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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.

Moore, AM, Martini MJ, Akella S, Arango HG, Balmaseda M, Bertino L, Ciavatta S, Cornuelle B, Cummings J, Frolov S, Lermusiaux P, Oddo P, Oke PR, Storto A, Teruzzi A, Vidard A, Weaver AT, Assimilation GOVD.  2019.  Synthesis of ocean observations using data assimilation for operational, real-time and reanalysis systems: A more complete picture of the state of the ocean. Frontiers in Marine Science. 6   10.3389/fmars.2019.00090   AbstractWebsite

Ocean data assimilation is increasingly recognized as crucial for the accuracy of real-time ocean prediction systems and historical re-analyses. The current status of ocean data assimilation in support of the operational demands of analysis, forecasting and reanalysis is reviewed, focusing on methods currently adopted in operational and real-time prediction systems. Significant challenges associated with the most commonly employed approaches are identified and discussed. Overarching issues faced by ocean data assimilation are also addressed, and important future directions in response to scientific advances, evolving and forthcoming ocean observing systems and the needs of stakeholders and downstream applications are discussed.

Rudnick, DL, Gopalakrishnan G, Cornuelle BD.  2015.  Cyclonic eddies in the Gulf of Mexico: Observations by underwater gliders and simulations by numerical model. Journal of Physical Oceanography. 45:313-326.   10.1175/jpo-d-14-0138.1   AbstractWebsite

Circulation in the Gulf of Mexico (GoM) is dominated by the Loop Current (LC) and by Loop Current eddies (LCEs) that form at irregular multimonth intervals by separation from the LC. Comparatively small cyclonic eddies (CEs) are thought to have a controlling influence on the LCE, including its separation from the LC. Because the CEs are so dynamic and short-lived, lasting only a few weeks, they have proved a challenge to observe. This study addresses that challenge using underwater gliders. These gliders' data and satellite sea surface height (SSH) are used in a four-dimensional variational (4DVAR) assimilation in the Massachusetts Institute of Technology (MIT) general circulation model (MITgcm). The model serves two purposes: first, the model's estimate of ocean state allows the analysis of four-dimensional fields, and second, the model forecasts are examined to determine the value of glider data. CEs have a Rossby number of about 0.2, implying that the effects of flow curvature, cyclostrophy, to modify the geostrophic momentum balance are slight. The velocity field in CEs is nearly depth independent, while LCEs are more baroclinic, consistent with the CEs origin on the less stratified, dense side of the LCE. CEs are formed from water in the GoM, rather than the Atlantic water that distinguishes the LCE. Model forecasts are improved by glider data, using a quality metric based on satellite SSH, with the best 2-month GoM forecast rivaling the accuracy of a global hindcast.

Edwards, CA, Moore AM, Hoteit I, Cornuelle BD.  2015.  Regional ocean data assimilation. Annual Review of Marine Science, Vol 7. 7:21-42.   10.1146/annurev-marine-010814-015821   AbstractWebsite

This article reviews the past 15 years of developments in regional ocean data assimilation. A variety of scientific, management, and safety-related objectives motivate marine scientists to characterize many ocean environments, including coastal regions. As in weather prediction, the accurate representation of physical, chemical, and/or biological properties in the ocean is challenging. Models and observations alone provide imperfect representations of the ocean state, but together they can offer improved estimates. Variational and sequential methods are among the most widely used in regional ocean systems, and there have been exciting recent advances in ensemble and four-dimensional variational approaches. These techniques are increasingly being tested and adapted for biogeochemical applications.

Hoteit, I, Hoar T, Gopalakrishnan G, Collins N, Anderson J, Cornuelle B, Kohl A, Heimbach P.  2013.  A MITgcm/DART ensemble analysis and prediction system with application to the Gulf of Mexico. Dynamics of Atmospheres and Oceans. 63:1-23.   10.1016/j.dynatmoce.2013.03.002   AbstractWebsite

