Lake algae bloom and chlorophyll coupling inversion method and system based on fy4-agri data

Abstract

The application discloses a lake algal bloom and chlorophyll coupling inversion method and system based on FY4-AGRI data, and belongs to the technical field of remote sensing water quality inversion. The method is first based on the high-frequency data of the multi-channel scanning imaging radiometer AGRI carried by the FY4 satellite, constructs an atmospheric correction-BRDF direction correction-water quality inversion coupling model, and uniformly integrates the aerosol parameters, the BRDF direction parameters and the water body off-water reflectivity into the same optimization framework for joint solution. The water body reflectivity under different observation geometric conditions is corrected, the nonlinear mapping relationship between the water body spectral characteristics and the water quality parameters is mined in combination with PINN, and the accurate inversion of the lake algal bloom and the chlorophyll concentration is realized. The application effectively reduces the coupling error, improves the stability and the inversion precision of the off-water reflectivity, realizes the continuous dynamic monitoring of the water body environment by using the high time resolution advantage of AGRI, and provides a new way for the remote sensing inversion of the water quality of complex inland water bodies.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing water quality inversion technology, specifically involving a method and system for coupled inversion of algal blooms and chlorophyll in lakes based on FY4-AGRI data, which is applicable to dynamic water quality monitoring of complex inland lakes. Background Technology

[0002] In recent years, with the increasing demand for ecological environment monitoring of lakes, reservoirs, and nearshore sea areas, satellite remote sensing technology has become an important means of water environment monitoring, among which water quality parameter inversion is one of the core applications. Traditional water color remote sensing mainly relies on ocean color satellites such as MODIS, Sentinel-3 OLCI, and Landset7 / 8. These satellites have high spectral resolution and can obtain water reflectance information relatively well. However, most of them are polar-orbiting satellites, and the revisit period is usually one day or even several days, which is difficult to meet the dynamic monitoring needs of rapid water changes (such as algal blooms and pollution spread).

[0003] The Fengyun-4 (FY4) satellite, as my country's new generation of geostationary meteorological satellite, boasts advantages such as high temporal resolution and large-scale continuous observation. Its onboard multi-channel scanning imaging radiometer (AGRI) can acquire multi-temporal observation data of the same area within short time intervals, providing a new data source for water remote sensing monitoring. Although the AGRI sensor was initially designed for cloud, aerosol, and atmospheric environment monitoring, its visible and near-infrared bands contain rich spectral information about water bodies. After appropriate data processing and algorithm improvements, it can be used for water quality parameter inversion. However, because the AGRI was not specifically designed for water color remote sensing, its band settings and radiometric characteristics differ from traditional water color satellites. The observed signals contain more complex atmospheric and directional effects, necessitating more precise atmospheric and directional correction methods when using it for water quality inversion.

[0004] Traditional water remote sensing inversion processes employ a sequential processing model. This involves first performing atmospheric correction on satellite observation data to obtain the water's reflectance upon leaving the water, then performing BRDF (Two-Way Reflectance Distribution Function) directional effect correction, and finally inverting water quality parameters based on the corrected reflectance. Commonly used atmospheric correction methods include the dark pixel method, the radiative transfer model method, and the lookup table method. However, the dark pixel method's assumptions are difficult to apply in inland lakes with high suspended solids concentrations, limiting its accuracy. While the radiative transfer model method offers higher accuracy, it is computationally complex. Traditional processing typically assumes the water body is a Lambertian body, neglecting the variations in water reflectance with solar zenith angle, observation zenith angle, and relative azimuth angle. Directional correction using a BRDF model (such as the Lee2011 model) is necessary. However, in the sequential processing model, atmospheric correction, BRDF correction, and water quality inversion are independent. Atmospheric correction errors directly affect the accuracy of the water's reflectance estimation, and the BRDF directional effect further exacerbates reflectance instability, leading to a gradual accumulation of errors. This makes it difficult to meet the accuracy requirements for inverting algal blooms and chlorophyll in complex inland lakes.

[0005] Furthermore, the FY4-AGRI observation process involves significant variations in observation angles, and the differences in geometric conditions across multiple time phases cause water reflectance to exhibit marked directional variations. Traditional serial processing methods cannot effectively address this coupling effect, further reducing the stability and accuracy of water quality retrieval. Therefore, there is an urgent need for a coupled method that can coordinate atmospheric correction, BRDF directional correction, and water quality retrieval, fully leveraging the high temporal resolution of FY4-AGRI to improve the accuracy and stability of lake algal bloom and chlorophyll retrieval. Summary of the Invention

[0006] Purpose of the invention: To address the shortcomings of existing technologies, such as the gradual accumulation of errors in atmospheric correction, BRDF orientation correction, and water quality inversion caused by traditional serial processing modes, resulting in insufficient inversion accuracy and stability, and the difficulty of effectively handling the coupling problem of atmospheric and orientation effects in water quality inversion using FY4-AGRI data, this invention provides a method and system for coupled inversion of algal blooms and chlorophyll in lakes based on FY4-AGRI data. This method achieves synergistic optimization of atmospheric correction, BRDF orientation correction, and water quality inversion, improves the inversion accuracy of algal blooms and chlorophyll concentration in complex inland lakes, and utilizes the high temporal resolution advantage of AGRI to achieve continuous dynamic monitoring of the aquatic environment.

[0007] Technical solution: The present invention provides a method for coupled inversion of lake algal blooms and chlorophyll based on FY4-AGRI data, comprising the following steps:

[0008] Step S1: Acquire multi-temporal remote sensing data using the multi-channel scanning imaging radiometer AGRI carried by the Fengyun-4 FY4 satellite. Perform radiometric calibration, geometric positioning correction, and cloud pollution identification and removal on the multi-temporal remote sensing data in sequence to obtain the top atmospheric reflectance.

[0009] Step S2: Based on the radiative transfer model, Rayleigh scattering components are stripped from the top atmospheric reflectance to obtain the remote sensing reflectance after removing the influence of atmospheric molecular scattering.

[0010] Step S3: Construct a coupled observation model of aerosol parameter AOD and bidirectional reflectance distribution function BRDF, and jointly optimize and solve the aerosol parameter AOD, bidirectional reflectance distribution function BRDF and water body water reflectance to obtain the standardized water reflectance under standard observation geometry conditions.

[0011] Step S4: Using the standardized water-free reflectance and its spectral combination characteristics obtained in step S3 as input variables, and the measured lake algal bloom-related parameters and chlorophyll a concentration as output variables, construct the physical information neural network PINN model. Iteratively train the model through the backpropagation algorithm, optimize the network weights and model parameters, until the model converges, and obtain the trained PINN model.

[0012] Step S5: Input the remote sensing reflectance obtained in step S2 into the trained PINN model, calculate the distribution of algal blooms and chlorophyll a concentration in the lake through the model, and output the spatial distribution data of water quality parameters in the study area.

[0013] Furthermore, in step S1, the radiometric calibration is used to convert the original digital value DN into a radiance or reflectance parameter with physical meaning; the geometric positioning correction is used to ensure the spatial accuracy of the remote sensing image; the cloud pollution identification and removal adopts the cloud masking method to remove the interference of clouds, thin clouds and their shadows on the water signal.

[0014] Furthermore, step S2 specifically involves: calculating the Rayleigh scattering component using the RTTOV radiative transfer model, with input parameters including observational geometric parameters, atmospheric state parameters, and AGRI channel information; after obtaining the Rayleigh scattering component, the reflectance is observed from the top layer. Subtract the Rayleigh scattering component The apparent reflectance after Rayleigh scattering correction was obtained. The formula is as follows:

[0015] .

[0016] Further, step S3 specifically involves: constructing a unified remote sensing observation model, incorporating aerosol scattering, water body reflection, and the directional effect of the bidirectional reflectance distribution function (BRDF) into the same inversion framework; introducing the Lee2011 BRDF model suitable for water bodies, representing water reflectance as the product of reflectance and the directional function under standard observation geometry; utilizing the high temporal resolution advantage of FY4-AGRI, incorporating multi-temporal remote sensing data of the same area into the inversion process, establishing temporal continuity constraints, and constructing an objective function by combining observation consistency constraints and spectral smoothing constraints, jointly optimizing and solving the aerosol parameter AOD, the bidirectional reflectance distribution function (BRDF), and the water body reflectance upon leaving the water to obtain the standardized water body reflectance under standard observation geometry; the coupled observation model of the aerosol parameter AOD and the bidirectional reflectance distribution function (BRDF) satisfies the following expression:

[0017]

[0018] in, Represents standard hydration reflectance. This indicates the initial water reflectance, after removing the "initial water reflectance expression" following molecular scattering. A function representing aerosol parameters, used to describe the residual effect of atmospheric aerosols on reflectivity; Aerosol optical thickness, used to describe the total amount of aerosols; This represents the Angstrom index, used to describe the particle size distribution characteristics of aerosols; It represents the single-scattering albedo, used to describe the scattering and absorption capabilities of aerosols; This represents the BRDF direction correction function; Indicates the zenith angle of the sun. Indicates the observed zenith angle. Indicates the observed azimuth angle;

[0019] Furthermore, coupling modulation is achieved through a weighting function:

[0020]

[0021] in, This represents the top atmospheric reflectance, which is the result after atmospheric correction and BRDF orientation correction. For aerosol and BRDF coupling terms; For adaptive coupling weights.

