Wang, He, Robert Hallberg, A Wallcraft, Brian K Arbic, and Eric P Chassignet, April 2024: Improving global barotropic tides with sub-grid scale topography. Journal of Advances in Modeling Earth Systems, 16(4), DOI:10.1029/2023MS004056. Abstract
In recent years, efforts have been made to include tides in both operational ocean models as well as climate and earth system models. The accuracy of the barotropic tides is often limited by the model topography, which is in turn limited by model horizontal resolution. In this work, we explore the reduction of barotropic tidal errors in an ocean general circulation model (Modular Ocean Model version 6; MOM6) using sub-grid scale topography representation. We follow the methodology from Adcroft (2013, https://doi.org/10.1016/j.ocemod.2013.03.002), which utilizes statistics from finer resolution topographic data sets to represent sub-grid scale features with a light computational cost in a structured finite volume formulation. The geometric effect from sub-grid scale topography can be introduced to the model with only a few parameters at each grid cell. The porous barriers, which are implemented at the walls of the grid cells, are used to modify transport between grid cells. Our results show that the globally averaged tidal error in lower-resolution simulations is significantly reduced with the use of porous barriers. We argue this method is a potentially useful tool to improve simulations of tides (and other flows) in low-resolution simulations.
Zhang, Wenda, Stephen M Griffies, Robert Hallberg, Yi-Hung Kuo, and Christopher L P Wolfe, June 2024: The role of surface potential vorticity in the vertical structure of mesoscale eddies in wind-driven ocean circulations. Journal of Physical Oceanography, 54(6), DOI:10.1175/JPO-D-23-0203.11243-1266. Abstract
The vertical structure of ocean eddies is generally surface-intensified, commonly attributed to the dominant baroclinic modes arising from the boundary conditions (BCs). Conventional BC considerations mostly focus on either flat- or rough-bottom conditions. The impact of surface buoyancy anomalies—often represented by surface potential vorticity (PV) anomalies—has not been fully explored. Here, we study the role of the surface PV in setting the vertical distribution of eddy kinetic energy (EKE) in an idealized adiabatic ocean model driven by wind stress. The simulated EKE profile in the extratropical ocean tends to peak at the surface and have an e-folding depth typically smaller than half of the ocean depth. This vertical structure can be reasonably represented by a single surface quasigeostrophic (SQG) mode at the energy-containing scale resulting from the large-scale PV structure. Due to isopycnal outcropping and interior PV homogenization, the surface meridional PV gradient is substantially stronger than the interior PV gradient, yielding surface-trapped baroclinically unstable modes with horizontal scales comparable to or smaller than the deformation radius. These surface-trapped eddies then grow in size both horizontally and vertically through an inverse energy cascade up to the energy-containing scale, which dominates the vertical distribution of EKE. As for smaller horizontal scales, the EKE distribution decays faster with depth. Guided by this interpretation, an SQG-based scale-aware parameterization of the EKE profile is proposed. Preliminary offline diagnosis of a high-resolution simulation shows the proposed scheme successfully reproducing the dependence of the vertical structure of EKE on the horizontal grid resolution.
The use of coarse resolution and strong grid-scale dissipation has prevented global ocean models from simulating the correct kinetic energy level. Recently parameterizing energy backscatter has been proposed to energize the model simulations. Parameterizing backscatter reduces long-standing North Atlantic sea surface temperature (SST) and associated surface current biases, but the underlying mechanism remains unclear. Here, we apply backscatter in different geographic regions to distinguish the different physical processes at play. We show that an improved Gulf Stream path is due to backscatter acting north of the Grand Banks to maintain a strong deep western boundary current. An improved North Atlantic Current path is due to backscatter acting around the Flemish Cap, with likely an improved nearby topography-flow interactions. These results suggest that the SST improvement with backscatter is partly due to the resulted strengthening of resolved currents, whereas the role of improved eddy physics requires further research.
Loose, Nora, Gustavo Marques, Alistair Adcroft, Scott D Bachman, Stephen M Griffies, Ian Grooms, Robert Hallberg, and Malte Jansen, December 2023: Comparing two parameterizations for the restratification effect of mesoscale eddies in an isopycnal ocean model. Journal of Advances in Modeling Earth Systems, 15(12), DOI:10.1029/2022MS003518. Abstract
There are two distinct parameterizations for the restratification effect of mesoscale eddies: the Greatbatch and Lamb (1990, GL90, https://journals.ametsoc.org/view/journals/phoc/20/10/1520-0485_1990_020_1634_opvmom_2_0_co_2.xml?tab_body=abstract-display) parameterization, which mixes horizontal momentum in the vertical, and the Gent and McWilliams (1990, GM90, https://journals.ametsoc.org/view/journals/phoc/20/1/1520-0485_1990_020_0150_imiocm_2_0_co_2.xml) parameterization, which flattens isopycnals adiabatically. Even though these two parameterizations are effectively equivalent under the assumption of quasi-geostrophy, GL90 has been used much less than GM90, and exclusively in z-coordinate models. In this paper, we compare the GL90 and GM90 parameterizations in an idealized isopycnal coordinate model, both from a theoretical and practical perspective. From a theoretical perspective, GL90 is more attractive than GM90 for isopycnal coordinate models because GL90 provides an interpretation that is fully consistent with thickness-weighted isopycnal averaging, while GM90 cannot be entirely reconciled with any fully isopycnal averaging framework. From a practical perspective, the GL90 and GM90 parameterizations lead to extremely similar energy levels, flow and vertical structure, even though their energetic pathways are very different. The striking resemblance between the GL90 and GM90 simulations persists from non-eddying through eddy-permitting resolution. We conclude that GL90 is a promising alternative to GM90 for isopycnal coordinate models, where it is more consistent with theory, computationally more efficient, easier to implement, and numerically more stable. Assessing the applicability of GL90 in realistic global ocean simulations with hybrid coordinate schemes should be a priority for future work.
We present the development and evaluation of MOM6-COBALT-NWA12 version 1.0, a 1/12∘ model of ocean dynamics and biogeochemistry in the northwest Atlantic Ocean. This model is built using the new regional capabilities in the MOM6 ocean model and is coupled with the Carbon, Ocean Biogeochemistry and Lower Trophics (COBALT) biogeochemical model and Sea Ice Simulator version-2 (SIS2) sea ice model. Our goal was to develop a model to provide information to support living-marine-resource applications across management time horizons from seasons to decades. To do this, we struck a balance between a broad, coastwide domain to simulate basin-scale variability and capture cross-boundary issues expected under climate change; a high enough spatial resolution to accurately simulate features like the Gulf Stream separation and advection of water masses through finer-scale coastal features; and the computational economy required to run the long simulations of multiple ensemble members that are needed to quantify prediction uncertainties and produce actionable information. We assess whether MOM6-COBALT-NWA12 is capable of supporting the intended applications by evaluating the model with three categories of metrics: basin-wide indicators of the model's performance, indicators of coastal ecosystem variability and the regional ocean features that drive it, and model run times and computational efficiency. Overall, both the basin-wide and the regional ecosystem-relevant indicators are simulated well by the model. Where notable model biases and errors are present in both types of indicator, they are mainly consistent with the challenges of accurately simulating the Gulf Stream separation, path, and variability: for example, the coastal ocean and shelf north of Cape Hatteras are too warm and salty and have minor biogeochemical biases. During model development, we identified a few model parameters that exerted a notable influence on the model solution, including the horizontal viscosity, mixed-layer restratification, and tidal self-attraction and loading, which we discuss briefly. The computational performance of the model is adequate to support running numerous long simulations, even with the inclusion of coupled biogeochemistry with 40 additional tracers. Overall, these results show that this first version of a regional MOM6 model for the northwest Atlantic Ocean is capable of efficiently and accurately simulating historical basin-wide and regional mean conditions and variability, laying the groundwork for future studies to analyze this variability in detail, develop and improve parameterizations and model components to better capture local ocean features, and develop predictions and projections of future conditions to support living-marine-resource applications across timescales.
Forced global ocean/sea-ice hindcast simulations are subject to persistent surface mass flux estimation biases, for example, configurations with an explicit-free surface may not take into account the seasonal storage of water on land when constraining sea level. We present a physically motivated surface mass flux closure, that results in: reduced watermass drift from initialization; improved Atlantic meridional overturning cirulation intensity; and more realistic rates of ocean heat uptake, in simulations using global ocean/sea-ice/land (MOM6/SIS2/LM3) model configurations, forced with atmospheric reanalysis data. In addition to accounting for the land storage, the area-integrated subpolar-to-polar (40°–90°N/S) surface mass fluxes are constrained, using a climatological estimate derived from the the CMIP6 historical ensemble, which helps to further improve hindcast performance. Simulations using MERRA-2 and JRA55-do forcing, subject to identical hydrologic constraints, exhibit similar reductions in drift.
We describe an idealized primitive-equation model for studying mesoscale turbulence and leverage a hierarchy of grid resolutions to make eddy-resolving calculations on the finest grids more affordable. The model has intermediate complexity, incorporating basin-scale geometry with idealized Atlantic and Southern oceans and with non-uniform ocean depth to allow for mesoscale eddy interactions with topography. The model is perfectly adiabatic and spans the Equator and thus fills a gap between quasi-geostrophic models, which cannot span two hemispheres, and idealized general circulation models, which generally include diabatic processes and buoyancy forcing. We show that the model solution is approaching convergence in mean kinetic energy for the ocean mesoscale processes of interest and has a rich range of dynamics with circulation features that emerge only due to resolving mesoscale turbulence.
Turbulent mixing in the ocean surface boundary layer leads to the presence of a surface mixed layer. This mixed layer is important for many phenomena including large-scale ocean dynamics, ocean-atmosphere coupling, and biological and biogeochemical processes. Analysis of the ocean mixed layer requires one to estimate its vertical extent, for which there are various definitions. Correspondingly, there are uncertainties on how to best identify an ocean surface mixed layer for a given application. We propose defining the mixed layer depth (MLD) from energetic principles through the potential energy (PE). The PE based MLD is based on the concept of PE anomaly, which measures the stratification of a layer of seawater by estimating its energetic distance from a well-mixed state. We apply the PE anomaly to diagnose the MLD as the depth to which a given energy could homogenize a layer of seawater. We evaluate the MLD defined by common existing methods and demonstrate that they contain a wide range of PE anomalies for the same MLD, particularly evident for deep winter mixed layers. The MLD defined from the PE anomaly ensures a more consistent MLD identified for a large range of stratifications. Furthermore, the PE method relates to the turbulent kinetic energy budget of the ocean surface boundary layer, which is fundamental to upper ocean mixing processes and parameterizations. The resulting MLD is more representative of active boundary layer turbulence, and is more robust to small anomalies in seawater properties.
Fox-Kemper, Baylor, Helene T Hewitt, Cunde Xiao, Guðfinna Aðalgeirsdóttir, Sybren Drijfhout, Tamsin L Edwards, Nicholas R Golledge, Mark A Hemer, Robert E Kopp, Gerhard Krinner, Alan C Mix, Dirk Notz, Sophie Nowicki, Intan Suci Nurhati, Lucas Ruiz, Jean-Baptiste Sallée, Aimee B A Slangen, Yongqiang Yu, and Robert Hallberg, et al., in press: Ocean, Cryosphere and Sea Level Change. In Climate Change 2021: The Physical Science Basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, , Cambridge University Press. August 2021.
Melet, Angelique, Robert Hallberg, and David Marshall, September 2021: Role of ocean mixing in climate change In Ocean Mixing: Drivers, Mechanisms and Impacts [Meredith, M. P. and A. Naraveira Garabato (eds.)], Elsevier, . Abstract
Many different physical processes contribute to mixing in the ocean, and this mixing plays a significant role in shaping the mean state of the ocean and its response to changing climate, as well as in shaping other features of the climate system. This chapter provides a review of some recent work to understand the role of ocean mixing in the climate system and techniques for parameterizing the various mixing processes in climate models. Improving our collective understanding of the dynamics of these mixing processes will lead to greater confidence in our projections of how the climate system will evolve and the feedbacks that will act to regulate this evolution.
We develop a parameterization for representing the effects of submesoscale symmetric instability (SI) in the ocean interior. SI may contribute to water mass modification and mesoscale energy dissipation in flow systems throughout the World Ocean. Dense gravity currents forced by surface buoyancy loss over shallow shelves are a particularly compelling test case, as they are characterized by density fronts and shears susceptible to a wide range of submesoscale instabilities. We present idealized experiments of Arctic shelf overflows employing the GFDL-MOM6 in z* and isopycnal coordinates. At the highest resolutions, the dense flow undergoes geostrophic adjustment and forms bottom- and surface-intensified jets. The density front along the topography combined with geostrophic shear initiates SI, leading to onset of secondary shear instability, dissipation of geostrophic energy, and turbulent mixing. We explore the impact of vertical coordinate, resolution, and parameterization of shear-driven mixing on the representation of water mass transformation. We find that in isopycnal and low-resolution z* simulations, limited vertical resolution leads to inadequate representation of diapycnal mixing. This motivates our development of a parameterization for SI-driven turbulence. The parameterization is based on identifying unstable regions through a balanced Richardson number criterion and slumping isopycnals toward a balanced state. The potential energy extracted from the large-scale flow is assumed to correspond to the kinetic energy of SI which is dissipated through shear mixing. Parameterizing submesoscale instabilities by combining isopycnal slumping with diapycnal mixing becomes crucial as ocean models move toward resolving mesoscale eddies and fronts but not the submesoscale phenomena they host.
