Method and system for predicting buried depth of underground water in drainage farmland

Abstract

The invention discloses a drainage farmland underground water burial depth prediction method and system, and belongs to the technical field of agricultural prediction. Obtaining daily actual evapotranspiration, lateral displacement and groundwater burial depth prediction values through physical process model simulation; determining an actual absolute error of a daily groundwater burial depth predicted value output by the physical model, determining a daily moisture balance intermediate variable, taking the daily moisture balance intermediate variable and the groundwater burial depth predicted value as input variables, and performing training according to the corresponding actual absolute error to obtain an absolute error prediction network; according to the absolute error prediction network, the predicted value of the absolute error is obtained and serves as the correction amount, the groundwater burial depth predicted value obtained through physical process model simulation is corrected, the corrected groundwater burial depth predicted value is obtained, and the method can more accurately and reliably simulate GWD dynamic changes under different drainage conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of groundwater depth prediction, and more particularly to a method and system for predicting groundwater depth in drained farmland. Background Art

[0002] Groundwater in coastal areas is typically shallow and highly mineralized, significantly impacting the dynamics of soil moisture and solutes in farmland, as well as the closely related root absorption and evapotranspiration processes. Scientific and rational regulation of these dynamics is crucial. Open ditches, concealed pipes, and vertical shafts are crucial drainage systems for regulating groundwater levels in farmland, thereby improving soil moisture conditions. Accurately predicting or simulating the dynamics of groundwater levels under drainage conditions is crucial for understanding soil moisture and solute dynamics in the root zone and optimizing field drainage system layout and water management strategies.

[0003] Influenced by numerous factors, including climate, soil, vegetation, topography, and human activities, the changing process of groundwater levels is extremely complex. Currently, these processes are primarily simulated using process-driven physical models. These models are often based on the theory of porous media fluid dynamics and the principle of mass conservation, effectively reflecting the mechanisms of soil water migration and the inherent logical relationships between these models and various influencing factors. Among these, the physical process model DRAINMOD uses a water balance equation to calculate soil gas storage volume and then estimates groundwater depth (GWD) based on the steady-state transformation relationship between gas storage volume and groundwater level. DRAINMOD requires relatively few parameters, and its principles are simple to understand and operate. It is suitable for simulating GWD in farmland under different artificial drainage conditions and has been widely used in the optimization design of farmland drainage systems and water management practices in different regions around the world.

[0004] DRAINMOD also inevitably includes some idealistic assumptions and simplifications. For example, the quantitative relationship between GWD and soil gas storage volume, upward water flux, and infiltration-related parameters is based on the assumption of steady-state conditions. In most cases, complex and changing environments make it difficult to meet this assumption, which undoubtedly introduces significant uncertainty into the assessment of the water balance of the soil-groundwater system and the GWD process. To simplify the calculation process, DRAINMOD artificially divides the soil layer between the surface and the GWD into dry and wet zones. This cannot reasonably reflect the impact of actual soil water and salt distribution on crop root water absorption and evaporation, which can easily lead to large deviations in GWD simulation results. This problem is particularly prominent during periods of persistent drought or frequent rainfall.

[0005] In summary, due to the numerous influencing factors and their complex interrelationships in the simulation process, as well as the widespread existence of soil spatial variability, the changes in field GWD are very complex and often highly uncertain, which will greatly affect the accuracy of the simulation results of the physical process model DRAINMOD. Summary of the Invention

[0006] In response to the problems existing in the above-mentioned fields, the present invention proposes a method and system for predicting the groundwater depth of drained farmland. By integrating physical process models and dynamic neural networks, a physical-data hybrid model suitable for predicting the groundwater depth of drained farmland is constructed. This model can more comprehensively and accurately consider the complex impact of the changing environment on the changes in the groundwater level in drained farmland, thereby more accurately and reliably simulating the dynamic changes of GWD under different drainage conditions.

[0007] To solve the above technical problems, the present invention discloses a method for predicting the depth of groundwater in drained farmland, comprising the following steps: The drainage system parameters, soil parameters, meteorological parameters, and crop parameters of the drained farmland are input into the physical process model of the farmland-scale hydrological simulation to obtain the actual daily evapotranspiration, lateral drainage, and groundwater depth prediction values ​​through simulation. Based on the daily groundwater depth prediction and measured values, determine the actual absolute error of the daily groundwater depth prediction output by the physical model; The daily water balance intermediate variable is determined based on the measured daily rainfall, the actual daily evapotranspiration and lateral drainage obtained through simulation. The absolute error prediction network is trained using the daily water balance intermediate variable and the predicted groundwater depth as input variables, and the corresponding actual absolute error. According to the absolute error prediction network, the predicted value of the absolute error is obtained; the predicted value of the absolute error is used as a correction value to correct the predicted value of the groundwater depth obtained by simulating the physical process model, and the corrected predicted value of the groundwater depth is obtained.

[0008] Preferably, the determining of the water balance intermediate variable specifically includes: According to the daily rainfall P , daily actual evapotranspiration predicted by the physical process model ET a and lateral displacement D , calculate the intermediate variables of water balance Δ for: The actual daily evapotranspiration is determined by comparing the sum of the daily maximum upward flux and the root zone soil water supply with the magnitude of the potential evapotranspiration; When the sum of the daily maximum upward flux and the root zone soil water supply is greater than the potential evapotranspiration, the daily actual evapotranspiration is the potential evapotranspiration; when the sum of the daily maximum upward flux and the root zone soil water supply is less than the potential evapotranspiration, the daily actual evapotranspiration is the sum of the maximum upward flux and the root zone soil water supply; The soil water supply to the root zone was calculated based on potential evapotranspiration and the average soil water potential in the root zone; The calculation of lateral drainage is divided into two cases: when the groundwater level is below the surface, the lateral drainage is calculated using the Hooghoudt equation; when water accumulates on the surface, the lateral drainage is calculated using the Kirkham equation.

