Mesoscale eddies, as a ubiquitous phenomenon in the ocean, play a critical role in the transport of heat, salt, and nutrients in the ocean (Huang et al., 2012; Munk, 2001; Zhang et al., 2016). Studies have demonstrated that mesoscale eddies can lead to anomalous upward heat fluxes (Klein and Lapeyre, 2009; McWilliams et al., 2009; Su et al., 2018), control the nutrient budget, and enhance the primary production in the euphoric layer (Dandapat and Chakraborty, 2016; Zhang and Qiu, 2020). Microwave remote sensing is an essential means of ocean eddy detection, using altimeters to track and observe eddies. With the development of satellite observations, mesoscale eddies with horizontal scales above one hundred kilometers have been solved by traditional altimeters (Chen et al., 2020; Li et al., 2019b; Zhang et al., 2014). However, to date, only sea surface height (SSH) along the satellite orbits has been measured by nadir altimeters, and there are wide gaps between two tracks, which causes the altimeters to limit the spatial resolution of sea surface topography to exceed 100 km (Gaultier et al., 2016). Therefore, a significant part of the mesoscale dynamic process with a scale below 100 km is difficult to characterize by traditional altimeters (Durand et al., 2010; Trott et al., 2019). In the literature, eddies are named in terms of their dynamic or morphological properties. The baroclinic Rossby deformation radius is a dividing line for oceanographers to define mesoscale and submesoscale eddies (Alpers et al., 2013; Zhang et al., 2019a). However, it depends on latitude and oceanographic parameters, which do not have fixed values. Therefore, in this paper, we call eddies with scales below 100 km smaller mesoscale eddies (SMEs) according to the observation limitation of altimeters (Trott et al., 2019), although some literature called them submesoscale eddies (Fu and Le Traon, 2006). Based on the conclusion that mesoscale eddies with smaller sizes have a larger number (Zheng et al., 2015), there are abundant SMEs in the ocean, although altimeters do not accurately observe them. Observations of SMEs are helpful to understand the energy and material transfer from mesoscale eddies to submesoscale eddies and make up for the cognitive gaps in the limitation of traditional altimeters.

The application of satellite altimeters in the field of eddy observation is entering a platform stage. Infrared remote sensing and ocean color remote sensing have attracted much attention due to their advantages in smaller-scale observation. Eddies drive local water upwelling (cyclones) or downwelling (anticyclones) and leave signals on the SST field as cold (warm) features (Dong et al., 2011), which can be monitored by infrared remote sensing. SST maps with high spatial resolution are ideal for researching smaller mesoscale eddies (Gula et al., 2015; Qiu and Chen, 2005). Tedesco et al. (2019) proved that barotropic instability is a generation mechanism of smaller mesoscale eddies by using a numerical model and SST map; the generation process was marked by the transmission of kinetic energy from the mean flow to an eddy. Furthermore, sea surface temperature anomaly (SSTA) data can eliminate the effect of background flow in the sea surface on eddy detection. The study proves that the location of the SSTA is identical to sea surface height anomalies induced by eddies (Sun et al., 2016). To date, automatic algorithms based on SST images have been applied to observe and identify eddies (Dong et al., 2011). However, sea surface temperature (SST) is affected by solar radiation and heat exchange between the ocean and atmosphere, which is susceptible to the environment. Hence, the algorithm based on SST probably has noticeable noise. Ocean color remote sensing based on the principle of substance tracing provides a different view to observe and characterize SMEs. Eddies, which have a strong ability to carry and transport substances, not only cause SSH and SST anomalies but also lead to different chlorophyll concentrations (Chls) in the upper ocean. The linkage between mesoscale eddies and Chl a has been studied, cyclonic eddies might have a profound influence on the mesoscale variability in Chl a (Chelton et al., 2011; Shafeeque et al., 2021). Studies have found that upwelling caused by the vertical movement of cyclones can bring nutrients and increase biological productivity and chlorophyll concentration at the sea surface (McGillicuddy, 2016; Williams, 2011); conversely, anticyclones cause chlorophyll concentration to fall (Yang et al., 2020). In summary, SST and Chl anomalies are utilizable indicators to manifest the signal of smaller mesoscale eddies on the sea surface (Alpers et al., 2013; Zatsepin et al., 2019). The fusion of SSTA and Chl maps is a beneficial attempt to improve the reliability of eddy identification results by dual authentication.