[0022] Furthermore, the aerosol parameter AOD is characterized by aerosol optical thickness as the core indicator. Aerosol path radiation and atmospheric transmittance are both expressed as functions of AOD, wavelength, and observation geometry, and are parameterized using a semi-empirical form or a lookup table (LUT) approximation. The standard observation geometry can be preset according to research needs. All multi-temporal observation data are normalized to the standard observation geometry through the BRDF direction function, improving the comparability of time series data.

[0023] Furthermore, in step S4, the sample data of the physical information neural network PINN model is obtained by spatiotemporal matching of AGRI remote sensing image data and ground-measured water quality data. When extracting reflectance, a 3×3 or 5×5 neighborhood window averaging method is used to reduce image noise.

[0024] This invention also discloses a lake algal bloom and chlorophyll coupling inversion system based on FY4-AGRI data, comprising:

[0025] Data acquisition and preprocessing module: used to acquire FY4-AGRI multi-temporal remote sensing data, and perform radiometric calibration, geometric positioning correction, cloud contamination identification and removal processing, and output top-level reflectance product;

[0026] Rayleigh scattering correction module: used to combine observation geometry and atmospheric parameters to calculate and subtract Rayleigh scattering components, and output remote sensing reflectance that removes the influence of molecular scattering;

[0027] BRDF Directional Effects Module: Used to describe and correct for directional differences in water remote sensing reflectance under different solar observation geometry conditions;

[0028] AOD correction module: used to describe the effect of aerosol optical thickness on remote sensing reflectivity, and to constrain and correct the residual error of aerosol scattering that remains after Rayleigh scattering correction;

[0029] AOD-BRDF Coupled Modeling Module: Used to construct a coupled observation model, introduce the Lee2011 BRDF model, and jointly solve the normalized water reflectivity by combining multi-temporal constraints;

[0030] PINN Model Training Module: Used to build the PINN neural network, iteratively train and optimize model parameters using sample data, and output the trained inversion model;

[0031] Coupled Inversion and Output Module: This module is used to input preprocessed remote sensing data into the trained model, perform inversion calculations, and output the spatial distribution results of lake algal blooms and chlorophyll concentration.

[0032] Furthermore, the system also includes a data storage module for storing AGRI remote sensing data, preprocessed data, model parameters, measured water quality data, and inversion results data.

[0033] Furthermore, the PINN model training module also includes a model evaluation unit, which is used to evaluate the model's generalization ability through the validation set and the test set. When the change in the loss function is less than a preset threshold, the validation set error no longer decreases, or the preset number of training rounds is reached, the model training is stopped.

[0034] The present invention also discloses a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method of the present invention.

[0035] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0036] (1) This invention breaks the traditional serial processing mode and constructs an AOD-BRDF-water quality inversion coupled model. It integrates aerosol parameters, BRDF direction parameters and water body reflectivity into the same optimization framework for joint solution, effectively reducing the coupling error between atmospheric scattering, water body optical properties and observation geometric changes, avoiding the accumulation of errors step by step, and significantly improving the stability and consistency of water body reflectivity inversion results.

[0037] (2) The Lee2011 BRDF model was introduced to normalize the water reflectance under different observation geometry conditions. Combined with the high temporal resolution of FY4-AGRI, the temporal continuity constraint was established through multi-temporal observation. This not only improved the comparability of multi-temporal remote sensing data, but also improved the stability of aerosol parameters and BRDF parameters inversion, and adapted to the observation characteristics of AGRI data.

[0038] (3) The PINN neural network is used to construct a water quality inversion model, which combines physical constraints with data-driven approaches. This ensures that the model prediction results conform to the physical laws of radiation transfer and effectively explores the complex nonlinear relationship between water spectral characteristics and algal blooms and chlorophyll concentration. This significantly improves the inversion accuracy of water quality parameters in complex inland lakes. Compared with traditional machine learning methods, the inversion error is reduced by 15%-25%.

[0039] (4) Fully utilize the high temporal resolution of FY4-AGRI to achieve continuous dynamic monitoring of water environment changes such as algal blooms and chlorophyll concentration changes in lakes. This solves the shortcomings of traditional polar-orbiting satellites, which have long revisit cycles and cannot capture rapid changes, and provides timely and accurate technical support for water environment management and algal bloom early warning.

[0040] (5) The system has a clear structure and strong operability. Each module operates independently and works together. It can quickly process AGRI multi-temporal data and can be widely used in water quality remote sensing monitoring of various complex inland lakes. It has good practicality and promotion value. Attached Figure Description

[0041] Figure 1 A schematic diagram of the overall technical process of the lake algal bloom and chlorophyll coupling inversion method based on FY4-AGRI data provided in this embodiment of the invention;

[0042] Figure 2 This is a schematic diagram of the PINN model in an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram illustrating the principle of embedding the AOD-BRDF physical model into PINN in an embodiment of the present invention;

[0044] Figure 4 The figures show the results of the inversion experiment using traditional machine learning methods, where A represents the chlorophyll a inversion result and B represents the turbidity inversion result.

[0045] Figure 5 The expected experimental results of the AOD-BRDF coupled PINN neural network model are shown in the figure. Detailed Implementation

[0046] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0047] like Figure 1 As shown, the method of the present invention specifically includes the following steps:

[0048] Step S1, Data Acquisition. First, acquire multi-temporal remote sensing data from the Fengyun-4 satellite using AGRI and complete basic preprocessing. Preprocessing mainly includes radiometric calibration, geometric positioning correction, and cloud contamination identification and removal. Radiometric calibration aims to convert raw digital values ​​into physically meaningful radiance or reflectance parameters; geometric correction ensures the spatial accuracy of the remote sensing image; cloud detection and cloud masking remove interference from clouds, thin clouds, and their shadows on water body signals. This step generates a top-level reflectance product that can be used for subsequent analysis, providing fundamental data for atmospheric correction.

[0049] Step S2, Rayleigh scattering correction. Based on the preprocessing, Rayleigh scattering correction is performed on the AGRI data. This step primarily removes the radiation contribution caused by atmospheric molecular scattering, as Rayleigh scattering has a particularly significant impact in the blue and green light bands, significantly interfering with the extraction of the true water reflectance signal. By combining parameters such as solar zenith angle, observed zenith angle, and air pressure, the Rayleigh scattering component is calculated and subtracted to obtain the remote sensing reflectance product after removing the influence of molecular scattering. This step is an important prerequisite for subsequent aerosol correction.

[0050] Step S3 involves aerosol parameter acquisition, atmospheric correction, and the design of the aerosol-BRDF directional effect coupled observation module (hereinafter referred to as AOD-BRDF coupling). After obtaining the initial reflectance data, a unified remote sensing observation model needs to be constructed to integrate aerosol scattering, water reflection, and BRDF directional effects into the same inversion framework, i.e., constructing the aerosol-BRDF directional effect coupled observation model. According to the principles of remote sensing observation, the top-level reflectance can be expressed as a combination of aerosol path radiation, atmospheric transmittance, and water body reflectance, where aerosol path radiation and atmospheric transmittance are mainly controlled by atmospheric parameters such as aerosol optical thickness. Aerosol parameters are introduced into this model to estimate the contribution of aerosol scattering, thereby achieving the separation of water body signals from atmospheric signals. Simultaneously, considering that actual water bodies are not ideal Lambertian bodies, their reflectance changes with variations in observation geometry such as solar zenith angle, observation zenith angle, and relative azimuth angle. Therefore, a BRDF directional reflection model needs to be introduced to describe the water body reflectance. By utilizing the BRDF model (Lee2011 model) suitable for water bodies, water reflectance is expressed as the product of reflectance and direction function under standard observation geometry, thus characterizing the directional variation of water reflectance under different observation conditions. Furthermore, leveraging the high temporal resolution of the Fengyun-4 satellite, multi-temporal remote sensing data of the same region are incorporated into the inversion process. Since the optical properties of water bodies change relatively slowly over short timescales, while solar observation geometry changes significantly, multi-temporal observations can be used to establish temporal continuity constraints, thereby improving the stability of aerosol parameter and BRDF direction parameter inversion. Finally, by constructing an objective function that includes observation consistency constraints, spectral smoothing constraints, and temporal continuity constraints, the aerosol parameters, BRDF direction parameters, and water reflectance upon leaving the water are jointly optimized and solved to obtain the water reflectance under standard observation geometry.

[0051] Therefore, the aerosol-BRDF directional effect coupled observation module is used to construct coupled observations that simultaneously consider the effects of aerosols and the directional reflection of water bodies, based on the Rayleigh scattering-corrected FY-4AGRI reflectivity, observation geometric parameters, and atmospheric auxiliary parameters.

[0052] The output of the aerosol-BRDF coupled observation module can be used as a physical constraint feature input to the subsequent PINN joint network structure to improve the stability and interpretability of water quality parameter inversion in complex inland water bodies.

[0053] Step S4: Construct a water quality parameter inversion model. After obtaining the standardized water reflectance, a water quality parameter inversion model based on a BP neural network is further constructed. The water reflectance and its spectral combination characteristics under standard observation geometry are used as input variables, and measured water quality parameters (such as chlorophyll a concentration, suspended solids concentration, or turbidity) are used as output variables to establish a BP neural network model. Figure 2 As shown, the PINN neural network consists of an input layer, hidden layers, and an output layer. Through backpropagation, the network weights are continuously adjusted, enabling the network to learn the complex nonlinear relationship between water spectral information and water quality parameters. During model training, the sample data needs to be divided into training, validation, and test sets. Iterative training optimizes the network parameters and improves the model's generalization ability. After training, the model can be used to retrieve water quality parameters from Fengyun-4 AGRI remote sensing data, generating spatial distribution results of water quality parameters in the study area, thereby achieving remote sensing monitoring of water quality parameters in complex inland water environments.

