A method for predicting spatial distribution of lake algae blooms based on near-surface wind vector and Bi-GRU-Attention model

Abstract

This invention discloses a method for predicting the spatial distribution of algal blooms in lakes based on near-surface wind vectors and a Bi-GRU-Attention model. The invention employs Empirical Orthogonal Function (EOF) analysis to extract the dominant mode of algal bloom spatial distribution and time coefficients that represent the temporal variation characteristics of algal bloom spatial patterns. Then, a bidirectional gated cyclic unit model based on an attention mechanism is constructed to extract key dynamic features from the wind vector time series and identify wind periods that significantly contribute to the formation of algal bloom spatial distribution patterns. Finally, the time coefficients of the dominant mode of algal bloom spatial distribution are predicted using the wind vector time series state, and the spatial distribution of algal blooms is reconstructed by combining the corresponding spatial modes. This invention provides a new approach for the study of wind-driven algal bloom spatial distribution.

Description

Technical Field

[0001] This invention belongs to the field of water environment science and technology, and in particular relates to the technology for predicting the spatial distribution of algal blooms in lakes. Background Technology

[0002] Algal blooms refer to the formation of visible algal communities in water bodies, which can accumulate on the surface in severe cases, forming green algal paste or even algal mats. They are widely found in eutrophic lakes, reservoirs, ponds, and enclosed or semi-enclosed water bodies such as bays. Algal toxins or odorous substances released during the growth and death of blooming algae can accumulate in organisms and, through biomagnification, threaten human health. Long-term field observations show that large-scale algal blooms in a short period are not caused by the accumulated biomass of algal growth. Because algal cells contain pseudovacuoles, they easily rise to the surface and form algal patches. Under the influence of mild and stable wind fields, these patches drift horizontally downwind and accumulate, leading to a redistribution of algal biomass in the horizontal space. This results in abnormal proliferation of algal biomass and aggravated blooms in local lake areas. Therefore, the spatial distribution of algal blooms is closely related to wind field characteristics.

[0003] In recent years, machine learning methods have been widely used in predicting algal blooms and analyzing the impact of environmental factors on algal blooms. For example, models based on algorithms such as Extreme Gradient Boosting (XGBoost) and Random Forest (RF) have been used to predict the occurrence and time-series trends of algal blooms. Furthermore, methods combining deep learning algorithms such as Long Short-Term Memory (LSTM) and Convolutional Neural Networks (CNN) with remote sensing data have also been used for short-term algal bloom prediction. However, existing machine learning models focus on predictive metrics such as chlorophyll-a concentration, algal density, and whether an algal bloom has occurred. These metrics primarily reflect the temporal dynamics and overall intensity of algal blooms, rather than their spatial distribution. The spatial distribution pattern of algal blooms is often influenced by hydrological and meteorological factors. Studies have shown that wind-driven currents are the main form of current in shallow lakes and play a significant role in the spatial distribution of algae. However, simple functional relationships are insufficient to describe the impact of wind on the spatial distribution of algal blooms. Summary of the Invention

[0004] Purpose of the invention: To address the technical problems existing in the prior art, this invention provides a method for predicting the spatial distribution of algal blooms in lakes based on near-surface wind vectors and the Bi-GRU-Attention model.

[0005] Technical Solution: To achieve the above-mentioned objectives, this invention adopts the following technical solution: a method for predicting the spatial distribution of algal blooms in lakes based on near-surface wind vectors and a Bi-GRU-Attention model, comprising the following steps:

[0006] S1, Data Acquisition: Acquire MODIS surface reflectance data and ERA5-land reanalysis data for the target area, and calculate the phytoplankton index accordingly. and near-surface wind vector ;

[0007] S2, spatial feature extraction of algal blooms: through EOF analysis, the spatial distribution of algal blooms is decomposed into dominant modes that do not change with time, and time coefficients that can represent their temporal variation characteristics are obtained.

[0008] S3, Construction of the spatial distribution model of algal blooms: Construct a bidirectional gated recurrent unit model Bi-GRU-Attention based on the attention mechanism, extract key dynamic features of near-surface wind vector time series, and identify wind conditions that significantly contribute to the formation of the spatial distribution pattern of algal blooms;

[0009] S4. The temporal coefficients of the dominant spatial mode of algal bloom are obtained by predicting the temporal state of wind vectors, and the spatial distribution of algal bloom coverage is obtained by reconstructing the corresponding spatial modes.

[0010] Furthermore, in step S1, MODIS surface reflectance data of the target area is obtained, and the phytoplankton index is calculated using the following formula. ,

[0011]

[0012]

[0013] In the formula, , , They represent the center wavelengths respectively. Red light band, center wavelength Near-infrared band and center wavelength Reflectivity in the shortwave infrared band; This represents the near-infrared band baseline reflectance obtained by linear interpolation of the red band and the short-wave infrared band.

