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Hursky, P, Porter MB, Cornuelle BD, Hodgkiss WS, Kuperman WA.  2004.  Adjoint modeling for acoustic inversion. Journal of the Acoustical Society of America. 115:607-619.   10.1121/1.1636760   AbstractWebsite

The use of adjoint modeling for acoustic inversion is investigated. An adjoint model is derived from a linearized forward propagation model to propagate data-model misfit at the observation points back through the medium to the medium perturbations not being accounted for in the model. This adjoint model can be used to aid in inverting for these unaccounted medium perturbations. Adjoint methods are being applied to a variety of inversion problems, but have not drawn much attention from the underwater acoustic community. This paper presents an application of adjoint methods to acoustic inversion. Inversions are demonstrated in simulation for both range-independent and range-dependent sound speed profiles using the adjoint of a parabolic equation model. Sensitivity and error analyses are discussed showing how the adjoint model enables calculations to be performed in the space of observations, rather than the often much larger space of model parameters. Using an adjoint model enables directions of steepest descent in the model parameters (what we invert for) to be calculated using far fewer modeling runs than if a forward model only were used. (C) 2004 Acoustical Society of America.

Ponte, AL, Cornuelle BD.  2013.  Coastal numerical modelling of tides: Sensitivity to domain size and remotely generated internal tide. Ocean Modelling. 62:17-26.   10.1016/j.ocemod.2012.11.007   AbstractWebsite

The propagation of remotely generated superinertial internal tides constitutes a difficulty for the modelling of regional ocean tidal variability which we illustrate in several ways. First, the M2 tidal solution inside a control region located along the Southern California Bight coastline is monitored while the extent of the numerical domain is increased (up to 512 x 512 km). While the amplitude and phase of sea level averaged over the region is quasi-insensitive to domain size, a steady increase of kinetic energy, predominantly baroclinic, is observed with increasing domain size. The increasing flux of energy into the control region suggests that this trend is explained by the growing contribution from remote generation sites of internal tide which can propagate up to the control region. Increasing viscosities confirms this interpretation by lowering baroclinic energy levels and limiting their rate of increase with domain size. Doubling the grid spacing allows consideration of numerical domains 2 times larger. While the coarse grid has lower energy levels than the finer grid, the rate of energy increase with domain size appears to be slowing for the largest domain of the coarse grid simulations. Forcing the smallest domain with depth-varying tidal boundary conditions from the simulation in the largest domain produces energy levels inside the control region comparable to those in the control region for the largest domain, thereby confirming the feasibility of a nested approach. In contrast, simulations forced with a subinertial tidal constituent (K1) show that when the propagation of internal tide is limited, the control region kinetic energy is mostly barotropic and the magnitudes of variations of the kinetic energy with domain size are reduced. (C) 2012 Elsevier Ltd. All rights reserved.

Worcester, PF, Lynch JF, Morawitz WML, Pawlowicz R, Sutton PJ, Cornuelle BD, Johannessen OM, Munk WH, Owens WB, Shuchman R, Spindel RC.  1993.  Evolution of the Large-Scale Temperature-Field in the Greenland Sea During 1988-89 from Tomographic Measurements. Geophysical Research Letters. 20:2211-2214.   10.1029/93gl02373   AbstractWebsite

The Greenland Sea Ocean Acoustic Tomography Experiment was conducted during 1988-89, as one component of the international Greenland Sea Project, to study deep water formation and the response of the gyre to variations in wind stress and ice cover. Six acoustic transceivers moored in an array 200-km across transmitted to one another at four hour intervals. Near the end of February, 1989, a sub-surface temperature maximum at several hundred meters depth disappeared over a suprisingly large area of the central Greenland Sea . While the water column was modified to about 1000 m depth over much of the gyre, the surface remained colder than the deeper water, contrary to what might be expected from simple models of convective renewal.

Kim, SY, Terrill EJ, Cornuelle BD, Jones B, Washburn L, Moline MA, Paduan JD, Garfield N, Largier JL, Crawford G, Kosro PM.  2011.  Mapping the U.S. West Coast surface circulation: A multiyear analysis of high-frequency radar observations. Journal of Geophysical Research-Oceans. 116   10.1029/2010jc006669   AbstractWebsite

The nearly completed U. S. West Coast (USWC) high-frequency radar (HFR) network provides an unprecedented capability to monitor and understand coastal ocean dynamics and phenomenology through hourly surface current measurements at up to 1 km resolution. The dynamics of the surface currents off the USWC are governed by tides, winds, Coriolis force, low-frequency pressure gradients (less than 0.4 cycles per day (cpd)), and nonlinear interactions of those forces. Alongshore surface currents show poleward propagating signals with phase speeds of O(10) and O(100 to 300) km day(-1) and time scales of 2 to 3 weeks. The signals with slow phase speed are only observed in southern California. It is hypothesized that they are scattered and reflected by shoreline curvature and bathymetry change and do not penetrate north of Point Conception. The seasonal transition of alongshore surface circulation forced by upwelling-favorable winds and their relaxation is captured in fine detail. Submesoscale eddies, identified using flow geometry, have Rossby numbers of 0.1 to 3, diameters in the range of 10 to 60 km, and persistence for 2 to 12 days. The HFR surface currents resolve coastal surface ocean variability continuously across scales from submesoscale to mesoscale (O(1) km to O(1000) km). Their spectra decay with k(-2) at high wave number (less than 100 km) in agreement with theoretical submesoscale spectra below the observational limits of present-day satellite altimeters.

