Bibliography - Stephen Griffies

1. Griffies, Stephen, Robert W Hallberg, A Pirani, Bonita L Samuels, and Michael Winton, et al., January 2009: Coordinated ocean-ice reference experiments (COREs). Ocean Modelling, 26(1-2), doi:10.1016/j.ocemod.2008.08.007.
   [ Abstract ]

   Coordinated Ocean-ice Reference Experiments (COREs) are presented as a tool to explore the behaviour of global ocean-ice models under forcing from a common atmospheric dataset. We highlight issues arising when designing coupled global ocean and sea ice experiments, such as difficulties formulating a consistent forcing methodology and experimental protocol. Particular focus is given to the hydrological forcing, the details of which are key to realizing simulations with stable meridional overturning circulations. The atmospheric forcing from [Large, W., Yeager, S., 2004. Diurnal to decadal global forcing for ocean and sea-ice models: the data sets and flux climatologies. NCAR Technical Note: NCAR/TN-460+STR. CGD Division of the National Center for Atmospheric Research] was developed for coupled-ocean and sea ice models. We found it to be suitable for our purposes, even though its evaluation originally focussed more on the ocean than on the sea-ice. Simulations with this atmospheric forcing are presented from seven global ocean-ice models using the CORE-I design (repeating annual cycle of atmospheric forcing for 500 years). These simulations test the hypothesis that global ocean-ice models run under the same atmospheric state produce qualitatively similar simulations. The validity of this hypothesis is shown to depend on the chosen diagnostic. The CORE simulations provide feedback to the fidelity of the atmospheric forcing and model configuration, with identification of biases promoting avenues for forcing dataset and/or model development.

2. Griffies, Stephen, Alistair Adcroft, Ventakramani Balaji, Robert W Hallberg, Sonya Legg, T Martin, and A Pirani, et al., February 2009: Sampling Physical Ocean Field in WCRP CMIP5 Simulations: CLIVAR Working Group on Ocean Model Development (WGOMD) Committee on CMIP5 Ocean Model Output, International CLIVAR Project Office, CLIVAR Publication Series No. 137, 56pp.
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3. Griffies, Stephen, and Alistair Adcroft, 2008: Formulating the equations of ocean models In Ocean Modeling in an Eddying Regime, Geophysical Monograph 177, M. W. Hecht, and H. Hasumi, eds., Washington, DC, American Geophysical Union, 281-318.
   [ Abstract PDF ]

   We formulate mathematical equations describing the thermo-hydrodynamics of the ocean and introduce certain numerical methods employed by models used for ocean simulations.

4. Griffies, Stephen, H Banks, and A Pirani, 2008: Furthering the science of ocean climate modelling. Clivar Exchanges, 13(1), 281-318.
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5. Pirani, A, Stephen Griffies, and H Banks, 2008: Report from the CLIVAR Working Group on ocean model development (WGOMD). Clivar Exchanges, 13(1), 30-32.
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6. Gnanadesikan, Anand, Stephen Griffies, and Bonita L Samuels, 2007: Effects in a climate model of slope tapering in neutral physics schemes. Ocean Modelling, 16(1-2), doi:10.1016/j.ocemod.2006.06.004.
   [ Abstract ]

   In many global ocean climate models, mesoscale eddies are parameterized as along isopycnal diffusion and eddy-induced advection (or equivalently skew-diffusion). The eddy-induced advection flattens isopycnals and acts as a sink of available potential energy, whereas the isopycnal diffusion mixes tracers along neutral directions. While much effort has gone into estimating diffusivities associated with this closure, less attention has been paid to the details of how this closure (which tries to flatten isopycnals) interacts with the mixed layer (in which vertical mixing tries to drive the isopycnals vertical). In order to maintain numerical stability, models often stipulate a maximum slope S_max which in combination with the thickness diffusivity A_gm defines a maximum eddy-induced advective transport A_gm*S_max. In this paper, we examine the impact of changing S_max within the GFDL global coupled climate model. We show that this parameter produces significant changes in wintertime mixed layer depth, with implications for wintertime temperatures in key regions, the distribution of precipitation, and the vertical structure of heat uptake. Smaller changes are seen in details of ventilation and currents, and even smaller changes as regards the overall hydrography. The results suggest that not only the value of the coefficient, but the details of the tapering scheme, need to be considered when comparing isopycnal mixing schemes in models.

