1 Introduction

Impacts of global warming on specific regions of the ocean have become increasingly important in recent years as human societies are confronted with the requirement to take appropriate actions to mitigate the adverse effects of global warming. Sea-level rise by as much as several meters, for example, will have negative social and economic consequences, including coastal inundation and flooding. Detailed global warming projections, including uncertainties, are needed to minimize the risks associated with climate change effects.

Several previous studies have explored the response of the western North Pacific to global warming. Sakamoto et al (2005) used a coupled atmosphere-ocean model with an eddy-permitting ocean model to show that the velocity of the Kuroshio Current and the Kuroshio Extension (KE) will increase as a result of atmospheric CO\(_2\) concentrations increased by 1% year\(^{-1}\). Sato et al (2006) have pointed out that a global warming projection based on the A2 scenario of the Intergovernmental Panel on Climate Change (IPCC) Special Report on Emission Scenarios leads to a poleward extension of the subtropical gyre. Liu et al (2016) have estimated future sea-level change in the western North Pacific by dynamical downscaling with an eddy-permitting ocean model under the RCP8.5 scenario. Li et al (2017) have used a Kuroshio-resolving, atmosphere–ocean coupled model to find that the KE system is intensified under the RCP4.5 scenario and that its path state tends to move poleward. Terada and Minobe (2018) have used Coupled Model Intercomparison Project Phase 5 (CMIP5) (Taylor et al 2012) data for both the RCP4.5 and RCP8.5 scenarios to investigate future changes in the dynamic sea level over the North Pacific and its relation to formation of subtropical mode water.

Despite these previous studies, there is presently no consensus about the response of the North Pacific to global warming. There are several reasons for this lack of consensus. First, the response of the ocean to global warming depends on the choice of greenhouse gas (GHG) emission scenario. For example, whether the pattern of global warming over the North Pacific exhibits a response like the Arctic Oscillation or the El Niño-Southern Oscillation (Yamaguchi and Noda 2006) leads to different responses by the North Pacific. Second, the simulated response of the ocean to global warming also depends on the horizontal resolution of the ocean general circulation models (OGCMs). In the western North Pacific, the Kuroshio and the KE flow as inertial jets accompanied by energetic eddies. The flow paths are strongly affected by the coastal geometry and the bottom topography. The simulation of these currents therefore requires a horizontal resolution fine enough to represent these oceanographic structures. Third, the simulated response of the ocean to global warming depends on the characteristics of the coupled models of the atmosphere and ocean. Each model has its own model biases and errors. Coupled models also include unforced internal variability. These factors make it difficult to interpret results in a single simulation.

There is, hence, a need to estimate the uncertainty of future predictions on ocean model downscaling in the western North Pacific. Regional, high-resolution ocean models are quite useful for regional climate prediction, because high-horizontal-resolution OGCMs can more accurately simulate regional climates than the conventional OGCMs (i.e., eddy-less or eddy-permitting ocean models). Ensemble simulations can help to identify biases and errors in a single simulation, and they provide information about the uncertainty of projections. The next step is therefore to perform an ensemble simulation with high-resolution models and to estimate the range of uncertainty of predicted climate changes.

In this study, we made predictions about climate change effects based on ensemble simulations using a high-resolution North Pacific OGCM with a horizontal resolution of 10 km, and we evaluated the uncertainty of the predictions. No previous ensemble simulations have used a model with a horizontal resolution of 10 km or finer. In addition to ocean circulation and temperature, we also focused on two issues that have rarely been examined in the previous studies: sea levels along the coast of Japan and sea ice in the Sea of Okhotsk.

This paper is organized as follows. In Sect. 2, we describe the model and experimental design. In Sect. 3, we present the simulation of the present climate in western North Pacific, including the Kuroshio, sea surface temperature (SST), sea ice in the Okhotsk Sea, and sea surface height (SSH). We present the projected climate changes in Sect. 4, and we discuss their relationship with atmospheric changes in Sect. 5. Section 6 includes a summary and concluding remarks.

2 Methodology

The projections for the western North Pacific in the present study are based on the Future Ocean Regional Projection dataset (FORP). The FORP dataset was created by the Japan Agency for Marine-Earth Science and Technology under the research program Social Implementation Program of Climate Change Adaptation Technology, which was sponsored by the Ministry of Education, Culture, Sports, Science and Technology (Grant Number: JPMXD0715667163). The purpose of this project was to identify climate change adaptation measures for local governments. Detailed descriptions of the dateset and experimental procedure can be found in Nishikawa et al (2020) and Nishikawa et al (2021).

2.1 Ocean model

As the ocean model, we used the MRI.COMv4 model (Tsujino et al 2017) developed by the Meteorological Research Institute. The MRI.COM is a depth-coordinate model that solves the primitive equations under the hydrostatic and Boussinesq approximations. The model uses spherical coordinates in the horizontal domain and the z coordinate in the vertical. The model domain is the entire North Pacific, from 100 \(^{\circ }\) E to 75 \(^{\circ }\) W and from 15 \(^{\circ }\) S to 70 \(^{\circ }\) N. The horizontal resolution is 1/10 \(^{\circ }\) in the zonal direction and 1/10 \(^{\circ }\) in the meridional direction. The model has 54 levels in the vertical, and interval thickness increases from 1 m at the surface to 600 m at the bottom.

The model adopts a high-precision, second-order moment scheme (Prather 1986) for advection of tracers. The horizontal viscosity is a biharmonic friction with a Smagorinsky-like viscosity (Griffies and Hallberg 2000); the horizontal diffusion is biharmonic. The model uses the vertical turbulent mixing scheme of Noh and Kim (1999).

The model also includes sea ice processes. The sea ice model is a five-category model in which the sea ice is classified according to its thickness. The thermodynamics is based on Mellor and Kantha (1989), and the dynamics is based on the elastic–viscous–plastic rheology of Hunke and Dukowicz (1997). The model does not include processes such as river runoff, tides, thermal expansion, and sea-level change due to atmospheric pressure.

The surface fluxes are computed using the bulk formulas of Large and Yeager (2004). Daily variations of solar altitude are taken into account by the scheme of Ishizaki and Yamanaka (2010).

2.2 Experiments

The historical and future ocean state projections were produced by integration of the ocean model forced by surface atmospheric states taken from CMIP5 models during the period 1960–2100. Compared to the time-slice experiments that have been conventionally adopted because of computer resource limitations, this approach enabled us to conduct a seamless analysis from the present climate to the future climate.

Four CMIP5 models (GFDL-ESM2M, MRI-CGCM3, MIROC5, and IPSL-CM5A-MR) were selected for surface boundary conditions based on the restrictions imposed by data availability and computational costs. We selected CMIP5 models for which external forcing data were available at 3-h time intervals. Atmospheric variables obtained every 3 h from the models were used for the entire period from 1960 to 2100. Continuous calculations were performed with these four surface forcing datasets; thus, we had four ensemble members that differed in terms of surface forcing. The present climate simulation experiment was performed from 1960 to 2005, and the simulation of the future climate was carried out for the time interval 2006–2100.

