Method for estimating rice yield based on allometric growth framework with accumulated temperature constraint

Abstract

The application discloses a rice yield estimation method based on an allometric growth framework constrained by accumulated temperature, and comprises the following steps: performing cultivation tests under different varieties and nitrogen fertilizer environments, sampling and measuring the dry matter and nitrogen content of leaves, stems and plants in the growth period to obtain accumulated temperature and yield data; constructing critical nitrogen dilution curves of leaves, stems and plants to calculate nitrogen nutrition indexes of various organs; introducing a leaf-stem nitrogen distribution deviation penalty term into the nitrogen nutrition index of the plant based on a leaf-stem nitrogen accumulation amount reference distribution relationship to establish a comprehensive nitrogen nutrition index; normalizing the relative growth length to represent the growth process, taking the nitrogen nutrition indexes and the comprehensive nitrogen nutrition index as objects to construct a dynamic model, and integrating adjacent growth stages to obtain integrated nitrogen nutrition indexes and comprehensive integrated nitrogen nutrition indexes; and adopting a linear plus platform model to represent the response relationship between the three types of nitrogen nutrition indexes and the relative grain yield. The method comprehensively considers the cooperation of multiple organs and the constraint of accumulated temperature, and improves the accuracy of yield estimation.

Description

Technical Field

[0001] This invention relates to the fields of crop yield prediction, nitrogen nutrition diagnosis and agricultural information technology, and in particular to a method for predicting rice yield based on an accumulated temperature-constrained allometric growth framework. Background Technology

[0002] Rice (Oryza sativa L.) is one of the world's major food crops, with nearly half of the global population relying on it as their staple food. With continued population growth, decreasing arable land, and increasing uncertainty regarding the impact of climate change on food production, ensuring high and stable rice yields is of paramount importance for safeguarding national food security and socio-economic development. Rice yield is significantly influenced by nitrogen fertilizer application; while high nitrogen input can increase yield, it also leads to environmental pollution. Optimizing nitrogen fertilizer management strategies has been proven to improve rice yield, nitrogen use efficiency (NUE), and environmental benefits. However, traditional nitrogen fertilizer application strategies are based on the mathematical relationship between nitrogen application rate and yield, and few studies utilize nitrogen status during phenological stages to estimate the optimal nitrogen application rate for rice yield. Therefore, it is necessary to redefine the nitrogen nutrient status for achieving high and stable yields, which is crucial for predicting rice yield and ensuring food security.

[0003] Existing methods for diagnosing nitrogen nutrition in rice mainly fall into two categories: direct fertilization recommendations based on soil nitrogen supply and diagnostic regulation based on plant nitrogen nutrition status. Because the latter directly reflects the nitrogen nutrition level within the crop and can respond more accurately to differences in genetic characteristics across different growth stages and varieties, it is widely used in precision agriculture. Previous research on plant nitrogen diagnosis has proposed the nitrogen nutrient index (NNI) method based on the critical nitrogen dilution curve (CNDC), which assesses crop nitrogen status by comparing the ratio of actual nitrogen concentration to critical nitrogen concentration. Furthermore, a comprehensive nitrogen nutrient index (NNI) has been developed based on this method. inte This method reflects the dynamic changes in nitrogen by accumulating NNI at each growth stage. NNI... inteThis method can better characterize the nitrogen accumulation effect of crops throughout their entire growth period, thus offering higher predictive accuracy compared to single-point diagnosis. Currently, most rice nitrogen diagnostic models can diagnose the nitrogen status of plants at specific growth stages. However, factors influencing rice yield formation include not only nitrogen concentration at a single time point but also the dynamic distribution of nitrogen among different functional organs and the synergistic effect of nitrogen status between source and sink organs. Previous studies have shown that rice yield formation depends on the synergistic contribution of leaf (source) photosynthesis and stem (sink) material translocation. The ratio of nitrogen distribution between leaves and stems directly determines the allocation efficiency of photosynthetic nitrogen and translocated nitrogen, thereby affecting dry matter accumulation and grain yield. However, most existing nitrogen diagnostic methods focus only on a single organ (such as based on aboveground dry matter or only on leaves), failing to effectively integrate the synergistic constraints of nitrogen distribution across multiple organs. In particular, they cannot diagnose the imbalance in nitrogen distribution between leaves and stems, making it difficult to accurately assess the nitrogen requirements for achieving high and stable yields.