We document the development and simulation characteristics of the next generation modeling system for seasonal to decadal prediction and projection at the Geophysical Fluid Dynamics Laboratory (GFDL). SPEAR (Seamless System for Prediction and EArth System Research) is built from component models recently developed at GFDL ‐ the AM4 atmosphere model, MOM6 ocean code, LM4 land model and SIS2 sea ice model. The SPEAR models are specifically designed with attributes needed for a prediction model for seasonal to decadal time scales, including the ability to run large ensembles of simulations with available computational resources. For computational speed SPEAR uses a coarse ocean resolution of approximately 1.0o (with tropical refinement). SPEAR can use differing atmospheric horizontal resolutions ranging from 1o to 0.25o. The higher atmospheric resolution facilitates improved simulation of regional climate and extremes. SPEAR is built from the same components as the GFDL CM4 and ESM 4 models, but with design choices geared toward seasonal to multidecadal physical climate prediction and projection. We document simulation characteristics for the time‐mean climate, aspects of internal variability, and the response to both idealized and realistic radiative forcing change. We describe in greater detail one focus of the model development process that was motivated by the importance of the Southern Ocean to the global climate system. We present sensitivity tests that document the influence of the Antarctic surface heat budget on Southern Ocean ventilation and deep global ocean circulation. These findings were also useful in the development processes for the GFDL CM4 and ESM 4 models.
We describe the baseline coupled model configuration and simulation characteristics of GFDL's Earth System Model Version 4.1 (ESM4.1), which builds on component and coupled model developments at GFDL over 2013–2018 for coupled carbon‐chemistry‐climate simulation contributing to the sixth phase of the Coupled Model Intercomparison Project. In contrast with GFDL's CM4.0 development effort that focuses on ocean resolution for physical climate, ESM4.1 focuses on comprehensiveness of Earth system interactions. ESM4.1 features doubled horizontal resolution of both atmosphere (2° to 1°) and ocean (1° to 0.5°) relative to GFDL's previous‐generation coupled ESM2‐carbon and CM3‐chemistry models. ESM4.1 brings together key representational advances in CM4.0 dynamics and physics along with those in aerosols and their precursor emissions, land ecosystem vegetation and canopy competition, and multiday fire; ocean ecological and biogeochemical interactions, comprehensive land‐atmosphere‐ocean cycling of CO2, dust and iron, and interactive ocean‐atmosphere nitrogen cycling are described in detail across this volume of JAMES and presented here in terms of the overall coupling and resulting fidelity. ESM4.1 provides much improved fidelity in CO2 and chemistry over ESM2 and CM3, captures most of CM4.0's baseline simulations characteristics, and notably improves on CM4.0 in (1) Southern Ocean mode and intermediate water ventilation, (2) Southern Ocean aerosols, and (3) reduced spurious ocean heat uptake. ESM4.1 has reduced transient and equilibrium climate sensitivity compared to CM4.0. Fidelity concerns include (1) moderate degradation in sea surface temperature biases, (2) degradation in aerosols in some regions, and (3) strong centennial scale climate modulation by Southern Ocean convection.
This paper provides a primer on the mathematical, physical, and numerical foundations of ocean models that are formulated using finite volume generalized vertical coordinate equations and that use the vertical Lagrangian‐remap method to evolve the ocean state. We consider the mathematical structure of the governing ocean equations in both their strong formulation (partial differential equations) and weak formulation (finite volume integral equations), thus enabling an understanding of their physical content and providing a physical‐mathematical framework to develop numerical algorithms. A connection is made between the Lagrangian‐remap method and the ocean equations as written using finite volume generalized vertical budgets. Thought experiments are offered to exemplify the mechanics of the vertical Lagrangian‐remap method and to compare with other methods used for ocean model algorithms.
We present a neutral diffusion operator appropriate for an ocean model making use of general vertical coordinates. The diffusion scheme uses polynomial reconstructions in the vertical, along with a horizontally local but vertically nonlocal stencil for estimates of tracer fluxes. These fluxes are calculated on a vertical grid that is the superset of model columns in a neutral density space. Using flux-limiters, the algorithm dissipates tracer extrema locally, and no new extrema are created. A demonstration using a linear equation of state in an idealized configuration shows that the algorithm is perfectly neutral. When using the nonlinear TEOS-10 equation of state with a constant reference pressure, the algorithm compares nearly exactly to a case discretized onto isopycnal surfaces and using along-layer diffusion. The algorithm's cost is comparable to that of tracer advection and can be readily implemented into ocean general circulation models.
Abram, Nerilie J., Carolina Adler, Nathaniel L Bindoff, Lijing Cheng, So-Min Cheong, William W L Cheung, Matthew Collins, Chris Derksen, Alexey Ekaykin, Thomas L Frölicher, Matthias Garschagen, Jean-Pierre Gattuso, Bruce Glavovic, Stephan Gruber, Valeria Guinder, and Robert Hallberg, et al., in press: Summary for Policymakers. In IPCC Special Report on the Ocean and Cryosphere in a Changing Climate [H.-O. Pörtner, D.C. Roberts, V. Masson-Delmotte, P. Zhai, M. Tignor, E. Poloczanska, K. Mintenbeck, A. Alegría, M. Nicolai, A. Okem, J. Petzold, B. Rama, N.M. Weyer (eds.)], , . December 2019.
We document the configuration and emergent simulation features from the Geophysical Fluid Dynamics Laboratory (GFDL) OM4.0 ocean/sea‐ice model. OM4 serves as the ocean/sea‐ice component for the GFDL climate and Earth system models. It is also used for climate science research and is contributing to the Coupled Model Intercomparison Project version 6 Ocean Model Intercomparison Project (CMIP6/OMIP). The ocean component of OM4 uses version 6 of the Modular Ocean Model (MOM6) and the sea‐ice component uses version 2 of the Sea Ice Simulator (SIS2), which have identical horizontal grid layouts (Arakawa C‐grid). We follow the Coordinated Ocean‐sea ice Reference Experiments (CORE) protocol to assess simulation quality across a broad suite of climate relevant features. We present results from two versions differing by horizontal grid spacing and physical parameterizations: OM4p5 has nominal 0.5° spacing and includes mesoscale eddy parameterizations and OM4p25 has nominal 0.25° spacing with no mesoscale eddy parameterization.
MOM6 makes use of a vertical Lagrangian‐remap algorithm that enables general vertical coordinates. We show that use of a hybrid depth‐isopycnal coordinate reduces the mid‐depth ocean warming drift commonly found in pure z* vertical coordinate ocean models. To test the need for the mesoscale eddy parameterization used in OM4p5, we examine the results from a simulation that removes the eddy parameterization. The water mass structure and model drift are physically degraded relative to OM4p5, thus supporting the key role for a mesoscale closure at this resolution.
Bindoff, Nathaniel L., William W L Cheung, James G Kairo, Javier Aristegui, Valeria Guinder, and Robert Hallberg, et al., in press: Changing Ocean, Marine Ecosystems, and Dependent Communities. In IPCC Special Report on the Ocean and Cryosphere in a Changing Climate [H.-O. Pörtner, D.C. Roberts, V. Masson-Delmotte, P. Zhai, M. Tignor, E. Poloczanska, K. Mintenbeck, A. Alegría, M. Nicolai, A. Okem, J. Petzold, B. Rama, N.M. Weyer (eds.)], , . December 2019.
We revisit the challenges and prospects for ocean circulation models following Griffies et al. (2010). Over the past decade, ocean circulation models evolved through improved understanding, numerics, spatial discretization, grid configurations, parameterizations, data assimilation, environmental monitoring, and process-level observations and modeling. Important large scale applications over the last decade are simulations of the Southern Ocean, the Meridional Overturning Circulation and its variability, and regional sea level change. Submesoscale variability is now routinely resolved in process models and permitted in a few global models, and submesoscale effects are parameterized in most global models. The scales where nonhydrostatic effects become important are beginning to be resolved in regional and process models. Coupling to sea ice, ice shelves, and high-resolution atmospheric models has stimulated new ideas and driven improvements in numerics. Observations have provided insight into turbulence and mixing around the globe and its consequences are assessed through perturbed physics models. Relatedly, parameterizations of the mixing and overturning processes in boundary layers and the ocean interior have improved. New diagnostics being used for evaluating models alongside present and novel observations are briefly referenced. The overall goal is summarizing new developments in ocean modeling, including: how new and existing observations can be used, what modeling challenges remain, and how simulations can be used to support observations.
We describe GFDL's CM4.0 physical climate model, with emphasis on those aspects that may be of particular importance to users of this model and its simulations. The model is built with the AM4.0/LM4.0 atmosphere/land model and OM4.0 ocean model. Topics include the rationale for key choices made in the model formulation, the stability as well as drift of the pre‐industrial control simulation, and comparison of key aspects of the historical simulations with observations from recent decades. Notable achievements include the relatively small biases in seasonal spatial patterns of top‐of‐atmosphere fluxes, surface temperature, and precipitation; reduced double Intertropical Convergence Zone bias; dramatically improved representation of ocean boundary currents; a high quality simulation of climatological Arctic sea ice extent and its recent decline; and excellent simulation of the El Niño‐Southern Oscillation spectrum and structure. Areas of concern include inadequate deep convection in the Nordic Seas; an inaccurate Antarctic sea ice simulation; precipitation and wind composites still affected by the equatorial cold tongue bias; muted variability in the Atlantic Meridional Overturning Circulation; strong 100 year quasi‐periodicity in Southern Ocean ventilation; and a lack of historical warming before 1990 and too rapid warming thereafter due to high climate sensitivity and strong aerosol forcing, in contrast to the observational record. Overall, CM4.0 scores very well in its fidelity against observations compared to the Coupled Model Intercomparison Project Phase 5 generation in terms of both mean state and modes of variability and should prove a valuable new addition for analysis across a broad array of applications.
Hieronymus, M, Jonas Nycander, J Nilsson, K Döös, and Robert Hallberg, February 2019: Oceanic overturning and heat transport: The role of background diffusivity. Journal of Climate, 32(3), DOI:10.1175/JCLI-D-18-0438.1. Abstract
The role of oceanic background diapycnal diffusion for the equilibrium climate state is investigated in the coupled climate model CM2G. Special emphasis is put on the oceanic meridional overturning and heat transport. Six runs with the model, differing only by their value of the background diffusivity, are run to steady state and the statistically steady integrations are compared. The diffusivity changes have large scale impacts on many aspects on the climate system. Two examples are the volume mean potential temperature that increases by 3.6 °C between the least and most diffusive run and the Antarctic sea ice extent, which reduces rapidly as the diffusivity increases. The overturning scaling with diffusivity is found to agree rather well with classical theoretical results for the upper but not for the lower cell. An alternative empirical scaling with the mixing energy is found to give good results for both cells. The oceanic meridional heat transport increases strongly with the diffusivity, an increase that can only partly be explained by increases in the meridional overturning. The increasing poleward oceanic heat transport is accompanied by a decrease in its atmospheric counterpart, which keeps the increase in the planetary energy transport small compared to that in the ocean.
Six recent Langmuir turbulence parameterization schemes and five traditional schemes are implemented in a common single column modeling framework and consistently compared. These schemes are tested in scenarios versus matched large eddy simulations (LES), across the globe with realistic forcing (JRA55‐do, WAVEWATCH‐III simulated waves) and initial conditions (Argo), and under realistic conditions as observed at ocean moorings. Traditional non‐Langmuir schemes systematically under‐predict LES vertical mixing under weak convective forcing, while Langmuir schemes vary in accuracy. Under global, realistic forcing Langmuir schemes produce 6% (‐1% to 14% for 90% confidence) or 5.2 m (‐0.2 m to 17.4 m for 90% confidence) deeper monthly mean mixed layer depths (MLD) than their non‐Langmuir counterparts, with the greatest differences in extratropical regions, especially the Southern Ocean in austral summer. Discrepancies among Langmuir schemes are large (15% in MLD standard deviation over the mean): largest under wave‐driven turbulence with stabilizing buoyancy forcing, next largest under strongly wave‐driven conditions with weak buoyancy forcing, and agreeing during strong convective forcing. Non‐Langmuir schemes disagree with each other to a lesser extent, with a similar ordering. Langmuir discrepancies obscure a cross‐scheme estimate of the Langmuir effect magnitude under realistic forcing, highlighting limited understanding and numerical deficiencies. Maps of the regions and seasons where the greatest discrepancies occur are provided to guide further studies and observations.
