Link between the internal variability and the baroclinic instability in the Bohai and Yellow Sea

A regional ocean ensemble simulation with slightly different initial conditions demonstrates that internal variability is formed (not only) in the Bohai and Yellow Sea. In this paper, we analyze the relationship between the internal variability and the baroclinic instability, (represented by the Eady predicted theoretical diffusivity Kt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}_{t}$$\end{document}; the larger the Kt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}_{t}$$\end{document}, the stronger the baroclinic instability level). In the ensemble, with tidal forcing, the spatial correlation between the Eady predicted theoretical diffusivity Kt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}_{t}$$\end{document} and the internal variability amounts to 0.80. Also, the time evolution trends of baroclinic instability and internal variability are similar. Based on this evidence, baroclinic instability may be a significant driver for internal variability. This hypothesis is validated using an additional ensemble of simulations, which is identical to the first ensemble, but this time, the tides are inactivated. This modification leads to an increase in internal variability, combined with the strengthening of baroclinic instability. In addition, the baroclinic instability level and internal variability variation co-vary consistently when comparing summer and winter seasons, both with and without tides. Our interpretation is that a stronger baroclinic instability causes more potential energy to be transformed into kinetic energy, allowing the unforced disturbances to grow.


Introduction
Ocean variability arises from the external forcing (for example, surface forcing) and internal processes associated with the nonlinearity and multi-scale integrations within the system (Hasselmann 1976).Such variability caused by internal processes is named internal variability, which is intrinsic, unprovoked, and chaotic, and cannot be linked directly to external forcing of the details of the initial state (von Storch et al. 2001).
The ocean is a turbulent fluid displaying chaotic properties from scales of a few centimeters (short scales) to hundreds of kilometers (large scales) (Ilıcak et al. 2008).Such turbulent nature indicates that a fraction of its variability is unpredictable and internally generated (Lorenz 1963).
Due to the existence of internal variability, the numerical simulation can capture the internal variability of the ocean.Quantities of previous works demonstrate that the internal variability can be shown from the model ensemble results (Büchmann and Söderkvist 2016;Geyer et al. 2021;Grégorio et al. 2015;Hirschi et al. 2013;Tang et al. 2019Tang et al. , 2020)).For example, the OCCIPUT (Oceanic Chaos-Impacts, Structure, Predictability) project shows that substantially different temporal and spatial scales of internal variability appear in the model result.It is used in the OCCIPUT that ensemble simulations consist of 50 NEMO (Nucleus for European Modelling of the Ocean) simulation members with slightly different but consistent initial conditions (Penduff et al. 2018).Hirshi et al. use twin-simulation with eddying (1/4°) and non-eddying (1°) to investigate the chaotic variability of the meridional overturning circulation, and the model configuration within the eddying (/ non-eddying) ensemble is the same except the initial conditions (Hirschi et al. 2013).In our paper, we use the ensemble simulation method, following the customary way, to detect and analyze internal variability in the Bohai and Yellow Sea.
What is considered "internal" and what is "external" depends on the context.In terms of numerical simulations, everything that is prescribed through and traced back to boundary and surface forcing is external.In the case of global warming, for instance, the "weather variations" in the coupled atmosphere-ocean system, including ENSO, AMOC, etc., are internal, while the effect of elevated greenhouse gases is external.In our case, "external" is the variability induced by the prescribed fluxes at the surface of the sea.In an ensemble, the effect of external causes is reflected in the ensemble mean, whereas internal variability is reflected in deviations from the ensemble mean (Grégorio et al. 2015;Hasselmann 1979;Penduff et al. 2019;Tang et al. 2019Tang et al. , 2020;;Benincasa 2023).Such definition can be understood as that the ensemble mean of the simulation shows the joint response of each simulation of an ensemble to the same atmospheric forcing, that is, the variability directly controlled by atmospheric forcing.The deviation of each simulation to the ensemble mean reflects the different development trajectories of each simulation with the same atmospheric forcing, which reflects the internal variability.
