Relationships Between Strong Internal Waves
and Their Surface Signatures

R. A. Kropfli*, L. A. Ostrovsky**, T. P. Stanton***, E. A. Skirta****,
A. N. Keane**, and V. G. Irisov**

*) NOAA/Environmental Technology Lab., Boulder, CO;
**) Univ. of Colorado, CIRES/ NOAA Environmental Technology Lab., Boulder, CO;
***) Naval Postgraduate School, Monterey, CA;
****) Dept. of Mathematics, Univ. of Toledo, Toledo, OH
MPEG video, 26 Sep 1995   (5 Mbytes), 25 Sep 1995  (5.4 Mbytes)


Strong internal waves (IW) in the form of soliton groups were observed off the Oregon coast with in-situ and remote sensors, including shore-based Doppler radars and an airborne microwave radiometer. Here, we analyze the relationships between isotherm vertical displacements, internal currents, radar backscatter cross-sections, along with Doppler velocity signals at horizontal (HH) and vertical (VV) polarizations.Analysis of these observations shows that the phase of radar-signal modulation with respect to the IW is such that the minimum radar signal intensity and lowest microwave brightness temperature lies close to the maximum of the IW thermocline depression or, equivalently, the maximum horizontal current excursion near the surface.

I. Introduction

Theoretical and observational studies of nonlinear internal waves (IW) in a shallow sea have a long history. The observational data show that tidally-generated internal solitons are a ubiquitous phenomenon in coastal zones with stratification, generally during the summer months, and suggest that they may consume a non-negligible part of tidal energy. Remote observations of surface signatures are now a common way to study IWs. Satellite images of IWs have been obtained routinely since the 1970s by photography and by synthetic aperture radar (SAR). Systematic physical studies of this phenomenon started with the works of Hughes and Grant [1978].

However, in spite of a relatively large body of prior work, a thorough understanding of relationships between IW characteristics and those of centimeter-range SWs is still lacking. It is especially true for internal solitons and bores in shelf zones where the IWs may have pulse-like shapes and very large amplitudes so that even a description of subsurface IW currents is a complicated problem.

We describe here the results of observations of extremely large amplitude internal solitons on the East Pacific Shelf during the Coastal Ocean Probing Experiment (COPE) in which strong correlations were observed between IW hydrophysical parameters and radar signals.

2. Experiment

COPE was performed off the coast of northern Oregon from September 12 through October 7, 1995. This area was selected because of the frequency and intensity of internal waves caused by diurnal tidal flow over a well-defined shelf break about 70 km offshore. The Columbia River, just 50 km to the north, was the source of warm, fresh water which generated a sharp and shallow pycnocline on which the IW packets could propagate.

Numerous sensors were mounted on the Scripps Institute Floating Instrument Platform, FLIP, moored about 25 km offshore in 150 m of water. These sensors enabled us to measure wind near the surface, air and sea surface temperatures, wave characteristics, and profiles of current, small-scale turbulence, temperature, salinity, and density. In addition, three arrays of thermistor chains and an inverted echo sounder operated by the Canadian Institute for Ocean Science were moored 6 km offshore in 75 m of water.

The K-band and X-band Doppler radars, 34.6 GHz and 9.3 GHz respectively, developed by the NOAA Environmental Technology Laboratory (ETL) were operated from a nearby hillside about 4 km from the shore and 744 m above sea level. Other ETL remote sensors, e.g., microwave radiometers, were operated at moderate incidence angles.

At the first stage, we concentrated on three cases in which the ETL radars operated in a fixed-beam mode and were directed at the ocean surface near FLIP, where current and temperature profiles were measured continuously along with near-surface wind. The in situ measurements were made from FLIP with a Loose-tethered Micro-structure Profiler (LMP), which provided temperature and salinity measurements at 0.1 m resolution. Current measurements were made with five ultrasonic travel time current sensors.

The measurements of temperature, salinity and density profiles prior to the passage of the IW front has indicated a very shallow (5-7 m) position of the pycnocline that is apparently due to the proximity of Columbia River. At the same time, during the strong spring tides, the14EC isotherm, which is near the depth of the maximum density gradient, indicated up to 26 m displacements from the undisturbed depth. These extreme displacements suggest a very strongly non-linear wave which was the greatest thermocline displacement observed during COPE. Displacements were routinely observed in the range of 15 to 20 m. The initial displacement was usually followed by a train of pulses; we refer to these pulses as solitons when they are well-separated. Peak current magnitudes in the strongest solitons were also unusually large, up to 0.8 m/s, just slightly less than the IW speed of 0.9 m/s (see below).