7. Griffies, Stephen, C Böning, and A M Treguier, 2007: Design considerations for coordinated ocean-ice reference experiments. Flux News, 3, 3-5.
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8. Griffies, Stephen, Matthew J Harrison, Ronald C Pacanowski, and Anthony Rosati, 2007: Ocean modelling with MOM. Clivar Exchanges, 12(3), 3-5, 13.
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9. Delworth, Thomas L., Anthony J Broccoli, Anthony Rosati, Ronald J Stouffer, Ventakramani Balaji, J A Beesley, W F Cooke, Keith W Dixon, John Dunne, Krista A Dunne, J W Durachta, Kirsten L Findell, Paul Ginoux, Anand Gnanadesikan, C Tony Gordon, Stephen Griffies, Rich Gudgel, Matthew J Harrison, Isaac Held, Richard S Hemler, Larry Horowitz, Stephen A Klein, Thomas R Knutson, P J Kushner, A R Langenhorst, H C Lee, Shian-Jiann Lin, Jian Lu, S Malyshev, P C D Milly, V Ramaswamy, J L Russell, M Daniel Schwarzkopf, Elena Shevliakova, Joseph J Sirutis, Michael J Spelman, William F Stern, Michael Winton, Andrew T Wittenberg, Bruce Wyman, Fanrong Zeng, and Rong Zhang, 2006: GFDL's CM2 Global Coupled Climate Models. Part I: Formulation and Simulation Characteristics. Journal of Climate, 19(5), doi:10.1175/JCLI3629.1.
   [ Abstract ]

   The formulation and simulation characteristics of two new global coupled climate models developed at NOAA's Geophysical Fluid Dynamics Laboratory (GFDL) are described. The models were designed to simulate atmospheric and oceanic climate and variability from the diurnal time scale through multicentury climate change, given our computational constraints. In particular, an important goal was to use the same model for both experimental seasonal to interannual forecasting and the study of multicentury global climate change, and this goal has been achieved. Two versions of the coupled model are described, called CM2.0 and CM2.1. The versions differ primarily in the dynamical core used in the atmospheric component, along with the cloud tuning and some details of the land and ocean components. For both coupled models, the resolution of the land and atmospheric components is 2° latitude × 2.5° longitude; the atmospheric model has 24 vertical levels. The ocean resolution is 1° in latitude and longitude, with meridional resolution equatorward of 30° becoming progressively finer, such that the meridional resolution is 1/3° at the equator. There are 50 vertical levels in the ocean, with 22 evenly spaced levels within the top 220 m. The ocean component has poles over North America and Eurasia to avoid polar filtering. Neither coupled model employs flux adjustments. The control simulations have stable, realistic climates when integrated over multiple centuries. Both models have simulations of ENSO that are substantially improved relative to previous GFDL coupled models. The CM2.0 model has been further evaluated as an ENSO forecast model and has good skill (CM2.1 has not been evaluated as an ENSO forecast model). Generally reduced temperature and salinity biases exist in CM2.1 relative to CM2.0. These reductions are associated with 1) improved simulations of surface wind stress in CM2.1 and associated changes in oceanic gyre circulations; 2) changes in cloud tuning and the land model, both of which act to increase the net surface shortwave radiation in CM2.1, thereby reducing an overall cold bias present in CM2.0; and 3) a reduction of ocean lateral viscosity in the extratropics in CM2.1, which reduces sea ice biases in the North Atlantic. Both models have been used to conduct a suite of climate change simulations for the 2007 Intergovernmental Panel on Climate Change (IPCC) assessment report and are able to simulate the main features of the observed warming of the twentieth century. The climate sensitivities of the CM2.0 and CM2.1 models are 2.9 and 3.4 K, respectively. These sensitivities are defined by coupling the atmospheric components of CM2.0 and CM2.1 to a slab ocean model and allowing the model to come into equilibrium with a doubling of atmospheric CO2. The output from a suite of integrations conducted with these models is freely available online (see http://nomads.gfdl.noaa.gov/). Manuscript received 8 December 2004, in final form 18 March 2005