The generation of internal variability is partly because of the nonlinearity, partly through the integration of shortterm variability as described by the stochastic climate model by Hasselmann (1976).In the global ocean and deep regional oceans, such as the South China Sea (e.g., Zhang et al. 2019), mesoscale eddies contribute to internal variability.That baroclinic instability is a source of internal variability was investigated in previous studies (Dawe and Thompson 2005;Gastineau et al. 2018;Waldman et al. 2018).Gastineau et al. (2018) found that a 20-year period of intrinsic decadal variability exists in the Atlantic subpolar basin, which is related to the density anomalies at 55°N in the eastern subpolar basin.The transient temperature fluxes play an important role in extracting the potential energy from the mean flow to grow perturbation, which indicates that a large-scale baroclinic instability of mean flow induces decadal variability in the model.
The internal variability of marginal seas received little attention over a long period of time, until recently, the researchers realize that the significance of shallow area internal variability is equal to the open ocean.Penduff et al.'s work finds that low-frequency internal variability leaves an imprint on the sea level variation in the coastal areas (2019).Figure 3 of Penduff et al. (2019) (hereinafter referred to as "PT3") shows the signal-to-noise ratio of sea level trends (ensemble mean divided by the ensemble standard deviation) in the Northwest Pacific, the Northwest Atlantic, the Northwest Indian, and around the south of Africa.A larger signal-to-noise ratio demonstrates that the variability is mostly attributed by external forcing; by contrast, a smaller signal-to-noise ratio indicates the variability is dominated by internal variability.In Penduff et al.'s (2019) research, the variability is mostly caused by external forcing where the signal-to-noise ratio is larger than 2; while if the signal-to-noise ratio is smaller than 2, then the variability is mostly attributed by internal variability.In PT3 the redder the color, the more important the internal variability.The black contours encircle the area where the signal-to-noise ratio is smaller than 2. From PT3, we find that in the Bohai and Yellow Sea, the sea level trend may be blurred by internal variability, because the whole Bohai and Yellow Sea signal-to-noise ratio is smaller than 2 (Penduff et al. 2019).In the Bohai and Yellow Sea, the formation of the internal variability is shown and proved in the variables temperature, salinity, and velocity, though the intensity differs in various variables (Lin et al. 2022).Above all, the internal variability analysis in the Bohai and Yellow Sea has been a question of interest.
The Bohai is a shallow basin in the northwestern of the Yellow Sea, connecting the Yellow Sea through the Bohai strait, and its average depth is 18 m.The Yellow Sea is a semi-enclosed marginal sea in the mid-latitude area, of which the depth is only 44 m on average.The topography of the Yellow Sea includes the well-developed shallow continental shelf and the north-south direction Yellow Sea trough.
The Bohai and Yellow Sea shows obvious seasonal variation because of the monsoon and its shallowness (Chu et al. 2005;Xia et al. 2006;Zhou et al. 2017).However, the water in the Yellow Sea trough shows less seasonality (Wang et al. 2014).In winter, due to the strong wind, the seawater temperature is almost uniform from the surface to the bottom; in spring, the water temperature in the surface layer becomes warm with the increasing solar radiation, but the water in the central trough remains cold owing to depth (Zhang et al. 2008;Zhu and Wu 2018).The temperature gradient between the warm surface and the cold bottom water appears in spring and becomes greater in summer.The temperature gradient further prohibits heat transformation from the surface layer to the bottom layer.Until autumn, the temperature gradient from the surface to the bottom starts to disappear (Park et al. 2011).
The tidal characteristics have complex structures, and the dissipation of M 2 tidal energy reaches 180 GW because of the joint effects of bottom friction and large tidal energy flux input (Choi 1980;Choi et al. 2003;Fang 2004;Larsen et al. 1985).Tides play a significant role in the hydrodynamics in the Bohai and Yellow Sea with considerable momentum and energy fluxes.Previously, we analyze the tidal effect on the internal variability and find that the internal variability increases when the tides are turned off (Lin et al. 2022).In this paper, we will investigate the possible driver of internal variability and why the internal variability level decreases when tides are turned off.
The model configurations, ensemble simulation design, and validation are described in Section 2. In Section 3, we shortly show the effects of the tide on internal variability.In Section 4, we discuss the possible driver of the internal variability and compare the difference in baroclinic instability between with and without tidal forcing situations.In the end, we draw the main conclusion of the paper.

