Numerical Simulation of the Regional Ocean Circulation in the Coastal Areas of China

The regional ocean circulation in the coastal areas of China (including a part of the western PacificOcean, the South China Sea and the Bay of Bengal et al.) is simulated by using the improved Princeton University ocean circulation model (POM). Compared with the modeling results obtained by the large-scaleocean general circulation model (OGCM), the basic ocean circulation features simulated by the regionalocean circulation model al-e in good agreement with that simulated by OGCM and some detailed characteristics such as the regional ocean circulation, sea temperature, salinity and flee sea surface height have alsobeen obtained which are in good accord with the observations. These results indicate that the regional oceancirculation model has good capability to produce the legional ocean circulation characteristics and it can beused to develop coupled legional ocean-atmospheric model systems.

An extended variable-grid global ocean circulation model and its preliminary results of the equatorial Pacific circulation

To investigate the interaction between the tropical Pacific and China seas a variable-grid global ocean circulation model with fine grid covering the area from 20°S to 50°N and from 99° to 150°E is developed. Numerical computation of the annually cyclic circulation fields is performed. The results of the annual mean zonal currents and deep to abyssal western boundary currents in the equatorial Pacific Ocean are reported. The North Equatorial Current,the North Equatorial Countercurrent, the South Equatorial Current and the Equatorial Undercurrent are fairly well simulated. The model well reproduces the northward flowing abyssal western boundary current.From the model results a lower deep western boundary current east of the Bismarck-Solomon-New Hebrides Island chain at depths around 2 000 m has been found. The model results also show that the currents in the equatorial Pacific Ocean have multi-layer structures both in zonal currents and western boundary currents, indicating that the global ocean overturning thermohaline circulation appears of multi-layer pattern.

Review on observational studies of western tropical Pacific Ocean circulation and climate

The Western Tropical Pacific(WTP) Ocean holds the largest area of warm water(>28℃) in the world ocean referred to as the Western Pacific Warm Pool(WPWP),which modulates the regional and global climate through strong atmospheric convection and its variability.The WTP is unique in terms of its complex 3-D ocean circulation system and intensive multiscale variability,making it crucial in the water and energy cycle of the global ocean.Great advances have been made in understanding the complexity of the WTP ocean circulation and associated climate impact by the international scientific community since the 1960 s through field experiments.In this study,we review the evolving insight to the 3-D structure and multi-scale variability of the ocean circulation in the WTP and their climatic impacts based on in-situ ocean observations in the past decades,with emphasis on the achievements since 2000.The challenges and open que stions remaining are reviewed as well as future plan for international study of the WTP ocean circulation and climate.

A two-time-level split-explicit ocean circulation model (MASNUM) and its validation

A two-time-level, three-dimensional numerical ocean circulation model（named MASNUM） was established with a two-level, single-step Eulerian forward-backward time-differencing scheme. A mathematical model of large-scale oceanic motions was based on the terrain-following coordinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-backward method was adopted to replace the most preferred leapfrog scheme as the time-differencing method for both barotropic and baroclinic modes. The forward-backward method is of second-order of accuracy, computationally efficient by requiring only one function evaluation per time step, and free of the computational mode inherent in the three-level schemes. This method is superior to the leapfrog scheme in that the maximum time step of stability is twice as large as that of the leapfrog scheme in staggered meshes thus the computational efficiency could be doubled. A spatial smoothing method was introduced to control the nonlinear instability in the numerical integration. An ideal numerical experiment simulating the propagation of the equatorial Rossby soliton was performed to test the amplitude and phase error of this new model. The performance of this circulation model was further verified with a regional（northwest Pacific） and a quasi-global（global ocean simulation with the Arctic Ocean excluded） simulation experiments. These two numerical experiments show fairly good agreement with the observations. The maximum time step of stability in these two experiments were also investigated and compared between this model and that model which adopts the leapfrog scheme.