Roemmich, Dean, M H Alford, H Claustre, K S Johnson, Brian King, J Moum, P Oke, W B Owens, S Pouliquen, S Purkey, M Scanderbeg, T Suga, Susan E Wijffels, N Zilberman, D Bakker, M O Baringer, M Belbeoch, H C Bittig, E S Boss, P Calil, F Carse, T Carval, Fei Chai, D Conchubhair, O Diarmuid, F d'Ortenzio, G Dall'Olmo, D Desbruyeres, K Fennel, I Fer, R Ferrari, G Forget, H J Freeland, T Fujiki, Marion Gehlen, B Greenan, and Robert Hallberg, et al., August 2019: On the Future of Argo: A Global, Full-Depth, Multi-Disciplinary Array. Frontiers in Marine Science, 6, DOI:10.3389/fmars.2019.00439. Abstract
The Argo Program has been implemented and sustained for almost two decades, as a global array of about 4000 profiling floats. Argo provides continuous observations of ocean temperature and salinity versus pressure, from the sea surface to 2000 dbar. The successful installation of the Argo array and its innovative data management system arose opportunistically from the combination of great scientific need and technological innovation. Through the data system, Argo provides fundamental physical observations with broad societally-valuable applications, built on the cost-efficient and robust technologies of autonomous profiling floats. Following recent advances in platform and sensor technologies, even greater opportunity exists now than 20 years ago to (i) improve Argo’s global coverage and value beyond the original design, (ii) extend Argo to span the full ocean depth, (iii) add biogeochemical sensors for improved understanding of oceanic cycles of carbon, nutrients, and ecosystems, and (iv) consider experimental sensors that might be included in the future, for example to document the spatial and temporal patterns of ocean mixing. For Core Argo and each of these enhancements, the past, present, and future progression along a path from experimental deployments to regional pilot arrays to global implementation is described. The objective is to create a fully global, top-to-bottom, dynamically complete, and multidisciplinary Argo Program that will integrate seamlessly with satellite and with other in situ elements of the Global Ocean Observing System (Legler et al., 2015). The integrated system will deliver operational reanalysis and forecasting capability, and assessment of the state and variability of the climate system with respect to physical, biogeochemical, and ecosystems parameters. It will enable basic research of unprecedented breadth and magnitude, and a wealth of ocean-education and outreach opportunities.
Arbic, Brian K., M H Alford, Joseph K Ansong, Maarten C Buijsman, R B Ciotti, J Thomas Farrar, and Robert Hallberg, et al., September 2018: A Primer on Global Internal Tide and Internal Gravity Wave Continuum Modeling in HYCOM and MITgcm In New Frontiers in Operational Oceanography, Tallahassee, Florida, GODAE OceanView, 307-392. Abstract
Oceanic heat uptake (OHU) is a significant source of uncertainty in both the transient and equilibrium responses to increasing the planetary radiative forcing. OHU differs among climate models and is related in part to their representation of vertical and lateral mixing. This study examines the role of ocean model formulation – specifically the choice of vertical coordinate and strength of background diapycnal diffusivity (Kd) – in the millennial-scale near-equilibrium climate response to a quadrupling of atmospheric CO2. Using two fully-coupled Earth System Models (ESMs) with nearly identical atmosphere, land, sea ice, and biogeochemical components, it is possible to independently configure their ocean model components with different formulations and produce similar near-equilibrium climate responses. The SST responses are similar between the two models (r2 = 0.75, global average ∼ 4.3 °C) despite their initial pre-industrial climate mean states differing by 0.4 °C globally. The surface and interior responses of temperature and salinity are also similar between the two models. However, the Atlantic Meridional Overturning Circulation (AMOC) responses are different between the two models, and the associated differences in ventilation and deep water formation have an impact on the accumulation of dissolved inorganic carbon in the ocean interior. A parameter sensitivity analysis demonstrates that increasing the amount of Kd produces very different near-equilibrium climate responses within a given model. These results suggest that the impact of the ocean vertical coordinate on the climate response is small relative to the representation of sub-gridscale mixing.
Greenland Ice Sheet (GIS) might have lost a large amount of its volume during the last interglacial and may do so again in the future due to climate warming. In this study, we test whether the climate response to the glacial meltwater is sensitive to its discharging location. Two fully coupled atmosphere–ocean general circulation models, CM2G and CM2M, which have completely different ocean components are employed to do the test. In each experiment, a prescribed freshwater flux of 0.1 Sv is discharged from one of the four locations around Greenland—Petermann, 79 North, Jacobshavn and Helheim glaciers. The results from both models show that the AMOC weakens more when the freshwater is discharged from the northern GIS (Petermann and 79 North) than when it is discharged from the southern GIS (Jacobshavn and Helheim), by 15% (CM2G) and 31% (CM2M) averaged over model year 50–300 (CM2G) and 70–300 (CM2M), respectively. This is due to easier access of the freshwater from northern GIS to the deepwater formation site in the Nordic Seas. In the long term (> 300 year), however, the AMOC change is nearly the same for freshwater discharged from any location of the GIS. The East Greenland current accelerates with time and eventually becomes significantly faster when the freshwater is discharged from the north than from the south. Therefore, freshwater from the north is transported efficiently towards the south first and then circulates back to the Nordic Seas, making its impact to the deepwater formation there similar to the freshwater discharged from the south. The results indicate that the details of the location of meltwater discharge matter if the short-term (< 300 years) climate response is concerned, but may not be critical if the long-term (> 300 years) climate response is focused upon.
This paper presents a method to parameterize vertical turbulent mixing coefficients within the ocean surface boundary layer (OSBL) for climate applications. The new method is specifically constructed to satisfy two requirements. The first aspect is to explicitly consider the mechanical energy budget of the turbulence that drives mixing. This constraint ensures a realistic and robust simulation of the OSBL, which is critical for coupled climate simulations. The second aspect is that the model should be formulated so that it is not sensitive to the numerical limitations common to climate simulations, such as long time-steps and coarse vertical grids. This goal is achieved by combining an existing resolved shear-driven mixing parameterization (here Jackson et al., 2008) with a new method to avoid time step sensitivity. The new method is motivated by the Kraus-Turner-Niiler type bulk boundary layer parameterization, but relaxes the requirement for vertical homogeneity. The non-dimensional coefficients m* and n* from the Kraus-Turner-Niiler approach are parameterized for the new method based on results of simulations using a previously tested parameterization at high resolution. The resulting parameterization is evaluated by comparing simulations with the new parameterization to simulations with the parameterization over a wide range of combinations of surface wind stress, surface buoyancy flux, and latitudes. The new method for vertical turbulent OSBL mixing is therefore proposed as a computationally efficient, implicitly energetically constrained option appropriate for ocean climate modeling applications.
Russell, Joellen L., I V Kamenkovich, C M Bitz, R Ferrari, Sarah T Gille, P J Goodman, Robert Hallberg, K S Johnson, K Khazmutdinova, I Marinov, Matthew R Mazloff, S C Riser, and Jorge L Sarmiento, et al., May 2018: Metrics for the Evaluation of the Southern Ocean in Coupled Climate Models and Earth System Models. Journal of Geophysical Research: Oceans, 123(5), DOI:10.1002/2017JC013461. Abstract
The Southern Ocean is central to the global climate and the global carbon cycle, and to the climate's response to increasing levels of atmospheric greenhouse gases, as it ventilates a large fraction of the global ocean volume. Global coupled climate models and earth system models, however, vary widely in their simulations of the Southern Ocean and its role in, and response to, the ongoing anthropogenic trend. Due to the region's complex water-mass structure and dynamics, Southern Ocean carbon and heat uptake depend on a combination of winds, eddies, mixing, buoyancy fluxes, and topography. Observationally-based metrics are critical for discerning processes and mechanisms, and for validating and comparing climate and earth system models. New observations and understanding have allowed for progress in the creation of observationally-based data/model metrics for the Southern Ocean. Metrics presented here provide a means to assess multiple simulations relative to the best available observations and observational products. Climate models that perform better according to these metrics also better simulate the uptake of heat and carbon by the Southern Ocean. This report is not strictly an intercomparison, but rather a distillation of key metrics that can reliably quantify the “accuracy” of a simulation against observed, or at least observable, quantities. One overall goal is to recommend standardization of observationally-based benchmarks that the modeling community should aspire to meet in order to reduce uncertainties in climate projections, and especially uncertainties related to oceanic heat and carbon uptake.
This study examines the relative roles of the Arctic freshwater exported via different pathways on deep convection in the North Atlantic and the Atlantic Meridional Overturning Circulation (AMOC). Deep water feeding the lower branch of the AMOC is formed in several North Atlantic marginal seas, including the Labrador Sea, Irminger Sea and the Nordic Seas, where deep convection can potentially be inhibited by surface freshwater exported from the Arctic. The sensitivity of the AMOC and North Atlantic to two major freshwater pathways on either side of Greenland is studied using numerical experiments. Freshwater export is rerouted in global coupled climate models by blocking and expanding the channels along the two routes. The sensitivity experiments are performed in two sets of models (CM2G and CM2M) with different control simulation climatology for comparison. Freshwater via the route east of Greenland is found to have a larger direct impact on Labrador Sea convection. In response to the changes of freshwater route, North Atlantic convection outside of the Labrador Sea changes in the opposite sense to the Labrador Sea. The response of the AMOC is found to be sensitive to both the model formulation and mean state climate.
MacKinnon, J A., M H Alford, Joseph K Ansong, Brian K Arbic, A Barna, B P Briegleb, F O Bryan, Maarten C Buijsman, Eric P Chassignet, Gokhan Danabasoglu, S Diggs, Stephen M Griffies, Robert Hallberg, S R Jayne, M Jochum, J Klymak, E Kunze, William G Large, Sonya Legg, B Mater, and Angelique Melet, et al., November 2017: Climate Process Team on Internal-Wave Driven Ocean Mixing. Bulletin of the American Meteorological Society, 98(11), DOI:10.1175/BAMS-D-16-0030.1. Abstract
Recent advances in our understanding of internal-wave driven turbulent mixing in the ocean interior are summarized. New parameterizations for global climate ocean models, and their climate impacts, are introduced.
Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatio-temporal patterns of mixing are largely driven by the geography of generation, propagation and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last five years and under the auspices of US CLIVAR, a NSF- and NOAA-supported Climate Process Team has been engaged in developing, implementing and testing dynamics-based parameterizations for internal-wave driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here we review recent progress, describe the tools developed, and discuss future directions.
Zanowski, Hannah, and Robert Hallberg, December 2017: Weddell Polynya Transport Mechanisms in the Abyssal Ocean. Journal of Physical Oceanography, 47(12), DOI:10.1175/JPO-D-17-0091.1. Abstract
Weddell Polynya transport mechanisms in the deep and abyssal oceans are examined in the NOAA Geophysical Fluid Dynamics Laboratory’s (NOAA/GFDL) coupled climate model, CM2G. During an 1820-year-long integration of the model, polynyas are forced every 29 years in the Weddell Sea via an increase in the diapycnal diffusivity. Composites of the events are used to examine the mechanisms responsible for transporting polynya signals away from the Weddell Sea. Polynya signal transport is governed by two dynamical mechanisms that act on different timescales and spread at different rates. Large-scale waves, such as Kelvin and planetary and topographic Rossby waves, propagate the polynya signal rapidly, on interannual-to-decadal timescales, while advection transports the signal more slowly, on decadal-to-centennial timescales. Despite their different spreading rates, these mechanisms can act contemporaneously, and it is often their combined effect that governs the property changes in the global deep and abyssal oceans. Both waves and advection cause temperature changes on isobaths. In the deep Atlantic, advection accounts for <15% of the total temperature change in the model, indicating that waves are strongly dominant there. Elsewhere, waves are still the stronger contributor, but advection accounts for 20%-40% of the total temperature change.
Ban, Raymond J., Cecilia M Bitz, Andy R Brown, John A Dutton, and Robert Hallberg, et al., 2016: In Next Generation Earth System Prediction: Strategies for Subseasonal to Seasonal Forecasts, Washington, DC, The National Academies Press, DOI:10.17226/21873.
Griffies, Stephen M., Gokhan Danabasoglu, Paul J Durack, Alistair Adcroft, V Balaji, C Böning, Eric P Chassignet, Enrique N Curchitser, Julie Deshayes, H Drange, Baylor Fox-Kemper, Peter J Gleckler, Jonathan M Gregory, Helmuth Haak, Robert Hallberg, Helene T Hewitt, David M Holland, Tatiana Ilyina, J H Jungclaus, Y Komuro, John P Krasting, William G Large, S J Marsland, S Masina, Trevor J McDougall, A J George Nurser, James C Orr, Anna Pirani, Fangli Qiao, Ronald J Stouffer, Karl E Taylor, A M Treguier, Hiroyuki Tsujino, P Uotila, M Valdivieso, Michael Winton, and Stephen G Yeager, September 2016: OMIP contribution to CMIP6: experimental and diagnostic protocol for the physical component of the Ocean Model Intercomparison Project. Geoscientific Model Development, 9(9), DOI:10.5194/gmd-9-3231-2016. Abstract
The Ocean Model Intercomparison Project (OMIP) aims to provide a framework for evaluating, understanding, and improving the ocean and sea-ice components of global climate and earth system models contributing to the Coupled Model Intercomparison Project Phase 6 (CMIP6). OMIP addresses these aims in two complementary manners: (A) by providing an experimental protocol for global ocean/sea-ice models run with a prescribed atmospheric forcing, (B) by providing a protocol for ocean diagnostics to be saved as part of CMIP6. We focus here on the physical component of OMIP, with a companion paper (Orr et al., 2016) offering details for the inert chemistry and interactive biogeochemistry. The physical portion of the OMIP experimental protocol follows that of the interannual Coordinated Ocean-ice Reference Experiments (CORE-II). Since 2009, CORE-I (Normal Year Forcing) and CORE-II have become the standard method to evaluate global ocean/sea-ice simulations and to examine mechanisms for forced ocean climate variability. The OMIP diagnostic protocol is relevant for any ocean model component of CMIP6, including the DECK (Diagnostic, Evaluation and Characterization of Klima experiments), historical simulations, FAFMIP (Flux Anomaly Forced MIP), C4MIP (Coupled Carbon Cycle Climate MIP), DAMIP (Detection and Attribution MIP), DCPP (Decadal Climate Prediction Project), ScenarioMIP (Scenario MIP), as well as the ocean-sea ice OMIP simulations. The bulk of this paper offers scientific rationale for saving these diagnostics.
