Submesoscale Eddy Spatiotemporal Variability Comparison Between Kuroshio Current and Open-Ocean Regions of the Western Pacific

Abstract

This study examines the 3D attributes of submesoscale eddies identified over a 12-month period within the Western Pacific Ocean. Composite parameters of cyclonic submesoscale eddies (CSMEs) occurring within and away from the Kuroshio Current system are compared and analyzed for their surface and subsurface features, as well as the seasonality of their core properties. Within the Kuroshio Current (KC) region, CSMEs are faster, stronger and deeper than in the open water (OW) region, with composite eddy depths of 97.5 m and 77.5 m, or 2.8 and 2.0 times the mixed layer depth, respectively. Prominent dipolar divergence patterns both at the surface and at depth reveal the presence of ageostrophic influence, with KC CSME cores deviating 48% and OW CSMEs deviating 40% from geostrophic balance at the surface. This imbalance drives strong vertical motion with maximum upward velocities of 19.2 m day⁻¹ at 57.7 m and 9.3 m day⁻¹ at 157.1 m within the KC and OW region CSME cores, respectively. Subsurface extrema analysis reveals structural differences in CSMEs between dynamic regions. These results provide a useful model-based estimate for subsurface CSME features which are difficult to quantify with observations.

1. Introduction

In recent years, the advent of increased computational power has allowed for finer resolution in numerical simulations, leading to an increased focus on submesoscale ocean features at spatiotemporal scales of 1–50 km over hours to days [1,2,3,4]. Submesoscale motions are characterized by a Rossby number (the ratio of inertial forces to Coriolis forces in a rotating system) of O(1) or greater. As the length scale decreases and Rossby number increases, the influence of the Coriolis force diminishes and geostrophic equilibrium breaks down, leading to nonlinear momentum advection and strong vertical motion in the upper boundary layer [1,5]. Many previous studies have investigated the submesoscale field as a whole [3,6,7,8,9]. For example, Su et al. showed that submesoscale motions contributed five times greater than mesoscale motions to the global heat budget by providing upward heat transport to the atmospheric boundary layer [8,10]. Dong et al. showed that submesoscale phenomena are responsible for up to 34% of the turbulent energy production within the ocean boundary layer [11]. These results hint at the importance of submesoscale motions in Earth’s oceans, which are likely underrepresented in ocean-only and coupled ocean–atmosphere models, warranting further exploration.

Within the submesoscale regime, oceanic structures such as filaments, meanders, fronts and eddies are defined [2]. This study is focused specifically on submesoscale eddies (SMEs). SMEs exist in the upper ocean and are characterized by strong rotational and vertical flow. Previous studies have provided valuable characterizations of SMEs at the ocean surface within specific, energetic regions. For example, Payandeh et al. utilized a collection of surface current measurements observed via high-frequency radar measurements in the Southern California Bight from 2012 to 2021 to identify and describe the occurrence, variability and potential drivers of SMEs [12], while Ernst et al. utilized sea surface height fields provided by NASA’s ECCO (Estimating the Circulation and Climate of the Ocean) project to identify and characterize SME-like variabilities in the Gulf of America over a 14-month period [13].

While submesoscale features have been explored at the ocean surface, studies on the subsurface dynamics of SMEs are also gaining momentum. D’addezio et al. investigated the physical characteristics of SMEs at the surface and at depth using statistical analysis based on high-resolution simulations with a focus on error covariance analysis for data assimilation applications [14]. Other recent research has investigated the subsurface contribution of SMEs to the stratification of the upper ocean and the overall heat budget. For example, X. Zhang et al. utilized a 1 km resolution model within the upper Kuroshio Extension to examine the vertical buoyancy flux within mesoscale and submesoscale eddies, highlighting the influence of baroclinic instabilities, frontogenesis and turbulent thermal wind balance on the restratification of the mixed layer [15]. They focused primarily on the seasonality of vertical mesoscale and submesoscale eddy buoyancy flux without focusing heavily on the SME structure.

Though essential, these analyses do not fully address the seasonally varying dynamics of SMEs at depth, nor do they provide a comparative analysis of SMEs influenced by a strong background current with those formed in a more passive, open water environment. Consequently, gaps remain in the analysis of seasonal SME parameters at depth, which impact applications such as acoustic propagation, search and rescue operations and ocean prediction systems [16,17,18,19,20]. We address this gap by defining and analyzing two dynamically distinct regions—one within the energetic Kuroshio Current and one in the adjacent open water. With this experimental design, we can isolate the impact of currents and investigate the differences in the resulting SME characteristics. The year-long study presented herein will focus on the physical properties and structure of SMEs with a higher horizontal and vertical resolution model than previous work to better quantify the vertical attributes of SMEs within the Western Pacific Ocean over a complete seasonal cycle.

In this investigation, we utilize a high-resolution ocean model simulation within the Western Pacific Ocean, encompassing the Kuroshio Current. The primary goal of this paper is to examine the seasonality and 3D structure of cyclonic submesoscale eddies, comparing those influenced by and contained within the Kuroshio Current system with those found in open water. The Kuroshio Current is responsible for the northward transport of warm water and significant thermal gradients which contribute to a highly active submesoscale landscape in the region. The Kuroshio Current and surrounding ocean is an appropriate location for the study of submesoscale features, as the diverse energy content of this region supports the creation of submesoscale flows which facilitate mixing and ultimately form SMEs [21,22].