This paper describes the development of an advanced ensemble Kalman filter (EnKF)-based ocean data assimilation system for prediction of the evolution of the loop current in the Gulf of Mexico (GoM). The system integrates the Data Assimilation Research Testbed (DART) assimilation package with the Massachusetts Institute of Technology ocean general circulation model (MITgcm). The MITgcm/DART system supports the assimilation of a wide range of ocean observations and uses an ensemble approach to solve the nonlinear assimilation problems. The GoM prediction system was implemented with an eddy-resolving 1/10th degree configuration of the MITgcm. Assimilation experiments were performed over a 6-month period between May and October during a strong loop current event in 1999. The model was sequentially constrained with weekly satellite sea surface temperature and altimetry data. Experiments results suggest that the ensemble-based assimilation system shows a high predictive skill in the GoM, with estimated ensemble spread mainly concentrated around the front of the loop current. Further analysis of the system estimates demonstrates that the ensemble assimilation accurately reproduces the observed features without imposing any negative impact on the dynamical balance of the system. Results from sensitivity experiments with respect to the ensemble filter parameters are also presented and discussed. (C) 2013 Elsevier B.V. All rights reserved.

Zhang, XB, Cornuelle B, Roemmich D.  2012.  Sensitivity of Western Boundary Transport at the Mean North Equatorial Current Bifurcation Latitude to Wind Forcing. Journal of Physical Oceanography. 42:2056-2072.   10.1175/jpo-d-11-0229.1   AbstractWebsite

The bifurcation of the North Equatorial Current (NEC) plays an important role in the heat and water mass exchanges between the tropical and subtropical gyres in the Pacific Ocean. The variability of western boundary transport (WBT) east of the Philippine coast at the mean NEC bifurcation latitude (12 degrees N) is examined here. A tropical Pacific regional model is set up based on the Massachusetts Institute of Technology general circulation model and its adjoint, which calculates the sensitivities of a defined meridional transport to atmospheric forcing fields and ocean state going backward in time. The adjoint-derived sensitivity of the WBT at the mean NEC bifurcation latitude to surface wind stress is dominated by curl-like patterns that are located farther eastward and southward with increasing time lag. The temporal evolution of the adjoint sensitivity of the WBT to wind stress resembles wind-forced Rossby wave dynamics but propagating with speeds determined by the background stratification and current, suggesting that wind-forced Rossby waves are the underlying mechanism. Interannual-to-decadal variations of the WBT can be hindcast well by multiplying the adjoint sensitivity and the time-lagged wind stress over the whole model domain and summing over time lags. The analysis agrees with previous findings that surface wind stress (especially zonal wind stress in the western subtropical Pacific) largely determines the WBT east of the Philippines, and with a time lag based on Rossby wave propagation. This adjoint sensitivity study quantifies the contribution of wind stress at all latitudes and longitudes and provides a novel perspective to understand the relationship between the WBT and wind forcing over the Pacific Ocean.

Muccino, JC, Arango HG, Bennett AF, Chua BS, Cornuelle BD, Di Lorenzo E, Egbert GD, Haidvogel D, Levin JC, Luo H, Miller AJ, Moore AA, Zaron ED.  2008.  The Inverse Ocean Modeling system. Part II: Applications. Journal of Atmospheric and Oceanic Technology. 25:1623-1637.   10.1175/2008jtecho522.1   AbstractWebsite

The Inverse Ocean Modeling (IOM) System is a modular system for constructing and running weak-constraint four-dimensional variational data assimilation (W4DVAR) for any linear or nonlinear functionally, smooth dynamical model and observing array. The IOM has been applied to four ocean models with widely varying characteristics. The Primitive Equations Z-coordinate-Harmonic Analysis of Tides (PEZ-HAT) and the Regional Ocean Modeling System (ROMS) are three-dimensional, primitive equations models while the Advanced Circulation model in 2D (ADCIRC-2D) and Spectral Element Ocean Model in 2D (SEOM-2D) are shallow-water models belonging to the general finite-element family. These models. in conjunction with the IOM, have been used to investigate a wide variety of scientific phenomena including tidal. mesoscale, and wind-driven circulation. In all cases, the assimilation of data using the IOM provides a better estimate of the ocean state than the model alone.

