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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.

Kim, SY, Terrill E, Cornuelle B.  2007.  Objectively mapping HF radar-derived surface current data using measured and idealized data covariance matrices. Journal of Geophysical Research-Oceans. 112   10.1029/2006jc003756   AbstractWebsite

Surface currents measured by high-frequency radars are objectively mapped using covariance matrices computed from hourly surface current vectors spanning two years. Since retrievals of surface radial velocities are inherently gappy in space and time, the irregular density of surface current data leads to negative eigenvalues in the sample covariance matrix. The number and the magnitude of the negative eigenvalues depend on the degree of data continuity used in the matrix computation. In a region of 90% data coverage, the negative eigenvalues of the sample covariance matrix are small enough to be removed by adding a noise term to the diagonal of the matrix. The mapping is extended to regions of poorer data coverage by applying a smoothed covariance matrix obtained by spatially averaging the sample covariance matrix. This approach estimates a stable covariance matrix of surface currents for regions with the intermittent radar coverage. An additional benefit is the removal of baseline errors that often exist between two radar sites. The covariance matrices and the correlation functions of the surface currents are exponential in space rather than Gaussian, as is often assumed in the objective mapping of oceanographic data sets. Patterns in the decorrelation length scale provide the variabilities of surface currents and the insights on the influence of topographic features (bathymetry and headlands). The objective mapping approach presented herein lends itself to various applications, including the Lagrangian transport estimates, dynamic analysis through divergence and vorticity of current vectors, and statistical models of surface currents.

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.

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]

Morris, M, Roemmich D, Cornuelle B.  1996.  Observations of variability in the South Pacific subtropical gyre. Journal of Physical Oceanography. 26:2359-2380.   10.1175/1520-0485(1996)026<2359:oovits>;2   AbstractWebsite

Variability of the subtropical gyre in the South Pacific Ocean was investigated using high-resolution expendable bathythermograph sections along a repeated track between New Zealand and Hawaii. The southern part of the section sampled most of the zonal flow in the subtropical gyre with the eastward flowing branch between New Zealand and Fiji and the westward branch extending north of Fiji to approximately 10 degrees S. The time series began in September 1987 and extended through 1994, averaging four cruises every year. The geostrophic shear field was calculated, relative to 800 m, with the aid of a mean T-S relationship. Variability was present at a broad range of spatial and temporal scales but annual fluctuations were particularly prominent. The authors conclude that 30 snapshots of temperature, measured over a period of seven years, are sufficient to resolve the annual cycle of the gyre scale circulation along the transect. The shape and intensity of the gyre varied seasonally throughout the water column (0-800 m). Geostrophic transport was most intense (15 Sv, where Sv=10(6)m(3)s(-1)) in November. At this time, the northern edges of eastward dow at the surface and in the thermocline were closest together and the ratio of thermocline to surface transport was highest. Most intense flow occurred approximately two to three months after the basinwide seasonal peak in Ekman pumping. Transport was weakest(ll Sv) in May and was associated with an increase in the poleward slant of the gyre center with depth and a decrease in the ratio of thermocline to surface transport. Seasonal wind forcing was considered as a possible mechanism for the observed annual intensification of the gyre-scale circulation. A simple linear model of thermocline response to local changes in wind stress curl explained a significant fraction of the observed annual variability. Conservation of potential vorticity q yielded an estimate for the absolute mean how (-1 cm s(-1) at 800 m), consistent with direct measurements in the region. Interannual variability, possibly related to the El Nino-Southern Oscillation cycle, was observed. The cold event of 1988/89 appeared to be associated with relatively weak gyre-scale transport. After 1991, gyre-scale transport was more intense and a prominent change in the small-scale circulation occurred, with a shift in the alongtrack wavenumber spectral energy to higher wavenumbers.

