A multi-index comprehensive decision-based method for reservoir operation without data

Abstract

This invention relates to a data-free reservoir scheduling method based on multi-index comprehensive decision-making, comprising: constructing a unified reservoir operation simulation framework; conducting multi-rule parallel simulation and obtaining the outflow process sequence; constructing a multi-dimensional performance evaluation index system and conducting quantitative evaluation; optimizing reservoir scheduling rules based on the multi-index comprehensive decision-making SMAA-TOPSIS model; and realizing multi-reservoir scheduling rule optimization, credibility evaluation, and result output. This invention, by constructing a unified reservoir operation simulation framework, integrates and parallelizes multiple data-free reservoir scheduling rules in a modular manner under consistent inflow and boundary conditions; calculates multi-dimensional performance evaluation indices for each scheduling rule based on a unified process, forming a deterministic evaluation index matrix; and, in cases where index weight information is incomplete, introduces SMAA to randomly sample weights and combines it with TOPSIS to perform multiple sorting and statistical analyses of each candidate rule, thereby achieving differentiated scheduling rule optimization and credibility expression oriented towards single-reservoir characteristics.

Description

Technical Field

[0001] This invention relates to a data-free reservoir scheduling method based on multi-index comprehensive decision-making, which is a hydraulic engineering calculation method and a method for reservoir data analysis and regulation. Background Technology

[0002] Reservoirs, as crucial engineering facilities for watershed water resource allocation, flood control and disaster reduction, and water supply and power generation regulation, significantly impact downstream runoff processes, flood peaks, temporal distribution of water volume, and regional water security patterns. In practice, with complete scheduling procedures and operational records, fine-grained runoff regulation can be implemented by following existing procedures and charts. However, at regional or large-scale watershed levels, scheduling procedures, rule parameters, and operational records are often difficult to obtain or standardize, thus limiting traditional modeling methods. Particularly in large-scale watershed (regional) and hydrological simulation and climate change impact assessment studies, the sheer number of reservoirs and significant data discrepancies necessitate the development of a "generalized reservoir scheduling rule" to effectively characterize the operational processes of reservoirs with limited or no data.

[0003] Currently, several technical approaches have been developed for generalized schemes for reservoirs without data, mainly including: segmented flood control rules, seasonal storage and release logic, daily adjustment schemes for target reservoir capacity, and empirical reservoir capacity-outflow functions. These schemes describe the outflow characteristics of reservoirs through parametric methods and have been widely applied in watershed hydrological modeling, flood impact analysis, and water resource assessment, providing crucial numerical simulation support. Furthermore, in evaluating the scheduling effectiveness, existing studies typically use multiple statistical indicators (such as goodness of fit, water volume deviation, and flood peak reproduction capability) to assess the consistency between simulated and observed outflows from multiple perspectives. Despite the significant progress made by these methods, from the perspective of unifying practical engineering needs with scientific research applications, existing technologies still have the following shortcomings:

[0004] (1) Existing schemes mostly adopt a mode of uniformly promoting and applying a single generalized scheduling rule at the regional scale, that is, the same rule is used for multiple reservoirs at the same time. However, different reservoirs have significant differences in functional positioning, reservoir capacity, inflow characteristics and operational preferences. A single rule is difficult to guarantee the best simulation performance of all reservoirs at the same time, which can easily lead to a significant accumulation and amplification of simulation deviations in the outflow process of some reservoirs, thereby affecting the accuracy and reliability of the overall regional hydrological simulation results.

[0005] (2) Existing studies have focused more on improving a single scheduling rule or making limited comparisons among a small number of rules. There is a lack of a unified technical framework that can integrate multiple scheduling rules in parallel and carry out systematic comparative analysis. It is difficult to automatically, objectively and reasonably select the optimal scheduling scheme from multiple candidate rules for specific reservoir or regional scenarios.

[0006] (3) The quantitative evaluation of the reservoir scheduling simulation effect relies on multiple indicators for judgment. Existing studies mainly focus on the parallel comparison of multiple indicators, lacking a unified multi-indicator comprehensive decision-making mechanism. At the same time, if fixed weights are used for weighted ranking in the comprehensive evaluation, subjectivity will be introduced and the ranking result will be sensitive to the weight setting, making it difficult to ensure the robustness of the rule selection process.

[0007] Therefore, improving the accuracy and reliability of hydrological simulation and flood risk analysis results at the regional and large-basin scales is a problem that needs to be solved. Summary of the Invention

[0008] To overcome the problems of existing technologies, this invention proposes a data-free reservoir scheduling method based on multi-index comprehensive decision-making. The method integrates and couples multiple typical data-free reservoir scheduling rules within a unified framework, fuses multi-dimensional performance indicators, and explicitly characterizes the uncertainty caused by incomplete indicator weight information. This enables the scientific identification and robust selection of applicable scheduling rules for different reservoirs, thereby significantly improving the accuracy and reliability of regional and large-basin-scale hydrological simulations and flood risk analysis results.

[0009] The objective of this invention is achieved as follows: a data-free reservoir scheduling method based on multi-index comprehensive decision-making, the steps of which are as follows:

[0010] Step 1: Construct a unified reservoir operation simulation framework, including the following sub-steps:

[0011] Sub-step 101, Basic Data Collection and Preprocessing: Collect historical hydrological and meteorological data, topographic data, river network data, land use data, soil and hydrogeological data, and data on human water use in the study area; simultaneously, collect design and operation data of multiple reservoirs in the study area, including reservoir capacity, characteristic reservoir capacity parameters, and minimum discharge flow; and, where data conditions permit, supplement with water level-storage capacity relationship curves and water level-discharge capacity curves; collect measured data on reservoir operation, including initial water level, inflow, outflow, and water storage process; and perform coordinate transformation, spatial interpolation, and time scale consistency preprocessing according to the input requirements of the selected watershed hydrological model and reservoir scheduling module.

[0012] Sub-step 102, construct and calibrate the watershed hydrological model: construct the watershed hydrological model based on the preprocessed data, calibrate and verify the main hydrological parameters, and ensure that the simulation accuracy of the natural water inflow process meets the needs of engineering and research.