We considered four Representative Concentration Pathways (RCPs) corresponding to GHG concentration trajectories RCP2.6, RCP4.5, RCP6.0, and RCP8.5 as future GHG emission scenarios for the CMIP5. We chose the RCP8.5 and RCP2.6 scenarios for this study, because they corresponded to the upper and lower bound among the four RCPs.

During the model integration, sea surface salinity (SSS) was relaxed to the World Ocean Atlas (WOA) climatological SSS (Monterey and Levitus 1997) with a time constant of 2 days, so that the modeled SSS did not drift significantly. Temperature and salinity were relaxed as lateral boundary conditions to the climatological temperature and salinity values of the WOA as well as to the temperature and salinity anomalies derived from the four CMIP5 parent models.

Because the modeled volume of the ocean was conserved using the Boussinesq approximation and virtual salinity flux instead of surface freshwater flux, it was necessary to separately evaluate the volume change due to the expansion and contraction of seawater and the inflow and outflow of fresh water. A Boussinesq ocean model should be adjusted by a globally uniform time-dependent factor to account for changes in global mean sea level associated with changes in global mean thermodynamic forcing (e.g., Greatbatch 1994). The globally uniform factor is diagnostically calculated by the net expansion/contraction of the global ocean (e.g., Griffies and Greatbatch 2012). As shown by Mellor and Ezer (1995), the globally uniform factor can correct a Boussinesq model on timescales longer than barotropic adjustments, so that it closely approximates the corresponding non-Boussinesq model. This correction is based on two assumptions. The first assumption is that the local sea-level change induced by the net expansion/contraction of the water column is rapidly distributed over the entire domain by the barotropic wave. The second assumption is that the slower baroclinic adjustments to vertical distributions of density change, which alter regional sea-level patterns, are well represented in Boussinesq ocean models. The latter assumption has been validated by the previous studies (e.g., Hsieh and Bryan 1996; Bryan 1996; Losch et al 2004; Yin et al 2010). The assessment of Mellor and Ezer (1995) shows that these assumptions are reasonable, and thus, we adopt this approach so as to correct errors arising from the Boussinesq approximation. In addition to the globally uniform factor, a regional ocean model needs a correction of sea level to account for its rise and fall over the entire model area (Mellor and Ezer 1995).

Thus, in a Boussinesq regional model, the total sea-level change (\(\eta \)) can be written as follows:

$$\begin{aligned} \eta (x, y, t) = \eta _\mathrm{m} (x, y, t) + \eta _\mathrm{g} (t) + \eta _\mathrm{r} (t), \end{aligned}$$
(1)

where \(\eta _\mathrm{m}\) is the local sea-level change calculated by a Boussinesq regional model, \(\eta _\mathrm{g}\) is the global mean sea-level change due to expansion/contraction of the water column and inflow/outflow of fresh water, and \(\eta _\mathrm{r}\) is the area-averaged sea-level change over the model domain due to transport across open boundaries of regional models. The introduction of these corrections (\(\eta _\mathrm{g}\) and \(\eta _\mathrm{r}\)) enables us to evaluate the regional contribution of steric sea level due to thermodynamic forcing.

We added the global mean sea-level (GMSL) rise (\(\eta _\mathrm{g}\)) derived from IPCC Special Report on Ocean and Cryosphere in a Changing Climate (SROCC) (Portner et al 2019) to the sea level calculated by the model. The GMSL rise at the end of the 21st century (2081–2100) was estimated to be 0.39 m (0.26–0.53 m) under the RCP2.6 scenario and 0.71 m (0.51–0.92 m) under the RCP8.5 scenario. In addition, we estimated the area-averaged sea level over the model domain (\(\eta _\mathrm{r}\)) from the averages of the changes simulated by the four CMIP5 parent models. The area-averaged sea-level rise at the end of the 21st century was estimated to be \(+0.034\) m under the RCP2.6 scenario and \(-0.026\) m under the RCP8.5 scenario.

We performed experiments similar to the OGCM simulations but using a 1.5-layer reduced-gravity (RG) model (Qiu et al 2013) to make it easy to get a linear response to a wind stress. The domain of the RG model covered the entire North Pacific (115 \(^{\circ }\) E–66 \(^{\circ }\) W, 15 \(^{\circ }\) S–60 \(^{\circ }\) N). The horizontal resolution was 0.25 \(^{\circ }\) \(\times \) 0.25 \(^{\circ }\), and the layer thickness was 500 m. We used a reduced-gravity constant of 1.8 cm\(^{2}\) s\(^{-1}\) to match the observed phase speed of the first baroclinic mode Rossby waves in the Pacific Ocean. The horizontal viscosity coefficient was \(1 \times 10^5\) cm\(^{2}\) s\(^{-1}\). The RG model was driven by the same surface boundary conditions but for the wind stress only during the period 1960–2100. The RG model was also driven by the JRA-55 (Kobayashi et al 2015) wind stress during the period 1960–2018 to evaluate the performance.

2.3 Observational data

The performance of the North Pacific high-resolution ocean model was evaluated by comparing the present climate results with observed data over the same period. The simulated SST and sea ice were compared with the COBESST2 dataset (Hirahara et al 2014). The temporal resolution of the COBESST2 dataset is monthly, and its spatial resolution is 1 \(^{\circ }\) \(\times \) 1 \(^{\circ }\). Comparisons were made for the period 1986–2005.

The simulated Kuroshio and offshore SSH were compared with the Copernicus Marine Environmental Monitoring Services (CMEMS) dataset (Mertz et al 2018). The temporal resolution of the CMEMS dataset is monthly and its spatial resolution is 0.25 \(^{\circ }\) \(\times \) 0.25 \(^{\circ }\). Comparisons were made during the period 1993–2005.

Monthly averages of the model results were used for the analysis. The timeframe of the present climate at the end of the 20th century was defined to be 1986–2005, and the timeframe for the future climate at the end of the 21st century was defined to be 2081–2100.

2.4 Estimation of uncertainty of future projection

To estimate the uncertainty of the projection at the end of the 21st century relative to the end of the 20th century, we used the method of Wakamatsu et al (2017) and the results of the ensemble simulations. The results included yearly outputs during the 20 years with the four atmospheric boundary conditions for the present climate and those with the four atmospheric boundary conditions for the future climate. We evaluated the uncertainty based on the differences of those results. We assumed that the 20-year average in each member was the average of a mixture distribution, and we estimated the uncertainty due to multiple experiments, internal variability, and resampling by adopting a mixture distribution and bootstrap resampling. The variance of the mixture distribution (T) was estimated as the sum of the variance due to the model (M), the variance due to the internal variations (V), and the variance due to data sampling (B):

$$\begin{aligned} T= & {} M + V + B \end{aligned}$$
(2)
$$\begin{aligned} M= & {} \frac{1}{N_\mathrm{m}} \sum _{m=1}^{N_\mathrm{m}} \left[ \mu _m - \mu \right] ^2 \end{aligned}$$
(3)
$$\begin{aligned} V= & {} \frac{1}{N_\mathrm{m}} \sum _{m=1}^{N_\mathrm{m}} \sigma _{\mathrm{m}}^2 \end{aligned}$$
(4)
$$\begin{aligned} B= & {} \frac{1}{N_\mathrm{i} - 1} \sum _{i=1}^{N_\mathrm{i}} \left[ \mu ^{\prime } - \frac{1}{N_\mathrm{i}} \sum _{i=1}^{N_\mathrm{i}} \mu ^{\prime } \right] ^2, \end{aligned}$$
(5)

where \(N_\mathrm{m}\) is the ensemble size (4), \(N_\mathrm{i}\) is the iteration size (10,000) of the bootstrap method, \(\mu \) is the ensemble mean of all model members and times, \(\mu _\mathrm{m}\) is the time-averaged mean of each model member, \(\mu ^\prime \), and \(\sigma _m\) is the standard deviation of each model member output.

