We use the Geophysical Fluid Dynamics Laboratory global ocean–sea ice model (GFDL-OM4) as documented by , with OM4 having an eddy-permitting grid spacing of 0.25∘. This relatively fine-resolution grid is especially suitable for our study of tropical Pacific sea level (defined as the region within the 20∘ S–20∘ N zonal band inside the Pacific basin) given that it simulates boundary currents and ocean eddies better than the more commonly used 1∘ class of models. In addition, due to the larger Rossby radius of deformation in the tropical region compared to the midlatitudes, the eddies over the tropical region have a larger spatial scale which can be captured by the model relatively well. Furthermore, OM4 makes use of a hybrid geopotential–isopycnal vertical coordinate , which is particularly useful in maintaining a realistic tropical Pacific thermocline, whereas many z-coordinate models have an overly diffuse thermocline .

We force OM4 with the two atmospheric datasets used for OMIP versions I and II . The OMIP protocol is detailed in and , with the use of two forcing datasets allowing us to assess robustness of simulated features and to better attribute biases. Following , all simulations are spun up by running for five cycles of the respective forcing datasets, over which time the upper ocean reaches a quasi-equilibrium state. We then present our analysis for the sixth forcing cycle.

Total sea level changes can be derived from satellite altimetry. The Copernicus Marine Environment Monitoring Service (CMEMS) provides a gridded sea level dataset by combining multi-mission altimeter satellite data starting from 1993 (https://resources.marine.copernicus.eu/, last access: 1 July 2019). The monthly sea surface height (SSH) anomaly from the geoid is used in this study. Following the definition of dynamic sea level (DSL) according to OMIP , the area-weighted global mean is removed from the observational data and model data to make them comparable.

For steric sea level anomaly and the depth-integrated density changes, we use version 4 of the Met Office Hadley Centre “EN” series (EN4) of datasets of global quality-controlled ocean temperature and salinity profile, which provides quality-controlled subsurface ocean temperature and salinity profiles based on objective analyses (https://www.metoffice.gov.uk/hadobs/en4/, last access: 13 August 2019). The gridded temperature and salinity profiles are used to derive density changes at all available grid cells. We also calculate the density changes solely caused by the thermal expansion .

To investigate the possible bias of the wind forcing, we use the Wave and Anemometer-based Sea Surface Wind (WASwind) data . The WASwind provides a global coverage of zonal and meridional wind stress based on wind observation from the International Comprehensive Ocean-Atmosphere Dataset at the monthly frequency with 4∘ by 4∘ grid resolution from 1950–2009. Through height correction for the anemometer-measured winds, the WASwind is not subjected to the spurious upward trend due to increases of anemometer height in the ship-based measurement. The dataset also incorporates the estimated winds from wind wave height. We find this dataset to be suitable for our analysis of the tropical Pacific, and it complements the assessment from , who focused on upwelling patterns in the global ocean.

Following , we separate time tendencies in sea level, η, into mass and steric contributions (see Eq. 2 in ): 1∂η(x,y,t)∂t=1gρ0∂(pb(x,y,t)-pa(x,y,t))∂t-1ρ0∫-H(x,y)η(x,y,t)∂ρ(x,y,z,t)∂tdz.

In this equation, g is the gravitational acceleration, pa is the pressure at the ocean surface due to atmospheric mass loading (which is zero in this study when discussing DSL variation in the model), and pb is the pressure at the ocean bottom. The first term on the right-hand side measures local sea level change due to changes in mass within a seawater column. In the second right-hand-side term, ρ is the in situ seawater density, with density changes integrated over the depth of a water column (from the ocean bottom at z=-H to the surface at z=η and as normalized by the reference density ρ0=1025 kg m-3), yielding sea level changes from density (steric) effects. The minus sign on the steric term arises since decreases in density, as from ocean warming or freshening, lead to increases in sea level. As noted earlier, the global mean sea level time series is subtracted from all regional sea levels from observations and models to allow for direct comparisons of the resulting DSL.

Based on the 1993–2017 observational data of regional mean sea level from CMEMS and steric sea level from EN4, we find that the sea level change over this period is dominated by steric effects in the tropical Pacific (defined as the region within the 20∘ S–20∘ N zonal band inside the Pacific basin). The regional averaged steric signal accounts for more than 75 % of the variance in the total sea level change over the eastern Pacific (180∘–eastern boundary) and accounts for more than 85 % of the variance in the western Pacific (120∘ E–180∘) (Fig. ). Particularly, the steric signal within the upper 400 m accounts for more than 95 % of the variance in the total steric signal in both the eastern and western tropical Pacific. This result shows the central role of density changes in the upper 400 m, which mainly relates to the thermocline depth changes, in accounting for patterns of sea level variability. The residual of the sea level variance is related to the mass component (Eq. ). These results are consistent with earlier analysis from CORE simulations documented by .

Density changes in the tropical Pacific are dominated by temperature changes in the upper 400 m (Fig. ). For the upper 400 m, such changes can arise from surface heat fluxes as well as lateral and vertical ocean heat transport. The surface heat flux provides a thermodynamical forcing that directly causes a local thermosteric sea level change (sea level changes due to thermal expansion) through diabatic heating. Surface wind forcing, on the other hand, induces a dynamical effect related to Ekman transport that causes light surface waters to diverge or converge, which in turn modifies sea level. Surface wind stress curl causes Sverdrup transport associated with both Ekman transport near the surface and geostrophic transport below. The internal wave propagation, like Rossby waves and Kelvin waves, at the seasonal and interannual timescales also has a large effect on the sea level variations in the tropical Pacific. All these effects can have very different contributions to sea level at different timescales and different spatial scales. In this study, we aim to characterize mechanisms that cause sea level variations and trends, and determine reasons for simulation biases.

