Isopycnal Coordinates Research Articles

On the hydrostatic limit of stably stratified fluids with isopycnal diffusivity

This article is concerned with rigorously justifying the hydrostatic limit for continuously stratified incompressible fluids under the influence of gravity. The main distinction of this work compared to previous studies is the absence of any (regularizing) viscosity contribution added to the fluid-dynamics equations; only thickness diffusivity effects are considered. Motivated by applications to oceanography, the diffusivity effects in this work arise from an additional advection term, the specific form of which was proposed by Gent and McWilliams in the 1990s to model the effective contributions of geostrophic eddy correlations in non-eddy-resolving systems. The results of this paper heavily rely on the assumption of stable stratification. We establish the well-posedness of the hydrostatic equations and the original (non-hydrostatic) equations for stably stratified fluids, along with their convergence in the limit of vanishing shallow-water parameter. These results are obtained in high but finite Sobolev regularity and carefully account for the various parameters involved. A key element of our analysis is the reformulation of the systems using isopycnal coordinates, enabling us to provide meticulous energy estimates that are not readily apparent in the original Eulerian coordinate system.

Benefit of vertical localization for sea surface temperature assimilation in isopycnal coordinate model

Sea surface temperature (SST) observations are a critical data set for long-term climate reconstruction. However, their assimilation with an ensemble-based data assimilation method can degrade performance in the ocean interior due to spurious covariances. Assimilation in isopycnal coordinates can delay the degradation, but it remains problematic for long reanalysis. We introduce vertical localization for SST assimilation in the isopycnal coordinate. The tapering functions are formulated empirically from a large pre-industrial ensemble. We propose three schemes: 1) a step function with a small localization radius that updates layers from the surface down to the first layer for which insignificant correlation with SST is found, 2) a step function with a large localization radius that updates layers down to the last layer for which significant correlation with SST is found, and 3) a flattop smooth tapering function. These tapering functions vary spatially and with the calendar month and are applied to isopycnal temperature and salinity. The impact of vertical localization on reanalysis performance is tested in identical twin experiments within the Norwegian Climate Prediction Model (NorCPM) with SST assimilation over the period 1980–2010. The SST assimilation without vertical localization greatly enhances performance in the whole water column but introduces a weak degradation at intermediate depths (e.g., 2,000–4,000 m). Vertical localization greatly reduces the degradation and improves the overall accuracy of the reanalysis, in particular in the North Pacific and the North Atlantic. A weak degradation remains in some regions below 2,000 m in the Southern Ocean. Among the three schemes, scheme 2) outperforms schemes 1) and 3) for temperature and salinity.

Diagnosing Frontal Dynamics From Observations Using a Variational Approach

AbstractIntensive hydrographic and horizontal velocity measurements collected in the Alboran Sea enabled us to diagnose the three‐dimensional dynamics of a frontal system. The sampled domain was characterized by a 40 km diameter anticyclonic eddy, with an intense front on its eastern side, separating the Atlantic and Mediterranean waters. Here, we implemented a multi‐variate variational analysis (VA) to reconstruct the hydrographic fields, combining the 1‐km horizontal resolution of the Underway Conductivity‐Temperature‐Depth (CTD) system with information on the flow shape from the Acoustic Doppler Current Profiler velocities. One advantage of the VA is given by the physical constraint, which preserves fine‐scale gradients better than the classical optimal interpolation (OI). A comparison between real drifter trajectories and virtual particles advected in the mapping quantified the improvements in the VA over the OI, with a 15% larger skill score. Quasi‐geostrophic (QG) and semi‐geostrophic (SG) omega equations enabled us to estimate the vertical velocity (w) which reached 40 m/day on the dense side of the front. How nutrients and other passive tracers leave the mixed‐layer and subduct is estimated with 3D advection from the VA, which agreed with biological sampling from traditional CTD casts at two eddy locations. Downwelling warm filaments are further evidence of subduction, in line with the w from SG, but not with QG. SG better accounted for the along‐isopycnal component of w in agreement with another analysis made on isopycnal coordinates. The multi‐platform approach of this work and the use of variational methods improved the characterization and understanding of (sub)‐mesoscale frontal dynamics.