Thermal expansion of the ocean in response to warming is an important component of historical sea-level rise1. Observational studies show that the Atlantic and Southern oceans are warming faster than the Pacific Ocean2, 3, 4, 5. Here we present simulations using a numerical atmospheric-ocean general circulation model with an interactive carbon cycle to evaluate the impact of carbon emission rates, ranging from 2 to 25 GtC yr−1, on basin-scale ocean heat uptake and sea level. For simulations with emission rates greater than 5 GtC yr−1, sea-level rise is larger in the Atlantic than Pacific Ocean on centennial timescales. This basin-scale asymmetry is related to the shorter flushing timescales and weakening of the overturning circulation in the Atlantic. These factors lead to warmer Atlantic interior waters and greater thermal expansion. In contrast, low emission rates of 2 and 3 GtC yr−1 will cause relatively larger sea-level rise in the Pacific on millennial timescales. For a given level of cumulative emissions, sea-level rise is largest at low emission rates. We conclude that Atlantic coastal areas may be particularly vulnerable to near-future sea-level rise from present-day high greenhouse gas emission rates.
Turbulent mixing driven by breaking internal tides plays a primary role in the meridional overturning and oceanic heat budget. Most current climate models explicitly parameterize only the local dissipation of internal tides at the generation sites, representing the remote dissipation of low-mode internal tides which propagate away through a uniform background diffusivity. In this study, a simple energetically-consistent parameterization of the low-mode internal tide dissipation is derived and implemented in Geophysical Fluid Dynamics Laboratory’s ESM2G Earth System Model. The impact of remote and local internal tide dissipation on the ocean state is examined using a series of simulations with the same total amount of energy input for mixing, but with different scalings of the vertical profile of dissipation with the stratification and with different idealized scenarios for the distribution of the low-mode internal tide energy dissipation: uniformly over ocean basins, continental slopes, or continental shelves. In these idealized scenarios, the ocean state, including the meridional overturning circulation, ocean ventilation, main thermocline thickness and ocean heat uptake, is particularly sensitive to the vertical distribution of mixing by breaking low-mode internal tides. Less sensitivity is found to the horizontal distribution of mixing, provided that distribution is in the open ocean. Mixing on coastal shelves only impacts the large-scale circulation and water mass properties where it modifies water masses originating on shelves. More complete descriptions of the distribution of the remote part of internal-tide driven mixing, particularly in the vertical and relative to water mass formation regions, are therefore required to fully parameterize ocean turbulent mixing.
Farneti, Riccardo, S M Downes, Stephen M Griffies, S J Marsland, E Behrens, M Bentsen, D Bi, A Biastoch, C Böning, A Bozec, V M Canuto, Eric P Chassignet, Gokhan Danabasoglu, S Danilov, N Diansky, H Drange, P G Fogli, A Gusev, Robert Hallberg, A Howard, M Ilicak, T Jung, M Kelley, William G Large, A Leboissetier, Matthew C Long, J Lu, S Masina, A Mishra, A Navarra, A J George Nurser, L Patara, and Bonita L Samuels, et al., September 2015: An assessment of Antarctic Circumpolar Current and Southern Ocean Meridional Overturning Circulation during 1958–2007 in a suite of interannual CORE-II simulations. Ocean Modelling, 93, DOI:10.1016/j.ocemod.2015.07.009. Abstract
In the framework of the second phase of the Coordinated Ocean-ice Reference Experiments (CORE-II), we present an analysis of the representation of the Antarctic Circumpolar Current (ACC) and Southern Ocean Meridional Overturning Circulation (MOC) in a suite of seventeen global ocean-sea ice models. We focus on the mean, variability and trends of both the ACC and MOC over the 1958–2007 period, and discuss their relationship with the surface forcing. We aim to quantify the degree of eddy saturation and eddy compensation in the models participating in CORE-II, and compare our results with available observations, previous fine-resolution numerical studies and theoretical constraints. Most models show weak ACC transport sensitivity to changes in forcing during the past five decades, and they can be considered to be in an eddy saturated regime. Larger contrasts arise when considering MOC trends, with a majority of models exhibiting significant strengthening of the MOC during the late 20th and early 21st century. Only a few models show a relatively small sensitivity to forcing changes, responding with an intensified eddy-induced circulation that provides some degree of eddy compensation, while still showing considerable decadal trends. Both ACC and MOC interannual variability are largely controlled by the Southern Annular Mode (SAM). Based on these results, models are clustered into two groups. Models with constant or two-dimensional (horizontal) specification of the eddy-induced advection coefficient κ show larger ocean interior decadal trends, larger ACC transport decadal trends and no eddy compensation in the MOC. Eddy-permitting models or models with a three-dimensional time varying κ show smaller changes in isopycnal slopes and associated ACC trends, and partial eddy compensation. As previously argued, a constant in time or space κ is responsible for a poor representation of mesoscale eddy effects and cannot properly simulate the sensitivity of the ACC and MOC to changing surface forcing. Evidence is given for a larger sensitivity of the MOC as compared to the ACC transport, even when approaching eddy saturation. Future process studies designed for disentangling the role of momentum and buoyancy forcing in driving the ACC and MOC are proposed.
It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held, I.M., Larichev, V.D., 1996. A scaling theory for horizontally homogeneous baroclinically unstable ow on a beta plane. J. Atmos. Sci. 53, 946–952., which ignores the effect of bottom friction.
It has recently been proposed to formulate eddy diffusivities in ocean models based on a mesoscale eddy kinetic energy (EKE) budget. Given an appropriate length scale, the mesoscale EKE can be used to estimate an eddy diffusivity based on mixing length theory. This paper discusses some of the open questions associated with the formulation of an EKE budget and mixing length, and proposes an improved energy budget-based parameterization for the mesoscale eddy diffusivity. A series of numerical simulations is performed, using an idealized flat-bottomed β-plane channel configuration with quadratic bottom drag. The results stress the importance of the mixing length formulation, as well as the formulation for the bottom signature of the mesoscale EKE, which is important in determining the rate of EKE dissipation. In the limit of vanishing planetary vorticity gradient, the mixing length is ultimately controlled by bottom drag, though the frictional arrest scale predicted by barotropic turbulence theory needs to be modified to account for the effects of baroclinicity. Any significant planetary vorticity gradient, β, is shown to suppress mixing, and limit the effective mixing length to the Rhines scale. While the EKE remains moderated by bottom friction, the bottom signature of EKE is shown to decrease as the appropriately non-dimensionalized friction increases, which considerably weakens the impact of changes in the bottom friction compared to barotropic turbulence. For moderate changes in the bottom-friction, eddy fluxes are thus reasonably well approximated by the scaling relation proposed by Held and Larichev (1996), which ignores the effect of bottom friction.
Internal lee waves generated by geostrophic flows over rough topography are thought to be a significant energy sink for eddies and energy source for deep ocean mixing. The sensitivity of the energy flux into lee waves from pre-industrial, present and possible future climate conditions is explored in this study using linear theory. The bottom stratification and geostrophic velocity fields needed for the calculation of the energy flux into lee waves are provided by Geophysical Fluid Dynamics Laboratory’s global coupled carbon-climate Earth System Model, ESM2G. The unresolved mesoscale eddy energy is parameterized as a function of the large-scale available potential energy. Simulations using historical and Representative Concentration Pathway (RCP) scenarios were performed over the 1861-2200 period. Our diagnostics suggest a decrease of the global energy flux into lee waves of order 20% from pre-industrial to future climate conditions under the RCP8.5 scenario. In the Southern Ocean, the energy flux into lee waves exhibits a clear annual cycle with maximum values in austral winter. The long-term decrease of the global energy flux into lee waves and the annual cycle of the energy flux in the Southern Ocean are mostly due to changes in bottom velocity.
The sensitivity of large scale ocean circulation and climate to overflow representation is studied using coupled climate models, motivated by the differences between two models differing only in their ocean components: CM2G (which uses an isopycnal–coordinate ocean model) and CM2M (which uses a z-coordinate ocean model). Analysis of the control simulations of the two models shows that the Atlantic Meridional Overturning Circulation (AMOC) and the North Atlantic climate have some differences, which may be related to the representation of overflow processes. Firstly, in CM2G, as in the real world, overflows have two branches flowing out of the Nordic Seas, to the east and west of Iceland, respectively, while only the western branch is present in CM2M. This difference in overflow location results in different horizontal circulation in the North Atlantic. Secondly, the diapycnal mixing in the overflow downstream region is much larger in CM2M than in CM2G, which affects the entrainment and product water properties. Two sensitivity experiments are conducted in CM2G to isolate the effect of these two model differences: in the first experiment, the outlet of the eastern branch of the overflow is blocked, and the North Atlantic horizontal circulation is modified due to the absence of the eastern branch of the overflow, although the AMOC has little change; in the second experiment, the diapycnal mixing downstream of the overflow is enhanced, resulting in changes in the structure and magnitude of the AMOC.
Zanowski, Hannah, Robert Hallberg, and Jorge L Sarmiento, November 2015: Abyssal Ocean Warming and Salinification after Weddell Polynyas in the GFDL CM2G Coupled Climate Model. Journal of Physical Oceanography, 45(11), DOI:10.1175/JPO-D-15-0109.1. Abstract
The role of Weddell Sea polynyas in establishing deep ocean properties is explored in the NOAA Geophysical Fluid Dynamics Laboratory’s (GFDL) coupled climate model, CM2G. Using statistical composite analysis of over 30 polynya events that occur in a 2,000-year-long preindustrial control run, the temperature, salinity, and water mass changes associated with the composite event are quantified. For the time period following the composite polynya cessation, termed the ‘recovery,’ warming between 0.002°C decade-1 and 0.019°C decade-1 occurs below 4200 m in the Southern Ocean basins. Temperature and salinity changes are strongest in the Southern Ocean and the South Atlantic near the polynya formation region. Comparison of the model results with abyssal temperature observations reveals that the composite polynya recovery signal could account for 10±8% of the recent warming in the abyssal Southern Ocean. For individual Southern Ocean basins, this percentage is as little as 6±11% or as much as 34±13%.
This paper describes a technique for obtaining sums of floating point values that are independent of the order-of-operations, and thus attractive for use in global sums in massively parallel computations. The basic idea described here is to convert the floating point values into a representation using a set of long integers, with enough carry-bits to allow these integers to be summed across processors without need of carries at intermediate stages, before conversion of the final sum back to a real number. This approach is being used successfully in an earth system model, in which reproducibility of results is essential.
The sensitivity of the Atlantic circulation and watermasses to biases in the convergence of moisture into the basin is examined in this study using two different general circulation models. For a persistent positive moisture flux into the tropical Atlantic, the average salinity and temperature in the basin is reduced, mainly below mid-depths and in high latitudes. A transient reduction in the Atlantic overturning strength occurs in this case, with a recovery timescale of 1–2 centuries. In contrast, a similar amount of freshwater directed into the Subpolar North Atlantic results in a persistent reduction in overturning and an increase in basin heat and salt content. In the unperturbed pre-industrial simulations, the Atlantic is unambiguously warmer and saltier than historical observations below mid-depths and in the Nordic Seas. The models’ tropical freshwater flux sensitivities project strongly onto the spatial pattern of this bias, suggesting a common atmospheric deficiency. The integrated Atlantic plus Arctic surface freshwater flux in these models is between −0.5 and −0.6 Sv, compared with an observational estimate of −0.28 Sv. Our results suggest that shortcomings in the models’ ability to reproduce realistic bulk watermass properties are due to an overestimation of the inter-basin moisture export from the tropical Atlantic.
Diapycnal mixing plays a key role in maintaining the ocean stratification and meridional overturning circulation (MOC). In the ocean interior, it is mainly sustained by breaking internal waves. Two important classes of internal waves are internal tides and lee waves, respectively generated by barotropic tides and geostrophic flows interacting with rough topography. Currently, regarding internal-wave driven mixing, most climate models only explicitly parameterize the local dissipation of internal tides. In this study, we explore the combined effects of internal tide and lee wave driven mixing on the ocean state. We perform a series of sensitivity experiments using the CM2G ocean-ice-atmosphere coupled model, including a parameterization of lee wave driven mixing using a recent estimate for the global map of energy conversion into lee waves, in addition to the tidal mixing parameterization. We show that although the global energy input in the deep ocean into lee waves (0.2 TW) is small compared to that into internal tides (1.4 TW), lee wave driven mixing makes a significant impact on the ocean state, notably on the ocean thermal structure and stratification, as well as on the MOC. The vertically-integrated circulation is also impacted in the Southern Ocean, which accounts for half the lee wave energy flux. Finally, we show that the different spatial distribution of the internal tide and lee wave energy input impacts the sensitivity described in this study. These results suggest that lee wave driven mixing should be parameterized in climate models, preferably using more physically-based parameterizations that allow the internal lee wave driven mixing to evolve in a changing ocean.
