Simulation method for expansion rate of lake group under influence of climate change

Abstract

The application discloses a simulation method for expansion rate of lake group under influence of climate change and relates to the technical field of hydrological analysis and calculation. The method comprises the following steps: collecting historical observation and reanalysis data in a basin range, unifying time and space scales, obtaining optical remote sensing images and DEM of a research area, extracting lake hydrological elements, and performing pretreatment; constructing an XGBoost machine learning model; inputting future meteorological driving sequences into the trained and verified model; predicting upstream water sequences; calculating future lake storage sequences; relying on the constructed lake water level-area-storage relationship; realizing lake group storage, water level and area evolution simulation; and dynamically quantifying and analyzing expansion rate, area, water level and water volume trends. The method breaks through the dependence on ground measured hydrological data, is suitable for application in data-free areas, can identify change characteristics of the lake group in expansion, overflow and stable stages, and thus realizes dynamic quantification and trend analysis of the future expansion rate of the lake group, thereby providing scientific support for lake group expansion risk judgment.

Description

Technical Field

[0001] This invention relates to the field of hydrological analysis and calculation technology, and in particular to a method for simulating the expansion rate of lake groups under the influence of climate change. Background Technology

[0002] In recent years, global climate change has significantly exacerbated the hydrological evolution of inland lakes. Influenced by rising temperatures and changing precipitation patterns, numerous lakes in the Qinghai-Tibet Plateau and surrounding areas have experienced continuous expansion or rapid shrinkage. Glacier melting, increased precipitation, and changes in evapotranspiration are key factors driving changes in lake volume. Since inland lakes are mostly located in closed basins and lack outflow channels, their water volume regulation mainly relies on lake surface evaporation and hydraulic connections between lakes. When lake levels rise to the critical elevation of the basin watershed, excess water will flow into neighboring lakes through overflow outlets, thereby strengthening the hydraulic connections between lake groups. This hydrological connectivity between lakes not only affects the regional water balance pattern but also has a profound impact on downstream river runoff, wetland ecosystems, and the production and lives of residents along the banks. Therefore, there is an urgent need to establish a comprehensive method that can simultaneously consider climate change drivers, lake hydrological processes, and the mutual replenishment relationships among lake groups to quantitatively predict future lake volume evolution and potential risks.

[0003] Currently, research on lake water volume and level changes mainly relies on traditional water balance models and statistical regression models, simulating lake hydrological processes using observational data such as precipitation, evaporation, and runoff. With the rapid development of remote sensing technology, large-scale, long-term lake area and water level inversion has become an important data acquisition method. In recent years, machine learning models, with their advantages in handling high-dimensional variables, nonlinear relationships, and time-series features, have been gradually applied to lake hydrological simulation and prediction. By integrating meteorological elements, hydrological driving factors, remotely sensed lake parameters, and digital elevation model (DEM) topographic information, a prediction model combining data-driven and topographic constraints can be constructed. This can improve the accuracy of lake water volume simulation and overflow risk identification to a certain extent, providing technical support for lake response analysis and water resource risk management under climate change.

[0004] While traditional water balance models and statistical methods have a certain physical basis, their simulation and prediction accuracy is often limited when input data is uncertain and hydrological processes exhibit strong nonlinearity and spatiotemporal heterogeneity. Although remote sensing and machine learning-based methods can fit complex nonlinear relationships well, most models still focus on simulating the water volume or water level of a single lake, rarely considering the hydraulic connections between lake groups in a closed watershed, the overflow process controlled by topography, and the mutual replenishment of multiple lakes. They are unable to fully present the chain response mechanism of climate-driven—lake hydrological processes—lake group linkage evolution, and still have significant limitations in the quantitative prediction of lake water volume evolution and overflow risk under multiple future scenarios. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a method for simulating the expansion rate of lake groups under the influence of climate change. Through the systematic integration of multi-source data and multiple technical dimensions, it achieves accurate simulation of the interconnected evolution and overflow processes of lake groups in closed watersheds. This effectively solves the technical problems that traditional methods and existing machine learning models are unable to present the chain response of lake groups and cannot quantitatively predict the risks of lake expansion and overflow.

[0006] This invention is implemented as follows:

[0007] A method for simulating the expansion rate of lake groups under the influence of climate change includes the following steps:

[0008] Step S1, Data Preparation and Climate Driving Factor Calculation:

[0009] Historical observation and reanalysis data within the watershed were collected, including precipitation, air temperature, wind speed, incident shortwave radiation, and longwave radiation; potential evapotranspiration was calculated using the Penman–Monteith method, and land surface evapotranspiration was extrapolated by combining crop coefficients; lake surface evaporation was calculated based on the energy balance equation; precipitation phases were distinguished by the temperature threshold method and snow and ice melt was calculated by combining the degree-day factor method, and glacial runoff was extrapolated.

