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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.

Fujii, Y, Cummings J, Xue Y, Schiller A, Lee T, Balmaseda MA, Remy E, Masuda S, Brassington G, Alves O, Cornuelle B, Martin M, Oke P, Smith G, Yang XS.  2015.  Evaluation of the Tropical Pacific Observing System from the ocean data assimilation perspective. Quarterly Journal of the Royal Meteorological Society. 141:2481-2496.   10.1002/qj.2579   AbstractWebsite

The drastic reduction in the number of observation data from the Tropical Atmospheric Ocean (TAO)/Triangle Trans-Ocean Buoy Network (TRITON) array since 2012 has given rise to a need to assess the impact of those data in ocean data assimilation (DA) systems. This article provides a review of existing studies evaluating the impacts of data from the TAO/TRITON array and other components of the Tropical Pacific Observing System (TPOS) on current ocean DA systems used for a variety of operational and research applications. It can be considered as background information that can guide the evaluation exercise of TPOS. Temperature data from TAO/TRITON array are assimilated in most ocean DA systems which cover the tropical Pacific in order to constrain the ocean heat content, stratification, and circulation. It is shown that the impacts of observation data depend considerably on the system and application. The presence of model error often makes the results difficult to interpret. Nevertheless there is consensus that the data from TAO/TRITON generally have positive impacts complementary to Argo floats. In the equatorial Pacific, the impacts are generally around the same level or larger than those of Argo. We therefore conclude that, with the current configuration of TPOS, the loss of the TAO/TRITON data is having a significant detrimental impact on many applications based on ocean DA systems. This conclusion needs to be kept under review because the equatorial coverage by Argo is expected to improve in the future.

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.

Verdy, A, Mazloff MR, Cornuelle BD, Kim SY.  2014.  Wind-driven sea level variability on the California coast: An adjoint sensitivity analysis. Journal of Physical Oceanography. 44:297-318.   10.1175/jpo-d-13-018.1   AbstractWebsite

Effects of atmospheric forcing on coastal sea surface height near Port San Luis, central California, are investigated using a regional state estimate and its adjoint. The physical pathways for the propagation of nonlocal [O(100 km)] wind stress effects are identified through adjoint sensitivity analyses, with a cost function that is localized in space so that the adjoint shows details of the propagation of sensitivities. Transfer functions between wind stress and SSH response are calculated and compared to previous work. It is found that (i) the response to local alongshore wind stress dominates on short time scales of O(1 day); (ii) the effect of nonlocal winds dominates on longer time scales and is carried by coastally trapped waves, as well as inertia-gravity waves for offshore wind stress; and (iii) there are significant seasonal variations in the sensitivity of SSH to wind stress due to changes in stratification. In a more stratified ocean, the damping of sensitivities to local and offshore winds is reduced, allowing for a larger and longer-lasting SSH response to wind stress.

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.

Zhang, XB, Cornuelle B, Roemmich D.  2011.  Adjoint Sensitivity of the Nino-3 Surface Temperature to Wind Forcing. Journal of Climate. 24:4480-4493.   10.1175/2011jcli3917.1   AbstractWebsite

The evolution of sea surface temperature (SST) over the eastern equatorial Pacific plays a significant role in the intense tropical air-sea interaction there and is of central importance to the El Nino-Southern Oscillation (ENSO) phenomenon. Effects of atmospheric fields (especially wind stress) and ocean state on the eastern equatorial Pacific SST variations are investigated using the Massachusetts Institute of Technology general circulation model (MITgcm) and its adjoint model, which can calculate the sensitivities of a cost function (in this case the averaged 0-30-m temperature in the Nino-3 region during an ENSO event peak) to previous atmospheric forcing fields and ocean state going backward in time. The sensitivity of the Nino-3 surface temperature to monthly zonal wind stress in preceding months can be understood by invoking mixed layer heat balance, ocean dynamics, and especially linear equatorial wave dynamics. The maximum positive sensitivity of the Nino-3 surface temperature to local wind forcing usually happens similar to 1-2 months before the peak of the ENSO event and is hypothesized to be associated with the Ekman pumping mechanism. In model experiments, its magnitude is closely related to the subsurface vertical temperature gradient, exhibiting strong event-to-event differences with strong (weak) positive sensitivity during La Nina (strong El Nino) events. The adjoint sensitivity to remote wind forcing in the central and western equatorial Pacific is consistent with the standard hypothesis that the remote wind forcing affects the Nino-3 surface temperature indirectly by exciting equatorial Kelvin and Rossby waves and modulating thermocline depth in the Nino-3 region. The current adjoint sensitivity study is consistent with a previous regression-based sensitivity study derived from perturbation experiments. Finally, implication for ENSO monitoring and prediction is also discussed.