2. Materials and Methods

2.1. Model Setup

In this work, the Navy Coastal Ocean Model (NCOM, version 4.6.8; NRL, Stennis Space Center, Hancock County, MS, USA) [23,24] is employed in the area of the Kuroshio Current system, located within the Western Pacific ocean. NCOM is a baroclinic, hydrostatic and Boussinesq regional ocean model which uses a free surface that allows for a hybrid σ-z vertical coordinate system to handle complex bathymetric conditions. NCOM has been shown to produce realistic analysis and forecast fields for a variety of research and operational applications [25,26,27]. In this study, we employ a free-running non-assimilative configuration to isolate and investigate the physics within NCOM without external influences, as has been done in previous studies [14,28,29,30]. Though atmospheric forcing and ocean boundary conditions come from data-assimilative models, the choice to run NCOM without data assimilation is deliberate and allows us to study SMEs as they emerge from the self-consistent dynamics of our model.

The NCOM modeled domain covers the area between 119.5° and 134.5° E and 17° and 28° N (Figure 1). The model is configured with a 0.01° horizontal grid resolution, consisting of 1501 × 1100 grid points with 100 vertical layers extending from the surface to a depth of 5500 m. The vertical grid spacing follows a logarithmic depth profile starting from 0.5 m for the first layer, with the highest concentration of levels in the upper 500 m. NCOM was run in 24 h forecast cycles from 1 November 2021 through 1 January 2023 with a 15 s timestep. Bathymetric data were obtained from the Navy’s two-minute resolution Digital Bathymetric Data Base (DBDB2; Naval Oceanographic Office, Stennis Space Center, MS, USA) [31], which was smoothed through a 9-point central median and two-step Hanning box filter. Initial and boundary conditions for NCOM were provided by the Hybrid Coordinate Ocean Model (HYCOM, version 2.2.98; NRL, Stennis Space Center, MS, USA), which is a primitive equation global and regional assimilative model that is often used to provide boundary conditions to finer regional models [32]. A Mellor–Yamada 2.0 vertical mixing scheme [33] and a third order upwind horizontal advection [34] were applied. Tides are provided from the global hydrodynamic tidal Finite Element Solutions (FES99; LEGOS/GRGS/CLS, Toulouse, France) database [35].

Hourly atmospheric surface forcing for NCOM was produced from the Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS, version 2021.5; NRL, Stennis Space Center, MS, USA) atmospheric model, which is a regional forecasting model which allows for high-resolution air–sea coupling [36]. The COAMPS atmospheric model configuration consists of 27, 9 and 3 km horizontal resolution nests. The 3 km nest (406 × 394 grid points), stretching from 13.5° to 29.5° N and 119°–137° E with 60 terrain-following vertical levels provides forcing to the ocean domain. Atmospheric boundary conditions were provided by the 0.5° Navy Global Environmental Model (NAVGEM, version 2.0; NRL, Monterey, CA, USA) [37]. Unlike the ocean model, data assimilation is included for the atmospheric model through the NRL Atmospheric Variational Data Assimilation System (NAVDAS; NRL, Monterey, CA, USA) [38]. On a 6 h update cycle, the NAVDAS includes atmospheric observations from radiosondes, aircraft, satellites, ships, and surface stations. For a more complete list of included atmospheric observation types and processing, the reader is referred to [39]. The atmospheric model was also run in 24 h forecast cycles from 00 UTC 1 November 2021 through 00 UTC 1 January 2023 with a 75 s time step.

The full modeled ocean domain is separated into two regions: one encompassing the Kuroshio Current system and continental shelf and the other encompassing only open water (Figure 1). The Kuroshio Current (KC) region extends from 119.5° to 123.5° E for latitudes 17° to 24° N and from 119.5° to 129° E for latitudes 24° to 28° N. In this region, the interaction of stronger currents with sharp bathymetric features together with topographic influences generate submesoscale wakes, vortex streets and SMEs [40,41,42]. The open water (OW) region includes the generally open ocean domain extending from 123.5° to 134.5° E for latitudes 17° to 24° N and from 129° to 134.5° E for latitudes 24° to 28° N. The bathymetry in this region is largely free of islands and generally much deeper compared to the KC region. Given the differences in ocean currents, bathymetry and topography between the KC and OW regions, we expect the physics influencing SMEs to differ as well.

2.2. Scale Separation and SME Identification

In order to highlight the influences of small-scale features and processes, the model output fields are separated into large- and small-scale components [8,13,14]. Specifically, the model field (X) is spatially filtered into a large-scale (X_L) and a small-scale (X_S) component as defined by $\mathrm{X}{-\mathrm{X}}_{\mathrm{L}}={\mathrm{X}}_{\mathrm{S}}$. While ocean dynamics occur on a continuum of scales, we must choose a length cutoff to isolate small-scale features for analysis. The minimum SME radius is set to 5.55 km, or 5 times the model horizontal grid resolution, and represents the physically resolvable length scale [10]. We choose to define the spatial separation between large and small scale as the length at which geostrophic balance breaks down and ageostrophic dynamics become significant (i.e., the first baroclinic Rossby radius of deformation [43]). At the modeled latitudes, the first baroclinic Rossby radius of deformation is approximately 50 km. Thus, we apply a 50 km Gaussian spatial filter to separate the large-scale from the small-scale components.

