A crop growth simulation method and system based on Gaussian process structure error correction and EnKF assimilation coupling

Abstract

A crop growth simulation method and system based on Gaussian process structure error correction and EnKF assimilation coupling, relating to the field of smart agriculture technology, is disclosed. The method comprises the following steps: Step 1: Acquiring multi-source remote sensing images, field observation data, and meteorological data of the study area; Step 2: Extracting vegetation index and canopy temperature information of the study area; Step 3: Performing sensitivity analysis on the WOFOST crop growth model; Step 4: Constructing a structure error model; Step 5: Constructing a structure error correction model using the Gaussian process (GP) regression algorithm; Step 6: Outputting the optimized simulation results. This invention can provide technical support for crop growth monitoring, dynamic assessment of soil moisture, identification of water stress, optimization of irrigation regimes, and yield prediction. Compared with traditional single-model simulation or single remote sensing monitoring methods, this invention can form a complete technical chain of "remote sensing observation—model simulation—data assimilation—error correction—result optimization," and has good practical application value.

Description

Technical Field

[0001] This invention relates to the field of smart agriculture technology, and in particular to a crop growth simulation method and system based on Gaussian process structure error correction and EnKF assimilation coupling. Background Technology

[0002] With the rapid rise of smart agriculture, fast and accurate spatiotemporal detection of crop dynamics is a crucial foundation for optimizing farmers' field management. This information can also assist relevant government departments in formulating agricultural policies, thereby improving agricultural productivity and management levels under increasingly variable climate conditions. In the field of agricultural production, process-based (PB) crop models and data-driven statistical models are widely used to simulate crop growth processes. Currently, process-based crop growth models such as WOFOST, DSSAT, and AquaCrop are widely used for crop growth simulation, yield estimation, and irrigation decision analysis. These models can capture the impact of environmental conditions, variety characteristics, and agricultural management on crop growth, describe crop growth dynamics, and have strong mechanistic explanation capabilities. However, in practical applications, these models are easily affected by factors such as meteorological input errors, soil parameter uncertainties, regional differences in crop parameters, and model simplification. The models cannot fully express the root zone water redistribution, canopy response, and water stress regulation processes caused by different irrigation methods, resulting in certain systematic biases and structural errors in the simulation results. Data assimilation techniques can integrate multi-source observation data into crop models, using measurement data to update selected model parameters, state variables, or both. This can effectively reduce model uncertainty and improve model simulation accuracy. Among them, sequential assimilation methods, represented by the ensemble Kalman filter (EnKF) algorithm, reduce model uncertainty and simulation time, and have become one of the most commonly used assimilation algorithms.

[0003] While EnKF's potential in improving model simulation accuracy has been widely validated, its optimization effectiveness remains constrained by model structural errors. Since crop models are simplified representations of real growth processes, they inevitably neglect some physiological mechanisms and their complex interactions with meteorological, soil, and management measures. Updating only one or two state variables does not always correct crop model behavior. When crop models exhibit structural biases in processes such as canopy growth, water stress response, dry matter accumulation, and yield formation, simply relying on state updates cannot completely eliminate error propagation in subsequent simulations and may even cause discontinuities in the temporal sequence of state variables or deviations of model parameters from reasonable ranges.

[0004] In recent years, machine learning methods have been used for crop growth index inversion, yield prediction, and model error correction. This data-driven approach based on machine learning algorithms does not rely on mechanistic processes and abandons parameter-based assumptions, effectively capturing the complex nonlinear relationships between feature variables and crop physiological indicators, thus enabling it to decouple complex crop growth patterns. However, this purely data-driven approach inherently lacks explicit expression of crop physiological and ecological processes. Its application in crop growth simulation is limited by the amount of data and its black-box nature, making it difficult to reveal the intrinsic regulatory mechanisms of key growth processes such as water stress, dry matter accumulation and distribution. Furthermore, due to limitations imposed by different agricultural ecological environments, different time series, and the unique growth patterns of different varieties, the universality and extrapolation ability of this predictive framework are weak.

[0005] To overcome the limitations of individual methods, research frameworks coupling crop models and machine learning algorithms have emerged. This knowledge-guided machine learning (KGML) framework fully leverages the ability of crop models to meticulously characterize crop physiological processes and the advantage of machine learning in effectively capturing and decoupling nonlinear processes, thereby providing more accurate predictions. It is primarily implemented through integration logic, such as physical prior constraints in data-driven methods or data-driven optimization of physical processes. However, these methods often implicitly assume that the introduced mechanistic models or domain knowledge are reliable. But if the process model itself has structural biases, the prior information, constraints, or training samples generated by it may also transmit these biases to the machine learning model, thus affecting the prediction results. On the other hand, existing KGML methods often enhance the physical rationality of the model by introducing known constraints. However, these constraints usually only cover some explicitly expressible mechanisms, and often lack a unified representation of comprehensive biases formed by multiple unknown sources such as model simplification, parameter errors, input errors, and environmental heterogeneity. Therefore, although these methods can improve local prediction results in complex agricultural scenarios, they still face problems such as insufficient process identification and limited cross-scenario generalization ability.

