A thorough analysis of the stability of a coupled version of an inter-hemispheric 3-box model of Thermohaline Circulation (THC) is presented. This study follows a similarly structured analysis on an uncoupled version of the same model presented in Part I. We study how the strength of THC changes when the system undergoes forcings representing global warming conditions. Each perturbation to the initial equilibrium is characterized by the total radiative forcing realized, by the rate of increase, and by the North-South asymmetry. The choice of suitably defined metrics allows us to determine the boundary dividing the set of radiative forcing scenarios that lead the system to equilibria characterized by a THC pattern similar to the present one, from those that drive the system to equilibria where the THC is reversed. We also consider different choices for the atmospheric transport parameterizations and for the ratio between the high latitude to tropical radiative forcing. We generally find that fast forcings are more effective than slow forcings in disrupting the present THC pattern, forcings that are stronger in the northern box are also more effective in destabilizing the system, and that very slow forcings do not destabilize the system whatever their asymmetry, unless the radiative forcings are very asymmetric and the atmospheric transport is a relatively weak function of the meridional temperature gradient. The changes in the strength of the THC are primarily forced by changes in the latent heat transport in the hemisphere, because of its sensitivity to temperature that arises from the Clausius-Clapeyron relation.
Within a simple model context, the sensitivity and stability of the thermohaline circulation to finite amplitude perturbations is studied. A new approach is used to tackle this nonlinear problem. The method is based on the computation of the so-called Conditional Nonlinear Optimal Perturbation (CNOP) which is a nonlinear generalization of the linear singular vector approach (LSV). It is shown that linearly stable thermohaline circulation states can become nonlinearly unstable and the properties of the perturbations with optimal nonlinear growth are determined. An asymmetric nonlinear response …
Using the coupled climate model CLIMBER-3a, we investigate changes in sea surface elevation due to a weakening of the thermohaline circulation (THC). In addition to a global sea level rise due to a warming of the deep sea, this leads to a regional dynamic sea level change which follows quasi-instantaneously any change in the ocean circulation. We show that the magnitude of this dynamic effect can locally reach up to ~1m, depending on the initial THC strength. In some regions the rate of change can be up to 20-25 mm/yr. The emerging patterns are discussed with respect to the oceanic circulation…
The ocean thermohaline circulation, also called meridional overturning circulation, is caused by water density contrasts. This circulation has large capacity of carrying heat around the globe and it thus affects the energy budget and further affects the climate. We consider a thermohaline circulation model in the meridional plane under external wind forcing. We show that, when there is no wind forcing, the stream function and the density fluctuation (under appropriate metrics) tend to zero exponentially fast as time goes to infinity. With rapidly oscillating wind forcing, we obtain an averagin…
We reconsider the problem of the stability of the thermohaline circulation as described by a two-dimensional Boussinesq model with mixed boundary conditions. We determine how the stability properties of the system depend on the intensity of the hydrological cycle. We define a two-dimensional parameters' space descriptive of the hydrology of the system and determine, by considering suitable quasi-static perturbations, a bounded region where multiple equilibria of the system are realized. We then focus on how the response of the system to finite-amplitude surface freshwater forcings depends on t…
The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic chang…
A thorough analysis of the stability of the uncoupled Rooth interhemispheric 3-box model of thermohaline circulation (THC) is presented. The model consists of a northern high latitudes box, a tropical box, and a southern high latitudes box, which respectively correspond to the northern, tropical and southern Atlantic ocean. We adopt restoring boundary conditions for the temperature variables and flux boundary conditions for the salinity variables. We study how the strength of THC changes when the system undergoes forcings that are analogous to those of global warming conditions by applying to …
In this work, we study the impact of non-Gaussian alpha-stable Levy motion on transitions between metastable equilibrium states (or attractors) in a stochastic Stommel two-box model for thermohaline circulation (THC). By maximizing the probability density of the solution process associated with a nonlocal Fokker-Planck equation, we compute maximal likely pathways and identify corresponding maximal likely stable equilibrium states. Our numerical results indicate weakened THC may be induced by perturbation with very small noise intensity in a certain range of stability index. Moreover, larger no…
