Quantitative Analysis Methods for the Physical-Biological Effects of Vortices of Different Polarities in Upwelling Systems

Abstract

This invention provides a quantitative analysis method for the physical-biological effects of vortices of different polarities in upwelling systems. Based on multi-source satellite remote sensing data and reanalysis data, this method constructs a systematic quantitative analysis technology system for vortices and chlorophyll-a concentration (CHL). It integrates vortex identification and tracking methods based on complex empirical orthogonal functions (CEOF), methods for calculating vortex geometric features and dynamic parameters, methods for calculating vortex radial CHL gradients, and methods for calculating vortex enhancement differentiation. This enables a detailed characterization of the dynamic characteristics and spatiotemporal distribution differences of cyclonic vortices (CEs) and anticyclonic vortices (AEs), and quantitatively assesses the regulatory mechanisms of vortices of different polarities on upwelling biological productivity. This reveals the coupling relationship between physical processes and biological responses in upwelling systems, providing a scientific basis and technical support for ecological environment monitoring and water environment management in upwelling systems.

Description

Technical Field

[0001] This invention relates to satellite remote sensing technology and its applications, and in particular to a quantitative analysis method for the physical-biological effects of vortices of different polarities in upwelling systems. Background Technology

[0002] Mesoscale eddies are core dynamic structures widely distributed in the ocean, playing a crucial role in marine physical processes and biogeochemical cycles. They regulate global heat balance, marine carbon sinks, nutrient redistribution, mixing layer depth changes, and primary productivity, significantly impacting climate change and marine ecosystem dynamics. Based on satellite-observed near-surface chlorophyll-a (CHL) concentration data, combined with fusion analysis of CHL at eddy centers, the spatial distribution patterns of eddy-driven phytoplankton have been preliminarily identified. In the low-latitude sea areas of 20°S–20°N, eddies exhibit prominent nonlinear characteristics, and their dynamic properties are typically characterized by the U / c ratio (the ratio of the eddy's circumferential average maximum geostrophic velocity to its propagation velocity). When U / c > 1, the eddy possesses the ability to capture and transport water during propagation.

[0003] Existing global-scale studies have found that the effect of eddies on CHL (concentrated hygroscopic vorticity) is primarily through agitation of surrounding water, rather than simple water capture. Furthermore, extreme CHL values ​​are mostly distributed at the eddy edge, exhibiting a dipole distribution, which contradicts the unipolar distribution characteristic dominated by capture mechanisms. The dynamic regulatory mechanism of this anomaly has not yet been systematically explained. Related research indicates that the transformation of eddies from a capture-dominated unipolar structure to a flow-dominated dipole structure is jointly regulated by two nonlinear parameters: Rossby number (Ro) and U / c. Theoretically, when U / c > 1, eddies can maintain structural coherence, but an increase in Ro disrupts quasi-geostrophic equilibrium, inducing strain frontogenesis and non-geostrophic secondary circulation, weakening the eddy boundary, making it a flow-capture hybrid structure, and even causing decoupling between surface biosignals and internal density structure.

[0004] Mesoscale eddy activity is frequent in the ocean regions affected by global upwelling systems. Large eddies (GWs) dominate regional circulation during the monsoon season. Influenced by the southwest monsoon, strong inversion flows and jet streams exist in the region, placing eddies in a complex and variable dynamic forcing environment. Currently, research in this region has not systematically compared the differences in the regulation of near-surface CHL by cyclonic eddies and anticyclonic eddies during upwelling and non-upwelling periods. The physical-biological coupling mechanisms of eddies of different polarities under variable dynamic backgrounds remain unclear. Targeted quantitative analysis methods are urgently needed to reveal the regulatory laws of eddies on the biological productivity of upwelling systems. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a quantitative analysis method for the physical-biological interactions of vortices of different polarities in upwelling systems, comprising the following steps:

[0006] S1. Acquire Argo buoy profile data, satellite chlorophyll-a concentration data, satellite sea level anomaly data, and mesoscale eddy trajectory data within the study area;

[0007] S2. Based on the complex empirical orthogonal function, the sea level anomaly data is processed to extract the main spatial modes and the corresponding dominant activity areas. Spatial masks are generated through Monte Carlo significance test, and then cyclones and anticyclones that occur in the upwelling system are screened.

[0008] S3. Calculate the vortex principal axis orientation, aspect ratio, propagation direction, westward propagation ratio, Rossby number, vortex nonlinear parameters, and Okubo–Weiss parameters to provide a quantitative description of the vortex's geometry and dynamic characteristics.

[0009] S4. Project the horizontal gradient of chlorophyll-a concentration onto the radial direction with the vortex center as a reference, calculate the radial chlorophyll-a concentration gradient of the vortex, and characterize the lateral redistribution effect of the vortex on the surrounding biomass.

[0010] S5. Statistically determine the area proportion of regions where the chlorophyll-a concentration inside the vortex abnormally exceeds the threshold, and quantify the enhancing effect of the vortex on biological productivity.

[0011] S6. Based on the obtained geometric, dynamic and biological parameters, quantitatively evaluate the regulatory mechanism of different polarity eddies on upwelling biological productivity, and reveal the coupling relationship between physical processes and biological responses in upwelling systems.

