Mixing parameterizations in ocean climate modeling

Results of numerical experiments with an eddy-permitting ocean circulation model on the simulation of the climatic variability of the North Atlantic and the Arctic Ocean are analyzed. We compare the ocean simulation quality with using different subgrid mixing parameterizations. The circulation model is found to be sensitive to a mixing parametrization. The computation of viscosity and diffusivity coefficients by an original splitting algorithm of the evolution equations for turbulence characteristics is found to be as efficient as traditional Monin–Obukhov parameterizations. At the same time, however, the variability of ocean climate characteristics is simulated more adequately. The simulation of salinity fields in the entire study region improves most significantly. Turbulent processes have a large effect on the circulation in the long-term through changes in the density fields. The velocity fields in the Gulf Stream and in the entire North Atlantic Subpolar Cyclonic Gyre are reproduced more realistically. The surface level height in the Arctic Basin is simulated more faithfully, marking the Beaufort Gyre better. The use of the Prandtl number as a function of the Richardson number improves the quality of ocean modeling.     

A note on the direct injection of turbulence by breaking waves

We investigate the turbulence induced by wave-breaking at the ocean surface. Two recent models use a mechanism of direct depth injection of turbulent kinetic energy (TKE) by breaking waves. Those models aim to reproduce the near-surface mean and turbulent properties, in particular the TKE dissipation rates. Of critical importance are the injection depth of each breaking wave and the size distribution of those breaking waves. The models by Sullivan et al. (2007) and by Kudryavtsev et al. (2008) have very different parameterizations, and those differences are reviewed here and compared to available observations. Using realistic parameterizations in these models leads to TKE injections too shallow to compare to observations, in particular for developed seas. The near-surface turbulence is thus still not well understood to the zeroth order. For instance, whether developed seas produce deeper or shallower mixing than young seas is neither well understood nor well modelled. Additional dedicated measurements as well as investigations of breaking non-breaking wave interactions are needed.     

海浪破碎对海洋上混合层中湍能量收支的影响

海浪破碎产生一向下输入的湍动能通量,在近海表处形成一湍流生成明显增加的次层,加强了海洋上混合层中的湍流垂向混合。为了研究海浪破碎对混合层中湍能量收支的影响,文中分析了海浪破碎对海洋上混合层中湍流生成的影响机制,采用垂向一维湍封闭混合模式,通过改变湍动能方程的上边界条件,引入了海浪破碎产生的湍动能通量,并分别对不同风速下海浪破碎的影响进行了数值研究,分析了混合层中湍能量收支的变化。当考虑海浪破碎影响时,近海表次层中的垂直扩散项和耗散项都有显著的增加,该次层中被耗散的湍动能占整个混合层中耗散的总的湍能量的92.0%,比无海浪破碎影响的结果增加了近1倍;由于平均流场切变减小,混合层中的湍流剪切生成减小了3.5%,形成一种存在于湍动能的耗散和垂直扩散之间的局部平衡关系。在该次层以下,局部平衡关系与壁层定律的结论一致,即湍动能的剪切生成与耗散相平衡。研究结果表明,海浪破碎在海表产生的湍动能通量影响了海洋上混合层中的各项湍能量收支间的局部平衡关系。     

Effect of roughness formulation on the performance of a coupled wave,hydrodynamic, and sediment transport model

A variety of algorithms are available for parameterizing the hydrodynamic bottom roughness associated with grain size, saltation, bedforms, and wave–current interaction in coastal ocean models. These parameterizations give rise to spatially and temporally variable bottom-drag coefficients that ostensibly provide better representations of physical processes than uniform and constant coefficients. However, few studies have been performed to determine whether improved representation of these variable bottom roughness components translates into measurable improvements in model skill. We test the hypothesis that improved representation of variable bottom roughness improves performance with respect to near-bed circulation, bottom stresses, or turbulence dissipation. The inner shelf south of Martha’s Vineyard, Massachusetts, is the site of sorted grain-size features which exhibit sharp alongshore variations in grain size and ripple geometry over gentle bathymetric relief; this area provides a suitable testing ground for roughness parameterizations. We first establish the skill of a nested regional model for currents, waves, stresses, and turbulent quantities using a uniform and constant roughness; we then gauge model skill with various parameterization of roughness, which account for the influence of the wave-boundary layer, grain size, saltation, and rippled bedforms. We find that commonly used representations of ripple-induced roughness, when combined with a wave–current interaction routine, do not significantly improve skill for circulation, and significantly decrease skill with respect to stresses and turbulence dissipation. Ripple orientation with respect to dominant currents and ripple shape may be responsible for complicating a straightforward estimate of the roughness contribution from ripples. In addition, sediment-induced stratification may be responsible for lower stresses than predicted by the wave–current interaction model.     