Over the tropical Pacific, distribution of DSL can be explained well by the surface wind stress in the mean state (Fig. a). Especially in the Northern Hemisphere, the large-scale Ekman transport toward the northwest Pacific, induced by trade winds, results in the notable DSL ridge related to the subtropical gyre. This DSL ridge creates a downgradient sea level toward the eastern basin that generates the eastward pressure gradient force that balances the Coriolis force plus the westward wind stress. To calculate the mean state bias, we calculate the time-mean DSL during the common period of 1993–2007 for JRA55-do and CORE, and subtract the CMEMS mean state from the simulations (Fig. b, c). Both simulations show a negative bias in most of the tropical Pacific basin except along the zonal band of 10∘ N.

Because the bias shows largely zonal structures, we investigate the zonal mean DSL and wind stress in the tropical Pacific. Figure a shows that the DSL in the simulation is generally lower than the observation by about 0.02 m except near 10∘ N. The meridional gradient of the zonal mean DSL, which is highly correlated with the narrow zonal currents in the tropical Pacific, is comparable with the observation in the Southern Hemisphere. The Northern Hemisphere, on the other hand, shows underestimated DSL gradient in two zonal bands, 9–20∘ N and 4–9∘ N due to the lack of DSL trough around 9∘ N and DSL ridge at 4∘ N. Between 9–20∘ N, the downgradient DSL toward the Equator is associated with the strength of North Equatorial Current (NEC). Between 4–9∘ N, the upgradient DSL toward the Equator is associated with the strength of North Equatorial Countercurrent (NECC). Therefore, the smaller or missing DSL gradient in both simulations could lead to underestimated NEC and NECC.

For the mean state of surface wind forcing, we compare the wind stress curl and the associated circulation strength (defined as the maximum value of the Sverdrup stream function along each latitude) between the forcing dataset and the observation from WASwind. The Sverdrup stream function is defined as 2Ψ=-∫EBx∇×τβρ0dx, where EB indicates the eastern boundaries of the tropical Pacific at each latitude, τ is the wind stress vector, β=df/dy is the meridional derivative of the Coriolis parameter, f, and ρ0=1025 kg m-3 is the reference density. Figure b–d show the zonal mean of zonal wind stress (τx), wind stress curl (∇×τ) bias, and circulation strength bias, respectively. The wind stress curl bias is dominated by the zonal wind shear bias (Fig. c). Although the zonal wind stress is generally similar between observations and simulations (Fig. b), the wind stress curl bias is sensitive to even small differences. The wind stress curl bias shows a large positive bias at around 4∘ N and a negative bias at around 9∘ N (Fig. c). The JRA55-do and CORE do not exactly capture some subtle features in the observation, such as the sharp zonal wind shear across the Intertropical Convergence Zone (ITCZ) and the comparatively uniform zonal wind stress in 0–5∘ N latitudes. This difference creates a negative bias in Sverdrup stream function (counterclockwise circulation bias) at 4∘ N and positive bias (clockwise circulation bias) at 9∘ N (Fig. d). Since the geostrophic flow components dominate the Sverdrup stream function, the counterclockwise circulation bias represents a negative DSL bias at the circulation center, and the clockwise circulation bias represents a positive DSL bias at the circulation center. These opposite DSL biases induced by the wind stress flatten the DSL ridge and trough in this region, thus decreasing the sea level gradient in both zonal bands. This analysis highlights the importance of an accurate representation of the zonal wind stress shear for simulating the DSL trough and the associated zonal currents in the 4–9∘ N band of the tropical Pacific.

To analyze the impact of zonal currents on heat, we consider two boxes within the tropical Pacific and assess the mean heat advection and volume transport from individual currents. For this purpose, we define a western box (Wbox, with boundaries 120∘ E–180∘; 20∘ S–20∘ N; 0–400 m) and an eastern box (Ebox, with boundaries 180∘–eastern boundary; 20∘ S–20∘ N; 0–400 m), as shown in Fig. , and express the heat budget as 3∭V∂Q∂tdV=Fsrf-ρ0Cp∬S(u⋅n^)(T-Tm)dS+<residual>. In this equation, ∭V∂Q∂tdV is the heat content changes in a box, which is related to the thermosteric sea level changes, and Fsrf is the area integrated net surface heat flux. Tm represents the volume mean temperature inside a box. For Wbox, Tm=Tmw and for Ebox, Tm=Tme. We calculate the heat advective transport term following the analysis of and . The residual term accounts for transport from small-scale processes including vertical mixing, subgrid-scale processes; these processes are not of concern here and are small compared to the role of currents.

