Fast algorithm for dynamic storage capacity of variable backwater area of river type reservoir

Abstract

The invention relates to the technical field of reservoir dispatching, and provides a quick algorithm for dynamic reservoir capacity of a variable backwater area of a river-type reservoir, comprising the following steps: acquiring basic parameters of the river-type reservoir; the initial water level, the end water level, the initial storage flow and the end storage flow in the flood regulation process are obtained; based on the starting water level and the ending water level, static reservoir capacity changes are calculated according to the basic features of the river; determining a starting natural water level and an ending natural water level from the dam site natural water level and flow relation curve based on the starting reservoir flow and the ending reservoir flow; calculating an initial water return length and an end water return length based on the initial water level, the end water level, the initial natural water level, the end natural water level and the river channel gradient; and based on the initial water return length, the ending water return length, the initial storage flow, the ending storage flow, the initial water level and the ending water level, calculating dynamic storage capacity change by using a parabolic water return curve equation, and calculating the ratio of the dynamic storage capacity change to static storage capacity change.

Description

Technical Field

[0001] This invention relates to the field of reservoir scheduling technology, and in particular to a fast algorithm for calculating the dynamic reservoir capacity of the backwater zone in a river-type reservoir. Background Technology

[0002] Due to the narrow and long channels of river-type reservoirs, and the fact that water depth and surface width are much smaller than reservoir length, significant gradients and flow velocities exist in the reservoir area during floods, leading to large discrepancies between the static storage capacity method or backwater curve method and the actual dynamic storage capacity. Traditional methods mainly use hydrodynamic flood evolution models for dynamic storage capacity calculation, but this method has stringent requirements for basic data, demanding detailed underwater topography or large-section data, making data collection difficult. It also requires constructing complex hydrodynamic models, relying on high-configuration computing power, and the calculation time increases significantly with grid density, river length, and flood process complexity, resulting in low efficiency. Furthermore, traditional methods only support a "forward calculation" mode (deriving water level changes from a given scheduling plan), which cannot meet the "backward calculation" requirements in flood control scheduling (deriving available storage capacity from a given target water level), limiting its flexibility and practicality in real-time scheduling decisions. Therefore, there is an urgent need for a fast dynamic storage capacity algorithm that requires less data, is computationally simple, and supports bidirectional calculations to improve the accuracy and efficiency of flood control scheduling for river-type reservoirs. Summary of the Invention

[0003] To address the aforementioned shortcomings, the present invention aims to propose a rapid algorithm for calculating the dynamic storage capacity of the backwater zone in river-type reservoirs. This algorithm utilizes limited basic data such as river gradient, water level-storage capacity, and water level-discharge relationship to construct a parabolic backwater curve model, thereby enabling rapid and accurate calculation of dynamic storage capacity and quantification of static storage capacity ratio. This, in turn, improves the accuracy, efficiency, and flexibility of flood control scheduling for river-type reservoirs.

[0004] To achieve this objective, the present invention adopts the following technical solution: A fast algorithm for the dynamic reservoir capacity of the variable backwater zone in a river-type reservoir includes: Obtain the basic parameters of the river-type reservoir, including the river gradient, riverbed elevation at the dam site, water level-reservoir capacity relationship curve, and natural water level-discharge relationship curve at the dam site. Obtain the initial water level, final water level, initial inflow, and final inflow during the flood control process; Based on the initial and final water levels, the static reservoir capacity change is calculated according to the basic characteristics of the river channel. Based on the initial inflow and the final inflow, the initial natural water level and the final natural water level are determined from the natural water level-discharge relationship curve at the dam site. Based on the initial water level, the final water level, the initial natural water level, the final natural water level, and the river gradient, calculate the initial backwater length and the final backwater length; Based on the initial backflow length, the final backflow length, the initial inflow rate, the final inflow rate, the initial water level, and the final water level, the dynamic storage capacity change is calculated using the parabolic backflow curve equation, and the ratio of the dynamic storage capacity change to the static storage capacity change is calculated.

[0005] Preferably, the calculation of static storage capacity change satisfies the following relationship: ; in, This indicates the average width of the downstream river channel. Indicates the rise in water level in front of the dam during the flood control process and , and These are the initial water level and the final water level, respectively. Indicates the average width of the upstream river channel Average width of downstream river channel The ratio, , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level. and It is obtained by calculating the topography of the reservoir area or the cross-section of the river channel, or by... Calculation, where Indicates water level. This indicates the riverbed elevation at the dam site. This indicates the gradient of the river channel.

[0006] Preferably, when the inflow remains constant, the calculation of the change in dynamic reservoir capacity satisfies the following relationship: ; in, Indicates dynamic storage capacity. Indicates the average width of the river channel. Indicates the initial water level Compared with the original water level before the dam was built The difference and , Indicates the end water level Compared with the original water level before the dam was built The difference and , Indicates the initial return water length of the dynamic reservoir and , Indicates the length of the reservoir's return water at the end of its operation and , This indicates the gradient of the river channel; The ratio of dynamic storage capacity change to static storage capacity change satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio and , Indicates static storage capacity. Indicates the rise in water level in front of the dam during the flood control process and , Indicates the average width of the upstream river channel Average width of downstream river channel The ratio and , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

[0007] Preferably, when the inflow increases, the calculation of the change in dynamic reservoir capacity satisfies the following relationship: ; in, Indicates dynamic storage capacity. Indicates the average width of the river channel. Indicates the end water level Original water level before dam construction corresponding to the final flow rate The difference and , Indicates the length of the reservoir's return water at the end of its operation and , Denotes the coefficients of the initial state water surface line equation and ,in Indicates the initial water level Original water level before dam construction corresponding to the initial flow rate The difference and , The x-coordinate of the intersection point of the initial backwater curve and the natural river surface line at the end of flood regulation is given. ,in Indicates the initial return water length of the dynamic reservoir and , This indicates the gradient of the river channel. and These are the initial natural water level and the final natural water level, determined by the initial inflow and the final inflow through the natural water level-flow relationship curve at the dam site. The ratio of dynamic storage capacity change to static storage capacity change satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio and , Indicates static storage capacity. Indicates the rise in water level in front of the dam during the flood control process and , Indicates the average width of the upstream river channel Average width of downstream river channel The ratio and , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

[0008] Preferably, the calculation of dynamic reservoir capacity change when inflow decreases includes: Determine the intersection of the final water surface line and the initial water surface line. When the following conditions are met... If the water level is high, the water will intersect at the backwater section of the initial water surface line; otherwise, the water will intersect at the natural inflow section of the initial water surface line. in , , , and These are the initial water level and the final water level, respectively. and These are the initial and final natural water levels, determined by the initial and final inflow rates through the natural water level-flow relationship curve at the dam site. Based on the initial water level Compared with the initial natural water level End water level With the end of natural water level Establish the initial state water surface line equation and the equation of the final state water surface line ,in , , This indicates the gradient of the river channel; Calculate the initial return water length and the length of the end return water The following relation is satisfied: ; based on and Establish the initial state of the natural inflow water surface line equation and the equation of the natural water surface line at the end state ; Based on the water surface line equation, the natural inflow water surface line equation, and the intersection point, the first water body formed by the decrease in natural inflow water level and the second water body formed by the rise in reservoir water level are calculated, along with the dynamic reservoir capacity. It is the sum of the volumes of the first water body and the second water body.

