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Gopalakrishnan, G, Hoteit I, Cornuelle BD, Rudnick DL.  2019.  Comparison of 4DVAR and EnKF state estimates and forecasts in the Gulf of Mexico. Quarterly Journal of the Royal Meteorological Society. 145:1354-1376.   10.1002/qj.3493   AbstractWebsite

An experiment is conducted to compare four-dimensional variational (4DVAR) and ensemble Kalman filter (EnKF) assimilation systems and their predictability in the Gulf of Mexico (GoM) using the Massachusetts Institute of Technology general circulation model (MITgcm). The quality of the ocean-state estimates, forecasts, and the contribution of ensemble prediction are evaluated. The MITgcm-Estimating the Circulation and Climate of the Ocean (ECCO) 4DVAR (MITgcm-ECCO) and the MITgcm-Data Assimilation Research Testbed (DART) EnKF (MITgcm-DART) systems were used to compute two-month hindcasts (March-April, 2010) by assimilating satellite-derived along-track sea-surface height (SSH) and gridded sea-surface temperature (SST) observations. The estimates from both methods at the end of the hindcast period were then used to initialize forecasts for two months (May-June, 2010). This period was selected because a loop current (LC) eddy (Eddy Franklin: Eddy-F) detachment event occurred at the end of May 2010, immediately after the Deepwater Horizon (DwH) oil spill. Despite some differences between the setups, both systems produce analyses and forecasts of comparable quality and both solutions significantly outperformed model persistence. A reference forecast initialized from the 1/12 degrees Hybrid Coordinate Ocean Model (HYCOM)/NCODA global analysis also performed well. The EnKF experiments for sensitivity to filter parameters showed enhanced predictability when using more ensemble members and stronger covariance localization, but not for larger inflation. The EnKF experiments varying the number of assimilation cycles showed enhanced short-term (long-term) predictability with fewer (more) assimilation cycles. Additional hindcast and forecast experiments at other times of significant LC evolution showed mixed performance of both systems, which depends strongly on the background state of the GoM circulation. The present work demonstrates a practical application of both assimilation methods for the GoM and compares them in a limited number of realizations. The overall conclusion showing improved short-term (long-term) predictability for EnKF (4DVAR) carries an important caveat that the results from this study are specific to a few 4DVAR and EnKF LC eddy separation experiments in the GoM and cannot be generalized to conclude the relative performance of both methods, especially in other applications. However, some of the concepts and methods should carry over to other applications.

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.

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.

Gopalakrishnan, G, Cornuelle BD, Hoteit I.  2013.  Adjoint sensitivity studies of loop current and eddy shedding in the Gulf of Mexico. Journal of Geophysical Research: Oceans. 118:3315-3335.   10.1002/jgrc.20240   AbstractWebsite

Adjoint model sensitivity analyses were applied for the loop current (LC) and its eddy shedding in the Gulf of Mexico (GoM) using the MIT general circulation model (MITgcm). The circulation in the GoM is mainly driven by the energetic LC and subsequent LC eddy separation. In order to understand which ocean regions and features control the evolution of the LC, including anticyclonic warm-core eddy shedding in the GoM, forward and adjoint sensitivities with respect to previous model state and atmospheric forcing were computed using the MITgcm and its adjoint. Since the validity of the adjoint model sensitivities depends on the capability of the forward model to simulate the real LC system and the eddy shedding processes, a 5 year (2004–2008) forward model simulation was performed for the GoM using realistic atmospheric forcing, initial, and boundary conditions. This forward model simulation was compared to satellite measurements of sea-surface height (SSH) and sea-surface temperature (SST), and observed transport variability. Despite realistic mean state, standard deviations, and LC eddy shedding period, the simulated LC extension shows less variability and more regularity than the observations. However, the model is suitable for studying the LC system and can be utilized for examining the ocean influences leading to a simple, and hopefully generic LC eddy separation in the GoM. The adjoint sensitivities of the LC show influences from the Yucatan Channel (YC) flow and Loop Current Frontal Eddy (LCFE) on both LC extension and eddy separation, as suggested by earlier work. Some of the processes that control LC extension after eddy separation differ from those controlling eddy shedding, but include YC through-flow. The sensitivity remains stable for more than 30 days and moves generally upstream, entering the Caribbean Sea. The sensitivities of the LC for SST generally remain closer to the surface and move at speeds consistent with advection by the high-speed core of the current, while sensitivities to SSH generally extend to deeper layers and propagate more slowly. The adjoint sensitivity to relative vorticity deduced from the sensitivities to velocity fields suggests that advection of cyclonic (positive) relative vorticity anomalies from the YC or the LCFEs accelerate the LC eddy separation. Forward model perturbation experiments were performed to complement and check the adjoint sensitivity analysis as well as sampling the predictability and nonlinearity of the LC evolution. The model and its adjoint can be used in four-dimensional variational assimilation (4D-VAR) to produce dynamically consistent ocean state estimates for analysis and forecasts of the circulation of the GoM.

Gopalakrishnan, G, Cornuelle BD, Hoteit I, Rudnick DL, Owens BW.  2013.  State estimates and forecasts of the loop current in the Gulf of Mexico using the MITgcm and its adjoint. Journal of Geophysical Research: Oceans. 118:3292-3314.   10.1002/jgrc.20239   AbstractWebsite

An ocean state estimate has been developed for the Gulf of Mexico (GoM) using the MIT general circulation model and its adjoint. The estimate has been tested by forecasting loop current (LC) evolution and eddy shedding in the GoM. The adjoint (or four-dimensional variational) method was used to match the model evolution to observations by adjusting model temperature and salinity initial conditions, open boundary conditions, and atmospheric forcing fields. The model was fit to satellite-derived along-track sea surface height, separated into temporal mean and anomalies, and gridded sea surface temperature for 2 month periods. The optimized state at the end of the assimilation period was used to initialize the forecast for 2 months. Forecasts explore practical LC predictability and provide a cross-validation test of the state estimate by comparing it to independent future observations. The model forecast was tested for several LC eddy separation events, including Eddy Franklin in May 2010 during the deepwater horizon oil spill disaster in the GoM. The forecast used monthly climatological open boundary conditions, atmospheric forcing, and run-off fluxes. The model performance was evaluated by computing model-observation root-mean-square difference (rmsd) during both the hindcast and forecast periods. The rmsd metrics for the forecast generally outperformed persistence (keeping the initial state fixed) and reference (forecast initialized using assimilated Hybrid Coordinate Ocean Model 1/12° global analysis) model simulations during LC eddy separation events for a period of 1̃2 months.