Seasonal Cycle of the Confluence of the Tsugaru Warm, Oyashio, and Kuroshio Currents East of Japan

AbstractThe Sanriku Confluence east of Japan is the region of confluence of the Tsugaru Warm Current from the Sea of Japan, the Oyashio Current from the western subarctic gyre and the Sea of Okhotsk, and Kuroshio water that has detached from the subtropical gyre. It is a field of vigorous stirring driven by variability in current systems, but transition processes between water masses have yet to be clarified. High‐resolution underwater conductivity‐temperature‐depth observations were undertaken during each of the four seasons to test a hypothesis that the water‐mass gradient in the Sanriku Confluence is set without full stirring. Analyses in isopycnal coordinates indicate the seasonal occurrence of prominent fronts of both salinity and displacement, related to the emergence of various water masses. After fitting error functions to frontal features, the seasonally emerging isopycnal salinity fronts often became extremely sharp with widths typically narrower than 3 km, supporting the hypothesis. Disturbances distinguished from frontal structures indicate variance peaks with ranges similar to or slightly greater than the baroclinic Rossby radius, likely stirring the large‐scale tracer gradient at this scale. Elevated variances in isopycnal salinity were often observed around the fronts, and variances caused by isolated patches with salinity anomalies were also large. By determining the horizontal scales at which the effects of internal wave heaving becomes dominant, we were able to calculate the potential vorticity (PV) of the balanced flow field. As the PV becomes negative or near zero around the fronts, symmetric instability might have developed.

On the impact of vertical coordinate choice for innovation when assimilating hydrographic profiles into isopycnal ocean models

Assimilation of hydrographic profiles into isopycnal model is not trivial, since one is in z-level coordinate and the other is discretized in potential density coordinate. There are two ways to calculate innovation. One realizes innovation in the observation vertical space and the other in the model isopycnal coordinates. This work aims to better understand the impacts and accuracy of each one. Three experiments were conducted over the South Atlantic with HYCOM employing the Ensemble Optimal Interpolation (EnOI) each 3 days during six years, in which the last four years were used for evaluation. The first experiment assimilated Argo data with innovations in isopycnal coordinates (ARGOdp). The second assimilated Argo data with innovation in z-levels (ARGOz). The third assimilated only Argo temperature with innovation in z-levels (ARGOzT). A Control run with no assimilation was also used for comparison.Considering the hindcast, a reduction of 12%, 17% and 18% was observed on temperature RMSD with respect to Control, and of 15%, 20% and 5% on salinity for ARGOdp, ARGOz and ARGOzT, respectively. Major impacts were observed in sea surface height (SSH) and ocean heat content (OHC) in the subtropical gyre region (10°S–40°S), especially near the coast. ARGOdp generally reduced SSH increasing model bias, while ARGOz managed to correct SSH towards AVISO and ARGOzT produced small negative impacts. This was confirmed by SSH spatial correlation with respect to AVISO, which was 0.754, 0.723, 0.756 and 0.740 for Control, ARGOdp, ARGOz, and ARGOzT, respectively. The overall mean of OHC in the top 2000 m was 42.84, 41.98, 41.41, 42.18 and 42.00 Mega Joule per square metre (MJ m−2) for WOA18, Control, ARGOdp, ARGOz and ARGOzT, respectively. A correct uplift of model isopycnals considering climatology was verified at the vertical cross-section along 42.5°W and around 28°S for ARGOz and ARGOzT, and an excessively uplift for ARGOdp. This led to stronger and thicker Intermediate Western Boundary Current and weaker Brazil Current (BC). Between 20°S and 27°S Control, ARGOz and ARGOzT presented a BC mean transport in agreement with literature, while ARGOdp underestimated it. The results indicate that innovation in observation space is more adequate than in model vertical space, particularly for low vertical model resolutions.