Model setup
The 3-D Finite-Volume Coastal Ocean Model (FVCOM) simulations are used in this paper (Chen et al. 2003).The model domain is illustrated in Fig. 1 (the shading area).The horizontal grid resolutions of Bohai and the Yellow Sea are about 4 km and 8 km; vertically, the model has 30 sigma layers.The open boundary is from Qidong, along the China coast to the southern tip of the Korean Peninsula.The Huanghe, Huaihe, and Haihe are considered, and the river discharges are from the "China Sediment Bulletin (2019)." The surface forcing data are prescribed every 6 h with the resolution of 0.2 • × 0.2 • , as prepared by NCEP's Cli- mate Forecast System Version 2. It includes the cloud cover, precipitation, evaporation, sea surface temperature, air pressure, specific humidity, surface wind forcing, and heat flux.The surface forcing dataset has been validated of good quality in previous work (Ding et al. 2019(Ding et al. , 2020)).The vertical viscosity and diffusivity are calculated by the Mellor and Yamada level 2.5 (MY-2.5)scheme (Mellor and Yamada 1982).For horizontal diffusivity, the Smagorinsky eddy parameterization method is chosen.At the open boundary, we use the tidal elevation to introduce the effect of the tides.The time-varied elevation consists of 8 tidal components (M 2 , S 2 , N 2 , K 2 , K 1 , O 1 , P 1 , Q 1 ) , which are obtained from TPXO8 (Egbert and Erofeeva 2002).
Earlier on, we examined two ensembles of simulations of the hydrodynamics in the Yellow Sea and the Bohai; tidal forcing is turned on in one ensemble (hereinafter referred to as "tide-ensemble"), and the other ensemble with tidal forcing turned off ("no-tide ensemble").Within tide-ensemble (/no-tide ensemble), the set-up of the five numerical simulations is the same, except for different times of initialization.In both ensembles, five simulations are initialized 24, 14, 12, 9, and 2 months prior to 1 January 2019, thus representing each one random trajectory in phase space.Two 5-member ensembles all covered the year 2019, and model integration ended on 31 December 2019.We chose the whole 2019 data for further internal variability analysis.To make sure the initial conditions of each ensemble are consistent in general but with slight differences, we first conducted a 9-year climatological simulation, and the initial conditions of the tide-ensemble and no-tide ensemble are taken from the above climatological simulation.It has been proven that each simulation of the ensemble is stable after at least 2 months from the initial time to Jan of 2019, and that slightly different initial time does not matter in detail, which only introduces a small difference and makes the internal variability form, as we mentioned in Section 1.