[0009] Preferably, when they intersect at the backwater section of the initial water surface line, the calculations of the first water body and the second water body satisfy the following relationship: The volume of the first water body Satisfying the relation: ; The volume of the second water body Satisfying the relation: ; in, Indicates the average width of the river channel. This represents the horizontal distance from the dam site to the intersection of the final water surface line and the initial water surface line, and satisfies the following relationship: ; and These are the initial and final backwater lengths of the dynamic reservoir, respectively. and These represent the initial natural water level and the final natural water level, respectively. Indicates the initial water level Compared with the initial natural water level The difference, Indicates the end water level With the end of natural water level The difference, This indicates the rise in water level in front of the dam during the flood control process. and These are the coefficients of the initial and final water surface line equations, respectively. This indicates the gradient of the river channel; Depend on The ratio of the change in dynamic storage capacity to the change in static storage capacity satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio, i.e. , Indicates static storage capacity. Indicates the average width of the upstream river channel Width of the river channel upstream of the downstream dam The ratio, i.e. , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

[0010] Preferably, when the intersection occurs at the natural inflow section of the initial water surface line, the calculations of the first water body and the second water body satisfy the following relationship: The volume of the first water body Satisfying the relation: ; The volume of the second water body Satisfying the relation: ; in, Indicates the average width of the river channel. The coefficients of the final state water surface line equation are represented. This represents the horizontal distance from the dam site to the intersection of the final water surface line and the initial water surface line, and is determined by the equation... Solving for the problem, This indicates the rise in water level in front of the dam during the flood control process. Indicates the initial water level Compared with the initial natural water level The difference, Indicates the initial backwater length of the dynamic reservoir; Depend on The ratio of the change in dynamic storage capacity to the change in static storage capacity satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio, i.e. , Indicates static storage capacity. Indicates the average width of the upstream river channel Average width of downstream river channel The ratio, and These represent the static reservoir capacity and river surface length corresponding to the initial and final water levels, respectively.

[0011] One of the above technical solutions has the following advantages or beneficial effects: This invention replaces the underwater topography and detailed cross-sectional data required by traditional methods with easily measurable macroscopic parameters such as river gradient and relationship curves. This reduces the basic data requirements from massive surveying data to routine hydrological observation results, significantly lowering the difficulty and cost of data collection. Secondly, it uses existing water level-reservoir-dam site natural water level-discharge relationship curves for rapid calculation of static reservoir capacity and natural water level, avoiding the complex process of constructing and discretizing hydrodynamic equations, and significantly reducing reliance on high-performance computing equipment. More importantly, it adopts a simplified physical model of parabolic backwater curve equations, which can directly output the ratio of dynamic reservoir capacity change to static reservoir capacity change through integral calculations. This transforms the time-consuming grid iteration solution in traditional methods into a one-time formula calculation, not only shortening the calculation cycle but also breaking through the limitation of traditional models that only support "forward calculations," achieving bidirectional calculation capabilities under both given scheduling schemes and target water levels. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0013] Figure 1 This is a fast algorithm for calculating the dynamic reservoir capacity of the variable backwater zone of a river-type reservoir, provided in this embodiment of the invention. Figure 2 This is a schematic diagram of the static storage capacity decomposition geometric model provided in an embodiment of the present invention; Figure 3 This is a first structural schematic diagram of the dynamic storage capacity provided in an embodiment of the present invention; Figure 4 This is a second structural schematic diagram of the dynamic storage capacity provided in an embodiment of the present invention; Figure 5 This is a third structural schematic diagram regarding the dynamic storage capacity provided in an embodiment of the present invention; Figure 6 This is a fourth structural schematic diagram regarding the dynamic storage capacity provided in an embodiment of the present invention; Figure 7 This is a fifth structural schematic diagram regarding the dynamic storage capacity provided in an embodiment of the present invention; Figure 8 This is the water level-discharge relationship curve at the Wantou Hub dam site provided in this embodiment of the invention; Figure 9 This is the water level and reservoir capacity curve of the Wantou Hub provided in this embodiment of the invention. Detailed Implementation

[0014] Embodiments of the present invention will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, where like or similar reference numerals designate like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the accompanying drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention.

[0015] In the present invention, the terms "comprising", "including" or any other variation thereof are intended to cover a non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the phrase "comprising a..." does not exclude the presence of additional identical elements in the process, method, article or device comprising the element.

[0016] A quick algorithm for the variable storage capacity in the variable backwater area of a river-channel reservoir, as Figure 1 shown, a preferred embodiment of the present invention includes the following steps: S1: Obtain the basic parameters of the river-channel reservoir. The basic parameters include the river slope, the river bottom elevation at the dam site, the water level-storage capacity relationship curve, and the natural water level-discharge relationship curve at the dam site; It should be noted that the river slope refers to the elevation drop per unit river length, which characterizes the longitudinal inclination degree of the river channel and is the core parameter for calculating the length of the backwater curve, usually expressed in thousandths or ten-thousandths. For example, in the case of the Wantou Junction ; the river bottom elevation at the dam site is the elevation of the river bed bottom at the location of the reservoir dam, serving as the elevation reference zero point for calculating the backwater length; the water level-storage capacity relationship curve is a curve describing the functional relationship between the water level in front of the dam and the total static water storage in the reservoir area, constructed from measured topographic data or cross-section data, and is used for directly querying or interpolating to calculate the static storage capacity; the natural water level-discharge relationship curve at the dam site is a curve describing the relationship between the discharge and the corresponding water level in the natural state at the dam site cross-section, and is used to determine the elevation of the natural river water surface line under different inflow discharges. The above basic parameters together constitute the physical boundary conditions and conversion relationships for calculating the variable storage capacity.

[0017] S2: Obtain the starting water level, ending water level, starting inflow discharge, and ending inflow discharge of the flood regulation process; It should be noted that the initial water level refers to the water level in front of the dam at the beginning of the flood control calculation period, which is the benchmark for calculating the initial reservoir capacity and water surface line; the final water level refers to the water level in front of the dam at the end of the flood control calculation period, reflecting the reservoir status after the operation; the initial inflow refers to the natural river flow entering the reservoir at the beginning of the period, which determines the initial natural water surface line shape; and the final inflow refers to the inflow at the end of the period, which may change due to changes in upstream water inflow or inter-regional confluence. These four parameters define the time boundary conditions and driving conditions for flood control calculation, and are key variables for distinguishing different operation scenarios (such as constant inflow, rising water, and falling water).

[0018] Understandably, step S2 essentially clarifies the specific operating conditions of the calculation object. By setting the starting and ending water levels and flow rates, the continuous flood process is discretized into calculable typical time periods. The difference between the starting and ending water levels determines the magnitude of reservoir capacity changes, while the changes in the starting and ending flow rates determine the dynamic adjustment requirements of the natural water surface line. By transforming the target water level control and inflow forecast in actual flood control scheduling into calculation inputs, it can support both forward deduction of given scheduling rules and reverse reservoir capacity calculation under the target water level, effectively overcoming the limitation of traditional methods that only support unidirectional calculations.

