In this study, we perform online sea ice bias correction within a Geophysical Fluid Dynamics Laboratory global ice-ocean model. For this, we use a convolutional neural network (CNN) which was developed in a previous study (Gregory et al., 2023, https://doi.org/10.1029/2023ms003757) for the purpose of predicting sea ice concentration (SIC) data assimilation (DA) increments. An initial implementation of the CNN shows systematic improvements in SIC biases relative to the free-running model, however large summertime errors remain. We show that these residual errors can be significantly improved with a novel sea ice data augmentation approach. This approach applies sequential CNN and DA corrections to a new simulation over the training period, which then provides a new training data set to refine the weights of the initial network. We propose that this machine-learned correction scheme could be utilized for generating improved initial conditions, and also for real-time sea ice bias correction within seasonal-to-subseasonal sea ice forecasts.
Deficiencies in upper ocean vertical mixing parameterizations contribute to tropical upper ocean biases in global coupled general circulation models, affecting their simulated ocean heat uptake and ENSO variability. To better understand these deficiencies, we develop a suite of ocean model experiments including both idealized single column models and realistic global simulations. The vertical mixing parameterizations are first evaluated using large eddy simulations as a baseline to assess uncertainties and evaluate their implied turbulent mixing. Global models are then developed following NOAA/GFDL's 0.25° nominal horizontal grid spacing OM4 (uncoupled) configuration of the MOM6 ocean model, with various modifications that target biases in the original model. We test several enhancements to the existing mixing schemes and evaluate them against observational constraints from Tropical Atmosphere Ocean moorings and Argo floats. In particular, we find that we can improve the diurnal variability of mixing in OM4 via modifications to its surface boundary layer mixing scheme, and can improve the net mixing in the upper thermocline by reducing the background vertical viscosity, allowing for more realistic, less diffuse currents. The improved OM4 model better represents the mixing, leading to improved diurnal deep-cycle variability, a more realistic time-mean tropical thermocline structure, and a better Pacific Equatorial Undercurrent.
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.
Data assimilation is often viewed as a framework for correcting short-term error growth in dynamical climate model forecasts. When viewed on the time scales of climate however, these short-term corrections, or analysis increments, can closely mirror the systematic bias patterns of the dynamical model. In this study, we use convolutional neural networks (CNNs) to learn a mapping from model state variables to analysis increments, in order to showcase the feasibility of a data-driven model parameterization which can predict state-dependent model errors. We undertake this problem using an ice-ocean data assimilation system within the Seamless system for Prediction and EArth system Research (SPEAR) model, developed at the Geophysical Fluid Dynamics Laboratory, which assimilates satellite observations of sea ice concentration every 5 days between 1982 and 2017. The CNN then takes inputs of data assimilation forecast states and tendencies, and makes predictions of the corresponding sea ice concentration increments. Specifically, the inputs are states and tendencies of sea ice concentration, sea-surface temperature, ice velocities, ice thickness, net shortwave radiation, ice-surface skin temperature, sea-surface salinity, as well as a land-sea mask. We find the CNN is able to make skillful predictions of the increments in both the Arctic and Antarctic and across all seasons, with skill that consistently exceeds that of a climatological increment prediction. This suggests that the CNN could be used to reduce sea ice biases in free-running SPEAR simulations, either as a sea ice parameterization or an online bias correction tool for numerical sea ice forecasts.
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.
Sane, Aakash, Brandon G Reichl, Alistair Adcroft, and Laure Zanna, October 2023: Parameterizing vertical mixing coefficients in the ocean surface boundary layer using neural networks. Journal of Advances in Modeling Earth Systems, 15(10), DOI:10.1029/2023MS003890. Abstract
Vertical mixing parameterizations in ocean models are formulated on the basis of the physical principles that govern turbulent mixing. However, many parameterizations include ad hoc components that are not well constrained by theory or data. One such component is the eddy diffusivity model, where vertical turbulent fluxes of a quantity are parameterized from a variable eddy diffusion coefficient and the mean vertical gradient of the quantity. In this work, we improve a parameterization of vertical mixing in the ocean surface boundary layer by enhancing its eddy diffusivity model using data-driven methods, specifically neural networks. The neural networks are designed to take extrinsic and intrinsic forcing parameters as input to predict the eddy diffusivity profile and are trained using output data from a second moment closure turbulent mixing scheme. The modified vertical mixing scheme predicts the eddy diffusivity profile through online inference of neural networks and maintains the conservation principles of the standard ocean model equations, which is particularly important for its targeted use in climate simulations. We describe the development and stable implementation of neural networks in an ocean general circulation model and demonstrate that the enhanced scheme outperforms its predecessor by reducing biases in the mixed-layer depth and upper ocean stratification. Our results demonstrate the potential for data-driven physics-aware parameterizations to improve global climate models.