In this paper, an eddy detection algorithm by fusing satellite infrared remote sensing and ocean color remote sensing was proposed to provide the possibility of SME observations. Subsequently, the algorithm was implemented in the Kuroshio Extension (KE, 28°–40°N, 138°–180°E) region. The KE is a strong eastward western boundary current extension formed by the Kuroshio separating from the coast of Japan (Qiu et al., 1991; Wang et al., 2020) and is recognized as an ocean current system with large amplitude meanders (Yasuda et al., 1992) (Fig. 1). The KE has the highest number of eddies of various scales in the North Pacific (Sasai et al., 2010). Eddy interactions are significant in modulating the decadal variability of the Kuroshio Extension System (Jia et al., 2019; Qiu and Chen, 2010) and affecting biogeochemical processes in the upper ocean (Uchiyama et al., 2017). Therefore, the KE is ideal for carrying out our algorithm. Recently, scientific discussions have shifted studies of mesoscale eddies to smaller mesoscale eddies, especially their generation. In the KE, Ji et al. (2018) characterized the spatial and temporal distribution of mesoscale eddies and suggested a role of horizontal shear instability in eddy generation based on Argo floats and ocean general circulation model for the Earth Simulation numerical model data. Luo et al. (2020) described that the smaller mesoscale flows on the edge of eddies have a close relationship with the frontal sharpening initiated by the mesoscale strain in the KE. Moreover, the spatial structure and temporal variation in vortices generated by the interaction between the Kuroshio and island obstacles were shown (Hsu et al., 2020; Isoguchi et al., 2009). However, these studies on smaller mesoscale eddies depend on numerical models or in-situ data, remote sensing observation of SMEs in the KE is needed.

The remainder of this paper is organized as follows. In Sections 2 and 3, a brief description of the data and method is given. Section 4 contributes to expressing the statistical results of SMEs from applying the algorithm in the KE. Simple spatial and temporal distributions and analyses of the generation of SMEs are carried out. Section 5 summarizes and discusses the method and results.

Eddy can be defined as the rotational motion of the fluid mass, in which the velocity field is represented as a rotating flow. The rotating direction of the velocity vector can be clockwise or counterclockwise. SST data can be convoluted with the Sobel operator to obtain the thermal-wind velocity (V) for eddy detection. And, the vertical movement of SMEs contributes to variations in chlorophyll concentrations. Thus, based on the effect of eddies on SSTAs and chlorophyll a concentrations, a fusion algorithm incorporating Chl based on SST is used to identify SMEs. The basic idea of the algorithm is to extract eddy features from SST and Chl images respectively, and then detect eddies both in information derived from SST and Chl data.

There are four main steps: (1) data preprocessing; (2) eddy feature extraction; (3) tracking; (4) credibility assessment (Fig. 2).

Step 1: data preprocessing. The SSTA data are calculated by original SST grid data from REMSS (SSTA=SST− $ {\mathrm{S}\mathrm{S}\mathrm{T}}_{\mathrm{a}\mathrm{v}\mathrm{g}} $; $ {\mathrm{S}\mathrm{S}\mathrm{T}}_{\mathrm{a}\mathrm{v}\mathrm{g}} $ is the daily climate average of the SST, which is calculated by the daily SST data from January 1, 2011 to December 31, 2018). Gaussian smoothing is used to smooth SSTA and Chl data for reducing the noise of the original images. A Sobel gradient operator is then implemented to convolute SSTA data to obtain the thermal-wind velocity. The operation uses two 3×3 kernels to compute approximations of spatial derivatives (${{{\boldsymbol{G}}}}_{{y}}$ and ${{{\boldsymbol{G}}}}_{{x}})$ of SSTA and Chl:

where x and y are the coordinate axes for space and correspond to the measurements to the east and north, respectively; * represents the 2-D convolution operation; A means the matrix extracted from the SSTA and Chl grid data; ${{{\boldsymbol{G}}}}_{{x}}$ and ${{{\boldsymbol{G}}}}_{{y}}$ represent two approximations of the zonal and meridional derivatives for each point, respectively (${{{\boldsymbol{G}}}}_{{x}\text{-}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{a}}$ and ${{{\boldsymbol{G}}}}_{{y}\text{-}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{a}}$ derived from SSTA images, ${{{\boldsymbol{G}}}}_{{x}\text{-}\mathrm{c}\mathrm{h}\mathrm{l}}$ and ${{{\boldsymbol{G}}}}_{{y}\text{-}\mathrm{c}\mathrm{h}\mathrm{l}}$ derived from Chl images).