[0019] S3: Based on the initial and final water levels, calculate the static reservoir capacity change according to the basic characteristics of the river channel; It should be noted that the basic characteristics of a river channel are different from the fundamental parameters. The fundamental parameters are the raw observation data collected in advance (such as the river gradient, the riverbed elevation at the dam site, and the water level-reservoir capacity curve), while the basic characteristics of a river channel are morphological parameters extracted from the fundamental parameters and used for subsequent calculations, such as the average width of the upstream channel. Average width of downstream river channel ,as well as and Static storage capacity change specifically refers to the increase in storage capacity corresponding to the rise of the reservoir water level from an initial value to an end value under ideal static conditions, ignoring the influence of water surface gradient. It serves as the benchmark reference quantity in dynamic storage capacity calculation. By consulting the water level-storage capacity relationship curve, the static storage capacity corresponding to the initial water level and the static storage capacity corresponding to the end water level can be directly obtained or calculated through interpolation; the difference between the two is the static storage capacity change. The water level-storage capacity relationship curve can be stored in tabular or functional form, reflecting the water storage capacity determined by the reservoir's geometry, and serves as the baseline value distinguishing dynamic effects from static volume.

[0020] Understandably, step S3 aims to establish a static benchmark for reservoir capacity calculation, quickly obtaining the theoretical reservoir capacity value without considering dynamic effects through curve lookup. Using the static reservoir capacity as the denominator or reference system provides a comparative basis for subsequent quantification of the relative size of the dynamic reservoir capacity. This allows the additional effects of the dynamic reservoir capacity to be clearly expressed using the dimensionless index of the dynamic / static reservoir capacity ratio, facilitating horizontal comparisons and experience summaries between different reservoirs or under different operating conditions.

[0021] S4: Based on the initial inflow and the final inflow, determine the initial natural water level and the final natural water level from the natural water level-discharge relationship curve at the dam site; It should be noted that the initial natural water level refers to the water level at the dam site cross-section when the initial inflow passes through the natural river channel under conditions unaffected by reservoir backwater; the final natural water level refers to the natural water level at the end of the inflow. These two parameters characterize the water surface elevation of the river channel without reservoir construction and are important references for constructing the dynamic reservoir capacity water level curve baseline. The natural water level-discharge relationship curve at the dam site can be established based on measured hydrological data downstream of the dam site, unaffected by backwater.

[0022] Understandably, step S4 aims to quantify the impact of inflow changes on the natural water surface line by converting flow parameters into water level parameters through curve lookup. Under a steady flow scenario with constant inflow, the initial and final natural water levels are equal, and the dynamic reservoir capacity is solely caused by changes in the upstream water level. Under a scenario of changing inflow, the natural water level difference directly affects the calculation boundary of the dynamic reservoir capacity, determining the relative position of the backwater curve and the natural water surface line. In summary, integrating flow forecast information into the calculation framework, enabling the dynamic reservoir capacity calculation to reflect the dynamic coupling effects during the actual flood evolution process, is a crucial step in distinguishing the differences in dynamic reservoir capacity under different inflow conditions.

[0023] S5: Calculate the initial backwater length and the final backwater length based on the initial water level, the final natural water level, the final natural water level, and the river gradient; It should be noted that, in one embodiment, the initial backwater length refers to the horizontal distance from the dam site upstream to the point where the backwater curve is tangent to the natural water surface line in the initial state, and the final backwater length refers to the corresponding distance at the end of flood control. These two parameters quantitatively describe the longitudinal range of the backwater's influence and are the spatial boundaries for integral calculation of dynamic reservoir capacity. The calculation is based on the backwater balance theory. The backwater length is directly proportional to the superelevation of the water level in front of the dam (the difference between the water level in front of the dam and the natural water level) and inversely proportional to the river gradient. Its physical meaning is the natural extension distance of the backwater curve when gravity and jacking force are in balance, which determines the spatial distribution range of the dynamic reservoir water body.

[0024] Understandably, step S5 aims to convert the water level parameter into a spatial scale parameter, providing clear upper and lower limits for the dynamic storage capacity integral. The length of the backwater directly determines the longitudinal influence range of the dynamic storage capacity; a longer backwater length means a more significant dynamic storage capacity effect. By introducing the river gradient, the geometric characteristics of the reservoir are coupled with the hydrodynamic characteristics, enabling the dynamic storage capacity calculation to reflect the influence of different river steepness levels.

[0025] S6: Based on the initial return water length, the final return water length, the initial inflow rate, the final inflow rate, the initial water level, and the final water level, calculate the dynamic storage capacity using the parabolic return water curve equation, and calculate the ratio of the change in dynamic storage capacity to the change in static storage capacity.

[0026] It should be noted that the parabolic backwater curve equation is a hydraulic mathematical model describing the parabolic shape of the water surface in the backwater section of the reservoir. Its standard form is: ,in The coefficient relating to the river gradient and the superelevation upstream of the dam is derived based on the theory of gradually varying flow. It assumes the backwater curve is tangent to the x-axis upstream of the dam and smoothly connects to the natural water surface upstream. The dynamic reservoir volume is obtained by integrating the area between this curve and the baseline and multiplying it by the average river width. The ratio of dynamic reservoir volume change to static reservoir volume change is a core indicator for quantifying the relative importance of dynamic reservoir volume. It directly reflects the significance of the dynamic effects of river-type reservoirs and serves as the basis for determining whether dynamic reservoir volume correction needs to be considered in scheduling decisions.

[0027] Understandably, the parabolic equation is first used to characterize the water surface morphology under different operating conditions. Then, the volume of the wedge-shaped water body between the initiation and termination water surface lines is calculated through piecewise integration. This volume represents the additional reservoir capacity formed by the backwater. The computational effect of step S6 is reflected in transforming the complex unsteady flow problem into a deterministic mathematical integration problem, significantly reducing computational complexity and computational power requirements. The calculated ratio of dynamic reservoir capacity to static reservoir capacity can intuitively reflect the magnitude of the dynamic effect. For example, when the ratio exceeds 0.3, it indicates that the dynamic reservoir capacity cannot be ignored and needs to be corrected in flood control calculations, thereby improving the accuracy and reliability of flood control scheduling.