Zhang, Cheng, Pavel Perezhogin, Cem Gultekin, Alistair Adcroft, Carlos Fernandez-Granda, and Laure Zanna, October 2023: Implementation and evaluation of a machine learned mesoscale eddy parameterization into a numerical ocean circulation model. Journal of Advances in Modeling Earth Systems, 15(10), DOI:10.1029/2023MS003697. Abstract
We address the question of how to use a machine learned (ML) parameterization in a general circulation model (GCM), and assess its performance both computationally and physically. We take one particular ML parameterization (Guillaumin & Zanna, 2021, https://doi.org/10.1002/essoar.10506419.1) and evaluate the online performance in a different model from which it was previously tested. This parameterization is a deep convolutional network that predicts parameters for a stochastic model of subgrid momentum forcing by mesoscale eddies. We treat the parameterization as we would a conventional parameterization once implemented in the numerical model. This includes trying the parameterization in a different flow regime from that in which it was trained, at different spatial resolutions, and with other differences, all to test generalization. We assess whether tuning is possible, which is a common practice in GCM development. We find the parameterization, without modification or special treatment, to be stable and that the action of the parameterization to be diminishing as spatial resolution is refined. We also find some limitations of the machine learning model in implementation: (a) tuning of the outputs from the parameterization at various depths is necessary; (b) the forcing near boundaries is not predicted as well as in the open ocean; (c) the cost of the parameterization is prohibitively high on central processing units. We discuss these limitations, present some solutions to problems, and conclude that this particular ML parameterization does inject energy, and improve backscatter, as intended but it might need further refinement before we can use it in production mode in contemporary climate models.
We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length scales larger than ℓ by smaller scale (subscale) turbulence. We use the first term in a multiscale gradient expansion due to Eyink [J. Fluid Mech. 549, 159 (2006)], which exhibits excellent correlation with the exact subscale physics when the partitioning length ℓ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/antidiffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced nondivergent velocity, v∗, that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity,¯¯¯uℓ, but by the effective velocity,
¯¯¯uℓ+v∗, the physics of which may improve commonly used LES models.
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.
Large tabular icebergs account for the majority of ice mass calved from Antarctic ice shelves, but are omitted from climate models. Specifically, these models do not account for iceberg breakup and as a result, modeled large icebergs could drift to low latitudes. Here, we develop a physically based parameterization of iceberg breakup based on the “footloose mechanism” suitable for climate models. This mechanism describes breakup of ice pieces from the iceberg edges triggered by buoyancy forces associated with a submerged ice foot fringing the iceberg. This foot develops as a result of ocean-induced melt and erosion of the iceberg freeboard explicitly parameterized in the model. We then use an elastic beam model to determine when the foot is large enough to trigger calving, as well as the size of each child iceberg, which is controlled with the ice stiffness parameter. We test the breakup parameterization with a realistic large iceberg calving-size distribution in the Geophysical Fluid Dynamics Laboratory OM4 ocean/sea-ice model and obtain simulated iceberg trajectories and areas that closely match observations. Thus, the footloose mechanism appears to play a major role in iceberg decay that was previously unaccounted for in iceberg models. We also find that varying the size of the broken ice bits can influence the iceberg meltwater distribution more than physically realistic variations to the footloose decay rate.
In December 2020, giant tabular iceberg A68a (surface area 3900 km2) broke up in open ocean much deeper than its keel, indicating that the breakage was not immediately caused by collision with the seafloor. Giant icebergs with lengths exceeding 18.5 km account for most of the calved ice mass from the Antarctic Ice Sheet. Upon calving, they drift away and transport freshwater into the Southern Ocean, modifying ocean circulation, disrupting sea ice and the marine biosphere, and potentially triggering changes in climate. Here, we demonstrate that the A68a breakup event may have been triggered by ocean-current shear, a new breakup mechanism not previously reported. We also introduce methods to represent giant icebergs within climate models that currently do not have any representation of them. These methods open opportunities to explore the interactions between icebergs and other components of the climate system and will improve the fidelity of global climate simulations.
Kenigson, Jessica, Alistair Adcroft, Scott D Bachman, Frederic Castruccio, Ian Grooms, P J Pegion, and Zofia Stanley, March 2022: Parameterizing the impact of unresolved temperature variability on the large-scale density field: 2. Modeling. Journal of Advances in Modeling Earth Systems, 14(3), DOI:10.1029/2021MS002844. Abstract
Ocean circulation models have systematic errors in large-scale horizontal density gradients due to estimating the grid-cell-mean density by applying the nonlinear seawater equation of state to the grid-cell-mean water properties. In frontal regions where unresolved subgrid-scale (SGS) fluctuations are significant, dynamically relevant errors in the representation of current systems can result. A previous study developed a novel and computationally efficient parameterization of the unresolved SGS temperature variance and resulting density correction. This parameterization was empirically validated but not tested in an ocean model. In this study, we implement deterministic and stochastic variants of this parameterization in the pressure-gradient force term of a coupled ocean-sea ice configuration of the community Earth system model-modular ocean model version 6 and perform a suite of hindcast sensitivity experiments to investigate the ocean response. The parameterization leads to coherent changes in the large-scale ocean circulation and hydrography, particularly in the Nordic Seas and Labrador Sea, which are attributable in large part to changes in the seasonally varying upper-ocean exchange through Denmark Strait. In addition, the separated Gulf Stream strengthens and shifts equatorward, reducing a common bias in coarse-resolution ocean models. The ocean response to the deterministic and stochastic variants of the parameterization is qualitatively, albeit not quantitatively, similar, yet qualitative differences are found in various regions.
