A method for optimizing parameters of a nested watershed hydrological model

Abstract

The present invention discloses a method for optimizing parameters of a nested watershed hydrological model, comprising the following steps: determining a research area of the watershed, stratifying the research area by elevation within the research area to obtain n sub-regions at different elevation levels; constructing a hydrological model equation for each sub-region at an elevation level; constructing a vector of dynamic parameters, performing crossover and mutation on the dynamic parameters within the vector using a fitness function, and screening for the optimal offspring individual vector; starting from the sub-region at the highest elevation level and sequentially optimizing the dynamic parameters of the hydrological model equation for each sub-region at an elevation level from top to bottom until the optimization of the dynamic parameters of the hydrological model equation for the research area is completed. The present invention proposes a method for optimizing parameters of a nested watershed hydrological model, which greatly shortens the optimization time required for watershed parameter optimization and effectively improves the efficiency of parameter optimization.

Description

Technical Field

[0001] The present invention relates to the field of hydrological research, and particularly relates to a method for optimizing parameters of a nested basin hydrological model. Background Art

[0002] In the process of hydrological research, it is crucial to use a hydrological model to predict hydrological data. The optimization of model parameters is a key content in hydrological simulation research and application, and the quality of model parameters directly affects the accuracy of model calculation results. How to make full use of existing observation data and improve the optimization efficiency has always been an important research direction. In most current studies, parameter calibration only uses data from outlet stations for parameter calibration, making it difficult to ensure the accuracy of hydrological forecasts. For basins with complex nested structures, existing methods often have difficulty accurately considering the influence of the interaction between different levels of basins on parameters, resulting in low accuracy of model simulation results, low efficiency in dealing with a large number of parameters, and being prone to falling into local optimal solutions, etc. Summary of the Invention

[0003] In view of the above deficiencies of the prior art, the present invention provides a method for optimizing parameters of a nested basin hydrological model.

[0004] To achieve the above invention objective, the technical solution adopted by the present invention is as follows:

[0005] Provide a method for optimizing parameters of a nested basin hydrological model, which includes the following steps:

[0006] S1: Determine the research area of the basin, and use elevation to stratify the research area within the research area to obtain n sub-regions with different elevation levels;

[0007] S2: Construct a hydrological model equation for each sub-region with an elevation level;

[0008] S3: Extract the dynamic parameters that affect the calculation results of the hydrological model equation, construct a vector about the dynamic parameters, perform crossover and mutation on the dynamic parameters in the vector using a fitness function, screen the optimal offspring individual vector, use the individuals within the optimal offspring individual vector as the optimized dynamic parameters, and output the optimized dynamic parameters to update the hydrological model equation;

[0009] S4: According to the n sub-regions with different elevation levels divided within the research area, loop and execute step S3, starting from the sub-region with the highest elevation level, optimize the dynamic parameters of the hydrological model equation for each sub-region with an elevation level from top to bottom in sequence until the dynamic parameters of the hydrological model equation for the research area are optimized.

[0010] Further, step S1 includes: determining the research area of the basin, and obtaining the elevation range [h min , h max, set the number n of elevation level sub-region divisions, and calculate the elevation of each elevation level sub-region

[0011] Further, the hydrological model equation for each elevation level sub-region in step S2 is:

[0012]

[0013] where i is the number of the elevation level sub-region, t is the statistical moment of hydrological data, V i (t) is the water storage at time t, P i (t) is the precipitation input at time t, E i (t) is the evaporation at time t, Qout,i(t) is the outflow at time t, j is the inflow path, Q in,j (t) is the inflow at time t, J i is the number of inflow paths, P 0,i (t) is the direct precipitation, α i is the precipitation distribution coefficient, k is the distribution path of the previous elevation level sub-region, K is the total amount of distribution paths, P k (t) is the outflow of the distribution path k at time t, αk is the distribution coefficient of the previous elevation level sub-region, ΔR i is the radiation value suffered, ρ is the air density, c is the specific heat at constant pressure of air, e 1 is the saturated water vapor pressure, e 0 is the actual water vapor pressure, Δk is the slope of the saturated water vapor pressure - temperature curve, r′ is the air resistance, r 0 is the surface resistance, γ is the resistance coefficient, β i is the influence coefficient of vegetation, n i is the Manning roughness coefficient, A i is the cross-sectional area of flow, R i is the hydraulic radius, S i is the slope of the basin water surface.