[0009] Preferably, the training to obtain an absolute error prediction network specifically includes: The daily groundwater depth predictions obtained by simulating the physical process model and the intermediate variables of water balance Δ As input, the predicted value of absolute error is output, and the absolute error prediction network is constructed with the goal of minimizing the error between the actual absolute error and the predicted value of absolute error; In the training phase, the actual absolute error is used as feedback input to train the constructed absolute error prediction network in an open-loop mode; In the prediction stage, the output results of the absolute error prediction network are fed back to the input, and the absolute error of the groundwater depth is dynamically simulated through a closed-loop mode to generate an absolute error prediction sequence.

[0010] Preferably, the training of the constructed absolute error prediction network in an open-loop mode specifically includes: During the training process, the actual absolute error is used as an input variable to participate in the training; setting different t d × HN combination, in which t d Delay time for input / output variables, HN is the maximum number of hidden layer nodes, which is obtained by evaluating the sample size. The network is trained by the LM algorithm until the root mean square error RMSE between the actual absolute error and the predicted value of the absolute error is minimized, and the optimal t d × HN combination.

[0011] Preferably, the dynamic simulation of the absolute error of the groundwater depth in a closed-loop mode specifically includes: During the prediction process, the predicted value of the absolute error is used as the output variable of the absolute error prediction network. The output result is fed back to the input layer as the input of the absolute error prediction network to dynamically simulate the absolute error.

[0012] Preferably, the physical process model is further verified, specifically by inputting drainage system parameters, soil parameters, meteorological parameters, crop parameters and measured farmland groundwater depth to calibrate and verify the physical process model, wherein: Drainage system parameters include drainage depth, drainage spacing, surface water depth, and effective drainage radius; Soil parameters include soil moisture characteristic curve, saturated hydraulic conductivity, relationship between groundwater depth and soil gas storage volume, relationship between groundwater depth and maximum upward flux of groundwater, and relationship between groundwater depth and infiltration parameters; Meteorological parameters include rainfall, temperature, relative humidity, and reference crop evapotranspiration; Crop parameters include potential evapotranspiration correction factor and effective rooting depth.

[0013] Preferably, the physical process model is a physical model DRAINMOD.

[0014] Preferably, the corrected groundwater depth prediction value is the sum of the correction amount and the groundwater depth prediction value obtained by simulating the physical model DRAINMOD.

[0015] Preferably, a drainage farmland groundwater depth prediction system is also included, including: The data acquisition module is used to input the acquired drainage system parameters, soil parameters, meteorological parameters, and crop parameters of the drained farmland into the physical process model of the farmland-scale hydrological simulation, and obtain the actual daily evapotranspiration, lateral drainage, and groundwater depth prediction values ​​through simulation; based on the daily groundwater depth prediction values ​​and the measured values, the actual absolute error of the daily groundwater depth prediction values ​​output by the physical model is determined; The absolute error prediction network construction module is used to determine the daily water balance intermediate variable based on the daily measured rainfall, the actual daily evapotranspiration and lateral drainage obtained through simulation; the absolute error prediction network is trained using the daily water balance intermediate variable and the predicted groundwater depth as input variables and the corresponding actual absolute error; The groundwater depth prediction module is used to obtain the predicted value of absolute error based on the absolute error prediction network; the predicted value of absolute error is used as a correction value to correct the groundwater depth prediction value obtained by simulating the physical process model to obtain a corrected groundwater depth prediction value.

[0016] Compared with the prior art, the present invention has the following beneficial effects: The proposed method for predicting groundwater depth in drained farmland uses a physical process model to simulate daily evapotranspiration, lateral drainage, and predicted groundwater depth. Furthermore, the actual absolute error (AED) of the daily groundwater depth prediction output by the physical model is determined by comparing it with the measured AED, providing theoretical support for the subsequent construction of an absolute error network. Based on the daily measured rainfall, the actual daily evapotranspiration and lateral drainage obtained through simulation, the daily water balance intermediate variable is determined. The water balance intermediate variable and the predicted groundwater depth are used as input variables, and the network is trained according to the corresponding actual absolute error until the error between the actual absolute error and the predicted absolute error is minimized, thereby obtaining an absolute error prediction network. This method integrates the physical process model and the data-driven model. By establishing a physical-data hybrid model of the groundwater depth of drained farmland, it can more comprehensively and accurately consider the complex impact of the changing environment on the groundwater level changes in drained farmland, thereby more accurately and reliably simulating the dynamic changes of GWD under different drainage conditions. Its mechanism interpretability, error controllability, and extrapolation and generalization capabilities are significantly improved, providing a reliable tool for the dynamic prediction of groundwater depth in drained farmland. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a flow chart of the physical-data hybrid modeling for groundwater depth prediction proposed in the present invention; Figure 2 Dynamic comparison results of the predicted and measured groundwater depth (GWD) simulations for two winter wheat-summer corn rotation seasons provided by the embodiments of the present invention; Figure 3 NARX provided by the embodiment of the present invention GWD and NARX ε In different t d × HN RMSE between the predicted and measured values ​​of groundwater depth GWD and absolute error under the combination; Figure 4 Comparison results of the predicted and measured absolute errors in different simulation periods (P1-P7 and P1'-P7') of two winter wheat-summer corn rotation seasons provided by the embodiment of the present invention; Figure 5 The GWD results predicted by different methods in different simulation periods (P1-P7 and P1'-P7') of two winter wheat-summer corn rotation seasons provided by the embodiment of the present invention; Figure 6 DRAINMOD model and DRAINMOD-NARX under different drainage spacing (L) provided by the embodiment of the present invention ε Results of GWD predicted by the hybrid model; Figure 7The different drainage depths (D d ) DRAINMOD model and DRAINMOD-NARX ε Results of GWD predicted by the hybrid model. DETAILED DESCRIPTION