[0006] In view of this, we propose a crop growth simulation method and system based on Gaussian process structure error correction and EnKF assimilation coupling. Summary of the Invention

[0007] The core invention of this invention is to introduce Gaussian process regression into the WOFOST-EnKF crop model assimilation framework, to explicitly model and correct the residual structural errors that still exist after assimilation, and further improve the simulation accuracy of crop growth state variables, the physiological rationality of time series, and the yield prediction ability through DVS growth stage constraints and embedded GP-EnKF cyclic correction mechanism.

[0008] A crop growth simulation method based on Gaussian process structure error correction coupled with EnKF assimilation comprises the following steps:

[0009] Step 1: Acquire multi-source remote sensing images, field observation data, and meteorological data of the study area;

[0010] Step 2: Extract vegetation index and canopy temperature information of the study area, combine it with ground measurement data, and construct an inversion model using grey relational analysis and BP algorithm;

[0011] Step 3: Using Simlab software, the EFAST method is employed to perform sensitivity analysis on the WOFOST crop growth model, thereby achieving parameter localization;

[0012] Step 4: Use the EnKF algorithm to assimilate LAI and SM into the crop model, further extract the systematic deviation sequences of the model at different growth stages, construct a structural error sequence dataset, and construct a structural error model;

[0013] Step 5: Construct a structural error correction model using the Gaussian process (GP) regression algorithm;

[0014] Step 6: Output the optimized simulation results and evaluate the optimization effect of the three error calibration models under different irrigation treatments.

[0015] Preferably, step 1 further includes acquiring multispectral images and thermal infrared images. The multispectral images include green light, red light, red edge, and near-infrared bands, and the thermal infrared images are used to acquire canopy temperature information.

[0016] Preferably, in step 2, vegetation index, canopy temperature information and related spectral characteristic parameters are extracted, and leaf area index and soil moisture inversion models are constructed in combination with field measurement data to obtain crop growth status observation data.

[0017] Preferably, in step 3, meteorological data, soil parameters, crop parameters, and field management parameters are input into the WOFOST crop growth model to simulate the growth and development process of crops under different drip irrigation conditions.

[0018] Preferably, in step 3, the first-order sensitivity index and the total sensitivity index of each parameter are obtained by analyzing the influence of the input factors on the output variance.

[0019] Preferably, in step 4, based on the WOFOST model simulation, the EnKF algorithm is introduced to dynamically assimilate and update state variables such as LAI and SM.

[0020] Preferably, in step 5, a Gaussian process regression model is constructed; the Gaussian process regression model can learn the nonlinear mapping relationship between the model state variables and the residual structural error, and output the error prediction mean and uncertainty.

[0021] Preferably, in step 5, the structural error correction model is: an unconstrained GP structural error model, a GP model under DVS growth function constraints, or an embedded GP-EnKF coupled assimilation calibration model; any one of the three.

[0022] Preferably, in step 6, the optimized simulation results of LAI, SM and Yield under different drip irrigation treatments are output; the open-loop simulation results, EnKF assimilation results, unconstrained GP correction results, DVS constrained GP correction results and embedded GP-EnKF correction results are compared using evaluation indicators such as root mean square error (RMSE) and coefficient of determination (R²).

[0023] A crop growth simulation system based on Gaussian process structure error correction and EnKF assimilation coupling also includes:

[0024] The data acquisition module is used to acquire UAV multispectral images, thermal infrared images, field observation data, and meteorological data;

[0025] The remote sensing feature extraction and parameter inversion module is used to extract vegetation indices, canopy temperature, and spectral features, and to invert LAI and SM.

[0026] The crop growth simulation module is used to simulate crop growth processes under different drip irrigation methods and irrigation levels based on the WOFOST model.

[0027] The EnKF data assimilation module is used to assimilate LAI and SM observation data into the WOFOST model and dynamically update crop growth status.

[0028] The residual structure error extraction module is used to calculate the residual error between the observations and the EnKF assimilation results, and to construct structural error training samples.

[0029] The Gaussian process structure error correction module is used to construct three types of structure error correction models: unconstrained GP, DVS-constrained GP, and embedded GP-EnKF.

[0030] The results output module is used to output the optimized LAI, SM, and Yield simulation results and to evaluate the model accuracy.

[0031] Yield is the final grain yield.