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.
Range, Molly M., Brian K Arbic, Brandon C Johnson, Theodore C Moore, Vasily V Titov, Alistair Adcroft, Joseph K Ansong, Christopher J Hollis, Jeroen Ritsema, Christopher R Scotese, and He Wang, October 2022: The Chicxulub impact produced a powerful global tsunami. AGU Advances, 3(5), DOI:10.1029/2021AV000627. Abstract
The Chicxulub crater is the site of an asteroid impact linked with the Cretaceous-Paleogene (K-Pg) mass extinction at ∼66 Ma. This asteroid struck in shallow water and caused a large tsunami. Here we present the first global simulation of the Chicxulub impact tsunami from initial contact of the projectile to global propagation. We use a hydrocode to model the displacement of water, sediment, and crust over the first 10 min, and a shallow-water ocean model from that point onwards. The impact tsunami was up to 30,000 times more energetic than the 26 December 2004 Indian Ocean tsunami, one of the largest tsunamis in the modern record. Flow velocities exceeded 20 cm/s along shorelines worldwide, as well as in open-ocean regions in the North Atlantic, equatorial South Atlantic, southern Pacific and the Central American Seaway, and therefore likely scoured the seafloor and disturbed sediments over 10,000 km from the impact origin. The distribution of erosion and hiatuses in the uppermost Cretaceous marine sediments are consistent with model results.
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.
The mechanical interactions between ice floes in the polar sea-ice packs play an important role in the state and predictability of the sea-ice cover. We use a Lagrangian-based numerical model to investigate such floe-floe interactions. Our simulations show that elastic and reversible deformation offers significant resistance to compression before ice floes yield with brittle failure. Compressional strength dramatically decreases once pressure ridges start to form, which implies that thicker sea ice is not necessarily stronger than thinner ice. The mechanical transition is not accounted for in most current sea-ice models that describe ice strength by thickness alone. We propose a parameterization that describes failure mechanics from fracture toughness and Coulomb sliding, improving the representation of ridge building dynamics in particle-based and continuum sea-ice models.
Efforts to manage living marine resources (LMRs) under climate change need projections of future ocean conditions, yet most global climate models (GCMs) poorly represent critical coastal habitats. GCM utility for LMR applications will increase with higher spatial resolution but obstacles including computational and data storage costs, obstinate regional biases, and formulations prioritizing global robustness over regional skill will persist. Downscaling can help address GCM limitations, but significant improvements are needed to robustly support LMR science and management. We synthesize past ocean downscaling efforts to suggest a protocol to achieve this goal. The protocol emphasizes LMR-driven design to ensure delivery of decision-relevant information. It prioritizes ensembles of downscaled projections spanning the range of ocean futures with durations long enough to capture climate change signals. This demands judicious resolution refinement, with pragmatic consideration for LMR-essential ocean features superseding theoretical investigation. Statistical downscaling can complement dynamical approaches in building these ensembles. Inconsistent use of bias correction indicates a need for objective best practices. Application of the suggested protocol should yield regional ocean projections that, with effective dissemination and translation to decision-relevant analytics, can robustly support LMR science and management under climate change.
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.
The next‐generation seasonal prediction system is built as part of the Seamless System for Prediction and EArth System Research (SPEAR) at the Geophysical Fluid Dynamics Laboratory (GFDL) of the National Oceanic and Atmospheric Administration (NOAA). SPEAR is an effort to develop a seamless system for prediction and research across time scales. The ensemble‐based ocean data assimilation (ODA) system is updated for Modular Ocean Model Version 6 (MOM6), the ocean component of SPEAR. Ocean initial conditions for seasonal predictions, as well as an ocean state estimation, are produced by the MOM6 ODA system in coupled SPEAR models. Initial conditions of the atmosphere, land, and sea ice components for seasonal predictions are constructed through additional nudging experiments in the same coupled SPEAR models. A bias correction scheme called ocean tendency adjustment (OTA) is applied to coupled model seasonal predictions to reduce model drift. OTA applies the climatological temperature and salinity increments obtained from ODA as three‐dimensional tendency terms to the MOM6 ocean component of the coupled SPEAR models. Based on preliminary retrospective seasonal forecasts, we demonstrate that OTA reduces model drift—especially sea surface temperature (SST) forecast drift—in coupled model predictions and improves seasonal prediction skill for applications such as El Niño–Southern Oscillation (ENSO).
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.
