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Hoteit, I, Cornuelle B, Kohl A, Stammer D.  2005.  Treating strong adjoint sensitivities in tropical eddy-permitting variational data assimilation. Quarterly Journal of the Royal Meteorological Society. 131:3659-3682.: Royal Meteorological Society, 104 Oxford Rd. Reading Berks RG1 7LL UK   10.1256/qj.05.97   AbstractWebsite

A variational data assimilation system has been implemented for the tropical Pacific Ocean using an eddy-permitting regional implementation of the MITgcm. The adjoint assimilation system was developed by the Estimation of the Circulation and the Climate of the Ocean consortium, and has been extended to deal with open boundaries. This system is used to adjust the model to match observations in the tropical Pacific region using control parameters which include initial conditions, open boundaries and time-dependent surface fluxes. This paper focuses on problems related to strong adjoint sensitivities that may impede the model fit to the observations. A decomposition of the velocities at the open boundaries into barotropic and baroclinic modes is introduced to deal with very strong sensitivities of the model sea surface height to the barotropic component of the inflow. Increased viscosity and diffusivity terms are used in the adjoint model to reduce exponentially growing sensitivities in the backward run associated with nonlinearity of the forward model. Simplified experiments in which the model was constrained with Levitus temperature and salinity data, Reynolds sea surface temperature data and TOPEX/POSEIDON altimeter data were performed to demonstrate the controllability of this assimilation system and to study its sensitivity to the starting guesses for forcing and initial conditions.

Skarsoulis, EK, Cornuelle BD.  2004.  Travel-time sensitivity kernels in ocean acoustic tomography. Journal of the Acoustical Society of America. 116:227-238.   10.1121/1.1753292   AbstractWebsite

Wave-theoretic ocean acoustic propagation modeling is combined with the peak arrival approach for tomographic travel-time observables to derive the sensitivity kernel of travel times with respect to sound-speed variations. This is the Born-Frechet kernel relating the three-dimensional spatial distribution of sound-speed variations with the induced travel-time variations. The derivation is based on the first Born approximation of the Green's function. The application of the travel-time sensitivity kernel to an ocean acoustic waveguide gives a picture close to the ray-theoretic one in the case of high frequencies. However, in the low-frequency case, of interest in ocean acoustic tomography, for example, there are significant deviations. Low-frequency travel times are sensitive to sound-speed changes in Fresnel-zone-scale areas surrounding the eigenrays, but not on the eigenrays themselves, where the sensitivity is zero. Further, there are areas of positive sensitivity, where, e.g., a sound-speed increase results in an increase of arrival times, i.e., a further delay of arrivals, in contrast with the common expectation. These findings are confirmed by forward acoustic predictions from a coupled-mode code. (C) 2004 Acoustical Society of America.

Skarsoulis, EK, Cornuelle BD, Dzieciuch MA.  2009.  Travel-time sensitivity kernels in long-range propagation. Journal of the Acoustical Society of America. 126:2223-2233.   10.1121/1.3224835   AbstractWebsite

Wave-theoretic travel-time sensitivity kernels (TSKs) are calculated in two-dimensional (2D) and three-dimensional (3D) environments and their behavior with increasing propagation range is studied and compared to that of ray-theoretic TSKs and corresponding Fresnel-volumes. The differences between the 2D and 3D TSKs average out when horizontal or cross-range marginals are considered, which indicates that they are not important in the case of range-independent sound-speed perturbations or perturbations of large scale compared to the lateral TSK extent. With increasing range, the wave-theoretic TSKs expand in the horizontal cross-range direction, their cross-range extent being comparable to that of the corresponding free-space Fresnel zone, whereas they remain bounded in the vertical. Vertical travel-time sensitivity kernels (VTSKs)-one-dimensional kernels describing the effect of horizontally uniform sound-speed changes on travel-times-are calculated analytically using a perturbation approach, and also numerically, as horizontal marginals of the corresponding TSKs. Good agreement between analytical and numerical VTSKs, as well as between 2D and 3D VTSKs, is found. As an alternative method to obtain wave-theoretic sensitivity kernels, the parabolic approximation is used; the resulting TSKs and VTSKs are in good agreement with normal-mode results. With increasing range, the wave-theoretic VTSKs approach the corresponding ray-theoretic sensitivity kernels. (C) 2009 Acoustical Society of America. [DOI: 10.1121/1.3224835]

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.

