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A
Agnon, Y, Malanotterizzoli P, Cornuelle BD, Spiesberger JL, Spindel RL.  1989.  The 1984 bottom-mounted Gulf Stream tomographic experiment. Journal of the Acoustical Society of America. 85:1958-1966.   10.1121/1.397849   AbstractWebsite

In this paper, data from a Gulf Stream tomographic experiment carried out in October 1984 are analyzed. The experiment used acoustic sources and receivers bottom mounted beneath the stream to measure Gulf Stream dynamics. However, due to an unfortunate electronic malfunction of the source, only 2 days of acoustically measured travel time data are available. Nevertheless, some new and positive results are obtained. Bottom reflected acoustic rays having up to two bottom bounces are unambiguously identified by solving the direct problem of tracing rays both in a reference climatological profile and in actual range‐dependent sound‐speed sections from a hydrographic survey carried out during the experiment. It is also shown that these rays do not appear to be affected by important nonlinearities so that they can be used to provide consistent results in inverse solutions.

Andrew, RK, Howe BM, Mercer JA, Group NPAL, Cornuelle B, Colosi J.  2005.  Transverse horizontal spatial coherence of deep arrivals at megameter ranges. Journal of the Acoustical Society of America. 117:1511-1526.   10.1121/1.1854851   AbstractWebsite

Predictions of transverse horizontal spatial coherence from path integral theory are compared with measurements for two ranges between 2000 and 3000 km. The measurements derive from a low-frequency (75 Hz) bottom-mounted source at depth 810 m near Kauai that transmitted m-sequence signals over several years to two bottom-mounted horizontal line arrays in the North Pacific. In this paper we consider the early arriving portion of the deep acoustic field at these arrays. Horizontal coherence length estimates, on the order of 400 m, show good agreement with lengths calculated from theory. These lengths correspond to about 1 degrees in horizontal arrival angle variability using a simple, extended, spatially incoherent source model, Estimates of scintillation index, log-amplitude variance, and decibel intensity variance indicate that the fields were partially saturated. There was no significant seasonal variability in these measures. The scintillation index predictions agree quite well with the dataset estimates; nevertheless, the scattering regime predictions (fully saturated) vary from the regime classification (partially saturated) inferred from observation. This contradictory result suggests that a fuller characterization of scattering regime metrics may be required. (c) 2005 Acoustical Society of America.

B
Baggeroer, AB, Birdsall TG, Clark C, Colosi JA, Cornuelle BD, Costa D, Dushaw BD, Dzieciuch M, Forbes AMG, Hill C, Howe BM, Marshall J, Menemenlis D, Mercer JA, Metzger K, Munk W, Spindel RC, Stammer D, Worcester PF, Wunsch C.  1998.  Ocean climate change; comparison of acoustic tomography, satellite altimetry, and modeling. Science. 281:1327-1332., Washington, DC, United States (USA): American Association for the Advancement of Science, Washington, DC   10.1126/science.281.5381.1327   AbstractWebsite

Comparisons of gyre-scale acoustic and direct thermal measurements of heat content in the Pacific Ocean, satellite altimeter measurements of sea surface height, and results from a general circulation model show that only about half of the seasonal and year-to-year changes in sea level are attributable to thermal expansion. Interpreting climate change signals from fluctuations in sea level is therefore complicated. The annual cycle of heat flux is 150 ± 25 watts per square meter (peak-to-peak, corresponding to a 0.2°C vertically averaged temperature cycle); an interannual change of similar magnitude is also detected. Meteorological estimates of surface heat flux, if accurate, require a large seasonal cycle in the advective heat flux.

Behringer, D, Birdsall T, Brown M, Cornuelle B, Heinmiller R, Knox R, Metzger K, Munk W, Spiesberger J, Spindel R, Webb D, Worcester P, Wunsch C.  1982.  A demonstration of ocean acoustic tomography. Nature. 299:121-125.   10.1038/299121a0   AbstractWebsite

Over the past decade oceanographers have become increasingly aware of an intense and compact ocean ‘mesoscale’ eddy structure (the ocean weather) that is superimposed on a generally sluggish large-scale circulation (the ocean climate). Traditional ship-based observing systems are not adequate for monitoring the ocean at mesoscale resolution. A 1981 experiment mapped the waters within a 300 × 300 km square south-west of Bermuda, using a peripheral array of moored midwater acoustic sources and receivers. The variable acoustic travel times between all source–receiver pairs were used to construct the three-dimensional (time-variable) eddy fields, using inverse theory. Preliminary results from inversions are consistent with the shipborne and airborne surveys.

