We focus on a joint region of Northeast Indian Ocean−South China Sea−Northwest Pacific Ocean (0°–40°N, 70°–140°E; see Fig. 2), where profiling floats have been deployed more than 500 since the last two decades (Liu et al., 2023). The local circulations in this region are complex and variable. Multiple equatorial currents and western boundary currents play key roles in the latitudinal and longitudinal heat, mass transport and the exchange process between Pacific−Indian Ocean basins and hemispheres, directly affecting and modulating the variation of the intersection area and local ocean-atmosphere interactions. Besides, the above region directly links the four gyres of the Indo−Pacific low-latitude basin, including the North Pacific Tropical Gyre (NPTG; Wijffels et al., 1998), the South Pacific Tropical Gyre (SPTG; Roemmich et al., 2007), the South China Sea Gyre (SCSG; Shaw et al., 1999; Liu et al., 2008), and the Indian Ocean Tropical Gyre (IOTG; Du et al., 2019; Wu et al., 2020).

To simulate mesoscale motions of profiling floats within the region, we use ECCO2 velocity field (available at http://ecco2.org/; see Menemenlis et al., 2005) configured for the Pacific Ocean-the South China Sea-North Indian Ocean. ECCO2 is an assimilating version of the MIT General Circulation Model (MITgcm). We use the “Cube 92” solution, which is run on a “cubed sphere” with 18-km (eddy permitting) horizontal grid spacing and 50 vertical levels unevenly distributed between the surface and 6000 m (Menemenlis et al., 2008). ECCO2 was optimized via Green’s function methodology (Menemenlis et al., 2005) to best represent observed hydrography. ECCO2 fields do not resolve high-frequency or high-wavenumber dynamics, and simulated floats will not be influenced by processes that ECCO2 does not resolve. For the analysis, we use archived 3-day average ECCO2 fields that have been interpolated to a regular 0.25° × 0.25° grid.

The comparison of ECCO2 sea surface height (SSH) field to the AVISO-mapped satellite altimetry product gives a qualitative assessment of the surface circulation and its variability during the float simulation period (January 1, 2015 to December 31, 2022). As an example of the South China Sea and the West Pacific, the mean sea surface height of the inner region of the South China Sea and the Luzon Strait depicted by the ECCO2 model is basically consistent with the observation from the AVISO satellite (as shown in Figs 3a and b), which is characterized by low values in the northern part of the South China Sea and high values in the outer sea of the Luzon Strait, with a value of about 1.1 m. The variance of SSH anomaly also reflects the consistency between ECCO2 and AVISO observations, with the maximum value (about 0.2 m) appearing in the middle of the South China Sea and the Kuroshio pathway. In addition, the vertical dynamic process depicted by the ECCO2 model is also close to the observation. Taking the vertical temperature and salinity change characteristics of the Luzon Strait as an example, both the ECCO2 model and Argo profile observation can depict the intrusion process of the Kuroshio water (Figures not shown), and the core of the intrusion of the high-salinity Kuroshio water is 100–200 m, which is consistent with the basic observational facts. The standard deviation (STD) of the two SSH products shows a similar structure (Figs 3c and d). High variance occurs in the middle of South China Sea, the Kuroshio pathway. Like the mean, the structure is patchy as a result of the relative brevity of the time series. Despite variability differences at specific locations, both the model and the AVISO product have roughly equal levels of SSH variability.

Float trajectories are simulated using an Argo module of the offline particle tracking model Octopus (http://github.com/jinbow/Octopus/; see e.g., Tamsitt et al., 2017; van Sebille et al., 2018; Wang et al., 2018, 2020, 2021). The model integrates float trajectories using daily average horizontal velocities from the (1/4)°–resolution model and vertical velocities derived from real Argo floats. Float trajectories are integrated via a Lagrangian advection scheme: $ {{\partial {{\boldsymbol{X}}_{\boldsymbol{i}}}} /{\partial t}}{{ = }}{{\boldsymbol{V}}_{\boldsymbol{i}}} $, where X_i is the (vector) position of the i-th particle, t is the time and V_i is the velocity vector mapped to the numerical float position using three-dimensional linear interpolation. In addition to the model velocities, Octopus Lagrangian tracking model also includes a stochastic velocity component to account for the float displacement caused by processes (such as turbulence) that are unresolved by the ECCO2 model. The subgrid-scale processes are parameterized by $ {{\Delta }}{{\boldsymbol{X}}_{{i}}} = \sqrt {2{\boldsymbol{K}}\delta t}\; \omega (t) $, where K represents the diffusivity tensor $ ({K_x},{K_y},{K_z}) $, $ \omega $ represents a Wiener process (stochastic random walk displacements) with unit variance, and $ \delta t $ denotes the time step for the Lagrangian integration (e.g., van Sebille et al., 2018). The particle trajectory in discrete form becomes