[0013] Sub-step 103, integrating multiple data-unavailable reservoir scheduling rules: deploying reservoir control units in the watershed hydrological model framework, defining the interface relationship between reservoir inflow, storage capacity and outflow, embedding several typical data-unavailable reservoir scheduling rules into the model system in a modular manner, forming an integrated reservoir scheduling simulation model that can be called in parallel under unified input conditions;

[0014] Step 2 involves conducting multi-rule parallel simulations and obtaining the outbound process sequence, including the following sub-steps:

[0015] Sub-step 201: Determine the simulation time range and time step according to research needs, and uniformly set the meteorological input scenario, initial reservoir capacity conditions, and downstream boundary conditions. Based on this, conduct daily operation simulations for each target reservoir using different data-free scheduling rules. The water balance equation for the r-th reservoir at time t using the m-th scheduling rule can be expressed as:

[0016]

[0017] In the formula, and These represent the water storage at the end of time t and the beginning of time t, respectively; and These represent the inflow and outflow rates of the reservoir at time t, respectively. This represents the sum of leakage and evaporation losses in the reservoir. For time step;

[0018] Sub-step 202 involves systematically organizing and structuring the simulation results of different scheduling rules, extracting the reservoir outflow process or water storage change process with stable long-sequence observation data, and forming a reservoir scheduling simulation result database for subsequent performance evaluation and comprehensive decision analysis.

[0019] Step 3: Construct a multi-dimensional performance evaluation index system and conduct quantitative evaluation: Based on the evaluation requirements and research scenario, construct an N-dimensional reservoir operation simulation performance evaluation index system. Quantitatively characterize the comprehensive performance of different scheduling rules from several aspects, including overall fitting ability, water volume deviation, statistical consistency, and flood peak reproduction ability. Quantitatively evaluate the simulation results of each scheduling rule.

[0020] After calculating the above indicators, the indicator results obtained from different reservoirs under different scheduling rules are uniformly organized and normalized to form a comprehensive performance evaluation indicator matrix with a three-dimensional structure of "reservoir-scheduling rule-performance indicator"; among which, the indicator matrix of the r-th reservoir ( ) is represented as:

[0021]

[0022] In the formula: This represents the calculated value of the nth evaluation index for the r-th reservoir under the m-th data-free scheduling rule; M is the total number of scheduling rules; N is the total number of evaluation indicators; R is the number of reservoirs; and this is applied to all R reservoirs. A set of indicator matrices;

[0023] Step 4, optimize reservoir scheduling rules based on the multi-index comprehensive decision-making SMAA-TOPSIS model, including the following sub-steps:

[0024] Sub-step 401, index normalization processing: for Normalization is performed to obtain a set of normalized index matrices. :

[0025]

[0026] In the formula: The value is the normalized indicator value, with a trend range of [0, 1]. The larger the value, the better the overall performance. and These represent the maximum and minimum values ​​of the nth index for the r-th reservoir among the M candidate scheduling rules, respectively; N + and N － These represent the set of benefit-type attribute indicators and the set of cost-type attribute indicators, respectively.

[0027] Sub-step 402: Introducing weights and modeling weight uncertainty using SMAA, including the following sub-steps:

[0028] Step 4021: Set the indicator weight vector :

[0029]

[0030] Step 4022: Define the feasible region of weights. :

[0031]

[0032] Step 4023, in Internal sampling of P group samples :

[0033]

[0034] In the formula: To characterize the probability distribution of weight uncertainty, a uniform distribution on the simplex is taken to reflect the weight uncertainty without prior preferences. Let p be the weight of the p-th group;

[0035] Sub-step 403: Construct the weighted matrix and calculate the TOPSIS proximity:

[0036] Step 4031, for each group of weights Construct a weighted normalized matrix :

[0037]

[0038] In the formula: This represents the weighted normalized index value under different weights;

[0039] Step 4032: Determine the positive and negative ideal solutions:

[0040]

[0041] In the formula: and These represent the positive and negative ideal solutions for the r-th reservoir under the p-th weight group, respectively. and These represent the maximum and minimum values ​​of the weighted normalized value of the nth indicator among the M candidate scheduling rules, respectively.

[0042] Step 4033: Calculate the Euclidean distance between each scheduling rule and the positive and negative ideal solutions:

[0043]

[0044] In the formula: and Let represent the distances between the m-th candidate scheduling rule and the positive and negative interpretations, respectively;

[0045] Step 4034: Calculate the relative proximity of each scheduling rule. :

[0046]

[0047] In the formula: The larger the value, the closer the m-th candidate scheduling rule is to the positive ideal solution and the further away it is from the negative ideal solution, and the better its overall performance.

[0048] Sub-step 404, Statistical analysis of ranking results based on multi-weighted samples: for each group of weighted samples Below, based on proximity Sort the M reservoir scheduling rules and record the optimal scheduling rule under that weight:

[0049] ;

[0050] By repeatedly calculating the weighted samples of group P, the optimal rule set under different weight preference conditions is obtained. ;

[0051] Sub-step 405, Robustness Statistics and Optimal Rule Determination: Under P-group weight sampling, statistically analyze the percentage of candidate scheduling rules that are determined to be the optimal rule under different weight conditions:

[0052]

[0053] In the formula, This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise.

[0054] The optimal scheduling rule for the r-th reservoir is finally determined as follows:

[0055]

[0056] Synchronize the acceptability probability corresponding to the optimal scheduling rule As a representation of credibility;

[0057] Step 5: Implement multi-reservoir scheduling rule optimization, credibility assessment and result output: Perform Step 4 for each of the multiple reservoirs in the study area to determine the recommended scheduling rules for each reservoir and their credibility and comprehensive evaluation results, and summarize them to form a multi-reservoir differentiated rule optimization result set.

[0058] Furthermore, the hydrological model in step 1 is the distributed hydrological model WEP.

[0059] Furthermore, the data-free reservoir scheduling rules in step 2 include at least: outflow rule W10 based on empirical parameterization, scheduling rule Z17 based on the concept of flood control segmentation control, scheduling rule D22 based on seasonal target reservoir capacity, generalized flood control scheduling rule H22 based on reservoir capacity segmentation control, and improved generalized flood control scheduling rule F25 based on reservoir capacity segmentation.

[0060] Furthermore, the reservoir operation simulation performance evaluation indicators in step 3 include at least the following typical indicators: Nash-Sutcliffe efficiency coefficient (NSE), coefficient of determination (R²), Kling-Gupta efficiency coefficient (KGE), relative error (RE), and peak flood error index (PDE), calculated using the following formulas:

[0061]

[0062]

[0063]

[0064]

[0065] Where: T represents the model validation period; and These represent the measured and simulated values ​​of reservoir outflow or water storage at time t, respectively. and These represent the complete measured sequence and the model-simulated sequence within time period T, respectively. This represents the correlation coefficient between the measured runoff sequence and the simulated runoff sequence; and These are the average values ​​of the measured and simulated sequences, respectively. and Then, let be the standard deviation of the measured and simulated sequences, respectively.

