An inland water level inversion precision improvement method based on SWOT satellite data

Abstract

The present application relates to the technical field of hydrodynamics, in particular to a method for improving water level inversion accuracy of inland water area based on SWOT satellite data, which comprises the following steps: obtaining SWOT data and independent reference water level data of the target water area, identifying effective overlapping observation points and constructing water level difference sequence; based on the error propagation mechanism of interferometric measurement, establishing a design matrix with baseline roll angle error (linear term) and baseline length error (quadratic term) as the core, using least squares method or optimal inversion method to solve system error parameters; and then applying parameter correction to the original data for iterative optimization. The method overcomes the shortcomings of traditional marine correction model under the condition of sparse inland data, and can realize high-precision estimation and elimination of system errors only by relying on limited reference data, effectively improving the water level monitoring accuracy and reliability of inland lakes, reservoirs and other water areas, and providing support for water resources management and hydrological research.

Description

Technical Field

[0001] This invention relates to the field of hydrodynamics, specifically to a method for improving the accuracy of inland water level inversion based on SWOT satellite data. Background Technology

[0002] The Surface Water and Ocean Topography (SWOT) satellite mission, through its innovative Ka-band radar interferometer (KaRIn), has achieved, for the first time, two-dimensional wide-swath elevation observations of global surface water bodies. This technology, hailed as a revolution in hydrological remote sensing, has one of its core objectives: to monitor water level changes in inland lakes, reservoirs, and rivers with high frequency and high spatial resolution, thereby providing unprecedented data support for water resource management, hydrological model validation, and global water cycle research. However, the accuracy of the SWOT interferometry system is profoundly affected by the geometric stability of its baseline (i.e., the virtual connection between the two antennas). During in-orbit operation, minute changes in baseline parameters (especially baseline roll angle and baseline length) caused by factors such as thermal deformation and platform micro-vibrations introduce systematic biases into the retrieved water level data. This bias is not random noise but rather an error with a specific spatial distribution pattern; without precise correction, it will severely limit the reliability of SWOT data in quantitative applications in inland waters.

[0003] Traditionally, the correction of these systematic errors has primarily drawn on the experience of marine hydrology, relying on large-scale, high-density observational data from "cross-points" or "overlapping zones" in open ocean areas to estimate and eliminate these errors through global or regional adjustment models. This approach is effective in marine environments because the ocean surface is homogeneous, spatially continuous, and data overlaps sufficiently. However, inland waters differ fundamentally from oceans in their spatial configuration: they are typically limited in area, irregular in shape, spatially discrete, and subject to strong interference from complex topography and land signals. Therefore, within inland target waters, it is often difficult to obtain a sufficient number of high-quality SWOT data cross-points with ideal spatial distribution to construct a robust global correction model. Directly applying marine correction strategies can lead to inaccurate or even ineffective estimation of correction parameters due to insufficient "samples" and differences in the applicability of error spatial patterns in inland areas, failing to effectively eliminate systematic water level deviations within the target water area.

[0004] Currently, a common approach to improving the quality of SWOT data for inland waters is to heavily rely on external high-precision reference data, such as coastal hydrological stations and laser altimetry satellite data, for simple local difference corrections or empirical fitting. While this method can improve local consistency to some extent, it fails to fundamentally analyze and separate the inherent, physically significant systematic error components of SWOT (such as roll angle error and baseline length error). Its correction effectiveness is highly dependent on the accuracy, spatiotemporal representativeness, and distribution density of the reference data itself, exhibiting weak universality and physical basis. When reference data is scarce or spatiotemporally mismatched, the correction capability of this method drops sharply, and it is difficult to reliably extend the correction parameters to areas of the same water body without reference data.

[0005] Therefore, existing technologies face a prominent contradiction and challenge: on the one hand, systematic errors in SWOT interferometry must be eliminated to unlock the application potential of its data in inland waters; on the other hand, global correction models suitable for the ocean are not well-suited for inland applications, while simple local empirical corrections lack physical foundations and are constrained by reference data. This contradiction constitutes one of the main bottlenecks in the application of SWOT inland hydrology. Developing a specialized correction method that can adapt to the spatial characteristics of inland waters, utilize limited and potentially unevenly distributed reference data, and perform systematic error estimation and elimination based on the physical mechanisms of interferometry has significant technical and application value. This is not only key to improving the accuracy of single observations but also a prerequisite for ensuring the consistency of long-term data series and achieving high-precision hydrodynamic research. Summary of the Invention

[0006] The purpose of this invention is to provide a method for improving the accuracy of inland water level inversion based on SWOT satellite data. By constructing a local cross-correction model, the method uses limited reference data to estimate and eliminate systematic biases caused by baseline roll angle and length errors, thereby significantly improving the accuracy of water level inversion.

