A hydrological model construction method based on embedded neural network

Abstract

The application discloses a hydrological model construction method based on embedded neural networks, comprising the following steps: step 1, splitting a basic hydrological model into modules; step 2, determining the corresponding embedded neural network types of the modules; step 3, determining the corresponding embedded neural network parameters of the modules; step 4, designing a new hydrological model structure according to standard embedded neural networks; and step 5, establishing a new hydrological model according to the new hydrological model structure. The application uses embedded neural networks to replace model modules, determines network parameters through end-to-end training, explores a more optimal hydrological model structure in a combination structure of standardized networks, can break out of the basic paradigm of traditional hydrological models, and lays a foundation for flexible adjustment of the model structure; the application establishes a new hydrological model according to the newly designed hydrological model structure, interprets the model structure, has regional applicability, and improves the model simulation precision.

Description

Technical Field

[0001] This invention belongs to the field of hydrology and deep learning technology, and in particular relates to a method for constructing hydrological models based on embedded neural networks. Background Technology

[0002] Flood forecasting is a crucial technical means for flood control and disaster reduction, and hydrological models are the most widely used method in operational applications. Due to the inherent complexity of the hydrological cycle, traditional hydrological models often employ numerous empirical formulas to simplify actual physical processes. This directly leads to decreased model performance and deviations of intermediate variables from their physical meaning. For example, the soil moisture content output by the model can have a systematic deviation of up to 300 mm from the measured value. The proportion of water in runoff before an event may exceed 80%, and even with accurate flow fitting, the proportion of runoff components can vary significantly. Preferred flows with confluence velocities 1-2 orders of magnitude faster than groundwater runoff are widespread but typically not considered by the model. Accurate descriptions of more complex processes often require more parameters, which hinders the development of hydrological models.

[0003] In contrast, pure deep learning hydrological models are directly data-driven, relying almost entirely on hydrological knowledge and avoiding excessive assumptions. Their core advantage lies in their ability to simultaneously absorb data from different spatiotemporal scales and capture information about the temporal and spatial changes in model parameters. However, as a black-box model, the output of a pure deep learning model is difficult to interpret explicitly; even from the model structure and parameters, it is hard to directly obtain effective physical information. Furthermore, as a data-driven model, its performance is directly related to the quantity and quality of available data, which severely limits the application scope of pure deep learning models. To combine the advantages of hydrological models and deep learning models, some hybrid models based on embedded neural networks have been researched, but their limitations are also very obvious: they can only provide ways to improve a single module and cannot indicate the direction for optimizing the overall model structure.

[0004] Therefore, how to establish a high-performance hydrological model that is applicable to a specific region, and can simultaneously absorb the commonalities and individual characteristics of big data to improve the model's simulation accuracy, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] The purpose of this invention is to provide a method for constructing a hydrological model based on an embedded neural network to solve the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention discloses a method for constructing a hydrological model based on an embedded neural network, the method comprising the following steps:

[0008] Step 1: Decompose the basic hydrological model into modules: Decompose the basic hydrological model into modules. The basic hydrological model is a lumped rainfall-runoff model. It uses rainfall, water surface evaporation and the initial state of the watershed as inputs to predict the flow process at the watershed outlet. Decompose a single formula or several related formulas in the basic hydrological model into a module. The decomposed modules have temporal or physical uniformity.

[0009] Step 2: Determine the embedded neural network type corresponding to each module: Divide the embedded neural networks into three types according to the number of recursion steps: stateless networks (Type I), single-step recursive networks (Type II), and multi-step recursive networks (Type III). Stateless networks are networks with no explicit time dependency between input and output, and have 0 recursion steps. Single-step recursive networks are networks whose input includes the output of the previous time step, and have 1 recursion step. Multi-step recursive networks are networks whose output depends on long sequence information. Determine the embedded neural network type corresponding to each module based on the definitions of different network types.

[0010] Step 3: Determine the embedded neural network parameters for each module: First, establish a hybrid model, that is, replace each module of the basic hydrological model (i.e., the original hydrological model) with an equivalent replacement network, while keeping the rest of the structure as it is, and establish a series of hybrid models; then train the original hydrological model and the hybrid model at the same time, and modify the network parameters to make the loss functions of the two equal. At this time, the network parameters can make the network replace the original module, thereby determining the embedded neural network parameters for each module.

