Winter wheat grain yield prediction method and system based on theoretical uncertainty assimilation remote sensing growth period and LAI

Abstract

The invention discloses a winter wheat grain yield prediction method and system based on theoretical uncertainty assimilation remote sensing growth period and LAI, and the method comprises the steps: firstly obtaining a multi-source time sequence remote sensing image, and extracting wheat growth period information and a leaf area index of a key growth period; secondly, constructing a theoretical uncertainty model considering the change of a remote sensing inversion error along with time and canopy density, and using the theoretical uncertainty model to dynamically characterize the credibility of a growth period and an LAI remote sensing estimated value; thirdly, the growth period and the LAI are assimilated into crop growth models such as WheatGrow in a layered mode under the constraint of theoretical uncertainty, phenology-related parameters and substance accumulation-related parameters are optimized respectively, and time-space continuous growth period, LAI and grain yield simulation results are obtained. Compared with a method which only depends on experience uncertainty or a single assimilation index, the method has the advantages that error transmission can be effectively inhibited, the wheat yield prediction precision of county and field scale is improved, and reliable technical support is provided for regional grain yield monitoring, precise fertilization and agricultural insurance.

Description

Technical Field

[0001] This invention belongs to the field of agricultural remote sensing and crop growth model technology, specifically involving a method and system for predicting winter wheat grain yield based on theoretical uncertainty assimilation of remote sensing growth period and LAI. Background Technology

[0002] Wheat is one of the world's major food crops, ranking first in both sown area and total yield. Therefore, timely and accurate monitoring of wheat growth and yield forecasting in major wheat-producing areas are of great significance for understanding the status of grain production, guiding field production management, and ensuring food security.

[0003] Crop growth models describe the crop growth and development process using mathematical formulas with physical meaning. Remote sensing can acquire key state variables describing growth in the model over a large area in real time, such as leaf area index (LAI), leaf nitrogen content, and growth stage. Combining the two can predict crop yield over a large area. However, the process of retrieving crop growth parameters from remote sensing involves certain uncertainties, which may arise from atmospheric noise, soil background effects, and vegetation saturation issues. Crop growth models also introduce uncertainties due to the spatiotemporal variability of meteorological, soil, and crop variety parameters, as well as the systematic errors inherent in the crop growth models themselves. Therefore, combining remote sensing observations and model simulations with their uncertainties using data assimilation algorithms to derive analytical solutions for state variables is a mainstream method for remote sensing model coupling.

[0004] Variational assimilation and sequential assimilation algorithms are two main algorithms for assimilating remote sensing data and models. The four-dimensional variational assimilation algorithm (4DVar), as a primary variational assimilation algorithm, couples all remote sensing estimates within a time window into a dynamic mechanism model and derives the optimal analytical solution of the model by minimizing the cost function through optimizing the model input parameters. The uncertainties of model simulation and remote sensing estimates are included in the cost function of the variational assimilation algorithm, thus effectively mitigating the problem of ill-conditioned inversion during the optimization process.

[0005] In data assimilation studies, quantifying the uncertainties of remote sensing estimates and model simulations is a crucial step. Remote sensing estimation errors and model simulation errors are represented by the observation error covariance and background error covariance, respectively. The observation error covariance is typically calculated using the standard deviation of the remote sensing estimation error or, based on the assumption of a normal distribution of remote sensing estimation bias, the root mean square error (RMSE) of the remote sensing estimate compared to field measurements, and is assumed to be constant across the spatiotemporal scales. The background error covariance is empirically determined and is usually assumed to be normally distributed. However, without field measurements, it is difficult to quantify the uncertainties of remote sensing observations and model backgrounds, and previous studies have demonstrated that the optimal uncertainty varies across different years. Furthermore, constant remote sensing and model uncertainties cannot describe the heterogeneity of remote sensing estimates and model background values, as well as their uncertainties across the spatiotemporal scales.

[0006] Theoretical uncertainty dynamically quantifies the quality of LAI products based on LAI estimates or reflectance and has the potential to serve as an input parameter for data assimilation. It is generally accepted in academia that reflectance saturation under dense canopies and interference from non-target variables (such as leaf pigment, leaf angle, soil background, and atmospheric noise) contribute to the uncertainty in remotely sensed LAI estimates. Many LAI products include quality assessment layers to evaluate the theoretical error of LAI estimates at the pixel scale, but the modeling process of nonparametric models results in a lack of mechanistic explanation for their theoretical uncertainty. For example, the theoretical uncertainty of CYCLOPES is calculated through the residuals between neural network estimates and corresponding input values. Gaussian process regression models provide an uncertainty interval related to mean predictions through Bayesian statistical inference. Although MODIS LAI is a physical method based on the radiative transfer equation, its theoretical uncertainty is the standard deviation of all acceptable numerical solutions on a lookup table. Effective MODIS-based LAI products, such as JRC-TIP and GA-TIP, are also based on lookup table methods, and their quality assessment indices (QQIs) are highly dependent on pre-defined model parameters because the prior probability density function of LAI is included in the cost function. Intuitively describing the response of LAI uncertainty to confounding factors can improve researchers' understanding of theoretical uncertainty and enhance its stability.

[0007] In recent years, the impact of crop phenology on yield estimation has attracted attention. Although researchers have optimized phenological parameters by assimilating the growth period index (LAI) in previous data assimilation studies, the accuracy of the corresponding growth period simulation remains questionable, as many studies using LAI as the sole assimilation index have found significant errors in non-LAI state variables. Recently, researchers have developed a new method that stratifies growth period and LAI to optimize the simulation of growth period. However, in-depth analysis of the impact of growth period assimilation on LAI and yield estimation accuracy is still lacking.

[0008] Numerous methods have been developed for large-scale estimation of vegetation growth stages, which can be categorized into time-series methods and classification methods. Time-series methods estimate growth stages by extracting features from smoothed vegetation index curves; classification methods extract growth stage information by training classification models using spectral features of the target growth stage. Both methods perform well in estimating crop sowing, heading, and maturity stages, but time-series methods estimate sowing dates by detecting crop emergence, as emergence occurs shortly after the actual sowing date. Recently, researchers have proposed a method to directly identify sowing dates by distinguishing soil reflectance characteristics between sown and unsown fields; however, time gaps in remote sensing image sequences introduce uncertainty.