The heat advection across the 180∘ transect dominates the heat content changes (thermosteric sea level changes, Fig. ) in the Wbox (Fig. ), whereas a compensation between surface heat flux and heat advection across the 180∘ transect is important in the Ebox. For the Ebox, the compensation between 180∘ heat advection and surface heat flux shows the eastern tropical Pacific as an important region for heat to enter the ocean and then to participate in the global energy cycle, which is consistent with the finding of diabatic heating at the surface controlling the heat movement over the ocean . Despite the large net surface heat flux in the Ebox, the heat is not stored in the eastern tropical Pacific but flushed to the western tropical Pacific. We find that, with larger net heat flux over the Ebox, the heat advection across the 180∘ transect is also larger in CORE than JRA55-do (see the detailed comparison in the next paragraph). For the Wbox, the main heat loss occurs at the 120∘ E transect, which advects the heat out with the magnitude a little less than half of the heat coming from the eastern tropical Pacific. Heat loss also occurs across the other three boundaries of the Wbox but is considerably smaller than across the 120∘ E transect. Besides some small differences in surface heat flux and the heat advection at the 180∘ transect, we do not see significant differences in the mean state heat budget between the simulations forced by CORE and JRA55-do.

Due to the importance of zonal heat transport between the two boxes, we look into the dominant currents and their relative contributions to the 180∘ transect (Fig. b, c). We define the current based on the time mean of the zonal velocity (Fig. d). The South Equatorial Current (SEC) is defined by the westward mean zonal velocity within 20∘ S to 5∘ N zonal band and above 400 m. Both CORE- and JRA55-do-forced simulations show that the SEC makes the largest contribution to the heat content changes in Wbox and Ebox with similar magnitude. The NEC, which is defined by the westward mean zonal velocity within 5–20∘ N zonal band and above 400 m, shows the second-largest contribution. The heat advection of NEC in CORE is around 50 % larger than JRA55-do. This difference in heat advection is a result of the larger mean zonal current speed in the CORE-forced simulation (Fig. c). Interestingly, we also see a higher energy input in the northern part of Ebox (Fig. ) in CORE, which reiterates the concept that the energy input in the Ebox is always flushed toward the Wbox in the simulations. The Equatorial Undercurrent (EUC), which is defined by the eastward mean zonal velocity within 2.5∘ S–2.5∘ N zonal band, largely compensates for the westward heat advection by the SEC and the NEC in both JRA55-do and CORE forcing. Both the NECC, defined by the eastward mean zonal velocity within the 2.5 to 10∘ N zonal band, and South Equatorial Countercurrent (SECC), defined by the eastward mean zonal velocity within the 2.5 to 10∘ S zonal band, show little contribution to heat content change for both boxes.

To check for current biases, we compare the speed and volume transport of each current system in JRA55-do and CORE with the available observational data (Table ). The EUC is well represented, with a simulated maximum value of 1.2 m s-1 at approximately 100 m depth at 138∘ W in JRA55-do and 1.2 m s-1 at approximately 100 m depth at 129∘ W in CORE along the Equator, which compares to an observed value of 1.1 m s-1 at approximately 86 m at 130∘ W from . The meridional extension of the EUC is also well simulated compared to the observed current confined between 2∘ S and 2∘ N at 180∘ in JRA55-do and 2∘ S and 3∘ N in CORE which skews more toward the Northern Hemisphere . The SEC at 180∘ shows good agreement in strength with the observed maximum value of 0.2 m s-1 for both JRA55-do and CORE . Due to the underestimated DSL gradient in the Northern Hemisphere and the missing DSL trough, weaker NEC and NECC in JRA55-do and CORE are expected. The observed NECC strength is 0.4 m s-1, while the simulations show a much weaker value of 0.1 m s-1. The weak NECC bias exists in the JRA55-do-forced simulation as well as the CORE-forced simulation, with attributing the CORE simulation biases to an inaccurate wind stress representation. Unfortunately, the improved surface wind forcing from JRA55-do did not resolve the underestimation of the NECC. The NEC is also underestimated due to the flattening of the DSL trough for both simulations. Namely, the NEC transport in the JRA55-do-forced simulation is 23 and 29 Sv in CORE, whereas the Argo-derived value is near 40 Sv .

When we compare NECC and NEC in both model simulations, the heat advection between Wbox and Ebox from the NEC is significantly larger than that from the NECC. Therefore, the Northern Hemisphere heat content changes in Ebox and Wbox are dominated by the NEC. Heat content changes are related to thermosteric sea level changes, so that a stronger NEC heat advection can explain the stronger east–west gradient in the DSL trend found in the Northern Hemisphere in CORE relative to JRA55-do (Fig. b, c). However, the weak NEC bias and difference between CORE and JRA55-do cannot explain the consistent underestimation of the DSL trend along the 10∘ N–20∘ N zonal band in both the CORE- and JRA55-do-forced simulations (Fig. a, b).

To help reveal mechanisms for the underestimation of the DSL trend, we investigate the wind stress forcing in CORE and JRA55-do and compare it with the WASwind observational product. We calculate the wind stress trend bias by subtracting the WASwind wind stress trend from CORE and JRA55-do. During 1993–2007, there is no statistically significant trend bias in wind stress that can help explain the DSL trend bias. For the trend significance test, the null hypothesis in the statistical test is zero long-term trend with an effective degree of freedom considering the autocorrelation of the time series. The large variability of wind stress and the small number of samples during this period result in an inconclusive statistical test. However, with the increased number of samples during a longer period (1958–2007), a statistically significant zonal wind bias in JRA55-do and CORE can be found (Fig. ).

