A 3D triple configuration potential evapotranspiration fusion method and system considering neighborhood spatiotemporal non-stationary errors

Abstract

The present invention provides a three-dimensional triple configuration potential evapotranspiration fusion method and system that considers neighborhood spatiotemporal non-stationary errors, relating to the technical field of potential evapotranspiration estimation. The method includes: obtaining potential evapotranspiration observations from meteorological stations in a target watershed and three independent potential evapotranspiration datasets and unifying the spatiotemporal resolution; calculating a Gaussian kernel function that matches a predetermined spatiotemporal window and using the kernel function to perform data standardization; constructing a variance calculation model for the three-dimensional triple configuration error to obtain the variance of the error of each dataset containing neighborhood dimensional spatiotemporal information within the predetermined spatiotemporal window; and constructing a data fusion model based on a least squares framework to determine the optimal fusion weights and achieve fusion of multi-source potential evapotranspiration data. The present invention solves the problems of local spatiotemporal non-stationary errors and the scale effect of the spatiotemporal window affecting fusion accuracy when fusing potential evapotranspiration data, effectively improving the accuracy of fused potential evapotranspiration data.

Description

Technical Field

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

[0002] Potential evapotranspiration (ET) is a key variable measuring atmospheric evapotranspiration demand and surface energy supply. It can also be used as an important indicator for predicting the occurrence of extreme weather events and is widely used in areas such as agricultural irrigation and drought monitoring. Due to the difficulty of actual observation, obtaining large-scale, long-sequence potential ET data typically relies on datasets generated through remote sensing inversion, reanalysis models, and land surface model simulations. These datasets are obtained indirectly and generally contain certain errors compared to actual observations.

[0003] To effectively improve data accuracy, fusing multiple potential evapotranspiration data has become a mainstream approach. Among these, Chinese invention patent publication number CN118551528A discloses a multi-source data fusion method based on the pixel-scale error covariance matrix. This method only addresses pixel errors at the regional scale and fails to fully consider local spatiotemporal nonstationary errors, making it unable to effectively capture subtle variations in potential evapotranspiration data within a local area.

[0004] Chinese invention patent publication number CN117010262A discloses a deep learning-based method for spatiotemporal fusion of global terrestrial evapotranspiration. While using a deep learning model for spatiotemporal data fusion improves data fusion accuracy, it relies on a large amount of ground observation station data for model training, making it highly data-dependent. Furthermore, deep learning methods often suffer from poor model interpretability and generalizability, significantly limiting their applicability in areas without sufficient observational data.

[0005] In summary, current research focuses on how to overcome the spatiotemporal nonstationary errors in potential evapotranspiration data while addressing the spatiotemporal window scale effect. Data fusion in areas lacking sufficient observational data support is therefore crucial for improving the accuracy and stability of potential evapotranspiration data through multi-source fusion of potential evapotranspiration data that considers spatiotemporal nonstationary errors in neighboring regions. Summary of the Invention

[0006] Purpose of the invention: To propose a three-dimensional triple configuration potential evapotranspiration fusion method that takes into account the 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 weight of each point in the neighborhood, the system effectively reduces the influence of local spatiotemporal non-stationary errors and spatiotemporal window scale effects in areas without sufficient observation data support, provides more accurate potential evapotranspiration fusion information, and provides solid and effective data support for drought monitoring and water resources management, effectively solving the above-mentioned problems existing in the existing technology.

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

[0008] Step 1: Obtain three independent sets of potential evapotranspiration data and meteorological station observation data in the target basin, convert all data into a unified unit, and unify the temporal and spatial resolution;

[0009] Step 2: Calculate the Gaussian kernel function that matches 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 the standardized potential evapotranspiration dataset;

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

[0011] Step 4: Based on the variance of the error containing the spatiotemporal information of the neighborhood dimension described in step 3, a constrained least squares optimization model is constructed and the optimal fusion weight is determined. The three independent sets of potential evapotranspiration data are linearly weighted fused according to the optimal fusion weight to obtain the potential evapotranspiration fusion dataset.

