A deep-sea basalt buoy underwater drift speed estimation method based on modal constraint

Abstract

The present application relates to the technical field of ocean observation equipment and ocean dynamic data, in particular to a deep-sea basalt buoy underwater drift speed estimation method based on modal constraint, comprising: obtaining multi-source ocean data and deep-sea basalt buoy operation information; constructing target area density stratification and vertical mode; calculating the vertical structure of geostrophic flow and carrying out modal projection; screening the dominant mode based on AVISO sea surface dynamic signal; estimating the underwater drift speed of the target depth based on the dominant mode and calculating the stage average drift speed; fusing the buoy endpoint constraint speed and outputting the uncertainty and quality control result. The present application reduces the direct dependence on external three-dimensional reanalysis flow field; makes AVISO sea surface height, sea surface height anomaly, absolute dynamic topography or sea surface geostrophic flow as the sea surface dynamic constraint, instead of being directly equivalent to the deep flow velocity; provides engineering usable speed results for deep-sea buoy trajectory correction and underwater position estimation.

Description

Technical Field

[0001] This invention relates to the field of marine observation equipment and marine dynamic data technology, and in particular to a method for estimating the underwater drift velocity of deep-sea basaltic buoys based on modal constraints. Background Technology

[0002] Deep-sea profiling buoys are crucial equipment for acquiring profile observation data such as temperature, salinity, and pressure in the deep sea. These buoys typically operate back and forth between the sea surface and the deep sea according to a preset cycle. During the surface phase, they acquire data transmission and location information via satellite communication and GPS positioning, but they usually lack positioning capabilities during the underwater phase.

[0003] Taking a deep-sea basalt buoy as an example, its operational cycle typically includes surface communication and positioning, diving, hovering, continuing to dive to the set maximum profile pressure, surfacing for profile observation, and resurfacing for communication. Since real-time position cannot be directly obtained underwater, the buoy experiences horizontal drift due to ocean currents during its operation. This underwater drift directly affects the profile observation position, the bottom sounding point position, the accuracy of trajectory reconstruction, and the assessment of positional uncertainty. Therefore, estimating the drift velocity of the deep-sea basalt buoy during its underwater operation is a key issue in deep-sea buoy data processing and trajectory correction.

[0004] In existing Deep Argo or deep-sea profiling buoy position processing, the following methods are typically used to address underwater drift issues: First, the closest GPS positioning result in time is selected as the approximate position based on the bottoming or profiling observation time; second, the periodic average drift velocity is estimated based on the difference in the GPS endpoint position of the sea surface in the current or adjacent period; and third, three-dimensional reanalysis flow fields such as GLORYS12 are introduced into the shore-based processing to correct the buoy's underwater drift.

[0005] While the methods described above can provide underwater drift correction information to some extent, they still have significant limitations. First, deep-sea buoys lack direct positioning information during their underwater phase; relying solely on the GPS endpoint position at the sea surface only yields equivalent drift results on a periodic scale, failing to reflect the differences in drift velocity at various stages. The accuracy of external three-dimensional reanalysis flow fields in deep, near-bottom, strong-current, and complex topographic regions is limited by model resolution, data assimilation capabilities, observational coverage, and regional applicability. For the deep and near-bottom operating phases of deep-sea basalt buoys, which are of interest, the reanalysis flow field may contain vertical structural biases or local velocity errors, easily introducing uncertainties when directly used for buoy drift correction. Satellite altimeter data such as AVISO primarily reflect sea surface height, sea surface height anomalies, absolute dynamic topography, and sea surface geostrophic signals, effectively describing sea surface and upper ocean dynamic processes, but they do not directly represent deep or near-bottom current velocities. Directly using AVISO sea surface geostrophic currents as deep-sea drift velocity ignores the vertical structural characteristics of ocean current velocity variations with depth.

[0006] Existing methods for estimating underwater drift velocity typically lack constraints on thermo-salinity stratification, buoyancy frequency, and vertical modal structure. In reality, the influence of sea surface dynamic signals on deeper layers is jointly controlled by local stratification structure, water depth, topography, and dynamic modes. Without vertical modal constraints, directly using surface current fields or external three-dimensional current fields to correct for deep-sea buoy underwater drift makes it difficult to guarantee the physical consistency of deep-sea drift velocity estimates.

[0007] Therefore, a novel method for estimating the underwater drift velocity of deep-sea basaltic buoys is needed. This method should be able to construct the density stratification and vertical modal structure of the target sea area using WOA isotherm and salinity data, and constrain the dominant mode using sea surface dynamic signals such as AVISO. This allows the sea surface dynamic information to be extended to the target buoy's operating depth according to a reasonable vertical structure, thus providing physically constrained velocity estimation results for underwater drift correction, bottom sounding point inversion, and uncertainty assessment of deep-sea basaltic buoys. Summary of the Invention

[0008] This invention provides a method for estimating the underwater drift velocity of deep-sea basaltic buoys based on modal constraints, in order to improve the problems of the inability to directly locate the deep-sea basaltic buoys during their underwater operation, insufficient deep-sea current field data, the difficulty in directly using sea surface dynamic signals for deep-sea drift correction, and the lack of stratified modal constraints in existing methods.

[0009] This invention provides a method for estimating the underwater drift velocity of deep-sea basaltic buoys based on modal constraints, comprising the following steps: S1, acquires multi-source oceanographic data and deep-sea basalt buoy operational information; Acquire multi-source oceanographic data within the target sea area, target time period, and target depth range, as well as operational information of deep-sea basalt buoys; S2, construct the density stratification and vertical modes of the target region; Based on multi-source ocean data, the density, potential density and buoyancy frequency of the target area are calculated to obtain the background stratification structure of the target area and construct the vertical mode. S3, calculate the vertical structure of geostrophic flow and perform modal projection; Calculate the vertical structure of geostrophic flow in the target region and project it onto the vertical modes; S4, based on AVISO sea surface dynamic signals to screen dominant modes; Extract AVISO sea surface dynamic signals within the target area and time period, and match them with the expression of each mode at the sea surface or near-surface layer to screen the dominant mode or combination of dominant modes; S5, estimate the underwater drift velocity at the target depth based on the dominant mode and calculate the stage average drift velocity; Based on the dominant modes or combinations of dominant modes obtained through screening, the AVISO sea surface dynamic signal is extended to the operating depth of the deep-sea basaltic buoy target according to the vertical mode structure to obtain the underwater drift velocity with stratified mode constraints. S6 integrates the buoy endpoint constraint velocity and outputs uncertainty and quality control results; When a deep-sea basalt buoy has a surface GPS endpoint position in the current or adjacent period, the endpoint constraint equivalent drift velocity is calculated based on the buoy endpoint position and then fused with the underwater drift velocity with stratified mode constraints.