[0028] In one embodiment, such as Figure 8 and 9 As shown, taking the Wantou Hub in the upper reaches of the Beijiang River as an example, this hub is located in the lower reaches of the Zhenjiang River, with a catchment area of ​​[missing information]. Total storage capacity Flood control capacity The reservoir area is long and narrow, exhibiting typical characteristics of a river-type reservoir. Firstly, the upstream 30 meters of the reservoir area were surveyed using river channel measurements. The average gradient of the main channel is At the same time, two core relationship curves were collected and established: one is the water level-discharge relationship curve at the dam site (i.e., Figure 8 The first is the natural river channel flow rate, which reflects the mapping relationship between water level and natural river channel flow; the second is the water level-reservoir capacity curve (i.e., Figure 9 This accurately depicts the functional relationship between the water level in front of the dam and the total static water storage. When the inflow is 4000... When the inflow remains constant, with an initial water level of 63 meters and an ending water level of 68 meters, the dynamic storage capacity / static storage capacity ratio can be calculated to be 0.725. When the initial inflow is 4000 cubic meters per second and the ending inflow is 5000 cubic meters per second, with an initial water level of 63 meters and an ending water level of 68 meters, the dynamic storage capacity / static storage capacity ratio can be calculated to be 0.52. When the initial inflow is 4000 cubic meters per second and the ending inflow is 3000 cubic meters per second, with an initial water level of 63 meters and an ending water level of 68 meters, the dynamic storage capacity / static storage capacity ratio can be calculated to be 0.436.

[0029] Preferably, the calculation of static storage capacity change satisfies the following relationship: ; in, This indicates the average width of the downstream river channel. Indicates the rise in water level in front of the dam during the flood control process and , and These are the initial water level and the final water level, respectively. Indicates the average width of the upstream river channel Average width of downstream river channel The ratio, , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level. and It is obtained by calculating the topography of the reservoir area or the cross-section of the river channel, or by... Calculation, where Indicates water level. This indicates the riverbed elevation at the dam site. This indicates the gradient of the river channel.

[0030] like Figure 2 As shown, it should be noted that the static storage capacity change... Essentially, it refers to the increase in static water storage volume corresponding to the rise in water level during flood regulation. This invention decomposes it into a truncated pyramidal reservoir capacity. With wedge-shaped storage capacity The sum of . prism The volume of the water body that was already filled at the initial water level between the end of the backwater and the dam site is determined by the upstream cross-sectional area. Downstream cross-sectional area and bottom length Together, the volume formula is determined as follows: wedge The volume of the water body formed by the newly added backwater section during the rise from the initial water level to the final water level is determined by the upstream cross-sectional area. With length increment The decision is made using the following formula: Average width of the downstream channel This refers to the average width of the water surface at or near the dam site, serving as the geometric reference for wedge calculations; the rise in water level in front of the dam. It is the end water level Compared with the initial water level The difference directly determines the range of change in static reservoir capacity; the average width of the upstream river channel It is a representative river width in the upper reaches of the reservoir area, and Together they constitute the rate of change of river channel width Reflects the contraction or diffusion characteristics of the river channel along its course; static reservoir capacity and river surface length. and The longitudinal distances corresponding to the influence range of the backwater at the initial and final water levels represent the extent of the static water body in the reservoir area at different water levels; the riverbed elevation at the dam site. This serves as the baseline for calculating the water surface length. In general, these parameters, through geometric generalization, transform the actual irregular river channel into an equivalent regular shape, providing geometric constraints for analytical calculations.

[0031] Understandably, the complex reservoir area morphology is first abstracted into an upstream width. Downstream width A regular geometric solid whose length varies with the water level is then used to divide the water body during flood control into a frustum of existing water storage and a wedge of newly added water storage. An integral expression is established using elementary geometric volume formulas, and finally, the width ratio is used to... After normalizing the multivariate data, we obtain a result containing only... , , , , Algebraic equations can be transformed from complex calculations requiring integrals along the path or discrete summations into one-time parameter substitution calculations, significantly reducing computational load and data dependency. This can be achieved by limiting... , It can be calculated either by actual cross-section measurement or by... Approximate calculations are used, thus this invention provides a dual approach that balances accuracy and efficiency. The former is suitable for important reservoirs with detailed data, while the latter is suitable for rapid assessment in areas lacking data, effectively expanding the scope of application.

[0032] Preferably, when the inflow remains constant, the calculation of the change in dynamic reservoir capacity satisfies the following relationship: ; in, Indicates dynamic storage capacity. Indicates the average width of the river channel. Indicates the initial water level Compared with the original water level before the dam was built The difference and , Indicates the end water level Compared with the original water level before the dam was built The difference and , Indicates the initial return water length of the dynamic reservoir and , Indicates the length of the reservoir's return water at the end of its operation and , This indicates the gradient of the river channel; The ratio of dynamic storage capacity change to static storage capacity change satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio and , Indicates static storage capacity. Indicates the rise in water level in front of the dam during the flood control process and , Indicates the average width of the upstream river channel Average width of downstream river channel The ratio and , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

[0033] like Figure 3 As shown, it should be noted that the dynamic storage capacity... Specifically refers to the dynamic additional reservoir capacity formed by changes in the shape of the backwater curve. Under the scenario of constant inflow, its physical meaning is the wedge-shaped water volume between the two backwater parabolas at the start and end times. Average channel width. It is the lateral scale parameter in integral calculation, which converts the two-dimensional water surface area into a three-dimensional volume. and These represent the superelevation values ​​of the water level in front of the dam relative to the natural river channel at the beginning and end times, respectively. Their magnitude directly determines the curvature and influence range of the backwater curve and is a coefficient of the parabola equation. and The only variable. and The spatial boundary for calculating dynamic reservoir capacity corresponds to the tangent points between the backwater curve and the natural water surface at the start and end times, respectively. Its calculation formula... Based on the balance between the parabolic geometry and the channel gradient, the integration interval ensures coverage of the entire backwater influence area. The ratio of the average channel width to the downstream width (dynamic reservoir capacity). Yes The correction factor is used when the average width is used in the calculation of dynamic storage capacity. The downstream width used in static storage capacity calculation When there is an inconsistency, through Ensure dimensional consistency and geometric compatibility in ratio calculations to improve calculation accuracy.

[0034] Understandably, for the most basic and common scheduling scenario of constant water inflow, a purely analytical calculation path for dynamic reservoir capacity was established. First, the original water level before dam construction was obtained using the water level-discharge relationship curve. As a reference plane, calculate and This allows us to determine the coefficients and integration interval of the equation for the backwater parabola. , ; then the initial parabola With the end of the parabola Perform a definite integral over the region between them, combined with the average width of the river channel. The dynamic storage capacity is obtained by analysis. Finally, the width ratio is introduced. By combining the static reservoir capacity formula with the dynamic reservoir capacity ratio, we can obtain the dynamic reservoir capacity ratio. In general, this avoids the complex operations of grid division and time step iteration in numerical simulation, compresses the dynamic reservoir capacity calculation into several algebraic operations, and improves the computational efficiency by several orders of magnitude. Moreover, since the integration process strictly follows the hydraulic backwater curve theory, the calculation accuracy is sufficient to meet the needs of engineering scheduling, providing an immediately usable dynamic reservoir capacity correction tool for real-time flood control decision-making.