The most obvious bias is the excessive westerly wind trend in CORE and JRA55-do than WASwind located at the central and eastern Pacific, with the trend bias particularly large in CORE (Fig. c). A westerly trend in CORE extending from 10∘ S to 15∘ N can also be seen in the zonal average over the tropical Pacific (Fig. ). The westerly trend is significantly reduced in the JRA55-do. On top of the westerly trend bias, there is an easterly trend bias in the 15–25∘ N zonal band for both JRA55-do and CORE (Fig. b, c). JRA55-do has an easterly trend bias only west of 150∘ W, while CORE extends across the entire Pacific basin. The existence of both the westerly and easterly trend biases in CORE generates a strong positive wind stress curl trend in the 8–20∘ N zonal band (Fig. b). The JRA55-do simulation also has a positive wind stress curl trend bias in the same zonal band but is roughly 3 times smaller than the CORE simulation (Fig. ). The smaller wind stress curl trend bias with JRA55-do is mainly due to the missing westerly trend bias in the 10∘ S to 10∘ N region.

The westerly trend bias in CORE forcing data is a result of the multiplicative factor (Rs) applied to the vector winds in the reanalysis data by . The multiplicative factor is determined by the 5-year mean (2000–2004) ratio between reanalysis data and observational data. Since the factor is designed to make the mean state of wind amplitude in reanalysis data better fit the observation, applying the same factor to the entire time series could result in biases across different timescales. In this case, the factor designed to correct the mean state causes an overestimation of the trend in the westerly wind in the eastern tropical Pacific where the factor has the highest value in the tropical Pacific (see Fig. 2a in ). The modified multiplicative factor that is actually used as an offsetting factor to correct JRA-55 wind in has a better adjustment without introducing the westerly trend bias. On the other hand, the easterly bias in the 15–25∘ N zonal band exists in both the JRA55-do and CORE forcing data.

We conclude from this analysis that the positive wind stress curl trend bias west of 150∘ W, found in both CORE and JRA55-do, is mainly due to the easterly wind stress trend bias. Additionally, the positive wind stress curl trend bias east of 150∘ W in the CORE forcing is due to the combined effect of easterly and westerly trend biases. The positive wind stress curl trend bias in the zonal band creates an artificial Ekman suction that causes the DSL trend in the simulations to be biased low.

We now examine how the barotropic geostrophic response affects the DSL trend. From the trend bias in the Sverdrup stream function, we can see how the geostrophic flow trend bias can cause the DSL trend bias. The Sverdrup stream function (Ψ) is calculated following Eq. (). The CORE simulation shows a negative stream function trend bias in the 10–20∘ N zonal band, whereas the JRA55-do trend bias is relatively small (Fig. a, b). The negative trend bias which corresponds to a trend of counterclockwise geostrophic current is related to the negative DSL trend bias across the Pacific basin.

To further investigate the dominant causes, we perform the same Sverdrup stream function calculation starting from the eastern boundary. However, in this calculation, we stop at 150∘ W, where the largest westerly wind trend bias is located, and keep the remaining basin as zeros until we reach the western boundary (Fig. c, d). This calculation helps to identify the contribution from the westerly trend bias in the eastern tropical Pacific. In particular, it reveals the importance of the westerly trend bias in the eastern tropical Pacific in driving the large-scale counterclockwise circulation trend bias, while the easterly wind bias along the 10–20∘ N latitude band west of 150∘ W strengthens the circulation trend bias in the CORE simulation. The Southern Hemisphere also shows the same negative DSL trend bias that can be explained by the same Ekman suction and the large-scale Sverdrup balance during 1958–2007. This analysis shows the significant effect of zonal wind stress trend biases near the Equator on the off-equatorial DSL trend biases from geostrophic balance and Ekman suction.

The large interannual to decadal variability in DSL can affect the trend and trend bias estimates over a shorter period . Based on the improved forcing from JRA55-do, we calculate the DSL trend during 1993–2017 and compared with the available observational data. Despite the reduced trend bias compared to 1993–2007, Fig.  still shows the trend bias in the 10–20∘ N zonal band, which also shows the existence of the DSL trend bias is not due solely to interannual variability over a short time period.

The above analyses mainly focus on the tropical Pacific. To give a quantitative comparison, we also analyze the zonal mean bias across three major basins to demonstrate the significance of tropical Pacific sea level bias (Fig. ). Pacific trend bias over the tropics in CORE is the largest across all three major basins. JRA55-do significantly reduces the bias over the tropical Pacific but has a negative bias in the extratropical region and other basins in both the Northern Hemisphere and Southern Hemisphere.

The seasonal variation of DSL in the 2 to 10∘ N zonal band is a result of the Rossby wave propagation that is generated in the eastern and central tropical Pacific by the local wind stress curl . Figure  shows the spatial pattern of the wind stress curl anomaly and the DSL anomaly in the eastern tropical Pacific between 2 and 10∘ N.

The Hovmöller diagram of the meridional mean from 2 to 10∘ N shows the propagation of this seasonal DSL signal and its relation with the Ekman pumping derived from wind stress curl (Fig. ). The DSL signal propagation speed matches the theoretical value of the first baroclinic Rossby wave of approximately 0.3 m s-1 . The calculation is based on Fig.  from 110∘ W to 150∘ E from January to December, which also matches with . A dipole structure appears across the zonal band when the previously generated signal reaches the central Pacific, while a newly generated opposite signal starts in the eastern tropical Pacific. The zonal dipole DSL does not reverse the absolute DSL gradient since the DSL difference between the east and west is 0.6 m in the mean state, while the Rossby wave created a east–west dipole that has an amplitude of only 0.1 m.

