Drainage basin rainfall runoff prediction method and device fusing mechanism model and machine learning model, and program product

Abstract

The invention discloses a drainage basin rainfall runoff prediction method and device fusing a mechanism model and a machine learning model, and a program product. The method comprises the following steps: firstly, constructing a seasonal Markov chain model by taking a seasonal rainfall state transition probability as a conditional transition probability; simulating the rainfall state of each day in a preset simulation period by adopting a seasonal Markov chain model, simulating the rainfall capacity of each day according to the distribution obeyed by the rainfall capacity of each seasonal characteristic time period, and generating a rainfall sequence in the preset simulation period; predicting the runoff yield of each day under a specified rainfall sequence in a preset simulation period by adopting a drainage basin mechanism model, and counting the earlier-stage accumulated rainfall capacity and seasonal characteristics as the input characteristics of runoff yield prediction; and finally, taking the input features of all runoff prediction in a preset simulation period and the corresponding runoff simulation values as a data set, training a machine learning model, and predicting the runoff in the future by adopting the trained machine learning model. The method is high in prediction efficiency and high in prediction precision.

Description

Technical Field

[0001] The present invention relates to a watershed rainfall runoff prediction technology, and in particular to a watershed rainfall runoff prediction method, device and program product integrating a mechanism model and a machine learning model. Background Art

[0002] Basin rainfall runoff prediction refers to predicting the corresponding runoff based on a rainfall process in the basin. Traditional basin rainfall runoff prediction mainly relies on mechanism models, such as semi-distributed hydrological models HSPF (HydrologicalSimulation Program Fortran) and LSPC (Loading Simulation Program C). These models are based on physical process simulation and require a large number of complex numerical calculations, which leads to long calculation time of the model and makes it difficult to meet the needs of real-time prediction and rapid response. In the simulation of large-scale data or long time series, the demand for computing resources is more significant. In addition, if rapid deduction is required, the calculation time for on-site deduction using mechanism models is long and cannot meet decision-making needs.

[0003] With the widespread application of machine learning models, some researchers have begun to use machine learning models for basin rainfall prediction, such as patent documents such as 202210642420, 202011375784.8, and 202310968062.0. Although machine learning models have advantages in pattern recognition and nonlinear mapping, machine learning models need to be trained with a large amount of high-quality training data. However, in the field of hydrology and water environment, measured data are often limited, especially data on extreme events are more scarce, which limits the learning of machine learning models for complex hydrological processes, reduces the generalization ability of the model, and reduces the prediction accuracy. Moreover, machine learning models are usually regarded as "black boxes" and lack the ability to explain physical processes, which makes it difficult for hydrological experts and decision makers to trust the prediction results of machine learning models, reducing their credibility in practical applications. In addition, the features of existing machine learning models are not comprehensive, resulting in the inability of the models to capture the impact of other factors related to rainfall and runoff in addition to rainfall, reducing the prediction accuracy. Summary of the invention

[0004] In view of the problems existing in the prior art, the purpose of the present invention is to provide a method, device and program product for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model with high prediction efficiency and high prediction accuracy.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions: A basin rainfall runoff prediction method integrating a mechanism model and a machine learning model comprises the following steps: (1) Obtain historical rainfall data of the basin and perform preprocessing; (2) Divide a year into several seasonal characteristic time periods, and calculate the seasonal rainfall state transition probability of each seasonal characteristic time period and the distribution of rainfall in each seasonal characteristic time period based on historical rainfall data; (3) The seasonal rainfall state transition probability is used as the conditional transition probability to construct a seasonal Markov chain model, and the rainfall state of each day within the preset simulation period is simulated according to the seasonal Markov chain model; (4) According to the distribution of rainfall in each seasonal characteristic time period and the daily rainfall state in the preset simulation period, the daily rainfall state and the corresponding rainfall in the rainfall state sequence are combined as the seasonal simulated rainfall sequence; (5) Based on the seasonal simulated rainfall sequence, the basin mechanism model is used to simulate the rainfall runoff in the basin and obtain the simulated runoff value for each day in the simulation period; (6) Extract the cumulative rainfall and seasonal characteristics of the previous several days of each day within the preset simulation period, and integrate them with the rainfall of the day as the input features for runoff prediction; (7) using the input features of all runoff predictions in a preset simulation period and the corresponding runoff simulation values ​​as a data set to train a machine learning ensemble model, wherein the machine learning ensemble model is a weighted integration of several machine learning sub-models; (8) Input the input features of the target watershed runoff prediction into the trained machine learning ensemble model to predict future runoff.

[0006] Furthermore, step (1) specifically includes: (1-1) Obtain historical rainfall data of the basin; (1-2) Identify whether there are abnormal rainfall values ​​in the historical rainfall data, and if so, delete the abnormal rainfall; (1-3) Check whether there are missing values ​​in the historical rainfall data. If so, interpolate the missing values; (1-4) Check whether the historical rainfall data is in a unified time format and unit. If not, unify them.

[0007] Furthermore, step (2) specifically includes: (2-1) According to the historical rainfall data, the daily rainfall status is determined according to the following formula: , In the formula, S t represents the rainfall status of the tth day in the historical rainfall data. Rainfall status 1 indicates rainfall, and rainfall status 0 indicates no rainfall. threshold represents the rainfall threshold, P trepresents the rainfall on day t in the historical rainfall data; (2-2) Divide a year into several seasonal characteristic time periods, and count the number of rainfall state transitions in each seasonal characteristic time period in the basin: , , In the formula, The rainfall state transition indicator variable indicates whether the rainfall state i is transferred to the rainfall state j on the tth day. Indicates yes, Indicates no, represents the number of rainfall state transitions from rainfall state i to rainfall state j within the seasonal characteristic time period s, represents the seasonal characteristic time period s; (2-3) Calculate the seasonal rainfall state transition probability for each seasonal characteristic time period according to the number of rainfall state transitions: , In the formula, represents the rainfall state transition probability from rainfall state i to rainfall state j in seasonal characteristic time period s, represents the number of times rainfall state i occurs within the seasonal characteristic time period s; (2-4) For each seasonal characteristic time period, the rainfall on all dates with rainfall is obtained, and the distribution of the rainfall in the seasonal characteristic time period is obtained by fitting based on the rainfall, wherein the distribution is specifically a Gamma distribution.