We follow the SME detection method described by [14], in which SMEs are identified within small-scale surface current fields based on the Okubo–Weiss (W) parameter. This parameter is a useful criterion in detecting coherent SME structures in the inherently noisy small-scale field and is used to separate vorticity-dominated features (negative W values) from strain-dominated ones (positive W values). The W parameter [44,45] is defined as

$$\mathrm{W}={{\mathrm{S}}_{\mathrm{n}}}^2+{{\mathrm{S}}_{\mathrm{s}}}^2-{\mathsf{\zeta }}^2$$

(1)

where the normal strain (${\mathrm{S}}_{\mathrm{n}}$), shear strain (${\mathrm{S}}_{\mathrm{s}}$) and surface relative vorticity ($\mathsf{\zeta })$ are defined as

$${\mathrm{S}}_{\mathrm{n}}={\displaystyle \frac{\partial \mathrm{u}}{\partial \mathrm{x}}}-{\displaystyle \frac{\partial \mathrm{v}}{\partial \mathrm{y}}}$$

(2)

$${\mathrm{S}}_{\mathrm{s}}={\displaystyle \frac{\partial \mathrm{v}}{\partial \mathrm{x}}}+{\displaystyle \frac{\partial \mathrm{u}}{\partial \mathrm{y}}}$$

(3)

$$\mathsf{\zeta }={\displaystyle \frac{\partial \mathrm{v}}{\partial \mathrm{x}}}-{\displaystyle \frac{\partial \mathrm{u}}{\partial \mathrm{y}}}$$

(4)

Here, $\mathrm{u}$ is the eastward velocity, $\mathrm{v}$ is the northward velocity, $\mathrm{x}$ is the east-pointing vector and $\mathrm{y}$ is the north-pointing vector. Because the W parameter is noisy and covers a wide range of values, it is common practice to normalize W by its standard deviation over the domain as ${\mathrm{W}}_{\mathrm{n}}={\displaystyle \frac{\mathrm{W}}{{\mathsf{\sigma }}_{\mathrm{w}}}}$ [46]. A 3-grid point 2D spatial Gaussian filter is applied to further smooth the ${\mathrm{W}}_{\mathrm{n}}$ field and highlight coherent features. To isolate the rotational motion indicative of SMEs, closed contours of −0.2 from the smoothed ${\mathrm{W}}_{\mathrm{n}}$ field are identified as potential SMEs; this standard threshold value has been used in previous studies to define the unambiguous cores of vorticity-dominated features [14,46,47,48]. Closed contours within 0.5° of the domain extents or within 25 km of land are excluded to avoid boundary conditions and land influences.

The circularity of potential SMEs is evaluated to ensure more circular contours are retained while more elongated contours are excluded. The centers of the potential SMEs are defined as the location of maximum surface vorticity within the closed contour, and radii are defined by the average distance from the center to the closed contour. Circularity of the SMEs are qualified by the deviation of each closed contour (${\mathrm{A}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{u}\mathrm{r}}$) from a fitted circle having an equivalent radius (${\mathrm{A}}_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}\mathrm{l}\mathrm{e}}$) as

$${\displaystyle \frac{{\mathrm{A}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{u}\mathrm{r}}-{\mathrm{A}}_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}\mathrm{l}\mathrm{e}}}{{\mathrm{A}}_{\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}\mathrm{l}\mathrm{e}}}}\times 100\le 35$$

(5)

A threshold value of 35 is chosen to remove elongated, filament-like structures and ensures the retained population consists of features that represent physically realistic SME structures [49]. The Coriolis parameter, which describes the apparent force acting on oceanic bodies due to Earth’s rotation, is defined as $\mathrm{f}=2 \mathrm{\ast } \mathsf{\Omega }\sin \left(\mathsf{\varphi }\right)$, where $\mathsf{\Omega }$ is the angular velocity of Earth and $\mathsf{\varphi }$ represents latitude. A Coriolis-normalized relative vorticity threshold defined by $\left|\mathsf{\zeta }/\mathrm{f}\right|\ge 1$ is applied to each detected contour to exclude weakly rotating and geostrophically dominated features [1,2,50,51]. Only closed contours that meet all these criteria are considered SMEs. From the identified SMEs, the degree and direction of rotation is determined, and the SMEs are characterized by their magnitude of normalized vorticity as cyclonic SMEs (CSMEs) having a positive small-scale vorticity or anticyclonic SMEs (ASMEs) having a negative small-scale vorticity.

As an example of scale separation, single timesteps of the resulting large-scale and small-scale ocean relative surface vorticity normalized by the Coriolis parameter (referred to simply as large-scale and small-scale vorticity throughout this section) are shown for the full domain on 12 UTC on 12 January 2022 and 12 UTC on 12 July 2022 in Figure 2. These were selected based on examination of the entire time series as representative of the typical winter and summer conditions throughout the domain across an interval of 6 months. The large-scale vorticity is characterized by features with length scales greater than 50 km in Figure 2a,b. In the KC region, the large-scale vorticity pattern is split into a positive portion to the left of the Kuroshio Current (indicated by the 1 m s⁻¹ contour) and a negative portion to the right of the Kuroshio Current, while in the OW region, large-scale vorticity varies throughout the region. Little variation exists in the range of large-scale vorticity feature magnitudes between regions and seasons. Small-scale vorticity, which encompasses all features smaller than 50 km, including eddies, fronts, and filaments, is shown in Figure 2c,d. At the small scale, vorticity shows stronger magnitudes and a greater variability than at the large scale, especially in the area immediately surrounding the Kuroshio Current, indicating that small-scale motions and influences dominate the large scale. Furthermore, greater variability in small-scale vorticity can be seen in the winter than in summer, indicating significant seasonal differences in the conditions which allow for SMEs. This increase in small-scale ocean activity in the cooler months and decrease in the warmer months is in agreement with previous studies and has been found to be correlated strongly with the seasonal cycle in mixed layer depth [15,52]. The deepening of the mixed layer coincides with an increase in available potential energy in the winter months, leading to the formation of balanced instabilities at this scale [1,7,53,54]. Consequently, a highly varying and intensified small-scale vorticity field exists in winter months while a more homogenized, weaker field is present in the summer months. This seasonality is also evident in the difference between SMEs identified in Figure 2e,f, with more SMEs identified in winter compared to summer throughout the domain. Within this domain, ASMEs are largely confined to areas near the Kuroshio Current in the KC region, while CSMEs are scattered throughout the full domain.