[0014] Further, step S3 includes:

[0015] S31: Extract the dynamic parameters that affect the calculation results of the hydrological model equation. The dynamic parameters include the precipitation distribution coefficient α i , the distribution coefficient α k , the slope Δk, the resistance coefficient γ, the influence coefficient β i ; Construct a vector X about the dynamic parameters. The number of elements m in the vector X is 5;

[0016] S32: According to the water storage V(t,X) calculated by the hydrological model equation determined by the elements in the vector X and the actual water storage V at time t in the elevation level sub-region 0(t) Construct a fitness function;

[0017]

[0018] Among them, F(X) is the fitness value calculated based on the vector X, and T is the basin hydrological observation period; the fitness value characterizes the accuracy in the genetic iteration process of dynamic parameters and is used to evaluate the adaptability of the genetic iteration process;

[0019] S33: During the observation period, according to the historical water storage observations and calculation results, construct any two individual vectors of the elements in the vector X The observation times of the two individual vectors are different, and the individuals in any two individual vectors are used as two different parents. is the m-th dynamic parameter in the first parent. is the m-th dynamic parameter in the second parent;

[0020] S34: Determine the crossover point u within the two individual vectors to obtain the crossed offspring individual vectors;

[0021]

[0022] Among them, is the k-th individual in the first parent, and k is the crossover point. is the k-th individual in the second parent;

[0023] S35: Set the range for random mutation of each individual within the offspring individual vectors, and randomly select two corresponding offspring individuals within the two offspring individual vectors x′ 1 and x′ 2 to perform random mutation within the range of random mutation. Substitute the two mutated offspring individual vectors x′ 1 and x′ 2 into the hydrological model equation respectively to calculate the fitness value, and calculate the acceptance probability p of the mutated offspring individual vectors x′ 1 and x′ 2 ;

[0024]

[0025] Among them, w is the mutation iteration coefficient. The more mutation iterations, the smaller the mutation iteration coefficient.

[0026] When p = 1, select the offspring individual vector corresponding to the maximum fitness value among F(x′ 1 ) and F(x′ 2 ) as the optimal offspring individual vector;

[0027] When p ≠ 1, set the acceptance probability threshold p 阈值 ;

[0028] If p ≤ p 阈值 , then take the corresponding offspring individual vector as the optimal offspring individual vector;

[0029] Otherwise, re - mutate the offspring individuals within the offspring individual vectors x′ 1 、x′ 2 until the optimal offspring individual vector is output;

[0030] S36: The individuals within the optimal offspring individual vector are used as the optimized dynamic parameters, and the optimized dynamic parameters are output to update the hydrological model equation.

[0031] The beneficial effects of the present invention are as follows: The present invention proposes a nested - type watershed hydrological model parameter optimization method, which hierarchically processes the research area of the nested - type watershed to form multiple sub - regions with different elevations. Corresponding hydrological model equations are established for each layer of watershed sub - regions, and the dynamic parameters of the model are iteratively optimized through an optimization algorithm; effectively overcoming the deficiency that the existing hydrological model parameter optimization only uses the observed data of the hydrological station at the watershed outlet, making full use of the existing effective historical measured data, obtaining hydrological parameters that can better represent the hydrological characteristics of the watershed. The results simulated by these parameters can better represent the hydrological processes occurring within the watershed, which has important practical significance. Greatly shortening the optimization time required for watershed parameter optimization and effectively improving the efficiency of parameter optimization. Description of the Drawings

[0032] Figure 1 It is a flow chart of a nested - type watershed hydrological model parameter optimization method. Specific Embodiments

[0033] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0034] As Figure 1 shown, a nested - type watershed hydrological model parameter optimization method includes the following steps:

[0035] S1: Determine the research area of the watershed, and hierarchically divide the research area within the research area using elevation to obtain sub - regions at different elevation levels. Step S1 specifically includes: Determine the research area of the watershed, obtain the elevation range [h min , h max of the research area, set the number n of sub - region divisions at elevation levels, and calculate the elevation of each sub - region at elevation levels This layering method can reflect the differences in different altitude regions during the hydrological change process because altitude affects processes such as precipitation and runoff. In high-altitude areas, there may be more diverse forms of precipitation (such as snowfall), and water flows from high altitude to low altitude under the action of gravity, with different confluence characteristics in different altitude layers.

