A method for evaluating reservoir group inflow variation decoupling and step-by-step gain transmission

Abstract

The application discloses a reservoir group incoming water variation decoupling and step-by-step gain transmission evaluation method, which firstly extracts the annual runoff variation coefficient and the runoff annual wet and dry ratio of the leading incoming water as the benchmark statistics, and constructs two types of independent controlled disturbances, namely, the interannual runoff variation disturbance and the annual distribution deviation disturbance, in the logarithmic domain parameter space; then, the Monte Carlo reservoir water balance simulation is carried out under the disturbance conditions of each node of the reservoir group, the ratio of the annual outflow variation coefficient to the annual inflow variation coefficient is calculated, and the net evaporation correction factor is multiplied as the gain function; finally, each node is determined to be attenuation, transmission or amplification according to the determination tolerance, and the variation transmission pattern of each node and the whole reservoir group is identified. The method decouples the interannual runoff variation and the annual distribution deviation variation into independent dimensions, quantifies the gain transmission effect of the reservoir group on the incoming water variation at each node, and provides a quantitative basis for the hydrological risk analysis and the beneficial regulation scheme evaluation of the reservoir group.

Description

Technical Field

[0001] This invention relates to hydrological and water resources analysis technology, specifically to a method for decoupling and evaluating the variability of inflow in a reservoir group. Background Technology

[0002] The uneven spatial and temporal distribution of water resources is a fundamental characteristic affecting the development and utilization of water resources in river basins. Influenced by monsoon climate and complex topography, river runoff exhibits significant interannual alternations of abundant and dry periods, and the seasonal distribution of flood and dry seasons within a single year is also extremely uneven. In recent years, global warming has intensified the atmospheric water cycle, and some river basins have observed trends such as increased annual runoff variability and deviations in the annual runoff abundance / dryness ratio from historical averages, increasing the difficulty of water resource regulation. Cascade reservoir systems are an important engineering means of water resource regulation in river basins, achieving beneficial goals such as water supply, irrigation, and power generation through reservoir capacity regulation. The essence of beneficial water resource regulation lies in utilizing the runoff regulation capacity of reservoirs to buffer the adverse effects of inflow fluctuations, and the magnitude and structure of inflow variability are key hydrological boundary conditions determining the feasibility of the regulation scheme and its beneficial effects.

[0003] The variability of inflow can be characterized from two independent dimensions. One is the interannual runoff variability, expressed as the annual runoff variation coefficient. The measurement reflects the intensity of the interannual alternation between abundant and scarce runoff; The larger the volume of water, the greater the reservoir capacity required for multi-year regulation, and the more difficult it is to maintain the water supply guarantee rate. Secondly, there is the annual distribution of wet and dry seasons, measured by the annual wet-dry ratio (the ratio of the multi-year average runoff during the flood season to the multi-year average runoff during the dry season), reflecting the degree of concentration of runoff over time within the year; the larger the annual wet-dry ratio, the heavier the flood control pressure during the flood season and the more prominent the water replenishment gap during the dry season. Under the background of climate change, the variability of the above two dimensions may change independently, or even evolve in opposite directions: in some watersheds... In some watersheds, the annual runoff ratio tends to stabilize while the ratio of wet to dry periods increases, while in others the opposite occurs. Therefore, it is necessary to decouple the two dimensions into independent and controllable analytical variables in order to accurately determine the gain transmission effect after the variability of each dimension is passed down step by step.

[0004] The existing methods for analyzing the inflow variability of cascade reservoirs have the following shortcomings: (1) Most studies focus on statistical analysis of a single dimension, or change two dimensions at the same time without independent control, making it difficult to distinguish the contributions of interannual runoff variability and intra-annual distribution shift variability to the cascade gain transfer effect; (2) There is a lack of methods to track the variability transfer law node by node within the cascade: Existing analyses usually take the entire cascade or the end section of the cascade as the object, which cannot reveal the differentiated gain transfer effect of each intermediate node; (3) Some methods simplify actual engineering factors such as evaporation loss, scheduling rules and physical reservoir capacity constraints in water balance simulation, resulting in deviations between the simulation results and the actual engineering, and making it impossible to accurately quantify the regulatory contribution of each node reservoir to the inflow variability.

[0005] In summary, there is currently a lack of analytical methods that can decouple interannual runoff variability from intra-annual distribution shift variability into independent controlled dimensions, quantify the cascade gain transfer effect node by node, and identify the variability transfer patterns at each node. This invention addresses these shortcomings. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a method for decoupling and evaluating the variability of inflow in a reservoir group. This method can decouple interannual runoff variability and intra-annual distribution shift variability into independent controlled dimensions, quantify the cascade gain transfer effect node by node, and identify the variability transfer pattern of each node.

[0007] Technical solution: The present invention provides a method for decoupling and evaluating the inflow variation of a reservoir group and the stepwise gain transfer, comprising:

[0008] Water inflow statistical feature extraction and controlled disturbance construction: The annual runoff variation coefficient and the annual wet-dry ratio of the cascade headwaters were extracted from the historical monthly runoff sequences of the cascade headwaters as baseline statistics, along with the logarithmic domain Thomas-Fiering model parameters of the headwaters and the inflows between each level. Based on the baseline statistics and model parameters, two types of controlled disturbances were constructed in the logarithmic domain parameter space: interannual runoff variation disturbance and intra-annual distribution shift disturbance. The interannual runoff variation disturbance only scaled the monthly standard deviation of the logarithmic domain to change the annual runoff variation coefficient, while the intra-annual distribution shift disturbance shifted the monthly mean of the flood and dry seasons in the logarithmic domain to change the intra-annual wet-dry ratio of the runoff. At the same time, standard deviation compensation scaling was added to keep the annual runoff variation coefficient unchanged. The two types of disturbances were applied independently, and each type of disturbance had no less than three intensity levels.

[0009] Monte Carlo simulation and gain function calculation for cascade scheduling: Monte Carlo reservoir water balance simulation is carried out node by node in series on the cascade system for two types of controlled disturbance conditions; the same set of random number sequences is shared for the simulation implementation of each disturbance condition in the same disturbance experimental group. During the simulation implementation, the gain function and the standard error of the gain function are calculated node by node. The number of simulation implementations is gradually increased so that the standard error does not exceed half of the pre-set judgment tolerance.

[0010] Identification of Variability Transmission Patterns: For interannual runoff variability disturbances and intra-annual distribution shift disturbances, a gain response matrix is ​​constructed using the calculation results of the gain functions of each node, with the disturbance conditions as rows and the cascade nodes as columns. Disturbance conditions and node combinations that are not marked as inapplicable by the gain function are considered as valid combinations. The judgment tolerance is compared with the values ​​in the gain response matrix, and the regulation type of each node is determined as attenuation, transmission, or amplification based on the comparison results, thereby identifying the variability regulation type and transmission pattern of each node and the entire cascade.

[0011] Furthermore, the interannual runoff variability disturbance is constructed as follows: the monthly standard deviations of the logarithmic domain are multiplied by an equal scaling factor;

[0012] The proportional scaling factor is determined by trial calculation and piecewise linear interpolation to make the annual runoff variation coefficient of the composite sequence reach the target value. The composite sequence is generated by running the logarithmic domain Thomas-Fiering model with the same random number sequence at each trial point. The annual runoff variation coefficient obtained by the trial calculation increases monotonically with the proportional scaling factor.