[0009] Post-flowering dry matter assimilated from leaves and ears accounts for 70-90% of wheat grain yield. Wheat grain yield originates from dry matter assimilation during the reproductive growth stage and dry matter redistribution during the vegetative growth stage. In the Simple Algorithm For Yield (SAFY) model, grain yield is only related to the leaf area index (LAI) during the grain-filling stage. In the World Food Studies (WOFOST) model, there is a high correlation between post-heading LAI and grain yield. However, there is a conflict between the optimal yield prediction time window and the yield formation mechanism. Researchers have found that in the multiple linear regression method, the highest yield estimation accuracy is achieved when inputting vegetation indices (VIs) from the jointing stage to the heading stage. The key to improving yield estimation accuracy lies in comprehensively considering the physiological basis of yield formation and the estimation accuracy of the assimilation model, and ultimately determining the optimal assimilation time window. Summary of the Invention

[0010] The purpose of this invention is to overcome the problems of coarse setting of remote sensing uncertainty, easy pathological inversion of assimilation parameters, and limited yield prediction accuracy in existing remote sensing-crop model assimilation methods. This invention proposes a method and system for predicting winter wheat grain yield based on theoretical uncertainty assimilation of remote sensing growth period and LAI, so as to achieve high-precision and spatiotemporally continuous prediction of winter wheat grain yield.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] On the one hand, this invention provides a method for predicting winter wheat grain yield based on the assimilation of theoretical uncertainty with remote sensing growth period and LAI, comprising the following steps:

[0013] Step 1: Remote sensing data acquisition and preprocessing: Acquire multi-source remote sensing images covering the target area during the winter wheat growing season, and preprocess the multi-source remote sensing images to construct a time-series reflectance dataset;

[0014] Step 2, Remote sensing estimation of wheat growth period and quantification of theoretical uncertainty: Based on time series vegetation index or soil spectral information, identify unsown and sown soils; by fitting the vegetation index time series, extract the time characteristics of heading and maturity periods, and construct theoretical uncertainty models and error covariance matrices for remote sensing estimation values ​​of sowing, heading and maturity periods based on satellite revisit cycle, observation time interval and sample point measurement error;

[0015] Step 3, LAI Remote Sensing Estimation and Theoretical Uncertainty Quantification: Based on the radiative transfer model or empirical / semi-empirical inversion model, wheat LAI at different time phases is inverted using medium spatial resolution satellite imagery or UAV multispectral imagery. Further, a synthetic dataset is constructed based on the PROSAIL forward radiative transfer model. The distribution characteristics of LAI estimation error under different canopy density conditions are analyzed. The functional relationship between LAI estimation value and estimation error is constructed, and this relationship is converted into the theoretical uncertainty and error covariance corresponding to the LAI remote sensing estimation value.

[0016] Step 4: Crop growth model construction and calibration: Select a crop growth model suitable for winter wheat, input meteorological, soil, management and variety parameters of the study area, and use the measured growth period, LAI and grain yield data of the experimental sample points to calibrate the variety parameters in the model related to growth period, material accumulation and yield, and obtain an unbiased background parameter set;

[0017] Step 5: Hierarchical Assimilation Based on Theoretical Uncertainty: Under the 4DVar four-dimensional variational assimilation framework, the model background value, remote sensing observation value and its uncertainty are integrated in the form of a cost function and solved using a global optimization algorithm. The first layer uses remotely estimated sowing, heading, and maturity dates as observations, selects growth period-related parameters as parameters to be optimized, and constructs an observation error covariance matrix using the theoretical uncertainty of the growth period to optimize the growth period parameters and their spatial distribution. The second layer, under the condition of fixed growth period parameters, uses remotely sensed LAI as an observation, selects parameters related to material accumulation and canopy structure as parameters to be optimized, constructs an observation error covariance matrix using the theoretical uncertainty of LAI, and assimilates and optimizes the material accumulation-related parameters to obtain a spatiotemporally continuous and error-controlled LAI and growth state.

[0018] Step 6, Yield Forecasting and Spatial Mapping: Using the parameters optimized by hierarchical assimilation to drive the crop growth model, simulate the dry matter accumulation, distribution and grain yield formation of wheat throughout the growing season, generate spatial distribution maps of winter wheat grain yield at the county or field scale, and calculate the statistical indicators of yield per unit area in each region.

[0019] Furthermore, in step 1, the multi-source remote sensing images include high temporal resolution optical satellite images for estimating fertility period and medium spatial resolution satellite images or UAV multispectral images for LAI estimation, wherein the high temporal resolution optical satellite images are PlanetScope images and the medium spatial resolution satellite images are Sentinel-2 images; the preprocessing includes radiometric calibration, atmospheric correction, geometric correction and cloud / shadow removal of the remote sensing images.

[0020] Furthermore, in step 2, the single-class support vector machine OCSVC is used to identify unsown soil and sown soil, with identification dates t1 and t2 respectively. This was used as an estimate of the sowing date; and by fitting the vegetation index time series with a double logistic function, the time characteristics of the heading and maturity periods were extracted. The double logistic function is expressed as follows:

[0021]

[0022] Where x is the accumulated day DOY, y is the NDVI, and y max is the maximum value of the NDVI time series, and a, b, c, and d are the fitting parameters;

[0023] The heading and maturity periods can be determined by analyzing the extreme values ​​and threshold positions of the first or second derivatives of the fitted curve.

[0024] Furthermore, in step 2, the theoretical uncertainty model for the remote sensing estimate of the sowing date is constructed as follows: assuming the error follows a normal distribution, ... The root mean square error (RMSE) of the sowing date estimation is used, where t1 and t2 are the observation times when unsown and sown soils were identified, respectively. The variance of the sowing date observation error is derived from this. Combining the measured growth period data of the sample points and the remote sensing estimation error, the error statistical characteristics of the remote sensing estimation values ​​of the heading and maturity periods are determined, and these are used to construct the error covariance matrix of the growth period estimation values.