[0011] Step 4: Design a new hydrological model structure based on standard embedded neural networks: First, define the standard forms of three types of embedded neural networks, determined by the average values ​​of the embedded neural network parameters; that is, the number of hidden layers and hidden units of the standard type I network is the average value of the parameters of all type I networks involved in the hybrid model, the number of hidden layers and hidden units of the standard type II network is the average value of the parameters of all type II networks involved in the hybrid model, and the number of hidden layers and hidden units of the standard type III network is the average value of the parameters of all type III networks involved in the hybrid model. If the average value is not an integer, it is rounded down to the nearest integer.

[0012] Then, a structured deep learning model was constructed using three types of standard embedded neural networks, and its performance was tested. The performance was measured using the Hydrological Information Criterion (HIC), and the construction method adopted a greedy algorithm. Specifically, the number of units in the initial structured deep learning model was set to 1, that is, only one standard type I network was used. Then, a standard type I, II, or III network was added to it in an arbitrary connection manner to form a new structure. The HIC values ​​of each structure were tested. In order to balance computational efficiency and search breadth, the two best structures were used as the basis, and an arbitrary type I, II, or III network was added to each of them in an arbitrary connection manner. The structure with the smallest HIC value was selected as the optimal sub-unit. The two optimal sub-units were connected in series or parallel to obtain the new hydrological model structure.

[0013] Step 5: Establish a new hydrological model based on the new hydrological model structure: Interpret the meaning of each module in the new hydrological model structure using the following methods: Type I networks represent evapotranspiration and fixed losses; Type II networks represent state-dependent hydrological processes, including runoff generation and linear reservoir runoff; Type III networks represent long-term time-dependent processes, including unit hydrographs, lag algorithms, and long-term processes involving deep soil layers; thereby establishing a new hydrological model based on the new hydrological model structure.

[0014] Furthermore, the basic hydrological models in step 1 include the Xin'anjiang model, the dual-supermodel, and the Sacramento model.

[0015] Furthermore, when the two optimal sub-units in step 4 are connected in series or parallel, the following principles shall be followed:

[0016] (1) Standard Class I networks should avoid cascading;

[0017] (2) Standard Class II networks form a parallel structure;

[0018] (3) Standard Class III network is essential.

[0019] Furthermore, the calculation formula for the Hydrological Information Criterion (HIC) in step 4 is as follows:

[0020]

[0021] In the formula: MSE represents the mean squared error achieved by the model after training; λ is the tradeoff coefficient; and k is the number of parameters in the model.

[0022] The beneficial effects of the present invention are as follows:

[0023] (1) This invention uses an embedded neural network to replace the model module, determines the network parameters through end-to-end training, and explores a better hydrological model structure by combining standardized networks. This can break away from the basic paradigm of first generating runoff and then converging runoff in traditional hydrological models, laying the foundation for flexible adjustment of the model structure.

[0024] (2) This invention defines the Hydrological Information Criterion (HIC) to measure the cost-effectiveness of structured deep learning models, seeks the best balance between optimization ability and structural complexity, and uses this as the objective function to determine the quality of the structure, providing a theoretical basis for the design of model structure.

[0025] (3) The present invention uses a greedy algorithm to design the model structure and stops optimization after the number of modules reaches 3. It uses existing superior structures to splice together a hydrological model, which overcomes the disadvantages of the variable arrangement of modules and the difficulty of exhaustive enumeration and traversal, and provides a feasible solution for the design of the model structure.

[0026] (4) The present invention establishes a new hydrological model based on the newly designed hydrological model structure and interprets the model structure. It has regional applicability and can absorb both the commonalities and individualities in big data, thereby improving the model simulation accuracy.

[0027] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the method flow described in this invention;

[0029] Figure 2 This is a schematic diagram of the parameter adjustment process for an embedded neural network.

[0030] Figure 3 This is a schematic diagram of the Liulin small watershed system in Example 1;

[0031] Figure 4 This is a schematic diagram of the design results of the structured deep learning model in Example 1;

[0032] Figure 5 This is a schematic diagram of the design results of the new hydrological model structure in Example 1;

[0033] Figure 6 This is a schematic diagram illustrating the simulation effects of some flood scenarios in Example 1. Detailed Implementation

[0034] This invention discloses a method for constructing a hydrological model based on an embedded neural network, such as... Figure 1 As shown, the method includes the following steps:

[0035] Step 1: Decompose the basic hydrological model into modules: The basic hydrological model is decomposed into modules. The basic hydrological model is a lumped rainfall-runoff model, using rainfall, water surface evaporation, and the initial state of the watershed as inputs to predict the flow process at the watershed outlet. Common models include the Xin'anjiang model, the dual-supermodel, the Sacramento model, etc. This module decomposition differs from the traditional division of natural processes such as evapotranspiration, runoff generation, and confluence. Here, a single formula or several related formulas are decomposed into a module, and the decomposed modules have temporal or physical uniformity. For example, in the Xin'anjiang model, runoff generation and water source allocation occur simultaneously and can be combined into one module. The runoff generation module in the Xin'anjiang model describes different hydrological processes in terms of runoff calculation and soil moisture content update, and can also be decomposed into two modules.

