Hydrological hybrid modeling method based on differentiable parameter learning

Abstract

The invention discloses a hydrological hybrid modeling method based on differentiable parameter learning. The hydrological hybrid modeling method comprises the following steps: performing differentiable reconstruction on a hydrological model; establishing a parameter learning neural network; and coupling the parameter learning neural network into the reconstructed hydrological model to form a hybrid model coupling data driving and a traditional hydrological model. The method has the advantage that the parameter learning neural network is introduced before the hydrological model. And learning parameters required for predicting the hydrological model from the collected data, and predicting the runoff by using the hydrological model. Meanwhile, the observation value of the runoff serves as the constraint of the parameter learning neural network and is used for adjusting the output of the parameter learning neural network, a partial black box hydrological model is formed, the influence of time and space variation of hydrological characteristics caused by current climate change and human activities on the prediction precision of a traditional hydrological model is solved, and the prediction accuracy of the hydrological model is improved. And the runoff prediction precision is improved.

Description

Technical Field

[0001] The invention relates to the technical field of watershed intelligent forecasting, and is particularly suitable for a hydrological hybrid modeling method based on differentiable parameter learning. Background Art

[0002] Conducting a systematic quantitative assessment of regional water resources and implementing a reasonable water resource allocation strategy is not only an effective means to resolve the contradiction between water supply and demand, but also a key measure to fundamentally alleviate the water resource crisis.

[0003] Hydrological models are currently the main tool for describing the formation mechanism and changing laws of basin hydrological phenomena. These models usually use a series of model parameters to describe the basin hydrological cycle process, so the accuracy of model parameters will directly affect the model prediction accuracy.

[0004] However, due to climate change and human activities, the characteristics of the basin will change, resulting in increased variability in the temporal and spatial variability of key hydrological characteristic parameters of the basin, which makes the hydrological model parameters have significant uncertainty. At the same time, due to the complexity of the basin's hydrological processes, little is known about the potential sources of errors, making it difficult to develop useful and efficient error correction methods. Therefore, a practical modeling strategy is urgently needed to reduce the requirements for information on model error sources.

[0005] Currently, Earth observation has entered the era of big data, and data-driven methods have developed rapidly. Such methods, represented by machine learning, have flexible data adaptability and are good at discovering hidden relationships in high-dimensional data features. They are potential strategies for addressing the above-mentioned challenges of model uncertainty. However, such methods often establish black box models that lack interpretability.

[0006] Therefore, there is an urgent need to explore a practical and efficient modeling strategy that, by coupling data-driven methods with hydrological models, can not only improve the prediction accuracy of the model, but also enhance its ability to explain the spatiotemporal variability of parameters, so as to cope with the uncertainty challenges of hydrological models and provide a scientific basis for regional water resources management. Summary of the invention

[0007] The purpose of the present invention is to provide a hydrological hybrid modeling method based on differentiable parameter learning, which is used to solve the problems faced by current hydrological models, such as high parameter uncertainty and low prediction accuracy, and the lack of interpretability of machine learning models based on big data.

[0008] To achieve the above object, the present invention adopts the following technical solutions: The hydrological hybrid modeling method based on differentiable parameter learning of the present invention comprises the following steps: S1, differentiable reconstruction of the hydrological model; S2, establishing a parameter learning neural network; the output of the parameter learning neural network corresponds to the hydrological model parameters; S3, the parameter learning neural network is coupled to the reconstructed hydrological model to form a hybrid model that couples data-driven and traditional hydrological models.

[0009] Furthermore, the hydrological model is specifically the Xin'anjiang model.

[0010] Furthermore, according to the time-varying characteristics of the parameters in the hydrological model, a static parameter learning neural network and a dynamic parameter learning neural network are constructed respectively; the static parameter learning network adopts a multilayer perceptron model; and the dynamic parameter learning network adopts a long short-term memory network model.