[0032] Compared with existing technologies, this invention provides a crop growth simulation method and system based on Gaussian process structure error correction and EnKF assimilation coupling, which has the following beneficial effects:

[0033] This invention can explicitly correct residual structural errors after crop model assimilation, thereby improving simulation accuracy. Based on the WOFOST crop growth model and the EnKF data assimilation framework, this invention further introduces a Gaussian process regression model to learn and compensate for residual errors that still exist between observed values ​​and assimilation results. Compared with methods that rely solely on EnKF for state variable updates, this invention can explicitly characterize systematic biases caused by model structure simplification, parameter uncertainty, and complex irrigation scenarios, thereby further improving the simulation accuracy of state variables such as leaf area index and soil moisture.

[0034] This invention integrates UAV remote sensing observation with crop model mechanism simulation to improve data utilization efficiency. It utilizes UAV multispectral imagery, thermal infrared imagery, and field measurement data to retrieve LAI and SM, and uses them as EnKF assimilation input, enabling high spatiotemporal resolution remote sensing observation to dynamically participate in the crop growth simulation process. This approach leverages the advantages of UAV remote sensing in rapidly acquiring crop growth and water status while retaining the WOFOST model's ability to express the mechanism of crop growth processes, thus improving the utilization efficiency of multi-source data in crop simulation.

[0035] This invention can adapt to the crop growth simulation needs under different drip irrigation methods and irrigation levels; it can be applied to different drip irrigation methods such as surface drip irrigation, subsurface drip irrigation, and shallow buried drip irrigation, and can also be applied to crop growth simulation under conditions of full irrigation and different degrees of deficit irrigation; by learning and correcting structural errors under different irrigation scenarios, this invention can improve the adaptability of the model under complex water management conditions and provide technical support for the optimization of precision irrigation systems.

[0036] This invention balances the accuracy of state variables, the rationality of the process, and the ability to predict yield. It sets up three types of structural error correction strategies: unconstrained GP, DVS-constrained GP, and embedded GP-EnKF. Among them, unconstrained GP is more conducive to reducing the numerical errors of LAI and SM; DVS-constrained GP is more conducive to improving the morphological rationality of crop growth process; and embedded GP-EnKF is more conducive to exploring the propagation effect of structural errors on the yield formation process. The three strategies complement each other, enabling this invention to select the appropriate correction method according to different application objectives.

[0037] This invention provides a reliable basis for precision irrigation management and agricultural production decision-making. By outputting optimized LAI, SM, and Yield simulation results, this invention can provide technical support for crop growth monitoring, dynamic assessment of soil moisture, identification of water stress, optimization of irrigation regimes, and yield prediction. Compared with traditional single-model simulation or single-remote sensing monitoring methods, this invention can form a complete technical chain of "remote sensing observation—model simulation—data assimilation—error correction—result optimization," and has good practical application value. Attached Figure Description

[0038] Figure 1 This is a flowchart of a crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling according to the present invention;

[0039] Figure 2 A schematic diagram showing the grey relational degree between various variables during the maize growth period and leaf area index and soil moisture at different depths, as well as the combination of input variables;

[0040] Figure 3 Remote sensing prediction results and overall accuracy map of leaf area index and soil moisture at different growth stages of maize;

[0041] Figure 4 The graph shows the results of first-order and full-order sensitivity analyses of maize yield.

[0042] Figure 5 The results of first-order and full-order sensitivity analyses of LAI are shown in the figure.

[0043] Figure 6 The graph shows the results of first-order and full-order sensitivity analyses of SM.

[0044] Figure 7 A comparison chart of LAI optimization results under different error correction models;

[0045] Figure 8 A comparison chart of SM optimization results under different error correction models;

[0046] Figure 9 A comparison chart showing the yield optimization results under different error correction models. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] The experimental crop of this invention is spring maize. The spring maize experiment was conducted at the Irrigation Experiment Center Station in Minqin County, Wuwei City, Gansu Province. The experimental area is located in the northeastern part of the Hexi Corridor and the lower reaches of the Shiyang River Basin. It is surrounded by the Badain Jaran and Tengger Deserts on the east, west and north sides, with geographical coordinates of 103.20°E, 38.71°N. It has a typical continental desert climate with scarce and uneven rainfall, high evaporation, and dry climate.

[0049] The soil type in the 0-60cm soil layer of the experimental site was clay loam, and the soil type below 60cm was sandy loam, with a soil bulk density of 1.68g / cm³. -3 The porosity is 42.8%, the field water holding capacity is 23.0%, the pH value is 8.04, and the irrigation water is groundwater with a burial depth greater than 30 cm and a mineralization of 0.91 g / L. −1 .

[0050] Spring maize was sown on April 23, 2024. Each experimental plot had 10 rows of maize with a row spacing of 0.7m, and each experimental plot had an area of ​​5m*7m.

[0051] This experiment employed three irrigation methods: film drip irrigation (FDI), shallow buried drip irrigation (SBDI), and surface drip irrigation (SDI); and three irrigation treatments: 100% (full irrigation), 80% (moderate deficit irrigation), and 60% (severe deficit irrigation).