[0010] As a preferred technical solution, in S1, the multi-source ocean data includes climatological data, AVISO sea surface dynamic data, and topographic and depth data; wherein, the climatological data includes WOA temperature, salinity, pressure, and depth; and the AVISO sea surface dynamic data includes AVISO sea surface height, sea surface height anomaly, absolute dynamic topography, and sea surface geostrophic data. The deep-sea basalt buoy operation information includes the buoy cycle number, surface communication time, dive start time, hovering depth and hovering pressure, maximum profile depth and maximum profile pressure, surface emergence time, pressure-time path, surface GPS endpoint position, and target estimation stage; the target estimation stage includes at least one of the following: dive stage, hovering stage, continued dive stage, bottom contact stage, surfacing stage, and complete underwater cycle.

[0011] As a preferred technical solution, the process of constructing the vertical mode in S2 is as follows: Establish the spatial coordinates and vertical coordinates of the target area; where, Indicates the horizontal coordinates to the east. Indicates the horizontal coordinates to the north. Indicates vertical coordinates; assuming sea level. seabed ,in Indicates the water depth in the target area; According to WOA temperature ,salinity and pressure Calculate the density of seawater:

[0012] in, Indicates depth Seawater density at that location Indicates depth The salinity at that location Indicates depth The temperature at that location Indicates depth Pressure at the location, Represents the equation of state for seawater; Buoyancy frequency squared The calculation is as follows:

[0013] in, Indicates the buoyancy frequency. Represents gravitational acceleration. Indicates the reference density. Indicates depth Seawater density at that location Represents the vertical coordinate; In obtaining Then, combined with the water depth of the target area Construct the vertical modal equations; The vertical mode is represented as:

[0014] in, Indicates the first Vertical mode, Indicates the modal order. Indicates the maximum modal order involved in the calculation; The vertical modal equation is expressed as:

[0015] in, Indicates the first The eigenvalues ​​corresponding to the first mode, Indicates the first Vertical mode, Represents the square of the buoyancy frequency; boundary conditions are set as follows:

[0016]

[0017] in, Indicates the sea surface boundary. Indicates the seabed boundary; Normalize the vertical modes:

[0018] in, This represents the weighting function.

[0019] As a preferred technical solution, in S3, based on the WOA density field, dynamic height, and the relationship between thermal wind, the vertical structure of the geostrophic flow in the target area is calculated. The calculation process is as follows: Calculation of vertical shear in geostrophic flow using the thermal wind relationship:

[0020] in, Indicates the eastward flow velocity. Indicates the northward geostrophic flow velocity. Represents gravitational acceleration. Represents the Coriolis parameter. Indicates the reference density. Indicates the density of seawater. Indicates the horizontal coordinates to the east. Indicates the horizontal coordinates to the north. Represents the vertical coordinate; Based on the thermal wind relationship, the vertical integration yields the result relative to the reference layer. Relative geotransfer structure:

[0021] in, Indicates depth The relative geotransfer vector at a point relative to the reference layer. Indicates depth Geostrophic vector at that location, Represents the reference layer Geostrophic vector at the location; After obtaining the vertical structure of the geostrophic flow, it can be represented as a superposition of several vertical modes:

[0022] in, Indicates depth The horizontal velocity vector at that location, Indicates the first Vertical mode, Indicates the first First mode amplitude, Indicates the maximum modal order involved in the expansion; No. The amplitude of the first mode is obtained by projection:

[0023] in, Indicates the first First mode amplitude, This represents the vertical structure of the geostrophic flow to be projected. Indicates the first Vertical mode, Represents the weighting function. Indicates the water depth in the target area; For the horizontal velocity vector, the eastward and northward velocity components can be projected separately:

[0024]

[0025] in, Indicates the first The eastward velocity amplitude corresponding to the first mode, Indicates the first The northward velocity amplitude corresponding to the first mode, Indicates the eastward velocity component. This represents the northbound velocity component.

[0026] As a preferred technical solution, in S4, the AVISO sea surface dynamic signal includes at least one of sea surface height, sea surface height anomaly, absolute dynamic topography, eastward sea surface land slew, northward sea surface land slew, and sea surface land slew velocity vector.

[0027] As a preferred technical solution, the process of screening the dominant mode or combination of dominant modes is as follows: For the The first mode, expressed at the sea surface or near-surface, is as follows:

[0028] in, Indicates the first First mode at sea surface or near-surface Speed ​​expression at the location, Indicates the first The first mode at time modal amplitude, Indicates the first The modal values ​​of the first mode at or near the sea surface. Indicates the depth at or near the sea surface; The first Correlation analysis was conducted between sea surface representation of the first mode and AVISO sea surface geostrophic flow:

[0029] in, Indicates the first The correlation coefficient between the first mode and the AVISO sea surface dynamic signal. Indicates the first Velocity representation of first-order modes at the sea surface or near the surface. Represents the AVISO sea surface geostrophic velocity vector or its components; Calculate the correlation coefficients for eastward and northward velocities respectively:

[0030]

[0031] in, This represents the correlation coefficient of eastward velocity. This represents the correlation coefficient of northbound speed. and They represent the first The first mode is expressed in the eastward and northward velocities at the sea surface or near-surface. and These represent the eastward and northward velocity components of the AVISO sea surface geostrophic current, respectively; Construct a comprehensive score :

[0032] in, Indicates the first The comprehensive score of the first mode, Represents the correlation coefficient. This represents the variance explained. Indicator of consistency in velocity direction This represents the mean squared error or reconstructed residual. , , and This indicates the preset weighting coefficient; A mode is determined to be the dominant mode when it meets the following conditions. :

[0033] in, This indicates a preset scoring threshold; when multiple modalities meet the screening criteria, a dominant modality set can be constructed.