[0025] Furthermore, in step 3, the synthetic dataset constructed based on the PROSAIL radiative transfer model uses Gaussian or uniform distribution sampling to sample input parameters including leaf area index (LAI), chlorophyll content (Cab), and mean leaf tilt angle (ALA) (as shown in Table 1). The corresponding spectral reflectance is simulated using the PROSAIL model, the inversion error under different LAI levels is analyzed, and an empirical function between the LAI estimate and the error standard deviation is fitted to obtain the LAI theoretical uncertainty model. The LAI theoretical uncertainty model gives a larger observation error variance to high LAI under dense canopy conditions and a smaller observation error variance to low LAI under sparse canopy conditions, thereby reducing the weight of LAI observations in the saturation zone during the assimilation process.

[0026] Table 1 Input parameters of the PROSAIL model

[0027]

[0028] Furthermore, in step 4, the crop growth model is the WheatGrow model; the variety parameters include: growth period-related parameters PVT, IE, PS, TS and FDF, LAI-related parameters SLA, LT, TA, EIN and MPR, and yield-related parameters 1000-grain weight GW and harvest index HI; the meteorological parameters include daily maximum temperature, daily minimum temperature, sunshine duration and rainfall; the soil parameters include soil layers, particle size structure, organic carbon content, pH, cation exchange capacity, total nitrogen content, bulk density, soil wilt coefficient, field water holding capacity and saturated water content; and the management parameters include sowing date, seeding rate, sowing depth and nitrogen, potassium and phosphorus application rates; as detailed in Table 2.

[0029] Table 2 Input parameters of the WheatGrow model

[0030]

[0031] Furthermore, in step 5, the four-dimensional variational assimilation cost function is:

[0032]

[0033] Where K represents the number of parameters to be optimized. Input parameters to the model, B represents the background value of the input parameters, and B is the background error covariance matrix. These are remote sensing observations, where N represents the number of remote sensing observations. These are the corresponding model simulation values. The observation error covariance matrix;

[0034] The cost function is solved using either the particle swarm optimization algorithm or the SCE-UA algorithm.

[0035] Furthermore, in step 6, the parameter-driven crop model after hierarchical assimilation optimization is used to simulate the dry matter accumulation, distribution, and grain yield formation of wheat throughout the growing season; a spatial distribution map of winter wheat grain yield at the county or field scale is generated, and statistical indicators of yield per unit area in each region are calculated; the yield results can further provide decision-making basis for precision fertilization, drought and flood mitigation, agricultural insurance, etc.

[0036] On the other hand, the present invention also provides a winter wheat grain yield prediction system based on theoretical uncertainty assimilation of remote sensing growth period and LAI, comprising:

[0037] The remote sensing data acquisition and preprocessing module is used to acquire multi-source remote sensing images covering the winter wheat growing season, and to perform radiometric calibration, atmospheric correction, geometric correction and cloud / shadow removal on them, and output a time series reflectance dataset.

[0038] The module for estimating the growth period and theoretical uncertainty is used to identify the sowing date of sown and unsown soils based on time-series vegetation index and / or soil spectral information, extract the heading and maturity periods by fitting vegetation index curves, and construct a theoretical uncertainty model and error covariance matrix of the remote sensing estimate of the growth period based on satellite revisit cycle, observation time interval and sample point residuals.

[0039] The LAI inversion and theoretical uncertainty module is used to invert LAI using a radiative transfer model or an empirical / semi-empirical inversion model, analyze LAI estimation errors based on the PROSAIL synthetic dataset, construct a theoretical uncertainty model for LAI, and output LAI observations and their error covariance matrix.

[0040] The crop growth model module is used to run the winter wheat crop growth model, receive meteorological, soil, management and variety parameters, and calibrate the model variety parameters through experimental sample point measured data to obtain the background parameter set;

[0041] The hierarchical assimilation module is used to perform a first-level assimilation optimization of fertility period-related parameters using observed values ​​and theoretical uncertainties of fertility period within a four-dimensional variational assimilation framework, and to perform a second-level assimilation optimization of material accumulation and canopy structure-related parameters using observed values ​​of LAI and theoretical uncertainties under the condition that fertility period parameters are fixed.

[0042] The yield prediction and spatial mapping module is used to drive a crop growth model with parameters optimized by hierarchical assimilation, output winter wheat grain yield and generate yield spatial distribution maps and statistical indicators.

[0043] Furthermore, the remote sensing data acquisition and preprocessing module is configured to receive PlanetScope, Sentinel-2 and UAV multispectral images, and reconstruct cloudless reflectance time series through cloud masking and time series interpolation.

[0044] Furthermore, the reproductive period estimation and theoretical uncertainty module is configured as follows:

[0045] The single-class support vector machine OCSVC was used to identify unsown and sown soils and to calculate the estimated sowing date.

[0046] The vegetation index time series was fitted with a double logistic function, and the heading and maturity stages were extracted based on curve features.

[0047] according to The RMSE of the sowing period was estimated, and the covariance matrix of the observation error of the growth period was constructed by combining the statistical results of the residuals of the sample points, where t1 and t2 are the observation times when the unsown soil and the sown soil were identified, respectively.

[0048] Furthermore, the LAI inversion and theoretical uncertainty module is configured as follows:

[0049] Based on the PROSAIL model, a synthetic sample library is generated, the estimation error at different LAI levels is analyzed, and the functional relationship between the LAI estimation value and the error standard deviation is fitted to obtain the theoretical uncertainty model of LAI.

[0050] Furthermore, the hierarchical assimilation module employs a four-dimensional variational assimilation cost function in both assimilation layers and solves it through a global optimization algorithm, outputting optimized results for winter wheat growth period, LAI, and grain yield at different spatial scales.

[0051] The beneficial effects of this invention are as follows:

[0052] Compared with methods that rely solely on empirical uncertainty or a single assimilation index, this invention can effectively suppress error propagation, improve the accuracy of wheat yield prediction at the county and field scales, and provide reliable technical support for regional grain yield monitoring, precision fertilization, and agricultural insurance. Attached Figure Description

[0053] Figure 1 A flowchart of a hierarchical assimilation strategy based on theoretical uncertainty;

[0054] Figure 2 Image features of different land cover types in PlantScope, from left to right: rice, rice straw residue, and wheat after sowing;

[0055] Figure 3 This is the theoretical uncertainty model for LAI;

[0056] Figure 4 (a), (b), and (c) are the production prediction results; (d), (e), and (f) are the results of hierarchical assimilation, traditional single-layer assimilation, and model simulation in Example 1, respectively; and (d), (e), and (f) are the results of hierarchical assimilation, traditional single-layer assimilation, and model simulation in Example 2, respectively. Detailed Implementation

[0057] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0058] like Figure 1 As shown, a method for predicting winter wheat grain yield based on theoretical uncertainty assimilation remote sensing estimation of growth period and LAI includes the following steps:

[0059] Step 1: Obtain multi-source remote sensing data and auxiliary data of winter wheat growing season in the study area, preprocess the remote sensing data, and construct a remote sensing time series dataset for growth period identification and LAI inversion;

[0060] Step 2: Construct a remote sensing estimation model for the growth period of winter wheat based on high temporal density remote sensing images, obtain the spatial distribution of key growth periods such as sowing date, heading date and maturity date, and construct a theoretical uncertainty model for remote sensing estimation of growth period.