3 Evaluation of present climate

The systematic bias of the OGCM simulations against observations was calculated to estimate errors in the simulated annual average SST and SSH. The mean SST and SSH at each location were the average values over 20 years and 13 years, respectively, for both simulations and observations (Fig. 1). The ensemble average was used for simulations. Figure 2 shows the SST and SSH biases. The mean area of sea ice in the Sea of Okhotsk was the average value over 20 years for both simulations and observations. Figure 3 shows the behavior of the model variables in the present climate, including the Kuroshio net transport, the SST trends, the seasonal evolution of the sea ice area, and sea-level variations along the coast of Japan. In future projections, we made no bias correction, because we assumed that the bias would cancel out in the comparison of the present climate to future climates.

Fig. 1
figure 1

SST climatology in the present climate (1986–2005) based on a observations (COBESST2) and b ensemble means of model results. The units are \(^{\circ }\) C. SSH (solid line) and the standard deviation of high-frequency (\(> 1 y^{-1}\)) variations (color) in the present climate (1993–2005) for c observations (CMEMS) and d ensemble means of model results. The units are in cm. The contour interval is 10 cm. A correction factor is added to SSH observations, so that an area average value is equal to that for model results

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Fig. 2
figure 2

Bias of the ocean model (model minus observation) in the present climate. a SST differences [\(^{\circ }\) C] based on observations (COBESST2) during 1986–2005. b SSH difference [cm] based on observations (CMEMS) during 1993–2005. Red and blue represent positive and negative bias, respectively

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Fig. 3
figure 3

The behavior of the model variables in the present climate. a Time-series of the Kuroshio net transport along 137\(^{\circ }\) E during 1967–2018. The units are Sv. Blue lines denote observation-based estimates based on the JMA repeat hydrographic observations. Black lines denote the simulated estimates based on the reduced-gravity model driven by the JRA-55 wind stress forcing. Thin (thick) lines denote monthly (3-year running mean) values. b SST trend (color) in ensemble means of model results during 1960–2005. Trend is given in \(^{\circ }\) C per 100 years. Contours indicate the mean SSTs during the same period. c Seasonal changes in the area of sea ice [\(10^6\) km\(^2\)] in the Sea of Okhotsk in the present climate (1986–2005). The red line and orange shading indicate monthly values for mean sea ice area and standard deviation among years and models. The black line and gray shading indicate the estimates of sea ice area based on observations (JMA analysis) and their interannual variations. d Sea-level anomalies along the coast of Japan during 1986–2005. The units are in cm. Anomalies are calculated using the monthly mean data. The 3-year running mean is applied to identify low-frequency variations. The black line denotes observations (JMA analysis). The red, green, purple, and blue lines denote GFDL-ESM2M, MRI-CGCM3, MIROC5, and IPSL-CM5A-MR, respectively. Global mean steric sea level estimated from each CMIP5 parent model is added to the model

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3.1 Kuroshio

The Kuroshio Current flows south of Japan, separates from the coast of Japan at the Boso Peninsula, and then flows eastward as the KE at \(\sim \) 35 \(^{\circ }\) N (Fig. 1c). A part of the KE returns southwestward and forms the Kuroshio recirculation. Overall, the model was able to represent the average features of the Kuroshio Current around Japan (Fig. 1d). The model realistically expressed the separation of the Kuroshio at the Boso peninsula, and the reproducibility of the average Kuroshio flow path and the position of the KE was generally good. This realistic simulation of the Kuroshio reflected the 10-km resolution of the model, which was fine enough to resolve coastal topography and mesoscale eddies. Short-term variations associated with eddy activities were also nicely simulated by the model. Note that the simulation of the Kuroshio has not been satisfactory in the conventional OGCMs (eddy-less or eddy-permitting ocean models) because of the overshoot of the Kuroshio (e.g., Liu et al 2016; Toda and Watanabe 2020).

In this study, we estimated the net transport of the Kuroshio and the latitude of the KE in the following way. We defined the Kuroshio net transport as the maximum value of the Sverdrup transport at 137\(^{\circ }\) E between 20\(^{\circ }\) Nand the south coast of Japan. We calculated the Sverdrup transport using the 1.5-layer, RG model described in Sect. 2.2. The KE latitude was defined as the latitude where the maximum of the meridional gradient of the yearly SSH zonally averaged between 145\(^{\circ }\) E and 160\(^{\circ }\) E was located.

The variations of the observed Kuroshio net transport have been satisfactorily explained by variations of the wind stress (Aoki and Kutsuwada 2008). There have been no significant trends in the observed net transport of the Kuroshio since the 1970s (JMA 2020). In the present climate, the Kuroshio net transport simulated by the RG model captured the observed features of the Kuroshio net transport (Fig. 3a). Consistent with observations, we observed no significant trend in the simulated Kuroshio net transport during the period 1967–2018.

3.2 Sea surface temperature

The observational data exhibited a pattern of zonally uniform SST, except for the region of the western boundary current, where a northward tilt of the contours was apparent (Fig. 1a). The observational data also showed a large meridional SST gradient off Sanriku at 36\(^{\circ }\)-42\(^{\circ }\) N, which is called the subarctic frontal zone (SAFZ) (e.g., Kida et al 2015; Nakano et al 2018), and in the middle of the Sea of Japan around 39\(^{\circ }\) N, which is called the polar front (e.g., Isoda et al 1991). The model not only simulated a realistic SST distribution, but because of its high horizontal resolution of 10 km, it also revealed structures associated with the western boundary current that were finer than those that observations revealed (Fig. 1b). The SAFZ off Sanriku at 36\(^{\circ }\)–42\(^{\circ }\) N and the polar front in the middle of the Sea of Japan around 39\(^{\circ }\) N were also captured by the model. Note that the SAFZ, which corresponds to the subtropical-subpolar gyre boundary, is distinctly separated from the KE jet at \(\sim \) 35\(^{\circ }\) N in the high-resolution model (Fig. 1d). This separation, however, is not clearly apparent in eddy-less or eddy-permitting models because of the overshoot of the Kuroshio (e.g., Liu et al 2016; Toda and Watanabe 2020). The mechanism of the separation, in which the eastward extension jet is located far south of the northern boundary of the subtropical gyre, has been investigated in a simple, two-layer, quasigeostrophic model (Sue and Kubokawa 2015).