[0011] Furthermore, the output of the static parameter learning neural network corresponds to the constant parameters of the hydrological model; and the output of the dynamic parameter learning neural network corresponds to the constant parameters and time-varying parameters of the hydrological model.

[0012] Furthermore, the expression of the hybrid prediction model is ,in When learning a network for static parameters, equal ; When learning a network for dynamic parameters, equal ; F is the reconstructed hydrological model, x is the parameter of the hydrological model; , is the constant parameter of the hydrological model of the ith basin; Learning neural networks for static parameters; The static attribute data of the ith watershed for the static parameter learning neural network; , is the parameter of the hydrological model of the ith basin at time t; Learning neural networks for dynamic parameters; The dynamic characteristic data of the ith watershed at the tth moment for the dynamic parameter learning neural network.

[0013] Furthermore, the coupling process is specifically as follows: using the simulated value of the target variable output by the hydrological model, constructing a loss function of the simulated value and the actual observed value, adjusting the output of the parameter learning neural network through gradient back propagation, and then using the output of the parameter learning neural network as the input of the reconstructed hydrological model to predict the target variable.

[0014] The advantage of the present invention is that a parameter learning neural network is introduced before the hydrological model, and the parameters required for predicting the hydrological model are learned from the collected data using the parameter learning neural network, and the runoff is predicted using the hydrological model. At the same time, the observed values ​​can be used as constraints for the parameter learning neural network to adjust the output of the parameter learning neural network. In other words, the present invention combines big data mining prediction with traditional hydrological models to form a partially black-boxed hydrological model, which solves the impact of the temporal and spatial variations of hydrological characteristics caused by current climate change and human activities on the prediction accuracy of traditional hydrological models. At the same time, using the observed values ​​to constrain the parameter learning neural network in turn can reduce errors and improve the prediction accuracy of runoff. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is a flow chart of the hydrological hybrid modeling method based on differentiable parameter learning described in the present invention.

[0016] Figure 2 Comparison curve of daily runoff simulation accuracy among regression function method, static parameter learning network and dynamic parameter learning network.

[0017] Figure 3 The spatial distribution of the average tensile water capacity (WM) of the basin in different models.

[0018] Figure 4 The spatial distribution of the tension water storage capacity curve index (B) in different models.

[0019] Figure 5 Time series graphs of parameter WM (a), parameter B (b), runoff (c), rainfall (d), potential evapotranspiration (e), soil water (f) and vegetation index (g) in the watershed where the USGS 01057000 station is located.

[0020] Figure 6 Time series graphs of parameter WM (a), parameter B (b), runoff (c), rainfall (d), potential evapotranspiration (e), soil water (f) and vegetation index (g) in the watershed where the USGS 08070000 station is located. DETAILED DESCRIPTION

[0021] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] like Figure 1As shown, the hydrological hybrid modeling method based on differentiable parameter learning of the present invention comprises the following steps: S1, Differentiable reconstruction of the hydrological model.

[0023] S2, establish a parameter learning neural network; the output of the parameter learning neural network corresponds to the hydrological model parameters. According to the time-varying characteristics of the parameters in the hydrological model, a static parameter learning neural network and a dynamic parameter learning neural network are constructed respectively; the static parameter learning network adopts a multilayer perceptron model; the dynamic parameter learning network adopts a long short-term memory network model. The output of the static parameter learning neural network corresponds to the constant parameters of the hydrological model; the output of the dynamic parameter learning neural network corresponds to the constant parameters and time-varying parameters of the hydrological model.

[0024] S3, the parameter learning neural network is coupled to the reconstructed hydrological model to form a hybrid model that couples data-driven and traditional hydrological models.