Modeling of the Turbulence in the Water Column under Breaking Wind Waves

Past studies have shown that there is a wave-enhanced, near-surface mixed-layer in which the dissipation rate is greater than that derived from the “law of the wall”. In this study, turbulence in water columns under wind breaking waves is investigated numerically and analytically. Improved estimations of dissipation rate are parameterized as surface source of turbulent kinetic energy (TKE) for a more accurate modelling of vertical profile of velocity and TKE in the water column. The simulation results have been compared with the experimental results obtained by Cheung and Street (1988) and Kitaigorodskii et al. (1983), with good agreement. The results show that the numerical full model can well simulate the near-surface wave-enhanced layer and suggest that the vertical diffusive coefficients are highly empirical and related to the TKE diffusion, the shear production and the dissipation. Analytical solutions of TKE are also derived for near surface layer and in deep water respectively. Near the surface layer, the dissipation rate is assumed to be balanced by the TKE diffusion to obtain the analytical solution; however, the balance between the dissipation and the shear production is applied at the deep layer. The analytical results in various layers are compared with that of the full numerical model, which confirms that the wave-enhanced layer near the surface is a diffusion-dominated region. The influence of the wave energy factor is also examined, which increases the surface TKE flux with the wave development. Under this region, the water behavior transits to satisfy the classic law of the wall. Below the transition depth, the shear production dominantly balances the dissipation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Algorithm of the <Emphasis Type="Italic">k</Emphasis>–ω Turbulence Equations Solution for the Ocean General Circulation Model

The algorithm for splitting k–ω turbulence equations is used to parameterize viscosity and diffusion coefficients in the ocean general circulation model. The k–ω equations are split into stages describing the transport-diffusion and generation-dissipation of the turbulent kinetic energy and frequency function ω. At the generation-dissipation stage, the equations are solved analytically. Calculations of circulation in the North Atlantic–Arctic Ocean for 1948–2009 have been carried out. The experiments demonstrate an adequate reproduction of hydrophysical characteristics and high efficiency of the algorithm. It is shown that considering the climatic annual mean buoyancy frequency in the turbulence equations at the generation-dissipation stage is an important factor in improving the accuracy of simulated fields.     

海浪破碎对北太平洋海表面温度模拟的影响

基于海浪模式WAVEWATCH Ⅲ模拟北太平洋海浪要素,结合NDBC浮标资料进行验证,发现模拟出的有效波高与浮标测量值具有很好的一致性。基于改进型白冠覆盖率耗散模型,利用海浪模式模拟出的有效波高、有效波周期和摩擦速度等海浪要素计算出单位面积水柱内因海浪破碎产生的湍动能通量。通过改变环流模式sbPOM湍动能方程的上边界条件,引入海浪破碎产生的湍动能通量,并探究海浪破碎对北太平洋海表面温度模拟的影响。研究表明,由于海浪破碎的引入,环流模式sbPOM对北太平洋海表面温度模拟的准确程度得到提升,这为大气模式提供一个准确的北太平洋下边界条件具有重要意义。     

Resolution convergence and sensitivity studies with North Atlantic circulation models. Part I: The western boundary current system

