Jean-Michel Campin

Implementation of an Atmosphere–Ocean General Circulation Model on the Expanded Spherical Cube

A hydrodynamical kernel that drives both an atmospheric and oceanic general circulation model is implemented in general orthogonal curvilinear coordinates using the finite-volume method on the sphere. The finite-volume method naturally describes arbitrary grids, and use of the vector-invariant form of the momentum equations simplifies the generalization to arbitrary coordinates. Grids based on the expanded spherical cube of Rancic et al., which contain eight singular points, are used. At these singularities the grid is nonorthogonal. The combined use of vector-invariant equations and the finite-volume method is shown to avoid degeneracy at these singular points. The model is tested using experiments proposed by Williamson et al. and Held and Saurez. The atmospheric solutions are examined seeking evidence of the underlying grid in solutions and eddy statistics. A global ocean simulation is also conducted using the same code. The solutions prove to be accurate and free of artifacts arising from the cubic grid.

Conservation of properties in a free-surface model

In height coordinate ocean models, natural conservation of tracers (temperature, salinity or any passive tracer) requires that the thickness of the surface cell varies with the free-surface displacement, leading to a non-linear free-surface formulation (NLFS). However, NLFS does not guarantee exact conservation unless special care is taken in the implementation, and in particular the time stepping scheme, as pointed out by Griffies et al. (Monthly Weather Rev. 129 (2001) 1081). This paper presents a general method to implement a NLFS in a conservative way, using an implicit free surface formulation. Details are provided for two tracer time stepping schemes, both second order in time and space: a two time-level scheme, such as Lax–Wendroff scheme, guarantees exact tracer conservation;a three time-level scheme such as the Adams–Bashforth II requires further adaptations to achieve exact local conservation and accurate global conservation preventing long term drift of the model tracer content. No compromise is required between local and global conservation since the method accurately conserves any tracer. In addition to the commonly used backward time stepping, the implicit free surface formulation also offers the option of a Crank–Nickelson time stepping which conserves the energy. The methods are tested in idealized experiments designed to emphasize problems of tracer and energy conservation. The tests show the ability of the NLFS method to conserve tracers, in contrast to the linear free-surface formulation. At test of energy conservation reveals that free-surface backward time-stepping strongly damps the solution. In contrast, Crank–Nickelson time stepping exactly conserves energy in the pure linear case and confirms the NLFS improvement relative to the linear free-surface when momentum advection is included. � 2003 Elsevier Ltd. All rights reserved.

Atmosphere–Ocean Modeling Exploiting Fluid Isomorphisms

Mathematical isomorphisms between the hydrostatic equations that govern the evolution of a compressible atmosphere and an incompressible ocean are described and exploited to guide the design of a hydrodynamical kernel for simulation of either fluid.

Mean Climate and Variability of the Atmosphere and Ocean on an Aquaplanet

Numerical experiments are described that pertain to the climate of a coupled atmosphere–ocean–ice system in the absence of land, driven by modern-day orbital and CO2 forcing. Millennial time-scale simulations yield a mean state in which ice caps reach down to 55° of latitude and both the atmosphere and ocean comprise eastward- and westward-flowing zonal jets, whose structure is set by their respective baroclinic instabilities. Despite the zonality of the ocean, it is remarkably efficient at transporting heat meridionally through the agency of Ekman transport and eddy-driven subduction. Indeed the partition of heat transport between the atmosphere and ocean is much the same as the present climate, with the ocean dominating in the Tropics and the atmosphere in the mid–high latitudes. Variability of the system is dominated by the coupling of annular modes in the atmosphere and ocean. Stochastic variability inherent to the atmospheric jets drives variability in the ocean. Zonal flows in the ocean exhibit decadal variability, which, remarkably, feeds back to the atmosphere, coloring the spectrum of annular variability. A simple stochastic model can capture the essence of the process. Finally, it is briefly reviewed how the aquaplanet can provide information about the processes that set the partition of heat transport and the climate of Earth.