[0025] The expression of the mixed model is ,in When learning a network for static parameters, equal ; When learning a network for dynamic parameters, equal ; F is the reconstructed hydrological model, x is the parameter of the hydrological model; , is the constant parameter of the hydrological model of the ith basin; Learning neural networks for static parameters; The static attribute data of the ith watershed for the static parameter learning neural network; , are the parameters of the hydrological model of the ith basin at time t; Learning neural networks for dynamic parameters; The dynamic characteristic data of the ith watershed at the tth moment for the dynamic parameter learning neural network.

[0026] The coupling process is specifically as follows: using the simulated value of the target variable output by the hydrological model, constructing a loss function between the simulated value and the actual observed value, adjusting the output of the parameter learning neural network through gradient back propagation, and then using the output of the parameter learning neural network as the input of the reconstructed hydrological model to predict the target variable.

[0027] Example 2 The hydrological model described in the present invention is specifically the Xin'anjiang model. The Xin'anjiang model is taken as an example to illustrate the hydrological hybrid modeling method based on differentiable parameter learning of the present invention.

[0028] Step 1: Most existing deep learning algorithms support automatic differentiation technology for gradient tracking, but traditional programming environments do not support this feature. Therefore, it is necessary to use specific operations in neural networks to reconstruct the submodule equations of the Xin'anjiang model to achieve differentiable reconstruction of the Xin'anjiang model. The reconstructed Xin'anjiang model requires that each calculation formula can be derived. This embodiment realizes the coupling of the Xin'anjiang model and the machine learning algorithm in the PyTorch environment, so the reconstructed Xin'anjiang model is written into the PyTorch environment, and functions such as torch.clamp, torch.mul, torch.min, and torch.max are applied.

[0029] The Xin'anjiang model consists of four parts: evapotranspiration calculation, runoff calculation, water source division calculation and confluence calculation.

[0030] The calculation formula of the evapotranspiration module of the Xinanjiang model is as follows: (1) (2) (3) (4) Where: WU and WL is the tension water storage of the upper and lower basins, EU , EL , ED They are the evapotranspiration of the upper, lower and deep layers of the basin, E represents the total evaporation of the three layers, P For rainfall, C is the deep evapotranspiration diffusion coefficient, WLM is the tension water capacity of the lower layer, EP is the potential evapotranspiration. C Except for , the units of other variables are mm.

[0031] The Xin'anjiang model adopts the full-storage runoff mechanism. The runoff calculation includes two parts: one is the runoff on the permeable area, and the other is the runoff on the impermeable area. The runoff calculation formula is as follows: (5) (6) (7) (8) (9) Where: PE represents the net rainfall, WMM It represents the maximum tensile water capacity of a single point in the soil. Bis the tension water storage capacity curve index, A Indicates the previous period affects the rainfall, R Indicates the total flow, WM represents the average tension water capacity of the basin, EY Indicates that the evaporation process consumes rainfall. B Except for , the units of other variables are mm.

[0032] The Xinanjiang model divides water sources into surface runoff, subsoil flow and groundwater runoff according to the free water reservoir. The calculation formula for water source division is as follows: (10) (11) (12) (13) Where: S 0 Indicates the free water storage in the current runoff area, SX Indicates the free water storage under a certain state. RS , RI and RG It is expressed as surface runoff, subsoil flow and underground runoff. SMM is the maximum free water capacity at a single point, SM Indicates free water capacity, the unit is mm. KI and KG represents the outflow coefficient of subsoil flow and underground runoff, AU It is expressed as the vertical coordinate corresponding to the water storage capacity curve, EX An index of the curve representing the free water storage capacity.

[0033] In the confluence calculation of the Xin'anjiang model, the model is divided into slope confluence and river network confluence. Among them, the surface runoff, subsoil flow and underground runoff in the slope confluence are calculated using the linear reservoir method, and the river network confluence formula uses the unit line formula based on the Gamma distribution.

[0034] (14) (15) (16) (17) (18) (19) Where: Q , QS , QI and QGIt is expressed as total flow, surface runoff, subsoil flow and underground runoff, all in m 3 / s. CS , CI and CR It is expressed as the mid-flow recession coefficient, groundwater recession coefficient and river network flow recession coefficient. and represent shape parameter and time parameter respectively. t max Indicates the maximum duration in days.