[0008] Furthermore, step (3) specifically includes: (3-1) Take the set of all possible rainfall states {0,1} as the state space, and the set of all seasonal rainfall state transition probabilities as the conditional probability set to construct a seasonal Markov chain model; (3-2) According to the rainfall frequency corresponding to the first day of the preset simulation cycle, the simulated rainfall state of the first day is randomly set ; (3-3) Based on the seasonal Markov chain model, the rainfall state of the next day is calculated according to the rainfall state of the previous day according to the corresponding seasonal transition probability, so as to simulate the simulated rainfall state sequence of the preset simulation period. ,in, It represents the simulated rainfall state of the τth day in the simulated rainfall state sequence, and N represents the total number of days in the preset simulation cycle.

[0009] Furthermore, step (4) specifically includes: (4-1) Extracting the dates with rainfall from the simulated rainfall state sequence, and simulating the corresponding rainfall according to the distribution of rainfall in the corresponding seasonal characteristic time period; (4-2) Set the rainfall on the date when the rainfall status is no rainfall to 0; (4-3) The simulated rainfall state and corresponding rainfall amount of each day within the preset simulation period are combined as a seasonal simulated rainfall sequence.

[0010] Furthermore, step (5) specifically includes: (5-1) Obtain the basin’s meteorological data, elevation data, soil parameters, land use data, and vegetation cover data; (5-2) Input seasonal simulated rainfall series, meteorological data, elevation data, soil parameters, land use data and vegetation cover data into the watershed mechanism model to simulate the rainfall-runoff process in the watershed and obtain the simulated runoff value for each day; (5-3) The flow simulation values ​​are formatted in a unified format and then output as a flow time series.

[0011] Furthermore, step (6) specifically includes: (6-1) Calculate the cumulative rainfall of the previous days based on the daily rainfall in the preset simulation period; (6-2) Determine seasonal characteristics based on the seasonal characteristic time period of each day in the preset simulation cycle; (6-3) Standardize daily rainfall, cumulative rainfall, and seasonal characteristics; (6-4) The standardized rainfall, accumulated rainfall, and seasonal characteristics are concatenated to form the input features for runoff prediction.

[0012] Furthermore, step (7) specifically includes: (7-1) Construct several machine learning sub-models based on different machine learning algorithms; (7-2) forming a data set with input features of all runoff predictions and corresponding runoff simulation values ​​within a preset simulation period, and dividing the data set into a first training set, a second training set, a first validation set, a second validation set, a first test set and a second test set; (7-3) Using the first training set to train each machine learning sub-model, using the first validation set to tune the hyperparameters of all machine learning sub-models, and using the first test set to test the capabilities of the machine learning sub-models; (7-4) establishing a machine learning ensemble model, wherein the machine learning ensemble model is a weighted set of all machine learning sub-models; (7-5) Using the second training set to train the machine learning ensemble model, using the second validation set to tune the weights in the machine learning ensemble model to obtain an optimized machine learning ensemble model, and using the second test set to test the capability of the optimized machine learning ensemble model.

[0013] A basin rainfall runoff prediction device integrating a mechanism model and a machine learning model, comprising: The historical rainfall data preprocessing module is used to obtain the historical rainfall data of the basin and perform preprocessing; The transition probability and distribution calculation module is used to calculate the seasonal rainfall state transition probability of each seasonal characteristic time period and the distribution of rainfall in each seasonal characteristic time period according to historical rainfall data; A rainfall state generation module is used to construct a seasonal Markov chain model using the seasonal rainfall state transition probability as a conditional transition probability, and simulate the rainfall state of each day within a preset simulation period according to the seasonal Markov chain model; A rainfall sequence generation module is used to simulate the daily rainfall according to the distribution of rainfall in each seasonal characteristic time period and the daily rainfall state in a preset simulation period, and combine the daily rainfall state and corresponding rainfall in the preset simulation period as a seasonal simulated rainfall sequence; The flow generation simulation module is used to simulate the flow generation of the basin rainfall using the basin mechanism model according to the seasonal simulated rainfall sequence, and obtain the simulated flow generation value of each day in the simulation period; The runoff prediction input feature extraction module is used to extract the cumulative rainfall and seasonal characteristics of the previous several days of each day within the preset simulation period, and merge them with the rainfall of the day as the input features of runoff prediction; A machine learning model integration module is used to train and optimize the machine learning integration model by taking the input features of all runoff predictions in a preset simulation period and the corresponding runoff simulation values ​​as a data set, wherein the machine learning integration model is a weighted integration of several machine learning sub-models; The future runoff prediction module is used to input the input features of the runoff prediction of the target watershed into the trained machine learning model to predict the future runoff production.

[0014] A computer program product comprises a computer program / instruction, wherein the computer program / instruction implements the above method when executed by a processor.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention uses Markov chain and Gamma distribution model, combined with seasonal characteristics, to generate a long-term seasonal simulated rainfall sequence, and uses the seasonal simulated rainfall sequence as basic data to train the machine learning model, breaking through the limitation of historical data length, enriching the training samples of the model, and enhancing the model's adaptability to different rainfall scenarios. It overcomes the defect of poor model generalization ability caused by insufficient samples in the prior art, and improves the prediction accuracy; 2. The present invention inputs the generated virtual rainfall data into the watershed mechanism model to perform large-scale hydrological process simulation and obtain the corresponding daily flow data. Thus, a large amount of high-precision flow simulation data is obtained, which provides sufficient samples for the training of machine learning models, makes up for the shortcoming of insufficient measured flow data, and further improves the prediction accuracy; 3. The input features of the model of the present invention include the previous accumulated rainfall and seasonal characteristics, taking into account a variety of factors affecting runoff generation, and are rich in features, which improves the sensitivity of the model to factors affecting runoff generation and enhances the prediction ability of the model. It solves the problem of low model accuracy caused by single features in the prior art and further improves the prediction accuracy; 4. The present invention uses multiple machine learning sub-models for training, optimizes the weights of each machine learning sub-model, and constructs a machine learning ensemble model that integrates multiple machine learning sub-models. This fully exploits the advantages of different models, reduces the bias and variance of a single model, improves the accuracy and robustness of prediction, and overcomes the shortcomings of the prior art in that a single model has limited performance; 5. The present invention integrates the physical mechanism of the mechanism model and the nonlinear mapping capability of the machine learning model, so that the prediction results are not only highly accurate but also have certain physical significance, thereby enhancing the credibility of the model; 6. The present invention applies the trained model to actual rainfall runoff prediction, provides real-time prediction capabilities, supports rapid response of decision-making departments, improves the efficiency of flood prevention warning and water resource scheduling, and fills the gap in the poor timeliness of prediction in the prior art. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a flow chart of a method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model provided by the present invention; Figure 2 It is a structural schematic diagram of a basin rainfall runoff prediction device that integrates a mechanism model and a machine learning model provided by the present invention. DETAILED DESCRIPTION

[0017] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0018] Embodiment 1.

