Estimating temperature and current using a pair of transceivers in a harbor environment

An efficient method to obtain the horizontal distribution of temperature and current fields within the water column is to measure the acoustic travel time between several horizontally-separated transceivers. Most studies^1,2 of coastal acoustic tomography (CAT) use only the travel times of the first acoustic arrivals between any pair of the transceivers to invert for the spatial fields. Nakano et al.³ designed a bi-static sonar system to utilize the acoustic reflections from the artificial reflectors placed at different distances away from the beach for monitoring the rip currents. In harbor environments the reflections from man-made structures and debris may provide information on the spatial variation of temperature and current.

This study estimates the spatial distribution of temperature and current in a harbor environment by analyzing the reciprocal travel time data collected on a pair of transceivers in an experiment conducted at a narrow channel in Bachimen Harbor, Keelung, Taiwan. The observed multipath arrivals are identified using the ray simulations in both the vertical and horizontal planes. In addition to the reflected pulses from the surface and seafloor, some of the observed arrival pulses are dominated by the energy components horizontally reflected from the harbor banks. The differences in the temperatures and currents estimated along these two ray paths show the spatial variation in this harbor environment.

Given a pair of transceivers horizontally separated by a distance R, and the times of acoustic pulses traveling with the current (t⁺) and against the current (t⁻), one can infer the path-averaged sound speed $cm$ and the path-averaged current projected along the propagation path $vm$⁠; these parameters are related to the travel times as follows:² 

To separate the small travel-time changes induced by the current from the much larger effects due to sound speed, we employ mean and differential travel times as follows:

where $tm=(t++t−)/2$ and $td=(t−−t+)/2$ are the mean and differential travel times obtained from the reciprocal travel time measurements, respectively.

A reciprocal acoustic transmission experiment was conducted between two acoustic stations in Bachimen Harbor between Hoping Island and Keelung City, Taiwan [the lower right-hand corner of Fig. 1(a)]⁴ on December 4, 2009. Two acoustic stations, A and B, were placed at the northern bank. The stations were separated by a distance of 488 m. The experiment was conducted during the flood tide [Fig. 1(b)]. Simultaneous point measurements were taken using a Horizontal Acoustic Doppler Current Profiler (HADCP) equipped with a Conductivity-Temperature-Depth (CTD) sensor deployed at the northwest bank. Figure 1(c) shows the time evolution of HADCP-measured current (projected onto $AB→$⁠) as a function of distance from the bank. The currents, flowing in the direction from Stations B to A, decreased in magnitude with increasing water level.

For the reciprocal acoustic transmission, we used the CAT system developed by the underwater acoustics team in Hiroshima University, Japan.¹ Each system consists of a microprocessor with an electronic circuit board for signal processing, a transducer for both transmitting and receiving acoustic signals (referred to as a transceiver), and a GPS receiver providing the 1-Hz signal to synchronize the timing of transmission and reception with an accuracy of about 1 μs. The transmitted signal is a phase-encoded maximum-length shift-register sequence (referred to as an m-sequence) with one cycle per digit at a center frequency of 10 kHz. These specifications would yield a digit length of 0.1 ms. The sequence length is 1023 (corresponding to a 10th order m-sequence) and thus the period of the sequence is 0.1023 s. The number of periods transmitted is 10, corresponding to a total signal length of approximately 1.023 s. The time period of alternate transmissions between two stations is 90 s.

The uncertainties of current and temperature measurements directly depend on the uncertainty of travel-time measurements, which in turn depends on the sampling of the acoustic signals. The received raw data are digitized and recorded at a sampling rate of 20 kHz. To achieve a temporal resolution higher than the sampling rate, an interpolation technique using a sinc function⁵ is applied, resulting in an improvement of about a factor of 10 (attaining a temporal resolution of about 5 μs); the travel-time precision obtained by the interpolation is comparable with the theoretical achievable limit of 5 μs calculated from the root-mean-square bandwidth of 10 kHz used in the experiment and the observed signal-to-noise ratio of 25.5 dB. For the ray path length of 488 m, the resulting uncertainty of sound speed estimates due to the travel-time uncertainty (5 μs) amounts to about 0.02 m/s, equivalent to the uncertainty in temperature of about 0.01  °C using the Mackenzie sound-speed equation⁶ in which the mean temperature and salinity are set to 19.15  °C and 34.14‰, respectively. Consequently, the uncertainty in the estimate of current speed is about 0.02 m/s.