C
Colosi, JA, Baggeroer AB, Cornuelle BD, Dzieciuch MA, Munk WH, Worcester PF, Dushaw BD, Howe BM, Mercer JA, Spindel RC, Birdsall TG, Metzger K, Forbes AMG.  2005.  Analysis of multipath acoustic, field variability and coherence in the finale of broadband basin-scale transmissions in the North Pacific Ocean. Journal of the Acoustical Society of America. 117:1538-1564.   10.1121/1.1854615   AbstractWebsite

The statistics of low-frequency, long-range acoustic transmissions in the North Pacific Ocean are presented. Broadband signals at center frequencies of 28, 75, and 84 Hz are analyzed at propagation ranges of 3252 to 5171 km, and transmissions were received on 700 and 1400 in long vertical receiver arrays with 35 in hydrophone spacing. In the analysis we focus on the energetic "finale" region of the broadband time front arrival pattern, where a multipath interference pattern exists. A Fourier analysis of 1 s regions in the finale provide narrowband data for examination as well. Two-dimensional (depth and time) phase unwrapping is employed to study separately the complex field phase and intensity. Because data sampling occured in 20 or 40 min intervals followed by long gaps, the acoustic fields are analyzed. in terms of these 20 and 40 min and multiday observation times. An analysis of phase, intensity, and complex envelope variability as a function of depth and time is presented in terms of mean fields, variances, probability density functions (PDFs), covariance, spectra, and coherence. Observations are compared to a random multipath model of frequency and vertical wave number spectra for phase and log intensity, and the observations are compared to a broadband multipath model of scintillation index and coherence. 2005 Acoustical Society of America.

Colosi, JA, Grp A.  1999.  A review of recent results on ocean acoustic wave propagation in random media: Basin scales. Ieee Journal of Oceanic Engineering. 24:138-155.   10.1109/48.757267   AbstractWebsite

Measurements of basin-scale acoustic transmissions made during the last four years by the Acoustic Thermometry of Ocean Climate (ATOC) program have allowed for the study of acoustic fluctuations of low-frequency pulse propagation at ranges of 1000 to 5000 km, Analysis of data from the ATOC Acoustic Engineering Test conducted in November 1994 has revealed new and unexpected results for the physics of ocean acoustic wave propagation in random media, In particular, use of traditional Lambda, Phi methods (using the Garrett-Munk (GM) internal wave model) to identify the wave propagation regime for early identifiable wavefronts predict the saturated regime, whereas observations of intensity probability density functions, intensity variance, and pulse time spread and wander suggest that the propagation is more likely near the border between the unsaturated and partially saturated regimes. Calculations of the diffraction parameter Lambda are very sensitive to the broad-band nature of the transmitted pulse, with CW calculations differing from a simplistic broad-band calculation by 10(3)! A simple model of pulse propagation using the Born approximation shows that CW and broad-band cases are sensitive to a random medium very differently and a theoretical description of broad-band effects for pulse propagation through a random media remains a fundamental unsolved problem in ocean acoustics. The observations show that, at 75-Hz center frequency, acoustic normal mode propagation is strongly nonadiabatic due to random media effects caused by internal waves. Simulations at a lower frequency of 28 Hz suggest that the first few modes might be treated adiabatically even in a random ocean. This raises the possibility of using modal techniques for ocean acoustic tomography, thereby increasing the vertical resolution of thermometry. Finally, the observation of unsaturated or partially saturated propagation for 75-Hz broad-band transmissions, like those of ATOC, suggests that ray-based tomography will be robust at basin-scales. This opens up the possibility of ray-based internal wave tomography using the observables of travel time variance, and vertical and temporal coherence, Using geometrical optics and the GM internal wave spectrum, internal wave tomography for an assortment of parameters of the GM model can be formulated in terms of a mixed linear/nonlinear inverse, This is a significant improvement upon a Monte Carlo approach presented in this paper which is used to infer average internal wave energies as a function of depth for the SLICE89 experiment. However, this Monte Carlo approach demonstrated, for the SLICE89 experiment, that the GM model failed to render a consistent inverse for acoustic energy which sampled the upper 100 m of the ocean, Until a new theory for the forward problem is advanced, internal wave tomography utilizing the signal from strong mode coupling can only be carried out using time-consuming Monte Carlo methods.