Wind-Driven Ocean Circulation in Shallow Water Lattice Boltzmann Model

A lattice Boltzmann (LB) model with overall second-order accuracy is applied to the 1.5-layer shallow water equation for a wind-driven double-gyre ocean circulation. By introducing the second-order integral approximation for the collision operator, the model becomes fully explicit. In this case, any iterative technique is not needed. The Coriolis force and other external forces are included in the model with second-order accuracy, which is consistent with the discretized accuracy of the LB equation. The numerical results show correct physics of the ocean circulation driven by the double-gyre wind stress with different Reynolds numbers and different spatial resolutions. An intrinsic low-frequency variability of the shallow water model is also found. The wind-driven ocean circulation exhibits subannual and interannual oscillations, which are comparable to those of models in which the conventional numerical methods are used.

Modeling the ocean circulation in the Bering Sea

With parameterized wave mixing, the circulation and the tidal current in the Bering Sea were simulated simultaneously using the three-dimensional Princeton Ocean Model. The simulated circulation pattern in the deep basin is relatively stable, cyclonic, and has little seasonal change. The Bering Slope Current between 200-1000 m isobaths was estimated to be 5 Sv in volume transport. The Kamchatka Current was estimated to be 20 Sv off the Kamchatka Peninsula. The Bering shelf circulations vary with season, driven mainly by wind. These features are consistent with historical esti- mates. A counter current was captured flowing southeastward approximately along the 200 m isobath of the Bering Slope, opposite to the northwestward Bering Slope Current, which needs to be validated by observations. An upwelling current is located in the shelf break （ 120-1000 m） area, which may imply the vertical advection of nutrients for supporting the Bering Sea Green Belt seasonal plankton blooms in the breakslope area. The Bering Slope Current is located in a downwelling area.

Wind-Driven,Double-Gyre,Ocean Circulation in a Reduced-Gravity,2.5-Layer,Lattice Boltzmann Model

A coupled lattice Boltzmann （LB） model with second-order accuracy is applied to the reduced-gravity, shallow water, 2.5-layer model for wind-driven double-gyre ocean circulation. By introducing the secondorder integral approximation for the collision operator, the model becomes fully explicit. The Coriolis force and other external forces are included in the model with second-order accuracy, which is consistent with the discretization accuracy of the LB equation. The feature of the multiple equilibria solutions is found in the numerical experiments under different Reynolds numbers based on this LB scheme. With the Reynolds number increasing from 3000 to 4000, the solution of this model is destabilized from the anti-symmetric double-gyre solution to the subtropic gyre solution and then to the subpolar gyre solution. The transitions between these equilibria states are also found in some parameter ranges. The time-dependent variability of the circulation based on this LB simulation is also discussed for varying viscosity regimes. The flow of this model exhibits oscillations with different timescales varying from subannual to interannual. The corresponding statistical oscillation modes are obtained by spectral analysis. By analyzing the spatiotemporal structures of these modes, it is found that the subannual oscillation with a 9-month period originates from the barotropic Rossby basin mode, and the interarmual oscillations with periods ranging from 1.5 years to 4.6 years originate from the recirculation gyre modes, which include the barotropic and the baroclinic recirculation gyre modes.

The numerical simulation of Pacific Ocean circulation with five-level model

A five-level oceanic primitive equation model has been developed. This model is integrated numerically with annual mean wind stress and heat flux at sea surface for 30 a. The ocean circulations tend to quasi-stability. The simulated results show that the computed annual mean currents and sea surface temperature agree well with the observations.

A modification to the Munk wind-driven ocean circulation theory

In order to fulfill the no-slip condition at the western and eastern boundaries of the ocean basin, introduced ＂effective wind stress＂, which has much larger spatial variations towards the boundaries than in the ocean interior. The effective wind stress can thus be decomposed into spatially slow-varying and fast varying components. Careful scale analysis on the classical Munk winddriven ocean circulation theory, which consists of the interior Sverdrup flow and the western boundary current but of no eastern boundary current, shows that the wind stress curl appearing in the Sverdrup equation must have negligible spatial variations. In the present model the spatially slow-varying component of the wind stress appears in the Sverdrup equation, and the spatially fastvarying component becomes the forcing term of the boundary equations. As a result, in addition to the classical Munk solution the present model has an extra term at the western boundary which （Northern Hemisphere） increases the northward transport as well as the southward return transport, and has a term at the eastern boundary corresponding to the eastern boundary current.

