Three-dimensional triple configuration potential evapotranspiration fusion method and system considering neighborhood space-time non-stationary error

Abstract

The invention provides a three-dimensional triple configuration potential evapotranspiration fusion method and system considering neighborhood space-time non-stationary errors, and relates to the technical field of potential evapotranspiration estimation. The method comprises the following steps: obtaining a potential evapotranspiration observation value of a target watershed meteorological station and three sets of independent potential evapotranspiration data sets, and unifying temporal-spatial resolution; calculating a Gaussian kernel function matched with the predetermined space-time window, and performing data standardization by using the kernel function; constructing a variance calculation model of the three-dimensional triple configuration error, and obtaining a variance of an error of neighborhood dimension spatio-temporal information contained in each data set under a predetermined spatio-temporal window; and constructing a data fusion model based on a least square framework, determining an optimal fusion weight and realizing fusion of the multi-source potential evapotranspiration data. According to the method, the problems that local space-time non-stationary errors exist during fusion of the potential evapotranspiration data and the fusion precision is influenced by the scale effect of the space-time window are solved, and the precision of the potential evapotranspiration fusion data is effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of potential evapotranspiration estimation, and particularly to a three-dimensional triple-configuration potential evapotranspiration fusion method and system considering neighborhood spatio-temporal non-stationary errors. Background Art

[0002] Potential evapotranspiration is a key variable for measuring the atmospheric evapotranspiration demand and surface energy supply, and can also be used as an important basis for judging whether extreme meteorological events occur. It is widely used in fields such as agricultural irrigation and drought monitoring. Limited by the actual observation difficulty, obtaining large-scale and long-term potential evapotranspiration data usually relies on datasets generated by remote sensing inversion, reanalysis models, and land surface model simulations. The aforementioned datasets are all obtained indirectly and generally have certain errors compared with actual observation data.

[0003] To effectively improve data accuracy, fusing multiple potential evapotranspiration data has become the mainstream method. Among them, the Chinese invention patent with the publication number CN118551528A discloses a multi-source data fusion method based on the pixel-scale error covariance matrix. This method only processes the pixel errors at the regional scale and does not deeply consider the local spatio-temporal non-stationary errors, and cannot effectively capture the fine changes of potential evapotranspiration data in the local area.

[0004] The Chinese invention patent with the publication number CN117010262A discloses a method for spatio-temporal fusion of global terrestrial evapotranspiration based on deep learning. Although using a deep learning model for spatio-temporal fusion of data improves the data fusion accuracy, it relies on a large amount of ground observation site data for model training and has a strong dependence on data. At the same time, deep learning methods often face problems such as poor model interpretability and insufficient generalization ability, and their applicability is significantly limited in areas without sufficient observation data support.

[0005] In summary, how to overcome the spatio-temporal non-stationary errors of potential evapotranspiration data while paying attention to the spatio-temporal window scale effect and data fusion in areas without sufficient observation data support is the current research focus. Therefore, carrying out research on multi-source data fusion of potential evapotranspiration considering neighborhood spatio-temporal non-stationary errors has become the key to improving the accuracy and stability of potential evapotranspiration data. Summary of the Invention

[0006] Objective of the invention: To propose a three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors, and further construct a system for implementing the above method. By integrating multi-source potential evapotranspiration data and introducing a spatiotemporal geographically weighted regression model to dynamically determine the influence weights of each point in the neighborhood, the influence of local spatiotemporal non-stationary errors and spatiotemporal window scale effects is effectively reduced in areas without sufficient observational data support, providing more accurate potential evapotranspiration fusion information and providing solid and effective data support for drought monitoring and water resource management, effectively solving the above problems existing in the prior art.

[0007] In the first aspect of the present invention, a three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors is proposed, including the following steps:

[0008] Step 1: Obtain three sets of independent potential evapotranspiration data and meteorological station observational data in the target basin, perform unified unit conversion on all data, and unify the spatiotemporal resolution.

[0009] Step 2: Calculate a Gaussian kernel function matching the predetermined spatiotemporal sliding window, calculate the neighborhood mean and neighborhood standard deviation through the spatiotemporal sliding window, and then perform zero-mean unit-variance standardization to obtain a standardized potential evapotranspiration dataset.