[0012] Further, in step S2, firstly, the sea level anomaly data is preprocessed by removing the long-term average and monthly average, and then normalized according to the standard deviation, serving as input for the complex empirical orthogonal function analysis; secondly, the first mode of the complex empirical orthogonal function analysis is extracted as the dominant spatial mode, and the significance of the sea level anomaly time series is tested using the Monte Carlo phase randomization method to generate a statistically significant spatial mask; finally, vortices whose trajectories intersect with the mask region are selected based on the spatial mask, and the vortex synthesis analysis is divided into three stages—pre-upwelling, peak upwelling, and post-upwelling—based on the evolution characteristics of the principal component time series of the dominant mode.

[0013] Furthermore, in step S3, the vortex geometry is obtained by principal component analysis to perform eigenvalue decomposition on the vortex shape; the dynamic features include the Rossby number and vortex nonlinear parameters.

[0014] Furthermore, the vortex nonlinear parameter is the ratio of the vortex rotational speed scale U to its translational speed c, when When the value is greater than 1, it indicates that the vortex has significant nonlinear characteristics.

[0015] Further, in step S4, the vortex radial chlorophyll-a concentration gradient is calculated using the following formula:

[0016] ;

[0017] in, This represents the radial unit vector pointing outward from the center of the vortex, where T represents the tracer inside the vortex, r is the normalized radial distance, and x and y are coordinates with the center of the vortex as the origin.

[0018] Further, in step S5, the vortex enhancement fraction is calculated using the following formula:

[0019] ,in, This indicates that the tracer quantity T inside the vortex exceeds the reference value T. The area is 1.2 times larger than the region. The tracer quantity representing the central region of the vortex. Indicates the normalized radius The total area of ​​the defined vortex core region.

[0020] Further, in step S6, the regulatory mechanism includes: determining that during the upwelling season, when the correlation between the abnormal surface chlorophyll-a concentration and the abnormal subsurface density drops to near zero, the dominant mechanism changes from a vertical process to a lateral redistribution process driven by background strain.

[0021] Furthermore, step S6 also includes quantitatively evaluating the vortex's capture capacity and nonlinear behavior by analyzing the scaling relationship between the Rossby number and the vortex nonlinear parameter. When the vortex nonlinear parameter is much greater than 1, it is determined that the vortex has the ability to maintain water capture.

[0022] Furthermore, in step S3, the geostrophic velocity field is solved by SLA based on the geostrophic relationship, and the Okubo–Weiss parameters are calculated.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] This invention constructs a systematic quantitative analysis technology system for vortices and CHL. This system integrates vortex identification and tracking methods based on complex empirical orthogonal functions (CEOF), methods for calculating vortex geometric features and dynamic parameters, methods for calculating vortex radial chlorophyll-a concentration (CHL) gradients, and methods for calculating vortex enhancement differentiation, achieving a detailed characterization of the dynamic characteristics and spatiotemporal distribution differences of cyclonic eddies (CEs) and anticyclonic eddies (AEs). Based on this, the regulatory effects and mechanisms of vortices of different polarities on the biological productivity of upwelling systems are further quantitatively evaluated, revealing the coupling relationship between physical processes and biological responses in upwelling systems, providing a scientific basis and technical support for upwelling ecological environment monitoring and water environment management. Compared with existing technologies, this invention, based on multi-source satellite remote sensing data and reanalysis data, systematically analyzes the dynamic characteristics of vortices of different polarities at different stages of upwelling systems and their impact mechanisms on biological productivity. The proposed method has good universality and scalability, and can be extended to other upwelling regions globally, providing new technical means and scientific basis for upwelling ecological environment monitoring and biological productivity assessment. Attached Figure Description

[0025] Figure 1 This diagram illustrates the distribution of climatological chlorophyll-a concentration, sea-level anomalies, and mesoscale eddies in the upwelling region of the upwelling system. (a) shows the distribution of average climatological chlorophyll-a concentration (shaded) and sea-level anomalies (contour lines) from June to September 1997 to 2025; (b) shows the distribution of the first mode of the complex empirical orthogonal function calculated from sea-level anomaly data retaining the seasonal cycle; (c) shows the distribution of the first mode of the complex empirical orthogonal function calculated from sea-level anomaly data removing the seasonal cycle; (d) shows a spatial mask map generated based on statistically significant regions of seasonal and non-seasonal complex empirical orthogonal functions; (e) shows the principal component time series plots corresponding to the first mode of the seasonal and non-seasonal complex empirical orthogonal functions; (f) shows the distribution of anticyclonic vortex trajectory segments intersecting with the spatial mask region; and (g) shows the distribution of cyclonic vortex trajectory segments intersecting with the spatial mask region.

[0026] Figure 2 The diagram shows the abnormal chlorophyll-a complex distribution centered on vortices. (a) shows the abnormal chlorophyll-a complex distribution of anticyclonic vortices during the early upwelling period (March-May); (b) shows the abnormal chlorophyll-a complex distribution of anticyclonic vortices during the upwelling period (June-September); (c) shows the abnormal chlorophyll-a complex distribution of anticyclonic vortices during the late upwelling period (October-December); (d) shows the abnormal chlorophyll-a complex distribution of cyclonic vortices during the early upwelling period (March-May); (e) shows the abnormal chlorophyll-a complex distribution of cyclonic vortices during the upwelling period (June-September); and (f) shows the abnormal chlorophyll-a complex distribution of cyclonic vortices during the late upwelling period (October-December).

