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.     

Evaluation of various vertical mixing parameterizations in a tropical Pacific Ocean GCM

Coupled general circulation models (GCMs) have had weak El Niño/Southern Oscillation variability that has been attributed to a diffuse thermocline in the modeled equatorial Pacific Ocean. Consequently, there have been many attempts to improve the thermocline by developing new or improved ocean vertical mixing schemes. This paper investigates the influence of gradient Richardson Number-based vertical mixing scheme profiles in a tropical Pacific Ocean GCM. It has been common for vertical mixing schemes to be assessed in tropical Pacific Ocean models that have a limited latitudinal domain bounded by zonal walls with sponge layers. However, recent work has shown that warm surface water can accumulate in these models and stop them from achieving the observed sharp equatorial thermocline. The present model employs a parameterized wall heat transport scheme that prevents warm surface water from accumulating. Thus we are able assess the influence of vertical mixing profiles in an ocean model that does not allow warm surface water to accumulate and influence the thermocline.In this paper we evaluate the equatorial performance of three different Richardson number (Ri)-based vertical mixing profiles: an integer power (IP) profile based on the observations of Peters, Gregg and Toole; a form of the Pacanowski and Philander profile modified to have low background mixing; and the Max Planck Institute profile. With the accumulation of warm surface water prevented, each of these profiles is able to achieve a sharp thermocline. When compared with observations, the IP profile achieves a better upwelling velocity distribution. We also examine the influence on equatorial performance of very high mixing coefficients at low Richardson number, and of low background mixing coefficients.     

The improvement of the one-dimensional Mellor-Yamada and K-profile parameterization turbulence schemes with the non-breaking surface wave-induced verticalmixing

Both the level 2.5 Mellor-Yamada turbulence closure scheme(MY) and K-profile parameterization(KPP) are popularly used by the ocean modeling community.The MY and the KPP are improved through including the non-breaking surface wave-induced vertical mixing(Bv),and the improved schemes were tested by using continuous data at the Papa ocean weather station(OWS) during 1961–1965.The numerical results showed that the Bv can make the temperature simulations fit much better with the continuous data from Papa Station.The two improved schemes overcame the shortcomings of predicting too shallow upper mixed layer depth and consequently overheated sea surface temperature during summertime,which are in fact common problems for all turbulence closure models.Statistical analysis showed that the Bv effectively reduced the mean absolute error and root mean square error of the upper layer temperature and increased the correlation coefficient between simulation and the observation.Furthermore,the performance of vertical mixing induced by shear instability and the Bv is also compared.Both the temperature structure and its seasonal cycle significantly improved by including the Bv,regardless of whether shear instability was included or not,especially for the KPP mixing scheme,which suggested that Bv played a dominant role in the upper ocean where the mean current was relatively weak,such as at Papa Station.These results may provide a clue to improve ocean circulation models.     

Comparative quantification of physically and numerically induced mixing in ocean models

A diagnostic method for calculating physical and numerical mixing of tracers in ocean models is presented. The physical mixing is defined as the turbulent mean tracer variance decay rate. The numerical mixing due to discretisation errors of tracer advection schemes is shown to be the decay rate between the advected square of the tracer variance and the square of the advected tracer and can be easily implemented into any ocean model. The applicability of the method is demonstrated for four test cases: (i) a one-dimensional linear advection equation with periodic boundary conditions, (ii) a two-dimensional flat-bottom lock exchange test case without mixing, (iii) a two-dimensional marginal sea overflow study with mixing and entrainment and (iv) the DOME test case with a dense bottom current propagating down a broad linear slope. The method has a number of advantages over previously introduced estimates for numerical mixing.     

Developments in ocean climate modelling

This paper presents some research developments in primitive equation ocean models which could impact the ocean component of realistic global coupled climate models aimed at large-scale, low frequency climate simulations and predictions. It is written primarily to an audience of modellers concerned with the ocean component of climate models, although not necessarily experts in the design and implementation of ocean model algorithms.     