[0036] Step 2: Determine the type of embedded neural network corresponding to each module: Divide the embedded neural networks into three types according to the number of recursion steps: stateless network (Type I network), single-step recursive network (Type II network), and multi-step recursive network (Type III network). These three types of networks can cover all modules decomposed from the hydrological model.

[0037] (1) Stateless network (Type I network): y t =f(x t ).

[0038] A network whose input and output have no explicit time dependency is a stateless network. Stateless networks have zero recursion steps, no state records, and reflect a time-invariant mapping relationship. They can be implemented using simple fully connected layers. Because the network's outputs are explicitly involved in subsequent calculations, the outputs retain a clear physical meaning during training. The water source differentiation module of the Xin'anjiang model can be considered a type I network.

[0039] (2) Single-step recursive network (Type II network): [y t , h t ]=f(x t , h t-1 ).

[0040] A network whose input includes the output of the previous time step is a single-step recursive network. A single-step recursive network has one recursion step, records the state of the previous time period, and reflects the time-varying mapping relationship. It can be implemented using a fully connected network structure that introduces the state variable of the previous time period as input. Since the network state may not directly participate in subsequent calculations, the absolute value of the state variable h is not meaningful; usually, an additional mapping is needed to project h into a reasonable range. The evapotranspiration module, runoff generation module, and underground runoff confluence module of the Xin'anjiang model can all be considered as Type II networks.

[0041] (3) Multi-step recursive network (Class III network): y=f(x).

[0042] Networks whose output depends on long-sequence information are called multi-step recursive networks, such as Long Short-Term Memory (LSTM) networks and Gated Recursive Networks (GRN), which can capture long-term dependencies. Their dependence on the number of time steps is variable and usually cannot be determined in advance. For example, a surface runoff confluence module can be considered a type III network. Multi-step recursive networks have a more complex structure and a larger number of parameters, and they have a stronger ability to fit time-series data. When using multi-step recursive networks to replace internal modules of a hydrological model, the number of hidden neurons must be strictly controlled so that the network performance is roughly equivalent to convolution operations, to prevent the performance of the type III network from overshadowing the role of other modules.

[0043] The type of embedded neural network corresponding to each module is determined based on the definition of different types of networks. For example, the two-source division module of the Xin'anjiang model can be equivalent to two Class I networks, the linear reservoir confluence modules of evapotranspiration, runoff generation, and groundwater runoff can each be equivalent to a Class II network, and the unit linear confluence module of surface runoff can be equivalent to a Class III network.

[0044] Step 3: Determine the embedded neural network parameters for each module: First, establish hybrid models, that is, replace each module of the basic hydrological model (original hydrological model) with an equivalent replacement network one by one, while keeping the rest of the structure unchanged, and establish a series of hybrid models. For example, if the original hydrological model is divided into 4 modules A, B, C, and D, then 4 hybrid models need to be established, including: a hybrid model in which module A is replaced with the corresponding type of embedded neural network, while B, C, and D remain unchanged; a hybrid model in which module B is replaced with the corresponding type of embedded neural network, while A, B, and C remain unchanged; a hybrid model in which module C is replaced with the corresponding type of embedded neural network, while A, B, and D remain unchanged; and a hybrid model in which module D is replaced with the corresponding type of embedded neural network, while A, B, and D remain unchanged.

[0045] Then determine the embedded neural network parameters for each module. The process for adjusting the embedded neural network parameters is as follows: Figure 2 As shown, the original hydrological model and the hybrid model are trained simultaneously. By modifying network parameters such as the number of hidden layers and the number of neurons in the hidden layers, the loss functions of the two models are made equal, i.e., Loss of the original model ≈ Loss of the hybrid model. At this point, the network parameters allow the network to perfectly replace the original modules without causing underfitting or overfitting, thus determining the embedded neural network parameters corresponding to each module. For datasets with large sample sizes, the number of hidden layers can be set to 2, while for small datasets of about 20 floods, the number of hidden layers can be set to 1. The initial value of the number of neurons in the hidden layers should be on the same order of magnitude as the sum of the network's input and output units.