Roemmich, D, Cornuelle B.  1990.  Observing the Fluctuations of Gyre-Scale Ocean Circulation - a Study of the Subtropical South-Pacific. Journal of Physical Oceanography. 20:1919-1934.   10.1175/1520-0485(1990)020<1919:otfogs>;2   AbstractWebsite

Seasonal and interannual variability of the subtropical gyre in the South Pacific Ocean are investigated by means of a time series of expendable bathythermograph (XBT) sections between New Zealand (36-degrees-S, 175-degrees-E) and Fiji (18-degrees-S, 178-degrees-E). The experiment spans much of the subtropical gyre and is a protype for future basin-scale observations. Eddy-resolving transects along the precisely repeating ship track, spanning four years, are used to estimate the mean field and fluctuations of temperature and geostrophic velocity. The mean field dominates on very large spatial scales while the fluctuations dominate on small scales. Mean and fluctuations have equal energy at a horizontal wavelength of about 2000 km. The study region contains three recurring small-scale features. These are the East Auckland Current, flowing eastward along the New Zealand continental slope, a front at about 29-degrees-S which is likely an extension of the Tasman Front, and a weaker feature, the Tropical Convergence at about 22-degrees-S. At lower latitudes in the study region, the entire thermocline migrates vertically at annual period. This annual oscillation ends near the front at 29-degrees-S. Farther poleward, the only substantial subsurface annual variation is in the strength of the East Auckland Current. Interannual variability of circulation during 1986-90 consisted of rapid transitions between two rather steady states. In one state, which persisted through 1987-88 and from mid-1989 to the present (mid-1990), the eastward flowing limb of the gyre was relatively strong and narrow, with a reversal in velocity at the ocean surface south of Fiji.

Dushaw, B, Bold G, Chiu CS, Colosi J, Cornuelle B, Desaubies Y, Dzieciuch M, Forbes A, Gaillard F, Gavrilov A, Gould J, Howe BM, Lawrence M, Lynch J, Menemenlis D, Mercer J, Mikhalevsky PN, Munk W, Nakano I, Schott F, Send U, Spindel R, Terre T, Worcester P, Wunsch C.  2001.  Observing the ocean in the 2000's: A strategy for the role of acoustic tomography in ocean climate observation. Observing the Oceans in the 21st Century. ( Koblinsky C, Smith NR, Eds.).:391-418., Melbourne: Bureau of Meteorology Abstract
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, 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.

Worcester, P, Cornuelle B.  1982.  Ocean acoustic tomography: Currents. Current Measurement, Proceedings of the 1982 IEEE Second Working Conference on. 2:131-135., Hilton Head Island, South CArolina   10.1109/ccm.1982.1158437   Abstract

Synoptic maps of the geostrophic current structure of the mesoscale field can be constructed from the three-dimensional density field provided by ocean acoustic tomography with unidirectional acoustic transmissions. Reciprocal acoustic transmissions can extend the technique by permitting one to directly measure the current field, including the barotropic component. A preliminary reciprocal acoustic transmission experiment at long range (300 km) and low frequency (400 Hz) is planned for autumn 1982.

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
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.

Haidvogel, DB, Arango H, Budgell WP, Cornuelle BD, Curchitser E, Di Lorenzo E, Fennel K, Geyer WR, Hermann AJ, Lanerolle L, Levin J, McWilliams JC, Miller AJ, Moore AM, Powell TM, Shchepetkin AF, Sherwood CR, Signell RP, Warner JC, Wilkin J.  2008.  Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the Regional Ocean Modeling System. Journal of Computational Physics. 227:3595-3624.   10.1016/   AbstractWebsite

Systematic improvements in algorithmic design of regional ocean circulation models have led to significant enhancement in simulation ability across a wide range of space/time scales and marine system types. As an example, we briefly review the Regional Ocean Modeling System, a member of a general class of three-dimensional, free-surface, terrain-following numerical models. Noteworthy characteristics of the ROMS computational kernel include: consistent temporal averaging of the barotropic mode to guarantee both exact conservation and constancy preservation properties for tracers; redefined barotropic pressure-gradient terms to account for local variations in the density field; vertical interpolation performed using conservative parabolic splines; and higher-order, quasi-monotone advection algorithms. Examples of quantitative skill assessment are shown for a tidally driven estuary, an ice-covered high-latitude sea, a wind- and buoyancy-forced continental shelf, and a mid-latitude ocean basin. The combination of moderate-order spatial approximations, enhanced conservation properties, and quasi-monotone advection produces both more robust and accurate, and less diffusive, solutions than those produced in earlier terrain-following ocean models. Together with advanced methods of data assimilation and novel observing system technologies, these capabilities constitute the necessary ingredients for multi-purpose regional ocean prediction systems. (c) 2007 Elsevier Inc. All rights reserved.