Figure 2(a) shows typical examples of the reciprocal pulse responses. There exist multiple arrivals in this environment due to the small width of the harbor. Comparing the measured pulse responses between the opposite directions, we observe that the overall structure of the reciprocal pulse responses is similar to each other. When the tidal current flows toward Station A with a relatively high speed [Fig. 2(a-1)], the acoustic pulse traveling in the direction from B to A (solid line) arrives earlier than that in the reversed direction (dashed line). When the current speed is low [Fig. 2(a-2)], the reciprocal pulse responses overlap. Figure 2(b) shows the amplitude of the measured pulse responses as a function of transmission time (Tx time). Two dominant groups, which arrive at the receiver around 321.8 ms (referred to as Group 1) and 323.5 ms (Group 2), are persistently observed. A preliminary data analysis was reported in Ref. 7.

To identify the propagation path of acoustic arrivals in the measured data, the three-dimensional acoustic propagation is approximated by decomposing the field into the two-dimensional (2D) fields in vertical and horizontal planes. A series of 2D simulations are conducted using the BELLHOP⁸ ray tracing program.

From the bathymetry survey, the water depth is approximately 1 m near the stations and increases to 5 m, as the distance increases 2 m in range away from Station B [Fig. 3(a-1)]. In such a shallow environment the water column is well mixed, therefore the water sound speed may assume to be uniform and is about 1518 m/s based upon the CTD measurement. A semi-infinite sub-bottom seafloor is adopted, and from the observation the sediment in the area is sandy silt. The values of geoacoustic parameters were initially determined using the data compiled by Hamilton and Bachman⁹ and were then tuned to fit the magnitude of the observed pulse response as follows: compressional sound speed of 1580 m/s, attenuation of 0.3 dB/λ, and density of 1.8 g/cm³.

The eigenray tracing in the vertical plane [Figs. 3(a-1) and 3(a-2)] shows the rays whose arrival times are less than 322.5 ms; those are: the direct ray (labeled as D; indicated by a black solid line), surface-reflected ray (S; red solid line), bottom-reflected ray (B; blue solid line), both bottom- and surface-reflected rays [BS and SB; blue and red dashed heavy lines], as well as the rays with multiple surface and bottom interactions arriving about 0.6-ms later [(BS)⁵B²SB, (BS)⁹B, (SB)⁹B; black, blue and red dashed thin lines]. Due to the finite bandwidth, the D, S, B, BS, and SB rays cannot be resolved in the time domain and they form the first peak in the Group 1 pulse response. The rays with many surface and bottom interactions suffer a higher loss than the first peak [Fig. 3(a-2)]; therefore, they might appear as small peaks in the received pulse responses. Those rays arriving later than 322.5 ms are omitted from the plot due to a much higher loss. The modeled ray arrivals in the vertical plane cannot predict Group 2 (with arrival time of about 323.5 ms) observed in the measured data.

To launch rays propagating in the horizontal plane, we first define a coordinate system: Station A as the origin and the transmission line between Stations A and B as the x axis. Then the outlines of the harbor are taken from the Google Earth image to describe the northern and southern boundaries. Where multiple y values occurred for a given x, such as the pier on the south bank, the datum was trimmed to have only one y-value.

Figures 3(b-1) and 3(b-2) show the eigenrays found in the horizontal plane. The direct ray (black solid line) is identical to the D ray in the vertical plane, traveling through the central area of the harbor channel. The ray with one reflection from the northwest bank very close to A (black dashed line) has a similar path to the direct ray. The two rays reflected from the northeast bank (blue solid and blue dashed lines) sample the area near the bank. Due to the longer propagation path these two rays arrive about 2 ms later than the direct ray. Thus, the observed acoustic arrivals having travel time of about 323.5 ms are associated with the rays reflected from the northeast bank. These rays constitute Group 2.

