4DVAR data assimilation in the Intra-Americas Sea with the Regional Ocean Modeling System (ROMS)

Abstract We present the background, development, and preparation of a state-of-the-art 4D variational (4DVAR) data assimilation system in the Regional Ocean Modeling System (ROMS) with an application in the Intra-Americas Sea (IAS). This initial application with a coarse model shows the efficacy of the 4DVAR methodology for use within complex ocean environments, and serves as preparation for deploying an operational, real-time assimilation system onboard the Royal Caribbean Cruise Lines ship Explorer of the Seas. Assimilating satellite sea surface height and temperature observations with in situ data from the ship in 14 day cycles over 2 years from January 2005 through March 2007, reduces the observation-model misfit by over 75%. Using measures of the Loop Current dynamics, we show that the assimilated solution is consistent with observed statistics.

[1]  J. Willis,et al.  Interannual variability in upper ocean heat content, temperature, and thermosteric expansion on global scales , 2004 .

[2]  W. Sturges,et al.  Circulation in the Gulf of Mexico: Observations and Models: Sturges/Circulation in the Gulf of Mexico: Observations and Models , 2005 .

[3]  Alexander F. Shchepetkin,et al.  The regional oceanic modeling system (ROMS): a split-explicit, free-surface, topography-following-coordinate oceanic model , 2005 .

[4]  P. Courtier,et al.  A strategy for operational implementation of 4D‐Var, using an incremental approach , 1994 .

[5]  N. Walker,et al.  Advances in satellite radiometry for the surveillance of surface temperatures, ocean eddies and upwelling processes in the Gulf of Mexico using GOES‐8 measurements during summer , 2003 .

[6]  Carl Wunsch,et al.  Estimating air‐sea fluxes of heat, freshwater, and momentum through global ocean data assimilation , 2004 .

[7]  George L. Mellor,et al.  Continuous assimilation of Geosat altimeter data into a three-dimensional primitive equation Gulf Stream model , 1994 .

[8]  Tal Ezer,et al.  An exercise in forecasting loop current and eddy frontal positions in the Gulf of Mexico , 2005 .

[9]  S. Gorshkov,et al.  World ocean atlas , 1976 .

[10]  R. Leben,et al.  Eddy energy and shelf interactions in the Gulf of Mexico , 2001 .

[11]  R. Leben,et al.  Accuracy Assessment of Jason-1 and TOPEX/POSEIDON Along-Track Sea Surface Slope Special Issue: Jason-1 Calibration/Validation , 2003 .

[12]  E. F. Bradley,et al.  Bulk parameterization of air‐sea fluxes for Tropical Ocean‐Global Atmosphere Coupled‐Ocean Atmosphere Response Experiment , 1996 .

[13]  L. Amarouche,et al.  Comparison of the Ku-Band Range Noise Level and the Relative Sea-State Bias of the Jason-1, TOPEX, and Poseidon-1 Radar Altimeters Special Issue: Jason-1 Calibration/Validation , 2003 .

[14]  C. Wunsch.  The Ocean Circulation Inverse Problem , 1996 .

[15]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[16]  John Sapper,et al.  The development and operational application of nonlinear algorithms for the measurement of sea surface temperatures with the NOAA polar‐orbiting environmental satellites , 1998 .

[17]  Hernan G. Arango,et al.  Weak and strong constraint data assimilation in the inverse Regional Ocean Modeling System (ROMS): Development and application for a baroclinic coastal upwelling system , 2007 .

[18]  Ralph F. Milliff,et al.  Mesoscale Correlation Length Scales from NSCAT and Minimet Surface Wind Retrievals in the Labrador Sea , 2003 .

[19]  Hyun-chul Lee,et al.  Effects of winds and Caribbean eddies on the frequency of Loop Current eddy shedding: A numerical model study , 2003 .

[20]  H. Hurlburt,et al.  A Numerical Study of Loop Current Intrusions and Eddy Shedding , 1980 .

[21]  Hernan G. Arango,et al.  Developments in terrain-following ocean models: intercomparisons of numerical aspects , 2002 .