Stanley, Zofia, Ian Grooms, William Kleiber, Scott D Bachman, Frederic Castruccio, and Alistair Adcroft, December 2020: Parameterizing the impact of unresolved temperature variability on the large-scale density field: Part 1. Theory. Journal of Advances in Modeling Earth Systems, 12(12), DOI:10.1029/2020MS002185. Abstract
Unresolved temperature and salinity fluctuations interact with a nonlinear seawater equation of state to produce significant errors in the ocean model evaluation of the large-scale density field. It is shown that the impact of temperature fluctuations dominates the impact of salinity fluctuations and that the error in density is, to leading order, proportional to the product of a subgrid-scale temperature variance and a second derivative of the equation of state. Two parameterizations are proposed to correct the large-scale density field: one deterministic and one stochastic. Free parameters in both parameterizations are fit using fine-resolution model data. Both parameterizations are computationally efficient as they require only one additional evaluation of a nonlinear equation at each grid cell. A companion paper will discuss the climate impacts of the parameterizations proposed here.
Tsujino, Hiroyuki, Shogo Urakawa, Stephen M Griffies, Gokhan Danabasoglu, Alistair Adcroft, A E Amaral, T Arsouze, M Bentsen, Raffaele Bernardello, C Böning, A Bozec, Eric P Chassignet, S Danilov, and Raphael Dussin, et al., August 2020: Evaluation of global ocean–sea-ice model simulations based on the experimental protocols of the Ocean Model Intercomparison Project phase 2 (OMIP-2). Geoscientific Model Development, 13(8), DOI:10.5194/gmd-13-3643-2020. Abstract
We present a new framework for global ocean–sea-ice model simulations based on phase 2 of the Ocean Model Intercomparison Project (OMIP-2), making use of the surface dataset based on the Japanese 55-year atmospheric reanalysis for driving ocean–sea-ice models (JRA55-do). We motivate the use of OMIP-2 over the framework for the first phase of OMIP (OMIP-1), previously referred to as the Coordinated Ocean–ice Reference Experiments (COREs), via the evaluation of OMIP-1 and OMIP-2 simulations from 11 state-of-the-science global ocean–sea-ice models. In the present evaluation, multi-model ensemble means and spreads are calculated separately for the OMIP-1 and OMIP-2 simulations and overall performance is assessed considering metrics commonly used by ocean modelers. Both OMIP-1 and OMIP-2 multi-model ensemble ranges capture observations in more than 80 % of the time and region for most metrics, with the multi-model ensemble spread greatly exceeding the difference between the means of the two datasets. Many features, including some climatologically relevant ocean circulation indices, are very similar between OMIP-1 and OMIP-2 simulations, and yet we could also identify key qualitative improvements in transitioning from OMIP-1 to OMIP-2. For example, the sea surface temperatures of the OMIP-2 simulations reproduce the observed global warming during the 1980s and 1990s, as well as the warming slowdown in the 2000s and the more recent accelerated warming, which were absent in OMIP-1, noting that the last feature is part of the design of OMIP-2 because OMIP-1 forcing stopped in 2009. A negative bias in the sea-ice concentration in summer of both hemispheres in OMIP-1 is significantly reduced in OMIP-2. The overall reproducibility of both seasonal and interannual variations in sea surface temperature and sea surface height (dynamic sea level) is improved in OMIP-2. These improvements represent a new capability of the OMIP-2 framework for evaluating process-level responses using simulation results. Regarding the sensitivity of individual models to the change in forcing, the models show well-ordered responses for the metrics that are directly forced, while they show less organized responses for those that require complex model adjustments. Many of the remaining common model biases may be attributed either to errors in representing important processes in ocean–sea-ice models, some of which are expected to be reduced by using finer horizontal and/or vertical resolutions, or to shared biases and limitations in the atmospheric forcing. In particular, further efforts are warranted to resolve remaining issues in OMIP-2 such as the warm bias in the upper layer, the mismatch between the observed and simulated variability of heat content and thermosteric sea level before 1990s, and the erroneous representation of deep and bottom water formations and circulations. We suggest that such problems can be resolved through collaboration between those developing models (including parameterizations) and forcing datasets. Overall, the present assessment justifies our recommendation that future model development and analysis studies use the OMIP-2 framework.
GFDL's new CM4.0 climate model has high transient and equilibrium climate sensitivities near the middle of the upper half of CMIP5 models. The CMIP5 models have been criticized for excessive sensitivity based on observations of present‐day warming and heat uptake and estimates of radiative forcing. An ensemble of historical simulations with CM4.0 produces warming and heat uptake that are consistent with these observations under forcing that is at the middle of the assessed distribution. Energy budget‐based methods for estimating sensitivities based on these quantities underestimate CM4.0's sensitivities when applied to its historical simulations. However, we argue using a simple attribution procedure that CM4.0's warming evolution indicates excessive transient sensitivity to greenhouse gases. This excessive sensitivity is offset prior to recent decades by excessive response to aerosol and land use changes.
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.
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.