[0004] Among existing rice nitrogen diagnosis techniques, although some scholars have used the cumulative nitrogen nutrient index (NNI)... inte To reflect the dynamic changes during the reproductive period, but NNI inte The calculations are still mainly based on single-organ parameters, lacking a quantitative description of the synergistic relationship of nitrogen allocation among multiple organs such as leaves and stems. In particular, existing technologies cannot identify and correct situations where "the overall nitrogen level is sufficient but the allocation among organs is unbalanced." That is, when the nitrogen ratio between leaves and stems deviates from the optimal allocation ratio, even if the overall nitrogen content (NNI) is within the appropriate range, yield loss will occur due to the imbalance of photosynthetic source-sink relationships. Meanwhile, studies have also indicated that the nitrogen allocation ratio among different organs significantly affects the accumulation and translocation of crop photosynthetic products, ultimately impacting yield formation. Therefore, constructing a dynamic nitrogen diagnosis method based on the synergistic constraints of nitrogen allocation among multiple organs, and correcting the nitrogen nutrient index by introducing a penalty mechanism for deviations in nitrogen allocation among organs, is particularly important for improving the accuracy of nitrogen management and achieving high and stable yields.

[0005] This invention analyzes the nitrogen allocation characteristics of multiple organs in different rice varieties at different growth stages. Addressing the limitation of existing technologies where single-organ diagnosis cannot reflect the rationality of nitrogen allocation, this invention explores the nitrogen-driven mechanism of yield formation and constructs a comprehensive nitrogen nutrition index model based on the synergistic constraints of whole-plant nitrogen nutrition level and inter-organ nitrogen allocation. This method can provide a technical approach to improve nitrogen use efficiency in rice and achieve high and stable yields. Summary of the Invention

[0006] To address the problems existing in the prior art, the purpose of this invention is to provide a method for predicting rice yield based on an accumulated temperature-constrained allometric growth framework. This invention characterizes the rice growth process uniformly by using relative growth degree days, and combines the nitrogen nutrition status of leaves, stems, and the whole plant to construct a single-time-point nitrogen nutrition index, an integral nitrogen nutrition index, and a comprehensive integral nitrogen nutrition index. It also establishes a linear plus plateau response relationship between these indices and relative yield, which is used for yield prediction and comparison of the effects of dynamic nitrogen nutrition indices at different growth stages.

[0007] To achieve the above objectives, the technical solution adopted by this invention is: a method for predicting rice yield based on an accumulated temperature-constrained allometric growth framework, comprising:

[0008] Rice cultivation experiments were conducted on different varieties and under different nitrogen fertilizer conditions. During the experiment, rice populations were sampled at key growth stages to measure the dry matter and nitrogen content of leaves, stems and plants, and to obtain corresponding meteorological accumulated temperature data and yield data.

[0009] The experimental data were analyzed, and critical nitrogen dilution curves based on leaf dry matter, stem dry matter, and plant dry matter were constructed respectively. The nitrogen nutrition index of each nitrogen nutrition diagnostic object was calculated based on the critical nitrogen dilution curves.

[0010] Based on the reference distribution of nitrogen accumulation in leaves and stems, when the plant is in Nitrogen nutritional index during the period Based on this, a penalty term for deviation in nitrogen allocation from leaf and stem is introduced. Establish a comprehensive nitrogen nutrition index model ;

[0011] Based on relative growth days The rice growth process was normalized and characterized using different nitrogen nutrition diagnostic subjects. and based on plants Comprehensive nitrogen nutrient index after correction penalty As a modeling object, construct its subsequent A dynamic model of change is used, and integration is performed over adjacent reproductive stages to obtain the integral nitrogen nutrition index. and the comprehensive nitrogen nutrition index

[0012] A linear plus plateau model was used to characterize the response relationship between the three nitrogen nutrition indices and relative grain yield (RY). Relative grain yield was expressed as the ratio of grain yield of each treatment to the highest grain yield, which was used to eliminate the influence of yield level differences between years, varieties or experimental conditions.