Pacific-Indian interocean circulation of the Antarctic Intermediate Water around South Australia

On the basis of the salinity distribution of isopycnal（σ_0=27.2 kg/m^3） surface and in salinity minimum, the Antarctic Intermediate Water（AAIW） around South Australia can be classified into five types corresponding to five regions by using in situ CTD observations. Type 1 is the Tasman AAIW, which has consistent hydrographic properties in the South Coral Sea and the North Tasman Sea. Type 2 is the Southern Ocean（SO） AAIW, parallel to and extending from the Subantarctic Front with the freshest and coldest AAIW in the study area. Type 3 is a transition between Type 1 and Type 2. The AAIW transforms from fresh to saline with the latitude declining（equatorward）. Type 4, the South Australia AAIW, has relatively uniform AAIW properties due to the semienclosed South Australia Basin. Type 5, the Southeast Indian AAIW, progressively becomes more saline through mixing with the subtropical Indian intermediate water from south to north. In addition to the above hydrographic analysis of AAIW, the newest trajectories of Argo（Array for real-time Geostrophic Oceanography） floats were used to constructed the intermediate（1 000 m water depth） current field, which show the major interocean circulation of AAIW in the study area. Finally, a refined schematic of intermediate circulation shows that several currents get together to complete the connection between the Pacific Ocean and the Indian Ocean. They include the South Equatorial Current and the East Australia Current in the Southwest Pacific Ocean, the Tasman Leakage and the Flinders Current in the South Australia Basin, and the extension of Flinders Current in the southeast Indian Ocean.

The influence of explicit tidal forcing in a climate ocean circulation model

The eight main tidal constituents have been implemented in the global ocean general circulation model with approximate 1° horizontal resolution.Compared with the observation data,the patterns of the tidal amplitudes and phases had been simulated fairly well.The responses of mean circulation,temperature and salinity are further investigated in the global sense.When implementing the tidal forcing,wind-driven circulations are reduced,especially those in coastal regions.It is also found that the upper cell transport of the Atlantic meridional overturning circulation（AMOC） reduces significantly,while its deep cell transport is slightly enhanced from 9×106m3/s to 10×106 m3/s.The changes of circulations are all related to the increase of a bottom friction and a vertical viscosity due to the tidal forcing.The temperature and salinity of the model are also significantly affected by the tidal forcing through the enhanced bottom friction,mixing and the changes in mean circulation.The largest changes occur in the coastal regions,where the water is cooled and freshened.In the open ocean,the changes are divided into three layers：cooled and freshened on the surface and below 3 000 m,and warmed and salted in the middle in the open ocean.In the upper two layers,the changes are mainly caused by the enhanced mixing,as warm and salty water sinks and cold and fresh water rises;whereas in the deep layer,the enhancement of the deep overturning circulation accounts for the cold and fresh changes in the deep ocean.

Influences of Freshwater from Major Rivers on Global Ocean Circulation and Temperatures in the MIT Ocean General Circulation Model

Responses of global ocean circulation and temperature to freshwater runoff from major rivers were studied by blocking regional runoff in the global ocean general circulation model （OGCM） developed at the Massachusetts Institute of Technology. Runoff into the tropical Atlantic, the western North Pacific, and the Bay of Bengal and northern Arabian Sea were selectively blocked. The blocking of river runoff first resulted in a salinity increase near the river mouths （2 practical salinity units）. The saltier and, therefore, denser water was then transported to higher latitudes in the North Atlantic, North Pacific, and southern Indian Ocean by the mean currents. The subsequent density contrasts between northern and southern hemispheric oceans resulted in changes in major ocean currents. These anomalous ocean currents lead to significant temperature changes （I^C -2~C） by the resulting anomalous heat transports. The current and temperature anomalies created by the blocked river runoff propagated from one ocean basin to others via coastal and equatorial Kelvin waves. This study suggests that river runoff may be playing an important role in oceanic salinity, temperature, and circulations; and that partially or fully blocking major rivers to divert freshwater for societal purposes might significantly change ocean salinity, circulations, temperature, and atmospheric climate. Further studies are necessary to assess the role of river runoff in the coupled atmosphere-ocean system.