[0034] in, This represents the set of dominant modes.

[0035] As a preferred technical solution, the underwater drift velocity calculation process with layered mode constraints in S5 is as follows: When a single dominant mode is adopted At that time, the modal constraint velocity is expressed as:

[0036] in, Indicates depth ,time Modal constraints on underwater drift velocity, Indicates the dominant mode At any moment modal amplitude, Indicates the dominant mode in depth Modal values ​​at; Dominant mode amplitude It can be determined by the AVISO sea surface landslide velocity and the modal values ​​of the dominant mode at the sea surface or near the surface:

[0037] in, Indicates time AVISO sea surface land rotation velocity vector This indicates that the dominant mode is at or near the sea surface. The modal value at the location; when processing the eastward and northward velocity components separately, it is written as:

[0038]

[0039] in, This represents the eastward velocity amplitude corresponding to the dominant mode. This represents the northward velocity amplitude corresponding to the dominant mode. and These represent the eastward and northward velocity components of the AVISO sea surface geostrophic current, respectively; When multiple dominant modes are combined, the modal constraint velocity is expressed as:

[0040] in, Represents the set of dominant modes. Indicates the first The dominant mode at time modal amplitude, Indicates the first Vertical mode; After obtaining the modal constrained velocity field, and combining it with the pressure-time path of the deep-sea basalt buoy, the buoy is positioned at time... The running depth is represented as:

[0041] in, Indicates the buoy's position at time The corresponding runtime depth; for the target runtime stage The stage-average underwater drift velocity is calculated as follows:

[0042] in, This represents the modally constrained average underwater drift velocity during the target phase. Indicates the start time of the target phase. Indicates the end time of the target phase. Indicates the buoy at time ,depth Modal constraint velocity at the location; The horizontal displacement estimate for the target stage is:

[0043] in, This represents the horizontal displacement vector obtained from the modal constraint velocity estimation during the target stage.

[0044] As a preferred technical solution, in S6, the process of calculating the equivalent drift velocity of the endpoint constraint and fusing it with the underwater drift velocity is as follows: Let the starting endpoint position of the buoy target period be... The end point position is The corresponding times are respectively and Then the equivalent drift velocity of the endpoint constraint is:

[0045]

[0046] in, This represents the equivalent drift velocity obtained from the buoy endpoint constraint. Indicates the starting endpoint position. Indicates the end point position. Indicates the time corresponding to the start and end points. Indicates the time corresponding to the end endpoint; Weighted fusion of endpoint constraint velocity and modal constraint velocity:

[0047] in, This represents the final estimated underwater drift velocity after fusion. This represents the equivalent drift velocity of the endpoint constraints. Indicates the modal constraint drift velocity. Let represent the fusion weights, and satisfy:

[0048] Fusion weights It can be determined based on endpoint position error, AVISO data error, WOA layering applicability, modal correlation coefficient, modal reconstruction residual, and target stage length; The fusion weights can be expressed as:

[0049] in, This represents the uncertainty of the endpoint constraint velocity. This represents the uncertainty of the modal constraint velocity; when the uncertainty of the endpoint constraint velocity is small, Increase; when the modal constraint velocity uncertainty is small, Decrease; The uncertainty of the final fusion rate is expressed as:

[0050] in, This represents the uncertainty in the final fusion rate. Indicates the uncertainty of the endpoint constraint velocity. This represents the uncertainty of the modal constraint velocity. This indicates the fusion residual or unmodeled error; The uncertainty of the modal constraint velocity can be determined by the following error terms:

[0051] in, This indicates the uncertainty caused by errors in the WOA stratification data. This indicates the uncertainty caused by errors in AVISO sea surface dynamic data. Indicates modal projection error, Indicates modal correlation error. This indicates the deep extension error of the sea surface dynamic signal.

[0052] As a preferred technical solution, the quality control results include reliable, low reliability, and unusable.

[0053] When the correlation coefficient of the dominant mode is greater than the preset threshold, the modal reconstruction residual is less than the preset threshold, the AVISO data is complete, the WOA stratification is stable, and the target stage is within the effective water depth range, the quality control result is set to reliable. When some conditions are not met but a velocity estimation result can still be formed, the quality control result is set to low confidence. When AVISO data is missing, WOA stratification is abnormal, the water depth in the target area does not meet the modal solution conditions, the Coriolis parameter is too small, the correlation of the dominant mode is lower than the preset threshold, or the modal extension results are abnormal, the quality control results will be set to unavailable.

[0054] This invention provides a method for estimating the underwater drift velocity of deep-sea basaltic buoys based on modal constraints, which has the following beneficial effects: This invention utilizes WOA temperature, salinity, and pressure data to calculate the density stratification, buoyancy frequency, and vertical modes of a target sea area, and uses these as vertical structural constraints for estimating the underwater drift velocity of deep-sea basaltic buoys. Compared to methods that directly call external three-dimensional reanalysis flow fields such as GLORYS12, this invention does not rely on a single external flow field product to directly provide deep-sea velocities. Instead, it uses the stratification structure of the target sea area itself to constrain the vertical morphology of the sea surface dynamic signal extending into the deep layers, thereby improving the physical consistency and regional applicability of underwater drift velocity estimation in deep, near-bottom, and complex topographic areas.

[0055] This invention uses AVISO sea surface height, sea surface height anomalies, absolute dynamic topography, or sea surface geostrophic currents as sea surface dynamic constraints, rather than directly equating AVISO surface current velocity with the buoy's deep-sea drift velocity. By projecting the vertical structure of the WOA geostrophic current onto different vertical modes and performing correlation matching between the sea surface representations of each mode and the AVISO sea surface dynamic signals, this invention can screen out the dominant modes or mode combinations that have a strong correlation with sea surface dynamic changes, and then perform deep-sea extrapolation based on the dominant modes. This avoids the bias caused by directly applying surface dynamic signals to deep-sea drift correction, improving the rationality of using sea surface satellite data in deep-sea buoy underwater drift estimation.

