Evaluation of Nonbreaking Wave-Induced Mixing Parameterization Schemes Based on a One-Dimensional Ocean Model

Surface waves have a considerable effect on vertical mixing in the upper ocean.In the past two decades,the vertical mixing induced through nonbreaking surface waves has been used in ocean and climate models to improve the simulation of the upper ocean.Thus far,several nonbreaking wave-induced mixing parameterization schemes have been proposed;however,no quantitative comparison has been performed among them.In this paper,a one-dimensional ocean model was used to compare the performances of five schemes,including those of Qiao et al.(Q),Hu and Wang(HW),Huang and Qiao(HQ),Pleskachevsky et al.(P),and Ghantous and Babanin(GB).Similar to previous studies,all of these schemes can decrease the simulated sea surface temperature(SST),increase the subsurface temperature,and deepen the mixed layer,thereby alleviating the common thermal deviation problem of the ocean model for upper ocean simulation.Among these schemes,the HQ scheme exhibited the weakest wave-induced mixing effect,and the HW scheme exhibited the strongest effect;the other three schemes exhibited roughly the same effect.In particular,the Q and P schemes exhibited nearly the same effect.In the simulation based on observations from the Ocean Weather Station Papa,the HQ scheme exhibited the best performance,followed by the Q scheme.In the experiment with the HQ scheme,the root-mean-square deviation of the simulated SST from the observations was 0.43℃,and the mixed layer depth(MLD)was 2.0 m.As a contrast,the deviations of the SST and MLD reached 1.25℃ and 8.4 m,respectively,in the experiment without wave-induced mixing.

What induced the trend shift of mixed-layer depths in the Antarctic Circumpolar Current region in the mid-1980s?

An obvious trend shift in the annual mean and winter mixed layer depth(MLD)in the Antarctic Circumpolar Current(ACC)region was detected during the 1960–2021 period.Shallowing trends stopped in mid-1980s,followed by a period of weak trends.The MLD deepening trend difference between the two periods were mainly distributed in the western areas in the Drake Passage,the areas north to Victoria Land and Wilkes Land,and the central parts of the South Indian sector.The newly formed ocean current shear due to the meridional shift of the ACC flow axis between the two periods is the dominant driver for the MLD trends shift distributed in the western areas in the Drake Passage and the central parts of the South Indian sector.The saltier trends in the regions north to Victoria Land and Wilkes Land could be responsible for the strengthening mixing processes in this region.

Influence of the upper mixed layer depth on Langmuir turbulence characteristics

The upper mixed layer depth(h)has a significant seasonal variation in the real ocean and the low-order statistics of Langmuir turbulence are dramatically influenced by the upper mixed layer depth.To explore the influence of the upper mixed layer depth on Langmuir turbulence under the condition of the wind and wave equilibrium,the changes of Langmuir turbulence characteristics with the idealized variation of the upper mixed layer depth from very shallow(h=5 m)to deep enough(h=40 m)are studied using a non-hydrostatic large eddy simulation model.The simulation results show that there is a direct entrainment depth induced by Langmuir turbulence(h_(LT))within the thermocline.The normalized depthaveraged vertical velocity variance is smaller and larger than the downwind velocity variance for the ratio of the upper mixed layer to a direct entrainment depth induced by Langmuir turbulence h/h_(LT)<1 and h/h_(LT)>1,respectively,indicating that turbulence characteristics have the essential change(i.e.,depth-averaged vertical velocity variance(DAVV)DADV for Langmuir turbulence)between h/h_(LT)<1 and h/h_(LT)>1.The rate of change of the normalized depth-averaged low-order statistics for h/h_(LT)<1 is much larger than that for h/h_(LT)>1.The reason is that the downward pressure perturbation induced by Langmuir cells is strongly inhibited by the upward reactive force of the strong stratified thermocline for h/h_(LT)<1 and the eff ect of upward reactive force on the downward pressure perturbation becomes weak for h/h_(LT)>1.Hence,the upper mixed layer depth has significant influences on Langmuir turbulence characteristics.