[0061] Step 3: Construct an LAI inversion model based on medium- and high-resolution optical or UAV multispectral imagery to obtain remote sensing estimates of LAI at different reproductive stages, and construct a theoretical uncertainty model for LAI remote sensing estimation by combining radiative transfer mechanism and synthetic dataset.

[0062] Step 4: Based on meteorological, soil, management and variety data, construct a wheat growth model suitable for the study area, perform initial setting and basic calibration of model parameters, and obtain background values ​​of growth period-related parameters and material accumulation-related parameters.

[0063] Step 5: Under the four-dimensional variational (4DVar) assimilation framework, the sowing date, heading date and maturity date estimated by remote sensing are used as observations. The uncertainty of the growth period theory is introduced to construct the observation error covariance matrix. The sensitive parameters related to the growth period in the WheatGrow model, such as sowing date, basic precocity and grain filling duration, are assimilated and optimized to obtain the optimized growth period parameters and the spatial distribution of continuous growth period.

[0064] Step 6: Under the condition of fixed growth period parameters, using remote sensing inversion of LAI as the observation, introduce the theoretical uncertainty of LAI to construct the observation error covariance matrix, and perform second-level assimilation optimization on the sensitive parameters related to material accumulation and canopy structure in the WheatGrow model to obtain spatiotemporally continuous and error-controlled simulation results of LAI and growth status.

[0065] Step 7: Use the parameter set optimized by hierarchical assimilation to drive the WheatGrow model to dynamically simulate the entire winter wheat growing season, output the cumulative dry matter and grain yield at the pixel scale or field scale, and generate a spatial distribution map and statistical indicators of winter wheat grain yield.

[0066] Example 1: Taking Xinghua City, Jiangsu Province as the study area, the applicability and accuracy of the winter wheat yield prediction method based on theoretical uncertainty hierarchical assimilation were verified at the county scale.

[0067] In step 1, data acquisition and preprocessing include:

[0068] Remote sensing data: PlanetScope high temporal resolution optical imagery and Sentinel-2 multispectral imagery covering the 2021–2022 winter wheat growing season were acquired. PlanetScope imagery was used for identification of sowing, heading, and maturity dates, with a temporal resolution better than 5 days; Sentinel-2 imagery was used for LAI inversion, with a spatial resolution of 10 m and a temporal resolution of approximately 5 days.

[0069] Meteorological data: Daily maximum and minimum temperatures, precipitation, wind speed and sunshine duration were collected from Xinghua meteorological station, and spatial interpolation methods were used to obtain meteorological driving data at the study area scale.

[0070] Soil and management data: Obtain 1:50,000 soil type maps and typical soil profile attributes (bulk density, organic matter content, field water holding capacity, etc.) of Xinghua County, and collect survey data such as sowing date, fertilizer application rate, and irrigation system provided by the local agricultural department for use as input to construct the WheatGrow model.

[0071] Radiometric calibration, atmospheric correction, geometric fine correction, and resampling were performed on PlanetScope and Sentinel-2 images, respectively. Cloud and cloud shadow pixels were identified using cloud mask products and thresholding methods. Missing phases were reconstructed using time series interpolation methods to form a reflectance time series dataset with a uniform spatial resolution of 10 m and a time interval of approximately 5 days.

[0072] In step 2, the process of remote sensing estimation of the reproductive period and construction of theoretical uncertainties is as follows:

[0073] First, field-measured sowing, heading, and maturity data from typical sampling sites in Xinghua County were selected. Combined with red and near-infrared reflectance data from PlanetScope before and after sowing, a soil spectral sample library was constructed. Figure 2 As shown, different soil types exhibit significant spectral differences. One-class support vector machine (OCSVC) was used to identify the sowing soil state over time, extracting the sowing date for each pixel to achieve pixel-level spatial mapping of sowing dates.

[0074] Secondly, using the Normalized Difference Vegetation Index (NDVI) as the main indicator, the PlanetScope time series NDVI was fitted with a double Logistic function or Asymmetric Gaussian. Based on the extreme positions of the first and second derivatives of the curve, the dates corresponding to the heading and maturity stages were obtained, thus obtaining a spatial distribution map of the heading and maturity stages within Xinghua County.

[0075] Furthermore, considering the PlanetScope revisit cycle, the uneven time interval caused by cloud cover, and the rate of change in the growth period, a theoretical derivation of the sowing date estimation error is performed. Assuming that sowing occurs between two cloudless images, the upper and lower bounds of the sowing date error are proportional to the time interval between the two images, thus constructing the theoretical uncertainty interval for the sowing date. This interval is then transformed into the variance under the assumption of a normal distribution, which yields the covariance of the sowing date observation error.

[0076] For the heading and maturity stages, the theoretical uncertainties of the heading and maturity stages are obtained by fitting the error distribution based on the residuals between the measured growth period of the sample points and the remote sensing estimates, and taking into account the revisit period and curve fitting error. A growth period observation error covariance matrix composed of the three is then constructed for growth period assimilation.

[0077] In step 3, the process of LAI remote sensing estimation and theoretical uncertainty construction is as follows:

[0078] Using measured LAI data from sampling points in Xinghua County and synchronously acquired Sentinel-2 reflectance data, a training set for LAI retrieval was constructed by selecting green, red, near-infrared, and two red-edge bands. A synthetic sample library containing multiple parameter combinations, including LAI, chlorophyll content (Cab), and average leaf inclination angle (ALA), was generated using the PROSAIL radiative transfer model to simulate the corresponding reflectance. A mapping relationship between reflectance / vegetation index and LAI was established on the synthetic samples.