Colosi, JA, Scheer EK, Flatte SM, Cornuelle BD, Dzieciuch MA, Munk WH, Worcester PF, Howe BM, Mercer JA, Spindel RC, Metzger K, Birdsall TG, Baggeroer AB.  1999.  Comparisons of measured and predicted acoustic fluctuations for a 3250-km propagation experiment in the eastern North Pacific Ocean. Journal of the Acoustical Society of America. 105:3202-3218.   10.1121/1.424650   AbstractWebsite

During the Acoustic Engineering Test (AET) of the Acoustic Thermometry of Ocean Climate (ATOC) program, acoustic signals were transmitted from a broadband source with 75-Hz center frequency to a 700-m-long vertical array of 20 hydrophones at a distance of 3252 km receptions occurred over a period of-six days. Each received pulse showed early identifiable timefronts, followed by about 2 s of highly variable energy. For the identifiable timefronts, observations of travel-time variance, average pulse shape, and the probability density function (PDF) of intensity are presented, and calculations of internal-wave contributions to those fluctuations are compared to the observations. Individual timefronts have rms travel time fluctuations of 11 to 19 ms, with time scales of less than 2 h. The pulse time spreads are between 0 and 5.3 ms rms, which suggest that internal-wave-induced travel-time biases are of the same magnitude. The PDFs of intensity for individual ray arrivals are compared to log-normal and exponential distributions. The observed PDFs are closer to the log-normal distribution, and variances of log intensity are between (3.1 dB)(2) (with a scintillation index of 0.74) for late-arriving timefronts and (2.0 dB)(2) (with a scintillation index of 0.2) for the earliest timefronts. Fluctuations of the pulse termination time of the transmissions are observed to be 22 ms rms. The intensity PDF of nonidentified peaks in the pulse crescendo are closer to a log-normal distribution than an exponential distribution, but a Kolmogorov-Smimov test rejects both distributions. The variance of the nonidentified peaks is (3.5 dB)(2) land the-scintillation index is 0.92. As a group, the observations suggest that the propagation is on the border of the unsaturated and partially saturated regimes. After improving the specification of the. ray weighting function, predictions of travel-time variance using the Garrett-Munk (GM) internal-wave spectrum at one-half the reference energy are in good agreement with the observations, and the one-half GM energy level compares well with XBT data taken along the transmission path. Predictions of pulse spread and wave propagation regime are in strong disagreement with the observations. Pulse time spread estimates are nearly two orders of magnitude too large, and Lambda-Phi methods for predicting the wave propagation regime predict full saturation. (C) 1999 Acoustical Society of America. [S0001-4966(99)04606-8].

Colosi, JA, Van Uffelen LJ, Cornuelle BD, Dzieciuch MA, Worcester PF, Dushaw BD, Ramp SR.  2013.  Observations of sound-speed fluctuations in the western Philippine Sea in the spring of 2009. Journal of the Acoustical Society of America. 134:3185-3200.   10.1121/1.4818784   AbstractWebsite

As an aid to understanding long-range acoustic propagation in the Philippine Sea, statistical and phenomenological descriptions of sound-speed variations were developed. Two moorings of oceanographic sensors located in the western Philippine Sea in the spring of 2009 were used to track constant potential-density surfaces (isopycnals) and constant potential-temperature surfaces (isotherms) in the depth range 120-2000 m. The vertical displacements of these surfaces are used to estimate sound-speed fluctuations from internal waves, while temperature/salinity variability along isopycnals are used to estimate sound-speed fluctuations from intrusive structure often termed spice. Frequency spectra and vertical covariance functions are used to describe the space-time scales of the displacements and spiciness. Internal-wave contributions from diurnal and semi-diurnal internal tides and the diffuse internal-wave field [related to the Garrett-Munk (GM) spectrum] are found to dominate the sound-speed variability. Spice fluctuations are weak in comparison. The internal wave and spice frequency spectra have similar form in the upper ocean but are markedly different below 170-m depth. Diffuse internal-wave mode spectra show a form similar to the GM model, while internal-tide mode spectra scale as mode number to the minus two power. Spice decorrelates rapidly with depth, with a typical correlation scale of tens of meters.