where n represents the time step number. In practice, the random number generator should be carefully chosen, because not all numbers are suitable for use in random walk models (Hunter et al., 1993). Here we implement the normal random number generator algorithm described by Kinderman and Monahan (1977), with a horizontal diffusivity of 1 m²/s, which is consistent with the diffusivities of the ECCO2 dataset.

Simulated profiling floats are configured to follow the same cycle as the real Argo floats, as defined in Fig. 4, including an initial descent to 1 000 m, parking time at 1 000 m, a further descent to 2 000 m, then ascent from 2 000 m depth to the surface, and finally an interval of time at the ocean surface to transmit data via satellite. For the period from 2015 to 2022, cycle timings for the delayed-mode BD float data were obtained from the observation and research station of global ocean Argo system (Hangzhou) (ftp://ftp.argo.org.cn/pub/ARGO/china/) within the research basin. Ocean currents are nonuniform in the vertical, which affects the true trajectories and how we interpret float displacements.

Simulation of profiling floats (parking at 1 000 m depth) trajectory requires parameterization of Argo based on observation data, including Argo working cycle time, vertical ascent/descent rate and float deployment scheme (including deployment position, scale and deployment time of virtual floats). By taking each variable as the initial condition of virtual floats, the Lagrangian tracking algorithm can be used to calculate and output the three-dimensional position of virtual float in the background model flow field. The Argo parameters configured in this work are shown in Fig. 4, including surface drifting, descending, parking, ascending and surface stages. In the simulation, the time of each stage is selected according to Table 1, and the single working cycle is about 5 d. All the Argo clock schedules are configured to approximate an “average” float, with cycle times and parking depths representing the weighted average of cycle times.

In December 2020, China designed a special project from which about 500 profiling floats were deployed across the Northwest Pacific, South China Sea, and the Indian Ocean. The majority of these floats were equipped with a communication system covered by Beidou-2 satellites. In order to optimize the float deployment position design, to avoid the float drifting into shallow waters (such as East China Sea) and out of the coverage of Beidou-2 satellite short message, and to ensure the normal working life of the whole fleet, four deployment experiments have been carried out in this work (see the details in Table 2). To maximize the statistical samples using a model of limited duration, we carry out repeated simulated-float releases, separated by time intervals large enough to produce statistically independent trajectories. The autocorrelations of mid-layer velocities (corresponding to core Argo floats) imply that the decorrelation time scales are about 5 d (Wang et al., 2018). The simulated floats are thus released at 30-day intervals starting on Day 1, and with the last release on Day 2791. Thus, there are at most 94 independent release times during the 8-year (January 1, 2015 to December 31, 2022) of the model run for each releasing experiments.

The marginal seas of China (including the Bohai Sea, Yellow Sea, East China Sea, and South China Sea) are all affected by the Kuroshio and its branches. The range of Kuroshio intrusion into the East China Sea shelf in different seasons is different, and it has obvious seasonal characteristics. Although the Kuroshio water constitutes a transport channel for material from east of the Luzon Strait to the East China Sea, the shallow water depth of the East China Sea (as shown in Fig. 2) hinders the entry of profiling floats which drift in the middle layer (1000 m). However, historically, some floats deployed east of the Luzon Strait and Taiwan Island (20°–28°N, 122°–127°E) had entered the East China Sea following Kuroshio and beached on the continental shelf. Therefore, the possibility of floats released east of the Luzon Strait drifting into the East China Sea should be investigated. In this section, the deployment region of the simulated floats is 20°–28°N, 122°–127°E, (as shown in Fig. 2, also see Table 2), and the grid setting is 0.5° × 0.4° with a single deployment of 100 floats. We select the floats deployed in August of each year in the overall simulation experiment (the deployment time of floats in the observational condition is August 2021), and the total number of deployments is 8 times.

Simulation results showed that under the influence of the South China Sea summer circulations and Kuroshio, the overall flow direction of simulated float trajectories deployed in August in recent years is northeastward (shown in Fig. 5). The number of simulated floats entering the East China Sea is very small (only 3 from 800), and the spilling effect is not significant, so it can be expected that the floats deployed in Luzon Strait will only have a small probability of entering the East China Sea under the influence of the ambient currents, which is consistent with theoretical deduction.

