Assessment of turbulence closure models for resonant inertial response in the oceanic mixed layer using a large eddy simulation model

Large eddy simulation (LES) of the resonant inertial response of the upper ocean to strong wind forcing is carried out; the results are used to evaluate the performance of each of the two second-order turbulence closure models presented by Mellor and Yamada (Rev Geophys Space Phys 20:851–875, 1982) (MY) and by Nakanishi and Niino (J Meteorol Soc Jpn 87:895–912, 2009) (NN). The major difference between MY and NN is in the formulation of the stability functions and the turbulent length scale, both strongly linked with turbulent fluxes; in particular, the turbulent length scale in NN, unlike that in MY, is allowed to decrease with increasing density stratification. We find that MY underestimates and NN overestimates the development of mixed layer features, for example, the strong entrainment at the base of the oceanic mixed layer and the accompanying decrease of sea surface temperature. Considering that the stability functions in NN perform better than those in MY in reproducing the vertical structure of turbulent heat flux, we slightly modify NN to find that the discrepancy between LES and NN can be reduced by more strongly restricting the turbulent length scale with increasing density stratification.     

Extending the k–ω turbulence model towards oceanic applications

Four different two-equation turbulence models for geophysical flows are compared: The k–ϵ model, two new versions of the k–ω model, and the Mellor–Yamada model. An extension of the k–ω model for buoyancy affected and rotating flows is suggested. Model performance is evaluated for a few typical oceanic flows. First, new analytical solutions of the models for the surface layer affected by breaking surface waves are discussed. The deficiencies of earlier attempts are high-lighted, and it is demonstrated why the Mellor–Yamada model and the k–ϵ model fail. It is illustrated that only one version of the k–ω model computes correct decay rates for turbulent quantities under breaking waves. Second, it is demonstrated that all models predict almost identical mixed layer depths and profiles for the turbulent kinetic energy in a classical stratified shear-entrainment experiment if the buoyancy term in the second equation is appropriately weighted. Third, the accuracy and numerical robustness of the new k–ω model in realistic oceanic situations is confirmed by comparison with the data-set of the Ocean Weather Ship ‘Papa’.     

A note on modeling double diffusive mixing in the global ocean

Though ubiquitous in the global oceans, double diffusive mixing has been largely ignored or poorly represented in the models of turbulent mixing in the ocean and in 3-D ocean models, until recently. Salt fingers occur in the interior of many marginal seas and ocean basins, the Tyrrhenian Sea and the subtropical Atlantic being two examples. Diffusive convection type of double diffusion occurs in the upper layers of many sub-polar seas and polar oceans due to cold melt water from sea ice. Consequently, it is important to be able to properly parameterize double diffusive mixing in basin scale and global ocean models, so that the water mass structure in the interior of the ocean can be properly simulated. This note describes a model for double diffusive mixing in the presence of background shear, based on Mellor–Yamada type second moment closure, more specifically Kantha, 2003, Kantha and Clayson, 2004 second moment closure models of resulting turbulence, following Canuto et al. (2008a) but employing a different strategy for modeling the pertinent terms in the second moment equations. The resulting model is suitable for inclusion in ocean general circulation models.     

Parameterization of vertical mixing in the Weddell Sea

A series of vertical mixing schemes implemented in a circumpolar coupled ice–ocean model of the BRIOS family is validated against observations of hydrography and sea ice coverage in the Weddell Sea. Assessed parameterizations include the Richardson number-dependent Pacanowski–Philander scheme, the Mellor–Yamada turbulent closure scheme, the K-profile parameterization, a bulk mixed layer model and the ocean penetrative plume scheme (OPPS). Combinations of the Pacanowski–Philander parameterization or the OPPS with a simple diagnostic model depending on the Monin–Obukhov length yield particularly good results. In contrast, experiments using a constant diffusivity and the traditional convective adjustment cannot reproduce the observations. An underestimation of wind-driven mixing in summer leads to an accumulation of salt in the winter water layer, inducing deep convection in the central Weddell Sea and a homogenization of the water column. Large upward heat fluxes in these simulations lead to the formation of unrealistic, large polynyas in the central Weddell Sea after only a few years of integration. Furthermore, spurious open-ocean convection affects the basin-scale circulation and leads to a significant overestimation of meridional overturning rates. We conclude that an adequate parameterization of both wind-induced mixing and buoyancy-driven convection is crucial for realistic simulations of processes in seasonally ice-covered seas.     