[0010] Step 3: Construct a variance calculation model for the three-dimensional error based on triple configuration, match the spatiotemporal sliding window, and calculate the variance of the error containing neighborhood dimension spatiotemporal information.

[0011] Step 4: According to the variance of the error containing neighborhood dimension spatiotemporal information in Step 3, construct a constrained least squares optimization model and determine the optimal fusion weights, and linearly weight and fuse the three sets of independent potential evapotranspiration data according to the optimal fusion weights to obtain a potential evapotranspiration fusion dataset.

[0012] In a further embodiment of the first aspect, the three sets of independent potential evapotranspiration data in the target basin in Step 1 include: reanalysis data, remote sensing inversion data, and land surface model driven data;

[0013] Accumulate or decompose the time resolutions of the reanalysis data, remote sensing inversion data, land surface model driven data, and meteorological station observational data to unify the time resolution;

[0014] Perform spatial interpolation on the spatial resolutions of the reanalysis data, remote sensing inversion data, land surface model driven data, and meteorological station observational data to unify the spatial resolution.

[0015] In a further embodiment of the first aspect, the calculation of the Gaussian kernel function matching the predetermined spatiotemporal sliding window in Step 2 specifically includes:

[0016] Construct a spatio-temporal sliding window centered at with a time radius of T and a space radius of :

[0017]

[0018] In the formula, represents the time dimension, ; and represent the space dimensions in the X and Y directions respectively, , ;

[0019] Calculate the unnormalized Gaussian weight within the spatio-temporal sliding window , and the formula is as follows:

[0020]

[0021] In the formula, is any point in ; , , represent the degree of deviation from the center ; , , represent the smoothing intensities in time, longitude, and latitude respectively;

[0022] Normalize the Gaussian weight, calculate the sum S of all grid points in the target domain, and obtain the Gaussian kernel function ;

[0023]

[0024]

[0025] In the formula, T represents the time radius; and represent the space radius.

[0026] In a further embodiment of the first aspect, step 2 further includes:

[0027] Based on the Gaussian kernel function , calculate the neighborhood mean when point is normalized within the spatio-temporal sliding window :

[0028]

[0029] In the formula, denote the potential evapotranspiration value of the points within the neighborhood;

[0030] Based on the Gaussian kernel function , calculate the point in the spatio-temporal sliding window of the neighborhood standard deviation :

[0031]

[0032] wherein, is the neighborhood mean value when the point is normalized in the spatio-temporal sliding window ; is the mean value of the square of the neighborhood when the point is normalized in the spatio-temporal sliding window ; is the square of the neighborhood mean value when the point is normalized in the spatio-temporal sliding window ;

[0033] According to the neighborhood standard deviation and the neighborhood mean value calculate the standardized value according to the zero-mean unit-variance standardization :

[0034]

[0035] wherein, is the standardized anomaly value at the time step and the spatial grid ( ); is the base value of the time step and the spatial grid ( ).

[0036] In a further embodiment of the first aspect, the process of constructing the variance calculation model of the three-dimensional error based on the triple configuration in step 3 specifically includes:

[0037] Initialize the variance calculation model of the three-dimensional error based on the triple configuration, and represent the observed data of the data set with the true value and the error :

[0038]

[0039] wherein, is the observed data of the d dimension of the i-th data set; is its corresponding random error; i is different data sets; d is the time or space dimension; is the true value of the corresponding dimension; and is the regression coefficient of the i-th dataset and the true value in the d dimension.

[0040] In a further embodiment of the first aspect, the spatio-temporal sliding window is matched, and the variance of the error containing the spatio-temporal information of the neighborhood dimension is calculated. This process specifically includes:

[0041] Calculate the observed data of the d dimension of the i-th dataset and the observed data of the d dimension of the j-th dataset Covariance :

[0042]

[0043] In the formula, is the variance; is the regression coefficient; is the residual;

[0044] According to the covariance , solve the variance of the one-dimensional error of the i-th dataset in the d dimension :

[0045]

[0046] In the formula, j and k respectively represent two other datasets; , are the covariances corresponding to dataset i and dataset k respectively; if d takes the time dimension T, capture the spatially non-stationary error in time; if d takes the spatial dimension S, capture the temporally non-stationary error in space;

[0047] Match the spatio-temporal sliding window , calculate the variance taking into account the time error and the variance of the spatial error

[0048]

[0049] In the formula, is the neighborhood time step; is the number of grid points within the neighborhood spatial range; T represents the time radius; and represent the spatial radius.