The CORE simulation also shows a larger seasonal DSL bias than JRA55-do. The larger bias in CORE is mainly due to the wrong timing of the wind stress curl in the eastern tropical Pacific. Generally, the seasonal amplitude of DSL forced by CORE is closer to the observed amplitude than JRA55-do. However, the timing of the DSL signal is delayed by 3 months, especially in the initiation region of 90∘ W (Fig. ). The positive DSL anomaly only starts in May for CORE, while JRA55-do and observations show a positive anomaly as early as February along 90∘ W. The DSL lag results in a much longer and larger negative DSL anomaly signal around 100∘ W in the CORE simulation.

The missed timing in CORE is related to the weaker Ekman pumping/suction east of 90∘ W throughout the year, thus causing significant DSL biases compared to observations. The timing of the JRA55-do simulation is relatively close to observations but with underestimated amplitudes in both Ekman pumping and DSL. This analysis shows the importance of resolving dynamics near the ocean boundary as they can strongly affect the basin-scale DSL variation on seasonal timescales.

Outside the initiation region, both forcing data show weaker Ekman suction during JJA and weaker Ekman pumping during DJF between 150∘ W and 180∘ when compared to observations (Fig. b, d). The weaker forcing does not affect the propagation of the DSL signal, but it causes the DSL signal in both simulations to be biased low west of 150∘ W due to the lack of continuous external forcing.

The vertical Ekman-induced velocity in the Ekman layer is given by 4WE=k⋅∇×τρ0f=1ρ0f∂τy∂x-∂τx∂y+τxfβ. In the tropics, a vertical velocity in the Ekman layer can be generated with zero wind stress curl but strong zonal wind due to the large β effect. Therefore, the weaker Ekman suction during JJA and weaker pumping during DJF could be related to the underestimated wind stress curl or zonal wind stress between 150∘ W and 180∘. The wind stress curl does not show bias as Ekman pumping/suction bias (Fig. f, h). The zonal wind stress, on the other hand, shows the negative bias (easterly bias) during JJA and positive bias (westerly) during DJF between 150∘ W and 180∘ in both JRA55-do and CORE, which is similar to the bias in Ekman pumping/suction (Fig. b, d). This result indicates that the westerly (during JJA) and easterly (during DJF) winds between 150∘ W and 180∘ are not strong enough in both JRA55-do and CORE, which leads to the underestimated Ekman suction and pumping, respectively.

The other interesting fact is the compensating effect between zonal wind stress and wind stress curl on the Ekman mechanism in this zonal band. In other words, the first two terms on the right-hand side of Eq. () which represent the wind-stress-curl-induced Ekman effect compensate for the last term which represents the zonal-wind-stress-induced Ekman effect. Figure  quantitatively visualizes this compensating effect perfectly, which shows the zonal-wind-related Ekman contribution and wind-stress-curl-related Ekman contribution. During JJA, the westerly wind dominates the zonal band due to cross-equatorial flow from the Southern Hemisphere, converging toward the ITCZ located in the Northern Hemisphere (Fig. a). The cross-equatorial flow, at the same time, provides a negative wind stress curl with Ekman pumping that compensates the effect of westerly wind on generating the Ekman suction (Fig. a, e). During DJF, the easterly component is generated due to the dominant northeasterly wind converging toward the ITCZ with little zonal wind south of the ITCZ (Fig. b). The difference in zonal wind near the ITCZ creates a positive wind stress curl with Ekman suction that also compensates the effect of the easterly wind on generating the Ekman pumping. Due to the compensating effect, the bias of zonal wind at around 120∘ W in the CORE simulation is compensated by the bias in wind stress curl (Fig. d, h). In other words, the Ekman mechanism at 120∘ W in the CORE simulation, though close to the observations like JRA55-do, is right for the wrong reason. Particularly in the tropical Pacific, this compensation effect should be further examined in the future when evaluating simulations to better understand the underlying biases.

We now examine the thermodynamical contribution from the surface heat flux to the seasonal DSL variation in JRA55-do. The latent heat flux and solar radiation control the net surface heat flux at the seasonal timescale (Fig. a–c). At the seasonal timescale, sea surface temperature (SST) is determined by the surface net heat flux with a roughly 3-month time lag (Fig. a, d). The mixed layer depth follows the SST which deepens during low SST because of the reduced stratification near the ocean surface and shoals during high SST because of the enhanced stratification (Fig. d, e). This mixed layer pattern can not be used to explain the spatiotemporal pattern seen in DSL seasonal variation (Fig. ). Instead, we find that the 20 ∘C isotherm shows the same wave propagation as the DSL, thus indicating the baroclinic nature of this seasonal Rossby wave propagation and the dominant role of ocean dynamics on the DSL variation. The seasonal analysis over the tropical Pacific shows the important role of ocean dynamics on the DSL variation which is quite different from the midlatitudes where the thermodynamic forcing dominates the changes of seasonal DSL .

