A daily runoff prediction method based on a water balance equation-guided deep learning model

Abstract

The present invention discloses a daily runoff prediction method of a deep learning model guided by a water balance equation, which comprises the following steps: 1. obtaining runoff and meteorological data in the study basin; 2. determining the physical mechanism; 3. establishing an LSTM model; 4. constructing a respective PG-LSTM model at each meteorological station; 5. establishing a total PG-LSTM model of the basin. The present invention has the following beneficial effects: the deep learning model guided by the physical mechanism constructed by the present invention not only has higher simulation accuracy in the simulation and prediction of the daily runoff process, but also has better physical consistency of the simulation results.

Description

Technical Field

[0001] The present invention relates to a method for simulating regional daily runoff, in particular to a method for predicting daily runoff based on a deep learning model guided by a monotonic relationship between precipitation and runoff. Background Art

[0002] Runoff is an important part of the water cycle. It determines the water resources and ecological environment in a certain area to a certain extent. It is particularly important to obtain the dynamic changes of river runoff on different time scales in a timely and accurate manner. Runoff prediction is one of the key tasks of effective water resources management. Its purpose is to obtain the runoff in a certain basin through certain prior knowledge and technical means, and to formulate relevant plans and policies based on the runoff prediction results. Accurate runoff prediction can enable people to take corresponding measures early on in drought and flood prevention, water abandonment and water storage, and make overall arrangements, so as to maximize the comprehensive benefits under the premise of safety.

[0003] The current runoff prediction models are mainly divided into two categories: one is process-driven models and the other is data-driven models. Generally speaking, traditional rainfall-runoff models predict runoff based on hydrological processes, and these sub-processes are driven by physical mechanisms in a nonlinear manner, including evapotranspiration, interception, infiltration, soil moisture and groundwater exchange, as well as the impact of water conservancy projects and other human activities. Based on past observational studies, people have formed mechanism approximations for these hydrological processes and given them certain physical meanings. However, the actual hydrological cycle process is very complex, and the research on some of its mechanisms is also insufficient. Therefore, people often need to simplify complex hydrological processes or make assumptions instead, which makes it impossible to use simple physical laws and mathematical equations to explain all hydrological processes and make accurate hydrological forecasts [3].

[0004] Compared with process-driven models, data-driven models do not need to consider the complex practical principles of the hydrological cycle. They can directly learn the relationship between input data and output runoff from hydrological big data and obtain excellent prediction results. Data-driven models do not need to call assumptions and approximations for specific problems, nor do they ignore the physical laws behind the data set. They only consider the correlation between the input data set and the output, and use their powerful data processing capabilities to build a system model about the relationship between input and output from scratch. The performance of the constructed model is often better than that of the process-driven model. However, this data-driven model does not rely on expert knowledge at all. The relationship between input and output is mined from the input data set itself, is invisible, and lacks consistency with the physical principles of the real world. Although the model has high prediction performance, their prediction results lack physical interpretability.

[0005] In summary, data-driven models can provide highly accurate runoff predictions, but the prediction results lack physical interpretability. On the contrary, the prediction results based on process-driven models are more convincing in terms of interpretability, but due to its complex hydrological cycle, it is difficult to achieve a good breakthrough in prediction accuracy. Coupling these two methods and using physical mechanisms to fill the lack of physical knowledge in data-driven models can make the runoff prediction accuracy relatively high while also having a certain degree of physical consistency. Summary of the invention

[0006] In view of the above-mentioned deficiencies in the prior art, the object of the present invention is to provide a method for daily runoff prediction based on a deep learning model guided by the monotonic relationship between precipitation and runoff, so as to further improve the runoff simulation accuracy and physical consistency.

[0007] In order to solve the above problems, the present invention adopts the following technical solutions.

[0008] 1. Obtain runoff and meteorological data within the study basin;

[0009] 2. Determine the physical mechanism: Use the meteorological data and runoff data obtained in step 1 to analyze and determine the monotonic relationship between rainfall and runoff;

[0010] 3. Establish LSTM model: Using the data obtained in step 1, establish LSTM runoff prediction model on a single weather station;

[0011] 4. Build a PG-LSTM model at each weather station: Add the physical mechanism determined in step 2 to the activation function of the LSTM model established in step 3, build a new activation function and a new PG-LSTM model;

[0012] 5. Establish the total PG-LSTM model of the watershed: Use the PG-LSTM model established in step 4 to assign the weight of each meteorological station and establish the PG-LSTM model of the complete watershed;