Jansen, Malte, Alistair Adcroft, and Sina Khani, et al., August 2019: Towards an energetically consistent, resolution aware parameterization of ocean mesoscale eddies. Journal of Advances in Modeling Earth Systems, 11(8), DOI:10.1029/2019MS001750. Abstract
A subgrid‐scale eddy parameterization is developed which makes use of an explicit eddy kinetic energy (EKE) budget and can be applied at both “non‐eddying” and “eddy permitting” resolutions. The subgrid‐scale eddies exchange energy with the resolved flow in both directions via a parameterization of baroclinic instability (based on the established formulation of Gent and McWilliams) and bi‐harmonic and negative Laplacian viscosity terms. This formulation represents the turbulent cascades of energy and enstrophy consistent with our current understanding of the turbulent eddy energy cycle. At the same time, the approach is simple and general enough to be readily implemented in ocean climate models, without adding significant computational cost.
The closure has been implemented in the Modular Ocean Model (MOM6) and tested in the “Neverworld” configuration, which employs an idealized analytically defined topography designed as a testbed for mesoscale eddy parameterizations. The parameterization performs well over a range of resolutions, seamlessly connecting non‐eddying and eddy resolving regimes.
General circulation models use subgrid‐scale (SGS) parameterizations to represent the effects of unresolved mesoscale eddies on large‐scale motions. Most of the current SGS parameterizations are based on a theoretical understanding of transient eddies, where the mean flow is a temporal average. Here, we use a spatial filtering analysis to better understand the scale‐dependent characteristics of the SGS fluxes. Specifically, we apply the filtering approach to diagnose SGS eddy volume fluxes and eddy velocity scales in a hierarchy of model configurations from a flat‐bottom channel to an idealized Southern Hemisphere. Importantly, SGS volume fluxes include significant contributions from standing meanders; unlike for transient eddies, the vertically integrated SGS volume flux does not necessarily integrate to zero. To accommodate net vertically integrated eddy fluxes, we define a SGS eddy diffusivity based on planetary potential vorticity (PV) diffusion. We diagnose the transient and standing contributions to SGS fluxes and associated effective diffusivities. In the presence of bottom topography or continental barriers the standing component of the PV diffusivity becomes dominant at large filter scales in the westerly wind region, while the transient component remains dominant in the easterly wind region. Our results suggest that the diagnosed PV diffusivity can be parameterized using mixing length theory based on a priori estimates of SGS velocity and length scales.
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.
Exchanges between coastal and oceanic waters shape both coastal ecosystem processes and signatures that they impart on global biogeochemical cycles. The time‐scales of these exchanges, however, are poorly represented in current‐generation, coarse‐grid climate models. Here we provide a novel global perspective on coastal residence time (CRT) and its spatio‐temporal variability using a new age tracer implemented in global ocean models. Simulated CRTs range widely from several days in narrow boundary currents to multiple years on broader shelves and in semi‐enclosed seas, in agreement with available observations. Overall, CRT is better characterized in high‐resolution models (1/8° and 1/4°) than the coarser (1° and 1/2°) versions. This is in large part because coastal and open ocean grid cells are more directly connected in coarse models, prone to erroneous coastal flushing and an underestimated CRT. Additionally, we find that geometric enclosure of a coastal system places an important constraint on CRT.
Most ocean climate models do not represent ice shelf calving in a physically realistic way, even though the calving of icebergs is a major component of the mass balance for Antarctic ice shelves. The infrequency of large calving events together with the difficulty of placing observational instruments around icebergs means that little is known about how calving icebergs affect the ocean. In this study we present a novel model of an ice shelf coupled to an ocean circulation model, where the ice shelf is constructed of Lagrangian elements that allow simulation of iceberg calving. The Lagrangian ice shelf model is used to simulate the flow beneath a static idealized ice shelf, to verify that it can reproduce the results of an existing Eulerian model simulation with an identical configuration. The Lagrangian model is then used to simulate the ocean's response to a calved iceberg drifting away from the ice shelf. The results show how a calving event and subsequent iceberg drift affect the ocean. At the ice front, the calving event leads to a warming of the ocean surface and cooling of the water column at depth, allowing cooler waters to enter the ice shelf cavity, leading to reduced melt rates within the cavity. A Taylor column is observed below the iceberg, which moves with the iceberg as it drifts into the open ocean. As the iceberg drifts further from the ice shelf, the circulation within the ice shelf cavity tends toward a new steady state, consistent with the new ice shelf geometry.
Lagrangian models of sea‐ice dynamics have several advantages over Eulerian continuum models. Spatial discretization on the ice‐floe scale is natural for Lagrangian models and offers exact solutions for mechanical non‐linearities with arbitrary sea‐ice concentrations. This allows for improved model performance in ice‐marginal zones, where sea ice is fragmented. Furthermore, Lagrangian models can explicitly simulate jamming processes that occur when sea ice moves through narrow confinements. While difficult to parameterize in continuum formulations, jamming emerges spontaneously in dense granular systems simulated in a Lagrangian framework. Here, we present a flexible discrete‐element framework for approximating Lagrangian sea‐ice mechanics at the ice‐floe scale, forced by ocean and atmosphere velocity fields. Our goal is to evaluate the potential of simpler models than the traditional discrete‐element methods for granular dynamics. We demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to produce jamming, and describe two different approaches based on Coulomb‐friction and cohesion which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model displays jamming behavior which is similar to the more complex model with Coulomb friction and ice‐floe rotation at larger scales, and has significantly lower computational cost.