[0046] Step 4: Design a new hydrological model structure based on standard embedded neural networks: First, define the standard forms of three types of embedded neural networks, determined by the average value of the embedded neural network parameters determined in Step 3; that is, the number of hidden layers and hidden units of the standard type I network is the average value of the parameters of all type I networks involved in the hybrid model in Step 3, the number of hidden layers and hidden units of the standard type II network is the average value of the parameters of all type II networks involved in the hybrid model in Step 3, and the number of hidden layers and hidden units of the standard type III network is the average value of the parameters of all type III networks involved in the hybrid model in Step 3. If the average value is not an integer, it is rounded down to the nearest integer.

[0047] Then, a structured deep learning model was constructed using three types of standard embedded neural networks, and its performance was tested. Performance was measured using the Hydrological Information Criterion (HIC), and the construction method employed a greedy algorithm. Specifically, the initial structured deep learning model had only one unit, i.e., using only one standard type I network. Subsequently, a standard type I, II, or III network was added to it in any way to form a new structure. The HIC values ​​of each structure were tested. To balance computational efficiency and search breadth, the two best structures were used as the basis for further construction. In each case, any type I, II, or III network was added in any way, and the structure with the smallest HIC value was selected as the optimal subunit. The two optimal subunits were connected in series or parallel to obtain the new hydrological model structure.

[0048] The formula for calculating the Hydrological Information Criterion (HIC) is as follows:

[0049]

[0050] In the formula: MSE represents the mean squared error achieved by the model after training; λ is the tradeoff coefficient, which can be 0.1; k is the number of parameters in the model; the smaller the HIC value, the higher the cost-effectiveness of the model.

[0051] The new hydrological model structure obtained above, which is to splice the optimal sub-units in series and parallel, should meet the following principles: (1) Standard Class I networks should avoid series connection; (2) Standard Class II networks should form parallel structures as much as possible; (3) Standard Class III networks are indispensable. If there are multiple splicing methods that meet the above principles, the one with the best HIC should be selected as the new hydrological model structure.

[0052] Step 5: Establish a new hydrological model based on the new hydrological model structure: Interpret the meaning of each module in the new hydrological model structure using the following methods: Type I networks typically represent single-valued mappings such as evapotranspiration, fixed losses, and others; Type II networks typically represent state-dependent hydrological processes, such as runoff generation and linear reservoir runoff; Type III networks typically represent long-term dependent processes, such as the unit hydrograph method, lag-based algorithms, and long-term processes involving deep soil layers. Thus, a new hydrological model is established based on the new hydrological model structure.

[0053] The method described in this invention is based on adjusting the embedded neural network structure using a hybrid model. It designs the model structure using hydrological information criteria and a greedy algorithm, and then applies physical interpretation or modeling methods to design a regionally adaptable hydrological model. This method can fully grasp the regional runoff generation and confluence characteristics and avoid the failure of traditional hydrological models in local areas, which is of great significance for flood control and disaster reduction.

[0054] Example 1

[0055] This embodiment is an application example of the above method.

[0056] This embodiment utilizes the Liulin small watershed in Neiqiu County, Xingtai City, located in a semi-arid and semi-humid region (e.g., Figure 3 (As shown) Based on the measured rainfall-runoff data from 1982 to 2022, a better model structure suitable for this region was designed using the method described in this invention. The basic hydrological model adopted is the Xin'anjiang dual-source model, with surface runoff using the Nash unit hydrograph and groundwater runoff using the linear reservoir method. This embodiment selected 24 floods with a time step of 1 hour, of which the first 19 were for calibration and the last 5 were for validation. All models were built in the Python environment using torch, and the mean squared error loss function was selected.

[0057] Step 1: Decompose the basic hydrological model into modules: Divide the Xin'anjiang model into modules X1~X5. Each module is written in the form of "[output1, output2,...]=module(input1, input2,...;parameter1, parameter2,...)".

[0058] (1) Evaporation module: [PE] t , TP t ]=X1(P t , TP t-1 ; D, EP);

[0059] Let P be the rainfall in time period t. t The cumulative rainfall before the start of time period t is TP (mm). t-1 The initial loss is D, mm, and the evaporation capacity over a given period is EP, mm. If TP t-1 If the value exceeds D, then the rainfall PE due to evapotranspiration is deducted in time period t.t =max{P t -EP, 0}; otherwise, calculate the cumulative rainfall TP at the end of period t t = TP t-1 + P t , if TP t still does not exceed D, then PE t =0, otherwise PE t =max{TP t - D -EP, 0}.

