A method for determining suitable flow velocity for fish breeding period based on reverse balance of fish metabolic energy

Abstract

The application discloses a fish breeding period suitable flow velocity determination method based on fish metabolic energy reverse balance, belongs to the field of aquatic ecological protection and environmental hydraulics, and comprises the following steps: in-situ investigation is carried out at the beginning and end of the fish breeding period, fish breeding ecological scenes representing ecological average levels of the fish breeding period are constructed, and average energy change amounts of fish individuals per unit time are obtained; an energy balance equation taking flow velocity v as a variable and taking the average energy change amount of fish individuals per unit time as a constraint is constructed, and individual scale flow velocity analysis result sets are obtained by reverse solution; uncertainty sampling is performed on uncertain parameters to determine population scale flow velocity analysis result sets, and the population scale flow velocity analysis result sets are mapped into ecological management indexes. The application obtains a fish breeding period suitable flow velocity range with a mechanical explanation under limited field investigation conditions, reduces dependence on large-scale frequency investigation, and is suitable for reservoir ecological regulation, gate dam discharge control, river regulation and fish habitat restoration engineering.

Description

Technical Field

[0001] This invention belongs to the fields of aquatic ecological protection, hydraulics and ecological regulation technology, and specifically relates to a method for determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy. Background Technology

[0002] River flow velocity is a crucial hydrodynamic factor influencing fish habitat, feeding, migration, spawning, and the survival of larvae and juveniles. For rivers affected by hydropower development, river channel management, and water resource allocation, the natural hydrodynamic processes are altered, impacting habitat distribution and reproductive success rates during the fish breeding season. Therefore, in determining ecological flow, reservoir scheduling, fish habitat restoration, and river ecological management, it is typically necessary to obtain the suitable flow velocity range for the target fish species' breeding season and translate this into actionable flow indicators for reservoir operation.

[0003] In existing technologies, suitable flow velocities for fish are typically determined through methods such as statistical analysis of fish occurrence frequency in the wild and expert-assigned values. For example, a common method for constructing habitat suitability curves involves statistically analyzing water depth, flow velocity, and substrate conditions corresponding to fish occurrence locations to generate a suitability curve, which is then further combined with a hydrodynamic model to calculate a weighted usable area. This type of method can reflect the spatial distribution characteristics of fish within a specific survey period, but its results are easily affected by factors such as survey frequency, sampling location, hydrological processes, and fish behavioral stages.

[0004] Specifically, existing methods for determining suitable flow velocities based on frequency of occurrence or empirical statistics have the following shortcomings: First, field surveys are labor-intensive, typically requiring multiple samplings at different flow rates, seasons, and river sections, resulting in high costs. Second, the frequency of fish occurrence does not necessarily equate to true physiological suitability; some fish may appear in suboptimal habitats due to predation, disturbance avoidance, or failure to compete. Third, existing suitability curves are difficult to directly apply when factors such as water temperature, food density, and river morphology change. Fourth, traditional methods often output a single threshold or empirical range, failing to adequately express the uncertainties of parameter errors and individual differences, making it difficult to meet the risk management needs in ecological scheduling. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy, which can effectively solve the above-mentioned problems.

[0006] The technical solution adopted in this invention is as follows:

[0007] This invention provides a method for determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy, comprising:

[0008] Step S1: Establish a database of fish bioenergetics parameters and obtain bioenergetics parameter data of the target fish species;

[0009] Step S2: Conduct in-situ surveys during the fish breeding season in the target river section; construct a fish breeding ecological scenario that represents the average ecological level during the fish breeding season through statistical calculations, including the mean values ​​of individual fish characteristics, environmental characteristics, and food characteristics; and obtain the measured average change in individual fish energy per unit time.

[0010] Step S3: Construct an energy balance equation with flow velocity v as the variable and measured average change in individual fish energy per unit time as the constraint. The energy balance equation describes the net energy intake per unit time obtained by the difference between feeding benefits per unit time and total metabolic cost per unit time, which reaches a balance with the measured average change in individual fish energy per unit time.

[0011] Step S4: Using the target fish bioenergetics parameters and the fish reproductive ecological scenario as input parameters, the energy balance equation is solved inversely within a preset flow velocity domain. This inversely deduces two flow velocity values ​​when the net energy intake per unit time of the target fish and the measured average change in individual fish energy per unit time reach equilibrium. Both flow velocity values ​​represent flow velocity values ​​that match the measured average change in individual fish energy per unit time. A net energy intake relationship curve is constructed, showing the relationship between net energy intake per unit time and flow velocity. A comprehensive analysis of the net energy intake relationship curve and the two matched flow velocity values ​​yields a set of flow velocity analysis results at the individual scale during the fish reproductive period, including the suitable flow velocity range for individuals, the optimal flow velocity v* for individuals, and the lower limit flow velocity for individual ecological tolerance.

[0012] Step S5: Select uncertain parameters from the input parameters and perform uncertainty sampling to generate multiple sets of input parameter samples. Step S4 is executed for each set of input parameter samples to obtain a set of individual optimal flow velocities v*. Based on the set of individual optimal flow velocities v*, determine the population-scale flow velocity analysis result set.

[0013] Step S6: Map the population-scale flow velocity analysis results set into ecological management indicators, and output at least the population-scale suitable flow velocity range, ecological tolerance lower limit, and corresponding ecological flow recommendations during the fish breeding season.

[0014] The method for determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy provided by this invention has the following advantages:

[0015] First, this invention uses flow velocity as a common control variable for both feeding benefits and swimming energy consumption, and inversely infers the suitable flow velocity during the fish breeding season through energy balance, thus explaining the fish's response to flow velocity from a physiological energy mechanism perspective. Second, this invention uses measured changes in growth or reproductive energy at the beginning and end of the breeding season as constraints, rather than solely relying on fish occurrence frequency, reducing the need for large-scale, multi-flow, and multi-season field frequency surveys. Third, this invention introduces boundary conditions such as water temperature, food abundance, fish size, and metabolic parameters to update the suitable flow velocity inversion results under different years, river sections, and body structures, exhibiting good transferability. Fourth, this invention uses Monte Carlo, Latin hypercube, or Sobol sequence sampling to propagate parameter uncertainties, outputting suitable flow velocity ranges, confidence intervals, and ecological tolerance lower limits, thereby supporting risk management in ecological scheduling. Fifth, this invention can be coupled with two-dimensional or three-dimensional hydrodynamic models, Manning's formula, or cross-sectional hydraulic relationships to convert physiologically suitable flow velocity thresholds into executable ecological flow, discharge ranges, and scheduling constraints, demonstrating good practicality. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the overall process of determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy, as provided in an embodiment of the present invention.