[0014] The near-surface wind vector This can be expressed by the following formula:

[0015]

[0016] In the formula, This represents the near-surface wind vector on day t. Indicates the east-west wind speed component. Indicates the north-south wind speed component. The nonlinear enhancement term representing the east-west wind speed. This represents the nonlinear enhancement term for north-south wind speed.

[0017] Furthermore, step S2, the extraction of spatial features of algal blooms, specifically includes the following steps:

[0018] S21, based on the phytoplankton index within the target area. The 60th percentile of all pixels greater than -0.004 is used as the threshold for the day;

[0019] S22, the target area is gridded, and the algal bloom coverage of the grid is calculated using the following formula.

[0020]

[0021] In the formula, Indicates the first Heavenly Algal bloom coverage within each grid Indicates the first Heavenly The number of pixels in a grid whose FAI value is higher than the daily threshold. This represents the total number of valid cells within the grid.

[0022] S23, Construct a gridded spatiotemporal matrix of algal bloom coverage for EOF analysis. ,

[0023]

[0024]

[0025] In the formula, Indicates the first The spatial distribution vector of the gridded algal bloom coverage over the day. The spatiotemporal matrix representing the gridded algal bloom coverage is denoted by N, where N represents the total number of grids in the target area and T represents the number of valid observation days.

[0026] S24, spatiotemporal matrix of gridded algal bloom coverage Perform anomaly processing to obtain the anomaly matrix. ,

[0027]

[0028]

[0029] In the formula, , This represents the average spatial distribution vector for all observed dates; Indicates the number of valid observation days;

[0030] S25, the anomaly matrix is ​​calculated using the following formula. covariance matrix And perform eigenvalue decomposition.

[0031]

[0032]

[0033] In the formula, Indicates the number of valid observation days. For the first There are 1 spatial mode, corresponding to an N×1 column vector. These are the corresponding eigenvalues, used to characterize the variance explained by this mode;

[0034] S26. Project each row of the anomaly matrix onto each spatial mode, and calculate the time coefficient of each spatial mode using the following formula. ,

[0035]

[0036] In the formula, Indicates the first The mode in the th ... The time coefficient for a given day represents the date spatial distribution for the k-th spatial mode. The response intensity; Indicates the first The spatial distance vector of the sky, through No. The transpose of the row is obtained.

[0037] Furthermore, the feature is that, in step S23, during the construction of the gridded algal bloom coverage spatiotemporal matrix... This also includes spatial downsampling of the original grid resolution.

[0038] Furthermore, the feature is that step S3, the construction of the spatial distribution model of algal blooms, specifically includes the following steps:

[0039] S31, extract the temporal features of the wind vector sequence using GRU, and output the hidden state of the current time step in both the orthogonal and reverse order of the wind vector sequence. ,

[0040]

[0041] In the formula, This is a positive hidden state. This is the reversed hidden state;

[0042] S32 introduces an attention mechanism, calculating the hidden state at each time step using the following formula. Attention score ,

[0043]

[0044] In the formula, Here is the attention weight matrix. For bias terms, Represents the hyperbolic tangent function. These are trainable weight vectors;

[0045] S33, the hidden state at each time step Attention score After normalization and weighting, we obtain the attention-weighted feature vector. :

[0046]

[0047]

[0048] In the formula, It is the normalized time step Attention weight coefficient, This represents the attention score at time step j. This represents the attention-weighted feature vector;

[0049] S34, the attention-weighted feature vector By inputting a multilayer fully connected regression network and performing nonlinear mapping, the predicted values ​​of the time coefficients for each modality on the target date are obtained. Output vector , indicating the first Before the spatial distribution of Tianzaohua The time coefficients of each EOF mode.

[0050] Furthermore, in step S3, the Bi-GRU-Attention model is trained using mean squared error (MSE) as the loss function.

[0051] Furthermore, in step S4, the time coefficients estimated by the model are used. The spatial distribution vector of the gridded algal bloom coverage is obtained by reconstructing the corresponding modalities using the following formula: ,

[0052]

[0053]

[0054] In the formula, The first estimated by the model The one in the first The time coefficient of a day For the corresponding spatial mode vector, This represents the average spatial distribution vector obtained by averaging the spatial distribution vectors of algal bloom coverage over all observation dates. This represents the spatial distance vector.

[0055] Beneficial effects: Compared with existing technologies, it has the following advantages:

[0056] (1) The dominant spatial modes and time coefficients extracted by the EOF analysis method in this invention can effectively reflect the interannual variation of the spatial pattern of algal blooms in Taihu Lake.

[0057] (2) The feasibility of the model of this invention is confirmed by the significant linear correlation between the wind vector sequence and the dominant mode time coefficient of the spatial distribution of algal bloom.