[0060] (2)Runoff production module: [R t , W t =X2(PE t , W t-1 ; WM, B);

[0061] Let the rainfall after subtracting evapotranspiration in the t-th period be PE t , in mm, the soil water content at the end of the t-1-th period is W t-1 , in mm, the average tension water storage capacity of the watershed is WM, in mm, and the exponent of the storage capacity distribution curve is B. First calculate the maximum single-point tension water storage capacity of the watershed WMM=(1+B)∙WM, in mm. If W t-1 >WM, then the ordinate value A of the corresponding curve t-1 =WMM, otherwise A t =WMM, otherwise A t =WMM∙[1-(1-W t-1 / WM)^(1 / (B+1))], the unit of A t is mm. If PE t +A t <WMM, then the runoff R in the period t =PE t -WM+W t-1 +WM∙[1-(PE t +A t ) / WMM]^(1+B), otherwise R t = PE t -WM+W t-1 , the unit of R t is mm. Finally update the soil water content W at the end of the t-th period t = PE t -R t +W t-1 .

[0062] (3)Runoff separation module: [RS t , RG t =X3(R t , PEt ; FC);

[0063] Let the surface runoff and groundwater runoff at time t be RS, respectively. t , and RG t The stable infiltration rate during the time period is FC, mm / h. If the precipitation PE due to evapotranspiration is deducted during time period t... t >0, then RG t = R t ∙min{PE t , FC} / PE t RS t =R t -RG t Otherwise RG t = RS t =0.

[0064] (4) Subsurface runoff collection module: [QG t ]=X4(RG t QG t-1 ; CG);

[0065] Remember QG t-1 Let QG be the groundwater runoff at the end of time period t-1, in m³ / s, and CG be the groundwater retreat coefficient. According to the linear reservoir method, the groundwater runoff at the end of time period t is QG. t =CG∙QG t-1 +(1-CG)∙RG t • F / 3.6 / dt, in m³ / s, where the catchment area F (in km²) and time step dt (in h) are known constants.

[0066] (5) Surface runoff collection module: [QS]=X5(RS; N, K);

[0067] According to Nash's unit hydrograph method, let N be the number of equivalent linear reservoirs in series, and K be the confluence time. Then the unit hydrograph UH... t =1 / K / Γ(N)∙(t / K)^(N-1)∙exp(-t / K), thus obtaining the surface runoff time series QS= RS*UH∙F / 3.6 / dt, in m³ / s, where RS is the surface runoff time series in mm, and the symbol "*" indicates convolution.

[0068] Remember Q sim =QS + QG, where QS is the time series of surface runoff and QG is the time series of groundwater runoff, then Q sim This represents the simulation results of the model. The meaning and value range of each parameter in the model are shown in Table 1.

[0069] Table 1

[0070]

[0071] Step 2: Determine the type of embedded neural network corresponding to each module: According to the number of recursion steps, embedded neural networks are divided into three categories: stateless networks (Type I networks), single-step recursive networks (Type II networks), and multi-step recursive networks (Type III networks). The discrimination method can be summarized as follows: Type I networks do not use their own output as input, Type II networks use their output from the previous time period as input to form a recursion of one time period, while Type III networks use the outputs from multiple past time periods as input to form a long sequence of recursion.

[0072] The equivalent substitution network type for each module is determined based on the number of recursive steps: The cumulative rainfall TP of evapotranspiration module X1 exists in both input and output, and there is a recursion over one time period, so a type II network is selected; the soil moisture content W of runoff generation module X2 exists in both input and output, and there is a recursion over one time period, so a type II network is selected; the water source distribution module X3 does not include its own output in its input, so a type I network is selected; the groundwater runoff flow rate QG of groundwater runoff collection module X4 exists in both input and output, and there is a recursion over one time period, so a type II network is selected; the surface runoff collection module X5 has multi-step time dependence, requiring a full series of input networks to obtain a full series of results, so a type III network is selected.

[0073] Step 3: Determine the embedded neural network parameters corresponding to each module: First, establish 5 hybrid models. Since the original hydrological model is split into 5 modules X1~X5, their corresponding equivalent embedded network types are II, II, I, II, and III, respectively. Therefore, 5 hybrid models need to be established, including: Hybrid model M1 replaces module X1 with a type II network, while X2~X5 remain unchanged; Hybrid model M2 replaces module X2 with a type II network, while X1 and X3~X5 remain unchanged; Hybrid model M3 replaces module X3 with a type I network, while X1~X2 and X4~X5 remain unchanged; Hybrid model M4 replaces module X4 with a type II network, while X1~X3 and X5 remain unchanged; Hybrid model M5 replaces module X5 with a type III network, while X1~X4 remain unchanged.