[0010] Step S2: Extract lake hydrological elements based on remote sensing imagery and DEM:

[0011] Optical remote sensing images of the study area were acquired and preprocessed. Water body information was extracted from the preprocessed images to construct a lake area sequence. Lake water levels were retrieved using satellite altimetry data. Based on a high-precision DEM, a regional growing method was used to construct the mathematical relationship between water level (H), area (A), and reservoir capacity (V). The least squares method was used to eliminate elevation offset, resulting in a corrected H-A-V curve. Historical lake reservoir capacity sequences were retrieved. Evolutionary characteristics were quantitatively characterized based on time-series data of lake area, water level, and water volume. The expansion rate of area, water level, and water volume was used to characterize the expansion intensity.

[0012] Step S3, Machine Learning Model Construction:

[0013] Using hydrological driving factors and the lake area and water level of the previous period as inputs, and the upstream water inflow of the lake as output, an XGBoost regression model is constructed and trained; the hydrological driving factors include lake surface precipitation, lake surface evaporation, watershed land surface evapotranspiration, land surface precipitation, and glacial runoff;

[0014] Step S4, Future Scenario Prediction and Lake Evolution Simulation:

[0015] The CMIP6 multi-scenario climate data, corrected by quantile mapping, is input into the trained model to predict future lake storage sequences. Overflow is calculated by combining the lowest watershed elevation of the lake basin. The H-A-V curve is mapped to water level and area to obtain the expansion rate of future lake area, water level, and water volume, completing the interannual evolution analysis of lakes under different emission scenarios. This enables dynamic quantification and trend analysis of the future expansion rate of the lake group.

[0016] Furthermore, in step 1, the Penman–Monteith method is used to calculate potential evapotranspiration, and the watershed land surface evapotranspiration is estimated by combining the crop coefficient. The calculation formula is as follows:

[0017]

[0018]

[0019] In the formula: Potential evaporation; G is the net radiation of the canopy surface; T is the soil heat flux; T is the daily average temperature; u is the wind speed. It is the saturated vapor pressure; This is the actual water vapor pressure; This is the saturated water vapor pressure difference; The slope of the water vapor pressure curve; This is the hygrometer constant; This represents the actual evapotranspiration in the basin. Let be the area weight of the i-th class; The crop coefficient is determined using the empirical formula or literature value of NDVI.

[0020] Land surface evapotranspiration in the basin and Represented as the same physical quantity, i.e. .

[0021] Furthermore, in step 1, the calculation of lake surface evaporation based on the energy balance equation is performed using the following formula:

[0022]

[0023] In the formula: Evaporation rate per unit area of ​​lake surface; Latent heat of vaporization; Net radiation from the lake surface; The slope of the water vapor pressure curve; This is the hygrometer constant; For the net radiation of the lake surface, This is the saturated water vapor pressure difference; Let wind speed be a function, according to the empirical formula. Determine, among which The wind speed is 2m.

[0024] Furthermore, in step 1, the calculation method for glacier runoff is as follows:

[0025] Precipitation was decomposed into rain and snow using the temperature threshold method. Rainfall amount The calculation formula is as follows:

[0026]

[0027] In the formula, Total precipitation; Rainfall; The current temperature; and These are the critical temperatures for precipitation and snowfall, respectively.

[0028] Glacial meltwater is calculated using the diurnal factor method, defining positive accumulated temperature, and the calculation formula is as follows:

[0029]

[0030] Therefore, snow and ice melt volume is calculated. :

[0031]

[0032]

[0033] In the formula, The day-to-day factor representing snow / ice;

[0034] The combined glacier runoff is calculated using the following formula:

[0035]

[0036] In the formula, The effective glacier runoff during time period t is represented by r, which is the refreezing or retention rate.

[0037] Furthermore, in step 2, the lake water level is retrieved by combining satellite altimetry data. The lake water level sequence is obtained based on ICESat-2 ATL13 / ATL12 products or Envisat, CryoSat-2, and Sentinel-3 altimetry satellite data. Outliers are eliminated through lake boundary screening and shore distance constraints, and a weighted average is used to obtain the lake surface elevation H at time t. t The calculation formula is as follows:

[0038]

[0039]

[0040] In the formula, Let be the lake surface elevation at the j-th elevation measurement point; M is the number of available elevation measurement points within the time period. As weight; The measurement error of the j-th altimeter is the accuracy bandwidth given in the satellite product.

[0041] Furthermore, in step 2, the mathematical relationship between water level H, area A, and reservoir capacity V is constructed using the region growing method based on a high-precision DEM, first determining the elevation of the lowest point in the lake basin. This is the starting point, with a preset fixed step size. Raise the water level step by step to construct a water level sequence ;

[0042] When the water level reaches At that time, the set of pixels Submerged, among them The elevation of pixel i;

[0043] Based on this data, the lake area and reservoir capacity at the corresponding water levels are obtained, calculated using the following formula:

[0044]

[0045]

[0046] In the formula, Let i be the area of ​​pixel i; Water level The area of ​​the lake below; For lake storage capacity, This is the elevation of the lowest point in the lake basin. For the kth water level, This is a preset fixed step size.