[0066] The advantages and beneficial effects of this invention are as follows: This invention constructs a unified reservoir operation simulation framework, integrating and parallelizing various data-unavailable reservoir scheduling rules in a modular manner under consistent inflow and boundary conditions; it calculates multi-dimensional performance evaluation indicators for each scheduling rule based on a unified process, forming a deterministic evaluation indicator matrix; in cases where indicator weight information is incomplete, it introduces SMAA to randomly sample weights and combines it with TOPSIS to perform multiple sorting and statistical analyses of each candidate rule, outputting the acceptability probability and robustness evaluation results of each rule, thereby achieving differentiated scheduling rule selection and credibility expression oriented towards single-reservoir characteristics. Based on this, this invention has the following advantages:

[0067] (1) Reduce the risk of systematic deviation: By evaluating multiple scheduling rules in parallel for the same reservoir and implementing differentiated optimization, the systematic deviation caused by the "unified application of a single rule" and its cumulative amplification risk in regional simulation can be effectively reduced.

[0068] (2) Achieve standardized and reproducible cross-rule comparison and evaluation: The unified simulation framework and structured result output enable different scheduling rules to be directly compared under consistent input conditions, reducing the arbitrariness of human selection and improving the reproducibility and traceability of the process.

[0069] (3) Improve the robustness and objectivity of the comprehensive ranking: explicitly incorporate the uncertainty of indicator weights into the SMAA framework, and obtain robustness quantitative indicators such as acceptability probability based on multiple ranking statistics of TOPSIS, thereby reducing the sensitivity of the conclusion to subjective weighting.

[0070] (4) Improve the transparency and applicability of results: In addition to providing recommended rules, the system also outputs credibility information such as acceptability probability and closeness statistics, making the basis for rule selection more transparent and facilitating comparison, verification and interpretation in engineering management and scientific research.

[0071] (5) Enhance the applicability and scalability in scenarios with no or little data: rule selection can be completed by relying only on the basic attributes of the reservoir and the available verification sequence (or equivalent alternative sequence); at the same time, it supports the expansion of candidate rule sets, indicator systems and weight constraints to adapt to different regions and different reservoir types.

[0072] In summary, this invention enables parallel comparison, robust optimization, and credibility expression of various data-unavailable scheduling rules under conditions of incomplete weight information and limited reservoir data, thereby improving the reliability and engineering application value of reservoir operation simulation and regional hydrological simulation results. Attached Figure Description

[0073] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0074] Figure 1 This is a flowchart of the reservoir scheduling method described in Embodiment 1 of the present invention;

[0075] Figure 2 This is a flowchart of the process of optimizing reservoir scheduling rules based on the SMAA-TOPSIS model in the reservoir scheduling method described in Embodiment 1 of the present invention;

[0076] Figure 3 This is a schematic diagram of the research area for an application example in Embodiment 4 of the present invention, which is a distribution map of cascade reservoirs in the Yalong River Basin;

[0077] Figure 4 This is a schematic diagram comparing the outflow runoff simulation of Jinping Level 1 Reservoir (a) and Ertan Reservoir (b) in the application example of Embodiment 4 of the present invention;

[0078] Figure 5 The following is a three-dimensional bar chart of the acceptability (credibility) of candidate scheduling rule ranking based on SMAA–TOPSIS, which is an application example in Embodiment 4 of the present invention: Jinping I Reservoir (a) and Ertan Reservoir (b). Detailed Implementation

[0079] Example 1:

[0080] This embodiment presents a data-free reservoir scheduling method based on multi-index comprehensive decision-making. The steps of the method are as follows, and the process is as follows: Figure 1 As shown:

[0081] Step 1: Construct a unified reservoir operation simulation framework: Collect basic data information of the study area, establish an integrated reservoir scheduling simulation platform using a watershed hydrological model, and embed various typical reservoir scheduling rules without data under the same inflow conditions to achieve parallel comparative calculations; including the following sub-steps:

[0082] Sub-step 101, Basic Data Collection and Preprocessing: First, determine the watershed hydrological model to be used and define the time frame. Based on the requirements of the determined watershed hydrological model and time frame, collect historical hydrological and meteorological data, topographic data, river network data, land use data, soil and hydrogeological data, and basic information on human water use within the study area. This information serves as the main driving data for the watershed hydrological model. Simultaneously, collect design and operation data for multiple reservoirs within the study area, including necessary information such as reservoir capacity, characteristic capacity parameters, and minimum discharge flow. When data availability permits, supplement with extended data such as water level-storage capacity curves and water level-discharge capacity curves to improve the accuracy of the scheduling rules. Furthermore, collect measured data on reservoir operation (such as initial water level, inflow, outflow, and water storage process), primarily for comparative analysis and performance evaluation of subsequent simulation results. Preprocessing, including coordinate transformation, spatial interpolation, and time scale consistency, is performed uniformly according to the input requirements of the selected watershed hydrological model and reservoir scheduling module, providing a reliable data foundation for model construction and evaluation.

[0083] The watershed hydrological model described in this embodiment can be the distributed hydrological model WEP (Water and Energy transfer process), or the SWAT (Soil and Water Assessment Tool) model, the VIC (Variable Infiltration Capacity) model, or other hydrological models that have similar watershed hydrological process simulation capabilities and can output daily runoff sequences.

[0084] Sub-step 102, construct and calibrate the watershed hydrological model: construct the watershed hydrological model based on the preprocessed data, calibrate and verify the main hydrological parameters, and ensure that the simulation accuracy of the natural water inflow process meets the needs of engineering and research.

[0085] When using the WEP model, preprocessed basic data can be used to drive the model, while measured daily runoff data can be used simultaneously to calibrate and validate key hydrological parameters of the model, thus initially constructing a natural water cycle simulation module to reproduce the natural inflow process of the river channel. Based on this, a social water use module of the WEP model can be further coupled to consider the impact of human water use activities on the watershed water cycle.