The thermal-wind velocity is obtained by the vector corresponding to the baroclinic velocity component contributed by the temperature based on the thermal-wind relationship and the first-order (linear) water state equation (Dong et al., 2011). To ensure that V has the correct rotating direction on both hemispheres, the V derived from SSTA images is defined as (${-{{\boldsymbol{G}}}}_{{x}\text{-}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{a}}$, ${{{\boldsymbol{G}}}}_{{y}\text{-}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{a}})$ in the Northern Hemisphere and (${{{\boldsymbol{G}}}}_{{x}\text{-}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{a}}$, ${{{\boldsymbol{G}}}}_{{y}\text{-}\mathrm{s}\mathrm{s}\mathrm{t}\mathrm{a}})$ in the Southern hemisphere. The gradient amplitude $\mathrm{\Delta }{f}$ was calculated by

Step 2: eddy feature extraction. Nencioli et al. (2010) proposed a vector-geometry eddy detection algorithm that can identify eddies from any velocity field because it is entirely based on the geometry of the flow field. Dong et al. (2011) applied this scheme to detect eddies based on thermal-wind velocity derived from SST data in the KE region. Referring to the vector-geometry algorithm, we fused the judgment of SST and Chl abnormal areas to identify SMEs, which characterized eddies by the following conditions.

Check each grid point for detecting eddy centers: (1) the eddy center is the local maximum (anticyclone) or minimum (cyclone) in a 5×5 neighborhood grid on the SSTA and Chl gradient amplitude; (2) around the eddy center, the direction of V has to change with a constant sense of rotation, and the components of V have to reverse in sign across the eddy center along with the zonal and meridional directions.

Detect eddy shapes once eddy centers are determined: (1) the eddy shape is the maximum gradient amplitude contour around the eddy center on the SSTA and Chl maps; (2) the SSTA and Chl gradient values gradually increase from the eddy center to the eddy shape. Cyclones manifest closed-contour negative SSTA, anticlockwise rotation, and positive Chl. Anticyclones manifest closed-contour positive SSTA and clockwise rotation.

The eddy features satisfying the above conditions are extracted from SST and Chl data respectively. Figure 3 shows examples of the V derived for a cold and a warm SME in the KE, which indicates how eddies are identified from SSTA. Figure 4 shows an example of SME identification from SST and Chl data over a wide area (28°–40°N, 138°–160°E). It can be seen that the algorithm is feasible to identify eddies by extracting SSTA and chlorophyll concentration anomaly. Moreover, Chl data with high spatial resolution help to identify smaller-scale eddies ignored by SST to some extent.

Step 3: tracking. An eddy tracking algorithm proposed by Dong et al. (2011) is used to track eddies. In summary, eddy tracks are determined by comparing the centers of the same type at successive time steps. The track of an eddy is updated by searching for eddy centers at time t+1 within a searching area of N×N grid points centered around the eddy location at time t. To avoid dividing a successive track into multiple tracks, eddies cannot be captured outside the searching area from time t to time t+1. Depending on the spatial and temporal resolution of the dataset, as well as the characteristics of the mean flow field, the size of the searching area is determined. Because the moving speed of eddies that are advected by the local flow is approximately on a scale of 10 cm/s and the temporal sampling frequency of our data is daily, the search radius is built as 15 km (Dong et al., 2011).

According to the tracking algorithm, the lifetime of eddies can be obtained. Considering the SST data are easily affected by complicated signals from the environment, we filter out eddies with lifetimes less than two days to reduce the impact of SST variability resulting from uncertain factors.

Step 4: credibility assessment. To obtain more accurate detection results, a parameter (P) was established to measure anomalies on a time scale, comparing the anomalies recorded in given months over the years (2011–2018). The higher the value, the more reliable the result is.

To calculate the parameter, a 0.1°×0.1° grids is first built, where grid dots within eddy shapes derived from SST or Chl are marked as 1, eddy shapes derived both from SST and Chl are marked as 2, and those without eddy shapes are marked as 0 (Figs 5a, b). The parameter$ \left(P\right) $ calculated at grid dots is defined as follows:

where i, j represent the row and column number of grids, respectively; $ {P}_{(i,j)} $ is the probability that there is an eddy at pixel (i, j); ${P}_{\mathrm{SSTA}(i,j)}$ and ${P}_{\mathrm{Chl}(i,j)}$ are the probabilities calculated based on the SSTA and Chl maps. The ${P}_{\mathrm{Chl}(i,j)}$ is calculated by the following equations,