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

[0013] Accumulating or decomposing the temporal resolutions of the reanalysis data, remote sensing inversion data, land surface model driven data, and meteorological station observation data to unify the temporal resolution;

[0014] The spatial resolutions of the reanalysis data, remote sensing inversion data, land surface model driven data and meteorological station observation data are spatially interpolated to unify the spatial resolution.

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

[0016] Build with As the center, the time radius is T, and the space radius is The spatiotemporal sliding window :

[0017]

[0018] Where, represents the time dimension, ; and Represents the spatial dimensions in the X and Y directions respectively, , ;

[0019] Sliding window in space and time Calculate the unnormalized Gaussian weights internally , the formula is as follows:

[0020]

[0021] Where, For Any point in 、 、 Compared to the center The degree of deviation; 、 、 Represents the smoothing intensity in time, longitude, and latitude respectively;

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

[0023]

[0024]

[0025] Where, T represents the time radius; and Indicates the space radius.

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

[0027] Based on Gaussian kernel function , calculation point Sliding window in space and time Neighborhood mean during normalization :

[0028]

[0029] Where, express Potential evapotranspiration value of points within the neighborhood;

[0030] Based on Gaussian kernel function , calculation point Sliding window in space and time Neighborhood standard deviation :

[0031]

[0032] Where, for point Sliding window in space and time Neighborhood mean when normalized; for point Sliding window in space and time The mean of the neighborhood squares when normalized; for point Sliding window in space and time The square of the neighborhood mean when normalized;

[0033] Based on the neighborhood standard deviation and neighborhood mean Calculate the standardized value according to zero mean and unit variance standardization :

[0034]

[0035] Where, For the time step and spatial grid ( ) at the standardized outlier value; is the time step and spatial grid ( )'s base value.

[0036] In a further embodiment of the first aspect, the process of constructing a variance calculation model of a three-dimensional error based on a 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 observation data of the dataset with the true value and error :

[0038]

[0039] Where, is the d-dimensional observation data of the i-th data set; is the corresponding random error; i is a different data set; d is the time or space dimension; is the true value of the corresponding dimension; and is the regression coefficient between the i-th data set and the true value in dimension d.

[0040] In a further embodiment of the first aspect, matching the spatiotemporal sliding window and calculating the variance of the error containing the spatiotemporal information of the neighborhood dimension specifically includes:

[0041] Calculate the d-dimensional observation data of the i-th data set The observation data of dimension d of the jth dataset The covariance of :

[0042]

[0043] Where, 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 data set in the d dimension :

[0045]

[0046] In the formula, j and k represent the other two data sets respectively; 、 are the covariances corresponding to dataset i and dataset k respectively; if d takes the time dimension T, it captures the spatial error that is non-stationary in time; if d takes the spatial dimension S, it captures the time error that is non-stationary in space;

[0047] Matching spatiotemporal sliding windows , calculate the variance of the time error Variance of spatial error The variance of the three-dimensional neighborhood error :

[0048]

[0049] Where, is the neighborhood time step; is the number of grid points in the neighborhood space; T represents the time radius; and Indicates the space radius.

[0050] In a further embodiment of the first aspect, the potential evapotranspiration fusion dataset in step 4 It is expressed as follows:

[0051]

[0052] Where, 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 comprises:

[0054] Solving for potential evapotranspiration fusion dataset Error :

[0055]

[0056] Where, 、 、 are the errors corresponding to data sets i, j, and k respectively;

[0057] The variance of the error considering the neighborhood dimension of the potential evapotranspiration fusion dataset containing spatiotemporal information is expressed as , calculate the optimal weights according to the least squares framework :

[0058]

[0059] Where, is the optimal weight of data set i; is the variance of the three-dimensional neighborhood error; the subscript t is the time dimension, s is the spatial dimension, and i, j, and k represent different data sets.

[0060] A second aspect of the present invention discloses a three-dimensional triple configuration potential evapotranspiration fusion system, comprising 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, the instructions being executed by the processor to implement the three-dimensional triple configuration potential evapotranspiration fusion method that considers neighborhood spatiotemporal non-stationary errors disclosed in the first aspect and further embodiments thereof.