Parameterization of Submesoscale Symmetric Instability in Dense Flows Along Topography

AbstractWe develop a parameterization for representing the effects of submesoscale symmetric instability (SI) in the ocean interior. SI may contribute to water mass modification and mesoscale energy dissipation in flow systems throughout the World Ocean. Dense gravity currents forced by surface buoyancy loss over shallow shelves are a particularly compelling test case, as they are characterized by density fronts and shears susceptible to a wide range of submesoscale instabilities. We present idealized experiments of Arctic shelf overflows employing the GFDL‐MOM6 in z* and isopycnal coordinates. At the highest resolutions, the dense flow undergoes geostrophic adjustment and forms bottom‐ and surface‐intensified jets. The density front along the topography combined with geostrophic shear initiates SI, leading to onset of secondary shear instability, dissipation of geostrophic energy, and turbulent mixing. We explore the impact of vertical coordinate, resolution, and parameterization of shear‐driven mixing on the representation of water mass transformation. We find that in isopycnal and low‐resolution z* simulations, limited vertical resolution leads to inadequate representation of diapycnal mixing. This motivates our development of a parameterization for SI‐driven turbulence. The parameterization is based on identifying unstable regions through a balanced Richardson number criterion and slumping isopycnals toward a balanced state. The potential energy extracted from the large‐scale flow is assumed to correspond to the kinetic energy of SI which is dissipated through shear mixing. Parameterizing submesoscale instabilities by combining isopycnal slumping with diapycnal mixing becomes crucial as ocean models move toward resolving mesoscale eddies and fronts but not the submesoscale phenomena they host.

Potential vorticity diagnostics based on balances between volume integral and boundary conditions

Taking advantage of alternative expressions for potential vorticity (PV) in divergence forms, we derive balances between volume integral of PV and boundary conditions, that are then applied to practical computations of PV:•We propose a new method for diagnosing the Ertel potential vorticity from model output, that preserves the balances;•We show how the expression of PV can be derived in general coordinate systems. This is here emphasised with isopycnic coordinates by generalising the PV expression to the general Navier-Stokes equations;•We propose a generalised derivation for the Haynes-McIntyre impermeability theorem, which highlights the role of the bottom boundary condition choice (e.g. no-slip vs free-slip) and mixing near the bottom boundary for the volume integral of PV.The implications of balances between volume integral of PV and boundary conditions are then analysed for specific processes at various scales:•At large scale, we show how an integral involving surface observations (derived from satellite observations) is linked to the integral of PV within a layer (between two isopycnals). This surface integral can be calculated for models and observations and can be used for validation;•At mesoscale or sub-mesoscale, we analyse the relationship between net PV anomalies and net surface density anomalies for idealised vortices and 2D fronts. This can help determining vortex or jet structures for idealised studies or empirical methodologies;•We also confirm and integrate previous results on the modification of PV within a bottom boundary layer into a single diagnostic taking into account the effect of density and velocity modifications by diabatic processes along the topography and diapycnal mixing within the boundary layer.

Eddy dynamics over continental slopes under retrograde winds: Insights from a model inter-comparison

Mesoscale eddies are ubiquitous in the ocean and play a key role in exchanges across continental slopes. In this study the properties of wind-driven baroclinic turbulence are investigated using eddy-resolving process simulations, focusing on the case of retrograde winds that arises around the margins of the subtropical gyres. In contrast to a flat-bottomed ocean, over steep slopes eddies develop from baroclinic instabilities are confined to the top few hundred meters. Deeper in the water column baroclinic instability and vertical momentum transfer are suppressed, so wind-input momentum is exported toward the open ocean by eddies before traversing down to the ocean bed. Close to the sloping topography, eddy energy sourced from the upper ocean is converted to potential energy, steepening isopycnals and driving bottom-trapped prograde flows. This process is associated with upgradient lateral buoyancy fluxes and downgradient isopycnal potential vorticity fluxes, and cannot be reproduced via linear stability calculations.These properties of wind-driven shelf/slope turbulence are contrasted against simulations with flat bathymetry. The key differences described above hinge on the flow close to the steep topographic slope, which may be sensitive to the model’s vertical coordinate system. The simulations are therefore replicated using models that employ geopotential coordinates, terrain-following coordinates, and isopycnal coordinates. Quantitative inter-model discrepancies in the momentum and energy budgets are much more pronounced in the presence of a steep bottom slope. However, the key findings of this study are consistent across the models, suggesting that they are robust and warrant incorporation into parameterizations of eddy transfer across continental slopes.