[0058] (3) The predicted values ​​obtained by the wind vector time series information in this invention can characterize the dominant structural features of the spatial distribution of algal blooms in independent samples, reproduce the location and range of the main distribution area of ​​algal blooms, and show that the wind vector time series status is the core factor driving the spatial heterogeneity of lake algal blooms. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the spatial distribution prediction method for lake algal blooms based on near-surface wind vectors and the Bi-GRU-Attention model described in this invention.

[0060] Figure 2 This is the wind speed field of Taihu Lake from 2009 to 2023 in this embodiment of the invention. (a) Fitted curve of Weibull distribution of wind speed in Taihu Lake, (b) Multi-year average wind direction rose diagram.

[0061] Figure 3 This refers to the multi-year average distribution of algal blooms in Taihu Lake from 2009 to 2023 and the spatial modes of EOF1 to EOF4 in this embodiment of the invention.

[0062] Figure 4 This is the annual average algal bloom frequency distribution from 2009 to 2023 in the embodiments of the present invention.

[0063] Figure 5 This is the daily variation and annual average distribution of the time coefficients of the first four EOF modes of algal blooms in Taihu Lake from 2009 to 2023 in this embodiment of the invention.

[0064] Figure 6 This is a correlation analysis of the algal bloom coverage rate of Taihu Lake from 2009 to 2023 with PC1–PC4 in an embodiment of the present invention.

[0065] Figure 7 This is a heat map showing the correlation coefficients between the EOF1-EOF4 time coefficients and the wind field factor in an embodiment of the present invention.

[0066] Figure 8 This is a graph showing the relationship between the predicted and actual values ​​of the time coefficients EOF1-EOF4 in this embodiment of the invention.

[0067] Figure 9 This is a spatial comparison of FAI data and the actual distribution and model-predicted distribution of algal bloom frequency on different dates in the embodiments of the present invention. Detailed Implementation

[0068] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0069] To characterize the complex relationship between wind vector sequences and the spatial distribution of algal blooms, this invention takes Taihu Lake as the research object. First, EOF analysis is used to decompose the spatial distribution of algal blooms into dominant modes that do not change over time, simultaneously obtaining time coefficients (PCs) that represent their temporal variation characteristics. Then, a Bi-GRU-Attention model based on an attention mechanism is constructed to extract key dynamic features of the wind vector sequence and identify wind periods that significantly contribute to the formation of the spatial distribution pattern of algal blooms. Finally, these features are used to estimate the time coefficients of the dominant spatial modes of algal blooms, and the spatial distribution of algal blooms is reconstructed by combining these features with the corresponding spatial modes. This invention, by combining EOF analysis with deep learning temporal modeling, provides a new approach to the study of the spatial distribution of algal blooms driven by wind.

[0070] The following examples provide a detailed description and explanation of the specific technical approach and steps of the present invention.

[0071] This invention provides a method for predicting the spatial distribution of algal blooms in lakes based on near-surface wind vectors and a Bi-GRU-Attention model, specifically including the following steps:

[0072] Step S1, Data Acquisition and Preprocessing

[0073] (1) Phytoplankton index data

[0074] Taking Taihu Lake as the research object, we used MODIS surface reflectance products MOD09GA (Terra) and MYD09GA (Aqua) as remote sensing data sources to acquire images of the Taihu Lake area from May to November each year from 2009 to 2023. Image preprocessing was performed on the Google Earth Engine (GEE) platform. After removing images affected by cloud cover, a total of 1318 days of valid observation data were obtained. The images from 2009–2021 (1136 days) were used as the training set for model training; the images from 2022–2023 were used as an independent test set (182 days) to evaluate the model's predictive performance on the spatial pattern of algal blooms.

[0075] The Planktonic Algal Index (FAI) can effectively enhance the remote sensing response of floating algal blooms while suppressing background signals and some atmospheric influences, making it suitable for large-scale spatial distribution studies of algal blooms in lakes. A threshold of -0.004 was used to identify algal blooms in Taihu Lake. The FAI index calculation formula is as follows:

[0076] (1)

[0077] (2)

[0078] In the formula, , , These represent the reflectance in the red light (645 nm), near-infrared (859 nm), and short-wave infrared (1240 nm) bands, respectively. , and These represent the center wavelengths of the corresponding bands: 645, 859, and 1240 nm.

[0079] (2) Near-surface wind vector data

[0080] The wind vector data comes from the ERA5-Land reanalysis dataset released by the European Centre for Medium-Range Weather Forecasts (ECMWF), selecting the horizontal wind speed components at a height of 10 m from 2009 to 2023: east-west component. ( The time indicates the wind vector pointing east (corresponding to westerly winds, in m / s) and its north-south component. ( The time (in meters per second) indicates that the wind vector points north, corresponding to a southerly wind. Both components together describe the direction and intensity of the wind vector on the horizontal plane. Wind vector data processing was also performed on the GEE platform. First, hourly data for the study area was extracted. , The data is divided into components, and the data for each 24-hour period is averaged; subsequently, a daily average is generated. , Component data.