The radars used in this study were originally designed and operated by ETL for meteorological research but were recently modified for detailed studies of the ocean. Here we used primarily fixed-beam data obtained when the antenna was directed near FLIP for several hours at a time while IW packets propagated through FLIP's position and, subsequently, the nearby radar sample gates.

The images collected in a 26-days period suggest that the structure and amplitude of IWs vary markedly with the strength of tidal forcing. Relatively strong spring tides generated rather regular and horizontally extended IW fronts. Weaker tidal forcing from neap tides seemed to generate IWs with greater curvature, distinctly separated from each other, as though they had been forced by sources associated with smaller-scale, localized features on the shelf break. In all cases, the IWs are presumably generated by tidal currents interacting with bottom topography near the shelf break located approximately 70 km off shore. These observations of IW structure suggest that the generating mechanisms during spring and neap tides might be different (such as lee waves in the former case and scattering on local bottom features in the latter).

The IW propagation velocity can be accurately determined from the slope of the wave fronts in range-time plots. Based on the slopes of the modulations in the range-time plot, the IW near FLIP was propagating onshore at .90 m/s.

Internal waves are observable to radars because of their strong modulations of the surface wave spectrum. Radar images, as described above, show bands of relatively high signal strength, where the SWs are enhanced by the IW, separated by low intensity bands where the surface waves are suppressed. Note that the direction of the near-surface current measured from FLIP is opposite to that of the Doppler velocity excursions in the weakly reflecting region of the IW, giving credence to the interpretation that observed modulations in Doppler velocity excursions are not caused directly by IW current.

3. Comparison of in-situ and radar data

Even cursory examinations of the radar data and the data obtained from FLIP show that they have highly correlated and unmistakably strong modulations during the IW passages (Fig.1).

FLIP parameters such as isotherm depth and current were plotted along with temporally-lagged radar measurements such as VV, HH, and Doppler velocity. In all analyzed cases the propagation direction of the IWs was such that our radar measurements near FLIP can be considered to be directly across the IW phase fronts.

Figure 1. Temporal records of Doppler velocity (a); VV-signal intensity (b)
(both from the ETL Ka-band radar); 37 GHz brightness temperature (c);
horizontal current at 4.4 m depth (d); and depth of 14 C isotherm (e)
for September 25/26, 1995


Generally, minima in radar signals are nearly coincident with maxima in the seaward component of Doppler velocity, with maxima in isotherm depths and maxima in IW-generated near-surface currents toward the shore. In particular, the near-surface current excursions are inferred to be toward the east in zones of minimum radar backscatter which we observe to have Doppler velocity excursions toward the west.

The brightness temperature as a function of time based on data taken from the radiometer during two passes by an airship over the IW were interpolated to FLIP's position from the observed positions of the smooth areas. The result shows that the 37 GHz brightness temperatures exactly in phase with the radar signal modulations. The radar and radiometric signals are well-correlated as expected because the small scale roughness is known to cause increases in both the radiometric brightness temperature and radar back scattering intensity. A remarkable feature is that the growth of the scattered radar signal level begins prior to the arrival of the IW train. This suggests that a 'precursor' to the IW is present in the spectrum of short surface waves. A similar phenomenon was reported before [Basovich et al., 1987; Gotwols & Sterner, 1988]. Finally, we note that the amplitude of modulations for both HH and VV polarizations increases monotonously with the isotherm displacement.

4. On mechanisms of SW-IW interaction

To choose between different candidate hydrodynamic processes which can explain the observed results, one should consider the main qualitative features of the signal modulation, in particular its depth and phasing between radar modulation and isotherm or current variations. A detailed theoretical consideration of the problem is beyond the scope of this work. Here we briefly discuss most relevant models which seem to fit the observations.

1. Effect of surface-active films

A possible candidate mechanism to explain the influence of IW-induced currents on short surface waves is the effect of surface-active films. This problem was considered in a number of works [e.g., Ermakov et al., 1980]). Horizontal currents induced by IWs could redistribute the surfactant which then damps the surface waves causing SW modulations. It is easy to show that in a steady-state regime,, the film is concentrated over the solitons (where the IW current is minimal in the reference frame moving with the IW phase speed, where the current is stationary). In our case, the film concentration modulation can be strong. Because the short-wave damping rate is the greatest where film concentration is the greatest, the slick should be observed as a minimum in the radar signal directly over the solitons, which agrees with our observations. Unfortunately, surfactants are difficult to measure in open ocean environments and were not measured during COPE. The action of surfactants readily explains the phasing of maxima and minima of radar scattering with respect to IW described above. However, this mechanism fails to explain the observed Doppler-signal anomalies and the presence of precursors due to its local character.