Physical uniqueness of higher-order Korteweg-de Vries theory for continuously stratified fluids without background shear

The 2nd-order Korteweg-de Vries (KdV) equation and the Gardner (or extended KdV) equation are often used to investigate internal solitary waves, commonly observed in oceans and lakes. However, application of these KdV-type equations for continuously stratified fluids to geophysical problems is hindered by nonuniqueness of the higher-order coefficients and the associated correction functions to the wave fields. This study proposes to reduce arbitrariness of the higher-order KdV theory by considering its uniqueness in the following three physical senses: (i) consistency of the nonlinear higher-order coefficients and correction functions with the corresponding phase speeds, (ii) wavenumber-independence of the vertically integrated available potential energy, and (iii) its positive definiteness. The spectral (or generalized Fourier) approach based on vertical modes in the isopycnal coordinate is shown to enable an alternative derivation of the 2nd-order KdV equation, without encountering nonuniqueness. Comparison with previous theories shows that Parseval’s theorem naturally yields a unique set of special conditions for (ii) and (iii). Hydrostatic fully nonlinear solutions, derived by combining the spectral approach and simple-wave analysis, reveal that both proposed and previous 2nd-order theories satisfy (i), provided that consistent definitions are used for the wave amplitude and the nonlinear correction. This condition reduces the arbitrariness when higher-order KdV-type theories are compared with observations or numerical simulations. The coefficients and correction functions that satisfy (i)-(iii) are given by explicit formulae to 2nd order and by algebraic recurrence relationships to arbitrary order for hydrostatic fully nonlinear and linear fully nonhydrostatic effects.

Optimising assimilation of hydrographic profiles into isopycnal ocean models with ensemble data assimilation

Hydrographic profiles are crucial observational datasets for constraining ocean models and their vertical structure. In this study, we investigate a key implementation setup for optimising their assimilation into isopycnal ocean models. For this purpose, we use the Norwegian Climate Prediction Model (NorCPM), which is a fully-coupled climate prediction system based on the Norwegian Earth System Model and the ensemble Kalman filter. First, we revisit whether it is more accurate to assimilate observations in their original coordinate (z-level coordinate) or to transform them into isopycnal coordinates prior to assimilation. The analysis is performed with a single assimilation step using synthetic observations that mimic the characteristic properties of hydrographic profiles: varying vertical resolutions, profiles of only temperature and observations only in the top 1000 m. Assimilating profiles in their native coordinate (z-level coordinates) performs best because converting observations into isopycnal coordinates is strongly non-linear which reduces the efficiency of the assimilation. Secondly, we investigate how to set the horizontal localisation radius for our system. A radius that varies with latitude following a bimodal Gaussian function fits the system well. Thirdly, we estimate observation error, which consists of both instrumental error and representativeness error. In the proposed formulation only the instrumental error decreases with the number of observations during superobing, because the representativeness error is dominated by model limitation. Finally, we demonstrate the impact of assimilating hydrographic profiles from the observational EN4 dataset into NorCPM. An analysis of 10 years with monthly assimilation is performed with special focus on assessing the accuracy and the reliability of our analysis. The assimilation of hydrographic profiles into NorCPM is found to efficiently reduce the model bias and error, and the ensemble spread is found to be a reliable estimator for the forecast error in most regions.

Numerical instabilities of vector‐invariant momentum equations on rectangular C‐grids

The linear stability of two well‐known energy‐ and enstrophy‐conserving schemes for the vector‐invariant hydrostatic primitive equations is examined. The problem is analyzed for a stably stratified Boussinesq fluid on an f‐plane with a constant velocity field, in height and isopycnal coordinates, by separation of variables into vertical normal modes and a linearized form of the shallow‐water equations (SWEs). As found by Hollingsworth et al. the schemes are linearly unstable in height coordinate models, due to non‐cancellation of terms in the momentum equations. The schemes with the modified formulations of kinetic energy proposed by Hollingsworth et al. are shown to have Hermitian stability matrices and hence to be stable to all perturbations. All perturbations in isopycnal models are also shown to be neutrally stable, even with the original formulations for kinetic energy. Analytical expressions are derived for the smallest equivalent depths obtained using Charney–Phillips and Lorenz vertical grids, which show that the Lorenz grid has larger growth rates for unstable schemes than the Charney–Phillips grid. Test cases are proposed for assessing the stability of new numerical schemes using the SWEs.