[0035] Preferably, when the inflow increases, the calculation of the change in dynamic reservoir capacity satisfies the following relationship: ; in, Indicates dynamic storage capacity. Indicates the average width of the river channel. Indicates the end water level Original water level before dam construction corresponding to the final flow rate The difference and , Indicates the length of the reservoir's return water at the end of its operation and , Denotes the coefficients of the initial state water surface line equation and ,in Indicates the initial water level Original water level before dam construction corresponding to the initial flow rate The difference and , The x-coordinate of the intersection point of the initial backwater curve and the natural river surface line at the end of flood regulation is given. ,in Indicates the initial return water length of the dynamic reservoir and , This indicates the gradient of the river channel. and These are the initial natural water level and the final natural water level, determined by the initial inflow and the final inflow through the natural water level-flow relationship curve at the dam site. The ratio of dynamic storage capacity change to static storage capacity change satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio and , Indicates static storage capacity. Indicates the rise in water level in front of the dam during the flood control process and , Indicates the average width of the upstream river channel Average width of downstream river channel The ratio and , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

[0036] like Figure 4 and Figure 5 As shown, it should be noted that the scenario of increased inflow refers to the situation where the inflow rate increases from the initial value to the final value during flood regulation, causing the water level of the natural river channel to rise synchronously, thereby encroaching on part of the reservoir capacity and reducing the effective dynamic reservoir capacity. (The x-axis of the intersection point is shown.) It is the initial return water parabola With the natural river water level at the end of flood control The intersection point, in physical terms, is the spatial turning point where the natural water flow re-intersects the initial backwater curve after flood regulation. The area to the left of this point is controlled by the initial backwater curve, while the area to the right is controlled by the natural water surface line after flood regulation. The dynamic reservoir capacity calculation interval is divided into two sub-segments to accurately deduct the impact of natural water level rises. (Coefficient) Riverbed gradient at the start time with extremely high values The curvature of the initial backwater curve is determined jointly. The length of the backwater at the end of the dam is determined by the difference between the water level upstream of the dam and the natural water level at the end of the dam. ; Characterizing the rise of the natural water level after flood regulation relative to the initial water level in front of the dam is a key factor in correcting dynamic reservoir capacity. The above parameters work together to ensure that the actual backwater volume can still be accurately quantified under complex conditions of enhanced inflow.

[0037] Understandably, in the face of scenarios with increased inflow, this invention aims to address the dynamic correction problem of reduced effective dynamic reservoir capacity caused by the rise of the natural water surface line when the inflow increases. Firstly, the natural water level corresponding to the initial and final flow rates is obtained using the natural water level-discharge relationship curve at the dam site. and Determine the range of change in the natural water surface line; then construct the initial backwater parabola. With the natural water surface line after flood regulation And solve for the intersection points This intersection divides the dynamic reservoir water body into a dual control zone above the initial parabola and above the natural water surface line; then the interval... integral , for interval integral The equation of the natural river surface at the end of flood control is: The reservoir capacity occupied by natural water level rise is accurately deducted through piecewise integration; finally, the width ratio is introduced. This achieves geometric unification with the static reservoir capacity formula. In general, transforming the coupling effect of flow and water level changes in unsteady flow into an analytically solvable set of algebraic equations avoids the complexity of traditional methods that require reconstructing a full-area hydrodynamic model for unsteady flow simulation. It maintains computational efficiency and engineering accuracy even during floods with significant inflow variations, providing a rapid assessment tool for real-time scheduling in response to complex conditions such as sudden surges in upstream inflows or inter-regional confluence.

[0038] Preferably, the calculation of dynamic reservoir capacity change when inflow decreases includes: Determine the intersection of the final water surface line and the initial water surface line. When the following conditions are met... If the water level is high, the water will intersect at the backwater section of the initial water surface line; otherwise, the water will intersect at the natural inflow section of the initial water surface line. in , , , and These are the initial water level and the final water level, respectively. and These are the initial and final natural water levels, determined by the initial and final inflow rates through the natural water level-flow relationship curve at the dam site. Based on the initial water level Compared with the initial natural water level End water level With the end of natural water level Establish the initial state water surface line equation and the equation of the final state water surface line ,in , , This indicates the gradient of the river channel; Calculate the initial return water length and the length of the end return water The following relation is satisfied: ; based on and Establish the initial state of the natural inflow water surface line equation and the equation of the natural water surface line at the end state ; Based on the water surface line equation, the natural inflow water surface line equation, and the intersection point, the first water body formed by the decrease in natural inflow water level and the second water body formed by the rise in reservoir water level are calculated, along with the dynamic reservoir capacity. It is the sum of the volumes of the first water body and the second water body.

[0039] like Figure 6 and 7 As shown, it should be noted that reduced inflow refers to the hydrological condition where the inflow at the end of the flood control process is less than the initial inflow. At this time, although the water level in front of the dam rises due to the flood control effect, the natural river level drops as the flow decreases, creating a special hydraulic condition where the upstream natural water level is lower than the reservoir water level. Intersection judgment conditions. In and These two inequalities represent the degree of backwater elevation relative to the natural water level at the beginning and end of the reservoir. By comparing the ordinate of the water surface line at the beginning backwater length with that of the water surface line at the end, this mathematically rigorous definition of the spatial topological relationship between the two parabolic water surface lines is crucial. Its physical essence lies in determining whether the vertex of the backwater curve at the end is low enough to ensure that the intersection of the two curves falls within the range of the backwater section at the beginning. The first water body refers to the reservoir capacity vacated by the drop in water level in the original natural river channel due to a decrease in natural inflow. The cross-section of this water body is formed by the difference in the ordinates of the two natural water surface lines at the beginning and end, and its longitudinal distribution extends upstream from the dam site to the intersection of the two natural water surface lines. The second water body refers to the backwater elevation volume formed by the rise in water level in front of the dam during flood regulation. Its cross-section is formed by the difference in the ordinates of the two backwater curves at the beginning and end. When the water surface line at the end is entirely below the water surface line at the beginning, this water body represents a negative value, indicating a net decrease in the actual water storage capacity of the reservoir due to the reduced inflow. The backwater section specifically refers to the length from the dam site upstream to the backwater. Within the range, the parabolic backwater curve section is significantly affected by the reservoir's backwater effect, resulting in a quadratic curve shape for the water surface. The natural inflow section refers to the upstream river section beyond the backwater length; in this section, the water surface recovers the natural river channel slope, exhibiting linear characteristics. River channel gradient. As a core parameter, in the coefficients of the parabola equation and The calculations demonstrate the control effect of reservoir geometry on the curvature of the water surface curve. The larger the value, the steeper the backflow curve and the shorter the range of water backflow.