[0013] Furthermore, the method for constructing the annual allocation offset perturbation is as follows:

[0014] In the logarithmic field, the logarithmic mean of each month during the flood season. Apply flood season offset The logarithmic mean of each month during the dry season Apply dry season offset ;in, This is the scaling factor for the theoretical mean of monthly runoff during the flood season; This is the scaling factor for the theoretical mean of monthly runoff during the dry season; and The solution is obtained by simultaneously solving the constraint of conservation of the expected annual runoff and the constraint of the annual ratio of abundant to dry runoff;

[0015] Apply flood season offset and dry season offset Then, a proportionally compensated scaling factor is applied to the logarithmic field standard deviation of each month. This brings the annual runoff variation coefficient back to the model baseline variation coefficient; wherein, the proportional compensation scaling factor... The annual wet-dry ratio of each target runoff was determined independently using the same trial calculation and piecewise linear interpolation method as the interannual runoff variability disturbance.

[0016] Furthermore, the expression for the conservation constraint of the expected annual runoff is as follows:

[0017] ;

[0018] The expression for the target runoff annual wet-dry ratio constraint is as follows:

[0019] ;

[0020] in, For the log-normal model, the first Theoretical mean of monthly runoff; The target is the ratio of wet to dry seasons in annual runoff.

[0021] Furthermore, the gain function is defined as the ratio of the annual outflow variation coefficient to the annual inflow variation coefficient of the current node multiplied by the net evaporation correction factor; wherein, the net evaporation correction factor is equal to 1 minus the ratio of the average annual net evaporation to the average annual inflow of the current node; when the average annual inflow does not exceed zero or the average annual outflow does not exceed zero, or the annual inflow variation coefficient is less than a preset lower limit, or the ratio of the average annual net evaporation to the average annual inflow is greater than a preset upper limit, the gain function is marked as inapplicable.

[0022] Furthermore, the Monte Carlo reservoir water balance simulation is implemented node-by-node in the cascade system for the two types of controlled disturbance conditions, including:

[0023] Calculate the monthly inflow at each node, and establish a monthly water balance equation based on the monthly inflow at each node; then, using the reservoir capacity-area curve and historical average net evaporation depth, calculate the monthly net evaporation at each node; finally, determine the monthly outflow at each node as follows:

[0024] After obtaining the initial outflow rate using the target water storage tracking method based on the regular curve, the following three constraint checks are performed in sequence: the first step is to limit the outflow rate between the minimum discharge rate and the maximum discharge capacity; the second step is to increase the outflow rate according to the upper limit of the water storage at the end of the month; and the third step is to decrease the outflow rate according to the lower limit of the dead storage capacity. Among these, the dead storage capacity constraint takes precedence over the minimum discharge constraint.

[0025] Once the outflow rate is determined, the monthly water balance equation is substituted back to calculate the monthly water storage. The inflow, storage, and outflow processes of each level of reservoir are then deduced sequentially from the leading node to the terminal node for each month.

[0026] Furthermore, the monthly inflow of each node is calculated as follows:

[0027] ;

[0028] In the formula, For the first node Monthly revenue; The current monthly runoff from the tap is the synthetic runoff under the current disturbance conditions. For the first Nodes Monthly outflow; For the first Nodes Monthly revenue; For the first Nodes Water flow during the lunar cycle;

[0029] The expression for the monthly water balance equation is as follows:

[0030]

[0031] In the formula, for Nodes The water storage at the beginning of the month, as End-of-month water storage; For the first The node Water storage at the beginning of the month; For the first Nodes Monthly revenue; For the first Nodes Monthly outflow; For the first Nodes Net evaporation from the water surface in a given month.

[0032] Furthermore, the standard error of the gain function is calculated as follows:

[0033] Each simulation is treated as an independent group. The gain function is calculated separately for each group according to its definition. Groups that are not applicable to the gain function are removed to obtain the effective groups. The standard error is calculated by dividing the sample standard deviation of the gain function values ​​of the effective groups by the square root of the number of effective groups. If the number of effective groups is less than 3, the combination is marked as inapplicable.

[0034] Furthermore, the step of comparing the judgment tolerance with the values ​​in the gain response matrix, and determining the variability of each node as attenuation, transmission, or amplification based on the comparison result, thereby identifying the variability transmission pattern of each node and the entire cascade, includes:

[0035] The gain function value is less than It is determined to be attenuation; the gain function value is greater than If it is determined to be amplified, otherwise it is determined to be transparent; among which, The decision tolerance is predetermined; if all effective combination adjustment types of the same node are consistent, it is determined to be a stable node; otherwise, it is determined to be a condition change node, and the adjacent disturbance condition intervals where the type change occurs are recorded.

[0036] Furthermore, the log-domain Thomas-Fiering model serves as a synthetic runoff generation model. The model parameters include the log-domain mean for each month, the log-domain standard deviation for each month, and the monthly Pearson correlation coefficient. Each model parameter is extracted by taking the natural logarithm of the historical monthly runoff sequence and then statistically analyzing it over a complete hydrological year. When there is a zero value in the historical monthly runoff, it is replaced by one-thousandth of the smallest positive value in the current sequence before taking the natural logarithm.

[0037] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0038] (1) In this invention, interannual runoff variability disturbance and intra-annual distribution offset disturbance are constructed in the logarithmic parameter space, and the two types of disturbances are ensured to be mutually independent by standard deviation compensation scaling. The two dimensions are decoupled into independent and controllable analytical variables, which solves the problem that the existing methods do not independently control the two dimensions, resulting in the inability to distinguish the contribution of each dimension's variability to the cascade gain transfer effect.

[0039] (2) The present invention performs Monte Carlo reservoir water balance simulation node by node and calculates the gain function node by node, which can reveal the differential gain transfer effect of each intermediate node. This solves the problem that the existing methods only take the whole cascade or the end section as the object, lack the internal node tracking of the cascade, and cannot reveal the differential regulation characteristics of each intermediate node.

[0040] (3) The present invention incorporates reservoir capacity-area curve, net evaporation of water surface, regular curve scheduling and three-step constraint verification including minimum discharge, maximum discharge and dead storage capacity in water balance simulation, which solves the problem that the simulation results are deviated from the actual engineering due to the simplification of actual engineering factors in the existing methods.

[0041] (4) This invention achieves variance reduction by sharing a random number sequence within the same perturbation experimental group, and determines the number of simulations by using the standard error adaptive convergence criterion, thus balancing computational efficiency and statistical accuracy.

[0042] (5) The present invention constructs a gain response matrix, and combines the judgment tolerance to determine each node as attenuation, transmission or amplification, and distinguishes between stable and condition-transition nodes, providing a quantitative basis for evaluating the beneficial scheduling scheme. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the process of the present invention;

[0044] Figure 2 This is a schematic diagram of the Cv perturbation gain response matrix in this invention;

[0045] Figure 3 This is a schematic diagram of the SR perturbation gain response matrix in this invention. Detailed Implementation

[0046] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0047] like Figure 1 As shown, the present invention provides a method for decoupling and evaluating the inflow variation of a reservoir group and the stepwise gain transfer, comprising the following steps:

[0048] S1. Extraction of statistical features of inflow and construction of controlled disturbances: The annual runoff variation coefficient and the annual wet-dry ratio of the inflow of the cascade headwaters are extracted from the historical monthly runoff sequences of the cascade headwaters as baseline statistics, along with the logarithmic domain Thomas-Fiering model parameters of the headwaters and the inflows of each level interval. Based on the baseline statistics and model parameters, two types of controlled disturbances are constructed in the logarithmic domain parameter space: interannual runoff variation disturbance and intra-annual distribution shift disturbance. Among them, the interannual runoff variation disturbance only scales the monthly standard deviation of the logarithmic domain to change the annual runoff variation coefficient, and the intra-annual distribution shift disturbance shifts the monthly mean of the logarithmic domain during the flood season and the dry season to change the intra-annual wet-dry ratio of the runoff. At the same time, standard deviation compensation scaling is added to keep the annual runoff variation coefficient unchanged. The two types of disturbances are applied independently, and each type of disturbance has no less than 3 intensity levels.