[0035] Step 2: The parameters used in the Xin'anjiang model include constant parameters and time-varying parameters. According to the time-varying characteristics of the parameters in the Xin'anjiang model, static parameter learning neural networks are constructed respectively. g A and dynamic parameter learning neural networks g Z .

[0036] The static parameter learning neural network uses a multi-layer perceptron model to map the collected basin static attribute features A to the constant parameters of the Xinanjiang model through a neural network. .

[0037] Static characteristic data A include daily average precipitation (mm / day), daily average potential evapotranspiration (mm / day), precipitation seasonality and temporal distribution, proportion of precipitation falling as snow, drought index (ratio of average potential evapotranspiration to average precipitation), frequency of heavy precipitation days (days / year), average duration of heavy precipitation events (days), frequency of dry days (days / year), average duration of dry periods (days), average elevation (m), average slope (m / km), basin area (km 2 ), percentage of forest land, maximum monthly mean of leaf area index, difference between maximum and minimum monthly mean of leaf area index, maximum monthly mean of green vegetation, difference between maximum and minimum monthly mean of green vegetation index, main land use type, proportion of catchment area associated with main land cover, root depth (m), bedrock depth (m), soil depth (m), volume porosity, saturated hydraulic conductivity (cm / hr), maximum water content (m), percentage of sand (%), percentage of silt (%), percentage of clay (%), most common geological category, proportion of catchment area characterized by most common geological category, second most common geological category, proportion of catchment area characterized by second most common geological category, proportion of catchment area covered by carbonate sedimentary rocks, subsurface porosity, subsurface permeability (m 2 ).

[0038] The size of the hidden layer of the static parameter learning neural network (hidden_size) is set to 256, the number of samples contained in each batch (batch_size) is set to 200, and the activation function is ReLU.

[0039] Dynamic parameter learning neural network g Z The long short-term memory network model is used to collect static characteristic data A and dynamic characteristic data related to hydrology. As input, it is mapped to the time-varying parameters of the Xinanjiang model through a neural network. . Dynamic feature data Including daily potential evapotranspiration (mm / day), daily precipitation (mm / day), daily vegetation index, daily soil water (m 3 / m 3 ), etc., covering climate factors, vegetation conditions, and soil moisture. g Z In the present study, the mean tension water capacity (WM) of the basin and the tension water storage capacity curve index (B) are considered as time-varying parameters, while other parameters are assumed to remain constant over time.

[0040] Dynamic parameter learning neural network g Z The hidden_size of the hidden layer is set to 256, the batch_size is 200, the time length (rho) in each batch is 365 days, and the optimizer is Adadelta.

[0041] It should be noted that the collected static feature data A and dynamic feature data do not allow missing data. If there is missing data, interpolation is required.

[0042] Static parameter learning neural network and constant parameters of Xinanjiang model The corresponding expression is shown in formula (20); the time-varying parameters of the dynamic parameter learning neural network and the Xinanjiang model The corresponding expression is shown in formula (21); (20) (twenty one) in, is the constant parameter of the hydrological model in the ith basin; Learning neural networks for static parameters; The static attribute data of the ith watershed for the static parameter learning neural network; is the parameter of the hydrological model of the ith basin at time t; The dynamic characteristic data of the ith watershed at the tth moment for the dynamic parameter learning neural network.

[0043] The data required for the Xinanjiang model include: daily potential evapotranspiration (mm / day) and daily precipitation (mm / day).

[0044] Step 3: Parameterize the neural network h Coupling to the reconstruction of Xinanjiang model F In the above formula, the black-boxed Xinanjiang model is formed to form a hybrid prediction model, which is expressed as formula (22): (twenty two) In the formula, There are two cases: when learning the network for static parameters, equal ; When learning a network for dynamic parameters, equal .

