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

Ruibin Xia Bingrui Li Chen Cheng

Ruibin Xia, Bingrui Li, Chen Cheng. Response of the mixed layer depth and subduction rate in the subtropical Northeast Pacific to global warming[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-021-1818-y
Citation: Ruibin Xia, Bingrui Li, Chen Cheng. Response of the mixed layer depth and subduction rate in the subtropical Northeast Pacific to global warming[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-021-1818-y

doi: 10.1007/s13131-021-1818-y

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

Funds: The National Natural Science Foundation of China under contract No. 41606217; the Open Fund of the Key Laboratory of Research on Marine Hazards Forecasting under contract No. LOMF1702; the Open Fund of Key Laboratory for Polar Science, Polar Research Institute of China, Ministry of Natural Resources under contract No. KP201702; the Open Fund of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences under contract No. KLOCW1903; the Natural Science Foundation of Jiangsu Province under contract No. BK20191405.
More Information
  • Figure  1.  The February–March mean MLD (shading, interval: 20 m) from the historical simulation of the 9 models (a–i) and ensemble mean result (j). The contours indicate the mean MLD difference (RCP8.5 minus historical), dashed lines (negative values) means the MLD shoals in a much warmer climate. Magenta points represent the location of the MLD front in historical simulation.

    Figure  2.  The MLD maximum (a), the intensity of the MLD front mean (b) during February–March in the 9 CMIP5 models and ensemble mean result. The colors represent historical simulation (blue), RCP8.5 experiment (red), and their differences (gray). Percentages represent changes compared to corresponding historical simulation.

    Figure  3.  Differences (RCP 8.5 minus historical) of Ekman pumping rate (shading, downward is positive) mean during February–March of the 9 models (a–i) and ensemble mean result (j). The positive values indicate the Ekman pumping trend to downward and contribute to deepening the MLD. The contours indicate the difference (RCP8.5 minus historical) in MLD mean during February–March (contours, interval: 10 m). The magenta points represent the location of the MLD front in historical simulation.

    Figure  5.  Differences (RCP 8.5 minus historical) of temperature advection (shading) mean during February–March of the 9 models (a–i) and ensemble mean result (j). The positive values indicate warm advection increased or cold advection decreased in the upper ocean and contribute to shoaling the MLD. The contours indicate the difference (RCP8.5 minus historical) in MLD mean during February–March (contours, interval: 10 m). The magenta points represent the location of the MLD front in historical simulation.

    Figure  4.  Differences (RCP 8.5 minus historical) of heat flux (shading) mean during February–March of the 9 models (a–i) and ensemble mean result (j). The positive values indicate the ocean release more heat to the atmosphere and contribute to deepening the MLD. The contours indicate the difference (RCP8.5 minus historical) in MLD mean during February–March (contours, interval: 10 m). The magenta points represent the location of the MLD front in historical simulation.

    Figure  6.  Differences (RCP 8.5 minus historical) of the subduction rate (shading, downward is positive) and subduction in historical simulation (contours, only over $ 2\times{10}^{6} $ m/s are shown) during February–March in the 9 models (a–i) and ensemble mean (j) result. The magenta points represent the location of the MLD front in historical simulation.

    Table  1.   The 9 models from CMIP5 analyzed in this study

    ModelInstitutionCountry
    CCSM4National Center for Atmospheric ResearchUSA
    CNRM-CM5Centre National de Recherches MeteorologiquesFrance
    GFDL-ESM2GNOAA/Geophysical Fluid Dynamics LaboratoryUSA
    GFDL-ESM2MNOAA/Geophysical Fluid Dynamics LaboratoryUSA
    IPSL-CM5A-LRInstitute Pierre-Simon LaplaceFrance
    IPSL-CM5A-MRInstitute Pierre-Simon LaplaceFrance
    MIROC-ESMUniversity of TokyoJapan
    MPI-ESM-LRMax Planck Institute for MeteorologyGermany
    MRI-CGCM3Meteorological Research InstituteJapan
    下载: 导出CSV

    Table  2.   Qualitative comparison of the contribution of the three major factors to MLD change after global warming