Van Roekel, L, Alistair Adcroft, Gokhan Danabasoglu, Stephen M Griffies, B Kauffman, William G Large, Michael Levy, and Brandon G Reichl, et al., November 2018: The KPP boundary layer scheme for the ocean: revisiting its formulation and benchmarking one‐dimensional simulations relative to LES. Journal of Advances in Modeling Earth Systems, 10(11), DOI:10.1029/2018MS001336. Abstract
We evaluate the Community ocean Vertical Mixing (CVMix) project version of the K‐profile parameterization (KPP) for modeling upper ocean turbulent mixing. For this purpose, one‐dimensional KPP simulations are compared across a suite of oceanographically relevant regimes against horizontally averaged large eddy simulations (LES). We find the standard configuration of KPP consistent with LES across many forcing regimes, supporting its physical basis. Our evaluation also motivates recommendations for KPP “best practices” within ocean circulation models, and identifies areas where further research is warranted.
The original treatment of KPP recommends the matching of interior diffusivities and their gradients to the KPP predicted values computed in the ocean surface boundary layer (OSBL). However, we find that difficulties in representing derivatives of rapidly changing diffusivities near the base of the OSBL can lead to loss of simulation fidelity. To mitigate this difficulty, we propose and evaluate two computationally simpler approaches: (1) match to the internal predicted diffusivity alone, (2) set the KPP diffusivity to zero at the OSBL base.
We find the KPP entrainment buoyancy flux to be sensitive to vertical grid resolution and details of how to diagnose the KPP boundary layer depth. We modify the KPP turbulent shear velocity parameterization to reduce resolution dependence. Additionally, an examination of LES vertical turbulent scalar flux budgets shows that the KPP parameterized non‐local tracer flux is incomplete due to the assumption that it solely redistributes the surface tracer flux. This result motivates further studies of the non‐local flux parameterization.
Gibson, A H., Andrew McC Hogg, A E Kiss, C J Shakespeare, and Alistair Adcroft, November 2017: Attribution of horizontal and vertical contributions to spurious mixing in an Arbitrary Lagrangian-Eulerian ocean model. Ocean Modelling, 119, DOI:10.1016/j.ocemod.2017.09.008. Abstract
We examine the separate contributions to spurious mixing from horizontal and vertical processes in an ALE ocean model, MOM6, using reference potential energy (RPE). The RPE is a global diagnostic which changes only due to mixing between density classes. We extend this diagnostic to a sub-timestep timescale in order to individually separate contributions to spurious mixing through horizontal (tracer advection) and vertical (regridding/remapping) processes within the model. We both evaluate the overall spurious mixing in MOM6 against previously published output from other models (MOM5, MITGCM and MPAS-O), and investigate impacts on the components of spurious mixing in MOM6 across a suite of test cases: a lock exchange, internal wave propagation, and a baroclinically-unstable eddying channel.
The split RPE diagnostic demonstrates that the spurious mixing in a lock exchange test case is dominated by horizontal tracer advection, due to the spatial variability in the velocity field. In contrast, the vertical component of spurious mixing dominates in an internal waves test case. MOM6 performs well in this test case owing to its quasi-Lagrangian implementation of ALE. Finally, the effects of model resolution are examined in a baroclinic eddies test case. In particular, the vertical component of spurious mixing dominates as horizontal resolution increases, an important consideration as global models evolve towards higher horizontal resolutions.
Large tabular icebergs calved from Antarctic ice shelves have long lifetimes (due to their large size), during which they drift across large distances, altering ambient ocean circulation, bottom-water formation, sea-ice formation, and biological primary productivity in the icebergs' vicinity. However, despite their importance, the current generation of ocean circulation models usually do not represent large tabular icebergs. In this study we develop a novel framework to model large tabular icebergs submerged in the ocean. In this framework, tabular icebergs are represented by pressure-exerting Lagrangian elements that drift in the ocean. The elements are held together and interact with each other via bonds. A breaking of these bonds allows the model to emulate calving events (i.e. detachment of a tabular iceberg from an ice shelf) and tabular icebergs breaking up into smaller pieces. Idealized simulations of a calving tabular iceberg, its drift, and its breakup demonstrate capabilities of the developed framework.
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.
Icebergs calved from the Antarctic continent act as moving sources of freshwater while drifting in the Southern Ocean. The lifespan of these icebergs strongly depends on their original size during calving. In order to investigate the effects (if any) of the calving size of icebergs on the Southern Ocean, we use a coupled general circulation model with an iceberg component. Iceberg calving length is varied from 62 m up to 2.3 km, which is the typical range used in climate models. Results show that increasing the size of calving icebergs leads to an increase in the westward iceberg freshwater transport around Antarctica. In simulations using larger icebergs, the reduced availability of meltwater in the Amundsen and Bellingshausen Seas suppresses the sea-ice growth in the region. In contrast, the increased iceberg freshwater transport leads to increased sea-ice growth around much of the East Antarctic coastline. These results suggest that the absence of large tabular icebergs with horizontal extent of tens of kilometers in climate models may introduces systematic biases in sea-ice formation, ocean temperatures and salinities around Antarctica.