The fidelity of numerical simulations of the general circulation of the North Atlantic Ocean in basin- to global-scale models have improved considerably in the last several years. This improvement appears to represent a regime shift in the dynamics of the simulated flow as the horizontal grid spacing decreases to around 10 km. Nevertheless, some significant biases in the simulated circulation and substantial uncertainties about the robustness of these results with respect to parameterization choices remain. A growing collection of simulations obtained with the POP primitive equation model allow us to investigate the convergence properties and sensitivity of high resolution numerical simulations of the North Atlantic, with particular attention given to Gulf Stream separation and the subsequent path of the North Atlantic Current into the Northwest Corner. Increases in resolution and reductions in dissipation both contribute to the improvements in the circulation seen in recent studies. We find that our highest resolution eddy-resolving simulations retain an appreciable sensitivity to the closure scheme. Our most realistic simulations of the Gulf Stream are not obtained at the lowest levels of dissipation, while the simulation of the North Atlantic Current continues to improve as dissipation is reduced to near the numerical stability limit. In consequence, there is a limited range of parameter space where both aspects of the simulated circulation can be brought into agreement with observations. This experience gained with the comparatively affordable regional North Atlantic model is now being used to configure the next generation of ocean climate 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.     

Reconstructing the upper ocean thermal profiles using one-dimensional numerical model

The observation data for 5 d at a station in the South China Sea is presented.After brief analysis of the wind speed,air temperature from the ship-borne meteorological instruments and temperature and salinity profiles from the CTD (conductivity,temperature,depth recorder) data,the authors find that the CTD casts are too sparse for us to understand the diurnal evolution of the thermal structure in the upper ocean.A one-dimensional (1D) numerical code based on Mellor-Yamada turbulence closure model is used to reconstruct the upper ocean thermal structure,utilizing the atmospheric forcing data from ship-borne weather station.The simulation results show good agreement with the observational data;the significance of breaking waves is also briefly discussed.The evolution of turbulence kinetic energy (TKE) and the contribution from shear production and buoyancy production are discussed respectively.Finally,several possible factors which might influence the numerical results are briefly analyzed.     

A numerical study of swash flows generated by bores

The dynamic processes of bore propagation over a uniform slope are studied numerically using a 2-D Reynolds Averaged Navier–Stokes (RANS) solver, coupled to a non-linear k − ε turbulence closure and a volume of fluid (VOF) method. The dam-break mechanism is used to generate bores in a constant depth region. Present numerical results for the ensemble-averaged flow field are compared with existing experimental data as well as theoretical and numerical results based on non-linear shallow water (NSW) equations. Reasonable agreement between the present numerical solutions and experimental data is observed. Using the numerical results, small-scale bore behaviors and flow features, such as the bore collapse process near the still-water shoreline, the ‘mini-collapse’ during the runup phase and the ‘back-wash bore’ in the down-rush phase, are described. In the case of a strong bore, the evolution of the averaged turbulence kinetic energy (TKE) over the swash zone consists of two phases: in the region near the still-water shoreline, the production and the dissipation of TKE are roughly in balance; in the region farther landwards of the still-water shoreline, the TKE decay rate is very close to that of homogeneous grid turbulence. On the other hand, in the case of a weak bore, the bore collapse generated turbulence is confined near the bottom boundary layer and the TKE decays at a much slower rate.     

Modelling of the upper turbulent layer in the ocean

A differential model of the upper turbulent layer in the ocean is considered. A closed system of equations includes equations of motion, balance, and dissipation of kinetic turbulence energy. Boundary conditions at the surface are determined using a solution of the atmospheric problem taking into account the interaction between the two media. The formulated algorithm allows for a relationship between turbulent energy dissipation and flux and the parameters of wind disturbance. The vertical profiles of turbulence and drift current characteristics are presented as well as parameters of the ocean-atmosphere interaction for various values of impulse jump within the limits of the wave layer with waves collapsing and not collapsing.UDK 551.456.152     

Observational and numerical modeling methods for quantifying coastal ocean turbulence and mixing