[0018] The following is a combination of the embodiments of the present invention Figure 1-Figure 7 , the technical solutions in the embodiments of the present invention are clearly and completely described. It should be understood that the terms used in the present invention are only used to describe specific implementation methods and are not intended to limit the present invention.

[0019] With the rapid development of computer technology and artificial intelligence, an increasing number of data-driven time series models have been used for dynamic simulation of GWD. Unlike physical process models, time series models do not consider the complex internal mechanisms of the system. Instead, they primarily identify model input and output data and minimize the error between the model output and the measured value. Model building can avoid various simplifications or assumptions, significantly reducing the impact of environmental complexity and uncertainty. Artificial neural network models are one of the most widely used time series models. They have a strong ability to fit the inherent laws of complex nonlinear systems and have been widely used in GWD dynamic simulation research. NARX is a commonly used dynamic neural network that organically links the current target prediction variable with its historical state and environmental influencing variables. Compared with static neural networks, NARX has a significant advantage in continuous dynamic simulation of GWD.

[0020] However, most current NARX models are mainly constructed based on easily accessible meteorological environmental variables, and are often only targeted at specific environmental conditions. They are unable to reflect the impact of changes in farmland drainage management parameters on GWD, greatly weakening their ability to be extrapolated under different types of drainage conditions, resulting in the inability to accurately obtain the dynamics of farmland GWD changes in the study area.

[0021] Therefore, the present invention constructs a physical-data hybrid model suitable for predicting the groundwater depth in drained farmland by integrating the physical process model and the dynamic neural network. It can more comprehensively and accurately consider the complex impact of the changing environment on the changes in the groundwater level in drained farmland, thereby more accurately and reliably simulating the dynamic changes of GWD under different drainage conditions.

[0022] like Figure 1 As shown, the present invention proposes a method for predicting the depth of groundwater in drained farmland, comprising the following steps: S1: Obtain drainage system parameters (including drainage depth, drainage spacing, surface water depth, and effective drainage radius), soil parameters (including soil moisture characteristic curve, saturated hydraulic conductivity, the relationship between groundwater depth and soil gas storage volume, the relationship between groundwater depth and maximum upward groundwater flux, and the relationship between groundwater depth and infiltration parameters), meteorological parameters (rainfall, temperature, relative humidity, and reference crop evapotranspiration), and crop parameters (including potential evapotranspiration correction factor and effective rooting depth) for drained farmland. Input these into a physical process model and simulate to obtain daily actual evapotranspiration, lateral drainage, and predicted groundwater depth. S2: Determine the actual absolute error of the daily predicted groundwater depth for drained farmland based on the daily predicted and measured groundwater depths; S3: Determine the water balance intermediate variable based on the daily measured rainfall, the daily actual evapotranspiration and lateral drainage obtained through prediction; use the daily water balance intermediate variable and the predicted groundwater depth as input variables, and train the absolute error prediction network based on the corresponding actual absolute error; S4: Obtain a predicted value of the absolute error according to the absolute error prediction network; use the predicted value of the absolute error as a correction value to correct the predicted value of the groundwater depth obtained by simulating the physical process model, and obtain a corrected predicted value of the groundwater depth.

[0023] Specifically, in step S2, the actual absolute error of the daily groundwater depth prediction value output by the physical model is defined as: in, is the actual absolute error, is the predicted value of groundwater depth, It is the measured value of groundwater depth.

[0024] In step S3, the water balance intermediate variables are determined, specifically including: According to the daily rainfall P , daily actual evapotranspiration predicted by the physical model ET a and lateral displacement D , calculate the intermediate variables of water balance Δ for: The daily actual evapotranspiration is determined by comparing the sum of the daily maximum upward flux and the root zone soil water supply with the magnitude of the potential evapotranspiration: Where, ET p is potential evapotranspiration, cm d -1, calculated by the Penman-Monteith formula; q u is the maximum upward flux, cm d -1 ; ET r is the soil water supply to the root zone, cm d -1 .

[0025] ET r Calculated based on potential evapotranspiration and average soil water potential in the root zone: Where, φ is the average soil water matrix potential in the root zone, cm; ρ is a fitting parameter that represents the attenuation degree of soil water supply capacity with the decrease of soil water matrix potential, which is provided by the model internally; φ 0.5 for ET r = 0.5 ET p Time φ , cm.

[0026] The calculation of lateral drainage is divided into two cases: when the groundwater level is below the ground surface, the lateral drainage D Calculated using the Hooghoudt equation: Where, k is the effective lateral hydraulic conductivity, cm d -1 ; L is the drainage ditch spacing, cm; m is the distance between the groundwater level in the middle of the parallel drainage ditch and the ditch water level, cm; d e is the equivalent drainage depth, cm.