Corresponding to the plots in Figure 2, histograms are shown for large-scale vorticity (Figure 3a,b), small-scale vorticity (Figure 3c,d), and the small-scale vorticity found only within the SME contours (Figure 3e,f). The distribution of large-scale vorticity (Figure 3a,b) is similar between winter and summer with a narrow spread and peaks close to zero for both regions. The distribution of small-scale vorticity (Figure 3c,d) displays a greater spread of values compared to the large scale. A negative small-scale vorticity bias exists for both regions and timesteps peaking at −0.18 (KC) and −0.10 (OW) in the winter and at −0.14 (KC) and −0.06 (OW) in the summer, indicating a domain-wide predominance of anticyclonic small-scale features throughout the year. With a stronger peak and narrower distribution, the small-scale vorticity in the summertime has less variability and a weaker magnitude compared to the wintertime, particularly in the OW region, as shown in Figure 2. In contrast, the histograms of small-scale vorticity located within the identified SME contours (Figure 3e,f) reveal positively skewed distributions peaking at 1.74 (KC) and 1.37 (OW) in the winter and 1.71 (KC) and 1.51 (OW) in the summer. This contrast can be attributed to the submesoscale dynamics characteristic of this domain, in which stability criteria have been shown to favor the formation of cyclonic vortices [6,14,55]. The KC region SMEs show an overall higher magnitude small-scale vorticity frequency peak than in the OW region year-round. In the summer there is a much smaller, flatter distribution of SMEs that tend to have a stronger small-scale vorticity than in winter for both regions. These distributions indicate a strong dominance of CSMEs over ASMEs throughout the domain year-round. Due to the significantly lower occurrence of ASMEs within the model domain and timeframe, the scope of this study will focus on CSMEs, and the contributions of ASMEs will be explored in future research.

3. Results and Discussion

The CSME attributes across each region were evaluated both at the surface (Section 3.1) and at depth (Section 3.2). With two months of model spinup lasting from 1 November 2021 to 1 January 2022, small-scale composite properties are extracted from the model output from 1 January 2022 to 1 January 2023 at 3 h timesteps for all valid individual CSMEs that have been identified with the approach outlined in Section 2.2. Within this study the term seasonality refers to a single annual cycle, as in previous studies [7,15,56]. While this single annual cycle may not capture full climatological variability, it provides a robust foundation for probing the varying physical processes present within SMEs throughout the year. The small-scale properties investigated include horizontal and vertical current velocities, temperature, salinity, density, divergence and surface elevation. Large-scale horizontal current velocities and surface wind stress are also considered. Individual CSME attributes are normalized by radius throughout the water column. Within both regions, CSMEs showed comparable 12-month mean radii of 7.09 km, which is in line with similar studies such as [12]. Therefore, within our study, a reference radius of 7.09 km was used for normalization.

The daily number of identified CSMEs per 10⁶ km² are shown for both regions in Figure 4. Throughout the domain, CSMEs (and submesoscale features in general) are more prevalent in the winter. In the OW region, shallow mixed layer depths (MLDs) and weaker flow-field interactions cause a significant decrease in CSME counts in the summer. This cycle is comparatively weaker in the KC region, where currents supply stronger flow-field interactions year-round. As such, a higher density of CSMEs exists near the KC throughout most of the year. It is important to note that the maturity and lifetime of the detected CSMEs is not considered, and CSMEs at every stage of development are included in the composites within this section.

3.1. CSME Surface Features

We begin the characterization of CSMEs within the KC and OW regions at the ocean surface where 12-month small-scale horizontal current, sea surface temperature (SST), sea surface salinity (SSS), density and sea surface height (SSH) are composited along with large-scale horizontal current and full-field wind stress. From the small-scale currents, normalized vorticity and divergence are calculated and composited, and from the small-scale SSH, geostrophic current is derived in order to evaluate the extent of ageostrophic influence present within CSMEs. Daily mean CSME small-scale surface parameters of current velocity magnitude, normalized vorticity, SST, SSS, density, SSH and radius are presented, and their seasonality is examined. It is important to note that while composites presented in this study include the unweighted contribution of CSMEs year-round, the time series reflect the daily average properties of CSMEs. In this way, we see both the seasonality and bulk characteristics of CSME properties.

