As demonstrated above, various signals of temperature and salinity variabilities can be extracted by the EEMD method for different time scales, including interannual, decadal, interdecadal and trend components. Large salinity interdecadal variability in the western equatorial Pacific is seen to play an important role in contributing to density anomalies. The relative contributions of temperature and salinity anomalies to density can be further quantified by separating their individual effects. In this section, we present some related analyses, with a focus on interdecadal component.
The reconstructed interdecadal components of temperature and salinity anomalies can be added onto their climatological parts to form total fields: S = Sclim + Sinterde, T = Tclim + Tinterde. A diagnostic analysis is then performed to quantify the individual contributions of salinity and temperature anomalies to a field of interest (F); its interdecadal anomalies can be calculated from contributions of temperature and salinity anomalies by considering temperature and salinity to be interdecadally varying (Tinterde and Sinterde) or climatological (Tclim and Sclim), respectively. F(Tinterde, Sinterde) denotes a reference analysis in which both temperature and salinity fields are taken to be interdecadally varying in calculating F; F(Tinterde, Sclim) is for a thermosteric analysis in which temperature field is taken as interdecadally varying but salinity field is taken as climatological; F(Tclim, Sinterde) is for a halosteric analysis in which salinity is taken as interdecadally varying but temperature field is taken to be climatological; F(Tclim, Sclim) is a climatological field in which both temperature and salinity climatological fields are taken in calculating F, serving as a climatology from which interdecadal anomalies are calculated. As demonstrated above, density anomalies in the western region can be equally importantly contributed from salinity anomalies, whereas they are dominantly determined by temperature in the central and eastern equatorial Pacific. So, a focused analysis is placed on the western equatorial Pacific in the region A (2.5◦S–2.5◦N, 160◦E–180◦). Detailed attribution analyses are given below for relative contributions of temperature and salinity anomalies to interdecadal anomalies of density and N2, respectively. Table 1 quantifies the relative effects of Tinterde and Sinterde anomalies on density and N2 in the western equatorial Pacific during interdecadal evolution as represented by some representative periods.
Table 1. Interdecadal anomalies of temperature, salinity and some derived fields in the western equatorial Pacific, including sea surface density (SSD), the mixed layer (ML) depth (MLD), oceanic density at the base of ML (DENS_MLD), N2 near the sea surface at 5m (N2_5 m) and at the base of ML (N2_MLD), respectively. Three calculations are performed to quantify their individual contributions to a field of interest, in which temperature and salinity fields can be taken as interdecadally varying or climatological. Results are shown for the western equatorial Pacific (the region A) during the different periods of the interdecadal evolution, which correspond to the persistent phases in 1979-1996 and 1999-2016, and to transitional periods as represented in 1998 and 2017, respectively.
(1). Density (ρ)
Figure 10 displays the results from diagnostic calculations performed to quantify the relative contributions of interdecadal components of Tinterde and Sinterde to density anomalies in the upper ocean of the western equatorial Pacific (the region A); the corresponding time series are shown in Fig. 11 for the sea surface and at subsurface depth of 200 m, respectively. As evident, ρ(Tinterde, Sinterde) is nearly the sum of ρ(Tinterde, Sclim) and ρ(Tclim, Sinterde). Inspection of these anomaly fields indicates that the way density is affected in the upper ocean is varying during interdecadal evolutions. In the subsurface layers, the situation is quite simple (Fig. 11b), in which salinity and temperature anomalies are largely of the same sign, with density anomalies being dominantly attributed from temperature anomalies. Indeed, ρ(Tinterde, Sinterde) follows closely with ρ(Tinterde, Sclim) in the subsurface layer (Fig. 11b).
The situation is more complicated in the surface layer (Fig. 11a), which will be our focus in the following analyses. As demonstrated above, salinity in the surface layer can have both uncompensated and compensated effects on density. During the persistent phases, SSS and SST anomalies are largely of the opposite sign, and their contributions to density anomalies are in the same direction, acting to increase density anomalies. The relative effects of Tinterde and Sinterde on density are well reflected in these three calculations for density anomalies (Fig. 10 and Fig. 11a). During persistent phases, for example, SSS and SST anomalies are of the opposite sign and the corresponding ρ(Tinterde, Sclim) and ρ(Tclim, Sinterde) fields are not compensated, making the amplitude of ρ(Tinterde, Sinterde) larger. During transitional periods, on the other hand, SSS and SST anomalies can be of the same sign and their effects are density-compensated. So, the ρ(Tinterde, Sclim) and ρ(Tclim, Sinterde) fields make the amplitude of ρ(Tinterde, Sinterde) smaller, consistent with the analyses in the Sect. 4. One striking feature is that the sign and amplitude of ρ(Tinterde, Sinter) is determined by ρ(Tclim, Sinterde) due to the dominant effect of salinity anomalies.
One interesting case can be illustrated in more details during the transitional periods as indicated during 1995–2003, when anomalies of SST, SSS and SSD indicate the differences in their sign transitions (Fig. 9). As analyzed above, for example, negative SST anomalies are accompanied with negative SSS anomalies, acting to produce negative density anomalies (Fig. 9a), which are dominantly contributed from the negative density anomalies during 1995–1999. The delayed effects on sign transitions of density anomalies are well reflected in these three density calculations (Fig. 11a). For example, ρ(Tinterde, Sclim) takes a lead in transition into positive anomaly in 1995; ρ(Tclim, Sinterde) takes a late transition into positive anomaly in 2002 (a lag); ρ(Tclim, Sinterde) remains to be negative anomaly until 1999 and then transits into positive anomaly, a lag caused by salinity effects relative to ρ(Tinterde, Sclim). The comparison among these three density calculations indicates that negative salinity anomaly is making a dominant contribution to the negative SSD anomaly (Fig. 11a).