[0040] Understandably, the core challenge in calculating dynamic reservoir capacity under reduced inflow conditions lies in the inverse coupling effect between the decline in natural river water level and the rise in reservoir water level. Traditional methods typically ignore the correction effect of inflow changes on dynamic reservoir capacity or directly employ complex unsteady flow numerical simulations. This embodiment achieves accurate analysis of dynamic reservoir capacity under inverse hydrological conditions by constructing a volume balance model containing two water bodies. The necessity of introducing an intersection judgment mechanism lies in the fact that, when inflow decreases, the final state water surface line may be lower than the initial state water surface line due to the excessive drop in natural water level. At this time, the location of the intersection point of the two curves determines whether the integral boundary of the second water body is limited to the backwater section or extends to the natural inflow section. This judgment directly determines the selection of subsequent integral equations, avoiding errors in volume calculation. Secondly, the innovation of decomposing dynamic reservoir capacity into a first water body and a second water body lies in the fact that the first water body objectively reflects the channel storage released due to the reduction in natural inflow, while the second water body quantifies the actual increase in flood control water storage. The superposition of the two can accurately describe the change in net water storage under conditions of reduced inflow. This decomposition method overcomes the deficiency of single-water-body models in distinguishing the main controlling factors of water level changes. Furthermore, by establishing a natural water surface line equation... and The method transforms the drawdown caused by flow changes into an integrable linear function, forming a geometrically closed region with the parabolic backwater curve equation. This allows the dynamic reservoir capacity calculation under reverse hydrological conditions to still be completed through elementary function integration without iterative solutions, fundamentally ensuring computational efficiency. By organically combining geometric topological judgment and volume decomposition, the technical problem of the uncertainty of the direction of dynamic reservoir capacity calculation when the inflow decreases is solved, ensuring the applicability of this invention across all operating conditions.

[0041] Preferably, when they intersect at the backwater section of the initial water surface line, the calculations of the first water body and the second water body satisfy the following relationship: The volume of the first water body Satisfying the relation: ; The volume of the second water body Satisfying the relation: ; in, Indicates the average width of the river channel. This represents the horizontal distance from the dam site to the intersection of the final water surface line and the initial water surface line, and satisfies the following relationship: ; and These are the initial and final backwater lengths of the dynamic reservoir, respectively. and These represent the initial natural water level and the final natural water level, respectively. Indicates the initial water level Compared with the initial natural water level The difference, Indicates the end water level With the end of natural water level The difference, This indicates the rise in water level in front of the dam during the flood control process. and These are the coefficients of the initial and final water surface line equations, respectively. This indicates the gradient of the river channel; Depend on The ratio of dynamic storage capacity change to static storage capacity change satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio, i.e. , Indicates static storage capacity. Indicates the average width of the upstream river channel Width of the river channel upstream of the downstream dam The ratio, i.e. , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

[0042] It should be noted that, under the condition of intersecting the initial water surface line at the backwater section, the first water body The calculation requires segmented analytical processing based on the geometric relationships shown in the attached diagram. According to the parabolic backwater curve theory in the hydraulic calculation handbook, such as... Figure 7 As shown, when the natural inflow decreases, the water body formed by the drop in reservoir water level can be divided into three characteristic segments: The section is the starting natural water surface line. With the end of the natural waterline At the dam site The horizontal length of the triangular shaded area within the range The volume of this region is calculated using the triangle area formula. calculate; The segment is the two natural water surface lines mentioned above. to The rectangular shaded area within the range has a horizontal length of The volume of this region is calculated using the formula for the area of ​​a rectangle. calculate; The section represents the final state of the backwater curve. With the end of the natural waterline exist to The volume of the shaded area within the range of curves must be obtained by integration. Calculation: Add the volumes of the three sections together and multiply by the average width of the river channel. Thus, the original expression for the first water body is obtained: Substitute and After defining the specific expression and expanding the integral terms, we eliminate intermediate variables by algebraically combining like terms. and Ultimately simplified to This simplification process utilizes This relationship of water flow length combines the volumes of the triangle and the rectangle into one. The compact form This approach avoids the quadratic error introduced by linear approximation. Second water body The integration interval is The integrand is The integral result is ,in This represents the difference in curvature between the initial and final return water curves. Represents a constant water level rise. Intersection point. Calculation formula Solving geometric equations Derived from this, the explicit expression compares the intersection point location with the relative elevation ratio. Water level rise Direct association enables the parsing of intersection point location.

[0043] Understandably, the physical basis for using a three-segment decomposition calculation for the first water body lies in the segmented changes in the reservoir's water surface line caused by the reduction in natural water inflow. and The segment is directly composed of the linear difference between the starting and ending natural water surface lines, while The section then exhibits a non-linear variation due to the influence of the backwater curve. Segment triangle and The technical effect of segment rectangle merging is that it reduces the number of intermediate variables required compared to the original process. and The calculation process is compressed into only containing and The expression significantly reduces the number of parameters and calculation steps, while The introduction of this term precisely corrects the discrepancy between the linear approximation and the actual shape of the parabola, ensuring the accuracy of volume calculations. The necessity of integrating the interval rather than using a simple geometric approximation lies in the fact that the interval is formed by a parabola. With a straight line The shape of the boundary of the enclosure cannot be precisely described by elementary geometry; it can be determined through integral operations. The volume of this irregular region can be precisely obtained, and the integral result shows... The term corresponds to the parabolic component. The item corresponds to linear deduction. The terms correspond to constant components, and together they constitute the complete curve volume. The second water volume partition interval is limited to... The technical significance lies in the fact that this range represents the initial backwater curve. With the end of the backwater curve The area where they directly intersect in space exceeds... The initial curve has now transformed into a natural water surface profile, therefore only within this interval is needed. Integration accurately yields the pure increment of flood control and water storage, avoiding redundant calculations introduced by an excessively large integration range. (Intersection point) The explicit expression is the core of the entire simplified calculation; traditional methods require iterative solutions. This is a nonlinear equation, which this scheme obtains directly through algebraic transformations. and The proportional relationship, the proportionality coefficient This comprehensively reflects the coupling effect between the relative backwater level at the end of the flood and the rise in water level, enabling the intersection point to be located within a constant time, fundamentally guaranteeing the computational efficiency advantage of this invention. In summary, through geometric decomposition, integral refinement, and algebraic explicitness, the system systematically solves the volume calculation problem arising from the coupling of reverse hydrological conditions and positive flood regulation under reduced inflow conditions, ensuring the analytical accuracy and efficiency of dynamic reservoir capacity calculation across all operating conditions.

[0044] Preferably, when the intersection occurs at the natural inflow section of the initial water surface line, the calculations of the first water body and the second water body satisfy the following relationship: The volume of the first water body Satisfying the relation: ; The volume of the second water body Satisfying the relation: ; in, Indicates the average width of the river channel. The coefficients of the final state water surface line equation are represented. This represents the horizontal distance from the dam site to the intersection of the final water surface line and the initial water surface line, and is determined by the equation... Solving for the problem, This indicates the rise in water level in front of the dam during the flood control process. Indicates the initial water level Compared with the initial natural water level The difference, Indicates the initial backwater length of the dynamic reservoir; Depend on The ratio of the change in dynamic storage capacity to the change in static storage capacity satisfies the following relationship: ; in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio, i.e. , Indicates static storage capacity. Indicates the average width of the upstream river channel Average width of downstream river channel The ratio, and These represent the static reservoir capacity and river surface length corresponding to the initial and final water levels, respectively.