where ${\mathrm{C}\mathrm{h}\mathrm{l}}_{\mathrm{s}\left({i},{j}\right)}$ represents the sum of chlorophyll concentration value (${\mathrm{C}\mathrm{h}\mathrm{l}}_{({i},{j})}$) dataset from the chlorophyll value of the month over the years in pixel (i, j) (y equals the number of years that we use to calculate the monthly average Chl and d equals the number of days in the month);$\overline{{\mathrm{C}\mathrm{h}\mathrm{l}}_{\mathrm{s}\left({i},{j}\right)}}$ represents the monthly average of ${\mathrm{C}\mathrm{h}\mathrm{l}}_{\mathrm{s}({i},{j})}$ over the years; and ${\mathrm{C}\mathrm{h}\mathrm{l}}_{\mathrm{d}({i},{j})}$ is the chlorophyll value on the day that the eddy is identified. Similarly, ${{P}}_{\mathrm{S}\mathrm{S}\mathrm{T}\mathrm{A}({i},{j})}$ is calculated by the same formula.

$ \alpha $ and $ \beta $ represent the empirical weight coefficients of SSTA and Chl for the eddy, respectively. There is a significant correction (approximately 0.5–0.7) between the mesoscale variability of Chl and SST and the influence of eddies (Shafeeque et al., 2021). The accuracy of the algorithm based on the SSTA is discussed by comparison with a 10-year global mesoscale eddy dataset based on SLA in the KE. The results indicated that true eddies account for more than 70% of the total number of detected eddies (Qian et al., 2021). For these reasons, the empirical value α is set to 0.7, and β is 0.3 in the KE accordingly. The two parameters give flexibility to the algorithm, which can be adjusted appropriately.

The algorithm filters eddies by detecting the P-value both in the eddy shapes derived from SST and Chl. Theoretically, the higher the P-value is, the more likely the detected result is an eddy and the more accurate the algorithm. To objectively assess the algorithm accuracy, a validation area (28°–33°N, 148°–153°E) is built. SMEs with different values of P are evaluated on a random basis for 12 days (one day per month) in the area. For these days, detection accuracy (DA) is defined as the number of true eddies (Nt) detected by the algorithm divided by the total number of eddies (N). True eddies are manually detected according to the eddy definition as a selection criterion. Table 1 shows the DA results in the 12 maps selected for validation. Accordingly, a high DA value (90%; P≈0.7) is selected to obtain a credible result. As long as there is one point in the eddy where P-value satisfies the condition, the eddy will be taken as the final result (Fig. 5d). The information (shapes and centers) of eddies is mainly determined by the SST when there is a spatial divergence between SST and Chl.

According to the detection algorithm, SMEs were detected, including their centers, shapes, types, sizes, and lifetimes. The size of SME is defined as the radius of the circle that has the same area as the region with the shape.

Microwave remote sensing is entering a platform stage in the field of eddy observation. Infrared remote sensing and ocean color remote sensing instead of traditional altimeters provide potential feasibility to characterize SMEs because of their advantage of high accuracy and resolution. A detection algorithm that allows identifying eddies on the base of satellite SST and Chl data is presented. Eddies are extracted depending on their characteristics in the temporal and spatial distribution of SST and Chl anomaly. The algorithm was applied to a high-eddy-activity zone, the Kuroshio Extension. Further, the distribution and generation of SMEs in the KE were observed and analyzed by combining altimetry, drifter, and wind data.

The distribution of SMEs shows obvious seasonal variations, and the SMEs tend to be distributed on both sides of the KC spindle. Three types of SME formation are successfully observed based on the eddy detection method. Typical examples are shown in the previous section. According to observations, SMEs always form on the edge of mesoscale eddies due to horizontal strain instability, mainly located near the meandering current of the KC. SMEs are always encountered on the Japanese coast, restricted by the geographic distribution. Atmospheric forces, especially wind, maybe important influencing factors causing the formation of SMEs.

The algorithm is capable of providing a method for SME identification, and it also has weaknesses. The weight coefficient between SST and Chl in the algorithm needs to be further studied by exploring the quantitative effects of SST and Chl on SMEs or optimizing by deep learning. Moreover, a strict assessment condition is established to identify eddies as accurately as possible, which might prevent some eddies from being observed. Ideally, the ultimate goal is to identify all oceanic eddies with satisfactory accuracy. In reality, it can never be realized but can gradually be approached. With the advent of ocean radar satellites, upcoming wide-swath interferometric altimeters (such as “SWOT”, Surface Water and Ocean Topography, and “Guanlan”) will hopefully characterize the sea surface height at smaller scales that have never been resolved before (Chen et al., 2019; Durand et al., 2010). In the future, we hope to couple the new-generation interferometric altimeters to optimize the detection algorithm and realize more accurate observations of smaller mesoscale eddies.