Sutton, PJ, Worcester PF, Masters G, Cornuelle BD, Lynch JF.  1993.  Ocean Mixed Layers and Acoustic Pulse-Propagation in the Greenland Sea. Journal of the Acoustical Society of America. 94:1517-1526.   10.1121/1.408128   AbstractWebsite

A simple one-dimensional ocean mixed layer model is used to study the effect of the transition between summer and winter conditions in the Greenland Sea on range-independent acoustic propagation. Acoustic normal modes propagated through the evolving sound-speed profile simulate broadband acoustic receptions from the Greenland Sea Tomography Experiment. The resulting changes in arrival structure and travel time are compared with data recorded between two of the tomographic moorings. The starting state for the model is the average of measured summer temperature and salinity profiles. At each time step the surface layer is modified by the removal of heat (modeling heat loss to the atmosphere) and the removal of fresh water (modeling evaporation minus precipitation). When necessary, static stability is maintained by mixing the surface layer into deeper layers. The acoustic normal modes exhibit large changes in behavior as the profile changes. In both summer (seasonal thermocline) and winter (adiabatic sound-speed profile) individual modes show minimal frequency dispersion. Intermediate profiles with a shallow surface mixed layer give highly dispersive modes, delaying the final acoustic energy cutoff by several hundred milliseconds relative to the summer and winter cases. This is the largest travel time signal observed in the data. The largest peak in the late continuous acoustic energy is due to minimally dispersed modes and corresponds to ray arrivals with near horizontal receiver angles. The amplitude of the arrival is low when significant dispersion is present.

Pinkel, R, Munk W, Worcester P, Cornuelle BD, Rudnick D, Sherman J, Filloux JH, Dushaw BD, Howe BM, Sanford TB, Lee CM, Kunze E, Gregg MC, Miller JB, Merrifield MA, Luther DS, Firing E, Brainard R, Flament PJ, Chave AD, Moum JM, Caldwell DR, Levine MD, Boyd T, Egbert GD.  2000.  Ocean mixing studied near Hawaiian Ridge. Eos, Transactions American Geophysical Union. 81:545-553.   10.1029/EO081i046p00545-02   AbstractWebsite

The Hawaii Ocean Mixing Experiment (HOME) is a grassroots program to study turbulent mixing processes near the Hawaiian Ridge. The HOME is motivated by the desire to understand diffusive aspects of the advective-diffusive balance that mediates the general circulation of the oceans. HOME is focused on tidally driven mixing, given the ubiquity of the tide as a deep-sea energy source. As the sea surface cools at high latitude, surface waters sink. Subsidence rate is sufficient to fill the worlds ocean with cold bottom water in approximately 3,000 years. Diffusive processes that transfer heat into the abyssal ocean are required to maintain a steady-state thermal structure. An effective eddy diffusivity of order Kp=10−4 m2 s−1, 700 times the molecular diffusivity of heat, is necessary [Munk, 1966]. Such a diffusivity might be supported by either mechanical mixing (turbulent transport) or thermodynamic (so-called doubly diffusive) processes.

Dushaw, BD, Worcester PF, Cornuelle BD, Howe BM.  1993.  On Equations for the Speed of Sound in Seawater. Journal of the Acoustical Society of America. 93:255-275.   10.1121/1.405660   AbstractWebsite

Long-range acoustic transmissions made in conjunction with extensive environmental measurements and accurate mooring position determinations have been used to test the accuracy of equations used to calculate sound speed from pressure, temperature, and salinity. The sound-speed fields computed using the Del Grosso equation [ V. A. Del Grosso, J. Acoust. Soc. Am. 56, 1084-1091 (1974)] give predictions of acoustic arrival patterns which agree significantly better with the long-range measurements than those computed using the Chen and Millero equation [ C. Chen and F. J. Millero, J. Acoust. Soc. Am. 62, 1129-1135 (1977) The predicted ray travel times and travel time error have been calculated using objectively mapped sound-speed fields computed from conductivity, temperature, depth (CTD) and expendable bathythermograph (XBT) data. Using the measured and predicted ray travel times, a negligible correction to Del Grosso's equation of + 0.05 +/- 0.05 m/s at 4000-m depth is calculated.