Localization of Deep Water Formation: Role of Atmospheric Moisture Transport and Geometrical Constraints on Ocean Circulation

A series of coupled atmosphere‐ocean‐ice aquaplanet experiments is described in which topological constraints on ocean circulation are introduced to study the role of ocean circulation on the mean climate of the coupled system. It is imagined that the earth is completely covered by an ocean of uniform depth except for the presence or absence of narrow barriers that extend from the bottom of the ocean to the sea surface. The following four configurations are described: Aqua (no land), Ridge (one barrier extends from pole to pole), Drake (one barrier extends from the North Pole to 358S), and DDrake (two such barriers are set 908 apart and join at the North Pole, separating the ocean into a large basin and a small basin, connected to the south). On moving from Aqua to Ridge to Drake to DDrake, the energy transports in the equilibrium solutions become increasingly ‘‘realistic,’’ culminating in DDrake, which has an uncanny resemblance to the present climate. Remarkably, the zonal-average climates of Drake and DDrake are strikingly similar, exhibiting almost identical heat and freshwater transports, and meridional overturning circulations. However, Drake and DDrake differ dramatically in their regional climates. The small and large basins of DDrake exhibit distinctive Atlantic-like and Pacific-like characteristics, respectively: the small basin is warmer, saltier, and denser at the surface than the large basin, and is the main site of deep water formation with a deep overturning circulation and strong northward ocean heat transport. A sensitivity experiment with DDrake demonstrates that the salinity contrast between the two basins, and hence the localization of deep convection, results from a deficit of precipitation, rather than an excess of evaporation, over the small basin. It is argued that the width of the small basin relative to the zonal fetch of atmospheric precipitation is the key to understanding this salinity contrast. Finally, it is argued that many gross features of the present climate are consequences of two topological asymmetries that have profound effects on ocean circulation: a meridional asymmetry (circumpolar flow in the Southern Hemisphere; blocked flow in the Northern Hemisphere) and a zonal asymmetry (a small basin and a large basin).

How Sensitive are Coarse General Circulation Models to Fundamental Approximations in the Equations of Motion

The advent of high-precision gravity missions presents the opportunity to accurately measure variations in the distribution of mass in the ocean. Such a data source will prove valuable in state estimation and constraining general circulation models (GCMs) in general. However, conventional GCMs make the Boussinesq approximations, a consequence of which is that mass is not conserved. By use of the height‐pressure coordinate isomorphism implemented in the Massachusetts Institute of Technology general circulation model (MITGCM), the impact of non-Boussinesq effects can be evaluated. Although implementing a non-Boussinesq model in pressure coordinates is relatively straightforward, making a direct comparison between height and pressure coordinate (i.e., Boussinesq and non-Boussinesq) models is not simple. However, a careful comparison of the height coordinate and the pressure coordinate solutions ensures that only non-Boussinesq effects can be responsible for the observed differences. As a yardstick, these differences are also compared with those between the Boussinesq hydrostatic and models in which the hydrostatic approximation has been relaxed, another approximation commonly made in GCMs. Model errors (differences) caused by the Boussinesq and hydrostatic approximations are demonstrated to be of comparable magnitude. Differences induced by small changes in subgrid-scale parameterizations are at least as large. Therefore, non-Boussinesq and nonhydrostatic effects are most likely negligible with respect to other model uncertainties. However, because there is no additional cost incurred in using a pressure coordinate model, it is argued that non-Boussinesq modeling is preferable simply for tidiness. It is also concluded that even coarse-resolution GCMs can be sensitive to small perturbations in the dynamical equations.