[0027] When water accumulates on the surface, D Calculated using the Kirkham equation: Where, H m is the depth of water accumulation, cm; r is the drainage radius, cm; D d is the depth of the drainage ditch, cm; c is the Kirkham coefficient.

[0028] The construction process of the absolute error prediction network includes: The daily groundwater depth prediction value obtained by simulating the physical process model GWD t,sim , and the calculated intermediate variables of water balance Δ As input, the absolute error of the prediction ε t,sim As an output item, during the training phase, the actual absolute error As the input variable, the absolute error prediction network is trained in open-loop mode; in the prediction stage, the predicted value of the absolute error is used as the output variable of the absolute error prediction network, and the output result is fed back to the input layer as the input of the absolute error prediction network to dynamically simulate the absolute error. The absolute error prediction network is dynamically simulated in closed-loop mode to generate the absolute error. ε t,sim Predict the sequence.

[0029] Where, U t-1 for t -1 time and past exogenous input variables, including daily groundwater depth predictions simulated by a calibrated physical process model GWD t,sim , intermediate variable of water balance Δ , past absolute error feedback value ε t-n ; ε t,sim is the output variable of the absolute error prediction network; l and n are the time delay orders of input and output respectively.

[0030] In particular, the physical process model is verified, specifically by inputting the drainage system parameters, soil parameters, meteorological parameters, crop parameters and the measured farmland groundwater depth in step S1, and calibrating and verifying the physical process model. The physical process model is specifically the physical model DRAINMOD.

[0031] In step S4, the corrected groundwater depth prediction value is obtained by taking the predicted value of the absolute error as the correction amount and summing it with the predicted value of the groundwater depth obtained by simulating the physical model DRAINMOD, that is: Where, GWD t,adj is the corrected predicted groundwater depth, cm.

[0032] Specifically, the absolute error prediction network is trained in an open-loop mode, including: During the training process, the actual absolute error is directly used as input to participate in the training, making the training more accurate and efficient; setting different t d × HN combination( t d Delay time for input / output variables, HN The network is trained using the efficient and reliable Levenberg–Marquardt (LM) algorithm until the root mean square error (RMSE) between the actual absolute error and the predicted absolute error is minimized, and the optimal t d × HN combination.

[0033] Dynamic simulation of the absolute error of groundwater depth is performed through a closed-loop model, including: During the prediction process, the predicted value of the absolute error is used as the output variable of the absolute error prediction network and fed back to the input layer as the input of the network, thereby realizing the dynamic simulation of the absolute error.

[0034] The present invention also proposes a drainage farmland groundwater depth prediction system, comprising: The data acquisition module is used to input the acquired drainage system parameters, soil parameters, meteorological parameters, and crop parameters of the drained farmland into the physical process model of the farmland-scale hydrological simulation, and obtain the actual daily evapotranspiration, lateral drainage, and groundwater depth prediction values ​​through simulation; based on the daily groundwater depth prediction values ​​and the measured values, the actual absolute error of the daily groundwater depth prediction values ​​output by the physical model is determined; The absolute error prediction network construction module is used to determine the daily water balance intermediate variable based on the daily measured rainfall, the actual daily evapotranspiration and lateral drainage obtained through simulation; the absolute error prediction network is trained using the daily water balance intermediate variable and the predicted groundwater depth as input variables and the corresponding actual absolute error; The groundwater depth prediction module is used to obtain the predicted value of absolute error based on the absolute error prediction network; the predicted value of absolute error is used as a correction value to correct the groundwater depth prediction value obtained by simulating the physical process model to obtain a corrected groundwater depth prediction value.

[0035] This invention established a hybrid prediction method for groundwater depth in drained farmland by integrating physical processes and data-driven models. Its mechanism interpretability, error controllability, and extrapolation and generalization capabilities are significantly improved, which can greatly improve the prediction accuracy of groundwater depth in drained farmland and provide a reliable tool for dynamic prediction of groundwater depth in drained farmland.

[0036] Example This embodiment involves the physical model DRAINMOD, the data driven model NARX GWD DRAINMOD-NARX, a hybrid model for groundwater depth prediction constructed by integrating dynamic neural network and the two ε The three models are intended to use the measured data of soil parameters (including soil moisture characteristic curve, saturated hydraulic conductivity, the relationship between groundwater depth and soil gas storage volume, the relationship between groundwater depth and maximum upward flux of groundwater, the relationship between groundwater depth and infiltration parameters, etc.), meteorological parameters (including rainfall, temperature, relative humidity, reference crop evapotranspiration, etc.), crops (including parameter potential evapotranspiration correction factor, effective rooting depth, etc.) and field management (including drainage depth, drainage spacing, irrigation conditions, etc.) of the first winter wheat-summer maize rotation season (October 7, 2019 to September 30, 2020) to calibrate or train the above three groundwater depth prediction models respectively, and use the measured data of the second winter wheat-summer maize rotation season (October 6, 2020 to September 30, 2021) to verify and evaluate them.

[0037] For the physical model DRAINMOD, calibration mainly uses a trial-and-error method. By adjusting parameters such as maximum surface water storage, Kirkham depth, ET correction factor, and lateral saturated hydraulic conductivity, the root mean square error (RMSE) between the GWD predicted values ​​based on the simulation output of the physical model DRAINMOD and the measured values ​​is minimized, thus obtaining the calibrated physical model DRAINMOD.