    IDModelNorthern regionSouthern region
    Contribution of factorMLD
    trend
    Contribution of factorMLD
    trend
    $ {w}_{\rm{e}} $QTad$ {w}_{\rm{e}} $QTad
    aCCSM4+$ \downarrow $+++$ \uparrow $
    bCNRM-CM5++$ \downarrow $+$ \downarrow $
    cGFDL-ESM2G++$ \downarrow $+++$ \uparrow $
    dGFDL-ESM2M+$ \downarrow $++$ \downarrow $
    eIPSL-CM5A-LR++$ \downarrow $+$ \uparrow $
    fIPSL-CM5A-MR++$ \downarrow $+$ \uparrow $
    gMIROC-ESM+$ \downarrow $+$ \downarrow $
    hMPI-ESM-LR++$ \downarrow $++$ \downarrow $
    iMRI-CGCM3++$ \downarrow $+$ \downarrow $
    Note: $ {w}_{\rm{e}} $, Q, and Tad represent the Ekman pumping, net heat flux, and upper-ocean heat advection, respectively; + means it contributes to the MLD deepening, while – means it helps to shallow the MLD; the red color represents that factor is dominant to the actual MLD change. MLD trend represents the final change of MLD; $ \uparrow $ means the MLD deepened, and $ \downarrow $ means the MLD shallowed.
    下载: 导出CSV
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  • 收稿日期:  2020-12-22
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Response of the mixed layer depth and subduction rate in the subtropical Northeast Pacific to global warming

doi: 10.1007/s13131-021-1818-y
    基金项目:  The National Natural Science Foundation of China under contract No. 41606217; the Open Fund of the Key Laboratory of Research on Marine Hazards Forecasting under contract No. LOMF1702; the Open Fund of Key Laboratory for Polar Science, Polar Research Institute of China, Ministry of Natural Resources under contract No. KP201702; the Open Fund of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences under contract No. KLOCW1903; the Natural Science Foundation of Jiangsu Province under contract No. BK20191405.
    通讯作者: E-mail: xiarb@nuist.edu.cn

English Abstract

Ruibin Xia, Bingrui Li, Chen Cheng. Response of the mixed layer depth and subduction rate in the subtropical Northeast Pacific to global warming[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-021-1818-y
Citation: Ruibin Xia, Bingrui Li, Chen Cheng. Response of the mixed layer depth and subduction rate in the subtropical Northeast Pacific to global warming[J]. Acta Oceanologica Sinica. doi: 10.1007/s13131-021-1818-y
    • The ocean mixed layer links the atmosphere to the deep ocean and plays a critical role in climate variability. Atmospheric fluxes of momentum, heat and freshwater through the ocean surface drive vertical mixing and provide the source of almost all oceanic motions (de Boyer Montégut et al., 2004). The ocean mixed layer is often defined as the layer where the temperature, density or vertical gradients are smaller than some values near the sea surface. So ocean mixed layer depth (MLD) is one of the most important quantities of the upper ocean as it defines the quasi-homogeneous surface region of density that directly interacts with the atmosphere (Kara et al., 2003).

      There are many kinds of research about the variability and dynamics of the MLD since the last century (Levitus, 1982; Monterey and Levitus, 1997; Carton and Giese, 2008). The variability of the MLD is usually linked to many processes occurring in the mixed layer (surface forcing, ocean advection, etc.). For example, the seasonal variability of the MLD in the Kuroshio Extension is controlled by sea surface heat flux (Qiu and Kelly, 1993). Both sea surface heat flux and vertical pumping impact the mixed layer temperature seasonal variability in the three North Pacific subtropical mode water formation regions, but the contribution of ocean advection is relatively small (Pan et al., 2011). The annual and decadal variabilities of the MLD in the North Pacific are also connected with the variabilities of wind and heat flux induced by the Pacific Decadal Oscillation (Qiu and Chen, 2006; Dawe and Thompson, 2007). Previous research suggests that ocean advection could be more important than other factors for the MLD variability in some regions (Liu and Lu, 2016; Xia et al., 2018). Ocean advection changes the ocean vertical density gradient, impact the stratification, and then contribute to the ocean mixing process. Recently, some studies focus on the ocean eddy effect on MLD and they indicate that eddies could influence the winter MLD, leading to the low potential vorticity (PV) water mass change under mixed layer depth (Wang et al., 2020a; Wen et al., 2020; Xu et al., 2016). Their results also highlight the importance of the advection on the MLD changes in ocean mesoscale processes.