[0013] As a further improvement of the present invention, the model of the critical nitrogen dilution curve is as follows: ,in, For the first Critical nitrogen concentrations for nitrogen-like nutrient diagnostic subjects, including leaves, stems, and plants; Dry weight; and The fitting parameters are: The model for the nitrogen nutrient index is: ,in, For the first Nitrogen-like nutrition diagnostic subjects in Nitrogen nutrient index during the period, including leaves stem and plants ; For the first Nitrogen-like nutrition diagnostic subjects in Measured nitrogen concentration during the period; These represent specific growth stages, including the tillering stage, jointing stage, heading stage, heading stage, and grain-filling stage.

[0014] As a further improvement of the present invention, the comprehensive nitrogen nutrient index model is as follows: ,in, This indicates a deviation from the nitrogen allocation penalty term. This represents the corresponding penalty intensity coefficient.

[0015] As a further improvement to the present invention, a nitrogen partition deviation penalty term is included. Represented using a piecewise function: ,in, Indicates the deviation index of nitrogen allocation in leaves and stems. For the first When the nitrogen allocation in the leaf-stem region deviates from the penalty tolerance threshold at each growth stage node, when At that time, it was considered that the deviation in nitrogen allocation from leaf and stem distribution was within the tolerable range. 0, no penalty is imposed on the plant's nitrogen nutrient index; when At that time, only the deviation exceeding the tolerance threshold is subject to a squared penalty; the leaf-stem nitrogen allocation deviation index Represented as: ,in, Indicates the first Reference ratio of leaf and stem nitrogen allocation for high-yielding samples at each growth stage ; Indicates the first Leaf nitrogen accumulation at each growth stage; Indicates the first Stalk nitrogen accumulation at each growth stage; To preset the high-yield screening threshold, This indicates that high-yield samples that meet the preset high-yield screening criteria are selected. This represents the median of the ratio of nitrogen accumulation in leaves and stems among the selected high-yield samples.

[0016] As a further improvement of the present invention, the integral nitrogen nutrient index and the comprehensive nitrogen nutrition index The unified representation is: ;in, These correspond to four adjacent growth stages: tillering-jointing, jointing-booting, booting-heading, and heading-filling. and The first The relative growth days corresponding to the start and end points of adjacent reproductive stages; ,when hour, Recorded as ;when hour, Recorded as The relative growth rate daily model is as follows: , ,in, For relative growth days; To accumulate growth over time; The total growth during the entire reproductive period; This refers to the number of days within this sampling phase. The first The highest and lowest temperatures of the day, Base temperature.

[0017] As a further improvement to the present invention, the linear addition plateau model is expressed as: , In the formula, Indicates the first Nitrogen-like nutritional index , respectively corresponding , and ; The first Intercept, slope, and plateau value of a linear plus plateau model; This corresponds to the critical value under the nitrogen nutrient index; when hour, Follow Increases linearly; when hour, Reaching the platform level.

[0018] As a further improvement of the present invention, the sampling of key growth periods covers at least three growth stages before flowering, including tillering, jointing, and heading; and heading and grain-filling stages, to form no fewer than five growth period nodes. Dynamic data.

[0019] As a further improvement to the present invention, the first Reference ratio of leaf and stem nitrogen allocation for high-yielding samples at each growth stage Determined from high-yield samples with a relative yield of not less than 0.90; The preferred range is the 25th percentile to the 75th percentile of the ratio of leaf-stem nitrogen accumulation in high-yield samples at the corresponding growth stage.

[0020] As a further improvement of the present invention, the first Leaf and stem nitrogen allocation at each growth stage deviates from the penalty tolerance threshold and penalty intensity coefficient From the corresponding adjacent reproductive stages and Assigning value to the first Nodes of adjacent reproductive stages ,make = , = In determining the first When combining corrective parameters for adjacent reproductive stages The candidate range is 0-0.35. The candidate range is 0-12, and candidate parameter combinations are generated through grid search. Leave-one-out cross-validation is used to evaluate the yield estimation error, and the candidate parameter combination with the smallest leave-one-out cross-validation error is taken as the optimal correction parameter combination for the corresponding interval.