Stability of algebraic non-equilibrium second-order closure models

Stability problems of algebraic non-equilibrium second-moment closure models have given rise to the so-called quasi-equilibrium versions in which turbulence equilibrium is used as an additional constraint. In this paper, we investigate reasons for the failure of the G.L. Mellor, T. Yamada [Reviews of Geophysics 20 (1982) 851] level 2.5 closure model and suggest a remedy for this. We further discuss a new non-equilibrium closure model by V.M. Canuto, A. Howard, Y. Cheng, M.S. Dubovikov (Journal of Physical Oceanography, 2000, accepted for publication) which has proven to allow for stable calculations. All models are then numerically tested with a simple wind entrainment experiment motivated by the H. Kato, O.M. Phillips [Journal of Fluid Mechanics 37 (1969) 643] laboratory experiment, with the aid of which the instability of the Mellor and Yamada (1982) and the stability of the Canuto et al. (2000) model are confirmed. The Canuto et al. (2000) model has three advantages compared to the Mellor and Yamada (1982) which are (i) the symmetry of stability functions, (ii) a higher critical Richardson number, and (iii) that the normalised shear stress increases with normalised shear for turbulence equilibrium. The latter advantage of the new model causes its high physical and numerical stability.     

A coupled 1-D biological/physical model of the northeast subarctic Pacific Ocean with iron limitation

The recent NE subarctic Pacific study of the Canadian JGOFS project was designed primarily to address why phytoplankton biomass and production at Ocean Station Papa (OSP: 50°N, 145°W) are not as high as the nitrate concentrations could potentially support. To examine the possible role of iron (Fe) limitation in concert with microzooplankton grazing and physical supply of nitrate, we have coupled a four-compartment Nitrogen–Phytoplankton–Zooplankton–Detritus planktonic ecosystem model with a 60-layer (each 2 m thick) one-dimensional mixed-layer model (Mellor–Yamada level 2.5), driven by annual forcing characteristic of OSP. Both the physical and ecological models are forced with the same annual heat budget, mean phytoplankton concentration was tuned with the equilibrium solution of the model, and the zooplankton parameter values were chosen to be representative of microzooplankton. Modelled sea surface temperature ranged between 6 (fixed – late winter) and 13–14°C, depending on the distribution and amount of phytoplankton and detritus calculated by the model. Simulations with Fe limitation reducing the maximum specific growth rate of phytoplankton (for Fe-replete conditions) by a factor of ∼3 best reproduced the annual cycle of surface layer nitrate, although the resulting annual f-ratio calculated from the fluxes into and out of the nitrogen compartment was marginally higher than recent estimates of f-ratio based on observations at OSP. The best simulations with Fe limitation agreed with observations of the annual cycle of surface nitrate concentration, the f-ratio, particulate nitrogen concentration in the euphotic layer, the export production, and the remineralization depth scale for sinking detritus, to within ∼50%, probably within the range of observational uncertainty and/or seasonal and interannual variability. Possible modifications include separating the detrital pool into suspended and sinking organic matter, decreasing the rate of remineralization with increasing depth, and examining the supply of nitrate to the surface layer by means of horizontal advection. The observational basis required to formulate these processes is marginal at present.     