Wiggins, SM, Dorman LM, Cornuelle BD.  1997.  Topography can affect linearization in tomographic inversions. Geophysics. 62:1797-1803.   10.1190/1.1444280   AbstractWebsite

Linearized inverse techniques commonly are used to solve for velocity models from traveltime data. The amount that a model may change without producing large, nonlinear changes in the predicted traveltime data is dependent on the surface topography and parameterization. Simple, one-layer, laterally homogeneous, constant-gradient models are used to study analytically and empirically the effect of topography and parameterization on the linearity of the model-data relationship. If, in a weak-velocity-gradient model, rays turn beneath a valley with topography similar to the radius of curvature of the raypaths, then large nonlinearities will result from small model perturbations. Hills, conversely, create environments in which the data are more nearly linearly related to models with the same model perturbations.

Dushaw, BD, Egbert GD, Worcester PF, Cornuelle BD, Howe BM, Metzger K.  1997.  A TOPEX/POSEIDON global tidal model (TPXO.2) and barotropic tidal currents determined from long-range acoustic transmissions. Progress in Oceanography. 40:337-367.   10.1016/s0079-6611(98)00008-1   AbstractWebsite

Tidal currents derived from the TPXO.2 global tidal model of Egbert, Bennett, and Foreman are compared with those determined from long-range reciprocal acoustic transmissions. Amplitudes and phases of tidal constituents in the western North Atlantic are derived from acoustic data obtained in 1991-1992 using a pentagonal array of transceivers. Small, spatially coherent differences between the measured and modeled tidal harmonic constants mostly result from smoothing assumptions made in the model and errors caused in the model currents by complicated topography to the southwest of the acoustical array. Acoustically measured harmonic constants (amplitude, phase) of M-2 tidal vorticity (3-8 x 10(-9) s(-1), 210-310 degrees) agree with those derived from the TPXO.2 model (2-5 x 10(-9) s(-1), 250-300 degrees), whereas harmonic constants of about (1-2 x 10(-9) s(-1), 350-360 degrees) are theoretically expected from the equations of motion. Harmonic constants in the North Pacific Ocean are determined using acoustic data from a triangular transceiver array deployed in 1987. These constants are consistent with those given by the TPXO.2 tidal model within the uncertainties. Tidal current harmonic constants determined from current meters do not generally provide a critical test of tidal models. The tidal currents have been estimated to high accuracy using long-range reciprocal acoustic transmissions; these estimates will be useful constraints on future global tidal models. (C) 1998 Elsevier Science Ltd. All rights reserved.

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.

Sohn, RA, Webb SC, Hildebrand JA, Cornuelle BD.  1997.  Three-dimensional tomographic velocity structure of upper crust, CoAxial segment, Juan de Fuca ridge: Implications for on-axis evolution and hydrothermal circulation. Journal of Geophysical Research-Solid Earth. 102:17679-17695.   10.1029/97jb00592   AbstractWebsite