[0021] As a further improvement of the present invention, the rice samples were sampled in at least three replicates, and the leaves, stems and panicles of the rice were separated. The samples were blanched at 105℃ for 30 min, dried at 80℃ to constant weight and then weighed to obtain the plant biomass. Finally, the dried samples were ground into powder and sieved. The total nitrogen content of each organ was determined by semi-micro Kjeldahl nitrogen determination method using an AA3 type continuous flow analyzer.

[0022] This invention addresses the problem that existing single-organ, single-time-point nitrogen diagnostic methods are insufficient to accurately characterize changes in the growth process, nitrogen allocation in multiple organs, and leaf-stem synergy mechanisms during rice yield formation. This invention uses cumulative growth days or relative growth days (RGDD) as a unified normalized growth process variable based on accumulated temperature. It constructs a multi-level critical nitrogen dilution curve (CNDC) system for leaf, stem, and whole-plant dry matter, calculates the organ-specific nitrogen nutrient index (NNI), and dynamically integrates these indices within adjacent growth stages to form the integrated nitrogen nutrient index (NNI). inteThe invention further establishes a high-yield reference population based on preset high-yield screening conditions, determines the reference ratio of leaf nitrogen accumulation to stem nitrogen accumulation according to the growth stage, establishes a leaf-stem nitrogen allocation benchmark value, and constructs a leaf-stem nitrogen allocation deviation index and deviation penalty term accordingly. A leaf-stem nitrogen allocation deviation correction is introduced on the basis of the whole-plant nitrogen nutrition index to form a comprehensive nitrogen nutrition index. The optimal mathematical parameters for each adjacent growth stage are determined through a joint master analysis grid search using the allowable deviation threshold δ and the penalty coefficient λ, combined with leave-one-out cross-validation, thereby improving the stability and predictive reliability of the model parameters. Based on the quantitative relationship model between various nitrogen nutrition indices and relative yield (RY), a rice yield prediction model for different growth stages is established for yield estimation and comparison of the effects of different dynamic nitrogen nutrition indices. This invention comprehensively considers the synergistic contribution of leaf photosynthetic nitrogen source, stem nitrogen pool, and whole-plant nitrogen nutrition status to yield formation. It overcomes the limitations of traditional methods that rely solely on single dry matter, leaf area index, or single-time-point nitrogen status for diagnosis. This invention can more accurately capture the critical nitrogen demand values ​​during key growth stages of rice, and effectively reduces random errors from single-point sampling through integrated dynamic indices, achieving precise dual control of nitrogen fertilizer application timing and amount. This invention requires fewer parameters, has strong mechanistic implications, and is widely applicable, effectively guiding high and stable rice yields. It is easily coupled to crop growth models, significantly improving the model's ability to simulate and predict dry matter accumulation, nitrogen translocation, and final yield. This invention is applicable to different varieties, planting densities, and nitrogen fertilizer treatments, and the dynamic nitrogen nutrition index accurately characterizes the nitrogen supply status of rice throughout its entire growth period.

[0023] The beneficial effects of this invention are:

[0024] 1. This invention constructs multi-organ critical nitrogen dilution curves using Bayesian hierarchical modeling, which can obtain the posterior distribution and 95% confidence interval of CNDC parameters. Compared with the point estimation of the traditional least squares method, this method provides a complete uncertainty quantification framework. At the same time, the Bayesian method can effectively separate the effects of different water treatments (such as dryland and flooded) on CNDC parameters (A1 and A2), and judge the significance of differences between treatments by the degree of overlap of the 95% confidence interval, which significantly improves the robustness and generalization ability of the critical nitrogen concentration model under complex environmental conditions.

[0025] 2. This invention constructs a comprehensive nitrogen nutrition index model by introducing a penalty function for nitrogen allocation deviation among organs. This model can identify and correct the situation where "the nitrogen level of the whole plant is sufficient but the allocation among organs is unbalanced". That is, when the nitrogen ratio between leaves and stems deviates from the optimal allocation ratio, even if the nitrogen content of the whole plant is within the appropriate range, the diagnostic result can be corrected by the penalty term to avoid yield loss caused by the imbalance of photosynthetic source-sink relationship.