[0047] Furthermore, in step 2, the elevation offset is eliminated using the least squares method to obtain the corrected H-A-V curve, as follows:

[0048] The least squares method is used to eliminate elevation deviation, and the calculation formula is as follows:

[0049]

[0050] in, This is the optimal water level correction amount. This represents the water level correction offset, the original observed water level during time period t. The lake area observed by remote sensing during time period t. The corrected water level corresponds to the lake area;

[0051] The revised H–A–V relationship is calculated as follows:

[0052]

[0053]

[0054] in, To determine the lake area corresponding to the corrected water level h, The lake capacity corresponding to the corrected water level h.

[0055] Furthermore, in step 3, the objective function of the XGBoost regression model consists of a loss function and a regularization term, calculated as follows:

[0056]

[0057] Where n is the total number of samples; Here is the loss function; y i The true value of sample i; The complexity penalty term for the k-th tree is calculated using the following formula:

[0058]

[0059] Where T is the number of leaf nodes; w j γ is the weight of the j-th leaf node; γ is the leaf node penalty coefficient; and λ is the L2 regularization coefficient.

[0060] By performing a second-order Taylor expansion on the loss function, XGBoost approximates the objective function as a quadratic function of the leaf node weights and derives the formulas for the optimal weights and split gain, thereby improving fitting accuracy while effectively preventing overfitting.

[0061] Furthermore, in step 3, the method for constructing the XGBoost regression model includes:

[0062] Historical data was divided into 70% training set, 15% validation set and 15% test set in chronological order. The training set was used for model fitting, the validation set was used for hyperparameter selection and early stopping strategy, and the test set was used for independent evaluation of model performance. Rolling validation was used to verify the stability of the model in time series prediction.

[0063] Standardize all input variables on the training set and apply the standardized parameters to the validation and test sets to ensure causal consistency.

[0064] The XGBoost regression model was tuned using a combination of grid search and cross-validation. The tuned hyperparameters included the maximum tree depth, learning rate, subsampling ratio, column sampling ratio, and regularization parameter. and ;

[0065] Using the coefficient of determination The root mean square error (RMSE) and mean absolute error (MAE) are used to evaluate the accuracy of the model.

[0066] Furthermore, in step 4, the expansion rates of the future lake area, water level, and water volume are calculated, using the following specific method:

[0067] The lake water balance equation is expressed as follows, and the calculation formula is as follows:

[0068]

[0069] Substituting the upstream inflow predicted by the model into the above formula, the future lake storage sequence is calculated. The lake water level is mapped using the modified H–A–V relationship. With area The calculation formula is as follows:

[0070]

[0071]

[0072] Combined with the lowest watershed elevation of the lake basin When predicting lake water levels When the critical value is exceeded, an overflow will occur and replenish the adjacent lake; when the overflow volume is insufficient, no secondary overflow occurs in the adjacent lake, or the water levels of the upstream and downstream lakes tend to be equal, the overflow process will end.

[0073] The lake overflowed, and the overflow volume was... The calculation formula is as follows:

[0074]

[0075] This overflow will serve as an additional inflow to the adjacent lake, causing the water volume of the replenished lake to increase rapidly; after receiving the overflow at time t, the reservoir capacity of the adjacent lake j is updated as follows:

[0076]

[0077] The water level and area are updated using their H–A–V curve mapping, and the calculation formula is as follows:

[0078]

[0079]

[0080] in, , , The updated reservoir capacity, water level, and area;

[0081] Within the lake group, water volume and level are iteratively updated lake by lake to simulate the overflow connectivity and expansion process between lakes. After completing the simulation of the future evolution of the lake group's capacity, water level, and area, the calculation formulas for the future lake area, water level, and water volume expansion rate are as follows:

[0082]

[0083]

[0084]

[0085] In the formula, , , Let t be the predicted area, water level, and water volume at time t.

[0086] The beneficial effects of this invention are as follows: This invention addresses the problems of high difficulty in hydrological analysis and calculation of inland lakes and the difficulty of existing methods in simulating the overflow and interconnected evolution of lake groups. By fusing multi-source meteorological and remote sensing data, extracting lake area over time, constructing models to predict reservoir capacity evolution, and combining the elevation of the lowest watershed of the lake basin to determine the overflow and water replenishment process of lake groups, this invention effectively makes up for the shortcomings of traditional models that rely on measured data and are difficult to present the hydraulic connection and overflow mechanism of lake groups, thus having significant technical advantages.

[0087] 1. Overcomes the limitations of hydrological simulation in areas with no data, and has a wider range of applications.

[0088] The entire calculation process is completed using reanalysis meteorological data and optical remote sensing images. It does not rely on ground water level and flow observations and can be widely applied to lakes in remote and closed watersheds such as the Qinghai-Tibet Plateau, solving the problem that traditional hydrological models are difficult to apply in areas with scarce data.

[0089] 2. Enables long-term evolution and multi-scenario prediction of lakes, resulting in more complete simulations.