[0017] Figure 2 A schematic diagram illustrating the relationship between dietary benefits, total metabolic cost, and net energy intake as a function of flow rate, provided in an embodiment of the present invention.

[0018] Figure 3 A schematic diagram of the probability distribution of individual optimal flow velocity obtained by uncertainty sampling provided in an embodiment of the present invention. Detailed Implementation

[0019] To make the technical problems solved, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of protection of this invention. The survey data, parameters, and calculation results involved in the embodiments are exemplary data used to illustrate the feasibility of this invention. These data conform to the general value ranges for fish physiological and ecological surveys and river hydrodynamic conditions, and do not constitute a limitation on the scope of protection of this invention.

[0020] The inventors discovered that a bioenergetics-based habitat assessment method can explain the fish's selection mechanism for current velocity from the perspectives of energy intake and consumption, and energy input for growth and reproduction. For drifting-feeding fish, current velocity determines food transport flux on the one hand, and increases swimming energy consumption on the other; for benthic-feeding fish, current velocity affects the availability of benthic food, feeding efficiency, and the energy required to maintain position. Therefore, by using current velocity as a variable in the energy balance equation and constraining the model with measured changes in growth or reproduction energy during the breeding season, it is possible to infer the appropriate current velocity required for target fish to maintain energy balance or achieve reproductive input under limited survey conditions.

[0021] Therefore, this invention provides a method for determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy, in order to solve the problems of existing methods for determining appropriate flow velocity, such as strong dependence on large-scale field occurrence frequency surveys, insufficient explanation of mechanisms, weak mobility, and insufficient expression of uncertainty. It also provides executable flow velocity and flow control indicators for reservoir ecological scheduling, dam discharge control, and habitat restoration.

[0022] This invention provides a method for determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy. By constructing an energy balance equation with flow velocity as the variable to be determined and using measured changes in growth or reproduction energy during the breeding season as constraints, the optimal flow velocity for individual fish during the breeding season is solved in reverse. Then, the appropriate flow velocity range and ecological tolerance lower limit at the population scale are determined through uncertainty sampling, thereby improving the explanatory power, transferability and practicality of determining the appropriate flow velocity for fish.

[0023] Example 1:

[0024] Please see Figure 1 This embodiment provides a method for determining the appropriate flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy, including the following steps S1 to S6:

[0025] Step S1: Establish a database of fish bioenergetics parameters and obtain bioenergetics parameter data of the target fish species;

[0026] As one implementation method, the fish bioenergetics parameter database is established by means of literature retrieval, indoor metabolic experiments, swimming ability experiments, feeding experiments, historical ecological survey data, or parameter migration of similar species. The fish bioenergetics parameter database can be indexed according to fish species, body length, body weight, water temperature, feeding type, and reproductive stage, so as to be automatically retrieved under different individual fish sample conditions.

[0027] Among them, fish bioenergetics parameters include metabolic parameters, swimming ability parameters, and feeding parameters; the metabolic parameters include the energy loss coefficient due to defecation. and excretion energy loss coefficient The swimming ability-related parameters include the swimming energy consumption index x and the swimming energy consumption coefficient. Critical swimming speed U crit Reference temperature T ref The parameters include temperature correction parameter τ, standard metabolic scaling factor α, and body mass allotropy index β; the feeding-related parameters include the initial value of predation response distance. , No. Empirical coefficient of similar bait , No. Flow rate inflection parameters of bait And the specific dynamic action coefficient SDA.

[0028] Step S2: Conduct in-situ surveys during the fish breeding season in the target river section; construct a fish breeding ecological scenario that represents the average ecological level during the fish breeding season through statistical calculations, including the mean values ​​of individual fish characteristics, environmental characteristics, and food characteristics; and obtain the measured average change in individual fish energy per unit time.

[0029] In this step, the mean individual characteristics of the fish include the mean body mass. and average body length The average environmental characteristics include the average water temperature. and the average range of water temperature changes per unit time The average characteristics of the bait include the first... Average feed concentration of similar baits , No. Mean energy density of similar baits and the Mean coefficient of variation of feed concentration for similar baits , , This represents the quantity and variety of food consumed by the target fish species; based on this, the fish reproductive ecological scenario is represented as: ;

[0030] The measured average change in individual fish energy per unit time is expressed as: , which is the measured average change in the growth energy or reproductive energy of an individual fish per unit time.

[0031] It should be noted that the present invention does not limit the specific method of conducting in-situ surveys, as long as it can obtain the fish reproductive ecological scenario that characterizes the average level of fish reproductive period and the measured average change in individual fish energy per unit time during the fish reproductive period.

[0032] As one implementation method, this step can be specifically implemented using steps S21 to S25:

[0033] In-situ surveys were conducted at the beginning and end of the fish breeding season in the target river section. For example, one or more breeding season monitoring sections or habitat survey units were set up in the target river section to collect samples of the target fish and measure the body weight W, body length L, and visceral body weight W of each fish. b Gonadal quality W g Body tissue energy density ρ b and gonadal energy density ρ g Individual fish data were collected. Samples of drifting food, benthic food, or attached algae were collected simultaneously to determine or estimate food concentration, food energy density, and coefficient of variation of food concentration. In addition, water temperature T was continuously monitored during the fish breeding season to obtain water temperature sequences.

[0034] Based on the initial and final in-situ survey results and water temperature sequences, a fish reproductive ecological scenario was constructed and the measured average change in individual fish energy per unit time was obtained.