10. Gnanadesikan, Anand, Keith W Dixon, Stephen Griffies, Ventakramani Balaji, M Barreiro, J A Beesley, W F Cooke, Thomas L Delworth, R Gerdes, Matthew J Harrison, Isaac Held, William J Hurlin, H C Lee, Z Liang, G Nong, Ronald C Pacanowski, Anthony Rosati, J L Russell, Bonita L Samuels, Qian Song, Michael J Spelman, Ronald J Stouffer, C Sweeney, G A Vecchi, Michael Winton, Andrew T Wittenberg, Fanrong Zeng, Rong Zhang, and John Dunne, 2006: GFDL's CM2 Global Coupled Climate Models. Part II: The baseline ocean simulation. Journal of Climate, 19(5), doi:10.1175/JCLI3630.1.
    [ Abstract ]

    The current generation of coupled climate models run at the Geophysical Fluid Dynamics Laboratory (GFDL) as part of the Climate Change Science Program contains ocean components that differ in almost every respect from those contained in previous generations of GFDL climate models. This paper summarizes the new physical features of the models and examines the simulations that they produce. Of the two new coupled climate model versions 2.1 (CM2.1) and 2.0 (CM2.0), the CM2.1 model represents a major improvement over CM2.0 in most of the major oceanic features examined, with strikingly lower drifts in hydrographic fields such as temperature and salinity, more realistic ventilation of the deep ocean, and currents that are closer to their observed values. Regional analysis of the differences between the models highlights the importance of wind stress in determining the circulation, particularly in the Southern Ocean. At present, major errors in both models are associated with Northern Hemisphere Mode Waters and outflows from overflows, particularly the Mediterranean Sea and Red Sea.

11. Jackett, D R., T J McDougall, R Feistel, D Wright, and Stephen Griffies, 2006: Algorithms for Density, Potential Temperature, Conservative Temperature, and the Freezing Temperature of Seawater. Journal of Atmospheric and Oceanic Technology, 23(12), doi:10.1175/JTECH1946.1.
    [ Abstract ]

    Algorithms are presented for density, potential temperature, conservative temperature, and the freezing temperature of seawater. The algorithms for potential temperature and density (in terms of potential temperature) are updates to routines recently published by McDougall et al., while the algorithms involving conservative temperature and the freezing temperatures of seawater are new. The McDougall et al. algorithms were based on the thermodynamic potential of Feistel and Hagen; the algorithms in this study are all based on the “new extended Gibbs thermodynamic potential of seawater” of Feistel. The algorithm for the computation of density in terms of salinity, pressure, and conservative temperature produces errors in density and in the corresponding thermal expansion coefficient of the same order as errors for the density equation using potential temperature, both being twice as accurate as the International Equation of State when compared with Feistel’s new equation of state. An inverse function relating potential temperature to conservative temperature is also provided. The difference between practical salinity and absolute salinity is discussed, and it is shown that the present practice of essentially ignoring the difference between these two different salinities is unlikely to cause significant errors in ocean models.

12. Gerdes, R, William J Hurlin, and Stephen Griffies, 2005: Sensitivity of a global ocean model to increased run-off from Greenland. Ocean Modelling, 12(3-4), doi:10.1016/j.ocemod.2005.08.003.
    [ Abstract ]

    We study the reaction of a global ocean–sea ice model to an increase of fresh water input into the northern North Atlantic under different surface boundary conditions, ranging from simple restoring of surface salinity to the use of an energy balance model (EBM) for the atmosphere. The anomalous fresh water flux is distributed around Greenland, reflecting increased melting of the Greenland ice sheet and increasing fresh water export from the Arctic Ocean. Depending on the type of surface boundary condition, the large circulation reacts with a slow-down of overturning and gyre circulations. Restoring of the total or mean surface salinity prevents a large scale redistribution of the salinity field that is apparent under mixed boundary conditions and with the EBM. The control run under mixed boundary conditions exhibits large and unrealistic oscillations of the meridional overturning. Although the reaction to the fresh water flux anomaly is similar to the response with the EBM, mixed boundary conditions must thus be considered unreliable. With the EBM, the waters in the deep western boundary current initially become saltier and a new fresh water mass forms in the north-eastern North Atlantic in response to the fresh water flux anomaly around Greenland. After an accumulation period of several decades duration, this new North East Atlantic Intermediate Water spreads towards the western boundary and opens a new southward pathway at intermediate depths along the western boundary for the fresh waters of high northern latitudes.