Using the Mellor–Yamada mixing scheme in seasonally ice-covered seas—Corrigendum to: Parameterization of vertical mixing in the Weddell Sea [Ocean Modelling 6 (2004) 83–100]

A coding error in the s-Coordinate Primitive Equation Model (SPEM) has led to misleading statements about the behaviour of the Mellor–Yamada level 2 parameterization of vertical mixing. It has been claimed that the scheme removes static instability only very slowly and preserves statically unstable stratifications for an unrealistic long time. This note corrects this statement by demonstrating that the Mellor–Yamada mixing scheme, if implemented correctly, tends to overestimate rather than underestimate vertical mixing in seasonally ice-covered seas. Similar to other mixing schemes with the same behaviour, this leads to spurious open ocean deep convection, an unrealistic homogenization of the water column, and a significant reduction of sea ice volume.     

渤海夏季潮致-风生-热盐环流的数值诊断计算

基于正交曲线坐标的ECOMSED三维水动力模式,并考虑了潮汐、风和实测温盐场,诊断计算了渤海夏季三维潮致-风生-热盐环流,分析了渤海夏季潮致余流、风生和热盐环流的分布结构。结果显示,在夏季,渤海中部海区明显存在一个顺时针向的涡旋,同时渤海还存在着多个逆时针向的涡旋。通过分析和比较各个分量在总环流中的作用,认为夏季潮致余流是相对弱的;热盐环流在夏季总环流中占主要成分。     

Simulation of the ocean surface mixed layer under the wave breaking

A one-dimensional mixed-layer model, including a Mellor-Yamada level 2.5 turbulence closure scheme, was implemented to investigate the dynamical and thermal structures of the ocean surface mixed layer in the northern South China Sea. The turbulent kinetic energy released through wave breaking was incorporated into the model as a source of energy at the ocean surface, and the influence of the breaking waves on the mixed layer was studied. The numerical simulations show that the simulated SST is overestimated in summer without the breaking waves. However, the cooler SST is simulated when the effect of the breaking waves is considered, the corresponding discrepancy with the observed data decreases up to 20% and the MLD calculated averagely deepens 3.8 m. Owing to the wave-enhanced turbulence mixing in the summertime, the stratification at the bottom of the mixed layer was modified and the temperature gradient spread throughout the whole thermocline compared with the concentrated distribution without wave breaking.     

Fractionation during remineralization of organic matter in the ocean

Remineralization ratios (–O₂:P, C_org.:P, N:P) in the ocean are estimated from ocean tracer data using a new approach, which takes into account the effects of local exchange across neutral surfaces. This approach is applied to temperature, salinity, phosphate, nitrate, dissolved oxygen, alkalinity, and dissolved inorganic carbon data from the low- and mid-latitude Pacific, Indian, and South Atlantic Oceans. The consideration of local exchange effects tends to reduce the –O₂:P and C_org.:P remineralization estimates above 1500 m compared to earlier estimates. Below 1500 m, exchange effects can be neglected (except in the South Atlantic) and earlier estimates appear robust. In the deep South Atlantic, the consideration of these effects leads to increased –O₂:P and C_org.:P remineralization ratio estimates, bringing them more in line with the robust deep ocean estimates. For reasonable, open ocean mixing coefficient values and several choices for phosphate remineralization rate profiles, –O₂:P (C_org.:P) remineralization ratios in the ocean increase from about 140 (100) at 750 m depth to about 170 (130) at 1500 m and remain so deeper down. Such an increase down through the upper ocean thermocline implies significant fractionation during remineralization of organic matter—nutrients are released higher in the water column than inorganic carbon. These results also argue for a –O₂:P (C_org.:P) uptake ratio in new production of about 140–150 (100–110). N:P remineralization ratios decrease from about 15 at 750 m to about 12 at 1500–2000 m. This may reflect a “true” N:P remineralization (and uptake) ratio of about 16, modified by denitrification.These results imply that applications of derived, quasi-conservative tracers, based on the assumption of constant remineralization ratios, may be subject to significant error for depths less than 1500 m. In addition, present Ocean General Circulation Models of the natural carbon cycle in the ocean–atmosphere system assume remineralization to occur without fractionation but have problems simulating observed, pre-industrial levels of atmospheric pCO₂, given observed ocean inventories of alkalinity and dissolved inorganic carbon. Implementation of uptake and (depth-dependent) remineralization ratios estimated here would likely reduce this problem considerably. Furthermore, calculations with a simple global carbon cycle model show that fractionation in the modern ocean, as estimated in the present work, has reduced atmospheric pCO₂ by more than 20 ppm below the level it would have had without fractionation.     