The received arrival patterns of reciprocal transmissions are formed into the reciprocal pulse responses. The multiple arrival peaks between the reciprocal responses are paired by selecting the nearest peaks in the aligned responses with the time lag reaching the maximum correlation between the reciprocal. Since the number of arrivals and their spacing are similar [e.g., Figs. 2(a-1) and 2(a-2)], it is expected that the nearest peaks in the aligned reciprocal pulses are the reciprocal pair.

For each ray group the mean travel time is estimated from the first arrival pair in the group to reduce the influence of the ray path length uncertainty induced by the change in the water level. The differential travel time is obtained by averaging the travel time differences of the pairs whose mean travel times within 1 ms from that of the first pair. When the travel time data are absent, due to the failure of a power supply, they are interpolated linearly from the adjacent data. After interpolation the mean and differential travel times are low-pass filtered by a 7-point boxcar window (10.5-min moving-average).

Figure 4(a) shows the time series of the path-averaged temperatures estimated by the mean travel times as well as the measurement using the temperature sensor at the northern bank. The path-averaged temperature is converted from the sound speed via the Mackenzie sound-speed equation⁶ using the measured salinity of 34.14‰. During the experiment the temperature at the northern bank (solid line) varied from 19.1  °C to 19.3  °C, while the path-averaged temperatures (dashed and dotted lines) show a similar trend but with a larger temporal variation. A noticeable difference between the two groups is observed during the last hour of the experiment. Although the path-length perturbation induced by the water-level change may contribute to this temperature (sound speed) change, the estimated maximum path-length change of the first peak is less than 1 cm, corresponding to a temperature change of 0.01  °C. Thus, we conclude that the observed higher frequency acoustically-determined temperature fluctuations and the differences between the two ray groups are indicative of spatial variability that is unresolved by the single temperature sensor.

Figure 4(b) shows the time series of path-averaged currents obtained from the differential travel times and the currents derived from the HADCP. The HADCP-derived currents show that when the current is strong (at early times) a considerable spatial variation is observed with a relatively high magnitude near the center of the channel (solid gray line), and as the current decreases its variation subsides. The path-averaged currents show similar temporal variations to the HADCP-derived currents. The decrease of currents at the Tx time of 0.5 h is observed in both measurements. The currents estimated by the differential travel times are slightly higher than the HADCP-derived current during the last half period. We interpret the difference between the path-averaged currents estimated from Group 1 (blue dashed line) and Group 2 (red dotted line) to indicate the spatial variation of the current field. The relatively small differences between the acoustic paths are consistent with the environment geometry since some part of Group 2 (reflected path) travels in the area near Group 1 (direct path) as indicated in Fig. 3(b-2).

This paper is based upon an acoustic experiment with a self-developed transceiver system conducted in a harbor environment. The purpose is to demonstrate the possibility of extracting the spatial variation of the currents and temperatures using the multipath acoustic propagation due to reflections from the sea surface/bottom and the harbor bank. Through a detailed analysis, the results have shown that, using a pair of transceivers, it is possible to obtain spatial information about the temperature and current fields in a highly reverberant environment by using horizontally reflected rays. In particular, in this experimental site, the estimated currents along the paths of Group 2 (the horizontally reflected paths) are weaker than those of Group 1 (the direct path) at the beginning of the flood tide. The larger variation observed in the path-averaged temperatures indicates that the temporal variation of the temperature field is larger along the ray paths than that near the northern bank. Also, due to a nearly uniform temperature distribution over the entire water volume, it is expected that the horizontal and vertical ray geometries remain stable without refractive effects. This work suggests future directions, including smaller space scale verification, measurements over a complete tidal cycle, and modeling the flow to better understand the spatial variability.

This work is supported by the Ministry of Science and Technology (MOST) of Taiwan, R.O.C. through Contract No. 104-2611-M-002-008. The authors would like to thank Professor Arata Kaneko, Hiroshima University for providing the CAT systems.