[0027] Figure 3 This is a distribution map of the radial chlorophyll-a anomaly gradient of the vortex superimposed with sea level anomaly contour lines, grouped as (a)-(f). Figure 2 Consistent, corresponding to radial chlorophyll-a anomalous gradient distributions in different seasons and different polar vortices;

[0028] Figure 4 This is a seasonal relationship diagram between anticyclonic eddies and cyclonic eddies, showing the chlorophyll-a content, density anomalies, and mixing layer depth. (a)-(c) represent data corresponding to anticyclonic eddies, and (d)-(f) represent data corresponding to cyclonic eddies. (a) and (d) are scatter plots of data from the early upwelling phase (March-May); (b) and (e) are scatter plots of data from the upwelling phase (June-September); and (c) and (f) are scatter plots of data from the late upwelling phase (October-December).

[0029] Figure 5 Scatter plot of Rossby number and nonlinear parameters for all identified vortices. Detailed Implementation

[0030] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0031] Example 1: 1. Data Acquisition

[0032] (1) Argo Buoy Profile Data: Argo buoy profile data (2001-2025) for the study area were obtained from the Global Ocean Data Assimilation Experiment, which provides delayed model temperature-salinity (TS) profile data from the global Argo observation network. Based on these profile data, the potential density anomaly was calculated according to the 2010 seawater thermodynamic equation (TEOS-10). Conservative temperature (CT) and absolute salinity (SA). Mixed layer depth (MLD) is determined using a density threshold (CT). ) and temperature threshold ( And it was estimated using 10m as the reference depth for the surface.

[0033] (2) Satellite CHL data: CHL is used as an important indicator of phytoplankton productivity. This invention uses the multi-sensor fusion CHL product (Version 6.0, unit: mgm) provided by the Ocean Color Climate Change Initiative. -3The data spans from 1997 to 2025, with a spatial resolution of 4 km and a temporal resolution of 8 days. Sourced from the European Space Agency, this data was constructed by fusing observations from multiple ocean color sensors. Systematic biases between different sensors were corrected during processing to ensure the consistency of the time series and the reliability of radiometric calibration.

[0034] (3) Satellite Sea Level Anomaly Data: Sea level anomaly (SLA) data are derived from the L4 sea surface height and its derived variables dataset of the global ocean grid published by the Copernicus Ocean Service. This dataset was generated using the optimal interpolation method, with a spatial resolution of 1 / 4° and a daily temporal resolution, and incorporates along-orbit L3 altimeter observations from a consistent dual-satellite configuration. To extract mesoscale variation information, this paper refers to existing research and performs spatial high-pass filtering on the SLA data.

[0035] (4) Mesoscale vortex trajectory data: The mesoscale vortex trajectory data for the study area is derived from the global mesoscale vortex trajectory product (delayed time data version 3.2), which was generated by SSALTO / DUACS and released through the Copernicus Climate Data Storage Center. This dataset identifies and tracks mesoscale vortices globally, with a spatial resolution of 1 / 4° and a temporal resolution of daily, covering the period from January 1993 to February 2022. Vortex identification is based on a single extreme value criterion, with a minimum amplitude threshold of 0.4 cm and a minimum lifespan of 10 days. The dataset also provides multiple characteristic parameters for cyclonic vortices and anticyclonic vortices, including the latitude and longitude of the vortex center (°), amplitude (m), radius (km), and axial propagation velocity (ms). -1 (and other geometric and dynamic properties.)

[0036] 2. Vortex Identification and Tracking

[0037] This invention extracts cyclonic and anticyclonic vortices occurring in upwelling systems (48°E–60°E, 2°N–12°N) from global mesoscale vortex trajectory data. Given that this study focuses on mesoscale vortices directly interacting with nearshore upwelling, the location of large vortices (GWs) was first identified during the analysis, and target vortices were then selected accordingly. GWs are quasi-stationary, significantly seasonal mesoscale structures that dominate during the summer monsoon and directly interact with nearshore upwelling systems. These vortices recur during the summer monsoon, with their center typically oscillating within the range of 5°N–10°N. GWs not only interact with nearshore upwelling but also influence other coherent vortex structures, thus playing a crucial role in upwelling dynamics and regional circulation during the summer monsoon. Based on this, this invention constructs a spatial mask of the GW's main activity region and filters all vortices with complete lifecycles within this region.

[0038] To identify the main activity areas of GW, this invention employs the Complex Empirical Orthogonal Function (CEOF) method, which is suitable for identifying dynamic structures with propagation characteristics, such as mesoscale eddies. Specifically, sea surface height anomaly (SLA) data, after removing long-term and monthly averages and normalizing by standard deviation, is used as input for CEOF analysis (Formula 1) to extract its main spatial modes and corresponding dominant activity areas.

[0039] (1);

[0040] in, This represents the time series of daily sea surface height anomalies (SLA). It is a preprocessed, standardized SLA sequence, where x, y, and t represent longitude, latitude, and time (days), respectively. Indicates at each pixel The SLA multi-year average value is obtained over the time dimension (t). This represents the standard deviation of the corresponding pixel.

[0041] To identify the main active regions of GW, this invention employs the Complex Empirical Orthogonal Function (CEOF) method, which is suitable for identifying dynamic structures with propagation characteristics, such as mesoscale vortices.