[0038] For the dynamic neural network model NARX GWD , using the efficient and reliable LM algorithm to train the network. GWD The inputs are the measured daily rainfall, atmospheric temperature and relative humidity, and the output is the predicted value of groundwater depth. t d and the number of hidden layer nodes HN , which can effectively avoid NARX GWD The network appears overfitting phenomenon and improves the operation efficiency. Therefore, the present invention sets different t d × HN Combination, training NARX under each combination GWD The network is used until the RMSE between the simulated value and the measured value of GWD is minimized, thereby determining the optimal t d × HN To simplify the calculation, let NARX GWD Inputs to the model (precipitation P , temperature T and relative humidity RH ) and output( GWD ) variables have the same delay, and the range of variation is 1 ~ 10 d, with a step size of 1 d; the maximum number of hidden layer nodes is HN m Based on the amount of samples available for training N Evaluate:

[0039] The number of samples available for training in the first winter wheat-summer corn rotation season N = 360 (2019 / 10 / 7~2020 / 9 / 30), so HN m = 2, so 10 × 2 = 20 types can be generated by comparison t d × HN The simulation accuracy of the combination is used to determine the best combination.

[0040] For hybrid models DRAINMOD-NARX ε The key is to build the absolute error prediction network NARX ε The training methods used, t d scope, HN The determination method is the same as NARX GWD Model consistent. NARX ε The input items are the daily groundwater depth prediction values ​​and water balance intermediate variables obtained by the physical model DRAINMOD simulation Δ The output is the predicted absolute error. The daily groundwater depth predictions, actual evapotranspiration, and lateral drainage required during the training process are all simulated and generated using the physical model DRAINMOD. Since the size, distribution and interaction relationship of these variables will undoubtedly be greatly affected by the initial groundwater level and simulation time interval, in order to increase the training sample size and make the network training results more representative and applicable, combined with the change law of GWD in the experimental base, the first rotation season is divided into 7 different periods P1~P7, and their starting times (corresponding initial GWD, sample size) are 2019 / 10 / 7 (73.7 cm, 360), 2020 / 2 / 1 (90.2 cm, 243), 2020 / 3 / 1 (98.4 cm, 214), 2020 / 4 / 1 (111.4 cm, 183), 2020 / 5 / 1 (134.2 cm, 153), 2020 / 6 / 1 (110.0 cm, 122) and 2020 / 7 / 1 (85.9 cm, 92), and the end time is 2020 / 9 / 30. A total of 1367 sets of data are obtained for training NARX ε . Accordingly, we can estimate HN m = 3. These simulation cycles basically cover the range of GWD variation within the wheat-corn rotation season in the region, which can provide representative data for the physical model DRAINMOD simulation, thereby making NARX ε The training is more reliable and applicable.

[0041] After all models were calibrated and trained, they were further tested and verified using the measured data from the second winter wheat-summer corn rotation season (October 6, 2020 to September 30, 2021). Similar to the previous rotation season, the constructed groundwater depth absolute error prediction dynamic neural network NARX was used. ε For verification, the data were also divided into 7 different periods (P1'~P7') according to the changes in GWD. The corresponding starting times (initial GWD, sample size) were 2020 / 10 / 6 (73.2 cm, 360), 2021 / 2 / 1 (93.1 cm, 242), 2021 / 3 / 1 (93.8 cm, 214), 2021 / 4 / 1 (103.4 cm, 183), 2021 / 5 / 1 (108.2 cm, 153), 2021 / 6 / 1 (117.0 cm, 122) and 2021 / 7 / 1 (96.4 cm, 92), and the end time was 2021 / 9 / 30. The total number of data samples in the verification set was 1,366.

[0042] The present invention uses four statistical indicators to evaluate the model simulation effect, including the coefficient of determination R 2 , root mean square error RMSE, relative RMSE (NRMSE) and Nash efficiency coefficient NSE: Where, is the sample size; and are simulated values ​​and measured values, respectively; is the mean of the simulation values; is the mean of the measured values.

[0043] R 2 The higher the NSE, or the lower the RMSE and NRMSE, the better the model simulation effect.

[0044] For the physical model DRAINMOD, Figure 2The results of the dynamic comparison between the predicted and measured GWD values ​​of two winter wheat-summer maize rotation seasons simulated by the physical model DRAINMOD are presented, among which, Figure 2 (a) is the comparison result from October 7, 2019 to September 30, 2020 in the first quarter (calibration phase). Figure 2 (b) is the comparison result from October 6, 2020 to September 30, 2021 in the second season (verification phase). The results show that the GWD simulated based on the physical model DRAINMOD can better reflect the changing trend of the measured values ​​in different rotation seasons, which is often manifested as a decrease in GWD after rainfall, and then gradually increases as the soil moisture is continuously lost through evaporation and drainage. R 2 , RMSE, NRMSE and NSE were 0.83, 16.3cm, 18.3% and 0.49 respectively. The GWD simulated in the second quarter was significantly different from the measured values. R 2 , RMSE, NRMSE and NSE are 0.72, 14.8cm, 16.6% and 0.40 respectively.

[0045] For the dynamic neural network model NARX GWD , Figure 2 (a) and 2(b) also show the NARX-based GWD ( t d × HN The optimal combination is 2 × 2, such as Figure 3 (a) shows the comparison between the simulated GWD and the measured values ​​in the two rotation seasons. In different rotation seasons, the simulated GWD and the measured values ​​have a high degree of agreement. R 2 , RMSE, NRMSE and NSE are 0.91, 7.8 cm, 8.7% and 0.89 respectively; and 0.67, 11.1 cm, 12.5% ​​and 0.65 respectively in the second season. GWD The phenomenon of GWD being overestimated and underestimated during the relatively dry (March 15th to June 30th) and wet (July 15th to September 15th) periods was effectively alleviated. R 2 and NSE increased by 1.8 and 62.1% respectively, while RMSE (NRMSE) decreased by 38.5%, indicating that NARX GWD It has more advantages in the dynamic prediction of groundwater level.