13. Griffies, Stephen, 2005: Some ocean model fundamentals In Ocean Weather Forecasting: An Integrated View of Oceanography, Berlin, Germany, Springer, 19-74.
    [ Abstract ]

    The purpose of these lectures is to present elements of the equations and algorithms used in numerical models of the large-scale ocean circulation. Such models generally integrate the ocean's primitive equations, which are based on Newton's Laws applied to a continuum fluid under hydrostatic balance in a spherical geometry, along with linear irreversible thermodynamics and subgrid scale (SGS) parameterizations. During formulations of both the kinematics and dynamics, we highlight issues related to the use of a generalized vertical coordinate. The vertical coordinate is arguably the most critical element determining how a model is designed and applications to which a model is of use.

14. Griffies, Stephen, Anand Gnanadesikan, Keith W Dixon, John Dunne, R Gerdes, Matthew J Harrison, Anthony Rosati, J L Russell, Bonita L Samuels, Michael J Spelman, Michael Winton, and Rong Zhang, 2005: Formulation of an ocean model for global climate simulations. Ocean Science, 1, 45-79.
    [ Abstract PDF ]

    This paper summarizes the formulation of the ocean component to the Geophysical Fluid Dynamics Laboratory's (GFDL) climate model used for the 4th IPCC Assessment (AR4) of global climate change. In particular, it reviews the numerical schemes and physical parameterizations that make up an ocean climate model and how these schemes are pieced together for use in a state-of-the-art climate model. Features of the model described here include the following: (1) tripolar grid to resolve the Arctic Ocean without polar filtering, (2) partial bottom step representation of topography to better represent topographically influenced advective and wave processes, (3) more accurate equation of state, (4) three-dimensional flux limited tracer advection to reduce overshoots and undershoots, (5) incorporation of regional climatological variability in shortwave penetration, (6) neutral physics parameterization for representation of the pathways of tracer transport, (7) staggered time stepping for tracer conservation and numerical efficiency, (8) anisotropic horizontal viscosities for representation of equatorial currents, (9) parameterization of exchange with marginal seas, (10) incorporation of a free surface that accomodates a dynamic ice model and wave propagation, (11) transport of water across the ocean free surface to eliminate unphysical "virtual tracer flux" methods, (12) parameterization of tidal mixing on continental shelves. We also present preliminary analyses of two particularly important sensitivities isolated during the development process, namely the details of how parameterized subgridscale eddies transport momentum and tracers.

15. Sweeney, C, Anand Gnanadesikan, Stephen Griffies, Matthew J Harrison, Anthony Rosati, and Bonita L Samuels, 2005: Impacts of shortwave penetration depth on large-scale ocean circulation and heat transport. Journal of Physical Oceanography, 35(6), 1103-1119.
    [ Abstract PDF ]

    The impact of changes in shortwave radiation penetration depth on the global ocean circulation and heat transport is studied using the GFDL Modular Ocean Model (MOM4) with two independent parameterizations that use ocean color to estimate the penetration depth of shortwave radiation. Ten to eighteen percent increases in the depth of 1% downwelling surface irradiance levels results in an increase in mixed layer depths of 3-20 m in the subtropical and tropical regions with no change at higher latitudes. While 1D models have predicted that sea surface temperatures at the equator would decrease with deeper penetration of solar irradiance, this study shows a warming, resulting in a 10% decrease in the required restoring heat flux needed to maintain climatological sea surface temperatures in the eastern equatorial Atlantic and Pacific Oceans. The decrease in the restoring heat flux is attributed to a slowdown in heat transport (5%) from the Tropics and an increase in the temperature of submixed layer waters being transported into the equatorial regions. Calculations were made using a simple relationship between mixed layer depth and meridional mass transport. When compared with model diagnostics, these calculations suggest that the slowdown in heat transport is primarily due to off-equatorial increases in mixed layer depths. At higher latitudes (5°-40°), higher restoring heat fluxes are needed to maintain sea surface temperatures because of deeper mixed layers and an increase in storage of heat below the mixed layer. This study offers a way to evaluate the changes in irradiance penetration depths in coupled ocean-atmosphere GCMs and the potential effect that large-scale changes in chlorophyll a concentrations will have on ocean circulation.