The main objective of this and its accompanying articles is to derive a mathematical theory associated with the thermohaline circulations (THC). This article provides a general transition and stability theory for the Boussinesq system, governing the motion and states of the large-scale ocean circulation. First, it is shown that the first transition is either to multiple steady states or to oscillations (periodic solutions), determined by the sign of a nondimensional parameter $K$, depending on the geometry of the physical domain and the thermal and saline Rayleigh numbers. Second, for both the…
The relatively warm climate found in the North- Western Europe is due to the gulf stream that circulates warm saline water from southern latitudes to Europe. In North Atlantic ocean the stream gives out a large amount of heat, cools down and sinks to the bottom to complete the Thermohaline circulation. There is considerable debate on the stability of the stream to inputs of fresh water from the melting ice in Greenland and Arctic. The circulation, being switched off, will have massive impact on the climate of Europe. Intergovernmental panel on climate change (IPCC) has warned of this danger in…
A combination of analytical and numerical techniques are used to efficiently determine the qualitative and quantitative behaviour of a one-basin zonally averaged thermohaline circulation ocean model. In contrast to earlier studies which use time stepping to find the steady solutions, the steady state equations are first solved directly to obtain the multiple equilibria under identical mixed boundary conditions. This approach is based on the differentiability of the governing equations and especially the convection scheme. A linear stability analysis is then performed, in which the normal modes…
Predictability of the North Atlantic thermohaline circulation (THC) variability as simulated in the GFDL coupled ocean-atmosphere general circulation model is established for a set of ensemble experiments. The ensembles consist of identical oceanic initial conditions underneath a model atmosphere chosen randomly from the model climatology. This experimental design is based on the separation in time scales present in the model which motivates the assumption that the predictability deduced from these ensembles provides an upper limit to the model's THC predictability. The climatology is taken fr…
The present study investigates how global thermodynamic properties of the climate system are affected by the changes in the intensity of the imposed oceanic heat transport in an atmospheric general circulation model in aqua-planet configuration. Increasing the poleward oceanic heat transport results in an overall increase in the surface temperature and a decrease in the equator-to-pole surface temperature difference as a result of the ice-albedo feedback. Following the classical ansatz by Stone, the atmospheric heat transport changes in such a way that the total poleward heat transport remains…
The global ocean overturning circulation, critically dependent on the global density stratification, plays a central role in regulating climate evolution. While it is well-known that the global stratification profile exhibits a strong dependence to Southern Ocean dynamics and in particular to wind and buoyancy forcing, we demonstrate here that the stratification is also acutely sensitive to the mesoscale eddy energy dissipation time-scale. Within the context of a global ocean circulation model with an energy constrained mesoscale eddy parameterization, it is shown that modest variations in the…
This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical approximations and does not employ additional phenomenological arguments to the model. The new approximate deconvolution model is tested in the numerical simulation of the wind-driven circulation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics. The model employs the barotropic vorticity equation driven by a symmetric double-gyre wind fo…
In the framework of the PARIS Beta project, fundamental milestones have been reached for the definition of future GNSS-R (Global Navigation Satellite System signal Reflections) altimetry missions (the PARIS concept). The most important one is the confirmation of the significant impact that GNSS-R data can have on mesoscale oceanography, as we discuss here. In this report, we first briefly review the contribution of satellite altimetry to mesoscale oceanography. We then summarise recent results obtained on the mapping capabilities of existing and future altimeter missions. From these analyses, …
The complexity of comprehensive ocean models poses an important question for parameterisations: is there a minimum set of equations that should be parameterised, on the one hand, to reduce the development to a minimum, and, on the other hand, to ensure an accurate representation of large-scale flow patterns? This work seeks to answer this to assist modern parameterisations be more selective in their targets. For this, we considered a North Atlantic configuration of the MIT general circulation model and studied contributions of different model equations to the accuracy of representation of the …
