A diapycnal diffusion algorithm for isopycnal ocean circulation models with special application to mixed layers

An algorithm is presented for solving the one-dimensional diffusion equation for density, written in terms of density (or a like surrogate) as the independent variable. The algorithm maintains nonnegative layer thicknesses, the premise of the transformation to density as the independent coordinate, under certain restrictions. Near-zero thickness layers can be maintained at the boundaries to accommodate future inflation in response to heating from the boundary. Layers can shrink to near-zero thickness in response to cooling from the boundary. A slight modification of the algorithm permits layers to have diffusion coefficients which differ by orders of magnitude. This provides a natural framework for a surface mixed layer in an isopycnal model, in which the mixed layer is distinguished as a zone of very high turbulent diffusivity overlying an ocean interior of much smaller turbulent diffusivity. The “mixed layer” may be an aggregation of several isopycnal layers rather than just one. A substantial jump in density at the mixed layer base can be represented by several near-zero thickness isopycnal layers. The specification of the thickness of the mixing zone, i.e., the mixed layer depth, is external to the algorithm. An illustration is given using a Kraus–Turner-type specification.     

利用全球温盐观测剖面计划资料估算太平洋上层跨等密度面混合

基于全球多年来积累的大量温盐观测剖面计划资料,利用精细尺度参数化方案估算了太平洋上层600米区域内的跨等密度面混合系数。结果表明,在不同季节跨等密度面混合系数的整体分布类似,但是细节上存在很大的不同。跨等密度面混合系数的加强与底部摩擦、海表面近惯性能量输入、赤道效应等因素密切相关。由于粗糙的地形,混合在东北太平洋门多西诺断裂带附近存在明显加强。同时,在南大洋西风带区域,由于大风引起的近惯性能量输入也导致了混合的强化。 与前人的研究结果相比,本文的估算具有更好的空间覆盖率以及更高的分辨率,更重要的是我们的结果体现了季节性变化。由于我们给出的是网格化产品,非常适合在数值模式中的应用。     

Spurious diapycnal mixing in terrain-following coordinate models: The problem and a solution

In this paper, we identify a crucial numerical problem in sigma coordinate models, leading to unacceptable spurious diapycnal mixing. This error is a by-product of recent advances in numerical methods, namely the implementation of high-order diffusive advection schemes. In the case of ROMS, spurious mixing is produced by its third-order upwind advection scheme, but our analysis suggests that all diffusive advection schemes would behave similarly in all sigma models. We show that the common idea that spurious mixing decreases with resolution is generally false. In a coarse-resolution regime, spurious mixing increases as resolution is refined, and may reach its peak value when eddy-driven lateral mixing becomes explicitly resolved. At finer resolution, diffusivities are expected to decrease but with values that only become acceptable at resolutions finer than the kilometer. The solution to this problem requires a specifically designed advection scheme. We propose and validate the RSUP3 scheme, where diffusion is split from advection and is represented by a rotated biharmonic diffusion scheme with flow-dependent hyperdiffusivity satisfying the Peclet constraint. The rotated diffusion operator is designed for numerical stability, which includes improvements of linear stability limits and a clipping method adapted to the sigma-coordinate. Realistic model experiments in a southwest Pacific configuration show that RSUP3 is able to preserve low dispersion and diffusion capabilities of the original third-order upwind scheme, while preserving water mass characteristics. There are residual errors from the rotated diffusion operator, but they remain acceptable. The use of a constant diffusivity rather than the Peclet hyperdiffusivity tends to increase these residual errors which become unacceptable with Laplacian diffusion. Finally, we have left some options open concerning the use of time filters as an alternative to spatial diffusion. A temporal discretization approach to the present problem (including implicit discretization) will be reported in a following paper.     

