar of ERS-1 and for near-threshold winds, the same accentuated decrease of backscatter cross section is expected if cm-scale waves are excluded, and only dm-scale waves contribute to the backscatter. For wind speeds near-threshold, as discussed above, dm-scale waves are excited but cm-scale Bragg waves may be absent or exist with very small amplitude. In this case the background backscatter level falls to the NEs ₀ (or below it) and single positive sign IWs are observed as a result of the very strong modulation to which the dm-scale waves are exposed due to resonance with the IW. Presumably, this modulation is so strong that the backscatter signal of the strained surface waves over the IW crests rises above the NEs ₀.

6. Conclusions

Processing of ERS-1 SAR images over the shelf zone has revealed three types of SAR signatures of short-period IWs: positive/negative, negative and positive sign variations of radar backscatter. At low to moderate wind velocities (higher than 2 m/s) positive/negative and negative signatures are observed for range propagating IWs; for azimuth propagating IWs the negative signature prevails. At very low wind velocities (of order 2m/s and less) strong single positive sign SAR signatures have been observed. The last can be considered as a particular case of IW radar signatures when the backscatter background level is comparable with the radar noise level. The cm-scale waves are not excited due to film damping over all the profile of IW but dm-waves can be excited and are strongly intensified due to the kinematic effect. In this case we have strong positive contrasts as the background spectrum is very small.

Acknowledgements.

J.C. da S. gratefully acknowledge the EU Human Capital and Mobility program (ERSBCHBITC941008) for a scholarship to study ocean slicks and the Portuguese JNICT for partial support. ERS-1 SAR image data were provided by ESA as part of the AO project AO2.UK123. D.R.G. Jeans processed the thermistor chain and ADCP data.

References

[1]. Vesecky, J.F. and R.H Stwart, The observation of ocean surface radar phenomena using imagery from the Seasat Synthetic Aperture Radar: An assessment. J. Geophys. Res., 87, 3397-3430, 1982.

[2]. Alpers W, Theory of radar imaging of internal waves., Nature, pg. 245-247,vol 314, 1985.

[3]. Thompson D. R. and R. F. Gasparovic, Intensity modulation in SAR images of internal waves, Nature, vol. 320, pg. 345-348, 1986.

[4.] Onstott, R and Rufenach, C., Shipboard active and passive microwave measurements of ocean surface slicks off the southern california coast, J. Geophys. Res., 97 (C4), pg 5315-5323, 1992.

[5]. Ewing, G, Slicks, surface films and internal waves, J. Marine Resear., vol. IX, pg 161-187, 1950.

[6]. Ermakov, S.A. and Pelinovsky, E.N., Variation of the spectrum of wind ripple on coastal waters under the action of internal waves, Dynamics of Atmospheres and Oceans, 8, 95-100, 1984.

[7]. Ermakov, SA, Salashin, SG and Panchenko, AR, Film slicks on the sea surface and some mechanisms of their formation., Dynamics of Atmospheres and Oceans, pg. 279-304, vol. 16, 1992.

[8]. da Silva, J.C., Ermakov, S.A., Robinson, I.S., Jeans, D.R.G. and S.V. Kijashko, The role of surface films in ERS SAR signatures of Internal Waves on the shelf. I. Short-period Internal Waves., submitted to J. Geophys. Research, 1997.

[9]. Laur, H., Derivation of Backscattering Coefficient s ⁰ in ERS-1.SAR.PRI Products, ESA Report: ERS-1 SAR Calibration, Issue 1, Rev. 0, 1992.

[10]. Hasselmann, K., Weak interaction theory of ocean waves, in Basic developments in fluid dynamics, ed. M. Holt, Academic press. N.Y. V. 2, 117-182, 1968.

[11]. Frew, N, and Nelson, R, Scaling of marine microlayer film surface pressure-area isotherms using chemical attributes, J. Geophys. Res., 97 (C4), pg 5291-5300, 1992.