[0079] Within the synthetic data space, the inversion errors at different LAI levels were statistically analyzed. It was found that under high LAI conditions, there is a significant saturation effect, with the error increasing with increasing LAI. Based on this, an empirical function (such as an exponential function or a piecewise linear function) was fitted to the equation "LAI estimate - error standard deviation" to obtain a theoretical uncertainty model for LAI. Figure 3 The figure shows a theoretical uncertainty model constructed based on the Xinghua dataset.

[0080] By combining the theoretical uncertainty model with the actual Sentinel-2 inversion of LAI, the corresponding observation error variance is calculated for each pixel and each time phase, forming the spatiotemporal variation of LAI observation error covariance, which is used for LAI assimilation.

[0081] In step 4, the WheatGrow model is built and localized:

[0082] Based on the growth characteristics of the main winter wheat varieties cultivated in Xinghua, parameters such as basal temperature, effective accumulated temperature, specific leaf area, photosynthetic efficiency, and dry matter partition coefficient were initially set. The model was calibrated using multi-stage observations (including growth period, LAI, and grain yield) at typical experimental sites in Xinghua to ensure that the model simulation results under unassimilated conditions were as consistent as possible with the measured data. The calibrated parameter set served as background parameters for growth period assimilation and LAI assimilation.

[0083] In step 5, reproductive period stratification and assimilation are performed:

[0084] Within the 4DVar framework, a growth period cost function is constructed using sowing date, heading date, and maturity date as observations. The background term constrains deviations of sowing date (SD), basic early maturity parameter (IE), and grain-filling duration (FDF) from background values. The observation term characterizes the difference between the model-simulated growth period and the remote sensing-estimated growth period. The observation error covariance is provided by the theoretical uncertainty in step 2.

[0085] The cost function was iteratively optimized using either the particle swarm optimization algorithm or the SCE-UA global optimization algorithm. The algorithm was solved independently for each pixel or agricultural management unit within Xinghua County to obtain a spatially continuous set of optimal growth period parameters, generating updated spatial distribution maps of sowing, heading, and maturity dates. Results showed that after growth period assimilation, the RMSE between the model-simulated growth period and the measured growth period at the sample sites could be controlled within approximately 4 days.

[0086] In step 6, LAI hierarchical assimilation is performed:

[0087] Under the condition of fixed growth period parameters, LAI assimilation cost function is constructed using multi-temporal Sentinel-2 inversion as the observation. Parameters related to material accumulation and canopy structure, such as seeding rate, nitrogen application rate, and specific leaf area, are selected as parameters to be optimized to ensure that the growth period parameters are not disturbed. The observation error covariance is generated using the theoretical uncertainty of LAI constructed in step 3, so that the high LAI stage is given a larger observation error, avoiding excessive constraints on parameter inversion by observations in the saturation zone.

[0088] Similarly, a global optimization algorithm was used to optimize parameters within a selected time window (e.g., from jointing to grain filling stage) to obtain the spatial distribution of parameters such as optimal seeding rate and nitrogen application rate at the county scale, and output spatiotemporally continuous LAI simulation results. Validation results show that after LAI assimilation, the RMSE of LAI decreased from approximately 1.0 to 0.6–0.75.

[0089] In step 7, the production forecast and accuracy evaluation are as follows:

[0090] Using the parameter set optimized by stratification and assimilation of the growth period and LAI, the WheatGrow model was driven to complete the simulation of the entire growing season under the condition of no remote sensing observation constraints. The model output the daily dry matter accumulation and grain moisture content changes, and the grain dry weight was extracted at the maturity stage as the winter wheat grain yield at the pixel scale.

[0091] The pixel-scale yield was aggregated to the field and county scales and compared with the agricultural statistical yield and sample point measured yield in Xinghua County. The coefficient of determination (R²) and root mean square error (RMSE) were used as indicators to evaluate the prediction accuracy. The results show that the RMSE of grain yield at the Xinghua County scale using the method of this invention is approximately 800-900 kg·ha⁻¹. Significantly higher than the schemes that did not assimilate and only assimilated LAI ( Figure 4 This demonstrates the effectiveness of the hierarchical assimilation strategy for theoretical uncertainty.

[0092] Example 2: Winter wheat yield prediction at the field scale in Rugao City

[0093] This embodiment uses the experimental station in Rugao City, Jiangsu Province, and surrounding farmland as the study area. At the field scale, multispectral remote sensing data from UAVs and field measurement data are used to verify the method of the present invention at a more refined scale.

[0094] In step 1, data acquisition and preprocessing include:

[0095] Unmanned aerial vehicle (UAV) imagery: During key growth stages of winter wheat, such as jointing, heading, and grain filling, UAVs equipped with multispectral cameras (including blue, green, red, red-edge, and near-infrared bands) were used to conduct aerial photography of the experimental area, achieving a ground resolution better than 0.2 m. The UAV reflectance was cross-referenced with ground-based spectrometer observations through radiometric calibration and atmospheric correction.

[0096] Ground observation: Multiple transects and quadrats were set up in the Rugao experimental field to record the sowing date, nitrogen application level and irrigation system under different treatments. LAI, growth period and dry matter accumulation were measured at each key growth stage, and grain yield was obtained by harvesting the quadrats at maturity.

[0097] Meteorology and Soil: Daily meteorological data from Rugao Meteorological Station were obtained, and soil samples from the experimental field were collected to analyze soil texture, organic matter, and bulk density, which were used as driving data and parameter background for the WheatGrow model.

[0098] Geometric correction and mosaicking of UAV imagery were performed, and ground control points were used to ensure spatial positioning accuracy. Relative radiometric correction was applied to flight paths with uneven illumination to eliminate striping effects. Finally, a multi-temporal, multispectral reflectance dataset at the field scale was generated.

[0099] In step 2, the remote sensing estimation of the reproductive period and the uncertainty are constructed as follows:

[0100] By using aerial images of bare land and seedlings taken by drones before and after the event, spectral differences between soil and early canopy were extracted. Combined with sowing and seedling emergence dates recorded in the field, a sowing date identification rule applicable to the field scale was established to ensure that the sowing date information is strictly aligned with drone observations.