[0081] Step S2, Characterization of the spatial features of algal blooms

[0082] To analyze the spatial heterogeneity and variation patterns of algal blooms in Taihu Lake, and further explore the correlation between wind vectors and the spatial distribution of algal blooms, the EOF analysis method was used to decompose the spatiotemporal data of gridded algal bloom coverage into mutually orthogonal spatial modes and corresponding time coefficients.

[0083] S21. First, a gridded spatiotemporal data matrix of algal bloom coverage was constructed for EOF analysis. The 60th percentile of all pixels with FAI greater than −0.004 across the entire lake was used as the daily threshold, and the study area was divided into a regular grid of 20×20 pixels.

[0084] S22, calculate the proportion of pixels in each grid that exceed the threshold as the algal bloom coverage of that grid, let the first... Heavenly Algal bloom coverage within each grid for:

[0085] (3)

[0086] In the formula, For the first Heavenly The number of pixels in a grid whose FAI value is higher than the daily threshold. This represents the total number of valid cells within the grid.

[0087] S23, regarding the above The grid undergoes spatial downsampling, using the mean of each 2×2 pixel block as the output, forming... The low-resolution grid yields a low-dimensional gridded spatial distribution vector of algal bloom coverage. Let the first... The spatial distribution vector of the sky for:

[0088] (4)

[0089] In the formula, This represents the number of grid cells after downsampling. Arranging the spatial distribution vectors of all dates in chronological order allows us to construct a gridded spatiotemporal data matrix of algal bloom coverage. Each row of matrix X corresponds to an observation on a given date, and each column corresponds to a spatial grid point.

[0090] (5)

[0091] In the formula, This represents the number of valid observation days.

[0092] S24. Based on this, an EOF analysis is performed on the above matrix. To eliminate the influence of the multi-year average background field, the matrix is ​​first... Perform anomaly processing. Let... This represents the multi-year average spatial distribution vector (N×1 column vector) obtained by averaging the spatial distribution vectors of algal bloom coverage over all observation dates, minus for each row of X. The distance matrix is ​​obtained as follows:

[0093] (6)

[0094] In the formula, , This represents the average spatial distribution vector for all observed dates; Indicates the number of valid observation days.

[0095] S25, then calculate the anomaly matrix. Covariance matrix:

[0096] (7)

[0097] And the covariance matrix Perform eigenvalue decomposition and solve the characteristic equation:

[0098] (8)

[0099] In the formula, For the first There are N spatial modes (N×1 column vectors). These are the corresponding eigenvalues, used to characterize the variance explained by this mode.

[0100] S26, Calculate the time coefficients for each mode, i.e., the anomaly matrix. Each row is projected onto each spatial mode:

[0101] (9)

[0102] In the formula, For the first The spatial distance vector of the sky (i.e.) No. (transpose of a line) For the first The mode in the th ... The time coefficient for a given day represents the date spatial distribution for the k-th spatial mode. The response intensity.

[0103] Step S3, Reconstructing the Spatial Distribution Model of Algal Blooms Based on Wind Vector Sequences

[0104] To simulate the spatial distribution of algal blooms in Taihu Lake using near-surface wind vectors, a spatial distribution reconstruction model based on wind vector sequences was constructed. This model first estimates the time coefficients of each spatial mode, and then reconstructs the spatial distribution of the algal blooms by combining the corresponding modes. The model input consists of the target date and the wind vector sequences for the preceding three days, where the input vector for each day is represented as:

[0105] (10)

[0106] In the formula, For sequence length, The earliest day, The target date is [date]. Each time step contains four variables: east-west wind speed component. North-south wind speed components And nonlinear enhancement terms introduced to improve the model's sensitivity to changes in wind speed intensity. , .

[0107] S31, the model first encodes the wind vector sequence using a GRU to extract its temporal features. For a unidirectional GRU, its time step in the wind vector sequence... The state update process can be represented as follows:

[0108] (11)

[0109] (12)

[0110] (13)

[0111] (14)

[0112] In the formula, and These represent the hidden states of the previous time step and the current time step, respectively. In the candidate hidden state, and These represent updating the door and resetting the door, respectively. For time steps The hidden state, , This is the weight matrix. For bias terms, Represents the hyperbolic tangent function. This represents the Sigmoid activation function. This represents element-wise product.

[0113] In the bidirectional GRU structure, the forward and reverse hidden states are calculated separately according to the temporal order and reverse order of the wind vector sequence, and then the two are concatenated to obtain the expression for each time step in the wind vector sequence:

[0114] (15)

[0115] In the formula, This is a positive hidden state. This is the reversed hidden state.

[0116] S32, building upon this, introduces an attention mechanism to weight each time step of the wind vector sequence to evaluate the relative contribution of the wind vector state at different time steps. Specifically, it weights the hidden states at each time step. Calculate attention score:

[0117] (16)

[0118] In the formula, Here is the attention weight matrix. For bias terms, Represents the hyperbolic tangent function. This is a trainable weight vector.