[0007] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0008] A method for improving the accuracy of inland water level inversion based on SWOT satellite data includes:

[0009] S1. Obtain SWOT level 2 data of the target inland water area and its spatiotemporal correlation independent reference water level data;

[0010] S2. Preprocess and perform spatiotemporal matching on the obtained data;

[0011] S3. Within the target water area, identify and extract the effective overlapping observation points between the SWOT data and the reference water level data, and their water level difference sequence L, where L=H KaRIn - HRef H KaRIn For SWOT observations, H Ref For reference water level values;

[0012] S4. Using the water level difference sequence L, construct and solve a local cross-correction model to estimate and correct the systematic bias in the SWOT data caused by at least the baseline roll angle error and the baseline length error, wherein the model is configured to be solved under the condition of limited overlap of observations in the inland waters;

[0013] S5. Correct the original SWOT data by applying the estimated system error parameters;

[0014] S6. Evaluate the accuracy of the corrected data and iteratively optimize the correction process based on the evaluation results.

[0015] Furthermore, in step S4, the local cross-calibration model is solved using the least squares method, and the estimated system error parameter R is obtained by the following formula:

[0016] R = B -1 ·L

[0017] Where R is the system error parameter vector, and B is the design matrix constructed based on SWOT observation geometry and error characteristics.

[0018] Furthermore, in step S4, the local cross-calibration model is solved using the optimal inversion method based on the error covariance structure, and the estimated system error parameter R is obtained by the following formula:

[0019] R = (B T C n -1 B) -1 ·B T C n -1 L

[0020] or,

[0021] R = (B T C n -1 B + C r -1 ) -1 ·B T C n -1 L

[0022] Among them, C n To observe the noise covariance matrix, C r This is the constraint information matrix for the system error parameters.

[0023] Furthermore, the design matrix B is constructed based on the following: the baseline roll angle error introduces a linear deviation characteristic in the cross-track direction in the SWOT observation data, and the baseline length error introduces a quadratic deviation characteristic.

[0024] Furthermore, if there are insufficient directly overlapping observation points in step S3, the effective observation information that can be used for correction can be expanded by one of the following methods: utilizing internal overlapping observations between different swaths of the SWOT satellite; or performing time interpolation on areas with gentle water level changes to generate virtual synchronous observation points.

[0025] Furthermore, the iterative optimization in step S6 includes adjusting one or more of the following parameters or strategies: the selection of overlapping observation regions, the weight allocation of observations in the calibration model, and the error covariance matrix C used. n Or C r Or the type of system error parameter to be estimated.

[0026] Furthermore, the independent reference water level data includes: nadir radar altimetry satellite data, laser altimetry satellite data, measured data from ground hydrological stations, or reference water surface elevation data output by hydrological models.

[0027] Furthermore, the inland water areas include lakes, reservoirs, marshes, wetlands, and low-velocity river sections; the corrected water level data is used for hydrological monitoring, water resource management, or related scientific research.

[0028] The beneficial effects of this invention are:

[0029] This invention effectively solves the problem of model failure in inland waters caused by data sparsity in existing correction methods based on globally overlapping data by constructing a local cross-correction model applicable to inland waters. It limits the correction scope to the target water area, directly solving for the parameter vector characterizing the SWOT systematic error using only limited synchronous observation data within that area. By designing a matrix to establish a mathematical relationship between the water level difference sequence and specific parameters reflecting baseline roll angle and baseline length errors, robust estimation of the systematic bias can still be achieved under limited data constraints, breaking through the dependence of traditional methods on large-area continuous overlapping data.