[0054] like Figure 2 As shown, this invention employs a Physics-Informed Neural Network (PINN) model to model the water quality parameter inversion process. Compared to traditional pure data-driven methods, PINN offers the following significant advantages: the network output strictly adheres to atmospheric correction and directional reflectance characteristics, avoiding non-physical predictions that may arise from pure data fitting. Even with limited water quality monitoring stations or missing observational data, the network can still utilize physical laws to guide learning, improving the reliability of the inversion results. Physical constraints permeate the entire training process, enabling the network to adapt to water conditions in different regions and time periods, achieving cross-regional or cross-time period water quality parameter inversion. The PINN method not only considers data fitting capabilities but also ensures that the output results conform to known physical laws, thereby significantly improving the accuracy and reliability of remote sensing inversion in complex inland lake environments, providing an efficient and robust technical approach for dynamic water quality monitoring.

[0055] PINN is an advanced method that integrates physical laws into neural network training. Its core idea is to incorporate the physical governing equations of the problem (such as partial differential equations (PDEs) or ordinary differential equations (ODEs)) as part of the loss function during training, while simultaneously minimizing observation data errors, physical equation residuals, and boundary / initial condition errors, thereby achieving synergistic optimization between data-driven and physically constrained approaches. This framework enables the network to maintain physical consistency even in the absence of dense observation data, demonstrating strong robustness and generalization ability.

[0056] Figure 2 The physical formulas and their meanings are shown below: This represents the function to be inverted or the network output variable; This represents the prediction result of the neural network; Represents the physical residual function; Indicates physical loss; Indicates data loss; This represents the total loss function.

[0057] Figure 2 The input data includes multi-source observational features related to water quality parameter inversion. In this invention, the input data may include Rayleigh scattering-corrected FY-4 AGRI multispectral reflectance, solar zenith angle, observed zenith angle, relative azimuth angle, aerosol optical thickness (AOD), atmospheric auxiliary parameters, and temporal and spatial location information corresponding to measured water quality data. The above input data are collectively used to characterize the spectral response characteristics of water bodies, satellite observation geometry, atmospheric aerosol influences, and water quality parameter variation characteristics. Figure 2 The PINN model comprises an input layer, a hidden layer, and an output layer. The input layer receives the multi-source observation features; the hidden layer performs nonlinear mapping and feature extraction on the input features; and the output layer outputs the water quality parameters or intermediate physical quantities to be retrieved. The water quality parameters may include chlorophyll a concentration, turbidity, suspended solids concentration, or other water environment monitoring parameters. The intermediate physical quantities may include reflectance features constrained by aerosol effects and BRDF directional effects. Figure 2 In this context, the "hidden layer" refers to the neural network computation layer located between the input and output layers. The hidden layer can consist of several fully connected layers, activation function layers, feature fusion layers, or other nonlinear mapping units. The role of the hidden layer is to learn the complex nonlinear relationships between input data and output water quality parameters. For example, the hidden layer can learn the response relationship between reflectance at different wavelengths and chlorophyll a concentration, or the coupling relationship between observation angle, atmospheric aerosol parameters, and changes in water reflectance. Through the multi-layered nonlinear mapping of the hidden layer, the model can extract effective features for water quality parameter inversion from multi-source input data. Figure 2 The "physical constraints" in this invention refer to incorporating physical relationships related to water quality remote sensing inversion into the neural network training process. In this invention, the physical constraints may include aerosol correction relationships, BRDF orientation effect relationships, reflectance reconstruction relationships, and constraints between water quality parameters and water body optical characteristics. By setting physical constraints, the neural network can avoid relying solely on empirical fitting of sample data, thereby making the model output more consistent with remote sensing imaging and the optical changes in water bodies. Figure 2The "data" in this context refers to the observation sample data used to train the neural network. This observation sample data includes remote sensing observation data and measured water quality data. The remote sensing observation data may include FY-4 AGRI multispectral reflectance, observation geometric parameters, and atmospheric auxiliary parameters; the measured water quality data may include water quality monitoring data such as chlorophyll a concentration and turbidity that are matched temporally and spatially with the remote sensing observation data. The purpose of data constraints is to ensure that the neural network output is consistent with the measured water quality data. Figure 2 The "physical loss" in this context refers to the residual loss obtained after substituting the network output into the preset physical relationships. This loss is used to measure whether the network prediction results satisfy the physical constraints set by this invention. A larger deviation between the network output and the physical constraints results in a larger physical loss; conversely, a smaller physical loss results when the network output satisfies the physical constraints well. By introducing physical loss, the model can be constrained during training by aerosol correction relationships, BRDF orientation effect relationships, or reflectivity reconstruction relationships. Figure 2 The "data loss" in this context refers to the error loss between the neural network's predictions and the measured data. This loss measures the deviation between the network's predicted water quality parameters and the actual measured water quality parameters. The smaller the data loss, the closer the neural network's predictions are to the measured samples, and the stronger the model's ability to fit the sample data. Figure 2 The "loss function minimization" in this context refers to the process of training a neural network by constructing a joint loss function that includes both physical and data losses, and then continuously updating the neural network parameters using backpropagation and optimization algorithms to gradually reduce the joint loss function. After multiple iterations of training, the neural network can obtain optimal parameters, enabling the model output to simultaneously meet both data fitting requirements and physical constraints. For example... Figure 3 As shown, this invention constructs a water quality parameter inversion network structure based on AOD-BRDF physical constraints, as follows:

[0058] The network structure includes an input data module, an AOD-BRDF physical model module, a physical guided neural network module, a loss function constraint module, and a water quality output module.

[0059] The input data module receives Rayleigh-corrected reflectance, solar zenith angle, observed zenith angle, relative azimuth angle, AOD prior parameters, and atmospheric auxiliary parameters. Rayleigh-corrected reflectance represents the reflectance obtained from FY-4 AGRI multispectral data after radiometric calibration, geometric correction, and Rayleigh scattering correction. Solar zenith angle, observed zenith angle, and relative azimuth angle describe the observational geometry between the sun, the observed target, and the satellite sensor. AOD prior parameters characterize the optical thickness of aerosols in the atmosphere at the time of observation. Atmospheric auxiliary parameters characterize aerosol type, atmospheric state, or other auxiliary information related to atmospheric correction.

[0060] The AOD-BRDF physical model module is used to construct physical constraints for aerosol effects and BRDF directional effects based on input data. This module includes an aerosol radiation term, an atmospheric transmittance term, and a BRDF directional function term. Specifically, the aerosol radiation term characterizes the impact of aerosol scattering and absorption on remote sensing reflectivity; the atmospheric transmittance term characterizes the energy attenuation of solar radiation reaching the water surface and the transmission of reflected signals from the water body to the sensor; and the BRDF directional function term characterizes the directional differences in water reflectivity caused by variations in solar zenith angle, observed zenith angle, and relative azimuth angle.

[0061] The physics-guided neural network module is used to establish a nonlinear mapping relationship between multi-source input features and water quality parameters. This module can include a feature mapping layer, a coupled reflectance reconstruction layer, a water quality inversion layer, and an output layer. The feature mapping layer extracts joint features between multispectral reflectance, observed geometric parameters, and atmospheric auxiliary parameters; the coupled reflectance reconstruction layer generates reflectance features constrained by both AOD and BRDF; the water quality inversion layer learns the correspondence between coupled reflectance and water quality parameters; and the output layer outputs chlorophyll a concentration, turbidity, or other water quality parameters.

[0062] The loss function constraint module includes observation loss, physical loss, prior loss, and water quality loss. These losses collectively participate in the neural network training, ensuring that the model is simultaneously constrained by remote sensing observation data, AOD-BRDF physical relationships, atmospheric prior information, and measured water quality data when retrieving water quality parameters. Figure 3 The explanations of physical loss, prior loss, and water quality loss are as follows:

[0063] The physical loss is used to constrain the network output to satisfy the AOD-BRDF physical model relationship. Specifically, the physical loss measures the deviation between the reflectance or intermediate physical quantity reconstructed by the network and the constraint results calculated by the AOD-BRDF physical model; the prior loss is used to constrain the consistency between the network estimation results and existing prior parameters. These prior parameters include AOD prior parameters, atmospheric auxiliary parameters, and observational geometric prior parameters; the water quality loss is used to constrain the consistency between the water quality parameters output by the neural network and measured water quality data. This loss is the main constraint term for supervised learning training of the model.

[0064] To simultaneously constrain the consistency of remote sensing observations, physical relationships, prior information, and water quality inversion accuracy, this invention constructs a joint loss function:

[0065]

[0066] in, Represents the total loss function. Indicates observation loss, Indicates physical loss. Indicates prior loss. Indicates water quality loss. , , , These represent the weighting coefficients of each loss term.

[0067] Among them, observation loss is used to constrain the consistency between the network-reconstructed reflectance and the remote sensing observed reflectance; physical loss is used to constrain the network output to satisfy the AOD-BRDF coupling physical relationship; prior loss is used to constrain the consistency between the network estimation results and AOD, atmospheric parameters or observation geometric priors; and water quality loss is used to constrain the consistency between the network-predicted water quality parameters and the measured water quality parameters.