[0101] The NDVI or red-edge vegetation index of the UAV time series were fitted. Since there are few time points of the UAV, field observation records were used as a supplement. The starting dates of jointing, heading and grain filling were determined by a combination of interpolation and fitting methods to form high-precision growth period observation data.

[0102] Unlike county-level data, field-level data has more diverse measured data on the reproductive period. Therefore, in the Rugao implementation, theoretical uncertainty and statistical error are combined: on the one hand, the time uncertainty of each reproductive period observation is determined based on the UAV flight plan and operability; on the other hand, the observation error variance is estimated based on the measured values ​​of the reproductive period and the residuals of the reproductive period inverted by the UAV, and the reproductive period observation error covariance matrix is ​​constructed in a comprehensive manner.

[0103] In step 3, the uncertainties in LAI inversion and theory are as follows:

[0104] After each drone aerial photograph, LAI measurement points were simultaneously deployed within the field. LAI was measured using an LAI meter, and the drone reflectivity corresponding to each point was recorded. Based on this sample data, LAI inversion models were established using methods such as random forest and support vector regression. The best-performing model was selected through cross-validation for field-scale LAI inversion.

[0105] Simultaneously, a synthetic sample library for the Rugao experimental field was generated using the PROSAIL model. The input parameter range was set based on prior information such as leaf inclination angle, chlorophyll content, and specific leaf area of ​​local varieties. A functional relationship between LAI estimation error and LAI size was established on the synthetic samples to obtain the theoretical uncertainty of LAI.

[0106] By combining the theoretical uncertainty of LAI with LAI based on UAV inversion, a larger error variance is assigned to the inversion results in the stage of dense canopy (larger LAI), and a smaller error variance is assigned in the stage of sparse canopy, thus constructing a field-scale LAI observation error covariance for LAI assimilation.

[0107] In step 4, the WheatGrow model localization process is as follows:

[0108] The control treatment (conventional fertilization and management) in the Rugao experimental field was selected as the baseline sample point. Using its complete growth period, LAI, and yield observations, the parameters related to temperature integration, photosynthetic efficiency, and dry matter distribution in the WheatGrow model were calibrated to ensure that the model could accurately reproduce the growth curve in the control field. For other treatments with different nitrogen application levels and management practices, the corresponding synchronous mathematical parameters were retained, and only the seeding rate and nitrogen application rate parameters were adjusted to form the background parameter set for each treatment.

[0109] In step 5, growth period assimilation is implemented at the field scale:

[0110] Using observations of the growth period (sowing date, heading date, and maturity date) of the control and different fertilization treatments as observations, a field-scale cost function was constructed within the 4DVar framework. Since the field area is relatively small, each field can be treated as a single pixel. The optimization objective is to ensure that the model's simulated growth period is consistent with field observations, and the parameter variation range is constrained by theoretical uncertainty and observation error covariance.

[0111] The optimization results show that after reproductive period assimilation, the simulation error of reproductive period for different treatments is generally less than 3-4 days, which lays a unified time frame for subsequent LAI assimilation.

[0112] In step 6, LAI assimilation is carried out at the field scale:

[0113] After fixing the growth period parameters, the LAI (Leaf Area) inversion results from multiple UAV aerial photographs were used as observations, and seeding rate, nitrogen application rate, and specific leaf area were selected as parameters to be optimized. Based on the synthetic data, a theoretical uncertainty model of LAI was constructed. The observation weights were reduced during the high LAI stage and increased during the early and middle stages of growth, thus maintaining the model's insensitivity to the high LAI saturation zone.

[0114] The optimal parameter set for each nitrogen application treatment was obtained by assimilating the LAI during the jointing to grouting period using a global optimization algorithm. The results show that the RMSE between the model-simulated LAI and the UAV-inverted LAI after LAI assimilation can be reduced to about 0.6, which is significantly better than the unassimilated case.

[0115] In step 7, the parameter set after two layers of assimilation is used to simulate the dry matter and yield formation process at the field scale. Grain dry weight is extracted at maturity and compared with the measured yield in the field. The predictive performance was evaluated using RMSE. Results showed that, at the Rugao field scale, the RMSE for grain yield prediction using the method of this invention was approximately 900–1000 kg·ha. -1 , Reaching 0.7 or above ( Figure 4 This allows for a better differentiation of yield differences among different fertilization treatments.

[0116] Two examples, one at the Xinghua county scale and the other at the Rugao field scale, demonstrate that the hierarchical assimilation method proposed in this invention, which assimilates remote sensing growth period and LAI based on theoretical uncertainty, can stably improve the accuracy of winter wheat yield prediction at different spatial scales, and has good scalability and engineering application prospects.

[0117] To support the above method, this invention also designs a winter wheat grain yield prediction system based on theoretical uncertainty assimilation of remote sensing growth period and LAI, comprising:

[0118] The remote sensing data acquisition and preprocessing module is used to acquire multi-source remote sensing images covering the winter wheat growing season, and to perform radiometric calibration, atmospheric correction, geometric correction and cloud / shadow removal on them, and output a time series reflectance dataset.

[0119] The module for estimating the growth period and theoretical uncertainty is used to identify the sowing date of sown and unsown soils based on time-series vegetation index and / or soil spectral information, extract the heading and maturity periods by fitting vegetation index curves, and construct a theoretical uncertainty model and error covariance matrix of the remote sensing estimate of the growth period based on satellite revisit cycle, observation time interval and sample point residuals.

[0120] The LAI inversion and theoretical uncertainty module is used to invert LAI using a radiative transfer model or an empirical / semi-empirical inversion model, analyze LAI estimation errors based on the PROSAIL synthetic dataset, construct a theoretical uncertainty model for LAI, and output LAI observations and their error covariance matrix.

[0121] The crop growth model module is used to run the winter wheat crop growth model, receive meteorological, soil, management and variety parameters, and calibrate the model variety parameters through experimental sample point measured data to obtain the background parameter set;

[0122] The hierarchical assimilation module is used to perform a first-level assimilation optimization of fertility period-related parameters using observed values ​​and theoretical uncertainties of fertility period within a four-dimensional variational assimilation framework, and to perform a second-level assimilation optimization of material accumulation and canopy structure-related parameters using observed values ​​of LAI and theoretical uncertainties under the condition that fertility period parameters are fixed.