[0049] Assume the cascade system consists of ( It consists of 10 reservoir nodes connected in series along the same main stream. , As the leader, (For the end point). The inflow at the first node (faucet) is external water from the cascade system; the... ( The water inflow between the nodes is the natural inflow between the dam site of the previous node and the dam site of this node.

[0050] Known engineering characteristic parameters of each reservoir node include: water level-storage capacity curve; storage capacity-area curve, where the value at the upper limit is taken when the storage exceeds the upper limit of the curve's domain, and the value at the lower limit is taken when the storage is below the lower limit; scheduling procedure rule curve, including the monthly target water level, flood control limit water level and its applicable months, and normal storage water level. The applicable months for the flood control limit water level are the same for each node, where the monthly target water level for the applicable month is not higher than the flood control limit water level, and the monthly target water level for other months is not higher than the normal storage water level; historical average net evaporation depth of each month; monthly minimum discharge flow and monthly maximum discharge capacity, both given in flow rate units, where the monthly minimum discharge flow is not greater than the corresponding monthly maximum discharge capacity; dead storage capacity; and continuous, uninterrupted historical monthly runoff sequences for the cascade headwater reservoirs and the water inflow between each level.

[0051] The specific implementation method of step S1 is as follows:

[0052] S1.1 Extract the annual runoff variation coefficient and the intra-year wet-dry ratio of the runoff from the historical monthly runoff series of the cascade headwater reservoirs as benchmark statistics, as follows:

[0053] In this invention, the starting month of the hydrological year is determined according to the watershed scheduling regulations, and the month number is... This corresponds to the first month of the hydrological year. In this invention, the sample standard deviation is calculated by dividing by the sample size by 1.

[0054] Based on the historical monthly runoff sequences (i.e., total monthly runoff in volume units) of the cascade headwater reservoirs, and according to hydrological year statistics (only hydrological years with both complete beginnings and ends are included in the statistics, with at least 3 complete hydrological years), two types of statistical quantities are extracted:

[0055] (a) Annual runoff variation coefficient : The ratio of the sample standard deviation to the sample mean of the total annual runoff for each historical hydrological year.

[0056] (b) Intra-annual runoff ratio The ratio of the sum of the multi-year average monthly runoff during the flood season to the sum of the multi-year average monthly runoff during the dry season, i.e.

[0057]

[0058] In the formula, For the first The multi-year average of monthly runoff; This is a collection of data for the months of the flood season. This is a collection of dry season months. and All are non-empty sets. , The division between the flood season and the dry season is determined according to the river basin management regulations, and is based on complete months. and Monthly serial number It is consistent with the monthly and yearly sequence numbers defined in this method.

[0059] The above statistics (annual runoff variation coefficient) and the ratio of abundant to scarce runoff within the year The values ​​directly extracted from historical sequences are used as historical baseline values ​​and are denoted as annual runoff variation coefficients. historical benchmark and the ratio of abundant to scarce runoff within the year historical benchmark It is used as a reference to determine the range of variation of various disturbance target parameters.

[0060] S1.2 Extract the logarithmic domain Thomas-Fiering model parameters of the inflow from the cascaded headwater reservoirs and the inflow from each level interval from the historical monthly runoff sequence, as follows:

[0061] The log-domain Thomas-Fiering model is used as a synthetic runoff generation model. The model parameters include the log-domain mean, log-domain standard deviation, and monthly Pearson correlation coefficient for each month. The model parameters are extracted by taking the natural logarithm of the historical monthly runoff series and then statistically analyzing them over a complete hydrological year. When there is a zero value in the historical monthly runoff, it is replaced by one-thousandth of the smallest positive value in the current series before taking the natural logarithm.

[0062] In this embodiment, the cascade headwater reservoir ( The natural logarithm of the monthly runoff in the historical monthly runoff series (using the same complete hydrological year range as S1.1) is taken; when there is a zero value in the historical monthly runoff, the zero value is replaced with one-thousandth of the smallest positive value among all monthly runoff records within the aforementioned complete hydrological year range before taking the logarithm. The monthly mean of the logarithmic domain is extracted. Monthly standard deviation of the logarithmic domain and the Moon and the Monthly Pearson correlation coefficient of monthly logarithmic runoff (For the sake of brevity, the node subscripts are omitted for the logarithmic field statistical parameters of the leading node, and the same applies below;) There are 12 parameters in each category, among which... Take one month now ), which serve as the baseline parameters for the logarithmic field Thomas-Fiering model.

[0063] Record No. Logarithmic monthly runoff ,in, For the first Monthly runoff. The recursive formula for the logarithmic domain Thomas-Fiering model is:

[0064]

[0065] In the formula, These are consecutive monthly step numbers. express Corresponding month number All in the formula All subscripts are taken ; They are mutually independent standard normal random variables. The composite monthly runoff is obtained by inverse transformation. get.

[0066] Extracting water from between each level of the cascade ( Logarithmic domain monthly runoff statistics (logarithmic domain mean of each month) Standard deviation of the logarithmic field for each month Pearson correlation coefficient for each month (The cyclic connection method is the same as above). As parameters of the logarithmic domain Thomas-Fiering model for water inflow at each level interval, the recursive formula is the same as that of the faucet, and each parameter is based on the first... Substitute the corresponding values ​​for each level interval. The above parameters must satisfy the logarithmic field standard deviation for each month. and Statistical characteristics were extracted from the historical monthly runoff sequences of each interval, with each interval's runoff sequence containing at least three complete hydrological years. Zero-value handling of interval runoff was performed in the same manner as for tap water.

[0067] S1.3. Based on the baseline statistics and model parameters, two types of controlled disturbance conditions are constructed in the logarithmic parameter space: interannual runoff variability disturbance and intra-annual distribution shift disturbance, as detailed below:

[0068] In step S1.3, all parameters for each type of disturbance are determined using the same set of random number sequences (including the baseline run and trial runs for that type of disturbance). For tap water, the Thomas-Fiering model is run using the baseline parameters (i.e., the logarithmic mean, standard deviation, and monthly correlation coefficients are all extracted from S1.2) to generate a composite sequence. After deducting the warm-up period, the effective length is no less than 10,000 hydrological years. The logarithmic runoff for the first month of the sequence is taken as the logarithmic mean for that month under the current parameter conditions. The warm-up period is no less than 5 hydrological years. The warm-up period data is discarded before calculating the statistics. This composite sequence replaces the historical sequence. The annual runoff variation coefficient and the annual runoff abundance / dryness ratio calculated according to the definitions in S1.1 are used as the model baseline variation coefficients for that type of disturbance. and the model baseline annual wet-dry ratio of runoff (Subsequent steps for all types of disturbances will use the model baseline values ​​of this class).

[0069] Based on the aforementioned baseline parameters, two types of controlled disturbances are constructed: interannual runoff variability disturbance and intra-annual distribution shift disturbance. The two types of disturbances are applied separately, without any cross-combination. Neither type of disturbance alters the monthly correlation coefficient. . and The target variation level range of the disturbance, i.e., the target annual runoff variation coefficient. Range of values, target annual runoff ratio The range of values ​​is determined based on the actual statistical characteristics of the watershed inflow and the needs of the actual analysis, but must include the corresponding model baseline values. The construction methods for interannual runoff variability disturbances and intra-annual distribution shift disturbances are as follows:

[0070] (a) Interannual runoff variability disturbances (disturbance)

[0071] The monthly standard deviations in the logarithmic domain are multiplied by a scaling factor; the scaling factor is determined by trial calculations and piecewise linear interpolation to make the annual runoff variation coefficient of the composite sequence reach the target value; the composite sequence is generated by running the logarithmic domain Thomas-Fiering model with the same random number sequence at each trial point, and the annual runoff variation coefficient obtained by the trial calculations increases monotonically with the scaling factor.