Seasonal variability of the isopycnal surface circulation in the South China Sea derived from a variable-grid global ocean circulation model

In this study, we develop a variable-grid global ocean general circulation model （OGCM） with a fine grid （1/6）° covering the area from 20°S-50°N and from 99°-150°E, and use the model to investigate the isopycnal surface circulation in the South China Sea （SCS）. The simulated results show four layer structures in vertical： the surface and subsurface circulation of the SCS are characterized by the monsoon driven circulation, with basin-scaled cyclonic gyre in winter and anti-cyclonic gyre in summer. The intermediate layer circulation is opposite to the upper layer, showing anti-cyclonic gyre in winter but cyclonic gyre in summer. The circulation in the deep layer is much weaker in spring and summer, with the maximum velocity speed below 0.6 cm/s. In fall and winter, the SCS deep layer circulation shows strong east boundary current along the west coast of Philippine with the velocity speed at 1.5 m/s, which flows southward in fall and northward in winter. The results have also revealed a fourlayer vertical structure of water exchange through the Luzon Strait. The dynamics of the intermediate and deep circulation are attributed to the monsoon driving and the Luzon Strait transport forcing.

Algorithm for simulating ocean circulation on a quantum computer

The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential equations with multiple variables.In this paper,we present for the first time an algorithm for simulating ocean circulation on a quantum computer to achieve a computational speedup.Our approach begins with using primitive equations describing the ocean dynamics and then discretizing these equations in time and space.It results in several linear system of equations(LSE)with sparse coefficient matrices.We solve these sparse LSE using the variational quantum linear solver that enables the present algorithm to run easily on near-term quantum computers.Additionally,we develop a scheme for manipulating the data flow in the algorithm based on the quantum random access memory and l∞norm tomography technique.The efficiency of our algorithm is verified using multiple platforms,including MATLAB,a quantum virtual simulator,and a real quantum computer.The impact of the number of shots and the noise of quantum gates on the solution accuracy is also discussed.Our findings demonstrate that error mitigation techniques can efficiently improve the solution accuracy.With the rapid advancements in quantum computing,this work represents an important first step toward solving the challenging problem of simulating ocean circulation using quantum computers.

Numerical simulations of Atlantic meridional overturning circulation(AMOC)from OMIP experiments and its sensitivity to surface forcing

Atlantic meridional overturning circulation(AMOC)plays an important role in transporting heat meridionally in the Earth’s climate system and is also a key metrical tool to verify oceanic general circulation models.Two OMIP(Ocean Model Intercomparison Project phase 1 and 2)simulations with LICOM3(version 3 of the LASG/IAP Climate System Ocean Model)developed at the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics(LASG),Institute of Atmospheric Physics(IAP),are compared in this study.Both simulations well reproduce the fundamental characteristics of the AMOC,but the OMIP1 simulation shows a significantly stronger AMOC than the OMIP2 simulation.Because the LICOM3 configurations are identical between these two experiments,any differences between them must be attributed to the surface forcing data.Further analysis suggests that sea surface salinity(SSS)differences should be mainly responsible for the enhanced AMOC in the OMIP1 simulation,but sea surface temperature(SST)also play an unignorable role in modulating AMOC.In the North Atlantic,where deep convection occurs,the SSS in OMIP1 is more saline than that in OMIP1.We find that in the major region of deep convection,the change of SSS has more significant effect on density than the change of SST.As a result,the SSS was more saline than that in OMIP2,leading to stronger deep convection and subsequently intensify the AMOC.We conduct a series of numerical experiments with LICOM3,and the results confirmed that the changes in SSS have more significant effect on the strength of AMOC than the changes in SST.

NUMERICAL MODELLING OF THE QUASI-GLOBAL OCEAN CIRCULATION BASED ON POM

A free surface quasi-global ocean circulation model, Princeton Ocean Model(POM), was adopted to simulate the climatological circulation. The horizontal resolution of themodel was 1/2° x 1/2° with 16 vertical sigma layers. The initial temperature and salinity fieldsof the model were interpolated from the Levitus data, and the COADS (Comprehensive Ocean-AtmosphereData Set) monthly mean SST and wind fields were used as the surface forcing. The integral timelength is 6a. The main general circulation components such as the equatorial current, the equatorialundercurrent, the south and north equatorial currents, the Antarctic Circumpolar Current (ACC), theKuroshio and the Gulf Stream were well reconstructed. The volume transports of PN section and ACCa-gree well with the estimations on field survey. Up to now there is no global or quasi-globalcirculation model results u-sing POM in literature. Our results demonstrate that POM has soundability to simulate the coastal circulation as well as the general ocean circulation. And thisresult can provide open boundary conditions for fine resolution regional ocean circulation models.