Validation
The tides and water levels are validated in the previous studies (Lin et al. 2022).In this paper, we further validate and compare the temperature and salinity model results with Research Vessel (RV) Dongfanghong 2 observation data.The RV Dongfanghong 2 research cruises were conducted in the spring and summer of 2018 in the Yellow Sea (The sites within the model domain are shown in Fig. 1).The RV Dongfanghong 2 observation data come from the publication Tian et al. (2022).Ensemble mean of the with-tide simulations are used for validation, and an exception is that as we only collect the observations data of temperature and salinity of 2018, considering that three of four members cover the time period of RV Dongfanghong 2 observation cruise, we calculate the average of these three members for temperature and salinity comparisons.
The simulated results of surface and bottom SST in spring and summer are generally consistent with the measured results in terms of spatial distribution (Fig. 2).In spring, the temperature difference between the surface layer and the bottom layer is small.In summer, the surface temperature is significantly higher than the bottom layer temperature, and a cold center exists at the bottom of the Yellow Seas.The Figure 3 shows the simulated salinity against observations.It can be seen that in Laizhou Bay near the shore, there is a low salinity area in both the measured and simulated results.However, the salinity in the interior bay is lower in the measured results, which may be because that the model river discharge data are estimated based on the "China Sediment Bulletin (2019)," as the measured river discharge is difficult to obtain.The model fails to simulate the low salinity area in the South Yellow Sea, which may be because the model simulation area does not include the Yangtze River estuary, so the influence of the Yangtze River on the South Yellow Sea has not been considered.The RMSEs between the model results and observations are 0.68 and 0.66 for surface and bottom salinity in the spring, respectively; the RMSEs are 0.92 and 0.66 for surface and bottom salinity in the summer, respectively.
The depth-mean circulations of the Bohai and Yellow Sea are in Fig. 4 during summer in 2019, from which we find the basic circulation distributions are well simulated.
In the Bohai, it consists of an anticyclonic gyre in the center of the Bohai and the inflow and outflow across the Bohai Strait.The Bohai circulation patterns are consistent with previous research (Guan 1994;Wei et al. 2003;Xu et al. 2023;Zhou et al. 2017).In the Yellow Sea, a cyclonic circulation basically exists, including the Korean Coastal Current flowing northward along the Korean coastline and changing direction in the Bohai Strait, the along coast currents flowing northward along the Shandong Peninsula.The simulated circulation patterns are in agreement with previous studies (Meng et al. 2020;Xia et al. 2006;Yuan et al. 2008).

Tidal effect on the internal variability
As mentioned in the introduction, the deviation of each simulation represents the variability to the ensemble mean that cannot trace back to the external causes.To compare the tidal forcing effect on the internal variability, we calculate the standard deviation of these deviations for the with-tide and no-tide ensemble, separately.
We calculate the spatial mean of the standard deviations of depth-averaged velocity anomalies u ′ , with u ′ representing the deviations to the ensemble mean at each day and at each model grid.For each day, we first calculate the difference of the depth-averaged velocities to the ensemble means, and then the standard deviation across all ensemble members in each model grid.Then, we get a time series of standard deviation of u ′ for each model grid and take the spatial mean at the end.The same process is applied for the tide-ensemble and no-tide ensemble, respectively.As u ′ are the deviations to the ensemble mean, it represents the internal variability intensities variations.
From Fig. 5, we find that the internal variability level is much reduced when the tides are activated (cf.Lin et al. 2022).
In addition, we find a seasonal variation of the internal variability, being weak in winter, starting to grow in spring, being strongest in summer, and receding gradually in autumn.We will discuss the reason of the seasonal signal in the next section.
Above are the time variations of the internal variability; Fig. 6a and b show spatial distributions of the yearly mean of the standard deviations of depth-averaged velocity anomalies u ′ .Here, for each model grid, we calculate the standard deviation of u ′ at each day and then take the yearly average.Figure 6 shows that a consistent spatial pattern exists in both with-tide and no-tide simulations, being highest in the center of the Yellow Sea and lowest along the coast.Furthermore, in the central of Yellow Sea, the internal variability level is higher in no-tide simulation than in with-tide simulation.