[22]  Hernan G. Arango,et al.  A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model , 2004 .

[23]  G. S. Fargion,et al.  Loop Current Eddy Paths in the Western Gulf of Mexico , 1999 .

[24]  Andrew F. Bennett,et al.  An inverse ocean modeling system , 2001 .

[25]  L. Oey.  Simulation of Mesoscale Variability in the Gulf of Mexico: Sensitivity Studies, Comparison with Observations, and Trapped Wave Propagation , 1996 .

[26]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. I: Theory , 2007 .

[27]  L. M. Berliner,et al.  A Bayesian tutorial for data assimilation , 2007 .

[28]  John C. Warner,et al.  Performance of four turbulence closure models implemented using a generic length scale method , 2005 .

[29]  Alexander F. Shchepetkin,et al.  Open boundary conditions for long-term integration of regional oceanic models , 2001 .

[30]  J. Sheinbaum,et al.  Flow structure and transport in the Yucatan Channel , 2002 .

[31]  Remy Baraille,et al.  The HYCOM (HYbrid Coordinate Ocean Model) data assimilative system , 2007 .

[32]  Smith,et al.  Satellite measurements of sea surface temperature through clouds , 2000, Science.

[33]  Edward J. Kearns,et al.  Five years of Florida current structure and transport from the Royal Caribbean cruise ship explorer of the Seas , 2008 .

[34]  Eric P. Chassignet,et al.  Deep flow variability in the vicinity of the Yucatan Straits from a high‐resolution numerical simulation , 2005 .

[35]  J. C. Evans,et al.  Separation of Warm-Core Rings in the Gulf of Mexico , 1993 .

[36]  D. Chelton,et al.  Geographical Variability of the First Baroclinic Rossby Radius of Deformation , 1998 .

[37]  M. Ghil,et al.  Data assimilation in meteorology and oceanography , 1991 .

[38]  Larry L. Stowe,et al.  Scientific basis and initial evaluation of the CLAVR-1 global clear cloud classification algorithm f , 1999 .

[39]  Ichiro Fukumori,et al.  Assimilation of TOPEX/Poseidon altimeter data into a global ocean circulation model: How good are the results? , 1999 .

[40]  H. Ngodock,et al.  Cycling the representer algorithm for variational data assimilation with a nonlinear reduced gravity ocean model , 2007 .

[41]  L. Oey,et al.  A Synopsis of the Circulation in the Gulf of Mexico and on its Continental Margins , 2013 .

[42]  James C. McWilliams,et al.  A method for computing horizontal pressure‐gradient force in an oceanic model with a nonaligned vertical coordinate , 2003 .

[43]  Michael H. Freilich,et al.  Wind Stress Curl and Wind Stress Divergence Biases from Rain Effects on QSCAT Surface Wind Retrievals , 2004 .

[44]  John Derber,et al.  A Global Oceanic Data Assimilation System , 1989 .

[45]  G. Dibarboure,et al.  Use of a High-Resolution Model to Analyze the Mapping Capabilities of Multiple-Altimeter Missions , 2001 .

[46]  J. Sheinbaum,et al.  Nonlinear Processes in Geophysical Fluid Dynamics , 2003 .

[47]  Carl Wunsch,et al.  Volume, heat, and freshwater transports of the global ocean circulation 1993-2000, estimated from a general circulation model constrained by World Ocean Circulation Experiment (WOCE) data , 2003 .

[48]  W. Collins,et al.  The NCEP–NCAR 50-Year Reanalysis: Monthly Means CD-ROM and Documentation , 2001 .

[49]  Ananda Pascual,et al.  Mesoscale mapping capabilities of multisatellite altimeter missions: First results with real data in the Mediterranean Sea , 2007 .

[50]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[51]  Paul J. Martin,et al.  A Real-Time Coastal Ocean Prediction Experiment for MREA04 , 2008 .

[52]  John Derber,et al.  The National Meteorological Center's spectral-statistical interpolation analysis system , 1992 .

[53]  X.-H. Lin,et al.  Altimetry and drifter data assimilations of loop current and eddies , 2007 .