[0013] The step 4 includes the following sub-steps:

[0014] Step 4.1: When there is precipitation, if the duration of precipitation reaches the hyperparameter threshold of whether the soil moisture content in the watershed is saturated, then the constraint of the physical loss function is added to the activation function of the LSTM model established in step 3; if the duration of precipitation is short, then the constraint of the physical loss function is not added to the activation function of the LSTM model established in step 3;

[0015] Step 4.2: When there is no precipitation, form corresponding physical constraints according to the water balance equation;

[0016] The loss function of the physics-guided LSTM is as follows:

[0017] Loss = λ data Loss MSE +λ PHY (Loss PHY1 +Loss PHY2 )

[0018] Where Loss is the loss function; λ data is the weight coefficient of simulated runoff; Loss MSE is the mean square error of the LSTM model simulating runoff; PHY is the weight coefficient corresponding to monotonicity; Loss PHY1 and Loss PHY2 They are the physical constraints when there is continuous precipitation and when there is no precipitation, respectively.

[0019] The present invention has the following beneficial effects:

[0020] (1) The present invention uses the water balance equation to guide neural network modeling, constructs a PG-LSTM model guided by a physical loss function, uses the monotonic relationship between precipitation and runoff in the water balance equation to form an inequality constraint, and uses recent precipitation as the weight of the physical constraint. The physical inequality constraint is used as an additional term to the original loss function to guide the training of the model. In short, the present invention uses a physical loss function constructed using known physical laws, which plays a role of physical regularization in deep learning training.

[0021] (2) The present invention applies a method combining a new physical mechanism with deep learning to the prediction of runoff in the upper reaches of the Heihe River, which improves the prediction accuracy while ensuring its physical consistency, produces results with physical significance, and provides important decision-making basis for scientifically formulating water use plans, improving water resource utilization, and alleviating the contradiction between supply and demand.

[0022] In summary, the constructed physical mechanism-guided deep learning model not only has higher simulation accuracy in the simulation and prediction of daily runoff processes, but also has better physical consistency of the simulation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 The overall method flow chart proposed by the present invention DETAILED DESCRIPTION

[0024] The present invention is further described in detail below with reference to the accompanying drawings and examples.

[0025] like Figure 1As shown, the present invention is a method for predicting runoff by using a water balance equation to guide neural network modeling and constructing a PG-LSTM model guided by a physical loss function. The purpose of optimizing the model is achieved by adding the physical mechanism that rainfall runoff has monotonicity to the activation function of the LSTM model. The method proposed in the present invention uses a water balance equation to guide neural network modeling and constructs a PG-LSTM model guided by a physical loss function to predict runoff, which can be summarized into three major links:

[0026] ⑴ Determine the monotonicity between rainfall and runoff:

[0027] After obtaining the rainfall-runoff data from the three meteorological stations of Qilian, Tuole, and Yeniugou in the upper reaches of the Heihe River and the Yingluoxia hydrological station, the monotonic relationship between rainfall and runoff was determined:

[0028] q t =p t -e t -Δs t (1)

[0029] Where q t is the flow yield of the basin; p t is the precipitation in the basin; e t is the evapotranspiration in the basin; Δs t It is the change of soil moisture content in the basin.

[0030] The water balance equation above clearly shows the dynamic interaction between runoff and precipitation intensity, evapotranspiration, infiltration and soil water storage. Precipitation is the only source of water in the watershed system. To a certain extent, precipitation intensity determines the intensity of runoff, and the relationship between precipitation and runoff should be monotonic, that is, at the current time step, if precipitation increases slightly, the runoff should also be greater.

[0031] (2) Constructing PG-LSTM models on three weather stations:

[0032] First, it is necessary to build a traditional LSTM model based on the maximum temperature, minimum temperature and rainfall at each weather station, and then design a physics-based loss function through the monotonic relationship between precipitation and runoff to build a new PG-LSTM model.

[0033] There are two common ways to construct loss functions guided by physical mechanisms: equality constraints based on physical equations and inequality constraints using properties such as monotonicity. The following equation is used to represent the physical relationship between the target variable Y and other physical variables Z:

[0034] G(Y,Z)=0(2)

[0035] H(Y,Z)≤0(3)

[0036] Where G and H are general forms of equations based on physical mechanisms, which can be algebraic operations of Y and Z or their partial differentials. For equality constraints, they can be converted into specific loss values ​​by squaring, and for inequality constraints, they can be converted into specific loss values ​​by using the Re-LU function, as follows:

[0037]

[0038] As can be seen from the formula, the physical loss function does not require actual observation of the target variable Y, so compared with the traditional loss function, it can even allow the training samples to contain data without the target variable Y and evaluate sample data without labels.