A spectral barotropic model of the wind-driven world ocean

A global spectral barotropic ocean model is introduced to describe the depth-averaged flow. The equations are based on vorticity and divergence (instead of horizontal momentum); continents exert a nearly infinite drag on the fluid. The coding follows that of spectral atmospheric general circulation models using triangular truncation and implicit time integration to provide a first step for seamless coupling to spectral atmospheric global circulation models and an efficient method for filtering of ocean wave dynamics. Five experiments demonstrate the model performance: (i) Bounded by an idealized basin geometry and driven by a zonally uniform wind stress, the ocean circulation shows close similarity with Munk’s analytical solution. (ii) With a real land–sea mask the model is capable of reproducing the spin-up, location and magnitudes of depth-averaged barotropic ocean currents. (iii) The ocean wave-dynamics of equatorial waves, excited by a height perturbation at the equator, shows wave dispersion and reflection at eastern and western coastal boundaries. (iv) The model reproduces propagation times of observed surface gravity waves in the Pacific with real bathymetry. (v) Advection of tracers can be simulated reasonably by the spectral method or a semi-Langrangian transport scheme. This spectral barotropic model may serve as a first step towards an intermediate complexity spectral atmosphere–ocean model for studying atmosphere–ocean interactions in idealized setups and long term climate variability beyond millennia.     

Observation of wave-enhanced turbulence in the near-surface layer of the ocean during TOGA COARE

Dissipation rate statistics in the near-surface layer of the ocean were obtained during the month-long COARE Enhanced Monitoring cruise with a microstructure sensor system mounted on the bow of the research vessel. The vibration contamination was cancelled with the Wiener filter. The experimental technique provides an effective separation between surface waves and turbulence, using the difference in spatial scales of the energy-containing surface waves and small-scale turbulence. The data are interpreted in the coordinate system fixed to the ocean surface. Under moderate and high wind-speed conditions, we observed the average dissipation rate of the turbulent kinetic energy in the upper few meters of the ocean to be 3–20 times larger than the logarithmic layer prediction. The Craig and Banner (J. Phys. Oceanogr. 24 (1994) 2546) model of wave-enhanced turbulence with the surface roughness length from the water side z₀ parameterized according to the Terray et al. (J. Phys. Oceanogr. 26 (1996) 792) formula z₀=cH_s provides a reasonable fit to the experimental dissipation profile, where z is the depth (defined here as the distance to the ocean surface), c≈0.6, and H_s is the significant wave height. In the wave-stirred layer, however, the average dissipation profile deviates from the model (supposedly because of extensive removing of the bubble-disturbed areas close to the ocean surface). Though the scatter of individual experimental dissipation rates (10-min averages) is significant, their statistics are consistent with the Kolmogorov's concept of intermittent turbulence and with previous studies of turbulence in the upper ocean mixed layer.     

The effect of ocean tides on a climate model simulation

We implemented an explicit forcing of the complete lunisolar tides into an ocean model which is part of a coupled atmosphere–hydrology–ocean–sea ice model. An ensemble of experiments with this climate model shows that the model is significantly affected by the induced tidal mixing and nonlinear interactions of tides with low frequency motion. The largest changes occur in the North Atlantic where the ocean current system gets changed on large scales. In particular, the pathway of the North Atlantic Current is modified resulting in improved sea surface temperature fields compared to the non-tidal run. These modifications are accompanied by a more realistic simulation of the convection in the Labrador Sea. The modification of sea surface temperature in the North Atlantic region leads to heat flux changes of up to 50 W/m². The climate simulations indicate that an improvement of the North Atlantic Current has implications for the simulation of the Western European Climate, with amplified temperature trends between 1950 and 2000, which are closer to the observed trends.     