In this review paper, state-of-the-art observational and numerical modeling methods for small scale turbulence and mixing with applications to coastal oceans are presented in one context. Unresolved dynamics and remaining problems of field observations and numerical simulations are reviewed on the basis of the approach that modern process-oriented studies should be based on both observations and models. First of all, the basic dynamics of surface and bottom boundary layers as well as intermediate stratified regimes including the interaction of turbulence and internal waves are briefly discussed. Then, an overview is given on just established or recently emerging mechanical, acoustic and optical observational techniques. Microstructure shear probes although developed already in the 1970s have only recently become reliable commercial products. Specifically under surface waves turbulence measurements are difficult due to the necessary decomposition of waves and turbulence. The methods to apply Acoustic Doppler Current Profilers (ADCPs) for estimations of Reynolds stresses, turbulence kinetic energy and dissipation rates are under further development. Finally, applications of well-established turbulence resolving particle image velocimetry (PIV) to the dynamics of the bottom boundary layer are presented. As counterpart to the field methods the state-of-the-art in numerical modeling in coastal seas is presented. This includes the application of the Large Eddy Simulation (LES) method to shallow water Langmuir Circulation (LC) and to stratified flow over a topographic obstacle. Furthermore, statistical turbulence closure methods as well as empirical turbulence parameterizations and their applicability to coastal ocean turbulence and mixing are discussed. Specific problems related to the combined wave-current bottom boundary layer are discussed. Finally, two coastal modeling sensitivity studies are presented as applications, a two-dimensional study of upwelling and downwelling and a three-dimensional study for a marginal sea scenario (Baltic Sea). It is concluded that the discussed methods need further refinements specifically to account for the complex dynamics associated with the presence of surface and internal waves.     

An oceanic general circulation model framed in hybrid isopycnic-Cartesian coordinates

A newly developed hybrid-coordinate ocean circulation model is documented and tested. Coordinate surfaces in this model adhere to isopycnals wherever this does not violate minimum layer thickness requirements; elsewhere, coordinate surfaces are geometrically constrained. The intent of this approach, some of whose features are reminiscent of the Arbitrary Lagrangian–Eulerian (ALE) technique, is to combine the best features of isopycnic-coordinate and fixed-grid circulation models within a single framework. The hybrid model is an offshoot of the Miami Isopycnic Coordinate Ocean Model whose solutions, obtained under identical geographic and forcing conditions, serve as reference. Century-scale simulations on a coarse-mesh near-global domain show considerable similarities in the modeled thermohaline-forced circulation. Certain architectural details, such as the choice of prognostic thermodynamic variables (ρ,S versus T,S) and the algorithm for moving coordinate surfaces toward their reference isopycnals, are found to only have a minor impact on the solution. Emphasis in this article is on the numerical resiliency of the hybrid coordinate approach. Exploitation of the model's flexible coordinate layout in areas of ocean physics where pure isopycnic coordinate models only have limited options, such as mixed-layer turbulence parameterization, will be the subject of forthcoming articles.     

涡分辨率的南海区域海洋环流模式构建技术研究

针对复杂海洋中尺度现象模拟仿真的技术难题,利用区域海洋环流模式ROMS,通过模式的网格构建、地形处理以及模式的初始场和强迫场处理技术,构建出一套涡分辨率南海区域海洋环流模式。通过模式模拟结果与卫星遥感实测资料等对比,发现该模式能够较好地模拟出南海涡旋及其引发的海温异常等海洋中小尺度过程,说明该模式可作为研究复杂海洋中尺度现象影响海军武器装备效能的环境数值仿真手段。     

Microstructure measurements and finescale parameterization assessment of turbulent mixing in the northern South China Sea

Both microscale and finescale measurements were conducted along 20°N and 21°N in the northern South China Sea (SCS) during July 2007. Spatial variability of turbulent kinetic energy (TKE) dissipation rate was examined, and two finescale parameterizations were assessed and compared. TKE dissipation rates along the 21°N section were found to be much higher than those along 20°N; in particular, remarkably high TKE dissipation rates existed near the Luzon Strait and around the Dongsha Plateau, which were likely caused by internal tides and internal solitary waves, respectively. The Gregg–Henyey scaling does not work well in the northern SCS, while the MacKinnon–Gregg scaling with a modified parameter matches the observations in both magnitude and variability. One explanation is that the large-scale/low-mode shear mainly comes from low-frequency internal waves such as internal tides, which are not described well by the Garrett–Munk spectrum.     