[0039] Generally speaking, the standard approach to deep learning model training is to minimize its model simulation value. The empirical loss on the training set is as follows:

[0040]

[0041] Therefore, the complete loss function of the physics-guided deep learning model can be expressed as:

[0042]

[0043] where λ and λ PHY is a hyperparameter that controls the relative importance of the empirical loss and physical loss functions.

[0044] When there is precipitation, if the precipitation lasts for a certain period of time, it is considered that the soil moisture content in the basin is saturated, and the runoff increase is more obvious, so the physical loss function constraint is added; if the precipitation lasts for a short period of time, it is considered that the soil moisture content in the basin is not saturated, and the increase in runoff due to precipitation is not obvious. To prevent overfitting, such a situation is ignored. The details are as follows:

[0045]

[0046] Where T is the total number of training samples in each batch; L is the number of days of precipitation; a is the hyperparameter threshold for determining whether the soil moisture content in the basin is saturated. If the number of days of precipitation is greater than or equal to a, the soil moisture content is considered to be saturated and the impact of precipitation on runoff is large. Otherwise, the soil moisture content is considered to be unsaturated and the impact of precipitation on runoff is not obvious; M is the number of days for which recent precipitation is selected as the physical constraint weight; P t-m is the precipitation at time tm; ReLU(·) is a piecewise linear function that changes all negative values ​​to 0 while keeping positive values ​​unchanged; is the simulated runoff value of the deep learning model at time t; Y t-1 is the actual observed runoff value at time t-1.

[0047] First, determine whether the number of days of precipitation has reached the threshold, and impose physical constraints on the sample data that has reached the threshold. When it rains continuously, if the runoff increases, is positive, then is 0; if runoff decreases, is negative, then If it is greater than 0, a constraint will be formed. At the same time, precipitation is also used as a weight indicator, which combines the recent precipitation accumulation with The multiplication result is used to constrain model training, where the greater the precipitation, the greater the weight it has and the greater the penalty caused by reduced runoff.

[0048] When there is no precipitation, if it continues to be rainless, there is no water input into the basin. According to the water balance equation, it is believed that the runoff will decrease (at least not increase), thus forming a physical constraint, as follows:

[0049]

[0050] Where b is the duration threshold for determining that there is no precipitation in the basin. If the number of days without precipitation is greater than or equal to b, it is believed that the runoff will not increase without reason. Otherwise, it is impossible to determine whether the runoff is affected by recent precipitation.

[0051] First, determine whether the number of days without precipitation reaches the threshold, and impose physical constraints on the sample data that reaches the threshold. When it does not rain, if the runoff decreases, is negative, then is 0; if runoff increases, is positive, then If it is greater than 0, a constraint will be formed.

[0052] Combining the physical loss function principle and the monotonic relationship between precipitation and runoff to construct the loss function of the physically guided LSTM is as follows:

[0053] Loss = λ data Loss MSE +λ PHY (Loss PHY1 +Loss PHY2 ) (9)

[0054] Where Loss is the loss function; λ data is the weight coefficient of simulated runoff; Loss MSE is the mean square error of the LSTM model simulating runoff; PHY is the weight coefficient corresponding to monotonicity; Loss PHY1 and Loss PHY2are the physical constraints under continuous precipitation and no precipitation, respectively. Formula (9) expresses the method of adding the physical mechanism to the activation function of the LSTM model, constructing a new activation function and a new PG-LSTM model.

[0055] The above processing can be summarized as follows: when there is precipitation, if the precipitation lasts for a certain period of time, it is considered that the soil moisture content in the basin is saturated, the runoff increase is more obvious, and the constraint of the physical loss function is added; if the precipitation lasts for a short period of time, it is considered that the soil moisture content in the basin is not saturated, and the increase in runoff due to precipitation is not obvious. In order to prevent overfitting, such a situation is ignored:

[0056] When there is no precipitation, if it continues without rain and there is no water input into the basin, according to the water balance equation, it is believed that the runoff will decrease (at least not increase), thus forming a physical constraint.

[0057] ⑶ Assign weights to each weather station, build a PG-LSTM model for the entire basin and evaluate it.

[0058] The weights of the three meteorological stations in the upper reaches of the Heihe River were set equal. After multiple experimental evaluations, the weight of each meteorological station was set to 0.1, forming an LSTM model with a data weight of 0.7 and a physical mechanism of the meteorological station of 0.3.