[0072] In this embodiment, the degree of interannual runoff variability in the composite sequence is altered by scaling the monthly standard deviations of the logarithmic domain proportionally. Let the scaling factor be... ( That is, the monthly standard deviation of the scaled logarithmic field. The logarithmic mean of each month remains unchanged after scaling.

[0073] The scaling factor was determined using trial and error and piecewise linear interpolation. Initial trial range is taken as follows: Within the trial calculation range, select no fewer than 5. Value (inclusive) Arrange them in ascending order, and the trial range should cover the annual runoff variation coefficient of the corresponding composite sequence. If the initial trial calculation range fails to cover the value, the range should be appropriately expanded and the calculation recalculated (while still satisfying the requirements). If the area is still not covered after expansion, then it will still not be covered. Level exclusion. The random number sequence for each trial point is run on the same basis as the baseline for this type of disturbance. The logarithmic runoff for the first month is taken as the logarithmic mean of that month under the current parameters, and the warm-up period length is the same as the baseline. For each trial value, the Thomas-Fiering model is run with scaled logarithmic parameters to generate a composite sequence. After deducting the warm-up period, the effective length of the composite sequence is no less than 10,000 hydrological years, and the corresponding annual runoff variation coefficient is calculated. During implementation, the corresponding values ​​for each adjacent trial point should be verified. The value is monotonically increasing; if this condition is not met, then such a perturbation will not be implemented. Given... The desired result is obtained through piecewise linear interpolation. value.

[0074] Under various disturbance conditions Within the range of variation, at least three intensity levels (inclusive) are considered. corresponding ).

[0075] (b) Intra-year allocation offset disturbance ( (disturbance)

[0076] In the logarithmic field, the logarithmic mean of each month during the flood season. Apply flood season offset The logarithmic mean of each month during the dry season Apply dry season offset After mapping back to the original runoff basin, it is equivalent to multiplying the theoretical mean of monthly runoff during the flood season and the dry season by . and .in, This is the scaling factor for the theoretical mean of monthly runoff during the flood season; This is the scaling factor for the theoretical mean of monthly runoff during the dry season; and The solution is obtained by simultaneously solving the constraint of conservation of the expected annual runoff and the constraint of the annual ratio of abundant to dry runoff;

[0077] Apply flood season offset and dry season offset Then, a proportionally compensated scaling factor is applied to the logarithmic field standard deviation of each month. This brings the annual runoff variation coefficient back to the model baseline variation coefficient; where the scaling factor is compensated proportionally. The annual wet-dry ratio of each target runoff was determined independently using the same trial calculation and piecewise linear interpolation method as the interannual runoff variability disturbance.

[0078] In this embodiment, the offset of the monthly mean runoff during the flood season and the dry season is first determined by constraining the conservation of the expected annual runoff volume, and then standard deviation compensation scaling is applied. Specifically, in the logarithmic domain, the logarithmic mean of each month during the flood season is calculated. Apply flood season offset (Right now , ), the logarithmic mean of each month in the dry season Apply dry season offset (Right now , The standard deviation of each month in the logarithmic domain remains constant during the mean shift step. The above... and Solve by simultaneously solving the following two constraints:

[0079] The conservation constraint on the expected value of annual runoff is expressed as follows:

[0080] ;

[0081] The target runoff annual wet-dry ratio constraint is expressed as follows:

[0082] ;

[0083] in, For the log-normal model, the first Theoretical mean of monthly runoff, ; The target is the ratio of wet to dry seasons in annual runoff. and All values ​​are baseline values ​​extracted in step S1.2. Solve by simultaneously solving the above two equations. and .

[0084] Solving for the results , Then, the standard deviation of the logarithmic field for each month was calculated. Apply proportional compensation scaling factor (i.e., the standard deviation of the logarithmic field for each month) This brings the annual runoff variation coefficient back to the model baseline variation coefficient. Scaling factor compensation is proportional. The same trial-and-error and piecewise linear interpolation method as in step S1.3(a) was used to calculate the annual wet-dry ratio of each target runoff. Independently determined: The initial trial range is the same as in step S1.3(a). The mean of the logarithmic domain for each trial point after offset is used. Standard deviation of the logarithmic field for each month after compensation scaling The constant monthly correlation coefficient The Thomas-Fiering model was run with the same random number sequence as the baseline for this type of disturbance. The logarithmic runoff for the first month was taken as the logarithmic mean of that month under the current parameters, and the warm-up period length was the same as the baseline. If expanding the trial range still fails to bring the annual runoff variation coefficient back to normal... Then the Level exclusion.

[0085] Under various disturbance conditions Within the range of variation, at least three intensity levels should be selected (including the baseline condition without SR perturbation: this condition should be directly taken). , Without solving the constraint equations, its That is ).

[0086] Each intensity level of various disturbances constitutes its own disturbance test group, and each list contains no fewer than three effective intensity levels.

[0087] S2. Monte Carlo simulation and gain function calculation for cascade scheduling: Monte Carlo reservoir water balance simulation is performed node by node in series on the cascade system for two types of controlled disturbance conditions; the same set of random number sequences is shared for the simulation implementation of each disturbance condition in the same disturbance experimental group; the gain function and the standard error of the gain function are calculated node by node during the simulation implementation process, and the number of simulation implementations is gradually increased so that the standard error does not exceed half of the pre-set judgment tolerance.

[0088] In step S2, for each perturbation condition in the perturbation experimental group (using... Numbering perturbation conditions, , (Total number of perturbation conditions in the experimental list), Monte Carlo reservoir water balance simulation is performed in series from the leading node to the terminal node in the cascade system, with each perturbation condition being simulated. Sub-Monte Carlo simulation implementation (i.e., single sample path), with Each simulation was numbered. , The random number should be a positive integer of at least 3, and different implementations should use independent random number sequences. An initial random number sequence should be selected during implementation. After completing all calculations from S2.1 to S2.2, if the maximum standard error of the gain function in each effective combination exceeds... Then gradually increase Using the complete set of valid data from the simulation, re-execute steps S2.1 and S2.2 until the maximum value mentioned above does not exceed [the specified value]. ;like If the convergence condition is not met even after reaching 50, the combination that still does not meet the condition is marked as inapplicable. If all combinations have been marked as inapplicable, the simulation process for that perturbation experimental group is terminated.

[0089] in, This is a pre-defined decision tolerance. The [number]th [period] under all perturbation conditions within the same perturbation experimental group. The simulation achieves the sharing of the same set of random number sequences: the standard normal random number sequence of the inflow from the tap and the standard normal random number sequence of the inflow from each interval remain the same under different disturbance conditions; the synthetic runoff from the tap varies under different disturbance conditions due to different parameters, and the inflow from each interval is completely consistent under all disturbance conditions, so as to reduce sampling noise between disturbance conditions. Disturbance and The random number sequences between the perturbation experimental groups are independent of each other.

[0090] The specific implementation process of step S2 is as follows:

[0091] S2.1. For the two types of controlled disturbance conditions, Monte Carlo reservoir water balance simulations are performed node-by-node in the cascade system. Details are as follows:

[0092] (1) Runoff sequence generation

[0093] Each implementation uses a random number sequence independent of the random number sequence used in the parameter determination process of step S1.3. The inflow sequence of the headwater reservoir uses the logarithmic domain statistical characteristics extracted in step S1.2 as the baseline parameter, and adjusts the logarithmic domain parameters according to the current disturbance conditions determined in step S1.3. Perturbation maintains mean Unchanged, adjusted standard deviation is ; The disturbance adjusted mean is Standard deviation is Afterwards, a synthetic monthly logarithmic runoff sequence is generated using the logarithmic domain Thomas-Fiering model. Each generation begins in the first month of the hydrological year (i.e.,...). Corresponding The logarithmic runoff for the first month is taken as the logarithmic mean of that month under the current disturbance conditions, and subsequent months are continuously generated by a recursive formula. The inverse transformation yields the synthetic monthly runoff from the tap under the current disturbance conditions, denoted as... .