[0052] The remote sensing image acquisition and ground data collection for the spring maize experiment took place at four time points: May 31, June 17, July 13, and August 31. At each sampling time point, leaf area index (LAI), soil moisture content (SM) data (at depths of 20 cm, 40 cm, and 60 cm), and multispectral remote sensing information were collected from each sampling point within the experimental area.

[0053] Example 1:

[0054] like Figures 1-9 ,

[0055] Step 1: Within the target farmland area, acquire multi-source remote sensing images, field observation data, and meteorological data using drones. Additionally, utilize the drone platform to acquire multispectral and thermal infrared images of crops during key growth stages; the multispectral images include green, red, red-edge, and near-infrared bands, while the thermal infrared images are used to obtain canopy temperature information.

[0056] During drone flight, ground reflection calibration plates and temperature calibration targets can be set simultaneously to improve the accuracy of radiometric and temperature correction of remote sensing images. At the same time, field measurements can be carried out on the drone flight dates to obtain observational data such as leaf area index, soil moisture in different soil layers, and final yield.

[0057] Meteorological data, including maximum and minimum temperatures, precipitation, solar radiation, wind speed, and water vapor pressure, are used to drive the operation of subsequent crop growth models.

[0058] Soil moisture was measured at soil layers of 0–20 cm, 20–40 cm, and 40–60 cm. Yield data could be obtained at crop maturity through plot harvesting or sample plant yield measurement.

[0059] The study aimed to acquire multi-source remote sensing images, field observation data, and meteorological data of the study area using drones. Specifically, DJI Movic 3M / 3T drones, equipped with a visible light camera, a multispectral camera, and a thermal infrared sensor, were used to acquire drone-based visible light images, multispectral images, and thermal infrared images of the study area.

[0060] Field observation data includes LAI, SM, and measured yield data.

[0061] Meteorological data includes crop model-driven data such as temperature, precipitation, solar radiation, wind speed, and water vapor pressure.

[0062] Step 2: Extract vegetation index and canopy temperature information of the study area, combine with ground measurement data, and construct an inversion model using grey relational analysis and BP algorithm.

[0063] Remote sensing feature parameters were extracted and LAI and SM were inverted; UAV multispectral images and thermal infrared images were preprocessed to obtain spatially registered orthophoto images, reflectance images and canopy temperature images; on this basis, feature parameters such as vegetation index, spectral band features and canopy temperature were extracted.

[0064] Vegetation indices may include Normalized Difference Vegetation Index (NDVI), Normalized Greenness Difference Vegetation Index (GNDVI), Chlorophyll Index (LCI), Normalized Difference Red Edge Index (NDRE), and Optimized Soil Adjusted Vegetation Index (OSAVI).

[0065] Furthermore, using extracted vegetation indices, spectral bands, and canopy temperature as input variables, and field-measured LAI and SM as target variables, a crop growth state inversion model is constructed to obtain the spatial distribution results of LAI and SM within the study area. The inversion model can employ grey relational analysis to screen sensitive features and combine BP neural networks, random forests, or other machine learning methods to achieve LAI and SM inversion. In this embodiment, the inverted LAI and SM are used as observation inputs for subsequent ensemble Kalman filter (EnKF) data assimilation to dynamically correct the simulated state of the WOFOST crop growth model.

[0066] WOFOST (WOrd Food Studies) is a mechanistic crop growth model developed by Wageningen University and the World Centre for Food Research in the Netherlands. It dynamically simulates the growth, development, and yield formation of annual field crops (wheat, corn, rice, etc.) in daily increments.

[0067] UAV remote sensing image preprocessing. Based on multispectral and thermal infrared images of maize in the study area acquired by UAVs, image stitching, spatial correction, and radiometric correction are first performed.

[0068] Based on this, vegetation index, canopy temperature and related spectral characteristic parameters were extracted, and leaf area index and soil moisture inversion models were constructed in combination with field measurement data to obtain crop growth status observation data as input for subsequent data assimilation.

[0069] like Figure 2 This paper presents a grey relational diagram showing the relationship between various variables during the maize growth period and leaf area index and soil moisture at different depths, as well as a schematic diagram of input variable combinations.

[0070] Figure 2 In the table, (a), (b), (c) and (d) represent the correlation analysis results at the four sampling time points, and (e) represents the correlation analysis results for the entire reproductive period.

[0071] SM20, SM40, and SM60 represent the average SM values ​​at depths of 0-20 cm, 20-40 cm, and 40-60 cm, respectively.

[0072] like Figure 3 This is a remote sensing prediction result and overall accuracy map of leaf area index and soil moisture at different growth stages of maize.

[0073] Figure 3 In the diagram, (a) and (b) represent the inversion results of the training and test sets of LAI, respectively; (c) and (d) represent the inversion results of the training and test sets of SM20, respectively; (e) and (f) represent the inversion results of the training and test sets of SM40, respectively; and (g) and (h) represent the inversion results of the training and test sets of SM60, respectively.