Seasonal variability of the mixed layer depth determined using an improved maximum angle method in the Arctic basins

To investigate the spatiotemporal variations in the mixed layer depth(MLD)in the Arctic basins,a new criterion to determine the MLD,called the improved maximum angle method(IMAM),was developed.A total of 45123 potential density profiles collected using Ice-Tethered Profilers(ITPs)in the Arctic basins during 2005-2021 were used to demonstrate the method’s effectiveness.By comparing the results obtained by the fixed threshold method(FTM),percentage threshold method(PTM),and maximum gradient method(MGM)for profiles in the Canada Basin,Makarov Basin,and Eurasian Basin,we determined that the quality index(1.0 for perfect identification of the MLD)of the IMAM regarding the assessment of the MLD determination method reached 0.94,which is much greater than those of other criteria.Moreover,two types of the density profiles were identified based on the mixed layer development stage.The MLDs of the typical profiles determined using the IMAM were found to have better consistency with the original definition.By utilizing the new mixed layer criterion,the seasonal variations and regional differences in the MLD in the Arctic basins were analyzed.Spatially,the summer and winter MLDs in the Canada Basin were the shallowest(13.55 m in summer,26.76 m in winter)than those in the Makarov(29.51 m in summer,49.08 m in winter)and Eurasian(20.36 m in summer,46.81 m in winter)basins due to the stable stratification in the upper ocean and the subsequent small effects of dynamic and thermodynamic processes(wind-driven stirring and brine rejection)in the Canada Basin.Seasonally,in the three Arctic basins,the average MLD was shallowest(22.77 m)in summer;it deepened through autumn and reached a winter maximum(41.12 m).

Seasonal Variation of the Sea Surface Temperature Growth Rate of ENSO

El Ni?o–Southern Oscillation(ENSO) exhibits a distinctive phase-locking characteristic, first expressed during its onset in boreal spring, developing during summer and autumn, reaching its peak towards winter, and decaying over the next spring. Several studies have demonstrated that this feature arises as a result of seasonal variation in the growth rate of ENSO as expressed by the sea surface temperature(SST). The bias towards simulating the phase locking of ENSO by many state-of-the-art climate models is also attributed to the unrealistic depiction of the growth rate. In this study, the seasonal variation of SST growth rate in the Ni?o-3.4 region(5°S–5°N, 120°–170°W) is estimated in detail based on the mixed layer heat budget equation and recharge oscillator model during 1981–2020. It is suggested that the consideration of a variable mixed layer depth is essential to its diagnostic process. The estimated growth rate has a remarkable seasonal cycle with minimum rates occurring in spring and maximum rates evident in autumn. More specifically, the growth rate derived from the meridional advection(surface heat flux) is positive(negative) throughout the year. Vertical diffusion generally makes a negative contribution to the evolution of growth rate and the magnitude of vertical entrainment represents the smallest contributor. Analysis indicates that the zonal advective feedback is regulated by the meridional immigration of the intertropical convergence zone, which approaches its southernmost extent in February and progresses to its northernmost location in September, and dominates the seasonal variation of the SST growth rate.

The connection of phytoplankton biomass in the Marguerite Bay polynya of the western Antarctic Peninsula to the Southern Annular Mode

Antarctic coastal polynyas are biological hotspots in the Southern Ocean that support the abundance of hightrophic-level predators and are important for carbon cycling in the high-latitude oceans.In this study,we examined the interannual variation of summertime phytoplankton biomass in the Marguerite Bay polynya(MBP)in the western Antarctic Peninsula area,and linked such variability to the Southern Annular Mode(SAM)that dominated the southern hemisphere extratropical climate variability.Combining satellite data,atmosphere reanalysis products and numerical simulations,we found that the interannual variation of summer chlorophyll-a(Chl-a)concentration in the MBP is significantly and negatively correlated with the spring SAM index,and weakly correlated with the summer SAM index.The negative relation between summer Chl-a and spring SAM is due to weaker spring vertical mixing under a more positive SAM condition,which would inhibit the supply of iron from deep layers into the surface euphotic layer.The negative relation between spring mixing and spring SAM results from greater precipitation rate over the MBP region in positive SAM phase,which leads to lower salinity in the ocean surface layer.The coupled physical-biological mechanisms between SAM and phytoplankton biomass revealed in this study is important for us to predict the future variations of phytoplankton biomasses in Antarctic polynyas under climate change.