We describe carbon system formulation and simulation characteristics of two new global coupled carbon-climate Earth System Models, ESM2M and ESM2G. These models demonstrate good climate fidelity as described in Part I while incorporating explicit and consistent carbon dynamics. The two models differ almost exclusively in the physical ocean component; ESM2M uses Modular Ocean Model version 4.1 with vertical pressure layers while ESM2G uses Generalized Ocean Layer Dynamics with a bulk mixed layer and interior isopycnal layers. On land, both ESMs include a revised land model to simulate competitive vegetation distributions and functioning, including carbon cycling among vegetation, soil and atmosphere. In the ocean, both models include new biogeochemical algorithms including phytoplankton functional group dynamics with flexible stoichiometry. Preindustrial simulations are spun up to give stable, realistic carbon cycle means and variability. Significant differences in simulation characteristics of these two models are described. Due to differences in oceanic ventilation rates (Part I) ESM2M has a stronger biological carbon pump but weaker northward implied atmospheric CO2 transport than ESM2G. The major advantages of ESM2G over ESM2M are: improved representation of surface chlorophyll in the Atlantic and Indian Oceans and thermocline nutrients and oxygen in the North Pacific. Improved tree mortality parameters in ESM2G produced more realistic carbon accumulation in vegetation pools. The major advantages of ESM2M over ESM2G are reduced nutrient and oxygen biases in the Southern and Tropical Oceans.
Two comprehensive Earth System Models, identical apart from their oceanic components, are used to estimate the uncertainty in projections of 21st century sea level rise due to representational choices in ocean physical formulation. Most prominent among the formulation differences is that one (ESM2M) uses a traditional z-coordinate ocean model, while the other (ESM2G) uses an isopycnal-coordinate ocean. As evidence of model fidelity, differences in 20th century global-mean steric sea level rise are not statistically significant between either model and observed trends. However, differences between the two models’ 21st century projections are systematic and both statistically and climatically significant. By 2100, ESM2M exhibits 18% higher global steric sea level rise than ESM2G for all four radiative forcing scenarios (28 to 49 mm higher), despite having similar changes between the models in the near-surface ocean for several scenarios. These differences arise primarily from the vertical extent over which heat is taken up and the total heat uptake by the models (9% more in ESM2M than ESM2G). The fact that the spun-up control state of ESM2M is warmer than ESM2G also contributes, by giving thermal expansion coefficients that are about 7% larger in ESM2M than ESM2G. The differences between these models provide a direct estimate of the sensitivity of 21st century sea level rise to ocean model formulation, and, given the span of these models across the observed volume of the ventilated thermocline, may also approximate the sensitivities expected from uncertainties in the characterization of interior ocean physical processes.
Mesoscale eddies play a substantial role in the dynamics of the ocean, but the dominant length-scale of these eddies varies greatly with latitude, stratification and ocean depth. Global numerical ocean models with spatial resolutions ranging from 1° down to just a few kilometers include both regions where the dominant eddy scales are well resolved and regions where the model’s resolution is too coarse for the eddies to form, and hence eddy effects need to be parameterized. However, common parameterizations of eddy effects via a Laplacian diffusion of the height of isopycnal surfaces (a Gent-McWilliams diffusivity) are much more effective at suppressing resolved eddies than in replicating their effects. A variant of the Phillips model of baroclinic instability illustrates how eddy effects might be represented in ocean models. The ratio of the first baroclinic deformation radius to the horizontal grid spacing indicates where an ocean model could explicitly simulate eddy effects; a function of this ratio can be used to specify where eddy effects are parameterized and where they are explicitly modeled. One viable approach is to abruptly disable all the eddy parameterizations once the deformation radius is adequately resolved; at the discontinuity where the parameterization is disabled, isopycnal heights are locally flattened on the one side while eddies grow rapidly off of the enhanced slopes on the other side, such that the total parameterized and eddy fluxes vary continuously at the discontinuity in the diffusivity. This approach should work well with various specifications for the magnitude of the eddy diffusivities.
Melet, Angelique, Robert Hallberg, Sonya Legg, and Kurt L Polzin, March 2013: Sensitivity of the Ocean State to the Vertical Distribution of Internal-Tide Driven Mixing. Journal of Physical Oceanography, 43(3), DOI:10.1175/JPO-D-12-055.1. Abstract
The ocean interior stratification and meridional overturning circulation are largely sustained by diapycnal mixing. The breaking of internal tides is a major source of diapycnal mixing. Many recent climate models parameterize internal-tide breaking using the scheme of St Laurent et al. (2002). While this parameterization dynamically accounts for internal-tide generation, the vertical distribution of the resultant mixing is ad hoc, prescribing energy dissipation to decay exponentially above the ocean bottom with a fixed length scale. Recently, Polzin (2009) formulated a dynamically based parameterization, in which the vertical profile of dissipation decays algebraically with a varying decay scale, accounting for variable stratification using WKB stretching. We compare two simulations using the St Laurent and Polzin formulations in the CM2G ocean-ice-atmosphere coupled model, with the same formulation for internal-tide energy input. Focusing mainly on the Pacific Ocean, where the deep low-frequency variability is relatively small, we show that the ocean state shows modest but robust and significant sensitivity to the vertical profile of internal-tide driven mixing. Therefore, not only the energy input to the internal tides matters, but also where in the vertical it is dissipated.
Climate models simulate a wide range of climate changes at high northern latitudes in response to increased CO2. They also have substantial disagreement on projected changes of the Atlantic meridional overturning circulation (AMOC). Here we use two pairs of closely related climate models - each containing members with large and small AMOC declines - to explore the influence of AMOC decline on the high latitude response to increased CO2. The models with larger AMOC decline have less high latitude warming and sea ice decline than their small AMOC decline counterpart. By examining differences in the perturbation heat budget of the 40�90�N region, it is shown that AMOC decline diminishes the warming by weakening poleward ocean heat transport and increasing the ocean heat uptake. The cooling impact of this AMOC forced surface heat flux perturbation difference is enhanced by shortwave feedback and diminished by longwave feedback and atmospheric heat transport differences. The magnitude of the AMOC decline within model pairs is positively related to the magnitudes of control climate AMOC and Labrador Sea convection. Because the 40degree 90degree N region accounts for up to 40% of the simulated global ocean heat uptake over one hundred years, the process described here influences the global heat uptake efficiency.
Straneo, F, P Heimbach, Olga V Sergienko, G Hamilton, G Catania, Stephen M Griffies, and Robert Hallberg, et al., August 2013: Challenges to Understand the Dynamic Response of Greenland's Marine Terminating Glaciers to Oceanic and Atmospheric Forcing. Bulletin of the American Meteorological Society, 94(8), DOI:10.1175/BAMS-D-12-00100.1. Abstract
The recent retreat and speedup of outlet glaciers, as well as enhanced surface melting around the ice sheet margin, have increased Greenland's contribution to sea level rise to 0.6±0.1 mm/yr and its discharge of freshwater into the North Atlantic. The widespread, near-synchronous glacier retreat, and its coincidence with a period of oceanic and atmospheric warming, suggest a common climate driver. Evidence points to the marine margins of these glaciers as the region from which changes propagated inland. Yet the forcings and mechanisms behind these dynamic responses are poorly understood and either missing or crudely parameterized in climate and ice sheet models. Resulting projected sea level rise contributions from Greenland by 2100 remain highly uncertain.
This paper summarizes current state of knowledge and highlights key physical aspects of Greenland's coupled ice-sheet/ocean/atmosphere system. Three research thrusts are identified to yield fundamental insights into ice sheet, ocean, sea ice and atmosphere interactions, their role in Earth's climate system, and probable trajectories of future changes: (1) focused process studies addressing critical glacier, ocean, atmosphere and coupled dynamics; (2) sustained observations at key sites; and (3) inclusion of relevant dynamics in Earth System Models.
Understanding the dynamic response of Greenland's glaciers to climate forcing constitutes both a scientific and technological frontier given the challenges of obtaining the appropriate measurements from the glaciers' marine termini and the complexity of the dynamics involved, including the coupling of the ocean, atmosphere, glacier and sea ice systems. Interdisciplinary and international cooperation are crucial to making progress on this novel and complex problem.
Capsule: An interdisciplinary and multi-faceted approach is needed to understand the forcings and mechanisms behind the recent retreat and acceleration of Greenland's glaciers and its implications for future sea level rise
We examine the influence of alternative ocean and atmosphere subcomponents on climate model simulation of transient sensitivities by comparing three GFDL climate models used for the CMIP5. The base model ESM2M is closely related to GFDL's CMIP3 climate model CM2.1, and makes use of a depth coordinate ocean component. The second model, ESM2G, is identical to ESM2M but makes use of an isopycnal coordinate ocean model. We compare the impact of this "ocean swap" with an "atmosphere swap" that produces the CM3 climate model by replacing the AM2 atmosphere with AM3 while retaining a depth coordinate ocean model. The atmosphere swap is found to have much larger influence on sensitivities of global surface temperature and Northern Hemisphere sea ice cover. The atmosphere swap also introduces a multi-decadal response timescale through its indirect influence on heat uptake. Despite significant differences in their interior ocean mean states, the ESM2M and ESM2G simulations of these metrics of climate change are very similar, except for an enhanced high latitude salinity response accompanied by temporarily advancing sea ice in ESM2G. In the ESM2G historical simulation this behavior results in the establishment of a strong halocline in the subpolar North Atlantic during the early 20th century and an associated cooling which are counter to observations in that region. The Atlantic meridional overturning declines comparably in all three models.
We describe the physical climate formulation and simulation characteristics of two new global coupled carbon-climate Earth System Models, ESM2M and ESM2G. These models demonstrate similar climate fidelity as the Geophysical Fluid Dynamics Laboratory’s previous CM2.1 climate model while incorporating explicit and consistent carbon dynamics. The two models differ exclusively in the physical ocean component; ESM2M uses Modular Ocean Model version 4.1 with vertical pressure layers while ESM2G uses Generalized Ocean Layer Dynamics with a bulk mixed layer and interior isopycnal layers. Differences in the ocean mean state include the thermocline depth being relatively deep in ESM2M and relatively shallow in ESM2G compared to observations. The crucial role of ocean dynamics on climate variability is highlighted in the El Niño-Southern Oscillation being overly strong in ESM2M and overly weak ESM2G relative to observations. Thus, while ESM2G might better represent climate changes relating to: total heat content variability given its lack of long term drift, gyre circulation and ventilation in the North Pacific, tropical Atlantic and Indian Oceans, and depth structure in the overturning and abyssal flows, ESM2M might better represent climate changes relating to: surface circulation given its superior surface temperature, salinity and height patterns, tropical Pacific circulation and variability, and Southern Ocean dynamics. Our overall assessment is that neither model is fundamentally superior to the other, and that both models achieve sufficient fidelity to allow meaningful climate and earth system modeling applications. This affords us the ability to assess the role of ocean configuration on earth system interactions in the context of two state-of-the-art coupled carbon-climate models.
Goldberg, D N., Christopher M Little, Olga V Sergienko, Anand Gnanadesikan, Robert Hallberg, and M Oppenheimer, June 2012: Investigation of land ice-ocean interaction with a fully coupled ice-ocean model, Part 2: Sensitivity to external forcings. Journal of Geophysical Research: Earth Surface, 117, F02038, DOI:10.1029/2011JF002247. Abstract
A coupled ice stream-ice shelf-ocean cavity model is used to assess the sensitivity of the coupled system to far-field ocean temperatures, varying from 0.0 to 1.80C, as well as sensitivity to the parameters controlling grounded ice flow. A response to warming is seen in grounding line retreat and grounded ice loss that cannot be inferred from the response of integrated melt rates alone. This is due to concentrated thinning at the ice shelf lateral margin, and to processes that contribute to this thinning. Parameters controlling the flow of grounded ice have a strong influence on the response to sub-ice shelf melting, but this influence is not seen until several years after an initial perturbation in temperatures. The simulated melt rates are on the order of that observed for Pine Island Glacier in the 1990s. However, retreat rates are much slower, possibly due to unrepresented bedrock features.
Goldberg, D N., Christopher M Little, Olga V Sergienko, Anand Gnanadesikan, Robert Hallberg, and M Oppenheimer, June 2012: Investigation of land ice-ocean interaction with a fully coupled ice-ocean model, Part 1: Model description and behavior. Journal of Geophysical Research: Earth Surface, 117, F02037, DOI:10.1029/2011JF002246. Abstract
Antarctic ice shelves interact closely with the ocean cavities beneath them, with ice shelf geometry influencing ocean cavity circulation, and heat from the ocean driving changes in the ice shelves, as well as the grounded ice streams that feed them. We present a new coupled model of an ice stream-ice shelf-ocean system that is used to study this interaction. The model is capable of representing a moving grounding line and dynamically responding ocean circulation within the ice shelf cavity. Idealized experiments designed to investigate the response of the coupled system to instantaneous increases in ocean temperature show ice-ocean system responses on multiple timescales. Melt rates and ice shelf basal slopes near the grounding line adjust in 1-2 years, and downstream advection of the resulting ice shelf thinning takes place on decadal timescales. Retreat of the grounding line and adjustment of grounded ice takes place on a much longer timescale, and the system takes several centuries to reach a new steady state. During this slow retreat, and in the absence of either an upward-or downward-sloping bed or long-term trends in ocean heat content, the ice shelf and melt rates maintain a characteristic pattern relative to the grounding line.