[0046] For hybrid models DRAINMOD-NARX ε, build and verify the absolute error prediction network NARX ε is the key. t d (1~10 d)× HN (1-3) combinations (30), using 1367 sets of data from daily water balance intermediate variables, groundwater depth prediction values ​​and corresponding absolute errors obtained by DRAINMOD simulation based on the physical model in the first rotation season during the 7 cycles P1-P7, the network was trained in open-loop mode until different t d × HN The RMSE between the predicted and measured values ​​of the absolute error under the combination is the smallest. Figure 3 (b) shows NARX GWD and NARX ε In different t d × HN The RMSE between the actual absolute error and the predicted absolute error under the combination shows that when t d = 3 d, HN = 3, RMSE is the smallest among all combinations, so NARX ε middle t d × HN The optimal combination is 3 × 3.

[0047] like Figure 4 As shown, it shows the ε Comparison of the simulated absolute errors and the actual absolute errors in different periods of the two rotation seasons. As can be seen from the figure, the simulated absolute errors in the calibration seasons P1 to P7 are in good agreement with the calculated actual absolute errors. R 2 and RMSE ranged from 0.52 (P7) to 0.90 (P1) and 7.7 (P1) to 13.8 cm (P7), respectively. R 2 and RMSE are 0.73 and 9.8 cm respectively; the difference between the simulated absolute error and the calculated actual absolute error is even greater in the validation season P1'~P7'. R 2 and RMSE vary between 0.43 (P7') and 0.72 (P1') and 8.4 (P1') and 12.5 cm (P7'), respectively. R 2 The above error analysis results show that the constructed NARX under different GWD initial conditions and time intervals isε It can be used to evaluate the absolute error generated by the physical model DRAINMOD simulation. However, since the error estimation model itself inevitably contains certain modeling errors, if this error is uncontrollable, the GWD simulation error may be further amplified, causing the gap between the GWD predicted values ​​obtained by the physical model DRAINMOD simulation and the measured values ​​to widen. In theory, if the error estimation results are used to correct the groundwater depth predicted values ​​obtained by the physical model DRAINMOD simulation to improve the simulation accuracy of the GWD, the following should be ensured:

[0048] Analyzing the properties of the above formula, we can see that the relationship between the actual absolute error and the predicted value of the absolute error mainly depends on two characteristic lines: ε t,sim = 0 and ε t,sim = 2 ε t,mea As the two characteristic lines change, ε t,sim -ε t,mea The 1:1 relationship diagram is divided into four areas: I, II, III and IV. Figure 4 (a) and Figure 4 (b) shows: when ε t,sim fall into (Zone I) or (III zone), use ε t,sim After the groundwater level is corrected, the absolute error will be closer to the actual value; otherwise, when ε t,sim in (Zone II, representing a more serious overestimation of the revised GWD) or (Zone IV, indicating that the revised GWD will be more seriously underestimated), the revised GWD will deviate further from the actual absolute error, resulting in the phenomenon of error amplification.

[0049] Figure 4 (a) and Figure 4 (b) shows that, whether it is calibration or verification season, through NARX ε Most of the obtained ε t,simAll of them are located in zones I and III (error reduction zones), of which the data points in zones I and III account for 30.5% and 53.6% of all data points respectively in the calibration season, totaling 84.1%, and the data points in zones I and III account for 38.3% and 49.2% respectively in the validation season, totaling 87.5%. Only a small number of them are located in zones II and IV (error amplification zones), of which the data points in zones II and IV account for 13.5% and 2.4% of all data points respectively in the calibration season, and the data points in zones II and IV account for 5.8% and 6.7% respectively in the validation season, and most of the data points in zones II and IV are concentrated in the and The smaller the area, the more accurate the GWD simulation will be. ε It can be used to evaluate the absolute error generated by the physical model DRAINMOD, and then used to correct the simulation results of the physical model DRAINMOD to improve the GWD simulation accuracy.

[0050] To this end, the absolute error prediction network NARX is constructed ε Obtained ε t,sim By superimposing the GWD simulated by the physical model DRAINMOD, the corrected GWD of the two rotation seasons can be obtained, such as Figure 2 (a) and (b). The results show that the GWD simulated by the hybrid model is in good agreement with the measured values ​​in both the calibration and validation seasons. R 2 ≥ 0.87, RMSE ≤ 8.4cm, NRMSE ≤ 9.4% and NSE ≤ 0.81. Compared with the physical model DRAINMOD, the hybrid model effectively alleviated the phenomenon of GWD being overestimated and underestimated in relatively dry and wet periods. R 2 and NSE increased by 18.0% and 213.1% respectively, while NRMSE decreased by 55.4%; compared with NARX GWD , the hybrid model also shows great advantages, R 2 The NSE and NSE increased by 15.0% and 7.7%, respectively, while the NRMSE decreased by 16.2%. The advantage of the hybrid model likely stems from its integration or integration of the strengths of both the DRAINMOD and NARX physical models. For example, the DRAINMOD physical model rationally and quantitatively considers the processes and mechanisms of water balance in farmland systems, while NARX demonstrates a strong ability to fit the complex relationships between influencing variables and errors.