Contrasting physical mechanisms of yellowfin tuna fluctuations between the western and eastern Indian Ocean

As an economically critical pelagic migratory species,yellowfin tuna(Thunnus albacores,YFT)is very sensible to physical and environmental conditions,such as sea surface temperature(SST),ocean heat content(OHC),and the mixed layer depth(MLD).We investigated the impact of SST,OHC,and MLD on fluctuations of YFT catch in the western/eastern Indian Ocean using the long time series of 63-year environmental and YFT datasets.We found that the impact of SST on YFT was heavily overestimated in the past,and MLD plays a more critical role in the YFT catch fluctuation.When the MLD deepens(>34.8 m),SST was more influential in predicting the catches of YFT than OHC in the western Indian Ocean,and OHC was more critical to YFT than SST in the eastern Indian Ocean.However,when the MLD shallows(<34.8 m),MLD was more vital to predict the catch per unit effort(CPUE)of YFT than SST/OHC in the western.After 2000,there was an asynchronous pattern of YFT CPUE induced by higher frequency variations and ocean hiatus of SST/OHC signals in the western and eastern Indian Oceans basins.The impact of the subsurface hiatus may induce the decrease of YFT in the eastern Indian Ocean.The above findings clarified a non-stationary relationship between the environmental factors and catches of YFT and provided new insights into variations in YFT abundance.

Simulation and Exploration of the Mechanisms Underlying the Spatiotemporal Distribution of Surface Mixed Layer Depth in a Large Shallow Lake

The aquatic eco-environment is significantly affected by temporal and spatial variation of the mixed layer depth （MLD） in large shallow lakes. In the present study, we simulated the three-dimensional water temperature of Taihu Lake with an unstructured grid with a finite-volume coastal ocean model （FVCOM） using wind speed, wind direction, short-wave radiation and other meteorological data measured during 13-18 August 2008. The simulated results were consistent with the measurements. The temporal and spatial distribution of the MLD and the possible relevant mechanisms were analyzed on the basis of the water temperature profile data of Taihu Lake. The results indicated that diurnal stratification might be established through the combined effect of the hydrodynamic conditions induced by wind and the heat exchange between air and water. Compared with the net heat flux, the changes of the MLD were delayed approximately two hours. Furthermore, there were significant spatial differences of the MLD in Taihu Lake due to the combined impact of thermal and hydrodynamic forces. Briefly, diurnal stratification formed relatively easily in Gonghu Bay, Zhushan Bay, Xukou Bay and East Taihu Bay, and the surface mixed layer was thin. The center of the lake region had the deepest surface mixed layer due to the strong mixing process. In addition, Meiliang Bay showed a medium depth of the surface mixed layer. Our analysis indicated that the spatial difference in the hydrodynamic action was probably the major cause for the spatial variation of the MLD in Taihu Lake.

On the subtropical Northeast Pacific mixed layer depth and its influence on the subduction

The present climate simulations of the mixed layer depth（MLD） and the subduction rate in the subtropical Northeast Pacific are investigated based on nine of the CMIP5 models. Compared with the observation data,spatial patterns of the MLD and the subduction rate are well simulated in these models. The spatial pattern of the MLD is nonuniform, with a local maximum MLD（〉140 m） region centered at（28°N, 135°W） in late winter. The nonuniform MLD pattern causes a strong MLD front on the south of the MLD maximum region, controls the lateral induction rate pattern, and then decides the nonuniform distribution of the subduction rate. Due to the inter-regional difference of the MLD, we divide this area into two regions. The relatively uniform Ekman pumping has little effect on the nonuniform subduction spatial pattern, though it is nearly equal to the lateral induction in values. In the south region, the northward warm Ekman advection（–1.75×10–7 K/s） controls the ocean horizontal temperature advection（–0.85×10–7 K/s）, and prevents the deepening of the MLD. In the ensemble mean, the contribution of the ocean advection to the MLD is about –29.0 m/month, offsetting the sea surface net heat flux contribution（33.9 m/month）. While in the north region, the southward cold advection deepens the MLD（21.4 m/month） as similar as the heat flux（30.4 m/month）. In conclusion, the nonuniform MLD pattern is dominated by the nonuniform ocean horizontal temperature advection. This new finding indicates that the upper ocean current play an important role in the variability of the winter MLD and the subduction rate.