A single-layer, quasi-geostrophic (QG), large-scale ocean circulation model is developed in this paper to study available ocean current energy potentials harnessed by using the ocean current turbines. Power extraction is modeled by adding a parameterized Rayleigh friction term in the barotropic vorticity equation. Numerical assessments are performed by simulating a set of mid-latitude ocean basins in the beta plane, which are standard prototypes of more realistic ocean dynamics considering inter-decadal variability in turbulent equilibrium. A sensitivity analysis with respect to the turbine pa…
Since the advent of satellite altimetry, our perception of the oceanic circulation has brought into focus the pervasiveness of mesoscale eddies that have typical scales of tens to hundreds of kilometers [5], are the ocean's analogue of weather systems, and are often thought of as the peak of the ocean's kinetic energy (KE) wavenumber spectrum [7, 19, 23]. Yet, our understanding of the ocean's spatial scales has been derived mostly from Fourier analysis in small representative regions (e.g. [16, 14, 4]), typically a few hundred kilometers in size, that cannot capture the vast dynamic range at p…
Climate and ocean circulation changes toward a modern snowball Earth
Japan Agency for Marine-Earth Science and Technology（日本海洋地球科学技术局）；Earth-Life Science Institute (ELSI), Institute of Future Science, Institute of Science Tokyo（东京科学大学未来科学研究所生命起源研究所）；Atmosphere and Ocean Research Institute, The University of Tokyo（东京大学大气海洋研究所）；University of the Ryukyus（冲绳大学）；Department of Geophysics, Graduate School of Science, Tohoku University（东北大学理学研究科地球物理学科）；National Institute of Polar Research（国立极地研究所）；The Graduate University for Advanced Studies, SOKENDAI（综合研究大学院大学）
A box model of the inter-hemispheric Atlantic meridional overturning circulation is developed, including a variable pycnocline depth for the tropical and subtropical regions. The circulation is forced by winds over a periodic channel in the south and by freshwater forcing at the surface. The model is aimed at investigating the ocean feedbacks related to perturbations in freshwater forcing from the atmosphere, and to changes in freshwater transport in the ocean. These feedbacks are closely connected with the stability properties of the meridional overturning circulation, in particular in respon…
Internal redox reactions may irreversibly alter the mantle composition and volatile inventory of terrestrial and super-Earth exoplanets and affect the prospects for atmospheric observations. The global efficacy of these mechanisms, however, hinges on the transfer of reduced iron from the molten silicate mantle to the metal core. Scaling analysis indicates that turbulent diffusion in the internal magma oceans of sub-Neptunes can kinetically entrain liquid iron droplets and quench core formation. This suggests that the chemical equilibration between core, mantle, and atmosphere may be energetica…
The interdecadal variability of a stochastically forced four-box model of the oceanic meridional thermohaline circulation (THC) is described and compared to the THC variability in the coupled ocean-atmosphere GCM of Delworth, Manabe, and Stouffer (1993). The box model is placed in a linearly stable thermally dominant mean state under mixed boundary conditions. A linear stability analysis of this state reveals one damped oscillatory THC mode in addition to purely damped modes. The variability of the model under a moderate amount of stochastic forcing, meant to emulate the random variability of …
The global stratification and circulation of the ocean and their sensitivities to changes in forcing depend crucially on the representation of the mesoscale eddy field. Here, a geometrically informed and energetically constrained parameterization framework for mesoscale eddies --- termed GEOMETRIC --- is proposed and implemented in three-dimensional primitive equation channel and sector models. The GEOMETRIC framework closes mesoscale eddy fluxes according to the standard Gent--McWilliams scheme, but with the eddy transfer coefficient constrained by the depth-integrated eddy energy field, prov…
A general circulation model of intermediate complexity with an idealized earthlike aquaplanet setup is used to study the impact of changes in the oceanic heat transport on the global atmospheric circulation. Focus is put on the Lorenz energy cycle and the atmospheric mean meridional circulation. The latter is analysed by means of the Kuo-Eliassen equation. The atmospheric heat transport compensates the imposed oceanic heat transport changes to a large extent in conjunction with significant modification of the general circulation. Up to a maximum about 3PW, an increase of the oceanic heat trans…
We present a set of idealised numerical experiments of a solstitial aquaplanet ocean and examine the thermodynamic and dynamic implications of surface gravity waves (SGWs) upon its mean state. The aquaplanet's oceanic circulation is dominated by an equatorial zonal jet and four Ekman driven meridional overturning circulation (MOC) cells aligned with the westerly atmospheric jet streams and easterly trade winds in both hemispheres. Including SGW parameterization (representing modulations of air-sea momentum fluxes, Langmuir circulation and Stokes-Coriolis force) increases mixed layer vertical m…