[0074] Step 3: Using Simlab software, the EFAST method is used to perform sensitivity analysis on the WOFOST crop growth model to achieve parameter localization.

[0075] EFAST (Extended Fourier Amplitude Sensitivity Test) is a global sensitivity analysis method used to quantitatively assess the influence of model input parameters on output results (first-order + interaction). It is most commonly used in crop models (such as WOFOST).

[0076] Crop growth simulations were conducted using the WOFOST model. Meteorological data, soil parameters, crop parameters, and field management parameters were input into the WOFOST crop growth model to simulate the growth and development process of crops under different drip irrigation conditions. The model outputs included LAI (Lower Irrigation Area), SM (Soil Surface Area), and final yield.

[0077] SimLab is a free, open-source uncertainty and sensitivity analysis software developed by the Joint Research Centre of the European Commission (JRC). It is the preferred tool for EFASTing crop models (WOFOST / APSIM / DSSAT).

[0078] Drip irrigation methods include surface drip irrigation (SDI), subsurface drip irrigation (FDI), and shallow buried drip irrigation (SBDI); irrigation levels include full irrigation (100%), moderate deficit irrigation (80%), and severe deficit irrigation (60%); the model was run under different combinations of drip irrigation methods and irrigation levels to obtain crop growth simulation results under each treatment condition; to improve the local applicability of the WOFOST model, parameter sensitivity analysis and parameter calibration can be carried out before the model is run.

[0079] Specifically, the EFAST global sensitivity analysis method can be used to screen key parameters that have a significant impact on LAI, SM, and Yield, and the sensitive parameters can be locally calibrated in conjunction with field observation data.

[0080] WOFOST model parameter calibration: This study uses the EFAST method to perform parameter sensitivity analysis on the WOFOST model. By analyzing the influence of input factors on output variance, the first-order sensitivity index and the overall sensitivity index of each parameter are obtained. First, 3250 sets of parameters are randomly sampled using Simlab, followed by WOFOST simulation. Based on the variance quantification of the parameters' influence on LAI, SM, and yield, sensitive parameters are screened.

[0081] like Figure 4 The graph shows the results of first-order and full-order sensitivity analyses of maize yield.

[0082] like Figure 5 The results of first-order and full-order sensitivity analyses of LAI are shown in the figure.

[0083] like Figure 6 The graph shows the results of first-order and full-order sensitivity analyses of SM.

[0084] Step 4-1: Use the EnKF algorithm to assimilate LAI and SM into the crop model, further extract the systematic deviation sequences of the model at different growth stages, construct the structural error sequence dataset, and construct the structural error model.

[0085] The main function of EnKF is to assimilate, update, correct, or optimize model state variables.

[0086] The EnKF algorithm is used to assimilate the LAI and SM obtained by inversion into the crop model, thereby obtaining the assimilation results of LAI and SM. Then, by comparing with the measured LAI and SM data, a structural error sequence dataset is constructed.

[0087] The EnKF algorithm was used to assimilate LAI and SM to update the model state variables, thereby obtaining the optimized crop growth status and soil moisture status.

[0088] Specifically, the EnKF algorithm is used to assimilate the LAI and SM state variables; based on the WOFOST model simulation, the EnKF algorithm is introduced to dynamically assimilate and update the LAI and SM state variables.

[0089] First, several set members are generated based on model parameters, meteorological drivers, and initial states, and then the prediction set at each time step is obtained by forward prediction using the WOFOST model. When LAI and SM data obtained by UAV inversion or field observation exist at a certain time step, the observation data is introduced into the EnKF update step.

[0090] EnKF calculates the Kalman gain based on the covariance of the prediction set error and the covariance of the observation error, and updates the state of each set member using the difference between the observed and predicted values; the updated LAI and SM state variables continue to participate in the WOFOST model prediction in the next time period.

[0091] This step allows the model to dynamically absorb external observation information, thereby reducing simulation errors caused by parameter uncertainties, input errors, and initial state deviations in open-loop simulations.

[0092] The specific calculation process is as follows:

[0093] In the prediction phase, the prediction set is generated using the previously analyzed set. The set members of the state variables can be represented as:

[0094] in, It is the predicted value of the random state variable at time t; It is the WOFOST model; It is a forecast set, which in this study refers to LAI and SM; It is meteorological data; It is the model parameter vector; It is the model error, assumed to follow a model with a mean of zero and a covariance matrix of... The Gaussian distribution.

[0095] for The set members, and the set mean and covariance matrix of the predicted state variables are:

[0096]

[0097]

[0098] in, It is the mean of the state variables; It is the error variance matrix of the state prediction values.

[0099] When external observation data is available, it is assimilated into the model to update the state variables.