[0056] This invention combines modal-constrained velocity fields with the pressure-time path of a deep-sea basaltic buoy, enabling the calculation of the average underwater drift velocity for a target phase along the buoy's actual trajectory. The target phase can be a complete underwater cycle or a specified depth layer and time window. Compared to methods that obtain the periodic average velocity solely based on the difference in the outflow endpoint position, this invention provides phased drift velocity results that more closely reflect the buoy's actual movement, thus better serving buoy trajectory correction, profile position correction, bottom-touching phase velocity correction, and underwater horizontal displacement estimation.

[0057] This invention can further integrate GPS endpoint constrained velocities from the buoy's sea surface and combine errors from WOA stratification data, AVISO sea surface dynamic data, dominant mode correlation errors, and endpoint position errors to output drift velocity uncertainty, horizontal displacement uncertainty, and quality control results. Therefore, this invention not only provides underwater drift velocity estimates but also simultaneously provides a reliability assessment of the results, making it easy to integrate into a deep-sea basaltic buoy shore-based data processing system for automated trajectory correction, anomaly result screening, and enhanced velocity input in subsequent bottom sounding point latitude and longitude inversion. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of the underwater drift velocity estimation method for deep-sea basaltic buoys based on modal constraints according to the present invention; Figure 2 This is a schematic diagram of vertical mode decomposition based on WOA layered data; Figure 3 The diagram shows the projection of the vertical structural modes of geostrophic flow and the results of the selection of dominant modes. Figure 4 This is a flowchart for calculating the stage-average drift velocity based on the dominant mode. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0061] Furthermore, the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article, unless otherwise specified, generally indicates that the preceding and following related objects have an "or" relationship.

[0062] The embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0063] Example 1: See Figure 1 This invention provides a method for estimating the underwater drift velocity of deep-sea basaltic buoys based on modal constraints, comprising the following steps: S1, acquires multi-source oceanographic data and deep-sea basalt buoy operational information; S2, construct the density stratification and vertical modes of the target region; S3, calculate the vertical structure of geostrophic flow and perform modal projection; S4, based on AVISO sea surface dynamic signals to screen dominant modes; S5, estimate the underwater drift velocity at the target depth based on the dominant mode and calculate the stage average drift velocity; S6 integrates the buoy endpoint constraint velocity and outputs uncertainty and quality control results.

[0064] Specifically,

[0065] In S1, multi-source oceanographic data within the target sea area, target time period, and target depth range are acquired, along with operational information of deep-sea basalt buoys (within the target period).

[0066] The multi-source oceanographic data includes climatological data, AVISO sea surface dynamic data, and topographic and depth data. Climatological data includes WOA temperature, salinity, pressure, or depth; AVISO sea surface dynamic data includes AVISO sea surface height, sea surface height anomalies, absolute dynamic topography, or sea surface geostrophic data.

[0067] Among them, climatological data are used to calculate the background density stratification, buoyancy frequency and vertical modes of the target sea area; AVISO sea surface dynamic data are used to provide sea surface dynamic constraints at the target time or during the target time period; topographic and depth data are used to determine the water depth of the target area, the depth range for mode solving and the effective depth range near the bottom.

[0068] The deep-sea basalt buoy operation information includes the buoy cycle number, surface communication time, dive start time, hovering depth or hovering pressure, maximum profile depth or maximum profile pressure, surface exit time, pressure-time path, surface GPS endpoint location, and target estimation stage.

[0069] The target estimation phase includes at least one of the following: the descent phase, the hovering phase, the continued descent phase, the phase before and after bottoming out, the surfacing phase, or the complete underwater cycle.

[0070] Step S1 unifies external oceanographic data, topographic data, and buoy operational information to provide input data for subsequent stratification mode construction, sea surface dynamic matching, and underwater drift velocity estimation.

[0071] In S2, based on WOA temperature, salinity, and pressure data, the density, potential density, and buoyancy frequency of the target region are calculated to obtain the background stratification structure of the target region, and vertical modes are constructed. See the process below. Figure 2 The specific steps are as follows: Establish the spatial and vertical coordinates of the target area. Among them, Indicates the horizontal coordinates to the east. Indicates the horizontal coordinates to the north. Represents the vertical coordinate. Let the sea level be... seabed ,in Indicates the water depth of the target area.

[0072] According to WOA temperature ,salinity and pressure Calculate the density of seawater:

[0073] in, Indicates depth Seawater density at that location Indicates depth The salinity at that location Indicates depth The temperature at that location Indicates depth Pressure at the location, This represents the equation of state for seawater.

[0074] Buoyancy frequency squared The calculation is as follows:

[0075] in, Indicates the buoyancy frequency. Represents gravitational acceleration. Indicates the reference density. Indicates depth Seawater density at that location Represents the vertical coordinate.

[0076] When the vertical coordinate is taken as the sea level When the seabed value is negative, under stable stratification conditions, it usually satisfies To avoid the impact of anomalous stratification on modal solutions, the density profile or buoyancy frequency profile can be smoothed, outliers removed, and stabilized.

[0077] In obtaining Then, combined with the water depth of the target area Construct the vertical modal equations. The vertical mode is represented as:

[0078] in, Indicates the first Vertical mode, Indicates the modal order. This indicates the maximum modal order involved in the calculation.

[0079] The vertical modal equation is expressed as:

[0080] in, Indicates the first The eigenvalues ​​corresponding to the first mode, Indicates the first Vertical mode, This represents the square of the buoyancy frequency. The boundary conditions are set as follows:

[0081]

[0082] in, Indicates the sea surface boundary. This indicates the seabed boundary. Depending on the target sea area conditions and specific application requirements, other boundary conditions applicable to the geostrophic mode or internal wave mode may also be used.

[0083] To facilitate subsequent modal projection, the vertical modes are normalized:

[0084] in, This represents the weighting function. The weighting function can be a constant. It can also be determined based on buoyancy frequency, effective observation depth, target operating depth range, or data reliability.

[0085] Step S2 transforms the WOA temperature, salinity, and climatology data into stratification constraints and vertical structure functions for the target sea area, so that subsequent underwater drift velocity estimation no longer depends solely on external flow field values, but is constrained by local stratification and water depth conditions.

[0086] In S3, based on the WOA density field, dynamic height, or thermo-wind relationship, the vertical structure of the geostrophic flow in the target region is calculated and projected onto the vertical mode obtained in S2.