[0035] The specific method is as follows:

[0036] Step S21: Conduct in-situ surveys at the beginning and end of the fish breeding season in the target river section to obtain the mean values ​​of measured data of multiple target fish individuals at the beginning, including the initial average body weight W0, the initial average body length L0, and the initial average visceral body weight W. b0 and initial average gonadal quality W g0 ; Obtain the mean values ​​of measured data for multiple target fish individuals at the final stage, including the mean body mass W1, mean body length L1, and mean visceral body mass W at the final stage. b1 and the average gonadal mass W at the end of life g1 ;

[0037] Simultaneously collect samples of each type of feed consumed by the target fish, and determine or estimate the feed concentration, feed energy density, and feed concentration variation coefficient for each type of feed; in addition, continuously monitor the water temperature T during the fish breeding season to obtain the water temperature sequence;

[0038] Step S22: Take the average of the initial average body weight W0 and the final average body weight W1 as the average body weight reflecting the average body weight level of fish during the breeding season. The average body length L0 at the beginning and L1 at the end are taken as the average body length reflecting the average body length of fish during the breeding season. ;

[0039] Step S23: Take the average value of the water temperature series continuously monitored during the fish breeding season as the average water temperature value reflecting the average water temperature level during the fish breeding season. The average value of water temperature variation per unit time during the fish breeding season is taken as the average water temperature variation range per unit time, reflecting the average level of water temperature variation per unit time during the fish breeding season. ;

[0040] Step S24, for the initial and final stages of the first... The average feed concentration for each type of bait was taken, and the values ​​were compared between the initial and final stages. The average energy density of the feed for this type of bait is taken, and the values ​​are compared between the initial and final stages. The mean value of the coefficient of variation of feed concentration for each type of feed was used to obtain the first value reflecting the characteristics of the corresponding feed elements during the fish breeding season. Average feed concentration of similar baits , No. Mean energy density of similar baits and the Mean coefficient of variation of feed concentration for similar baits ;

[0041] Step S25: Based on the change in individual fish growth energy or reproductive energy at the end of the period relative to that at the beginning of the period, divide by the number of fish per unit time Δt during the reproductive period to obtain the measured average change in individual fish energy per unit time. ;

[0042] If the research focuses only on reproductive energy input, and only calculates the energy consumption of the gonads based on changes in gonadal energy or the gonadal energy consumption before and after egg laying, then... If the research focuses on both the growth and reproductive inputs of body tissues, then the total energy change of body tissues and gonads is used for calculation. The formula is as follows:

[0043] (1)

[0044] (2)

[0045] (3)

[0046] in: and These represent the energy density of body tissues and the energy density of gonads, respectively. and These represent the total energy of the individual's body tissues and gonads in the initial stage and the total energy of the individual's body tissues and gonads in the final stage, respectively. and These represent the survey times at the beginning and end of the fish's breeding season, respectively.

[0047] Step S3: Construct an energy balance equation with flow velocity v as the variable and measured average change in individual fish energy per unit time as the constraint. The energy balance equation describes the net energy intake per unit time obtained by the difference between feeding benefits per unit time and total metabolic cost per unit time, which reaches a balance with the measured average change in individual fish energy per unit time.

[0048] As a form of expression, the energy balance equation is characterized as follows:

[0049] (4)

[0050] in: Represents the energy function of food intake; The benefit of food intake per unit of time; Represents the energy loss coefficient during defecation; Represents the energy loss coefficient during excretion; Represents a specific dynamic action coefficient Effects on the energy function of food intake The energy consumption term for the specific dynamic action obtained thereafter; Represents the total metabolic energy expenditure function. Represents the flow velocity, which is the variable to be determined. Represents water temperature; and The sum represents the total metabolic cost per unit of time.

[0051] When the target fish primarily feeds on drifting invertebrates, the feeding energy function The mechanism of drifting feeding was established and characterized as follows:

[0052] (5)

[0053] in: The model calibration coefficients represent the accessibility and connectivity of feeding in river sections. Representing the The concentration of a type of bait, including volume concentration or biomass concentration; Represents the cross-sectional area of ​​the fish's predation response; Representing the The energy density of a type of bait, i.e., the energy content per unit; Represents the time scale and unit conversion factor, used to convert the feed flux through the predator-prey response cross section per unit time into feed energy per unit time; This represents the quantity of different types of bait.

[0054] Represents the cross-sectional area of ​​the fish's predation response, which is determined by the predation response distance. Determined; predator reaction distance It is related to body length L and flow velocity v, increasing with increasing body length and decreasing with increasing flow velocity. One way to express it is as follows: , λ represents the initial value of the predator response distance determined based on the body length L, and λ represents the predator response distance velocity decay coefficient, which is used to characterize the rate at which the predator response distance decreases as the velocity v increases.

[0055] Representing the The probability of successful predation of this type of bait is given when the current velocity v is not less than the critical swimming velocity U. crit hour, Set to 0 to reflect the constraint that fish cannot stably feed or maintain their position under excessively high current speeds; The decreasing trend of flow velocity v can be characterized by an S-shaped function or an exponential decay function.

[0056] The sigmoid function is characterized as follows:

[0057] (6)

[0058] The exponential decay function is characterized as:

[0059] (7)

[0060] in: Representing the Empirical coefficients for similar baits Representing the Flow velocity inflection parameters for bait-like materials.

[0061] When the target fish primarily feeds on benthic organisms or attached algae, i.e., for benthic-feeding fish or algae-feeding fish, the feeding energy function... The empirical function can be constructed using a hump-shaped empirical function, a monotonically increasing empirical function, or a food availability function. Its parameters are obtained by fitting the amount of food consumed or the energy intake rate per unit time under different flow velocities to characterize the effect of flow velocity on food renewal, feeding efficiency, and benthic attachment stability.

[0062] As a form of expression, the total metabolic energy expenditure function It includes standard metabolic energy expenditure and swimming-active metabolic energy expenditure, and incorporates corrections for body mass W and water temperature T, characterized as follows:

[0063] (8)

[0064] in: Represents standard metabolic energy consumption. α represents the standard metabolic scale coefficient, which controls the overall scale or baseline level of standard metabolic energy consumption; β represents the body mass allotropic index, which controls the power function rate of change of standard metabolic energy consumption with increasing body mass W. This represents the active metabolic energy expenditure of swimming. , This represents the energy consumption coefficient of swimming.

[0065] In addition, total metabolic energy consumption function Standard metabolic energy consumption can also be used. Maximum metabolic rate The normalized expression for the critical swimming speed:

[0066]

[0067] In this embodiment, the flow velocity v is used as a variable that simultaneously affects the food intake gain per unit time and the metabolic energy expenditure of swimming activity.

[0068] Step S4: Using the target fish bioenergetics parameters and the fish reproductive ecological scenario as input parameters, the energy balance equation is solved inversely within a preset flow velocity domain. This inversely deduces two flow velocity values ​​when the net energy intake per unit time of the target fish and the measured average change in individual fish energy per unit time reach equilibrium. Both flow velocity values ​​represent flow velocity values ​​that match the measured average change in individual fish energy per unit time. A net energy intake relationship curve is constructed, showing the relationship between net energy intake per unit time and flow velocity. A comprehensive analysis of the net energy intake relationship curve and the two matched flow velocity values ​​yields a set of flow velocity analysis results at the individual scale during the fish reproductive period, including the suitable flow velocity range for individuals, the optimal flow velocity v* for individuals, and the lower limit flow velocity for individual ecological tolerance.