[0094] No. The incoming water from the first-level interval is extracted according to step S1.2. Based on the baseline statistical characteristics of the interval (without perturbation), the synthetic monthly runoff series was independently generated using the logarithmic domain Thomas-Fiering model (the logarithmic runoff of the first month was taken as...). ), denoted as The inflow sequences for each interval are generated separately from each other and from the faucet inflow sequence, all under the assumption of statistical independence.

[0095] Each implementation involves a synthetic monthly runoff sequence with a length no less than the sum of the warm-up period and the effective simulation period. The effective simulation period is... For each hydrological year, the same perturbation conditions and realizations are taken in the same perturbation experimental group. value, No less than 1,000 hydrological years.

[0096] (2) Series water balance simulation

[0097] The initial water storage and preheating period settings for each implementation are shown in (3) Preheating period settings.

[0098] First, calculate the monthly inflow for each node, as follows:

[0099]

[0100] In the formula, For the first node Monthly revenue; The current monthly runoff from the tap is the synthetic runoff under the current disturbance conditions. For the first Nodes Monthly outflow; For the first Nodes Monthly revenue; For the first Nodes Water flow during the lunar cycle;

[0101] Secondly, a monthly water balance equation is established by combining the monthly inflow at each node. The expression of the monthly water balance equation is as follows:

[0102]

[0103] In the formula, for Nodes The water storage at the beginning of the month, as End-of-month water storage; For consecutive monthly step numbers, month number . For the first The node Water storage at the beginning of the month; For the first Nodes Monthly revenue; For the first Nodes Monthly outflow; For the first Nodes The net evaporation from the water surface in a month. All water quantities in the formula use a uniform unit of volume.

[0104] Next, combining the monthly inflow at each node, the net evaporation at each node in each month is calculated using the reservoir capacity-area curve and the historical average net evaporation depth, as detailed below:

[0105] First, calculate the net evaporation for each month, then determine the outflow rate. The formula for calculating net evaporation is as follows:

[0106]

[0107] In the formula, For the first The node The historical average net evaporation depth of the water surface in a given month For the first The node Water storage at the beginning of the month The corresponding water surface area can be obtained from the reservoir capacity-area curve.

[0108] Finally, the outflow of each node for each month is determined as follows:

[0109] After obtaining the initial outflow rate using the target water storage tracking method based on the regular curve, the following three constraint checks are performed in sequence: the first step is to limit the outflow rate between the minimum discharge rate and the maximum discharge capacity; the second step is to increase the outflow rate according to the upper limit of the water storage at the end of the month; and the third step is to decrease the outflow rate according to the lower limit of the dead storage capacity. Among these, the dead storage capacity constraint takes precedence over the minimum discharge constraint.

[0110] In this embodiment, the monthly outflow is determined at each node using the regular curve target water storage tracking method. The target water storage volume at the end of the month, given by the scheduling procedure rule curve. (Converted from the target water level via the water level-reservoir capacity curve) To track the target, the preliminary outflow is calculated by taking the month-end water storage as equal to the target water storage using the water balance equation. ,when season Then, perform constraint verification in the following steps in sequence (the outflow rate corrected in the previous step is the current value for each step; the month-end water storage volume mentioned in each step is substituted with the current outflow rate for that step). Calculations; the minimum discharge flow and maximum discharge capacity for each month are converted to monthly water volume based on the number of days in the month, and then compared with... Compare):

[0111] ① The outflow rate shall be limited to no less than the converted minimum monthly outflow rate and no more than the converted maximum monthly outflow capacity;

[0112] ② Check the upper limit of water storage at the end of the month ( (For months with flood control limits, the reservoir capacity is taken as the corresponding water level; for other months, the reservoir capacity is taken as the corresponding water level.) If the water level at the end of the month is higher than the upper limit, the outflow is increased until the water level at the end of the month is equal to the upper limit, but not exceeding the converted maximum discharge capacity for each month. If the water level at the end of the month is still higher than the upper limit after the outflow is at the converted maximum discharge capacity for each month, the outflow is at the converted maximum discharge capacity for each month, and the water level at the end of the month is recorded as the actual value.

[0113] ③ Verify the lower limit of month-end water storage: If the month-end water storage is lower than the dead storage capacity, reduce the outflow until the month-end water storage equals the dead storage capacity (water storage constraints take precedence over minimum discharge constraints; in this case, the outflow is allowed to be less than the converted minimum discharge flow for each month); if the month-end water storage is still lower than the dead storage capacity after reducing the outflow to zero, then take... The water storage at the end of the month is based on the actual value. Record.

[0114] Once the outflow rate is determined, the monthly water balance equation is substituted back to calculate the monthly water storage. The inflow, storage, and outflow processes of each level of reservoir are then deduced sequentially from the leading node to the terminal node for each month.

[0115] (3) Preheating period settings

[0116] The above water balance simulation requires a preheating period; the preheating period data is not included in the subsequent gain function calculation. The preheating period in this step is... The number of years (not less than 5 years) and the preheating period in step S1.3 can be taken separately. The beginning water storage volume of each node in the first month of each implementation is taken as the reservoir capacity corresponding to the normal water storage level of that node.

[0117] S2.2 During the simulation, the gain function and its standard error are calculated node by node, and the number of simulations is gradually increased until the standard error does not exceed half of the pre-set tolerance. Specifically:

[0118] S2.2.1 Gain Function Calculation:

[0119] The gain function is defined as the ratio of the annual outflow variation coefficient to the annual inflow variation coefficient of the current node, multiplied by the net evaporation correction factor. The net evaporation correction factor is equal to 1 minus the ratio of the average annual net evaporation to the average annual inflow of the current node. When the average annual inflow does not exceed zero, or the average annual outflow does not exceed zero, or the annual inflow variation coefficient is less than the preset lower limit, or the ratio of the average annual net evaporation to the average annual inflow is greater than the preset upper limit, the gain function is marked as inapplicable.

[0120] In this embodiment, each implementation removes the preceding... After collecting the preheating period data for each hydrological year, all valid data will be merged, and the annual inflow and outflow of each node will be calculated by hydrological year (the sum of the monthly inflow and outflow of each month in that hydrological year), as well as the annual net evaporation (the sum of the monthly net evaporation of each month in that hydrological year).

[0121] For the first The node at the node Under each disturbance condition, the coefficient of variation is calculated according to the same definition as in step S1.1. The coefficient of variation of annual inflow and annual outflow for each sample hydrological year:

[0122]

[0123] In the formula, Indicates the sample standard deviation; and The first Under the first disturbance condition, the first The node Annual inflow and annual outflow for each sample hydrological year Each time the preheating period is deducted, there is All effective hydrological years Total of times One sample hydrological year; and All The mean annual inflow and mean annual outflow for each sample.

[0124] No. Under the first disturbance condition, the first The gain function of each node is defined as:

[0125]

[0126] In the formula, For the first Under the first disturbance condition, the first All nodes The average annual net evaporation for each sample hydrological year. The net evaporation correction factor is... .when or or or When the perturbation condition is such that the gain function of the node is not calculated, it is marked as not applicable.

[0127] S2.2.2 Statistical Uncertainty Assessment of the Gain Function

[0128] In step S2.2.2, the standard error of the gain function needs to be calculated. The calculation method is as follows: treat all simulations as independent groups, calculate the gain function for each group according to the definition of the gain function, remove groups that are not applicable to the gain function, and obtain the effective groups. The standard error is the sample standard deviation of the gain function value of the effective group divided by the square root of the number of effective groups. If the number of effective groups is less than 3, the combination is marked as not applicable.