[0045] When the simulated values ​​output by the Xin'anjiang model have observed values, the loss function is constructed by combining the simulated values ​​obtained by the hydrological model with the actual observed values, and then the parameter learning neural network is constrained according to the gradient back propagation in the deep learning algorithm. The formula is as follows: (twenty three) The loss function of the present invention is a likelihood function described by the classic Nash-Sutcliffe Efficiency coefficient (NSE): (twenty four) Where Qobe and Qsim are the observed and simulated runoff values, respectively; Qave is the average observed value; and n is the number of data values.

[0046] Example 3 Taking 671 basins in North America as an example, the data set from 2003 to 2008 was selected as training data, and the data set from 2009 to 2012 was selected as evaluation data. The measured runoff data was used as the evaluation variable, and the Pearson correlation coefficient (Corr), NSE, the deviation percentage of the highest 2% flow range (FHV) and the deviation percentage of the lowest 30% flow range (FLV) were selected as evaluation indicators to evaluate the prediction accuracy of the static parameter learning network and the dynamic parameter learning network of the hydrological hybrid modeling using the differentiable parameter learning method of the present invention, and the hybrid model constructed by the present invention was compared with the traditional regression function method (fm), and different scenarios were set, as shown in Table 1.

[0047] Table 1 Among them, fm(WM) means that the parameter basin average tension water capacity (WM) is set as a time-varying parameter by using the regression function method; fm(B) means that the tension water storage capacity curve index (B) is set as a time-varying parameter by using the regression function method; fm(WM,B) means that the parameters WM and B are simultaneously set as time-varying parameters by using the regression function method; dPL-XAJ means a static parameter learning network; dPL-XAJ(WM) means that the parameter WM is set as a time-varying parameter in a dynamic parameter network; dPL-XAJ(B) means that the parameter B is set as a time-varying parameter in a dynamic parameter network; dPL-XAJ(WM,B) means that the parameters WM and B are simultaneously set as time-varying parameters in a dynamic parameter network.

[0048] like Figure 2 As shown in the figure, the evaluation indicators under different scenarios are: Pearson correlation coefficient (Corr) Figure 2 a. NSE Figure 2 b. Deviation percentage of the maximum 2% flow range (FHV) Figure 2 c and the percentage deviation of the lowest 30% flow range (FLV) Figure 2 d Comparison of runoff simulation accuracy.

[0049] like Figure 3 As shown, the spatial distribution characteristics of the time-varying parameter WM under different scenarios.

[0050] like Figure 4 As shown in Figure 2, the spatial distribution characteristics of the time-varying parameter B under different scenarios.

[0051] Two basins were selected, with USGS 01057000 and USGS 08070000 as the basin total outlet stations, and the temporal variation characteristics of each parameter were analyzed, such as Figure 5 and Figure 6 shown.

[0052] in, Figure 5 a Shows the temporal variation characteristics of the time-varying parameter WM in the basin where the USGS 01057000 station is located under the scenarios of fm(WM), fm(WM,B), dPL-XAJ(WM), and dPL-XAJ(WM,B).

[0053] Figure 5 b shows the temporal variation characteristics of the time-varying parameter B in the basin where the USGS 01057000 station is located under the scenarios of fm(B), fm(WM,B), dPL-XAJ(B), and dPL-XAJ(WM,B).

[0054] Figure 5 c is the temporal variation characteristics of runoff in the basin where the USGS 01057000 station is located under the seven scenarios shown in Table 1.

[0055] Figure 5 d is the temporal variation characteristics of rainfall in the basin where the USGS 01057000 station is located.

[0056] Figure 5 e shows the temporal variation characteristics of potential evapotranspiration in the basin where the USGS 01057000 station is located.

[0057] Figure 5 f is the temporal variation characteristics of soil water in the watershed where the USGS 01057000 station is located.