Due to the significant seasonal fluctuations in DSL within the tropical Pacific, we use the same box budget as in Fig.  to study the corresponding zonal current variations between Wbox and Ebox. The zonal current anomaly is strongly affected by the meridional DSL gradient. In the 2 to 10∘ N zonal band, we find one of the largest DSL variances. The corresponding meridional DSL gradient changes, in response to the Rossby wave propagation, can have a large impact on the seasonal changes of the NECC. Figure a, b show the seasonal amplitude and phase defined by the largest values of the monthly climatology and the corresponding month, respectively. The SEC and the EUC show comparable and dominating roles on seasonal heat advection between Ebox and Wbox. The seasonal amplitude of heat advection in the CORE simulation is larger than with JRA55-do for all currents, which is consistent with larger wind stress forcing and DSL amplitude in CORE.

All seasonal phases agreed between the two simulations except for the NECC and SEC. The SEC difference between the two simulations is mainly due to the small difference in the subseasonal signal that causes the difference in phase (Fig. c). For the NECC, the difference in phase can also be seen in the volume transport, which peaks in June for CORE and November for JRA55-do (Fig. b, c). The simulation forced by JRA55-do shows a better agreement with the observed NECC, which peaks in December . Due to the better simulation of the Rossby wave propagation which affects the DSL seasonal variation in the narrow zonal bend in JRA55-do, the seasonal variation of meridional DSL gradient is also better represented in the simulation which affects the timing of the NECC. At 180∘, the positive anomaly of meridional DSL gradient in CORE during the second half of the year creates an anomalous counterforce which counteracts the negative meridional DSL gradient that supports NECC strength (Fig. ). This effect can also be seen in Fig. c, where NECC in the CORE-forced simulation decreases in the second half of the year that deviates from the more accurate NECC simulation forced by JRA55-do.

The zonal current analysis confirms the importance of an accurate simulation of the DSL at the seasonal timescale. This analysis also demonstrates the crucial role of the surface wind stress timing near the eastern tropical Pacific, which influences the timing of heat advection and volume transport across the tropical Pacific. The NECC and SECC, though smaller than SEC and EUC in volume transport, are the only two currents that show a change of direction in the simulation at seasonal timescales (Fig. c). This current reversal, however, does not exist in the observations. In the simulations, the current reversals result from the underestimated mean state of the currents that leads to the incorrect seasonal heat and mass transport direction. However, due to the small contribution in volume and heat budgets from these two currents, the model simulation is not greatly affected by this reversal at the seasonal timescale.

We first focus on the zonal mean of the DSL variation in the tropical Pacific region during El Niño. A clear recharge–discharge oscillator affecting DSL can be seen evolving during El Niño (Fig. a, c, e) . According to the oscillator theory, the warm water volume continues to be charged into the equatorial region before it reaches the peak of an El Niño. It then discharges to higher latitude after the peak as a result of the Sverdrup transport response to wind forcing over the tropical Pacific. The SST lags the DSL positive anomaly before the peak and the negative anomaly after the peak of El Niño. This lag means that the subsurface processes build up the warm water volume before the SST starts to warm up during the charging stage. During the discharging stage, the subsurface processes release the warm water volume before the SST starts to cool down.

Consistent with the theory, DSL reaches the peak at the end of Year1 for both simulations during the charging stage, which increase the warm water volume near the Equator, and quickly changes to a negative anomaly, while the higher latitude changes from a negative to positive anomaly, which indicates the start of the discharging stage (Fig. a, c). The lag of the SST is also clear in both simulations. The CORE simulation shows a larger DSL bias which is consistent with the bias shown at other timescales (Fig. b, d). The recharge–discharge pattern can also be seen during the longer period composite (1958–2007) (Fig. e).

We separate the El Niño period into four different stages (Fig. ). The first is the initiation stage calculated as the mean of 7 months to 12 months prior to the maximum ONI (February, Year1 to July, Year1). In this stage, we see the positive DSL anomaly initiated in the central tropical Pacific along the Equator. The second stage is the mean of 6 months prior to the maximum ONI value (August, Year1 to January, Year2). The positive DSL anomaly propagates eastward due to the propagation of an equatorial downwelling Kelvin wave, while the negative DSL anomaly strengthens in the western tropical Pacific in both hemispheres . Based on the ENSO oscillator theories, the negative DSL anomaly in the western tropical Pacific is a result of two phenomena. One is the upwelling Rossby wave propagating westward on two sides of the Equator reaching the western boundary based on the delayed oscillator theory . The other is related to the shoaling of the off-Equator thermocline based on the western tropical Pacific oscillator theory . The latter also leads to the increase of sea level pressure due to decreasing SST and the associated easterly wind at the Equator in the third stage.

The third stage is the mean of 6 months following the maximum ONI value (January, Year2 to June, Year2). The positive anomaly in the eastern Pacific starts to dissipate through a coastal Kelvin wave moving heat toward the poles . The reflected downwelling Rossby wave on two sides of the Equator, on the other hand, tries to move the heat back to the warm pool in the western Pacific . Like in stage 2, the DSL drop in stage 3 over the western tropical Pacific is also a result of two phenomena. Based on the delay oscillator theory, the reflected upwelling Rossby-wave-related DSL drop in the western tropical Pacific starts showing at the Equator. On the other hand, the western tropical Pacific oscillator theory emphasizes the importance of equatorial easterly winds, due to the positive sea level pressure off-Equator, on generating the negative DSL anomaly at the Equator. This stage is also referring to the discharging stage in the recharge–discharge oscillator theory where the warm water volume is discharged poleward from the Equator. The final stage is calculated as the mean of 7 months to 12 months following the maximum ONI value (July, Year2 to December, Year2). In the final stage, the downwelling Rossby wave on two sides of the Equator shows in the western tropical Pacific for both simulations.