Quantitatively, Table 1 lists the relative contributions of salinity and temperature anomalies to density and the other related fields during different phases of the interdecadal evolution. These calculations indicate that salinity can play a dominant role in producing density anomalies during interdecadal transitional periods. For example, the negative SSD anomaly in 1998 (-0.003 kg m− 3 ) is attributed to the combined effects of a negative SSS anomaly (-0.058) and a negative temperature anomaly (-0.041), respectively. Also for the transitional period in 2017, the positive SSD anomaly in 2017 (+ 0.01 kg m− 3 ) is attributed to the combined effects of a positive SSS anomaly (+ 0.080) and a positive temperature anomaly (+ 0.064), respectively. Clearly, salinity anomalies play an important role in determining not only the amplitude but also the sign of density anomalies during the interdeadal evolution.
(2). The Brunt–Väisälä frequency squared (N 2 )
Density interdecadal anomalies are used to calculate its vertical gradient and the corresponding Brunt–Väisälä frequency squared (N2), a parameter representing the stratification stability. The vertical structure of interdecadal variability for N2 in the upper ocean of the western equatorial Pacific is shown in Fig. 12, which corresponds well to that for density (Fig. 8c). On interdecadal time scales, N2 anomalies exhibit well-defined see-saw patterns vertically with large anomalies centered at depths of 100m and 200m, respectively. During the interdecadal evolution, transitions take place between stable and unstable stratification conditions in the upper ocean. For example, during warm and fresh phases in the 1980s-1990s, the stratification is stable in the upper 150m, but unstable below it. A transition takes place during transitional period in the late 1970s and the late 1990s, respectively. During the cold and salty phases in the 2000s, the stratification becomes unstable in the upper layer of 150m but stable below it. Such changes can be explained by changes in density, which are attributed to temperature and salinity effects. In the subsurface layers, as demonstrated above, salinity and temperature anomalies are of the same sign and their effects are density-compensated during interdecadal evolution; so, N2 anomalies are dominantly determined by changes in the vertical structure of temperature.
The situation is quite complicated in the surface layer, where salinity can have both uncompensated and compensated effects on density during interdecadal evolution. As seen above, salinity anomalies exhibit the differences in its effects on density in the upper ocean: uncompensated effect in the surface layer acting to increase density anomalies, but compensated effect in the subsurface layers acting to reduce density anomalies, respectively. These salinity effects on density are well reflected in its vertical gradient (N2). For example, during warm and fresh persistent phases, negative salinity anomalies make the temperature-induced negative density anomalies more negative in the surface layer, thus making more stable stratification in the upper layer of 150m. Similarly, during cold and salty persistent phases, positive salinity anomalies make the temperature-induced positive density anomalies more positive, thus making less stable stratification. During transitional periods, the sign and amplitude of SSD anomalies can be dominantly determined by salinity anomalies, and so of N2 anomalies.
Similar attribution analyses are performed for the effects of Tinterde and Sinterde on N2 interdecadal anomalies. The extent to which N2 is affected by salinity is shown in Fig. 12 for three diagnostic calculations to quantify the relative contributions of Tinterde and Sinterde in the western equatorial Pacific; the corresponding time series are shown in Fig. 13 for the sea surface and at subsurface depth of 200 m, respectively. As evident, the sum of N2(Tinterde, Sclim) and N2(Tclim, Sinterde) almost recovers the signal of N2(Tinterde, Sinterde). In the subsurface layers (Fig. 13b), N2(Tinterde, Sinterde) is dominantly determined by temperature in the western equatorial Pacific so N2(Tinterde, Sinterde) follows closely with N2(Tinterde, Sclim). As shown in Fig. 13a, the salinity effects on N2 are mainly in the surface layer, where salinity plays a dominant role in producing N2 anomalies, with N2(Tinterde, Sinterde) following N2(Tclim, Sinterde). Indeed, the delayed effects on sign transitions of density are also reflected in its effects on N2 (Figs. 12–13). These analyses indicate that salinity effect in the surface layer makes dominant contribution to the stratification, including the amplitude and sign of N2 variability.
Quantitatively, Table 1 lists the relative contributions of salinity and temperature anomalies to N2 in the western equatorial Pacific during different periods. These calculations indicate that salinity can play a dominant role in producing N2 anomalies during interdecadal evolution. For example, the positive N2 anomaly (+ 1.078×10− 5 s− 2 ) for the transitional period in 1998 is attributed to the combined effects of a negative SSS anomaly (-0.058) and a negative temperature anomaly (-0.041), respectively. Also for the transitional period in 2017, the negative SSD anomaly in 2017 (-0.712×10− 5 s− 2 ) is attributed to the combined effects of a positive SSS anomaly (+ 0.080) and a positive temperature anomaly (+ 0.064), respectively. Clearly, salinity anomalies play an important role in determining not only the amplitude but also the sign of N2 anomalies during the transitional phase.