      The response of the upper-ocean and MLD to global warming is also a significant problem. For example, the sea surface temperature (SST) change is influenced obviously by ocean advection after global warming (Xie et al. 2010). The MLD in the 21st century decreases in most regions of the North Pacific, whereas the spatial pattern of the MLD is nearly unchanged (Jang et al., 2011). They consider the overall shoaling results in part from intensified upper-ocean stratification caused by both surface warming and freshening. A significant MLD decrease (>30 m) is found in the Kuroshio Extension, which is predominantly driven by reduced surface cooling, caused by the weakening of wind (Jang et al., 2011). However, some subsequent researches indicate that the MLD reduction would be non-uniform and most pronounced on the southern edge of the present deep-MLD region, due to the advection of temperature change in the upper 100 m by the mean eastward flow in the models (Zhang et al., 2016). Some long-timescale observation data shows that while the SST is rising at mid-latitudes, stratification is not unequivocally increasing nor is MLD shoaling (Somavilla et al., 2017). MLD variability reveals itself as a subtle interplay between circulation and atmospheric forcing at mid-latitudes (Somavilla et al., 2017). Besides, if MLD shoals uniformly in the whole region, this change could not lead to a large change of the MLD front. The studies above have implied that other processes, such as ocean advection, may play important roles in the MLD non-uniform change process under the warmer climate.

      Ocean ventilation, including the subduction and obduction process, is a key component of global oceanic circulation. Subduction and obduction have been widely used as tools describing kinematical and dynamical processes coupling the mixed layer and the ocean interior. The spatial pattern and temporal variation of the MLD both play important roles in the subduction and obduction process (Stommel, 1979; Woods, 1985; Marshall et al., 1993). Therefore, the MLD variability indirectly dominates many products caused by the subduction process, such as the mode water. Generally, sea surface net heat flux or surface wind field are considered as key factors on the MLD and then impact on the formation of the subduction rate and mode water (Hu et al., 2011; Qu and Chen, 2009; Xu et al., 2012). For example, both subantarctic mode water (SAMW) and Antarctic Intermediate Water (AAIW) are increased under intensified westerlies, increased heat loss and the lateral induction term change due to the deepening of the MLD (Liu et al., 2017). Xu et al. (2016, 2017) pointed out that PV distribution is asymmetric outside the anticyclonic eddy core, with enhanced subduction near the southeastern rim of the anticyclonic eddy. Katsura (2018) suggested the eastern subtropical mode water (ESTMW) and MLD is even related to the Pacific decadal oscillation from seasonal to interannual cycle. As the effective subduction generally occurs in late winter or early spring, when the MLD reaches its local maximum (Marshall et al., 1993), we use the February–March means to analyze the mechanism in this paper.

      There are two MLD local maximum regions in the subtropical North Pacific. The previous studies usually care more about the western region with relatively deeper MLD (e.g., Jang et al., 2011; Xu et al., 2012). While the eastern MLD local maximum region, accompanied by the subduction local maximum and formation of the ESTMW, is also important. Among all the subtropical low PV water masses in North Pacific, only ESTMW and the near-equatorial North Pacific low PV water mass (NELPVW) can migrate to the equatorial Pacific, and effect subsurface oceanic temperature there (Wang et al., 2020b). Their studies provided that the MLD and subduction variation could lead to a potential climate effect near-equatorial Pacific. Due to the lack of observation data, the long-timescale variation of MLD near the ESTMW formation region is not clear. Luckily, the Coupled Model Intercomparison Project Phase 5 (CMIP5) provides us the convenience to study the long-time variability of the MLD. We indicate that the ocean heat advection plays a critical role in the banded shoaling of MLD after global warming at the ESTMW formation region (Xia et al., 2015). Although the accuracy is limited by a single model simulation. Furthermore, with the 9 CMIP5 models, we show the MLD spatial pattern in historical climate simulation in detail and suggest that the non-uniform MLD pattern causes a strong MLD front. MLD front controls the lateral induction rate pattern and then decides the non-uniform distribution of the subduction rate (Xia et al., 2018). Therefore, we provide new questions and discuss them in this paper: How does the MLD respond to global warming in models? How does the MLD front change and why? What are the characteristics and mechanisms of the inter-model differences? What influences are these inter-model differences on the subduction process? Similar to the results in previous research (Xia et al., 2015, 2018), we propose that ocean advection change affects the MLD spatially non-uniform change, and then changes the MLD front and the subduction process to the increased forcing radiation. But the inter-model differences may be non-negligible, which depend on the various dominated mechanisms.

      The rest of the paper is organized as follows. A brief description of the data is introduced in Section 2. We examine the inter-model differences in the CMIP5 models, explore the mechanisms and the influence of the MLD on the subduction process in Section 3. Finally, Section 4 shows the summary and discussion.