[0061] Beneficial Effects: The proposed technical solution effectively reduces the impact of temporal and spatial window scale effects in potential evapotranspiration data fusion by accounting for neighborhood temporal and spatial non-stationary errors. This enhances the ability to capture local temporal and spatial non-stationary errors and reduces their impact. This method offers higher accuracy than traditional triple configuration and two-dimensional triple configuration methods, providing robust 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 This is a flowchart of Example 1 of the present invention.

[0063] Figure 2 This is a flow chart of Example 2 of the present invention.

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

[0065] Figure 4 This is a weighted spatial distribution map of the potential evapotranspiration of various basic data sets in the middle and upper reaches of the Yellow River during the study period in Example 3 of the present invention when they are fused.

[0066] Figure 5 This is a box plot of the accuracy evaluation results of the reference values of each site and different data sets during the study period in Example 3 of the present invention. DETAILED DESCRIPTION

[0067] In the following description, numerous specific details are provided to provide a more thorough understanding of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced without one or more of these details. In other instances, certain technical features well known in the art have not been described to avoid confusion with the present invention.

[0068] Example 1:

[0069] Current two-dimensional triple configuration potential evapotranspiration data fusion considering dual spatiotemporal errors usually uses the global time series and spatial domain when calculating the error variance, taking into account the error changes of the overall time series and the overall spatial domain, but ignores the local spatiotemporal non-stationary errors of the data. At the same time, the scale effect of the spatiotemporal window of the potential evapotranspiration data fusion is superimposed, which limits the improvement of the potential evapotranspiration data fusion accuracy.

[0070] To this end, this embodiment discloses a three-dimensional triple configuration potential evapotranspiration fusion method that takes into account neighborhood spatiotemporal non-stationary errors. This method can not only reduce the impact of spatiotemporal window scale effects when fusing potential evapotranspiration data, but also improve the ability to capture local spatiotemporal non-stationary errors and reduce their impact, providing solid and effective technical and data support for fields such as drought monitoring, agricultural irrigation, and ecological research. The method flow is shown in [1]. Figure 1 The specific steps are as follows:

[0071] Step 1: Obtain three independent potential evapotranspiration datasets for the target basin, including reanalysis, remote sensing inversion, and land surface model-driven data, as well as meteorological station observation data. Convert all datasets to a unified unit and unify their temporal and spatial resolutions.

[0072] Step 2: Based on the spatiotemporal geographically weighted regression model, the Gaussian kernel function matching the predetermined spatiotemporal window is calculated. The local mean and local standard deviation are calculated through the spatiotemporal sliding window, and then zero-mean unit variance standardization is performed to obtain the standardized potential evapotranspiration dataset.

[0073] Step 3: Construct a variance calculation model for the three-dimensional error based on the triple configuration, match the spatiotemporal sliding window corresponding to the normalization step, and calculate the variance of the error including the spatiotemporal information of the neighborhood dimension;

[0074] Step 4: Based on the variance of the neighborhood dimension error, a constrained least squares optimization model is constructed and the optimal fusion weight is determined. The three independent potential evapotranspiration datasets are linearly weighted fused according to the optimal weight to obtain the potential evapotranspiration fusion dataset.

[0075] Example 2:

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

[0077] Step 1: Obtain three independent potential evapotranspiration datasets (including reanalysis, remote sensing inversion, and land surface model-driven data) and meteorological station observation data for the target basin, convert all datasets to a unified unit, and unify the temporal and spatial resolution.

[0078] Step 11: Obtain target watershed reanalysis, remote sensing inversion, land surface model driven dataset, latitude and longitude of each grid center, and ground hydrological station observation information;

[0079] Step 12: Convert the physical dimensions of reanalysis, remote sensing inversion, land surface model-driven potential evapotranspiration datasets, and surface hydrological station observations to a unified unit.

[0080] Step 13: Accumulate or decompose the temporal resolutions of reanalysis, remote sensing inversion, land surface model-driven potential evapotranspiration datasets, and surface hydrological station observations to unify the temporal resolution;

[0081] Step 14: Interpolate the spatial resolutions of reanalysis, remote sensing inversion, land surface model-driven potential evapotranspiration datasets, and ground hydrological station observations to unify the spatial resolution.