16. Griffies, Stephen, 2004: Fundamentals of Ocean Climate Models, Princeton, NJ: Princeton University Press, 518 pp.
    [ Abstract ]

    This book sets forth the physical, mathematical, and numerical foundations of computer models used to understand and predict the global ocean climate system. Aimed at students and researchers of ocean and climate science who seek to understand the physical content of ocean model equations and numerical methods for their solution, it is largely general in formulation and employs modern mathematical techniques. It also highlights certain areas of cutting-edge research. Stephen Griffies presents material that spans a broad spectrum of issues critical for modern ocean climate models. Topics are organized into parts consisting of related chapters, with each part largely self-contained. Early chapters focus on the basic equations arising from classical mechanics and thermodynamics used to rationalize ocean fluid dynamics. These equations are then cast into a form appropriate for numerical models of finite grid resolution. Basic discretization methods are described for commonly used classes of ocean climate models. The book proceeds to focus on the parameterization of phenomena occurring at scales unresolved by the ocean model, which represents a large part of modern oceanographic research. The final part provides a tutorial on the tensor methods that are used throughout the book, in a general and elegant fashion, to formulate the equations.

17. Griffies, Stephen, Matthew J Harrison, Ronald C Pacanowski, and Anthony Rosati, 2004: A Technical Guide to MOM4, GFDL Ocean Group Technical Report No. 5, Princeton, NJ:: NOAA/Geophysical Fluid Dynamics Laboratory, 342 pp.
    [ Abstract PDF ]

    This manual provides a detailed description of the analytical, numerical, and computational aspects of the MOM4 ocean model.

18. Griffies, Stephen, 2003: An introduction to linear predictability analysis In Global Climate, Rodó, X., and F. A. Comín, eds., Berlin, Springer-Verlag, 80-101.
19. Griffies, Stephen, 2003: An introduction to ocean climate modeling In Global Climate, Rodó, X., and F. A. Comín, eds., Berlin, Springer-Verlag, 55-79.
20. Griffies, Stephen, Ronald C Pacanowski, M Schmidt, and Ventakramani Balaji, 2001: Tracer conservation with an explicit free surface method for z-coordinate ocean models. Monthly Weather Review, 129(5), 1081-1098.
    [ Abstract PDF ]

    This paper details a free surface method using an explicit time stepping scheme for use in z-coordinate ocean models. One key property that makes the method especially suitable for climate simulations is its very stable numerical time stepping scheme, which allows for the use of a long density time step, as commonly employed with coarse-resolution rigid-lid models. Additionally, the effects of the undulating free surface height are directly incorporated into the baroclinic momentum and tracer equations. The novel issues related to local and global tracer conservation when allowing for the top cell to undulate are the focus of this work. The method presented here is quasi-conservative locally and globally of tracer when the baroclinic and tracer time steps are equal. Important issues relevant for using this method in regional as well as large-scale climate models are discussed and illustrated, and examples of scaling achieved on parallel computers provided.

21. Stocker, T F., Thomas L Delworth, Stephen Griffies, Isaac Held, V Ramaswamy, and Brian J Soden, et al., 2001: Physical climate processes and feedbacks In Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge, UK, Cambridge University Press, 418-470.
22. Griffies, Stephen, 2000: Review of "Ocean Modeling and Parameterization," E. P. Chassignet and J. Verron, eds., 1998, Kluwer Academic Publishers. Bulletin of the American Meteorological Society, 81(3), 591-593.
23. Griffies, Stephen, C Böning, F O Bryan, E P Chassignet, R Gerdes, H Hasumi, A C Hirst, A M Treguier, and D Webb, 2000: Developments in ocean climate modelling. Ocean Modelling, 2, 123-192.
    [ Abstract PDF ]

    This paper presents some research developments in primitive equation ocean models which could impact the ocean component of realistic global climate models aimed at large-scale, low frequency climate simulations and predictions. It is written primarily to an audience of modellers concerned with the ocean component of climate models, although not necessarily experts in the design and implementation of ocean model algorithms.