[0026] 3. This invention constructs a comprehensive integral nitrogen nutrient index (NNI) by introducing the relative growth day (RGDD) time series parameter. inte This effectively eliminates the random errors and differences in growth period of single-point sampling diagnosis, and can continuously and accurately characterize the nitrogen supply status and cumulative effect of rice throughout the entire growth period, significantly improving the accuracy of nitrogen diagnosis and the reliability of yield prediction.

[0027] 4. This invention optimizes the tolerance threshold for deviation of nitrogen allocation in leaves and stems for different adjacent growth stages. and penalty intensity coefficient Candidate parameter combinations are generated through grid search, and the yield prediction effect of each combination is evaluated by leave-one-out cross-validation error. The parameter combination with the smallest cross-validation error is taken as the optimal correction parameter combination for the corresponding interval, thereby avoiding the subjectivity brought about by manually fixing parameters and improving the objectivity of the construction of the comprehensive integral nitrogen nutrition index for different growth stages and the stability of yield estimation. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the critical nitrogen dilution curves and parameter estimation results constructed based on the dry matter of leaves, stems and whole plants in an embodiment of the present invention.

[0029] Figure 2 This is a schematic diagram of NNI dynamic curve fitting based on relative growth rate day RGDD and integral calculation of adjacent growth period intervals in an embodiment of the present invention;

[0030] Figure 3 This is a reference ratio for nitrogen allocation in leaves and stems under high-yield samples in this embodiment of the invention. A diagram illustrating the differences in reproductive stages;

[0031] Figure 4 Nitrogen nutritional index in embodiments of the present invention Integral Nitrogen Nutrition Index and the comprehensive nitrogen nutrition index Relative grain yield A schematic diagram of the linear plus-plateau response relationship;

[0032] Figure 5 This is a schematic diagram comparing the yield prediction errors of three types of nitrogen nutrition indices in different growth stages according to an embodiment of the present invention.

[0033] Figure 6 In this embodiment of the invention, the nitrogen allocation in the leaf and stem deviates from the tolerance threshold. With penalty intensity coefficient A schematic diagram of the grid search and parameter response analysis results. Detailed Implementation

[0034] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0035] Example 1

[0036] A method for predicting rice yield based on an accumulated temperature-constrained allometric growth framework includes:

[0037] During the experiment, field meteorological data at the experimental site were recorded after rice transplanting, including daily maximum and minimum temperatures, and cumulative growth days (AGDD) were calculated based on the rice base temperature (10℃).

[0038] During the experiment, samples were taken at key growth stages of rice to obtain data such as dry weight and nitrogen concentration of leaves, stems and whole plants for each treatment.

[0039] The experimental data were analyzed using a Bayesian hierarchical modeling method, and critical nitrogen dilution curves (CNDCs) based on leaf dry matter, stem dry matter, and whole plant dry matter were constructed, as follows: Figure 1 As shown, (a) represents the critical nitrogen dilution curves (CNDCs) based on leaves, stems, and the whole plant, and (b) represents the corresponding posterior parameter estimates. The solid and dashed lines represent the critical nitrogen dilution curves and their confidence intervals, respectively. The parameter plots are used to represent the differences in critical nitrogen dilution curve parameters under different organs or treatment conditions, and to calculate the nitrogen nutrient index (NNI) for each organ. The critical nitrogen concentration dilution curves are uniformly represented as follows:

[0040]

[0041] in, For the first Critical nitrogen concentration for organoids For the first The dry matter content of organoids, and These are the parameters for the corresponding critical nitrogen dilution curve; This represents leaves, stems, or plants. The constructed critical nitrogen concentration dilution curves for leaves, stems, and plants are as follows:

[0042]

[0043]

[0044]

[0045] Calculate the nitrogen nutrient index for each organ based on the above critical nitrogen concentration:

[0046]

