Surfaces Of Constant Density Research Articles

Dynamical freeze-out criterion in event-by-event hydrodynamics

In hydrodynamical modelling of ultrarelativistic heavy-ion collisions the freeze-out is typically assumed to take place on a surface of constant temperature or energy density. In this work we apply a dynamical freeze-out criterion, which compares the hydrodynamical expansion rate with the pion scattering rate, to an event-by-event ideal hydrodynamics at the full RHIC collision energy. We present hadron spectra and elliptic flow calculated using (2+1)-dimensional ideal hydrodynamics, and show the differences between constant temperature and dynamical freeze-out criteria. We find that when the freeze-out ratio is fixed to one, the different freeze-out criteria lead to slightly different spectra and v2(pT) in the event-by-event calculations.

The response of superpressure balloons to gravity wave motions

Abstract. Superpressure balloons (SPB), which float on constant density (isopycnic) surfaces, provide a unique way of measuring the properties of atmospheric gravity waves (GW) as a function of wave intrinsic frequency. Here we devise a quasi-analytic method of investigating the SPB response to GW motions. It is shown that the results agree well with more rigorous numerical simulations of balloon motions and provide a better understanding of the response of SPB to GW, especially at high frequencies. The methodology is applied to ascertain the accuracy of GW studies using 12 m diameter SPB deployed in the 2010 Concordiasi campaign in the Antarctic. In comparison with the situation in earlier campaigns, the vertical displacements of the SPB were measured directly using GPS. It is shown using a large number of Monte Carlo-type simulations with realistic instrumental noise that important wave parameters, such as momentum flux, phase speed and wavelengths, can be retrieved with good accuracy from SPB observations for intrinsic wave periods greater than ca. 10 min. The noise floor for momentum flux is estimated to be ca. 10−4 mPa.

BAROCLINIC INSTABILITY IN STELLAR RADIATION ZONES

Surfaces of constant pressure and constant density do not coincide in differentially rotating stars. Stellar radiation zones with baroclinic stratification can be unstable. Instabilities in radiation zones are of crucial importance for angular momentum transport, mixing of chemical species and, possibly, for magnetic field generation. This paper performs linear analysis of baroclinic instability in differentially rotating stars. Linear stability equations are formulated for differential rotation of arbitrary shape and then solved numerically for rotation non-uniform in radius. As the differential rotation increases, r- and g-modes of initially stable global oscillations transform smoothly into growing modes of baroclinic instability. The instability can therefore be interpreted as stability loss to r- and g-modes excitation. Regions of stellar parameters where r- or g-modes are preferentially excited are defined. Baroclinic instability onsets at a very small differential rotation of below 1%. The characteristic time of instability growth is about one thousand rotation periods. Growing disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from baroclinic instability in differentially rotating radiation zones is, therefore, possible.

HIGH Q BPS MONOPOLE BAGS ARE URCHINS

It has been known for 30 years that 't Hooft–Polyakov monopoles of charge Q greater than one cannot be spherically symmetric. Five years ago, Bolognesi conjectured that, at some point in their moduli space, BPS monopoles can become approximately spherically symmetric in the high Q limit. In this paper, we determine the sense in which this conjecture is correct. We consider an SU(2) gauge theory with an adjoint scalar field, and numerically find configurations with Q units of magnetic charge and a mass which is roughly linear in Q, for example, in the case Q = 81 we present a configuration whose energy exceeds the BPS bound by about 54%. These approximate solutions are constructed by gluing together Q cones, each of which contains a single unit of magnetic charge. In each cone, the energy is largest in the core, and so a constant energy density surface contains Q peaks and thus resembles a sea urchin.

Rapid cross-density ocean mixing at mid-depths in the Drake Passage measured by tracer release

