1 INTRODUCTION

A westward flow called the North Equatorial Current (NEC), which is confined between 8°N–17°N in the surface layer of the North Pacific Ocean, is an important region for water mass exchange and mixing (e.g., Fine et al., 1994; Qu et al., 1998). The main body of the NEC is concentrated within a layer shallower than the 26.5–26.8 potential density (σ_θ) surfaces (Qiu et al., 2015). To the east of Mindanao Island, the NEC bifurcates into the southward-flowing Mindanao Current (MC) (e.g., Nitani, 1972; Hu and Cui, 1991; Wang et al., 2016) and the northwardflowing Kuroshio Current (KC) (e.g., Lien et al., 2014; Qiu et al., 2014; Chen et al., 2015).

On interannual timescales, NEC transport increases (decreases) during El Niño (La Niña) periods (Qiu and Lukas, 1996; Kim et al., 2004). Seasonally, the NEC is strong in spring and weak in autumn. Dynamically, the variability of the sea surface height anomaly and the NEC is attributed primarily to local winds and Rossby waves propagated from the eastern boundary of the Pacific Ocean (e.g., Qiu and Joyce, 1992; Qu et al., 2008; Kashino et al., 2009; Wang et al., 2019).

Using ocean models with high resolution and low dissipation, Richards et al. (2006) demonstrated that alternating jet-like structures occur between 30°N–55°N and in the tropics. Based on an ocean model of the North Pacific Ocean, Nakano and Hasumi (2005) found a series of zonal jets with meridional scale of 3°N–5°N. Alternating jets have also been discovered in the deep ocean following analysis of float data (Hogg and Owens, 1999). Based on profiling float temperature-salinity data, Qiu et al. (2013a and b) identified three well-defined eastwardflowing jets with velocity of 2–5 cm/s. The jets were centered around 9°N, 13°N, and 18°N within the 26.9–27.3 σ_θ surfaces along 130°E–135°E beneath the permanent westward-flowing NEC. Zhang et al. (2017) used direct mooring observations to reveal the existence of eastward zonal jets below the NEC at 10.5°N and 13.0°N.

Using the Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) products, it has been shown that three regions of high variability exist in the North Pacific Ocean: the Kuroshio/Kuroshio Extension southeast of Japan, North Equatorial Countercurrent along 5°N, and the region off the Pacific coast of Central America around 11°N (Qiu, 1999). In addition, there is a regional maximum of sea surface height variability with a root mean square value of >0.10 m in the area 19°N–25°N, 135°E–175°W (Wyrtki, 1975; Aoki and Imawaki, 1996; Qiu, 1999), where the northern part of the NEC is beneath the surface eastward-flowing North Pacific Subtropical Countercurrent (STCC). The instability of the STCC-NEC system has been discussed comprehensively based on baroclinic instability theory (Qiu, 1999; Kobashi and Kawamura, 2002).

If the bottom layer of the NEC and the upper layer of the zonal jets are considered a coupled system within the NEC basin, it is important to investigate its stability. Furthermore, although NEC stability has been discussed qualitatively by Qiu (1999), the key factors governing its stability remain to be determined. To address these issues, nine moorings were deployed at 8.5°N, 10.5°N, 11.0°N, 12.5°N, 13.0°N, 15.0°N, 15.5°N, 17.5°N, and 18.0°N along 130.0°E to clarify both the growth rate in the boundary layer of the NEC-zonal jets system and the relative contributions to the growth rate of different NEC parameters. The remainder of this paper is organized as follows. The data obtained from the nine moorings and the AVISO products are introduced in Section 2. In Section 3, the relative contributions to NEC stability from different parameters and the growth rate in the boundary layer of the NEC-zonal jets system are discussed. A short discussion and the derived conclusions are presented in Section 4.

2 DATA 2.1 Acoustic Doppler Current Profiler (ADCP) mooring data

To determine variability and vertical structure within the NEC basin, moorings were deployed along 130°E. The corresponding water depth is approximately 5 400–5 900 m. Moorings were deployed at 8.0°N, 10.5°N, 13.0°N, 15.5°N, and 18.0°N in September 2014 and retrieved one year later. From 2016, the mooring locations were changed to 8.5°N, 11.0°N, 12.5°N, 15.0°N, and 17.5°N (Fig. 1). It should be noted that mooring data during September 2014 to September 2015 at 8.0°N were lost, and that three ADCPs (two at 12.5°N and one at 15.0°N) failed during September 2015 to December 2016. Full details of the moorings are listed in Table 1.

