Backscattering of Sound from Salinity Fluctuations: Measurements off a Coastal River Estuary

Marcos M. Sastre-Córdova1

Raytheon Company Seapower Capability Center

1847 West Main Rd. Portsmouth, Rhode Island, 02871 USA

1 At the time of publication the author was a graduate student at: University of Massachusetts School of Marine Science and Technology 706 South Rodney French Blvd., New Bedford, MA 02744-1221 USA sastrem@raytheon.com

Abstract- In this work a set of near co-located acoustic intensity observations and environmental measurements is presented which allowed quantification of the source of the acoustic scattering and confirmation of backscattering contributions from salinity microstructure. Observations were made by the T-REMUS Autonomous Underwater Vehicle (AUV) in a fresh water plume off a coastal river estuary characterized by strong salinity stratification and intense turbulence. Velocity and density microstructure measurements were used to calculate the expected acoustic backscattering cross-section from salinity fluctuations, which was then compared to near coincident acoustic intensity measurements. Surrogate measures of discrete particle scattering sources (i.e., biologic and mineral) for comparison with measured backscattering were also obtained. A series of regression analyses (single and multi-variable) were performed in an attempt to account for the observed acoustic variability. It was found that most of the variability in the acoustic return signal was explained by a linear combination of the independent variables selected. The results suggest that most of these regressions were dominated by biological and microstructure sources, with a fair amount of cases that were either completely biologically or microstructure dominated. The results led to the conclusion that measurements of salinity backscattering agree with theoretical predictions within experimental error of +/-2dB (on average) for a wide range of turbulence levels, with an observed underestimate of the salinity backscattering of at least 1.5dB under high turbulence conditions. These results strongly support the idea of performing an inversion of the acoustic signal to obtain the salinity variance dissipation rate.

I. INTRODUCTION

Understanding how velocity, temperature, and salinity diffuse at molecular scales is one of the most challenging problems of modern oceanography. Phenomena occurring at these scales are commonly referred in the oceanographic literature as microstructure. Quantifying microstructure and its role in oceanographic and acoustic processes is severely limited by the ability to make measurements at sufficiently small scales, particularly those associated with the diffusion of temperature and salinity [10]. The use of high frequency acoustic scattering techniques offers the promise of achieving the goal of directly measuring salinity microstructure. This is because in the ocean density and sound speed variability,

which arise from temperature and salinity variability, induce acoustic impedance fluctuations which result in directional scattering of sound waves [5].

Laboratory experiments have confirmed acoustic scattering

from temperature variability [11]. Recent theoretical and observational research of [15], [16], [8], [13], and [12], have suggested that there are oceanic regions, particularly in the coastal ocean, where salinity fluctuations should be sufficiently large compared to particulate scattering that high frequency acoustic scattering from microstructure should be observable. These studies have addressed very important theoretical considerations but have the common shortcoming of limited amount of co-located acoustic and in-situ field observations to quantitatively validate theoretical predictions; particularly for the case of salinity dominated stratification. This paper summarizes key findings of an experiment producing near-coincident acoustic and environmental measurements by employing the use of an AUV.

II. FIELD DATA COLLECTION

A. T-REMUS AUV The SMAST T-REMUS AUV is a custom designed

extended REMUS 100 vehicle containing the Rockland Microstructure Measurements System (RMMS) developed by Rockland Electronics of Victoria, BC. The RMMS turbulence package consists of two orthogonal thrust probes, two FP07 fast response thermistors, three orthogonal accelerometers and a fast response pressure sensor. Also contained on the T-REMUS vehicle are an upward and downward looking 1.2 MHz Acoustic Doppler Current Profiler (ADCP), a FASTCAT CTD probe, a Wet Labs BB2F Combination Spectral Backscattering Meter/Chlorophyll Fluorometer, and a variety of “hotel” sensors measuring pitch, roll, yaw, and many other internal dynamical characteristics of the T-REMUS vehicle. This suite of sensors allows quantification of the key

1-4244-2523-5/09/$20.00 ©2009 IEEE

dynamical and kinematical turbulent and fine scale physical processes throughout the water column.