[0082] Step 2: Based on the spatiotemporal geographically weighted regression model, the Gaussian kernel function matching the predetermined spatiotemporal window is calculated. The mean and standard deviation are calculated through the spatiotemporal sliding window, and then zero-mean unit variance standardization is performed to obtain the standardized potential evapotranspiration dataset.

[0083] Step 21, build ( ) is the center, the time radius is T, and the space radius is ( , ) three-dimensional sliding window ;

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

[0085] Step 23: Based on Gaussian kernel function , calculation point Under the 3D sliding window Local mean when normalizing ;

[0086] Step 24: Based on Gaussian kernel function , calculation point Under the 3D sliding window The square of the local mean ;

[0087] Step 25: Based on Gaussian kernel function , calculation point Under the 3D sliding window The local standard deviation .

[0088] Step 3: Construct a variance calculation model for the three-dimensional error based on the triple configuration, match the spatiotemporal sliding window corresponding to the normalization step, and calculate the variance of the error considering the neighborhood dimension that includes spatiotemporal information;

[0089] Step 31: Initialize the variance calculation model of the three-dimensional error based on the triple configuration, and use the true value and error to represent the observation data of the data set. ;

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

[0091] Step 33: Match the spatiotemporal sliding window used in step 2 and calculate the variance of the error considering the neighborhood dimension including spatiotemporal information. .

[0092] Step 4: Based on the variance of the error considering the neighborhood dimension, a constrained least squares optimization model is constructed to determine the optimal fusion weight. The three independent potential evapotranspiration datasets are linearly weighted fused according to the optimal weight to obtain the fused potential evapotranspiration dataset.

[0093] Step 41: Linear fusion is used to fuse the data set. The fused data set can be expressed as ;

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

[0095] Step 43: Perform linear fusion of different data sets based on the solved optimal weights to obtain a fused data set.

[0096] Example 3:

[0097] The upper and middle reaches of the Yellow River, located between 95°-112° east longitude and 32°-42° north latitude, are important sections of the Yellow River, the second longest river in my country. The main stream of the Yellow River is about 5,464 km long, and the drainage 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. It has diverse climate types and a large altitude span. The average temperature over the years is about 2-14°C, and the average precipitation over the years is about 400-600mm. The precipitation is mainly concentrated in June-September and the interannual variation is significant. The basin is affected by multiple factors such as climate change, uneven temporal and spatial distribution of precipitation, and soil erosion. Especially in years with less precipitation and higher evaporation, water supply and agricultural irrigation face severe challenges, and potential evaporation in the region shows obvious spatiotemporal non-stationarity. This embodiment constructs a three-dimensional triple configuration potential evaporation fusion scenario taking into account the spatiotemporal non-stationary errors of the neighborhood in the middle and upper reaches of the Yellow River. Specifically:

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

[0099]

[0100] Where PET is the potential evapotranspiration value; is the slope of the saturated vapor pressure curve (kPa / ℃); is the net radiation ( ); G is the surface soil heat flux ( ); is a psychological 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). The potential evapotranspiration reference value of the study area was obtained according to the above method, and the unit of all data was unified into mm / day, the time scale was unified into 1 day, and the spatial scale was unified into 0.1°×0.1°.

[0101] S2): Neighborhood data normalization unit: First, determine the discrete window, in the time dimension, let , in the spatial dimension, let ; Then calculate the unnormalized kernel value, for each ( ) point, calculate first , and then calculate the sum of all grid points in the target area At this time there are: , through the above calculation, we can get a three-dimensional discrete Gaussian kernel , which sums to 1 and is concentrated in Nearby (the farther from the center, the smaller the value), by using different spatiotemporal windows ( Take 3 and 7, Take 3×3, 5×5, 7×7, 9×9, and 11×11 in sequence (a total of 10 cases) to obtain different Gaussian kernels for subsequent normalization, and obtain normalized results under different spatiotemporal windows.

[0102] S3): Three-dimensional error variance calculation unit: takes the standardized result data under different spatiotemporal windows as input, calculates the variance of the error of each data set based on the classic triple configuration principle under the corresponding spatiotemporal sliding window, and then calculates the variance of the three-dimensional error considering the neighborhood dimension.