[0030] The correction model established in this invention is based on the physical error propagation mechanism of SWOT interferometry, achieving accurate spatial modeling and elimination of systematic errors. By constructing the basis functions of the design matrix into linear and quadratic terms related to the cross-track coordinates, the model directly corresponds to the spatial deviation pattern introduced by hardware systematic errors within the observation span. The obtained parameter vector has a clear physical meaning, and the correction amount calculated accordingly can accurately offset the systematic distortion caused by the determined error source, thereby ensuring the physical consistency and reliability of the correction results.

[0031] To address the uneven quality and noise-related characteristics of localized data in inland water bodies, this invention employs a strategy combining optimal inversion based on the covariance matrix with regularization constraints, ensuring the numerical stability and accuracy of parameter solutions. By constructing an observation noise covariance matrix to reflect data quality differences and spatial correlations, and introducing a constraint information matrix into the inversion equation to incorporate prior knowledge, this effectively suppresses ill-conditioned problems that may occur when data is scarce or noise is high, thereby improving the method's adaptability and robustness under complex observation conditions.

[0032] This invention establishes a self-perfecting correction loop by setting up an iterative optimization process that includes independent verification and multiple adjustable stages. It allows for feedback adjustments to overlapping data selection, noise weight allocation, prior constraint strength, and model complexity based on verification results. Through multiple iterations, the correction process dynamically adapts to the data conditions and error characteristics of specific water areas, thereby systematically improving the accuracy and reliability of the final water level data and enabling SWOT data to meet the requirements of high-precision hydrological applications.

[0033] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0034] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a schematic diagram of the overall process of the present invention;

[0036] Figure 2 This is a schematic diagram of the local cross-correction of the present invention. Detailed Implementation

[0037] 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 embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] Example 1

[0039] This embodiment describes a method for improving the accuracy of inland water level retrieval based on SWOT satellite data. Addressing the fundamental differences between inland and ocean waters in terms of spatial scale, topographic complexity, and data overlap patterns, it abandons the traditional global cross-correction approach applicable to open oceans and proposes and implements a local cross-correction technique specifically suited for inland waters. Within the target water area, using limited and readily available synchronous or quasi-synchronous observation data, a local correction model for SWOT systematic errors is constructed and solved. This enables high-precision estimation and effective removal of these systematic biases under the reality of limited data sources, including:

[0040] During the data preparation phase, SWOT level 2 data for the target water area is acquired. This includes water surface elevation pixel point cloud data generated by the KaRIn interferometer, with each pixel containing pre-processed geographic location, elevation value, and relevant quality labeling. Simultaneously, external independent reference water level data matching the SWOT observation period and spatial range needs to be acquired. This reference data can originate from various independent Earth observation systems or ground-based measurement networks. For example, it could be radar altimetry data from contemporaneous satellites such as Jason-3, Sentinel-3, or Sentinel-6, whose along-orbit nadir observation points require precise lake waveform reorientation and other specialized processing to obtain reliable water level values; it could also be laser altimetry data from satellites such as ICESat-2; in suitable areas, continuous measured water level time series from coastal hydrological stations, moored buoys, or pressure sensors are preferred; additionally, reference water surface elevation fields output from rigorously validated high-resolution hydrological models or fusion products can also be considered. A common feature of these multi-source reference data is that their water level inversion principle is independent of the interferometric principle of SWOT, thus providing an independent benchmark for cross-calibration.

[0041] When preprocessing and spatiotemporally matching SWOT data and external reference data, a series of standardization processes are required for both. For SWOT pixel cloud data, necessary quality screening is required to remove pixels affected by land contamination, low signal-to-noise ratio, or invalid markers. For external altimetry data, instrument bias correction and atmospheric delay correction are necessary, and the data must be unified to the same geodetic datum and vertical reference frame as the SWOT data. Spatiotemporal matching refers to mapping the external reference data to the spatiotemporal location of each valid SWOT observation pixel through spatial interpolation and temporal alignment, thereby registering a reference water level value H for each SWOT pixel. Ref .

[0042] Subsequently, the core phase of constructing the local cross-calibration model begins. Within the target water area, existing SWOT valid observations H are identified. KaRIn And it was successfully registered with a reliable reference value H. RefThe pixels constitute the effective overlapping observation points. Calculate the water level difference sequence L at all overlapping points, where L... i =H KaRIn i - H Ref i This difference sequence L includes not only the SWOT systematic error signal that we want to estimate, but also the random observation noise of both the SWOT and reference data, as well as possible environmental errors that may not be completely eliminated.