[0123] The yield prediction and spatial mapping module is used to drive a crop growth model with parameters optimized by hierarchical assimilation, output winter wheat grain yield and generate yield spatial distribution maps and statistical indicators.

[0124] The remote sensing data acquisition and preprocessing module is configured to receive PlanetScope, Sentinel-2 and UAV multispectral images, and reconstruct cloudless reflectance time series through cloud masking and time series interpolation.

[0125] The module for estimating the reproductive period and addressing theoretical uncertainties is configured as follows:

[0126] The single-class support vector machine OCSVC was used to identify unsown and sown soils and to calculate the estimated sowing date.

[0127] The vegetation index time series was fitted with a double logistic function, and the heading and maturity stages were extracted based on curve features.

[0128] according to The RMSE of the sowing period was estimated, and the covariance matrix of the observation error of the growth period was constructed by combining the statistical results of the residuals of the sample points, where t1 and t2 are the observation times when the unsown soil and the sown soil were identified, respectively.

[0129] The LAI inversion and theoretical uncertainty module is configured as follows:

[0130] Based on the PROSAIL model, a synthetic sample library is generated, the estimation error at different LAI levels is analyzed, and the functional relationship between the LAI estimation value and the error standard deviation is fitted to obtain the theoretical uncertainty model of LAI.

[0131] The hierarchical assimilation module employs a four-dimensional variational assimilation cost function in both assimilation layers and solves it through a global optimization algorithm, outputting the optimized results of winter wheat growth period, LAI, and grain yield at different spatial scales.

[0132] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0133] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments do not limit the scope of protection of the present invention in any way, and all technical solutions obtained by equivalent substitution or other means fall within the scope of protection of the present invention. Parts not covered in this invention are the same as or can be implemented using existing technology.

Claims

1. A method for predicting winter wheat grain yield based on assimilating remote sensing phenological phase and LAI with theoretical uncertainty, characterized in that, Comprise the following steps: Step 1, remote sensing data acquisition and pretreatment: obtain multi-source remote sensing images covering the target area of winter wheat growing season, and pretreat the multi-source remote sensing images to construct a time series reflectivity dataset; Step 2, remote sensing estimation of wheat growth period and theoretical uncertainty quantification: based on time series vegetation index or soil spectrum information, identify unsown soil and sown soil; by fitting the time series of vegetation index, extract the time characteristics of heading stage and maturity stage, and based on satellite revisit period, observation time interval and sample measurement error, construct the theoretical uncertainty model and error covariance matrix of remote sensing estimation value of sowing period, heading stage and maturity stage; Step 3, remote sensing estimation of LAI and theoretical uncertainty quantification: based on radiation transfer model or empirical / semi-empirical inversion model, use medium spatial resolution satellite images or unmanned aerial vehicle multispectral images to retrieve wheat LAI at different time, further based on PROSAIL forward radiation transfer model, construct synthetic dataset, analyze the distribution characteristics of LAI estimation error under different crown density conditions, construct the functional relationship between LAI estimation value and estimation error, and convert the relationship into the theoretical uncertainty and error covariance corresponding to the remote sensing estimation value of LAI; Step 4, construction and calibration of crop growth model: select a crop growth model suitable for winter wheat, input meteorological, soil, management and variety parameters in the study area, and use the measured growth period, LAI and grain yield data of the test sample to calibrate the variety parameters related to growth period, material accumulation and yield in the model, and obtain the unbiased background parameter set; Step 5, hierarchical assimilation based on theoretical uncertainty: in the framework of four-dimensional variational assimilation 4DVar, integrate the model background value, remote sensing observation value and its uncertainty in the form of cost function, and solve by using global optimization algorithm; wherein, the first layer takes the remote sensing estimated sowing period, heading stage and maturity stage as observation, selects growth period related parameters as optimization parameters, uses growth period theoretical uncertainty to construct observation error covariance matrix, and optimizes to obtain growth period parameters and their spatial distribution; the second layer fixes the growth period parameters, takes remote sensing LAI as observation, selects parameters related to material accumulation and crown structure as optimization parameters, uses LAI theoretical uncertainty to construct observation error covariance matrix, and optimizes the assimilation of material accumulation related parameters to obtain time and space continuous and error controlled LAI and growth state; Step 6, yield prediction and spatial mapping: use the parameters optimized by hierarchical assimilation to drive the crop growth model, simulate the dry matter accumulation, distribution and grain yield formation of winter wheat in the whole growing season, generate county scale or field scale winter wheat grain yield spatial distribution map, and calculate the unit area yield statistical index of each region.

2. The method for predicting winter wheat grain yield based on assimilating remote sensing phenological period and LAI with theoretical uncertainty according to claim 1, characterized in that, In the step 1, the multi-source remote sensing images include high temporal resolution optical satellite images for growth stage estimation and medium spatial resolution satellite images or unmanned aerial vehicle multi-spectral images for LAI estimation, wherein the high temporal resolution optical satellite images are PlanetScope images, and the medium spatial resolution satellite images are Sentinel-2 images; the preprocessing includes radiometric calibration, atmospheric correction, geometric correction and cloud / shadow removal on the remote sensing images.

3. The method of predicting winter wheat grain yield based on assimilating remote sensing phenological period and LAI with theoretical uncertainty according to claim 1, characterized in that, In step 2, the unsown soil and sown soil are identified by using one-class support vector machine (OCSVC), and the identification dates are t1 and t2, respectively, so that as the estimated value of the sowing date; and by fitting the time series of the vegetation index with a double Logistic function, the time characteristics of the heading stage and the mature stage are extracted, and the double Logistic function is expressed as: where x is the accumulated day DOY, y is the NDVI, y max is the maximum value of the NDVI time series, and a, b, c, d are fitting parameters; The heading stage and the mature stage are determined by analyzing the first-order or second-order derivative extreme value and the threshold position of the fitting curve.

4. The method for predicting winter wheat grain yield based on assimilating remote sensing phenological period and LAI with theoretical uncertainty according to claim 1, characterized in that, In step 2, the theoretical uncertainty model of the remote sensing estimation value of the sowing period is constructed as follows: under the assumption that the error satisfies the normal distribution, the error of the remote sensing estimation value of the sowing period is calculated as The root mean square error RMSE of the sowing period estimation value is taken as the sowing period observation error variance, wherein t1 and t2 are the observation times of the unseeded soil and the seeded soil identified, respectively, and the sowing period observation error variance is derived; the error statistical characteristics of the remote sensing estimation values of the heading stage and the mature stage are determined in combination with the actual growth period data of the sample points and the remote sensing estimation error, and are used to construct the error covariance matrix of the growth period estimation value.