Diapycnal mixing (across density surfaces) is an important process in the global ocean overturning circulation. Mixing in the interior of most of the ocean, however, is thought to have a magnitude just one-tenth of that required to close the global circulation by the downward mixing of less dense waters. Some of this deficit is made up by intense near-bottom mixing occurring in restricted 'hot-spots' associated with rough ocean-floor topography, but it is not clear whether the waters at mid-depth, 1,000 to 3,000 metres, are returned to the surface by cross-density mixing or by along-density flows. Here we show that diapycnal mixing of mid-depth (∼1,500 metres) waters undergoes a sustained 20-fold increase as the Antarctic Circumpolar Current flows through the Drake Passage, between the southern tip of South America and Antarctica. Our results are based on an open-ocean tracer release of trifluoromethyl sulphur pentafluoride. We ascribe the increased mixing to turbulence generated by the deep-reaching Antarctic Circumpolar Current as it flows over rough bottom topography in the Drake Passage. Scaled to the entire circumpolar current, the mixing we observe is compatible with there being a southern component to the global overturning in which about 20 sverdrups (1 Sv = 10(6) m(3) s(-1)) upwell in the Southern Ocean, with cross-density mixing contributing a significant fraction (20 to 30 per cent) of this total, and the remainder upwelling along constant-density surfaces. The great majority of the diapycnal flux is the result of interaction with restricted regions of rough ocean-floor topography.

Declining Oxygen on the British Columbia Continental Shelf

The first thorough examination of oxygen concentrations in Canadian waters of the Pacific Ocean reveals several patterns in space and time. Sub-surface concentrations of oxygen tend to be lower in shelf waters than in deep-sea waters on the same isopycnal and lower in southern waters of the continental shelf than farther north. The lowest near-bottom concentration was 0.7 ml L−1 (31 μmol kg−1) in mid-shelf waters in summer off southwest Vancouver Island in the Juan de Fuca Eddy region. Oxygen concentration there declined at a rate of 0.019 ml L−1 y−1 (0.83 μmol kg−1 y−1) from 1979 to 2011. This decline is attributed mainly to changes in oxygen concentrations on the same density surfaces, rather than to changes in the depth of constant-density surfaces. A numerical simulation of ocean currents and nutrient concentrations in and surrounding the Juan de Fuca Eddy in summer reveals persistent upwelling into the centre of this eddy and slow bottom currents within the eddy. Upwelled water at bottom of the Juan de Fuca Eddy has water properties associated with the California Undercurrent on the 26.6 sigma-t surface at 200 m depth, where oxygen concentration is typically 2.0 ml L−1 (87 μmol kg−1) and declined at a rate of 0.025 ml L−1 y−1 (1.1 μmol kg−1 y−1) from 1981 to 2011, mainly as a result of changes on constant-density surfaces rather than to uplifting isopycnals. We propose that upwelling advects deep, oxygen-poor water onto the continental shelf bottom, and the slow bottom currents allow time for oxidation of organic material in bottom waters to further reduce the oxygen concentration. RÉSUMÉ [Traduit par la rédaction] Le premier examen approfondi des concentrations d'oxygène dans les eaux canadiennes de l'océan Pacifique révèle plusieurs configurations dans le temps et dans l'espace. Les concentrations d'oxygène sous la surface ont tendance à être plus faibles dans les eaux de la plate-forme continentale que dans les eaux de l'océan profond sur la même isopycne et plus faibles dans les eaux du sud de la plate-forme que plus loin au nord. La concentration la plus faible près du fond était de 0.7 ml L−1 (31 μmol kg−1) dans les eaux du milieu de la plate-forme en été au large du sud-ouest de l’île de Vancouver dans la région du remous de Juan de Fuca. Les concentrations en oxygène à cet endroit ont diminué au rythme de 0.019 ml L−1 a−1 (0.83 μmol kg−1 a−1) entre 1979 et 2011. Cette diminution est principalement attribuée aux changements dans les concentrations d'oxygène sur les surfaces d’égale densité plutôt qu'aux changements dans la profondeur des surfaces de densité constante. Une simulation numérique des courants océaniques et des concentrations de nutrients dans le remous de Juan de Fuca et dans les régions avoisinantes en été révèle des remontées d'eau froide persistantes vers le centre de ce remous et des courants de fond lents à l'intérieur du remous. L'eau qui a remonté au fond du remous de Juan de Fuca a des propriétés liées au sous-courant de Californie sur la surface sigma–t 26.6 à une profondeur de 200 m, où la concentration en oxygène est normalement de 2.0 ml L−1 (87 μmol kg−1), et a diminué au taux de 0.025 ml L−1 a−1 (1.1 μmol kg−1 a−1) de 1981 à 2011, principalement à cause des changements sur les surfaces de densité constante plutôt que du soulèvement des isopycnes. Nous pausons l'hypothèse que les remontées d'eau advectent des eaux profondes pauvres en oxygène au bas de la plate-forme continentale et que les lents courants de fond donnent le temps à l'oxydation de la matière organique dans les eaux de fond, ce qui réduit davantage la concentration de l'oxygène.