[0051] like Figure 5As shown in the figure (1:1), the physical models DRAINMOD and NARX are used to analyze the changes in the cropping seasons and different time periods (P1~P7 and P1'~P7'). GWD The comparison of the predicted groundwater depth obtained by the hybrid model and the measured value. In most simulation cycles, the simulation accuracy of the hybrid model is the highest (the average values ​​of the evaluation indicators in the 7 cycles are R 2 =0.85; RMSE = 10.0 cm; NRMSE = 12.7%; NSE = 0.82), NARX GWD Second ( R 2 = 0.77; RMSE = 12.1cm; NRMSE = 15.0%; NSE = 0.69), while the physical model DRAINMOD was the lowest ( R 2 = 0.80; RMSE = 19.2 cm; NRMSE = 24.1%; NSE = 0.55).

[0052] Adaptability in different management environments is an important issue in model development. The reliability and accuracy of NARX are closely related to the representativeness and coverage of the training data. Unless a large amount of statistical or measured data is available, general field experiments can only represent certain special cases. For example, the drainage scenario involved in the field experiment in this embodiment is very limited. It is obviously not representative of other drainage scenarios and lacks relevant data (such as lateral drainage volume) to support it. Therefore, NARX GWD These models are primarily trained and constructed using readily available meteorological data, but fail to account for the impact of changes in drainage management conditions (such as ditch depth and spacing) on ​​GWD. Consequently, their application in optimizing field drainage system layout and managing farmland soil moisture is inevitably limited. In contrast, the groundwater depth prediction absolute error dynamic neural network constructed in this paper offers significant advantages in this regard. It can clearly reflect the impact of changes in ditch depth and spacing on field drainage intensity and GWD, and can therefore be extrapolated to various drainage environments, demonstrating strong adaptability.

[0053] In order to further demonstrate the extrapolation and generalization ability of the proposed method for predicting groundwater depth in drained farmland, the response characteristics of field drainage conditions were simulated and analyzed using the physical model DRAINMOD and the hybrid model. L Usually between 50 and 210 m, the drainage depth D d Between 1 and 2.6 m, this embodiment sets 10 types L × D dCombination scenarios, including 5 L = 50, 90, 130, 170 and 210 m (at this time D d Fixed at 1.2 m, consistent with the fields involved in this invention) and 5 D d = 1, 1.4, 1.8, 2.2 and 2.6 m (at this time L The physical model DRAINMOD and the hybrid model proposed in this invention were used to simulate the dynamic changes of GWD under the above 10 scenarios in two crop rotation seasons. L In terms of the impact Figure 6 As shown, (due to the similarity of the change rules, in order to facilitate the distinction, Figure 6 Only the L = 50, 130, 210 m), different in the two rotation seasons L Under these conditions, the GWD variation trends of the hybrid model prediction method proposed in this paper and the physical model DRAINMOD are basically similar, and the Pearson correlation coefficient between the two is r Between 0.91 and 0.99 ( P <0.001); GWD L Increase and gradually decrease (such as L = 50→210 m, the average GWD values ​​simulated by the physical model DRAINMOD in the first and second cropping seasons were 101.2→85.6 cm and 106.1→82.2 cm, respectively, while the values ​​predicted by the hybrid model proposed in this paper were 95.2→83.7 cm and 102.0→85.5 cm). L The increase results in reduced lateral drainage intensity and thus reduced groundwater level drawdown rate.

[0054] Similarly, different D d Under these conditions, the variation trends of GWD simulated by the hybrid model prediction method proposed in this invention and the physical model DRAINMOD are also very similar ( r = 0.91~0.98, P <0.001) The GWD simulated by the two models were D d Increase and increase (such as Figure 7 As shown, D d = 1.0→2.6 m, DRAINMOD / simulated by the method proposed in this invention in the first and second cropping seasons GWDThe mean values ​​are 90.6→122.8 and 87.7→126.9 cm / 88.0→113.5 and 89.3→113.2 cm, respectively. This is because the increase in drainage depth leads to an increase in lateral drainage intensity, thereby accelerating the decline in groundwater levels. Based on the above analysis, it can be seen that the hybrid model proposed in the present invention has better inherited the powerful extrapolation and generalization capabilities of the physical model DRAINMOD under different drainage management conditions, and can more sensitively reflect the impact of changes in drainage parameters on groundwater levels. On the other hand, the hybrid model prediction method proposed in the present invention integrates NARX's powerful fitting ability for the internal relationships of complex nonlinear systems, and better avoids the situation where the simulated groundwater level rises rapidly and approaches or reaches the surface during periods of intensive rainfall, thereby making the simulated GWD dynamic change trend more in line with reality.

[0055] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

[0056] In addition, unless otherwise specified, all technical and scientific terms used in the present invention have the same meaning as commonly understood by those skilled in the art to which the present invention belongs. All documents mentioned in this specification are incorporated by reference to disclose and describe the methods related to the documents. In the event of any conflict with any incorporated document, the content of this specification shall prevail.