[0047] in, For the first Nitrogen-like nutrition diagnostic subjects in the first Nitrogen nutrition index at each reproductive stage The measured nitrogen concentration corresponds to the reproductive period. To determine the dry matter quality at the corresponding reproductive stage The critical nitrogen concentration obtained by substituting into equation (1);

[0048] Based on relative output not less than For high-yield samples, the reference ratio of nitrogen allocation in leaves and stems was determined according to the growth stage. Based on this, the nitrogen allocation deviation index of leaves and stems was calculated. The leaf-stem nitrogen allocation deviation index is expressed as:

[0049]

[0050] Reference ratio of nitrogen allocation in leaf and stem for high yield in formula (3) Represented as:

[0051]

[0052] in, and They represent the first Leaf nitrogen accumulation and stem nitrogen accumulation at each growth stage; It is used to characterize the degree of deviation of the ratio of leaf nitrogen accumulation to stem nitrogen accumulation at the current growth stage from the high-yield reference ratio.

[0053] like Figure 3 As shown, high-yield samples refer to samples with relative yield; the yield is determined by the median ratio of leaf nitrogen accumulation to stem nitrogen accumulation at the corresponding growth stage. Based on the reference distribution relationship of leaf and stem nitrogen accumulation in high-yield samples, the nitrogen nutrient index of the plant is used. Based on this, a penalty term for deviation in nitrogen allocation from leaf and stem is introduced. Construct a comprehensive nitrogen nutrition index The comprehensive nitrogen nutrient index model is as follows:

[0054]

[0055] in, This represents the penalty intensity coefficient corresponding to the reproductive period; Represented using a piecewise function with a tolerance threshold:

[0056]

[0057] in, For the first Leaf and stem nitrogen allocation deviates from the tolerance threshold during each growth stage. When, no penalty is imposed on the nitrogen nutrient index of the whole plant; when In this case, only the deviation exceeding the tolerance threshold is subject to a squared penalty. In equations (5) and (6) and And corresponding to adjacent reproductive stages and Assignment is possible, and These are the parameters to be optimized.

[0058] Living by relative growth As a normalized variable for accumulated temperature in reproductive progress, the nitrogen nutrition index of each nitrogen nutrition diagnostic subject was used. and comprehensive nitrogen nutrition index For the modeling object, construct its subsequent A dynamic model of change. For example... Figure 2 As shown, the dynamic model is integrated over adjacent reproductive stages to obtain the integrated nitrogen nutrition index. and the comprehensive nitrogen nutrition index Its unified representation is:

[0059]

[0060] in, ;when hour, This is recorded as the integral nitrogen nutritional index. ;when hour, This is recorded as the comprehensive nitrogen nutrition index. The adjacent growth stages include four intervals: tillering-jointing, jointing-booting, booting-heading, and heading-filling.

[0061] The relative growth rate daily model is as follows:

[0062]

[0063] in, For relative growth days; To accumulate growth over time; The total growth during the entire reproductive period; This refers to the number of days within this sampling phase. The first The highest and lowest temperatures of the day, The base temperature is 10℃ for rice.

[0064] like Figure 4 As shown, the above nitrogen nutrient index Integral nitrogen nutritional index and the comprehensive nitrogen nutrition index As a candidate dynamic nitrogen nutrition index A linear-platform model was used to characterize the response relationship between different nitrogen nutrient indices and relative grain yield. The linear-platform model is expressed as follows:

[0065]

[0066] In the formula, Indicates the first Nitrogen-like nutritional index , respectively corresponding , and ; The first Intercept, slope, and plateau value of a linear plus plateau model; This represents the critical value corresponding to the nitrogen nutrient index. When hour, Follow Increases linearly; when hour, Reaching the platform level.

[0067] Furthermore, such as Figure 5 As shown, the deviation of leaf and stem nitrogen allocation from the tolerance threshold and penalty intensity coefficient For the parameters to be optimized, a grid search was performed for each adjacent growth stage; for each combination of candidate parameters, the comprehensive nitrogen nutrient index was recalculated. and the comprehensive nitrogen nutrition index The yield estimation error was evaluated using leave-one-out cross-validation, and the candidate parameter combination with the smallest cross-validation error was selected as the optimal correction parameter combination for the corresponding fertility stage. Figure 6 As shown.