Evaluation of momentum and sensible heat fluxes in constant density coordinates: Application to superpressure balloon data during the VORCORE campaign

Expressions for momentum and heat fluxes using density as the vertical coordinate are derived. These are applied in the evaluation of fluxes using data from super‐pressure balloons drifting on constant density surfaces in the Antarctic lower stratosphere during the VORCORE campaign (September 2005 to February 2006). We focus on the core months of October and November. Vertical fluxes of zonal and meridional momentum are calculated using wind, pressure and height data and the vertical flux of sensible heat is calculated using temperature and height data. Calculations were performed in three band passes covering 1–13 h. We find that the largest fluxes are in the vicinity of the Antarctic Peninsula. In October the fluxes in the low period band pass (1–5 h) account for the main part of the total flux of zonal momentum, consistent with topographically forced waves. During November the vertical fluxes of zonal momentum are found mainly in longer period band passes, consistent with weaker winds. The peak campaign‐averaged flux of zonal momentum in the vicinity of the Antarctic Peninsula is ∼−30 mPa. These values are ∼60% larger over the peninsula than those inferred by other authors. The flux of zonal momentum provides a zonal body force of ∼5 m s−1 day−1 assuming a saturated spectrum. We infer downward sensible heat fluxes of ∼3 W m−2. The corresponding cooling rates assuming a saturated spectrum are ∼0.6 K day−1, a significant fraction of the net radiative imbalance in the springtime Antarctic lower stratosphere.

Observations of sound-speed fluctuations on the New Jersey continental shelf in the summer of 2006

Environmental sensors moored on the New Jersey continental shelf tracked constant density surfaces (isopycnals) for 35 days in the summer of 2006. Sound-speed fluctuations from internal-wave vertical isopycnal displacements and from temperature/salinity variability along isopycnals (spiciness) are analyzed using frequency spectra and vertical covariance functions. Three varieties of internal waves are studied: Diffuse broadband internal waves (akin to waves fitting the deep water Garrett/Munk spectrum), internal tides, and, to a lesser extent, nonlinear internal waves. These internal-wave contributions are approximately distinct in the frequency domain. It is found that in the main thermocline spicy thermohaline structure dominates the root mean square sound-speed variability, with smaller contributions coming from (in order) nonlinear internal waves, diffuse internal waves, and internal tides. The frequency spectra of internal-wave displacements and of spiciness have similar form, likely due to the advection of variable-spiciness water masses by horizontal internal-wave currents, although there are technical limitations to the observations at high frequency. In the low-frequency, internal-wave band the internal-wave spectrum follows frequency to the -1.81 power, whereas the spice spectrum shows a -1.73 power. Mode spectra estimated via covariance methods show that the diffuse internal-wave spectrum has a smaller mode bandwidth than Garrett/Munk and that the internal tide has significant energy in modes one through three.

Turbulent diapycnal mixing in the northwestern Pacific

Nearly vertical mixing in the oceans across surfaces of constant density (isopycnals), known as diapycnal mixing, transports heat, modifies water masses, and maintains stratification. This mixing needs to be included in models of large‐scale ocean circulation and climate models, but it is not fully understood. Some studies have suggested that wind is a key source of energy for diapycnal mixing in the deep ocean, but observational and modeling studies have been contradictory. To learn more, Jing et al. used data from recent hydrographic studies to study turbulent diapycnal mixing in the subtropical northwestern Pacific Ocean, a region that encompasses a range of ocean conditions, including both flat and rough seafloor. They examined spatial and seasonal variations as well as the role of eddies. They found that enhanced mixing occurred over rougher seafloor. Over flatter seafloor the researchers found that mixing is probably stirred by wind near the surface, with eddies playing an important role in enhancing mixing at greater depths. In the upper 600 meters of the ocean, the wind and diapycnal mixing varied seasonally, with stronger winds and mixing in winter and weaker winds and mixing in summer. This is different from the midlatitude northwestern Pacific, where seasonality of diapycnal mixing can be found at 1500‐meter depth. (Journal of Geophysical Research‐Oceans, doi:10.1029/2011JC007142, 2011)