Flow-dependent assimilation of sea surface temperature in isopycnal coordinates with the Norwegian Climate Prediction Model

We document a pilot stochastic re-analysis computed by assimilating sea surface temperature (SST) anomalies into the ocean component of the coupled Norwegian Climate Prediction Model (NorCPM) for the period 1950–2010 (doi: 10.11582/2016.00002). NorCPM is based on the Norwegian Earth System Model and uses the ensemble Kalman filter for data assimilation (DA). Here, we assimilate SST from the stochastic HadISST2 historical reconstruction. The accuracy, reliability and drift are investigated using both assimilated and independent observations. NorCPM is slightly overdispersive against assimilated observations but shows stable performance through the analysis period. It demonstrates skills against independent measurements: sea surface height, heat and salt content, in particular in the Equatorial and North Pacific, the North Atlantic Subpolar Gyre (SPG) region and the Nordic Seas. Furthermore, NorCPM provides a reliable monitoring of the SPG index and represents the vertical temperature variability there, in good agreement with observations. The monitoring of the Atlantic meridional overturning circulation is also encouraging. The benefit of using a flow-dependent assimilation method and constructing the covariance in isopycnal coordinates are investigated in the SPG region. Isopycnal coordinates discretisation is found to better capture the vertical structure than standard depth-coordinate discretisation, because it leads to a deeper influence of the assimilated surface observations. The vertical covariance shows a pronounced seasonal and decadal variability that highlights the benefit of flow-dependent DA method. This study demonstrates the potential of NorCPM to compute an ocean re-analysis for the 19th and 20th centuries when SST observations are available.

Characteristics of the Nordic Seas overflows in a set of Norwegian Earth System Model experiments

Global ocean models with an isopycnic vertical coordinate are advantageous in representing overflows, as they do not suffer from topography-induced spurious numerical mixing commonly seen in geopotential coordinate models. In this paper, we present a quantitative diagnosis of the Nordic Seas overflows in four configurations of the Norwegian Earth System Model (NorESM) family that features an isopycnic ocean model. For intercomparison, two coupled ocean-sea ice and two fully coupled (atmosphere-land-ocean-sea ice) experiments are considered. Each pair consists of a (non-eddying) 1° and a (eddy-permitting) 1/4° horizontal resolution ocean model. In all experiments, overflow waters remain dense and descend to the deep basins, entraining ambient water en route. Results from the 1/4° pair show similar behavior in the overflows, whereas the 1° pair show distinct differences, including temperature/salinity properties, volume transport (Q), and large scale features such as the strength of the Atlantic Meridional Overturning Circulation (AMOC). The volume transport of the overflows and degree of entrainment are underestimated in the 1° experiments, whereas in the 1/4° experiments, there is a two-fold downstream increase in Q, which matches observations well. In contrast to the 1/4° experiments, the coarse 1° experiments do not capture the inclined isopycnals of the overflows or the western boundary current off the Flemish Cap. In all experiments, the pathway of the Iceland-Scotland Overflow Water is misrepresented: a major fraction of the overflow proceeds southward into the West European Basin, instead of turning westward into the Irminger Sea. This discrepancy is attributed to excessive production of Labrador Sea Water in the model. The mean state and variability of the Nordic Seas overflows have significant consequences on the response of the AMOC, hence their correct representations are of vital importance in global ocean and climate modelling.