    • The present study primarily uses the output from the 9 global coupled climate models (Table 1) as part of the CMIP5 (Dunne et al., 2012; Taylor et al., 2012). We choose the historical simulation and the Representative Concentration Pathways (RCP) 8.5 scenario. The historical simulation simulates the 20th century climate forced by observed atmospheric composition changes. While in the RCP8.5 scenario, the radiative forcing increases throughout the 21st century before reaching a level of approximately 8.5 W/m2 at the end of the century respectively (Taylor et al., 2012). The present-day mean state is taken from 1951 to 2000 in the historical simulation and the future climatology is from 2051 to 2100 in the RCP8.5 scenarios. Fifty-year averaged variables in those scenarios are calculated to represent their mean state, and the variabilities between the historical and RCP8.5 scenarios represent the changes in global warming.

      Table 1.  The 9 models from CMIP5 analyzed in this study

      ModelInstitutionCountry
      CCSM4National Center for Atmospheric ResearchUSA
      CNRM-CM5Centre National de Recherches MeteorologiquesFrance
      GFDL-ESM2GNOAA/Geophysical Fluid Dynamics LaboratoryUSA
      GFDL-ESM2MNOAA/Geophysical Fluid Dynamics LaboratoryUSA
      IPSL-CM5A-LRInstitute Pierre-Simon LaplaceFrance
      IPSL-CM5A-MRInstitute Pierre-Simon LaplaceFrance
      MIROC-ESMUniversity of TokyoJapan
      MPI-ESM-LRMax Planck Institute for MeteorologyGermany
      MRI-CGCM3Meteorological Research InstituteJapan

      The spatial resolution varies between models and within the same model for atmospheric and oceanic variables. To facilitate comparison with each model and observations, we interpolated them onto a 1°×1° latitude-longitude grid. We investigate both the common features (ensemble mean) and the inter-model differences among models, focusing on the MLD variability and dynamics. The same member run (R1i1p1) is chosen in all models. The model outputs are freely available from the Program for Climate Model Diagnosis and Intercomparison (PCMDI) at the Lawrence Livermore National Laboratory (http://cmip-pcmdi.llnl.gov/cmip5/). The model in historical simulation has been examined with the Levitus-94 data (Levitus and Boyer, 1994) and Argo data (Xia et al., 2018). These data are both 1°×1° gridded and from the Asia-Pacific Data Research Center (APDRC, http://apdrc.soest.hawaii.edu/).

    • Single model simulation indicated that the MLD during February–March is banded shoaling in response to global warming, with a maximum shoaling of 50 m, leading to the lateral induction reduction (Xia et al., 2015). While more model simulation results (Fig. 1) indicate that the above conclusion may depend on the chosen model. In the RCP8.5 scenario experiments, all models show the MLD shoaling pattern in this region.

      Figure 1.  The February–March mean MLD (shading, interval: 20 m) from the historical simulation of the 9 models (a–i) and ensemble mean result (j). The contours indicate the mean MLD difference (RCP8.5 minus historical), dashed lines (negative values) means the MLD shoals in a much warmer climate. Magenta points represent the location of the MLD front in historical simulation.

      As shown in Fig. 1, the contours indicate the mean MLD difference (RCP8.5 minus historical), as the dashed lines (negative values) means the MLD shoals in a much warmer climate. MLD shoals in all models, which is similar to the single model result (Xia et al., 2015). But the MLD change pattern is relatively diverse in different models. We will discuss these similarities and differences in detail next, which will influence the MLD front change pattern directly. The MLD horizontal gradient $ {h}_{\rm{grad}} $ is calculated as

      $$ {\rm{}}{h_{{\rm{grad}}}} = \nabla {h_{\rm{m}}} = \frac{{\partial {h_{\rm{m}}}}}{{\partial x}}{\mathop i\limits^ \rightharpoonup} + \frac{{\partial {h_{\rm{m}}}}}{{\partial y}}{\mathop j\limits^ \rightharpoonup} ,$$ (1)

      where the unit of $ {h}_{\rm{grad}} $ is m/km. In this paper, we use MLD front intensity to represent the MLD horizontal gradient maximum.

      MLD in historical simulation (shading in Fig. 1) in all models show an inter-regional diversity, which is much deeper (>140 m) in the northern region and relatively shallower (<60 m) in the southern region. Thus we divide this area into two regions, while the MLD fronts (magenta points in Fig. 1) are suitable boundaries. The two regions are called “northern region” (north of the MLD front) and “southern region” (south of the MLD front) respectively (Xia et al., 2018). When concerned with the response of MLD (contours in Fig. 1) to the warmer climate, it is obvious that the MLD change is also divided by these boundaries in almost all models (except MRI-CGCM3). The MLD shoals more in the northern region, where the MLD maximum exists in historical simulation. The MLD maximum shoals over 30 m with increased radiation forcing in the ensemble mean result of the 9 CMIP5 models. As a result, the MLD front intensity weakens obviously from 0.24 m/km to 0.15 m/km (weakened by 33.9%). While with shallower MLD in historical simulation, the MLD change is much smaller in the southern region than that in the northern region. Especially, the MLD even slightly deepened in CCSM4, MIROC-ESM in the southern region. In other words, it seems that the deeper of MLD in historical simulation, the shallowerafter increased forcing radiation. The ensemble mean also reflects this characteristic. This non-uniform MLD change pattern is highly consistent with the non-uniform MLD pattern in historical simulation (Figs 1 and 2a), which significantly reduces the MLD front intensity. As shown in Fig. 2, the decrease of the MLD front (33.9%) is generally larger than the shoaling of MLD (22.2%) in the MLD maximum region.