The sampling frequency of the 75-kHz ADCPs deployed on our moorings was set to 1 h. At each mooring, two ADCPs (one looking upward and one looking downward) were attached at the depth of approximately 450 m. As each ADCP was set to observe 60 (8 m/bin) bins, the observation range of the two ADCPs was around 900 m. In fact, the measurement range of the ADCPs was variable because strong currents incline the mooring system and reduce the observational range. Before use in the analysis, the ADCP data underwent a strict quality control procedure. ADCP data with pitch or roll of >18°, current speed of >2 m/s, and < 80% good beam coverage were removed. Furthermore, the blank zone between adjacent ADCPs was filled by interpolation. Generally, most ADCP data were considered poor in the surface layer where beam emission echo is very strong; thus, data in the 0–50 m layer were deleted directly, except for the mooring at 13.0°N because the ADCP data were considered very good in the upper 50 m. The accuracy and resolution of the ADCPs were limited to within 1% velocity ±5 mm/s and < 1 mm/s, respectively. The ADCP data were processed as a daily dataset to remove tidal signals.

2.2 AVISO products

AVISO data were used in this study (Boebel and Barron, 2003; Barron et al., 2009). This altimetryobserved dataset comprises merged European Remote Sensing Satellite-1 and -2, Ocean Topography Experiment Topex/Poseidon, Geosat Follow-On, and Jason-1 and -2 data (Le Traon et al., 1998; Ducet et al., 2000). The 0.25°×0.25° resolution AVISO products (January 1, 1993 to December 31, 2015) that included daily sea surface height and corresponding geostrophic currents were downloaded from https://www.aviso.altimetry.fr.

3 RESULT 3.1 Mean structures of the NEC and zonal jets

The mean zonal velocities (red lines) and standard deviations (dashed blue lines) at the nine mooring stations are shown in Fig. 2. In this paper, the positive direction is defined as northward and eastward. It can be seen that the NEC is a surface-intensified feature. Generally, the intensity of the surface NEC increases from 8.5°N to 10.5°N and then decreases slowly with increasing latitude. Vertically, the main body of the NEC deepens with latitude. At 18°N, the NEC is completely below the sea surface layer. The greatest standard deviation of zonal velocity occurs at 76 m (8.5°N), 50 m (10.5°N), 63 m (11.0°N), 60 m (12.5°N), 62 m (13.0°N), 67 m (15.0°N), 50 m (15.5°N), 63 m (17.5°N), and 59 m (18.0°N). It is interesting that all depths are focused in the upper 100 m. The mean meridional velocities at the mooring stations are much smaller than the zonal velocities but their standard deviations are comparable (figure not shown).

It is worth emphasizing that eastward zonal jets exist beneath the NEC at 8.5°N, 10.5°N, 12.5°N, 13.0°N, and 17.5°N. The strongest zonal jet is found at 8.5°N with a value of 0.08 m/s at 455 m depth. To depict the zonal jets intuitively, latitude-depth sections of the mean zonal velocities interpolated from the ADCP data are shown in Fig. 3. Although zonal jets are found to exist at 10.5°N and 13.0°N, their intensity is smaller than at 8.5°N and 12.5°N. Furthermore, a zonal jet is evident at 17.5°N. Therefore, it is suggested that the zonal jets are concentrated at 8.5°N, 12.5°N, and 17.5°N along 130.0°E, consistent with the findings of Qiu et al.(2013a, b), who reported zonal jets centered around 9°N, 13°N, and 18°N along 130°E–135°E. In addition, the zonal jets deepen with latitude. For example, the zonal jet core is around 500 m depth at 8.5°N and 700 m depth at 12.5°N. At 17.5°N, the zonal jet is very weak above 800 m depth, which suggests that its core might be below 800 m. At 18.0°N, the STCC rather than the NEC occupies the upper layer; instead, the NEC is completely beneath the STCC.

3.2 NEC stability

Although Qiu (1999) discussed NEC stability qualitatively, the relationship between the NEC growth rate and several key parameters remains unclear yet. To investigate NEC stability quantitatively, a 2½-layer linearized reduced gravity model was utilized under the quasi-geostrophic approximation as follows:

where q_n is the perturbation potential vorticity, П_n is he mean potential vorticity, and ϕ_n is the perturbation stream function in the n-th layer. In the following, H₁/H₂ and U₁/U₂ denote the mean layer thickness and the mean zonal velocity in the surface (n=1) and second (n=2) layers, respectively. The potential vorticity and the meridional gradient of the mean potential vorticity are shown in the following:

where , , , β is the meridional gradient of the Coriolis parameter f₀, ▽² is the horizontal Laplacian operator, ρ₀ denotes the reference density.