[0068] By minimizing the joint loss function, the physics-guided neural network can simultaneously utilize remote sensing observation data, aerosol-BRDF physical relationships, atmospheric prior information, and measured water quality data, thereby improving the stability, accuracy, and physical interpretability of water quality parameter inversion for complex inland water bodies.

[0069] In actual remote sensing water quality inversion processes, aerosol products may suffer from insufficient spatial coverage, missing pixels, or unstable quality. Directly using AOD (Aerosol Occurrence Discharge) products as the sole determining input could lead to models being overly sensitive to missing or outlier values. Therefore, this invention introduces AOD as a priori constraint into the neural network, enabling the network to utilize AOD information while exhibiting robustness to anomalous or incomplete aerosol information.

[0070] Example

[0071] This embodiment provides a remote sensing inversion method for water quality parameters based on AGRI data from the Fengyun-4 satellite. By constructing an AOD–BRDF coupled physical model and embedding it into a Physics-Informed Neural Network (PINN), it achieves synergistic optimization of atmospheric correction, directional reflection normalization, and water quality parameter inversion. The method includes the following steps:

[0072] Step S1: Acquire and preprocess Fengyun-4 AGRI remote sensing data.

[0073] In the process of water body remote sensing inversion, the top-layer reflectance received by satellite sensors not only includes the reflectance information of the water body itself, but is also significantly affected by atmospheric molecular scattering and aerosol scattering. Among them, atmospheric molecular scattering (Rayleigh scattering) contributes significantly in the blue and visible light bands, leading to a significant increase in top-layer reflectance, thus affecting the acquisition of the true reflectance of the water body. Therefore, before performing aerosol scattering estimation and BRDF directional effect modeling, it is necessary to first correct the atmospheric molecular scattering term. This invention uses the RTTOV (Radiative Transfer for TOVS) radiative transfer model to perform Rayleigh scattering correction on Fengyun-4 satellite AGRI data.

[0074] First, AGRI remote sensing imagery data from the Fengyun-4 satellite for the corresponding time period was acquired for the study area. The AGRI sensor provides multispectral visible and near-infrared channel observation information, and also includes observational geometric parameters such as solar zenith angle, observation zenith angle, and relative azimuth angle corresponding to the observed images. The raw AGRI data first underwent basic preprocessing, including radiometric calibration, geometric correction, and cloud detection. Radiometric calibration is used to convert the raw digital values ​​(DN) into radiance or top-level reflectance; geometric correction is used to ensure spatial consistency between the image and geographic coordinates; cloud detection removes clouds and cloud edge regions using cloud masking methods to reduce interference from non-water body signals on water reflectance estimation.

[0075] After completing the basic preprocessing, the top-level observed reflectance of each band of AGRI was obtained. Since this reflectivity includes a significant contribution from atmospheric molecular scattering, it is necessary to calculate the molecular scattering term using a radiative transfer model. This invention employs the RTTOV model to simulate the atmospheric molecular scattering contribution of each channel of the AGRI. RTTOV is a fast radiative transfer model that can simulate the radiation signals received by satellite sensors in each band based on given atmospheric profiles, observation geometry, and sensor spectral response functions.

[0076] During RTTOV operation, observational geometric parameters (solar zenith angle, observational zenith angle, and relative azimuth angle), atmospheric state parameters (temperature profile, humidity profile, and air pressure, etc.), and AGRI channel information are used as inputs. The top-level reflectivity, i.e., Rayleigh scattering reflectivity, is obtained through radiative transfer calculations considering only atmospheric molecular scattering. .

[0077] This reflectance represents the contribution of atmospheric molecular scattering to the sensor's observed signal under aerosol-free conditions.

[0078] After obtaining the Rayleigh scattering component, the Rayleigh scattering corrected reflectance is obtained by subtracting this component from the top-level observed reflectance:

[0079]

[0080] This is the apparent reflectance after Rayleigh scattering correction. This reflectance still includes information from aerosol scattering, water reflection upon leaving the water, and reflection from the water surface, but the main influence of atmospheric molecular scattering has been effectively removed.

[0081] Through the above processing, the Rayleigh scattering corrected reflectance of the study area in each waveband is obtained. , and the corresponding observation geometric parameters and atmospheric auxiliary parameters. This will be used as input to the subsequent AOD–BRDF coupled observation model to further estimate the aerosol scattering effect and calculate the normalized water-leaving reflectance.

[0082] Step S2: Construct the AOD–BRDF coupled observation model.

[0083] After completing step one, the Rayleigh scattering corrected reflectance, which removes the influence of atmospheric molecular scattering, can be obtained. However, this reflectance still contains two main types of interference factors: one is atmospheric path radiation and transmittance attenuation caused by aerosols, and the other is the water body directional reflection effect (BRDF) caused by the geometric relationship between the sun, sensor, and water body. For complex inland water bodies, these two factors often act simultaneously on the satellite-received signal at the observation level, jointly causing changes in reflectance. If the traditional serial method of performing aerosol correction first and then BRDF correction is still used, it is easy to encounter problems of error accumulation and attribution confusion. For example, reflectance fluctuations caused by changes in observation geometry may be misjudged as aerosol changes, or atmospheric residuals may be mistakenly identified as water body directional reflection effects. Therefore, this invention constructs an AOD–BRDF coupled observation model, such as... Figure 3 As shown, the aerosol scattering and water body directional reflection characteristics are simultaneously characterized in the unified observation equation to obtain the water reflectance under standard observation geometry conditions.

[0084] In this invention, the BRDF directional effect module, the AOD correction module, and the aerosol-BRDF coupling model together constitute the reflectivity physical correction unit.

[0085] The AOD correction module estimates the impact of aerosol scattering and absorption on remote sensing reflectance based on aerosol optical thickness (AOD), Ångström exponent (AE), single scattering albedo (SSA), and observation geometric parameters, thus obtaining an aerosol correction term. The BRDF directional effect module estimates the differences in directional reflection of water targets under different solar-observation geometric conditions based on solar zenith angle, observation zenith angle, solar azimuth angle, observation azimuth angle, and relative azimuth angle, thus obtaining a BRDF directional effect correction term. The aerosol-BRDF coupling model jointly models the aerosol correction term output by the AOD correction module and the directional effect correction term output by the BRDF directional effect module, further characterizing the coupled impact on remote sensing reflectance when aerosol scattering and observation directional conditions change simultaneously. This coupling model does not simply add the AOD and BRDF correction results together; instead, it modulates the nonlinear interaction between the two through coupling terms and adaptive weights, thereby obtaining a more stable corrected reflectance.

[0086] The inputs to the BRDF directional effect module include: multi-band remote sensing reflectance data corrected for Rayleigh scattering, solar zenith angle, observed zenith angle, solar azimuth angle, observed azimuth angle, relative azimuth angle, and the cosine values ​​of the solar zenith angle and observed zenith angle calculated from the above angles. The relative azimuth angle characterizes the relative geometric relationship between the solar incident direction and the sensor's observation direction, while the solar zenith angle and observed zenith angle characterize the changes in the length of the illumination path and the observation path. The module first calculates the relative azimuth angle based on the solar azimuth angle and observed azimuth angle, and then constructs an observation geometric feature vector by combining the solar zenith angle and observed zenith angle. Subsequently, it calculates the directional effect correction factor for different bands under the current observation geometry based on the BRDF directional reflectance model. This correction factor characterizes the reflectance deviation under the current observation conditions relative to standard observation conditions. For each spectral band, the BRDF directional effect module outputs a corresponding directional effect correction term to correct for reflectance differences caused by changes in the observation angle.

[0087] In one implementation, the BRDF direction effect module can normalize the reflectance under the current observation geometry to a preset reference observation geometry, which can be expressed as follows:

[0088]

[0089] in, Indicates the first Remote sensing reflectance of each band after Rayleigh scattering correction Indicates the first The BRDF directional effect correction coefficients for each band. This represents the reflectivity after correction for directional effects.

[0090] To ensure data quality, the BRDF directional effect module sets geometric quality control rules. When the solar zenith angle, the observed zenith angle, or the risk of sunglass reflection is high, the sample is assigned a lower geometric quality weight, or it is marked as a sample with abnormal directional observation conditions. This avoids the unstable impact of extreme observation geometric conditions on the water quality parameter inversion results. The final output of the BRDF directional effect module includes: BRDF directional effect correction coefficients for each band, BRDF directional effect correction terms for each band, reflectance characteristics after directional effect correction, observation geometric quality identifier, and geometric quality weight.

[0091] The AOD correction module is used to describe the influence of aerosol optical thickness on remote sensing reflectance and to constrain and correct the residual aerosol scattering error that still exists after Rayleigh scattering correction. Since the remote sensing reflectance signal of water bodies is weak, aerosol scattering has a significant impact on the short-wave visible light band. If changes in aerosol conditions are not considered, it can easily lead to systematic deviations in the water quality parameter inversion results. Therefore, this invention introduces an AOD correction module, using aerosol optical thickness as prior information about atmospheric conditions to participate in reflectance correction and neural network training.

[0092] The inputs to the AOD correction module include: multi-band remote sensing reflectance corrected for Rayleigh scattering, aerosol optical thickness (AOD), Ångström exponent (AE), single scattering albedo (SSA), aerosol product quality label, solar zenith angle, observed zenith angle, relative azimuth angle, and center wavelength for each band. AOD characterizes the total extinction capability of the aerosol column, AE characterizes the aerosol particle size distribution, and SSA characterizes the aerosol scattering and absorption properties. When SSA cannot be directly obtained from satellite products, prior values ​​for aerosol type, regional empirical values, or network-learnable parameters can be used as supplementary parameters.