On sampling the ocean using underwater gliders

[1] The sampling characteristics of an underwater glider are addressed through comparison with contemporaneous measurements from a ship survey using a towed vehicle. The comparison uses the underwater glider Spray and the towed vehicle SeaSoar north of Hawaii along 158°W between 22.75°N and 34.5°N. A Spray dive from the surface to 1000 m and back took 5.6 h and covered 5.3 km, resulting in a horizontal speed of 0.26 m s−1. SeaSoar undulated between the surface and 400 m, completing a cycle in 11 min while covering 2.6 km, for a speed of 3.9 m s−1. Adjacent profiles of temperature and salinity are compared between the two platforms to prove that each is accurate. Spray and SeaSoar data are compared through sections, isopycnal spatial series, and wave number spectra. The relative slowness of the glider results in the projection of high-frequency oceanic variability, such as internal waves, onto spatial structure. The projection is caused by Doppler smearing because of finite speed and aliasing due to discrete sampling. The projected variability is apparent in properties measured on depth surfaces or in isopycnal depth. No projected variability is seen in observations of properties on constant density surfaces because internal waves are intrinsically filtered. Wave number spectra suggest that projected variability affects properties at constant depth at wavelengths shorter than 30 km. These results imply that isobaric quantities, like geostrophic shear, are valid at wavelengths longer than 30 km, while isopycnal quantities, like spice, may be analyzed for scales as small as a glider measures.

The transient response of the Southern Ocean pycnocline to changing atmospheric winds

The vertical density structure of the Southern Ocean is dynamically linked to wind stress at the surface, but the nature of this coupling is not fully understood. Observations from the last several decades show a significant increase in the strength of westerly winds over the Southern Ocean, but an appreciable change in the tilt of constant density surfaces (isopycnals) has not yet been detected there. Using a combination of theory and idealized numerical simulations, we show that the response of the density structure occurs on centennial timescales, making it difficult to detect significant changes with a few decades of hydrographic observations. Dynamic coupling between the circumpolar current and northern basins regulates the slow adjustment of the density structure. Our results provide a new interpretation for recent observations and highlight the importance of the interaction between regional Southern Ocean dynamics and global ocean circulation.

Quantifying the Consequences of the Ill-Defined Nature of Neutral Surfaces

Abstract In the absence of diapycnal mixing processes, fluid parcels move in directions along which they do not encounter buoyant forces. These directions define the local neutral tangent plane. Because of the nonlinear nature of the equation of state of seawater, these neutral tangent planes cannot be connected globally to form a well-defined surface in three-dimensional space; that is, continuous “neutral surfaces” do not exist. This inability to form well-defined neutral surfaces implies that neutral trajectories are helical. Consequently, even in the absence of diapycnal mixing processes, fluid trajectories penetrate through any “density” surface. This process amounts to an extra mechanism that achieves mean vertical advection through any continuous surface such as surfaces of constant potential density or neutral density. That is, the helical nature of neutral trajectories causes this additional diasurface velocity. A water-mass analysis performed with respect to continuous density surfaces will have part of its diapycnal advection due to this diasurface advection process. Hence, this additional diasurface advection should be accounted for when attributing observed water-mass changes to mixing processes. Here, the authors quantify this component of the total diasurface velocity and show that locally it can be the same order of magnitude as diasurface velocities produced by other mixing processes, particularly in the Southern Ocean. The magnitude of this diasurface advection is proportional to the ocean’s neutral helicity, which is observed to be quite small in today’s ocean. The authors also use a perturbation experiment to show that the ocean rapidly readjusts to its present state of small neutral helicity, even if perturbed significantly. Additionally, the authors show how seasonal (rather than spatial) changes in the ocean’s hydrography can generate a similar vertical advection process. This process is described here for the first time; although the vertical advection due to this process is small, it helps to understand water-mass transformation on density surfaces.