[0042] First, the raw daily sea surface height anomaly (SLA) data is preprocessed by removing the long-term mean and monthly mean, and then normalizing it according to the standard deviation, as shown in formula (1). This normalization process effectively eliminates the inhomogeneity of the long-term mean background field and spatial variance distribution in the raw SLA data, providing standardized input for subsequent complex empirical orthogonal function (CEOF) analysis.

[0043] Complex empirical orthogonal function (CEOF) analysis was conducted based on preprocessed SLA data. The results show that for SLA data after removing the long-term mean, the first mode can explain 12.3% of the total variance (corresponding to...). Figure 1 (b)), its spatial distribution corresponds to the SLA climatology from June to September (corresponding to Figure 1 The high agreement between the two modes (a) and (b) indicates that this mode primarily reflects signal characteristics related to seasonal variations. The complex empirical orthogonal function (CEOF) amplitude of this mode is significantly higher near (7.5°N, 53°E), (2°N, 48°E), and along the coast, consistent with the average location of the large vortex (GW), southern circulation (SG), and strong coastal currents during the southwest monsoon reported in existing studies. The second mode explains 8.82% of the total variance. Compared to the first mode, its GW center is located further south, around 5°N, reflecting the non-seasonally locked position of the GW.

[0044] To further assess the impact of seasonality, this invention re-performs complex empirical orthogonal function (CEOF) analysis on SLA data after removing the monthly climatological mean (i.e., taking the monthly mean as the average in equation (1)). The results show that the deseasoned dominant mode can explain 10.28% of the total variance (corresponding to...). Figure 1 (c) captured the strongest residual variability; the second mode explained 6.82% of the total variance, exhibiting temporal characteristics similar to but weaker than the dominant mode, and differing in spatial structure. The temporal concentration of each dominant mode remained between May and December (corresponding to...). Figure 1 (e) indicates that the dominant anomalous variability remains phase-locked with the season. The above results suggest that removing the seasonal cycle primarily redistributes variance across different modes without isolating additional, clearly independent physical processes in time.

[0045] Further analysis shows that the spatial structure of the second mode of the complex empirical orthogonal function (CEOF) calculated from the SLA data that preserves the seasonal signal is highly consistent with that of the first mode obtained from the deseasoned SLA data, proving that this mode is a robust and persistent dynamic feature. Therefore, the complex empirical orthogonal function (CEOF) analysis that preserves the seasonal cycle can effectively distinguish different variability features of the GW system: the first mode captures the variability region most strongly affected by seasonal modulation, while the second mode isolates the spatially stable mesoscale variability signal that is not phase-locked with the seasonal cycle.

[0046] Furthermore, the spatial patterns obtained from deseasonalized SLA data show good consistency with the analysis results based on 8-day synthetic data. Based on this consistency, this invention jointly constructs a spatial mask using the first mode of the complex empirical orthogonal function (CEOF) of seasonal SLA and the first mode of the complex empirical orthogonal function (CEOF) of deseasonalized SLA, to identify eddies intersecting with upwelling-affected areas at any stage of their lifecycle. The reason for choosing this combined mask is that the spatial distribution of the second mode of the complex empirical orthogonal function (CEOF) of seasonal SLA extends into the open ocean, including eddy trajectories with limited direct interaction with coastal upwelling; while the spatial distribution of the deseasonalized mode is more tightly confined to the nearshore area, i.e., the area with the strongest upwelling influence. Using both together allows for precise screening of target eddies.

[0047] Monte Carlo significance test was used to identify spatial regions that were statistically significant at a significance level of 0.05. By performing phase randomization on the SLA time series, the temporal phase was randomized while maintaining the original power spectrum characteristics, thus generating a series of phase-randomized SLA time series. For each randomized implementation, the complex empirical orthogonal function (CEOF) was recalculated, and the 95th percentile of the amplitude distribution of the obtained CEOF was used as the significance threshold. Regions where the observed CEOF amplitude exceeded this threshold (Equation (2)) were considered statistically significant and further used as spatial masks. Figure 1 (d) in the formula is used for vortex screening (equation (3)).

[0048] (2);

[0049] in, This represents the 95th percentile of the alternative amplitude distribution obtained through the Monte Carlo phase randomization method. This represents the amplitude corresponding to the s-th substitute sample. This represents the number of substitute samples, which is set to 100 here. Therefore, the saliency mask can be defined as:

[0050] (3);

[0051] in, This represents the amplitude of the m-th mode of the complex empirical orthogonal function (CEOF) at pixel (x,y). When the observed amplitude of the complex empirical orthogonal function (CEOF) exceeds this threshold, the corresponding pixel is considered statistically significant.

[0052] Figure 1 The study presents the climatological SLA and CHL fields from June to September, the spatial mask obtained based on the significance analysis of the Multiple Empirical Orthogonal Function (CEOF), and the vortex trajectories intersecting with this mask. Based on the temporal modal evolution of the principal components of the dominant CEOF, the vortex synthesis analysis is divided into three dynamically defined stages: the early GW stage (March–May), the peak GW stage (June–September), and the late GW stage (October–December). Although these stages do not strictly correspond to the traditional seasonal division, their division directly stems from the temporal variation characteristics of the consistent dominant CEOF modes. Figure 1 (e) indicates that the value intensifies from March to May, remains high from June to September, and then gradually declines. Therefore, this phase division reflects the intrinsic evolution of mesoscale dynamic processes related to the GW system and the upwelling season, rather than simply climatological seasonal variations.