5. The method of predicting winter wheat grain yield based on assimilating remote sensing phenological period and LAI with theoretical uncertainty according to claim 1, characterized in that, In the step 3, the synthetic dataset constructed based on the PROSAIL radiative transfer model adopts Gaussian distribution or uniform distribution sampling of input parameters including a leaf area index (LAI), a chlorophyll content (Cab) and an average leaf angle (ALA), simulates corresponding spectral reflectance through the PROSAIL model, analyzes the inversion error under different LAI levels, and fits an empirical function between the LAI estimation value and the error standard deviation to obtain an LAI theoretical uncertainty model; the LAI theoretical uncertainty model enables high LAI under dense canopy conditions to be assigned with larger observation error variance, and low LAI under sparse canopy conditions to be assigned with smaller observation error variance, so that the weight of the LAI observation in the saturation area is reduced in the assimilation process.

6. The method for predicting winter wheat grain yield based on assimilating remote sensing phenological period and LAI with theoretical uncertainty according to claim 1, characterized in that, In the step 4, the crop growth model is a WheatGrow model; the variety parameters include growth stage related parameters PVT, IE, PS, TS and FDF, LAI related parameters SLA, LT, TA, EIN and MPR, and yield related parameters thousand-grain weight GW and harvest index HI; the meteorological parameters include daily maximum temperature, daily minimum temperature, sunshine duration and rainfall, the soil parameters include soil layer, particle size structure, organic carbon content, pH, cation exchange capacity, total nitrogen content, bulk density, soil wilting coefficient, field water holding capacity and saturated water content, and the management parameters include sowing date, sowing amount, sowing depth and nitrogen, potassium and phosphorus application amounts.

7. The method of predicting winter wheat grain yield based on assimilating remote sensing phenological period and LAI with theoretical uncertainty according to claim 1, characterized in that, In the step 5, the four-dimensional variational assimilation cost function is: wherein K represents the number of parameters to be optimized, is the input parameter of the model, is the background value of the input parameter, B is the background error covariance matrix, is the remote sensing observation value, N represents the number of remote sensing observations, is the corresponding model simulation value, is the observation error covariance matrix; The cost function is solved by a particle swarm algorithm or an SCE-UA algorithm.

8. A system for predicting winter wheat grain yield based on assimilating remote sensing phenology and LAI with theoretical uncertainty, characterized in that, The method comprises the following steps: a remote sensing data acquisition and preprocessing module for acquiring multi-source remote sensing images covering the winter wheat growing season, and performing radiometric calibration, atmospheric correction, geometric correction and cloud / shadow removal on the images to output a time series reflectance dataset; a growth stage estimation and theoretical uncertainty module for identifying sowing soil and non-sowing soil to estimate the sowing date based on time series vegetation index and / or soil spectral information, extracting the heading stage and the mature stage by fitting the vegetation index curve, and constructing a theoretical uncertainty model of the growth stage remote sensing estimation value and an error covariance matrix based on a satellite revisit period, an observation time interval and a sample residual; an LAI inversion and theoretical uncertainty module for inverting LAI through a radiative transfer model or an empirical / semi-empirical inversion model, analyzing LAI estimation error based on a PROSAIL synthetic dataset, constructing an LAI theoretical uncertainty model, and outputting an LAI observation value and an error covariance matrix thereof; and a crop growth model updating module for updating the crop growth model based on the LAI observation value and the error covariance matrix. The crop growth model module is configured to run a winter wheat crop growth model, receive meteorological, soil, management, and variety parameters, and calibrate model variety parameters through measured data of test points to obtain a background parameter set; The hierarchical assimilation module is configured to perform first layer assimilation optimization on growth period related parameters by using observation values and their theoretical uncertainties of the growth period under a four-dimensional variational assimilation framework, and perform second layer assimilation optimization on material accumulation and canopy structure related parameters by using observation values and their theoretical uncertainties of LAI under the condition that the growth period parameters are fixed. The yield prediction and spatial mapping module is configured to drive the crop growth model by using the parameters optimized through hierarchical assimilation, output winter wheat grain yield, and generate a yield spatial distribution map and statistical indicators.

9. The system for predicting winter wheat grain yield based on assimilating remote sensing phenological phase and LAI with theoretical uncertainty according to claim 8, characterized in that, The remote sensing data acquisition and preprocessing module is configured to receive PlanetScope, Sentinel-2, and unmanned aerial vehicle multi-spectral images, and reconstruct a cloud-free reflectivity time series through cloud mask and time series interpolation.

10. The system for predicting winter wheat grain yield based on assimilating remote sensing phenological phase and LAI with theoretical uncertainty according to claim 8, characterized in that, The growth period estimation and theoretical uncertainty module is configured to: identify unplanted soil and planted soil by using one-class support vector machine (OCSVC), and calculate a sowing date estimation value; fit a double Logistic function to a vegetation index time series, and extract the heading stage and the mature stage based on curve characteristics; According to The RMSE of sowing date is estimated, and the observation error covariance matrix of the growth period is constructed combined with the sample residual statistical results, where t1 and t2 are the identified observation times of the unsown soil and the sown soil, respectively.

11. The system for predicting winter wheat grain yield based on assimilating remote sensing phenological phase and LAI with theoretical uncertainty according to claim 8, characterized in that, The LAI inversion and theoretical uncertainty module is configured to: generate a synthetic sample library based on the PROSAIL model, analyze estimation errors at different LAI levels, fit a functional relationship between LAI estimation values and error standard deviations, and obtain an LAI theoretical uncertainty model.

12. The system for predicting winter wheat grain yield based on assimilating remote sensing phenological phase and LAI with theoretical uncertainty according to claim 8, characterized in that, The hierarchical assimilation module adopts a four-dimensional variational assimilation cost function in both layers of assimilation, and solves the cost function through a global optimization algorithm to output optimization results of winter wheat growth period, LAI, and grain yield at different spatial scales.

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