[0069] This step can be implemented using steps S41 to S42:

[0070] Step S41: Construct the objective function based on the energy budget balance equation. :

[0071] (9)

[0072] Step S42, preset the flow velocity definition domain , Representing the upper limit of the velocity domain, the objective function is solved using an inverse algorithm. To solve the problem, for example, a grid search is performed in the velocity domain with an initial step size of 0.01 m / s, and the solution is refined using a bisection method within the candidate extremum interval. The two roots equal to 0 yield the first flow velocity value when the equilibrium state is reached. Second flow rate value Simultaneously, within the velocity domain, a characterization of net energy intake per unit time as a function of velocity is constructed. Changing net energy intake curve :

[0073] (10)

[0074] Please see here. Figure 2 In the net energy intake relationship curve In this study, the flow rate corresponding to the individual with the largest net energy intake per unit time is taken as the individual's optimal flow rate v*.

[0075] First flow velocity value Second flow rate value All represent flow velocity values ​​that match the measured average change in energy of individual fish per unit time, and satisfy the relationship... , the first flow rate value Second flow rate value Using the lower and upper limits of the individual's suitable flow velocity range as the respective lower and upper limits, the individual's suitable flow velocity range is constructed. Within the individual's suitable flow velocity range NE(v)≥G obs Characterizing flow velocity Within the individual's suitable flow velocity range At that time, the physiological responses of the target fish were all better than or equal to the first flow velocity value. Second flow rate value The target fish physiological response at that time, i.e., better than or equal to the measured average change in individual fish energy per unit time. ;

[0076] The flow velocity range corresponding to NE(v)≥0 is used as the ecological tolerance flow velocity range for maintaining individual survival or basic activities, and the lower limit of the ecological tolerance flow velocity range is used as the lower limit flow velocity for individual ecological tolerance.

[0077] It should be noted that this invention does not address the objective function. The solution method is limited. For example, the reverse solution can be solved using the bisection method, Newton's method, secant method, grid search, or a combination thereof.

[0078] Step S5: Select uncertain parameters from the input parameters, perform uncertainty sampling on the uncertain parameters, generate multiple sets of input parameter samples, and execute step S4 for each set of input parameter samples to obtain a set of individual optimal flow velocities v*; determine the population-scale flow velocity analysis results based on the set of individual optimal flow velocities v*.

[0079] This step can be implemented using steps S51 to S54:

[0080] Step S51: Select an uncertainty parameter from the input parameters to quantify the uncertainty including individual differences in fish sampling, temperature fluctuations, feed fluctuations, model empirical coefficients, and survey errors;

[0081] Uncertain parameters may include water temperature, food concentration, food energy density, body mass, and initial value of predation response distance. Energy loss coefficient during excretion, energy loss coefficient during defecation, specific dynamic action coefficient, critical swimming speed, and the first Empirical coefficient of similar bait , No. Flow rate inflection parameters of bait One or more of the following;

[0082] For each uncertain parameter, its probability distribution type is determined based on prior knowledge or historical data, including normal distribution, uniform distribution and log-normal distribution, and the probability distribution is assigned a value based on the value of the corresponding parameter in the target fish bioenergetics parameter data or the fish reproductive ecological scenario to obtain a specific probability distribution;

[0083] Step S52: Sample according to the specific probability distribution of each uncertain parameter to generate multiple sets of input parameter samples. Step S4 is executed for each set of input parameter samples to obtain a set of individual optimal flow velocities v*.

[0084] It should be noted that when performing uncertain sampling in this step, the uncertain sampling can be Monte Carlo random sampling, and Latin hypercube sampling, Sobol low-difference sequence sampling, or Bootstrap resampling can be selected to generate multiple sets of parameter samples, thereby constructing a suitable flow velocity range or quantile range.

[0085] Step S53: Based on the set of individual optimal flow velocities v*, determine the distribution peak, mean, median, preset quantile interval or confidence interval to determine the population-scale flow velocity analysis result set, including one or more of the population-scale optimal flow velocity, robust suitable flow velocity interval, extended suitable flow velocity interval and ecological tolerance lower limit flow velocity.

[0086] For example, the 10th to 90th percentiles are used as the robust and suitable flow velocity range at the population scale, the 5th percentile is used as the lower limit of ecological conservatism at the population scale, and the median is used as the recommended optimal flow velocity at the population scale.

[0087] Step S54: The input parameter samples and the corresponding population-scale velocity analysis results form a sample-result relationship. A global sensitivity analysis is performed on the sample-result relationship of all groups to identify key parameters that affect the suitable velocity inversion results, so as to guide subsequent investigations and parameter calibration.

[0088] When performing global sensitivity analysis in this step, sensitivity analysis can be based on variance decomposition, regression coefficients, permutation importance, or Sobol index to determine the environmental parameters, fish physiological parameters, or empirical coefficients that have the greatest impact on the individual optimal flow velocity v*.

[0089] Step S6: Map the population-scale flow velocity analysis results set into ecological management indicators, and output at least the population-scale suitable flow velocity range, ecological tolerance lower limit, and corresponding ecological flow recommendations during the fish breeding season.

[0090] This step may specifically include the following implementation methods:

[0091] When a two-dimensional or three-dimensional hydrodynamic model of the target river section is available, the area-weighted average velocity, median velocity, or quantile velocity within the target spawning habitat area are obtained using the two-dimensional or three-dimensional hydrodynamic model. Based on this, an ecological flow that satisfies the requirement that the flow velocity is within the appropriate velocity range at the population scale is searched in the candidate discharge or flow condition set.

[0092] For example, under a set of candidate ecological flow or discharge conditions, the spatial distribution of flow velocity within the target spawning habitat is simulated, the area-weighted average flow velocity, median flow velocity, quantile flow velocity or suitable area ratio is calculated, and the flow range that satisfies the flow velocity being within the suitable flow velocity range at the population scale is searched.

[0093] In the absence of two-dimensional or three-dimensional hydrodynamic models, the boundary velocity threshold of the population-scale suitable velocity range can be mapped to the flow threshold using the Manning formula, measured water level-discharge relationship, or cross-sectional hydrodynamic relationship, and the corresponding ecological flow suggested range can be output.