[0053] 3. Vortex Geometry and Dynamics

[0054] To obtain the dominant direction of the vortex ( This invention employs Principal Component Analysis (PCA) to decompose the vortex morphology into eigenvalues, thereby determining its principal axis and corresponding direction. The direction angle is calculated using the arctangent function of the ratio of the projections of the principal axis onto the x and y directions. Furthermore, the aspect ratio of the vortex is defined as the ratio of the length of the secondary axis to the length of the principal axis, used to characterize the shape of the vortex. When this ratio is close to 1, it indicates that the vortex morphology approaches a circle.

[0055] Direction of dissemination ( The average direction angle is obtained by calculating the direction angle of the line connecting adjacent positions on the vortex trajectory. The average direction angle and the average propagation direction are calculated using the circular statistical method, and weighted by the vortex area and the displacement distance between adjacent positions, respectively.

[0056] The proportion of westward-propagating vortices ( This is calculated based on the latitudinal displacement along each vortex trajectory. Negative latitudinal displacement is considered westward motion, and the proportion of such displacement is defined as... .

[0057] Rossby number ( The ratio of relative vorticity to planetary vorticity is given by f, where f is the Coriolis parameter and L is the characteristic length scale, which is taken as the vortex radius R here. The velocity scale U is defined as the maximum vortex velocity averaged along the circumference of the vortex.

[0058] vortex nonlinear parameters ( The vortex velocity scale (U) is defined as the ratio of its rotational velocity scale (U) to its translational velocity (c), where the translational velocity (c) is calculated from the displacement between adjacent positions on the vortex trajectory. This parameter measures the vortex's ability to capture and transport water within its core region. When the value is greater than 1, it indicates that the vortex has significant nonlinear characteristics and is capable of transporting the trapped fluid and its associated physical and biogeochemical properties; while when... When the value is less than 1, the vortex more closely resembles a linear wave. This index has been widely used to characterize the dynamics of mesoscale vortices.

[0059] The Okubo–Weiss parameters (OW) are estimated based on the velocity field calculated from SLA data, following standard altimeter vortex diagnostic methods. First, the geostrophic zonal velocity (u) and meridional velocity (v) are calculated from the SLA using the geostrophic relationship:

[0060] ;

[0061] Where g is the gravitational acceleration, f is the Coriolis parameter, and η is the SLA. Subsequently, the relative vorticity (ζ) and strain components are calculated using the spatial derivative of the velocity field:

[0062] ;

[0063] The normal strain component characterizes the degree of tensile or compressive deformation of the fluid along the velocity direction; The tangential strain component characterizes the degree of shear deformation of the fluid perpendicular to the velocity direction.

[0064] The total strain intensity (S) is calculated as follows:

[0065] ;

[0066] The Okubo-Weiss parameters are calculated as follows:

[0067] ;

[0068] Spatial derivatives were calculated using a second-order central difference method based on NumPy numerical differential functions. All velocity components (u, v) and their derivatives (S, ζ, and Okubo-Weiss) were calculated in a vortex-centered normalized coordinate system. This normalized spatial extent was extended to 4R to reduce boundary effects while adequately characterizing the influence of the surrounding background flow field.

[0069] (4) Vortex radial CHL gradient

[0070] The radial gradient of the tracer T is calculated by projecting its horizontal gradient onto the radial direction with reference to the vortex center:

[0071] ;

[0072] in, , , This represents the distance from the center of the vortex to the corresponding point. This is the polar angle of the corresponding point in the local coordinate system. This distance is calculated from the x and y coordinates normalized relative to the vortex radius R:

[0073] ;

[0074] The above expression can be equivalently written as

[0075] ;

[0076] in, This represents the radial unit vector pointing outward from the center of the vortex.

[0077] (5) Vortex enhancement partition

[0078] Vortex enhancement discrimination ( This is used to quantify the area proportion of the CHL-increased region within the vortex range, and is defined as follows:

[0079] ;

[0080] in, This indicates that the tracer quantity T inside the vortex exceeds the reference value T. The area is 1.2 times larger than the surrounding area. Indicates the normalized radius Total area of ​​the defined vortex core region. Normalized radial distance. Defined as:

[0081] ;

[0082] Where x and y are coordinates in a reference frame centered on the vortex, and R is the vortex radius. CHLA is used as the tracer, and its expression in log space is considered. The expression can be equivalently written as the following expression:

[0083] ;

[0084] Among them, 0.079 is Approximate value. Reference value CHLA( Defined as the normalized radius. The median of CHLA within the range is used to represent the vortex core signal.