Three-dimensional models of compressional velocity and azimuthal anisotropy from tomographic inversions using 23,564 ocean bottom seismometer P wave arrivals define systematic lateral variations in seismic structure of the CoAxial segment of the Juan de Fuca Ridge (JdFR). Over much of the segment the across-axis structure is roughly axisymmetric, characterized by a progressive increase in dike velocities moving away from the ridge axis. This trend is most apparent in the basal dikes, where on-axis velocities are about 800 m/s slower than those measured elsewhere within the rift valley. The on-axis sheeted dikes also exhibit ridge-oriented azimuthal anisotropy, with a peak-to-peak amplitude of about 600 m/s. Outboard of the rift valley, beneath ridge flanks with fault scarps, velocities in the upper 1500 m of crust are reduced. The maximum amplitude of this anomaly is about 700 m/s, located near the top of the sheeted dikes. Variations in the three-dimensional velocity model are believed to reflect changes in crustal porosity, from which we infer an axisymmetric porosity model for seismic layer 2 of the CoAxial segment. As the crust ages, the evolution of layer 2 porosity could occur in the following way: (1) the porosity of zero-age, on-axis dikes is set at formation by the contraction of molten material, (2) hydrothermal alteration fills pore spaces as the dikes move away from the center of the axial valley, and (3) normal faulting on the ridge flank scarps opens fractures and increases porosity of the upper dikes as they move off-axis. At the north end of the segment, dike velocities are several hundred meters per second slower, on average, and the across-axis structure is lost. The transition from a coherent, aligned seismic structure to a less distinct pattern with reduced velocities may represent a shift from magmatic to amagmatic extension moving away from the Cobb hotspot on the ridge axis. The porosity structure we have derived for the CoAxial segment suggests an alternative to the usual hydrothermal circulation model of cross-axis convection cells. A circulation model with along-axis convection cells located entirely within the axial valley appears to be more compatible with our data.

Morawitz, WML, Sutton PJ, Worcester PF, Cornuelle BD, Lynch JF, Pawlowicz R.  1996.  Three-dimensional observations of a deep convective chimney in the Greenland sea during Winter 1988/89. Journal of Physical Oceanography. 26:2316-2343.   10.1175/1520-0485(1996)026<2316:tdooad>2.0.co;2   AbstractWebsite

All available temperature data, including moored thermistor. hydrographic, and tomographic measurements, have been combined using least-squares inverse methods to study the evolution of the three-dimensional temperature field in the Greenland Sea during winter 1988/89. The data are adequate to resolve features with spatial scares of about 40 km and larger. A chimney structure reaching depths in excess of 1000 m is observed to the southwest of the gyre center during March 1989. The chimney has a spatial scale of about 50 km, near the limit of the spatial resolution of the data, and a timescale of about 10 days, The chimney structure breaks up and disappears in only 3-6 days. A one-dimensional vertical heat balance adequately describes changes in total heat content in the chimney region from autumn 1988 until the time of chimney breakup, when horizontal advection becomes important. A simple one-dimensional mixed layer model is surprisingly successful in reproducing autumn to winter bulk temperature and salinity changes, as well as the observed evolution of the mixed layer to depths in excess of 1000 m. Uncertainties in surface freshwater fluxes make it difficult to determine whether net evaporation minus precipitation, or ice advection, is responsible for the observed depth-averaged salinity increase from autumn to winter in the chimney region. Rough estimates of the potential energy balance In the mixed laver suggest that potential energy changes are reasonably consistent with turbulent kinetic energy (TKE) production terms. Initially the TKE term parameterizing wind forcing and shear production is important, but as the mixed layer deepens the surface buoyancy production term dominates. The estimated average annual deep-water production rate in the Greenland Sea for 1988/89 is about 0.1 Sverdrups, comparable to production rates during the 1980s and early 1990s derived from tracer measurements. The location of the deep convection observed appears to be sensitively linked to the amount of Arctic Intermediate Water (AIW) present from autumn through spring. Although AIW is an important source of salt for the surface waters, too much AIW overstratifies the water column, preventing deep convection from occurring.

Todd, RE, Rudnick DL, Mazloff MR, Cornuelle BD, Davis RE.  2012.  Thermohaline structure in the California Current System: Observations and modeling of spice variance. Journal of Geophysical Research-Oceans. 117   10.1029/2011jc007589   AbstractWebsite