[0129] In this embodiment, each of the M Monte Carlo simulations is treated as an independent group, and for each group... Calculate the gain function according to the formula in step S2.2.1. (At this point, the sample size in each formula is based on the effective hydrological years for that group.) replace If any individual group triggers the inapplicable condition of step S2.2.1, then that group is removed, thus obtaining an independent estimate of the gain function. Let the number of effective groups be... (equal (Subtracting the number of rejected groups), if the number of valid groups is less than 3, the standard error of the combination is marked as inapplicable. The standard error of the gain function is:

[0130] .

[0131] S3. Identification of Variability Transmission Patterns: For interannual runoff variability disturbances and intra-annual distribution shift disturbances, a gain response matrix is ​​constructed using the calculation results of the gain functions of each node, with the disturbance conditions as rows and the cascade nodes as columns. Disturbance conditions and node combinations that are not marked as inapplicable by the gain function are considered valid combinations. The judgment tolerance is compared with the values ​​in the gain response matrix. Based on the comparison results, the regulation type of each node is determined as attenuation, transmission, or amplification, thereby identifying the variability regulation type and transmission pattern of each node and the entire cascade.

[0132] The specific implementation process of step S3 is as follows:

[0133] S3.1. For interannual runoff variability disturbances and intra-annual distribution shift disturbances, a gain response matrix is ​​constructed using the calculation results of the gain functions of each node, with the disturbance conditions as rows and the cascade nodes as columns, as follows:

[0134] Construct the gain response matrix based on the calculation results of step S2. Disturbance and Each disturbance corresponds to its own gain response matrix. Each matrix has the disturbance condition corresponding to the disturbance type as the row and the cascade nodes as the column, with the gain function value recorded at each position. (Take all of the steps in S2.2.1) (values ​​calculated from each sample) and their standard error (Take the value calculated in step S2.2.2).

[0135] S3.2. Compare the judgment tolerance with the values ​​in the gain response matrix. Based on the comparison results, determine the adjustment type of each node as attenuation, pass-through, or amplification, and then identify the variability adjustment type and transmission pattern of each node and the entire stage, including:

[0136] The gain function value is less than It is determined to be attenuation; the gain function value is greater than If it is determined to be amplified, otherwise it is determined to be transparent; among which, The decision tolerance is predetermined; if all effective combination adjustment types of the same node are consistent, it is determined to be a stable node; otherwise, it is determined to be a condition change node, and the adjacent disturbance condition intervals where the type change occurs are recorded.

[0137] In this embodiment, each disturbance condition is based on its corresponding target parameter value ( Disturbance is , Disturbance is Arrange them from smallest to largest. For each type of disturbance, determine the adjustment type for each node using the gain response matrix. Utilize the aforementioned determination tolerance. The judgment rules are as follows:

[0138] when Under this disturbance condition, it is determined to be attenuation;

[0139] when At that time, it is determined to be a pass-through;

[0140] when At that time, it was determined to be magnified.

[0141] Combinations marked as inapplicable are not included in the type determination of that node; if all combinations of a node are inapplicable, then that node is not determined.

[0142] If all effective combination adjustment types of the same node are consistent, it is determined to be a stable node (stable attenuation, stable amplification, or stable transmission); otherwise, it is determined to be a condition change node, and the interval between each adjacent effective disturbance condition that causes the type change is recorded.

[0143] For each type of perturbation implemented, the following results are output:

[0144] (a) Gain response matrix;

[0145] (b) Variation adjustment type of each node: stable decay, stable amplification, stable transmission, conditional transition (with the adjacent effective disturbance condition intervals for each transition), or not applicable;

[0146] (c) Variation transmission pattern: the label sequence of adjustment types of each node arranged along the ladder.

[0147] When the same node exhibits inconsistent adjustment types under two types of disturbances, the adjustment types of the node under each type of disturbance should be recorded separately.

[0148] The method of the present invention is applicable to the monthly runoff process of each water inflow sequence (including tap water and water inflow in each interval), which can be reasonably described by the logarithmic domain Thomas-Fiering model described in step S1.2, and the cascade system in which the spatial correlation between each water inflow sequence is negligible.

[0149] This invention addresses the scenario of beneficial water allocation and, by applying controlled statistical parameter disturbances (including interannual runoff variability and intra-annual distribution offset disturbances) to the inflow at each cascade terminal, utilizes Monte Carlo simulation of cascade allocation to calculate the gain function (the ratio of the annual outflow variability coefficient to the annual inflow variability coefficient at each node, multiplied by the net evaporation correction factor) node by node. This yields the response characteristics of the gain function as a function of disturbance intensity and cascade node location; the gain function is less than... When it is determined to be attenuation, it is greater than When the value is between 1 and 2, it is considered magnification; when it falls between 1 and 2, it is considered pass-through. This method uses a pre-defined tolerance for judgment. It quantifies the gain propagation effect of cascade reservoirs on interannual and intra-annual runoff variability on a node-by-node basis, thereby aiding in the comparison and selection of optimal cascade scheduling schemes. This method is applicable to cascade systems where the monthly runoff processes of each inflow sequence can be fitted by a logarithmic domain Thomas-Fiering model, and where the spatial correlation between inflow sequences has a relatively small impact on the analysis conclusions. Before use, it is advisable to verify the method through goodness-of-fit and correlation tests.

[0150] The effectiveness of the present invention will be verified through a specific embodiment below.

[0151] Cascade System Overview: This embodiment focuses on a cascade system consisting of four reservoirs connected in series along the same main stream. The nodes are numbered... ,in As the leading node, This is the terminal node. The starting month of the hydrological year is June, and the month number is... Corresponding to June, the hydrological annual cycle runs from June of the current year to May of the following year. (This refers to the set of months for the flood season.) (Corresponding to June to September), Collection of dry season months (Corresponding to October to May of the following year). Tolerance is determined by... .

[0152] The engineering scale of the four reservoirs decreases sequentially from upstream to downstream, resulting in gradient differences in the runoff regulation capacity of each node in the cascade. The expected gain transfer effect within the same cascade will vary between nodes.

[0153] Longtou Reservoir 1 is a large-scale multi-year regulating reservoir with a normal storage level corresponding to a storage capacity of 2.5 billion m³, a dead storage capacity of 200 million m³, and a beneficial storage capacity of 2.3 billion m³. The reservoir's maximum discharge capacity is 600-700 m³ / s during the flood season, decreasing to 350-400 m³ / s during the dry season. The minimum discharge flow remains constant at 150 m³ / s throughout the year to meet downstream ecological flow demands. This relatively low upper limit of discharge capacity forces the reservoir to regulate water levels during years of heavy rainfall, and it is expected that the reservoir will have a strong effect on mitigating inflow variability.

[0154] Reservoir 2 is a medium-sized reservoir for annual regulation, with a normal storage level corresponding to a storage capacity of 1.4 billion m³ and a dead storage capacity of 100 million m³. Its maximum discharge capacity is between 800 and 900 m³ / s, and its minimum discharge is 100 m³ / s. This reservoir also has the capacity for annual runoff redistribution, but this is weaker than that of Reservoir 1.

[0155] Reservoir 3 is a small seasonal regulating reservoir with a normal storage level corresponding to a storage capacity of 900 million m³ and a dead storage capacity of 60 million m³. Its maximum discharge capacity is 1000~1400 m³ / s, which is significantly larger than that of the two upstream reservoirs, but its regulation capacity is relatively limited.

[0156] Reservoir 4 is a terminal runoff reservoir with a normal storage level corresponding to a storage capacity of 350 million m³ and a dead storage capacity of 30 million m³. Its maximum discharge capacity is as high as 3000 m³ / s, far exceeding the normal inflow level. Based on its engineering parameters, it can be inferred that this reservoir has limited ability to regulate the fluctuation characteristics of upstream water flow.