Generally, the normal mode solution is well described by the following form:

in which k and l are the zonal and meridional wave numbers, respectively, with amplitude A_n. To derive nontrivial solutions for A_n, Eq.2 is substituted into Eq.1, following which the equation about wave speed c is derived as follows:

where , .

In fact, c is composed of the real part c_r and the imaginary part c_i; thus, c≡_cr+ic_i, where c_r is the phase speed and kc_i represents the growth rate. If c_i=0, the system is stable; otherwise, it is unstable. Past studies have reported that the NEC is stable (Qiu, 1999; Kobashi and Kawamura, 2002); however, the reason for the stability of the NEC remains unresolved quantitatively. It seems that the Coriolis parameter f, shear gradient of zonal velocity, layer depth ratio δ, and stratification ratio γ are all closely associated with the growth rate of the NEC. Our calculations, which indicate that the growth rates at the nine mooring stations are all zero, suggest that the NEC is stable.

A series of idealized experiments was designed to discuss the relative contributions of key parameters to the NEC growth rate. First, all parameters except f were artificially set as constants, which tends to make the NEC unstable. The resultant relationship between latitude and growth rate is shown in Fig. 4a. As f is proportional to latitude, the NEC growth rate becomes larger with increasing latitude/f. Second, γ was similarly considered as the only variable, while all other parameters were set as constants, which also makes the NEC unstable. It is demonstrated in Fig. 4b that a lower value of γ corresponds to a greater growth rate. For U₁ and U₂, it is shown that a smaller value of U₁ or a greater value of U₂ leads to a higher growth rate of the NEC (Fig. 4c & d). In other words, the NEC growth rate is proportional to velocity shear. For the layer depth ratio δ, if H₁ is held constant, the increase of H₂ meridionally corresponds to the decrease of the H₁/H₂ ratio, which leads to decrease of the growth rate (Fig. 4e). If H₂ is held constant, the increase of H₁ meridionally corresponds to the increase of the H₁/H₂ ratio, which leads to decrease of the growth rate (Fig. 4f). In summary, the layer depth ratio δ always generates decrease of the NEC growth rate meridionally. The calculation shows that both the ratio γ and the shear of zonal velocity decrease with latitude in the NEC region. Therefore, f and γ lead to an increase of the NEC growth rate, while U₁−U₂ and δ generate a decrease of the NEC growth rate meridionally. In fact, as the NEC is stable, it would appear that the two inversed physical processes cancel each other, leading to zero growth rate of the NEC. Specifically, f and γ maintain NEC stability in low latitudes, while velocity shear and the layer depth ratio δ play an important role in NEC stability in high latitudes.

3.3 Instability in the boundary layer between the NEC and zonal jets

It is shown in Fig. 2 that the zonal jets are much stronger at 8.5°N and 12.5°N, where the standard deviation is comparable with that in the surface layer, in comparison with the other stations. At stations without zonal jets, or where the zonal jets are very weak, the standard deviations generally decrease with depth. It is very likely that the growth rate in the boundary layer comprising the bottom of the NEC (the first layer) and the upper zonal jets (the second layer) is no longer zero. Here, we choose 12.5°N as an example for which to calculate the growth rate in the boundary layer; the corresponding parameters are listed in Table 2. Specifically, ρ₁=26.0 σ_θ, ρ₂=26.5 σ_θ, ρ₃=27.0 σθ, H₁= 88 m, H₂= 186 m, and U₁ (U₂) is given by the mean zonal velocity between ρ₁ and ρ₂ (ρ₂ and ρ₃) based on the mooring observations at 12.5°N. Here, depth ρ₂ is set at the point of zero zonal velocity in the NEC-zonal jet system. For simplicity, 2πl is set as the mean value in the NEC region. The result shows that it is unstable. Similar calculation indicates that the growth rate in this layer is not zero at 8.5°N or 13.0°N (Fig. 5a), where both the zonal jets and the velocity shear between the NEC and the zonal jets are larger than at the other stations (Table 2). The smaller velocity shear at 13.0°N (compared with that at 8.5°N and 12.5°N) leads to the smaller growth rate. In comparison, the corresponding layers at 11.0°N, 15.0°N, 15.5°N, and 18.0°N without zonal jets are stable. It is striking that the growth rate is zero at both 10.5°N and 17.5°N, where zonal jets exist. At 17.5°N, the velocity shear is so small that the growth rate is equal to zero. At 10.5°N, although the velocity shear is comparable with that at 13.0°N, the lower latitude tends to attenuate the growth rate to zero. At 18.0°N, the layer comprising the bottom of the STCC and the upper NEC is unstable, consistent with previous research (Qiu, 1999; Kobashi and Kawamura, 2002). It is shown in Fig. 1b that the high variability of sea surface height along 130.0°E is concentrated around 8.0°N, 9.0°N–10.0°N, and 12.0°N–13.0°N. Meanwhile, the mooring data shown in Fig. 3 and Table 2 indicate that the zonal jets at 8.5°N, 12.5°N, and 13.0°N are stronger than at the other mooring stations, both of which support our calculations well.