Large eddy simulation of stratified mixing in two-dimensional dam-break problem in a rectangular enclosed domain

Mixing in both coastal and deep ocean emerges as one of the important processes that determines the transport of pollutants, sediments and biological species, as well as the details of the global thermohaline circulation. Both the observations, due to their lack in space and time resolution, and most coastal and general circulation models due to inadequate physics, can only provide partial information about oceanic mixing processes. A new class of nonhydrostatic models supplemented with physically based subgrid-scale (SGS) closures, or so-called large eddy simulation (LES), is put forth as another tool of investigation to complement observational and large-scale modeling efforts.However, SGS models have been developed primarily for homogeneous, isotropic flows. Here, four SGS models based on Smagorinsky eddy viscosity and diffusivity are tested for stratified flows in the context of 2D dam-break problem in a rectangular enclosed domain. This idealized testbed leads to a number of simplifications about the initial conditions, boundary conditions and geometry, while exhibiting the dynamically complex characteristics of stratified flows involving the interaction of shear-induced mixing and internal waves. Direct numerical simulations (DNS) at high resolutions are taken as benchmark solutions. Under-resolved simulations without SGS terms (so-called DNS¹) are used to quantify the impact of SGS stresses. The performance of LES is assessed by using the time evolution of the volume fraction of intermediate density water masses generated by mixing. The simulations are conducted using a nonhydrostatic high-order spectral element model Nek5000 developed to exhibit minimal numerical dissipation and dispersion errors, which is advantageous to quantify accurately the impact of SGS stresses.It is found that all tested SGS models lead to improved results with respect to those from DNS¹. Also, SGS models allow for simulations with coarse resolutions that blow up in DNS¹ due to lack of adequate dissipation where needed. The SGS model in which the vertical eddy diffusion is modulated via a function that depends on the Richardson number Ri shows the most faithful reproduction of mixed water masses at all resolutions tested.The sensitivity of the results to the tunable parameter of the SGS model, to changes in the Ri-dependent function and resolution of the turbulent overturning scales is shown.     

Comparing the overflow of dense water in isopycnic and cartesian models with tracer observations in the eastern Mediterranean

Isopycnic and cartesian model simulations for the overflow and spreading of dense water are compared with each other and with independent transient-tracer observations. This case study is performed for Adriatic dense water overflowing into the deep eastern Mediterranean with chlorofluoromethane (CFC-12) observations used to test the model simulations. The realism of both types of model simulation depends on the representation of diapycnal mixing. In the cartesian model, convective adjustment and mixing dilute the overflow of Adriatic dense water and lead to unrealistic vertical homogenization. Incorporating a modified convection scheme emphasizing the sinking of dense fluid, rather than its mixing, leads to a more realistic penetration of the dense overflow. In the isopycnic model, there is an improved simulation of the overflow, which leads to the density contrast of the deep Mediterranean waters being maintained. However, there is too low a CFC-12 concentration at mid-depths unless explicit diapycnal mixing is incorporated. In each model, the different spreading of dense water is associated with a different bottom pressure torque and depth-integrated transport, and hence with contrasting tracer distributions throughout the water column.     

Some consequences of a flood tide front in Loch Creran

Loch Creran is a small Scottish sea loch with two basins which are connected by a shallow narrows. A sharp front that forms just inside the narrows during flood tides producing a simple mechanism for flushing the top brackish layer of the inner basin. The mechanism is shown to be consistent with temperature and velocity data. Conservation equations are used with salinity data to estimate mixing and entrainment rates and thus the energy used. A bottom drag coefficient for the narrows is estimated from the tidal signals of velocity and pressure gradient, and the turbulent kinetic energy entering the inner loch from the narrows is calculated, so that finally a value for the flux Richardson number (the fraction of available energy used by mixing and entrainment) can be given.     