Inflationary infrared divergences: geometry of the reheating surface vs. δN formalism

We describe a simple way of incorporating fluctuations of the Hubble scale during the horizon exit of scalar perturbations into the δN formalism. The dominant effect comes from the dependence of the Hubble scale on low-frequency modes of the inflaton. This modifies the coefficient of the log-enhanced term appearing in the curvature spectrum at second order in field fluctuations. With this modification, the relevant coefficient turns out to be proportional to the second derivative of the tree-level spectrum with respect to the inflaton ϕ at horizonexit. A logarithm with precisely the same coefficient appears in acalculation of the log-enhancement of the curvature spectrum basedpurely on the geometry of the reheating surface. We take thisagreement as strong support for the proposed implementation of theδN formalism. Moreover, our analysis makes it apparent that the log-enhancement of the inflationary power-spectrum is indeed physical if this quantity isdefined using a global coordinate system on the reheating surface (or anyother post-inflationary surface of constant energy density). However, it can be avoided by defining the spectrum using invariant distances on this surface.

Observed space-time scales of internal waves and finescale intrusions on the New Jersey Shelf and their likely acoustic implications.

It has been known for some time that ocean density surfaces possess multi-scale variations in temperature (T) and salinity (S), termed spice (hot and salty, cold and fresh) by Munk in 1981. Compensating T and S variations along a surface of constant density have reinforcing sound speed anomalies and thus have important acoustic implications. With the advent of new technologies to observe small scale, rapidly changing ocean thermohaline structure, spice variations, and their acoustic effects are just starting to be understood. Better known are the impacts of internal waves which vertically advect ocean sound speed structure. This talk will present analysis of moored T and S observations on the New Jersey Shelf region during the SW06 experiment in which the sound speed effects of internal waves and spice can be approximately separated. These results will be contrasted with similar measurements made in the deep waters of the Philippine Sea. Using recent results from coupled mode theory, some discussion of the acoustic implications of the internal wave and spice structure will be presented. In particular, the phase randomizing effects of linear internal waves and spice will diminish the mean acoustical influence of intense but localized nonlinear internal waves.

Abel inversion of asymmetric plasma density profile at Aditya tokamak

In Aditya tokamak, at Institute for Plasma Research, till now, multi-channel microwave interferometer system is used to measure the cord averaged plasma density at predefined radial position. An inversion code is developed to determine the local density profile from the chord average density measurement of radially asymmetric plasma. The radial density profile is interpolated using Spline interpolation analytical technique for symmetric plasma density profile. Code implements the Slice and Stack method to determine localized density from asymmetric averaged plasma density measurement from interferometer. Inverted results are tested with various monotonically varying asymmetric radial density profiles of the plasma shots. It also provides the poloidal picture of plasma density distribution with circular constant density surfaces. Localized density measurements, which is very important for successful operation of tokamak, is in agreement with observation of other diagnostics.

Instantaneous liquid interfaces.

We describe and illustrate a simple procedure for identifying a liquid interface from atomic coordinates. In particular, a coarse-grained density field is constructed, and the interface is defined as a constant density surface for this coarse-grained field. In applications to a molecular dynamics simulation of liquid water, it is shown that this procedure provides instructive and useful pictures of liquid-vapor interfaces and of liquid-protein interfaces.

Influence of elastic deformations on the inner core wobble

SUMMARY The Earth’s longest free mode of nutation, the inner core wobble (ICW), consists of a prograde precession of the tilted figure of the inner core with respect to a fixed mantle. The dynamics of the ICW is controlled by coupling at the inner-core boundary (ICB) and by the torque exerted by the rest of the Earth on a tilted inner core. This mode has not yet been observed either directly or indirectly, though theoretical estimates suggest its period should be 2410 solar days or 6.6 yr. However, these estimates were based on models that did not properly take into account elastic deformations associated with a tilted inner core. In this work, we incorporate these elastic deformations in a model of free nutations that rests on an angular momentum formalism. We find that based on an elastic, oceanless and dissipationless earth model corresponding to PREM, elastic deformations within the inner core contribute to a lengthening of the period of the ICW from 2410 to 2715 solar days. The internal forcing caused by the misalignment between surfaces of constant density and centrifugal potential is the most important contribution to elastic deformations.

Transient electro-osmotic flow in cylindrical microcapillaries containing salt-free medium

A theoretical study on the transient electro-osmotic flow through a cylindrical microcapillary containing a salt-free medium is presented for both constant surface charge density and constant surface potential. The exact analytical solutions for the electric potential distribution and the transient electro-osmotic flow velocity are derived by solving the nonlinear Poisson-Boltzmann equation and the Navier-Stokes equation. Based on these results, a systematic parametric study on the characteristics of the transient electro-osmotic flow is detailed. The general behavior of transient electro-osmotic flow in a cylindrical tube is similar to that observed in a microchannel containing an electrolyte solution. However, the steady-state electro-osmotic flow significantly deviates from the typical plug flow at higher surface charge and the rate of increase in the electro-osmotic mobility is strongly suppressed due to the effect of counterion condensation. In addition, the applicability limit of these solutions is also discussed.