The simulated SST showed negative biases by as much as \(-1\) \(^{\circ }\) C, except near the coast of Japan (Fig. 2a). This negative bias may be partly related to the southward bias of the westerly winds, which were used to set the surface boundary conditions (Nishikawa et al 2021). The southward shift of the subtropical gyre, possibly caused by the southward bias of the westerly winds, led to the southward shift of the SST contours. The relationship between the north–south migration of the westerly winds and the associated changes in the subtropical gyre will be further discussed in Sect. 5.

The observed SSTs showed positive trends in the western North Pacific (JMA 2020). The rate of increase around Japan was estimated to be + 1.14 \(^{\circ }\) C per 100 years (statistically significant with a confidence level of 99%). The observed SSTs also showed decadal variations associated with major climate modes, such as the Pacific Decadal Oscillation (PDO) (Mantua et al 1997; Zhang et al 1997) and North Pacific Gyre Mode Oscillation (NPGO) (Lorenzo et al 2008), which are predominant modes of climatic variation in the North Pacific. The simulated SSTs captured spatial structures associated with the PDO and NPGO, as previously reported in CMIP5 models (e.g., Yim et al 2015; Wang and Li 2017). The long-term positive trend of the simulated, average SST around Japan was consistent with observations (Fig. 3b).

3.3 Sea ice in the Sea of Okhotsk

The Sea of Okhotsk is a seasonal sea ice region. Formation of the sea ice generally begins around the northwestern Siberian coast in December. The area of sea ice reaches a maximum in March, and the sea ice disappears in May. The simulation results generally captured this seasonal cycle (Fig. 3c). The positive biases and relatively large standard deviations compared with the observational data were due mainly to inconsistency among the models rather than to internal variability within individual models.

There was a negative temporal trend in the observed area of sea ice in March (JMA 2020). The rate of change was \(-6.2 \times 10^3\) km\(^2\) year\(^{-1}\) during the period 1971–2019 (statistically significant with a confidence level of 99%). The simulation results reproduced the consistently negative trend in the winter sea ice area (Table 1).

Table 1 Long-term trend in the sea ice area in the Sea of Okhotsk during March
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3.4 Sea surface height

The SSH is relatively high in the western subtropical gyre and relatively low in the western subpolar gyre (Fig. 1c). The steeper gradient of SSH in the western subtropical gyre is associated with the Kuroshio and KE. Short-term variations of SSH related to eddy activities are common in the region associated with KE east of Japan. The simulated SSH generally reproduced the distribution of SSHs in the western North Pacific (Fig. 1d). The magnitude of the short-term variations in the model was comparable to that of the observations. There was a positive bias to the simulated SSHs near the coast of Japan and a negative bias on the south side of KE (Fig. 2b). The latter may be related to the southward bias of the westerly winds, which were used as the surface boundary conditions, as mentioned in Sect. 3.2.

Sea level along the coast of Japan has shown decadal-to-interdecadal variations and a positive trend since the 1980s (JMA 2020). Previous studies have indicated that the decadal variations are caused by the westward propagation of oceanic Rossby waves that are produced by the wind stress curl over the North Pacific (Yasuda and Sakurai 2006; Sasaki et al 2014, 2017). The simulated sea level along the coast of Japan reproduced the observed features, although the phase of the decadal variations did not necessarily correspond to the observations (Fig. 3d). The amplitude of the decadal variability in the model was slightly smaller than the observed amplitude.

4 Projection of future climate change

4.1 Regional climate change uncertainty in the western North Pacific

Before addressing the climate at the end of the 21st century, we examine the variances of the projections based on Wakamatsu et al (2017). As mentioned in Sect. 2.4, the total variance includes model variance, internal variance, and bootstrap variance. Figure 4 shows the spatial distribution of the variances of the SST and SSH under the RCP8.5 scenario. We can see the spatial variation of the fraction of the total variance contributed by each of the three components of the variance.

Fig. 4
figure 4

(upper) Variances of SST at the end of the 21st century (2081–2100) under the RCP8.5 scenario. a Total SST variance, b SST variance due to model uncertainty, and c SST variance due to internal variations. The unit of variance is the square of the temperature in \(^{\circ }\) C. (lower) Same as a–c, but for the variance of SSH. d Total SSH variance, e SSH variance due to model uncertainty, and f SSH variance due to internal variations. The unit of variance is the square of the SSH in cm

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The total variance of SST was relatively large in the northern Sea of Japan, around Hokkaido, east of Sanriku, and in the Yellow Sea (Fig. 4a). The largest part of the variance resulted from the variance of the model (Fig. 4b). The difference in the atmospheric forcing based on the four CMIP5 datasets (GFDL-ESM2M, MRI-CGCM3, MIROC5, and IPSL-CM5A-MR) contributed to the variance in these regions. The variance associated with internal variations was relatively large in the region east of the Korea Peninsula and east of Japan (Fig. 4c). The fact that the variance associated with data sampling was negligible (not shown) indicates that the 20 years of samples in each experiment were adequate to capture the internal variability.

The total SSH variance was relatively large in the Kuroshio and the KE regions (Fig. 4d). In contrast to the SST variance, the largest part of the SSH variance resulted from the variance associated with internal variations (Fig. 4f). The implication is that variations of the Kuroshio and the KE path contributed much of the large SSH variance. The variance of the model was apparent in the region south of Japan (Fig. 4e). This variance was related to the variations of the Kuroshio path caused by the differences of atmospheric forcing. The variance associated with data resampling was negligible for the SSH variance (not shown), as was the case with the SST variance.

4.2 Kuroshio

As mentioned in Sect. 3.1, the observed changes in the Kuroshio Current are related to changes of the wind stress over the North Pacific subtropical gyre (Aoki and Kutsuwada 2008). The simulated changes in the Kuroshio are likely to reflect the changes of the wind stress obtained from the four CMIP5 datasets under the RCP8.5 and RCP2.6 scenarios.

The average value of the Kuroshio net transport simulated by the RG model decreased by about 3 Sv at the end of the 21st century relative to the end of the 20th century (Fig. 5a) under the RCP8.5 scenario. The range of the change, however, was within the standard deviation of the present climate. Under the RCP2.6 scenario, there was no clear change in the simulated net transport of the Kuroshio. Figure 5b shows the contribution of each variance to the total variance of the Kuroshio net transport. It is apparent that the model variance was the largest of the variances and was sufficient to explain almost all of the variance for both RCP scenarios. The internal variability accounted for a small part of the total variance, and the contribution of bootstrap variance was negligible.