Kohl, A, Stammer D, Cornuelle B.  2007.  Interannual to decadal changes in the ECCO global synthesis. Journal of Physical Oceanography. 37:313-337.   10.1175/jpo3014.1   AbstractWebsite

An estimate of the time-varying global ocean circulation for the period 1992 - 2002 was obtained by combining most of the World Ocean Circulation Experiment ( WOCE) ocean datasets with a general circulation model on a 1 horizontal grid. The estimate exactly satisfies the model equations without artificial sources or sinks of momentum, heat, and freshwater. To bring the model into agreement with observations, its initial temperature and salinity conditions were permitted to change, as were the time-dependent surface fluxes of momentum, heat, and freshwater. The estimation of these "control variables" is largely consistent with accepted uncertainties in the hydrographic climatology and meteorological analyses. The estimated time-mean horizontal transports of volume, heat, and freshwater, which were largely underestimated in the previous 2 optimization performed by Stammer et al., have converged with time-independent estimates from box inversions over most parts of the World Ocean. Trends in the model's heat content are 7% larger than those reported by Levitus and correspond to a global net heat uptake of about 1.1 W m(-2) over the model domain. The associated model trend in sea surface height over the estimation period resembles the observations from Ocean Topography Experiment ( TOPEX)/Poseidon over most of the global ocean. Sea surface height changes in the model are primarily steric but show contributions from mass redistributions from the subpolar North Atlantic Ocean and the Southern Ocean to the subtropical Pacific Ocean gyres. Steric contributions are primarily temperature based but are partly compensated by salt variation. However, the North Atlantic and the Southern Ocean reveal a clear contribution of salt to large-scale sea level variations.

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.

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.

Moore, AM, Arango HG, Di Lorenzo E, Cornuelle BD, Miller AJ, Neilson DJ.  2004.  A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Modelling. 7:227-258.   10.1016/j.ocemod.2003.11.001   AbstractWebsite

The regional ocean modelling system (ROMS) is a new generation ocean general circulation model that is rapidly gaining favour in the ocean modelling community. The tangent linear and adjoint versions of ROMS have recently been developed, and a new suite of tools that utilize these models for a variety of applications are now available to the ocean modelling community. In this paper we will describe the tangent linear and adjoint components of ROMS, and present examples from the tools that are currently available to ROMS users. In particular we will consider the finite time eigenmodes and the adjoint finite time eigenmodes of the tangent linear propagator, the singular vectors of the propagator, and its forcing singular vectors and stochastic optimals. The pseudospectra of the tangent linear resolvent matrix are also considered. Examples of each type of calculation will be presented for a time evolving double gyre ocean circulation in a rectangular ocean basin. (C) 2003 Elsevier Ltd. All rights reserved.

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.

Miller, AJ, Cornuelle BD.  1999.  Forecasts from fits of frontal fluctuations. Dynamics of Atmospheres and Oceans. 29:305-333.   10.1016/s0377-0265(99)00009-3   AbstractWebsite

A primitive equation ocean model is fit with strong constraints to non-synoptic hydrographic surveys in an unstable frontal current region, the Iceland-Faeroe Front. The model is first initialized from a time-independent objective analysis of non-synoptic data (spanning 2 to 6 days). A truncated set of eddy-scale basis functions is used to represent the initial error in temperature, salinity, and velocity. A series of model integrations, each perturbed with one basis function for one dependent variable in one layer, is used to determine the sensitivity to the objective-analysis initial state of the match to the non-synoptic hydrographic data. A new initial condition is then determined from a generalized inverse of the sensitivity matrix and the process is repeated to account for non-linearity. The method is first tested in 'identical twin' experiments to demonstrate the adequacy of the basis functions in representing initial condition error and the convergence of the method to the true solution. The approach is then applied to observations gathered in August 1993 in the Iceland-Faeroe Front. Model fits are successful in improving the match to the true data, leading to dynamically consistent evolution scenarios. However, the forecast skill (here defined as the variance of the model-data differences) of the model runs from the optimized initial condition is not superior to less sophisticated methods of initialization, probably due to inadequate initialization data. The limited verification data in the presence of strong frontal slopes may not be sufficient to establish Forecast skill, so that it must be judged subjectively or evaluated by other quantitative measures. (C) 1999 Elsevier Science B.V. All rights reserved.