Interannual variability of mixed layer depth and heat storage of upper layer in the tropical Pacific Ocean

By using the upper layer data(downloaded from the web of the Scripps Institution of Oceanography),the interannual variability of the heat storage of upper layer(from surface to 400 m depth) and the mixed layer depth in the tropical Pacific Ocean are investigated. The abnormal signal of the warm event comes from the central and west Pacific Ocean, whereas it is regarded that the abnormal signal of the warm event comes from the east Pacific Ocean in the popular viewpoint. From the viewpoint on the evolution of the interannual variability of the mixed layer depth and the heat storage of the whole upper layer, the difference between the two types of El Nino is so small that it can be neglected. During these two El Nino/La Nina events(1972/1973 and 1997/1998), other than the case of the heat storage or for the mixed layer depth, the abnormal signal propagates from the central and west Pacific Ocean to the east usually by the path along the equator whereas the abnormal signal propagates from the east to the west by the path northern to the equator. For the interannual variability, the evolution of the mixed layer depth corresponds to that of the heat storage in the upper layer very well. This is quite different from the evolution of seasonality.

Response of the mixed layer depth and subduction rate in the subtropical Northeast Pacific to global warming

The response of the mixed layer depth(MLD)and subduction rate in the subtropical Northeast Pacific to global warming is investigated based on 9 CMIP5 models.Compared with the present climate in the 9 models,the response of the MLD in the subtropical Northeast Pacific to the increased radiation forcing is spatially nonuniform,with the maximum shoaling about 50 m in the ensemble mean result.The inter-model differences of MLD change are non-negligible,which depend on the various dominated mechanisms.On the north of the MLD front,MLD shallows largely and is influenced by Ekman pumping,heat flux,and upper-ocean cold advection changes.On the south of the MLD front,MLD changes a little in the warmer climate,which is mainly due to the upper-ocean warm advection change.As a result,the MLD front intensity weakens obviously from 0.24 m/km to0.15 m/km(about 33.9%)in the ensemble mean,not only due to the maximum of MLD shoaling but also dependent on the MLD non-uniform spatial variability.The spatially non-uniform decrease of the subduction rate is primarily dominated by the lateral induction reduction(about 85%in ensemble mean)due to the significant weakening of the MLD front.This research indicates that the ocean advection change impacts the MLD spatially non-uniform change greatly,and then plays an important role in the response of the MLD front and the subduction process to global warming.

Changes in Mixed Layer Depth and Spring Bloom in the Kuroshio Extension under Global Warming

The mixed layer is deep in January-April in the Kuroshio Extension region. This paper investigates the response in this region of mixed layer depth （MLD） and the spring bloom initiation to global warming using the output of 15 models from CMIP5. The models indicate that in the late 21st century the mixed layer will shoal and the MLD reduction will be most pronounced in spring at about 33~N on the southern edge of the present deep-MLD region. The advection of temperature change in the upper 100 m by the mean eastward flow explains the spatial pattern of MLD shoaling in the models. Associated with the shoaling mixed layer, the onset of spring bloom inception is projected to advance due to the strengthened stratification in the warming climate.

Simulation and future projection of the mixed layer depth and subduction process in the subtropical Southeast Pacific

The present climate simulation and future projection of the mixed layer depth(MLD)and subduction process in the subtropical Southeast Pacific are investigated based on the geophysical fluid dynamics laboratory earth system model(GFDL-ESM2 M).The MLD deepens from May and reaches its maximum(>160 m)near(24°S,104°W)in September in the historical simulation.The MLD spatial pattern in September is non-uniform in the present climate,which shows three characteristics:(1)the deep MLD extends from the Southeast Pacific to the West Pacific and leads to a"deep tongue"until 135°W;(2)the northern boundary of the MLD maximum is smoothly near 18°S,and MLD shallows sharply to the northeast;(3)there is a relatively shallow MLD zone inserted into the MLD maximum eastern boundary near(26°S,80°W)as a weak"shallow tongue".The MLD nonuniform spatial pattern generates three strong MLD fronts respectively in the three key regions,promoting the subduction rate.After global warming,the variability of MLD spatial patterns is remarkably diverse,rather than deepening consistently.In all the key regions,the MLD deepens in the south but shoals in the north,strengthing the MLD front.As a result,the subduction rate enhances in these areas.This MLD antisymmetric variability is mainly influenced by various factors,especially the potential-density horizontal advection non-uniform changes.Notice that the freshwater flux change helps to deepen the MLD uniformly in the whole basin,so it hardly works on the regional MLD variability.The study highlights that there are regional differences in the mechanisms of the MLD change,and the MLD front change caused by MLD non-uniform variability is the crucial factor in the subduction response to global warming.