[0086] Sub-step 103 integrates multiple data-unavailable reservoir scheduling rules: Reservoir control units are deployed within the watershed hydrological model framework, defining the interface relationships between reservoir inflow, capacity, and outflow. Several typical data-unavailable reservoir scheduling rules are embedded into the model system in a modular manner, forming an integrated reservoir scheduling simulation model that can be invoked in parallel under unified input conditions. The data-unavailable reservoir scheduling rules include at least: outflow rules based on empirical parameterization, scheduling rules based on flood control segmentation control, scheduling rules based on seasonal target capacity, generalized flood control scheduling rules based on capacity segmentation control, and improved generalized flood control scheduling rules based on capacity segmentation, etc.

[0087] Step 2: Conduct multi-rule parallel simulation and obtain the outflow process sequence: Under unified hydrological conditions and model structure constraints, perform reservoir scheduling simulation calculations using different scheduling rules for the target reservoir, obtain the reservoir outflow process and water storage change sequence corresponding to each rule, and form a multi-rule simulation result set, which includes the following sub-steps:

[0088] Sub-step 201: Determine the simulation time range and time step according to research needs, and uniformly set the meteorological input scenario, initial reservoir capacity conditions, and downstream boundary conditions. Based on this, conduct daily operation simulations for each target reservoir using different data-free scheduling rules. The water balance equation for the r-th reservoir at time t using the m-th scheduling rule can be expressed as:

[0089]

[0090] In the formula, and These represent the water storage volume (m³) at the end of time t and the beginning of time t, respectively. 3 ); and Represent the inflow and outflow of the reservoir at time t (m³). 3 / s); This represents the sum of leakage and evapotranspiration losses in the reservoir (m). 3 ); The time step is in seconds (s).

[0091] Sub-step 202 involves systematically organizing and structuring the simulation results of different scheduling rules, extracting the reservoir outflow process or water storage change process with stable long-sequence observation data, and forming a reservoir scheduling simulation result database for subsequent performance evaluation and comprehensive decision analysis.

[0092] Step 3: Construct a multi-dimensional performance evaluation index system and conduct quantitative evaluation: Based on the evaluation requirements and research scenario, construct an N-dimensional reservoir operation simulation performance evaluation index system. Quantitatively characterize the comprehensive performance of different scheduling rules from several aspects, including overall fitting ability, water volume deviation, statistical consistency, and flood peak reproduction ability. Quantitatively evaluate the simulation results of each scheduling rule to form a comprehensive evaluation index matrix for each rule, which serves as the input for subsequent comprehensive decision-making.

[0093] After calculating all indicators, the indicator results obtained from different reservoirs under different scheduling rules were uniformly organized and normalized to form a comprehensive performance evaluation indicator matrix with a three-dimensional structure of "reservoir-scheduling rule-performance indicator," providing basic data support for subsequent multi-indicator comprehensive decision analysis. Among them, the indicator matrix of the r-th reservoir ( ) is represented as:

[0094]

[0095] In the formula: Let represent the calculated value of the nth evaluation index (e.g., NSE, KGE, R², RE, PDE) for the r-th reservoir under the m-th data-free scheduling rule; M is the total number of scheduling rules; N is the total number of evaluation indicators; R is the number of reservoirs; and for all R reservoirs, a set of evaluation indicators can be generated. A set of indicator matrices.

[0096] Step 4: Optimize reservoir scheduling rules based on the multi-criteria comprehensive decision-making SMAA-TOPSIS model: Introduce the stochastic multi-criteria acceptability analysis theory SMAA and the approximate ideal solution ranking method TOPSIS, explicitly consider the differences in evaluation index weights and their uncertainty effects, comprehensively rank each scheduling rule, output robustness indicators such as acceptability probability, and determine the optimal scheduling rule of the target reservoir and its credibility characterization.

[0097] This step employs SMAA-TOPSIS to optimize scheduling rules. Since the weights of evaluation indicators lack a unified objective basis, fixed weighting easily introduces subjectivity and leads to unstable ranking results. Considering that each evaluation indicator in this invention is calculated by comparing actual reservoir data with corresponding simulated sequences under a unified calculation process, and can be considered a deterministic evaluation value given the data and calculation rules, this invention only models the uncertainty of the weights: The weight vector is sampled within the feasible region of the weights, and TOPSIS proximity calculation and ranking are performed on each group of weights sequentially. The results of multiple rankings are statistically analyzed to obtain the acceptability index (or acceptability probability) of each candidate scheduling rule, which is used to characterize the robustness and reliability of the optimal rule. The process is as follows: Figure 2 As shown.

[0098] Includes the following sub-steps:

[0099] Sub-step 401, index normalization: Due to the different dimensions of different evaluation indicators, and the attribute differences between benefit-type indicators (larger index values ​​indicate better simulation results) and cost-type indicators (smaller index values ​​indicate smaller simulation errors and better results), in order to ensure that all indicators are comparable on the same scale and used for subsequent SMAA–TOPSIS integrated decision-making, the index matrix of the r-th reservoir output in step 3 ( The normalization process is performed to obtain the normalized index matrix set. :

[0100]

[0101] In the formula: The value is the normalized indicator value, with a trend range of [0, 1], and the larger the value, the better the overall performance; and These represent the maximum and minimum values ​​of the nth index for the r-th reservoir among the M candidate scheduling rules, respectively; N + and N － These represent the set of benefit-type attribute indicators (NSE, R², and KGE, etc.) and the set of cost-type attribute indicators (|PDE| and |RE|, etc.), respectively.

[0102] Sub-step 402: Introducing Weights and Modeling Weight Uncertainty (SMAA): Given that the comprehensive ranking of multiple indicators inevitably depends on indicator weights, and in the scenario of optimizing reservoir scheduling rules without data, the importance of each evaluation indicator lacks a unified objective basis, using fixed weights easily introduces subjectivity and makes the ranking results sensitive to the weight setting. To reduce subjectivity and explicitly characterize the uncertainty caused by incomplete indicator weight information, the weights of each evaluation indicator are treated as unknown variables under the SMAA framework, and their location is limited to a preset weight feasible region. By randomly sampling within the weight feasible region, multiple sets of candidate weight vectors are obtained, and the TOPSIS ranking calculation is repeated under each set of weight conditions. Furthermore, by statistically analyzing the frequency of each data-free reservoir scheduling rule being determined as the optimal solution under different weight conditions, the acceptability probability corresponding to each scheduling rule is obtained, which is used to characterize the robustness and reliability of the scheduling rule optimization results. The specific steps are as follows:

[0103] Step 4021: Set the indicator weight vector :

[0104]

[0105] in: The indicator has N components, where N is the total number of evaluation indicators. ;

[0106] Step 4022: Define the feasible region of weights. :

[0107]

[0108] Step 4023, in Internal sampling of P group samples :

[0109]

[0110] In the formula: To characterize the probability distribution of weight uncertainty, a uniform distribution on the simplex can be taken to reflect the weight uncertainty without prior preferences. Let be the weight of the p-th group.