Design and Numerical Simulation of an Arctic Ocean Circulation and Thermodynamic Sea－Ice Model

In this paper, the first version of a new Arctic Ocean circulation and thermodynamic sea-ice model is presentedby the authors based on the framework of a twenty-layer World Oceanic general circulation model developed byZhang et al. in 1994. The model's domain covers the Arctic Ocean and Greenland-Norwegian Seas with the horizontal resolution of 200 km×200 km on a stereographic projection plane. In vertical, the model uses the Eta-coordinate(Sigma modified to have quasi-horizontal coordinate surfaces) and has ten unevenly-spaced layers to cover the deepest water column of 3000 m. Two 150-year integrations of coupling the ocean circulation model with the sea-icemodel have been performed with seasonally cyclic surface boundary conditions. The only difference between the tWoexperiments is in the model's geography. Some preliminary analyses of the experimental results have been done focused on the following aspects: (1) surface layer temperature, salinity and current; (2) the' Atlantic Layer'; (3)sea-ice cover and its seasonal variation. In comparison with the available observational data, these results are acceptable with reasonable accuracy.

An ocean circulation model based on Eulerian forward-backward difference scheme and three-dimensional, primitive equations and its application in regional simulations

A two-time-level, three-dimensional numerical ocean circulation model is established with a two-level, single-step Eulerian time-difference scheme. The mathematical model of the large-scale oceanic motions is based on the terrain-following coo-rdinated, Boussinesq, Reynolds-averaged primitive equations of ocean dynamics. A simple but very practical Eulerian forward-back-ward method is adopted to replace the most preferred leapfrog scheme as the time-difference method for both barotropic and barocli-nic modes. The forward-backward method is of the second order of accuracy, requires only once of the function evaluation per time step, and is free of the computational mode inherent in the three-level schemes. It is superior in many respects to the original leapfrog and Asselin-filtered leapfrog schemes in the practical use. The performance of the newly-built circulation model is tested by simula-ting a barotropic （tides in marginal seas of China） and a baroclinic phenomenon （seasonal evolution of the Yellow Sea Cold Water Mass）, respectively. The three-year time histories of four prognostic variables obtained by the POM model and the two-time-level model are compared in a regional simulation experiment for the northwest Pacific to further show the reliability of the two-level scheme circulation model.

Advances in Studying Oceanic Circulation from Hydrographic Data with Applications in the South China Sea

Methods for studying oceanic circulation from hydrographic data are reviewed in the context of their applications in the South China Sea. These methods can be classified into three types according to their different dynamics as follows: (1) descriptive methods, (2) diagnostic methods without surface and bottom forcing, and (3) diagnostic methods with the above boundary forcing. The paper discusses the progress made in the above methods together with the advancement of study in the South China Sea circulation.

Modeling the Middle Jurassic ocean circulation

We present coupled ocean-sea-ice simulations of the Middle Jurassic（~165 Ma） when Laurasia and Gondwana began drifting apart and gave rise to the formation of the Atlantic Ocean. Since the opening of the Proto-Caribbean is not well constrained by geological records, configurations with and without an open connection between the Proto-Caribbean and Panthalassa are examined. We use a sea-floor bathymetry obtained by a recently developed three-dimensional（3D） elevation model which compiles geological, palaeogeographical and geophysical data. Our original approach consists in coupling this elevation model, which is based on detailed reconstructions of oceanic realms, with a dynamical ocean circulation model. We find that the Middle Jurassic bathymetry of the Central Atlantic and Proto-Caribbean seaway only allows for a weak current of the order of 2 Sv in the upper 1000 m even if the system is open to the West. The effect of closing the western boundary of the Proto-Caribbean is to increase transport related to barotropic gyres in the southern hemisphere and to change water properties, such as salinity, in the Neo-Tethys. Weak upwelling rates are found in the nascent Atlantic Ocean in the presence of this superficial current and we discuss their compatibility with deep-sea sedimentological records in this region.