This paper examines spurious dianeutral transport within a suite of ocean models (GOLD, MITgcm, MOM, and ROMS). We quantify such transport through a global diagnostic that computes the reference potential energy, whose evolution arises solely through transport between density classes. Previous studies have focused on the importance of accurate tracer advection schemes in reducing the spurious transport and closure. The present study highlights complementary issues associated with momentum transport. Spurious dianeutral transport is shown to be directly proportional to the lateral grid Reynolds number (ReΔ), with such transport significantly reduced when ReΔ<10.
Simulations with the isopycnal model GOLD provide a benchmark for the smallest level of spurious dianeutral transport realizable in our model suite. For idealized simulations with a linear equation of state, GOLD exhibits identically zero spurious dianeutral mixing, and thus maintains a constant reference potential energy when all physical mixing processes are omitted. Amongst the non-isopycnal models tested in idealized simulations, ROMS generally produces smaller spurious dianeutral mixing than MITgcm or MOM, since ROMS makes use of a higher order upwind-biased scheme for momentum transport that enforces a small ReΔ. In contrast, MITgcm and MOM both employ unbiased (centered) discretizations of momentum transport, and therefore rely on lateral friction operators to control the grid Reynolds number. We find that a lateral shear-dependent Smagorinsky viscosity provides an effective means to locally reduce ReΔ, and thus to reduce spurious dianeutral transport in MITgcm and MOM.
In addition to four idealized simulations, we quantify spurious dianeutral transport in realistic global ocean climate simulations using GOLD and MOM with a realistic equation of state for seawater, both with and without mesoscale eddies in the resolved flow field. The GOLD simulations have detectable levels of spurious cabbeling from along isopycnal advective truncation errors. Significantly larger spurious dianeutral transport arises in a non-eddying MOM simulation. In an eddying MOM simulation, spurious dianeutral transport is larger still but is reduced by increasing momentum friction.
A parameterization for the restratification by finite-amplitude, submesoscale, mixed layer eddies, formulated as an overturning streamfunction, has been recently proposed to approximate eddy fluxes of density and other tracers. Here, the technicalities of implementing the parameterization in the coarse-resolution ocean component of global climate models are made explicit, and the primary impacts on model solutions of implementing the parameterization are discussed. Three global ocean general circulation models including this parameterization are contrasted with control simulations lacking the parameterization. The MLE parameterization behaves as expected and fairly consistently in models differing in discretization, boundary layer mixing, resolution, and other parameterizations. The primary impact of the parameterization is a shoaling of the mixed layer, with the largest effect in polar winter regions. Secondary impacts include strengthening the Atlantic meridional overturning while reducing its variability, reducing CFC and tracer ventilation, modest changes to sea surface temperature and air-sea fluxes, and an apparent reduction of sea ice basal melting.
In this study, we investigate the dynamics of a dense gravity currents over different sizes of ridges and canyons. We employ a high resolution idealized isopycnal model and perform a large number of experiments changing the aspect ratio of a ridge/canyon, the Coriolis parameter, the reduced gravity, the background slope and initial overflow thickness. The control run (smooth topography) is in an eddy-regime and the frequencies of the eddies coincide with those of the Filchner overflow Darelius et al., 2009. Our idealized corrugation experiments show that corrugations steer the plume downslope, and that ridges are more effective than canyons in transporting the overflow to the deep ocean. We find that a corrugation Burger number (Buc) can be used as a parameter to describe the flow over topography. Buc is a combination of a Froude number and the aspect ratio. The maximum downslope transport of a corrugation can be increased when the height of the corrugation increases (Buc increases) or when the width of the corrugation decreases (Buc increases).
In addition, we propose a new parameterization of mixing as a function of Buc that can be used to account for unresolved shear in coarse resolution models. The new parameterization captures the increased local shear, thus increasing the turbulent kinetic energy and decreasing the gradient Richardson number. We find reasonable agreement in the overflow thickness and transport between the models with this parameterization and the high resolution models. We conclude that mixing effects of corrugations can be implemented as unresolved shear in an eddy diffusivity formulation and this parameterization can be used in coarse resolution models.
A simple model of the temperature-dependent biological decay of dissolved oil is embedded in
an ocean climate circulation model and used to simulate underwater plumes of dissolved and
suspended oil originating from a point source in the northern Gulf of Mexico. Plumes at different
source depths are considered and the behavior at each depth is found to be determined by the
combination of sheared current strength and vertical profile of decay rate. An upper bound on the
supply rate of dissolved and suspended oil is estimated for the interior water column from
contemporary analysis of the Deepwater Horizon blowout. For all plume scenarios, toxic levels
of dissolved oil are found to remain confined to the northern Gulf of Mexico, and abate within a
few weeks after the spill stops. An estimate of oxygen consumption due to microbial oxidation of
oil suggests that the presence of oil alone will not lead to hypoxia, but a deep plume of oil and
methane (which dissolves readily in water) does lead to localized regions of persistent hypoxia
and anoxia in the vicinity of the source.
Because ocean color alters the absorption of sunlight, it can produce changes in sea surface temperatures with further impacts on atmospheric circulation. These changes can project onto fields previously recognized to alter the distribution of tropical cyclones. If the North Pacific subtropical gyre contained no absorbing and scattering materials, the result would be to reduce subtropical cyclone activity in the subtropical Northwest Pacific by 2/3, while concentrating cyclone tracks along the equator. Predicting tropical cyclone activity using coupled models may thus require consideration of the details of how heat moves into the upper thermocline as well as biogeochemical cycling.
We overview problems and prospects in ocean circulation models, with emphasis on certain developments aiming to
enhance the physical integrity and flexibility of large-scale models used to study global climate. We also consider elements
of observational measures rendering information to help evaluate simulations and to guide development priorities.
http://www.oceanobs09.net/blog/?p=88
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.
Griffies, Stephen M., Alistair Adcroft, V Balaji, Robert Hallberg, Sonya Legg, Torge Martin, and Anna 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. PDF
In ocean models that use a mode splitting algorithm for time-stepping the internal- and external-gravity modes, the external and internal solutions each can be used to provide an estimate of the free surface height evolution. In models with time-invariant vertical coordinate spacing, it is standard to force the internal solutions for the free surface height to agree with the external solution by specifying the appropriate vertically averaged velocities; because this is a linear problem, it is relatively straightforward. However, in Lagrangian vertical coordinate ocean models with potentially vanishing layers, nonlinear discretizations of the continuity equations must be used for each interior layer. This paper discusses the options for enforcing agreement between the internal and external estimates of the free surface height, along with the consequences of each choice, and suggests an optimal, essentially exact, approach.
Legg, Sonya, Tal Ezer, Stephen M Griffies, Robert Hallberg, and L Jackson, et al., May 2009: Improving oceanic overflow representation in climate models: The gravity current entrainment climate process team. Bulletin of the American Meteorological Society, 90(5), DOI:10.1175/2008BAMS2667.1. Abstract
Oceanic overflows are bottom-trapped density currents originating in semienclosed basins, such as the Nordic seas, or on continental shelves, such as the Antarctic shelf. Overflows are the source of most of the abyssal waters, and therefore play an important role in the large-scale ocean circulation, forming a component of the sinking branch of the thermohaline circulation. As they descend the continental slope, overflows mix vigorously with the surrounding oceanic waters, changing their density and transport significantly. These mixing processes occur on spatial scales well below the resolution of ocean climate models, with the result that deep waters and deep western boundary currents are simulated poorly. The Gravity Current Entrainment Climate Process Team was established by the U.S. Climate Variability and Prediction (CLIVAR) Program to accelerate the development and implementation of improved representations of overflows within large-scale climate models, bringing together climate model developers with those conducting observational, numerical, and laboratory process studies of overflows. Here, the organization of the Climate Process Team is described, and a few of the successes and lessons learned during this collaboration are highlighted, with some emphasis on the well-observed Mediterranean overflow. The Climate Process Team has developed several different overflow parameterizations, which are examined in a hierarchy of ocean models, from comparatively well-resolved regional models to the largest-scale global climate models.
Muench, R D., A K Wåhlin, T M Özgökmen, Robert Hallberg, and L Padman, December 2009: Impacts of bottom corrugations on a dense Antarctic outflow: NW Ross Sea. Geophysical Research Letters, 36, L23607, DOI:10.1029/2009GL041347. Abstract
Prominent seabed corrugations, axially oriented roughly down-slope, are present along the Antarctic continental slope. We use analytical and numerical model results to assess the potential impact of these corrugations on outflows of dense shelf water that contribute to Antarctic Bottom Water. Down-slope flow increases with increasing corrugation height and varies with along-slope wavelength. For parameters appropriate to the northwest Ross Sea, where heights and wavelengths are ∼10–20 m and ∼1.5 km, respectively, we estimate that the corrugations increase the down-slope transport of dense water, relative to the smooth bottom case, by ∼13%. Corrugations enhance entrainment and reduce along-slope speed of the dense outflow. Larger amplitude corrugations (∼100 m) observed in other regions may impact outflows elsewhere around the poorly mapped Antarctic continental margin. Our results emphasize the need to consider small-scale local topography when modeling dense outflows.
White, Laurent, Alistair Adcroft, and Robert Hallberg, December 2009: High-order regridding–remapping schemes for continuous isopycnal and generalized coordinates in ocean models. Journal of Computational Physics, 228(23), DOI:10.1016/j.jcp.2009.08.016. Abstract
A hierarchy of high-order regridding–remapping schemes for use in generalized vertical coordinate ocean models is presented. The proposed regridding–remapping framework is successfully used in a series of idealized one-dimensional numerical experiments as well as two-dimensional internal wave and overflow test cases. The model is capable of replicating z-, sigma- and isopycnal-coordinate results, among others. Particular emphasis is placed on the design of a continuous isopycnal framework, which is a more general alternative to the layered isopycnal paradigm. Continuous isopycnal coordinates use target interface densities to define layers. In contrast to traditional layered isopycnal models, in which along-layer density gradients vanish, general coordinate approaches must deal with extra terms. For example, the calculation of pressure gradient force is more complicated and must be evaluated carefully. High-order reconstructions within boundary cells are crucial for obtaining sensible results and for reducing spurious diffusion near boundaries. Vertical advection is implicitly embedded in the remapping step and directly benefits from high-order schemes. Volume and all tracers are conserved to machine precision, which is a necessary ingredient for long-term ocean climate modeling. This hybrid vertical coordinate model provides the framework to easily capture the impact of different coordinate systems on dynamics.
Layered ocean models can exhibit spurious thermobaric instability if the compressibility of sea water is not treated accurately enough. We find that previous solutions to this problem are inadequate for simulations of a changing climate. We propose a new discretization of the pressure gradient acceleration using the finite volume method. In this method, the pressure gradient acceleration is exhibited as the difference of the integral “contact” pressure acting on the edges of a finite volume. This integral “contact” pressure can be calculated analytically by choosing a tractable equation of state. The result is a discretization that has zero truncation error for an isothermal and isohaline layer and does not exhibit the spurious thermobaric instability.
Fox-Kemper, Baylor, R Ferrari, and Robert Hallberg, 2008: Parameterization of mixed layer eddies. Part I: Theory and diagnosis. Journal of Physical Oceanography, 38(6), DOI:10.1175/2007JPO3792.1. Abstract
Ageostrophic baroclinic instabilities develop within the surface mixed layer of the ocean at horizontal fronts and efficiently restratify the upper ocean. In this paper a parameterization for the restratification driven by finite-amplitude baroclinic instabilities of the mixed layer is proposed in terms of an overturning streamfunction that tilts isopycnals from the vertical to the horizontal. The streamfunction is proportional to the product of the horizontal density gradient, the mixed layer depth squared, and the inertial period. Hence restratification proceeds faster at strong fronts in deep mixed layers with a weak latitude dependence. In this paper the parameterization is theoretically motivated, confirmed to perform well for a wide range of mixed layer depths, rotation rates, and vertical and horizontal stratifications. It is shown to be superior to alternative extant parameterizations of baroclinic instability for the problem of mixed layer restratification. Two companion papers discuss the numerical implementation and the climate impacts of this parameterization.
Fox-Kemper, Baylor, Gokhan Danabasoglu, R Ferrari, and Robert Hallberg, 2008: Parameterizing submesoscale physics in global climate models. Clivar Exchanges, 13(1), 3-5. PDF
Equatorial turbulent diffusivities resulting from breaking gravity waves may be more than a factor of 10 less than those in the midlatitudes. A coupled general circulation model with a layered isopycnal coordinate ocean is used to assess Pacific climate sensitivity to a
latitudinally varying background diapycnal diffusivity with extremely low values near the equator. The control experiments have a minimum upper-ocean diffusivity of 10−5 m2 s−1 and are initialized
from present-day conditions. The average depth of the σθ =
26.4 interface (z26.4) in the Pacific increases by 140
m after 500 yr of coupled model integration. This corresponds to a warming trend
in the upper ocean. Low equatorial diffusivities reduce the z26.4
bias by 30%. Isopycnal surfaces are elevated from the eastern boundary up to midlatitudes by cooling in the upper several hundred meters, partially compensated by freshening. Entrainment of intermediate water masses from below σθ
= 26.4 decreases by 1.5 Sv (1 Sv 106 m3 s−1), mainly in the western tropical Pacific. The Pacific heat uptake (30°S–30°N) from the atmosphere reduces by 0.1 PW. This is associated with warmer entrainment temperatures in the eastern equatorial Pacific upwelling region. Equatorward heat transport from the Southern Ocean increases by 0.07 PW.