[0019] The embodiment of the present invention provides a method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model. Figure 1 As shown, the following steps are included: S101. Obtain historical rainfall data of the basin and perform preprocessing.

[0020] In the specific implementation, the step specifically includes: S101-1. Obtain historical rainfall data for the basin; the sources of historical rainfall data include meteorological station observations, radar estimates, and satellite remote sensing data. Ensure that the data covers a sufficiently long period of time and covers various climate conditions and rainfall patterns, thereby providing a comprehensive data basis for subsequent analysis; S101-2. Identify whether there are abnormal rainfall values ​​in the historical rainfall data, such as using the interquartile range method (IQR). If so, delete the abnormal rainfall to ensure the accuracy of the data; S101-3. Check whether there are missing values ​​in the historical rainfall data. If so, interpolate the missing values. For example, use the similarity interpolation method to interpolate the data of stations in adjacent or similar basins based on the similarity between stations after linear regression analysis to ensure the continuity of the time series. S101-4. Check whether the historical rainfall data is in a unified time format and unit. If not, unify them to ensure that data from different sources are comparable.

[0021] It should be noted that in other embodiments, other methods may also be used for preprocessing.

[0022] S102, dividing a year into a number of seasonal characteristic time periods, and calculating the seasonal rainfall state transition probability of each seasonal characteristic time period and the distribution of rainfall in each seasonal characteristic time period based on historical rainfall data.

[0023] In the specific implementation, the step specifically includes: S102-1. Determine the daily rainfall status according to the following formula based on historical rainfall data:

[0024] In the formula, represents the rainfall status of the tth day in the historical rainfall data. Rainfall status 1 indicates rainfall, and rainfall status 0 indicates no rainfall. threshold Indicates the rainfall threshold, usually 0.1 mm, P t Represents the rainfall on day t in the historical rainfall data.

[0025] S102-2. Divide a year into several seasonal characteristic time periods, and count the number of rainfall state transitions in each seasonal characteristic time period in the basin: ,

[0026] In the formula, The rainfall state transition indicator variable indicates whether the rainfall state i is transferred to the rainfall state j on the tth day. Indicates yes, Indicates no, represents the number of rainfall state transitions from rainfall state i to rainfall state j within the seasonal characteristic time period s, represents the seasonal characteristic time period s; It should be noted that the seasonal characteristic time period can be divided in a variety of ways. For example, in this embodiment, a year is divided into four seasons, spring, summer, autumn and winter, and each season is used as a seasonal characteristic time period, with a total of 4 seasonal characteristic time periods and 4 seasonal rainfall state transition probabilities. In other embodiments, a year can also be divided into 12 months according to the month, and each month is used as a seasonal characteristic time period, with a total of 12 seasonal characteristic time periods and 12 seasonal rainfall state transition probabilities.

[0027] It should be noted that the rainfall state can be divided in many ways. In this embodiment, it is divided into two states: rainfall and no rainfall. In other embodiments, the rainfall state can also be divided into no rain, light rain, moderate rain, heavy rain, etc.

[0028] S102-3. Calculate the seasonal rainfall state transition probability for each seasonal characteristic time period according to the number of rainfall state transitions:

[0029] In the formula, represents the rainfall state transition probability from rainfall state i to rainfall state j in seasonal characteristic time period s, Represents the number of times rainfall state i occurs within the seasonal characteristic time period s.

[0030] S102-4. For each seasonal characteristic time period, the rainfall on all dates with rainfall is obtained, and the distribution of the rainfall in the seasonal characteristic time period is obtained by fitting the rainfall, wherein the distribution is specifically a Gamma distribution.

[0031] Among them, the distribution of rainfall in the seasonal characteristic time period is fitted, specifically the shape parameter α and scale parameter β of the Gamma distribution. Commonly used methods include moment estimation and maximum likelihood estimation, thereby obtaining the probability density function of the Gamma distribution based on the shape parameter α and scale parameter β: , , In the formula, f(x;α,β) represents the probability density function of the Gamma distribution, x represents the rainfall (the rainfall on a rainy day), the shape parameter α controls the shape of the rainfall distribution, and the scale parameter β controls the range and average value of the rainfall. is the Gamma function, which is a function of the shape parameter α, with subscripts α−1 and β α It is directly derived from the definition of Gamma distribution and is used to describe the distribution of rainfall.

[0032] It should be noted that here it is necessary to fit the rainfall distribution of different rainfall corresponding states. For example, in this embodiment, the rainfall distribution of the rainfall state is fitted. In other embodiments, if the rainfall state is divided into light rain, moderate rain, heavy rain, etc., then it is necessary to fit the distribution of rainfall obeyed by different rainfall levels respectively.

[0033] S103, constructing a seasonal Markov chain model using the seasonal rainfall state transition probability as a conditional transition probability, and simulating the rainfall state of each day within a preset simulation period according to the seasonal Markov chain model.

[0034] In specific implementation, this step includes: S103-1. Taking the set of all possible rainfall states {0,1} as the state space and the set of all seasonal rainfall state transition probabilities as the conditional probability set, a seasonal Markov chain model is constructed; S103-2. Randomly set the simulated rainfall state on the first day according to the rainfall frequency corresponding to the first day of the preset simulation cycle. ; Among them, the probability of rainfall occurrence can be obtained by dividing the number of days with rainfall in the corresponding seasonal characteristic time period by the total number of days; S103-3, based on the seasonal Markov chain model, the rainfall state of the next day is calculated according to the rainfall state of the previous day according to the corresponding seasonal transition probability, so as to simulate the simulated rainfall state sequence of the preset simulation period ,in, Indicates the simulated rainfall state of the τth day in the simulated rainfall state sequence, and N represents the total number of days in the preset simulation cycle. For example, assuming the preset simulation cycle is 2 years, the total number of days is 2*365 days.