Colosi, JA, Duda TF, Lin YT, Lynch JF, Newhall AE, Cornuelle BD.  2012.  Observations of sound-speed fluctuations on the New Jersey continental shelf in the summer of 2006. Journal of the Acoustical Society of America. 131:1733-1748.   10.1121/1.3666014   AbstractWebsite

Environmental sensors moored on the New Jersey continental shelf tracked constant density surfaces (isopycnals) for 35 days in the summer of 2006. Sound-speed fluctuations from internal-wave vertical isopycnal displacements and from temperature/salinity variability along isopycnals (spiciness) are analyzed using frequency spectra and vertical covariance functions. Three varieties of internal waves are studied: Diffuse broadband internal waves (akin to waves fitting the deep water Garrett/Munk spectrum), internal tides, and, to a lesser extent, nonlinear internal waves. These internal-wave contributions are approximately distinct in the frequency domain. It is found that in the main thermocline spicy thermohaline structure dominates the root mean square sound-speed variability, with smaller contributions coming from (in order) nonlinear internal waves, diffuse internal waves, and internal tides. The frequency spectra of internal-wave displacements and of spiciness have similar form, likely due to the advection of variable-spiciness water masses by horizontal internal-wave currents, although there are technical limitations to the observations at high frequency. In the low-frequency, internal-wave band the internal-wave spectrum follows frequency to the -1.81 power, whereas the spice spectrum shows a -1.73 power. Mode spectra estimated via covariance methods show that the diffuse internal-wave spectrum has a smaller mode bandwidth than Garrett/Munk and that the internal tide has significant energy in modes one through three. (C) 2012 Acoustical Society of America. [DOI: 10.1121/1.3666014]

Cornuelle, BD, Chereskin TK, Niiler PP, Morris MY, Musgrave DL.  2000.  Observations and modeling of a California undercurrent eddy. Journal of Geophysical Research-Oceans. 105:1227-1243.   10.1029/1999jc900284   AbstractWebsite

A deep, nonlinear warm eddy advecting water that was also anomalously saltier, lower in oxygen, and higher in nutrients relative to surrounding waters was observed in moored current and temperature measurements and in hydrographic data obtained at a site similar to 400 km off the coast of northern California. The eddy was reproduced using a nonlinear quasi-geostrophic model, initialized by an iterative procedure using time series of 2-day averaged moored current measurements. The procedure demonstrates how a data assimilative technique synthesizes and enhances the resolution of a relatively sparse data set by incorporating time-dependence and model physics. The model forecast showed significant skill above persistence or climatology for 40 days. Our hypothesis, that the eddy was generated at the coast in winter and subsequently moved 400 km offshore by May, is consistent with the eddy movement diagnosed by the model and with the observations and coastal climatology. The model evolution significantly underpredicted the temperature anomaly in the eddy owing in part to unmodeled salinity compensation in trapped California Undercurrent water. Together, observations and model results show a stable nonlinear eddy in the California Current System that transported water and properties southwestward through the energetic eastern boundary region. Coherent features such as this one may be a mechanism for property transfer between the eddy-rich coastal zone and the eddy desert of the eastern North Pacific Ocean.

Cornuelle, BD, Morris MY, Roemmich DH.  1993.  An Objective Mapping Method for Estimating Geostrophic Velocity from Hydrographic Sections Including the Equator. Journal of Geophysical Research-Oceans. 98:18109-18118.   10.1029/93jc01729   AbstractWebsite

Objective mapping can remove the equatorial singularity from the problem of estimating geostrophic shear from noisy density measurements. The method uses the complete thermal wind relation, so it is valid uniformly on and off the equator. Errors in the thermal wind balance are due to neglected terms in the momentum balance, which are treated as noise in the inverse problem. The question of whether the geostrophic balance holds near the equator is restated as a need to estimate the size of the ageostrophic noise in the thermal wind equation. Objective mapping formalizes the assumptions about the magnitudes and scales of the geostrophic currents and about the magnitudes and scales of the ageostrophic terms and measurement errors. The uncertainty of the velocity estimates is calculated as part of the mapping and depends on the signal to noise ratio (geostrophic density signal to ageostrophic ''noise'') in the data, as well as the station spacing and the scales assumed for the geostrophic velocities. The method is used to map zonal velocity from a mean Hawaii-Tahiti Shuttle density section. These are compared with previous velocity estimates for the same dataset calculated using other techniques. By choosing appropriate scales, the objective map can duplicate previous results. New temperature data are presented from a repeating, high-resolution expendable bathythermograph section crossing the equator at about 170-degrees-W with four cruises a year between 1987-1991. There appear to be significant differences between this mean temperature and the shuttle mean temperature. Temperature is converted to density with the aid of a mean T-S relation and geostrophic velocity maps are calculated for the 4-year mean. The mean geostrophic undercurrent obtained from our sections is weaker than in the shuttle estimate and is centered slightly north of the equator. Enforcing symmetry about the equator removes the offset of the current, giving a stronger, but narrow undercurrent. The density field apparently includes significant (O(0.5 kg M-3)) large-scale ageostrophic variability which makes velocity estimates from single cruises poorly determined near the equator.