[0045] It should be noted that the section intersecting the initial water surface line with the natural inflow section refers to the water surface line at the end of the flow. The water level at the intersection with the initial water level has exceeded the initial return water length. The range, that is At this point, the initial water level has returned to the natural river channel slope on the upstream side of the intersection, and its equation is: Second water volume expression middle, The term calculates the parabolic volume formed by the return water curve in the final state within the intersection interval by integration. The term is obtained by subtracting the linear volume occupied by the initial natural water surface line within the interval through integration. The term is the integral result of the constant term, representing the rise in water level in front of the dam. With initial congestion The cumulative effect in the intersection interval The item is a correction item, used to avoid in The initial backwater curve should have been used within the interval. However, the starting natural waterline was used incorrectly. The correction value for the volume calculation caused by this double counting is equal to the initial return water curve at... Integral over the interval Through algebraic transformations Can be converted The form of the intersection. From the equation The equation is established based on the geometric condition that the ordinate of the backwater curve at the intersection point is equal to the ordinate of the natural water surface at the initial state. Its explicit solution... Obtained through algebraic manipulation, avoiding numerical iteration, where the square root... The ratio representing the natural drawdown to the final uplift is used to indicate the point of intersection being closer to the dam site, while a larger ratio indicates the point of intersection extends further upstream. First water body. The calculation method is the same as when intersecting the backwater section at the initial water surface line. Understandably, when the inflow decreases and the intersection point exceeds the initial backflow length, the difficulty in calculating the second water body lies in the fact that the integration interval spans two different hydraulic characteristic regions: the backflow section and the natural section. Traditional methods typically cannot handle such cross-regional integration problems. However, this embodiment introduces a correction term. This successfully achieved a seamless connection between water volumes in different areas. (Intersection point) The explicit expression of the intersection point is crucial to the entire computational framework. Traditional hydraulic methods require solving a system of nonlinear equations to determine the intersection point, which is computationally inefficient and suffers from convergence problems. This embodiment uses algebraic transformation to... Represented as The product of the product of the relative water level difference and the square root of the difference allows the intersection point to be located within a constant time, fundamentally ensuring the computational efficiency advantage of this invention. In the calculation of the second water body volume, The physical meaning of the three terms is from the dam site to the intersection point. The volume of the region enclosed by the backwater curve at the end of the process and the natural water surface line at the beginning of the process is given. The boundary of this region is composed of a parabola and a straight line. The closed volume can be accurately obtained by integrating and subtracting the two curves. The terms then eliminated the intervals. The systematic errors introduced by the linear approximation are eliminated to ensure that the volume calculation strictly conforms to the actual water surface morphology. In this embodiment, through cross-regional integration and precise correction, the technical challenges of uncertain intersection points, inconsistent integration boundaries, and unsmooth regional transitions are effectively solved. This allows the invention to maintain analytical calculation capabilities even under the most complex extreme reverse hydrological conditions, avoiding the use of computationally expensive numerical simulation methods and providing an efficient and reliable technical path for engineering applications.

[0046] In another embodiment, when the inflow remains constant, the dynamic / static reservoir capacity values ​​corresponding to the flood control intervals at each water level are (with a water level difference of 1 meter):

[0047] The dynamic / static reservoir capacity values ​​corresponding to each level of flood control interval (with a water level difference of 2 meters) are as follows:

[0048] When the inflow increases, the dynamic storage capacity / static storage capacity ratio of each flood control interval at each water level is as follows (with a water level difference of 1 meter):

[0049] The dynamic storage capacity / static storage capacity ratio for each level of flood control interval (with a water level difference of 2 meters) is as follows:

[0050] When the inflow decreases, the dynamic storage capacity / static storage capacity ratio for each level of flood control zone is as follows (with a water level difference of 1 meter):

[0051] The dynamic storage capacity / static storage capacity ratio for each level of flood control interval (with a water level difference of 2 meters) is as follows:

[0052] The table above covers three typical operating conditions: constant inflow, increased inflow, and decreased inflow. Water level differences include two scheduling accuracies: 1 meter and 2 meters. The inflow rate ranges from 2000 cubic meters per second to 9000 cubic meters per second, progressively increasing or decreasing, comprehensively depicting the impact of dynamic changes in inflow rate and upstream water level on the dynamic reservoir capacity effect during torrential rain and floods. Data shows a significant correlation between the dynamic reservoir capacity coefficient and the range of water level rise, inflow rate, and changes in inflow. Under constant inflow conditions, within a fixed water level range (e.g., 67-68 meters), as the flow rate increases from 2000 cubic meters per second to 9000 cubic meters per second, the coefficient decreases from 0.960 to 0.098, indicating that under high flow conditions, the ratio of reservoir velocity to water surface gradient increases, and the proportion of dynamic storage capacity decreases significantly. Under a fixed flow rate (e.g., 4000 cubic meters per second), as the water level rises from 63-64 meters to 70-71 meters, the coefficient increases from 0.310 to 0.841, reflecting that the greater the flood regulation amplitude, the more significant the additional storage capacity formed by backwater. Within the same flow range, when the water level difference increases from 1 meter to 2 meters, the dynamic storage capacity coefficient increases by approximately 15%-25%. For example, in the 67-69 meter range, the coefficient increases from 0.677 to 0.711 at a flow rate of 4000 cubic meters per second, verifying the contribution of the cumulative effect of the flood regulation process to the dynamic storage capacity. The dynamic storage capacity coefficient under the condition of increased inflow is generally lower than that under the condition of constant inflow. For example, in the 67-68 meter range with a flow rate of 4000-5000 cubic meters per second, the coefficient is 0.677 when the inflow is constant, but drops to 0.650 when the inflow increases. This is because the increased inflow leads to a rise in the water level of the natural river channel, compressing the reservoir's backwater space and weakening the relative proportion of dynamic storage capacity. Conversely, the coefficient under the condition of decreased inflow is significantly higher than the previous two conditions. In the 67-68 meter range with a flow rate of 5000-4000 cubic meters per second (reverse), the coefficient is as high as 1.119, indicating that the reduced flow releases a large amount of river channel storage, and the dynamic storage capacity effect is significantly reduced. The table data also reveals nonlinear characteristics: in the low flow range (2000-3000 cubic meters per second), the dynamic reservoir capacity coefficient increases rapidly with rising water level, while in the high flow range (8000-9000 cubic meters per second), the increase tends to level off. This is closely related to the width-to-depth ratio and water flow area variation characteristics of river-type reservoirs. These pre-calculated and systematically organized parameters can be directly embedded into the flood control scheduling decision-making system. Scheduling personnel can quickly obtain the dynamic reservoir capacity correction coefficient by looking up the table based on real-time inflow, dam front water level, and predicted inflow trends. This allows for dynamic correction of the static reservoir capacity flood control calculation results, thereby significantly improving flood forecast accuracy and scheduling response efficiency. It avoids the computational delays and resource consumption caused by temporarily constructing complex hydrodynamic models, fully verifying the significant advantages of this invention in terms of engineering practicality and computational efficiency.