Fig. 5
figure 5

(upper) Kuroshio net transport [Sv] in the present climate (1986–2005) and at the end of the 21st century (2081–2100). a Kuroshio net transport. The vertical black line is the standard deviation of the estimate. b Variance of the Kuroshio net transport. The unit of variance is the square of the transport in Sv. V internal variation, M variance among models, B variance due to small sample size. (lower) Same as a–b but for the KE latitude [\(^{\circ }\)] in the present climate and at the end of the 21st century. c KE latitude. The vertical black line is the standard deviation of the estimate. d Variance of the KE latitude. The unit is the square of the latitude in degrees. V internal variation, M variance among models, B variance due to small sample size

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The latitude of the KE moved northward by about 0.2\(^{\circ }\) at the end of the 21st century relative to the end of the 20th century under the RCP8.5 scenario (Fig. 5c), but the range of the latitude change was within the standard deviation of the present climate. There was no clear change under the RCP2.6 scenario. An examination of the contribution of each component of the variance to the total variance reveals that, in contrast to the Kuroshio net transport, the variance associated with interannual variations accounts for a large part of the total variance under both RCP scenarios (Fig. 5d). The model variance was relatively small, and the contribution of bootstrap variance was negligible.

4.3 Sea surface temperature

The average simulated SSTs around Japan increased by as much as 5 \(^{\circ }\) C during the 21st century (Fig. 6). The simulated pattern was consistent with observed trends and CMIP5 model projections. The average SST increase around Japan at the end of the 21st century relative to the end of the 20th century was estimated to be 1.1 ± 0.6 \(^{\circ }\) C under the RCP2.6 scenario and by 3.6 ± 1.3 \(^{\circ }\) C under the RCP8.5 scenario. The stated uncertainties correspond to the 90 % confidence interval of the simulated change. These estimates are higher than the global average of SST changes, which was estimated to be 0.73 \(^{\circ }\) C under the RCP2.6 scenario and 2.58 \(^{\circ }\) C under the RCP8.5 scenario (Portner et al 2019).

Fig. 6
figure 6

Projected SST changes [\(^{\circ }\) C] (color) in the western North Pacific at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP2.6 (a) and the RCP8.5 (b) scenarios. Contours indicate the mean SST in the present climate (1986–2005)

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The SST increase around Japan was not spatially uniform. The increase was estimated to be large in the central Sea of Japan under the RCP2.6 scenario and offshore of Kushiro and Sanriku under the RCP8.5 scenario (Fig. 6). The pattern under the RCP2.6 scenario has been similar to the observed trends (JMA 2020).

4.4 Sea ice in the Sea of Okhotsk

The simulated annual maximum sea ice area in March decreased from the end of the 20th century to the end of the 21st century (see Figs. 3c and 7a). This result was consistent with the present trend and sea ice projections by the CMIP5 models. Our model results estimated that the rate of decrease would be 28 ± 34% under the RCP2.6 scenario and 70 ± 22% under the RCP8.5 scenario. The variance of the model projections was attributable mainly to model variance for both RCP scenarios (Fig. 7b). Under the RCP2.6 scenario, the decrease of sea ice area was relatively small, and the area of sea ice remained within the range associated with present climate variability. Under the RCP8.5 scenario, the reduction in sea ice area was significant (99% significance level) compared to the uncertainty in the projection. In addition, under the RCP8.5 scenario, the decrease in the sea ice area was significant throughout the freezing season. For example, the start of the period of freezing was predicted to shift from November to December, and the start of the period of complete melting of sea ice was predicted to shift from June to May (see Figs. 3c and 7a).

Fig. 7
figure 7

a Projected seasonal changes in the sea ice area [10\(^6\) km\(^2\)] in the Sea of Okhotsk at the end of the 21st century (2081–2100). The red (blue) line and orange (aqua) shading indicate monthly values for mean sea ice area and standard deviation among years and models under the RCP8.5 (RCP2.6) scenario. b Fractions of variance contributed by individual components in March: (red) difference among models, (green) internal variability, and (blue) uncertainty due to small sample size

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The advance of sea ice to the coast of Hokkaido was predicted to decrease as the area of sea ice formation decreased along the Siberian coast. The fraction of time when sea ice was present during March in the coastal area of Hokkaido was projected to decrease from 0.5–0.7 at the end of the 20th century to 0.2–0.5 under the RCP2.6 scenario and 0.1 under the RCP8.5 scenario at the end of the 21st century (Fig. 8).

Fig. 8
figure 8

Projected changes of concentrations of sea ice (color) in the Sea of Okhotsk in March at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP2.6 (a) and the RCP8.5 (b) scenarios. Contours indicate the projected sea ice concentration in the future climate (2081–2100)

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4.5 Sea surface height

The SSH in the offshore areas around Japan were projected to rise during the 21st century under both RCP scenarios. It should be noted that the projected SSH was obtained by adding the GMSL rise and the area-averaged elevation over the model domain to the SSH calculated by the model, as documented in Sect. 2.2. The projected rise of SSH was relatively large in the subtropical gyre, including the Kuroshio, but it was smaller in the Sea of Japan and even smaller in the subpolar region, including the Oyashio and the Sea of Okhotsk (Fig. 9). Under the RCP 8.5 scenario, the Pacific Ocean in southern Japan would rise by more than 0.8 m by the end of the 21st century; the corresponding rise in the Sea of Okhotsk would be only 0.6 m. The rate of rise of SSH may therefore vary between regions (e.g., Fig. 9). This variability is caused mainly by the thermal expansion and contraction of sea water due to changes in sea surface fluxes and changes in ocean circulation due to changes in wind fields.

Fig. 9
figure 9

Projected SSH changes [cm] (color) in the western North Pacific at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP2.6 (a) and the RCP8.5 (b) scenarios. Contours indicate the projected SSHs

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The average sea level along the coast of Japan was projected to rise during the 21st century, similar to the rise of GMSL. This result was consistent with observed trends since the 1980s and CMIP5 model predictions. An examination of the projected sea level at 16 tide stations along the coast of Japan (Fig. 10) revealed that from the end of the 20th century to the end of the 21st century, sea level was projected to increase by an average of 0.39 m (range 0.22–0.55 m) under the RCP2.6 scenario and by 0.71 m (range 0.46–0.97 m) under the RCP8.5 scenario. Under both RCP scenarios, the increase in the average sea level along the coast of Japan was thus expected to greatly exceed the amplitude of decadal variations (about 0.04 m). The estimated median values differed by less than 0.01 m from the projected GMSL rise. The fact that the estimated range of sea-level rise was larger than the range of the projected rise of GMSL reflects the large decade-scale variability in coastal sea level around Japan.

Fig. 10
figure 10

Projected areal averages of sea-level changes [m] along the coast of Japan at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP2.6 (a) and the RCP8.5 (b) scenarios. The error bar is the 5–95% confidence interval, light gray shades show the range of error of the global average, and colors show the range of error that also takes into account the error of variations along the coast of Japan

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There were no significant regional differences in sea-level rise along the coast of Japan by the end of the 21st century. Figure 10 shows the averages of the predicted sea-level rises at the grid points corresponding to the 16 tide stations divided into four areas (Region I–Region IV: see Fig. 9a). For the RCP2.6 scenario, the simulated sea-level rises in Region I, Region II, Region III, and Region IV were 0.38 m (0.22–0.55 m), 0.38 m (0.21–0.55 m), 0.39 m (0.22–0.56 m), 0.39 m (0.23–0.56 m), respectively. Under the RCP8.5 scenario, the corresponding rises were 0.70 m (0.45–0.95 m), 0.70 m (0.45–0.95 m), 0.74 m (0.47–1.00 m), 0.73 m (0.47–0.98m), respectively. The maximum difference in the rises of sea level between regions was 0.01 m, except in Regions III and IV under the RCP 8.5 scenario; in those cases, the simulated sea-level rises were larger than the average in all regions by 0.02–0.03 m. Because of the large uncertainties in the simulated results, there were no significant regional differences in the projected sea-level rise along the coast of Japan.