Discussion
Based on the analysis above, a conclusion is drawn that the tidal forcing leads to a strong decrease in internal variability.Furthermore, the variation of the standard deviation of the depth-averaged velocity, which represents the internal variability level, runs parallel to the development of the stratification.The stratification influences the baroclinic instability.Baroclinic instability can cause the release of potential energy to the kinetic energy of growing turbulence, which may further modulate the tendency of internal variability generation.As mentioned in the introduction, baroclinic instability may be a source of internal variability (Waldman et al. 2018).We hypothesize that internal variability stems from baroclinic instability through stratification modulation in the Bohai and Yellow Sea.We expect that the development of the internal variability varies with the intensity of the baroclinic instability in spatial and temporal distributions.
Baroclinic instability is a hydrodynamic instability that happens when south-north or vertical differences in pressure and density in the ocean or atmosphere (Stevens et al. 2013).In the real ocean state, there are inevitable disturbances, some of which are temporary, but some of which will interact with the basic state and take energy from the basic state, and the amplitudes of the disturbances will grow (Feng 2021; Gastineau et al. 2018).How long will a disturbance last depends on if the system can provide the environment to let the disturbance grow (Geyer et al. 2021).The spatial pattern distributions (Fig. 6) are both consistent with the hypothesis, in the center area of the Yellow Sea, the depth is deeper, which is suitable for the development of stratification in summer; while in the continental shelf, where the depths are shallow, the mixings by wind and tides are strong, so the seawater temperature and salinity are more uniform.
To further analyze our hypothesis, we aim at explaining the tidal forcing changes on internal variability intensities from the elementary baroclinic instability theory, Eady theory.
The Eady theory is a useful analytical concept about baroclinic instability.In this paper, we follow Stone (1972), Isachsen (2011), andWaldman et al. (2018) to calculate the theoretical diffusivity K t from wave number and the growth rate (hereinafter K t ).It shows an estimate of mesoscale turbulence transport capacity, modulating the restratification.
Based on the Eady theory, the growth rate is and wave number where f is the Coriolis coefficient, N is the buoyancy fre- quency, N = √ − g 0 z , 0 and are the reference and potential densities, U g is the geostrophic current, z U g = g , which is the depth-mean geostrophic current shear, and H is the water depth.Furthermore, the Eady theory predicted theoretical diffusivity is from which, it indicates that the K t is influenced by the topography and horizontal and vertical density gradients.The larger the K t , the stronger the baroclinic instability level.
The spatial and time mean of depth-averaged K t of the Bohai and Yellow Sea obtained from the tide-ensemble and no-tide ensemble are shown respectively in Tables 1  and 2. We find that the variations in the two ensembles co-vary, with a maximum in both ensembles in Experiment 5 and a minimum in Experiment 2. In the Bohai, the spatial correlations between the internal variability and K t are 0.67 and 0.57 in with-tide and no-tide ensembles, respectively.In the Yellow Sea, the correlations are 0.72 and 0.67 in with-tide and no-tide ensembles.
When comparing the spatial and time means of the depth-averaged K t pairwise, we find that the spatial mean K t is higher in the no-tide simulations.A t-test of the hypothesis of pairwise zero differences of the spatial and temporal mean of depth-averaged K t between the tide-ensemble and no-tide ensemble for the Bohai and Yellow Sea is rejected with a risk of less than 5%.Thus, the differences in Bohai and Yellow Sea are statistically significant.
To show the spatial patterns of depth-averaged K t of both ensembles, Fig. 7a and b show the time-and depthaveraged K t at each position.The depth-averaged K t exceeds 40m 2 ∕s in most of the center Yellow Sea in both tide-ensemble and no-tide ensemble.Based on Eq. ( 3), the Eady theory predicted theoretical diffusivity K t depends on the square of the water depth H, so that the K t is weak in shallow waters like the Bohai.The area encircled by 80 m 2 ∕s contour line is larger when tides are turned off, which indicates that the K t is larger in the center of the Yellow Sea in the no-tide simulation.Such spatial patterns of K t (Fig. 7a and b) are similar to the patterns of the standard deviation of u � .The spatial correlation between the standard deviations of u � and the K t predicted in with-tide and no-tide simulations is 0.80 and 0.61, respectively.The results illustrate a preliminary relationship between internal variability intensities and Eady theory predicted theoretical diffusivity K t .To further compare the relation between K t and internal variability intensities, we calculate the time correlation between these two variables.
The model domain averaged depth-mean K t shows a good agreement with the standard deviations of u � .These agreements show not only in the comparison between K t and spatial mean of u � (Fig. 8a and b), but also in the difference of two variables between with-tide and no-tide simulations (Fig. 8c).In with-tide and no-tide simulations, the spatial means of the standard deviation of u � are relatively weaker in winter, starting to increase in spring, reaching its maximum in summer, and beginning to decrease in autumn.These trends are consistent with the variations of K t .The correlations between the spatial mean of the standard deviation of u � and theoretical diffusivities are 0.60 and 0.66 in the tide-ensemble and no-tide ensemble, respectively.From Fig. 8c, we find that most of the time (except for winter), the spatial means of the standard deviations of u � in the notide simulation are larger than that in with-tide simulation.Furthermore, the difference in the spatial mean of u � varies consistently with the difference of K t between with-tide and no-tide simulations, and the correlation reaches 0.73.The above results suggested that the larger K t , representing an increased baroclinic instability, is associated with stronger internal variability intensities.