3.1.1. Currents

The 12-month composites of small-scale CSME surface current velocity (referred to simply as currents throughout Section 3.1) are shown for both regions in Figure 5a. Regardless of the region, currents are characterized by a counterclockwise flow surrounding the eddy core, defined as the CSME area within one normalized radius. The red arrows in Figure 5a indicate the 12-month mean magnitude and direction of large-scale CSME currents. Mean large-scale CSME currents follow the Kuroshio Current to the northwest at a rate of 0.31 m s⁻¹ in the KC region, while those within the OW CSMEs tend to be smaller and change direction seasonally, resulting in a much weaker annual mean large-scale current with a rate of 0.05 m s⁻¹ flowing towards the southwest. Current magnitudes in both areas follow the large-scale currents, and mean core currents in the KC region (0.33 m s⁻¹) are 38% greater in magnitude than those in the OW region (0.24 m s⁻¹) annually. A minimum near-zero current velocity is found at the CSME centers, with a radially increasing velocity throughout the core, followed by a decreasing velocity past one radius.

While the maximum current velocity is generally found at one radius (Figure 5a) the maximum is not constant surrounding the eddy core, particularly for the KC region. Instead, currents increase where the large-scale current flows in the same direction as the composite eddy rotation in each region. The strongest currents are typically located toward the east in the KC region. Within the OW region, CSMEs have a more uniform current profile due to the lack of any consistent directional, large-scale current influence in this region.

Figure 5b shows the daily time series of the mean core current, with KC and OW CSMEs showing a slight increase in mid-summer and early fall, respectively. The daily mean time series of the mean core CSME normalized small-scale surface vorticity (referred to simply as vorticity throughout Section 3.1) is shown in Figure 5c. Vorticity is strongest year-round within the KC region, corresponding to the stronger current velocities found in this region (Figure 5b). Vorticity in both regions increases slightly in the summer. In the KC region, the increase in current and vorticity occurs in early summer, while the increase in the OW region happens in late summer.

3.1.2. Temperature, Salinity, and Density

The 12-month composites of small-scale SST and small-scale SSS with contoured small-scale surface density (referred to in Section 3.1 as SST, SSS and density, hereafter) are shown in Figure 6a and Figure 6b, respectively. Regardless of the region, the CSMEs found within this domain are dominantly cold core eddies with higher SSS and density compared to the surrounding ocean. The SST, SSS and density signatures have correlated patterns, with areas of colder temperatures corresponding to higher salinity and density. In general, the SST and density are of similar magnitude between the KC and OW regions, which have a 12-month mean core SST of −0.40 °C and −0.42 °C, and a density of 0.144 kg m⁻³ and 0.140 kg m⁻³, respectively. SSS varies more by region with CSMEs having saltier surface values in the KC region with a 12-month mean core SSS of 0.032 psu compared to 0.018 psu for the OW region.

Regardless of the region, the SST, SSS, and density patterns show a significant asymmetry about the eddy center. This asymmetry is due to a combination of two primary factors: the natural distortion of eddies throughout their lifecycle and Ekman transport [57]. To demonstrate the Ekman transport from wind stress, the 12-month mean surface wind stress over the CSMEs is indicated in magnitude and direction by black arrows in Figure 6a,b, which show a consistent wind stress pointing to the southwest throughout both regions. The wind-forced Ekman transport causes deflection to the right of wind stress (i.e., to the northwest in each of these regions). A natural asymmetric decay of CSMEs over time leads to greater stretching in the longitudinal direction. This is reflected in the composites, which include CSMEs at every stage of the lifecycle. Following this asymmetry, density contours are more compact towards the east in both regions, indicating an asymmetric tightening of the density gradient in the area surrounding CSMEs, which impacts the MLD as will be discussed in Section 3.2.1.

Figure 7 shows the daily variability for small-scale CSME SST (Figure 7a), SSS (Figure 7b) and density (Figure 7c). SST and density show comparable daily mean trends for both regions. In the KC region more extreme positive and negative peaks in temperature (for example in June and November) correspond to more extreme negative and positive peaks in density. In the OW region, the more extreme positive peaks in SST (for example in July) instead correspond to positive peaks in salinity. Positive SST anomalies indicate the presence of warm-core CSMEs. Because the temperature and salinity change together, there is no corresponding peak seen with the density. The daily mean SSS are in close agreement between KC and OW for the first half of the year, but the trends diverge throughout the summer and early fall.

Because both temperature and salinity influence density, correlations are calculated to determine the dominant parameter driving the density patterns. Small-scale surface density has a positive correlation with small-scale SSS (with correlation values of 0.43 and 0.44 for the KC and OW regions respectively) and a negative correlation with small-scale SST (with correlation values of −0.84 and −0.78 for the KC and OW regions respectively). The relative strengths of these correlations indicate that changes in small-scale temperature have a greater impact than salinity on changes in density throughout the domain, as has been observed in submesoscale fronts [58].