[0119] S33, the attention score is normalized using the Softmax function to obtain the corresponding attention weight coefficients. :

[0120] (17)

[0121] In the formula, Indicates a time step. This represents an exponential function.

[0122] The attention weight coefficients for each time step are obtained based on the attention mechanism. The hidden states at each time step are weighted and summed to obtain the attention-weighted feature vector. :

[0123] (18)

[0124] Step S4: Spatial distribution prediction of algal bloom coverage

[0125] S34, Finally, the attention-weighted feature vector The input is processed by a multilayer perceptron, and the modal time coefficients for the target date are obtained through nonlinear mapping. This process can be represented as follows:

[0126] (19)

[0127] In the formula, The nonlinear mapping function of the multilayer perceptron, These are learnable parameters. Output vector. , indicating the first Before the spatial distribution of Tianzaohua The time coefficients of each EOF mode.

[0128] S4, Based on model prediction of the spatial distribution vector of gridded algal bloom coverage.

[0129] Time coefficients estimated using the model A linear combination of the corresponding modes reconstructs the spatial distribution of the predicted gridded algal bloom coverage. Reconstructed spatial distribution vector of the sky Predicted values:

[0130] (20)

[0131] In the formula, The first estimated by the model A time coefficient, For the corresponding mode vector, This is the multi-year average spatial distribution vector. This represents the spatial distance vector calculated using the time coefficient estimated by the model.

[0132] Step S5, Model Evaluation Metrics

[0133] The model performance is comprehensively evaluated from two aspects: its ability to estimate EOF time coefficients and its ability to reconstruct spatial distributions. To assess the model's ability to estimate time coefficients, the coefficient of determination (COD) between the estimated values ​​and the corresponding true values ​​is calculated. Its expression is as follows:

[0134] (twenty one)

[0135] In the formula, This is the overall mean of the time coefficients for all training samples.

[0136] Subsequently, the reconstructed spatial distribution was compared with the actual distribution calculated based on formulas (2) and (3), and various evaluation indicators were calculated, including the Nash–Sutcliffe efficiency coefficient (NSE), structural similarity index (SSIM), relative bias (PBIAS), and intersection-over-union ratio (IoU), to comprehensively evaluate the model's ability to reconstruct the spatial distribution of algal blooms. Among these, NSE evaluates the model's predictive performance by comparing the model's estimation error with the estimation error based on the observed mean. For the first... Heaven, based on all of that day The actual algal bloom coverage of each grid Estimated algal bloom coverage Calculate the date :

[0137] (twenty two)

[0138] In the formula, Indicates the first The mean coverage of algal blooms across all grids. The closer NSE is to 1, the higher the simulation accuracy of the model.

[0139] PBIAS measures the systematic bias of the model's simulated spatial distribution relative to the actual spatial distribution. A positive value indicates that the simulated values ​​are generally higher than the actual values, while a negative value indicates that the simulated values ​​are generally lower than the actual values. This metric is calculated globally across all dates and all grid cells in the test set. The closer its absolute value is to 0, the smaller the systematic bias of the model. The expression is:

[0140] (twenty three)

[0141] In the formula, and The meaning is consistent with formula (22). This indicates the number of valid observation days for the test set.

[0142] IoU is used to evaluate the degree of overlap between regions with algal bloom coverage greater than a threshold in simulated and real spatial distributions. First, based on the threshold... Binarize the algal bloom coverage of each grid: Coverage The grid is assigned a value of 1 if it is not a grid, and a value of 0 otherwise. Define the first... The sets of grid indices with a value of 1 in the actual and estimated algal bloom coverage are respectively... and , The IoU expression is: (twenty four)

[0143] in This indicates the number of grid indices within the set. A value closer to 1 indicates a higher degree of overlap between the simulated algal bloom coverage (greater than the threshold) and the actual distribution. At the spatial structure level, the SSIM index is introduced to assess the structural similarity between the simulated and actual spatial distributions. The sky will be the spatial distribution vector of the true algal bloom coverage. Reconstructed matrix (Corresponding to the downsampled low-resolution grid), prediction matrix Similarly, its expression is: (25)

[0144] in, and These are the mean and standard deviation of the matrix, respectively. For covariance; , ,constant , L represents the theoretical dynamic range of algal bloom coverage, so we take L=1. The range of values ​​for SSIM is... The closer the value is to 1, the higher the similarity of the spatial structure.