[0090] By constructing lake area sequences, training models, and retrieving reservoir capacity and water levels, the future evolution of lakes can be predicted. This method balances nonlinear hydrological response and temporal continuity, and its prediction accuracy and physical plausibility are superior to traditional statistical methods.

[0091] 3. Accurately simulates the overflow and linkage process of lake groups, making the mechanism more realistic.

[0092] Using the lowest watershed of the lake basin as the critical condition, the system automatically determines the states such as the initiation of overflow, replenishment by adjacent lakes, termination of overflow, and water level balance, so as to truly reflect the water transfer pattern among lake groups in a closed watershed and solve the key deficiency of existing models that generally ignore the hydraulic connection of lake groups.

[0093] The present invention will be explained in detail below with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0094] Figure 1 This is a flowchart illustrating the simulation method for the lake group expansion rate under the influence of climate change according to the present invention. Detailed Implementation

[0095] This embodiment presents a method for simulating the expansion rate of lake groups under the influence of climate change, such as... Figure 1 As shown, it includes the following steps:

[0096] Step S1, Data Preparation and Climate Driving Factor Calculation:

[0097] Historical observation and reanalysis data within the watershed were collected, and precipitation (P), air temperature (T), wind speed (U), and incident shortwave radiation were extracted. With longwave radiation Meteorological elements;

[0098] Spatial scale unification: For raster data, bilinear interpolation, cubic convolution interpolation, or nearest neighbor interpolation are used for resampling; for station observation data, Kriging interpolation, inverse distance weighted interpolation, and other methods are used for spatial interpolation to unify all elements to the target spatial resolution.

[0099] Time scale unification: Linear interpolation is used to fill time gaps in time series data, or time aggregation (summation / averaging) is used to perform scale transformation, unifying all elements to the target time step and completing time alignment correction.

[0100] Based on this, the land surface evapotranspiration E of the watershed is calculated. land Lake surface evaporation E lake With glacial runoff Q glacier Hydrological driving factors.

[0101] Potential evapotranspiration (ET0) was calculated using the Penman–Monteith method recommended by FAO-56, and combined with land cover or normalized difference vegetation index (NDVI), with a given crop coefficient K for each zone. c Calculate the actual evapotranspiration of the watershed The calculation formula is as follows:

[0102] (1)

[0103] (2)

[0104] In the formula: Potential evapotranspiration, mm / d; Net radiation at the canopy surface, MJ / m 2 d; G represents soil heat flux. T represents the daily average temperature. u represents wind speed, in m / s; e sThe saturated vapor pressure is kPa; e a The actual water vapor pressure is expressed in kPa. Δ represents the saturated water vapor pressure difference, in kPa; Δ is the slope of the water vapor pressure curve. ; This is the hygrometer constant. ;ET land The actual evapotranspiration of the watershed is expressed in mm / d. K represents the area weight of the i-th class coverage; c The crop coefficient can be obtained using the empirical formula NDVI or literature values.

[0105] Evapotranspiration from the land surface of the watershed and Representing the same physical quantity, i.e. .

[0106] Based on the principle of energy balance, the simplified form of the Penman–Monteith combined formula is used to calculate the lake surface evaporation E. lake The calculation formula is as follows:

[0107] (3)

[0108] In the formula: λ represents the evaporation rate per unit area of ​​the lake surface, in mm / d; λ represents the latent heat of vaporization, in MJ / kg. -1 ; Net radiation from the lake surface, MJ / m 2 d; f(U2) is the wind speed function, which can be derived by the empirical formula f(U2)=0.26(1+0.536U2), where U2 is the wind speed at 2m height, m / s; the meanings of the other symbols are the same as before.

[0109] Precipitation was decomposed into rain and snow using the temperature threshold method, with the rainfall amount P... rain,t The calculation formula is as follows:

[0110] (4)

[0111] In the formula, P t Total precipitation, mm; P rain,t Rainfall, in mm; T t The temperature for the current period is in °C; T r and T s These are the critical temperatures for precipitation and snowfall, respectively, in °C.

[0112] Glacial meltwater is calculated using the diurnal factor method, defining positive accumulated temperature, and the calculation formula is as follows:

[0113] (5)

[0114] Therefore, the snow and ice melt M is calculated.ice / snow :

[0115] (6)

[0116] (7)

[0117] In the formula, DDF snow / ice The day factor for snow / ice is mm / (d·℃).

[0118] The combined glacier runoff is calculated using the following formula:

[0119] (8)

[0120] In the formula, Q glacier,t The effective glacier runoff during time period t is represented by r, which is the refreezing or retention rate.

[0121] Step S2: Extract lake hydrological elements based on remote sensing imagery and DEM:

[0122] Optical remote sensing images (such as Landsat TM / ETM+ / OLI, Sentinel-2 MSI, Gaofen series, etc.) covering the study area were acquired and subjected to geometric, atmospheric, and radiometric corrections. After removing the effects of clouds and snow using known remote sensing preprocessing methods such as cloud detection algorithms and snow masking, the Normalized Difference Water Index (NDWI) or Modified Difference Water Index (MNDWI) was calculated. Water pixels were extracted using known remote sensing interpretation methods such as threshold segmentation or supervised classification to obtain the lake area sequence A. t .