The Effect of Boreal Summer Intraseasonal Oscillation on Mixed Layer and Upper Ocean Temperature over the South China Sea

Intraseasonal oscillation of the mixed layer and upper ocean temperature has been found to occur over the South China Sea(SCS)in the summer monsoon season based on the multiple reanalysis and observational data in this study.The method of composite analysis and an upper ocean temperature equation assisted the analysis of physical mechanisms.The results show that the mixed layer depth(MLD)in the SCS has a significant oscillation with a 30-60 d period over the SCS region,which is closely related to boreal summer intraseasonal oscillation(BSISO)activities.The MLD can increase(decrease)during the positive(negative)phase of the BSISO and usually lags behind by approximately one-eighth of the lifecycle(5 days)of the BSISO-related convection.The BSISO may cause periodic anomalies at the air-sea boundary,such as wind stress and heat flux,so it can play a dominant role in modulating the variation in MLD.There also are significant intraseasonal seawater temperature anomalies in both the surface and subsurface layers of the SCS.In addition,during the initial phase of the BSISO,the temperature anomaly signals of the thermocline are obviously opposite to the sea surface temperature(SST),especially in the southern SCS.According to the results from the analysis of the temperature equation,the vertical entrainment term caused by BSISO-related wind stress is stronger than the thermal forcing during the initial stage of convection,and it is more significant in the southern SCS.

On the Response of the Global Subduction Rate to Global Warming in Coupled Climate Models

The response of the global subduction rate to global warming was assessed based on a set of Intergovernmental Panel on Climate Change （IPCC） Fourth Assessment Report （AR4） models. It was found that the subduction rate of the global ocean could be significantly reduced under a warming climate, as compared to a simulation of the present-day climate. The reduction in the subduction volume was quantitatively estimated at about 40 Sv and was found to be= primarily induced by the decreasing of the lateral induction term due to a shallower winter mixed layer depth. The shrinking of the winter mixed layer would result from intensified stratification caused by increased heat input into the ocean under a warming climate. A reduction in subduction associated with the vertical pumping term was estimated at about 5 Sv. F^rther, in the Southern Ocean, a significant reduction in subduction was estimated at around 24 Sv, indicating a substantial contribution to the weakening of global subduction.

North Pacific Eastern Subtropical Mode Water simulation and future projection

The present climate simulation and future projection of the Eastern Subtropical Mode Water （ESTMW） in the North Pacific are investigated based on the Geophysical Fluid Dynamics Laboratory Earth System Model （GFDL-ESM2M）. Spatial patterns of the mixed layer depth （MLD） in the eastern subtropical North Pacific and the ESTMW are well simulated using this model. Compared with historical simulation, the ESTMW is produced at lighter isopycnal surfaces and its total volume is decreased in the RCP8.5 runs, because the subduction rate of the ESTMW decreases by 0.82×10？6 m/s during February–March. In addition, it is found that the lateral induction decreasing is approximately four times more than the Ekman pumping, and thus it plays a dominant role in the decreased subduction rate associated with global warming. Moreover, the MLD during February–March is banded shoaling in response to global warming, extending northeastward from the east of the Hawaii Islands （20°N, 155°W） to the west coast of North America （30°N, 125°W）, with a max-imum shoaling of 50 m, and then leads to the lateral induction reduction. Meanwhile, the increased north-eastward surface warm current to the east of Hawaii helps strengthen of the local upper ocean stratification and induces the banded shoaling MLD under warmer climate. This new finding indicates that the ocean surface currents play an important role in the response of the MLD and the ESTMW to global warming.