[0059] The efficiency coefficient (NSE), root mean square error (RMSE), correlation coefficient (r), volume error (Ve), relative error (RE) and relative difference of peak flow (RD) are used to evaluate the model accuracy and physical consistency. The formula is as follows:

[0060]

[0061] In the above formula, Q o refers to the observed value, Q m Refers to the analog value, Q t represents a value at time t, represents the grand average of the observations, Represents the total average of the simulated values. The present invention obtains results with high accuracy and certain physical explanatory power. The accuracy and physical consistency of the daily-scale runoff data simulated using the PG-LSTM model were evaluated, and the results showed that the new model has a significant improvement over the old model.

[0062] By adding the physical mechanism of rainfall runoff monotonicity to the activation function of the traditional deep learning neural network LSTM (Long Short-Term Memory Network, a variant of RNN), the LSTM model can be trained to converge quickly and accelerate the training of the model. The model constructed in this way has the advantages of high accuracy, strong physical interpretation, fewer training samples and faster training speed than the traditional deep learning LSTM model.

[0063] Finally, it should be noted that the above implementation examples are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to preferred examples, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A daily runoff prediction method based on a water balance equation guided deep learning model, characterized in that: It includes the following steps:

1. Obtain runoff and meteorological data within the study basin; 2. Determine the physical mechanism: Use the meteorological data and runoff data obtained in step 1 to analyze and determine the monotonic relationship between rainfall and runoff; 3. Establish LSTM model: Using the data obtained in step 1, establish LSTM runoff prediction model on a single weather station; 4. Build a PG-LSTM model at each weather station: Add the physical mechanism determined in step 2 to the activation function of the LSTM model established in step 3, build a new activation function and a new PG-LSTM model; 5. Establish the total PG-LSTM model of the watershed: Use the PG-LSTM model established in step 4 to assign the weight of each meteorological station and establish the PG-LSTM model of the complete watershed; The step 4 includes the following sub-steps: Step 4.1: When there is precipitation, if the duration of precipitation reaches the hyperparameter threshold of whether the soil moisture content in the watershed is saturated, then the constraint of the physical loss function is added to the activation function of the LSTM model established in step 3; if the duration of precipitation is short, then the constraint of the physical loss function is not added to the activation function of the LSTM model established in step 3; Step 4.2: When there is no precipitation, form corresponding physical constraints according to the water balance equation; The loss function of the physics-guided LSTM is as follows: Loss=λ data Loss MSE +λ PHY (Loss PHY1 +Loss PHY2 ) Where Loss is the loss function; λ data is the weight coefficient of simulated runoff; Loss MSE is the mean square error of the LSTM model simulating runoff; PHY is the weight coefficient corresponding to monotonicity; Loss PHY1 and Loss PHY2 They are the physical constraints when there is continuous precipitation and when there is no precipitation, respectively.

2. The daily runoff prediction method based on a water balance equation guided deep learning model according to claim 1 is characterized in that: The monotonic relationship between rainfall and runoff determined in step 2 is: q t =p t -e t -Δs t Among them, q t is the flow yield of the basin; p t is the precipitation in the basin; e t is the evapotranspiration in the basin; Δs t It is the change of soil moisture content in the basin.

3. The daily runoff prediction method based on a water balance equation guided deep learning model according to claim 1 or 2, characterized in that: It also includes step six: evaluating the accuracy and physical consistency of the model obtained in step five using efficiency coefficient, root mean square error, correlation coefficient, volume error, relative error and relative difference in peak flow.

4. A daily runoff prediction method based on a water balance equation guided deep learning model according to claim 1, 2 or 3, characterized in that: The step five includes the following sub-steps: Step 5.1: Determine the weight coefficients of data and physical functions in the loss function; Step 5.2: Assign the same weight coefficient to each site when building the overall PG-LSTM model.

5. The daily runoff prediction method based on a water balance equation guided deep learning model according to claim 4 is characterized in that: The weight coefficients of the data and the physical function in the loss function are: data accounts for 0.7, and the physical function accounts for 0.

3.

6. The daily runoff prediction method based on a water balance equation guided deep learning model according to claim 3 is characterized in that: The process of evaluating model performance is: Step 6.1: Use efficiency coefficient, root mean square error, and correlation coefficient to evaluate the accuracy of the model prediction results: Step 6.2: Assess the physical consistency of the model using volume error, relative error, and relative difference in peak flow.

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