[0035] S104, simulating the daily rainfall according to the distribution of rainfall in each seasonal characteristic time period and the daily rainfall state in the preset simulation period, and combining the daily rainfall state and corresponding rainfall in the rainfall state sequence as a seasonal simulated rainfall sequence.

[0036] In specific implementation, this step includes: S104-1. Extracting the rainfall state from the simulated rainfall state sequence as rainfall ( =1) and simulate the corresponding rainfall according to the distribution of rainfall in the corresponding seasonal characteristic time period; S104-2, set the rainfall status to no rainfall ( =0) is set to 0; S104-3. Combining the simulated rainfall state and corresponding rainfall amount for each day in a preset simulation period as a seasonal simulated rainfall sequence.

[0037] S105. According to the seasonal simulated rainfall sequence, the basin mechanism model is used to simulate the runoff generation of the basin rainfall to obtain the simulated runoff generation value for each day in the simulation period.

[0038] In specific implementation, this step includes: S105-1. Obtain the meteorological data, elevation data, soil parameters, land use data and vegetation coverage data of the watershed; meteorological data include temperature, wind speed, etc.; soil parameters include infiltration rate, saturated hydraulic conductivity, field water holding capacity, etc., which reflect the hydrological characteristics of the soil; vegetation coverage data include vegetation type, canopy interception, etc., which affect the interception and evapotranspiration of rainfall; S105-2, input seasonal simulated rainfall sequence, meteorological data, elevation data, soil parameters, land use data and vegetation cover data into the watershed mechanism model, simulate the rainfall runoff process in the watershed, including rainfall interception, infiltration, evapotranspiration, runoff and other processes, and obtain the daily runoff simulation value; wherein, the watershed mechanism model can select any suitable traditional mechanism model; S105-3. The flow generation simulation values ​​are formatted in a unified manner and then output as a flow generation time series.

[0039] Compared with the measured data, the seasonal simulated rainfall series and the corresponding runoff simulation values ​​have a large amount of data, which can make up for the lack of generalization ability of pure machine learning models due to limited training data. Through the training of machine learning models, the learning ability of complex hydrological processes can be improved.

[0040] S106: extract the accumulated rainfall and seasonal characteristics of the previous several days of each day within the preset simulation period, and merge them with the rainfall of the current day as input features for runoff prediction.

[0041] In specific implementation, this step includes: S106-1. Calculate the cumulative rainfall of the previous several days according to the daily rainfall in the preset simulation period; wherein, multiple time windows may be selected to realize the cumulative rainfall, for example, the cumulative rainfall of the previous 1 day, the previous 3 days, and the previous 5 days may be set respectively to reflect the impact of short-term rainfall, and the cumulative rainfall of the previous 7 days and the previous 15 days may be added to reflect the impact of medium-term rainfall, and the cumulative rainfall of the previous 30 days and the previous 60 days may be added to reflect the impact of long-term rainfall; S106-2, determining seasonal characteristics according to the seasonal characteristic time period of each day in the preset simulation cycle; for example, assuming that a certain date in the preset simulation cycle is November 11, when the seasonal characteristic time period is divided according to months, the seasonal characteristic corresponding to November 11 is November, and when the seasonal characteristic time period is divided according to seasons, the seasonal characteristic corresponding to November 11 is winter; S106-3. Standardize daily rainfall, cumulative rainfall, and seasonal characteristics, such as coding and unifying scales; S106-4. The standardized rainfall, accumulated rainfall and seasonal characteristics are combined to form input features for runoff prediction.

[0042] The input characteristics of runoff prediction take into account various factors that affect runoff generation, capture the impact of seasonal and previous rainfall conditions on runoff generation, and improve the model's adaptability and prediction accuracy to different rainfall processes.

[0043] S107, using the input features of all runoff predictions in a preset simulation period and the corresponding runoff simulation values ​​as a data set to train the machine learning model.

[0044] In specific implementation, this step includes: S107-1. Construct several machine learning sub-models based on different machine learning algorithms; Among them, the machine learning sub-models are the following models: Convolutional Neural Network (CNN): Good at processing spatiotemporal data, capturing local features and temporal patterns; XGBoost: A tree model based on gradient boosting with efficient feature processing capabilities; LightGBM: An improved gradient boosting framework with fast training speed and excellent performance; Random Forest: Improve the generalization ability of the model by integrating multiple decision trees.

[0045] The machine learning sub-model may also be other types of network models.

[0046] S107-2. Form a data set with the input features of all runoff predictions and the corresponding runoff simulation values ​​within a preset simulation period, and divide it into a first training set, a second training set, a first validation set, a second validation set, a first test set, and a second test set.

[0047] S107-3. Use the first training set to train each machine learning sub-model, use the first validation set to tune the hyperparameters of all machine learning sub-models, and use the first test set to test the capabilities of the machine learning sub-models.

[0048] During training, the mean square error (MSE) is used as the loss function to measure the difference between the predicted value and the true value and guide the update of the model parameters. During the training process, each machine learning sub-model learns according to the input features (such as month information, rainfall in the next m days, and cumulative rainfall in the previous n days) and the corresponding daily flow target, and continuously adjusts its internal parameters to gradually reduce the error with the true value.

[0049] After completing the initial training of each model, the first validation set is used to fine-tune the hyperparameters (non-directly learnable parameters) of all machine learning sub-models to prevent overfitting and maximize the model's prediction ability. The following are the key points in hyperparameter tuning for each machine learning sub-model: A. Convolutional Neural Network (CNN) Convolution kernel size: determines the network's receptive field for local features, such as 3×3, 5×5, etc. By comparing the effects of different convolution kernel sizes on the first validation set, the best configuration for capturing rainfall-runoff time series features is selected.