[0053] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0054] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

Claims

1. A fast algorithm for calculating the dynamic reservoir capacity of the variable backwater zone in a river-type reservoir, characterized in that, include: Obtain the basic parameters of the river-type reservoir, including the river gradient, riverbed elevation at the dam site, water level-reservoir capacity relationship curve, and natural water level-discharge relationship curve at the dam site. Obtain the initial water level, final water level, initial inflow, and final inflow during the flood control process; Based on the initial and final water levels, the static reservoir capacity change is calculated according to the basic characteristics of the river channel. Based on the initial inflow and the final inflow, the initial natural water level and the final natural water level are determined from the natural water level-discharge relationship curve at the dam site. Based on the initial water level, the final water level, the initial natural water level, the final natural water level, and the river gradient, calculate the initial backwater length and the final backwater length; Based on the initial backflow length, the final backflow length, the initial inflow rate, the final inflow rate, the initial water level, and the final water level, the dynamic storage capacity change is calculated using the parabolic backflow curve equation, and the ratio of the dynamic storage capacity change to the static storage capacity change is calculated.

2. The rapid algorithm for calculating the dynamic reservoir capacity of the variable backwater zone of a river-type reservoir according to claim 1, characterized in that, The calculation of static storage capacity change satisfies the following relationship: ； in, This indicates the average width of the downstream river channel. Indicates the rise in water level in front of the dam during the flood control process and , and These are the initial water level and the final water level, respectively. Indicates the average width of the upstream river channel Average width of downstream river channel The ratio, , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level. and It is obtained by calculating the topography of the reservoir area or the cross-section of the river channel, or by... Calculation, where Indicates water level. This indicates the riverbed elevation at the dam site. This indicates the gradient of the river channel.

3. The rapid algorithm for calculating the dynamic reservoir capacity of the variable backwater zone of a river-type reservoir according to claim 2, characterized in that, When the inflow remains constant, the calculation of changes in dynamic reservoir capacity satisfies the following relationship: ； in, Indicates dynamic storage capacity. Indicates the average width of the river channel. Indicates the initial water level Compared with the original water level before the dam was built The difference and , Indicates the end water level Compared with the original water level before the dam was built The difference and , Indicates the initial return water length of the dynamic reservoir and , Indicates the length of the reservoir's return water at the end of its operation and , This indicates the gradient of the river channel; The ratio of dynamic storage capacity change to static storage capacity change satisfies the following relationship: ； in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio and , Indicates static storage capacity. Indicates the rise in water level in front of the dam during the flood control process and , Indicates the average width of the upstream river channel Average width of downstream river channel The ratio and , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

4. The rapid algorithm for calculating the dynamic reservoir capacity of the variable backwater zone of a river-type reservoir according to claim 2, characterized in that, When the inflow increases, the calculation of the change in dynamic reservoir capacity satisfies the following relationship: ； in, Indicates dynamic storage capacity. Indicates the average width of the river channel. Indicates the end water level Original water level before dam construction corresponding to the final flow rate The difference and , Indicates the length of the reservoir's return water at the end of its operation and , Denotes the coefficients of the initial state water surface line equation and ,in Indicates the initial water level Original water level before dam construction corresponding to the initial flow rate The difference and , The x-coordinate of the intersection point of the initial backwater curve and the natural river surface line at the end of flood regulation is given. ,in Indicates the initial return water length of the dynamic reservoir and , This indicates the riverbed gradient. and These are the initial natural water level and the final natural water level, determined by the initial inflow and the final inflow through the natural water level-flow relationship curve at the dam site. The ratio of dynamic storage capacity change to static storage capacity change satisfies the following relationship: ； in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio and , Indicates static storage capacity. Indicates the rise in water level in front of the dam during the flood control process and , Indicates the average width of the upstream river channel Average width of downstream river channel The ratio and , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

5. The rapid algorithm for calculating the dynamic reservoir capacity of the variable backwater zone of a river-type reservoir according to claim 2, characterized in that, When the inflow decreases, the calculation of the change in dynamic reservoir capacity includes: Determine the intersection of the final water surface line and the initial water surface line. When the following conditions are met... If the water level is high, the water will intersect at the backwater section of the initial water surface line; otherwise, the water will intersect at the natural inflow section of the initial water surface line. in , , , and These are the initial water level and the final water level, respectively. and These are the initial and final natural water levels, determined by the initial and final inflow rates through the natural water level-flow relationship curve at the dam site. Based on the initial water level Compared with the initial natural water level End water level With the end of natural water level Establish the initial state water surface line equation and the equation of the final state water surface line ,in , , This indicates the gradient of the river channel; Calculate the initial return water length and the length of the end return water The following relation is satisfied: ； based on and Establish the initial state of the natural inflow water surface line equation and the equation of the natural water surface line at the end state ; Based on the water surface line equation, the natural inflow water surface line equation, and the intersection point, the first water body formed by the decrease in natural inflow water level and the second water body formed by the increase in reservoir water level are calculated, along with the dynamic reservoir capacity. It is the sum of the volumes of the first water body and the second water body.

6. The rapid algorithm for calculating the dynamic reservoir capacity of the variable backwater zone of a river-type reservoir according to claim 5, characterized in that, When they intersect at the backwater section of the initial water surface line, the calculations of the first water body and the second water body satisfy the following relationship: The volume of the first water body Satisfying the relation: ； The volume of the second water body Satisfying the relation: ； in, Indicates the average width of the river channel. This represents the horizontal distance from the dam site to the intersection of the final water surface line and the initial water surface line, and satisfies the following relationship: ; and These are the initial and final backwater lengths of the dynamic reservoir, respectively. and These represent the initial natural water level and the final natural water level, respectively. Indicates the initial water level Compared with the initial natural water level The difference, Indicates the end water level With the end of natural water level The difference, This indicates the rise in water level in front of the dam during the flood control process. and These are the coefficients of the initial and final water surface line equations, respectively. This indicates the gradient of the river channel; Depend on The ratio of the change in dynamic storage capacity to the change in static storage capacity satisfies the following relationship: ； in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio, i.e. , Indicates static storage capacity. Indicates the average width of the upstream river channel Width of the river channel upstream of the downstream dam The ratio, i.e. , This indicates the length of the river channel with the corresponding static reservoir capacity at the initial water level. This indicates the length of the river channel with the corresponding static reservoir capacity at the end of the water level.

7. The rapid algorithm for calculating the dynamic reservoir capacity of the variable backwater zone of a river-type reservoir according to claim 5, characterized in that, When the intersection occurs at the natural inflow section of the initial water surface line, the calculations for the first water body and the second water body satisfy the following relationship: The volume of the first water body Satisfying the relation: ； The volume of the second water body Satisfying the relation: ； in, Indicates the average width of the river channel. The coefficients of the final state water surface line equation are represented. This represents the horizontal distance from the dam site to the intersection of the final water surface line and the initial water surface line, and is determined by the equation... Solving for the problem, This indicates the rise in water level in front of the dam during the flood control process. Indicates the initial water level Compared with the initial natural water level The difference, Indicates the initial backwater length of the dynamic reservoir; Depend on The ratio of the change in dynamic storage capacity to the change in static storage capacity satisfies the following relationship: ； in, This represents the average channel width of the reservoir and the channel width upstream of the downstream dam. The ratio, i.e. , Indicates static storage capacity. Indicates the average width of the upstream river channel Average width of downstream river channel The ratio, and These represent the static reservoir capacity and river surface length corresponding to the initial and final water levels, respectively.

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