Effect of Langmuir circulation on upper ocean mixing in the South China Sea

Effect of Langmuir circulation (LC) on upper ocean mixing is investigated by a two-way wave-current coupled model. Themodel is coupled of the ocean circulationmodel ROMS (regional ocean modeling system) to the surface wave model SWAN (simulating waves nearshore) via the model-coupling toolkit. The LC already certified its importance by many one-dimensional (1D) research andmechanismanalysis work. This work focuses on inducing LC’s effect in a three-dimensional (3-D) model and applying it to real field modeling. In ROMS, theMellor-Yamada turbulence closuremixing scheme is modified by including LC’s effect. The SWAN imports bathymetry, free surface and current information fromthe ROMS while exports significant wave parameters to the ROMS for Stokes wave computing every 6 s. This coupled model is applied to the South China Sea (SCS) during September 2008 cruise. The results show that LC increasing turbulence and deepening mixed layer depth (MLD) at order of O (10 m) in most of the areas, especially in the north part of SCS where most of our measurements operated. The coupled model further includes wave breaking which will bringsmore energy into water. When LC works together with wave breaking,more energy is transferred into deep layer and accelerates the MLD deepening. In the north part of the SCS, their effects aremore obvious. This is consistent with big wind event in the area of the Zhujiang River Delta. The shallow water depth as another reasonmakes themeasy to influence the oceanmixing as well.     

Tidally driven mixing in a numerical model of the ocean general circulation

Astronomical data reveals that approximately 3.5 terawatts (TW) of tidal energy is dissipated in the ocean. Tidal models and satellite altimetry suggest that 1 TW of this energy is converted from the barotropic to internal tides in the deep ocean, predominantly around regions of rough topography such as mid-ocean ridges. A global tidal model is used to compute turbulent energy levels associated with the dissipation of internal tides, and the diapycnal mixing supported by this energy flux is computed using a simple parameterization.The mixing parameterization has been incorporated into a coarse resolution numerical model of the global ocean. This parameterization offers an energetically consistent and practical means of improving the representation of ocean mixing processes in climate models. Novel features of this implementation are that the model explicitly accounts for the tidal energy source for mixing, and that the mixing evolves both spatially and temporally with the model state. At equilibrium, the globally averaged diffusivity profile ranges from 0.3 cm² s⁻¹ at thermocline depths to 7.7 cm² s⁻¹ in the abyss with a depth average of 0.9 cm² s⁻¹, in close agreement with inferences from global balances. Water properties are strongly influenced by the combination of weak mixing in the main thermocline and enhanced mixing in the deep ocean. Climatological comparisons show that the parameterized mixing scheme results in a substantial reduction of temperature/salinity bias relative to model solutions with either a uniform vertical diffusivity of 0.9 cm² s⁻¹ or a horizontally uniform bottom-intensified arctangent mixing profile. This suggests that spatially varying bottom intensified mixing is an essential component of the balances required for the maintenance of the ocean’s abyssal stratification.     

An ERA40-based atmospheric forcing for global ocean circulation models

We develop, calibrate and test a dataset intended to drive global ocean hindcasts simulations of the last five decades. This dataset provides surface meteorological variables needed to estimate air-sea fluxes and is built from 6-hourly surface atmospheric state variables of ERA40. We first compare the raw fields of ERA40 to the CORE.v1 dataset of Large and Yeager (2004), used here as a reference, and discuss our choice to use daily radiative fluxes and monthly precipitation products extracted from satellite data rather than their ERA40 counterparts. Both datasets lead to excessively high global imbalances of heat and freshwater fluxes when tested with a prescribed climatological sea surface temperature. After identifying unrealistic time discontinuities (induced by changes in the nature of assimilated observations) and obvious global and regional biases in ERA40 fields (by comparison to high quality observations), we propose a set of corrections. Tropical surface air humidity is decreased from 1979 onward, representation of Arctic surface air temperature is improved using recent observations and the wind is globally increased. These corrections lead to a significant decrease of the excessive positive global imbalance of heat. Radiation and precipitation fields are then submitted to a small adjustment (in zonal mean) that yields a near-zero global imbalance of heat and freshwater. A set of 47-year-long simulations is carried out with the coarse-resolution (2° × 2°) version of the NEMO OGCM to assess the sensitivity of the model to the proposed corrections. Model results show that each of the proposed correction contributes to improve the representation of central features of the global ocean circulation.     

