Seasonal variability of the observed OBP in the world oceans
As shown in Fig. 1, OBP has significant seasonal variability. During boreal winter, negative OBP anomalies are located in the northern North Pacific and subtropical South Pacific, ranging from − 1 cm to − 3 cm. The vectors represent the Ekman transport anomalies (Sv per grid box). In above two regions, vectors’ pattern indicates the local divergence of mass, which accounts for negative anomalies of OBP to some extent. Positive OBP anomalies are found in the subtropical North Pacific, corresponding to the convergence of Ekman transport (Fig. 1a). In the South China Sea (SCS), positive OBP anomalies are located along the western boundary, and this is due to the Ekman transport driven by northeasterly wind during winter (Cheng and Qi 2010). North of 40 °S in the Indian Ocean, significant divergence is located in the central Indian Ocean, accounting for the negative OBP anomalies. Along the coast of northern Indian Ocean, positive OBP anomalies are caused by the strong onshore Ekman transport. In the North Atlantic Ocean, weak negative OBP anomalies are in the subpolar region, while positive OBP anomalies appear between 10 °N and 50 °N. In the Southern Ocean, strong positive OBP anomalies (~ 3 cm) are located in the southeastern Southern Indian Ocean and Southern Atlantic, corresponding to the convergent southward Ekman transport. The distribution of OBP during boreal spring is similar to that during winter, but somewhat weaker. The remarkable differences are the positive anomalies in the subpolar Pacific and Atlantic (Fig. 1b). During boreal summer (autumn), overall the wind direction is flipped, and the OBP pattern is opposite to that during winter (spring) (Fig. 1c and d).
Based on GRACE observations and numeric models, numerous studies have investigated seasonal variations of OBP in global ocean, with a particular focus on the North Pacific (e.g., Gill and Niiler 1973; Ponte 1999; Kanzow et al. 2005; Bingham and Hughes 2008; Ponte et al. 2007; Chambers 2011; Johnson and Chambers 2013; Piecuch and Ponte 2014; Piecuch et al. 2015). The seasonal distribution of OBP revealed in this study are similar to that of previous studies. Using longer timeseries of data, we can obtain more robust seasonal cycle. Furthermore, Fig. 1 illustrates the relation between OBP and Ekman transport more intuitively.
Figure 2a shows the annual cycle of sea level, steric sea level and OBP anomalies in the western tropical Pacific (160°−200 °E, 10 °S−10 °N, Box A in Fig. 1a). Sea level has significant seasonal variability, reaching the maximum during boreal winter (2 cm) and minimum during boreal summer (−3 cm). Steric sea level has an annual cycle similar to sea level, while the OBP has an opposite phase. Thus, in this region steric sea level dominates the sea level variations, indicating the importance of baroclinic processes at low latitudes. In western tropical Pacific, sea level anomaly is quite larger than the sum of steric and OBP anomalies. The unclosed sea level budget is likely due to the errors exist in observations. In the southeastern South Indian Ocean (80°−120 °E, 60°−40 °S, Box B in Fig. 1a), sea level has stronger positive (negative) anomaly during February−Apirl (July−September). The seasonal cycle of OBP anomaly is quite similar to that of sea level anomaly, while the seasonal cycle of steric sea level is different (Fig. 2b). This figure suggests that OBP dominates the sea level variations, indicating the important role of barotropic processes at high latitudes.
Diagnostic OBP
As shown in Fig. 1, OBP anomalies are closely linked to the Ekman transport divergence/convergence. Figure 3 shows the observed OBP and diagnosed OBP based on Eq. (1) in the North Pacific (Gill and Niiler 1973). Overall, the pattern and amplitude of the signals obtained from these two approaches are similar, especially for the large-scale feature in the open northern North Pacific during boreal winter (summer) (Fig. 3). However, the results from the diagnostic equation are different from observations in the regions with complicated bottom topography. When there exists closed contour of \(\mathcal{H}\), such as in the southern Indian Ocean and Pacific, the OBP cannot be obtained by integration along \(\mathcal{H}\) from eastern boundary. Under this circumstance, Eq. (1) will be invalid. At lower latitudes and longer periods, baroclinic processes also make considerable contributions to the OBP variations (Piecuch 2013,2015; Piecuch and Ponte 2014; Piecuch et al. 2015). In addition, the OBP adjusts around the world oceans. Therefore, to fully understand OBP variations, even on regional scale, a global model is needed.
Simulated OBP from PCOM model
Figure 4 shows the OBP anomalies in boreal winter and summer simulated by PCOM (Exp. 1). The model reproduces the observed OBP pattern quite well; for example, the OBP dipole in the North Pacific, South Pacific and Indian Oceans. Even in the marginal seas, such as the South China Sea and Gulf of Carpentaria, the OBP signal reversion in summer and winter are also simulated in the model. In the tropical western Pacific (Region A) and southeastern South Indian Ocean (Region B), the annual cycle of OBP, sea level and steric anomalies simulated by the model are quite similar to the observations (Figs. 2 and 5) and results based on volume-conserving models (e.g., Ponte 1999; Ponte et al. 2007; Bingham and Hughes 2008; Köhl et al. 2012; Kuhlmann et al. 2013; Poropat et al. 2018; Androsov et al. 2020). Figures 4 and 5 indicate that the PCOM can simulate the seasonal cycle of regional OBP quite well; thus, this model can be used to study the dynamics of OBP variability.