Decline of the Black Sea oxygen inventory

Abstract. We show that from 1955 to 2015, the inventory of oxygen in the Black Sea has decreased by 44 % and the basin-averaged oxygen penetration depth has decreased from 140 m in 1955 to 90 m in 2015, which is the shallowest annual value recorded during that period. The oxygenated Black Sea surface layer separates the world's largest reservoir of toxic hydrogen sulfide from the atmosphere. The threat of chemocline excursion events led to hot debates in the past decades arguing on the vertical stability of the Black Sea oxic/suboxic interface. In the 1970s and 1980s, when the Black Sea faced severe eutrophication, enhanced respiration rates reduced the thickness of the oxygenated layer. Re-increasing oxygen inventory in 1985–1995 supported arguments in favor of the stability of the oxic layer. Concomitant with a reduction of nutrient loads, it also supported the perception of a Black Sea recovering from eutrophication. More recently, atmospheric warming was shown to reduce the ventilation of the lower oxic layer by lowering cold intermediate layer (CIL) formation rates. The debate on the vertical migration of the oxic interface also addressed the natural spatial variability affecting Black Sea properties when expressed in terms of depth. Here we show that using isopycnal coordinates does not overcome the significant spatial variability of oxygen penetration depth. By considering this spatial variability, the analysis of a composite historical set of oxygen profiles evidenced a significant shoaling of the oxic layer, and showed that the transient "recovery" of the 1990s was mainly a result of increased CIL formation rates during that period. As both atmospheric warming and eutrophication are expected to increase in the near future, monitoring the dynamics of the Black Sea oxic layer is urgently required to assess the threat of further shoaling.

Evaluation of the arbitrary Lagrangian–Eulerian vertical coordinate method in the MPAS-Ocean model

The vertical coordinate of the Model for Prediction Across Scales-Ocean (MPAS-Ocean) uses the Arbitrary Lagrangian–Eulerian (ALE) method, which offers a variety of configurations. When fully Eulerian, the vertical coordinate is fixed like a z-level ocean model; when fully Lagrangian there is no vertical transport through the interfaces so that the mesh moves with the fluid; additional options for vertical coordinates exist between these two extremes, including z-star, z-tilde, sigma, and isopycnal coordinates. Here we evaluate spurious diapycnal mixing in MPAS-Ocean in several idealized test cases as well as real-world domains with full bathymetry. Mixing data is compared to several other ocean models, including the Parallel Ocean Program (POP) z-level and z-star formulations. In three-dimensional domains, MPAS-Ocean has lower spurious mixing that other ocean models. A series of simulations show that this is likely due to MPAS-Ocean’s hexagon-type horizontal grid cells combined with a flux-corrected transport tracer advection scheme designed for these unstructured meshes.The frequency-filtered vertical coordinate of Leclair and Madec (2011) (also called z-tilde) has been implemented and analyzed in MPAS-Ocean. This addition allows low-frequency vertical transport to pass through the vertical interface in an Eulerian manner, while high-frequency vertical oscillations, such as internal gravity waves, are treated in a Lagrangian manner. Z-tilde leads to a substantial reduction in vertical transport across layer interfaces, and a reduction in spurious diapycnal mixing.

Energetics of lateral eddy diffusion/advection: Part III. Energetics of horizontal and isopycnal diffusion/advection

Gravitational Potential Energy (GPE) change due to horizontal/isopycnal eddy diffusion and advection is examined. Horizontal/isopycnal eddy diffusion is conceptually separated into two steps: stirring and subscale diffusion. GPE changes associated with these two steps are analyzed. In addition, GPE changes due to stirring and subscale diffusion associated with horizontal/isopycnal advection in the Eulerian coordinates are analyzed. These formulae are applied to the SODA data for the world oceans. Our analysis indicates that horizontal/isopycnal advection in Eulerian coordinates can introduce large artificial diffusion in the model. It is shown that GPE source/sink in isopycnal coordinates is closely linked to physical property distribution, such as temperature, salinity and velocity. In comparison with z-coordinates, GPE source/sink due to stirring/cabbeling associated with isopycnal diffusion/advection is much smaller. Although isopycnal coordinates may be a better choice in terms of handling lateral diffusion, advection terms in the traditional Eulerian coordinates can produce artificial source of GPE due to cabbeling associated with advection. Reducing such numerical errors remains a grand challenge.