[0157] The water level-capacity curve and capacity-area curve of each reservoir are given by piecewise linear functions. The target water level at the end of each month is set according to the dispatching regulations: during the flood season, the water level is controlled below the flood limit level; in October, the water level is gradually restored to the normal storage level; and from February to May, the water level drops to the flood limit level.

[0158] Historical inflow sequences: The historical monthly runoff sequences for the cascade head reservoirs and the three inter-cascade intervals are all 40 complete hydrological years in length. The inflow to each inter-cascade interval is independent of the head reservoir, and the flow rate is approximately 10% to 20% of that of the head reservoir.

[0159] The method for decoupling and evaluating the inflow variation of a reservoir group according to the present invention includes the following steps:

[0160] S1. Extraction of statistical features of incoming water and construction of controlled perturbation, as detailed below: S1.1, Baseline Statistic

[0161] The baseline value of the annual runoff variation coefficient was extracted from the historical monthly runoff series of the Longtou Reservoir, which was summarized by hydrological year. Annual runoff abundance / dryness ratio baseline value .

[0162] S1.2, Parameters of the Thomas-Fiering model in the logarithmic field

[0163] The logarithmic mean, standard deviation, and monthly Pearson correlation coefficient for the historical monthly runoff of the Longtou Reservoir were extracted after taking the natural logarithm. Parameters for each interval of inflow were extracted independently, and those with a standard deviation greater than zero and a correlation coefficient less than 1 were determined.

[0164] S1.3 Controlled Disturbance Construction

[0165] Interannual runoff variability disturbance ( (disturbance)

[0166] The Thomas-Fiering model was run with baseline parameters to generate a composite sequence of 10,000 effective hydrological years (with a 5-year warm-up period), yielding the model baseline coefficient of variation. .exist Nine equally scaled factors were used for trial calculations within the range, and the coefficient of variation of annual runoff in the composite sequence at each trial calculation point was adjusted accordingly. It is strictly monotonically increasing, from 0.1379 to 1.6727. Six target levels were selected within the range (including those corresponding to the model baseline). The scaling factor for each level is determined by piecewise linear interpolation.

[0167] Intra-year allocation offset disturbance ( (disturbance)

[0168] The baseline model was run using an independent random number sequence to obtain the baseline coefficient of variation. Model baseline annual runoff wet-dry ratio .exist Six target runoff annual abundance / dryness ratio grades (including baseline conditions) were selected within the scope. For each target level, the annual total flow conservation constraint and the annual runoff abundance-dryness ratio constraint are solved simultaneously. and The compensation scaling factor was then determined through trial calculations and interpolation. The coefficient of variation was brought back to the model baseline value. The deviations in the annual wet-dry ratio and the annual total change rate of actual runoff at each level were all within 5%, indicating that all were effective.

[0169] The experimental lists for both types of disturbances each contain 6 valid levels, and both meet the requirement of having at least 3.

[0170] S2. Monte Carlo simulation and gain function calculation for cascade scheduling, as follows: For each type of disturbance, Monte Carlo simulation is performed in series on the cascade 4-node system according to all disturbance conditions in the disturbance experimental group. Effective simulation period. A hydrological year, warm-up period Year. Within the same perturbation experimental group, the same set of faucet and interval water inflow random number sequences are shared for all perturbation conditions with the same number, and the random number sequences of the two types of perturbations are independent of each other.

[0171] The perturbation converged after 7 iterations. The perturbation converges after five iterations.

[0172] S3. Identification of variation transmission patterns, as detailed below:

[0173] (1) The gain response matrix of the disturbance is shown in Table 1 and Figure 2 As shown.

[0174]

[0175] (2) The gain response matrix of the disturbance is shown in Table 2. Figure 3 As shown.

[0176]

[0177] (3) Variation transmission pattern under Cv perturbation

[0178] As shown in Table 1, the gain function of node 1 (the large reservoir) varies with... Increase and decrease significantly: when At lower values ​​(0.30~0.52), the gain function is between 0.97 and 0.99, falling within the pass-through range; when... When the gain is increased above 0.75, it drops below 0.90, showing a significant attenuation, especially at the maximum disturbance level ( The gain function at node 1 is only 0.679. This trend is consistent with the basic pattern of multi-year regulation of large reservoirs. Therefore, node 1... Under perturbation, it is determined to be a conditional transition node, and the transition occurs. The interval changes from pass-through to attenuation.

[0179] The gain function of node 2 (medium-sized reservoir) exhibits the opposite trend to that of node 1: at low... Under certain conditions, the gain function is approximately 0.86~0.92, falling within the attenuation range; with... As the flow rate increases, the gain function gradually rises to 0.96-0.97, entering the transmission range. The hydrological mechanism is as follows: when the inflow variability is low, node 1 essentially transmits the flow, while node 2 directly addresses and regulates the stronger upstream inflow fluctuations. However, when the inflow variability is high, node 1 has already attenuated most of the fluctuations, and the inflow variability reaching node 2 is relatively small, thus the gain transmission effect of node 2 is no longer significant. Therefore, node 2 is determined to be a condition transition node, with a transition range of [missing information]. It changes from attenuation to pass-through.

[0180] Node 3 (small reservoir) and Node 4 (run-off reservoir) are in all Under disturbance conditions, the gain functions are all between 0.98 and 1.00, indicating stable transmission. The gain function of node 4 is always 1.000, indicating that its discharge capacity far exceeds the inflow volume and has almost no regulating effect on runoff variability.

[0181] Based on the above results, The variability transmission pattern of the four-level ladder under perturbation is as follows:

[0182] Condition transition—Condition transition—Stable pass-through—Stable pass-through

[0183] (4) Variation transmission pattern under SR perturbation

[0184] As can be seen from Table 2, in Under the condition of disturbance (i.e., the change in the annual runoff abundance-difference ratio), the gain function of node 1 is at its minimum when the annual runoff abundance-difference ratio is ( The gain function (approaching equilibrium) is 0.936, indicating attenuation; as the annual runoff abundance / difference ratio increases to above 1.83, the gain function rises to 0.97-0.99, transitioning to transmission. Based on this, node 1 is determined to be a condition transition node, with a transition range of [missing information]. .

[0185] Node 2 is in all 6 The gain function under all perturbation conditions ranged from 0.918 to 0.932, and was lower than 0.932 under all six SR perturbation conditions. The attenuation threshold was determined to be a stable attenuation. This indicates that regardless of how the annual distribution of wet and dry seasons changes, this node consistently has a weakening effect on the interannual variability of inflows.

[0186] Nodes 3 and 4 in Under disturbance and in The performance under disturbances was consistent, and all were judged to be stable transmission.

[0187] The pattern of variability transmission under perturbation is as follows:

[0188] Conditional transition—stable decay—stable pass-through—stable pass-through

[0189] (5) Comprehensive comparison of the results of the two types of disturbances

[0190] It is worth noting that node 2 is in Conditional transition under disturbance (low) Attenuation, high (through transmission), and in The two conditions, stable decay under disturbance and stable conditions, are inconsistent. This difference indicates that the same node can exhibit different regulatory characteristics in response to different dimensions of inflow variability; if the two dimensions are not analyzed independently, the above differences will be masked.

[0191] From the perspective of the entire cascade system, in this embodiment's four-stage series system, the variability gain transmission effect is mainly concentrated in the first two nodes (large and medium-sized reservoirs), while the latter two nodes (small and run-of-river reservoirs) are essentially transparent. The latter two nodes have smaller beneficial storage capacity and limited ability to regulate inflow variability. Meanwhile, the regulation mode of the leading large reservoir changes with the intensity of disturbance, reflecting a threshold effect in reservoir regulation capacity: the reservoir's storage capacity is only fully utilized when inflow variability exceeds a certain level.