A general ecosystem model for applications to primary productivity and carbon cycle studies in the global oceans

We have developed a general 1-D multi-component ecosystem model that incorporates a skillful upper ocean mixed layer model based on second moment closure of turbulence. The model is intended for eventual incorporation into coupled 3-D physical–biogeochemical ocean models with potential applications to modeling and studying primary productivity and carbon cycling in the global oceans as well as to promote the use of chlorophyll concentrations, in concert with satellite-sensed ocean color, as a diagnostic tool to delineate circulation features in numerical circulation models. The model is nitrogen-based and the design is deliberately general enough and modular to enable many of the existing ecosystem model formulations to be simulated and hence model-to-model comparisons rendered feasible. In its more general form (GEM10), the model solves for nitrate, ammonium, dissolved nitrogen, bacteria and two size categories of phytoplankton, zooplankton and detritus, in addition to solving for dissolved inorganic carbon and total alkalinity to enable estimation of the carbon dioxide flux at the air–sea interface. Dissolved oxygen is another prognostic variable enabling air–sea exchange of oxygen to be calculated. For potential applications to HNLC regions where productivity is constrained by the availability of a trace constituent such as iron, the model carries the trace constituent as an additional prognostic variable. Here we present 1-D model simulations for the Black Sea, Station PAPA and the BATS site. The Black Sea simulations assimilate seasonal monthly SST, SSS and surface chlorophyll, and the seasonal modulations compare favorably with earlier work. Station PAPA simulations for 1975–1977 with GEM5 assimilating observed SST and a plausible seasonal modulation of surface chlorophyll concentration also compare favorably with earlier work and with the limited observations on nitrate and pCO₂ available. Finally, GEM5 simulations at BATS for 1985–1997 are consistent with the available time series. The simulations suggest that while it is generally desirable to employ a comprehensive ecosystem model with a large number of components when accurate depiction of the entire ecosystem is desirable, as is the prevailing practice, a simpler formulation such as GEM5 (N²PZD model) combined with assimilation of remotely sensed SST and chlorophyll concentrations may suffice for incorporation into 3-D prediction models of primary productivity, upper ocean optical clarity and carbon cycling.     

Southern Ocean transformation in a coupled model with and without eddy mass fluxes

A coupled air–sea general circulation model is used to simulate the global circulation. Different parameterizations of lateral mixing in the ocean by eddies, horizontal, isopycnal, and isopycnal plus eddy advective flux, are compared from the perspective of water mass transformation in the Southern Ocean. The different mixing physics imply different buoyancy equilibria in the surface mixed layer, different transformations, and therefore a variety of meridional overturning streamfunctions. The coupled‐model approach avoids strong artificial water mass transformation associated with relaxation to prescribed mixed layer conditions. Instead, transformation results from the more physical non‐local, nonlinear interdependence of sea‐surface temperature, air–sea fluxes, and circulation in the model's atmosphere and ocean. The development of a stronger mid‐depth circulation cell and associated upwelling when eddy fluxes are present, is examined. The strength of overturning is diagnosed in density coordinates using the transformation framework.     

Effect of Stokes drift on upper ocean mixing

Stokes drift is the main source of vertical vorticity in the ocean mixed layer. In the ways of Coriolis - Stokes forcing and Langmuir circulations, Stokes drift can substantially affect the whole mixed layer. A modified Mellor-Yamada 2. 5 level turbulence closure model is used to parameterize its effect on upper ocean mixing conventionally. Results show that comparing surface heating with wave breaking, Stokes drift plays the most important role in the entire ocean mixed layer, especially in the subsurface layer. As expected, Stokes drift elevates both the dissipation rate and the turbulence energy in the upper ocean mixing. Also, ilffluence of the surface heating, wave breaking and wind speed on Stokes drift is investigated respectively. Research shows that it is significant and important to assessing the Stokes drift into ocean mixed layer studying. The laboratory observations are supporting numerical experiments quantitatively.