[0050] The number of convolution kernels (number of channels): reflects the richness of the extracted features. If the number is insufficient, the network's expression ability is limited; if the number is too large, it is easy to cause overfitting and increase the computational overhead.

[0051] Number of network layers: The more layers there are, the better the model's ability to capture complex features, but the network is difficult to train and prone to overfitting.

[0052] Learning rate and regularization coefficient: By adjusting the learning rate (such as 0.001, 0.0005, etc.) and L2 regularization, a balance between error convergence speed and stability is sought in the first verification set.

[0053] B. XGBoost Learning rate (eta): controls the contribution of each weak learner to the overall model. If it is too large, it will lead to overfitting, while if it is too small, the training will be slow.

[0054] Maximum depth (max_depth): determines the complexity of a single tree. If it is too deep, it is easy to overfit, and if it is too shallow, the model will not express enough.

[0055] Subsample and colsample_bytree: Used to randomly select samples or features to improve the generalization ability of the model. Try different combinations in the first validation set.

[0056] Regularization parameters (lambda, alpha): limit the complexity of the tree, adjust the penalty for highly complex tree structures, and avoid overfitting of the tree.

[0057] C. LightGBM Learning rate (learning_rate): Similar to eta in XGBoost, it determines the single update step size, affecting the convergence speed and overfitting risk.

[0058] Maximum depth (max_depth) and number of leaf nodes (num_leaves): control the complexity and refinement of the tree. If num_leaves is too large, the model will easily capture noise and cause overfitting; if it is too small, the expression ability will be insufficient.

[0059] Histogram width (max_bin): LightGBM uses a histogram-based algorithm to discretize features. The larger the max_bin, the more detailed the feature division, but it will increase the amount of calculation.

[0060] Early stopping rounds: Set early stopping conditions in the first validation set, and stop training when the validation error does not improve after several rounds to prevent overfitting.

[0061] D. Random Forest Number of trees (n_estimators): A larger number of trees can reduce variance, but increase training and prediction overhead; insufficient number of trees will affect stability.

[0062] Maximum number of features (max_features): The number of features that can be selected when splitting each node. If it is too large, it may be overfitting, and if it is too small, it may be underfitting.

[0063] Maximum depth (max_depth): Limits the depth of a single tree. Too deep will cause the model to memorize details on the training set and lose generalization ability.

[0064] Minimum number of sample leaves (min_samples_leaf): controls the minimum number of samples in a leaf node. A larger value reduces the risk of overfitting and smoothes the prediction results.

[0065] Finally, the generalization ability of each machine learning sub-model is tested on the first test set to evaluate the effect of the machine learning sub-model on unseen data. Specifically, the evaluation index can be calculated using the first test set to measure the final performance of each sub-model. If the performance of the sub-model on the first test set is similar to that on the first validation set, it means that the model has robust generalization performance.

[0066] The evaluation indicators include: Mean Squared Error (MSE): measures the average squared difference between the predicted value and the true value; Root mean square error (RMSE): The square root of MSE, which more intuitively reflects the magnitude of the error; Mean Absolute Error (MAE): the average absolute difference between the predicted values ​​and the true values; The coefficient of determination (R 2 ): reflects the degree to which the model explains the variation of the true value.

[0067] S107-4. Establish a machine learning ensemble model, where the machine learning ensemble model is a weighted set of all machine learning sub-models.

[0068] The machine learning ensemble model is specifically: , st ,

[0069] Where J(w) is the optimization objective function, The weight matrix formed by the weights of all machine learning sub-models, w k represents the weight of the kth machine learning sub-model, K is the number of machine learning sub-models, and Y i represents the true value of the i-th sample, is the predicted value of the k-th machine learning sub-model for sample i, and N is the number of samples.

[0070] S107-5. Use the second training set to train the machine learning ensemble model, use the second validation set to tune the weights in the machine learning ensemble model to obtain an optimized machine learning ensemble model, and use the second test set to test the capability of the optimized machine learning ensemble model.

[0071] In the present invention, the machine learning ensemble model is not a simple integration of each machine learning sub-model, but is obtained by independent training and evaluation through the second training set, the second validation set, and the second test set. This ensures that the machine learning ensemble model learns the optimal combination weights on unused independent data, further improving the overall prediction performance.

[0072] First, the second training set is used to perform preliminary training on the machine learning ensemble model. On the second training set, the model no longer trains the machine learning sub-model itself, but performs preliminary learning on the combination of its prediction results based on the trained machine learning sub-model to obtain a preliminary weighted ensemble model. Specifically, for each sample, the trained machine learning sub-models first give prediction values, and then these prediction values ​​are paired with the true values ​​to form training features and targets. The difference between the combined output and the true flow production is measured by the mean square error and other losses, and the initial weights of each machine learning sub-model in the machine learning ensemble model are iteratively updated.

[0073] Then, the weights of the machine learning ensemble model are tuned using the second validation set, and the optimal weights are assigned to each machine learning sub-model, so that the combined prediction achieves the minimum error on the second validation set. Specifically, the non-negative least squares method (NNLS) or convex optimization method can be used to solve the optimal weight vector with the goal of minimizing the combined error. Assume that the output of the machine learning ensemble model is the weighted sum of the predicted values ​​of each machine learning sub-model, and continuously adjust the weights on the second validation set until the prediction error of the combined result is optimal.

[0074] Finally, the second test set is used to perform a final generalization test on the machine learning ensemble model to test the performance of the machine learning ensemble model on completely independent, unseen data and evaluate its adaptability to real scenarios. Specifically, the second test set can be input into each machine learning sub-model to obtain the prediction value of each machine learning sub-model, and then the weight combination obtained by tuning is used to generate the ensemble model output, as shown in the following formula:

[0075] The flow rate predicted by the machine learning ensemble model was compared with the corresponding flow rate in the second test set, and the capabilities of the machine learning ensemble model were tested including performance evaluation, error analysis, model robustness verification, and performance analysis under different scenarios.

[0076] Performance evaluation specifically evaluates the prediction performance of the integrated model on the test set and calculates various evaluation indicators.