1. Near-coincidence assumption In order to resolve the vertical density and velocity structure

the AUV is deployed in a yo-yo profiling pattern. Acoustic measurements taken with the on-board ADCP can lag or lead (depending if the acoustic sample is taken above or below the AUV) the in-situ sensor measurements by about 50 seconds but it is assumed that the statistics of volume variability, given that samples are taken at a fixed depth, do not change significantly within this time interval (or horizontal distance covered). All measurements taken with the AUV are synchronized, but the sampling volumes differ from sensor to sensor. Even under highly variable conditions, it is assumed that the statistics of the measured parameters do not change as much with range as they do with depth. This allows the comparison of acoustic and in-situ data since the depth covered by the in-situ sensor is not sampled acoustically at the same time. The mean difference between acoustic and in-situ samples is just under one minute, so no significant changes in the statistics of the measurements is expected. Fig. 1 shows the basic measurement configuration. The solid line shows the depth of the in-situ measurements, and the dashed line the center of the acoustic bins for the upward looking ADCP.

Figure 1. AUV in-situ and acoustic sampling across a down-range statistically

homogeneous volume

III. OCEAN MICROSTRUCTURE

In the oceans, microstructure refers to structures smaller than 1 meter all the way down to where molecular dissipation becomes important in the transfer of kinetic energy. Making accurate measurements down to this scale is particularly difficult for scalars (i.e., temperature and salinity) because naturally occurring turbulent motions directly affect the scale at which molecular dissipation takes place. This is even more

difficult for salinity measurements since conductivity, used to derive salinity, is strongly dependent on temperature and the probe response times are not small enough to detect variability at very high wavenumbers. The most important driving parameter for scalar dissipation is the turbulent dissipation of kinetic energy, which is a function of the velocity shear and can be measured to the smallest scales necessary.

A. Velocity microstructure The turbulent kinetic energy dissipation rate, ε, is estimated

from velocity shear measurements made along the AUV travel direction x. Assuming isotropy at the smaller scales, ε is given by

xw

xv

∂∂+

∂∂=

415ε (1)

where v and w are the horizontal and vertical components of velocity, respectively. The velocity shear measurements are first corrected for AUV motion and vibration by coherently subtracting the three components of acceleration. A description of the spectral correction procedure can be found in [6].

B. Salinity microstructure The parameter that better describes salinity microstructure is

the dissipation rate for salinity variance, χS. To directly measure χS one would need to make salinity measurements down to where molecular dissipation becomes important, which is currently unachievable. Alternatively, ε estimates can be used along with high resolution CTD measurements to indirectly estimate χS using

2

2

2⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂Γ=

zS

NSεχ (2)

where N is the buoyancy frequency, ∂S/∂z is the mean salinity gradient of a stably stratified vertical profile, and Γ is the mixing efficiency, which from laboratory measurements is known to have values of about 0.2 [7].

IV. MULTI-VARIABLE ANALYSIS

One of the key advantages of using an AUV is the synchronization and collocation of independent measurements which allow direct quantitative comparison of multiple variables. For the problem at hand, we need to compare acoustic returns to other in-situ measurements. Microstructure measurements allow quantification of the acoustic contributions expected from acoustic impedance fluctuations, and optical measurements serve as proxies for discrete acoustic scattering sources.

A. Salinity backscattering cross-section For salinity dominated scattering the acoustic cross-section

for volume variability reduces to the expression used in [14]:

κααακχσ

2

2/11

2/12

,)()2()(2

8)2/(

=

−⎟⎟⎠

⎞⎜⎜⎝

⎛−=

kBB

SsalV d

dfkqfk

DkqB (3)

where χS is the salinity variance dissipation rate, kB is the Batchelor wavenumber defined as kB = (ε/νD2)1/4, D is the scalar diffusivity, ν is the molecular diffusivity, q is a constant and has a value of 3.7, κ is the acoustic wavenumber, k is the physical wavenumber, B is a constant containing the haline contraction and sound speed variations, and α is a non-dimensional wavenumber, (k/kB)2q1/2, kept for convenience. The function f(α) is given by

⎟⎠⎞⎜

⎝⎛ −= ∫

∞ −− dxeef x

αα ααα 2/2/ 22

)( (4)

Another variable used as an indicator of acoustic variability due to salinity was the mean salinity variance <s2> for each salinity gradient estimate ∂S/∂z. These two variables are not necessarily related and both could properly describe the salinity microstructure acoustic variability.