Cornuelle, BD, Malanotterizzoli P.  1986.  A Maximum-Gradient Inverse for the Gulf-Stream System. Journal of Geophysical Research-Oceans. 91:566-580.   10.1029/JC091iC09p10566   AbstractWebsite

Acoustic tomography uses integrating measurements which require inverse methods to resolve the averages into estimates of spatial structure. Statistical inverse methods have been extensively used to solve the reconstruction problem over different tomographic ranges and configurations. These inverses become very difficult to apply in frontal regions like the Gulf Stream (GS) system, where the statistics are acutely inhomogeneous and anisotropic and the mean is not a likely representation of the GS front at any time. In this paper we propose an alternative inverse which asks for the solution which gives a front instead of asking for the smoothest solution. The inverse solution minimizes the errors in the fit to the data while simultaneously maximizing the sum of the squares of the gradients observed in the reconstructed section and minimizing the absolute value norm for stability. The inverse is aimed at detecting changes in the GS front, thus the data are used to estimate the perturbations to a previous estimate of the frontal structure, instead of reconstructing the entire front as a perturbation from some average state. This approach is intended to merge well with eventual dynamic updating schemes and can be used with various types of data, given a proper model. Several examples have been run intercomparing the traditional linear least squares (LLSI) with the maximum gradient inverse (MGI), from very idealized cases to a real Gulf Stream section reconstructed from hydrographic data. Different transceiver configurations were also compared and mid-depth instruments were found to be superior to bottom mounted instruments. The simplest cases show a significant improvement in the estimate of the Gulf Stream front by the MGI compared to the weighted least squares inverse (LLSI). As the cases became more complicated (and more realistic), the differences between inverse methods become less pronounced, although the strength and location of the perturbation maxima were always determined more accurately by the MGI. The decline is at least partially due to the numerical algorithm which lumps data misfits and external constraints (the maximum gradient) into a single penalty criterion which is minimized. The most immediate way to overcome this limitation is to break up the problem into a two-step procedure, first a least squares inverse to fit the data and second an iterative, nonlinear optimization maximizing the gradient and minimizing the absolute value norm.

Cornuelle, BD, Worcester PF.  1996.  Ocean Acoustic Tomography: Integral data and ocean models. Elsevier oceanography series. ( Malanotte-Rizzoli P, Ed.).:97-115., Amsterdam, New York: Elsevier Abstract
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Cornuelle, B.  1990.  Some practical aspects of ocean acoustic tomography. Oceanographic and geophysical tomography: Les Houches, session L, 1988. ( Desaubies Y, Tarantola A, Zinn-Justin J, Eds.)., Amsterdam: North-Holland Abstract
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Cornuelle, BD, Worcester PF, Hildebrand JA, Hodgkiss WS, Duda TF, Boyd J, Howe BM, Mercer JA, Spindel RC.  1993.  Ocean Acoustic Tomography at 1000-Km Range Using Wave-Fronts Measured with a Large-Aperture Vertical Array. Journal of Geophysical Research-Oceans. 98:16365-16377.   10.1029/93jc01246   AbstractWebsite

Broadband acoustic signals transmitted from a moored 250-Hz source to a 3-km-long vertical line array of hydrophones 1000 km distant in the north central Pacific Ocean were used to determine the amount of information available from tomographic techniques used in the vertical plane connecting a source-receiver pair. A range-independent, pure acoustic inverse to obtain the sound speed field using travel time data from the array is shown to be possible by iterating from climatological data without using any information from concurrent environmental measurements. Range-dependent inversions indicate resolution of components of oceanic variability with horizontal wavelengths shorter than 50 km, although the limited spatial resolution of concurrent direct measurements does not provide a strong cross-validation, since the typical cast spacing of 20-25 km gives a Nyquist wavelength of 40-50 km. The small travel time signals associated with high-wavenumber ocean variability place stringent but achievable requirements on travel time measurement precision. The forward problem for the high-wavenumber components of the model is found to be subject to relatively large linearization errors, however, unless the sound speed field at wavelengths greater than about 50 km is known from other measurements or from a two-dimensional tomographic array. The high-ocean-wavenumber resolution that is in principle available from tomographic measurements is therefore achievable only under restricted conditions.