Numerical Simulations of Sea Surface Cooling by a Mixed Layer Model during the Passage of Typhoon Rex

In order to investigate the formation mechanism of rapid decrease of maritime sea surface temperature (SST) observed by R/V Keifu Maru, the ocean response to Typhoon Rex is simulated using a mixed layer model. The rapid decrease of the maritime SST is successfully simulated with realistic atmospheric forcing and an entrainment scheme of which sources of turbulent kinetic energy (TKE) are production due to wind stress, generation during free convection, and production due to current shear. The rapid decrease at the observed station by R/V Keifu Maru is not produced by instant atmospheric forcing but is mainly produced by entrainment on the right side of the running typhoon as a part of cooling area during its passage, and remained during a few days. The sea surface cooling (SSC) is evident along the track and on the right side of the running typhoon, which is similar to the SSC of satellite observation by TRMM/TMI. The conspicuous SSC produced by both entrainment and upwelling is situated just under the track of typhoon when the typhoon moves slower. Intercomparison of entrainment schemes of the mixed layer model is implemented. Frictional velocity and buoyancy effects are effective for a gradual SSC covering the wide region. In contrast, the effect of current shear at the mixed layer base is related to the amount of SSC and the sharp horizontal gradient of SSC. The entrainment scheme including all three TKE sources has the best performance for SSC simulation.     

Comparison of gravity current mixing parameterizations and calibration using a high-resolution 3D nonhydrostatic spectral element model

In light of the pressing need for development and testing of reliable parameterizations of gravity current entrainment in ocean general circulation models, two existing entrainment parameterization schemes, K-profile parameterization (KPP) and one based on Turner’s work (TP), are compared using idealized experiments of dense water flow over a constant-slope wedge using the HYbrid Coordinate Ocean Model (HYCOM). It is found that the gravity current entrainment resulting from KPP and TP differ significantly from one another. Parameters of KPP and TP are then calibrated using results from the high-order nonhydrostatic spectral element model Nek5000. It is shown that a very good agreement can be reached between the HYCOM simulations with KPP and TP, even though these schemes are quite different from each other.     

Numerical study of the meridional overturning circulation with “mixing hotspots” in the Pacific Ocean

Using an idealized ocean general circulation model, we examine the effect of “mixing hotspots” (localized regions of intense diapycnal mixing) predicted based on internal wave-wave interaction theory (Hibiya et al., 2006) on the meridional overturning circulation of the Pacific Ocean. Although the assumed diapycnal diffusivity in the mixing hotspots is a little larger than the predicted value, the upwelling in the mixing hotspots is not sufficient to balance the deep-water production; out of 17 Sv of the downwelled water along the southern boundary, only 9.2 Sv is found to upwell in the mixing hotspots. The imbalance as much as 7.8 Sv is compensated by entrainment into the surface mixed layer in the vicinity of the downwelling region. As a result, the northward transport of the deep water crossing the equator is limited to 5.5 Sv, much less than estimated from previous current meter moorings and hydrographic surveys. One plausible explanation for this is that the magnitude of the meridional overturning circulation of the Pacific Ocean has been overestimated by these observations. We raise doubts about the validity of the previous ocean general circulation models where diapycnal diffusivity is assigned ad hoc to attain the current magnitude suggested from current meter moorings and hydrographic surveys.     

Ocean circulation and sea ice distribution in a finite element global sea ice–ocean model

A newly developed global Finite Element Sea Ice–Ocean Model (FESOM) is presented. The ocean component is based on the Finite Element model of the North Atlantic (FENA) but has been substantially updated and extended. In addition to a faster realization of the numerical code, state-of-the-art parameterizations of subgrid-scale processes have been implemented. A Redi/GM scheme is employed to parameterize the effects of mesoscale eddies on lateral tracer distribution. Vertical mixing and convection are parameterized as a function of the Richardson number and the Monin–Obukhov length. A finite element dynamic-thermodynamic sea ice–model has been developed and coupled to the ocean component. Sea ice thermodynamics have been derived from the standard AWI sea ice model featuring a prognostic snow layer but neglecting internal heat storage. The dynamic part offers the viscous-plastic and elastic-viscous-plastic rheologies. All model components are discretized on a triangular/tetrahedral grid with a continuous, conforming representation of model variables. The coupled model is run in a global configuration and forced with NCEP daily atmospheric reanalysis data for 1948–2007. Results are analysed with a slight focus on the Southern Hemisphere. Many aspects of sea ice distribution and hydrography are found to be in good agreement with observations. As in most coarse-scale models, Gulf Stream transport is underestimated, but transports of the Kuroshio and the Antarctic Circumpolar Current appear realistic. The seasonal cycles of Arctic and Antarctic sea ice extents and Antarctic sea ice thickness are well captured; long- and short-term variability of ice coverage is found to be reproduced realistically in both hemispheres. The coupled model is now ready to be used in a wide range of applications.     