[0123] Geometric correction and image registration: Geometric correction is performed using ground control points (GCP) combined with a polynomial or rational function model (RFM), and images from different time phases are registered to ensure spatial consistency of multi-time phase images;

[0124] Radiometric calibration and atmospheric correction: The image DN value is converted into radiance or apparent reflectance using calibration coefficients. Atmospheric correction models such as FLAASH, 6S or QUAC are used to convert the apparent reflectance into surface reflectance to eliminate the effects of atmospheric molecule and aerosol scattering.

[0125] Threshold segmentation method: The Otsu algorithm is used to automatically determine the segmentation threshold, or the threshold is set based on experience (e.g., NDWI>0) and manually judged.

[0126] Supervised classification: Based on training samples, classifiers such as maximum likelihood, support vector machine (SVM) or random forest are used to classify water pixels in remote sensing images;

[0127] The lake water level series was primarily obtained by inversion from ICESat-2 ATL13 / ATL12 products (or altimetry satellite data such as Envisat, CryoSat-2, and Sentinel-3). Outliers were eliminated through lake boundary screening and shore distance constraints, and a weighted average was used to obtain the lake surface elevation H at time t. t The calculation formula is as follows:

[0128] (9)

[0129] (10)

[0130] In the formula, h j Let be the lake surface elevation at the j-th elevation measurement point, in meters; M is the number of available elevation measurement points within the time period; w j σ is the weight; j Let m be the measurement error of the j-th altimeter (i.e., the accuracy bandwidth given in the satellite product).

[0131] The relationship between lake water level, area, and storage capacity (H–A–V) was constructed based on a high-precision DEM.

[0132] First, determine the elevation z of the lowest point in the lake basin. min Starting from this point, the water level is gradually increased by a preset fixed step size Δh to construct a water level sequence. .

[0133] When the water level reaches h k At that time, the set of pixels Submerged, of which z i Let i be the elevation of pixel i.

[0134] Based on this data, the lake area and reservoir capacity at the corresponding water levels are obtained, calculated using the following formula:

[0135] (11)

[0136] (12)

[0137] In the formula, a i Let A(h) be the area of ​​pixel i; k (h) represents the water level. k The area of ​​the lake below; V(h) k () represents the lake's reservoir capacity.

[0138] Because of the vertical reference bias in DEMs, the H–A–V curves constructed based on DEMs may not match satellite inversion observations. To reduce errors, the least squares method is used to estimate the elevation offset δz, and the calculation formula is as follows:

[0139] (13)

[0140] Thus, the corrected H–A–V relationship is obtained, and the calculation formula is as follows:

[0141] (14)

[0142] (15)

[0143] Finally, by combining the corrected H–A–V curve with the area-water level sequence retrieved from remote sensing, the historical lake water volume sequence V can be deduced. t .

[0144] To quantitatively characterize the evolution of lake groups, after obtaining the area, water level, and water volume sequences, the time series of the lake group as a whole is summarized; the lake expansion rate is introduced to reflect the intensity of lake expansion: the area expansion rate represents the relative increase per unit time, the water level expansion rate represents the speed of water level rise, and the water volume expansion rate represents the speed of reservoir capacity change.

[0145] The three are interconnected through the relationship of water level – area – water volume (H – A – V), and their difference form can be expressed as:

[0146] (16)

[0147] in, For the rate of water expansion, The rate of water level expansion. This represents the average lake surface area over the specified period.

[0148] Step S3, Machine Learning Model Construction:

[0149] Extreme Gradient Boosting (XGBoost) is used to predict lake water volume. XGBoost is an ensemble learning algorithm based on the gradient boosting framework. Its core idea is to iteratively train a Classification and Regression Tree (CART) and continuously optimize the model's predictions in each iteration using the gradient information of the objective function, thereby gradually approximating the actual observations.

[0150] Using the upstream water volume of a lake as the prediction target, this study aims to achieve accurate prediction of the upstream water volume of the lake, providing key hydrological input conditions for subsequent analysis of lake level changes, area expansion, water volume changes, and the overall evolution trend of the lake group.

[0151] The lake area sequence A is obtained according to step S2. t Based on the spatial extent of the watershed land surface, the precipitation data obtained in step S1 is spatially partitioned and statistically analyzed to extract the lake surface precipitation P.lake,t and land surface precipitation P land,t .

[0152] Constructing a training sample set , where x i Input features include: lake surface precipitation P lake,t Lake surface evaporation E lake,t Evapotranspiration from the land surface of the basin land,t Land surface precipitation P land,t glacial runoff Q glacier,t And the lake area A in the previous period t-1 With water level H t-1 Output variable y i The inflow of water from the upper reaches of the lake, Q in,t After the model is trained, its prediction function is denoted as f. XGB .