3.1.3. Small-Scale Surface Divergence

Horizontal surface divergence, defined as $\mathsf{\delta }={\displaystyle \frac{\partial \mathrm{u}}{\partial \mathrm{x}}}+{\displaystyle \frac{\partial \mathrm{v}}{\partial \mathrm{y}}}$, serves as an indicator of subsurface vertical motions and provides insight into the circulation dynamics of CSMEs. The 12-month composite CSME small-scale normalized surface divergence ($\mathsf{\delta }/\mathrm{f})$ by region is shown in Figure 8. An asymmetric central dipole divergence pattern is found in each region. Within one radius, KC region CSMEs slightly favor divergence at the surface with a mean core normalized divergence value of 0.004, which indicates upward subsurface vertical motion. In the OW region, convergence dominates, with a mean core normalized divergence value of −0.040. The difference in composite CSME surface divergence asymmetry is indicative of the differing physical forces that support CSMEs between the KC and OW regions. CSMEs in the OW region are primarily driven by intrinsic instabilities and show behavior typical of CSMEs in which convergence dominates at the surface [59]. However, in the KC region, CSMEs are also influenced by the high-energy dynamics and topographical features surrounding the Kuroshio Current, which impacts the surface divergence. The strong surface divergence patterns shown in the 12-month composite CSMEs suggest that these eddies are not in geostrophic balance and there are strong ageostrophic motions that must be considered to better describe this behavior.

3.1.4. Small-Scale SSH and Ageostrophic Influence

Our discussion on ageostrophic motion begins with a description of CSME SSH, from which ageostrophic current is derived. The 12-month composite CSME small-scale SSH (henceforth referred to simply as SSH) is shown for both regions in Figure 9a. Corresponding to the counterclockwise flow, which indicates a low-pressure center in the Northern Hemisphere, the CSMEs are shown to have negative SSH values, indicating a surface depression, at the eddy core. The overall SSH pattern is found to be influenced by the surrounding large-scale surface currents in the KC region where there is a strong large-scale current flow to the northeast (as shown by the red arrow in Figure 5a), leading to the composite CSME SSH showing a slight increase in elevation towards the southeast (to the right of the large-scale currents). This large-scale current influence is not prominent in the OW domain, which maintains a more symmetric SSH and current field.

Figure 9b shows the daily mean core SSH values for each region. In both regions, SSH is deepest in the summertime and shallowest in the wintertime. The KC region has a CSME annual mean core SSH of −5.10 cm with a minimum value of −10.7 cm, while the OW region composite CSME has an annual mean central small-scale core SSH value of −4.05 cm with a minimum value of −16.6 cm.

An inverse relationship exists between SSH and CSME radius values (taken at 3-hourly intervals over 12 months), as evidenced by a statistically significant (p-value < 0.05) SSH–radius correlation coefficient of −0.46 for KC and −0.59 for OW CSMEs. The daily mean CSME radius trends in Figure 9c show an increasing daily mean radius corresponding to a decreasing daily mean SSH and vice versa for CSMEs in both regions. Furthermore, local SSH minima in the OW trend correspond to spikes in the OW CSME radius trend, indicating the presence of large, deep CSMEs on those days. However, there are no significant corresponding peaks in the daily mean CSME core vorticity shown in Figure 5c, indicating that though those SMEs are larger with stronger centers, they are not rotating faster.

From the 12-month composite small-scale SSH fields, geostrophic surface currents (${\mathrm{u}}_{\mathrm{g}},{\mathrm{v}}_{\mathrm{g}})$ are derived from ${\mathrm{u}}_{\mathrm{g}}={\displaystyle \frac{-\mathrm{g}}{\mathrm{f}}}{\displaystyle \frac{\partial \mathrm{S}\mathrm{S}\mathrm{H}}{\partial \mathrm{x}}}$ and ${\mathrm{v}}_{\mathrm{g}}={\displaystyle \frac{\mathrm{g}}{\mathrm{f}}}{\displaystyle \frac{\partial \mathrm{S}\mathrm{S}\mathrm{H}}{\partial \mathrm{y}}}$, where g is the acceleration due to Earth’s gravity, defined as g = −9.81 m s⁻². By using the composite field, influences from tides are minimized. Both the 12-month composite small-scale currents (black arrows) and the 12-month composite small-scale geostrophic currents (red arrows) are also shown in Figure 9a. In an effort to quantify the extent of geostrophy present in the CSMEs, the percent change (PC) of the 12-month composite small-scale current from the 12-month composite small-scale geostrophic currents is calculated using Equation (6), and shown for each region in Figure 10a.

$$PC={\displaystyle \frac{\sqrt{{(u-u_g)}^2+{(v-v_g)}^2}}{\sqrt{{u_g}^2+{v_g}^2}}}\times 100$$

(6)

Based on the application of Equation (6), small-scale currents are in complete geostrophic balance for $PC$ values of 0 and are completely ageostrophic for $PC$ values of 100. For both regions, the CSMEs are strongly ageostrophic at the CSME cores with geostrophy increasing radially past the cores. The composite KC CSME core deviates 48% from geostrophic balance and the composite OW CSME core deviates 40% from geostrophic balance. This shows that both geostrophic and ageostrophic flow are present within the CSMEs at the resolvable scale used in this study, with ageostrophic influences dominating more in the KC region than in the OW region. This behavior highlights the continuum of dynamical influences present within CSMEs.

The small-scale geostrophic currents are shown to be stronger than small-scale currents within approximately two radii of the composite CSMEs for each of the regions (Figure 9a). As a result, small-scale ageostrophic currents flow against the CSME small-scale currents (clockwise flow). This ageostrophic motion, which opposes geostrophic motion, drives the observed surface divergence and subsequent vertical motion. To highlight the influence from ageostrophic motion on CSMEs, the normalized divergence is derived from only the CSME small-scale composite ageostrophic currents as shown in Figure 10b. For both regions, the divergence pattern computed from the composite ageostrophic currents is in excellent agreement with the 12-month composite divergence derived from the small-scale currents (Figure 8).