[0068] Finally, the critical nitrogen dilution curve construction, leaf-stem nitrogen allocation deviation correction, daily dynamic integration of relative growth degree, parameter grid search optimization, and linear + platform yield response model are integrated to obtain a rice yield prediction method based on an accumulated temperature-constrained allometric growth framework. This method can output the optimal combination of correction parameters, integral dynamic nitrogen nutrient index, and corresponding yield estimation model for different adjacent growth stages, and can be used for rice yield estimation and performance comparison of different dynamic nitrogen nutrient indices.

[0069] Example 2

[0070] The study was conducted on a base in 2024-2025. A two-factor split-plot design was used, with one rice variety, two irrigation levels, five nitrogen application levels, three replicates, and a total of 30 plots. Water was the primary treatment, with two irrigation levels: rainfed (W0) and flooded (W1). Nitrogen application was the secondary treatment, with one level of pure nitrogen (0 kg ha). -1 90 kg ha -1 180 kg ha -1 270kg ha -1 and 360kg ha -1 Five nitrogen application levels were implemented, with urea as the nitrogen fertilizer, applied in three separate applications: 40% before transplanting, 30% during the tillering stage, and 30% during the booting stage. The rice variety selected was Yongyou 4949, a leading agricultural variety in Sichuan Province in 2024. This variety is high-yielding and of high quality, suitable for machine transplanting and harvesting, with a row spacing of 30 cm and a plant spacing of 18 cm. Field management, including rice seedling raising, transplanting, plant protection, and harvesting, was uniformly carried out according to the local high-yield rice planting plan.

[0071] Example 3

[0072] The experiment was conducted in an industrial park in 2025. The experimental materials were the locally cultivated hybrid rice varieties Chuanzhongyou 3607 (V1) and Champion Rice Quanyou 607 (V2). Five nitrogen fertilizer gradients were set up: 0 kg / hm². 2 (N0), 75 kg / hm 2 (N1), 150 kg / hm 2 (N2), 225 kg / hm 2 (N3) and 300 kg / hm 2 (N4). A total of 10 treatments were combined: V1N0, V1N1, V1N2, V1N3, V1N4, V2N0, V2N1, V2N2, V2N3, and V2N4. All 10 treatments were sown in seedling trays in mid-to-late May. After the seedlings reached the three-leaf stage, seedlings with uniform growth were selected and transplanted to field plots. Irrigation, weeding, and pest and disease management were carried out according to local rice planting standards to avoid biotic and abiotic stress.

[0073] Meteorological data in the rice field after transplanting were recorded hourly by Dynamet-1K (Dynamet Inc., USA) near the experimental site, including daily minimum temperature (°C), daily maximum temperature (°C), and sunshine duration (h). Daily temperature was used to calculate cumulative growth days, an index that represents the time-dependent changes in rice growth and nitrogen dynamics, controlled by temperature variations during the rice growing season, and is the sum of growth days from transplanting to each sampling date.

[0074] Destructive sampling was conducted during key growth stages of rice, including tillering, jointing, booting, heading, and grain-filling stages. Three samples from each plot of uniformly growing rice were randomly selected. The leaves and stems were separated and placed in an oven for blanching at 105℃ for 30 min, followed by drying at 80℃ to constant weight. The dry weight of each organ was then measured, and the dry weight of the entire aboveground part of the plant was calculated. The dried and weighed leaf and stem samples were then pulverized, and the total nitrogen concentration was determined using the semi-micro Kjeldahl method with an AA3 continuous flow analyzer (SealAnalytical GmbH, Norderstedt, Germany). The nitrogen status of the leaves, stems, and the entire plant was calculated based on this result.

[0075] The collected data were organized by year, location, treatment, nitrogen application level, replication, and organ, and critical nitrogen dilution curves were constructed for leaves, stems, and whole plants, respectively. Figure 1 The nitrogen nutrient index (NNI) was calculated for each growth stage, and the dynamic relationship between NNI and RGDD was established using relative growth days (RGDD) as the time scale. Figure 2 ).