[0085] Example 2: 1. Seasonal Vortex Geometry and Dynamics

[0086] In mesoscale vortices within upwelling regions, one of the most significant seasonal signals, compared to changes in amplitude, radius, and propagation characteristics, is the reorientation of vortex geometry with polarity (Table 1). During the early upwelling phase (March-May, M3-5), both anticyclonic vortices (AEs) and cyclonic vortices (CEs) exhibit a predominantly northeast-southwest orientation, with average axis orientations of approximately 38° and 40°, respectively. As the upwelling phase begins in June (June-September, M6-9), cyclonic vortices (CEs) undergo significant rotation, shifting to a northwest-southeast orientation (approximately 109°), corresponding to a change of approximately 70°; in contrast, anticyclonic vortices (AEs) maintain a relatively stable orientation (approximately 53°). During the later upwelling phase (October-December, M10-12), anticyclonic vortices (AEs) remain predominantly northeast-southwest (approximately 23°), while cyclonic vortices (CEs) tend to adjust towards a more eastward direction (approximately 43°). Therefore, this seasonal reorientation is a robust and polarity-differentiated characteristic of vortex fields.

[0087] Table 1 shows the seasonal statistics for anticyclonic vortices (AEs) and cyclonic vortices (CEs). The number of vortices is based on unique trajectory numbers, while other statistics are calculated based on the instantaneous state of the vortices at each time point. Indicates the average direction of propagation. This indicates the dominant orientation angle of the main axis. An aspect ratio of 1 indicates that the vortex shape is circular. w This indicates the proportion of westward-propagating vortices within the boundary of the study area. M represents the month, and the statistical results are grouped according to the corresponding month (represented by numbers).

[0088] Table 1

[0089]

[0090] During the M6-9 period, the size of anticyclonic vortices (AEs) increased significantly (average radius approximately 135 km), a change consistent with the arrival of the gas vortex (GW), indicating that regional circulation has a significant influence on the size of anticyclonic vortices. Throughout all seasons, cyclonic vortices (CEs) consistently exhibited stronger energy characteristics than anticyclonic vortices (AEs), specifically larger amplitudes and higher axial velocities, while maintaining relatively smaller radii. The aspect ratios of both types of vortices remained consistently less than 0.8, indicating that their morphology was generally non-circular, and this characteristic did not change seasonally.

[0091] Although vortices generally propagate westward (accounting for 66-85%), their geometric orientation closely corresponds to the seasonal reversal of the background flow field, especially in cyclonic vortices (CEs). The significant reorientation of cyclonic vortices during M6-9 corresponds to the eastward flow dominated by the southwest monsoon. Therefore, the reorientation characteristics of cyclonic vortices are consistent with the deformation caused by background strain. In contrast, anticyclonic vortices (AEs) maintained a stable northeast-southwest orientation during this period, indicating their stronger resistance to strain-induced deformation.

[0092] Rossby number ( The magnitude of cyclonic eddies (CEs) increases significantly during M6–9, with cyclonic eddies (AEs) reaching approximately 0.45 and anticyclonic eddies (AEs) approximately 0.33, before weakening somewhat during M10–12. It is generally believed that when... At this time, the nonlinear advection term in the flow becomes dynamically important. Therefore, during the M6-9 period... The seasonal increase indicates an enhancement of nonlinear rotational dynamic processes, which is particularly pronounced in cyclones (CEs).

[0093] Okubo–Weiss( The diagnostic results further indicated that during the M6–9 period, the vorticity in the core region of cyclones (CEs) significantly increased, while a more pronounced strain-dominated region appeared on their periphery. This spatial distribution pattern is consistent with the reorientation process of cyclonic eddies and indicates that their morphological changes are influenced by seasonally enhanced background strain. In contrast, anticyclonic eddies (AEs) exhibit a more balanced strain-vorticity structure throughout the year, with their vorticity-dominant cores (AEs) during M6–9. This further expands. This indicates that the anticyclone vortex has stronger rotational consistency and relatively lower sensitivity to deformation.

[0094] In summary, these results indicate that seasonal background circulation selectively reshapes the structure of cyclonic eddies (CEs), while anticyclonic eddies (AEs) largely maintain their structural consistency. Based on this, the next step will be to utilize vortex center CHL fusion analysis to assess the modulation effect of these different dynamic characteristics on the spatial distribution of CHLs.

[0095] 2. Spatial structure of CHL fusion at the vortex center

[0096] The CHL fusion field at the vortex center exhibited a clear and stable polarity-dependent characteristic across three phases: the pre-upwelling phase (M3-5), the upwelling phase (M6-9), and the post-upwelling phase (M10-12). Lower CHL anomalies (CHLA) were observed within anticyclonic vortices (AEs), while higher anomalies were observed within cyclonic vortices (CEs). This result is consistent with the understanding that mesoscale vortices enhance biological productivity. Figure 2 ).

[0097] Although the principal axis geometry of cyclonic vortices (CEs) underwent significant reorientation during M6–9, the lateral redistribution of the surrounding CHL remained spatially consistent across seasons for both polar vortices. During M3–5, positive (negative) CHLA was concentrated on the north- to northwest side of anticyclonic vortices (AEs) (cyclonic vortices, CEs), respectively. With the onset of upwelling, these anomalies shifted northeastward in both types of vortices, and this distribution further expanded to cover most of the northern region in the later stages of upwelling, indicating a significant and seasonally evolving asymmetry in the surrounding CHL field. For mesoscale vortices in the Northern Hemisphere, this convergent distribution pattern is more consistent with the vortex churning effect on a CHL field dominated by zonal gradients, rather than the more commonly discussed meridional gradient. However, the anticyclonic vortex and cyclonic vortex core regions continued to exhibit low and high CHL values, respectively, indicating that the internal signals of the vortices were maintained throughout the seasonal evolution. This coexistence of core anomaly stability and peripheral asymmetric redistribution indicates that the eddy, during transport, can both maintain the water it captures and simultaneously redistribute surrounding primary productivity. To further isolate the effects of this lateral redistribution, the next step will be to analyze the spatial gradient characteristics driving the CHL redistribution.