The reason why there is a seasonal annual cycle of the spatial mean of the standard deviation of u � can be explained as follows: in winter, due to the strong winds, the energy input at the sea surface in both with-tide and no-tide simulations, the water column is well mixed and the temperature and salinity are mostly homogeneous from the surface to bottom.(Fig. 9a and b show the temperature distribution in winter in with-tide and no-tide simulations, respectively.)Thus, the baroclinic instability is weak, and unforced disturbance can hardly grow in winter.In addition, the differences between the temperature distribution of tide-ensemble and no-tide ensemble are far from evident, so that differences of internal variability intensities differences are not obvious.On the other hand, in summer, the temperature distributions of with-tide and no-tide ensemble are less similar.Compared with with-tide simulations, the temperature is higher at the surface layer and lower at the bottom layer in no-tide simulation (Fig. 9c and  d).In other words, the vertical temperature difference is larger in no-tide simulation, which is because the strength of vertical mixing caused by tides brings the cold water from the bottom layer upwards and mixes with the upper warm water in with-tide simulation (Lü et al. 2010;Moon et al. 2009;Xia et al. 2006).By contrast, the dense cold water lies stably at the bottom layer of the sea, with less mixing with the upper warm water, when the tides are turned off.The vertical density distribution shows a similar distribution with temperature (Fig. 10c and d), in which the density difference is larger in the no-tide ensemble.The K t distributions along 35°N sections in summer in tide-ensemble and no-tide ensemble are shown in Fig. 10a  and b.The greatest variances of K t are between 10 and 40 m, which is consistent with the pattern of the gradient of density (see also Benincasa 2023).Compared with the K t vertical distribution in the tide-ensemble (Fig. 10a), the K t maximum is higher in the no-tide ensemble.As we mentioned above, the cold and dense sea water with less density gradient emerges at the bottom of the Yellow Sea trough, but in the no-tide ensemble, sea water density still varies with depth below 50 m.Correspondingly, in withtide simulations, the theoretical diffusivities are mostly lower than 50 m 2 ∕s , while in no-tide simulations, more than half of the seawater theoretical diffusivities are above 50 m 2 ∕s .Based on the above analysis, the depth-averaged is larger in no-tide simulations.
The Eady theory predicted theoretical diffusivity K t is generally higher in no-tide simulations, which indicates the baroclinic instability is stronger so that the potential energy is easier to be released to kinetic energy.The available potential energy release feeds the kinetic energy of the growing turbulence and further gives the possibility to let the internal variability grow.
Baroclinic instability is a possible source of internal variability as suggested and validated in the Mediterranean Sea by Waldman et al. (2018).They suggested that internal variability is caused by a modulation of the background stratification by eddy activities.It seems to be also applicable in   2018) is that we are discussing how tides modify the stratification, adjust the baroclinic instability, and consequently influence the internal variability intensities.
One issue that needs to be noticed is that the K t distribu- tion in the no-tide ensemble is not higher than in the tideensemble at every grid point.In the whole model domain, the percentage of the grid points, of which Eady predicted theoretical diffusivities are greater (smaller) in the no-tide ensemble compared with the tide-ensemble, is 84.19% (15.81%).
When looking at the values across the ensemble members (Table 3), we notice that there is some co-variation, as demonstrated by the K t in Exp1, which is larger than in Exp 2, but smaller than in Exp 4, which is again smaller than in Exp 5-in both ensembles, with-tides and without-tides.Therefore, we do a t-test on the differences of K t (Exp i ) with-tides − K t (Exp i ) without-tides , whether their mean difference across experiments is consistent with a mean increase or a mean decrease.Since we have only 5 pairs of experiments, the number of degrees of freedom for the t-test is relatively small, namely, 5.
Such a t-test with a 5% significance level illustrates that there are 45.33% of the grid points, of which the theoretical diffusivities are statistically significantly increased when the tidal forcing is turned off; by contrast, there are only 5.29% of grid pints, where the theoretical diffusivity is statistically decreased when the tidal forcing is turned off.Here, the problem of multiple testing needs to be taken into account: allowing a risk of 5% of false rejections, then a rejection rate of 5% and a bit more is consistent with all rejections being false (von Storch and Zwiers 1999).
The theoretical diffusivities of two randomly selected grid points are shown in Table 3.For the grid point in 39°N 120°E, the K t values in all members in the no-tide ensemble are higher than those in the tide-ensemble.In addition, the t-test assesses the difference of K t between with and with- out tidal forcing ensemble as statistically significant.The K t at another grid point (38.1250°N122.875°E) appears to be different.The ensemble mean K t of tide-ensemble (47.25 m 2 ∕s ) is larger than in the no-tide ensemble (44.82 m 2 ∕s ), but K t is not always larger in the members of the with-tide ensemble-Exp1 is an exception.The t-test fails to assess the K t difference between with tidal forcing and without tidal forcing ensembles as statistically significant.
Regarding the grid points, which show larger K t in the tide-ensemble, we suggest an explanation from a statistical and a dynamic point of view: • Statistically: The percentage of grid points, at which K t is deemed to be significantly reduced when the tidal forcing is only about 5%, as explained above, which may be entirely within the expected false rejection rate of multiple testing.• Dynamically: The tidal forcing influences the location of the stratification.Taking a vertical profile (along 38.5°N) in autumn for example (Fig. 11), where the depth-averaged K t is larger from 122°E to 123.38°N in the with- tide ensemble.This may be so because the center of the main stratification in the zonal direction shifts from 122.5°E to 123.5°E.The greatest density gradient goes with the position of the stratification, thus the K t distribu- tion changes as well.But based on the results shown in Tables 1 and 2, the K t level is higher in most of the model domain when tides are turned off.