[0074] Then, the parameters of the embedded network were determined by training the hybrid model. Due to the small sample size, all hybrid models used a single hidden layer. The training results of the hybrid model are compared with the original hydrological model in Table 2.

[0075] Table 2

[0076]

[0077] Based on the principle that the origin and mixture of Loss should be as close as possible, the evapotranspiration module can be replaced by a Class II network with 2 hidden neurons, the runoff generation module can be replaced by a Class II network with 4 hidden neurons, the water source distribution module can be replaced by a Class I network with 3 hidden neurons, the underground runoff confluence module can be replaced by a Class II network with 4 hidden neurons, and the surface runoff confluence module can be replaced by a Class III network with 2 hidden neurons.

[0078] Step 4: Design a new hydrological model structure based on the standard embedded neural network: Define the standard forms of three types of embedded neural networks, which are determined by the average value of the embedded neural network parameters after parameter tuning in Step 3, as shown in Table 3.

[0079] Table 3

[0080]

[0081] Step 3 involves only one Class I network with one hidden layer and three hidden neurons. Therefore, a standard Class I network is defined as a stateless network with one hidden layer and three hidden neurons. Step 3 involves three Class II networks, each with one hidden layer and two, four, and four hidden neurons, respectively. Therefore, a standard Class II network is defined as a single-step recursive network with one hidden layer and approximately three (2+4+4) / 3. Step 3 involves only one Class III network with one hidden layer and two hidden neurons. Therefore, a standard Class III network is defined as a multi-step recursive network with one hidden layer and two hidden neurons.

[0082] Structured deep learning models are built based on three types of standard embedded neural networks: such as Figure 4 As shown, when building a structured deep learning model, the simplest standard Class I network is first selected, denoted as structure (1), with a HIC value of 695. An additional network is added to it in a series and parallel manner, so that the number of modules in the model reaches 2, resulting in structures (2) to (9). At this time, the most efficient structures are (4) and (8), with HIC values ​​of 220.7 and 147.3 respectively. Based on (4), a new additional network is added to it in a series and parallel manner, so that the number of modules in the model reaches 3, resulting in structures (10) to (21), with the most efficient structure being (16). Based on (8), a new additional network is added to it in a series and parallel manner, so that the number of modules in the model reaches 3, resulting in structures (22) to (32), with the most efficient structure being (23). Therefore, the final selected sub-units are (16) and (23).

[0083] Then, a new hydrological model structure is built based on the optimal sub-unit, such as... Figure 4As shown, taking the structure of the Xin'anjiang model as a reference, all five modules are replaced with standard embedded neural networks to obtain a structured deep learning model (a), with a HIC of 93.7; connected in the order of (16) → (23), a structured deep learning model (b) is obtained, with a HIC of 53.4; connected in the order of (23) → (16), since the end of (23) and the beginning of (16) are both standard Class I networks, in order to avoid repeated connection of Class I networks, only one is retained, resulting in a structured deep learning model (b), with a HIC of 52.7; connected in parallel with (16) and (23), a structured deep learning model (c) is obtained, with a HIC of 54.1. Therefore, structure (c) is taken as the optimal structure, which is significantly better than the structure (a) corresponding to the Xin'anjiang model.

[0084] Step 5: Establish a new hydrological model based on the new hydrological model structure: interpret the physical meaning implied by the new hydrological model structure, such as... Figure 5 As shown in the diagram, the structure (c) "→[Process A (Type I) + Process B (Type III)] → Process C (Type I) →[Process D (Type II) + Process E (Type II)] →" can be interpreted as follows: After rainfall, some rainwater directly forms "new water" runoff (Process A), while the other part pushes "old water" in the soil to form runoff (Process B). The two mix to obtain the total runoff (Process C). The runoff converges to the watershed outlet through two paths with different velocities (Processes D and E), thus obtaining the total watershed outflow. In this process, because the runoff generated by rainfall pushing "old water" is complex and slow, with a long time dependence, it needs to be described by a Type III network; because the direct runoff of "new water" is direct and rapid, almost unaffected by the watershed state, it is depicted by a Type I network; and the confluence of the two paths can be described by linear reservoirs, both of which have a time-dependent recursion, which is precisely what a Type II network can describe. This process is consistent with the analysis results of the latest isotope experiments.

[0085] A new hydrological model was established based on the new structure:

[0086] (1) New aquaculture flow module: [Rnew t ]=A(P t ; EP, FC).