      Figure 2.  The MLD maximum (a), the intensity of the MLD front mean (b) during February–March in the 9 CMIP5 models and ensemble mean result. The colors represent historical simulation (blue), RCP8.5 experiment (red), and their differences (gray). Percentages represent changes compared to corresponding historical simulation.

      The MLD change pattern (contours in Fig. 1) is non-uniform and its inter-model differences could not be ignored. This phenomenon indicates it is not accurate to discuss the mechanism with only one model. The inter-model differences mainly reflect in the following two aspects. First, in the northern region, though the MLD shoals larger than that in the southern region in all models, the maximum of MLD shoaling differs considerably in different models (Fig. 2a). The maximum of MLD shoaling is only about 20–30 m in CCSM4, IPSL-CM5A-MR, but increasing to 40–50 m in CNRM-CM5, GFDL-ESM2M, and arriving at the maximum 80 m in MIROC-ESM. Compared with the MLD in historical simulation, it is easy to find that the deeper of MLD in historical simulation, the shallower after increased forcing radiation. This characteristic occurs not only in the diverse regions in one model but also in the inter-model differences. Generally, the weakening magnitude of the MLD front is consistent with the shoaling of the MLD maximum. But the MLD front is weakened to the maximum in MRI-CGCM3, in which there is not the largest MLD shoaling maximum. Second, in the southern region, the MLD shoals small in all models RCP8.5 scenario experiments. But the changing pattern could be divided into two categories. First, although the shoaling magnitude and location are not consistent, a banded shoaling from southwest to northeast could be found in CNRM-CM5, GFDL-ESM2M, MPI-ESM-LR and MRI-CGCM3, similar to the previous research (Xia et al., 2015). Second, the MLD is shallowed a little or even deepened in some regions in the rest of the 5 models.

      In summary, the MLD change pattern (contours in Fig. 1) is non-uniform and its inter-model differences could not be ignored. Both the consistency of the models and the inter-model differences show that the change of MLD front is not only due to the maximum of MLD shoaling but also depended on the MLD non-uniform spatial variability. As a result, the decrease of the MLD front (33.9%) is generally larger than the shoaling of MLD (22.2%) in the MLD maximum region (Fig. 2). This result indicates that the subduction process may become much weaker, also depended on the MLD non-uniform spatial variability. We will discuss this question in Section 3.3.

    • The inter-model differences in both regions suggest that dominant factors of the MLD change depend on the models or regions. In this part, we will focus on these mechanisms. The response of dominant factors is various in the 9 models, due to variable regions, the external forcing, or parameterization designs. To discuss the influence of these factors clearly, we still use the two regions divided by the MLD front: the northern region and the southern region. Comparing these models, we could get more information about how do these factors influence the MLD change and which factor plays a dominant role in the long-time scales of the MLD change process.

      In the historical simulation, the spatial pattern of the Ekman pumping caused by sea surface wind stress is generally similar in all models and contributes to the winter MLD deepening in almost the whole region (Xia et al., 2018). However, compared with the RCP8.5 experiment, the Ekman pumping change patterns are disordered and inconsistent in different models (Fig. 3). Though the weakened Ekman pumping could make a positive contribution to the MLD shoaling in most models, the Ekman pumping change locations are not corresponding with the MLD change patterns. For example, the maximum locations of Ekman pumping weakening are far away from the MLD shoaling maximum cores in IPSL-CM5A-LR, IPSL-CM5A-MR, and MIROC-ESM.

      Figure 3.  Differences (RCP 8.5 minus historical) of Ekman pumping rate (shading, downward is positive) mean during February–March of the 9 models (a–i) and ensemble mean result (j). The positive values indicate the Ekman pumping trend to downward and contribute to deepening the MLD. The contours indicate the difference (RCP8.5 minus historical) in MLD mean during February–March (contours, interval: 10 m). The magenta points represent the location of the MLD front in historical simulation.