Dissipation of baroclinic tidal energy and diapycnal mixing in the White Sea

The modeling results obtained using the original version of the three-dimensional finite-element hydrostatic model QUODDY-4 testify that the spatial distributions of dissipation of baroclinic tidal energy and the related coefficient of diapycnal mixing in the deepwater stratified subdomain of the White Sea (the Basin and Kandalaksha and Dvina bays together) are highly similar to those found for low- and midlatitude oceans. It is in the open part of the sea that their values remain equal to the minimum possible values determined by the molecular kinematic viscosity; at its lateral boundaries (not all boundaries, but only individual segments (sites of mixing)), their values increase. In the shallow homogeneous subdomain of the White Sea, the dissipation of baroclinic tidal energy is considerably larger than in the deep stratified subdomain. Accordingly, the vertical eddy viscosity in the first subdomain is a few orders of magnitude higher than the coefficient of diapycnal mixing in the second subdomain. This is caused by an increased tidal velocity due to reduced depths.     

Spatial and seasonal variability of global ocean diapycnal transport inferred from Argo profiles

The global diapycnal transport in the ocean interior is one of the significant branches to return the deep water back toward near-surface. However, the amount of the diapycnal transport and the seasonal variations are not determined yet. This paper estimates the dissipation rate and the associated diapycnal transports at 500 m, 750 m and 1 000 m depth throughout the global ocean from the wide-spread Argo profiles, using the finescale parameterizations and classic advection-diff usion balance. The net upwelling is ~5.2±0.81 Sv (Sverdrup) which is approximately one fifth in magnitude of the formation of the deep water. The Southern Ocean is the major region with the upward diapycnal transport, while the downwelling emerges mainly in the northern North Atlantic. The upwelling in the Southern Ocean accounts for over 50% of the amount of the global summation. The seasonal cycle is obvious at 500 m and vanishes with depth, indicating the energy source at surface. The enhancement of diapycnal transport occurs at 1000min the Southern Ocean, which is pertinent with the internal wave generation due to the interaction between the robust deep-reaching flows and the rough topography. Our estimates of the diapycnal transport in the ocean interior have implications for the closure of the oceanic energy budget and the understanding of global Meridional Overturning Circulation.     

The effect of the wave-induced mixing on the upper ocean temperature in a climate model

The significant underestimation of sea surface temperature （SST） and the temperature in the upper ocean is one of common problems in present climate models. The influence of the wave-induced mixing on SST and the temperature in the upper ocean was examined based on a global climate model. The results from the model coupled with wave-induced mixing showed a significant improvement in the simulation of SST and the temperature in the upper ocean compared with those of the original model without wave effects. Although there has still a cold bias, the new simulation is much closer to the climatology, especially in the northern ocean and tropical ocean. This study indicates that some important physical processes in the accurate simulation of the ocean may be ignored in present climate models, and the wave-induced mixing is one of those factors. Thus, the wave-induced mixing （ or the effect of surface waves） should be incorporated properly into climate models in order to simulate or forecast the ocean, then climate system, more accurately.     