[0058] Figure 5 g is the temporal variation characteristics of the vegetation index in the watershed where the USGS 01057000 station is located.

[0059] in, Figure 6 a Shows the temporal variation characteristics of the time-varying parameter WM in the basin where the USGS 08070000 station is located under the scenarios of fm(WM), fm(WM,B), dPL-XAJ(WM), and dPL-XAJ(WM,B).

[0060] Figure 6 b shows the temporal variation characteristics of the time-varying parameter B in the basin where the USGS 08070000 station is located under the scenarios of fm(B), fm(WM,B), dPL-XAJ(B), and dPL-XAJ(WM,B).

[0061] Figure 6 c is the temporal variation characteristics of runoff in the basin where the USGS 08070000 station is located under the seven scenarios shown in Table 1.

[0062] Figure 6 d is the temporal variation characteristics of rainfall in the basin where the USGS 08070000 station is located.

[0063] Figure 6 e shows the temporal variation characteristics of potential evapotranspiration in the basin where the USGS 08070000 station is located.

[0064] Figure 6 f is the temporal variation characteristics of soil water in the watershed where the USGS 08070000 station is located.

[0065] Figure 6 g is the temporal variation characteristics of the vegetation index in the watershed where the USGS 08070000 station is located.

[0066] The results show that the static parameter learning network and dynamic parameter learning network of the hydrological hybrid modeling with differentiable parameter learning proposed in this invention are better than the traditional regression function method in terms of runoff estimation accuracy. Compared with the traditional regression function, the parameters WM and B obtained by the dynamic parameter learning network show more obvious spatial clustering characteristics, and their time distribution is also more reasonable.

Claims

1. A hydrological hybrid modeling method based on differentiable parameter learning, characterized in that: The following steps are involved: S1, differentiable reconstruction of the hydrological model; S2, establishing a parameter learning neural network; the output of the parameter learning neural network corresponds to the hydrological model parameters; S3, the parameter learning neural network is coupled to the reconstructed hydrological model to form a hybrid model that couples data-driven and traditional hydrological models.

2. The hydrological hybrid modeling method based on differentiable parameter learning according to claim 1, characterized in that: The hydrological model is specifically the Xin'anjiang model.

3. The hydrological hybrid modeling method based on differentiable parameter learning according to claim 1, characterized in that: According to the time-varying characteristics of the parameters in the hydrological model, a static parameter learning neural network and a dynamic parameter learning neural network are constructed respectively; the static parameter learning network adopts a multilayer perceptron model; and the dynamic parameter learning network adopts a long short-term memory network model.

4. The hydrological hybrid modeling method based on differentiable parameter learning according to claim 3 is characterized by: The output of the static parameter learning neural network corresponds to the constant parameters of the hydrological model; the output of the dynamic parameter learning neural network corresponds to the constant parameters and time-varying parameters of the hydrological model.

5. The hydrological hybrid modeling method based on differentiable parameter learning according to claim 1, characterized in that: The expression of the hybrid prediction model is: ,in When learning a network for static parameters, equal ; When learning a network for dynamic parameters, equal ; F is the reconstructed hydrological model, x is the parameter of the hydrological model; , is the constant parameter of the hydrological model of the ith basin; Learning neural networks for static parameters; The static attribute data of the ith watershed for the static parameter learning neural network; , is the parameter of the hydrological model of the ith basin at time t; Learning neural networks for dynamic parameters; The dynamic characteristic data of the ith watershed at the tth moment for the dynamic parameter learning neural network.

6. The hydrological hybrid modeling method based on differentiable parameter learning according to claim 1, characterized in that: The coupling process is specifically as follows: using the simulated value of the target variable output by the hydrological model, constructing a loss function between the simulated value and the actual observed value, adjusting the output of the parameter learning neural network through gradient back propagation, and then using the output of the parameter learning neural network as the input of the reconstructed hydrological model to predict the target variable.

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