[0145] Example

[0146] Based on the 5-day-scale near-surface wind vector data of Taihu Lake ERA from May to November 2023 (2009 to 2023), the annual daily-scale wind speed frequency statistics for each year were fitted with the Weibull distribution function. The shape parameter k characterizes the skewness and dispersion of the distribution curve, while the scale parameter c corresponds to the 63.2% quantile of wind speed under the fitted Weibull distribution. The results show that the shape parameter k of the wind speed distribution varies from 2.039 to 2.602 in different years, with a multi-year average of 2.293 and a coefficient of variation of 6.34%. The scale parameter c... The values ​​range from 3.274 to 3.839 m / s, with a multi-year average of 3.564 m / s and an interannual coefficient of variation of 3.82% (Table 1). The coefficient of determination for the fit (R²) is... 2 The values ​​are all greater than 0.7, indicating that the overall distribution of wind speed on an interannual scale is stable, and the typical wind speed level remains consistent. Figure 2 (a)). Regarding wind direction, interannual correlation analysis based on the frequency distribution of wind direction sectors showed that the average Pearson correlation coefficient between the wind direction distribution of Taihu Lake in different years and the multi-year average wind direction was 0.911, and the coefficient of variation was 4.1% (Table 1). The dominant wind direction in different years was concentrated in the range of southeast-east to southeast (112.5° to 135.0°). Figure 2 (b) The frequency variation range of the prevailing wind direction is 14.0% to 21.5% (as shown in Table 1), indicating that the prevailing wind direction of Taihu Lake is relatively stable on a multi-year scale.

[0147] Table 1. Statistical Analysis of the Consistency of Weibull Parameters and Wind Direction Frequency Distribution of Taihu Lake Wind Field from 2009 to 2023

[0148] To quantitatively analyze the spatial modes and variation characteristics of algal blooms in Taihu Lake, this study used EOF analysis to perform spatiotemporal decomposition of FAI image sequences from 2009 to 2023. Figure 2As shown, the results indicate that the cumulative variance explained by modes EOF1–EOF4 reached 57.7%, representing the main modes of spatial distribution variation of algal blooms in Taihu Lake. The average spatial distribution of algal blooms in Taihu Lake over many years shows a high-intensity aggregation along the northwestern shoreline, which is consistent with the higher frequency of algal blooms occurring in the northwestern lake area each year. Figure 3 ). Figure 3 Figures (a) to (e) illustrate the spatial variation characteristics of the EOF spatial modes after removing the multi-year average distribution. Among them, EOF1 (contribution rate 27.4%) represents the diffusion of algal blooms from the northwest coast towards the lake center, and is the most dominant mode in the spatial distribution of algal blooms. Figure 3 As shown in (b), EOF2 (12.5%) exhibits an increase in algal bloom intensity in Taihu Gonghu, Zhushanhu, and Meilianghu, while the algal bloom intensity decreases in the central lake area. Figure 3 As shown in (c); EOF3 (10.9%) is characterized by increased algal bloom intensity in the southwest lake area, especially the nearshore zone, while algal blooms are weakened in the central lake area, Meiliang Lake in the north, and Gong Lake, as shown in (c). Figure 3 As shown in (d); EOF4 (6.9%) exhibits a characteristic of algal blooms concentrating in localized western lake areas while weakening in other areas, as shown in (d). Figure 3 As shown in (e).

[0149] This invention analyzed the interannual variation characteristics of the time coefficients (PC1 to PC4) corresponding to the EOF1 to EOF4 modes of algal blooms in Taihu Lake. PC1 to PC4 all exhibited significant interannual differences, such as... Figure 4 As shown: PC1 remained at a low level between 2009 and 2014, was relatively high from 2015 to 2020, and then showed a downward trend from 2021 to 2023, reaching its maximum value (0.501) and minimum value (-0.855) in 2017 and 2023, respectively. Statistical analysis showed a significant linear positive correlation between the annual average PC1 value and the annual average algal bloom coverage (r = 0.928, p < 0.001), while the correlation between PC2–PC4 and the annual average algal bloom coverage was not significant. Figure 5 .

[0150] To quantitatively assess the driving effect of near-surface wind field on the dominant spatial distribution mode of algal blooms in Taihu Lake, this invention analyzes the correlation between the time coefficients corresponding to EOF1–EOF4 and wind speed and wind vector components (u, v). The results show that different spatial modes exhibit different response characteristics to wind field factors. Figure 6Among them, the time coefficient PC1 corresponding to EOF1 showed a significant negative correlation with wind speed (r = -0.271, p < 0.001), indicating that as wind speed increases, water mixing intensifies, making it difficult for floating cyanobacteria to form large-scale aggregations on the lake surface. It also showed a significant negative correlation with the v component of wind speed (r = -0.109, p < 0.001), indicating that weak northerly winds favor the diffusion of algal blooms from the northwest coast towards the lake center. Unlike EOF1, the time coefficient PC2 corresponding to EOF2 showed a significant positive correlation with wind speed (r = 0.164, p < 0.001) and also a significant positive correlation with the v component (r = 0.119, p < 0.001), but a significant negative correlation with the u component (r = -0.178, p < 0.001). Therefore, under the influence of the southeasterly wind field, EOF2 exhibits a spatial mode of increased algal bloom outbreaks in Zhushan Lake, Meiliang Lake, and Gong Lake in the northern part of Taihu Lake. The time coefficient PC4 corresponding to EOF4 shows a negative correlation with both the u component (r = -0.064, p = 0.023) and the v component (r = -0.099, p < 0.001), indicating that under the influence of northeasterly winds, algal blooms that have long accumulated along the northwest coast are more likely to accumulate in the western Taihu Lake area downwind. Overall, the correlation between the dominant spatial mode of algal blooms and wind speed and direction lays the foundation for constructing a spatial distribution model of algal blooms driven by near-surface wind vectors.