It should be noted that the above conclusions rely on the accuracy of the float simulation system and the model flow field (ECCO2). Due to the relatively poor simulation performance of ECCO2 in the nearshore area, discrepancies between the simulated float trajectories with observations may occur. In addition, a random motion module is an important component in the Octopus Lagrangian tracking model, which the subgrid random motion is used to present the mixing process caused by Brownian motion ($ {{\Delta }}{{\boldsymbol{X}}_{{i}}} = \sqrt {2{\boldsymbol{K}}\delta t}\; \omega (t) $, see details in Section 2.2). In the model, the horizontal diffusion coefficient (K) determines the strength of random motion, with the larger diffusion coefficient, the stronger the stochastic random walk displacements ($ { {\Delta {\boldsymbol{X}}}} $). In the float simulation system, the horizontal diffusivity coefficient is set to 1 m²/s, consistent with the background flow field. However, according to Batchelor (1952) theory, turbulent mixing leads to gradually separation of two adjacent fluid particles in the drifting process, which means that the random module would cause system uncertainty in the process of stepwise integration calculation of profiling floats position, and the uncertainty would increase with time. When the background flow field is added, this system uncertainty will be further amplified by the advection effect.

The Kuroshio is the main flow in this domain and worthy of further research. We thus select the floats trapped in the Kuroshio to assess its impact on their drift trajectory by analyzing statistical data. By analyzing the experimental results of Exp_1, we find a total of 32 sets of floats within the Kuroshio axis with a velocity exceeding 20 cm/s, which translates to 32 times 10 buoys. We select this part of the floats and mapped out their drift trajectories (shown in Fig. 6). During the simulation duration, approximately 2/3 (207) of the floats move northward along the strong front of the Kuroshio, while the remaining floats are trapped at the Luzon Strait. By calculating the drift distances of the floats, it is shown that the floats that remain on the Kuroshio axis have a significantly longer average drift distance, averaging 1090 km within 300 d, while the floats that are not on the Kuroshio axis have an average drift distance of only about 254 km within the same time period.

The Philippine Sea lies to the east and north of the Philippine Archipelago in the western North Pacific Ocean. The deepest part of the shelf is over 2500 m and it is the most important pathway for water and heat-salt exchange between the South China Sea and the western Pacific Ocean. When the Kuroshio flows northward along the Philippine Archipelago, passing the east side of the Luzon Strait, two typical paths of motion are often formed: one is a non-invasive direct crossing of the Luzon Strait to the north; the other is a westward intrusion to the South China Sea. Therefore, the complicated oceanic circulations in the Philippine Sea and the changes of west boundary currents of Pacific such as Kuroshio and Ryukyu currents at the Luzon Strait will have a strong influence on the float drifting in this area. This is manifested in the overall clockwise motion of the floats under the influence of the subtropical gyre in the North Pacific, as well as the intrusion of the Kuroshio into the South China Sea caused by meso-scale processes and to a certain extent, the intrusion of some floats into the East China Sea. Based on the simulation in Section 3.1, the releasing boundary was expanded to the Philippine Sea (8°–25°N, 127°–135°E), the simulated trajectory time length extended to 400 d (see more details in Table 2). The aim of this section is to discuss the drifting characteristics of float drifting in the Philippine Sea under the influence of Kuroshio and Ryukyu currents. Meanwhile, the coverage range of Beidou Satellite is proposed to be 5°–55°N and 70°–140°E. We will discuss the approximate time and location that simulated floats, which are operating in the Philippine Sea, drift out of the Beidou coverage range.