[0100] The transformation of external observation data at the same time can be expressed as:

[0101]

[0102] in, These are observed values; It is an observation operator used to transform the model state into the observation space; It is the actual state at time t; It is the observation error, which follows a mean of zero and a covariance matrix of... The Gaussian distribution.

[0103] During the update phase, the state variables of each set member are updated using prior estimates and the differences between the observed data and the prior estimates of these data in the prediction step.

[0104] The predicted state variables for each set member are updated according to the following equation:

[0105]

[0106]

[0107] in, It is the assimilated set of analytical states; It is the Kalman gain matrix.

[0108] Step 4-2: Extracting residual structural errors after assimilation; Although EnKF can correct the LAI and SM state variables at the observation time, residual errors that cannot be completely eliminated may still exist between the assimilated results and the measured values. These residual errors reflect the structural biases of the WOFOST model in the processes of crop canopy growth, water stress response, dry matter accumulation, and yield formation. Therefore, in this embodiment, the difference between the observed values ​​and the EnKF assimilation results is used as the structural error sample.

[0109] For LAI and SM, the residual structural error and It can be represented as:

[0110]

[0111]

[0112] in, and They represent the observed values, and These represent the assimilation results.

[0113] A crop growth simulation framework was constructed based on the WOFOST crop growth model and the EnKF data assimilation algorithm. Meteorological data, soil parameters, crop parameters, and different drip irrigation methods and irrigation levels were input into the model. EnKF was used to assimilate LAI and SM data obtained by machine learning algorithms into the WOFOST crop growth model, enabling the model to incorporate UAV remote sensing inversion results and field observation information, thereby reducing the simulation error of crop growth state variables.

[0114] Step 5-1: Construct a structural error correction model using the Gaussian process (GP) regression algorithm.

[0115] Construct a Gaussian process structure error correction model; using the input features obtained in step 4-1 as independent variables and the residual structure errors of LAI and SM obtained in step 4-2 as dependent variables, construct a Gaussian process regression model.

[0116] Gaussian process regression models can learn the nonlinear mapping relationship between model state variables and residual structural errors, and output the mean and uncertainty of error predictions. In practical implementation, LAI structural error correction models and SM structural error correction models can be constructed separately. For any sample to be corrected, its crop state variables are input into the trained Gaussian process regression model to obtain the corresponding structural error prediction value. This prediction error is then compensated into the EnKF assimilation result to obtain the corrected LAI and SM simulation results.

[0117] Specifically, the regression model constructed is as follows:

[0118]

[0119]

[0120] In the formula, and These represent the input and output of the training dataset, respectively. As latent variables; To follow the pattern with a mean of 0 and a variance of Gaussian noise term with normal distribution; Gaussian process The mean function can be used. Kernel Covariance Defined, and represented by vectors and matrices respectively, in the following forms:

[0121]

[0122]

[0123] Step 5-2:

[0124] Three structural error correction strategies were set up.

[0125] To adapt to different simulation targets, this embodiment sets up three Gaussian process structure error correction strategies.

[0126] The first approach: Unconstrained GP structure error correction strategy;

[0127] As a basic correction scheme, the model uses key state variables output by WOFOST (such as developmental stage (DVS), leaf area index (LAI), total aboveground biomass (TAGP), soil moisture content (SM), etc.) as input features and structural error sequence as output target to construct a Gaussian process regression model, which directly corrects the model assimilation results.

[0128] This strategy directly uses the state and process variables output by WOFOST-EnKF as inputs and the residual structural error as output to train a Gaussian process regression model, and performs offline error compensation on the EnKF assimilation results.

[0129] This strategy is suitable for situations where the primary goal is to reduce the simulation errors of LAI and SM, and can fully leverage the fitting ability of Gaussian process regression to nonlinear residuals.

[0130] The second approach: DVS-constrained GP structure error correction strategy;

[0131] Based on the unconstrained GP structural error model, crop development stage (DVS) is introduced as a prior physical constraint; by analyzing the evolution of the correction results with DVS, a smoothing constraint is applied to the prediction results of the GP model.

[0132] This strategy, based on unconstrained GP correction, introduces crop development stage DVS as a growth process constraint, ensuring that the LAI correction results conform to the stage-specific changes in canopy growth. Specifically, crop growth stages can be divided according to DVS, and smoothing constraints or stage function constraints can be applied to the GP-corrected LAI sequence. This causes LAI to gradually increase in the early growth stage, remain relatively stable at its peak, and gradually decrease at maturity, thereby reducing spikes, sawtooth fluctuations, and non-physical abrupt changes that may occur with purely data-driven correction.

[0133] The third approach: Embedded GP-EnKF coupling assimilation correction strategy;

[0134] GP-EnKF: Gaussian process-ensemble Kalman filter.