[0151] like Figure 7 As shown, the correlation between PC1–PC4 and wind speed and u and v components is illustrated. The spatial modal temporal coefficient prediction model for algal blooms, driven by wind vector sequence characteristics, exhibits a significant linear correlation between the predicted and actual values ​​of the temporal coefficients (PC1–PC4) for the first four modes (EOF1–EOF4) of algal blooms in Taihu Lake, with coefficients of determination (R²) of 0.906, 0.887, 0.849, and 0.619, respectively. This indicates that the temporal characteristics of wind vectors can characterize the temporal variation of the spatial distribution of algal blooms. Near-surface wind vector temporal sequences have a significant structural constraint on the spatial pattern of algal blooms, thus shaping the spatial distribution of algal blooms in Taihu Lake.

[0152] As shown in Table 2, the predicted values ​​of the model in this invention maintain good consistency with the actual values ​​on the independent test set in terms of overall trend. The Nash-Sutcliffe efficiency coefficient (NSE) is 0.514, indicating that the model has stable predictive ability. From a spatial structure perspective, the average structural similarity index (SSIM) and intersection-over-union ratio (IoU) of the predicted and actual spatial distributions of algal blooms are 0.629 and 0.821, respectively (Table 2). Furthermore, the bias analysis results show that the relative bias of the prediction (PBIAS) is -1.11%, indicating no significant systematic bias. In summary, within the prediction framework based on EOF decomposition, the spatial distribution of algal blooms reconstructed using the time coefficients predicted by wind vector time series information combined with the first ten EOF modes can effectively characterize the dominant structural features of the spatial distribution of algal blooms in independent samples, further verifying that wind vector time series information has a significant constraining effect on the dominant mode of the spatial distribution of algal blooms.

[0153] Table 2. Comprehensive evaluation index of the model's performance in reconstructing the spatial distribution of algal blooms.

[0154] Figure 8 A scatter plot showing the estimated time coefficients and their corresponding true values ​​obtained by mapping the wind vector sequence through a multilayer perceptron after feature extraction using GRU and attention mechanisms is presented, illustrating the linear relationship between the two. Figure 9 It demonstrates how the spatial distribution of gridded algal bloom coverage and the actual distribution on a given day can be reconstructed by linearly combining the estimated time coefficient with the corresponding spatial mode.

[0155] The dominant spatial modes extracted using the EOF analysis method in this invention exhibit a high degree of consistency with the interannual outbreak characteristics of algal blooms in Taihu Lake over time, effectively carrying the core information of the spatiotemporal variation of algal blooms in Taihu Lake. Wind vector sequences have a significant structural constraint effect on the dominant modes of algal bloom spatial distribution. The predicted values ​​obtained using wind vector temporal information can characterize the dominant structural features of algal bloom spatial distribution in independent samples, reproducing the location and range of the main algal bloom distribution areas, indicating that the temporal state of wind vectors is the core factor driving the spatial heterogeneity of algal blooms in Taihu Lake.

[0156] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for predicting the spatial distribution of algal blooms in lakes based on near-surface wind vectors and a Bi-GRU-Attention model, characterized in that, Includes the following steps: S1, Data Acquisition: Acquire MODIS surface reflectance data and ERA5-Land reanalysis data for the target area, and calculate the phytoplankton index accordingly. and near-surface wind vector ; S2, Algal bloom spatial feature extraction: The spatial distribution of algal blooms is decomposed into dominant modes that do not change with time through EOF analysis, and time coefficients that can represent the temporal variation characteristics of the dominant modes are obtained. S3, Construction of the spatial distribution model of algal blooms: Construct a bidirectional gated recurrent unit model Bi-GRU-Attention based on the attention mechanism, extract key dynamic features of near-surface wind vector time series, and identify wind conditions that significantly contribute to the formation of the spatial distribution pattern of algal blooms; S4. The temporal coefficients of the dominant spatial mode of algal bloom are obtained by predicting the temporal state of wind vectors, and the spatial distribution of algal bloom coverage is obtained by reconstructing the corresponding spatial modes.

