A physical mechanism-guided deep learning rainfall runoff simulation method

Abstract

This paper proposes a physical mechanism-guided deep learning rainfall-runoff simulation method. Combining hydrological physics and hydrometeorological big data, this method implements a physical mechanism-guided deep learning simulation solution by setting a penalty term in the optimization function. It also uses extreme event samples as penalties, taking into account both heavy rain events and long periods of no rain, and proposes a new calculation formula. Compared with traditional deep learning methods, the runoff simulation method provided by this method solves the problem of deep learning lacking physical mechanisms and avoids non-monotonicity in the simulation process. This method can be widely applied to rainfall-runoff simulation, and can systematically and comprehensively complete runoff simulation and prediction, providing a basis for scientific decision-making.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrological models, and in particular relates to a rainfall runoff simulation method guided by deep learning using physical mechanisms. Background Art

[0002] Runoff prediction is fundamental to water resource management, allocation, and efficient utilization. Hydrological models use meteorological data such as precipitation to calculate runoff for prediction and forecasting purposes.

[0003] Theory-based models are well-suited for representing processes conceptually well-understood based on known scientific principles. However, due to the inherent complexity of hydrological processes, traditional hydrological models struggle to express processes that are difficult to understand outside current knowledge. In these situations, theory-based models are often forced to make simplifying assumptions about physical processes and set conceptual parameters. This not only leads to poor model performance but also hinders a thorough understanding and analysis of runoff formation mechanisms.

[0004] Deep learning models rely on the information contained in data and are widely applicable in fields with large, representative data samples. Big data-based deep learning methods, as algorithms suitable for fitting highly nonlinear systems, have been applied to rainfall-runoff simulation. This approach ignores complex underlying surface conditions and hydrological processes, instead learning and storing a large number of input-output mapping relationships to understand and analyze runoff variations. However, it lacks physical mechanisms and can only capture correlations between variables, thus failing to fully address the goal of understanding causal relationships in scientific problems.

[0005] Data-driven rainfall-runoff simulation mainly adopts deep learning methods to solve time series problems, but the existing deep learning rainfall-runoff simulation methods have the following problems: (1) The probability of extreme rainfall in historical data is very low, which leads to large errors in the model's simulation of the peak flow of extreme rainstorms, and it is very easy to cause water imbalance; (2) It often leads to the occurrence of negative flow, and when faced with extreme conditions of long-term rainless periods, the model will also collapse; (3) When using hydrological models based on physical mechanisms to simulate runoff, the rainfall-runoff relationship is monotonic. The greater the rainfall, the greater the corresponding runoff, and the greater the evaporation, the smaller the corresponding runoff. However, traditional deep learning rainfall-runoff simulation methods cannot guarantee the monotonicity of the simulation. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a rainfall runoff simulation method guided by deep learning based on physical mechanisms in response to the above-mentioned problems, which uses physical theory and measured data in combination.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a physical mechanism-guided neural network rainfall runoff simulation method, characterized by comprising the following steps:

[0008] S1) Selecting a deep learning model for predicting and simulating hydrological time series;

[0009] S2) Based on the historical meteorological, hydrological, and time data of the current day and several days ago, the data is normalized and used as model input, and the runoff value is simulated according to the deep learning model.

[0010] S3) selecting the first 70% of the time series as a training set, selecting the objective function training model parameters, adding a penalty term for the hydrological physical process to the traditional mean square error optimization objective of the model, and determining the objective function calculation formula;

[0011] S4) The remaining 30% of the time series is used as a validation set to verify the model effect and obtain the runoff simulation value.

[0012] According to the above scheme, the historical meteorological data in step S2 includes precipitation p, maximum and minimum temperatures T max , T min , potential evapotranspiration e, solar radiation S, atmospheric pressure V p , the hydrological data is the runoff q, the simulated runoff value As follows:

[0013]

[0014] Where f is the simulation function of the deep learning method; X is the input data; and t is the time data.