[0087] Calculation of vertical shear in geostrophic flow using the thermal wind relationship:

[0088] in, Indicates the eastward flow velocity. Indicates the northward geostrophic flow velocity. Represents gravitational acceleration. Represents the Coriolis parameter. Indicates the reference density. Indicates the density of seawater. Indicates the horizontal coordinates to the east. Indicates the horizontal coordinates to the north. Represents the vertical coordinate.

[0089] Based on the thermal wind relationship, the vertical integration yields the result relative to the reference layer. Relative geotransfer structure:

[0090] in, Indicates depth The relative geotransfer vector at a point relative to the reference layer. Indicates depth Geostrophic vector at that location, Represents the reference layer The geostrophic flow vector at that location.

[0091] The geostrophic vertical structure obtained based on the WOA density field is not directly equivalent to the true absolute deep-sea velocity at the target time. When it is necessary to construct absolute velocity constraints, the AVISO sea surface geostrophic current can be combined with sea surface constraints, amplitude corrections, or reference layer shifts in subsequent steps.

[0092] After obtaining the vertical structure of the geostrophic flow, it can be represented as a superposition of several vertical modes:

[0093] in, Indicates depth The horizontal velocity vector at that location, Indicates the first Vertical mode, Indicates the first First mode amplitude, This indicates the maximum modal order involved in the expansion.

[0094] No. The amplitude of the first mode is obtained by projection:

[0095] in, Indicates the first First mode amplitude, This represents the vertical structure of the geostrophic flow to be projected. Indicates the first Vertical mode, Represents the weighting function. Indicates the water depth of the target area.

[0096] For the horizontal velocity vector, the eastward and northward velocity components can be projected separately:

[0097]

[0098] in, Indicates the first The eastward velocity amplitude corresponding to the first mode, Indicates the first The northward velocity amplitude corresponding to the first mode, Indicates the eastward velocity component. This represents the northbound velocity component.

[0099] Step S3 decomposes the geostrophic vertical structure obtained based on the WOA density structure into several vertical modal contributions with physical meaning, providing a basis for subsequent identification of dominant modes that have a strong correspondence with the AVISO sea surface dynamic signal.

[0100] In S4, AVISO sea surface dynamic signals within the target area and time period are extracted and matched with the expression of each mode at the sea surface or near-surface layer. Dominant modes or combinations of dominant modes are then selected. (See [link to relevant documentation]). Figure 3 The AVISO sea surface dynamic signal includes at least one of sea surface height, sea surface height anomaly, absolute dynamic topography, eastward sea surface landslide, northward sea surface landslide, or sea surface landslide velocity vector.

[0101] For the The first mode, expressed at the sea surface or near-surface, can be represented as:

[0102] in, Indicates the first First mode at sea surface or near-surface Speed ​​expression at the location, Indicates the first The first mode at time modal amplitude, Indicates the first The modal values ​​of the first mode at or near the sea surface. It indicates the depth at or near the sea surface.

[0103] The first Correlation analysis was conducted between sea surface representation of the first mode and AVISO sea surface geostrophic flow:

[0104] in, Indicates the first The correlation coefficient between the first mode and the AVISO sea surface dynamic signal. Indicates the first Velocity representation of first-order modes at the sea surface or near the surface. This represents the AVISO sea surface geostrophic velocity vector or its components.

[0105] Calculate the correlation coefficients for eastward and northward velocities respectively:

[0106]

[0107] in, This represents the correlation coefficient of eastward velocity. This represents the correlation coefficient of northbound speed. and They represent the first The first mode is expressed in the eastward and northward velocities at the sea surface or near-surface. and These represent the eastward and northward velocity components of the AVISO sea surface geostrophic current, respectively.

[0108] Construct a comprehensive score :

[0109] in, Indicates the first The comprehensive score of the first mode, Represents the correlation coefficient. This represents the variance explained. Indicator of consistency in velocity direction This represents the mean squared error or reconstructed residual. , , and This indicates the preset weighting coefficient.

[0110] A mode is determined to be the dominant mode when it meets the following conditions. :

[0111] in, This indicates a preset scoring threshold. When multiple modalities meet the screening criteria, a dominant modality set can be constructed.

[0112] in, This represents the set of dominant modes.

[0113] In step S4, the AVISO sea surface dynamic signal is used to screen the WOA stratification modes, so that the sea surface dynamic information is not used directly as deep current velocity, but is used to determine the dominant mode or mode combination that can characterize the sea surface-deep dynamic connection.

[0114] In S5, the calculation process for estimating the underwater drift velocity at the target depth based on the dominant mode and calculating the stage-average drift velocity is as follows: Figure 4 As shown.

[0115] Based on the dominant modes or combinations of dominant modes obtained through screening, the AVISO sea surface dynamic signal is extended to the operating depth of the deep-sea basaltic buoy according to the vertical mode structure, and the underwater drift velocity with stratified mode constraints is obtained.

[0116] When a single dominant mode is adopted At that time, the modal constraint velocity is expressed as:

[0117] in, Indicates depth ,time Modal constraints on underwater drift velocity, Indicates the dominant mode At any moment modal amplitude, Indicates the dominant mode in depth Modal values ​​at that location.

[0118] Dominant mode amplitude It can be determined by the AVISO sea surface landslide velocity and the modal values ​​of the dominant mode at the sea surface or near the surface:

[0119] in, Indicates time AVISO sea surface land rotation velocity vector This indicates that the dominant mode is at or near the sea surface. The modal value at that location. When processing the eastward and northward velocity components separately, it can be written as:

[0120]

[0121] in, This represents the eastward velocity amplitude corresponding to the dominant mode. This represents the northward velocity amplitude corresponding to the dominant mode. and These represent the eastward and northward velocity components of the AVISO sea surface geostrophic current, respectively.

[0122] When multiple dominant modes are combined, the modal constraint velocity is expressed as:

[0123] in, Represents the set of dominant modes. Indicates the first The dominant mode at time modal amplitude, Indicates the first Vertical mode.

[0124] After obtaining the modal constrained velocity field, and combining it with the pressure-time path of the deep-sea basalt buoy, the buoy is positioned at time... The running depth is represented as:

[0125] in, Indicates the buoy at time The corresponding runtime depth. For the target runtime phase. The stage-average underwater drift velocity is calculated as follows:

[0126] in, This represents the modally constrained average underwater drift velocity during the target phase. Indicates the start time of the target phase. Indicates the end time of the target phase. Indicates the buoy at time ,depth Modal constraint velocity at the location.