[0077] Error analysis includes residual analysis and outlier detection. Residual analysis is to calculate the prediction error, analyze the distribution characteristics of the residual, check whether there is systematic deviation or heteroscedasticity, and provide a basis for model improvement. Outlier detection is to identify samples with large prediction errors and analyze possible reasons, such as abnormal input features and the applicability of the model under specific conditions.

[0078] Model robustness verification includes repeated experiments and cross-validation. Repeated experiments are to repeat model training and evaluation under different random seeds or data partitions to observe the consistency of model performance and verify the stability of the model. Cross-validation uses K-fold cross-validation to comprehensively evaluate the generalization ability of the model and reduce the randomness of the evaluation results.

[0079] Performance analysis under different scenarios includes evaluation by rainfall magnitude and seasonal analysis. Evaluation by rainfall magnitude is to classify the test set by rainfall intensity, evaluate the prediction performance of the model under different rainfall scenarios, and ensure the comprehensive adaptability of the model. Seasonal analysis is to evaluate the performance of the model by season or month, analyze the impact of seasonal changes on the model, and ensure that the model can capture seasonal characteristics.

[0080] Finally, based on the evaluation results, it is determined whether the model meets the expected performance requirements, providing a basis for the improvement and practical application of the model.

[0081] S108. Input the input features of the runoff prediction of the target watershed into the trained machine learning ensemble model to predict future runoff.

[0082] Among them, the input features of runoff prediction of the target basin are obtained in the following way: Get future rainfall forecast: obtain the rainfall forecast data for each day in the next m days from the meteorological department or manually set; Calculate the previous cumulative rainfall: Use real-time data to calculate the cumulative rainfall in the previous n days; Extract seasonal features: Extract the month from the date and perform periodic encoding when necessary to capture seasonal features.

[0083] The input features of runoff prediction are then processed in the standardized manner used during training to ensure that the scale of the feature values ​​is consistent with that used during training.

[0084] Load the trained machine learning ensemble model, input the input features of runoff prediction, make predictions, and obtain the simulated runoff values ​​for the next m days.

[0085] Embodiment 2.

[0086] The embodiment of the present invention provides a basin rainfall runoff simulation device that integrates a mechanism model and a machine learning model. The device can be implemented in software and / or hardware and can be configured in a terminal device. Figure 2 As shown, the device comprises: The historical rainfall data preprocessing module 201 is used to obtain the historical rainfall data of the basin and perform preprocessing; The transition probability and distribution calculation module 202 is used to calculate the seasonal rainfall state transition probability of each seasonal characteristic time period and the distribution of rainfall in each seasonal characteristic time period according to historical rainfall data; A rainfall state generation module 203 is used to construct a seasonal Markov chain model using the seasonal rainfall state transition probability as a conditional transition probability, and simulate the rainfall state of each day within a preset simulation period according to the seasonal Markov chain model; The rainfall sequence generation module 204 is used to simulate the daily rainfall according to the distribution of the rainfall in each seasonal characteristic time period and the daily rainfall state in the preset simulation period, and combine the daily rainfall state and the corresponding rainfall in the preset simulation period as a seasonal simulated rainfall sequence; The flow generation simulation module 205 is used to simulate the flow generation of the basin rainfall using the basin mechanism model according to the seasonal simulated rainfall sequence, and obtain the simulated flow generation value of each day in the simulation period; The runoff prediction input feature extraction module 206 is used to extract the cumulative rainfall and seasonal characteristics of the previous several days of each day in a preset simulation period, and merge them with the rainfall of the day as the input features of the runoff prediction; The machine learning model integration module 207 is used to train the machine learning integration model by taking the input features of all runoff predictions in a preset simulation period and the corresponding runoff simulation values ​​as a data set, wherein the machine learning integration model is a weighted integration of several machine learning sub-models; The future runoff prediction module 208 is used to input the input features of the runoff prediction of the target watershed into the trained machine learning model to predict the future runoff.

[0087] The historical rainfall data preprocessing module 201 specifically includes: A data acquisition unit, used to obtain historical rainfall data of the basin; An outlier processing unit is used to identify whether there is an abnormal rainfall value in the historical rainfall data, and if so, delete the abnormal rainfall value; Missing value processing unit detects whether there are missing values ​​in the historical rainfall data, and if so, interpolates the missing values; The detection unit is used to detect whether the historical rainfall data is in a unified time format and unit. If not, it will be unified.

[0088] The transition probability and distribution calculation module 202 specifically includes: The rainfall status acquisition unit is used to determine the daily rainfall status according to the historical rainfall data according to the following formula:

[0089] In the formula, represents the rainfall status of the tth day in the historical rainfall data. Rainfall status 1 indicates rainfall, and rainfall status 0 indicates no rainfall. threshold represents the rainfall threshold, P t represents the rainfall on day t in the historical rainfall data; The state transition times calculation unit is used to divide a year into several seasonal characteristic time periods and count the number of rainfall state transitions in each seasonal characteristic time period of the basin:

[0090]

[0091] In the formula, The rainfall state transition indicator variable indicates whether the rainfall state i is transferred to the rainfall state j on the tth day. Indicates yes, Indicates no, represents the number of rainfall state transitions from rainfall state i to rainfall state j within the seasonal characteristic time period s, represents the seasonal characteristic time period s; The state transition probability calculation unit is used to calculate the seasonal rainfall state transition probability of each seasonal characteristic time period according to the number of rainfall state transitions:

[0092] In the formula, represents the rainfall state transition probability from rainfall state i to rainfall state j in seasonal characteristic time period s, represents the number of times rainfall state i occurs within the seasonal characteristic time period s; The rainfall distribution fitting unit is used to obtain the rainfall of all dates with rainfall status for each seasonal characteristic time period, and to obtain the distribution of the rainfall in the seasonal characteristic time period according to the rainfall fitting, wherein the distribution is specifically a Gamma distribution.

[0093] The rainfall status generating module 203 specifically includes: A seasonal Markov chain model building unit is used to take the set of all possible rainfall states {0,1} as the state space and the set of all seasonal rainfall state transition probabilities as the conditional probability set to build a seasonal Markov chain model; The initial state setting unit is used to randomly set the simulated rainfall state of the first day according to the rainfall frequency corresponding to the first day. ; A rainfall state simulation unit is used to calculate the rainfall state of the next day according to the rainfall state of the previous day according to the corresponding seasonal transition probability based on the seasonal Markov chain model, so as to simulate a simulated rainfall state sequence of a preset simulation period. ,in, It represents the simulated rainfall state of the τth day in the simulated rainfall state sequence, and N represents the total number of days in the preset simulation cycle.