[0135] After each EnKF assimilation is completed and the state is written back, GP structural error correction is further performed on the set members: for each member, its current state features are read in real time, the error is predicted by GP and the assimilated LAI and SM are corrected a second time. The corrected state will be fed back to the prediction step of the next time period until all external observations are assimilated into the model.

[0136] This strategy embeds Gaussian process structure error correction into the EnKF prediction-update loop. After each EnKF assimilation update, the state variables of the current set members are read, the trained GP model predicts the amount of structure error correction, and a secondary correction is applied to the assimilated LAI and SM. The corrected state variables are then written back to the WOFOST model to participate in the prediction of the next time period. In this way, structure error correction is no longer just a post-processing step, but enters the crop model state propagation process, further influencing dry matter accumulation and final yield formation.

[0137] Step 6: Output the optimized simulation results and evaluate the optimization effect of the three error calibration models under different irrigation treatments.

[0138] Output the optimized crop growth simulation results; after the above steps, output the optimized LAI, SM, and Yield simulation results under different drip irrigation treatments. Evaluation indicators such as root mean square error (RMSE) and coefficient of determination (R²) can be used to compare the open-loop simulation results, EnKF assimilation results, unconstrained GP correction results, DVS-constrained GP correction results, and embedded GP-EnKF correction results.

[0139] In one specific embodiment, the unconstrained GP structural error correction strategy can significantly reduce the simulation errors of LAI and SM; the DVS-constrained GP structural error correction strategy can enhance the continuity and physiological rationality of the LAI time series; and the embedded GP-EnKF coupling assimilation correction strategy can enable structural error correction to participate in the subsequent state propagation process and further optimize the yield simulation.

[0140] Compare and optimize crop model simulation results; systematically compare the optimization effects of three types of structural error correction frameworks under different drip irrigation methods and irrigation levels. Identify and compare the optimization performance of the three error correction models, and select the optimal solution.

[0141] To identify and explore the responses of three drip irrigation modes—shallow buried drip irrigation (SBDI), mulched drip irrigation (FDI), and surface drip irrigation (SDI)—to different error correction models.

[0142] like Figures 7-9 : , , , , These represent the evaluation parameters for open-loop simulation, EnKF assimilation results, unconstrained GP structural error model correction results, DVS-constrained structural error model, and embedded GP-EnKF coupled assimilation calibration model, respectively.

[0143] To address the structural error problem in crop models under different drip irrigation conditions, this invention provides a crop growth simulation method based on the coupling of GP structural error correction and EnKF assimilation. The purpose of this invention is to overcome the problems of insufficient simulation accuracy of existing crop growth models under complex drip irrigation conditions, residual structural errors remaining after data assimilation, lack of physiological constraints in machine learning correction results, and insufficient stability in yield prediction. This method integrates multi-source remote sensing data from UAVs, field measured data, meteorological data, the WOFOST crop growth model, the EnKF algorithm, and the GP regression model to achieve optimized simulation of crop growth indicators such as LAI, SM, and yield. The corresponding processing flow is as follows: Figure 1 As shown.

[0144] In summary, this invention proposes a crop growth simulation method and system based on the coupling of Gaussian process structure error correction and ensemble Kalman filter assimilation. This technique utilizes the EnKF method to couple UAV remote sensing data, machine learning algorithms, and the WOFOST crop model.

[0145] First, based on UAV imagery and ground-based measured data of maize during key growth stages in the study area obtained by the UAV platform, an inversion model was constructed using the BP neural network algorithm to obtain leaf area index and soil moisture rate data, which served as observational inputs for subsequent data assimilation.

[0146] By fusing LAI and SM data retrieved from UAVs using the EnKF method, a WOFOST-EnKF assimilation framework was constructed. By comparing the assimilation simulation results with ground-based measured data, the systematic bias sequence of the model at different growth stages, i.e., the structural error sequence, was extracted, providing a training dataset for the construction of subsequent error models.

[0147] Furthermore, Gaussian process regression (GP) was used to learn and correct the model structure error, and three error correction models were constructed: (a) unconstrained GP offline structure error correction model, (b) GP error correction model under DVS growth function constraint, and (c) embedded GP-EnKF coupled assimilation calibration model.

[0148] The system compared the optimization effects of three types of structural error correction frameworks under different drip irrigation methods and irrigation levels.

[0149] Example 2:

[0150] Based on Example 1, a crop growth simulation system based on Gaussian process structure error correction and EnKF assimilation coupling is proposed.

[0151] The system includes the following modules:

[0152] The data acquisition module is used to acquire UAV multispectral images, thermal infrared images, field observation data, and meteorological data;

[0153] The remote sensing feature extraction and parameter inversion module is used to extract vegetation indices, canopy temperature, and spectral features, and to invert LAI and SM.

[0154] The crop growth simulation module is used to simulate crop growth processes under different drip irrigation methods and irrigation levels based on the WOFOST model.

[0155] The EnKF data assimilation module is used to assimilate LAI and SM observation data into the WOFOST model and dynamically update crop growth status.