Atmosphere and ocean are coupled via air-sea interactions. The atmospheric conditions fuel the ocean circulation and its variability, but the extent to which ocean processes can affect the atmosphere at decadal time scales remains unclear. In particular, such low-frequency variability is difficult to extract from the short observational record, meaning that climate models are the primary tools deployed to resolve this question. Here, we assess how the ocean's intrinsic variability leads to patterns of upper-ocean heat content that vary at decadal time scales. These patterns have the potential …
A model of aluminium has been developed and implemented in an Ocean General Circulation Model (NEMO-PISCES). In the model, aluminium enters the ocean by means of dust deposition. The internal oceanic processes are described by advection, mixing and reversible scavenging. The model has been evaluated against a number of selected high-quality datasets covering much of the world ocean, especially those from the West Atlantic Geotraces cruises of 2010 and 2011. Generally, the model results are in fair agreement with the observations. However, the model does not describe well the vertical distribut…
Recent Atmosphere-Ocean Coupled General Circulation Model (AOGCM) simulations of the twentieth century climate, which account for anthropogenic and natural forcings, make it possible to study the origin of long-term temperature correlations found in the observed records. We study ensemble experiments performed with the NCAR PCM for 10 different historical scenarios, including no forcings, greenhouse gas, sulfate aerosol, ozone, solar, volcanic forcing and various combinations, such as it natural, anthropogenic and all forcings. We compare the scaling exponents characterizing the long-term corr…
Of profound astrobiological interest, Enceladus appears to have a global subsurface ocean that is salty, indicating water-rock reaction at present or in the past, important for its habitability. Here, we investigate how salinity and the partition of heat production between the silicate core and the ice shell affect ocean dynamics and the associated heat transport -- a key factor that determines the equilibrium ice shell geometry. Assuming steady state conditions, we show that the meridional overturning circulation of the ocean, driven by heat and salt exchange with the ice, has opposing signs …
The Meridional Overturning Circulation (MOC) in the Southern Ocean is investigated using hydrographic observations combined with satellite observations of sea-surface height. A three-dimensional (spatial and vertical) estimate of the isopycnal eddy-diffusivity in the Southern Ocean is obtained using the theory of Ferrari & Nikurashin (2010), that includes the influence of suppression of the diffusivity by the strong, time-mean flows. It is found that the eddy diffusivity is enhanced at depth, reaching a maximum at the "critical layer" near 1000m. The estimate of diffusivity is used with a simp…
Interaction between atmospheric mid-latitude flow and wind-driven ocean circulation is studied coupling two idealized low-order spectral models. The barotropic Charney-DeVore model with three components simulates a bimodal mid-latitude atmospheric circulation in a channel with two stable flow patterns induced by topography. The wind-driven ocean double gyre circulation in a square basin (of half the channel length) is modeled by an equivalent barotropic formulation of the Veronis model with 21 components, which captures Rossby-wave dynamics and nonlinear decadal variability. When coupled, the …
The Meridional Overturning Circulation (MOC) is a system of surface and deep currents encompassing all ocean basins, crucial to the Earth's climate. Detecting potential climatic changes in the MOC first requires a careful characterisation of its inherent variability. Key components of the MOC are the Atlantic MOC (AMOC) and the Antarctic Circumpolar Current (ACC). The role of boundary properties in determining the AMOC and ACC is investigated, as a function of cross-sectional coordinate and depth, using a hierarchy of general circulation models. The AMOC is decomposed as the sum of near-surfac…
Dissolved manganese (Mn) is a biologically essential element, and its oxidised form is involved in the removal of trace elements from ocean waters. Recently, a large number of highly accurate Mn measurements have been obtained in the Atlantic, Indian and Arctic Oceans as part of the GEOTRACES programme. The goal of this study is to combine these new observations with state-of-the-art modelling to give new insights into the main sources and redistribution of Mn throughout the ocean. To this end, we simulate the distribution of dissolved Mn using a global-scale circulation model. This first mode…
The mechanism that causes an interdecadal oscillation in a coarse resolution sector ocean model forced by mixed boundary conditions is studied. The oscillation is characterized by large fluctuations in convective activity and air/sea heat exchange on a decadal time scale. When the convective activity is large, a strengthening of the southeastward surface flow advects more relatively fresh water from the northwestern part of the basin into the convective area, which reduces the convective activity. Similarly, when the convective activity is small, the flow of relatively fresh water is weak, whi…