[0050] In a further embodiment of the first aspect, the potential evapotranspiration fusion dataset is represented as follows:

[0051]

[0052] In the formula, is the potential evapotranspiration dataset; , , are the fusion weights corresponding to datasets i, j, and k, respectively.

[0053] In a further embodiment of the first aspect, step 4 further includes:

[0054] Solving the error of the potential evapotranspiration fusion dataset :

[0055]

[0056] In the formula, , , are the errors corresponding to datasets i, j, and k, respectively;

[0057] The variance of the error considering the neighborhood dimension containing spatio-temporal information in the potential evapotranspiration fusion dataset is expressed as , and the optimal weight is calculated according to the least squares framework:

[0058]

[0059] In the formula, is the optimal weight of dataset i; is the variance of the three-dimensional neighborhood error; the subscript t represents the time dimension, s represents the space dimension, and i, j, k represent different datasets.

[0060] In a second aspect of the present invention, a three-dimensional triple configuration potential evapotranspiration fusion system is disclosed. The system includes at least one processor and a memory communicatively connected to at least one said processor; wherein: the memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors disclosed in the first aspect and its further embodiments.

[0061] Beneficial effects: The technical solution proposed by the present invention effectively reduces the influence of the spatio-temporal window scale effect of potential evapotranspiration data fusion by considering neighborhood spatio-temporal non-stationary errors, enhances the ability to capture local spatio-temporal non-stationary errors and reduces their influence. This method has higher accuracy compared to traditional triple configuration and two-dimensional triple configuration methods, and at the same time provides solid and effective technical and data support for fields such as drought monitoring, agricultural irrigation, and ecological research. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is the flowchart of Embodiment 1 of the present invention.

[0063] Figure 2 This is the flowchart of Embodiment 2 of the present invention.

[0064] Figure 3 This is the average spatial distribution map of the five-day cumulative value of the potential evapotranspiration in the middle and upper reaches of the Yellow River Basin from January 1, 1980 to December 31, 2021 in Embodiment 3 of the present invention.

[0065] Figure 4 This is the spatial distribution map of the weights when fusing the potential evapotranspiration of each basic dataset in the middle and upper reaches of the Yellow River Basin during the research period in Embodiment 3 of the present invention.

[0066] Figure 5 This is the box plot of the results of directly evaluating the accuracy of the reference values of each station and different datasets during the research period in Embodiment 3 of the present invention. Detailed implementation manners

[0067] In the following description, a large number of specific details are given to provide a more thorough understanding of the present invention. However, it is obvious to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features well known to the public are not described.

[0068] Embodiment 1:

[0069] When calculating the variance of the error in the current two-dimensional triple-configuration potential evapotranspiration data fusion considering double spatio-temporal errors, the global time series and spatial domain are usually used, taking into account the error changes in the overall time series and overall spatial domain, but ignoring the local spatio-temporal non-stationary errors of the data. At the same time, the scale effect of the spatio-temporal window of the potential evapotranspiration data fusion is superimposed, restricting the improvement of the accuracy of the potential evapotranspiration data fusion.

[0070] Therefore, this embodiment discloses a three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors, which can not only reduce the influence of the scale effect of the spatio-temporal window during the potential evapotranspiration data fusion, but also improve the ability to capture and reduce the influence of local spatio-temporal non-stationary errors, providing a solid and effective technical and data support for fields such as drought monitoring, agricultural irrigation, and ecological research. The process of this method is shown in Figure 1 as follows, and the specific steps are as follows:

[0071] Step 1: Obtain three sets of independent potential evapotranspiration datasets driven by reanalysis, remote sensing inversion, and land surface model in the target basin and the meteorological station observation data, and perform unified unit conversion and unified spatio-temporal resolution for all datasets;

[0072] Step 2: Based on the spatio-temporal geographically weighted regression model, calculate the Gaussian kernel function matching the predetermined spatio-temporal window. After calculating the local mean and local standard deviation through the spatio-temporal sliding window, perform zero-mean unit-variance standardization to obtain the standardized potential evapotranspiration dataset.