[0094] When the target fish species are multiple species, after obtaining the population-scale suitable flow velocity range for each species, the intersection of the population-scale suitable flow velocity ranges is taken as the common suitable range according to the management objectives, or the maximum value of the ecological tolerance lower limit flow velocity of each species is taken as the engineering control lower limit flow velocity according to the principle of ecological conservatism.

[0095] The ecological management indicators include one or more of the following: ecological flow lower limit, suitable ecological flow range, suitable flow velocity compliance rate, intraday flow change limit, interday flow change limit, minimum duration constraint, suitable flow velocity compliance rate indicator, and ecological scheduling early warning indicator.

[0096] The present invention has the following advantages:

[0097] First, this invention uses flow velocity as a common control variable for feeding benefits and swimming energy consumption, and inversely infers the suitable flow velocity for fish breeding season through energy balance, which can explain the fish's response to flow velocity from the perspective of physiological energy mechanisms.

[0098] Second, this invention uses measured changes in growth or reproductive energy at the beginning and end of the breeding season as constraints, and does not rely solely on the frequency of fish occurrence, which can reduce the need for large-scale, multi-flow, and multi-season field occurrence frequency surveys.

[0099] Third, this invention introduces boundary conditions such as water temperature, food abundance, fish size, and metabolic parameters to update the appropriate flow velocity inversion results under different years, different river sections, and different body structures, and has good transferability.

[0100] Fourth, by sampling and propagating parameter uncertainties using Monte Carlo, Latin hypercube, or Sobol sequences, this invention can output suitable flow velocity ranges, confidence intervals, and ecological tolerance lower limits, thereby supporting risk management in ecological scheduling.

[0101] Fifth, this invention can be coupled with two-dimensional or three-dimensional hydrodynamic models, Manning's formula, or cross-sectional hydraulic relationships to convert physiologically suitable flow velocity thresholds into executable ecological flow, discharge ranges, and scheduling constraints, thus having good practicality.

[0102] Example 2: Inversion of suitable current velocity during the breeding season of drifting-feeding fish

[0103] This embodiment uses river-drifting, feeding schizothorax fish as the target fish to illustrate the specific implementation process of this invention in determining the appropriate flow velocity threshold for the breeding season at the river section scale. The target river section is 3.2 km long and 45 m to 85 m wide, with the fish breeding season from late April to mid-June. According to historical surveys, the adult target fish are mostly 160 mm to 260 mm in length and 80 g to 260 g in weight, primarily feeding on drifting aquatic insect larvae and small crustaceans.

[0104] I. Survey Design and Data Acquisition

[0105] Four survey sections were set up in the target river section, and samples of the target fish were collected at the beginning and end of the breeding season. t0 and t1 represent the survey times at the beginning and end of the fish breeding season, respectively. In this embodiment, the unit of time is taken on a daily scale, and the number of fish per unit of time Δt during the breeding season is 42 days. Thirty fish were collected each time. After removing immature and damaged individuals, 24 samples with similar body length, body weight, and maturity were selected for energy calculation.

[0106] In this embodiment, the data for the initial stage of the reproductive period are as follows: the initial average body length L0 is 212 mm, the initial average body weight W0 is 168 g, and the initial average body weight after evisceration W... b0 The initial average gonadal weight was 145 g. g0 The average body length (L1) was 13.8 g; the data at the end of the reproductive period are as follows: the average body length (L1) at the end of the period was 216 mm, the average body weight (W1) at the end of the period was 176 g, and the average body weight (W after visceration) at the end of the period was 13.8 g. b1 The average gonadal mass at the end of the period was 150 g. g1 The weight was 19.6 g. The average water temperature during the breeding season was 12.4℃, with a daily average water temperature variation range of 9.8℃ to 15.1℃.

[0107] Simultaneously, drifting bait was collected at four cross-sections using drifting nets. Sample identification and biomass conversion revealed that the drifting bait mainly consisted of mayfly larvae, chironomid larvae, and trichome larvae. After conversion to water biomass concentration, the average concentrations of the three types of bait were 0.34 mg / m³. 3 0.51 mg / m 3 and 0.18 mg / m 3 The corresponding feed energy densities were 21.5 J / mg, 20.2 J / mg, and 22.8 J / mg, respectively. Based on the repeated measurements of the samples, the coefficient of variation of the feed concentration was taken as 0.25 to 0.35.

[0108] To calculate the measured energy change, the body tissue energy density ρ b Take 5.6 kJ / g, gonadal energy density ρ g Take 6.4 kJ / g. According to the formula... and We can obtain:

[0109] =145×5.6+13.8×6.4=900.32 kJ

[0110] =150×5.6+19.6×6.4=965.44 kJ

[0111] therefore, =1.55 kJ / d

[0112] G obs This indicates the average net energy accumulation requirement of the target fish species for body tissue growth and gonadal development during the current breeding season survey interval.

[0113] II. Parameter Library Construction

[0114] Based on metabolic experiments, swimming ability experiments, and literature parameters of similar schizothorax fish, a database of bioenergetic parameters for the target fish was established. In this embodiment, the energy loss coefficient due to defecation is... Take 0.18 as the energy loss coefficient for excretion. The specific dynamic action factor (SDA) is set to 0.07, and calculated as 0.17 of dietary energy intake. Standard metabolic items are presented in the form of body mass and temperature correction, with a reference temperature T. ref The temperature is set to 12℃, and the temperature correction parameter τ is set to 0.07. The swimming energy consumption index x is set to 2.1. The critical swimming speed U crit The value is taken as 1.05 m / s, and the parameter uncertainty range is taken as ±15%.

[0115] The predator-response distance RD(v) is expressed in the following form: Where RD0 is 0.32m and λ is 0.45.

[0116] Fish predation response cross-sectional area A react (v)=π·RD(v) 2 . No. Probability of successful predation by similar bait Using an S-shaped function: ;

[0117] For mayfly larvae, chironomid larvae, and trichomes, Take values ​​of 3.8, 3.2, and 4.3 respectively. Let's take values ​​of 0.85 m / s, 0.88 m / s, and 0.82 m / s respectively. When v ≥ U cri At that time, PC i (v)=0.