In this paper, the terms backscattering cross-section and

backscattering strength are used interchangeably. Cross-section values are presented in decibel scale referenced to 1 m2/m3 or 1 m-1.

B. Suspended sediments/minerals Sediments of mineral composition can be a very significant

source of acoustic scattering at high frequencies, particularly in coastal and estuarine environments. Acoustic inversion of backscattering signals has been used to obtain estimates of sediment concentration with various degrees of success [2]. Optical backscatter (OBS) measurements have proven more reliable than acoustics as surrogate measure of sediment concentrations under non-saturation conditions [1].

C. Biologic scatterers Zooplankton and fish generally contribute to acoustic

backscattering because their effective scattering length is comparable and sometimes larger than the acoustic wavelength used, which translates to geometric scattering. Unlike sediments, OBS is not a good surrogate for biologic scatterers, even for the smaller species of zooplankton. However, regions with a high density of zooplankton are generally characterized by high levels of phytoplankton, which are often measurable using optical techniques. For this work, we used chlorophyll-a fluorescence ([Chl-a]) data as a surrogate for biological scatterers concentration. The validity of this assumption strongly depends on the dynamics of the environment and the degree of bio-physical coupling [4].

D. Field observations: Merrimack River plume The Merrimack River is associated with a watershed

covering a significant portion of the New Hampshire and northeast Massachusetts land area. It discharges into the Gulf of Maine approximately 6 km south of the New Hampshire -

Massachusetts border. Discharge during the late spring time is typically between 500 and 1000 m3s-1. The density field in this environment is dominated by salinity, so the site provides excellent conditions for observing naturally occurring high frequency acoustic variability due to salinity fluctuations.

Field data was collected in late spring 2007 during a 2-day

experiment. The AUV was deployed close to the river mouth where it starts to navigate downstream in a yo-yo profiling pattern (1 degree slope) to sample the vertical structure of the fresh water interface. The downstream pass, approximately 3.5 km, is followed by a constant depth return upstream path under the plume (at about 5 m), where flow speeds are slower (data from this pass were not used in the analysis). Acoustic intensity derived from the ADCP was used to be compared against ε, temperature, salinity, density, optical scattering, and fluorometer measurements taken within (or in close vicinity of) the acoustically sampled volume. The intensity measurements were taken in 0.5 m acoustic bins during the first day of deployment and 0.25 m for the second, and converted to acoustic backscattering cross-section (volume scattering strength) values using the procedure described in [3].

TABLE I VARIABLES USED IN LINEAR REGRESSION ANALYSES SHOWING SOURCE INSTRUMENT, ORIGINAL SAMPLING RATE (SAMPLES PER SECOND) AND

PHYSICAL UNITS.

Variable Description Source Original Sampling Rate

Units

[Chl-a] Estimated chlorophyll-a concentration

BB2F 8 sps μg L-1

<dS/dz> Mean salinity gradient CTD 16 sps psu m-1

bb700 (OBS)

Optical backscattering coefficient at 700nm

BB2F 8 sps m-1

N Brunt-Vaisala (Buoyancy) frequency

CTD 16 sps Hz

<s2> Salinity variance CTD 16 sps psu2

ε Turbulent kinetic energy dissipation rate

µASTP 500 sps W kg-1

σv Acoustic backscattering cross-section

ADCP Intensity

0.3 sps m-1

σv,sal Salinity microstructure acoustic backscattering

i

CTD/µASTP 16 / 500 sps m-1

Note: Sampling rates are here provided for the source data, which do not necessarily correspond to the resolution of the end variable estimated.