[0087] Let P be the rainfall in time period t. t The evapotranspiration capacity during a given period is EP, mm, and the average steady-state infiltration rate of the watershed is FC, mm / h. If P t If the EP requirement cannot be met, there will be no new aquatic flow, Rnew. t =0, if P t If EP is met, then the precipitation PE due to evapotranspiration is deducted. t =P t-EP, if PE t Beyond FC, Rnew t =PE t -FC, otherwise Pnew t =0. The calculation of module A can be performed sequentially over time, and the model does not use its own output as input, which conforms to the structure of a type I network.

[0088] (2) Old water production module: [Rold]=B(P, G0; FC, GM, Bold, Nold, Kold).

[0089] Assume that the old water in the watershed is stored in the soil, with an initial content of G0 mm, a maximum storage capacity of GM mm, Bold as an index describing the spatial heterogeneity of the old water reservoir, Nold as the number of equivalent linear reservoirs required for the lag simulation of the old water reservoir, and Kold as the average time for the old water to flow through each tank. Let dF t The infiltration rate over a given period is expressed in mm, when PE t When FC is exceeded, dF t =FC, otherwise dF t =PE t Infiltrated rainfall first enters the old reservoir. The portion of rainfall that fills and overflows the old reservoir will generate old water runoff. It is necessary to first calculate the intermediate variables: the maximum old reservoir storage capacity at a single point in the basin, GMM = (1 + Bold)∙GM, and G... t-1 The corresponding ordinate value A of the curve t =GMM∙[1-(1-G t-1 If the overflow amount of the old water is Sold, then the overflow amount of the old water is Sold. t =dF t -GM+G t-1 +GM∙[1-(dF t +A t ) / GMM]^(1+Bold), where the unit is mm, and G t-1 Let be the average old water content at the end of time period t-1, in mm. The Nash unit hydrograph is used to further describe the lag of old water overflow, yielding the old water yield time series Rold = Sold * UH∙F / 3.6 / dt, m³ / s, where UH... t =1 / Kold / Γ(Nold)∙(t / Kold)^(Nold-1)∙exp(-t / Kold) is the unit curve, the symbol "*" indicates convolution, and the watershed area F and the computation time step dt are known constants. Module B requires the complete time series P as input to calculate the complete time series Rold. It cannot be calculated by splitting the calculation into time intervals t. The calculation formula has a long-term dependency and conforms to the structure of a type III network.

[0090] (3) New and old water mixing module: [R1 t R2 t ]=C(Rnew t Rold t G t ; GM, α, β, Nold, Kold).

[0091] New water flows into the ground faster than old water, but when soil moisture is scarce in the watershed, new water will be converted back into old water through infiltration. The conversion rate is defined as tr = (G... t / GM)^α, where α is a parameter. During each flow period, a certain proportion of new water (tr) is converted to old water. Since the average confluence time is Nold·Kold, the infiltrated new water and old water become Rnew. t '=Rnew t ·(1-tr^(Nold·Kold)), Rold t =Rold t +Rnew t ·tr^(Nold·Kold). Due to the complex watershed structure, the watershed is divided into two sub-regions with an area ratio of β. Then, the runoff generation process R1 in region 1 is... t =(Rnew t '+ Rold t ')·β, the runoff generation process R2 in region 2 t =(Rnew t '+ Rold t The computation of module C can be performed sequentially over time periods, and the model does not use its own output as input, which conforms to the structure of a type I network.

[0092] (4) The merging module of region 1: [Q1 t ]=D(R1 t Q1 t-1 ; C1).

[0093] Remember Q1 t-1 Let Q1 be the outlet flow of region 1 at the end of the previous time period, and C1 be the flow recession coefficient of region 1. According to the linear reservoir method, Q1... t =C1∙Q1 t-1 +(1-C1)∙R1 t • F / 3.6 / dt, where the catchment area F and the time step dt are known constants. The calculation of module D can be performed sequentially over time, and both the input and output of the model contain state variables Q1, which conforms to the structure of a type II network.

[0094] (5) The bus module of region 2: [Q2 t ]=E(R2 t Q2 t-1 (C2)

[0095] Remember Q2 t-1 Let Q2 be the outlet flow of region 2 at the end of the previous time period, and C2 be the flow recession coefficient of region 2. According to the linear reservoir method, Q2... t =C2∙Q2 t-1 +(1-C2)∙R2 t • F / 3.6 / dt, where the catchment area F and the time step dt are known constants. The calculation of module E can be performed sequentially over time, and both the input and output of the model contain the state variable Q2, which conforms to the structure of a type II network.

[0096] The parameters of the new hydrological model are shown in Table 4.

[0097] Table 4

[0098]

[0099] Based on 20 floods in the Liulin River Basin, the Xin'anjiang model and the newly constructed hydrological model were simultaneously calibrated. The simulation results during the calibration and validation periods are shown in Table 5. The simulation results for some flood events are shown in the figure. Figure 6 As shown.