[0153] In the t-th iteration, the predicted value for sample i is:

[0154] (17)

[0155] Among them, f k For the k-th base learner (regression tree); Let be the function space of the CART regression tree.

[0156] The objective function of the model consists of a loss function and a regularization term, and the calculation formula is as follows:

[0157] (18)

[0158] Where n is the total number of samples; l(·) is the loss function; y i Ω(f) represents the true value of sample i; k The term ) represents the complexity penalty for the k-th tree, calculated using the following formula:

[0159] (19)

[0160] Where T is the number of leaf nodes; w j γ is the weight of the j-th leaf node; γ is the leaf node penalty coefficient; and λ is the L2 regularization coefficient.

[0161] By performing a second-order Taylor expansion on the loss function, XGBoost approximates the objective function as a quadratic function of the leaf node weights and derives the formulas for the optimal weights and split gain, thereby effectively preventing overfitting while improving fitting accuracy.

[0162] To ensure the causal rationality and accuracy of the predictions, historical data was divided into a training set (70%), a validation set (15%), and a test set (15%) in chronological order. The training set was used for model fitting, while the validation set was used for hyperparameter selection and early stopping strategies. The early stopping strategy was implemented based on the loss function or prediction accuracy on the validation set; training stopped when the validation set metrics failed to improve for several consecutive rounds. The goal was to minimize the prediction error on the validation set, and the optimal hyperparameter combination was determined through grid search and cross-validation. The test set was used for independent evaluation of model performance. Rolling validation was also used to verify the model's stability in time series prediction.

[0163] In terms of feature processing, all input variables are standardized on the training set, and the parameters are applied to the validation and test sets to ensure causal consistency. Hyperparameter tuning employs a combination of grid search and cross-validation, mainly including the maximum tree depth, learning rate, subsampling ratio, column sampling ratio, and regularization parameter (…). ).

[0164] Accuracy evaluation uses the coefficient of determination R. 2 The three metrics are: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and others. A higher RMSE indicates a lower MAE. Lower RMSE and MAE indicate that the model performs better in terms of fitting accuracy and predictive ability.

[0165] The final trained extreme gradient boosting model can be expressed as follows, and the calculation formula is as follows:

[0166] (20)

[0167] Step S4, Future Scenario Prediction and Lake Evolution Simulation:

[0168] Future climate-driving data are derived from typical emission scenarios (such as SSP2-4.5) output by the CMIP6 model, including meteorological elements such as precipitation, temperature, wind speed, and radiation. Due to systematic biases in climate model outputs, quantile mapping (QM) is used to correct these biases.

[0169] Based on the corrected meteorological data, hydrological drivers related to lake water balance are calculated, following a calculation process consistent with historical periods. Future meteorological driver sequences are input into an XGBoost model trained and validated in historical periods to predict upstream inflow sequences, using the following formula:

[0170] (twenty one)

[0171] In the formula, This represents the lake area and water level as observed / predicted in the previous year, used as a lagged input.

[0172] The future simulation is based on the water balance equation and is recursively applied year by year. When predicting year t, the lake area and water level are taken from the observation or prediction results of the previous year to ensure the causal consistency of the simulation process and reflect the feedback effect of the lake geometry on the water balance.

[0173] The lake water balance equation is expressed as follows, and the calculation formula is as follows:

[0174] (twenty two)

[0175] Substituting the predicted upstream inflow into the above formula, we can calculate the future lake storage sequence. The lake water level is mapped using the modified H–A–V relationship. With area The calculation formula is as follows:

[0176] (twenty three)

[0177] (twenty four)

[0178] Combined with the lowest watershed elevation h of the lake basin spill When predicting lake water levels When the critical value is exceeded, an overflow will occur and replenish the adjacent lake; when the overflow volume is insufficient, no secondary overflow occurs in the adjacent lake, or the water levels of the upstream and downstream lakes tend to be equal, the overflow process will end.

[0179] The lake overflowed, and the overflow volume was... The calculation formula is as follows:

[0180] (25)

[0181] This overflow will serve as an additional inflow to the adjacent lake, causing the water volume of the replenished lake to increase more rapidly. After receiving the overflow at time t, the reservoir capacity of the adjacent lake j is updated as follows:

[0182] (26)

[0183] The water level and area are updated using their H–A–V curve mapping, and the calculation formula is as follows:

[0184] (27)

[0185] (28)

[0186] Iterative updates of water volume and level across the lake group can simulate the overflow connectivity and expansion process between lakes. After simulating the future evolution of the lake group's capacity, water level, and area, the future expansion rates of lake area, water level, and water volume are as follows:

[0187] (29)

[0188] (30)

[0189] (31)

[0190] In the formula, A t fut, H t fut, V t fut represents the predicted area, water level, and water volume at time t.

[0191] By combining the above steps, we can identify the changing characteristics of lake groups during their expansion, overflow, and stabilization phases, thereby enabling dynamic quantification and trend analysis of the future expansion rate of lake groups.