5 Response of the North Pacific subtropical gyre to atmospheric changes

In this section, we try to identify the causes of future changes of SST and SSH in the western North Pacific. The largest increase of SST was projected to occur east of Japan between 38\(^{\circ }\) N and 43\(^{\circ }\) N (Fig. 6), whereas the largest SSH rise was projected in the KE region and east of Japan between 32\(^{\circ }\) N and 40\(^{\circ }\) N (Fig. 9). The area with large increases of SST and SSH was not restricted to the region around Japan, but instead it extended to the east as far as \(\sim \) 160\(^{\circ }\) W (Fig. 11). This pattern suggests that basin-scale atmospheric and oceanic changes were responsible for these increases of SST and SSH. We thus looked for related changes in the atmospheric fields, especially under the RCP8.5 scenario, because the signals were clearer under the RCP8.5 than under the RCP2.6 scenario. We defined the mixed water (MW) region (140\(^{\circ }\)–160\(^{\circ }\) E, 38\(^{\circ }\)–43\(^{\circ }\) N) as the area with the most significant increase of SST, and the KE region (140\(^{\circ }\)–160\(^{\circ }\) E, 32\(^{\circ }\)–40\(^{\circ }\) N) as the area with the most significant SSH rise. We used ensemble average of the four members for the analysis.

Fig. 11
figure 11

Projected SST changes [\(^{\circ }\) C] (color) at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP2.6 scenario (a) and the RCP8.5 scenarios (b). Contours indicate the mean SST in the present climate. c, d Same as a, b, but for the projected SSH changes [cm]. The SSH changes were calculated after removal of the global mean sea-level rise and the area-averaged sea-level rise. Blue and green boxes denote the MW region (140\(^{\circ }\)–160\(^{\circ }\) E, 38\(^{\circ }\)–43\(^{\circ }\) N) and the KE region (140\(^{\circ }\)–160\(^{\circ }\) E, 32\(^{\circ }\)–40\(^{\circ }\) N), respectively

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First, simulated future changes of surface air temperature (SAT) revealed basin-wide warming over the North Pacific (Fig. 12a, b). The area with significant SAT rise that exceeded 4 \(^{\circ }\) C extended from east of Japan to the central North Pacific (40\(^{\circ }\) N, 180\(^{\circ }\) E). This area corresponded to the area with a significant increase of SST (Fig. 11a, b). A scatter diagram of average SST versus average SAT in the MW region revealed a significant positive correlation (\(r=0.98\)) (Fig. 13a). This result implies that SST was closely correlated with SAT in the MW region.

Fig. 12
figure 12

Projected atmospheric changes at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP8.5 scenario. a Surface air temperature [\(^{\circ }\) C], b same as a but shown on an enlarged map of the western North Pacific, c downward net surface heat flux [\(W/m^2\)], and d same as c but shown on an enlarged map of the western North Pacific

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Fig. 13
figure 13

Scatter diagram of future changes of a the SST [\(^{\circ }\) C] and SAT [\(^{\circ }\) C] and b the SST [\(^{\circ }\) C] and downward net surface heat flux [W/m\(^2\)] averaged in the MW region (140\(^{\circ }\)–160\(^{\circ }\) E, 38\(^{\circ }\)–43\(^{\circ }\) N) among ensemble members at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP8.5 scenario. The square, open circle, triangle, plus sign, and closed circle denote GFDL-ESM2M, MRI-CGCM3, MIROC5, IPSL-CM5A-MR, and the ensemble mean, respectively. Correlation coefficients and p values are shown for the regression lines (solid lines)

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Next, we examined downward net surface heat fluxes to determine where there was a cause-and-effect relationship between the SST and SAT in the MW region. Future changes in the downward net surface heat flux (positive when ocean gains heat) revealed basin-wide downward heat fluxes, except in the area east of Japan around 40\(^{\circ }\) N, where the dominant surface heat fluxes were upward (Fig. 12c, d). The latter area corresponded to a region where there was a significant increase of SST. There was a negative correlation (\(r=-0.70\)) between the average SSTs and the average downward net surface heat flux in the MW region (Fig. 13b). This correlation implies that the increases of SST in the MW region were caused not by local surface heat flux directly but by changes in the ocean itself. We then looked for atmospheric changes that might have been responsible for the changes in the upper ocean.

Sea-level pressure (SLP) indicated a positive anomaly at mid-latitudes of 30\(^{\circ }\)–50\(^{\circ }\) N and a negative anomaly at higher latitudes over the North Pacific (Fig. 14a). Such a dipole structure is recognized as a response to atmospheric warming (Stoacker et al 2013), because a similar pattern is found in the ensemble mean of the CMIP5 results. The high-pressure anomalies at 30\(^{\circ }\)–50\(^{\circ }\) N extended to the west, and they covered Japan south of 40\(^{\circ }\) N (Fig. 14b). The dipole structure of SLP resulted in enhanced westerlies and northward migration of the westerlies over the North Pacific. At the same time, anticyclonic circulation in the mid-latitudes of the North Pacific Ocean associated with the high-pressure anomaly caused negative wind stress curl anomalies around Japan (Fig. 14c, d). The wind stress curl zonally averaged between 140\(^{\circ }\) E and 140\(^{\circ }\) W indicated enhanced negative anomalies between 30\(^{\circ }\) N and 50\(^{\circ }\) N that corresponded to the high SLP anomalies mentioned above and to the positive anomalies in the southern part of the subtropical gyre (15\(^{\circ }\)–30\(^{\circ }\) N) (Fig. 14e). The implication is that the subtropical gyre had spun-up (spun-down) north (south) of 30 \(^{\circ }\) N.