Roles of vertical turbulent mixing in the ocean response to Typhoon Rex (1998)

How the role of vertical turbulent mixing (VTM) in sea surface cooling (SSC) varies with the moving speed of a tropical cyclone was examined for Typhoon Rex (1998) by using the Meteorological Research Institute Community Ocean Model (MRI.COM). The MRI.COM well reproduced TRMM/TMI three-day mean sea surface temperature (SST) fields along Rex’s track. During the fast-moving phase of Rex, SSC simulated by the MRI.COM was caused by shear-induced VTM on the right side of the track. During the slowly-moving phase, on the other hand, the Ekman-pumping area mostly overlapped the VTM area right behind Rex’s center. During the recurvature phase, cool water transported by the upwelling was more efficiently entrained into a mixed layer by the VTM for nearly a 1 near-inertial period after the passage of Rex. We then modified the entrainment formulation of Deardorff (1983), which was incorporated into a slab mixed-layer ocean model (SOM) so as to fit to the results simulated by the MRI.COM. The principal modifications are as follows: (1) consideration of turbulent kinetic energy (TKE) production caused by surface wave breaking; (2) increase in the coefficient for estimating dissipation to balance with TKE production due to turbulent transport; and (3) changing the initial guess for the critical Richardson number. These modifications led to an improvement of SST simulations by the SOM. The impact of the modifications on simulated SSTs turned out to be more significant than the impacts of initial mixed-layer depth and the difference between diurnally-varying and daily mean short-wave radiation.     

Evaluations of threshold and curvature mixed layer depths by various mixing schemes in the Mediterranean Sea

Predictive ability of five different embedded turbulent mixing models that range from second-order turbulent closure to bulk mixing parameterization is examined in the Mediterranean Sea. Each is embedded in the HYbrid Coordinate Ocean Model (HYCOM). Mixed layer depth (MLD), which is one of the most important upper ocean variables, is used to evaluate the treatment of turbulent processes in each model run. In addition to overall spatial and temporal variability, analyses of MLD are presented using an extensive set (3976) of temperature and salinity profiles from various data sources during 2003–2006. Results obtained from simulations (with no data assimilation and relaxation only to salinity) for the five mixing models are compared with observed MLDs obtained from in situ temperature and salinity profile observations. To ensure the robustness of the validation statistics MLD is computed using both curvature and threshold based methodologies. Results indicate that while all mixing schemes represent the MLD well, the bulk mixing models have substantial accuracy deficiencies relative to the higher order mixing models. The modeled MLDs are slightly deeper than observed MLDs with the mean bias error ∼10 m for the higher order mixing models while the bulk mixing model bias error is 15 m or more. The RMS error for the higher order mixing models is ∼40 m while it is ∼50 m for the bulk mixing models. The bulk mixing models had substantially larger errors particularly for the curvature MLD definition.     

On the eddy mixing and energetics of turbulence in a stable atmospheric boundary layer

Some changes in the eddy mixing in the atmospheric boundary layer (ABL) are investigated with the use of the mesoscale RANS turbulence model. It is found that the behavior of parameters of the eddy turbulence mixing is in compliance with the recently obtained data of laboratory and atmospheric measurements. In particular, the flow Richardson number (Ri _f ) during the transient flow to a strongly stable state can behave nonmonotonically, growing with the increasing gradient Richardson number (Ri _g ) to the state of saturation at a certain gradient Richardson number (Ri _g ? 1), which separates two different turbulent regimes: the regimes of strong mixing and weak mixing. An analysis of the energetics based on the balance equations of kinetic and potential turbulence energies shows, in particular, that the weak mixing (Ri _g > 1) is quite capable of transferring momentum. This phenomenon can be explained not only by the fact that the flow is sustained by propagating internal waves, which effectively transfer momentum under strong stratification conditions, but also by the fact that turbulence permanently arises in the free atmosphere and in the deep ocean at Ri _g ? 1.     