Conclusion
Based on the regional ocean model, ensemble simulations with slightly different initial conditions are conducted to investigate the tidal effect on the internal variability in the Bohai and Yellow Sea.The results reveal that the internal variability decreases, when the tidal forcing is considered.We analyze the tidal forcing damping effect on the internal variability by comparing the performance of internal variability development and the theoretical diffusivity K t as conceptualized by the Eady theory, which allows to estimate the level of baroclinicity.
Two pieces of evidence have shown that the internal variability intensity is associated with the baroclinic instability level: (1) In both with-tide and no-tide simulations, a seasonal signal appears in the internal variability time variation, which runs parallel to the development of the Eady theory predicted theoretical diffusivity K t .The time correlations between the K t and the internal variability reach 0.60 and 0.66, respectively, when tides are turned on and off.Such correlations reveal that the baroclinic instability is related with the internal variability.
(2) The difference in internal variability intensities between with-tide and no-tide simulations varies jointly with the difference of the K t with the correlation of 0.73.
Our results suggest that baroclinic instability is a driver of internal variability.With strong baroclinic instability, the potential energy is easier to be released to kinetic energy; meanwhile, it provides the chances for the unforced disturbances to grow.The earlier work has demonstrated that baroclinic instability is a source of internal variability through modulation of the background stratification by the mesoscale eddies (Waldman et al. 2018).But for the Bohai and Yellow Sea, of which the hydrodynamic is different from the deep ocean basins, it is the first time that the generation of the internal variability is explained from the perspective of baroclinic instability.This approach, based on baroclinic instability, also allows an explanation of the effect of the tides on the internal variability in the Bohai and Yellow Sea.
In conclusion, the tidal forcing influences the distribution of the stratification, more so in summer and less so in winter, which further has an impact on the baroclinic instability level.When the tidal forcing is considered, the vertical mixing strengthens, and the stratification is modulated, further weakening the baroclinic instability.Because the baroclinic instability is a possible source of internal variability, the internal variability is suppressed when the tidal forcing is turned on.
It should be noted that the baroclinic instability is not the only source of internal variability.Other processes may also contribute.The accumulation of short-term variability through the mechanism of the Stochastic Climate model (Hasselmann 1976) certainly also plays a role in these processes.
Our study suffers from the small ensembles of only 5 members.However, because of the seasonal change from winter to summer being consistent with the experimental change from no tide to with tide, including the statistical significance at many points, we believe that our result is qualitatively robust, even if enlarging the ensembles would Table 3 The Eady theory predicted theoretical diffusivity K t distributions of two randomly chosen model grid points.For one of the grid points (39°N 120°E), the ensemble mean K t of the without-tidal forcing ensemble (6.32 m 2 ∕s ) is greater than the value of the with-tidal forcing ensemble (3.51 m 2 ∕s ), and the t-test validates that the difference between the with-tidal forcing and without-tidal forcing is significant (thus, this point is labeled a "significant increase grid node").For another grid point (38.1250°N122.875°E), the ensemble mean K t of the without-tidal forcing ensemble (44.82 m 2 ∕s ) is smaller than the value of the with-tidal forcing ensemble (47.25 m 2 ∕s ), but the t-test fails to access the difference of the K t of this grid node as statistically significant (and the point is considered an "insignificant decrease grid node")