24. Griffies, Stephen, and Robert W Hallberg, 2000: Biharmonic friction with a Smagorinsky-like viscosity for use in large-scale eddy-permitting ocean models. Monthly Weather Review, 128(8), 2935-2946.
    [ Abstract PDF ]

    This paper discusses a numerical closure, motivated from the ideas of Smagorinsky, for use with a biharmonic operator. The result is a highly scale-selective, state-dependent friction operator for use in eddy-permitting geophysical fluid models. This friction should prove most useful for large-scale ocean models in which there are multiple regimes of geostrophic turbulence. Examples are provided from primitive equation geopotential and isopycnal-coordinate ocean models.

25. Griffies, Stephen, Ronald C Pacanowski, and Robert W Hallberg, 2000: Spurious diapycnal mixing associated with advection in a z-coordinate ocean model. Monthly Weather Review, 128(3), 538-564.
    [ Abstract PDF ]

    This paper discusses spurious diapycnal mixing associated with the transport of density in a z-coordinate ocean model. A general method, based on the work of Winters and collaborators, is employed for empirically diagnosing an effective diapycnal diffusivity corresponding to any numerical transport process. This method is then used to quantify the spurious mixing engendered by various numerical representations of advection. Both coarse and fine resolution examples are provided that illustrate the importance of adequately resolving the admitted scales of motion in order to maintain a small amount of mixing consistent with that measured within the ocean's pycnocline. Such resolution depends on details of the advection scheme, momentum and tracer dissipation, and grid resolution. Vertical transport processes, such as convective adjustment, act as yet another means to increase the spurious mixing introduced by dispersive errors from numerical advective fluxes.

26. Pacanowski, Ronald C., and Stephen Griffies, 1999: The MOM3 Manual, GFDL Ocean Group Technical Report No. 4, Princeton, NJ: NOAA/Geophysical Fluid Dynamics Laboratory, 680 pp.
27. Schneider, T, and Stephen Griffies, 1999: A conceptual framework for predictability studies. Journal of Climate, 12(10), 3133-3155.
    [ Abstract PDF ]

    A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information-theoretical principles, lies at the center of the framework. The PP is invarient under linear coordinate transformations and applies to multivariate predictions irrespective of assumptions about the probability distribution of prediction errors. For univariate Gaussian predictions, the PP reduces to conventional predictability measures that are based upon the ratio of the rms error of a model prediction over the rms error of the climatological mean prediction. Since climatic variability on intraseasonal to interdecadal timescales follows an approximately Gaussian distribution, the emphasis of this paper is on multivariate Gaussian random variables. Predictable and unpredictable components of multivariate Gaussian systems can be distinguished by predictable component analysis, a procedure derived from discriminant analysis: seeking components with large PP leads to an eigenvalue problem, whose solution yields uncorrelated components that are ordered by PP from largest to smallest. In a discussion of the application of the PP and the predictable component analysis in different types of predictability studies, studies are considered that use either ensemble integrations of numerical models or autoregressive models fitted to observed or simulated data. An investigation of simulated multidecadal variability of the North Atlantic illustrates the proposed methodology. Reanalyzing an ensemble of integrations of the Geophysical Fluid Dynamics Laboratory coupled general circulation model confirms and refines earlier findings. With an autoregressive model fitted to a single integration of the same model, it is demonstrated that similar conclusions can be reached without resorting to computationally costly ensemble integrations.