To close the overturning circulation, dense bottom water must upwell via turbulent mixing. Recent studies have identified thin bottom boundary layers (BLs) as locations of intense upwelling, yet it remains unclear how they interact with and shape the large-scale circulation of the abyssal ocean. The current understanding of this BL--interior coupling is shaped by 1D theory, suggesting that variations in locally produced BL transport generate exchange with the interior and thus a global circulation. Until now, however, this picture has been based on a 1D theory that fails to capture the local e…
We construct a climatology of Lagrangian coherent structures (LCSs), the concealed skeleton that shapes transport, with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy-Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent Lagrangian circulation patterns. cLCSs strongly constrain the ensemble-mean Lagrangian circulation of the instantaneous model velocity, thus we show that a climatological velocity may preserve meaningful transport information. Also, the …
In this paper, we set forth a 3-D ocean model of the radioactive trace isotopes Th-230 and Pa-231. The interest arises from the fact that these isotopes are extensively used for investigating particle transport in the ocean and reconstructing past ocean circulation. The tracers are reversibly scavenged by biogenic and lithogenic particles. Our simulations of Th-230 and Pa-231 are based on the NEMO-PISCES ocean biogeochemistry general circulation model, which includes biogenic particles, namely small and big particulate organic carbon, calcium carbonate and biogenic silica. Small and big lithog…
The distribution of dissolved aluminium in the West Atlantic Ocean shows a mirror image with that of dissolved silicic acid, hinting at intricate interactions between the ocean cycling of Al and Si. The marine biogeochemistry of Al is of interest because of its potential impact on diatom opal remineralisation, hence Si availability. Furthermore, the dissolved Al concentration at the surface ocean has been used as a tracer for dust input, dust being the most important source of the bio-essential trace element iron to the ocean. Previously, the dissolved concentration of Al was simulated reasona…
Density and sea level changes weaken the Atlantic Meridional Overturning Circulation through ocean bottom pressure
Rosenstiel School of Marine, Atmospheric, and Earth Science, University of Miami（迈阿密大学罗斯恩施泰尔海洋、大气和地球科学学院）；National Oceanography Centre, Southampton（南安普敦国家海洋中心）
Persistent memory and tail-risk amplification in Atlantic Meridional Overturning Circulation variability: a Volterra integral framework calibrated with CMIP6
Faculty of Engineering, Universidad del Desarrollo（发展大学工程学院）
Any type of non-buoyant material in the ocean is transported horizontally by currents during its sinking journey. This lateral transport can be far from negligible for small sinking velocities. To estimate its magnitude and direction, the material is often modelled as a set of Lagrangian particles advected by current velocities that are obtained from Ocean General Circulation Models (OGCMs). State-of-the-art OGCMs are strongly eddying, similar to the real ocean, providing results with a spatial resolution on the order of 10 km on a daily frequency. While the importance of eddies in OGCMs is we…
We address the question of how to use a machine learned parameterization in a general circulation model, and assess its performance both computationally and physically. We take one particular machine learned parameterization \cite{Guillaumin1&Zanna-JAMES21} 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…
In this study, we focus on Langmuir turbulence in the deep ocean with the presence of a large macroalgal farm using a Large Eddy Simulation method. The wave-current interactions are modelled by solving the wave-averaged equations. The hydrodynamic process over the farm is found to drive a persistent flow pattern similar to Langmuir circulations but is locked in space across the farm. These secondary circulations are generated because the cross-stream shear produced by the rows of canopy elements leads to a steady vertical vorticity field, which is then rotated to the downstream direction under…
Quantifying the mechanisms of tracer dispersion in the ocean remains a central question in oceanography, for problems ranging from nutrient delivery to phytoplankton, to the early detection of contaminants. Most analyses have been based on Lagrangian concepts of transport, focusing on the identification of features minimizing fluid exchange among regions, or more recently on network tools which focus on connectivity and transport pathways. Neither of these approaches allows ranking the geographical sites of major water passage and selecting them so that they monitor waters coming from separate…
The climate impact of ocean gateway openings during the Eocene-Oligocene transition is still under debate. Previous model studies employed grid resolutions at which the impact of mesoscale eddies has to be parameterized. We present results of a state-of-the-art eddy-resolving global ocean model with a closed Drake Passage, and compare with results of the same model at non-eddying resolution. An analysis of the pathways of heat by decomposing the meridional heat transport into eddy, horizontal, and overturning circulation components indicates that the model behavior on the large scale is qualit…