[0098] 3. Radial CHL gradient

[0099] Analysis results indicate that both anticyclonic eddies (AEs) and cyclonic eddies (CEs) exhibit significant radial gradient structures of chlorophyll-a anomalies (CHLA) (corresponding to...). Figure 3 Through the analysis of Field analysis reveals that the lateral moderating effect of eddies on the CHL field intensifies with seasonal progression, and this effect significantly exceeds the scope of enhanced local biological productivity. During the upwelling period (M6-9), the radial gradient of CHL from anticyclonic eddies (AEs) is most pronounced in the northern quadrant, while it is relatively weaker in the southwestern quadrant. The magnitude reached This corresponds to a relative increase of approximately 12% in CHL within a unit vortex radius. The northeastern edge of the vortex is the gradient peak region, with values ​​reaching [value missing]. If we take ΔR≈1 to characterize the radial scale from the vortex core to the edge, we can obtain... This confirms that the relative increase in CHL in the radial direction of the upwelling seasonal vortex is approximately 20%-40%.

[0100] The radial gradient structure of cyclonic vortices (CEs) exhibits symmetrical and opposite characteristics to that of anticyclonic vortices (AEs), with relatively weak spatial contrast. The magnitude of the gradient within the vortex is... This corresponds to approximately 30% variation in CHL. The local maximum gradient at the vortex edge migrates between different quadrants, which highly matches the reorientation characteristics of the cyclonic vortex geometry during the upwelling period (M6-9). The gradient in the cyclonic vortex core region remains weakly positive for most of the year, with only a slight enhancement in the southern part of the core during the upwelling period (M6-9), followed by a weakening again in the later upwelling period (M10-12). This period is consistent with the enhancement of CHL in the vortex core region relative to other seasons, indicating that the decrease in relative gradient amplitude is essentially a result of the enhancement of the core biomass signal, rather than a weakening of lateral contrast. While the above spatial gradient characteristics clarify the correlation between vortex signals and lateral CHL redistribution, the coupling between surface CHL distribution and vertical processes has not yet been revealed. Therefore, further comparative analysis of surface CHL and subsurface vortex structures is needed.

[0101] 4. Coupling relationship between surface CHL and surface vortex structure

[0102] Seasonal evolution has a significant regulatory effect on the coupling relationship between the surface CHL and the subsurface vortex density structure (corresponding to...) Figure 4During the upwelling phase (M6-9), the correlation between surface CHLA and subsurface density anomaly (DA) dropped to an extremely low level (r<0.06, p>0.2), indicating a clear decoupling between the two. However, in the early (M3-5) and late (M10-12) phases of the upwelling, CHLA and DA of both types of polar eddies showed significant correlations (r=0.38-0.43, p<0.05), confirming a close coupling between subsurface density structure and surface biological response during the non-peak upwelling phase.

[0103] From a seasonal perspective, both types of vortices exhibit higher DA values ​​during the early stage of upwelling (March); during the later stages of upwelling, high DA values ​​are mainly concentrated in the later part of the daily sequence within the year. The mixing layer depth (MLD) is generally deeper in anticyclonic vortices (AEs), exceeding 100m during the upwelling period (M6-9); cyclonic vortices (CEs) have relatively shallower MLDs (<100m), but higher DA values ​​(>24 kg⋅m). -3 Despite the aforementioned differences in subsurface structure, the surface CHL peak values ​​of both types of vortices are generally at similar levels (approximately 0.4 mg⋅m). -3 However, significant local bioenhancement exists within the anticyclone, with anomaly-high CHL values ​​reaching 0.61 mg⋅m⁻¹ during the upwelling phase. -3 Furthermore, the CHL values ​​of both types of vortices increased slightly in the later stages of the upwelling, reaching approximately 0.44 mg⋅m. -3 This observation result is compared with the spatially averaged CHL composite field (corresponding to...). Figure 2 A discrepancy exists, with the latter showing that the overall CHL level within the anticyclone is low. This difference reveals a fundamental difference between the satellite composite field and the Argo buoy point matching results, indicating that both local bio-enhancement effects and vortex-scale overall CHL dilution can coexist within the anticyclone. In summary, changes in surface CHL during upwelling are decoupled from the subsurface vortex density structure, and the dominant regulatory mechanism shifts to a CHL lateral redistribution process driven by enhanced background strain.

[0104] 5. Capture and Dynamic Vortex Evolution

[0105] Rossby number ( The estimation results show that its value is mostly higher than the commonly used threshold throughout the seasonal cycle. (Table 1) shows that the nonlinear advection process always plays an important role in dynamics. During the M6-9 period... The further increase in [value] reflects a further enhancement of the vortex system, which was already in a nonlinear state. This enhancement coincides with the period of strongest CHL gradient around the vortex, indicating that advection transport plays a particularly important role in the redistribution of matter during the upwelling season. Despite the enhanced advection, the vortex core still maintains relatively stable biological characteristic signals.