2. The method for predicting the spatial distribution of lake algal blooms based on near-surface wind vectors and the Bi-GRU-Attention model according to claim 1, characterized in that, In step S1, MODIS surface reflectance data of the target area is obtained, and the phytoplankton index is calculated using the following formula. , ， ， In the formula, , , They represent the center wavelengths respectively. Red light band, center wavelength Near-infrared band and center wavelength Reflectivity in the shortwave infrared band; This represents the near-infrared band baseline reflectance obtained by linear interpolation of the red band and the short-wave infrared band. The near-surface wind vector This can be expressed by the following formula: ， In the formula, This represents the near-surface wind vector on day t. Indicates the east-west wind speed component. Indicates the north-south wind speed component. The nonlinear enhancement term representing the east-west wind speed. This represents the nonlinear enhancement term for north-south wind speed.

3. The method for predicting the spatial distribution of lake algal blooms based on near-surface wind vectors and the Bi-GRU-Attention model according to claim 1, characterized in that, Step S2, the extraction of spatial features of algal blooms, specifically includes the following steps: S21, based on the phytoplankton index within the target area. The 60th percentile of all pixels greater than -0.004 is used as the threshold for the day; S22, the target area is gridded, and the algal bloom coverage of the grid is calculated using the following formula. ， In the formula, Indicates the first Heavenly Algal bloom coverage within each grid Indicates the first Heavenly The number of pixels in a grid whose FAI value is higher than the daily threshold. This represents the total number of valid cells within the grid. S23, Construct a gridded spatiotemporal matrix of algal bloom coverage for EOF analysis. , ， ， In the formula, Indicates the first The spatial distribution vector of the gridded algal bloom coverage over the day. The spatiotemporal matrix representing the gridded algal bloom coverage is denoted by N, where N represents the total number of grids in the target area and T represents the number of valid observation days. S24, spatiotemporal matrix of gridded algal bloom coverage Perform anomaly processing to obtain the anomaly matrix. , ， ， In the formula, , This represents the average spatial distribution vector for all observed dates; Indicates the number of valid observation days; S25, the anomaly matrix is ​​calculated using the following formula. covariance matrix And perform eigenvalue decomposition. ， ， In the formula, Indicates the number of valid observation days. For the first There are 1 spatial mode, corresponding to an N×1 column vector. These are the corresponding eigenvalues, used to characterize the variance explained by this mode; S26. Project each row of the anomaly matrix onto each spatial mode, and calculate the time coefficient of each spatial mode using the following formula. , ， In the formula, Indicates the first The mode in the th ... The time coefficient for a given day represents the date spatial distribution for the k-th spatial mode. The response intensity; Indicates the first The spatial distance vector of the sky, through No. The transpose of the row is obtained.

4. The method for predicting the spatial distribution of lake algal blooms based on near-surface wind vectors and the Bi-GRU-Attention model according to claim 3, characterized in that, In step S23, the spatiotemporal matrix of gridded algal bloom coverage is constructed. This also includes spatial downsampling of the original grid resolution.

5. The method for predicting the spatial distribution of lake algal blooms based on near-surface wind vectors and the Bi-GRU-Attention model according to claim 1, characterized in that, Step S3, constructing the spatial distribution model of algal blooms, specifically includes the following steps: S31, extract the temporal features of the wind vector sequence using GRU, and output the hidden state of the current time step in both the orthogonal and reverse order of the wind vector sequence. , ， In the formula, This is a positive hidden state. This is the reversed hidden state; S32 introduces an attention mechanism, calculating the hidden state at each time step using the following formula. Attention score , ， In the formula, Here is the attention weight matrix. For bias terms, Represents the hyperbolic tangent function. These are trainable weight vectors; S33, the hidden state at each time step Attention score After normalization and weighting, we obtain the attention-weighted feature vector. : ， ， In the formula, It is the normalized time step Attention weight coefficient, This represents the attention score at time step j. This represents the attention-weighted feature vector; S34, the attention-weighted feature vector By inputting a multilayer fully connected regression network and performing nonlinear mapping, the predicted values ​​of the time coefficients for each modality on the target date are obtained. Output vector , indicating the first Before the spatial distribution of Tianzaohua The time coefficients of each EOF mode.

6. The method for predicting the spatial distribution of lake algal blooms based on near-surface wind vectors and the Bi-GRU-Attention model according to claim 1, characterized in that, In step S3, the Bi-GRU-Attention model is trained using mean squared error (MSE) as the loss function.

7. The method for predicting the spatial distribution of lake algal blooms based on near-surface wind vectors and the Bi-GRU-Attention model according to claim 1, characterized in that, In step S4, the time coefficients estimated by the model are used. The spatial distribution vector of the gridded algal bloom coverage is obtained by reconstructing the corresponding modalities using the following formula: , ， ， In the formula, The first estimated by the model The one in the first The time coefficient of a day For the corresponding spatial mode vector, This represents the average spatial distribution vector obtained by averaging the spatial distribution vectors of algal bloom coverage over all observation dates. This represents the spatial distance vector.

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