[0118] III. Construction of Energy Equations

[0119] In this embodiment, the energy function of food intake Represented as ;in, Representing the time scale and unit conversion factor, used to convert the food flux passing through the predator-prey response cross section per unit time into the energy ingested per unit time. Based on the daily effective feeding time, in this embodiment, the daily effective feeding time is taken as 9 hours, and the feeding activity reduction factor is taken as 0.62. This is the model calibration coefficient, used to describe the accessibility and connectivity of feeding in the river section. In this embodiment, it is set to 0.51.

[0120] Total metabolic energy expenditure function Represented as ;in, This represents standard metabolic energy expenditure. This indicates the metabolic energy expenditure associated with active swimming. Based on the above parameters, in this embodiment, when the average body mass... =172 g, average water temperature At 12.4℃, the calculated standard metabolic energy consumption is approximately 5.82 kJ / d; when the flow velocities v are 0.30 m / s, 0.50 m / s, 0.70 m / s, and 0.90 m / s, the active metabolic energy consumption for swimming is approximately 0.46 kJ / d, 1.11 kJ / d, 2.17 kJ / d, and 3.65 kJ / d, respectively.

[0121] The feeding benefit and the energy loss coefficient of defecation Energy loss coefficient due to excretion Energy consumption items for specific dynamic actions Substituting metabolic energy consumption into the energy balance equation: .

[0122] IV. Inverse Solution of Individual Optimal Flow Velocity

[0123] Within the preset flow velocity domain [0.05, 1.20] m / s, a grid search was performed with an initial step size of 0.01 m / s, and the solution was refined using a bisection method within the candidate extreme value interval. The calculation results show that under low flow velocity conditions, the food transport flux is insufficient, resulting in low feeding benefits; under high flow velocity conditions, although the food flux increases, the probability of successful predation decreases and swimming energy consumption rises rapidly, leading to a reduction in net energy intake; under medium flow velocity conditions, a relatively optimal balance is achieved between feeding benefits and swimming energy consumption.

[0124] For mean body mass =172 g, average body length =214 mm, average water temperature =12.4 ℃, Net energy intake relationship curve The energy intake reaches its maximum near v = 0.58 m / s, with a maximum net energy intake of approximately 3.44 kJ / d. This satisfies NE(v) ≥ G. obs The flow velocity range is 0.27 m / s to 0.71 m / s; the ecological tolerance flow velocity range for NE(v)≥0 is 0.19 m / s to 0.81 m / s. Therefore, the optimal flow velocity v* for this individual fish sample during the breeding season is 0.58 m / s, the suitable flow velocity range is 0.27 m / s to 0.71 m / s, and the lower limit of ecological tolerance is 0.19 m / s.

[0125] V. Uncertainty Sampling and Determination of Suitable Flow Velocity at the Population Scale

[0126] To quantify the impact of individual differences, food fluctuations, and parameter uncertainties on the inversion results, this embodiment employs Monte Carlo sampling for uncertainty propagation. The number of sampling iterations M is set to 10,000. Body mass W follows a normal distribution N(172, 28). 2 )g, and limited to 90 g to 260 g; water temperature T adopts a uniform distribution U(9.8, 15.1) ℃; the first Feed concentration D of type of bait i The log-normal distribution was adopted, and the coefficient of variation of feed concentration was taken from the measured sample values; the excretion energy loss coefficient F adopted a uniform distribution U(0.14, 0.22); the excretion energy loss coefficient A uniform distribution U(0.05, 0.09) was used; the initial predation response distance was... The normal distribution N(0.32, 0.04²) m was used; the critical swimming speed U critThe normal distribution N(1.05,0.12²)m / s was adopted and restricted to 0.75 m / s to 1.35 m / s.

[0127] For each set of sampled parameters, the energy balance equation is repeatedly constructed and the optimal flow velocity v* is solved in reverse. (See also...) Figure 3 The v* distribution obtained from 10,000 simulations is approximately unimodal, with a mean of 0.48 m / s, a median of 0.50 m / s, and a standard deviation of 0.11 m / s. The 5th percentile is 0.34 m / s, the 10th percentile is 0.37 m / s, the 90th percentile is 0.62 m / s, and the 95th percentile is 0.66 m / s.

[0128] Accordingly, this embodiment determines the optimal flow velocity at the population scale during the target fish's breeding season to be 0.50 m / s; the robust suitable flow velocity range is 0.37 m / s to 0.62 m / s; the extended suitable flow velocity range is 0.34 m / s to 0.66 m / s; and the lower limit of ecological tolerance is 0.19 m / s. If the ecological regulation objective leans towards conservative protection, 0.37 m / s to 0.62 m / s can be used as the ecological flow velocity control range during the breeding season; if the inflow to the target river section is low and water supply or power generation needs to be considered, a flow velocity of no less than 0.19 m / s can be used as the minimum ecological tolerance control limit, and the proportion of time for the suitable flow velocity to be met should be increased.

[0129] VI. Sensitivity Analysis

[0130] Global sensitivity analysis based on variance contribution was used to evaluate the 10,000 samples. The results showed that the first-order sensitivity index of total food biomass concentration to v* was 0.31, and the critical swimming velocity U... crit The first-order sensitivity index is 0.22, and the predation response distance is from the initial value. The first-order sensitivity index for the sample was 0.17, the first-order sensitivity index for water temperature T was 0.11, and the total for the remaining parameters was 0.19. Therefore, under the conditions of this embodiment, food abundance, swimming ability, and predation response distance are the main factors affecting the inversion results of suitable current velocity. In engineering applications, priority should be given to improving the representativeness of food sampling, supplementing the target fish swimming ability test, and performing localized calibration of the response distance parameter.