In general, the model simulations show great resemblance in terms of spatial patterns and temporal changes. Both simulations demonstrate the oscillator theories well. However, asymmetry in the DSL changes on two sides of the Equator seem missing from the theories mentioned above during El Niño. The asymmetric pattern, like the negative DSL signal in the southwestern tropical Pacific, is related to other mechanisms dominating the DSL signal over certain regions, which reduces the symmetry along the Equator .

The negative DSL anomaly and the asymmetry of DSL in the southwestern tropical Pacific are not due to the lack of discharging of warm water from the Equator but instead due to the drop in DSL signal that is intensified after the peak ONI (stage 3) (Fig. e, f). This dropping DSL signal can also be found in the composite based on observations during 1993–2007 (Fig. ). We see that the Southern Hemisphere DSL drop is strongly related to the pressure difference between Australia and the Southern Hemisphere central to eastern tropical Pacific (Fig. ). This pressure difference, known as the Southern Oscillation Index (SOI), causes a negative wind stress curl in the region of DSL drop in stage 2 (Fig. c, d) and stage 3 (Fig. e, f), which results in Ekman suction and the associated negative DSL anomaly.

The negative DSL anomaly in the southwest tropical Pacific started before the ONI peak (stage 2) and reached maximum right after the peak (stage 3) (Fig. ). In stage 2, a high-pressure center is established near Australia, while a low-pressure center is formed near the southeast tropical Pacific (Fig. c,d). Between the two pressure systems, a strong geostrophic wind toward the Equator is formed and turns to the right near the Equator due to the low pressure at the eastern equatorial Pacific. This turning creates a negative wind stress curl in the southwestern tropical Pacific that causes Ekman suction and the associated negative DSL anomaly.

After the ONI peak, a low-pressure center is established in the south-central tropical Pacific (Fig. e, f). This low-pressure center, closer to the southwest tropical Pacific than in stage 2, causes a stronger negative wind stress curl than in stage 2 due to the increased pressure gradient that results in stronger Ekman suction and DSL drop. Eventually, the dropping DSL signal subsides due to decreased and reversed pressure contrast related to the Southern Oscillation (Fig. g, h). Since the composite based on observations only includes four El Niño events, the different sea level pressure amplitudes could be readily dominated by the strongest events. Therefore, the amplitude changes between longer (1958–2007) and shorter periods (1993–2007) should not be seen as a long-term trend but instead a sign of possible decadal variability of the ENSO/SOI strength.

The mechanism of the asymmetric sea level along Equator is missing in the known oscillator theories. The delayed oscillator theory can explain the DSL drop in the western tropical Pacific resulting from a westward propagation of upwelling Rossby wave in stage 2. The western tropical Pacific oscillator, on the other hand, emphasizes the importance of dropping SST in the western tropical Pacific due to the shoaling of the thermocline (dropping DSL) as a result of cyclonic wind generated from off-equatorial convection in stage 2. . Both theories cannot explain the maximum value of DSL drop in stage 3 in the Southern Hemisphere and the asymmetric response of DSL and sea level pressure between the north and south.

To better quantify the role of the wind stress curl on the DSL variation in the tropical Pacific during the composite period, we regress the wind stress curl with the DSL anomaly at each grid point (Fig. ). Figure b, d show the strong positive correlation (R>0.6) between DSL and wind stress curl in the region where the negative DSL anomaly is located (Fig. ) in both JRA55-do and CORE simulations. The regression shows a regression coefficient of around 1.2×10-8 N m-3 per 10 mm DSL change. Compared to the Southern Hemisphere, the maximum DSL drop in the Northern Hemisphere happens in stage 2. This drop is quickly restored toward the mean state in stage 3 (Fig. ) due to an increase of negative wind stress curl created by the high sea level pressure (Fig. ), which is a process described by the western tropical Pacific oscillator theory . This behavior is also shown in the regression maps where the wind stress curl is negatively correlated with the DSL anomaly in the region from 150∘ E to 180∘ and Equator to 20∘ N.

This analysis demonstrates the importance of sea level pressure evolution in the tropical Pacific on the DSL changes during El Niño. In stage 2, the combination of ocean wave propagation (delayed oscillator) and wind stress curl creates the maximum DSL drop in the northwest tropical Pacific. In stage 3, the air–sea interaction (western tropical Pacific oscillator) quickly restores the northwest tropical Pacific DSL to the mean state through the established high sea level pressure, while the negative wind stress curl established by the sea level pressure gradient in the Southern Hemisphere creates the maximum DSL drop in the southwest tropical Pacific. The different mechanisms between north and south indicate the lag in DSL signal is due to different forcings. It is not an energy redistribution or wave propagation between the northwestern and southwestern tropical Pacific. This asymmetry in the DSL dropping signal between the north and south of the western tropical Pacific can usually be seen during El Niño.