V. RESULTS

There were marked similarities in the spatial structure of the AUV measurements for both days of deployment. The overall structure of the upper 4m of the near-field river plume is characterized by strong acoustic backscatter in the 300-700m downstream region, which was more distinguishable during Day 1 (Figs. 2&3). Backscattering strength values (within 10th and 90th percentiles) ranged from -52 to -28 dB and -66 to -44

dB for days 1 and 2, respectively. A bimodal distribution in the aggregate scattering strength values was distinguishable for Day 1 with peaks at -44 and -30 dB (Fig. 4 – top right), but absent in Day 2 with a single peak at about -55 dB.

Figure 2. Contours of salinity microstructure backscattering strength, ADCP backscattering strength, chlorophyll-a concentration and optical backscatter at

700nm for Day 1 with sigma-t lines shown in white.

Figure 3. Contours of salinity microstructure backscattering strength, ADCP backscattering strength, chlorophyll-a concentration and optical backscatter at

700nm for Day 2 with sigma-t lines shown in white. At first glance there seems to be some correspondence of

OBS and σv but it is evident that the variation in acoustic backscattering, which spanned several orders of magnitude, could not have been explained linearly by OBS variability alone. The levels of OBS observed were low compared to those expected from high suspended sediment regions [1] and mostly on the order of what one would expect from dissolved or very small (<< 1mm) suspended minerals which would cause none to very little scattering of sound. In [9], the author

suggests enhanced backscattering due to turbulence at Bragg wavenumbers smaller than kη or in the inertial sub-range for velocity fluctuations, which could explain the OBS and σv discrepancy. However, it is clear that at the values of ε observed and the acoustic frequency used we are operating far beyond (higher wavenumber than) the inertial sub-range and therefore incoherent (random) acoustic scattering by sediments can be assumed.

Theoretical σv,sal values ranged from -85 to -48 dB with a distinct peak at -58 dB and -83 to -50 dB with a peak at -60 dB, for days 1 and 2 respectively (Fig. 4). Although salinity gradients were comparable on both days of sampling but there was a noticeable decrease in the values of ε observed on the second day. For Day 1 most ε values stayed above 10-7 W/kg with a peak at 6.3x10-7 W/kg, while for Day 2 most measurements remained under this value with another peak at 6.3x10-9 W/kg. This is strongly suggestive of an overall acoustic intensity reduction due exclusively to turbulent salinity microstructure, since a two-order reduction in ε (10-7 to 10-9) could correspond up to a 10dB reduction in backscattering strength per Equation (3).

Figure 4. Histograms of aggregated samples for selected variables. ADCP

scattering levels include data from all 8 beams (UP and DOWN). Fig. 5 shows the multi-variable regression analysis results

for each of the two days taking one of the downward-looking ADCP beams; this was representative of what was generally observed. Recall that during the first day deployment, the ADCP pulse length was set to 0.5 m which covers a scattering volume of approximately 170 ml at 1m away from the AUV. If there are discrete scatterers with an abundance of less than 1 every 170 ml or equivalently 5000 per m3 the measured intensity would show a “hit or miss” pattern over consecutive samples as the probability of hitting one of these scatterers on consecutive pings would be reduced. Equivalently, if the abundance of scatterers remains unchanged but the sampling volume is reduced, a “hit or miss” pattern in the acoustic data

is likely [12]. This was precisely what was observed during Day 2. Because of the shorter pulse length, resulting in a reduction of the sampling volume by 50%, it appears as if whatever caused the peak intensities observed during Day 1 was absent in Day 2 when in fact it was intermittently invisible to the acoustic bin size used.

The effect of this to the multi-regression analysis also

reduces to a “hit or miss” structure in the determination coefficient (Fig. 5). Because none of the measured proxies were able to fully explain some of the peak values observed (σv > -35dB) the multi-regression did not always produce significant fits (i.e., r2 > 0.5). Note that the ranges (distance from the initial point of descent) at which r2 < 0.5 correspond to where some of the peak values in σv were observed, particularly evident in Day 1 where r2 transitions from being statistically insignificant to about 0.9 within the first 700 m. This leads to the conclusion that the scatterer responsible for these peak values was not linearly described by any of the measured proxies.