[0111] Sub-step 403: Construct the weighted matrix and calculate the TOPSIS proximity:

[0112] Step 4031, for each group of weights Construct a weighted normalized matrix :

[0113]

[0114] In the formula: This represents the weighted normalized index value under different weights.

[0115] Step 4032: Determine the positive and negative ideal solutions:

[0116]

[0117] In the formula: and These represent the positive and negative ideal solutions for the r-th reservoir under the p-th weight group, respectively. and These represent the maximum and minimum values ​​of the weighted normalized value of the nth indicator among the M candidate scheduling rules, respectively.

[0118] Step 4033: Calculate the Euclidean distance between each scheduling rule and the positive and negative ideal solutions:

[0119]

[0120] In the formula: and Let represent the distances between the m-th candidate scheduling rule and the positive and negative interpretations, respectively.

[0121] Step 4034: Calculate the relative proximity of each scheduling rule. :

[0122]

[0123] In the formula: The larger the value, the closer the m-th candidate scheduling rule is to the positive ideal solution and the further away it is from the negative ideal solution, and the better its overall performance.

[0124] Sub-step 404, Statistical analysis of ranking results based on multi-weighted samples: for each group of weighted samples Below, based on proximity Sort the M reservoir scheduling rules and record the optimal scheduling rule under that weight:

[0125] .

[0126] By repeatedly calculating the weighted samples of group P, the optimal rule set under different weight preference conditions is obtained. .

[0127] Sub-step 405, Robustness Statistics and Optimal Rule Determination: Under P-group weight sampling, statistically analyze the percentage of candidate scheduling rules that are determined to be the optimal rule under different weight conditions.

[0128]

[0129] In the formula: This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise.

[0130] The optimal scheduling rule for the r-th reservoir is finally determined as follows:

[0131]

[0132] Synchronize the acceptability probability corresponding to the optimal scheduling rule As a representation of credibility.

[0133] Step 5: Implement multi-reservoir scheduling rule optimization, credibility assessment and result output: Perform Step 4 for each of the multiple reservoirs in the study area to determine the recommended scheduling rules for each reservoir and their credibility and comprehensive evaluation results, and summarize them to form a multi-reservoir differentiated rule optimization result set.

[0134] This step optimizes the multi-reservoir scheduling rules, assesses their reliability, and summarizes the results. Specifically, step 4 is performed on each of the R target reservoirs within the study area, based on their reliability. Determine the recommended scheduling rules for each reservoir. The results are compiled into a set consisting of "reservoir - recommended scheduling rules - credibility - comprehensive evaluation results". .

[0135] Example 2:

[0136] This embodiment is an improvement on the above embodiment, and is a refinement of the watershed hydrological model in the above embodiment. The watershed hydrological model described in this embodiment is the distributed hydrological model WEP (Water and Energy Transfer Process).

[0137] The WEP model is a physical-mechanism-based, dual-structure distributed hydrological model, named after the Water and Energy Transfer Process. Developed in 1995, it has been widely used and continuously improved in Japan, South Korea, the Netherlands, and China for over 20 years. Early versions of the WEP model used grids as the computational unit, making them suitable for small-scale watersheds. To address the complex topography of large-scale watersheds in my country, the WEP-L model, using "sub-watersheds with contour zones" as the computational unit, was further developed.

[0138] Example 3:

[0139] This embodiment is an improvement upon the above embodiment, detailing the reservoir scheduling module of the watershed hydrological model. The data-free reservoir scheduling regulations described in this embodiment include: outflow rule W10 based on empirical parameterization, scheduling rule Z17 based on the concept of segmented flood control, scheduling rule D22 based on seasonal target reservoir capacity, generalized flood control scheduling rule H22 based on segmented reservoir capacity control, and improved generalized flood control scheduling rule F25 based on segmented reservoir capacity.

[0140] Outflow gauge W10 based on empirical parameterization:

[0141]

[0142] in: The average inflow over many years (m 3 / s); and These are empirical parameters and can be set to values ​​of 0.16 and 0.60, respectively.

[0143] Dispatch rule Z17 based on the concept of segmented flood control:

[0144]

[0145] in: , and These represent the minimum discharge, normal discharge, and maximum safe discharge flow rates of the reservoir (m³). 3 / s). In the absence of actual measured operating data. , and The 5th, 30th, and 97th percentiles of natural daily runoff can be taken as empirical default values.

[0146] Scheduling rule D22 based on seasonal target storage capacity:

[0147]

[0148] in: , and These represent the minimum discharge, normal discharge, and maximum safe discharge flow rates of the reservoir (m³). 3 / s); k and r represent the index and correction coefficient of the severity of the flood entering the reservoir, respectively, by , and The calculation results in which The target storage capacity (m) per month (m) 3 In the absence of actual measured operational data, , and The 10th, 50th, and 99th percentiles of natural daily runoff can be taken as empirical default values.

[0149] Generalized flood control scheduling rule H22 based on reservoir capacity segmentation control:

[0150]

[0151] in: and These represent the normal discharge from the reservoir and the flood control activation threshold flow (m³). 3 / s), which can be taken as 30% of the multi-year average flow and the 100-year return period flow of the natural daily runoff series, respectively. k is the peak shaving adjustment coefficient, derived from... The calculation yielded, where The reservoir's catchment area (m²) 2 ).

[0152] Improved generalized flood control dispatching rule F25 based on reservoir capacity segmentation:

[0153]

[0154] in: This indicates that the flood control activation threshold flow is 30% of a 100-year return period flow. The average inflow over many years (m 3 / s); and These represent normal discharge and adjusted discharge flow rates (m³). 3 / s), respectively through and It was calculated.

[0155] In the above rules:

[0156] (1) General variables: , , ( , , , and )and Represent the time step (s) of the time simulation and the inflow (m) at time t, respectively. 3 / s), outflow at time t (m 3 / s) and water storage at time t (m³) 3 ).