The mean state bias of DSL persists in the simulations forced by JRA55-do when compared to CORE. The missing DSL trough along 9∘ N in both CORE- and JRA55-do-forced simulations shows the importance of sharp zonal wind stress changes near the ITCZ. In the 4∘ N to 9∘ N latitude band, the bias in the wind stress forcing causes flattening of the DSL gradient in the meridional direction that leads to biases in the geostrophic current. The bias in the geostrophic current directly impacts the mean strength of NECC and NEC. A future improvement of the zonal wind shear in the tropical Pacific is needed for a better DSL and zonal current representation in ocean model simulations.

The JRA55-do-forced simulation significantly improves the DSL trend bias over the tropical Pacific. The improved zonal wind stress trend in JRA55-do over the eastern equatorial Pacific is the main reason for the better DSL trend simulations. The trend analysis shows extra attention is needed for the method used for correcting the magnitude of the wind stresses found in reanalysis data. A single multiplicative factor applied to the entire time series of wind stress may not be appropriate since it can cause errors in variability and changes in other timescales. A DSL trend bias along 10∘ N, though improved, still exists in the JRA55-do-forced simulation. We identify an easterly wind trend bias, related to this persisting DSL trend bias in both CORE and JRA55-do, as a point of focus for improvements in the atmospheric forcing.

The JRA55-do-forced simulation also shows improved seasonal DSL variation due to a better representation of the wind stress curl forcing in the eastern tropical Pacific. The improved timing of wind stress curl in JRA55-do results in a more accurate Rossby wave propagation in the 0–10∘ N zonal band, thus leading to an improved NECC simulation. In this zonal band, both zonal wind stress and wind stress curl contribute to the Ekman pumping/suction with compensating effects at the seasonal timescale. Though the final effect of Ekman pumping/suction in CORE is similar to that in JRA55-do, the CORE forcing data have a relatively inaccurate representation of the zonal wind and wind stress curl. The reason for the similar Ekman pumping/suction is mainly due to the compensation effect in CORE between the bias in the zonal wind and the bias in wind stress curl. Detailed tropical ocean analysis is needed on the effect of Ekman pumping/suction in future model evaluation to avoid ignoring this bias compensation.

Both CORE and JRA55-do generate reasonable DSL variations during El Niño compared to observations, with smaller biases in the JRA55-do simulation. An asymmetry in the DSL change during an El Niño event on two sides of the Equator has not been explained in the existing oscillator theories. We find the asymmetry in the DSL pattern is strongly related to wind stress curl that follows the sea level pressure evolution during El Niño. An atmospheric sea level pressure gradient created by a pressure drop in the southeastern tropical Pacific and a pressure rise in Australia as well as the sea level pressure drop in the cold tongue region are the main contributors to the negative wind stress curl that drives the DSL drop. The high correlation between wind stress curl and DSL shows the dominant influence of local wind forcing on the DSL signal. The analysis demonstrates the importance of the external forcing on the off-Equator DSL changes during an El Niño event.

To reduce the time-mean bias of DSL in future OMIP simulations over the tropical Pacific, accurate zonal wind stress shear near the ITCZ is crucial. Especially over the 4 to 9∘ N zonal band, the biases in the time mean of the DSL can further affect the mean ocean current strength and cause an artificial seasonal ocean current reversal.

For the bias in the long-term trend of DSL, the JRA55-do has significantly improved the westerly wind bias at the eastern Pacific near the equatorial region (10∘ S to 10∘ N) that results in the reduction of DSL bias along 10∘ N. To further reduce this DSL bias along 10∘ N, we find easterly trend biases exist along 20∘ N in both the JRA55-do and CORE forcings that create the artificial positive wind stress curl along 10∘ N, resulting in the negative sea level bias. The multiplicative factor applied to correct the wind stress is highly related to the wind stress bias. A careful evaluation of the wind stress field across different timescales after applying the factor is necessary to reduce the bias of the simulated DSL.

For the seasonal variation of the DSL, the dominant external forcing is region specific. Over the deep tropics, from the Equator to around 10∘ N/S, ocean dynamics are the dominating factor which was mainly initiated at the eastern boundary near 90∘ W due to Ekman suction/pumping induced by local wind stress curl. Therefore, capturing the timing and strength of the local wind stress curl is crucial to better simulate the seasonal variation of the DSL. The accurate DSL variation can further improve the simulated ocean current in seasonal timescale, like the improved NECC in the JRA55-do compared to the CORE-forced simulation. However, the continuously underestimated DSL amplitude in the JRA55-do simulation, which is related to the underestimated wind stress curl in the same zonal band, needs further improvement. Besides the local boundary wind forcing near 90∘ W, the underestimated seasonal zonal wind stress variability between 150∘ W and 180∘ in both JRA55-do and CORE causes the underestimated DSL signal throughout the year. Due to the compensation effect of zonal wind stress and wind stress curl on the strength of Ekman suction/pumping in the tropics, a separated evaluation of both zonal wind stress and wind stress curl is needed in the future to avoid the compensated bias shown in the CORE forcing data.

For interannual variability, the El Niño-related DSL variation is well represented in JRA55-do and CORE for both the timing and the spatial pattern. However, we still see a amplitude bias for DSL in both CORE- and JRA55-do-forced simulations. JRA55-do does improve the amplitude bias compared to CORE.

The multiple timescale analyses in this study provide a comprehensive view of important variability, changes, and the associated biases in the tropical Pacific. Any improvement of the biases mentioned in this study will be very helpful to further a mechanistic understanding of tropical Pacific DSL patterns using OMIP simulations and by extension their related coupled climate models.