[0015] According to the above scheme, the objective function calculation formula in step S3 is as follows:

[0016] L(θ)=λ data MSE data +λ ∞ MSE ∞ +λ0MSE0+λ mcp MSE mcp +λ mce MSE mce

[0017]

[0018] Where L(θ) is the objective function; MSE data is the mean square error of the simulated runoff data using the deep learning method; data MSE data Weight coefficient; n tis the length of time data; MSE ∞ is the mean square error penalty term of the deep learning model in response to extreme rainstorm events; ∞ MSE ∞ The weight coefficient of MSE0 is the mean square error penalty term of the deep learning model in response to long-term rainless events; λ o is the weight coefficient of MSE0; mcp is the mean square error penalty term of the deep learning model to cope with the rainfall monotonicity constraint; mcp MSE mcp Weight coefficient; MSE mce is the mean square error penalty term of the deep learning model to cope with the evaporation monotonicity constraint; mce MSE mcp The weight coefficient of .

[0019] According to the above scheme, the penalty items include the following:

[0020] S41) The deep learning model uses the following formula to calculate the occurrence of extreme rainstorm events:

[0021] f[p ∞ ,t]-p ∞ =0 t>t F

[0022]

[0023] Where p ∞ is the rainfall value of the extreme rainstorm event; after the basin experiences a long period of heavy rain, the soil moisture content is close to the full state. At the full time t F After that, the rainstorm will be converted into runoff after deducting the evaporation loss; p is the number of different rainstorm levels;

[0024] S42) The deep learning model uses the following formula to calculate the occurrence of long-term rainless events:

[0025] f[p 0 , t]=0 t→∞

[0026]

[0027] Where p 0 is the rainfall value of a long-term rainless event, that is, 0 mm. When the basin experiences a long-term rainless situation, the soil moisture content is exhausted and no runoff occurs;

[0028] S43) The deep learning model should use the following formula to calculate the rainfall monotonicity constraint:

[0029] f[p1,t]-f[p2,t]≥0 p1>p2

[0030]

[0031] Where n p is the number of monotonic constraints for different rainfall levels from small to large; ReLU is the activation function, which excludes the non-negative terms that satisfy the monotonic relationship and only calculates the mean square error of the negative terms of the non-monotonic relationship; Δp i It is a small change of a certain magnitude added to the rainfall data;

[0032] S44) The deep learning model should use the following formula to calculate the evaporation monotonicity constraint:

[0033] f[e1,t]-f[e2,t]≤0 e1>e2

[0034]

[0035] Where n e is the number of monotonic constraints for different evaporation levels from small to large; Δe i It is a small change of a certain magnitude added to the evaporation data.

[0036] The beneficial effects of the present invention are: 1. It provides a rainfall runoff simulation method guided by deep learning of physical mechanisms, combines hydrological physical processes and hydrometeorological big data, and realizes a deep learning simulation scheme guided by physical mechanisms by setting the penalty term of the optimization function; 2. It uses samples of extreme events as penalties, considers both heavy rain events and long-term rainless events, and proposes a new calculation formula; 3. Compared with traditional deep learning methods, the provided runoff simulation method solves the problem of lack of physical mechanisms in deep learning and avoids non-monotonicity in the simulation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 The flowchart of one embodiment of the present invention is shown in FIG.

[0038] Figure 2a 、 Figure 2b A comparison chart of runoff simulation results in a watershed before and after adding a rainless sample, provided in one embodiment of the present invention.

[0039] Figure 3a 、 Figure 3b A comparison chart of runoff simulation results in a certain watershed before and after adding extreme rainstorm samples of different magnitudes, provided in one embodiment of the present invention.

[0040] Figure 4 A comparison chart of daily model result indicators for traditional deep learning and physical mechanism-guided deep learning, provided for one embodiment of the present invention. DETAILED DESCRIPTION

[0041] For a better understanding of the present invention, the present invention is further described below with reference to the accompanying drawings and embodiments.

[0042] like Figure 1 As shown, the present invention provides a rainfall runoff simulation method guided by deep learning based on physical mechanisms. The technical solution of the present invention specifically includes the following steps:

[0043] Step 1: Select a deep learning model for predicting and simulating hydrological time series, such as a long short-term memory neural network (LSTM) model;

[0044] Step 2: Based on the historical weather conditions of the day and a few days ago (precipitation p, maximum and minimum temperatures T max , T min , potential evapotranspiration e, solar radiation S, atmospheric pressure V p etc.), hydrological (runoff q), and time data are normalized and used as model inputs;

[0045]

[0046] Where, is the runoff value simulated by the deep learning method; f is the simulation function of the deep learning method; X is the input data; t is the time data.