[0043] The key to the local cross-correction model described in this invention lies in establishing the mathematical relationship between the water level difference sequence L and the SWOT systematic error parameter vector R to be determined. The systematic error parameter R includes at least a parameter reflecting the baseline roll angle error and a parameter reflecting the baseline length error. According to the geometric principles of SWOT interferometry, the baseline roll angle error introduces a systematic water level deviation that varies approximately linearly with the cross-track distance throughout the entire observation span; while the baseline length error introduces a systematic water level deviation that varies with the square of the cross-track distance. Based on this physical mechanism, a design matrix B can be constructed. Each row of matrix B corresponds to an overlapping observation point, and its number of columns is equal to the number of systematic error parameters to be estimated. For the i-th observation point, its corresponding row vector in matrix B includes the normalized cross-track coordinates and the values ​​of the basis functions such as the cross-track coordinates. The cross-track coordinates are used to fit the linear term, corresponding to the roll angle error; the square of the cross-track coordinates is used to fit the quadratic term, corresponding to the baseline length error.

[0044] Solving the above model under the condition of finitely overlapping observation points embodies the processing strategy of this invention. A direct and effective method is to use the least squares method. This method is simple and efficient, and suitable for situations where the quality of overlapping points is high and their distribution is relatively reasonable. However, when the observation noise is large or spatial correlation exists, a better choice is to use the optimal inversion method based on the error covariance structure. The core of this method is to construct and utilize the covariance matrix C of the observation noise. n Matrix C n The diagonal elements represent the uncertainty variance of the water level difference at each overlapping point, while the off-diagonal elements characterize the correlation of noise between different points. At this point, the optimal linear unbiased estimate of the system error parameter can be obtained through R = (B T C n -1 B) -1 ·B T C n -1 L is obtained. To further stabilize the solution process and prevent overfitting when the data is extremely sparse, constraints on the parameter R itself can be introduced into the objective function, i.e., a regularization term can be added. This corresponds to using a constraint information matrix C. r The estimation formula then expands to R = (B T C n-1 B + C r -1 ) -1 ·B T C n -1 L. Matrix C r The design matrix B can be set based on prior knowledge of the magnitude and range of systematic errors. For example, it can be set as a diagonal matrix, where the values ​​on the diagonal represent the expected constraint strength on the variation magnitude of each error parameter. It should be noted that the construction of the design matrix B is not limited to the linear and quadratic basis functions mentioned above. More complex basis functions that can more accurately describe its influence mode can be incorporated based on a deeper study of the characteristics of SWOT systematic errors.

[0045] After obtaining the estimated value R of the system error parameter, the original SWOT level 2 data product can be corrected. The correction process is the reverse of the above modeling: for each pixel in the SWOT data, based on its cross-track coordinates and other information, the deviation caused by the system error at that point is calculated using the model represented by the design matrix B, and then calculated from the original observation value H. KaRIn Subtract this deviation from the corrected water level value to obtain the corrected water level value.

[0046] To ensure the calibration effect and optimize the process, accuracy verification and iterative optimization are necessary. The calibrated water level data needs to be compared with another set of completely independent measured verification data that was not involved in the aforementioned model solution process, and quantitative indicators such as root mean square error, bias, and coefficient of determination are calculated. If the accuracy does not meet the preset requirements, the iterative optimization process is initiated. The objects of optimization may include, but are not limited to: reselecting the range or spatial distribution of overlapping observation areas to obtain more representative samples; adjusting the observation noise covariance matrix C. n Weighting different observation points in the matrix reduces the contribution of low-quality data; adjusting the constraint information matrix C r The strength of the correction is adjusted to balance data fitting and solution stability; it may even involve adding or removing certain parameter types from the system error parameter vector R. This iterative process can be repeated until the correction results meet the accuracy threshold required by the application.