Cornuelle, B, Howe BM.  1987.  High Spatial-Resolution in Vertical Slice Ocean Acoustic Tomography. Journal of Geophysical Research-Oceans. 92:11680-11692.   10.1029/JC092iC11p11680   AbstractWebsite

Most studies of ocean acoustic tomography have assumed that little horizontal information is available from the many acoustic multipath travel times observed in a single vertical plane (slice) between source and receiver moorings. There is in fact significant small-scale information present in such data sets. We examine single vertical slice tomography in spectral terms, and show that the acoustic measurements resemble a high-pass filter, which is more sensitive to small scales (shorter than 100 km) than to longer scales, with the exception of the mean, which is well measured. The sensitivity extends to scales smaller than 10 km, in theory, although the level of the ocean energy spectrum is so low at these scales that even small data errors limit the measurement. We use analytical calculations supplemented by numerical simulations with realistic data sets to show that accurate reconstructions of the high wave number features are possible out to the limits of the parameterization (9.2-km wavelength) when the power spectrum of the ocean features is white or red, the total measurement error is 1 ms, and multiple receivers are used. The ultimate limit of spatial resolution may be smaller still, depending on array configuration, measurement errors, and the shape of the power spectrum.

Cornuelle, B, Wunsch C, Behringer D, Birdsall T, Brown M, Heinmiller R, Knox R, Metzger K, Spiesberger J, Spindel R, Webb D, Worcester P.  1985.  Tomographic maps of the ocean mesoscale. Part 1: Pure acoustics. Journal of Physical Oceanography. 15:133-152.   10.1175/1520-0485(1985)015<0133:TMOTOM>2.0.CO;2   Abstract

A field test of ocean acoustic tomography was conducted in 1981 for a two month period in a 300 km square at 26°N, 70°W in the North Atlantic (just south of the MODE region). Nine acoustic deep-sea moorings with sea floor transponders for automated position keeping and with provisions for precise time keeping were set and recovered. From the measured travel times between moorings, various displays of the three-dimensional field of sound speed (closely related to temperature) have been obtained by inversion procedures. These procedures use historical ocean data as a reference, but all information from the in situ surveys has been withheld; the “pure” tomographic results were then compared to direct in situ observations. The tomographically derived spatial mean profile compares favorably to an equivalent profile from the in situ observations; both differ significantly from the historical average. Maps constructed at three day intervals for a two month period show a pattern of eddy structure in agreement with the direct observations within computed mapping errors, but these mapping errors are too large for many oceanographic purposes. The mapping errors are the result of an unexpectedly large noise variance in travel time. (A 1983 experiment, using sources with larger bandwidth, reduced this variance to acceptable limits.) The 1981 tomographic results strongly suggest that the ocean sometimes undergoes transitions too rapid to be mapped over such large areas by shipboard observations.

Cornuelle, B, Munk W, Worcester P.  1989.  Ocean Acoustic Tomography from Moving Ships. Journal of Geophysical Research-Oceans. 94:6232-6250.   10.1029/JC094iC05p06232   AbstractWebsite

Mesoscale mapping of the ocean sound speed field in a 1000×1000 km area by means of ocean acoustic tomography is greatly enhanced by augmenting a few acoustic moorings with a movable ship-based receiver. Computer simulations based on realistic noise levels in the measured acoustic travel times give 5% (1%) residual variance in ΔC(x;y,z) for four (six) acoustic source moorings in an ocean perturbed in the gravest baroclinic mode. For comparison, objective mapping based on traditional vertical profiles requires 3 times the steaming distance to yield equivalent residual error. Detailed results depend on many parameters: the assumed mesoscale spectrum and vertical mode structure, the number of observed multipaths, the mooring configuration, the number of ship stations and the travel time signal level (due to mesoscale eddies) and noise level (due to internal waves and position-keeping errors). These parameters have critical values, below which there is distinct deterioration and beyond which there is little gain. We believe that the critical values can be attained in practice so the ultimate limit on mesoscale mapping is imposed by the internal wave-induced travel time error. This assumes that position keeping of the submerged acoustic sources and receiver by a combination of satellite navigation and high-frequency acoustics can be achieved with ±10-m accuracy. The present study assumes a stationary ocean; a second paper will deal with reciprocal transmissions yielding currents and hence the barotropic mode. This is required in a dynamic ocean model for estimating ΔC(x,y,z;t). All this is preparatory to a tomography experiment in the Greenland Sea in 1988–1989.