[0047] Step 3: Select the first 70% of the time series as the training set and select the objective function training model parameters;

[0048] Step 4: Add the penalty term of hydrological physical process to the traditional mean square error optimization objective of the model and calculate it according to the following formula:

[0049] L(θ)=λ data MSE data +λ ∞ MSE ∞ +λ0MSE0+λ mcp MSE mcp +λ mce MSE mce (2)

[0050]

[0051] Where L(θ) is the objective function; MSE data is the mean square error of the simulated runoff data using the deep learning method; data MSE data Weight coefficient; n t is the length of time data; MSE ∞is the mean square error penalty term of the deep learning model in response to extreme rainstorm events; ∞ MSE ∞ The weight coefficient of MSE0 is the mean square error penalty term of the deep learning model in response to long-term rainless events; λ o is the weight coefficient of MSE0; mcp is the mean square error penalty term of the deep learning model to cope with the rainfall monotonicity constraint; mcp MSE mcp Weight coefficient; MSE mce is the mean square error penalty term of the deep learning model to cope with the evaporation monotonicity constraint; mce MSE mcp The weight coefficient of ; among them, the different objective penalty items of the hydrological physical process are as follows:

[0052] (1) The deep learning model uses the following formula to calculate the occurrence of extreme rainstorm events:

[0053] f[p ∞ ,t]-p ∞ =0 t>t F (4)

[0054]

[0055] Where p ∞ is the rainfall value of the extreme rainstorm event; after the basin experiences a long period of heavy rain, the soil moisture content is close to the full state. At the full time t F After that, the rainstorm (minus evaporation loss) will be completely converted into runoff; MSE ∞ is the mean square error penalty term of the deep learning model in response to extreme rainstorm events; n p is the number of different rainstorm levels.

[0056] (2) The deep learning model uses the following formula to calculate the occurrence of long-term rainless events:

[0057] f[p 0 , t]=0 t→∞ (6)

[0058]

[0059] Where p 0 is the rainfall value of a long-term rainless event (i.e., 0 mm). When the basin experiences a long-term rainless situation, the soil moisture content is exhausted and no runoff occurs. MSE0 is the mean square error penalty term of the deep learning model in response to long-term rainless events.

[0060] (3) The deep learning model should use the following formula to calculate the rainfall monotonicity constraint:

[0061] f[p1,t]-f[p2,t]≥0 p1>p2 (8)

[0062]

[0063] Where, MSE mcp is the mean square error penalty term of the deep learning model in response to rainfall monotonicity constraint; n p is the number of monotonic constraints for different rainfall levels (from small to large); ReLU is the activation function, which excludes the non-negative terms that satisfy the monotonic relationship and only calculates the mean square error of the negative terms of the non-monotonic relationship; Δp i It is a small change of a certain magnitude added to the rainfall data.

[0064] (4) The deep learning model should use the following formula to calculate the evaporation monotonicity constraint:

[0065] f[e l ,t]-f[e2,t]≤0 e1>e2 (10)

[0066]

[0067] Where, MSE mce is the mean square error penalty term of the deep learning model to cope with the evaporation monotonicity constraint; n e is the number of monotonic constraints for different evaporation levels (from small to large); Δe i It is a small change of a certain magnitude added to the evaporation data.

[0068] Step 5: Use the remaining 30% length time series as a validation set to verify the model effect and obtain the runoff simulation value.

[0069] As a specific embodiment, the evaluation index of hydrological forecast calculation accuracy adopts the Nash efficiency coefficient NSE, which can be calculated according to formula (12):

[0070]

[0071] Where Q obs is the model simulation flow, Q sim is the measured flow rate, is the average of the measured traffic, and N is the sequence length.

[0072] As a specific example, first, set the number of training iterations to 1000, the hidden layer size to 40, the number of stacking layers to 1, the learning rate to 5‰, the batch size to 1 / 10 of the total number of samples, and the max-min normalization method. The lag time is set to 20 days, the weight of traditional indicators can be 0.6, and the weight of other indicators can be 0.1.

[0073] In one specific example, a physics-based deep learning model was used to simulate rainfall and runoff from the Catchment Attributes and Meteorology for Large-sample Studies Dataset (Camels), a dataset of 671 consecutive river basins in the United States that were minimally impacted by human activities. The model was run on a daily time scale, with three sets of meteorological input data from different sources for each river basin. The rainfall and runoff simulation method was compared for different extreme rainstorms, long periods of no rainfall, and sample sizes, and the optimal sample number and sample size were determined based on the compared computational accuracy.