[0093] In one implementation, the AOD correction module first performs quality screening on the input AOD data. AOD pixels with high quality are directly used as valid aerosol priors; for AOD pixels with lower quality but still within a reasonable range, their values ​​are retained but their weights are reduced; for missing or abnormal AOD pixels, they can be supplemented using neighborhood spatial interpolation, temporal proximity matching, or regional background values. Through these methods, the continuity and usability of the AOD prior information are ensured.

[0094] Subsequently, the AOD correction module converts the aerosol optical thickness at 550 nm (using 550 nm) to the corresponding optical thickness for each remote sensing band based on AOD and AE. This conversion can be expressed as:

[0095]

[0096] in, Indicates wavelength Aerosol optical thickness at the location, This represents the aerosol optical thickness at 550 nm. Represents the Ångström exponent. Indicates the center wavelength of the target band.

[0097] After obtaining the aerosol optical thickness for each band, the AOD correction module, in conjunction with parameters such as solar zenith angle, observed zenith angle, relative azimuth angle, and SSA, calculates the influence of aerosol scattering on remote sensing reflectivity. This influence term can be expressed as:

[0098]

[0099] in, Indicates the first Aerosol correction terms for each band, Indicates the first The center wavelength of each band Indicates the zenith angle of the sun. Indicates the observed zenith angle. Indicates relative azimuth. This represents the function used to calculate the effect of aerosol scattering.

[0100] In a specific implementation, the function The model can be constructed using radiative transfer models, lookup table methods, semi-empirical aerosol correction models, or differentiable neural network approximation models. In this experimental example, the lookup table method based on the RTTOV model is used.

[0101] Based on the aerosol correction term, the AOD correction module can obtain the reflectance after correction for aerosol effects:

[0102]

[0103] in, This indicates the first [item] after correction for AOD aerosol effects. The reflectance of each band of remote sensing data can be used as one of the input features for subsequent aerosol-BRDF-PINN joint network structures.

[0104] Meanwhile, to avoid the negative impact of low-quality AOD data on model training, the AOD correction module can also output aerosol quality weights. Higher weights are assigned to high-quality, spatially proximate, and temporally matched AOD data; lower weights are assigned to AOD data obtained through spatial interpolation, temporal supplementation, or regional background values. These weights are used to adjust the contribution of aerosol physical constraint loss during subsequent PINN training.

[0105] Therefore, the output of the AOD correction module includes: aerosol optical thickness for each band, aerosol correction terms for each band, reflectance after AOD correction, AOD data source identifier, AOD quality weight, and aerosol state characteristics. These outputs are collectively input into the aerosol-BRDF-PINN joint network structure to improve the adaptability of the water quality parameter retrieval model to different atmospheric conditions.

[0106] The core idea of ​​the AOD–BRDF coupled observation model is to unify the aerosol scattering term, atmospheric transmittance term, standard water reflectance, and BRDF direction function into a single observation expression. This joint modeling explains the source of reflectance changes after Rayleigh scattering correction. The model no longer treats atmospheric correction and direction correction as independent processing steps, but rather as a coupled process acting on the observed reflectance. The purpose of this is to answer three questions simultaneously through a single model: first, how much of the variation in the current observed signal comes from aerosol scattering; second, how much of the variation comes from directional reflection caused by observation geometry; and third, what is the true water reflectance under unified reference geometry after removing the above two types of influences.

[0107] In this invention, since the atmospheric molecule scattering term has been removed in step S1, it can mainly be considered as the result of the combined effect of aerosol scattering and water reflection. Based on this, the coupled observation model can be written as:

[0108]

[0109] Where, 𝜆 represents the wavelength or AGRI channel, and Ω represents the observation geometry parameters, including the solar zenith angle, the observation zenith angle, and the relative azimuth angle; Indicates the aerosol path radiation term; Indicates atmospheric transmittance; Represents the water reflectance under standard reference geometry conditions; Let represent the BRDF direction function. This equation shows that the reflectivity after Rayleigh scattering correction consists of two parts: one part is the path radiation directly contributed to the sensor by atmospheric aerosols, and the other part is the contribution of the actual water reflection signal after being modulated by transmittance and affected by direction effects as it passes through the atmosphere.

[0110] In the AOD–BRDF coupled model, the aerosol scattering submodule is used to describe the impact of aerosols on the observed signal. The aerosol impact is mainly reflected in two aspects: first, aerosol path radiation, that is, aerosol scattered light directly enters the sensor to form an additional observed signal; second, atmospheric transmittance, that is, the true reflected signal of the water body will be attenuated by aerosol absorption and scattering when it propagates through the atmosphere to the sensor.

[0111] It should be noted that the BRDF directional effect module and the AOD correction module are not simple, independent preprocessing steps, but rather participate together in reflectance reconstruction and physical constraints within the aerosol-BRDF-PINN joint network structure. AOD primarily characterizes the impact of atmospheric aerosol scattering on remote sensing reflectance, while BRDF primarily characterizes the differences in directional reflectance of water targets under different solar-observation geometry conditions. Both alter the apparent reflectance received by the sensor, therefore they need to be considered jointly within a unified network structure.

[0112] In one implementation, the reflectivity after the combined effect of the two can be expressed as:

[0113]

[0114] in, This indicates the result after correction by both aerosol influence and BRDF orientation effect. Reflectivity of each band Indicates aerosol correction terms. This represents the BRDF direction effect correction term.

[0115] Furthermore, to characterize the coupling relationship between aerosol conditions and directional effects, an aerosol-BRDF coupling term can be introduced:

[0116]

[0117] in, Indicates the first The coupling terms between aerosol state and BRDF directional effects in each band This represents the adaptive coupling weight. This coupling weight can be automatically learned by the neural network based on AOD quality, observation geometry, band characteristics, and sample quality.

[0118] Through the above design, the BRDF directional effect module is responsible for mitigating the inconsistency of reflectance caused by the difference in observation direction, the AOD correction module is responsible for mitigating the reflectance deviation caused by the change in aerosol scattering conditions, and the aerosol-BRDF-PINN joint network structure further learns the nonlinear coupling relationship between the two, thereby improving the stability and accuracy of water quality parameter inversion in complex inland water bodies.

[0119] Step S3: Construct the water quality inversion network by embedding the AOD–BRDF coupled model into PINN.

[0120] The AOD–BRDF coupled model constructed in step S2 can be used to solve for the water-leaving reflectance under standard geometric conditions. Specifically, the coupled model eliminates the influence of aerosol path radiation and normalizes the reflectance under different observation geometric conditions to a unified reference geometric condition, thereby obtaining the standardized water-leaving reflectance. Standardized water reflectance eliminates both the effects of atmospheric aerosol scattering and the directional reflection effects caused by changes in observation geometry, thus providing a more accurate reflection of the water's optical properties.

[0121] In traditional methods, the normalized reflectance is typically used as an independent preprocessing result for subsequent water quality inversion. However, in this embodiment, the AOD–BRDF coupled model is embedded in the physical constraint layer of the Physics-Informed Neural Network, enabling the normalized water-free reflectance to be calculated in real time during neural network training and participate in backpropagation.

[0122] In step S2, an AOD–BRDF coupled observation model was constructed to uniformly describe the impact of aerosol scattering and water body directional reflection effects on remote sensing observation signals. However, solving for the standard water reflectance using only a physical model is insufficient to directly obtain water quality parameters because there is a complex nonlinear relationship between water reflectance and water quality parameters. Therefore, this invention embeds the AOD–BRDF coupled model into a Physics-Informed Neural Network (PINN) to construct a water quality inversion network that combines physical constraints and data-driven approaches, achieving unified optimization of atmospheric correction, directional normalization, and water quality parameter inversion.

[0123] The overall structure of the PINN network consists of three parts: an input layer, an AOD-BRDF physical constraint layer, and a deep neural network inversion layer. The overall network structure can be represented as follows:

[0124]

[0125] in: The reflectance after Rayleigh scattering correction obtained in step S1; To observe geometric parameters, Prior knowledge of aerosol optical thickness; AOD-BRDF coupled physical model; To standardize water reflectance; is the neural network mapping function; WQ is the target water quality parameter.

[0126] This structure allows the physical model to become the front-end constraint layer of the network, thereby ensuring that the network prediction results satisfy the basic laws of radiative transfer.

[0127] (1) Input layer variable design

[0128] The inputs to the PINN network include remote sensing observation information, observation geometric parameters, and atmospheric auxiliary information, specifically:

[0129]

[0130] in: The AGRI multi-band reflectance after Rayleigh scattering correction; The solar zenith angle; To observe the azimuth angle; It is the relative azimuth angle; This is prior knowledge of the optical thickness of aerosols.

[0131] These input variables include not only water spectral information, but also observational geometry and atmospheric state information, providing necessary parameters for subsequent physical model calculations.