As illustrated by the simulation results in Figs 7 and 8, with the advection of the Philippine Ocean currents, some floats released in August of each year can drift off Beidou coverage range through the eastern and southern boundaries. For example, in the 300 d simulation (Exp_2; see details in Table 2), out of the total 800 floats (100 floats × 8 groups), approximately 36 floats crossed out from the eastern boundary of Beidou coverage with a ratio of 4.5%. During the statistics calculation, if the float first breaches the eastern boundary during its operation, we will consider it to have drifted out of the Beidou coverage region and include it in the statistics. These floats mostly concentrated between 7°–21°N and were transported by the eastward zonal jets of the North Pacific (Xia and Du, 2022). The number of floats crossing out from the southern boundary of the Beidou coverage is much smaller, only 13 floats, with a ratio of 1.6%. This is due to the significant northward transport of Kuroshio, which largely prevents the floats from drifting southward. The floats crossing out from the southern boundary may be attributed to the presence of southward compensation currents such as the Mindanao Current, as well as mesoscale processes or diffusion processes. When the simulation was extended to 400 d, the results showed that more floats crossed out from both the eastern and southern boundaries of the Beidou coverage, with the number (ratio) reaching 64 (8%) and 21 (2.6%) respectively. In particular, in the 400-d simulation experiment, floats that are located on the Kuroshio Path will drift out of the Beidou coverage through the east boundary with the transport of Kuroshio Extension (KE) in the latitude range of 30°–34°N. This indicates that, in addition to considering the battery life limitation of the floats, the influence of KE on the float drifts should be taken into account to make sure the floats can operate in the Philippine Sea for more than one year. Therefore, it is suggested to avoid the strong frontal positions of Kuroshio and KE during deployment.

Under the strong seasonal gyre influences in the North Indian Ocean (e.g., Wyrtki, 1973; Swallow, 1984; Wu et al., 2020), there is a certain probability that the floats deployed in the eastern Sri Lanka will drift out of the Beidou coverage range, resulting in communication disconnection. This section is based on the outputs of Exp_3 (see Table 2), mainly discussing the drift trajectory of floats deployed in eastern Sri Lanka (6°–12°N, 83°–90°E) influenced by the North Indian Ocean circulation and the possibility of floats crossing the Beidou coverage area. The simulation results show that the floats deployed in the eastern Sri Lanka were mainly driven by the seasonal circulation of the Bay of Bengal, and most of the floats were still drifting in the Bay of Bengal within 400 d, while a small number of floats crossed the southern boundary of Beidou (as shown in Fig. 9). Due to the larger number of samples in Exp_3 (100 single deployments and 94 times of deployments), the number of floats crossing the southern boundary was much greater than the result of Exp_2. The statistical results show that the number of floats crossing the southern boundary is 743, accounting for 7.9% of the total samples (743/9400). The overall cross-border location of the floats is 73°–91°E, and the maximum probability cross-border location is approximately 81°E. It is inferred that the reason may be that the coastal current is strong due to Sri Lanka shore, resulting in a large amount of water transport, thus carrying more floats.

In this section, the float trajectory simulation system is used to try deploying a synthetic profiling float array with a resolution of 1.5° × 1.5° in joint oceans, namely the East Indian−South China Sea−Northwest Pacific Ocean (5°–40°N, 70°–140°E). This region is generally similar to the location of the present China float network, and performing a preliminary analysis on its Lagrangian trajectories, exploring the effectiveness and the maintenance strategy of subsequent observation networks. In the simulation, the releasing position of the float array is selected in the open oceans with the water depth greater than 1500 m. The initial position of the array is on a 1.5° × 1.5° grid and contains a random deviation less than 1°, which is compared with observation conditions. To ensure an adequate sample size, the deployment strategy of synthetic float array is multiple deployment (totally 23 times), from 2015 to 2020, with an interval of three months (January, April, July, and October) to ensure that the derived float trajectories contain seasonal characteristics (see details in Table 2).

There are 823 effective floats deployment launched in the regions with the maximum depth over than 2000 m (see Table 2). In general, judging from the distribution of the float array, it can be inferred that during the floats’ life span of two years, the 1.5° × 1.5° float array can cover the entire Eastern Indian Ocean, South China Sea and Northwest Pacific region to realize real-time monitoring of the upper ocean in this region. In the North Pacific, the background circulation is stronger than that in other oceans, so the drifting of the floats is more intense and the trajectories are longer, leading to a sparser distribution of float array over time (Fig. 10). It can be inferred that when deploying floats in the North Pacific, the spatial resolution of float array should be increased. For other oceans (e.g., the South China Sea and the Bay of Bengal), due to the strong seasonal circulations, the temporal resolution of the array should be densified, that is, the time interval of floats releasing should be shortened.

Optimization and maintenance of the float array in the western Pacific Ocean−South China Sea−North Indian Ocean should consider not only the working life of the battery (generally 2 years), but also the loss caused by the floats drifting out of the range of Beidou satellite short message coverage. According to the distribution of synthetic float array at different times under the model framework (as shown in Fig. 10), after 90 d of deployment, floats from the North Pacific began to drift out of the Beidou coverage area. At this time, the floats would be driven by the Kuroshio and North Pacific circulations to drift out of the eastern boundary of the Beidou coverage (in agreement with the conclusions of Section 3.1). The number of buoys drifting out from the North Pacific Ocean increases with time. Within 720 d after release, the floats can be driven as far as 165°E by the KE.