      Similar to Ekman pumping, the ocean releases heat flux to the atmosphere in all models and contributes to the winter MLD deepening spatial quite uniformly in the historical simulation (Xia et al., 2018). But the change of heat flux in a warmer climate is also relatively variable in those models. In the northern region, the ocean releases less heat in CCSM, CNRM-CM5, GFDL-ESM2G, and GFDL-ESM2M, which is consistent with the MLD shoaling; but releases more heat and blocks MLD shoaling in other models. In the southern region, the inter-model differences of heat flux change influence are also huge (see details in Table 2 and Fig. 4). Noticed that is interesting for the net heat flux change in MRI-CGCM3: the ocean releases more heat to the atmosphere in all regions after global warming. This change of heat flux provides a negative contribution and impedes the shoaling of MLD in the whole region.

      Table 2.  Qualitative comparison of the contribution of the three major factors to MLD change after global warming

      IDModelNorthern regionSouthern region
      Contribution of factorMLD
      trend
      Contribution of factorMLD
      trend
      $ {w}_{\rm{e}} $QTad$ {w}_{\rm{e}} $QTad
      aCCSM4+$ \downarrow $+++$ \uparrow $
      bCNRM-CM5++$ \downarrow $+$ \downarrow $
      cGFDL-ESM2G++$ \downarrow $+++$ \uparrow $
      dGFDL-ESM2M+$ \downarrow $++$ \downarrow $
      eIPSL-CM5A-LR++$ \downarrow $+$ \uparrow $
      fIPSL-CM5A-MR++$ \downarrow $+$ \uparrow $
      gMIROC-ESM+$ \downarrow $+$ \downarrow $
      hMPI-ESM-LR++$ \downarrow $++$ \downarrow $
      iMRI-CGCM3++$ \downarrow $+$ \downarrow $
      Note: $ {w}_{\rm{e}} $, Q, and Tad represent the Ekman pumping, net heat flux, and upper-ocean heat advection, respectively; + means it contributes to the MLD deepening, while – means it helps to shallow the MLD; the red color represents that factor is dominant to the actual MLD change. MLD trend represents the final change of MLD; $ \uparrow $ means the MLD deepened, and $ \downarrow $ means the MLD shallowed.

      The inter-model differences in upper-ocean temperature advection are also significant (Fig. 5). In the northern region, there is southward cold advection to contribute to the MLD deepening in historical simulation (Figs 5 and 6 in Xia et al., 2018). With increased radiation forcing, the cold advection is weakened in CCSM4, GFDL-ESM2M and MPI-ESM-LR, increased in CNRM-CM5, IPSL-CM5A-LR, IPSL-CM5A-MR and MRI-CGCM3, and changed little in the other two models. Compared with the changes of Ekman pumping and net heat flux, it is indicated that the cold ocean advection change contributes to the MLD shoaling mainly in CCSM4 and GFDL-ESM2M, and even plays the dominant role in MPI-ESM-LR in the northern region. In the southern region, the historical warm advection (Figs 5 and 6 in Xia et al., 2018) is strengthened in CNRM-CM5, GFDL-ESM2M, MPI-ESM-LR, and MRI-CGCM3, which is highly consistent with the MLD shoaling. In other models, warm advection reduces and helps to deepen the MLD in the southern region, especially in GFDL-ESM2G, IPSL-CM5A-LR, and IPSL-CM5A-MR.

      Figure 5.  Differences (RCP 8.5 minus historical) of temperature advection (shading) mean during February–March of the 9 models (a–i) and ensemble mean result (j). The positive values indicate warm advection increased or cold advection decreased in the upper ocean and contribute to shoaling the MLD. The contours indicate the difference (RCP8.5 minus historical) in MLD mean during February–March (contours, interval: 10 m). The magenta points represent the location of the MLD front in historical simulation.

      Because the inter-model differences are non-negligible, the ensemble mean is unrepresentative (Table 2). As mentioned in Section 3.1, we divided this area into the northern region and southern region by the MLD front. In the northern region, decreasing Ekman pumping dominates the MLD shoaling in IPSL-CM5A-LR, IPSL-CM5A-MR, and MRI-CGCM3. The ocean releases less heat flux to the atmosphere and plays the most important role in CNRM-CM5, MPI-ESM-LR. Only cold advection contributes to the MLD shoaling in MPI-ESM-LR. While in CCSM4 and GFDL-ESM2M, both the changes in heat flux and ocean cold advection are consistent with the MLD shoaling pattern.