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

[0104] Table 1: Evaluation index calculation reference table

[0105]

[0106] In the table, x represents the value of the selected dataset, y represents the value of the benchmark dataset, N represents the total number of samples, and r is the correlation coefficient CC in the KGE′ calculation process. is the standard deviation ratio (variability ratio), usually taken as , For the data set.

[0107] Table 2 shows the statistical index evaluation results of this method with a time step of hou. Each index takes the average value of the results of all stations in the complete time series (January 1, 1980 - December 31, 2021). For CC, the CC of all windows exceeds 0.78. Take 3 o'clock, The increase of has a significant effect on CC. RMSE, KGE', and IOA all show the same trend as CC. The increase of has a significant effect on the improvement of the index. =29 as the center, increasing upwards and decreasing downwards. Taking into account the correlation coefficient, error terms (RMSE, Bias) and two consistency indicators (KGE′, IOA), =3, =11 scheme ranked in the top 5% in all indicators, and this scheme was used in all subsequent analyses of this method.

[0108] Table 2: Statistical indicator evaluation results

[0109]

[0110] Figure 4 Figure 2 shows the spatial distribution of the weights used for the fusion of the underlying datasets. The figure shows that the single-source datasets exhibit significant systematic biases at both temporal resolutions: ERA5-Land and GLEAM exhibit overall underestimation, while GLDAS almost loses its spatial gradient due to oversaturation, resulting in a hou-scale average IOA of only around 0.3. The 3D triple-configuration potential evapotranspiration fusion method, which accounts for neighborhood spatiotemporal nonstationary errors, achieves weights ranging from 0.37-0.45 for ERA5 and 0.26-0.33 for GLDAS and GLEAM, exhibiting locally adaptive weight fields over the Loess Plateau and Hetao Plain. This dynamic balance effectively suppresses oversmoothing (ERA5) and jumps (GLEAM) in the single-source data, significantly improving spatial consistency. At the hou-scale, the 3D triple-configuration potential evapotranspiration fusion method, which accounts for neighborhood spatiotemporal nonstationary errors, achieves an IOA of 0.686, demonstrating its ability to handle nonstationary errors and validating its superiority in capturing spatiotemporal nonstationary errors and improving the accuracy of potential evapotranspiration estimates. Figure 5Box plots of various metrics for all datasets are shown. The median IOA and CC for the 3D triple-configuration potential evapotranspiration fusion method, which considers neighborhood temporal and spatial non-stationary errors, remain stable at around 0.90, while the KGE improves to the range of 0.75–0.83. Data dispersion is significantly reduced. The 3D triple-configuration potential evapotranspiration fusion method, which considers neighborhood temporal and spatial non-stationary errors, maintains RMSE of approximately 5.3–5.6 mm / 5 days, a 12–15% reduction compared to ERA5, and reduces the bias to less than 2.5 mm / 5 days, achieving a 50–70% reduction in bias. The box and whiskers of the 3D triple-configuration potential evapotranspiration fusion method, which considers neighborhood temporal and spatial non-stationary errors, are extremely short, indicating the most effective suppression of data dispersion and extreme errors, demonstrating 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 limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A three-dimensional triple configuration potential evapotranspiration fusion method considering the neighborhood spatiotemporal non-stationary error, characterized by: The steps include: Step 1: Obtain three independent sets of potential evapotranspiration data and meteorological station observation data in the target basin, convert all data into a unified unit, and unify the temporal and spatial resolution; Three independent sets of potential evapotranspiration data include: reanalysis data, remote sensing inversion data, and land surface model driven data; Accumulating or decomposing the temporal resolutions of the reanalysis data, remote sensing inversion data, land surface model driven data, and meteorological station observation data to unify the temporal resolution; performing 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; Step 2: Calculate the Gaussian kernel function that matches the predetermined spatiotemporal sliding window, specifically including: Build with As the center, the time radius is T, and the space radius is The spatiotemporal sliding window : ； Where, represents the time dimension, ; and Represents the spatial dimensions in the X and Y directions respectively, , ; Sliding window in space and time Calculate the unnormalized Gaussian weights internally , the formula is as follows: ； Where, For Any point in 、 、 Compared to the center The degree of deviation; 、 、 Represents the smoothing intensity in time, longitude, and latitude respectively; Normalize the Gaussian weights, calculate the sum S of all grid points in the target area, and obtain the Gaussian kernel function ; ； ； Where, T represents the time radius; and Indicates the space radius; The neighborhood mean and neighborhood standard deviation are calculated through a spatiotemporal sliding window and then normalized to zero mean and unit variance to obtain a standardized potential evapotranspiration dataset. Step 3: construct a three-dimensional error variance calculation model based on triple configuration, match the spatiotemporal sliding window, and calculate the variance of the error containing the spatiotemporal information of the neighborhood dimension; Step 4: Based on the variance of the error containing the spatiotemporal information of the neighborhood dimension described in step 3, a constrained least squares optimization model is constructed and the optimal fusion weight is determined. The three independent sets of potential evapotranspiration data are linearly weighted fused according to the optimal fusion weight to obtain the potential evapotranspiration fusion dataset.

2. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors according to claim 1 is characterized in that: Step 2 further includes: Based on Gaussian kernel function , calculation point Sliding window in space and time Neighborhood mean during normalization : ； Where, express Potential evapotranspiration value of points within the neighborhood; Based on Gaussian kernel function , calculation point Sliding window in space and time Neighborhood standard deviation : ； Where, for point Sliding window in space and time Neighborhood mean when normalized; for point Sliding window in space and time The mean of the neighborhood squares when normalized; for point Sliding window in space and time The square of the neighborhood mean when normalizing.

3. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors according to claim 2 is characterized in that: Step 2 further includes: Based on the neighborhood standard deviation and neighborhood mean Calculate the standardized value according to zero mean and unit variance standardization : ； Where, For the time step and spatial grid ( ) at the standardized outlier value; is the time step and spatial grid ( )'s base value.

4. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors according to claim 1 is characterized in that: The construction of the variance calculation model of the three-dimensional error based on the triple configuration described in step 3 specifically includes: Initialize the variance calculation model of the three-dimensional error based on the triple configuration, and represent the observation data of the dataset with the true value and error : ； Where, is the d-dimensional observation data of the i-th data set; is the corresponding random error; i is a different data set; d is the time or space dimension; is the true value of the corresponding dimension; and is the regression coefficient between the i-th data set and the true value in dimension d.

5. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors according to claim 4 is characterized in that: Matching the spatiotemporal sliding window and calculating the variance of the error containing the spatiotemporal information of the neighborhood dimension, specifically including: Calculate the d-dimensional observation data of the i-th data set The observation data of dimension d of the jth dataset The covariance of : ； Where, is the variance; is the regression coefficient; is the residual; According to the covariance , solve the variance of the one-dimensional error of the i-th data set in the d dimension : ； In the formula, j and k represent the other two data sets respectively; 、 are the covariances corresponding to dataset i and dataset k respectively; if d takes the time dimension T, it captures the spatial error that is non-stationary in time; if d takes the spatial dimension S, it captures the time error that is non-stationary in space; Matching spatiotemporal sliding windows , calculate the variance of the time error Variance of spatial error The variance of the three-dimensional neighborhood error : ； Where, is the neighborhood time step; is the number of grid points in the neighborhood space; T represents the time radius; and Indicates the space radius.

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

7. The three-dimensional triple configuration potential evapotranspiration fusion method considering neighborhood spatiotemporal non-stationary errors according to claim 6 is characterized in that: Step 4 also includes: Solving for potential evapotranspiration fusion dataset Error : ； Where, 、 、 are the errors corresponding to data sets i, j, and k respectively; The variance of the error considering the neighborhood dimension of the potential evapotranspiration fusion dataset containing spatiotemporal information is expressed as , calculate the optimal weights according to the least squares framework : ； Where, is the optimal weight of data set i; is the variance of the three-dimensional neighborhood error; the subscript t is the time dimension, s is the spatial dimension, and i, j, and k represent different data sets.

8. A three-dimensional triple configuration potential evapotranspiration fusion system, characterized in that: The system comprises at least one processor and a memory communicatively connected to at least one of the processors; wherein: The memory stores instructions that can be executed 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 spatiotemporal non-stationary errors according to any one of claims 1 to 7.

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