Claims

1. A method for predicting groundwater depth in drained farmland, characterized in that: include: The drainage system parameters, soil parameters, meteorological parameters, and crop parameters of the drained farmland are input into the physical process model of the farmland-scale hydrological simulation to obtain the actual daily evapotranspiration, lateral drainage, and groundwater depth prediction values ​​through simulation. Based on the daily groundwater depth prediction and measured values, determine the actual absolute error of the daily groundwater depth prediction output by the physical model; The daily water balance intermediate variable is determined based on the measured daily rainfall, the actual daily evapotranspiration and lateral drainage obtained through simulation. The absolute error prediction network is trained using the daily water balance intermediate variable and the predicted groundwater depth as input variables, and the corresponding actual absolute error. According to the absolute error prediction network, the predicted value of the absolute error is obtained; the predicted value of the absolute error is used as a correction value to correct the predicted value of the groundwater depth obtained by simulating the physical process model, and the corrected predicted value of the groundwater depth is obtained.

2. The method for predicting groundwater depth in drained farmland according to claim 1, characterized in that: The determination of the water balance intermediate variable specifically includes: According to the daily rainfall P , daily actual evapotranspiration predicted by the physical process model ET a and lateral displacement D , calculate the intermediate variables of water balance Δ for: The actual daily evapotranspiration is determined by comparing the sum of the daily maximum upward flux and the root zone soil water supply with the magnitude of the potential evapotranspiration; When the sum of the daily maximum upward flux and the root zone soil water supply is greater than the potential evapotranspiration, the daily actual evapotranspiration is the potential evapotranspiration; when the sum of the daily maximum upward flux and the root zone soil water supply is less than the potential evapotranspiration, the daily actual evapotranspiration is the sum of the maximum upward flux and the root zone soil water supply; The soil water supply to the root zone was calculated based on potential evapotranspiration and the average soil water potential in the root zone; The calculation of lateral drainage is divided into two cases: when the groundwater level is below the surface, the lateral drainage is calculated using the Hooghoudt equation; when water accumulates on the surface, the lateral drainage is calculated using the Kirkham equation.

3. The method for predicting the depth of groundwater in drained farmland according to claim 2, characterized in that: The training to obtain the absolute error prediction network specifically includes: The daily groundwater depth predictions obtained by simulating the physical process model and the intermediate variables of water balance Δ As input, the predicted value of absolute error is output, and the absolute error prediction network is constructed with the goal of minimizing the error between the actual absolute error and the predicted value of absolute error; In the training phase, the actual absolute error is used as feedback input to train the constructed absolute error prediction network in an open-loop mode; In the prediction stage, the output results of the absolute error prediction network are fed back to the input, and the absolute error of the groundwater depth is dynamically simulated through a closed-loop mode to generate an absolute error prediction sequence.

4. The method for predicting groundwater depth in drained farmland according to claim 3, characterized in that: The training of the constructed absolute error prediction network in the open-loop mode specifically includes: During the training process, the actual absolute error is used as an input variable to participate in the training; setting different t d × HN combination, in which t d Delay time for input / output variables, HN is the maximum number of hidden layer nodes, which is obtained by evaluating the sample size. The network is trained by the LM algorithm until the root mean square error RMSE between the actual absolute error and the predicted value of the absolute error is minimized, and the optimal t d × HN combination.

5. The method for predicting the depth of groundwater in drained farmland according to claim 4, characterized in that: The dynamic simulation of the absolute error of groundwater depth in a closed-loop mode specifically includes: During the prediction process, the predicted value of the absolute error is used as the output variable of the absolute error prediction network. The output result is fed back to the input layer as the input of the absolute error prediction network to dynamically simulate the absolute error.

6. The method for predicting groundwater depth in drained farmland according to claim 1, characterized in that: It also includes the verification of the physical process model, which is obtained by inputting drainage system parameters, soil parameters, meteorological parameters, crop parameters and the measured farmland groundwater depth to calibrate and verify the physical process model, including: Drainage system parameters include drainage depth, drainage spacing, surface water depth, and effective drainage radius; Soil parameters include soil moisture characteristic curve, saturated hydraulic conductivity, relationship between groundwater depth and soil gas storage volume, relationship between groundwater depth and maximum upward flux of groundwater, and relationship between groundwater depth and infiltration parameters; Meteorological parameters include rainfall, temperature, relative humidity, and reference crop evapotranspiration; Crop parameters include potential evapotranspiration correction factor and effective rooting depth.

7. The method for predicting the depth of groundwater in drained farmland according to claim 6, characterized in that: The physical process model is the physical model DRAINMOD.

8. The method for predicting groundwater depth in drained farmland according to claim 7, characterized in that: The corrected groundwater depth prediction value is the sum of the correction amount and the groundwater depth prediction value obtained by simulating the physical model DRAINMOD.

9. A drainage farmland groundwater depth prediction system, characterized in that: include: The data acquisition module is used to input the acquired drainage system parameters, soil parameters, meteorological parameters, and crop parameters of the drained farmland into the physical process model of the farmland-scale hydrological simulation, and obtain the actual daily evapotranspiration, lateral drainage, and groundwater depth prediction values ​​through simulation; based on the daily groundwater depth prediction values ​​and the measured values, the actual absolute error of the daily groundwater depth prediction values ​​output by the physical model is determined; The absolute error prediction network construction module is used to determine the daily water balance intermediate variable based on the daily measured rainfall, the actual daily evapotranspiration and lateral drainage obtained through simulation; the absolute error prediction network is trained using the daily water balance intermediate variable and the predicted groundwater depth as input variables and the corresponding actual absolute error; The groundwater depth prediction module is used to obtain the predicted value of absolute error based on the absolute error prediction network; the predicted value of absolute error is used as a correction value to correct the groundwater depth prediction value obtained by simulating the physical process model to obtain a corrected groundwater depth prediction value.

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