[0192] This invention addresses the technical challenges of simulating the interconnected evolution of lake groups, effectively coupling overflow processes with inter-lake recharge relationships, and quantitatively predicting lake expansion and overflow risks. Breaking away from the reliance on ground-based hydrological data, it integrates watershed meteorological elements, remote sensing data, and lake water levels extracted from DEMs to construct a lake water level-area-storage capacity (H-A-V) relationship. This couples climate scenario prediction, lake evolution simulation, DEM-based overflow threshold judgment of the lake basin's lowest watershed, and inter-lake recharge processes into a unified system, forming a complete technology chain of "data extraction—model construction—scenario prediction." Through this systematic integration of multiple technologies, it solves the problems of traditional methods and existing machine learning models failing to represent the chain response of lake groups and accurately simulate the interconnected evolution and overflow processes of lake groups in closed watersheds. It is adaptable to applications in data-free areas, compensating for the technical shortcomings of lake group simulation in these regions, and enabling dynamic quantification and trend analysis of future lake group expansion rates.

[0193] The above description is only used to illustrate the technical solutions of the present invention and is not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention (such as the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for simulating the expansion rate of lake groups under the influence of climate change, characterized in that, Includes the following steps: Step S1, Data Preparation and Climate Driving Factor Calculation: Historical observation and reanalysis data within the watershed were collected, including precipitation, air temperature, wind speed, incident shortwave radiation, and longwave radiation; potential evapotranspiration was calculated using the Penman–Monteith method, and land surface evapotranspiration was extrapolated by combining crop coefficients; lake surface evaporation was calculated based on the energy balance equation; precipitation phases were distinguished by the temperature threshold method and snow and ice melt was calculated by combining the degree-day factor method, and glacial runoff was extrapolated. Step S2: Extract lake hydrological elements based on remote sensing imagery and DEM: Optical remote sensing images of the study area were acquired and preprocessed. Water body information was extracted from the preprocessed images to construct a lake area sequence. Lake water levels were retrieved using satellite altimetry data. Based on a high-precision DEM, a regional growing method was used to construct the mathematical relationship between water level (H), area (A), and reservoir capacity (V). The least squares method was used to eliminate elevation offset, resulting in a corrected H-A-V curve. Historical lake reservoir capacity sequences were retrieved. Evolutionary characteristics were quantitatively characterized based on time-series data of lake area, water level, and water volume. The expansion rate of area, water level, and water volume was used to characterize the expansion intensity. Step S3, Machine Learning Model Construction: Using hydrological driving factors and the lake area and water level of the previous period as inputs, and the upstream water inflow of the lake as output, an XGBoost regression model is constructed and trained; the hydrological driving factors include lake surface precipitation, lake surface evaporation, watershed land surface evapotranspiration, land surface precipitation, and glacial runoff; Step S4, Future Scenario Prediction and Lake Evolution Simulation: The CMIP6 multi-scenario climate data, corrected by quantile mapping, is input into the trained model to predict future lake storage sequences. Overflow is calculated by combining the lowest watershed elevation of the lake basin. The H-A-V curve is mapped to water level and area to obtain the expansion rate of future lake area, water level, and water volume, completing the interannual evolution analysis of lakes under different emission scenarios. This enables dynamic quantification and trend analysis of the future expansion rate of the lake group.

2. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, In step 1, the Penman–Monteith method is used to calculate potential evapotranspiration, and the watershed land surface evapotranspiration is estimated by combining the crop coefficient. The calculation formula is as follows: In the formula: Potential evaporation; G is the net radiation of the canopy surface; T is the soil heat flux; T is the daily average temperature; u is the wind speed. It is the saturated vapor pressure; This is the actual water vapor pressure; This is the saturated water vapor pressure difference; The slope of the water vapor pressure curve; This is the hygrometer constant; This represents the actual evapotranspiration in the basin. Let be the area weight of the i-th class; The crop coefficient is determined using the empirical formula or literature value of NDVI. Land surface evapotranspiration in the basin and Represented as the same physical quantity, i.e. .

3. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, In step 1, the lake surface evaporation is calculated based on the energy balance equation, and the calculation formula is as follows: In the formula: Evaporation rate per unit area of ​​lake surface; Latent heat of vaporization; Net radiation from the lake surface; The slope of the water vapor pressure curve; This is the hygrometer constant; For the net radiation of the lake surface, This is the saturated water vapor pressure difference; Let wind speed be a function, according to the empirical formula. Determine, among which The wind speed is 2m.

4. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, In step 1, the calculation method for glacier runoff is as follows: Precipitation was decomposed into rain and snow using the temperature threshold method. Rainfall amount The calculation formula is as follows: In the formula, Total precipitation; Rainfall; The current temperature; and These are the critical temperatures for precipitation and snowfall, respectively. Glacial meltwater is calculated using the diurnal factor method, defining positive accumulated temperature, and the calculation formula is as follows: Therefore, snow and ice melt volume is calculated. : In the formula, The day-to-day factor representing snow / ice; The combined glacier runoff is calculated using the following formula: In the formula, The effective glacier runoff during time period t is represented by r, which is the refreezing or retention rate.

5. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, In step 2, the lake water level is retrieved by combining satellite altimetry data. The lake water level sequence is obtained based on ICESat-2 ATL13 / ATL12 products or Envisat, CryoSat-2, and Sentinel-3 altimetry satellite data. Outliers are eliminated through lake boundary screening and shore distance constraints, and a weighted average is used to obtain the lake surface elevation H at time t. t The calculation formula is as follows: In the formula, Let be the lake surface elevation at the j-th elevation measurement point; M is the number of available elevation measurement points within the time period. As weight; The measurement error of the j-th altimeter is the accuracy bandwidth given in the satellite product.

6. The method for simulating the lake group expansion rate under the influence of climate change according to claim 1, characterized in that, In step 2, the mathematical relationship between water level H, area A, and reservoir capacity V is constructed using the region growing method based on a high-precision DEM, first determining the elevation of the lowest point in the lake basin. This is the starting point, with a preset fixed step size. Raise the water level step by step to construct a water level sequence ; When the water level reaches At that time, the set of pixels Submerged, among them The elevation of pixel i; Based on this data, the lake area and reservoir capacity at the corresponding water levels are obtained, calculated using the following formula: In the formula, Let i be the area of ​​pixel i; Water level The area of ​​the lake below; For lake storage capacity, This is the elevation of the lowest point in the lake basin. For the kth water level, This is a preset fixed step size.

7. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, In step 2, the elevation offset is eliminated using the least squares method to obtain the corrected H-A-V curve, as follows: The least squares method is used to eliminate elevation deviation, and the calculation formula is as follows: in, This is the optimal water level correction amount. This represents the water level correction offset, the original observed water level during time period t. The lake area observed by remote sensing during time period t. The corrected water level corresponds to the lake area; The revised H–A–V relationship is calculated as follows: in, To determine the lake area corresponding to the corrected water level h, The lake capacity corresponding to the corrected water level h.

8. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, In step 3, the objective function of the XGBoost regression model consists of a loss function and a regularization term, and the calculation formula is as follows: Where n is the total number of samples; Here is the loss function; y i The true value of sample i; The complexity penalty term for the k-th tree is calculated using the following formula: Where T is the number of leaf nodes; w j γ is the weight of the j-th leaf node; γ is the leaf node penalty coefficient; and λ is the L2 regularization coefficient. By performing a second-order Taylor expansion on the loss function, XGBoost approximates the objective function as a quadratic function of the leaf node weights and derives the formulas for the optimal weights and split gain, thereby improving fitting accuracy while effectively preventing overfitting.

9. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, Step 3, the method for constructing the XGBoost regression model includes: Historical data was divided into 70% training set, 15% validation set and 15% test set in chronological order. The training set was used for model fitting, the validation set was used for hyperparameter selection and early stopping strategy, and the test set was used for independent evaluation of model performance. Rolling validation was used to verify the stability of the model in time series prediction. Standardize all input variables on the training set and apply the standardized parameters to the validation and test sets to ensure causal consistency. The XGBoost regression model was tuned using a combination of grid search and cross-validation. The tuned hyperparameters included the maximum tree depth, learning rate, subsampling ratio, column sampling ratio, and regularization parameter. and ; Using the coefficient of determination The root mean square error (RMSE) and mean absolute error (MAE) are used to evaluate the accuracy of the model.

10. The method for simulating the expansion rate of lake groups under the influence of climate change according to claim 1, characterized in that, In step 4, the expansion rates of the future lake area, water level, and water volume are calculated, using the following specific method: The lake water balance equation is expressed as follows, and the calculation formula is as follows: Substituting the upstream inflow predicted by the model into the above formula, the future lake storage sequence is calculated. The lake water level is mapped using the modified H–A–V relationship. With area The calculation formula is as follows: Combined with the lowest watershed elevation of the lake basin When predicting lake water levels When the critical value is exceeded, an overflow will occur and replenish the adjacent lake; when the overflow volume is insufficient, no secondary overflow occurs in the adjacent lake, or the water levels of the upstream and downstream lakes tend to be equal, the overflow process will end. The lake overflowed, and the overflow volume was... The calculation formula is as follows: This overflow will serve as an additional inflow to the adjacent lake, causing the water volume of the replenished lake to increase rapidly; after receiving the overflow at time t, the reservoir capacity of the adjacent lake j is updated as follows: The water level and area are updated using their H–A–V curve mapping, and the calculation formula is as follows: in, , , The updated reservoir capacity, water level, and area; Within the lake group, water volume and level are iteratively updated lake by lake to simulate the overflow connectivity and expansion process between lakes. After completing the simulation of the future evolution of the lake group's capacity, water level, and area, the calculation formulas for the future lake area, water level, and water volume expansion rate are as follows: In the formula, t, , Let t be the predicted area, water level, and water volume at time t.

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