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.
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.
We propose a new framework for parameterization of ocean convection processes. The new framework is termed “patchy convection” since our aim is to represent the heterogeneity of mixing processes that take place within the horizontal scope of a grid cell. We focus on applying this new scheme to represent the effect of pre-conditioning for deep convection by subgrid scale eddy variability. The nw parameterization separates the grid-cell into two regions of different stratification, applies convective mixing separately to each region, and then recombines the density profile to produce the grid-cell mean density profile. The scheme depends on two parameters: the areal fraction of the vertically-mixed region within the horizontal grid cell, and the density difference between the mean and the unstratified profiles at the surface. We parameterize this density difference in terms of an unresolved eddy kinetic energy. We illustrate the patchy parameterization using a 1D idealized convection case before evaluating the scheme in two different global ocean-ice simulations with prescribed atmospheric forcing; i) diagnosed eddy velocity field applied only in the Labrador Sea ii) diagnosed global eddy velocity field. The global simulation results indicate that the patchy convection scheme improves the warm biases in the deep Atlantic Ocean and Southern Ocean. This proof-of-concept study is a first step in developing the patchy parameterization scheme, which will be extended in future to use a prognostic eddy field as well as to parameterize convection due to under-ice brine rejection.
We present a porous medium approach to representing topography, and a new algorithm for the objective interpolation of topography, for use in ocean circulation models of fixed resolution. The representation and algorithm makes use of two concepts; impermeable thin walls and porous barriers. Impermeable thin walls allow the representation of knife-edge sub-grid-scale barriers that block lateral flow between model grid cells. Porous barriers permit the sub-grid scale geometry to modulate lateral transport as a function of elevation. We find that the porous representation and the resulting interpolated topography retains key features, such as overflow sill depths, without compromising other dynamically relevant aspects, such as mean ocean depth for a cell. The accurate representation of the ocean depth is illustrated in a simple model of a tsunami that has a cross-basin travel time very much less dependent on horizontal resolution than when using conventional topographic interpolation and representation.
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.
Wind power inputs at the surface ocean are dissipated through smaller-scale processes in the ocean interior and turbulent boundary layer. Simulations suggest that seafloor topography enhances turbulent mixing and energy dissipation in the ocean interior.
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.
Baughman, E, Anand Gnanadesikan, A DeGaetano, and Alistair Adcroft, November 2012: Investigation of the Surface and Circulation Impacts of Cloud Brightening Geoengineering. Journal of Climate, 25(21), DOI:10.1175/JCLI-D-11-00282.1. Abstract
Projected increases in greenhouse gases have prompted serious discussion on geoengineering the climate system to counteract global climate change. Cloud albedo enhancement has been proposed as a feasible geoengineering approach, but previous research suggests undesirable consequences of globally uniform cloud brightening. The present study uses GFDL�s CM2G global coupled model to simulate cloud albedo enhancement via increases in cloud condensation nuclei (CCN) to 1000 cm−3 targeted at the marine stratus deck of the Pacific Ocean, where persistent low clouds suggest a regional approach to cloud brightening. We investigate the impact of this regional geoengineering on global circulation and climate in the presence of a 1% annual increase of CO2. Surface temperatures returned to near Pre-Industrial levels over much of the globe with cloud modifications in place. In the first 40 years and over the 140 year mean, significant cooling over the Equatorial Pacific, continued Arctic warming, and large precipitation changes over the western Pacific, and a westward compression and intensification of the Walker Circulation were observed in response to cloud brightening. The cloud brightening caused a persistent La Nina condition associated with an increase in hurricane maximum potential intensity and genesis potential index, and decreased vertical wind shear between July and November in the tropical Atlantic, South China Sea, and to the east of Japan. Responses were similar with CCN = 500 cm−3.
We present results for simulated climate and climate change from a newly developed high-resolution global climate model (GFDL CM2.5). The GFDL CM2.5 model has an atmospheric resolution of approximately 50 Km in the horizontal, with 32 vertical levels. The horizontal resolution in the ocean ranges from 28 Km in the tropics to 8 Km at high latitudes, with 50 vertical levels. This resolution allows the explicit simulation of some mesoscale eddies in the ocean, particularly at lower latitudes.
We present analyses based on the output of a 280 year control simulation; we also present results based on a 140 year simulation in which atmospheric CO2 increases at 1% per year until doubling after 70 years.
Results are compared to the GFDL CM2.1 climate model, which has somewhat similar physics but coarser resolution. The simulated climate in CM2.5 shows marked improvement over many regions, especially the tropics, including a reduction in the double ITCZ and an improved simulation of ENSO. Regional precipitation features are much improved. The Indian monsoon and Amazonian rainfall are also substantially more realistic in CM2.5.
The response of CM2.5 to a doubling of atmospheric CO2 has many features in common with CM2.1, with some notable differences. For example, rainfall changes over the Mediterranean appear to be tightly linked to topography in CM2.5, in contrast to CM2.1 where the response is more spatially homogeneous. In addition, in CM2.5 the near-surface ocean warms substantially in the high latitudes of the Southern Ocean, in contrast to simulations using CM2.1.