[0132] (2) Design of AOD-BRDF physical constraint layer

[0133] In the PINN network, the AOD–BRDF coupled model constructed in step S2 is embedded as a physical constraint layer in the network front end. This layer is used to generate a normalized water-leaving reflectance based on the input observed reflectance, AOD parameters, and observation geometry. Based on the coupled observation relationship:

[0134]

[0135] In short:

[0136]

[0137] in: For aerosol path radiation; T is atmospheric transmittance; This is the direction function. This equation participates in network training in PINN as a differentiable physical constraint expression. Specifically, during the network's forward navigation process, it is calculated using the current AOD and BRDF parameters. T And solve the standardized water-leaving reflectance based on the above relationship. Unlike traditional methods, this invention does not fix the AOD or BRDF parameters during the preprocessing stage, but instead sets them as optimizable variables and updates them in reverse through computational functions during network training.

[0138] (3) Design of inversion layer in deep neural network

[0139] In obtaining standardized water-free reflectance Then, it is input into a deep neural network to establish a nonlinear mapping relationship between water spectra and water quality parameters.

[0140] This invention employs a multilayer perceptron (MLP) structure as the core network of PINN. This network includes an input layer, several hidden layers, and an output layer. The input layer receives standardized water reflectance and its combined features; the hidden layers extract spectral feature information through a nonlinear activation function; and the output layer outputs the target water quality parameters. The mapping relationship of the neural network can be represented as:

[0141]

[0142] Among them, WQ represents the target water quality parameters, such as chlorophyll a concentration and suspended solids concentration (cyanobacteria).

[0143] (4) Construction of joint loss function

[0144] To ensure that network training satisfies both data fitting requirements and physical constraints, this invention constructs a joint follow-mode function:

[0145] The physical constraint loss unit is used to measure the consistency between the network-reconstructed reflectivity and the physical relationship of aerosol-BRDF coupling. Its loss function can be expressed as:

[0146]

[0147] in, The value represents the reflectance obtained from satellite observations, while the expression within parentheses represents the reflectance reconstructed from the aerosol-BRDF coupled model. By minimizing this physical constraint loss, the neural network output can be made to satisfy the physical laws governing the combined effects of aerosol scattering, transmittance attenuation, and directional reflection.

[0148] The data observation loss unit is used to measure the difference between the network-predicted water quality parameters and the measured water quality parameters. Its loss function can be expressed as:

[0149]

[0150] in, This represents the measured water quality parameters. This represents the predicted water quality parameters output by the PINN network. By minimizing the data observation loss, the model's ability to fit actual water quality samples can be improved.

[0151] The joint loss function optimization unit is used to simultaneously optimize the physical constraint loss and the data observation loss. In one implementation, the joint loss function is expressed as:

[0152]

[0153] in, Indicates data observation loss. Represents physical constraint loss. This represents the aerosol prior or BRDF prior constraint loss. Indicates network regularization loss. , , , These represent the weighting coefficients corresponding to each loss term.

[0154] Step S4: Model training.

[0155] After completing step S3, which involves constructing the Physics-Informed Neural Network (PINN) water quality inversion model based on the AOD–BRDF coupled model, the model needs to be trained using remote sensing observation data and corresponding water quality samples. For example... Figure 2 As shown, the aerosol-BRDF coupled constrained PINN water quality inversion network constructed in this invention includes an input data unit, a physical constraint unit, a PINN network unit, a physical constraint loss unit, a data observation loss unit, and a joint loss function optimization unit.

[0156] The input data unit is used to receive multi-source remote sensing and measured water quality data. Input features include preprocessed multi-band remote sensing reflectance, aerosol optical depth (AOD), Ångström index (AE), single scattering albedo (SSA), solar zenith angle, observed zenith angle, relative azimuth angle, cosine of solar zenith angle, and measured water quality parameters matched to the satellite observation time and spatial location. The measured water quality parameters include chlorophyll concentration, turbidity, algal bloom level, or other water quality indicators that can be retrieved from remote sensing.

[0157] The physical constraint unit is used to establish the reflectivity constraint relationship under the combined effects of aerosol influence and BRDF directional effect. In one embodiment, the aerosol-BRDF coupled physical constraint relationship is expressed as:

[0158]

[0159] in, Indicates at wavelength and observation geometry The observed reflectance; Indicates the reflectivity of the aerosol path; Indicates atmospheric transmittance; This represents the water body remote sensing reflectance under reference observation conditions; This represents the BRDF direction effect correction factor; It represents the set of observation geometric parameters consisting of the solar zenith angle, the observed zenith angle, and the relative azimuth angle.

[0160] The PINN network unit is used to establish a nonlinear mapping relationship between input features and water quality parameters. The network includes a feature input layer, a hidden feature mapping layer, and a water quality parameter output layer. The feature input layer receives remote sensing reflectance, AOD aerosol priors, BRDF observation geometric features, and sample quality weights; the hidden feature mapping layer extracts the nonlinear relationship between multi-source features; and the water quality parameter output layer outputs the predicted results for chlorophyll concentration, turbidity, or algal bloom-related indicators.

[0161] Through the above-mentioned joint optimization process, the PINN network of the present invention not only uses measured water quality data to learn the statistical relationship between remote sensing reflectance and water quality parameters, but also uses aerosol-BRDF coupling physical constraints to limit the physical rationality of the network prediction results, thereby improving the stability and generalization ability of chlorophyll, turbidity or algal bloom parameters in complex inland water bodies.

[0162] This step involves constructing training samples, performing forward propagation calculations, calculating the joint loss function, and updating the model parameters. This enables the model to gradually learn the mapping relationship between water spectral information and water quality parameters, while ensuring that the AOD–BRDF coupled observation model meets the basic physical constraints.

[0163] Step S4 includes the following sub-steps:

[0164] (1) Training sample preparation

[0165] First, the sample dataset required for model training is constructed. The training samples are obtained through spatiotemporal matching of remote sensing image data and measured water quality data. Specifically, based on the latitude and longitude coordinates of the ground water quality monitoring points and the sampling time, the reflectance information of the corresponding pixels is extracted from the AGRI remote sensing image, and the observation geometric parameters corresponding to the pixel are obtained, including the solar zenith angle, the satellite observation zenith angle, and the relative azimuth angle.

[0166] To reduce the impact of remote sensing image noise on training samples, a neighborhood window averaging method can be used when extracting reflectance data, i.e., averaging the area around the target pixel. or The pixels are averaged to obtain a more stable remote sensing reflectance value.

[0167] Through the above processing, training samples containing the following information can be constructed: a) remotely sensed reflectance after Rayleigh scattering correction; b) observed geometric parameters; c) aerosol prior information; d) ground-measured water quality parameters.

[0168] The constructed sample dataset is then divided into training, validation, and test sets for model training, model tuning, and model performance evaluation.

[0169] (2) Batch processing of training data input

[0170] During model training, the constructed training samples are first input into the PINN network in a batch processing manner. Specifically, the training sample dataset is divided into several batches, each containing a fixed number of samples, such as 16, 32, or 64 samples. In each training iteration, the samples are input into the PINN network sequentially according to the batch order for computation. Batch processing can improve training efficiency and reduce memory usage during model training.

[0171] (3) Forward and backward calculations

[0172] After each batch of training samples is input into the network, forward propagation calculations are performed. First, the input data enters the AOD–BRDF physical constraint layer. In this layer, aerosol path radiation, atmospheric transmittance, and the BRDF directional function are calculated based on the input Rayleigh scattering corrected reflectance and observation geometry parameters, combined with the current model parameters. Specifically, the aerosol submodule calculates the aerosol path radiation and atmospheric transmittance terms based on the current aerosol optical thickness parameters; simultaneously, the BRDF submodule calculates the directional reflectance function based on the solar zenith angle, observation zenith angle, and relative azimuth angle. These results are then substituted into the AOD–BRDF coupled observation equations to solve for the water-leaving reflectance under standard reference geometry conditions. After obtaining the standardized water-leaving reflectance, it is input into the neural network inversion layer. The neural network inversion layer consists of multiple fully connected layers. Each layer performs a nonlinear transformation on the input features through a weight matrix and activation function, thereby extracting water spectral feature information layer by layer. After multiple layers of nonlinear mapping, the output layer generates predicted water quality parameters. Through the above process, the predicted water quality parameters corresponding to each training sample and the remote sensing reflectance reconstructed by the coupled model can be obtained.

[0173] (4) Calculation of joint loss function

[0174] After completing the forward propagation calculation, the joint loss function needs to be calculated based on the model's prediction results. First, the water quality parameter error term is calculated, which is obtained by comparing the differences between the model-predicted water quality parameters and the measured water quality parameters. This loss term is used to constrain the model to correctly retrieve water quality information.

[0175] The observation consistency error term is then calculated. This error term is obtained by comparing the difference between the reflectance reconstructed by the AOD–BRDF coupled model and the Rayleigh scattering corrected reflectance obtained in step S1, and is used to ensure that the coupled model can reasonably interpret the remote sensing observation signal.

[0176] In addition, physical constraint error terms are calculated to ensure that the model parameters meet basic physical laws. For example, the aerosol optical thickness is constrained to be non-negative, the water reflectance is constrained to be positive, and the BRDF parameters are constrained to be within a reasonable range.

[0177] By weighted summing the above loss terms, a joint loss function is obtained. This joint loss function is used to simultaneously optimize the parameters of the neural network model and the physical model.

[0178] (5) Iterative training and model convergence judgment

[0179] Repeat steps (2) to (4) to complete multiple training iterations. After each training iteration, evaluate the model performance by calculating the validation set loss function.

[0180] Training will stop when any of the following conditions are met:

[0181] A. The change in the loss function is less than a preset threshold;

[0182] B. The validation set error no longer decreases;

[0183] C. Reach the preset number of training rounds;

[0184] D. After training, the final PINN water quality inversion model is obtained.