[0047] Table 1. Comparison of root mean square error before and after local cross-correction (unit: cm)

[0048]

[0049] As shown in Table 1, at different SWOT data resolutions (0.25 km to 4 km), compared with using field-measured water levels or error-free simulated water levels as references, the root mean square error (RMSE) of the corrected water level data was significantly reduced in most cases. At a 1 km resolution, using error-free reference data, the correction reduced the RMSE from 12.6 cm to 9.6 cm, improving accuracy by 3.0 cm, demonstrating that the method of this invention can effectively estimate and remove the inherent systematic bias of SWOT. When the resolution is 2-4 km and an error-free reference is used, the corrected RMSE shows a slight increase, reflecting a possible slight overfitting of the model under highly smooth data conditions, highlighting the necessity of adjusting model parameters or performing iterative optimization based on data conditions. Figure 2 The invention demonstrated local cross-correction on Lake Baikal. SWOT systematic error correction was achieved using methods such as least squares. Results show that the method of this invention can substantially improve the accuracy of SWOT level inversion in inland waters using limited reference data.

[0050] In summary, this invention proposes a method to improve the accuracy of inland water level inversion based on SWOT satellite data. By acquiring SWOT data and independent reference water level data for the target water area, effective overlapping observation points are identified and a water level difference sequence is constructed. Based on the interferometric error propagation mechanism, a design matrix is ​​established with baseline roll angle error (linear term) and baseline length error (quadratic term) as its core. The system error parameters are solved using the least squares method or optimal inversion method. The original data is then iteratively optimized after parameter correction. This method overcomes the shortcomings of traditional marine correction models under sparse inland data conditions, achieving high-precision estimation and elimination of system errors with only limited reference data. It effectively improves the accuracy and reliability of water level monitoring in inland lakes, reservoirs, and other water bodies, providing support for water resource management and hydrological research.

[0051] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A method for improving the accuracy of inland water level retrieval based on SWOT satellite data, characterized in that, include: S1. Obtain SWOT level 2 data of the target inland water area and its spatiotemporal correlation independent reference water level data; S2. Preprocess and perform spatiotemporal matching on the obtained data; S3. Within the target water area, identify and extract the effective overlapping observation points between the SWOT data and the reference water level data, and their water level difference sequence L, where L=H KaRIn - H Ref H KaRIn For SWOT observations, H Ref For reference water level values; S4. Using the water level difference sequence L, construct and solve a local cross-correction model to estimate and correct the systematic bias in the SWOT data caused by at least the baseline roll angle error and the baseline length error, wherein the model is configured to be solved under the condition of limited overlap of observations in the inland waters; S5. Correct the original SWOT data by applying the estimated system error parameters; S6. Evaluate the accuracy of the corrected data and iteratively optimize the correction process based on the evaluation results.

2. The method as described in claim 1, characterized in that, In step S4, the local cross-calibration model is solved using the least squares method, and the estimated system error parameter R is obtained by the following formula: R = B -1 ·L Where R is the system error parameter vector, and B is the design matrix constructed based on SWOT observation geometry and error characteristics.

3. The method as described in claim 1, characterized in that, In step S4, the local cross-calibration model is solved using the optimal inversion method based on the error covariance structure. The estimated system error parameter R is obtained by the following formula: R = (B T C n -1 B) -1 ·B T C n -1 L or, R = (B T C n -1 B + C r -1 ) -1 ·B T C n -1 L Among them, C n To observe the noise covariance matrix, C r This is the constraint information matrix for the system error parameters.

4. The method as described in claim 2 or 3, characterized in that, The design matrix B is constructed based on the following: the baseline roll angle error introduces a linear deviation characteristic in the cross-track direction in the SWOT observation data, and the baseline length error introduces a quadratic deviation characteristic.

5. The method as described in claim 1, characterized in that, If there are insufficient directly overlapping observation points in step S3, the effective observation information that can be used for correction can be expanded by one of the following methods: utilizing internal overlapping observations between different swaths of the SWOT satellite; or performing time interpolation on areas with gentle water level changes to generate virtual synchronous observation points.

6. The method as described in claim 1, characterized in that, The iterative optimization in step S6 includes adjusting one or more of the following parameters or strategies: the selection of overlapping observation regions, the weighting of observations in the calibration model, and the error covariance matrix C used. n Or C r Or the type of system error parameter to be estimated.

7. The method as described in claim 1, characterized in that, The independent reference water level data includes: nadir radar altimetry satellite data, laser altimetry satellite data, measured data from ground hydrological stations, or reference water surface elevation data output by hydrological models.

8. The method as described in claim 1, characterized in that, The inland water areas include lakes, reservoirs, marshes, wetlands, and low-velocity river sections; the corrected water level data is used for hydrological monitoring, water resource management, or related scientific research.

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