Statistics of floats drifting out of the Beidou range are displayed in Fig. 11. The number of floats drifting out of the Beidou coverage increases linearly over time, with approximately 2% (18 ± 3 of totaling 823) in 300 d and 5% (42 ± 6) in 720 d. Due to the limited deployment time of the simulated floats, system errors may contribute to a large level of uncertainty in these statistics. However, the present results suggest that, if losses due to floats drifting out of Beidou coverage are taken into account (not considering the battery power losses), roughly 20 additional floats must be added to the 1.5° float array in order to ensure effective observation during one year of operation, and around 42 buoys for a two-year period.

The overall spread of the float array is a function of the domain size and the flow structure. We quantify the horizontal spreading of the floats using a discretized two-dimensional probability density function (2D-PDF) denoted as $ P(x,y,T,\Delta L) $, where $ x $ and $ y $ indicate geographic coordinates, $ T $ represents the elapsed time, and $ \Delta L $ is the grid size. The 2D-PDF is computed by counting the number of floats within a grid box centered at $ (x,y) $ and normalizing by the total number of floats and grid box area $ {(\Delta L)^2} $ after spreading time $ T $. Thus, for example, $ P\;({x_0},{y_0},{\text{100\;d,}} {\text {1.5°}}) $ = 6 means that six floats can be found within a 1.5° × 1.5° grid box centered at$ ({x_0},{y_0}) $ at 100 d. The PDF of the float array at different times provides predictions of the float positions, indicating if the array is converging or diverging, with higher values indicating a higher likelihood of floats clustering at that position.

The results shown in Fig. 12 indicates that the relatively weak currents in the inner of the Bay of Bengal and the South China Sea, both semi-enclosed basins, result in high PDF values (around 20) at Day 180, Day 360 and Day 720 (23 deployments in total). This indicates that the floats deployed in these locations are not largely dispersed within two years, thus there is no need to supplement additional floats (not considering the power limit). We further analyze the simulation results and find the locations where the number of floats has significantly changed by comparing the numerical difference between the above PDFs, and consider the regions where the floats have obviously decreased as the locations that need to be supplemented for floats deployment in subsequent maintenance work. The result shown in Fig. 13 indicates that the cold colored patches of PDF (representing the net divergence of floats) are mainly distributed in the Philippine Sea. Due to its open shelf-sea boundary, the Philippine Sea is affected by strong western boundary currents, such as the Kuroshio, which leads to a decrease in PDF, indicating the higher dissipation rate of floats in this region, which is in agreement with that in Section 3.2. Therefore, the Philippine Sea should be considered as a priority area for replenishment of floats in the float array.

In addition, the positions where PDF changes greatly also exist in the boundary currents and monsoon currents. In the strong front system, floats are usually transported downstream very quickly due to the driving force of intense currents and result in accumulations. We select the Kuroshio Extension (32°–38°N, 138°–164°E) and the Bay of Bengal Monsoon region (5°–12°N, 82°–93°E) for an intensified single deployment of simulated floats (see Exp_5 in Table 2) and then calculate the PDF (x, y, 100 d, 0.1°) . Theoretically, the PDF is approximately equal to 1, the flow at that location will not significantly converge or diverge. If the PDF is greater than 1, it indicates convergence, and if it is less than 1, it indicates divergence. The result shows that in the downstream of KE, especially in the positions with rich mesoscale eddies, the maximum of PDF is about 1.2, which proves the convergence effects of the floats (shown in Fig. 14). The reason might be that near strong currents eddies tend to bump floats into the currents (Wang et al., 2021). Similarly, in the downstream area of the strong summer monsoon in the Bay of Bengal, Argo floats were found to convergence. These results suggest that simulated floats tend to accumulate in downstream regions of strong currents or in areas with strong eddy activities. This explains why in Exp_4, high PDFs (greater than 40) are more likely to appear in the western boundaries of the oceans or in the strong current regions, such as the eastern boundary of the Bay of Bengal, the northwestern boundary of the South China Sea, and the western boundary of the Pacific Ocean. Meanwhile, low PDFs (less than 20) are also scattered in the aforementioned positions. In summary, it is suggested to deploy addition floats in the regions with relatively obvious weaking PDFs, such as the eastern boundary of the Bay of Bengal, the northwestern boundary of the South China Sea, and the upstream of the strong flow on the western boundary of the Pacific Ocean.