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.
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.
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.
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
Marshall, David, and Alistair Adcroft, April 2010: Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold’s first stability theorem. Ocean Modelling, 32(3-4), DOI:10.1016/j.ocemod.2010.02.001. Abstract
A family of eddy closures is studied that flux potential vorticity down-gradient and solve an explicit budget for the eddy energy, following the approach developed by Eden and Greatbatch (2008, Ocean Modelling). The aim of this manuscript is to demonstrate that when energy conservation is satisfied in this manner, the growth or decay of the parameterized eddy energy relates naturally to the instability or stability of the flow as described by Arnold’s first stability theorem. The resultant family of eddy closures therefore possesses some of the ingredients necessary to parameterize the gross effects of eddies in both forced-dissipative and freely-decaying turbulence. These ideas are illustrated through their application to idealized, barotropic wind-driven gyres in which the maximum eddy energy occurs within the viscous boundary layers and separated western boundary currents, and to freely-decaying turbulence in a closed barotropic basin in which inertial Fofonoff gyres emerge as the long-time solution. The result that these eddy closures preserve the relation between the growth or decay of eddy energy and the instability or stability of the flow provides further support for their use in ocean general circulation models.
Martin, Torge, and Alistair Adcroft, July 2010: Parameterizing the fresh-water flux from land ice to ocean with interactive icebergs in a coupled climate model. Ocean Modelling, 34(3-4), DOI:10.1016/j.ocemod.2010.05.001. Abstract
Icebergs are an important part of the fresh-water cycle and, until now, have not been explicitly represented in Intergovernmental Panel on Climate Change (IPCC) class coupled global circulation models (CGCMs) of the climate system. In this study we examine the impact of introducing interactive icebergs in a next-generation CGCM designed for 21st Century climate predictions. The frozen fresh-water discharge from land is used as calving to create icebergs in the coupled system which are then free to evolve and interact with the sea-ice and ocean components. Icebergs are fully prognostic, represented as point particles and evolve according to momentum and mass balance equations. About 100,000 individual particles are present at any time in the simulations but represent many more icebergs through a clustering approach. The various finite sizes of icebergs, which are prescribed by a statistical distribution at the calving points, lead to a finite life-time of icebergs ranging from weeks, for the smallest icebergs (60 m length), up to years for the largest (2.2 km length). The resulting melt water distribution seen by the ocean enhances deep-water formation, in particular on the continental shelves, relative to the model without icebergs.
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.
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.
Griffies, Stephen M., and Alistair Adcroft, 2008: Formulating the equations of ocean models In Ocean Modeling in an Eddying Regime, Geophysical Monograph 177, M. W. Hecht, and H. Hasumi, eds., Washington, DC, American Geophysical Union, 281-318. Abstract PDF
We formulate mathematical equations describing the thermo-hydrodynamics of the ocean and introduce certain numerical methods employed by models used for ocean simulations.
White, Laurent, and Alistair Adcroft, 2008: A high-order finite volume remapping scheme for nonuniform grids: The piecewise quartic method (PQM). Journal of Computational Physics, 227(15), DOI:10.1016/j.jcp.2008.04.026. Abstract
A hierarchy of one-dimensional high-order remapping schemes is presented and their performance with respect to accuracy and convergence rate investigated. The schemes are also compared based on remapping experiments in closed domains. The piecewise quartic method (PQM) is presented, based on fifth-order accurate piecewise polynomials, and is motivated by the need to significantly improve hybrid coordinate systems of ocean climate models, which require the remapping to be conservative, monotonic and highly accurate. A limiter for this scheme is fully described that never decreases the polynomial degree, except at the location of extrema. We assess the use of high-order explicit and implicit
(i.e., compact) estimates for the edge values and slopes needed to build the piecewise polynomials in both piecewise parabolic method (PPM) and PQM. It is shown that all limited PQM schemes perform significantly better than limited PPM schemes and that PQM schemes are much more cost-effective.
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.
Boccaletti, G, R Ferrari, Alistair Adcroft, D Ferreira, and J Marshall, 2005: The vertical structure of ocean heat transport. Geophysical Research Letters, 32, L10603, DOI:10.1029/2005GL022474. Abstract
One of the most important contributions the ocean makes to Earth's climate is through its poleward heat transport: about 1.5 PW or more than 30% of that accomplished by the ocean-atmosphere system (Trenberth and Caron, 2001). Recently, concern has arisen over whether global warming could affect this heat transport (Watson et al., 2001), for example, reducing high latitude convection and triggering a collapse of the deep overturning circulation (Rahmstorf, 1995). While the consequences of abrupt changes in oceanic circulation should be of concern, we argue that the attention devoted to deep circulations is disproportionate to their role in heat transport. For this purpose, we introduce a heat function which identifies the contribution to the heat transport by different components of the oceanic circulation. A new view of the ocean emerges in which a shallow surface intensified circulation dominates the poleward heat transport.