Based on the above analysis, it seems that the stronger the zonal jets, the higher the growth rate. Therefore, it is interesting to investigate whether an equivalent velocity shear at different velocities in the boundary layer produces the same growth rate. To clarify this point, we set an idealized experiment at 12.5°N. The growth rate was calculated with U₁=-0.05 and U₂=0.01 and with U₁=-0.10 and U₂=-0.04. It should be noted that the velocity shear (U₁−U₂) and all other parameters were the same in both cases. It is shown in Fig. 5b that the growth rates are different in the two cases, suggesting that the growth rate is associated not only with the shear gradient of the zonal velocities but also with the velocities in two layers. It would appear that when the signs of the two zonal velocities differ, the growth rate is more likely to become larger than when the signs of the two zonal velocities are the same.

To investigate the dynamics, a key factor D, based on Eq.3, is defined as follows:

It should be noted that factor D is the necessary and sufficient condition for stability/instability. As the term is always positive, the system might be unstable when Π_1yΠ_1y < 0 because the parameters R, γ, δ, and λ are all positive. In other words, a negative value of Π_1yΠ_2y is the necessary but not sufficient condition for instability. As the westward-flowing NEC and eastward-flowing zonal jets lead to a negative value of U₁−U₂, Π_1yΠ_2y can be written as follows:

The term in the second set of brackets is positive. However, as the absolute value of is larger than β, the term in the first set of brackets is negative, leading to a negative value of Π_1yΠ_2y; therefore, the boundary layer of the NEC-zonal jet system is possibly unstable.

In fact, U₁−U₂ and U₂ in Eq.4 could be considered as two variables:

where , , and . It is evident that factor D is controlled not only by the velocity shear but also by the velocity in the second layer. In addition, factor D is closely associated with the total wave number K. The relationship between the growth rate and both U₁ and U₂ is shown in Fig. 6. On the assumption of longwaves with k=5×10^-6/m, the growth rate increases with the value of U₁−U₂. When k>1.3×10^-5 /m, the growth rate is no longer proportional to the value of U₁−U₂; however, it always increases with U₂.

3.4 Variability in the NEC-zonal jet system

The time series of zonal velocities at the nine mooring stations along 130.0°E are shown in Figs. 7 & 8. Beneath the permanent NEC, eastward zonal jets and the vertically extended NEC exist alternately meridionally. At low latitudes, e.g., 8.5°N, the NEC is concentrated on the surface, and the zonal jets are centered at around 500 m. The main body of the NEC and the intermittent zonal jets deepen with latitude. In addition, the intensity of the zonal jets varies with latitude; it is strongest at 8.5°N on June 6, 2016 (i.e., 0.65 m/s) and weakest at 15.5°N. Generally, the zonal jets at both 8.5°N and 12.5°N are much stronger than at the other stations. At 11.0°N, 15.0°N, and 15.5°N, although there is no zonal jet climatologically, one does appear intermittently over time. At 18.0°N, the zonal jets disappear completely. To investigate the variability of the NEC-zonal jet system, a power spectrum analysis is shown in Figs. 9 & 10. A common peak of 70–120 d is almost coherent from the sea surface to the bottom of the range of ADCP measurements at all mooring stations, which is significant (insignificant) below (above) the thermocline at the 95% confidence level. It should be noted that measurements for the full two years were retrieved only at 8.5°N, 11.0°N, and 17.5°N; the time series at the other stations extended for approximately one year. A semiannual signal is evident at 8.5°N, 11.0°N, and 17.5°N. Specifically, it is concentrated in the upper 250 m at both 8.5°N and 11.0°N and below 400 m at 17.5°N at the 95% confidence level.