A REGIONAL COUPLED AIR-SEA-WAVE MODEL: SIMULATION OF UPPER-OCEAN RESPONSES TO AN IDEALIZED TROPICAL CYCLONE

In this study a coupled air-sea-wave model system, containing the model components of GRAPES-TCM, ECOM-si and WAVEWATCH III, is established based on an air-sea coupled model. The changes of wave state and the effects of sea spray are both considered. Using the complex air-sea-wave model, a set of idealized simulations was applied to investigate the effects of air-sea-wave interaction in the upper ocean. Results show that air-wave coupling can strengthen tropical cyclones while air-sea coupling can weaken them; and air-sea-wave coupling is comparable to that of air-sea coupling, as the intensity is almost unchanged with the wave model coupled to the air-sea coupled model.The mixing by vertical advection is strengthened if the wave effect is considered, and causes much more obvious sea surface temperature(SST) decreases in the upper ocean in the air-sea coupled model. Air-wave coupling strengthens the air-sea heat exchange, while the thermodynamic coupling between the atmosphere and ocean weakens the air-sea heat exchange: the air-sea-wave coupling is the result of their balance. The wave field distribution characteristic is determined by the wind field. Experiments are also conducted to simulate ocean responses to different mixed layer depths.With increasing depth of the initial mixed layer, the decrease of SST weakens, but the temperature decrease of deeper layers is enhanced and the loss of heat in the upper ocean is increased. The significant wave height is larger when the initial mixed layer depth increases.

On the Response of Subduction in the South Pacific to an Intensification of Westerlies and Heat Flux in an Eddy Permitting Ocean Model

Based on an eddy permitting ocean general circulation model, the response of water masses to two distinct climate scenarios in the South Pacific is assessed in this paper. Under annually repeating atmospheric forcing that is characterized by different westerlies and associated heat flux, the response of Subantarctic Mode Water（SAMW） and Antarctic Intermediate Water（AAIW） is quantitatively estimated. Both SAMW and AAIW are found to be warmer, saltier and denser under intensified westerlies and increased heat loss. The increase in the subduction volume of SAMW and AAIW is about 19.8 Sv（1 Sv =10-6m-3s-（-1））. The lateral induction term plays a dominant role in the changes in the subduction volume due to the deepening of the mixed layer depth（MLD）. Furthermore, analysis of the buoyancy budget is used to quantitatively diagnose the reason for the changes in the MLD. The deepening of the MLD is found to be primarily caused by the strengthening of heat loss from the ocean to the atmosphere in the formation region of SAMW and AAIW.

Barrier and compensation layers in the East China Sea

Climatology of the isothermal layer depth （ILD） and the mixed layer depth （MLD） has been produced from in-situ temperaturesalinity observations in the East China Sea （ECS） since 1925. The methods applied on the global are used to compute the ILD and the MLD in the ECS with a temperature criterion AT=0. 8 ℃ for the ILD, and a density criterion with a threshold △σθ corresponding to fixed △T=0. 8 ℃ for the MLD, respectively. With the derived climatology ILD and MLD, the monthly variations of the barrier layer （BL） and the compensation layer （CL） in the ECS are analyzed. The BL mainly exists in the shallow water region of the ECS during April-June with thickness larger than 15 m. From December to next March, the area along the shelf break from northeast of Taiwan Island to the northeast ECS is characterized by the CL. Two kinds of main temperature - salinity structures of the CL in this area are given.

Mixed layer in the Sea of Japan:numerical simulation andlong-term data analysis

Seasonal variation and topography of the mixed layer in the Sea of Japan are studied by comparison of results from long-term observation data analysis and from numerical simulation with the MHI oceanic model (Shapiro. 1998. Marine Hydrophysical Journal, 6: 26-40). The data are retrieved from Oceanographic A tlas of the Bering Sea, Okhotsk Sea, and Japan/East Sea (Rostov, Rostov, Dmitrieva, et al. 2003. Pacific Oceanography, 1(1):70-72). The simulated and long-term patterns are compared. An impact of surface buoyancy flux, wind, and convergence/divergence of surface currents upon the mixed layer in the Sea of Japan is analyzed.