[0127] Accordingly, the horizontal displacement estimate for the target stage is:

[0128] in, This represents the horizontal displacement vector obtained from the modal constraint velocity estimation during the target stage.

[0129] Step S5 converts the AVISO sea surface dynamic signal and WOA vertical mode constraints into the stage-averaged underwater drift velocity of the deep-sea basalt buoy along its actual operating path, enabling the results to directly serve buoy trajectory correction and underwater position estimation.

[0130] In S6, when the deep-sea basalt buoy has a GPS endpoint position on the sea surface in the current cycle or an adjacent cycle, the endpoint constraint equivalent drift velocity is calculated based on the buoy endpoint position and fused with the modal constraint drift velocity obtained in S5.

[0131] Let the starting point of the buoy target period be... The end point position is The corresponding times are respectively and Then the equivalent drift velocity of the endpoint constraint is:

[0132] in, This represents the equivalent drift velocity obtained from the buoy endpoint constraint. Indicates the starting endpoint position. Indicates the end point position. Indicates the time corresponding to the start and end points. This indicates the time corresponding to the end endpoint.

[0133] Weighted fusion of endpoint constraint velocity and modal constraint velocity:

[0134] in, This represents the final estimated underwater drift velocity after fusion. This represents the equivalent drift velocity of the endpoint constraints. Indicates the modal constraint drift velocity. Let represent the fusion weights, and satisfy:

[0135] Fusion weights It can be determined based on endpoint position error, AVISO data error, WOA layer suitability, modal correlation coefficient, modal reconstruction residual, and target stage length.

[0136] The fusion weights can be expressed as:

[0137] in, This represents the uncertainty of the endpoint constraint velocity. This represents the uncertainty of the modal constraint velocity. When the uncertainty of the endpoint constraint velocity is small, Increase; when the modal constraint velocity uncertainty is small, Decrease.

[0138] The uncertainty of the final fusion rate can be expressed as:

[0139] in, This represents the uncertainty in the final fusion rate. Indicates the uncertainty of the endpoint constraint velocity. This represents the uncertainty of the modal constraint velocity. This indicates the fusion residual or unmodeled error.

[0140] The uncertainty of the modal constraint velocity can be determined by the following error terms:

[0141] in, This indicates the uncertainty caused by errors in the WOA stratification data. This indicates the uncertainty caused by errors in AVISO sea surface dynamic data. Indicates modal projection error, Indicates modal correlation error. This indicates the deep extension error of the sea surface dynamic signal.

[0142] Based on the aforementioned uncertainty calculation results, and in conjunction with the dominant mode correlation, mode reconstruction residuals, stratification stability, and target stage effectiveness, the underwater drift velocity estimation results are assessed for quality control, and the quality control results are used for identification. The quality control assessment characterizes the reliability of the drift velocity estimation results for the current target stage and serves as the basis for determining whether to use these velocity results in subsequent trajectory correction and horizontal displacement estimation.

[0143] Quality control results are categorized into three types: reliable, low reliability, and unusable.

[0144] When the correlation coefficient of the dominant mode is greater than the preset threshold, the modal reconstruction residual is less than the preset threshold, the AVISO data is complete, the WOA stratification is stable, and the target stage is within the effective water depth range, the quality control result is set to reliable.

[0145] When some conditions are not met but a velocity estimation result can still be formed, the quality control result is set to low confidence.

[0146] When AVISO data is missing, WOA stratification is abnormal, the water depth in the target area does not meet the modal solution conditions, the Coriolis parameter is too small, the correlation of the dominant mode is lower than the preset threshold, or the modal extension results are abnormal, the quality control results will be set to unavailable.

[0147] This invention utilizes WOA temperature, salinity, and pressure data to calculate the density stratification, buoyancy frequency, and vertical modes of a target sea area, and uses these as vertical structural constraints for estimating the underwater drift velocity of deep-sea basaltic buoys. Compared to methods that directly call external three-dimensional reanalysis flow fields such as GLORYS12, this invention does not rely on a single external flow field product to directly provide deep-sea velocities. Instead, it uses the stratification structure of the target sea area itself to constrain the vertical morphology of the sea surface dynamic signal extending into the deep layers, thereby improving the physical consistency and regional applicability of underwater drift velocity estimation in deep, near-bottom, and complex topographic areas.

[0148] This invention uses AVISO sea surface height, sea surface height anomalies, absolute dynamic topography, or sea surface geostrophic currents as sea surface dynamic constraints, rather than directly equating AVISO surface current velocity with the buoy's deep-sea drift velocity. By projecting the vertical structure of the WOA geostrophic current onto different vertical modes and performing correlation matching between the sea surface representations of each mode and the AVISO sea surface dynamic signals, this invention can screen out the dominant modes or mode combinations that have a strong correlation with sea surface dynamic changes, and then perform deep-sea extrapolation based on the dominant modes. This avoids the bias caused by directly applying surface dynamic signals to deep-sea drift correction, improving the rationality of using sea surface satellite data in deep-sea buoy underwater drift estimation.

[0149] This invention combines modal-constrained velocity fields with the pressure-time path of a deep-sea basaltic buoy, enabling the calculation of the average underwater drift velocity for a target phase along the buoy's actual trajectory. The target phase can be a complete underwater cycle or a specified depth layer and time window. Compared to methods that obtain the periodic average velocity solely based on the difference in the outflow endpoint position, this invention provides phased drift velocity results that more closely reflect the buoy's actual movement, thus better serving buoy trajectory correction, profile position correction, bottom-touching phase velocity correction, and underwater horizontal displacement estimation.

[0150] This invention can further integrate GPS endpoint constrained velocities from the buoy's sea surface and combine errors from WOA stratification data, AVISO sea surface dynamic data, dominant mode correlation errors, and endpoint position errors to output drift velocity uncertainty, horizontal displacement uncertainty, and quality control results. Therefore, this invention not only provides underwater drift velocity estimates but also simultaneously provides a reliability assessment of the results, making it easy to integrate into a deep-sea basaltic buoy shore-based data processing system for automated trajectory correction, anomaly result screening, and enhanced velocity input in subsequent bottom sounding point latitude and longitude inversion.