[0036] S2: Construct the hydrological model equations for each sub-region of the altitude level;

[0037]

[0038] Among them, i is the number of the sub-region of the altitude level, t is the statistical moment of hydrological data, V i (t) is the water storage at time t, P i (t) is the precipitation input at time t, E i (t) is the evaporation at time t, Qout,i(t) is the outflow at time t, j is the inflow path, Q in,j (t) is the inflow at time t, J i is the number of inflow paths, P 0,i (t) is the direct precipitation, α i is the precipitation distribution coefficient, k is the distribution path of the previous altitude level sub-region, K is the total amount of distribution paths, P k (t) is the outflow of distribution path k at time t, αk is the distribution coefficient of the previous altitude level sub-region, ΔR i is the radiation value suffered, ρ is the air density, c is the specific heat at constant pressure of air, e 1 is the saturation water vapor pressure, e 0 is the actual water vapor pressure, Δk is the slope of the saturation water vapor pressure - temperature curve, r′ is the air resistance, r 0 is the surface resistance, γ is the resistance coefficient, β i is the influence coefficient of vegetation, n i is the Manning roughness coefficient, A i is the cross-sectional area of the water flow, R i is the hydraulic radius, S i is the slope of the water surface of the basin;

[0039] S3: Extract the dynamic parameters that affect the calculation results of the hydrological model equations. The dynamic parameters include the precipitation distribution coefficient α i 、the distribution coefficient α k 、the slope Δk, the resistance coefficient γ, the influence coefficient β i ; Construct a vector X about the dynamic parameters. The number of elements m in the vector X is 5;

[0040] S4: The water storage V(t,X) calculated according to the hydrological model equations determined by the elements in the vector X and the actual water storage V at time t in the sub-region of the altitude level0 (t) Construct a fitness function;

[0041]

[0042] Among them, F(X) is the fitness value calculated based on the vector X, and T is the basin hydrological observation period; the fitness value characterizes the accuracy in the genetic iteration process of dynamic parameters and is used to evaluate the adaptability of the genetic iteration process.

[0043] S5: During the observation period, according to the historical water storage observations and calculation results, construct any two individual vectors of the elements in the vector X The observation times of the two individual vectors are different, and the individuals in any two individual vectors are used as two different parent generations. is the m-th dynamic parameter in the first parent generation. is the m-th dynamic parameter in the second parent generation;

[0044] S6: Determine the crossover point u within the two individual vectors to obtain the crossed offspring individual vectors;

[0045]

[0046] Among them, is the k-th individual within the first parent generation, and k is the crossover point. is the k-th individual within the second parent generation;

[0047] S7: Set the range of random mutation for each individual within the offspring individual vectors, and randomly select two corresponding offspring individuals within the two offspring individual vectors x′ 1 、x′ 2 to perform random mutation within the range of random mutation, substitute the two mutated offspring individual vectors x′ 1 、x′ 2 into the hydrological model equation respectively, calculate the fitness value, and calculate the acceptance probability p of the mutated offspring individual vectors x′ 1 、x′ 2 ;

[0048]

[0049] Among them, w is the mutation iteration coefficient. The more mutation iterations, the smaller the mutation iteration coefficient.

[0050] When p = 1, select the offspring individual vector corresponding to the maximum fitness value in F(x′ 1 ) and F(x′ 2 ) as the optimal offspring individual vector;

[0051] When p ≠ 1, set the acceptance probability threshold p 阈值;

[0052] If p ≤ p 阈值 , then take the corresponding offspring individual vector as the optimal offspring individual vector;

[0053] Otherwise, re-mutate the offspring individuals within the offspring individual vectors x′ 1 , x′ 2 until the optimal offspring individual vector is output;

[0054] S8: The individuals within the optimal offspring individual vector are used as the optimized dynamic parameters, and the optimized dynamic parameters are output to update the hydrological model equation;

[0055] S9: According to the n elevation-level sub-regions divided within the study area, loop through steps S2 - S7, starting from the elevation-level sub-region with the highest elevation and optimizing the dynamic parameters of the hydrological model equation for each elevation-level sub-region from top to bottom in sequence until the dynamic parameters of the hydrological model equation for the study area are optimized.

[0056] The present invention proposes a nested watershed hydrological model parameter optimization method, which hierarchically processes the study area of the nested watershed to form multiple sub-regions with different elevations, establishes corresponding hydrological model equations for each layer of watershed sub-regions, and iteratively optimizes the dynamic parameters of the model through an optimization algorithm; effectively overcomes the deficiency that the existing hydrological model parameter optimization only uses the observed data of the watershed outlet hydrological station, makes full use of the existing effective historical measured data, obtains hydrological parameters that can better represent the watershed hydrological characteristics, and the results simulated by these parameters can better represent the hydrological processes occurring within the watershed, having important practical significance. Greatly shortens the optimization time required for watershed parameter optimization and effectively improves the efficiency of parameter optimization.