[0073] Step 3: Construct a variance calculation model for three-dimensional error based on triple configuration, match the spatio-temporal sliding window corresponding to the standardization step, and calculate the variance of the error containing spatio-temporal information in the neighborhood dimension.

[0074] Step 4: According to the variance of the error in the neighborhood dimension, construct a constrained least squares optimization model and determine the optimal fusion weight. Linearly weight and fuse the three sets of independent potential evapotranspiration datasets according to the optimal weight to obtain the potential evapotranspiration fusion dataset.

[0075] Example 2:

[0076] Based on Example 1, this example discloses a refined process of a three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary error, combined with Figure 1 and Figure 2 . It should be noted that the refined process disclosed in this example is only a feasible solution for the three-dimensional triple configuration potential evapotranspiration fusion considering neighborhood spatio-temporal non-stationary error. In actual application, deletions or additions can be made according to objective factors such as environment and equipment.

[0077] Step 1: Obtain three sets of independent potential evapotranspiration datasets driven by reanalysis, remote sensing inversion, and land surface model of the target basin and meteorological station observation data, and perform unified unit conversion and unified spatio-temporal resolution for all datasets.

[0078] Step 11: Obtain the reanalysis, remote sensing inversion, land surface model-driven datasets, the longitude and latitude of the center of each grid, and the observation information of ground hydrological stations in the target basin.

[0079] Step 12: Convert the physical dimensions of the potential evapotranspiration datasets driven by reanalysis, remote sensing inversion, and land surface model and the observation information of ground hydrological stations to unify the units.

[0080] Step 13: Accumulate or decompose the time resolution of the potential evapotranspiration datasets driven by reanalysis, remote sensing inversion, and land surface model and the observation information of ground hydrological stations to unify the time resolution.

[0081] Step 14: Perform spatial interpolation on the spatial resolution of the potential evapotranspiration datasets driven by reanalysis, remote sensing inversion, and land surface model and the observation information of ground hydrological stations to unify the spatial resolution.

[0082] Step 2: Based on the spatio-temporal geographically weighted regression model, calculate the Gaussian kernel function that matches the predetermined spatio-temporal window. After calculating the mean and standard deviation through the spatio-temporal sliding window, perform zero-mean unit-variance standardization to obtain the standardized potential evapotranspiration dataset.

[0083] Step 21: Construct a three-dimensional sliding window centered at ( ), with a time radius of T and a spatial radius of ( , ). ;

[0084] Step 22: Construct a Gaussian kernel function that determines the calculation weight by the influence of grid points in the neighborhood on the target point ;

[0085] Step 23: Based on the Gaussian kernel function , calculate the local mean of point during standardization under the three-dimensional sliding window ;

[0086] Step 24: Based on the Gaussian kernel function , calculate the square of the local mean of point under the three-dimensional sliding window ;

[0087] Step 25: Based on the Gaussian kernel function , calculate the local standard deviation of point under the three-dimensional sliding window .

[0088] Step 3: Construct a variance calculation model for three-dimensional errors based on triple configuration, match the spatio-temporal sliding window corresponding to the standardization step, and calculate the variance of errors considering the neighborhood dimension containing spatio-temporal information;

[0089] Step 31: Initialize the variance calculation model for three-dimensional errors based on triple configuration, and represent the observed data of the dataset with the true value and error ;

[0090] Step 32: Obtain the variance of one-dimensional errors in the method of the variance calculation model for three-dimensional errors based on triple configuration ;

[0091] Step 33: Match the spatio-temporal sliding window adopted in Step 2, and calculate the variance of errors considering the neighborhood dimension containing spatio-temporal information .

[0092] Step 4: Construct a constrained least squares optimization model to determine the optimal fusion weights based on the variance of the error considering the neighborhood dimension, and linearly weight and fuse the three sets of independent potential evapotranspiration datasets according to the optimal weights to obtain the fused potential evapotranspiration dataset.

[0093] Step 41: Use linear fusion to fuse the datasets. The fused dataset can be expressed as ;

[0094] Step 42: The variance of the error considering the neighborhood dimension of the fused dataset containing spatio-temporal information can be expressed as , and calculate the optimal weights according to the least squares framework ;

[0095] Step 43: Perform linear fusion of different datasets according to the solved optimal weights to obtain the fused dataset.