CFD analysis of thermal–hydraulic behavior in SCWR typical flow channels

Investigations on thermal–hydraulic behavior in SCWR fuel assembly have obtained a significant attention in the international SCWR community. However, there is still a lack of understanding and ability to predict the heat transfer behavior of supercritical water. In this paper, CFD analysis is carried out to study the flow and heat transfer behavior of supercritical water in sub-channels of both square and triangular rod bundles. Effect of various parameters, e.g. thermal boundary conditions and pitch-to-diameter ratio on the thermal–hydraulic behavior is investigated. Two boundary conditions, i.e., constant heat flux at the outer surface of cladding and constant heat density in the fuel pin are applied. The results show that the structure of the secondary flow mainly depends on the rod bundle configuration as well as the pitch-to-diameter ratio, whereas, the amplitude of the secondary flow is affected by the thermal boundary conditions, as well. The secondary flow is much stronger in a square lattice than that in a triangular lattice. The turbulence behavior is similar in both square and triangular lattices. The dependence of the amplitude of the turbulent velocity fluctuation across the gap on Reynolds number becomes prominent in both lattices as the pitch-to-diameter ratio increases. The effect of thermal boundary conditions on turbulent velocity fluctuation is negligibly small. For both lattices with small pitch-to-diameter ratios ( P/ D < 1.3), the mixing coefficient is about 0.022. Both secondary flow and turbulent mixing show unusual behavior in the vicinity of the pseudo-critical point. Further investigation is needed. A strong circumferential non-uniformity of wall temperature and heat transfer is observed in tight lattices at constant heat flux boundary conditions, especially in square lattices. In the case with constant heat density of fuel pin, the circumferential conductive heat transfer significantly reduces the non-uniformity of circumferential distribution of wall temperature and heat transfer, which is favorable for the design of SCWR fuel assemblies.

Learning about the ocean carbon cycle from observational constraints and model simulations of multiple tracers

A key question in studies of the potential for reducing uncertainty in climate change projections is how additional observations may be used to constrain models. We examine the case of ocean carbon cycle models. The reliability of ocean models in projecting oceanic CO2 uptake is fundamentally dependent on their skills in simulating ocean circulation and air–sea gas exchange. In this study we demonstrate how a model simulation of multiple tracers and utilization of a variety of observational data help us to obtain additional information about the parameterization of ocean circulation and air–sea gas exchange, relative to approaches that use only a single tracer. The benefit of using multiple tracers is based on the fact that individual tracer holds unique information with regard to ocean mixing, circulation, and air–sea gas exchange. In a previous modeling study, we have shown that the simulation of radiocarbon enables us to identify the importance of parameterizing sub-grid scale ocean mixing processes in terms of diffusive mixing along constant density surface (isopycnal mixing) and the inclusion of the effect of mesoscale eddies. In this study we show that the simulation of phosphate, a major macronutrient in the ocean, helps us to detect a weak isopycnal mixing in the upper ocean that does not show up in the radiocarbon simulation. We also show that the simulation of chlorofluorocarbons (CFCs) reveals excessive upwelling in the Southern Ocean, which is also not apparent in radiocarbon simulations. Furthermore, the updated ocean inventory data of man-made radiocarbon produced by nuclear tests (bomb 14C) enable us to recalibrate the rate of air–sea gas exchange. The progressive modifications made in the model based on the simulation of additional tracers and utilization of updated observational data overall improve the model’s ability to simulate ocean circulation and air–sea gas exchange, particularly in the Southern Ocean, and has great consequence for projected CO2 uptake. Simulated global ocean uptake of anthropogenic CO2 from pre-industrial time to the present day by both previous and updated models are within the range of observational-based estimates, but with substantial regional difference, especially in the Southern Ocean. By year 2100, the updated model estimated CO2 uptake are 531 and 133 PgC (1PgC = 1015 gram carbon) for the global and Southern Ocean respectively, whereas the previous version model estimated values are 540 and 190 PgC.