Figure 5. Multi-variable regression results for a representative beam-pass

combination. The top plot shows the determination coefficient for the regression with the practical 98% confidence level shown by the dashed line at 0.5. The bottom plot shows the f-statistic for each regression with threshold fc

shown by the black and red dashed lines.

The single and multivariable regression helped explain the vertical (depth) structure of the observed acoustic variability in most cases. Several profiles clearly show good agreement with variability observed in the independent variable set, suggesting an adequate selection of variables. We found a diverse set of scenarios that characterize most of the significant multivariate fits to the data. Most of them almost totally explained by σv,sal and [Chl-a] alone. These scenarios are: 1. salinity dominated scattering near the surface, 2. salinity dominated scattering at low turbulence, 3. salinity dominated scattering at high turbulence, 4. biologically dominated scattering, and 5. salinity variance dominated scattering. Fig. 6 illustrates a case with

salinity dominated scattering at high turbulence. Note that the correspondence of theoretical and measured backscattering is quite remarkable (top left graph), explaining over 94% of the variance.

Given these results a few cases were identified in where the

correspondence of theoretical and measured salinity backscattering was extremely significant (r2 > 0.9) and used the samples for an inversion of the acoustic scattering equation to produce estimates of χS, the salinity variance dissipation rate. These estimates (in the order of 10-3 to 10-2 psu2 s-1) were somewhat higher than those reported in the literature but by no means unreasonable given the environmental conditions of the experiment. Using these estimates the calculated mixing efficiency, Γ, ranged from 0.08 – 0.34 with an average of about 0.16 which is very close to the generally assumed value of 0.2.

Figure 6. Individual and multi-variable regression results showing σv,sal as the dominant scattering source under high turbulence. The top graphs show the

measured scattering and the corresponding partial regression for each independent variable in decibels, with the partial determination coefficient, r2,

shown in parenthesis next to the title. The bottom graphs show: 1. TKE dissipation rate for the profile, showing εLO as the ε lower bound above which

σv,sal ∝ κε1/2; 2. The multi-regression fit compared to the original backscattering strength measurements. The mean square error and

determination coefficient are noted.

VI. CONCLUSIONS

The AUV deployment proved to be successful for making near-coincident measurements of salinity microstructure and volume backscattering. The river plume environment provided high turbulence and strong salinity gradient conditions that resulted in observable backscattering due to microstructure. The time difference between acoustic and in-situ sensor samples - and the uncertainties in the respective volume sizes - did not prevent the analyses employed from reaching favorable and statistically significant results. The chosen variables for the linear regression analysis were adequate but incomplete. The regions of the plume showing the highest backscattering

values were only partially explained by the multi-variable linear model. The source of this scattering can not be verified with the data collected.

The comparisons resulted in confirmation that the

backscattering field was dominated by salinity microstructure with instances of high echo returns presumed to originate from biological sources. For both days, over 50% of the backscattering samples that correlated well with in-situ measurements indicated salinity microstructure to be dominant at 1.2 MHz. The acoustic resolution was also found to be important for discriminating discrete scatterers from microstructure. The presence of discrete scatterers affects the echo distributions and the mean backscattering level and both are function of the size and density of the scatterer. Since the measured backscattering due to salinity microstructure is less (if at all) affected by the acoustic sampling resolution, the distribution of salinity backscattering measured over various acoustic resolutions could be obtained.

ACKNOWLEDGMENT

The author would like to express his deepest gratitude to Dr. Louis Goodman for his guidance and mentoring during the course of the research leading up to the results here presented. Dr. Goodman and Dr. Daniel McDonald from SMAST are credited for data collection during the Merrimack River field work. Special thanks to Mr. Zhankun Wang from the Marine Turbulence Lab at SMAST for providing ε estimates for the Merrimack River data set.

This work was supported by the Raytheon Company

Advanced Study Program Fellowship and the School of Marine Science and Technology at the University of Massachusetts.

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