[0151] This invention provides a method for estimating the underwater drift velocity of deep-sea basaltic buoys based on modal constraints. It reduces direct dependence on external three-dimensional reanalysis flow fields by constraining the vertical distribution of underwater currents through local stratification. The method utilizes AVISO sea surface dynamic signals to screen dominant vertical modes and perform deep-layer extensions, treating AVISO sea surface height, sea surface height anomalies, absolute dynamic topography, or sea surface geostrophic currents as sea surface dynamic constraints, rather than directly equating them to deep-layer current velocities. Combining a stage-averaged underwater drift velocity estimation method with pressure-time path and sea surface endpoint constraints, the method outputs target stage drift velocity, horizontal displacement, uncertainty, and quality control results, providing engineering-usable velocity results for deep-sea buoy trajectory correction and underwater position estimation.

[0152] Of course, the present invention may have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can make various corresponding changes and modifications according to the present invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints, characterized in that, Includes the following steps: S1, acquires multi-source oceanographic data and deep-sea basalt buoy operational information; Acquire multi-source oceanographic data within the target sea area, target time period, and target depth range, as well as operational information of deep-sea basalt buoys; S2, construct the density stratification and vertical modes of the target region; Based on multi-source ocean data, the density, potential density and buoyancy frequency of the target area are calculated to obtain the background stratification structure of the target area and construct the vertical mode. S3, calculate the vertical structure of geostrophic flow and perform modal projection; Calculate the vertical structure of geostrophic flow in the target region and project it onto the vertical modes; S4, based on AVISO sea surface dynamic signals to screen dominant modes; Extract AVISO sea surface dynamic signals within the target area and time period, and match them with the expression of each mode at the sea surface or near-surface layer to screen the dominant mode or combination of dominant modes; S5, estimate the underwater drift velocity at the target depth based on the dominant mode and calculate the stage average drift velocity; Based on the dominant modes or combinations of dominant modes obtained through screening, the AVISO sea surface dynamic signal is extended to the operating depth of the deep-sea basaltic buoy target according to the vertical mode structure to obtain the underwater drift velocity with stratified mode constraints. S6 integrates the buoy endpoint constraint velocity and outputs uncertainty and quality control results; When the deep-sea basalt buoy has a surface GPS endpoint position in the current cycle or an adjacent cycle, the endpoint constraint equivalent drift velocity is calculated based on the buoy endpoint position and then fused with the underwater drift velocity with stratified mode constraints. In S2, the process of constructing the vertical mode is as follows: Establish the spatial coordinates and vertical coordinates of the target area; where, Indicates the horizontal coordinates to the east. Indicates the horizontal coordinates to the north. Indicates vertical coordinates; assuming sea level. seabed ,in Indicates the water depth in the target area; According to WOA temperature ,salinity and pressure Calculate the density of seawater: in, Indicates depth Seawater density at that location Indicates depth The salinity at that location Indicates depth The temperature at that location Indicates depth Pressure at the location, Represents the equation of state for seawater; Buoyancy frequency squared The calculation is as follows: in, Indicates the buoyancy frequency. Represents gravitational acceleration. Indicates the reference density. Indicates depth Seawater density at that location Represents the vertical coordinate; In obtaining Then, combined with the water depth of the target area Construct the vertical modal equations; The vertical mode is represented as: in, Indicates the first Vertical mode, Indicates the modal order. Indicates the maximum modal order involved in the calculation; The vertical modal equation is expressed as: in, Indicates the first The eigenvalues ​​corresponding to the first mode, Indicates the first Vertical mode, Represents the square of the buoyancy frequency; boundary conditions are set as follows: in, Indicates the sea surface boundary. Indicates the seabed boundary; Normalize the vertical modes: in, This represents the weighting function.

2. The method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints according to claim 1, characterized in that, In S1, the multi-source ocean data includes climatological data, AVISO sea surface dynamic data, and topographic and depth data; among which, climatological data includes WOA temperature, salinity, pressure, and depth; AVISO sea surface dynamic data includes AVISO sea surface height, sea surface height anomaly, absolute dynamic topography, and sea surface geostrophic data. The deep-sea basalt buoy operation information includes the buoy cycle number, surface communication time, dive start time, hovering depth and hovering pressure, maximum profile depth and maximum profile pressure, surface emergence time, pressure-time path, surface GPS endpoint position, and target estimation stage; the target estimation stage includes at least one of the following: dive stage, hovering stage, continued dive stage, bottom contact stage, surfacing stage, and complete underwater cycle.

3. The method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints according to claim 1, characterized in that, In S3, based on the WOA density field, dynamic height, and thermal wind relationship, the vertical structure of the geostrophic flow in the target region is calculated. The calculation process is as follows: Calculation of vertical shear in geostrophic flow using the thermal wind relationship: in, Indicates the eastward flow velocity. Indicates the northward geostrophic flow velocity. Represents gravitational acceleration. Represents the Coriolis parameter. Indicates the reference density. Indicates the density of seawater. Indicates the horizontal coordinates to the east. Indicates the horizontal coordinates to the north. Represents the vertical coordinate; Based on the thermal wind relationship, the vertical integration yields the result relative to the reference layer. Relative geotransfer structure: in, Indicates depth The relative geotransfer vector at a point relative to the reference layer. Indicates depth Geostrophic vector at that location, Represents the reference layer Geostrophic vector at the location; After obtaining the vertical structure of the geostrophic flow, it can be represented as a superposition of several vertical modes: in, Indicates depth The horizontal velocity vector at that location, Indicates the first Vertical mode, Indicates the first First mode amplitude, Indicates the maximum modal order involved in the expansion; No. The amplitude of the first mode is obtained by projection: in, Indicates the first First mode amplitude, This represents the vertical structure of the geostrophic flow to be projected. Indicates the first Vertical mode, Represents the weighting function. Indicates the water depth in the target area; For the horizontal velocity vector, the eastward and northward velocity components can be projected separately: in, Indicates the first The eastward velocity amplitude corresponding to the first mode, Indicates the first The northward velocity amplitude corresponding to the first mode, Indicates the eastward velocity component. This represents the northbound velocity component.

