Correction and commentary for "Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the regional ocean modeling system" by Haidvogel et al., J. Comp. Phys 227, pp 3595-3624

Although our names appear as co-authors in the above article (Haidvogel et al. (2008) [1], hereafter H2008), we were not aware of its existence until after it was published. In reading the article, we discovered that a significant portion of it (~40%, or 10 pages) repeats three large fragments from our own previously published work, Shchepetkin and McWilliams (2005) [2] (hereafter SM2005), but now presented in such a way that the motivation for the specific algorithmic choices made in ROMS and the relations among the different model components are no longer clear. The model equations appearing in H2008, Section 2.1 (taken from an earlier article, Haidvogel et al. (2000) [3]) are not entirely consistent with the actual equations solved in the ROMS code, resulting in contradictions within H2008 itself. In our view the description in H2008 does not constitute a mathematically accurate statement about the hydrodynamic core of ROMS. The purpose of this note is to clarify and correct this, as well as to explain some of the algorithmic differences among ROMS versions now in use.

[1]  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 .

[2]  J. Molines,et al.  On the seasonal variability and eddies in the North Brazil Current: insights from model intercomparison experiments , 2001 .

[3]  W. Dewar,et al.  Mode waters and subduction rates in a high-resolution South Atlantic simulation , 1999 .

[4]  Dale B. Haidvogel,et al.  Numerical Simulation of Flow around a Tall Isolated Seamount. Part II: Resonant Generation of Trapped Waves , 1993 .

[5]  C. Willmott Some Comments on the Evaluation of Model Performance , 1982 .

[6]  J. Dukowicz Reduction of Density and Pressure Gradient Errors in Ocean Simulations , 2001 .

[7]  Alistair Adcroft,et al.  Rescaled height coordinates for accurate representation of free-surface flows in ocean circulation models , 2004 .

[8]  L. Centurioni,et al.  Permanent Meanders in the California Current System , 2008 .

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

[10]  Alexander F. Shchepetkin,et al.  Algorithm for non-hydrostatic dynamics in the Regional Oceanic Modeling System , 2007 .

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

[12]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[13]  Robert L. Higdon,et al.  Barotropic-Baroclinic Time Splitting for Ocean Circulation Modeling , 1997 .

[14]  Jarle Berntsen,et al.  Internal pressure errors in sigma-coordinate ocean models—sensitivity of the growth of the flow to the time stepping method and possible non-hydrostatic effects , 2005 .

[15]  J. McWilliams,et al.  Mesoscale to Submesoscale Transition in the California Current System. Part I: Flow Structure, Eddy Flux, and Observational Tests , 2008 .

[16]  K. Ide,et al.  A Three-Dimensional Variational Data Assimilation Scheme for the Regional Ocean Modeling System , 2008 .

[17]  Y. Song,et al.  A General Pressure Gradient Formulation for Ocean Models. Part II: Energy, Momentum, and Bottom Torque Consistency , 1998 .

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

[19]  Dale B. Haidvogel,et al.  A semi-spectral primitive equation ocean circulation model using vertical sigma and orthogonal curvilinear horizontal coordinates , 1991 .

[20]  Akio Arakawa,et al.  Computational Design of the Basic Dynamical Processes of the UCLA General Circulation Model , 1977 .

[21]  A. Ciappa An operational comparative test of z-levels PGF schemes to reduce pressure gradient errors of the ocean model POM , 2006 .

[22]  P. Marchesiello,et al.  A sigma-coordinate primitive equation model for studying the circulation in the South Atlantic Part II: Meridional transports and seasonal variability , 1998 .

[23]  Robert L. Higdon,et al.  Stability Analysis of Operator Splitting for Large-Scale Ocean Modeling , 1996 .

[24]  R. Higdon Implementation of a Barotropic-Baroclinic Time Splitting for Isopycnic Coordinate Ocean Modeling , 1999 .

[25]  Yongqi Wang,et al.  A Semi-Implicit Semispectral Primitive Equation Model for Lake Circulation Dynamics and Its Stability Performance , 1998 .

[26]  L. Oey,et al.  Sigma Coordinate Pressure Gradient Errors and the Seamount Problem , 1998 .

[27]  Alistair Adcroft,et al.  Conservation of properties in a free-surface model , 2004 .

[28]  Dale B. Haidvogel,et al.  Numerical Ocean Circulation Modeling , 1999 .