Hoteit, I, Cornuelle B, Heimbach P.  2010.  An eddy-permitting, dynamically consistent adjoint-based assimilation system for the tropical Pacific: Hindcast experiments in 2000. Journal of Geophysical Research-Oceans. 115   10.1029/2009jc005437   AbstractWebsite

An eddy-permitting adjoint-based assimilation system has been implemented to estimate the state of the tropical Pacific Ocean. The system uses the Massachusetts Institute of Technology's general circulation model and its adjoint. The adjoint method is used to adjust the model to observations by controlling the initial temperature and salinity; temperature, salinity, and horizontal velocities at the open boundaries; and surface fluxes of momentum, heat, and freshwater. The model is constrained with most of the available data sets in the tropical Pacific, including Tropical Atmosphere and Ocean, ARGO, expendable bathythermograph, and satellite SST and sea surface height data, and climatologies. Results of hindcast experiments in 2000 suggest that the iterated adjoint-based descent is able to significantly improve the model consistency with the multivariate data sets, providing a dynamically consistent realization of the tropical Pacific circulation that generally matches the observations to within specified errors. The estimated model state is evaluated both by comparisons with observations and by checking the controls, the momentum balances, and the representation of small-scale features that were not well sampled by the observations used in the assimilation. As part of these checks, the estimated controls are smoothed and applied in independent model runs to check that small changes in the controls do not greatly change the model hindcast. This is a simple ensemble-based uncertainty analysis. In addition, the original and smoothed controls are applied to a version of the model with doubled horizontal resolution resulting in a broadly similar "downscaled'' hindcast, showing that the adjustments are not tuned to a single configuration (meaning resolution, topography, and parameter settings). The time-evolving model state and the adjusted controls should be useful for analysis or to supply the forcing, initial, and boundary conditions for runs of other models.

Hoteit, I, Cornuelle B, Kim SY, Forget G, Kohl A, Terrill E.  2009.  Assessing 4D-VAR for dynamical mapping of coastal high-frequency radar in San Diego. Dynamics of Atmospheres and Oceans. 48:175-197.   10.1016/j.dynatmoce.2008.11.005   AbstractWebsite

The problem of dynamically mapping high-frequency (HF) radar radial velocity observations is investigated using a three-dimensional hydrodynamic model of the San Diego coastal region and an adjoint-based assimilation method. The HF radar provides near-real-time radial velocities from three sites covering the region offshore of San Diego Bay. The hydrodynamical model is the Massachusetts Institute of Technology general circulation model (MITgcm) with 1 km horizontal resolution and 40 vertical layers. The domain is centered on Point Loma, extending 117 km offshore and 120 km alongshore. The reference run (before adjustment) is initialized from a single profile of T and S and is forced with wind data from a single shore station and with zero heat and fresh water fluxes. The adjoint of the model is used to adjust initial temperature, salinity, and velocity, hourly temperature, salinity and horizontal velocities at the open boundaries, and hourly surface fluxes of momentum, heat and freshwater so that the model reproduces hourly HF radar radial velocity observations. Results from a small number of experiments suggest that the adjoint method can be successfully used over 10-day windows at coastal model resolution. It produces a dynamically consistent model run that fits HF radar data with errors near the specified uncertainties. In a test of the forecasting capability of the San Diego model after adjustment, the forecast skill was shown to exceed persistence for up to 20 h. (C) 2008 Elsevier B.V. All rights reserved.

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.

Hoteit, I, Cornuelle B, Thierry V, Stammer D.  2008.  Impact of resolution and optimized ECCO forcing on Simulations of the tropical pacific. Journal of Atmospheric and Oceanic Technology. 25:131-147.   10.1175/2007jtecho528.1   AbstractWebsite

The sensitivity of the dynamics of a tropical Pacific Massachusetts Institute of Technology (MIT) general circulation model (MITgcm) to the surface forcing fields and to the horizontal resolution is analyzed. During runs covering the period 1992-2002, two different sets of surface forcing boundary conditions are used, obtained 1) from the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis project and 2) from the Estimating the Circulation and Climate of the Ocean (ECCO) assimilation consortium. The "ECCO forcing" is the "NCEP forcing" adjusted by a state estimation procedure using the MITgcm with a 1 degrees x 1 degrees global grid and the adjoint method assimilating a multivariate global ocean dataset. The skill of the model is evaluated against ocean observations available in situ and from satellites. The model domain is limited to the tropical Pacific, with open boundaries located along 26 degrees S, 26 degrees N, and in the Indonesian throughflow. To account for large-scale changes of the ocean circulation, the model is nested in the global time-varying ocean state provided by the ECCO consortium on a 1 grid. Increasing the spatial resolution to 1/3 degrees and using the ECCO forcing fields significantly improves many aspects of the circulation but produces overly strong currents in the western model domain. Increasing the resolution to 1/6 degrees does not yield further improvements of model results. Using the ECCO heat and freshwater fluxes in place of NCEP products leads to improved time-mean model skill (i.e., reduced biases) over most of the model domain, underlining the important role of adjusted heat and freshwater fluxes for improving model representations of the tropical Pacific. Combinations of ECCO and NCEP wind forcing fields can improve certain aspects of the model solutions, but neither ECCO nor NCEP winds show clear overall superiority.

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.