Energetics of lateral eddy diffusion/advection: Part IV. Energetics of diffusion/advection in sigma coordinates and other coordinates

Gravitational potential energy (GPE) source and sink due to stirring and cabbeling associated with sigma diffusion/advection is analyzed. It is shown that GPE source and sink is too big, and they are not closely linked to physical property distribution, such as temperature, salinity and velocity. Although the most frequently quoted advantage of sigma coordinate models are their capability of dealing with topography; the excessive amount of GPE source and sink due to stirring and cabbeling associated with sigma diffusion/advection diagnosed from our analysis raises a very serious question whether the way lateral diffusion/advection simulated in the sigma coordinates model is physically acceptable. GPE source and sink in three coordinates is dramatically different in their magnitude and patterns. Overall, in terms of simulating lateral eddy diffusion and advection isopycnal coordinates is the best choice and sigma coordinates is the worst. The physical reason of the excessive GPE source and sink in sigma coordinates is further explored in details. However, even in the isopycnal coordinates, simulation based on the Eulerian coordinates can be contaminated by the numerical errors associated with the advection terms.

Sensitivity of transient climate change to tidal mixing: Southern Ocean heat uptake in climate change experiments performed with ECHAM5/MPIOM

We investigate the sensitivity of the transient climate change to a tidal mixing scheme. The scheme parameterizes diapycnal diffusivity depending on the location of energy dissipation over rough topography, whereas the standard configuration uses horizontally con- stant diffusivity. We perform ensemble climate change experiments with two setups of MPIOM/ECHAM5, one setup with the tidal mixing scheme and the second setup with the standard configuration. Analysis of the responses of the transient climate change to CO2 increase reveals that the implementation of tidal mixing leads to a significant reduction of the transient surface warming by 9 %. The weaker surface warming in the tidal run is localized par- ticularly over the Weddell Sea, likely caused by a stronger ocean heat uptake in the Southern Ocean. The analysis of the ocean heat budget reveals that the ocean heat uptake in both experiments is caused by changes in convection and advection. In the upper ocean, heat uptake is caused by reduced convection and enhancement of the Deacon Cell, which appears also in isopycnal coordinates. In the deeper ocean, heat uptake is caused by reduction of convective cooling associated with the circulation polewards of 65S. Tidal mixing leads to stronger heat uptake in the Southern Ocean by causing stronger changes in advection, namely a stronger increase in the Deacon Cell and a stronger reduction in advective cooling by the circulation polewards of 65S. Counter-intuitively, the relation between tidal mixing and greater heat storage in the deep ocean is an indirect one, through the influence of tidal mixing on the circulation.

Diapycnal diffusivity at the upper boundary of the tropical North Atlantic oxygen minimum zone

A deliberate tracer release experiment in 2008–2010 was used to study diapycnal mixing in the tropical northeastern Atlantic. The tracer (CF3SF5) was injected on the isopycnal surface σΘ = 26.88 kg m−3, which corresponds to about 330 m depth. Three surveys, performed 7, 20, and 30 months after the release, sampled the vertically and laterally expanding tracer patch. The mean diapycnal mixing estimate over the entire region occupied by the tracer and the period of 30 months was found to be (1.19 ± 0.18) × 10−5 m2 s−1, or, alternatively, (3.07 ± 0.58) × 10−11 (kg m−3)2 s−1as computed from the advection‐diffusion equation in isopycnal coordinates with the thickness‐weighted averaging. The latter method is preferable in the regions of different stratification for it yields local diapycnal mixing estimates varying less with stratification than their Cartesian coordinate counterparts. Results of this study are comparable to the results of the North Atlantic tracer release experiment (NATRE). However, the internal wave‐wave interaction models predict reduced mixing from the breaking of internal waves at low latitudes. Thus, the diapycnal diffusivity found in this study is higher than parameterized by the low latitude of the site (4°N–12°N).

Strongly nonlinear, simple internal waves in continuously-stratified, shallow fluids

Abstract. Strongly nonlinear internal waves in a layer with arbitrary stratification are considered in the hydrostatic approximation. It is shown that "simple waves" having a variable vertical structure can emerge from a wide class of initial conditions. The equations describing such waves have been obtained using the isopycnal coordinate as a variable. Emergence of simple waves from an initial Gaussian impulse is numerically investigated for different density profiles, from two- and three-layer structure to the continuous one. Besides the first mode, examples of second- and third-mode simple waves are given.