Cornuelle, BD.  1982.  Acoustic Tomography. IEEE Transactions on Geoscience and Remote Sensing. 20:326-332.   10.1109/tgrs.1982.350450   AbstractWebsite

High-resolution measurements of the density field in the ocean are prohibitively expensive if traditional ship-borne instruments are used. Tomography uses acoustic remote sensing to infer ocean structure, and avoids many of the limitations of direct measurements. Sound pulses follow distinct trajectories through the water from source to receiver, and the travel time for a given pulse is a known functional of the sound speed field. This functional can be inverted to recover an estimate of the sound speed field through which it passed. The inversion is accomplished with either detenninistic linear matrix inversion or stochastic optimal estimation, and the sound speed field estimate returned can be converted to an estimate of density. A numerical simulation of the pilot tomography experiment is presented to demonstrate that tomography can be effective in reproducing significant ocean features.

Cornuelle, BD.  1985.  Simulations of Acoustic Tomography Array Performance with Untracked or Drifting Sources and Receivers. Journal of Geophysical Research-Oceans. 90:9079-9088.   10.1029/JC090iC05p09079   AbstractWebsite

Ocean tomography as originally proposed required all sources and recievers to be tautly moored and acoustically tracked to separate travel time perturbations due to mooring motion from those due to ocean features. It is possible to process the tomographic travel times to estimate both ocean sound speed perturbations and mooring offsets, effecting a separation without external tracking. A side effect of this processing is a check on the ray identification, since the varying instrument positions can be used as a synthetic array for estimating ray angle. Simulations and examples with actual data were used to contrast mapping performance with and without mooring tracking for a variety of ray data sets. In general, the ocean maps degrade when the tracking data are withheld. However, when many high-precision ray travel time measurements are available, the degradation is small; in these cases it would be possible to deploy free-drifting instruments as part of a monitoring experiment.

Crosby, SC, Cornuelle BD, O'Reilly WC, Guza RT.  2017.  Assimilating Global Wave Model Predictions and Deep-Water Wave Observations in Nearshore Swell Predictions. Journal of Atmospheric and Oceanic Technology. 34:1823-1836.   10.1175/jtech-d-17-0003.1   AbstractWebsite

Nearshore wave predictions with high resolution in space and time are needed for boating safety, to assess flood risk, and to support nearshore processes research. This study presents methods for improving regional nearshore predictions of swell-band wave energy (0.04-0.09 Hz) by assimilating local buoy observations into a linear wave propagation model with a priori guidance from global WAVEWATCH III (WW3) model predictions. Linear wave propagation, including depth-induced refraction and shoaling, and travel time lags, is modeled with self-adjoint backward ray tracing techniques. The Bayesian assimilation yields smooth, high-resolution offshore wave directional spectra that are consistent with WW3, and with offshore and local buoy observations. Case studies in the Southern California Bight (SCB) confirm that the nearshore predictions at independent (nonassimilated) buoy sites are improved by assimilation compared with predictions driven with WW3 or with a single offshore buoy. These assimilation techniques, valid in regions and frequency bands where wave energy propagation is mostly linear, use significantly less computational resources than nonlinear models and variational methods, and could be a useful component of a larger regional assimilation program. Where buoy locations have historically been selected to meet local needs, these methods can aid in the design of regional buoy arrays by quantifying the regional skill improvement for a given buoy observation and identifying both high-value and redundant observations. Assimilation techniques also identify likely forward model error in the Santa Barbara Channel, where permanent observations or model corrections are needed.

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Di Lorenzo, E, Moore AM, Arango HG, Cornuelle BD, Miller AJ, Powell B, Chua BS, Bennett AF.  2007.  Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system. Ocean Modelling. 16:160-187.   10.1016/j.ocemod.2006.08.002   AbstractWebsite

We describe the development and preliminary application of the inverse Regional Ocean Modeling System (ROMS), a four dimensional variational (4DVAR) data assimilation system for high-resolution basin-wide and coastal oceanic flows. Inverse ROMS makes use of the recently developed perturbation tangent linear (TL), representer tangent linear (RP) and adjoint (AD) models to implement an indirect representer-based generalized inverse modeling system. This modeling framework is modular. The TL, RP and AD models are used as stand-alone sub-models within the Inverse Ocean Modeling (IOM) system described in [Chua, B.S., Bennett, A.F., 2001. An inverse ocean modeling system. Ocean Modell. 35 137-165.]. The system allows the assimilation of a wide range of observation types and uses an iterative algorithm to solve nonlinear assimilation problems. The assimilation is performed either under the perfect model assumption (strong constraint) or by also allowing for errors in the model dynamics (weak constraints). For the weak constraint case the TL and RP models are modified to include additional forcing terms on the right hand side of the model equations. These terms are needed to account for errors in the model dynamics. Inverse ROMS is tested in a realistic 3D baroclinic upwelling system with complex bottom topography, characterized by strong mesoscale eddy variability. We assimilate synthetic data for upper ocean (0-450 m) temperatures and currents over a period of 10 days using both a high resolution and a spatially and temporally aliased sampling array. During the assimilation period the flow field undergoes substantial changes from the initial state. This allows the inverse solution to extract the dynamically active information from the synthetic observations and improve the trajectory of the model state beyond the assimilation window. Both the strong and weak constraint assimilation experiments show forecast skill greater than persistence and climatology during the 10-20 days after the last observation is assimilated. Further investigation in the functional form of the model error covariance and in the use of the representer tangent linear model may lead to improvement in the forecast skill. (c) 2006 Elsevier Ltd. All rights reserved.