[0096] Example 3:

[0097] The middle and upper reaches of the Yellow River, approximately between 95° - 112° east longitude and 32° - 42° north latitude, are an important section of the Yellow River, the second longest river in China. The main stream of the Yellow River is about 5464 km long, and the basin area of the study area is about 700,000 km 2 . The basin is located in the transition zone between the East Asian monsoon and the inland arid climate, with diverse climate types and a large elevation span. The average annual temperature is about 2 - 14 °C, and the average annual precipitation is about 400 - 600 mm. The precipitation is mainly concentrated in June - September and has significant interannual variations. Affected by multiple factors such as climate change, uneven spatio-temporal distribution of precipitation, and soil erosion, especially in years with less precipitation and large evaporation, water supply and agricultural irrigation face severe challenges, and potential evapotranspiration shows obvious spatio-temporal non-stationarity in this area. In this example, a three-dimensional triple configuration potential evapotranspiration fusion scenario considering neighborhood spatio-temporal non-stationary errors was constructed for the middle and upper reaches of the Yellow River. Specifically:

[0098] S1): Collect multi-source information and unify the spatio-temporal scale: Obtain the potential evapotranspiration data of ERA5-Land, GLDAS-Noah, and GLEAM 4.1 in the middle and upper reaches of the Yellow River Basin from January 1, 1980, to December 31, 2021 (see Figure 3 ), meteorological information such as the observed elevation, air pressure, sunshine hours, air temperature, relative humidity, and wind speed variables at ground hydrological stations. Currently, there is no method to directly obtain the potential evapotranspiration of natural water surfaces or the land surface, and it is often estimated by indirect means. The modified FAO56 Penman-Monteith formula is the method recommended by the Food and Agriculture Organization of the United Nations to calculate potential evapotranspiration, and its calculation results are considered reliable. The formula is as follows:

[0099]

[0100] In the formula, PET is the potential evapotranspiration value; is the slope of the saturated vapor pressure curve (kPa / °C); is the net radiation ( ); G is the surface soil heat flux ( ); is the psychrometric constant; is the wind speed at a height of 2 meters (m / s); is the saturated vapor pressure (kPa); is the actual water vapor partial pressure in the air (kPa). According to the above method, the reference value of potential evapotranspiration in the study area is obtained, and the units of all data are unified to mm / day, the time scale is unified to 1 day, and the spatial scale is unified to 0.1°×0.1°.

[0101] S2): Neighborhood data standardization unit: First, determine the discrete window. In the time dimension, let , and in the spatial dimension, let ; then calculate the unnormalized kernel value. For each ( ) point, first calculate , and then calculate the sum of all grid points in the target domain At this time, there is: , and a three-dimensional discrete Gaussian kernel can be obtained through the above calculation, which satisfies the sum of 1 and is concentrated near (the farther away from the center, the smaller the value). By using different spatio-temporal windows for the three basic data sets ( takes 3, 7, takes 3×3, 5×5, 7×7, 9×9, 11×11 in turn for a total of 10 combinations), different Gaussian kernels are obtained for subsequent standardization, and the standardization results under different spatio-temporal windows are obtained.

[0102] S3): Three-dimensional error variance calculation unit: Taking the standardized result data under different spatio-temporal windows as input, calculate the variance of the error of each data set based on the classical triple collocation principle under the corresponding spatio-temporal sliding window, and then calculate the three-dimensional error variance considering the neighborhood dimension.

[0103] S4): Output unit: After determining the optimal weight according to the calculation result of the error variance, fuse the three basic data sets to obtain the fusion result, and evaluate the accuracy according to the indicators in Table 1.

[0104] Table 1: Calculation reference table for evaluation indicators

[0105]

[0106] In the table, where x represents the value of the selected dataset for calculation, y represents the value of the benchmark dataset, N represents the total number of samples. During the calculation of KGE′, r is the correlation coefficient CC, is the standard deviation ratio (variation ratio), usually taking , as the dataset.