3.2. Subsurface CSME Structure and Properties

We turn now to the subsurface to further describe the 3D characteristics of CSMEs, where the 12-month composite parameters of MLD, horizontal and vertical current, temperature, salinity, density, vorticity and divergence are characterized at depth. Daily mean CSME small-scale parameters of MLD and bottom depth are also presented, and their seasonality is examined.

3.2.1. MLD, Horizontal Current and Bottom Depth

The behavior of SMEs is closely linked to the depth and stratification of the mixed layer. In this study, we define the MLD as the point below 10 m where the potential density changes by an amount equivalent to a 0.2 °C change in temperature [60,61]. The 10 m reference depth is used to avoid minor diurnal near-surface fluctuations. When the mixed layer is shallow (in the summer), stratification increases. This trend leads to more energetic, albeit shallower CSMEs in the summer, with the opposite behavior evident in wintertime CSMEs.

The 12-month composite MLD is shown for each region in Figure 11. Composite core CSME MLDs having values of 34.6 m (KC region) and 38.6 m (OW region) are 17.5% and 15.7% shallower than the full KC and OW region mean MLDs, respectively. This pattern of shoaling towards the center of CSMEs mirrors the behavior of mesoscale eddies which have been shown to thin the mixed layer [62,63]. Furthermore, MLD patterns are asymmetric about the center CSME axis, which has also been noted in mesoscale cyclonic eddies [64,65]. The sharper density gradients to the east (Figure 6) act to prevent mixing, leading to shallower MLDs.

The 12-month composite small-scale CSME currents are shown at depth in Figure 12 with center longitudinal and latitudinal vertical cross sections. CSME cores maintain a near-zero current magnitude. In both regions, maximum current magnitude occurs at the ocean surface near one radius, after which current magnitude decreases both radially and with depth. Small-scale vorticity is contoured in black in Figure 12, revealing the cone-shaped vortical structure of CSMEs. The small-scale vorticity contour is used here as an indicator of how far CSMEs extend throughout the water column. A threshold vorticity value of 1 s⁻¹ is used to define the CSME bottom depths in accordance with the SME identification criterion defined in Section 2.2. The regional composite CSME bottom depth value is noted by a red dashed line and the regional composite MLD is noted by a solid green line in Figure 12. The composite CSMEs are shown to extend well past the mixed layer with eddy bottom depths of 97.5 m (KC) and 77.5 m (OW) occurring at 2.8 (KC) and 2.0 (OW) times the mean core composite MLDs.

Figure 13a shows the daily mean core MLD values, along with the daily mean CSME bottom depths, while Figure 13b shows the ratio of the two for each region. The CSME bottom depths change more rapidly throughout the summer months compared to MLD (Figure 13) with a maximum bottom-to-MLD ratio also occurring in the summer months for both regions when the MLD is at its minimum. This trend reflects the tendency of CSME properties to shrink towards the surface as the MLD becomes shallow and more stratified. Though MLDs are slightly deeper in the OW CSME cores, the KC region CSMEs maintain deeper bottom depths throughout the year, owing to the greater horizontal current velocities within the KC region which propagate further into the water column of CSMEs.

3.2.2. Temperature and Salinity

Vertical cross sections of the 12-month composite CSME small-scale temperature are shown with density contours in Figure 14. While CSME currents (Figure 12) are greatest in magnitude at the surface, subsurface temperature patterns reveal a symmetric profile with colder and denser water located below the MLDs but above the CSME bottom depths. In the horizontal direction, the drastic horizontal change in both temperature and density indicates strong baroclinicity propagating well beyond the mixed layer. Vertical cross sections of the 12-month composite CSME small-scale salinity are shown in Figure 15, along with density contours. At depth, temperature has a much greater influence on the density profile than salinity does. The composite CSME salinity profiles roughly follow the patterns seen in temperature, showing a diffuse structure of positive salinity extending below the bottom depths along the CSME cores.

We can use extrema values as a reference to better understand the extent of influence CSMEs have within the upper ocean. Extrema values are calculated as the minimum temperature, minimum salinity, or maximum density along the CSME column located horizontally within one radius. CSME small-scale temperature extrema exist on average at 2.4 (KC) and 2.0 (OW) times the MLD and density extrema exist at 2.0 (KC) and 1.7 (OW) times the MLD. These results are comparable to the approximate small-scale temperature extrema depth to MLD ratio of 2 reported by [14]. The composite small-scale salinity extrema exist closer to the MLD in the KC region (1.3 times the MLD) than in OW (2.1 times the MLD), in which the composite salinity extrema exist below the CSME bottom depth. The seasonal trends in temperature and salinity extrema values in relation to the surface values and depths in relation to the MLDs are illustrated for both regions in Figure 16. The temperature extrema tend to be colder relative to the surface throughout the year (Figure 16a), though outliers exist in mid-summer in the OW region due to the warm SST anomalies mentioned in Section 3.1.2. The CSME salinity extrema are closer to the surface salinity values throughout the warmer months, coinciding with the extrema occurring deeper relative to the MLD in both regions.

3.2.3. Divergence and Vertical Motion

Vertical cross sections of the 12-month composite CSME small-scale divergence are shown with vertical velocity contours in Figure 17. A dipolar pattern of positive and negative small-scale divergence exists at the surface as discussed in Section 3.1.3. Below the surface, throughout the mixed layer, divergence dominates the CSME core within the mixed layer in both regions. The divergence within the CSME core is at a maximum at 15.2 m in KC and 13.7 m in OW, before diminishing in strength with depth and shifting to convergence dominating below the MLD.