Dynamics of seasonal variability of OBP
To explore the importance of each forcing, we carried out another four experiments (Exps. 2–5 in Table 1). There is no significant difference between results from Exp. 1 and Exp. 2 (Fig. 6a). As discussed by Huang and Jin (2001), heating creates no barotropic pressure signals; thus, local heating does not lead to OBP signals initially. However, nonuniform heating has an impact on the ocean circulation, and then causes slight mass redistribution in some regions indirectly. Overall, heat flux forcing is not important for the seasonal variability of OBP. The freshwater flux is tuned off in Exp. 3, the OBP pattern remains quite similar to that in Exp. 1 (Fig. 6b). Although precipitation can induce OBP signals, the horizontal scales of precipitation events are much smaller than the barotropic radius of deformation. As a result, the corresponding signals are mostly dispersed to the other parts of the world oceans, with negligible residuals left behind (Huang and Jin, 2002). Therefore, freshwater flux through precipitation has also little impact on regional bottom pressure.
The contribution to OBP from wind forcing is shown in Fig. 6c (Exp.1–Exp. 4). In the Pacific, Indian Ocean and Southern Ocean, OBP pattern is similar to that in Exp.1 (Fig. 4a), which suggests that wind forcing accounts for the dominant part of the regional OBP pattern observed by GRACE.
If the static effect based on the inverse barometer (IB) approximation is accurate, SLP anomaly should lead to no OBP signals. The difference of Exp. 1–Exp. 5 illustrates the contribution due to the non-static effect of SLP (Fig. 6d). The OBP difference in Fig. 6d is near zero in most regions on seasonal timescales, while it is relatively large in marginal seas and near the coasts (Fig. 6d). Sensitive experiments based on PCOM indicate that a model without subjected to the SLP can produce accurate results regarding to seasonal OBP and sea surface elevation in the open oceans; however, to accurately simulate the OBP in marginal seas and near the coasts, the model should include the SLP forcing as the upper boundary condition. Besides wind and SLP forcing, the bottom topography might also play a role in the regions with high STD values.
Non-static effect of the sea level pressure
Driven by climatological monthly mean atmospheric forcing, Exps. 1–5 cannot simulate the high-frequency variations of OBP. The non-static effect of SLP on the OBP is almost absent in the climatological runs. To check impacts of SLP on the high-frequency variations, additional three experiments were carried out by restarting from the spin-up run (Exps. 6–8 in Table 1).
The seasonal pattern of OBP for Exp. 6 is very similar to that for Exp.1, and the winter OBP difference for Exp. 6–Exp. 7 is also very close to that for Exp.1–Exp.5 (figures not shown). In terms of seasonal variations of OBP, almost no difference exists between experiments driven by the climatological monthly mean and the daily atmospheric forcing.
Figure 7a shows the standard deviation (STD) of OBP with period longer than 30 days for Exp. 6. OBP has strong variability in the north northern Pacific and Southern Ocean (maximum STD reaches to 5 cm). The amplitude and pattern of OBP for Exp.7 is very close to that for Exp. 6 (Fig. 7b). OBP time series at station A (100 °E, 50 °S) from Exp. 6 and 7 match very well, with a correlation coefficient of 0.99 (significant above 99% level). The STD of OBP for Exp. 8 is very small, except for the coastal and shallow water regions, such as the coast of China Sea, Australia, and Antarctica. In these regions, the non-static effect of SLP cannot be neglected (Fig. 7c). Figure 7 indicates that in the open oceans wind forcing dominates the OBP variations with period longer than 30 days, while non-static effect of SLP on OBP can be neglected.
To examine the OBP characters on the synoptic time scale, we analyze the STD of OBP with period shorter than 10 days for Exp. 6 (Fig. 8). High variance is located in the northern Pacific, northern Atlantic and the Southern Ocean (maximum STD reaches to 5 cm). The synoptic OBP variance accounts for a considerable part of the total OBP variance in the Southern Ocean. In the Antarctic Circumpolar Current (ACC) area, the strong OBP variance is related to resonance characteristics of the bathymetry at those periods (Poropat et al. 2018). Without SLP forcing, the OBP variance for Exp. 7 is weaker than that for Exp. 6 (Fig. 8a and b).
The difference between Exp. 6 and Exp. 7 is due to SLP forcing. As shown in Fig. 8c, the non-static effect of SLP is remarkable in the northern north Pacific, north western Atlantic and the Southern Ocean. The maximum STD of OBP forced by SLP is on the order of 3 cm in the southern Pacific, about half of the total variance (Fig. 8a and c). If the horizontal scales of initial perturbations are comparable to the barotropic radius of deformation, the initial pressure perturbations will be retained (Huang and Jin 2002). In the Southern Ocean, the spatial scale of SLP anomaly is on the order of thousands of kilometers, which is comparable with the barotropic Rossby radius of deformation. Therefore, the high-frequency SLP variance can affect the OBP. The phases of OBP time series at station A obtained from Exp. 6 and Exp.7 also match very well, with a correlation coefficient of 0.91 (significant above 99% level). The STD of OBP time series at station A is about 4.2 cm for Exp. 6 and 1.9 cm for Exp.8 (about 45% of the former). The differences among Exps. 6–8 indicate that the validity of IB correction is dependent on frequency and geographical location (Ponte et al. 1991; Ponte 1992, 1993). Figure 8 suggests that the non-static effect of SLP cannot be neglected on synoptic timescales.