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.

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=10āˆ’4 m2 sāˆ’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.

Kim, SY, Cornuelle BD, Terrill EJ, Jones B, Washburn L, Moline MA, Paduan JD, Garfield N, Largier JL, Crawford G, Kosro PM.  2013.  Poleward propagating subinertial alongshore surface currents off the US West Coast. Journal of Geophysical Research-Oceans. 118:6791-6806.   10.1002/jgrc.20400   AbstractWebsite

The network comprising 61 high-frequency radar systems along the U.S. West Coast (USWC) provides a unique, high resolution, and broad scale view of ocean surface circulation. Subinertial alongshore surface currents show poleward propagating signals with phase speeds of O(10) and O(100-300) kmd-1 that are consistent with historical in situ observations off the USWC and that can be possibly interpreted as coastally trapped waves (CTWs). The propagating signals in the slow mode are partly observed in southern California, which may result from scattering and reflection of higher-mode CTWs due to curvature of shoreline and bathymetry near Point Conception, California. On the other hand, considering the order of the phase speed in the slow mode, the poleward propagating signals may be attributed to alongshore advection or pressure-driven flows. A statistical regression of coastal winds at National Data Buoy Center buoys on the observed surface currents partitions locally and remotely wind-forced components, isolates footprints of the equatorward propagating storm events in winter off the USWC, and shows the poleward propagating signals year round.

Heimbach, P, Fukumori I, Hills CN, Ponte RM, Stammer D, Wunsch C, Campin JM, Cornuelle B, Fenty I, Forget G, Kohl A, Mazloff M, Menemenlis D, Nguyen AT, Piecuch C, Trossman D, Verdy A, Wang O, Zhang H.  2019.  Putting it all together: Adding value to the global ocean and climate observing systems with complete self-consistent ocean state and parameter estimates. Frontiers in Marine Science. 6   10.3389/fmars.2019.00055   AbstractWebsite

In 1999, the consortium on Estimating the Circulation and Climate of the Ocean (ECCO) set out to synthesize the hydrographic data collected by the World Ocean Circulation Experiment (WOCE) and the satellite sea surface height measurements into a complete and coherent description of the ocean, afforded by an ocean general circulation model. Twenty years later, the versatility of ECCO's estimation framework enables the production of global and regional ocean and sea-ice state estimates, that incorporate not only the initial suite of data and its successors, but nearly all data streams available today. New observations include measurements from Argo floats, marine mammal-based hydrography, satellite retrievals of ocean bottom pressure and sea surface salinity, as well as ice-tethered profiled data in polar regions. The framework also produces improved estimates of uncertain inputs, including initial conditions, surface atmospheric state variables, and mixing parameters. The freely available state estimates and related efforts are property-conserving, allowing closed budget calculations that are a requisite to detect, quantify, and understand the evolution of climate-relevant signals, as mandated by the Coupled Model Intercomparison Project Phase 6 (CMIP6) protocol. The solutions can be reproduced by users through provision of the underlying modeling and assimilation machinery. Regional efforts have spun off that offer increased spatial resolution to better resolve relevant processes. Emerging foci of ECCO are on a global sea level changes, in particular contributions from polar ice sheets, and the increased use of biogeochemical and ecosystem data to constrain global cycles of carbon, nitrogen and oxygen. Challenges in the coming decade include provision of uncertainties, informing observing system design, globally increased resolution, and moving toward a coupled Earth system estimation with consistent momentum, heat and freshwater fluxes between the ocean, atmosphere, cryosphere and land.

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.

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   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.

Powell, BS, Kerry CG, Cornuelle BD.  2013.  Using a numerical model to understand the connection between the ocean and acoustic travel-time measurements. Journal of the Acoustical Society of America. 134:3211-3222.   10.1121/1.4818786   AbstractWebsite

Measurements of acoustic ray travel-times in the ocean provide synoptic integrals of the ocean state between source and receiver. It is known that the ray travel-time is sensitive to variations in the ocean at the transmission time, but the sensitivity of the travel-time to spatial variations in the ocean prior to the acoustic transmission have not been quantified. This study examines the sensitivity of ray travel-time to the temporally and spatially evolving ocean state in the Philippine Sea using the adjoint of a numerical model. A one year series of five day backward integrations of the adjoint model quantify the sensitivity of travel-times to varying dynamics that can alter the travel-time of a 611 km ray by 200 ms. The early evolution of the sensitivities reveals high-mode internal waves that dissipate quickly, leaving the lowest three modes, providing a connection to variations in the internal tide generation prior to the sample time. They are also strongly sensitive to advective effects that alter density along the ray path. These sensitivities reveal how travel-time measurements are affected by both nearby and distant waters. Temporal nonlinearity of the sensitivities suggests that prior knowledge of the ocean state is necessary to exploit the travel-time observations. (C) 2013 Acoustical Society of America.

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.