An Ensemble Kalman Filter multi-tracer assimilation: Determining uncertain ocean model parameters for improved climate-carbon cycle projections

An Ensemble Kalman Filter is applied to assimilate observed tracer fields in various combinations in the Bern3D ocean model. Each tracer combination yields a set of optimal transport parameter values that are used in projections with prescribed CO₂ stabilization pathways. The assimilation of temperature and salinity fields yields a too vigorous ventilation of the thermocline and the deep ocean, whereas the inclusion of CFC-11 and radiocarbon improves the representation of physical and biogeochemical tracers and of ventilation time scales. Projected peak uptake rates and cumulative uptake of CO₂ by the ocean are around 20% lower for the parameters determined with CFC-11 and radiocarbon as additional target compared to those with salinity and temperature only. Higher surface temperature changes are simulated in the Greenland–Norwegian–Iceland Sea and in the Southern Ocean when CFC-11 is included in the Ensemble Kalman model tuning. These findings highlights the importance of ocean transport calibration for the design of near-term and long-term CO₂ emission mitigation strategies and for climate projections.     

悬对沙Mellor-Yamada海洋边界层模型计算结果的影响

为了分析海洋水体垂向水流紊动及紊动交换情况而采用了一维的海洋边界层模型(Mellor-Yamada)并利用数值实验的方法对悬沙、盐度、温度等数据进行分析。原模型未将悬沙考虑在内，本文试将它引入进去探讨由于它的存在对紊动混合特性的影响。2000年4月，Mellor将最初的模型引入了依赖于Richardson数的紊动动能耗散率。本文通过比较具有悬沙和不具有悬沙两种情况下的速度、温度和盐度垂向分布随时间的变化，分析讨论由于悬沙的存在所引发的密度层化对紊动混合作用的影响，并发现悬浮泥沙抑制了部分模拟时间的紊动混合作用。     

Inter-cohort differences in spatial and temporal settlement patterns of young-of-the-year windowpane (Scophthalmus aquosus) in southern New Jersey

The timing and location of settlement of two cohorts (spring and fall) of windowpane (Scophthalmus aquosus) were identified based on collections from 64 sampling locations along a corridor from the lower estuary, through the inlet, and on to the adjacent inner continental shelf in southern New Jersey. Spatio-temporal patterns of settlement during 1989–1998 were determined based on capture location and timing, and eye migration stage. Spring-spawned windowpanes were collected in estuarine, inlet and ocean habitats as larvae, during settlement, and after settlement. Densities of spring-spawned larvae (∼2–10 mm standard length (SL)) peaked in May in all habitats (estuary, inlet, and ocean). Initial settlement of spring-spawned windowpane occurred during May in the inlet and ocean when fish had grown to ∼7–8 mm SL (mid-point of eye migration), but fish did not appear in demersal estuarine collections until June when they were larger and more developmentally advanced (∼24–32 mm SL; post-eye migration). A transitional settlement period, comprised of a progressive habitat shift from pelagic to demersal habitats, is proposed for the spring cohort to explain the observed patterns. Fall-spawned fish of all developmental stages and sizes were virtually absent from estuarine collections. Fall-spawned larval (∼2–10 mm SL) densities peaked in October in inlet and ocean habitats and fish began settling there during the same month at sizes similar to the spring cohort (∼7–8 mm SL). This research confirms that there are important cohort-specific and life-stage dependent differences in young-of-the-year (YOY) windowpane habitat use in southern New Jersey and perhaps in other east coast US estuaries. These differences may affect the overall contribution that each cohort makes to a given year class and thus, may have an important role in determining the recruitment dynamics of this species.     