[0157] (2) Feature library capacity: , , and These represent dead storage capacity and normal storage capacity (m). 3 ), reservoir capacity corresponding to high flood levels and total reservoir capacity (m³) 3 ).in, The value needs to be determined in conjunction with the rules and the season: in rules Z17, H22, and F25, The first rule specifies the reservoir capacity corresponding to the flood control limit water level during the flood season; the second rule (D22) determines the capacity dynamically according to the season (the reservoir capacity corresponding to the flood control limit water level during the flood season, and the reservoir capacity corresponding to the normal storage water level during the non-flood season). Additionally, the H22 and F25 rules... , and These represent the reservoir capacity corresponding to the critical water level, the adjustment water level, and the emergency water level, respectively (m). 3 (This can be achieved through empirical formulas) , and It is calculated. When measured data is missing, the feature library capacity parameter can be estimated using inflow percentiles or satellite data: for example, in the Z17 rule, , and The total storage capacity can be approximated. 10%, 30%, and 97%; in the H22 and F25 regulations, It can be obtained by inverting the 75th percentile of the satellite remote sensing water surface area sequence in conjunction with the ReGeom global reservoir capacity-area relationship, or by using an empirical formula. ( The value is usually taken as 0.37, but 0.42 can be used for the Yangtze River Basin.

[0158] Example 4:

[0159] This embodiment is an improvement upon the above embodiment, refining the reservoir operation simulation performance evaluation indicators in step 3 of the above embodiment. The reservoir operation simulation performance evaluation indicators in step 3 of this embodiment include at least the following typical indicators: Nash-Sutcliffe efficiency coefficient (Wisseret number NSE), coefficient of determination (R²), Kling-Gupta efficiency coefficient (KGE), relative error (RE), and peak flood error index (PDE). The calculation formulas are as follows:

[0160]

[0161]

[0162]

[0163]

[0164] Where: T represents the model validation period; and These represent the measured and simulated values ​​of reservoir outflow or water storage at time t, respectively. and These represent the complete measured sequence and the model-simulated sequence within time period T, respectively. This represents the correlation coefficient between the measured runoff sequence and the simulated runoff sequence; and These are the average values ​​of the measured and simulated sequences, respectively. and Then, let be the standard deviation of the measured and simulated sequences, respectively.

[0165] Meanwhile, if the measured sequence is outflow runoff, the PDE can be used to reflect the model's ability to reproduce the flood peak process. The smaller the value, the more accurate the flood peak simulation. In the formula, N is the number of valid years participating in the calculation, that is, the years in the entire verification period T that have both reliable measured and simulated annual maximum flood peak flow records. and Let represent the measured and simulated maximum annual flood peak flow in year k, respectively.

[0166] Among the evaluation indicators, NSE and KGE both range from (−∞, 1], with values ​​closer to 1 indicating a stronger fit to the runoff process. R² ranges from [0, 1], with values ​​closer to 1 indicating a higher correlation and better statistical consistency between the simulated and measured sequences. A smaller |RE| indicates better overall water conservation performance. A smaller |PDE| value indicates more accurate model simulation of peak flood amplitude.

[0167] Application examples:

[0168] The invention implementation cases take the cascade reservoirs in the lower reaches of the Yalong River basin as the research object, see... Figure 3Five data-unsupported reservoir scheduling rules—W10 (Wisseret et al., 2010), Z17 (Zajac et al., 2017), D22 (Dong et al., 2022), H22 (Hanazaki et al., 2022), and F25 (Funato et al., 2025)—were selected as candidate schemes for comparison between simulation and comprehensive optimization. This application example illustrates the effectiveness of the data-unsupported reservoir scheduling rule optimization method based on multi-index comprehensive decision-making in this region, but does not constitute an undue limitation on the scope of protection of this invention.

[0169] The implementation method includes the following steps:

[0170] Step 1: Construct a unified reservoir operation simulation framework. Collect basic data information of the study area, establish an integrated reservoir scheduling simulation platform using a watershed hydrological model, and embed various typical reservoir scheduling rules without available data under the same inflow conditions to achieve parallel comparative calculations.

[0171] Sub-step 101: Basic Data Collection and Preprocessing. In this case, the distributed hydrological model WEP (Water and Energy Transfer Process) is first used as the basic watershed hydrological model. Based on this, basic data on hydrology, meteorology, topography, river network, land use, soil, hydrogeology, and human water consumption (including agricultural, industrial, and domestic water use) in the study area from 1980 to 2020 are collected. According to the input requirements of the WEP model, coordinate transformation, spatial interpolation, and time scale consistency processing are uniformly performed. At the same time, in order to clarify the composition and engineering attributes of the cascade reservoirs in the study area, data on the five major cascade hydropower stations built on the main stream as of 2020—Jinping I, Jinping II, Guandi, Ertan, and Tongzilin—are compiled to obtain reservoir capacity parameters, minimum discharge flow, water level-storage capacity relationship curves, water level-discharge capacity curves, and measured outflow and storage processes for each reservoir. Given that the WEP model uses a daily time step, and that reservoirs such as Jinping II, Guandi, and Tongzilin are primarily diurnal regulating reservoirs, their intra-day scheduling characteristics are difficult to effectively represent at a daily scale. Therefore, Ertan Reservoir (commissioned in March 2013) and Jinping I Reservoir (commissioned in December 1999), which possess seasonal or annual regulation capabilities, were selected as the objects for the optimization and verification of scheduling rules. Furthermore, during the period of 2010–2018, both reservoirs operated under independent scheduling modes, which facilitates comparative analysis of rule optimization.

[0172] Sub-step 102: Construct and calibrate the basic watershed hydrological model. Using preprocessed basic data to drive the WEP model, and simultaneously using measured daily runoff data to calibrate and validate key hydrological parameters of the model, a preliminary natural water cycle simulation module is constructed to reproduce the natural inflow process of the river channel. Based on this, the social water use module of the WEP model is further coupled to consider the impact of human water use activities on the watershed water cycle.

[0173] Sub-step 103 integrates multiple data-unavailable reservoir scheduling rules. First, based on the dam site locations of Ertan Reservoir and Jinping I Reservoir, reservoir calculation nodes are set up in the WEP hydrological model; then, the selected five typical data-unavailable reservoir scheduling rules are integrated into the model confluence module in a modular manner.