2. Cascade mechanism

It has been suggested by a number of observers [e.g., Hughes & Grant, 1978; Basovich et al, 1987] that IWs act primarily on surface gravity waves of few decimeters to few meters in wavelength, which, in turn, modulate the gravity-capillary waves that contribute to scattering at microwave frequencies. In these theories, surface gravity wavelengths affected the most by IWs are determined by the "group synchronism" criterion, i.e., the group velocity of surface waves cgr plus IW-induced surface current being nearly the same as the phase velocity of the IWs. Under this condition, "blocking" is possible: the wave reaches a turning point and reflected (or refracted), which, in turn, may radically change the surface wave configuration and produce a strong modulation even for moderate-amplitude IWs. IWs were observed in COPE to propagate with typical velocities of 0.7 to 0.9 m/s; surface waves with such group velocities have wavelengths in the range of 0.8 to 2.0 meters between solitons, where the IW current is weak, and should be much shorter, from few centimeters to few dozens of centimeters, over strong solitons, where the IW current is 0.5-0.8 m/s. Because more intense surface gravity waves tend to break and form the capillary ripples or enhance the scattering anyway, the radar signal minima will coincide with those of the suppressed surface gravity waves. Such a cascade mechanism can explain the observation of minimum scattering directly over the solitons fo weak winds; if the wind increases, the SW maximum will move toward the forward edge of the IW. This tendency is also seen in some of our COPE observations.

3. Direct modulation of SW by IW

As mentioned, the synchronous SW over the solitons, where the IW current is strong, are rather short and for strong currents can move into the centimeter wavelength range. It can be shown [Bakhanov, 1998], that while moderate current would amplify these waves, the current close to the IW phase velocity makes the opposite effect, and the wave intensity decreases oved the solitons. This may explain the observed phasing without considering a cascade, although not the "opposite" Doppler shifts mentioned above.

There are not enough observational data analyzed so far to choose with any certainty between these mechanisms. Moreover, they all might contribute to some degree to the short wave modulation and formation of radar images.

5. Conclusions

Extremely strong, tidally-generated, internal-wave soliton trains were observed during COPE by means of contact sensors and microwave radars during a three and a half week experiment off the coast of northern Oregon. Very distinct radar signatures of IWs were the result of strong influences of the IWs on the surface wave spectrum. Correlations as high as .9 were found between the radar signals and current/isotherm records made at FLIP. Stronger signal modulations were always observed at HH compared to VV and detectable modulations were easily observed at HH even at wind speeds as high as 15 m/s when VV modulations were not observable. Radar observations showed that the IW spatial structure was determined by the tidal strength, i.e., whether the forcing was from strong spring tides or weak neap tides. The opposition of the Doppler velocity excursions (from the mean) to the direction of near-surface current measurements on FLIP indicates that the Doppler velocity excursions were not representative of IW currents; more consistent with the measurements was the interpretation that the Doppler excursions were caused either by orbital motions of SWs or by parasitic capillary waves.

A careful positioning of data from a single radar range gate onto time records of current and thermocline depression showed that the maximum radar returns were not coincident with the regions of highest strain rate (that is rather typical of the observations of weak IW) but were found to lead the current pulse/thermocline depression as it progressed shoreward with average speeds of about .8 m/s. Particle velocities of nearly that magnitude attest to the strong non-linearity of these waves as does the extreme ratio of thermocline depression to ambient thermocline depth which was as great as 5:1. The portions of IWs weakly-reflecting to radars were roughly coincident with the solitons themselves, i.e., the current pulses/thermocline depressions.

A more detailed description of the results given above can be found in [1,2]


Support for this work was provided by the NOAA-DOD Advanced Sensor Applications Program and the Office of Naval Research Physical Oceanography Program.


1. T. P. Stanton and L. A. Ostrovsky, Observations of highly nonlinear internal solitons over the continental shelf. Geophys. Rev. Lett., 25, 14, 2695-2698, 1998.

2. R. A. Kropfli, L. A. Ostrovsky, T. P. Stanton, E. A. Skirta, A. Keane, and V. E. Irisov, Relationships between strong internal waves and their surface signatures. Accepted for J. Geophys. Res., 1998.