[0074] from Figure 2a and 2b It can be seen that adding virtual samples without rain can effectively reduce the occurrence of negative flow.

[0075] from Figure 3a and 3b It can be seen that adding virtual samples of extreme rainstorms can effectively improve the flood peak simulation and is related to the magnitude of the rainstorm.

[0076] The simulation results of the embodiment on 671 Camels basins are as follows Figure 4 As shown in the figure, preliminary results show that the forecast results after physical mechanism constraints (PHY-1, 2, and 3) are more accurate than the traditional deep learning forecast results (LTSM-1, 2, and 3). The NSE of the deep learning model based on the physical mechanism during the test period increased from a mean of 0.59 and a median of 0.66 to a mean of 0.62 and a median of about 0.69.

[0077] The target prediction error during the test period using the deep learning model based on physical mechanisms was significantly reduced: the mean square error of the extreme rainstorm constraint was reduced from a mean of 0.44 to a mean of 0.23; the mean square error of the long-term rainless constraint was reduced from a mean of 0.58 to a mean of 0.45; the mean square error of the rainfall monotonicity constraint was reduced from a mean of 0.20 to a mean of 0.07. The physical robustness of the deep learning model based on physical mechanisms has been greatly improved.

[0078] The rainfall runoff simulation method based on physical mechanism-guided deep learning provided by the embodiment of the present invention adds a penalty term of the hydrological physical process to the traditional mean square error optimization objective of the model, constrains the traditional deep learning model, solves the phenomenon that the deep learning model does not meet the physical mechanism constraints, and improves the simulation calculation accuracy, calculation efficiency and stability.

Claims

1. A rainfall runoff simulation method guided by deep learning based on physical mechanisms, characterized by: The steps include: S1) Selecting a deep learning model for predicting and simulating hydrological time series; S2) Based on the historical meteorological, hydrological, and time data of the current day and several days ago, the data is normalized and used as model input, and the runoff value is simulated according to the deep learning model. ; S3) Select the first 70% of the time series as the training set, select the objective function training model parameters, add the penalty term of the hydrological physical process to the traditional mean square error optimization objective of the model, and determine the objective function calculation formula as follows: Where, is the objective function; is the mean square error of the simulated runoff data using the deep learning method; for The weight coefficient of is the length of time data; is the mean square error penalty term of the deep learning model in response to extreme rainstorm events; for The weight coefficient of is the mean square error penalty term of the deep learning model in response to long-term rainless events; for The weight coefficient of is the mean square error penalty term for the deep learning model to cope with rainfall monotonicity constraints; for The weight coefficient of is the mean square error penalty term for the deep learning model to cope with the evaporation monotonicity constraint; for The weight coefficient of S4) The remaining 30% of the time series is used as a validation set to verify the model effect and obtain the runoff simulation value.

2. The rainfall-runoff simulation method based on physical mechanism-guided deep learning according to claim 1 is characterized in that: The historical meteorological data in step S2) includes precipitation , maximum and minimum temperatures , potential evapotranspiration , solar radiation , atmospheric pressure , the hydrological data is runoff , the simulated runoff value is as follows: Where, is the simulation function of the deep learning method; is the input data; For time data.

3. A rainfall-runoff simulation method guided by deep learning based on physical mechanisms according to claim 1 or 2, characterized in that: The penalty items include the following: S41) The deep learning model uses the following formula to calculate the occurrence of extreme rainstorm events: Where, is the rainfall value of the extreme rainstorm event; After a long period of heavy rain in the basin, the soil water content is close to full. After that, the rainstorm will be converted into runoff after deducting the evaporation loss; is the number of different rainstorm levels; S42) The deep learning model uses the following formula to calculate the occurrence of long-term rainless events: Where, is the rainfall value of a long-term rainless event, that is, 0 mm. When the basin experiences a long-term rainless situation, the soil moisture content is exhausted and no runoff will occur; S43) The deep learning model should use the following formula to calculate the rainfall monotonicity constraint: Where, is the number of monotonicity constraints for different rainfall levels from small to large; It is an activation function that excludes non-negative terms that satisfy the monotonic relationship and only calculates the mean square error of negative terms in the non-monotonic relationship. It is a small change of a certain magnitude added to the rainfall data; S44) The deep learning model should use the following formula to calculate the evaporation monotonicity constraint: Where, is the number of monotonic constraints for different evaporation levels from small to large; It is a small change of a certain magnitude added to the evaporation data.

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