[0174] Step 2: Conduct multi-rule parallel simulation and obtain the outbound process sequence.

[0175] Sub-step 201: In the WEP hydrological model, based on the start-up times of Jinping I Reservoir (commissioned in March 2013) and Ertan Reservoir (commissioned in December 1999), the start time of the reservoir scheduling module is set respectively; under the premise of keeping the hydrological drive, model structure and engineering constraints consistent, five reservoir scheduling rules, W10, Z17, D22, H22 and F25, are called to carry out parallel scheduling simulation to obtain the outflow and storage sequence under different rules.

[0176] Sub-step 202, combining the measured monthly outflow data of the two reservoirs, to ensure consistency between the simulation results and observation data in terms of time range and time scale, the simulation outputs of the five scheduling rules are uniformly organized, and the outflow simulation results of Jinping I Reservoir from 2015 to 2018 and Ertan Reservoir from 2010 to 2018 under each scheduling rule are extracted respectively, constructing a reservoir scheduling simulation result database of "reservoir-scheduling rule-time-outflow", such as... Figure 4 As shown.

[0177] Step 3: Construct a multi-dimensional performance evaluation index system and conduct quantitative assessment. In this application example, the measured reservoir data used is the monthly outflow process. Therefore, five evaluation indicators were selected: Nash-Sutcliffe efficiency coefficient (NSE), coefficient of determination (R²), Kling-Gupta efficiency coefficient (KGE), relative error (|RE|), and peak flow error (|PDE|). The outflow simulation results of each candidate scheduling rule were quantitatively evaluated and compared. The evaluation results are summarized in Table 1. Table 1 shows that for Jinping I Reservoir, except for W10, the other generalized scheduling rules can well characterize the actual operation characteristics of the reservoir; for Ertan Reservoir, the five compared scheduling rules can reasonably reflect the overall reservoir operation process.

[0178] Table 1 Simulation Assessment of Outflow Runoff

[0179]

[0180] Step 4: Optimize reservoir scheduling rules based on the multi-index comprehensive decision-making SMAA-TOPSIS model. Following the process described in sub-steps 401–405, conduct comprehensive ranking and robustness analysis on the evaluation results of Jinping I Reservoir and Ertan Reservoir under five candidate scheduling rules (W10, Z17, D22, H22, and F25) to determine the recommended scheduling rules for each reservoir and their reliability characterization. In this embodiment, the following implementation details are further clarified:

[0181] 1) In sub-step 401 (indicator normalization), the min-max method is used to normalize each evaluation index; among them, the three benefit-type indicators NSE, R² and KGE (the larger the value, the better the performance) are normalized by positive normalization, and the two cost-type indicators |RE| and |PDE| (the smaller the value, the better the performance) are normalized by negative normalization.

[0182] 2) In sub-step 402 (introducing weights and modeling weight uncertainty, SMAA), this application example satisfies... Within the weighted feasible region, a uniform sampling strategy is adopted, and 10,000 weighted samples are set for Jinping I Reservoir and Ertan Reservoir respectively. These samples are used to repeatedly perform TOPSIS proximity calculation and ranking statistics to obtain the acceptability probability and robustness evaluation results of each scheduling rule.

[0183] 3) In sub-steps 403–405, this application example performs TOPSIS ranking and robustness statistics on the five candidate scheduling rules according to the process described in sub-steps 401–405. Based on the repeated ranking results of the weighted samples, the ranking acceptability probability and ranking of each candidate scheduling rule are statistically obtained, and a ranking acceptability probability distribution chart is further drawn. See details. Figure 5 . Figure 5The results show that in Jinping I Reservoir, rule D22 has a probability of ranking first with a probability of 1.0, indicating that this rule remains optimal under uncertain weight information, demonstrating significant and robust overall advantages. The acceptability of the remaining rules is mainly distributed between ranking 2nd and 5th, indicating that these rules are more sensitive to weight settings and exhibit suboptimal and less robust characteristics overall. For Ertan Reservoir, rules F25 and Z17 have high acceptability probabilities in ranking first, constituting the main competing solutions; the acceptability of D22 and H22 is more concentrated in the middle rankings, reflecting the variability of ranking results under different weight preferences. In contrast, rule W10 has a probability of ranking 5th with a probability of 1.0, consistently ranking last, and can be considered unsuitable for Ertan Reservoir. This fully demonstrates that the SMAA-TOPSIS model framework can achieve optimal reservoir scheduling rules even when weight information is unknown.

[0184] Step 5 involves optimizing multi-reservoir scheduling rules, assessing their reliability, and outputting results. Step 4's ranking and robustness statistics are performed on Jinping I Reservoir and Ertan Reservoir respectively. The "acceptability probability (reliability) of ranking 1" is used as the criterion for recommending rules, resulting in a multi-reservoir optimization result set (see Table 2) comprising "reservoir—recommended scheduling rule—reliability—comprehensive evaluation result." This provides a basis for differentiated configuration of reservoir scheduling rules in the study area.

[0185] Table 2 Optimization Results of Differentiated Dispatch Rules for Multiple Reservoirs

[0186]