[0094] The rainfall sequence generation module 204 specifically includes: A rainfall day simulation unit is used to extract the date with rainfall status from the simulated rainfall status sequence, and simulate the corresponding rainfall according to the distribution of rainfall in the corresponding seasonal characteristic time period; The no-rainfall day simulation unit is used to set the rainfall on the date with no rainfall to 0; The simulated rainfall sequence acquisition unit is used to combine the simulated rainfall state and the corresponding rainfall amount of each day in a preset simulation period as a seasonal simulated rainfall sequence.

[0095] The flow simulation module 205 specifically includes: A data acquisition unit, used to acquire the meteorological data, elevation data, soil parameters, land use data and vegetation cover data of the watershed; The hydrological simulation unit is used to input seasonal simulated rainfall sequences, meteorological data, elevation data, soil parameters, land use data and vegetation cover data into the watershed mechanism model to simulate the rainfall-runoff process in the watershed and obtain the daily runoff simulation value; The format unification unit is used to unify the format of the flow generation simulation value and output the flow generation time series.

[0096] The runoff prediction input feature extraction module 206 specifically includes: The accumulated rainfall extraction unit is used to calculate the accumulated rainfall of several days before the current day according to the daily rainfall in the preset simulation period; A seasonal characteristic determination unit, used to determine seasonal characteristics according to the seasonal characteristic time period of each day in a preset simulation cycle; Standardization units are used to standardize daily rainfall, cumulative rainfall, and seasonal characteristics; The feature generation unit is used to concatenate the standardized rainfall, accumulated rainfall, and seasonal characteristics to form input features for runoff prediction.

[0097] Among them, the machine learning model integration module 207 specifically includes: A sub-model construction unit, used to construct a number of machine learning sub-models based on different machine learning algorithms; A data set acquisition unit, used to form a data set from all input features of runoff prediction and corresponding runoff simulation values ​​within a preset simulation period, and divide the data set into a first training set, a second training set, a first validation set, a second validation set, a first test set, and a second test set; A sub-model training unit, configured to train each machine learning sub-model using a first training set, to optimize hyperparameters of all machine learning sub-models using a first validation set, and to test capabilities of the machine learning sub-models using a first test set; A machine learning ensemble model building unit, used to build a machine learning ensemble model, wherein the machine learning ensemble model is a weighted set of all machine learning sub-models; The weight optimization unit is used to train the machine learning ensemble model using the second training set, to tune the weights in the machine learning ensemble model using the second validation set to obtain the optimized machine learning ensemble model, and to test the capability of the optimized machine learning ensemble model using the second test set.

[0098] The device provided in the embodiment of the present invention can be used to execute the method provided in the first embodiment of the present invention, and has the corresponding functions and beneficial effects of executing the method. For any details not provided, please refer to the method description and will not be repeated.

[0099] It is worth noting that in the embodiment of the above-mentioned device, the various units and modules included are only divided according to functional logic, but are not limited to the above-mentioned division, as long as the corresponding functions can be achieved; in addition, the specific names of the functional units are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of the present invention.

[0100] The embodiments described above are only illustrative, wherein the modules described as separate components may or may not be physically separated, and the components displayed as modules may or may not be physical modules, i.e., they may be located in one place, or they may be distributed on multiple network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, or of course, it can be implemented only by hardware, as long as the function or effect can be achieved.

[0101] Embodiment three.

[0102] The embodiment of the present invention also provides a computer program product, such as an app on a mobile phone or tablet, an installation program on a computer, etc., which includes a computer program / instruction, and the computer program / instruction is executed by a processor to implement the method described in Example 1. The code of the computer executable program for performing the operation of the present invention can be written in one or more programming languages ​​or a combination thereof, and the programming language includes an object-oriented programming language, such as Java, Smalltalk, C++, Python, and also includes a conventional procedural programming language, such as "C" language or similar programming language. The program code can be executed completely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer and partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computer (for example, using an Internet service provider to connect through the Internet).

Claims

1. A basin rainfall runoff prediction method integrating a mechanism model and a machine learning model, characterized in that: The steps include: (1) Obtain historical rainfall data of the basin and perform preprocessing; (2) Divide a year into several seasonal characteristic time periods, and calculate the seasonal rainfall state transition probability of each seasonal characteristic time period and the distribution of rainfall in each seasonal characteristic time period based on historical rainfall data; (3) The seasonal rainfall state transition probability is used as the conditional transition probability to construct a seasonal Markov chain model, and the rainfall state of each day within the preset simulation period is simulated according to the seasonal Markov chain model; (4) According to the distribution of rainfall in each seasonal characteristic time period and the daily rainfall state in the preset simulation period, the daily rainfall state and the corresponding rainfall in the rainfall state sequence are combined as the seasonal simulated rainfall sequence; (5) Based on the seasonal simulated rainfall sequence, the basin mechanism model is used to simulate the rainfall runoff in the basin and obtain the simulated runoff value for each day in the simulation period; (6) Extract the cumulative rainfall and seasonal characteristics of the previous several days of each day within the preset simulation period, and integrate them with the rainfall of the day as the input features for runoff prediction; (7) using the input features of all runoff predictions in a preset simulation period and the corresponding runoff simulation values ​​as a data set to train a machine learning ensemble model, wherein the machine learning ensemble model is a weighted integration of several machine learning sub-models; (8) Input the input features of the target watershed runoff prediction into the trained machine learning ensemble model to predict future runoff.

2. The method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model according to claim 1 is characterized in that: Step (1) specifically includes: (1-1) Obtain historical rainfall data of the basin; (1-2) Identify whether there are abnormal rainfall values ​​in the historical rainfall data, and if so, delete the abnormal rainfall; (1-3) Check whether there are missing values ​​in the historical rainfall data. If so, interpolate the missing values; (1-4) Check whether the historical rainfall data is in a unified time format and unit. If not, unify them.