Claims

1. A nested watershed hydrological model parameter optimization method, characterized in that: The following steps are involved: S1: Determine the study area of ​​the watershed, stratify the study area using elevation within the study area, and obtain n sub-areas of different elevation levels; S2: construct the hydrological model equations for each elevation level sub-region; Among them, i is the number of the elevation level sub-area, t is the statistical time of the hydrological data, V i (t) is the water storage capacity at time t, P i (t) is the precipitation input at time t, E i (t) is the evaporation at time t, Q out,i (t) is the outflow at time t, j is the inflow path, Q in,j (t) is the inflow at time t, J i is the number of inflow pathways, P 0,i (t) is direct precipitation, α i is the precipitation distribution coefficient, k is the distribution path of the sub-region of the previous elevation level, K is the total amount of the distribution path, P k (t) is the outflow of distribution path k at time t, α k is the distribution coefficient of the sub-area of ​​the previous elevation level, ΔR i is the radiation value received, ρ is the air density, c is the specific heat of air at constant pressure, e1 is the saturated water vapor pressure, e0 is the actual water vapor pressure, Δk is the slope of the saturated water vapor pressure-temperature curve, r′ is the air resistance, r0 is the surface resistance, γ is the resistance coefficient, β i is the influence coefficient of vegetation, n i is the Manning roughness coefficient, A i is the cross-sectional area of ​​water flow, R i is the hydraulic radius, S i is the slope of the water surface in the basin; S3: Extract the dynamic parameters that affect the calculation results of the hydrological model equation, construct a vector of the dynamic parameters, use the fitness function to perform crossover mutation on the dynamic parameters in the vector, screen the optimal offspring individual vector, use the individuals in the optimal offspring individual vector as the optimized dynamic parameters, and output the optimized dynamic parameters to update the hydrological model equation; S4: According to the n elevation level sub-areas divided in the study area, step S3 is executed repeatedly, and the dynamic parameters of the hydrological model equation of each elevation level sub-area are optimized from top to bottom starting from the elevation level sub-area with the largest elevation, until the dynamic parameters of the hydrological model equation of the study area are optimized.

2. The nested watershed hydrological model parameter optimization method according to claim 1, characterized in that: The step S1 includes: determining the research area of ​​the watershed, obtaining the elevation interval [h min ,h max ], set the number n of elevation level sub-areas, and calculate the elevation of each elevation level sub-area 3. The nested watershed hydrological model parameter optimization method according to claim 2, characterized in that: The step S3 comprises: S31: Extract dynamic parameters that affect the calculation results of the hydrological model equation, including the precipitation distribution coefficient α i , distribution coefficient α k , slope Δk, resistance coefficient γ, influence coefficient β i ; Construct a vector X about dynamic parameters, the number of elements in the vector X is m=5; S32: construct a fitness function based on the water storage V(t,X) calculated by the hydrological model equation determined by the elements in the vector X and the actual water storage V0(t) at time t in the elevation level sub-area; Among them, F(X) is the fitness value calculated based on vector X, and T is the basin hydrological observation period; the fitness value represents the accuracy of the dynamic parameter genetic iteration process and is used to evaluate the adaptability of the genetic iteration process; S33: During the observation period, based on the historical water storage observation and calculation results, construct any two individual vectors of the elements in vector X The observation times of two individual vectors are different, and the individuals in any two individual vectors are regarded as two different parents. is the mth dynamic parameter in the first parent, is the mth dynamic parameter in the second parent; S34: Determine a crossover point u in the two individual vectors, and obtain a descendant individual vector after the crossover; in, is the kth individual in the first parent generation, k is the crossover point, is the kth individual in the second parent generation; S35: setting a range for random mutation of each individual in the offspring individual vector, randomly selecting two corresponding offspring individuals in the two offspring individual vectors x′1 and x′2 to perform random mutation within the range of random mutation, substituting the two offspring individual vectors x′1 and x′2 after mutation into the hydrological model equation, calculating the fitness value, and calculating the acceptance probability p of the offspring individual vectors x′1 and x′2 after mutation according to the fitness value; Among them, w is the mutation iteration coefficient. The more mutation iterations, the smaller the mutation iteration coefficient. When p = 1, the offspring individual vector corresponding to the largest fitness value in F(x′1) and F(x′2) is selected as the optimal offspring individual vector; When p≠1, set the receiving probability threshold p 阈值 ; If p≤p 阈值 , then the corresponding offspring individual vector is taken as the optimal offspring individual vector; Otherwise, re-mutate the offspring individuals in the offspring individual vectors x′1 and x′2 until the optimal offspring individual vector is output; S36: The individuals in the optimal offspring individual vector are used as optimized dynamic parameters, and the optimized dynamic parameters are output to update the hydrological model equation.

Images