Fig. 14
figure 14

a Projected sea-level pressure [hPa] changes at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP8.5 scenario, b same as a but shown on an enlarged map of the western North Pacific, c same as a but for wind stress [0.1 N/m\(^2\)] (vector) and wind stress curl [\(10^{7}\) N/m\(^3\)] (color), d same as c but shown on an enlarged map of the western North Pacific. (e) Zonally averaged wind stress curl [\(10^{7}\) N/m\(^3\)] between 140\(^{\circ }\) E and 140\(^{\circ }\) W for the present climate (1986–2005; black), the future climate (2081–2100; red), and the difference (blue). f Scatter diagram of future changes of the SSH averaged in the KE region (140\(^{\circ }\)–160\(^{\circ }\) E, 32\(^{\circ }\)–40\(^{\circ }\) N) and the zero wind stress curl line (ZWCL), defined as the latitude of the zero wind stress curl averaged between 140\(^{\circ }\) E and 140\(^{\circ }\) W, at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP8.5 scenario. The square, open circle, triangle, plus sign, and closed circle denote GFDL-ESM2M, MRI-CGCM3, MIROC5, IPSL-CM5A-MR, and the ensemble mean, respectively. Correlation coefficients and p values are shown for the regression line (solid line)

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The negative wind stress curl anomalies in the northern part of the subtropical gyre (30\(^{\circ }\)–40\(^{\circ }\) N) were accompanied by a depression of the main pycnocline that led to positive sea-level anomalies around Japan (Fig. 14c, d). These positive sea-level anomalies corresponded to a northward expansion of the northern part of the subtropical gyre. Figure 14f shows a scatter diagram between the SSH averaged in the KE region and the zero-wind stress curl line (ZWCL), which is defined as the latitude of zero wind stress curl averaged between 140\(^{\circ }\) E and 140\(^{\circ }\) W, and is equivalent to the latitude of the subtropical–subpolar gyre boundary. The positive correlation between the SSH and the ZWCL (\(r=0.92\)) suggests that the northward migration of the ZWCL was related to the increase of SSH in the KE region.

The linear response of the subtropical gyre to the wind stress appeared more clearly in the RG model (Fig. 15). The fact that the projected SSH changes were negative between 15\(^{\circ }\) N and 30\(^{\circ }\) N and positive north of 30\(^{\circ }\) N reflected the wind stress curl anomalies (Fig. 14e). The negative SSH anomalies along 137 \(^{\circ }\) E were related to the decrease in the Kuroshio net transport documented in Sect. 4.2. A comparison of the results of the RG model with the results of the OGCM (Fig. 11d) revealed that positive (negative) SSH anomalies were more widely distributed in the subtropical (subpolar) gyre in the latter case. This difference probably reflects the fact that, in addition to dynamic processes, the positive SSH anomalies in the subtropical gyre may also have been related to thermodynamic processes, such as the decrease in density of subtropical mode water through heat uptake in the subtropical gyre (e.g., Suzuki and Ishii 2011; Terada and Minobe 2018; Suzuki and Tatebe 2020).

Fig. 15
figure 15

Projected SSH changes [cm] (colors) derived from a 1.5-layer reduced-gravity model at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP 8.5 scenario. White contours indicate the mean SSH in the present climate. The contour interval is 20 cm

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The northward expansion of the northern part of the subtropical gyre accompanied the increase of SST in the MW region east of Japan (Fig. 11b). The area with a significant increase of SST corresponded to the area with a large north–south gradient of the SST (the SAFZ) in the present climate. In the SAFZ, the northward migration of the subtropical–subpolar gyre boundary resulted in a large increase of SST. The net sea surface heat flux was therefore upward (Fig. 12d). In other areas, warming by the surface air accounted for the increase of SST.

These results suggest that the increase of SST in the SAFZ was caused by a change in ocean circulation. To test this hypothesis, we modified the SST distribution with a northward shift of 1\(^{\circ }\), which is comparable to the change in the ensemble mean of the ZWCL (Fig. 14f), and we imposed a basin-wide warming of 2.58 \(^{\circ }\) C, which is an estimation of the global mean increase of SST under the RCP8.5 scenario (Portner et al 2019). Figure 16 shows the reproduced SST changes, the pattern of which was similar to the future projection under the RCP8.5 scenario (see Figs. 6b and 11b). This result suggests that the northward shift of the subtropical gyre was associated with the SST increase in the MW region.

Fig. 16
figure 16

a The SST changes [\(^{\circ }\) C] expected from a 1 \(^{\circ }\) northward shift of the mean SST fields in the present climate (1986–2005) along with the basin-wide warming of 2.58 \(^{\circ }\) C (color). The contour shows the mean SST in the present climate. b Same as a but shown on an enlarged map of the western North Pacific region

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It has been pointed out that the influence of ocean circulation is one of the factors that causes the rate of increase in SST near Japan to be greater than that of the global mean SST. It has generally been estimated that the rate of SST increase from the 1900s to the present has been 2–3 times the global average increase in the western boundary region, including the ocean around Japan (Wu et al 2012; Stoacker et al 2013). According to an analysis based on simple ocean data assimilation (SODA) (Giese and Ray 2011), the poleward movement of the western boundary current after the 1900s was due to the poleward shift of the wind system. It has been pointed out that this trend may have contributed to the warming in the western boundary region (Wu et al 2012; Stoacker et al 2013). Another consideration is that the relatively large rate of increase of SST in the waters near the Asian continent may have been affected by the high rate of increase of temperature over the inland areas of the continent near Japan (JMA 2015). Recent studies using a coupled atmosphere-ocean model have shown that changes of ocean circulation accompanied by advection of warm air transported to the northwestern Pacific in the lower troposphere and the northward excursion of the Kuroshio have been factors that contributed to warming of the Kuroshio since the 1980s. It has been pointed out that both factors may have contributed to the increase of SST in the KE region (Toda and Watanabe 2020). The results of this study are consistent with those previous studies.

A high-pressure anomaly over the North Pacific was found in all ensemble members (Fig. 17), but the pattern of the anomaly differed between them. The high-pressure anomaly at 30\(^{\circ }\)–50\(^{\circ }\) N was more prominent in the MIROC5 and IPSL-CM5A-MR models and less prominent in the GFDL-ESM2M and MRI-CGCM3 models. This difference suggests that the simulated response of atmospheric warming may depend on the model. It should be kept in mind that the ensemble mean of the future SLP changes (Fig. 14a, b) is strongly affected by the MIROC5 and IPSL-CM5A-MR results.

Fig. 17
figure 17

Projected sea-level pressure changes [hPa] at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP8.5 scenario for the a GFDL-ESM2M b MRI-CGCM3, c MIROC5, and d IPSL-CM5AMR

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A trend of high pressure over the North Pacific was found not only in the future climate but also in the present climate. Toda and Watanabe (2020) used observations, atmospheric reanalysis, and ensemble-mean fields of a global climate model (MIROC5.2) to show that the high-pressure trend over the North Pacific during 1981–2010 was a combination of PDO-related internal variability and externally forced components, .

It is interesting to note that the northward migration of the ZWCL did not necessarily lead to the northward shift of the KE. Figure 18a shows a scatter diagram between the KE latitude and the ZWCL. The correlation coefficient (\(r=0.57\)) between them was low and not significant (\(p=0.52\)). The fact that the slope of the regression line (0.18) was much smaller than 1.0 implies that changes in the latitude of the KE were much smaller than those of the ZWCL. In low-resolution OGCMs that cannot represent the separation between the subtropical–subpolar gyre boundary and the KE jet, a northward overshoot of the western boundary current is often seen along with a northward shift of the westerly wind. However, in eddy-resolving OGCMs that can represent the separation latitude to the south of the ZWCL, changes in the KE latitude are much reduced, regardless of changes in westerly winds, because the KE jet is located at the latitude where the wind stress curl changes, and the resultant SSH changes are relatively small (see Figs. 14e and 15).