[0107] Table 2 shows the evaluation results of the statistical indicators with the time step of dekad for this method. The average value of the results of all stations for each indicator is taken from the complete time series (January 1, 1980 - December 31, 2021). For CC, all window CC values exceed 0.78. When taking as 3, the increase of significantly improves CC. For RMSE, KGE′, and IOA, they all show the same trend, which is the same as CC. the increase of significantly improves the indicators. For Bias, centered on = 29, it increases upward and decreases downward. Considering the correlation coefficient, error terms (RMSE, Bias), and two consistency indicators (KGE′, IOA), = 3, = 11, the indicators of the scheme are all in the top 5%. The subsequent analysis of this method will adopt the above - mentioned scheme.

[0108] Table 2: Evaluation Results of Statistical Indicators

[0109]

[0110] Figure 4 is the spatial distribution map of the weights of each basic dataset during fusion. It can be seen from the figure that the single - source datasets show significant systematic biases at both time resolutions: ERA5 - Land and GLEAM are overall underestimated, while GLDAS almost loses the spatial gradient due to over - saturated values, resulting in an average dekad IOA of only about 0.3. For the three - dimensional triple - configuration potential evapotranspiration fusion method considering neighborhood spatio - temporal non - stationary errors, the weight of ERA5 is between 0.37 - 0.45, and those of GLDAS and GLEAM are between 0.26 - 0.33, and a local adaptive weight field is shown in the Loess Plateau and Hetao Plain regions. Such a dynamic balance effectively suppresses the over - smoothing (ERA5) and jump (GLEAM) phenomena of single - source data, significantly improving the spatial consistency: at the dekad scale, the IOA of the three - dimensional triple - configuration potential evapotranspiration fusion method considering neighborhood spatio - temporal non - stationary errors is 0.686, reflecting the ability of this method to handle non - stationary errors and verifying its advantages in capturing spatio - temporal non - stationary errors and improving the estimation accuracy of potential evapotranspiration. Figure 5Box plots of various indicators for all datasets. For the box plots of various indicators of all datasets, the median values of IOA and CC of the three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors are both stable at around 0.90. The KGE is increased to the range of 0.75 - 0.83, and the data dispersion converges significantly. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors controls the RMSE at about 5.3 - 5.6 mm / 5d, a 12 - 15% reduction compared to ERA5, and reduces the Bias to less than 2.5 mm / 5d, achieving a 50 - 70% reduction in bias. The box and whiskers of the three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors are extremely short, indicating that it is the most effective in suppressing data dispersion and extreme errors, showing excellent robustness.

[0111] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as a limitation of the present invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the present invention as defined by the appended claims.

Claims

1. A three-dimensional triple configuration potential evapotranspiration fusion method considering spatio-temporal non-stationary errors in the neighborhood, characterized in that, It includes the following steps: Step 1: Obtain three sets of independent potential evapotranspiration data and meteorological station observation data in the target basin, perform unified unit conversion on all data, and unify the spatio-temporal resolution. Step 2: Calculate the Gaussian kernel function matching the predetermined spatio-temporal sliding window, calculate the neighborhood mean and neighborhood standard deviation through the spatio-temporal sliding window, and then perform zero-mean unit-variance standardization to obtain the standardized potential evapotranspiration data set. Step 3: Construct a variance calculation model for three-dimensional errors based on triple configuration, match the spatio-temporal sliding window, and calculate the variance of the errors containing spatio-temporal information in the neighborhood dimension. Step 4: According to the variance of the errors containing spatio-temporal information in the neighborhood dimension in Step 3, construct a constrained least-squares optimization model and determine the optimal fusion weights, and linearly weight and fuse the three sets of independent potential evapotranspiration data according to the optimal fusion weights to obtain the potential evapotranspiration fusion data set.

2. The three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to claim 1, characterized in that The three sets of independent potential evapotranspiration data in the target basin in Step 1 include: reanalysis data, remote sensing inversion data, and land surface model-driven data. Accumulate or decompose the time resolutions of the reanalysis data, remote sensing inversion data, land surface model-driven data, and meteorological station observation data to unify the time resolution. Perform spatial interpolation on the spatial resolutions of the reanalysis data, remote sensing inversion data, land surface model-driven data, and meteorological station observation data to unify the spatial resolution.