Claims

1. A method for decoupling and evaluating the variability of inflow in a reservoir group, characterized in that, include: Water inflow statistical feature extraction and controlled disturbance construction: The annual runoff variation coefficient and intra-year wet / dry ratio of the inflow from the cascade headwater reservoirs are extracted as baseline statistics from historical monthly runoff sequences. Logarithmic domain Thomas-Fiering model parameters for headwater inflow and inflow between each level are also included. Based on the baseline statistics and model parameters, two types of controlled disturbances are constructed in the logarithmic domain parameter space: interannual runoff variation disturbance and intra-year distribution shift disturbance. The interannual runoff variation disturbance only scales the monthly standard deviation in the logarithmic domain to change the annual runoff variation coefficient. The intra-year distribution shift disturbance shifts the monthly mean values ​​of the flood and dry seasons in the logarithmic domain to change the intra-year wet / dry ratio, while adding standard deviation compensation scaling to keep the annual runoff variation coefficient unchanged. The two types of disturbances are applied independently, with each type having at least three intensity levels. The construction method of the intra-year distribution shift disturbance is as follows: In the logarithmic field, the logarithmic mean of each month during the flood season. Apply flood season offset The logarithmic mean of each month during the dry season Apply dry season offset ;in, This is the scaling factor for the theoretical mean of monthly runoff during the flood season; This is the scaling factor for the theoretical mean of monthly runoff during the dry season; and The solution is obtained by simultaneously solving the constraint of conservation of the expected annual runoff and the constraint of the annual ratio of abundant to dry runoff; Apply flood season offset and dry season offset Then, a proportionally compensated scaling factor is applied to the logarithmic field standard deviation of each month. This brings the annual runoff variation coefficient back to the model baseline variation coefficient; wherein, the proportional compensation scaling factor... The annual wet-dry ratio of each target runoff was determined independently using the same trial calculation and piecewise linear interpolation method as the interannual runoff variability disturbance. Monte Carlo simulation and gain function calculation for cascade scheduling: For two types of controlled disturbance conditions, Monte Carlo reservoir water balance simulations are performed node-by-node in the cascade system. Simulations with the same number for each disturbance condition in the same disturbance experimental group share the same set of random number sequences. During the simulation process, the gain function and its standard error are calculated node-by-node, and the number of simulations is gradually increased to ensure the standard error does not exceed half of a pre-set tolerance. The step of performing Monte Carlo reservoir water balance simulations node-by-node in the cascade system for the two types of controlled disturbance conditions includes: Calculate the monthly inflow at each node, and establish a monthly water balance equation based on the monthly inflow at each node; then, using the reservoir capacity-area curve and historical average net evaporation depth, calculate the monthly net evaporation at each node; finally, determine the monthly outflow at each node as follows: After obtaining the initial outflow rate using the target water storage tracking method based on the regular curve, the following three constraint checks are performed in sequence: the first step is to limit the outflow rate between the minimum discharge rate and the maximum discharge capacity; the second step is to increase the outflow rate according to the upper limit of the water storage at the end of the month; and the third step is to decrease the outflow rate according to the lower limit of the dead storage capacity. Among these, the dead storage capacity constraint takes precedence over the minimum discharge constraint. Once the outflow rate is determined, the monthly water balance equation is substituted back to calculate the monthly water storage. The inflow, storage and outflow processes of each level of reservoir are then deduced sequentially from the leading node to the terminal node for each month. The gain function is defined as the ratio of the annual outflow variation coefficient to the annual inflow variation coefficient of the current node, multiplied by the net evaporation correction factor. Wherein, the net evaporation correction factor is equal to 1 minus the ratio of the average annual net evaporation to the average annual inflow at the current node; when the average annual inflow does not exceed zero or the average annual outflow does not exceed zero, or the annual inflow variation coefficient is less than the preset lower limit, or the ratio of the average annual net evaporation to the average annual inflow is greater than the preset upper limit, the gain function is marked as not applicable. Identification of Variability Transmission Patterns: For interannual runoff variability disturbances and intra-annual distribution shift disturbances, a gain response matrix is ​​constructed using the calculation results of the gain functions of each node, with the disturbance conditions as rows and the cascade nodes as columns. Disturbance conditions and node combinations that are not marked as inapplicable by the gain function are considered as valid combinations. The judgment tolerance is compared with the values ​​in the gain response matrix, and the regulation type of each node is determined as attenuation, transmission, or amplification based on the comparison results, thereby identifying the variability regulation type and transmission pattern of each node and the entire cascade.

2. The method for decoupling and evaluating the inflow variation of a reservoir group according to claim 1, characterized in that, The perturbation of interannual runoff variability is constructed as follows: the standard deviation of each month in the logarithmic domain is multiplied by an equal scaling factor; The proportional scaling factor is determined by trial calculation and piecewise linear interpolation to make the annual runoff variation coefficient of the composite sequence reach the target value. The composite sequence is generated by running the logarithmic domain Thomas-Fiering model with the same random number sequence at each trial point. The annual runoff variation coefficient obtained by the trial calculation increases monotonically with the proportional scaling factor.

3. The method for decoupling and evaluating the inflow variation of a reservoir group according to claim 1, characterized in that, The expression for the conservation constraint of the expected annual runoff is as follows: ； The expression for the target runoff annual wet-dry ratio constraint is as follows: ； in, For the log-normal model, the first Theoretical mean of monthly runoff; The target is the ratio of wet to dry seasons in annual runoff; This is a collection of months during the flood season; This is a collection of dry season months.

4. The method for decoupling and evaluating the inflow variation of a reservoir group according to claim 1, characterized in that, The monthly inflow of each node is calculated as follows: ； In the formula, For the first node Monthly revenue; The current monthly runoff from the tap is the synthetic runoff under the current disturbance conditions. For the first Nodes Monthly outflow; For the first Nodes Monthly revenue; For the first Nodes Water flow during the lunar cycle; The expression for the monthly water balance equation is as follows: ； In the formula, for Nodes The water storage at the beginning of the month, as End-of-month water storage; For the first The node Water storage at the beginning of the month; For the first Nodes Monthly revenue; For the first Nodes Monthly outflow; For the first Nodes Net evaporation from the water surface in a given month.

5. The method for decoupling and evaluating the inflow variation of a reservoir group according to claim 1, characterized in that, The standard error of the gain function is calculated as follows: Each simulation is treated as an independent group. The gain function is calculated separately for each group according to its definition. Groups that are not applicable to the gain function are removed to obtain the effective groups. The standard error is calculated by dividing the sample standard deviation of the gain function values ​​of the effective groups by the square root of the number of effective groups. If the number of effective groups is less than 3, the combination is marked as inapplicable.

6. The method for decoupling and evaluating the inflow variation of a reservoir group according to claim 1, characterized in that, The process of comparing the judgment tolerance with the values ​​in the gain response matrix, and determining the adjustment type of each node as attenuation, pass-through, or amplification based on the comparison result, thereby identifying the variability adjustment type and transmission pattern of each node and the entire stage, includes: The gain function value is less than It is determined to be attenuation; the gain function value is greater than If it is determined to be amplified, otherwise it is determined to be transparent; among which, The decision tolerance is predetermined; if all effective combinations of adjustment types of the same node are consistent, it is determined to be a stable node; otherwise, it is determined to be a condition change node, and the adjacent disturbance condition intervals where the type change occurs are recorded.

7. The method for decoupling and evaluating the inflow variation of a reservoir group according to claim 1, characterized in that, The log-domain Thomas-Fiering model serves as a synthetic runoff generation model. The model parameters include the log-domain mean for each month, the log-domain standard deviation for each month, and the monthly Pearson correlation coefficient. Each model parameter is extracted by taking the natural logarithm of the historical monthly runoff series and then statistically analyzing it over a complete hydrological year. When there is a zero value in the historical monthly runoff, it is replaced by one-thousandth of the smallest positive value in the current series before taking the natural logarithm.

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