Fig. 18
figure 18

Scatter diagrams of future changes of a the KE latitude [\(^{\circ }\)] and the ZWCL [\(^{\circ }\)], and b the SSH [cm] averaged in the KE region and coastal sea level (CSL) [cm] along the coast of Japan among ensemble members at the end of the 21st century (2081–2100) relative to the end of the 20th century (1986–2005) under the RCP8.5 scenario. The square, open circle, triangle, plus sign, and closed circle denote GFDL-ESM2M, MRI-CGCM3, MIROC5, IPSL-CM5A-MR, and the ensemble mean, respectively. Correlation coefficients and p values are shown for the regression lines (solid lines). The dashed lines indicate a slope of 1

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It is also noteworthy that the offshore sea-level rise in the western North Pacific is not directly related to the coastal sea-level rise along the coast of Japan. Figure 18b shows a scatter diagram between the rise of SSH averaged in the KE region and the coastal sea-level rise along the coast of Japan after removal of the GMSL rise. The correlation is positive (\(r=0.79\)), but the type-1 error rate is 0.45. The fact that the slope of the regression line (0.38) is smaller than 1.0 indicates that the coastal sea-level rise is smaller than the offshore sea-level rise. The implication is that the rise of coastal sea level along the coast of Japan is different from the offshore sea-level rise in the western North Pacific. Under the RCP8.5 scenario, the strengthening of both the North Pacific subtropical and subpolar gyres was apparent along with the strengthening of the westerlies. Negative SSH anomalies in the subpolar gyre propagate from the Kuril Islands to the Japanese archipelago via coastally trapped waves (CTWs) (e.g., Tsujino et al 2008; Minobe et al 2017). As a result, the rise in sea level along the coast of Japan is not closely associated with the rise in the offshore areas, and it is smaller than the rise offshore. This difference suggests that quantitative estimation of future changes in the coastal sea level will require a high-resolution ocean model capable of resolving CTWs.

6 Summary and concluding remarks

We used a high-resolution ocean model to project changes in the Kuroshio Current, SST, and SSH in the western North Pacific, and sea ice in the Sea of Okhotsk to the end of the 21st century under the RCP2.6 and RCP8.5 scenarios. An important goal of this study was to conduct high-resolution (i.e., 10-km-mesh) ensemble simulations. Using the results obtained from these high-resolution ensemble simulations, we obtained estimates of future climate changes in the western North Pacific along with information about the range of uncertainty (Fig. 4).

The projected future climate showed no significant change in the Kuroshio net transport and the latitude of the Kuroshio Extension (KE) with both RCP scenarios, in the sense that the changes were within the range of variabilities in the present climate (Fig. 5). The northern part of the subtropical gyre was enhanced and shifted northward under the RCP8.5 scenario. The projected SST showed robust increases throughout the entire western North Pacific (Fig. 6). The magnitude of the changes, however, depended on location and tended to be larger in northern regions than in southern regions. The projected sea ice area in the Sea of Okhotsk decreased under both RCP scenarios (Figs. 7, 8). The SSH in the western North Pacific showed a significant rise, especially in the subtropical gyre (Fig. 9). Much of the SSH rise was attributed to the global mean sea-level rise. In contrast, the spatial variation in sea level along the coast of Japan was small (Fig. 10). The mean sea-level rise along the coast of Japan was mostly comparable to the global mean sea-level rise.

Changes in projected ocean states were attributed to changes in basin-scale atmospheric forcing. The dipole structure of sea-level pressure (SLP), which is regarded as the atmospheric response to global warming, resulted in anticyclonic circulation anomalies at 30\(^{\circ }\)–50 \(^{\circ }\) N over the North Pacific under the RCP8.5 scenario (Fig. 14). These anomalies caused negative wind stress curl anomalies and thus positive SSH anomalies in the western part of the basin. Those anomalies led to northward migration of the North Pacific subtropical–subpolar gyre boundary (Fig. 11). In the simulation under the RCP8.5 scenario, the projected rate of increase in SST was large off Sanriku and off Kushiro (Fig. 6). These areas correspond to regions with a large north–south gradient of SST (i.e., the subarctic frontal zone) in the present climate (see Fig. 1b).

This study is one of the first efforts to project future climate changes and their uncertainties in the western North Pacific, including sea levels along the coast of Japan and sea ice in the Sea of Okhotsk, using a high-resolution ocean model. The uncertainty took account of model uncertainty, internal variability, and uncertainty due to small data size. The study revealed the fraction that each source of variability contributed to the total variance. The use of a high-resolution model enabled us not only to provide a realistic reproduction of the Kuroshio and the KE in the present climate but also to predict future climate changes in response to changes of the North Pacific subtropical gyre. We found that the northward shift of the subtropical-subpolar gyre boundary did not necessarily accompany the migration of the KE in a high-resolution model. Changes in sea level along the coast of Japan were quite different from those in the offshore areas. This difference was probably caused by the propagation of coastally trapped waves (CTWs), which was well resolved by the high-resolution ocean model. The CTWs mitigated the spatial variation of the SSH along the coast of Japan.

The rates of coastal sea-level rise depended on time and space. Those dependencies have been attributed largely to the impacts of basin-scale climate modes on coastal sea levels (Han et al 2019). One of the science issues to be answered was the extent to which sea level signals in the open ocean would affect coastal sea level where there is a continental shelf and slope. The finding of this study that CTWs affected the coastal sea level in a global warming climate may be applicable to understanding of the impact of climate modes on coastal sea-level rise.

It should be noted that future changes in coastal sea level could arise from several processes other than atmospheric and oceanic dynamics. Signals in coastal sea-level records can be caused by geophysical processes, such as the visco-elastic deformation of the Earth to land-ice melt, which is called glacial isostatic adjustment (Peltier 2004), instantaneous changes in the Earth’s gravity field due to land-ice mass changes (Mitrovica et al 2001, 2011), vertical land motion due to techtonic changes in the solid Earth (Austermann and Mitrovica 2015), and anthropogenic processes, such as subsidence from groundwater pumping (Wada et al 2012). Future changes due to these processes were beyond the scope of this study.

It is also noteworthy that the estimation of uncertainty in this study was not perfect. The ensemble size might have been insufficient. Because coupled atmosphere and ocean models include unforced internal variations, averaging over the ensemble would extract the forced response from internal variability. Large ensemble size, therefore, would effectively reduce the uncertainty. In addition, analysis of the SSH variance indicated that the fraction of the variance contributed by internal variability was relatively large in the KE region (Fig. 4f). The implication is that internal variability contributes more to the variance of SSH than external forcing in the KE region, where eddy activities would contribute to ocean dynamics. Ensemble simulations with different initial conditions as well as larger ensemble sizes are needed to more reliably quantify uncertainty for future projections of coastal sea-level rise. Carrying out such simulations will be the next step of this study.