Reducing the upper-ocean background diffusivity uniformly to 10−6 m2 s−1 cools the upper ocean from the tropics, but warms and freshens from the midlatitudes. Enhanced convergence into the Pacific of water lighter than σθ = 26.4 compensates the reduction in upwelling of intermediate waters in the tropics. Basin-averaged
z26.4 bias increases in the low background case. These results demonstrate basin-scale sensitivity to the observed suppression of equatorial background dissipation. This has clear implications for understanding oceanic heat uptake in the Pacific as well as other important aspects of the climate system. Diapycnal diffusivities due to truncation errors and other numerical artifacts in ocean models may need to be less than 10−6 m2 s−1 in order to accurately represent this effect in climate models.
This paper presents a new parameterization for shear-driven, stratified, turbulent mixing that is pertinent to climate models, in particular the shear-driven mixing in overflows and the Equatorial Undercurrent. This parameterization satisfies a critical requirement for climate applications by being simple enough to be implemented implicitly and thereby allowing the parameterization to be used with time steps that are long compared to both the time scale on which the turbulence evolves and the time scale with which it alters the large-scale ocean state.
The mixing is expressed in terms of a turbulent diffusivity that is dependent on the shear forcing and a length scale that is the minimum of the width of the low Richardson number region (Ri = N2/|uz|2, where N is the buoyancy frequency and |uz| is the vertical shear) and the buoyancy length scale over which the turbulence decays [Lb = Q1/2/N, where Q is the turbulent kinetic energy (TKE)]. This also allows a decay of turbulence vertically away from the low Richardson number region over the buoyancy scale, a process that the results show is important for mixing across a jet. The diffusivity is determined by solving a vertically nonlocal steady-state TKE equation and a vertically elliptic equilibrium equation for the diffusivity itself.
High-resolution nonhydrostatic simulations of shear-driven stratified mixing are conducted in both a shear layer and a jet. The results of these simulations support the theory presented and are used, together with discussions of various limits and reviews of previous work, to constrain parameters.
Legg, Sonya, L Jackson, and Robert Hallberg, 2008: Eddy-resolving modeling of overflows In Ocean Modeling in an Eddying Regime, Geophysical Monograph 177, M. W. Hecht, and H. Hasumi, eds., Washington, DC, American Geophysical Union, 63-82.
Little, Christopher M., Anand Gnanadesikan, and Robert Hallberg, October 2008: Large-scale oceanographic constraints on the distribution of melting and freezing under ice shelves. Journal of Physical Oceanography, 38(10), DOI:10.1175/2008JPO3928.1. Abstract
Previous studies suggest that ice shelves experience asymmetric melting and freezing. Topography may constrain oceanic circulation (and thus basal melt–freeze patterns) through its influence on the potential vorticity (PV) field. However, melting and freezing induce a local circulation that may modify locations of heat transport to the ice shelf. This paper investigates the influence of buoyancy fluxes on locations of melting and freezing under different bathymetric conditions. An idealized set of numerical simulations (the “decoupled” simulations) employs spatially and temporally fixed diapycnal fluxes. These experiments, in combination with scaling considerations, indicate that while flow in the interior is governed by large-scale topographic gradients, recirculation plumes dominate near buoyancy fluxes. Thermodynamically decoupled models are then compared to those in which ice–ocean heat and freshwater fluxes are driven by the interior flow (the “coupled” simulations). Near the southern boundary, strong cyclonic flow forced by melt-induced upwelling drives inflow and melting to the east. Recirculation is less evident in the upper water column, as shoaling of meltwater-freshened layers dissipates the dynamic influence of buoyancy forcing, yet freezing remains intensified in the west. In coupled simulations, the flow throughout the cavity is relatively insensitive to bathymetry; stratification, the slope of the ice shelf, and strong, meridionally distributed buoyancy fluxes weaken its influence.
The impact of the penetration length scale of shortwave radiation into the surface ocean is investigated with a fully coupled ocean, atmosphere, land and ice model. Oceanic shortwave radiation penetration is assumed to depend on the chlorophyll concentration. As chlorophyll concentrations increase the distribution of shortwave heating becomes shallower. This change in heat distribution impacts mixed-layer depth. This study shows that removing all chlorophyll from the ocean results in a system that tends strongly towards an El Niño state—suggesting that chlorophyll is implicated in maintenance of the Pacific cold tongue. The regions most responsible for this response are located off-equator and correspond to the oligotrophic gyres. Results from a suite of surface chlorophyll perturbation experiments suggest a potential positive feedback between chlorophyll concentration and a non-local coupled response in the fully coupled ocean-atmosphere system.
We note that there are essentially two methods of solving the hydrostatic primitive equations in general vertical coordinates: the quasi-Eulerian class of algorithms are typically used in quasi-stationary coordinates (e.g. height, pressure, or terrain following) coordinate systems; the quasi-Lagrangian class of algorithms are almost exclusively used in layered models and is the preferred paradigm in modern isopycnal models. These approaches are not easily juxtaposed. Thus, hybrid coordinate models that choose one method over the other may not necessarily obtain the particular qualities associated with the alternative method.
We discuss the nature of the differences between the Lagrangian and Eulerian algorithms and suggest that each has its benefits. The arbitrary Lagrangian-Eulerian method (ALE) purports to address these differences but we find that it does not treat the vertical and horizontal dimensions symmetrically as is done in classical Eulerian models. This distinction is particularly evident with the non-hydrostatic equations, since there is explicitly no symmetry breaking in these equations. It appears that the Lagrangian algorithms can not be easily invoked in conjunction with the pressure method that is often used in non-hydrostatic models. We suggest that research is necessary to find a way to combine the two viewpoints if we are to develop models that are suitable for simulating the wide range of spatial and temporal scales that are important in the ocean.
Hallberg, Robert, and Anand Gnanadesikan, 2006: The role of eddies in determining the structure and response of the wind-driven Southern Hemisphere overturning: Results from the modeling eddies in the Southern Ocean (MESO) project. Journal of Physical Oceanography, 36(12), 2232-2252. Abstract PDF
The Modeling Eddies in the Southern Ocean (MESO) project uses numerical sensitivity studies to examine the role played by Southern Ocean winds and eddies in determining the density structure of the global ocean and the magnitude and structure of the global overturning circulation. A hemispheric isopycnal-coordinate ocean model (which avoids numerical diapycnal diffusion) with realistic geometry is run with idealized forcing at a range of resolutions from coarse (2°) to eddy-permitting (1/6°). A comparison of coarse resolutions with fine resolutions indicates that explicit eddies affect both the structure of the overturning and the response of the overturning to wind stress changes. While the presence of resolved eddies does not greatly affect the prevailing qualitative picture of the ocean circulation, it alters the overturning cells involving the Southern Ocean transformation of dense deep waters and light waters of subtropical origin into intermediate waters. With resolved eddies, the surface-to-intermediate water cell extends farther southward by hundreds of kilometers and the deep-to-intermediate cell draws on comparatively lighter deep waters. The overturning response to changes in the winds is also sensitive to the presence of eddies. In noneddying simulations, changing the Ekman transport produces comparable changes in the overturning, much of it involving transformation of deep waters and resembling the mean circulation. In the eddy-permitting simulations, a significant fraction of the Ekman transport changes are compensated by eddy-induced transport drawing from lighter waters than does the mean overturning. This significant difference calls into question the ability of coarse-resolution ocean models to accurately capture the impact of changes in the Southern Ocean on the global ocean circulation.
Kunkel, C M., Robert Hallberg, and M Oppenheimer, 2006: Coral reefs reduce tsunami impact in model simulations. Geophysical Research Letters, 33, L23612, DOI:10.1029/2006GL027892. Abstract
Significant buffering of the impact of tsunamis by coral reefs is suggested by limited observations and some anecdotal reports, particularly following the 2004 Indian Ocean tsunami. Here we simulate tsunami run-up on idealized topographies in one and two dimensions using a nonlinear shallow water model and show that a sufficiently wide barrier reef within a meter or two of the surface reduces run-up on land on the order of 50%. We studied topographies representative of volcanic islands (islands with no continental shelf) but our conclusions may pertain to other topographies. Effectiveness depends on the amplitude and wavelength of the incident tsunami, as well as the geometry and health of the reef and the offshore distance of the reef. Reducing the threat to reefs from anthropogenic nutrients, sedimentation, fishing practices, channel-building, and global warming would help to protect some islands against tsunamis.
A series of idealised numerical simulations of dense water flowing down a broad uniform slope are presented, employing both a z-coordinate model (the MIT general circulation model) and an isopycnal coordinate model (the Hallberg Isopycnal Model). Calculations are carried out at several different horizontal and vertical resolutions, and for a range of physical parameters. A subset of calculations are carried out at very high resolution using the non-hydrostatic variant of the MITgcm. In all calculations dense water descends the slope while entraining and mixing with ambient fluid. The dependence of entrainment, mixing and down-slope descent on resolution and vertical coordinate are assessed. At very coarse resolutions the z-coordinate model generates excessive spurious mixing, and dense water has difficulty descending the slope. However, at intermediate resolutions the mixing in the z-coordinate model is less than found in the high-resolution non-hydrostatic simulations, and dense water descends further down the slope. Isopycnal calculations show less resolution dependence, although entrainment and mixing are both reduced slightly at coarser resolution. At intermediate resolutions the z-coordinate and isopycnal models produce similar levels of mixing and entrainment. These results provide a benchmark against which future developments in overflow entrainment parameterizations in both z-coordinate and isopycnal models may be compared.
Lagrangian- (and isopycnic-) vertical coordinate ocean models are subject to an exponentially growing numerical instability in weakly stratified regions when thermobaricity is not accurately compensated. Inaccurate compensation for compressibility in the pressure gradient terms leads to pressure gradient truncation errors (due to the vertical discretization) that can drive the Lagrangian coordinate surfaces to reinforce these errors. It is possible to avoid this instability while using the full non-linear equation of state for seawater by using an optimal alternate discretization of the pressure gradient terms and extracting a slowly spatially varying reference compressibility that approximates the compressibility of the ocean's mean state.
Arbic, Brian K., Stephen T Garner, Robert Hallberg, and H L Simmons, 2004: The accuracy of surface elevations in forward global barotropic and baroclinic tide models. Deep-Sea Research, Part II, 51(25-26), 3069-3101. Abstract PDF
This paper examines the accuracy of surface elevations in a forward global numerical model of 10 tidal constituents. Both one-layer and two-layer simulations are performed. As far as the authors are aware, the two-layer simulations and the simulations in a companion paper (Deep-Sea Research II, 51 (2004) 3043) represent the first published global numerical solutions for baroclinic tides. Self-consistent forward solutions for the global tide are achieved with a convergent iteration procedure for the self-attraction and loading term. Energies are too large, and elevation accuracies are poor, unless substantial abyssal drag is present. Reasonably accurate tidal elevations can be obtained with a spatially uniform bulk drag cd or horizontal viscosity KH, but only if these are inordinately large. More plausible schemes concentrate drag over rough topography. The topographic drag scheme used here is based on an exact analytical solution for arbitrary small-amplitude terrain, and supplemented by dimensional analysis to account for drag due to flow-splitting and low-level turbulence as well as that due to breaking of radiating waves. The scheme is augmented by a multiplicative factor tuned to minimize elevation discrepancies with respect to the TOPEX/POSEIDON (T/P)-constrained GOT99.2 model. The multiplicative factor may account for undersampled small spatial scales in bathymetric datasets. An optimally tuned multi-constituent one-layer simulation has an RMS elevation discrepancy of 9.54 cm with respect to GOT99.2, in waters deeper than 1000 m and over latitudes covered by T/P (66N to 66S). The surface elevation discrepancy decreases to 8.90 cm (92 percent of the height variance captured) in the optimally tuned two-layer solution. The improvement in accuracy is not due to the direct surface elevation signature of internal tides, which is of small amplitude, but to a shift in the barotropic tide induced by baroclinicity. Elevations are also more accurate in the two-layer model when pelagic tide gauges are used as the benchmark, and when the T/P-constrained TPXO6.2 model is used as a benchmark in deep waters south of 66S. For Antarctic diurnal tides, the improvement in forward model elevation accuracy with baroclinicity is substantial. The optimal multiplicative factor in the two-layer case is nearly the same as in the one-layer case, against initial expectations that the explicit resolution of low-mode conversion would allow less parameterized drag. In the optimally tuned two-layer M2 solution, local values of the ratio of temporally averaged squared upper layer speed to squared lower layer speed often exceed 10.
The energy flux out of barotropic tides and into internal waves ("conversion") is computed using a global domain multi-layer numerical model. The solution is highly baroclinic and reveals a global field of internal waves radiating way from generation sites of rough topography. A small number of sites where intense internal wave generation occurs accounts for most of the globally integrated work done on the barotropic tide and dominates sites such as the Mid-Atlantic ridge. The globally integrated conversion of the M2 barotropic tide is 891 Gigawatts and the globally integrated rate of working of the ocean by astronomical forcing is 2.94 Terawatts. Both of these estimates are close to accepted values derived from independent methods. Regional estimates of conversion are also similar to previous inferences, lending additional confidence that the solution has captured the essential physics of low-mode internal wave generation and that numerical prediction of conversion has skill in regions where no previous estimates are available.