[29]  John D. McCalpin A comparison of second‐order and fourth‐order pressure gradient algorithms in a σ‐co‐ordinate ocean model , 1994 .

[30]  P. Smolarkiewicz A Fully Multidimensional Positive Definite Advection Transport Algorithm with Small Implicit Diffusion , 1984 .

[31]  Robert Hallberg,et al.  Stable Split Time Stepping Schemes for Large-Scale Ocean Modeling , 1997 .

[32]  Thomas M. Powell,et al.  Multi‐scale modeling of the North Pacific Ocean: Assessment and analysis of simulated basin‐scale variability (1996–2003) , 2005 .

[33]  S. Levitus,et al.  World ocean atlas 2009 , 2010 .

[34]  T. McDougall,et al.  Minimal Adjustment of Hydrographic Profiles to Achieve Static Stability , 1995 .

[35]  James C. McWilliams,et al.  Equilibrium structure and dynamics of the California Current System , 2003 .

[36]  James C. McWilliams,et al.  Computational Kernel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations , 2009 .

[37]  S. Griffies,et al.  Tracer Conservation with an Explicit Free Surface Method for z-Coordinate Ocean Models , 2001 .

[38]  Edwin D. Mares,et al.  On S , 1994, Stud Logica.

[39]  Swapan K. Pandit,et al.  A transient higher order compact scheme for incompressible viscous flows on geometries beyond rectangular , 2007, J. Comput. Phys..

[40]  R. Easter Two Modified Versions of Bott's Positive-Definite Numerical Advection Scheme , 1993 .

[41]  J. Beckers On some stability properties of the discretization of damped propagation of shallow-water inertia–gravity waves on the Arakawa B-grid , 1999 .

[42]  Jean-Marc Molines,et al.  Circulation characteristics in three eddy-permitting models of the North Atlantic , 2001 .

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

[44]  J. Dukowicz,et al.  Approximate factorization as a high order splitting for the implicit incompressible flow equations , 1992 .

[45]  Yves Morel,et al.  Time splitting and linear stability of the slow part of the barotropic component , 2008 .

[46]  Kayo Ide,et al.  A three-dimensional variational data assimilation in support of coastal ocean observing systems , 2007, SPIE Optical Engineering + Applications.

[47]  J. McWilliams,et al.  Evaluation and application of the ROMS 1-way embedding procedure to the central california upwelling system , 2006 .

[48]  Aike Beckmann,et al.  A numerical model of the Weddell Sea: Large scale circulation and water mass distribution , 1999 .

[49]  James C. McWilliams,et al.  Quasi-Monotone Advection Schemes Based on Explicit Locally Adaptive Dissipation , 1998 .

[50]  J. Berntsen Internal Pressure Errors in Sigma-Coordinate Ocean Models , 2002 .

[51]  Dale B. Haidvogel,et al.  Numerical Simulation of Flow around a Tall Isolated Seamount. Part I: Problem Formulation and Model Accuracy , 1993 .

[52]  J. Verron,et al.  How Topographic Smoothing Contributes to Differences between the Eddy Flows Simulated by Sigma- and Geopotential-Coordinate Models , 2002 .

[53]  Dale B. Haidvogel,et al.  Dynamical simulations of filament formation and evolution in the Coastal Transition Zone , 1991 .

[54]  Piotr K. Smolarkiewicz,et al.  Predicting weather, climate and extreme events , 2008, J. Comput. Phys..

[55]  Comparing Two Topography-Following Primitive Equation Models for Lake Circulation , 1999 .

[56]  Y. Song,et al.  A General Pressure Gradient Formulation for Ocean Models. Part I: Scheme Design and Diagnostic Analysis , 1998 .

[57]  James C. McWilliams,et al.  Mesoscale to Submesoscale Transition in the California Current System. Part II: Frontal Processes , 2008 .

[58]  J. Molines,et al.  A sigma-coordinate primitive equation model for studying the circulation in the South Atlantic. Part I: Model configuration with error estimates , 1998 .

[59]  D. Haidvogel,et al.  A semi-implicit ocean circulation model using a generalized topography-following coordinate system , 1994 .

[60]  John C. Warner,et al.  Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the Regional Ocean Modeling System , 2008, J. Comput. Phys..

[61]  Kayo Ide,et al.  A three‐dimensional variational data assimilation scheme for the Regional Ocean Modeling System: Implementation and basic experiments , 2008 .

[62]  C. Willmott ON THE VALIDATION OF MODELS , 1981 .