28. Griffies, Stephen, 1998: The Gent-McWilliams skew flux. Journal of Physical Oceanography, 28(5), 831-841.
    [ Abstract PDF ]

    This paper formulates tracer stirring arising from the Gent-McWilliams (GM) eddy-induced transport in terms of a skew-diffusive flux. A skew-diffusive tracer flux is directed normal to the tracer gradient, which is in contrast to a diffusive tracer flux directed down the tracer gradient. Analysis of the GM skew flux provides an understanding of the physical mechanisms prescribed by GM stirring, which is complementary to the more familiar advective flux perspective. Additionally, it unifies the tracer mixing operators arising from Redi isoneutral diffusion and GM stirring. This perspective allows for a computationally efficient and simple manner in which to implement the GM closure in z-coordinate models. With this approach, no more computation is necessary than when using isoneutral diffusion alone. Additionally, the numerical realization of the skew flux is significantly smoother than the advective flux. The reason is that to compute the skew flux, no gradient of the diffusivity or isoneutral slope is taken, whereas such a gradient is needed for computing the advective flux. The skew-flux formulation also exposes a striking cancellation of terms that results when the GM diffusion coefficient is identical to the Redi isoneutral diffusion coefficient. For this case, the horizontal components to the tracer flux are aligned down the horizontal tracer gradient, and the resulting computational cost of Redi diffusion plus GM skew diffusion is roughly half that needed for Redi diffusion alone.

29. Griffies, Stephen, Anand Gnanadesikan, Ronald C Pacanowski, V D Larichev, J K Dukowicz, and R D Smith, 1998: Isoneutral diffusion in a z-coordinate ocean model. Journal of Physical Oceanography, 28(5), 805-830.
    [ Abstract PDF ]

    This paper considers the requirements that must be satisfied in order to provide a stable and physically based isoneutral tracer diffusion scheme in a z-coordinate ocean model. Two properties are emphasized: 1) downgradient orientation of the diffusive fluxes along the neutral directions and 2) zero isoneutral diffusive flux of locally referenced potential density. It is shown that the Cox diffusion scheme does not respect either of these properties, which provides an explanation for the necessity to add a nontrivial background horizontal diffusion to that scheme. A new isoneutral diffusion scheme is proposed that aims to satisfy the stated properties and is found to require no horizontal background diffusion.

30. Bryan, Kirk, and Stephen Griffies, 1997: Predictability of North Atlantic climate on decadal times scales estimated using a coupled ocean-atmosphere model. International WOCE Newsletter, 26, 5-9.
31. Griffies, Stephen, and Kirk Bryan, 1997: Predictability of North Atlantic multidecadal climate variability. Science, 275(5297), 181-184.
    [ Abstract PDF ]

    Atmospheric weather systems become unpredictable beyond a few weeks, but climate variations can be predictable over much longer periods because of the coupling of the ocean and atmosphere. With the use of a global coupled ocean-atmosphere model, it is shown that the North Atlantic may have climatic predictability on the order of a decade or longer. These results suggest that variations of the dominant multidecadal sea surface temperature patterns in the North Atlantic, which have been associated with changes in climate over Eurasia, can be predicted if an adequate and sustainable system for monitoring the Atlantic Ocean exists.

32. Griffies, Stephen, and Kirk Bryan, 1997: A predictability study of simulated North Atlantic multidecadal variability. Climate Dynamics, 13(7-8), 459-487.
    [ Abstract PDF ]

    The North Atlantic is one of the few places on the globe where the atmosphere is linked to the deep ocean through air-sea interaction. While the internal variability of the atmosphere by itself is only predictable over a period of one to two weeks, climate variations are potentially predictable for much longer periods of months or even years because of coupling with the ocean. This work presents details from the first study to quantify the predictability for simulated multidecadal climate variability over the North Atlantic. The model used for this purpose is the GFDL coupled ocean-atmosphere climate model used extensively for studies of global warming and natural climate variability. This model contains fluctuations of the North Atlantic and high-latitude oceanic circulation with variability concentrated in the 40-60 year range. Oceanic predictability is quantified through analysis of the time-dependent behavior of large-scale empirical orthogonal function (EOF) patterns for the meridional stream function, dynamic topography, 170 m temperature, surface temperature and surface salinity. The results indicate that predictability in the North Atlantic depends on three main physical mechanisms. The first involves the oceanic deep convection in the subpolar region which acts to integrate atmospheric fluctuations, thus providing for a red noise oceanic response as elaborated by Hasselmann. The second involves the large-scale dynamics of the thermohaline circulation, which can cause the oceanic variations to have an oscillatory character on the multidecadal time scale. The third involves non-local effects on the North Atlantic arising from periodic anomalous fresh water transport advecting southward from the polar regions in the East Greenland Current. When the multidecadal oscillatory variations of the thermohaline circulation are active, the first and second EOF patterns for the North Atlantic dynamic topography have predictability time scales on the order of 10-20 y, whereas EOF-1 of SST has predictability time scales of 5-7 y. When the thermohaline variability has weak multidecadal power, the Hasselmann mechanism is dominant and the predictability is reduced by at least a factor of two. When the third mechanism is in an extreme phase, the North Atlantic dynamic topography patterns realize a 10-20 year predictability time scale. Additional analysis of SST in the Greenland Sea, in a region associated with the southward propagating fresh water anomalies, indicates the potential for decadal scale predictability for this high latitude region as well. The model calculations also allow insight into regional variations of predictability, which might be useful information for the design of a monitoring system for the North Atlantic. Predictability appears to break down most rapidly in regions of active convection in the high-latitude regions of the North Atlantic.