[0106] Classical nonlinear standard ( ,See Figure 5 This further indicates that the vortex is always in a strongly nonlinear state. (See the horizontal red dashed line in the figure). The seasonal average of the scatter data ( Figure 5 )show, The value varies between approximately 2.1 and 4.3, meaning that the rotational speed of the vortex is about 2 to 4 times its translational speed. Under these conditions, fluid particles can circulate multiple times within the vortex before propagating a distance equal to the vortex radius, thus facilitating the continued presence of the captured water within the vortex core.

[0107] right and Comparing the seasonal averages reveals a stable relationship between the two: the ratio It varies between approximately 9 and 11. This indicates that its satisfying form is... k The scaling relation is such that k≈10. Substituting, we get This indicates that the propagation speed of the vortex is proportional to the product of the vortex size and the planetary vorticity. When k=10, we have That is, the propagation speed of the vortex is less than an order of magnitude of the rotational speed.

[0108] In summary, these diagnostic results indicate that the vortex in this region maintains a strong trapping capability. At the same time, it is also in a state of significant nonlinear dynamics. The coexistence of persistent core capture and seasonally enhanced advection redistribution suggests that the mesoscale eddies in this monsoon-type upwelling system can be viewed as an advection-capture hybrid with characteristics of both advection transport and material capture.

[0109] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A quantitative analysis method for the physical-biological effects of vortices of different polarities in an upwelling system, characterized in that, Includes the following steps: S1. Acquire Argo buoy profile data, satellite chlorophyll-a concentration data, satellite sea level anomaly data, and mesoscale eddy trajectory data within the study area; S2. Based on the complex empirical orthogonal function, the sea level anomaly data is processed to extract the main spatial modes and the corresponding dominant activity areas. Spatial masks are generated through Monte Carlo significance test, and then cyclones and anticyclones that occur in the upwelling system are screened. S3. Calculate the vortex principal axis orientation, aspect ratio, propagation direction, westward propagation ratio, Rossby number, vortex nonlinear parameters, and Okubo–Weiss parameters to provide a quantitative description of the vortex's geometry and dynamic characteristics. S4. Project the horizontal gradient of chlorophyll-a concentration onto the radial direction with the vortex center as a reference, calculate the radial chlorophyll-a concentration gradient of the vortex, and characterize the lateral redistribution effect of the vortex on the surrounding biomass. S5. Statistically determine the area proportion of regions where the chlorophyll-a concentration inside the vortex abnormally exceeds the threshold, and quantify the enhancing effect of the vortex on biological productivity. S6. Based on the obtained geometric, dynamic and biological parameters, quantitatively evaluate the regulatory mechanism of different polarity eddies on upwelling biological productivity, and reveal the coupling relationship between physical processes and biological responses in upwelling systems. The regulatory mechanism includes: determining that during the upwelling season, when the correlation between the abnormal surface chlorophyll-a concentration and the abnormal subsurface density drops to near zero, the dominant mechanism changes from a vertical process to a lateral redistribution process driven by background strain. Step S6 also includes quantitatively evaluating the vortex’s capture capacity and nonlinear behavior by analyzing the scaling relationship between the Rossby number and the vortex nonlinear parameter. When the vortex nonlinear parameter is much greater than 1, the vortex is determined to have the ability to maintain water capture.

2. The quantitative analysis method according to claim 1, characterized in that, In step S2, firstly, the sea level anomaly data is preprocessed by removing the long-term average and monthly average, and then normalized according to the standard deviation, which is used as the input for complex empirical orthogonal function analysis. Secondly, the first mode of complex empirical orthogonal function analysis is extracted as the dominant spatial mode, and the significance of the sea level anomaly time series is tested by Monte Carlo phase randomization method to generate a statistically significant spatial mask. Finally, based on the vortexes that intersect the spatial mask screening trajectory and the mask region, and according to the principal component time series evolution characteristics of the dominant mode, the vortex synthesis analysis is divided into three stages: the early stage of upflow, the peak stage of upflow, and the late stage of upflow.

3. The quantitative analysis method according to claim 1, characterized in that, In step S3, the vortex geometry is obtained by principal component analysis to perform eigenvalue decomposition on the vortex shape; the dynamic features include the Rossby number and vortex nonlinear parameters.

4. The quantitative analysis method according to claim 3, characterized in that, The vortex nonlinear parameter is the ratio of the vortex rotational speed scale U to its translational speed c. When the value is greater than 1, it indicates that the vortex has significant nonlinear characteristics.

5. The quantitative analysis method according to claim 1, characterized in that, In step S4, the vortex radial chlorophyll-a concentration gradient is calculated using the following formula: ； in, This represents the radial unit vector pointing outward from the center of the vortex, where T represents the tracer inside the vortex, r is the normalized radial distance, and x and y are coordinates with the center of the vortex as the origin.

6. The quantitative analysis method according to claim 1, characterized in that, In step S5, the vortex enhancement fraction is calculated using the following formula: ,in, This indicates that the tracer quantity T inside the vortex exceeds the reference value. The area is 1.2 times larger than the surrounding area. The tracer quantity representing the central region of the vortex. Indicates the normalized radius The total area of ​​the defined vortex core region.

7. The quantitative analysis method according to claim 1, characterized in that, In step S3, the geostrophic velocity field is solved by SLA based on the geostrophic relationship, and the Okubo–Weiss parameters are calculated.

Images