4. The method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints according to claim 1, characterized in that, In S4, the AVISO sea surface dynamic signal includes at least one of sea surface height, sea surface height anomaly, absolute dynamic topography, eastward sea surface landslide, northward sea surface landslide, and sea surface landslide velocity vector.

5. The method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints according to claim 4, characterized in that, The process of selecting the dominant mode or combination of dominant modes is as follows: For the The first mode, expressed at the sea surface or near-surface, is as follows: in, Indicates the first First mode at sea surface or near-surface Speed ​​expression at the location, Indicates the first The first mode at time modal amplitude, Indicates the first The modal values ​​of the first mode at or near the sea surface. Indicates the depth at or near the sea surface; The first Correlation analysis was conducted between sea surface representation of the first mode and AVISO sea surface geostrophic flow: in, Indicates the first The correlation coefficient between the first mode and the AVISO sea surface dynamic signal. Indicates the first Velocity representation of first-order modes at the sea surface or near the surface. Represents the AVISO sea surface geostrophic velocity vector or its components; Calculate the correlation coefficients for eastward and northward velocities respectively: in, This represents the correlation coefficient of eastward velocity. This represents the correlation coefficient of northbound speed. and They represent the first The first mode is expressed in the eastward and northward velocities at the sea surface or near-surface. and These represent the eastward and northward velocity components of the AVISO sea surface geostrophic current, respectively; Construct a comprehensive score : in, Indicates the first The comprehensive score of the first mode, Represents the correlation coefficient. This represents the variance explained. Indicator of consistency in velocity direction This represents the mean squared error or reconstructed residual. , , and Indicates the preset weighting coefficient; A mode is determined to be the dominant mode when it meets the following conditions. : in, This indicates a preset scoring threshold; when multiple modalities meet the screening criteria, a dominant modality set can be constructed. in, This represents the set of dominant modes.

6. The method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints according to claim 1, characterized in that, In S5, the underwater drift velocity calculation process with layered mode constraints is as follows: When a single dominant mode is adopted At that time, the modal constraint velocity is expressed as: in, Indicates depth ,time Modal constraints on underwater drift velocity, Indicates the dominant mode At any moment modal amplitude, Indicates the dominant mode in depth Modal values ​​at; Dominant mode amplitude It can be determined by the AVISO sea surface landslide velocity and the modal values ​​of the dominant mode at the sea surface or near the surface: in, Indicates time AVISO sea surface land rotation velocity vector This indicates that the dominant mode is at or near the sea surface. The modal value at the location; when processing the eastward and northward velocity components separately, it is written as: in, This represents the eastward velocity amplitude corresponding to the dominant mode. This represents the northward velocity amplitude corresponding to the dominant mode. and These represent the eastward and northward velocity components of the AVISO sea surface geostrophic current, respectively; When multiple dominant modes are combined, the modal constraint velocity is expressed as: in, Represents the set of dominant modes. Indicates the first The dominant mode at time modal amplitude, Indicates the first Vertical mode; After obtaining the modal constrained velocity field, and combining it with the pressure-time path of the deep-sea basalt buoy, the buoy is positioned at time... The running depth is represented as: in, Indicates the buoy at time The corresponding runtime depth; for the target runtime stage The stage-average underwater drift velocity is calculated as follows: in, This represents the modally constrained average underwater drift velocity during the target phase. Indicates the start time of the target phase. Indicates the end time of the target phase. Indicates the buoy at time ,depth Modal constraint velocity at the location; The horizontal displacement estimate for the target stage is: in, This represents the horizontal displacement vector obtained from the modal constraint velocity estimation during the target stage.

7. The method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints according to claim 1, characterized in that, In S6, the process of calculating the equivalent drift velocity of the endpoint constraint and fusing it with the underwater drift velocity is as follows: Let the starting endpoint position of the buoy target period be... The end point position is The corresponding times are respectively and Then the equivalent drift velocity of the endpoint constraint is: in, This represents the equivalent drift velocity obtained from the buoy endpoint constraint. Indicates the starting endpoint position. Indicates the end point position. Indicates the time corresponding to the start and end points. Indicates the time corresponding to the end endpoint; Weighted fusion of endpoint constraint velocity and modal constraint velocity: in, This represents the final estimated underwater drift velocity after fusion. This represents the equivalent drift velocity of the endpoint constraints. Indicates the modal constraint drift velocity. Let represent the fusion weights, and satisfy: Fusion weights It can be determined based on endpoint position error, AVISO data error, WOA layering applicability, modal correlation coefficient, modal reconstruction residual, and target stage length; The fusion weights can be expressed as: in, This represents the uncertainty of the endpoint constraint velocity. This represents the uncertainty of the modal constraint velocity; when the uncertainty of the endpoint constraint velocity is small, Increase; when the modal constraint velocity uncertainty is small, Decrease; The uncertainty of the final fusion rate is expressed as: in, This represents the uncertainty in the final fusion rate. Indicates the uncertainty of the endpoint constraint velocity. This represents the uncertainty of the modal constraint velocity. This indicates the fusion residual or unmodeled error; The uncertainty of the modal constraint velocity can be determined by the following error terms: in, This indicates the uncertainty caused by errors in the WOA stratification data. This indicates the uncertainty caused by errors in AVISO sea surface dynamic data. Indicates modal projection error, Indicates modal correlation error. This indicates the deep extension error of the sea surface dynamic signal.

8. The method for estimating the underwater drift velocity of a deep-sea basaltic buoy based on modal constraints according to claim 7, characterized in that, Quality control results can be categorized as reliable, low-reliability, or unusable. When the correlation coefficient of the dominant mode is greater than the preset threshold, the modal reconstruction residual is less than the preset threshold, the AVISO data is complete, the WOA stratification is stable, and the target stage is within the effective water depth range, the quality control result is set to reliable. When some conditions are not met but a velocity estimation result can still be formed, the quality control result is set to low confidence. When AVISO data is missing, WOA stratification is abnormal, the water depth in the target area does not meet the modal solution conditions, the Coriolis parameter is too small, the correlation of the dominant mode is lower than the preset threshold, or the modal extension results are abnormal, the quality control results will be set to unavailable.

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