33. Toggweiler, J R., E Tziperman, Y Feliks, Kirk Bryan, Stephen Griffies, and Bonita L Samuels, 1996: Reply. Journal of Physical Oceanography, 26(6), 1106-1110.
    [ Abstract PDF ]

    The comment by Rahmstorf suggests that a numerical problem in Tziperman et al. (1994, TTFB) leads to a noisy E - P field that invalidates TTFB's conclusions. The authors eliminate the noise, caused by the Fourier filtering used in the model, and show that TTFB's conclusions are still valid. Rahmstorf questions whether a critical value in the freshwater forcing separates TTFB's stable and unstable runs. By TTFB's original definition, the unstable runs in both TTFB and in Rahmstorf's comment have most definitely crossed a stability transition point upon switching to mixed boundary conditions. Rahmstorf finally suggests that the instability mechanism active in TTFB is a fast convective mechanism, not the slow advective mechanism proposed in TTFB. The authors show that the timescale of the instability is, in fact, consistent with the advective mechanism

34. Griffies, Stephen, and E Tziperman, 1995: A linear thermohaline oscillator driven by stochastic atmospheric forcing. Journal of Climate, 8(10), 2440-2453.
    [ Abstract PDF ]

    The interdecadal variability of a stochastically forced four-box model of the oceanic meridional thermohaline circulation (TMC) is described and compared to the THC variability in the coupled ocean-atmosphere GCM of Delworth, Manabe, and Stouffer. The box model is placed in linearly stable thermally dominant mean state under mixed boundary conditions. A linear stability analysis of this state reveals one damped oscillatory THC mode in additon to purely damped modes. The variability of the model under a moderate amount of stochastic forcing, meant to emulate the random variability of the atmosphere affecting the coupled model's interdecadal THC variability, is studied. A linear interpretation, in which the damped oscillatory mode is of primary importance, is sufficient for understanding the mechanism accounting for the stochastically forced variability. Direct comparison of the variability in the box model and coupled GCM reveals common qualitative aspects. Such a comparison supports, although does not verify, the hypothesis that the coupled model's THC variability can be interpreted as the result of atmospheric weather exciting a linear damped oscillatory THC mode.

35. Griffies, Stephen, and Kirk Bryan, 1994: Predictability of North Atlantic climate variability on multidecadal time scales In The Atlantic Climate Change Program, Proceedings from the principal investigators meeting, NOAA, University Corporation for Atmospheric Research, 77-80.
    [ Abstract ]

    A major goal of the ACCP program is to gain the understanding of North Atlantic climate variability required for making predictions. An essential first step in this direction is to assess the predictability of Atlantic climate variability from models. A methodology for doing this was first proposed by Lorenz (1965) for atmospheric models. Recently, predictability studies have been extended to coupled atmosphere-ocean models in connection with the El Niño/Southern Oscillation phenomenon (e.g., Cane and Zebiak, 1987; Goswami and Shukla, 1991). At present, no operational monitoring system exists to provide proper initial conditions for the ocean on a global basis or even for the North Atlantic. The goal of this study is to use the GFDL climate model to determine the value, in terms of practical prediction of multi-decadal climate variability, of an operational, deep-sea observing system. We present here preliminary results toward this goal.

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