Upper ocean thermohaline structure in the California Current System is investigated using sustained observations from autonomous underwater gliders and a numerical state estimate. Both observations and the state estimate show layers distinguished by the temperature and salinity variability along isopycnals (i.e., spice variance). Mesoscale and submesoscale spice variance is largest in the remnant mixed layer, decreases to a minimum below the pycnocline near 26.3 kg m(-3), and then increases again near 26.6 kg m(-3). Layers of high (low) meso-and submesoscale spice variance are found on isopycnals where large-scale spice gradients are large (small), consistent with stirring of large-scale gradients to produce smaller scale thermohaline structure. Passive tracer adjoint calculations in the state estimate are used to investigate possible mechanisms for the formation of the layers of spice variance. Layers of high spice variance are found to have distinct origins and to be associated with named water masses; high spice variance water in the remnant mixed layer has northerly origin and is identified as Pacific Subarctic water, while the water in the deeper high spice variance layer has southerly origin and is identified as Equatorial Pacific water. The layer of low spice variance near 26.3 kg m(-3) lies between the named water masses and does not have a clear origin. Both effective horizontal diffusivity, kappa(h), and effective diapycnal diffusivity, kappa(v), are elevated relative to the diffusion coefficients set in the numerical simulation, but changes in kappa(h) and kappa(v) with depth are not sufficient to explain the observed layering of thermohaline structure.

Worcester, PF, Cornuelle BD, Dzieciuch MA, Munk WH, Howe BM, Mercer JA, Spindel RC, Colosi JA, Metzger K, Birdsall TG, Baggeroer AB.  1999.  A test of basin-scale acoustic thermometry using a large-aperture vertical array at 3250-km range in the eastern North Pacific Ocean. Journal of the Acoustical Society of America. 105:3185-3201.   10.1121/1.424649   AbstractWebsite

Broadband acoustic signals were transmitted during November 1994 from a 75-Hz source suspended near the depth of the sound-channel axis to a 700-m long vertical receiving array approximately 3250 km distant in the eastern North Pacific Ocean. The early part of the arrival pattern consists of raylike wave fronts that are resolvable, identifiable, and stable. The later part of the arrival pattern does not contain identifiable raylike arrivals, due to scattering from internal-wave-induced sound-speed fluctuations. The observed ray travel times differ from ray predictions based on the sound-speed field constructed using nearly concurrent temperature and salinity measurements by more than a priori variability estimates, suggesting that the equation used to compute sound speed requires refinement. The range-averaged ocean sound speed can be determined with an uncertainty of about 0.05 m/s from the observed ray travel times together with the time at which the near-axial acoustic reception ends, used as a surrogate for the group delay of adiabatic mode 1. The change in temperature over six days can be estimated with an uncertainty of about 0.006 degrees C. The sensitivity of the travel times to ocean variability is concentrated near the ocean surface and at the corresponding conjugate depths, because all of the resolved ray arrivals have upper turning depths within a few hundred meters of the surface. (C) 1999 Acoustical Society of America. [S0001-4966(99)04506-3].

Sutton, PJ, Morawitz WML, Worcester PF, Cornuelle BD.  1997.  Temperature evolution of the upper ocean in the Greenland Sea January to march 1989. Journal of Geophysical Research-Oceans. 102:27861-27874.   10.1029/97jc02439   AbstractWebsite

Tomographic data obtained during early 1989 in the Greenland Sea have been analyzed at 4-8 hour resolution to give the range-averaged vertical temperature evolution in the upper 500 m for a 106 km path. The tomographic inversions used both ray travel time data and normal mode group velocity data in order to maximize near-surface resolution. Two major events are apparent in the results. The first is the warming of a cold (-1.9 degrees C) 100 m thick surface layer, and the second, 10 days later, is the cooling of a relatively warm (-0.9 degrees C) subsurface layer between 300 m and 500 m depth. This warm subsurface layer is a critical source of salinity and buoyancy for deep convection. The surface layer warming is consistent with a mixed layer deepening over a portion of the path, bringing up water from below. Special Sensor Microwave Imager (SSM/I) ice data indicate that the local ice field disappears 3-4 days after the surface warming. The cooling of the warm 300 m to 500 m layer is also consistent with a vertical process. There is no ice cover at this time, and so surface heat fluxes are large. A northerly wind event occurs at the onset of the cooling of the 300-500 m layer, suggesting that wind-induced mixing may have played a role in initiating the process. There is evidence of southward flow advecting warm water into the area both before and after the two events studied in detail here.