As discussed, the presence of divergence is a signature of ageostrophic motion and subsequently vertical motion. This resulting vertical motion is evident in the CSME small-scale vertical velocity, shown with red (upward velocity) and blue (downward velocity) contours in Figure 17. Within the CSME cores in both regions, upward vertical motion dominates throughout the eddy core. The strength of upward vertical motion is greater in the KC CSMEs cores, which also show stronger divergence. Though the divergence pattern throughout the eddy cores shows convergence below the MLD and divergence within the mixed layer, the vertical velocity remains positive.

To quantify the at-depth strength of vertical motion, Figure 18 shows the vertical current magnitude extrema profiles within the CSME cores. In the KC region, the core CSME maximum and minimum vertical current magnitudes of 19.2 m/day and −11.8 m/day appear below the MLDs (but above the CSME bottom depths) at 57.7 m and 53.5 m, respectively. The OW region maximum vertical current magnitude of 9.3 m/day appears below both the MLD and CSME bottom depth, at 157 m depth. However, the OW minimum vertical current magnitude profile has two comparable local maxima: one located above the MLD with a value of −6.5 m/day at 26.2 m and another value of −6.5 m/day at 168.3 m. These results further reflect a significant difference between the two distinct ocean environments we have distinguished for analysis. Furthermore, these profiles reveal the far-reaching impacts of CSMEs on vertical motion, which extend well beyond the CSME bottom depths.

4. Summary and Conclusions

Using the output from a year-long high-resolution ocean model simulation, submesoscale eddies were detected and analyzed within two distinct geographic regions in the Western Pacific Ocean: the Kuroshio Current region and the open water region. The distinction between these regions is necessary, as the SME dynamics differ dramatically. The KC region includes fast-flowing currents and topographically influenced areas, while the OW region includes generally slower currents and is largely unaffected by bottom effects due to the deeper water column. Within this study, cyclonic SMEs were targeted due to their dominance over anticyclonic SMEs.

One particularly novel aspect of this study is the determination of the 12-month CSME composite eddy parameters not only at the surface, but also throughout the upper ocean. By doing this for both the KC region and the OW region, a robust evaluation and comparison of the differences between the typical CSME structure and attributes identified within each region can be performed. Key findings of CSMEs within this study include the following.

• The counterclockwise flow and positive vorticity of CSMEs in the KC region are faster and stronger compared to those in the OW region. These current trends also lead to the vertical extent of the CSMEs, based on a vorticity threshold of 1 s⁻¹, to be deeper in the KC region despite the shallower MLD. Composite CSME bottom depths are found at 2.8 times the mean core composite MLDs in the KC region and at 2.0 times the mean core composite MLDs in the OW region. Seasonally, the eddy bottom depths follow the MLD trends, with shoaling in the summer and deepening in the winter.
• Surface ageostrophic currents, found to be flowing in the opposite direction of the geostrophic currents, within the CSMEs lead to a dipole divergence pattern, with divergence in the KC region having stronger magnitudes compared to the OW region. Ageostrophy dominates more in the KC region, where the composite CSME core deviates 48% from geostrophic balance, while the OW region composite CSME core shows a 40% deviation from geostrophic balance. Divergence dominates the eddy core throughout the mixed layer, with a switch to convergence below the MLD. The divergence pattern leads to upward vertical motion within the eddy core throughout the upper ocean. Maximum vertical velocities of 19.2 m day⁻¹ and 9.3 m day⁻¹ were found at 57.7 m and 157.1 m depth for the KC and OW regions, respectively.
• Following from the upward vertical motion within the CSME, the CSMEs have cold cores with increased salinity and density. The small-scale temperature, salinity, and density mean extrema values are found below the MLD at 62.2 m, 46.0 m, and 57.5 m for the KC region and 50.0 m, 57.5 m, 49.7 m for the OW region. The density patterns closely follow the temperature patterns, indicating strong baroclinic behavior within the CSMEs that extends well past both the MLD and the defined eddy bottom depths.

With the CSME structure and attributes discussed throughout this study, it is expected for these eddies to have substantial impacts on the surrounding ocean environment not only in the vicinity of strong boundary currents, but throughout the global ocean. While the magnitudes of the parameters discussed are generally larger in the KC region compared to the OW region, the influence of the typical CSME in the OW region is not insignificant. Future work related to this study includes evaluating CSME influences on ocean features and phenomena such as vertical heat and fluxes, stratification, acoustic parameters, and energy budgets. The three-dimensional nature of these phenomena, in particular, warrants deeper investigation in future work. Additionally, influences and feedback mechanisms between the SMEs and the atmosphere should be examined. As part of future work, the horizontal resolution and mixing scheme of the model must also be considered. Particularly in the summer when the MLD shoals, it is expected that many SMEs exist below the detection limit of what is used in this study.

In summary, we have addressed both the 12-month mean and seasonal behavior of CSMEs, showing a strong ageostrophic influence, upward vertical motion, and baroclinic structure. Furthermore, we have shown how regional flow-field attributes affect the small-scale parameters of current, divergence, SSH anomalies, temperature, salinity, and density. The composites discussed here represent the typical CSME found close to a boundary current region, as well as the typical CSME found in the open water. As such, the results presented are expected to be germane to regions outside of the Western Pacific Ocean as well.