3. The method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model according to claim 1 is characterized in that: Step (2) specifically includes: (2-1) According to the historical rainfall data, the daily rainfall status is determined according to the following formula: ， In the formula, represents the rainfall status of the tth day in the historical rainfall data. Rainfall status 1 indicates rainfall, and rainfall status 0 indicates no rainfall. threshold represents the rainfall threshold, P t represents the rainfall on day t in the historical rainfall data; (2-2) Divide a year into several seasonal characteristic time periods, and count the number of rainfall state transitions in each seasonal characteristic time period in the basin: ， ， In the formula, The rainfall state transition indicator variable indicates whether the rainfall state i is transferred to the rainfall state j on the tth day. Indicates yes, Indicates no, represents the number of rainfall state transitions from rainfall state i to rainfall state j within the seasonal characteristic time period s, represents the seasonal characteristic time period s; (2-3) Calculate the seasonal rainfall state transition probability for each seasonal characteristic time period according to the number of rainfall state transitions: ， In the formula, represents the rainfall state transition probability from rainfall state i to rainfall state j in seasonal characteristic time period s, represents the number of times rainfall state i occurs within the seasonal characteristic time period s; (2-4) For each seasonal characteristic time period, the rainfall on all dates with rainfall is obtained, and the distribution of the rainfall in the seasonal characteristic time period is obtained by fitting based on the rainfall, wherein the distribution is specifically a Gamma distribution.

4. The method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model according to claim 1 is characterized in that: Step (3) specifically includes: (3-1) Take the set of all possible rainfall states {0,1} as the state space, and the set of all seasonal rainfall state transition probabilities as the conditional probability set to construct a seasonal Markov chain model; (3-2) According to the rainfall frequency corresponding to the first day of the preset simulation cycle, the simulated rainfall state of the first day is randomly set ; (3-3) Based on the seasonal Markov chain model, the rainfall state of the next day is calculated according to the rainfall state of the previous day according to the corresponding seasonal transition probability, so as to simulate the simulated rainfall state sequence of the preset simulation period. ,in, Indicates the first The simulated rainfall status of the day, N represents the total number of days in the preset simulation cycle.

5. The method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model according to claim 1 is characterized in that: Step (4) specifically includes: (4-1) Extracting the dates with rainfall from the simulated rainfall state sequence, and simulating the corresponding rainfall according to the distribution of rainfall in the corresponding seasonal characteristic time period; (4-2) Set the rainfall on the date when the rainfall status is no rainfall to 0; (4-3) The simulated rainfall state and corresponding rainfall amount of each day within the preset simulation period are combined as a seasonal simulated rainfall sequence.

6. The method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model according to claim 1 is characterized in that: Step (5) specifically includes: (5-1) Obtain the basin’s meteorological data, elevation data, soil parameters, land use data, and vegetation cover data; (5-2) Input seasonal simulated rainfall series, meteorological data, elevation data, soil parameters, land use data and vegetation cover data into the watershed mechanism model to simulate the rainfall-runoff process in the watershed and obtain the simulated runoff value for each day; (5-3) The flow simulation values ​​are formatted in a unified format and then output as a flow time series.

7. The method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model according to claim 1 is characterized in that: Step (6) specifically includes: (6-1) Calculate the cumulative rainfall of the previous days based on the daily rainfall in the preset simulation period; (6-2) Determine seasonal characteristics based on the seasonal characteristic time period of each day in the preset simulation cycle; (6-3) Standardize daily rainfall, cumulative rainfall, and seasonal characteristics; (6-4) The standardized rainfall, accumulated rainfall, and seasonal characteristics are concatenated to form the input features for runoff prediction.

8. The method for predicting rainfall and runoff in a watershed by integrating a mechanism model and a machine learning model according to claim 1 is characterized in that: Step (7) specifically includes: (7-1) Construct several machine learning sub-models based on different machine learning algorithms; (7-2) forming a data set with input features of all runoff predictions and corresponding runoff simulation values ​​within a preset simulation period, and dividing the data set into a first training set, a second training set, a first validation set, a second validation set, a first test set and a second test set; (7-3) Using the first training set to train each machine learning sub-model, using the first validation set to tune the hyperparameters of all machine learning sub-models, and using the first test set to test the capabilities of the machine learning sub-models; (7-4) establishing a machine learning ensemble model, wherein the machine learning ensemble model is a weighted set of all machine learning sub-models; (7-5) Using the second training set to train the machine learning ensemble model, using the second validation set to tune the weights in the machine learning ensemble model to obtain an optimized machine learning ensemble model, and using the second test set to test the capability of the optimized machine learning ensemble model.

9. A basin rainfall runoff prediction device integrating a mechanism model and a machine learning model, characterized in that: include: The historical rainfall data preprocessing module is used to obtain the historical rainfall data of the basin and perform preprocessing; The transition probability and distribution calculation module is used to calculate the seasonal rainfall state transition probability of each seasonal characteristic time period and the distribution of rainfall in each seasonal characteristic time period according to historical rainfall data; A rainfall state generation module is used to construct a seasonal Markov chain model using the seasonal rainfall state transition probability as a conditional transition probability, and simulate the rainfall state of each day within a preset simulation period according to the seasonal Markov chain model; A rainfall sequence generation module is used to simulate the daily rainfall according to the distribution of rainfall in each seasonal characteristic time period and the daily rainfall state in a preset simulation period, and combine the daily rainfall state and corresponding rainfall in the preset simulation period as a seasonal simulated rainfall sequence; The flow generation simulation module is used to simulate the flow generation of the basin rainfall using the basin mechanism model according to the seasonal simulated rainfall sequence, and obtain the simulated flow generation value of each day in the simulation period; The runoff prediction input feature extraction module is used to extract the cumulative rainfall and seasonal characteristics of the previous several days of each day within the preset simulation period, and merge them with the rainfall of the day as the input features of runoff prediction; A machine learning model integration module is used to train and optimize the machine learning integration model by taking the input features of all runoff predictions in a preset simulation period and the corresponding runoff simulation values ​​as a data set, wherein the machine learning integration model is a weighted integration of several machine learning sub-models; The future runoff prediction module is used to input the input features of the runoff prediction of the target watershed into the trained machine learning model to predict the future runoff production.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the method according to any one of claims 1 to 8 is implemented.

Images