Fig. 1
Fig. 1 Model domain (the shading area) and station of spring (grey triangles) and summer (yellow cycles) Dongfanghong 2 research cruises

Fig. 2
Fig. 2 The comparison of observation and simulated results of the surface and bottom temperature.The first row (a-d) shows simulated temperature results; the second row (e-h) shows the observed temperature results; the first (a and e) and third columns (c and g) are the

Fig. 3
Fig. 3 Fig. 3 is the same as Fig. 2, but for the salinity comparison between observed results (a-d) and simulated (e-h)

Fig. 5 Fig. 6
Fig. 5 The time variation of the spatial-mean internal variability intensities.The pink and blue lines are for with-tide and no-tide ensembles, respectively

Fig. 7
Fig. 7 The time mean of the theoretical diffusivity predicted from Eady theory for tide-ensemble (a) and no-tide ensemble (b), respectively

Fig. 8 Fig. 9
Fig. 8 The time variations of Eady theory predicted theoretical diffusivity K t (blue dotted line) and the spatial mean of u � (pink solid line) in with-tide (a), no-tide simulations (b), and the difference between

Table 1
The spatial mean of Eady theory predicted theoretical diffusivity K t of the Bohai obtained from the with and without tidal forc-

Table 2
Same as Table 1, but for the Yellow Sea Without tidal forcing 47.86 39.05 49.62 50.12 37.48 lead to changes in some details, without compromising the main conclusion.