To investigate the variability of the relationship between the NEC and the zonal jets, the vertical mean NEC averaged from the sea surface to the depth of zero velocity (blue line), and the mean zonal jets (red line) averaged from the depth of zero velocity to the bottom of the range of the ADCP measurement are shown in Figs. 11 & 12. It should be noted that the depth of zero velocity at 11.0°N, 15.0°N, and 15.5°N is artificially defined at 300, 500, and 500 m, respectively. It is striking that the blue and red lines are well consistent with each other, suggesting that the intensity of the NEC is inversely proportional to the strength of the zonal jets. When the NEC is strong, it is not only a surface-intensified feature but it also extends to deeper layers. Vertical extension of the NEC could weaken the zonal jets or even lead to occupation of the region of the zonal jets. Sometimes the NEC is sufficiently strong that the zonal jets disappear completely. It should be noted that the blue and red lines at 18.0°N represent the STCC and the NEC, respectively. It can be seen that they are well coherent, suggesting that STCC variability is inversely proportional to the NEC at 18.0°N along 130.0°E.

It is interesting to check the growth rate in the boundary layer of the NEC-zonal jet system on the time node, when zonal jets exist beneath the NEC. Calculation shows the boundary layer is unstable during May 15 to June 15, 2016 at 8.5°N, and a similar calculation was applied to the other mooring stations. Quantitatively, in low latitudes, e.g., 8.5°N, when U₁−U₂ is >0.05 m/s, the system tends to be unstable. Around the bifurcation latitude of the NEC, e.g., 12.5°N, when U₁−U₂ is >0.04 m/s, the system is unstable. In high latitudes, e.g., 17.5°N, when U₁−U₂ is >0.01 m/s, the growth rate is not zero. In addition, the stronger the zonal jets, the higher the growth rate. It should be noted that the above analysis is based on the longwave assumption.

4 DISCUSSION AND CONCLUSION

This study was based on direct ADCP measurements obtained at 8.5°N, 10.5°N, 11.0°N, 12.5°N, 13.0°N, 15.0°N, 15.5°N, 17.5°N, and 18.0°N along 130.0°E. The observations extended vertically to depths of 800–1 000 m, providing a dataset convenient for investigation of the features of the NEC and its underlying zonal jets. The main body of the NEC is concentrated in the upper layer at 8.5°N but it deepens with increasing latitude. At 18.0°N, the NEC is completely below the sea surface layer, and the surface current is instead the eastward-flowing STCC. Climatologically, eastward-flowing intermittent zonal jets are concentrated around 8.5°N, 12.5°N, and 17.5°N, consistent with previous research (Qiu et al., 2013a, b) that found three eastward zonal jets centered around 9°N, 13°N, and 18°N within the 26.9–27.3 σ_θ surfaces along 130°E–135°E. Similar to the NEC, the main body of the zonal jets also deepens with latitude. Generally, the standard deviation decreases with depth. However, in regions where the zonal jets are strong, the standard deviation is comparable with that in the surface layer. During the observation period, zonal jets were found to exist intermittently. Calculation showed that the variability of the NEC is inversely proportional to the strength of the zonal jets. The power spectral density analysis demonstrated that intraseasonal signals of 70–120 d are common below the thermocline at the nine mooring stations along 130.0°E.

A series of idealized experiments was designed to investigate the growth rate of the NEC. As the Coriolis parameter, velocity shear, layer depth ratio, and stratification ratio are all closely related to the NEC growth rate, in the experiments, one parameter was set as the only variable, while all other parameters were held constant to maintain the NEC instability. It was found that the Coriolis parameter and stratification ratio play important roles in the stability of NEC at low latitudes, and that the velocity shear and the layer depth ratio maintain NEC stability at high latitudes.

In the boundary layer comprising the bottom NEC and upper zonal jets, the growth rate was found not zero at 8.5°N, 12.5°N, and 13.0°N, whereas it was zero at the other stations. Although zonal jets exist at 10.5°N and 17.5°N, the low latitude of 10.5°N and the weak velocity shear at 17.5°N lead to NEC stability at the two stations. At 18.0°N, the layer comprising the bottom STCC and upper NEC was found unstable, consistent with previous research (Qiu, 1999; Kobashi and Kawamura, 2002).

On the assumption of longwaves, the growth rate is mainly proportional to the velocity shear. In the low latitudes of the NEC basin, the boundary layer is unstable when the velocity shear is >0.05 m/s. Near the NEC bifurcation latitude, the boundary layer is unstable when the velocity shear is >0.04 m/s. The corresponding value is 0.01 m/s at high latitudes. On the assumption of shortwaves, the growth rate is unrelated to velocity shear, but it is well proportional to the velocity of the zonal jets. This could be attributed to the asymmetry of the velocities of different layers in Π_1y and Π_2y.

5 DATA AVAILABILITY STATEMENT

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

6 ACKNOWLEDGMENT

We thank all the scientists, technicians, and the crew of R/V Science for the deployment and retrieval of the moorings. The daily sea surface height and geostrophic currents from AVISO products can be downloaded from https://www.aviso.altimetry.fr/.