      As for the southern region, we defined two categories to distinguish the inter-model differences of the MLD change pattern in Section 3.1. In CNRM-CM5, GFDL-ESM2M, MPI-ESM-LR, and MRI-CGCM3, there are MLD banded shoaling from southwest to northeast, which is highly corresponding to the increasing upper-ocean warm advection. Upper-ocean warm advection contributes to strength the stratification and reduces the mixing. On the contrary, MLD changes little or even deepens in the other areas and the other 5 models. In these regions, the ocean advection change is negative. As the ocean advection is basically warm advection caused by Ekman advection in historical simulation (Xia et al., 2018). Therefore, the negative change means that the warm advection decreases and contributes to weakening the stratification and then deepening the MLD. Both above categories suggest that ocean advection change plays a key role in maintaining the MLD in the southern region. Our previous research has demonstrated that the shoaling contribution of the warm ocean advection could offset the deepening contribution of heat flux and Ekman pumping (Xia et al., 2018). This mechanism also works on the MLD change in RCP8.5 experiments.

      In conclusion, the inter-model differences are non-negligible and the dominant mechanisms of MLD change are quite diverse in individual regions or models. For the northern region, MLD shallow greatly and is influenced by the above three factors. The contribution proportions of these factors generally change due to the various models. For the southern region, MLD changes a little under the warmer climate, when the ocean becomes warmer and stratification is strengthened. In some models, there are MLD banded shoaling regions. Both situations in the southern region are mainly due to the upper ocean warm advection change, caused by the change of trade wind. Although large inter-model differences exist in other factors, the change of ocean advection is truly similar in all the models. The less shoaling of MLD in the southern region combines with obviously shoaling of MLD in the northern region, and then causes the significant weakening of the MLD front.

      Figure 4.  Differences (RCP 8.5 minus historical) of heat flux (shading) mean during February–March of the 9 models (a–i) and ensemble mean result (j). The positive values indicate the ocean release more heat to the atmosphere and contribute to deepening the MLD. The contours indicate the difference (RCP8.5 minus historical) in MLD mean during February–March (contours, interval: 10 m). The magenta points represent the location of the MLD front in historical simulation.

    • The subduction rate is defined as (Williams, 1991; Xu et al., 2012):

      $$ {\rm{}}{S_{{\rm{mean}}}} = - {\mathop {{u_{\rm{m}}}}\limits^ \rightharpoonup} \cdot \nabla {h_{\rm{m}}} + {w_{\rm{e}}}, $$ (2)

      where $ - {\mathop {{u_{\rm{m}}}}\limits^ \rightharpoonup} \cdot \nabla {h}_{\rm{m}} $ is the lateral induction, occurs at the current across the front of the MLD. The Ekman pumping velocity $ {w}_{\rm{e}} $ can be defined as $ {w_{\rm{e}}}={\rm{cur}}{{\rm{l}}_z}(\tau /f)/{\rho _0} $ (Pond and Pickard, 1983), where τ is the wind stress and f is the Coriolis parameter. As the effective subduction only occurs after the MLD reaches a maximum, we calculate the subduction rate during February–March from Eq. (2). The subduction rate maximum spatial patterns are similar in the 9 models in historical simulation (Fig. 6, contours). In the ensemble mean, the subduction maximum region forms a banded structure near the east-west direction, with the maximum 4×106 m/s at (24°N, 140°W). Previous research suggests this non-uniform subduction rate spatial pattern is almost dominated by the non-uniform lateral induction rate distribution (Xia et al., 2018). The latter is highly consistent with the position and intensity of the MLD front.

      Figure 6.  Differences (RCP 8.5 minus historical) of the subduction rate (shading, downward is positive) and subduction in historical simulation (contours, only over $ 2\times{10}^{6} $ m/s are shown) during February–March in the 9 models (a–i) and ensemble mean (j) result. The magenta points represent the location of the MLD front in historical simulation.

      In a warmer climate, subduction decreases in almost all the models (Fig. 6). In the ensemble mean, the subduction maximum changes from 3.03×10−6 m/s to 2.55×10−6 m/s, weakening about 0.48×10−6 m/s (15.7%). Surprisingly, the subduction decreasing maximum regions in all models is highly consistent with the historical subduction maximum regions, where is actually the source regions of ESTMW in historical simulation. Therefore, the reduction of subduction maximum pushes less water into the thermocline and leads to less mode water formation as a result directly. In the warmer climate, the lateral induction change caused by the MLD front change is still the dominant factor of the subduction change. In the ensemble mean, the lateral induction rate decreases by 0.4×106 m/s (about 29.1%) after global warming, and provides more than 85% of contribution to the subduction change. That is why the location of subduction decreasing is highly consistent with the historical MLD front (Fig. 6) in almost all the models.