Pacific ocean circulation based on observation

A thorough understanding of the Pacific Ocean circulation is a necessity to solve global climate and environmental problems. Here we present a new picture of the circulation by integrating observational results. Lower and Upper Circumpolar Deep Waters (LCDW, UCDW) and Antarctic Intermediate Water (AAIW) of 12, 7, and 5 Sv (10⁶ m³s⁻¹) in the lower and upper deep layers and the surface/intermediate layer, respectively, are transported to the North Pacific from the Antarctic Circumpolar Current (ACC). The flow of LCDW separates in the Central Pacific Basin into the western (4 Sv) and eastern (8 Sv) branches, and nearly half of the latter branch is further separated to flow eastward south of the Hawaiian Ridge into the Northeast Pacific Basin (NEPB). A large portion of LCDW on this southern route (4 Sv) upwells in the southern and mid-latitude eastern regions of the NEPB. The remaining eastern branch joins nearly half of the western branch; the confluence flows northward and enters the NEPB along the Aleutian Trench. Most of the LCDW on this northern route (5 Sv) upwells to the upper deep layer in the northern (in particular northeastern) region of the NEPB and is transformed into North Pacific Deep Water (NPDW). NPDW shifts southward in the upper deep layer and is modified by mixing with UCDW around the Hawaiian Islands. The modified NPDW of 13 Sv returns to the ACC. The remaining volume in the North Pacific (11 Sv) flows out to the Indian and Arctic Oceans in the surface/intermediate layer.     

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.     

Effects of sea ice formation and diapycnal mixing on the Okhotsk Sea intermediate water clarified with oxygen isotopes

Processes relating to the formation of dense shelf water and intermediate water in the Okhotsk Sea were studied by examining oxygen isotope ratios (δ¹⁸O), salinity, and temperature. The salinity and δ¹⁸O of the cold dense shelf water on the northern continental shelf showed peculiar relationship. The relationship indicates that 3% of the mixed-layer water, having salinity of 32.6, froze and the remaining 97% became dense shelf water of salinities of more than 33.2 (σ_θ>26.7) during the sea ice formation. The salinity–δ¹⁸O relationship also shows that 20% of the Okhotsk Sea Intermediate Water at the σ_θ=26.8 level was derived from the dense shelf water. The remaining 80% came from the Western Subarctic Pacific water modified by diapycnal mixing of water affected by the surface cooling and freshening within the Okhotsk Sea. The mixing with dense shelf water contributes to only 26% of the temperature difference or 8% of the salinity difference between the original Pacific water and the Okhotsk Sea Intermediate Water at σ_θ=26.8. This result suggests that the cold and less saline properties of the Okhotsk Sea Intermediate Water are produced mainly by diapycnal mixing, rather than by mixing of the Pacific water with the dense shelf water.     

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.     

Spatial distribution of turbulent diapycnal mixing along the Mindanao current inferred from rapid-sampling Argo floats

The Mindanao Current (MC) bridges the North Pacific low-latitude western boundary current system region and the Indonesian Seas by supplying the North Pacific waters to the Indonesian Throughflow. Although the previous study speculated that the diapycnal mixing along the MC might be strong on the basis of the water mass analysis of the gridded climatologic dataset, the real spatial distribution of diapycnal mixing along the MC has remained to be clarified. We tackle this question here by applying a finescale parameterization to temperature and salinity profiles obtained using two rapid-sampling profiling Argo floats that drifted along the MC. The western boundary (WB) region close to the Mindanao Islands and the Sangihe Strait are the two mixing hotspots along the MC, with energy dissipation rate ε and diapycnal diffusivity K_ρ enhanced up to?~?10^–6 W kg^?1 and?~?10^–3 m² s^?1, respectively. Except for the above two mixing hotspots, the turbulent mixing along the MC is mostly weak, with ε and K_ρ to be 10^–11–10^–9 W kg^?1 and 10^–6–10^–5 m² s^?1, respectively. Strong mixing in the Sangihe Strait can be basically attributed to the existence of internal tides, whereas strong mixing in the WB region suggests the existence of internal lee waves. We also find that water mass transformation along the MC mainly occurs in the Sangihe Strait where the water masses are subjected to strong turbulent mixing during a long residence time.