3. The three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to claim 1, characterized in that The calculation of the Gaussian kernel function matching the predetermined spatio-temporal sliding window in Step 2 specifically includes: Construct a -centered spatio-temporal sliding window with a time radius of T and a space radius of : ​ ； Wherein, represents the time dimension, ; and respectively represent the spatial dimensions in the X and Y directions, , ; In a spatio-temporal sliding window compute the unnormalized Gaussian weights , as follows: ； In the formula, is any point in ; , , represent the degree of deviation compared to the center ; , , respectively represent the smoothing intensities in time, longitude, and latitude; Normalized Gaussian weights, calculate the sum S of all grid points in the target domain to obtain the Gaussian kernel function ; ； ； Where T represents the time radius; and represents the space radius.

4. The three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to claim 3, wherein Step 2 further includes: Based on the Gaussian kernel function , calculate the point in the spatio-temporal sliding window when normalizing the neighborhood mean : ； Wherein, represents the potential evapotranspiration value of the points within the neighborhood; Based on the Gaussian kernel function , calculate the point in the spatio-temporal sliding window of the neighborhood standard deviation : ； Wherein, is the neighborhood mean value of point when normalized by the spatio-temporal sliding window ; is the mean value of the neighborhood squares of point when normalized by the spatio-temporal sliding window ; is the square of the neighborhood mean value of point when normalized by the spatio-temporal sliding window .

5. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to claim 4, wherein Step 2 further includes: According to the neighborhood standard deviation and the neighborhood mean Calculate the standardized value according to zero-mean unit-variance standardization : ； wherein, is the standardized outlier at the time step and the spatial grid ( ); is the base value of the time step and the spatial grid ( ).

6. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to claim 1, characterized in that The construction of the variance calculation model for three-dimensional errors based on triple configuration in Step 3 specifically includes: Initialize the variance calculation model of three-dimensional error based on triple configuration, and represent the observed data of the data set with true values and errors : ； wherein, is the d - dimensional observed data of the i - th data set; is its corresponding random error; i is different data sets; d is the time or space dimension; is the true value of the corresponding dimension; and are the regression coefficients of the i - th data set and the true value in the d dimension.

7. The three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors according to claim 6, characterized in that Matching the spatio-temporal sliding window and calculating the variance of the errors containing spatio-temporal information in the neighborhood dimension specifically includes: Calculate the observed data of the d - dimension for the i - th data set and the observed data of the d - dimension for the j - th data set covariance : ； In the formula, is the variance; is the regression coefficient; is the residual; According to the covariance , solve for the variance of the one-dimensional error of the $i$-th data set in dimension $d$ : ； where j and k respectively represent the other two data sets; and are the covariances corresponding to data set i and data set k respectively; if d takes the time dimension T, it captures the spatially non-stationary spatial error; if d takes the spatial dimension S, it captures the temporally non-stationary temporal error; Match spatio-temporal sliding window , calculate the variance considering time error and the variance of spatial error of the three-dimensional neighborhood error : ； In the formula, is the neighborhood time step; is the number of grid points within the neighborhood spatial range; T represents the time radius; and represent the spatial radius.

8. The three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to claim 1, characterized in that In step 4, the potential evapotranspiration fusion dataset is expressed as follows: ； In the formula, is the potential evapotranspiration dataset; , , are the fusion weights corresponding to datasets i, j, and k, respectively.

9. The three-dimensional triple-configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to claim 8, wherein Step 4 also includes: Solving the error of the potential evapotranspiration fusion dataset error : ； In the formula, , , are the errors corresponding to the data sets i, j, and k respectively; The variance of the error considering the neighborhood dimension of the potential evapotranspiration fusion dataset containing spatio-temporal information is expressed as , and the optimal weights are calculated according to the least squares framework : ； wherein, is the optimal weight of dataset i; is the variance of the three-dimensional neighborhood error; the subscript t represents the time dimension, s represents the spatial dimension, and i, j, k represent different datasets.

10. A three-dimensional triple-configuration potential evapotranspiration fusion system, characterized in that, It includes at least one processor and a memory communicatively connected to at least one of the processors; wherein: The memory stores instructions executable by the processor, and the instructions are used to be executed by the processor to implement the three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatio-temporal non-stationary errors according to any one of claims 1 to 9.

Images