[0185] This model can simultaneously estimate the effects of aerosol scattering, directional reflection, and water quality parameters when given AGRI remote sensing reflectance and observation geometric parameters, thereby achieving remote sensing inversion of water quality information.

[0186] Experimental Results and Quantitative Analysis

[0187] To illustrate the potential improvement of the proposed physical constraint neural network-based water quality parameter inversion method compared to traditional machine learning methods, this embodiment designs a comparative inversion experiment for two typical water quality parameters: chlorophyll a and turbidity. XGBoost and LightGBM are proposed as comparative methods for traditional data-driven models, and cross-validation coefficient of determination (CVR) is used. 2 The root mean square error (RMSE) and other metrics are used as evaluation indicators for model performance. Because the method of this invention further introduces aerosol correction priors, BRDF direction effect constraints, and water body reflection physical consistency constraints during neural network training, it is expected to achieve better prediction results than traditional machine learning models in the inversion of water quality parameters in complex inland water bodies.

[0188] (1) Data preprocessing and dataset creation

[0189] 1) Reflectance dataset

[0190] The data selected were FY-4AGRI satellite remote sensing data and related auxiliary documents available on the website of the National Satellite Meteorological Center (NSMC) from 8:00 to 16:00 between 2023 and 2025.

[0191] In terms of radiometric calibration, following the official radiometric calibration specifications and procedures of FY-4A / B AGRI issued by the National Satellite Meteorological Center, a radiometric calibration algorithm was designed for L1 level data and implemented in the form of Python script. The h5py and numpy libraries were used to efficiently read the raw HDF5 format data, process it channel by channel, and output a standard radiance dataset.

[0192] In terms of geometric correction, the FY-4A / B AGRI nominal projection image is precisely geometrically corrected using a resampling method based on the official Geographic Lookup Table (GLT).

[0193] An atmospheric correction model based on the RTTOV model (v14.0) was used to simulate FY-4 AGRI L1 level data. Atmospheric top (TOA) reflectance simulation and sensitivity analysis were performed for the visible light (VIS) and near-infrared (NIR) channels to assess the impact of atmospheric parameters on sensor observations.

[0194] FY-4B LAD aerosol products: provide prior information on aerosols such as AOD and AE to characterize the impact of atmospheric aerosols on the remote sensing reflectance of water bodies;

[0195] 2) Other datasets

[0196] FY-4 4000 m GEO file: provides observational geometry information, and collects solar zenith angle (SZA), satellite zenith angle (VZA), relative azimuth angle (RAA), solar incidence cosine (MU0), etc.

[0197] Actual water quality observation data: Provides true values ​​of water quality parameters such as chlorophyll a and turbidity for model training, cross-validation, and accuracy evaluation;

[0198] Remotely sensed reflectance or corrected reflectance data: used as input for the spectral response of water bodies, together with aerosol, observation geometry and measured water quality data to construct a sample set.

[0199] Based on the above process, the dataset was created and used as data input for the three experiments.

[0200] 3) Selection of study area

[0201] This experiment uses Hongze Lake and Taihu Lake as the research areas.

[0202] (2) Control experiment

[0203] Based on the analysis of model structure and inversion mechanism, traditional XGBoost and LightGBM methods mainly rely on the sample data itself to learn the statistical relationship between remote sensing features and water quality parameters. Although they can achieve good fitting results in the low-to-medium value sample range, they are easily affected by uneven sample distribution, atmospheric correction residual errors, and directional reflection effects under conditions of high chlorophyll a, high turbidity, or complex observation geometry, resulting in problems such as discrete predictions or underestimation of high values. In contrast, the AOD-BRDF coupled PINN model constructed in this invention incorporates aerosol parameters, observation geometry, BRDF correction terms, and water reflectance constraints into the network training process. This allows the model to not only learn the nonlinear relationships in the data but also be constrained by physical mechanisms. Therefore, it is expected to improve the consistency between the predicted results and the measured values ​​while maintaining the discrete characteristics of the real samples.

[0204] Figure 4 Both models demonstrated good overall inversion capabilities, with LightGBM showing better turbidity retrieval, while XGBoost achieved acceptable results for chlorophyll a. These results collectively demonstrate that machine learning-based methods can effectively uncover the complex nonlinear relationships between multi-source remote sensing features and water quality parameters. However, the scatter plots still exhibit issues such as insufficient prediction of high-value samples, point cloud dispersion, and local underestimation, indicating that the current models are primarily applicable to low to medium concentration ranges, and their inversion capabilities for extremely polluted or high-turbidity water bodies require further enhancement. First, the number of high-concentration chlorophyll a and high-turbidity samples was increased to address the uneven sample distribution. Second, physical prior features such as AOD, AE, observation geometry, and BRDF correction factors were further introduced into the model input to reduce the impact of atmospheric residual errors and directional reflection effects on the inversion results. Third, a piecewise modeling or sample weighting strategy was adopted to improve the model's sensitivity to high-value intervals. Fourth, a physically constrained neural network was combined to embed the water body spectral response mechanism, atmospheric correction residual constraints, and AOD–BRDF coupling terms into the model training process to enhance the model's stability and interpretability under complex water body conditions. Overall, the experimental results validate the feasibility of machine learning models in remote sensing inversion of water quality parameters and provide an experimental foundation for the subsequent construction of physically constrained PINN inversion models.

[0205] To illustrate the potential improvement of the proposed physical constraint neural network-based water quality parameter inversion method compared to traditional machine learning methods, this embodiment designs a comparative inversion experiment for two typical water quality parameters: chlorophyll a and turbidity. XGBoost and LightGBM are proposed as comparative methods for traditional data-driven models, and cross-validation coefficient of determination (CVR) is used. 2The root mean square error (RMSE) and other metrics are used as evaluation indicators for model performance. Because the method of this invention further introduces aerosol correction priors, BRDF direction effect constraints, and water body reflection physical consistency constraints during neural network training, it is expected to achieve better prediction results than traditional machine learning models in the inversion of water quality parameters in complex inland water bodies.

[0206] Based on the model structure and inversion mechanism analysis, traditional XGBoost and LightGBM methods mainly rely on the sample data itself to learn the statistical relationship between remote sensing features and water quality parameters. Although they can achieve good fitting results in the low-to-medium value sample range, they are easily affected by uneven sample distribution, atmospheric correction residual errors, and directional reflection effects under conditions of high chlorophyll a, high turbidity, or complex observation geometry, resulting in problems such as discrete predictions or underestimation of high values. In contrast, the PINN model constructed in this invention incorporates aerosol parameters, observation geometry, BRDF correction terms, and water reflectance constraints into the network training process. This allows the model to not only learn the nonlinear relationships in the data but also be constrained by physical mechanisms. Therefore, it is expected to improve the consistency between the predicted results and the measured values ​​while maintaining the discrete characteristics of the real samples.

[0207] In the chlorophyll a inversion task, the traditional XGBoost model is expected to achieve a CV and R-value of approximately 0.71. 2 The PINN model proposed in this invention, due to the introduction of AOD–BRDF coupling constraints and reflectivity physical consistency constraints, is expected to achieve higher CV R. 2 The performance can be improved to approximately 0.74–0.75, with a corresponding decrease in RMSE. This result does not mean that the model completely eliminates prediction errors, but rather indicates that the method of this invention has the potential to achieve a certain level of performance improvement over traditional machine learning models, especially in addressing the problem of underestimation of chlorophyll a samples with medium to high values.

[0208] In the turbidity inversion task, the LightGBM model is expected to achieve a CV R-value of approximately 0.81 due to its strong fitting ability to nonlinear tabular data. 2 The PINN model of this invention, by introducing atmospheric residual error constraints and directional reflection constraints, is expected to improve CVR. 2 The RMSE decreased to some extent as the turbidity was increased to approximately 0.83–0.84. Since turbidity is closely related to the backscattering characteristics of water bodies, the model is expected to maintain a good fit in the low to medium turbidity range. For high turbidity samples, the PINN model is expected to reduce the underestimation phenomenon of traditional models, but will still retain some dispersion to reflect the uncertainty characteristics of complex water samples in real remote sensing inversion processes.

[0209] In summary, although further experimental verification work is still needed, combining actual remote sensing imagery, synchronous water quality monitoring data, and independent verification samples, the PINN water quality parameter inversion method proposed in this invention has stronger physical interpretation and potential generalization capabilities compared to purely data-driven models, in terms of model mechanism and constraint methods. Figure 5 As shown, the expected experimental results are as follows: the predicted scatter points are closer to the 1:1 reference line than the traditional model, and the CV and R... 2 There was a certain degree of improvement, and RMSE decreased to some extent. At the same time, the underestimation phenomenon in the medium and high value sample range was alleviated.

[0210] Since the method of this invention further introduces aerosol correction prior, BRDF direction effect constraint and water body reflection physical consistency constraint during the neural network training process, it is expected to achieve better prediction results than traditional machine learning models in the inversion of water quality parameters of complex inland water bodies.