[54]  W. Johns,et al.  Moored Observations of Western Boundary Current variability and thermohaline circulation at 26.5°N in the subtropical north Atlantic , 1996 .

[55]  Yannick Trémolet,et al.  Diagnostics of linear and incremental approximations in 4D‐Var , 2004 .

[56]  D. Roemmich.  The Balance of Geostrophic and Ekman Transports in the Tropical Atlantic Ocean , 1983 .

[57]  David C. Smith,et al.  The Interaction of a Two-Layer Isolated Mesoscale Eddy With Bottom Topography , 1983 .

[58]  B. Cornuelle,et al.  Interannual to Decadal Changes in the ECCO Global Synthesis , 2007 .

[59]  L. Kantha,et al.  A Regional Data-Assimilative Model for Operational Use in the Gulf of Mexico , 2013 .

[60]  S. Lord,et al.  Ocean Data Assimilation and Initialization Procedure for the Coupled GFDL/URI Hurricane Prediction System , 2005 .

[61]  Timothy P. Boyer,et al.  World Ocean Atlas 1994. Volume 4. Temperature , 1994 .

[62]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[63]  Jérôme Vialard,et al.  Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks , 2003 .

[64]  H. Arango,et al.  A generalized reduced‐gravity ocean model , 1991 .

[65]  Carl Wunsch,et al.  Global ocean circulation during 1992-1997, estimated from ocean observations and a general circulation model , 2002 .

[66]  A. Romanou,et al.  Gulf of Mexico circulation within a high-resolution numerical simulation of the North Atlantic Ocean , 2004 .

[67]  C. Wunsch,et al.  Towards the general circulation of the North Atlantic ocean , 1982 .

[68]  George L. Mellor,et al.  A Gulf Stream model and an altimetry assimilation scheme , 1991 .

[69]  Thomas M. Smith,et al.  An Improved In Situ and Satellite SST Analysis for Climate , 2002 .

[70]  Alexander F. Shchepetkin,et al.  Model evaluation experiments in the North Atlantic Basin : simulations in nonlinear terrain-following coordinates , 2000 .

[71]  D. Roemmich.  Circulation of the Caribbean Sea: A well‐resolved inverse problem , 1981 .

[72]  P. Courtier,et al.  Correlation modelling on the sphere using a generalized diffusion equation , 2001 .

[73]  J. Sheinbaum,et al.  Canek: Measuring Transport in the Yucatan Channel , 2003 .

[74]  D. Dietrich,et al.  Numerical studies of eddy shedding in the Gulf of Mexico , 1994 .

[75]  Philip L. Richardson,et al.  Caribbean Current and eddies as observed by surface drifters , 2005 .

[76]  L. Oey.  Eddy‐ and wind‐forced shelf circulation , 1995 .

[77]  Serge Gratton,et al.  Limited‐memory preconditioners, with application to incremental four‐dimensional variational data assimilation , 2008 .

[78]  Worth D. Nowlin,et al.  General distribution of water masses within the eastern Caribbean Sea during the winter of 1972 and fall of 1973 , 1982 .

[79]  L. Oey,et al.  Near-Surface Currents in DeSoto Canyon (1997–99): Comparison of Current Meters, Satellite Observation, and Model Simulation , 2003 .

[80]  J. O'Brien,et al.  The connectivity of eddy variability in the Caribbean Sea, the Gulf of Mexico, and the Atlantic Ocean , 1999 .

[81]  L. Oey,et al.  Assimilation of drifter and satellite data in a model of the Northeastern Gulf of Mexico , 2004 .

[82]  A. Bennett,et al.  Inverse Modeling of the Ocean and Atmosphere , 2002 .

[83]  S. Glenn,et al.  Drifting buoy observations of a loop current anticyclonic eddy , 1993 .

[84]  F. Muller‐Karger,et al.  On the seasonal phytoplankton concentration and sea surface temperature cycles of the Gulf of Mexico as determined by satellites , 1991 .

[85]  O. Talagrand,et al.  Short-range evolution of small perturbations in a barotropic model , 1988 .