Seasonality of interannual atmosphere–ocean interaction in the South China Sea

The present study documents the atmosphere–ocean interaction in interannual variations over the South China Sea (SCS). The atmosphere–ocean relationship displays remarkable seasonality and regionality, with an atmospheric forcing dominant in the northern and central SCS during the local warm season, and an oceanic forcing in the northern SCS during the local cold season. During April–June, the atmospheric impact on the sea surface temperature (SST) change is characterized by a prominent cloud-radiation effect in the central SCS, a wind-evaporation effect in the central and southern SCS, and a wind-driven oceanic effect along the west coast. During November–January, regional convection responds to the SST forcing in the northern SCS through modulation of the low-level convergence and atmospheric stability. Evaluation of the precipitation–SST and precipitation–SST tendency correlation in 24 selected models from CMIP5 indicates that the simulated atmosphere–ocean relationship varies widely among the models. Most models have the worst performance in spring. On average, the models simulate better the atmospheric forcing than the oceanic forcing. Improvements are needed for many models before they can be used to understand the regional atmosphere–ocean interactions in the SCS region.     

Aggregation of the Arctic copepod Calanus hyperboreus over the ocean floor of the Greenland Sea

According to combined observations from vertical plankton tows, dredging with epibenthic nets 1 m above the ocean floor, video recordings and acoustic data from a scanning sonar obtained during descent and during deployment on the ocean floor, the calanoid copepod Calanus hyperboreus was aggregated in high concentrations near the ocean floor of the Greenland Sea between 2300 and 2500 m during late July and August. Concentrations were highest very close to the ocean floor and decreased rapidly further upward. These nearly mono-specific aggregations were apparently drifting in cloud-like formations with a horizontal extension of ca. 270 m with the near-bottom currents. Maximum abundances observed were up to 2 orders of magnitude higher than in the water column. The biomass in the bottom 20 m layer was around 18% of the biomass in the rest of the water column. Stage composition, reduced metabolic rates and insensibility to mechanical stimuli indicate that these C. hyperboreus were representing the resting population. The fact that high concentrations were observed during deployments lasting >1 d and in 3 years suggests that aggregation near the ocean floor is a regular, rather than an extraordinary, pattern in the life history of C. hyperboreus in the Greenland Sea, but there is need for comparison with other seas and eventually other Calanus species.     

Natural air–sea flux of CO2 in simulations of the NASA-GISS climate model: Sensitivity to the physical ocean model formulation

Results from twin control simulations of the preindustrial CO₂ gas exchange (natural flux of CO₂) between the ocean and the atmosphere are presented here using the NASA-GISS climate model, in which the same atmospheric component (modelE2) is coupled to two different ocean models, the Russell ocean model and HYCOM. Both incarnations of the GISS climate model are also coupled to the same ocean biogeochemistry module (NOBM) which estimates prognostic distributions for biotic and abiotic fields that influence the air–sea flux of CO₂. Model intercomparison is carried out at equilibrium conditions and model differences are contrasted with biases from present day climatologies. Although the models agree on the spatial patterns of the air–sea flux of CO₂, they disagree on the strength of the North Atlantic and Southern Ocean sinks mainly because of kinematic (winds) and chemistry (pCO₂) differences rather than thermodynamic (SST) ones. Biology/chemistry dissimilarities in the models stem from the different parameterizations of advective and diffusive processes, such as overturning, mixing and horizontal tracer advection and to a lesser degree from parameterizations of biogeochemical processes such as gravitational settling and sinking. The global meridional overturning circulation illustrates much of the different behavior of the biological pump in the two models, together with differences in mixed layer depth which are responsible for different SST, DIC and nutrient distributions in the two models and consequently different atmospheric feedbacks (in the wind, net heat and freshwater fluxes into the ocean).