[0131] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy, characterized in that, include: Step S1: Establish a database of fish bioenergetics parameters and obtain bioenergetics parameter data of the target fish species; Step S2: Conduct in-situ surveys during the fish breeding season in the target river section; A fish reproductive ecological scenario was constructed through statistical calculations to characterize the average ecological level of fish during the breeding season, including the mean values ​​of individual fish characteristics, environmental characteristics, and food characteristics. In addition, the average measured change in energy of individual fish per unit time was obtained; Step S3: Construct an energy balance equation with flow velocity v as the variable and measured average change in individual fish energy per unit time as the constraint. The energy balance equation describes the net energy intake per unit time obtained by the difference between feeding benefits per unit time and total metabolic cost per unit time, which reaches a balance with the measured average change in individual fish energy per unit time. Step S4: Using the target fish bioenergetics parameters and the fish reproductive ecological scenario as input parameters, the energy balance equation is solved inversely within a preset flow velocity domain. This inversely deduces two flow velocity values ​​when the net energy intake per unit time of the target fish and the measured average change in individual fish energy per unit time reach equilibrium. Both flow velocity values ​​represent flow velocity values ​​that match the measured average change in individual fish energy per unit time. A net energy intake relationship curve is constructed, showing the relationship between net energy intake per unit time and flow velocity. A comprehensive analysis of the net energy intake relationship curve and the two matched flow velocity values ​​yields a set of flow velocity analysis results at the individual scale during the fish reproductive period, including the suitable flow velocity range for individuals, the optimal flow velocity v* for individuals, and the lower limit flow velocity for individual ecological tolerance. Step S5: Select uncertain parameters from the input parameters and perform uncertainty sampling to generate multiple sets of input parameter samples. Step S4 is executed for each set of input parameter samples to obtain a set of individual optimal flow velocities v*. Based on the set of individual optimal flow velocities v*, determine the population-scale flow velocity analysis result set. Step S6: Map the population-scale flow velocity analysis results set into ecological management indicators, and output at least the population-scale suitable flow velocity range, ecological tolerance lower limit, and corresponding ecological flow recommendations during the fish breeding season.

2. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 1, characterized in that, The method for establishing the fish bioenergetic parameter database is as follows: the fish bioenergetic parameter database is established through literature retrieval, indoor metabolic experiments, swimming ability experiments, feeding experiments, historical ecological survey data, or parameter migration of similar species; the fish bioenergetic parameter database is indexed according to fish species, body length, body weight, water temperature, feeding type, and reproductive stage, and is used for automatic retrieval under different individual fish sample conditions; Among them, fish bioenergetics parameters include metabolic parameters, swimming ability parameters, and feeding parameters; the metabolic parameters include the energy loss coefficient due to defecation. and excretion energy loss coefficient The swimming ability-related parameters include the swimming energy consumption index x and the swimming energy consumption coefficient. Critical swimming speed U crit Reference temperature T ref The parameters include temperature correction parameter τ, standard metabolic scaling factor α, and body mass allotropy index β; the feeding-related parameters include the initial value of predation response distance. , No. Empirical coefficient of similar bait , No. Flow rate inflection parameters of bait And the specific dynamic action coefficient SDA.

3. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 1, characterized in that, The mean individual characteristics of the fish include the mean body weight. and average body length The average environmental characteristics include the average water temperature. and the average range of water temperature changes per unit time The average characteristics of the bait include the first... Average feed concentration of similar baits , No. Mean energy density of similar baits and the Mean coefficient of variation of feed concentration for similar baits , , This represents the quantity and variety of food consumed by the target fish species; based on this, the fish reproductive ecological scenario is represented as: ; The measured average change in individual fish energy per unit time is expressed as: , which is the measured average change in the growth energy or reproductive energy of an individual fish per unit time.

4. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 3, characterized in that, Step S2 includes: Step S21: Conduct in-situ surveys at the beginning and end of the fish breeding season in the target river section to obtain the mean values ​​of measured data of multiple target fish individuals at the beginning, including the initial average body weight W0, the initial average body length L0, and the initial average visceral body weight W. b0 and initial average gonadal quality W g0 ; Obtain the mean values ​​of measured data for multiple target fish individuals at the final stage, including the mean body mass W1, mean body length L1, and mean visceral body mass W at the final stage. b1 and the average gonadal mass W at the end of life g1 ; Simultaneously collect samples of each type of feed consumed by the target fish, and determine or estimate the feed concentration, feed energy density, and feed concentration variation coefficient for each type of feed; in addition, continuously monitor the water temperature T during the fish breeding season to obtain the water temperature sequence; Step S22: Take the average of the initial average body weight W0 and the final average body weight W1 as the average body weight reflecting the average body weight level of fish during the breeding season. The average body length L0 at the beginning and L1 at the end are taken as the average body length reflecting the average body length of fish during the breeding season. ; Step S23: Take the average value of the water temperature series continuously monitored during the fish breeding season as the average water temperature value reflecting the average water temperature level during the fish breeding season. The average value of water temperature variation per unit time during the fish breeding season is taken as the average water temperature variation range per unit time, reflecting the average level of water temperature variation per unit time during the fish breeding season. ; Step S24, for the initial and final stages of the first... The average feed concentration for each type of bait was taken, and the values ​​were compared between the initial and final stages. The average energy density of the feed for this type of bait is taken, and the values ​​are compared between the initial and final stages. The mean value of the coefficient of variation of feed concentration for each type of feed was used to obtain the first value reflecting the characteristics of the corresponding feed elements during the fish breeding season. Average feed concentration of similar baits , No. Mean energy density of similar baits and the Mean coefficient of variation of feed concentration for similar baits ; Step S25: Based on the change in individual fish growth energy or reproductive energy at the end of the period relative to that at the beginning of the period, divide by the number of fish per unit time Δt during the reproductive period to obtain the measured average change in individual fish energy per unit time. ; If the research focuses only on reproductive energy input, and only calculates the energy consumption of the gonads based on changes in gonadal energy or the gonadal energy consumption before and after egg laying, then... If the research focuses on both the growth and reproductive inputs of body tissues, then the total energy change of body tissues and gonads is used for calculation. The formula is as follows: （1） （2） （3） in: and These represent the energy density of body tissues and the energy density of gonads, respectively. and These represent the total energy of the individual's body tissues and gonads in the initial stage and the total energy of the individual's body tissues and gonads in the final stage, respectively. and These represent the survey times at the beginning and end of the fish's breeding season, respectively.

5. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 3, characterized in that, The energy balance equation is characterized as follows: （4） in: Represents the energy function of food intake; The benefit of food intake per unit of time; Represents the energy loss coefficient during defecation; Represents the energy loss coefficient during excretion; Represents a specific dynamic action coefficient Effects on the energy function of food intake The energy consumption term for the specific dynamic action obtained thereafter; Represents the total metabolic energy expenditure function. Represents flow rate, Represents water temperature; and The sum represents the total metabolic cost per unit of time.

6. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 5, characterized in that, When the target fish primarily feeds on drifting invertebrates, the feeding energy function The mechanism of drifting feeding was established and characterized as follows: （5） in: The model calibration coefficients represent the accessibility and connectivity of feeding in river sections. Representing the The concentration of a type of bait, including volume concentration or biomass concentration; Represents the cross-sectional area of ​​the fish's predation response; Representing the The energy density of a type of bait, i.e., the energy content per unit; Represents the time scale and unit conversion factor, used to convert the feed flux through the predator-prey response cross section per unit time into feed energy per unit time; This represents the quantity of different types of bait. Represents the cross-sectional area of ​​the fish's predation response, which is determined by the predation response distance. Determined; predator reaction distance It is related to body length L and flow velocity v, increasing with increasing body length and decreasing with increasing flow velocity. , λ represents the initial value of the predator response distance determined based on the body length L, and λ represents the predator response distance velocity decay coefficient, which is used to characterize the rate at which the predator response distance decreases as the velocity v increases. Representing the The probability of successful predation of this type of bait is given when the current velocity v is not less than the critical swimming velocity U. crit hour, Set to 0; The decreasing trend of flow velocity v with increasing velocity v is characterized by an sigmoid function or an exponential decay function. The sigmoid function is characterized as follows: （6） The exponential decay function is characterized as: （7） in: Representing the Empirical coefficients for similar baits Representing the Flow velocity inflection parameters for bait-like materials; When the target fish primarily feeds on benthic organisms or attached algae, i.e., for benthic-feeding fish or algae-feeding fish, the feeding energy function... The empirical functions were constructed using a hump-shaped empirical function, a monotonically increasing empirical function, or a food availability function. The parameters of these functions were obtained by fitting the feed intake or energy intake rate per unit time under different flow velocities to characterize the effects of flow velocity on food renewal, feeding efficiency, and benthic attachment stability.

7. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 5, characterized in that, Total metabolic energy expenditure function It includes standard metabolic energy expenditure and swimming-active metabolic energy expenditure, and incorporates corrections for body mass W and water temperature T, characterized as follows: （8） in: Represents standard metabolic energy consumption. , β represents the standard metabolic scale coefficient, which controls the overall scale or benchmark level of standard metabolic energy consumption, and β represents the body mass allotropic index, which controls the power function rate of change of standard metabolic energy consumption with increasing body mass W. This represents the active metabolic energy expenditure of swimming. , This represents the energy consumption coefficient of swimming.

8. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 5, characterized in that, Step S4 includes: Step S41: Construct the objective function based on the energy budget balance equation. : （9） Step S42, preset the flow velocity definition domain , Representing the upper limit of the velocity domain, the objective function is solved using an inverse algorithm. Solve and search The two roots equal to 0 yield the first flow velocity value when the equilibrium state is reached. Second flow rate value Simultaneously, within the velocity domain, a characterization of net energy intake per unit time as a function of velocity is constructed. Changing net energy intake curve : （10） In the net energy intake relationship curve In this study, the flow rate corresponding to the individual with the largest net energy intake per unit time is taken as the individual's optimal flow rate v*. First flow velocity value Second flow rate value All represent flow velocity values ​​that match the measured average change in energy of individual fish per unit time, and satisfy the relationship... , the first flow rate value Second flow rate value Using the lower and upper limits of the individual's suitable flow velocity range as the respective lower and upper limits, the individual's suitable flow velocity range is constructed. Within the individual's suitable flow velocity range NE(v)≥G obs Characterizing flow velocity Within the individual's suitable flow velocity range At that time, the physiological responses of the target fish were all better than or equal to the first flow velocity value. Second flow rate value The target fish physiological response at that time, i.e., better than or equal to the measured average change in individual fish energy per unit time. ; The flow velocity range corresponding to NE(v)≥0 is used as the ecological tolerance flow velocity range for maintaining individual survival or basic activities, and the lower limit of the ecological tolerance flow velocity range is used as the lower limit flow velocity for individual ecological tolerance.

9. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 1, characterized in that, Step S5 includes: Step S51: Select an uncertainty parameter from the input parameters to quantify the uncertainty including individual differences in fish sampling, temperature fluctuations, feed fluctuations, model empirical coefficients, and survey errors; For each uncertain parameter, its probability distribution type is determined based on prior knowledge or historical data, including normal distribution, uniform distribution and log-normal distribution, and the probability distribution is assigned a value based on the value of the corresponding parameter in the target fish bioenergetics parameter data or the fish reproductive ecological scenario to obtain a specific probability distribution; Step S52: Sample according to the specific probability distribution of each uncertain parameter to generate multiple sets of input parameter samples. Step S4 is executed for each set of input parameter samples to obtain a set of individual optimal flow velocities v*. Step S53: Based on the set of individual optimal flow velocities v*, determine the distribution peak, mean, median, preset quantile interval or confidence interval to determine the population-scale flow velocity analysis result set, including one or more of the population-scale optimal flow velocity, robust suitable flow velocity interval, extended suitable flow velocity interval and ecological tolerance lower limit flow velocity. Step S54: The input parameter samples and the corresponding population-scale velocity analysis results form a sample-result relationship. A global sensitivity analysis is performed on the sample-result relationship of all groups to identify key parameters that affect the suitable velocity inversion results, so as to guide the survey and parameter calibration.

10. The method for determining the suitable flow velocity during the fish breeding season based on the reverse balance of fish metabolic energy according to claim 1, characterized in that, Step S6 includes: When a two-dimensional or three-dimensional hydrodynamic model of the target river section is available, the area-weighted average velocity, median velocity, or quantile velocity within the target spawning habitat area are obtained using the two-dimensional or three-dimensional hydrodynamic model. Based on this, an ecological flow that satisfies the requirement that the flow velocity is within the appropriate velocity range at the population scale is searched in the candidate discharge or flow condition set. In the absence of two-dimensional or three-dimensional hydrodynamic models, the boundary velocity threshold of the population-scale suitable velocity range is mapped to the flow threshold using the Manning formula, measured water level-discharge relationship, or cross-sectional hydrodynamic relationship, and the corresponding ecological flow suggested range is output. When the target fish species are multiple species, after obtaining the population-scale suitable flow velocity range for each species, the intersection of the population-scale suitable flow velocity ranges is taken as the common suitable range according to the management objectives, or the maximum value of the ecological tolerance lower limit flow velocity of each species is taken as the engineering control lower limit flow velocity according to the principle of ecological conservatism. The ecological management indicators include one or more of the following: ecological flow lower limit, suitable ecological flow range, suitable flow velocity compliance rate, intraday flow change limit, interday flow change limit, minimum duration constraint, suitable flow velocity compliance rate indicator, and ecological scheduling early warning indicator.

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