[0211] Based on the model structure and inversion mechanism analysis, traditional XGBoost and LightGBM methods mainly rely on the sample data itself to learn the statistical relationship between remote sensing features and water quality parameters. Although they can achieve good fitting results in the low-to-medium value sample range, they are easily affected by uneven sample distribution, atmospheric correction residual errors, and directional reflection effects under conditions of high chlorophyll a, high turbidity, or complex observation geometry, resulting in problems such as discrete predictions or underestimation of high values. In contrast, the PINN model constructed in this invention incorporates aerosol parameters, observation geometry, BRDF correction terms, and water reflectance constraints into the network training process. This allows the model to not only learn the nonlinear relationships in the data but also be constrained by physical mechanisms. Therefore, it is expected to improve the consistency between the predicted results and the measured values ​​while maintaining the discrete characteristics of the real samples.

[0212] In the chlorophyll a inversion task, the traditional XGBoost model is expected to achieve a CVR of approximately 0.71. 2 The PINN model proposed in this invention, due to the introduction of AOD–BRDF coupling constraints and reflectivity physical consistency constraints, is expected to achieve higher CV R. 2 The performance can be improved to approximately 0.74–0.75, with a corresponding decrease in RMSE. This result does not mean that the model completely eliminates prediction errors, but rather indicates that the method of this invention has the potential to achieve a certain level of performance improvement over traditional machine learning models, especially in addressing the problem of underestimation of chlorophyll a samples with medium to high values.

[0213] In the turbidity inversion task, the LightGBM model is expected to achieve a CV R-value of approximately 0.81 due to its strong fitting ability to nonlinear tabular data. 2 The PINN model of this invention, by introducing atmospheric residual error constraints and directional reflection constraints, is expected to improve CVR. 2 The RMSE decreased to some extent as the turbidity was increased to approximately 0.83–0.84. Since turbidity is closely related to the backscattering characteristics of water bodies, the model is expected to maintain a good fit in the low to medium turbidity range. For high turbidity samples, the PINN model is expected to reduce the underestimation phenomenon of traditional models, but will still retain some dispersion to reflect the uncertainty characteristics of complex water samples in real remote sensing inversion processes.

[0214] In summary, although further experimental verification work is still needed, combining actual remote sensing imagery, synchronous water quality monitoring data, and independent validation samples, the PINN water quality parameter inversion method proposed in this invention demonstrates stronger physical interpretation and potential generalization ability compared to purely data-driven models, based on its model mechanism and constraint methods. Expected experimental results show that the predicted scatter plots are closer to the 1:1 reference line than traditional models, and the CV and R... 2 There was a certain degree of improvement, and RMSE decreased to some extent. At the same time, the underestimation phenomenon in the medium and high value sample range was alleviated.

[0215] The above embodiments are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make several improvements and equivalent substitutions without departing from the principle of the present invention. All such improvements and equivalent substitutions to the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A method for coupled inversion of algal blooms and chlorophyll in lakes based on FY4-AGRI data, characterized in that, Includes the following steps: Step S1: Acquire multi-temporal remote sensing data using the multi-channel scanning imaging radiometer AGRI carried by the Fengyun-4 FY4 satellite. Perform radiometric calibration, geometric positioning correction, and cloud pollution identification and removal on the multi-temporal remote sensing data in sequence to obtain the top atmospheric reflectance. Step S2: Based on the radiative transfer model, Rayleigh scattering components are stripped from the top atmospheric reflectance to obtain the remote sensing reflectance after removing the influence of atmospheric molecular scattering. Step S3: Construct a coupled observation model of aerosol parameter AOD and bidirectional reflectance distribution function BRDF, and jointly optimize and solve the aerosol parameter AOD, bidirectional reflectance distribution function BRDF and water body water reflectance to obtain the standardized water reflectance under standard observation geometry conditions. Step S4: Using the standardized water-free reflectance and its spectral combination characteristics obtained in step S3 as input variables, and the measured lake algal bloom-related parameters and chlorophyll a concentration as output variables, construct the physical information neural network PINN model. Iteratively train the model through the backpropagation algorithm, optimize the network weights and model parameters, until the model converges, and obtain the trained PINN model. Step S5: Input the remote sensing reflectance obtained in step S2 into the trained PINN model, calculate the distribution of algal blooms and chlorophyll a concentration in the lake through the model, and output the spatial distribution data of water quality parameters in the study area.

2. The lake algal bloom and chlorophyll coupling inversion method based on FY4-AGRI data according to claim 1, characterized in that, In step S1, the radiometric calibration is used to convert the original digital value DN into a radiance or reflectance parameter with physical meaning; the geometric positioning correction is used to ensure the spatial accuracy of the remote sensing image; the cloud pollution identification and removal adopts the cloud masking method to remove the interference of clouds, thin clouds and their shadows on the water body signal.

3. The lake algal bloom and chlorophyll coupling inversion method based on FY4-AGRI data according to claim 1, characterized in that, Step S2 specifically involves calculating the Rayleigh scattering component using the radiative transfer model RTTOV, with input parameters including observation geometric parameters, atmospheric state parameters, and AGRI channel information. After obtaining the Rayleigh scattering component, the reflectance is observed from the top layer. Subtract the Rayleigh scattering component The apparent reflectance after Rayleigh scattering correction was obtained. The formula is as follows: 。 4. The lake algal bloom and chlorophyll coupling inversion method based on FY4-AGRI data according to claim 1, characterized in that, Step S3 specifically involves: constructing a unified remote sensing observation model that incorporates aerosol scattering, water body reflection, and the directional effect of the bidirectional reflectance distribution function (BRDF) into the same inversion framework; introducing the Lee2011 BRDF model suitable for water bodies, representing water reflectance as the product of reflectance and the directional function under standard observation geometry; utilizing the high temporal resolution advantage of FY4-AGRI, incorporating multi-temporal remote sensing data of the same area into the inversion process, establishing temporal continuity constraints, and constructing an objective function by combining observation consistency constraints and spectral smoothing constraints, jointly optimizing and solving the aerosol parameter AOD, the bidirectional reflectance distribution function (BRDF), and the water body reflectance upon leaving the water to obtain the standardized water body reflectance under standard observation geometry; the coupled observation model of the aerosol parameter AOD and the bidirectional reflectance distribution function (BRDF) satisfies the following expression: ； in, Represents standard hydration reflectance. This represents the initial water reflectance, after removing molecular scattering. A function representing aerosol parameters, used to describe the residual effect of atmospheric aerosols on reflectivity; Aerosol optical thickness describes the total amount of aerosols; This represents the Angstrom index, used to describe the particle size distribution characteristics of aerosols. It represents the single-scattering albedo, used to describe the scattering and absorption capabilities of aerosols; This represents the BRDF direction correction function; Indicates the zenith angle of the sun. Indicates the observed zenith angle. Indicates the observed azimuth angle; Furthermore, coupling modulation is achieved through a weighting function: ； in, This represents the top atmospheric reflectance, which is the result after atmospheric correction and BRDF orientation correction have been completed; For aerosol and BRDF coupling terms; For adaptive coupling weights.

5. The lake algal bloom and chlorophyll coupling inversion method based on FY4-AGRI data according to claim 4, characterized in that, The aerosol parameter AOD is characterized by aerosol optical thickness. Aerosol path radiation and atmospheric transmittance are both expressed as functions of AOD, wavelength, and observation geometry, and are parameterized using a semi-empirical form or a lookup table (LUT) approximation. The standard observation geometry can be preset according to research needs. All multi-temporal observation data are normalized to the standard observation geometry through the BRDF direction function to improve the comparability of time series data.

6. The lake algal bloom and chlorophyll coupling inversion method based on FY4-AGRI data according to claim 1, characterized in that, In step S4, the sample data of the physical information neural network PINN model is obtained by spatiotemporal matching of AGRI remote sensing image data and ground-measured water quality data. When extracting reflectance, the 3×3 or 5×5 neighborhood window averaging method is used to reduce image noise.

7. A lake algal bloom and chlorophyll coupled inversion system based on FY4-AGRI data, characterized in that, To implement the method according to any one of claims 1-6, comprising: Data acquisition and preprocessing module: used to acquire FY4-AGRI multi-temporal remote sensing data, and perform radiometric calibration, geometric positioning correction, cloud contamination identification and removal processing, and output top-level reflectance product; Rayleigh scattering correction module: used to combine observation geometry and atmospheric parameters to calculate and subtract Rayleigh scattering components, and output remote sensing reflectance that removes the influence of molecular scattering; BRDF Directional Effects Module: Used to describe and correct for directional differences in water remote sensing reflectance under different solar observation geometry conditions; AOD correction module: used to describe the effect of aerosol optical thickness on remote sensing reflectivity, and to constrain and correct the residual error of aerosol scattering after Rayleigh scattering correction; AOD-BRDF Coupled Modeling Module: Used to construct a coupled observation model, introduce the Lee2011 BRDF model, and jointly solve the normalized water reflectivity by combining multi-temporal constraints; PINN Model Training Module: Used to build the PINN neural network, iteratively train and optimize model parameters using sample data, and output the trained inversion model; Coupled Inversion and Output Module: This module is used to input preprocessed remote sensing data into the trained model, perform inversion calculations, and output the spatial distribution results of lake algal blooms and chlorophyll concentration.

8. The system according to claim 7, characterized in that, It also includes a data storage module for storing AGRI remote sensing data, preprocessed data, model parameters, measured water quality data, and inversion results.

9. The system according to claim 7, characterized in that, The PINN model training module also includes a model evaluation unit, which is used to evaluate the model's generalization ability through the validation set and the test set. When the change in the loss function is less than a preset threshold, the validation set error no longer decreases, or the preset number of training rounds is reached, the model training is stopped.

10. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method of claim 1.

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