Papadakis, M P., Eric P Chassignet, and Robert Hallberg, 2003: Numerical simulations of the Mediterranean sea outflow: Impact of the entrainment parameterization in an isopycnic coordinate ocean model. Ocean Modelling, 5(4), 325-356. Abstract PDF
Gravity current entrainment is essential in determining the properties of the interior ocean water masses that result from marginal sea overflows. Although the individual entraining billows will be unresolvable in large-scale ocean models for the foreseeable future, some large-scale simulations are now being carried out that do resolve the intermediate scale environment which may control the rate of entrainment. Hallberg [Mon. Wea. Rev. 128 (2000) 1402] has recently developed an implicit diapycnal mixing scheme for isopycnic coordinate ocean models that includes the Richardson number dependent entrainment parameterization of Turner [J. Fluid Mech. 173 (1986) 431], and which may be capable of representing the gravity current evolution in large-scale ocean models. The present work uses realistic regional simulations with the Miami Isopycnic Coordinate Ocean Model (MICOM) to evaluate ability of this scheme to simulate the entrainment that is observed to occur in the bottom boundary currents downstream of the Mediterranean outflow. These simulations are strikingly similar to the observations, indicating that this scheme does produce realistic mixing between the Mediterranean outflow and the North Atlantic Central Water. Sensitivity studies identify the critical Richardson number below which vigorous entrainment occurs as a particularly important parameter. Some of these experiments also show meddies detaching from the Mediterranean undercurrent at locations that appear to be highly influenced by topographic features.
Gnanadesikan, Anand, and Robert Hallberg, 2002: Physical oceanography, thermal structure and general circulation In Encyclopedia of Physical Science and Technology, Vol. 12, New York, NY, Academic Press, 189-210. Abstract
Physical oceanography is concerned with the study of the physical processes which control the spatiotemporal structure of such fields as density, temperature, and velocity within the ocean. A major thrust of this field is the development of an understanding of the general circulation, namely the circulation of the ocean on large scales (of order 100-10,000 km) and over long times (decades to millennia). The general circulation is what determines the large-scale chemical and thermal structure of the ocean and plays a major role in global climate and biogeochemistry. The large-scale circulation can be broken down into three cells, a surface cell where wind driving is important, a deep cell where mixing is important, and an intermediate cell where potentially both wind and mixing are important. This article discusses the physical framework necessary to understand these circulations and presents standard models which explain some key features of the large-scale structure.
Thompson, L, K A Kelly, D Darr, and Robert Hallberg, 2002: Buoyancy and mixed layer effects on the sea surface height response in an isopycnal model of the North Pacific. Journal of Physical Oceanography, 32(12), 3657-3670. Abstract PDF
An isopycnal model of the North Pacific is used to demonstrate that the seasonal cycle of heating and cooling and the resulting mixed layer depth entrainment and detrainment cycle play a role in the propgation of wind-driven Rossby waves. The model is forced by realistic winds and seasonal heat flux to examine the interaction of nearly annual wind-driven Rossby waves with the seasonal mixed layer cycle. Comparison among four model runs, one adiabatic (without diapycnal mixing or explicit mixed layer dynamics), one diabatic (with diapycnal mixing and explicit mixed layer dynamics), one with the seasonal cycle of heating only, and one with only variable winds suggests that mixed layer entrainment changes the structure of the response substantially, particularly at midlatitudes. Specifically, the mixed layer seasonal cycle works against Ekman pumping in the forcing of first-mode Rossby waves between 17° and 28°N. South of there the mixed layer seasonal cycle has little influence on the Rossby waves, while in the north, seasonal Rossby waves do not propagate. To examine the first baroclinic mode response in detail, a modal decomposition of the numerical model output is done. In addition, a comparison of the forcing by diapycnal pumping and Ekman pumping is done by a projection of Ekman pumping and diapycnal velocities on to the quasigeostrophic potential vorticity equation for each vertical mode. The first baroclinic mode's forcing is split between Ekman pumping and diapycnal velocity at midlatitudes, providing an explanation for the changes in the response when a seasonal mixed layer response is included. This is confirmed by doing a comparison of the modal decomposition in the four runs described above, and by calculation of the first baroclinic mode Rossby wave response using the one-dimensional Rossby wave equation.
Hallberg, Robert, 2001: Reply. Journal of Physical Oceanography, 31(7), 1926-1930. PDF
Hallberg, Robert, and Anand Gnanadesikan, 2001: An exploration of the role of transient eddies in determining the transport of a zonally reentrant current. Journal of Physical Oceanography, 31(11), 3312-3330. Abstract PDF
The meridional Ekman transport in a zonally reentrant channel may be balanced by diabatic circulations, standing eddies associated with topography, or by Lagrangian mean eddy mass fluxes. A simple model is used to explore the interaction between these mechanisms. A key assumption of this study is that diabatic forcing in the poleward edge of the channel acts to create lighter fluid, as is the case with net freshwater fluxes into the Southern Ocean. For weak wind forcing or strong diabatic constraint, a simple scaling argument accurately predicts the level of baroclinic shear. However, given our understanding of the relative magnitudes of Ekman flux and deep upwelling, this is not the appropriate parameter range for the Antarctic Circumpolar Current. With stronger wind stresses, eddies are prominent, with baroclinic instability initially developing in the vicinity of large topography. Arguments have been advanced by a number of authors that baroclinic instability should limit the velocity shear, leading to a stiff upper limit on the transport of the current. However, in the simulations presented here baroclinic instability is largely confined to the region of topographic highs, and the approach to a current that is independent of the wind stress occurs gradually. Several recent parameterizations of transient eddy fluxes do not reproduce key features of the observed behavior.
Gnanadesikan, Anand, and Robert Hallberg, 2000: On the relationship of the Circumpolar Current to Southern Hemisphere winds in coarse-resolution ocean models. Journal of Physical Oceanography, 30(8), 2013-2034. Abstract PDF
The response of the Circumpolar Current to changing winds has been the subject of much debate. To date, most theories of the current have tried to predict the transport using various forms of momentum balance. This paper argues that it is also important to consider thermodynamic as well as dynamic balances. Within large-scale general circulation models, increasing eastward winds within the Southern Ocean drive a northward Ekman flux of light water, which in turn produces a deeper pycnocline and warmer deep water to the north of the Southern Ocean. This in turn results in much larger thermal wind shear across the Circumpolar Current, which, given relatively small near-bottom velocities, results in an increase in Antarctic Circumpolar Current (ACC) transport. The Ekman flux near the surface is closed by a deep return flow below the depths of the ridges. A simple model that illustrates this picture is presented in which the ACC depends most strongly on the winds at the northern and southern edges of the channel. The sensitivity of this result to the formulation of buoyancy forcing is illustrated using a second simple model. A number of global general circulation model runs are then presented with different wind stress patterns in the Southern Ocean. Within these runs, neither the mean wind stress in the latitudes of Drake Passage nor the wind stress curl at the northern edge of Drake Passage produces a prediction for the transport of the ACC. However, increasing the wind stress within the Southern Ocean does increase the ACC transport.
Griffies, Stephen M., and Robert 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.
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.
Hallberg, Robert, 2000: Time integration of diapycnal diffusion and Richardson number-dependent mixing in isopycnal coordinate ocean models. Monthly Weather Review, 128(5), 1402-1419. Abstract PDF
In isopycnal coordinate ocean models, diapycnal diffusion must be expressed as a nonlinear difference equation. This nonlinear equation is not amenable to traditional implicit methods of solution, but explicit methods typically have a time step limit of order t h2/ (where t is the time step, h is the isopycnal layer thickness, and is the diapycnal diffusivity), which cannot generally be satisfied since the layers could be arbitrarily thin. It is especially important that the diffusion time integration scheme have no such limit if the diapycnal diffusivity is determined by the local Richardson number. An iterative, implicit time integration scheme of diapycnal diffusion in isopycnal layers is suggested. This scheme is demonstrated to have qualitatively correct behavior in the limit of arbitrarily thin initial layer thickness, is highly accurate in the limit of well-resolved layers, and is not significantly more expensive than existing schemes. This approach is also shown to be compatible with an implicit Richardson number-dependent mixing parameterization, and to give a plausible simulation of an entraining gravity current with parameters like the Mediterranean Water overflow through the Straits of Gibraltar.
An important component of the ocean's thermohaline circulation is the sinking of dense water from continental shelves to abyssal depths. Such downslope flow is thought to be a consequence of bottom stress retarding the alongslope flow of density-driven plumes. In this paper the authors explore the potential for explicitly simulating the simple mechanism in z-coordinate models. A series of experiments are performed using a twin density-coordinate model simulation as a standard of comparison. The adiabatic nature of the experiments and the importance of bottom slope make it more likely that the density-coordinate model will faithfully reproduce the solution. The difficulty of maintaining the density signal as the plume descends the slope is found to be the main impediment to accurate simulation in the z-coordinate model. The results of process experiments suggest that the model solutions will converge when the z-coordinate model has sufficient vertical resolution to resolve the bottom viscous layer and horizontal grid spacing equal to its vertical grid spacing divided by the maximum slope. When this criterion is met it is shown that the z-coordinate model converges to an analytical solution for a simple two-dimensional flow.
Hallberg, Robert, 1997: Localized coupling between surface and bottom-intensified flow over topography. Journal of Physical Oceanography, 27(6), 977-998. Abstract PDF
Substantial bottom topography in a basin with planetary vorticity gradients strongly affects the vertical structure of the linear topographic and planetary Rossby waves that spin up the ocean circulation. There is no barotropic mode with large amplitude topography and stratification. It is shown that the lowest frequency two-layer quasigeostrophic waves that exist with stratification, planetary vorticity gradients, and large-amplitude bottom topography are more strongly concentrated in the vertical than Burger number 1 scaling would indicate (for most orientations of the wavevector) except where the bottom slope is nearly meridional. This concentration increases with decreasing frequency. Ray tracing in an ocean basin suggests that the two layers are linearly coupled in regions with parallel or antiparallel topographic and planetary vorticity gradients, but elsewhere small amplitude motion in the two layers is largely independent. Continuity within isopycnal layers implies that most of the circulation remains within isopycnal layers, even in the regions of linear coupling. The strength of surface(bottom)-intensified flow driven by coupling to bottom(surface)-intensified flow is approximately twice as strong as the surface(bottom) projection of the bottom(surface)-intensified flow. Primitive equation simulations concur with the quasigeostrophic results and indicate that the localized linear coupling between surface- and bottom-intensified flow pertains to a continuous stratification.
Hallberg, Robert, 1997: Stable split time stepping schemes for large-scale ocean modeling. Journal of Computational Physics, 135, 54-65. Abstract PDF
An explicit time integration of the primitive equations, which are often used for numerical ocean simulations, would be subject to a short time step limit imposed by the rapidly varying external gravity waves. One way to make this time step limit less onerous is to split the primitive equations into a simplified two-dimensional set of equations that describes the evolution of the external gravity waves and a much more slowly evolving three-dimensional remainder. The two-dimensional barotropic equations can be rapidly integrated over a large number of short time steps, while a much longer time step can be used with the much more complicated remainder. Unfortunately, it has recently been demonstrated that an inexact splitting into the fast and slow equations can lead to instability in the explicit integration of the slow equations. Here a more exact splitting of the equations is proposed. The proposed split time stepping scheme is demonstrated to be stable for linear inertia-gravity waves, subject to a time step limit based on the inertial frequency and internal gravity wave speeds.
Hallberg, Robert, and P Rhines, 1996: Buoyancy-driven circulation in an ocean basin with isopycnals intersecting the sloping boundary. Journal of Physical Oceanography, 26(6), 913-940. Abstract PDF
The dynamics that govern the spreading of a convectively formed water mass in an ocean with sloping boundaries are examined using an isopycnal model that permits the interface between the layers to intersect the sloping boundaries. The simulations presented here use a two-layer configuration to demonstrate some of the pronounced differences in a baroclinically forced flow between the response in a basin with a flat bottom and vertical walls and a more realistic basin bounded by a sloping bottom. Each layer has a directly forced signal that propagates away from the forcing along the potential vorticity (PV) contours of that layer. Paired, opposed boundary currents are generated by refracted topographic Rossby waves, rather than Kelvin waves. It is impossible to decompose the flow into globally independent baroclinic and barotropic modes; topography causes the barotropic (i.e., depth averaged) response to buoyancy forcing to be just as strong as the baroclinic response. Because layer PV contours diverge, boundary currents are pulled apart at different depths even in weakly forced, essentially linear, cases. Such barotropic modes, often described as "caused by the JEBAR effect," are actually dominated by strong free flow along PV contours. With both planetary vorticity gradients and topography, the two layers are linearly coupled. This coupling is evident in upper-layer circulations that follow upper-layer PV contours but originate in unforced regions of strong lower-layer flow. The interior ocean response is confined primarily to PV contours that are either directly forced or strongly coupled at some point to directly forced PV contours of the other layer. Even when the forcing is strong enough to generate a rich eddy field in the upper layer, the topographic PV gradients in the lower layer stabilize that layer and inhibit exchange of fluid across PV contours. The dynamic processes explored in this study are pertinent to both nonlinear flows (strongly forced) and linear flows (weakly forced and forerunners of strongly forced). Both small (f plane) and large (full spherical variation of the Coriolis parameter) basins are included. Transequatorial basins, in which the geostrophic contours are blocked, are not described here.