A comparison of two global ocean-ice coupled models with different horizontal resolutions

A global eddy-permitting ocean-ice coupled model with a horizontal resolution of 0.25 by 0.25 is established on the basis of Modular Ocean Model version 4 (MOM4) and Sea Ice Simulator (SIS). Simulation results are compared with those of an intermediate resolution ocean-ice coupled model with a horizontal resolution of about 1 by 1 . The results show that the simulated ocean temperature, ocean current and sea ice concentration from the eddy-permitting model are better than those from the intermediate resolution model. However, both the two models have the common problem of ocean general circulation models (OGCMs) that the majority of the simulated summer sea surface temperature (SST) is too warm while the majority of the simulated subsurface summer temperature is too cold. Further numerical experiments show that this problem can be alleviated by incorporating the non-breaking surface wave-induced vertical mixing into the vertical mixing scheme for both eddy-permitting and intermediate resolution models.     

Calculations of the evolution of the upper ocean based on the similarity theory

Several schemes of turbulent mixing in the upper ocean are considered, including a modified scheme based on the modified Monin-Obukhov similarity theory. The schemes have been used for the calculation of the evolution of the upper ocean. The results are compared with the data of automated buoys. It is shown that the scheme based on the similarity theory gives a result not worse than the commonly used ones and has several advantages, which makes it the most appropriate for including in the ocean circulation models and climate models.     

表面波浪对海洋上层混合的作用

A new three-dimensional numerical model is derived through a wave average on the primitive N-S equations, in which both the＂Coriolis-Stokes forcing＂ and the＂Stokes-Vortex force＂ are considered. Three ideal experiments are run using the new model applied to the Princeton ocean model （POM）. Numerical results show that surface waves play an important role on the mixing of the upper ocean. The mixed layer is enhanced when wave effect is considered in conjunction with small Langmuir numbers. Both surface wave breaking and Stokes production can strengthen the turbulent mixing near the surface. However, the influence of wave breaking is limited to a thin layer, but Stokes drift can affect the whole mixed layer. Furthermore, the vertical mixing coefficients clearly rise in the mixed layer, and the upper ocean mixed layer is deepened especially in the Antarctic Circumpolar Current when the model is applied to global simulations. It indicates that the surface gravity waves are indispensable in enhancing the mixing in the upper ocean, and should be accounted for in ocean general circulation models.     

The role of surface waves in the ocean mixed layer

Previously, most ocean circulation models have overlooked the role of the surface waves. As a result, these models have produced insufficient vertical mixing, with an under - prediction of the ,nixing layer （ML） depth and an over - prediction of the sea surface temperature （SST）, particularly during the summer season. As the ocean surface layer determines the lower boundary conditions of the atmosphere, this deficiency has severely limited the performance of the coupled ocean - atmospheric models and hence the climate studies. To overcome this shortcoming, a new parameterization for the wave effects in the ML model that will correct this systematic error of insufficient mixing. The new scheme has enabled the mixing layer to deepen, the surface excessive heating to be corrected, and an excellent agreement with observed global climatologic data. The study indicates that the surface waves are essential for ML formation, and that they are the primer drivers of the upper ocean dynamics; therefore, they are critical for climate studies.     

印度尼西亚海潮致混合研究现状与展望

印度尼西亚海(简称印尼海)位于热带太平洋和印度洋交汇的海域,是全球最大的内潮生成海域.内潮耗散导致强烈的潮致混合,一方面将温跃层以下的海水卷入上层,降低印尼海海表温度,之后通过海气相互作用产生显著的天气和气候效应;另一方面对穿越印尼海的印度尼西亚贯穿流的物质与能量输运也有着重要影响.自Ar-lindo计划以来,人们对印...