[0156] The residual structure error extraction module is used to calculate the residual error between the observations and the EnKF assimilation results, and to construct structural error training samples.

[0157] The Gaussian process structure error correction module is used to construct three types of structure error correction models: unconstrained GP, DVS-constrained GP, and embedded GP-EnKF.

[0158] The results output module is used to output the optimized LAI, SM, and Yield simulation results and to evaluate the model accuracy.

[0159] Through the above implementation methods, the present invention can organically combine UAV remote sensing observation, crop model simulation, ensemble Kalman filter assimilation, and Gaussian process structure error correction to achieve optimized simulation of crop growth status and yield under different drip irrigation conditions.

[0160] This method can improve the accuracy of numerical simulation of state variables, enhance the continuity and physiological rationality of crop growth processes, and provide technical support for precision irrigation management and yield prediction.

[0161] Components not described in detail in this article are existing technologies.

[0162] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A crop growth simulation method based on coupling of Gaussian process structural error correction and EnKF assimilation, characterized in that, The following steps are used: Step 1: Acquire multi-source remote sensing images, field observation data, and meteorological data of the study area; Step 2: Extract vegetation index and canopy temperature information of the study area, combine it with ground measurement data, and construct an inversion model using grey relational analysis and BP algorithm; Step 3: Using Simlab software, the EFAST method is employed to perform sensitivity analysis on the WOFOST crop growth model, thereby achieving parameter localization; Step 4: Use the EnKF algorithm to assimilate LAI and SM into the crop model, further extract the systematic deviation sequences of the model at different growth stages, construct a structural error sequence dataset, and construct a structural error model; Step 5: Construct a structural error correction model using the Gaussian process (GP) regression algorithm; Step 6: Output the optimized simulation results and evaluate the optimization effect of the three error calibration models under different irrigation treatments.

2. The method according to claim 1, wherein, In step 1; It also includes acquiring multispectral images and thermal infrared images. The multispectral images include green light, red light, red edge and near-infrared bands, and the thermal infrared images are used to acquire canopy temperature information.

3. The method according to claim 2, wherein, In step 2; Vegetation index, canopy temperature information and related spectral characteristic parameters were extracted, and leaf area index and soil moisture inversion models were constructed by combining field measurement data to obtain crop growth status observation data.

4. The crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling according to claim 1, characterized in that, In step 3; Meteorological data, soil parameters, crop parameters, and field management parameters are input into the WOFOST crop growth model to simulate the growth and development process of crops under different drip irrigation conditions.

5. The crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling according to claim 1, characterized in that, In step 3; By analyzing the influence of input factors on output variance, the first-order sensitivity index and the overall sensitivity index of each parameter are obtained.

6. The crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling according to claim 1, characterized in that, In step 4; Based on the WOFOST model simulation, the EnKF algorithm is introduced to dynamically assimilate and update state variables such as LAI and SM.

7. The crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling according to claim 1, characterized in that, In step 5; Construct a Gaussian process regression model; Gaussian process regression models can learn the nonlinear mapping relationship between model state variables and residual structural errors, and output the error prediction mean and uncertainty.

8. The crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling according to claim 1, characterized in that, In step 5; The structural error correction model is any one of the following: unconstrained GP structural error model, GP model under DVS growth function constraint, or embedded GP-EnKF coupled assimilation calibration model.

9. The crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling according to claim 1, characterized in that, In step 6; Output the optimized simulation results of LAI, SM, and Yield under different drip irrigation treatments; The results of open-loop simulation, EnKF assimilation, unconstrained GP correction, DVS-constrained GP correction, and embedded GP-EnKF correction were compared using evaluation metrics such as root mean square error (RMSE) and coefficient of determination (R²).

10. A crop growth simulation system based on Gaussian process structure error correction and EnKF assimilation coupling, based on the crop growth simulation method based on Gaussian process structure error correction and EnKF assimilation coupling as described in any one of claims 1-8, characterized in that, Also includes: The data acquisition module is used to acquire UAV multispectral images, thermal infrared images, field observation data, and meteorological data; The remote sensing feature extraction and parameter inversion module is used to extract vegetation indices, canopy temperature, and spectral features, and to invert LAI and SM. The crop growth simulation module is used to simulate crop growth processes under different drip irrigation methods and irrigation levels based on the WOFOST model. The EnKF data assimilation module is used to assimilate LAI and SM observation data into the WOFOST model and dynamically update crop growth status. The residual structure error extraction module is used to calculate the residual error between the observations and the EnKF assimilation results, and to construct structural error training samples. The Gaussian process structure error correction module is used to construct three types of structure error correction models: unconstrained GP, DVS-constrained GP, and embedded GP-EnKF. The results output module is used to output the optimized LAI, SM, and Yield simulation results and to evaluate the model accuracy.

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