      The inter-model difference of subduction is mainly caused by the inter-model difference of lateral induction (Xia et al., 2018). Comparing the historical simulation with the RCP8.5 scenario, we find inter-model differences still exist in the changes of subduction and lateral induction, but not as big as the MLD change factors mentioned in Section 3.2. A possible reason is that whichever controls the MLD change, the final result is to weaken the MLD front, and then impact on subduction. It is conspicuous that the lateral induction change is larger in GFDL-ESM2M, MPI-ESM-LR, MIROC-ESM, and MRI-CGCM3 (almost over 20%) than that in other models (Fig. 6), corresponding with the inter-model differences of MLD front intensity change (Fig. 2b). In other words, ocean advection seems almost the dominant factor in these four models (Table 2).

    • The objective of this study is to describe the possible response of the MLD and the subduction process after global warming and discuss the mechanisms. Comparing with the historical simulation and RCP8.5 experiment in 9 CMIP5 models, we find the MLD change pattern is non-uniform and its inter-model differences could not be ignored. The change of MLD front is not only due to the maximum of MLD shoaling, but also depended on the MLD non-uniform spatial variability. In the ensemble mean, the decrease of the MLD front is about 1.5 times as large as the shoaling of MLD maximum. As a result, the weekened subduction is mainly caused by the decreased lateral induction, while the latter comes from the MLD front reduction. In the ensemble mean, the lateral induction rate decreases by 0.4×106 m/s (about 29.1%), and provides more than 85% of contribution to the subduction change. To see a single model, the lateral induction change is larger in GFDL-ESM2M, MPI-ESM-LR, MIROC-ESM, and MRI-CGCM3 (almost over 20%) than that in other models, corresponding with the larger MLD front intensity change, where ocean advection is almost the dominated factor. Xu et al. (2012) found that the low PV water and Subtropical Countercurrent (STCC) first show a sharp weakening trend when the radiative forcing increases, but then reverse to a slow strengthening trend of smaller magnitude after the radiative forcing is stabilized. This is because the subsequent warming is greater at the subsurface than that at the sea surface, destabilizing the upper ocean and becoming favorable for the low PV water formation. Their result better supports our conclusion, because they used the RCP4.5 scenario to simulate the warmer climate and the concern region (western Pacific) also differs from ours. The radiative forcing is increased sharply to 4.5 W/m2 and then keeps stable in the RCP4.5 scenario (van Vuuren et al., 2011). But the radiative forcing maintains a linear growth in RCP8.5 (van Vuuren et al., 2011), which means the ocean fast response is not finished until 2100. This continually growing radiative forcing and the inter-regional difference may be the key reasons for MLD decreasing in this paper.

      The inter-model differences of MLD change are non-negligible, which rely on the variable dominant mechanisms in various regions or models. For the northern region, MLD shallows greatly and is influenced by all the three factors mentioned above. The contribution proportions of these factors are generally diverse among regions and models. In the southern region, MLD becomes a little deepening or slight banded shoaling. Both situations in the southern region are mainly due to the upper ocean warm advection change, caused by the change of trade wind. Although the inter-model differences of Ekman pumping and heat flux changes are large, the change of ocean advection in the southern region is quite similar in all the models. The less shoaling of MLD in the southern region combines with obviously shoaling of MLD in the northern region, leading to the significant weakening of the MLD front. As we know, climate change is affected by all kinds of forcings, and the individual climate effects of each force are difficult to analyze. A quantitative diagnostic is necessary for further work. Liang-Kleeman information flow method may be one useful method to establish a causal relationship (Jiang et al., 2019).

      Compared with observation data, the simulated MLD in models is usually deeper and non-uniform in the spatial pattern. Both amplified MLD front intensity and the lack of eddy dissipation cause larger subduction in CMIP5 models. As a result, mode water can be generated in a wider region and the low vorticity can be maintained and extended far to the south. In recent years, more and more researchers begin to focus on the eddy effects on the subduction and the mode water formation. It is found that eddy activities contribute to the MLD variation in various time scales (days to years), and then impact the subduction process in many regions (Wang et al., 2020a; Wen et al., 2020; Xu et al., 2016, 2017). With the development of high-resolution models in CMIP6, exploring the eddy effect in decadal to multi-annual cycles in a warmer or colder climate becomes realizable, which will be carried out in our future research.

    • We appreciate the World Climate Research Programme’s Working Group on Coupled Modeling, which is responsible for CMIP5. We thank the climate modeling groups (as listed in Table 1) for producing and making available their model output.

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