Di Lorenzo, E, Miller AJ, Neilson DJ, Cornuelle BD, Moisan JR.  2004.  Modelling observed California Current mesoscale eddies and the ecosystem response. International Journal of Remote Sensing. 25:1307-1312.   10.1080/01431160310001592229   AbstractWebsite

Satellite and in situ observations are used to test model dynamics for the California Current System (CCS). The model and data are combined to reconstruct the mesoscale ocean structure during a given three-week period. The resulting physical flow field is used to drive a 3D ecosystem model to interpret SeaWiFS and in situ chlorophyll-a (chl-a) variations. With this approach a more complete and consistent picture of the physical and ecosystem processes of the CCS is obtained, providing the basis for addressing fundamental questions about dynamics and predictability of the coastal ocean.

Duda, TF, Flatte SM, Colosi JA, Cornuelle BD, Hildebrand JA, Hodgkiss WS, Worcester PF, Howe BM, Mercer JA, Spindel RC.  1992.  Measured Wave-Front Fluctuations in 1000-Km Pulse-Propagation in the Pacific-Ocean. Journal of the Acoustical Society of America. 92:939-955.   10.1121/1.403964   AbstractWebsite

A 1000-km acoustical transmission experiment has been carried out in the North Pacific, with Pulses broadcast between a moored broadband source (250-Hz center frequency) and a moored sparse vertical line of receivers. Two data records are reported: a period of 9 days at a pulse rate of one per hour, and a 21 -h period on the seventh day at six per hour. Many wave-front segments were observed at each hydrophone depth, and arrival times were tracked and studied as functions of time and depth. Arrivals within the final section of the pulse are not trackable in time or space at the chosen sampling rates, however. Broadband fluctuations, which are uncorrelated over 10-min sampling and 60-m vertical spacing, are observed with about 40 (ms)2 variance. The variance of all other fluctuations (denoted as low-frequency) is comparable or smaller than the broadband value; this low-frequency variance can be separated into two parts: a wave-front segment displacement (with vertical correlation length greater than 1 km) that varies substantially between rays with different ray identifiers, and a distortion (with vertical correlation length between 60 m and 1 km) of about 2 (ms)2 variance. The low-frequency variance may be explained as the effect of internal waves, including internal tides. The variance of the broadband fluctuations is reduced somewhat but not eliminated if only high-intensity peaks are selected; this selection does not affect the statistics of the low-frequency fluctuations.

Duda, TF, Pawlowicz RA, Lynch JF, Cornuelle BD.  1995.  Simulated Tomographic Reconstruction of Ocean Features Using Drifting Acoustic Receivers and a Navigated Source. Journal of the Acoustical Society of America. 98:2270-2279.   10.1121/1.413341   AbstractWebsite

Numerically simulated acoustic transmission from a single source of known position (for example, suspended from a ship) to receivers of partially known position (for example, sonobuoys dropped from the air) are used for tomographic mapping of ocean sound speed. The maps are evaluated for accuracy and utility. Grids of 16 receivers are employed, with sizes of 150, 300, and 700 km square. Ordinary statistical measures are used to evaluate the pattern similarity and thus the mapping capability of the, system. For an array of 300 km square, quantitative error in the maps grows with receiver position uncertainty. The large and small arrays show lesser mapping capability than the mid-size array. Mapping errors increase with receiver position uncertainty for uncertainties less than 1000-m rms, but uncertainties exceeding that have less systematic effect on the maps. Maps of rms error of the field do not provide a complete view of the utility of the acoustic network. Features of maps are surprisingly reproducible for different navigation error levels, and give comparable information about mesoscale structures despite great variations in those levels. (C) 1995 Acoustical Society of America.