     

Direct measurements of diapycnal mixing in a fjord reach—Puget Sound's Main Basin

In the spring of 1988, time series of microstructure and ADCP current profiles were collected at four locations in the North Main Basin of Puget Sound, Washington. Depth and time averages of diapycnal diffusivity at the four stations (1.8−67.0×10⁻⁴ m² s⁻¹) were one to three decades above typical open-ocean thermocline levels. The buoyancy frequency-squared N² was near open-ocean levels, but unlike the open-ocean where N²S², finescale shear-squared S² was three to six times N² over significant portions of the water column at two of the stations. The time and space mean of all measurements ( ) is close to inferred vertical eddy diffusivity from a primitive equation model for Puget Sound (K_z=3×10⁻³ m² s⁻¹) (J. Geophys. Res. 96 (1991) 16779). Large time and space variability of K_ρ was found, with differences of inter-station, depth–time means over one decade. A simple scaling argument using the observed K_ρ suggests significant exchange of mass between the layers of the subtidal flow over the basin's residence time. Additionally, measurements show that local mixing may be comparable to volume-weighted sill mixing in modifying the Main Basin's stratification. Both are contrary to the “advective reach” simplification of fjord dynamics. The mixing levels were dominated by the passage of a mid-depth, southward-flowing density intrusion and what we interpret as a strongly advected, non-linear internal tide. These mechanisms elevated profile-averaged K_ρ by more than 10 times background levels, with sustained patches of K_ρ≥1×10⁻² m² s⁻¹. Critical 8-m gradient Richardson numbers (Ri₈<0.25) matching regions of overturns (>20 m) and strong turbulence suggest that shear instabilities dominated the turbulence production, though there was support for double-diffusive convection in the warm core of the density intrusion.     

The study of ocean circulation dynamics with numerical models

Summarized is the author's study of the ocean circulation dynamics with numerical models, for which he was honored by the Okada Prize (1979). Cited topics are formation of the western boundary current and its variation associated with imposed wind stress, some effects of a marine ridge on the boundary current, coastal upwelling circulation and coastal thermohaline front formation. Recent modelling efforts in Japan, specifically on numerical study of ocean circulation dynamics are also reviewed.     

The mixing mechanism in the formation of ocean shear waves

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Water mass exchange and diapycnal mixing at Bussol’ Strait revealed by water mass properties

Intensive CTD observations that resolve the mean and tidal components were done with a total of 129 casts in summer of 2001 at Bussol’ Strait. Based on these data and all the available historical data, we have revealed the outflow from Bussol’ Strait to the Pacific and the significant diapycnal mixing in the strait. In the range 27.0−27.3σ _θ , the water property in Bussol’ Strait is almost identical to that of the Kuril Basin Water (KBW). The KBW out of Bussol’ Strait forms a water mass front with the East Kamchatka Current Water (EKCW). This front also corresponds to the front of the Oyashio Current. In the lower part of the intermediate layer (27.3−27.6σ _θ ), part of the water in the strait is characterized by lower temperature, lower salinity, and higher dissolved oxygen than that of KBW and EKCW, which can be explained only by the diapycnal mixing. The strong diapycnal mixing in the strait can also be shown by the density inversion, occurrence frequency of which corresponds well to the amplitude distribution of the diurnal current. In the density range 26.7−26.8σ _θ , the water in Bussol’ Strait has the lowest potential vorticity, suggesting that it is a source region of the low potential vorticity water. Seasonal change of the water can reach up to a density of 26.8σ _θ around Bussol’ Strait. This leads us to propose that the combination of winter convection and local tidal mixing leads to effective ventilation of the intermediate layer.     

Effects of the deep ocean circulation on the reservoir characteristics of the ocean

To examine the effects of the deep ocean circulation on the characteristics of the ocean as a reservoir, age distributions of the material whose source and sink are at the ocean surface are calculated using an idealized vertical two-dimensional model of the ocean. The results show that the large-scale vertical circulation of the deep water accelerates the renewal of deep water and reduces the average age of the material. It is also shown that the multi-layered structures of the deep circulation are more realistic than the one-layered structure and promote the renewal of the deep water.