[0100] Table 5

[0101]

[0102] As can be seen, according to the method described in this invention, the new hydrological model structure designed based on embedded neural networks is significantly better than the original structure of the Xin'anjiang model, reducing the average relative peak error by 4%, the average relative flood volume error by 3%, and the average NSE by 0.04, thus proving the effectiveness of this invention.

[0103] Finally, it should be noted that the above description is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for constructing a hydrological model based on an embedded neural network, characterized in that, The method includes the following steps: Step 1: Decompose the basic hydrological model into modules: Decompose the basic hydrological model into modules. The basic hydrological model is a lumped rainfall-runoff model. It uses rainfall, water surface evaporation and the initial state of the watershed as inputs to predict the flow process at the watershed outlet. Decompose a single formula or several related formulas in the basic hydrological model into a module. The decomposed modules have temporal or physical uniformity. Step 2: Determine the embedded neural network type corresponding to each module: Divide the embedded neural networks into three types according to the number of recursion steps: stateless networks (Type I), single-step recursive networks (Type II), and multi-step recursive networks (Type III). Stateless networks are networks with no explicit time dependency between input and output, and have 0 recursion steps. Single-step recursive networks are networks whose input includes the output of the previous time step, and have 1 recursion step. Multi-step recursive networks are networks whose output depends on long sequence information. Determine the embedded neural network type corresponding to each module based on the definitions of different network types. Step 3: Determine the embedded neural network parameters for each module: First, establish a hybrid model, that is, replace each module of the basic hydrological model (i.e., the original hydrological model) with an equivalent replacement network, while keeping the rest of the structure as it is, and establish a series of hybrid models; then train the original hydrological model and the hybrid model at the same time, and modify the network parameters to make the loss functions of the two equal. At this time, the network parameters can make the network replace the original module, thereby determining the embedded neural network parameters for each module. Step 4: Design a new hydrological model structure based on standard embedded neural networks: First, define the standard forms of three types of embedded neural networks, determined by the average values ​​of the embedded neural network parameters; that is, the number of hidden layers and hidden units of the standard type I network is the average value of the parameters of all type I networks involved in the hybrid model, the number of hidden layers and hidden units of the standard type II network is the average value of the parameters of all type II networks involved in the hybrid model, and the number of hidden layers and hidden units of the standard type III network is the average value of the parameters of all type III networks involved in the hybrid model. If the average value is not an integer, it is rounded down to the nearest integer. Then, a structured deep learning model was constructed using three types of standard embedded neural networks, and its performance was tested. The performance was measured using the Hydrological Information Criterion (HIC), and the construction method adopted a greedy algorithm. Specifically, the number of units in the initial structured deep learning model was set to 1, that is, only one standard type I network was used. Then, a standard type I, II, or III network was added to it in an arbitrary connection manner to form a new structure. The HIC values ​​of each structure were tested. In order to balance computational efficiency and search breadth, the two best structures were used as the basis, and an arbitrary type I, II, or III network was added to each of them in an arbitrary connection manner. The structure with the smallest HIC value was selected as the optimal sub-unit. The two optimal sub-units were connected in series or parallel to obtain the new hydrological model structure. Step 5: Establish a new hydrological model based on the new hydrological model structure: Interpret the meaning of each module in the new hydrological model structure using the following methods: Type I networks represent evapotranspiration and fixed losses; Type II networks represent state-dependent hydrological processes, including runoff generation and linear reservoir runoff; Type III networks represent long-term time-dependent processes, including unit hydrographs, lag algorithms, and long-term processes involving deep soil layers; thereby establishing a new hydrological model based on the new hydrological model structure.

2. The method for constructing a hydrological model based on an embedded neural network according to claim 1, characterized in that, The basic hydrological models in Step 1 include the Xin'anjiang model, the dual-supermodel, and the Sacramento model.

3. The method for constructing a hydrological model based on an embedded neural network according to claim 1, characterized in that, When the two optimal sub-units in step 4 are connected in series or parallel, the following principles should be followed: (1) Standard Class I networks should avoid cascading; (2) Standard Class II networks form a parallel structure; (3) Standard Class III network is essential.

4. The method for constructing a hydrological model based on an embedded neural network according to claim 1, characterized in that, The formula for calculating the Hydrological Information Criterion (HIC) in step 4 is as follows: In the formula: MSE represents the mean squared error achieved by the model after training; λ is the tradeoff coefficient; and k is the number of parameters in the model.

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