[0187] Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to the preferred arrangement, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solution of the present invention (such as the form and distribution of reservoirs, the application of various formulas, the order of steps, etc.) without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A data-free reservoir scheduling method based on multi-index comprehensive decision-making, characterized in that, The steps of the method are as follows: Step 1: Construct a unified reservoir operation simulation framework, including the following sub-steps: Sub-step 101, Basic data collection and preprocessing: Collect historical hydrological and meteorological data, topographic data, river network system, land use, soil and hydrogeological data, and data on human water use in the study area; at the same time, collect design and operation data of multiple reservoirs in the study area, including reservoir capacity, characteristic reservoir capacity parameters and minimum discharge flow, and, when data conditions permit, supplement by obtaining water level-reservoir capacity relationship curves and water level-discharge capacity curves; Collect measured data on reservoir operation, including initial water level, inflow, outflow and water storage process; and perform coordinate transformation, spatial interpolation and time scale consistency preprocessing according to the input requirements of the selected watershed hydrological model and reservoir scheduling module. Sub-step 102, construct and calibrate the watershed hydrological model: construct the watershed hydrological model based on the preprocessed data, calibrate and verify the main hydrological parameters, and ensure that the simulation accuracy of the natural water inflow process meets the needs of engineering and research. Sub-step 103, integrating multiple data-unavailable reservoir scheduling rules: deploying reservoir control units in the watershed hydrological model framework, defining the interface relationship between reservoir inflow, storage capacity and outflow, embedding several typical data-unavailable reservoir scheduling rules into the model system in a modular manner, forming an integrated reservoir scheduling simulation model that can be called in parallel under unified input conditions; Step 2 involves conducting multi-rule parallel simulations and obtaining the outbound process sequence, including the following sub-steps: Sub-step 201: Determine the simulation time range and time step according to research needs, and uniformly set the meteorological input scenario, initial reservoir capacity conditions, and downstream boundary conditions. Based on this, conduct daily operation simulations for each target reservoir using different data-free scheduling rules. The water balance equation for the r-th reservoir at time t using the m-th scheduling rule can be expressed as: In the formula, and These represent the water storage at the end of time t and the beginning of time t, respectively; and These represent the inflow and outflow rates of the reservoir at time t, respectively. This represents the sum of leakage and evaporation losses in the reservoir. For time step; Sub-step 202 involves systematically organizing and structuring the simulation results of different scheduling rules, extracting the reservoir outflow process or water storage change process with stable long-sequence observation data, and forming a reservoir scheduling simulation result database for subsequent performance evaluation and comprehensive decision analysis. Step 3: Construct a multi-dimensional performance evaluation index system and conduct quantitative evaluation: Based on the evaluation requirements and research scenario, construct an N-dimensional reservoir operation simulation performance evaluation index system. Quantitatively characterize the comprehensive performance of different scheduling rules from several aspects, including overall fitting ability, water volume deviation, statistical consistency, and flood peak reproduction ability. Quantitatively evaluate the simulation results of each scheduling rule. After calculating the above indicators, the indicator results obtained from different reservoirs under different scheduling rules are uniformly organized and normalized to form a comprehensive performance evaluation index matrix with a three-dimensional structure of "reservoir-scheduling rule-performance index"; among which, the index matrix of the r-th reservoir ( ) is represented as: In the formula: This represents the calculated value of the nth evaluation index for the r-th reservoir under the m-th data-free scheduling rule; M is the total number of scheduling rules; N is the total number of evaluation indicators; R is the number of reservoirs; and this is applied to all R reservoirs. A set of indicator matrices; Step 4, optimize reservoir scheduling rules based on the multi-index comprehensive decision-making SMAA-TOPSIS model, including the following sub-steps: Sub-step 401, index normalization processing: for Normalization is performed to obtain a set of normalized index matrices. : In the formula: The value is the normalized indicator value, with a trend range of [0, 1]. The larger the value, the better the overall performance. and These represent the maximum and minimum values ​​of the nth index for the r-th reservoir among the M candidate scheduling rules, respectively; N + and N － These represent the set of benefit-type attribute indicators and the set of cost-type attribute indicators, respectively. Sub-step 402: Introducing weights and modeling weight uncertainty using SMAA, including the following sub-steps: Step 4021: Set the indicator weight vector : Step 4022: Define the feasible region of weights. : Step 4023, in Internal sampling of P group samples : In the formula: To characterize the probability distribution of weight uncertainty, a uniform distribution on the simplex is taken to reflect the weight uncertainty without prior preferences. Let p be the weight of the p-th group; Sub-step 403: Construct the weighted matrix and calculate the TOPSIS proximity: Step 4031, for each group of weights Construct a weighted normalized matrix : In the formula: This represents the weighted normalized index value under different weights; Step 4032: Determine the positive and negative ideal solutions: In the formula: and These represent the positive and negative ideal solutions for the r-th reservoir under the p-th weight group, respectively. and These represent the maximum and minimum values ​​of the weighted normalized value of the nth indicator among the M candidate scheduling rules, respectively. Step 4033: Calculate the Euclidean distance between each scheduling rule and the positive and negative ideal solutions: In the formula: and Let represent the distances between the m-th candidate scheduling rule and the positive and negative interpretations, respectively; Step 4034: Calculate the relative proximity of each scheduling rule. : In the formula: The larger the value, the closer the m-th candidate scheduling rule is to the positive ideal solution and the further away it is from the negative ideal solution, and the better its overall performance. Sub-step 404, Statistical analysis of ranking results based on multi-weighted samples: for each group of weighted samples Below, based on proximity Sort the M reservoir scheduling rules and record the optimal scheduling rule under that weight: ； By repeatedly calculating the weighted samples of group P, the optimal rule set under different weight preference conditions is obtained. ; Sub-step 405, Robustness Statistics and Optimal Rule Determination: Under P-group weight sampling, statistically analyze the percentage of candidate scheduling rules that are determined to be the optimal rule under different weight conditions: In the formula, This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise. The optimal scheduling rule for the r-th reservoir is finally determined as follows: Synchronize the acceptability probability corresponding to the optimal scheduling rule As a representation of credibility; Step 5: Implement multi-reservoir scheduling rule optimization, credibility assessment and result output: Perform Step 4 for each of the multiple reservoirs in the study area to determine the recommended scheduling rules for each reservoir and their credibility and comprehensive evaluation results, and summarize them to form a multi-reservoir differentiated rule optimization result set.

2. The method according to claim 1, characterized in that, The watershed hydrological model in step 1 is the distributed hydrological model WEP.

3. The method according to claim 1, characterized in that, The data-free reservoir scheduling rules in step 2 include at least: outflow rule W10 based on empirical parameterization, scheduling rule Z17 based on the concept of flood control segmentation, scheduling rule D22 based on seasonal target reservoir capacity, generalized flood control scheduling rule H22 based on reservoir capacity segmentation control, and improved generalized flood control scheduling rule F25 based on reservoir capacity segmentation.

4. The method according to claim 1, characterized in that, The reservoir operation simulation performance evaluation indicators in step 3 include at least the following typical indicators: Nash-Sutcliffe efficiency coefficient (NSE), coefficient of determination (R²), Kling-Gupta efficiency coefficient (KGE), relative error (RE), and peak flood error index (PDE). The calculation formulas are as follows: Where: T represents the model validation period; and These represent the measured and simulated values ​​of reservoir outflow or water storage at time t, respectively. and These represent the complete measured sequence and the model-simulated sequence within time period T, respectively. This represents the correlation coefficient between the measured runoff sequence and the simulated runoff sequence; and These are the average values ​​of the measured and simulated sequences, respectively. and Then, let be the standard deviation of the measured and simulated sequences, respectively.

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