On the Relationship between Decadal Buoyancy Anomalies and Variability of the Atlantic Meridional Overturning Circulation

AbstractOwing to the role of the Atlantic meridional overturning circulation (AMOC) in ocean heat transport, AMOC variability is thought to play a role in climate variability on a wide range of time scales. This paper focuses on the potential role of the AMOC in climate variability on decadal time scales. Coupled and ocean-only general circulation models run in idealized geometries are utilized to study the relationships between decadal AMOC and buoyancy variability and determine whether the AMOC plays an active role in setting sea surface temperature on decadal time scales. Decadal AMOC variability is related to changes in the buoyancy field along the western boundary according to the thermal wind relation. Buoyancy anomalies originate in the upper ocean of the subpolar gyre and travel westward as baroclinic Rossby waves. When the buoyancy anomalies strike the western boundary, they are advected southward by the deep western boundary current, leading to latitudinally coherent AMOC variability. The AMOC i...

Double-Diffusive Recipes. Part I: Large-Scale Dynamics of Thermohaline Staircases

AbstractThree-dimensional dynamics of thermohaline staircases are investigated using a series of basin-scale staircase-resolving numerical simulations. The computational domain and forcing fields are chosen to reflect the size and structure of the North Atlantic subtropical thermocline. Salt-finger transport is parameterized using the flux-gradient formulation based on a suite of recent direct numerical simulations. Analysis of the spontaneous generation of thermohaline staircases suggests that thermohaline layering is a product of the gamma instability, associated with the variation of the flux ratio with the density ratio . After their formation, numerical staircases undergo a series of merging events, which systematically increase the size of layers. Ultimately, the system evolves into a steady equilibrium state with pronounced layers 20–50 m thick. The size of the region occupied by thermohaline staircases is controlled by the competition between turbulent mixing and double diffusion. Assuming, in acc...

Ocean-Forced Ice-Shelf Thinning in a Synchronously Coupled Ice-Ocean Model

The first fully synchronous, coupled ice shelf-ocean model with a fixed grounding line and imposed upstream ice velocity has been developed using the MITgcm (Massachusetts Institute of Technology general circulation model). Unlike previous, asynchronous, approaches to coupled modeling our approach is fully conservative of heat, salt, and mass. Synchronous coupling is achieved by continuously updating the ice-shelf thickness on the ocean time step. By simulating an idealized, warm-water ice shelf we show how raising the pycnocline leads to a reduction in both ice-shelf mass and back stress, and hence buttressing. Coupled runs show the formation of a western boundary channel in the ice-shelf base due to increased melting on the western boundary due to Coriolis enhanced flow. Eastern boundary ice thickening is also observed. This is not the case when using a simple depth-dependent parameterized melt, as the ice shelf has relatively thinner sides and a thicker central “bulge” for a given ice-shelf mass. Ice-shelf geometry arising from the parameterized melt rate tends to underestimate backstress (and therefore buttressing) for a given ice-shelf mass due to a thinner ice shelf at the boundaries when compared to coupled model simulations.

Dynamic Adjustment of the Ocean Circulation to Self-Attraction and Loading Effects

The oceanic response to surface loading, such as that related to atmospheric pressure, freshwater exchange, and changes in the gravity field, is essential to our understanding of sea level variability. In particular, so-called self-attraction and loading (SAL) effects caused by the redistribution of mass within the land‐atmosphere‐ ocean system can have a measurable impact on sea level. In this study, the nature of SAL-induced variability in sea level is examined in terms of its equilibrium (static) and nonequilibrium (dynamic) components, using ageneralcirculationmodelthatimplicitlyincludesthephysicsofSAL.TheadditionalSALforcingisderivedby decomposing ocean mass anomalies into spherical harmonics and then applying Love numbers to infer associatedcrustaldisplacementsandgravitationalshifts.ThisimplementationofSALphysicsincursonlyarelatively small computational cost. Effects of SAL on sea level amount to about 10% of the applied surface loading on average but depend strongly on location. The dynamic component exhibits large-scale basinwide patterns, with considerable contributions from subweekly time scales. Departures from equilibrium decrease toward longer time scales but are not totally negligible in many places. Ocean modeling studies should benefit from using a dynamical implementation of SAL as used here.