[0076] The above data were organized by year, location, variety, treatment, nitrogen application level, replication, and nitrogen nutrition diagnostic subjects. Critical nitrogen dilution curves for leaves, stems, and whole plants were constructed, and the nitrogen nutrition index for each growth stage was calculated. Furthermore, using relative growth days as a variable of growth process, a dynamic relationship between the nitrogen nutrition index and relative growth days was constructed. The integral nitrogen nutrition index was obtained by integrating the data over four adjacent growth stages: tillering-jointing, jointing-booting, booting-heading, and heading-filling.

[0077] Furthermore, from the perspective of relative output not less than ( In high-yield samples with a nitrogen accumulation of 0.90, the median ratio of leaf nitrogen accumulation to stem nitrogen accumulation is calculated according to the growth stage and used as the reference ratio for high-yield leaf-stem nitrogen allocation at the corresponding growth stage. Then, the leaf-stem nitrogen allocation deviation index is calculated based on this reference ratio, and a leaf-stem nitrogen allocation deviation penalty term is introduced on the basis of the whole plant nitrogen nutrition index to obtain the comprehensive nitrogen nutrition index.

[0078] For each adjacent growth stage, the deviation tolerance threshold for leaf-stem nitrogen allocation and the penalty intensity coefficient are used as the parameters to be optimized. Candidate parameter combinations are generated through grid search, and leave-one-out cross-validation is used to evaluate the yield estimation error. The candidate parameter combination with the smallest cross-validation error is selected as the optimal correction parameter combination for the corresponding interval, and the comprehensive integral nitrogen nutrient index is calculated accordingly.

[0079] Finally, the nitrogen nutrition index, integral nitrogen nutrition index, and comprehensive integral nitrogen nutrition index were selected as candidate dynamic nitrogen nutrition indices and a linear-platform response relationship was established with relative grain yield to obtain rice yield estimation models for different growth stages. These models were then used for yield estimation and comparison of the effects of different dynamic nitrogen nutrition indices.

[0080] The embodiments described above are merely illustrative of specific implementations of the present invention, and while the descriptions are detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for predicting rice yield based on an accumulated temperature-constrained allometric growth framework, characterized in that, include: Rice cultivation experiments were conducted on different varieties and under different nitrogen fertilizer conditions. During the experiment, rice populations were sampled at key growth stages to measure the dry matter and nitrogen content of leaves, stems and plants, and to obtain corresponding meteorological accumulated temperature data and yield data. The experimental data were analyzed, and critical nitrogen dilution curves based on leaf dry matter, stem dry matter, and plant dry matter were constructed respectively. The nitrogen nutrition index of each nitrogen nutrition diagnostic object was calculated based on the critical nitrogen dilution curves. Based on the reference distribution of nitrogen accumulation in leaves and stems, when the plant is in Nitrogen nutritional index during the period Based on this, a penalty term for deviation in nitrogen allocation from leaf and stem is introduced. Establish a comprehensive nitrogen nutrition index model ; Based on relative growth days The rice growth process was normalized and characterized using different nitrogen nutrition diagnostic subjects. and based on plants Comprehensive nitrogen nutrient index after corrective punishment As a modeling object, construct its following A dynamic model of change was used, and the integral nitrogen nutrient index was obtained by integrating the results over adjacent reproductive stages. and the comprehensive nitrogen nutrition index ; A linear plus plateau model was used to characterize the response relationship between the three nitrogen nutrition indices and relative grain yield (RY). Relative grain yield was expressed as the ratio of grain yield of each treatment to the highest grain yield, which was used to eliminate the influence of yield level differences between years, varieties or experimental conditions.

2. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 1, characterized in that, The model for the critical nitrogen dilution curve is as follows: ,in, For the first Critical nitrogen concentrations for nitrogen-like nutrient diagnostic subjects, including leaves, stems, and plants; Dry weight; and The fitting parameters are: The model for the nitrogen nutrient index is: ,in, For the first Nitrogen-like nutrition diagnostic subjects in Nitrogen nutrient index during the period, including leaves stem and plants ; For the first Nitrogen-like nutrition diagnostic subjects in Measured nitrogen concentration during the period; These represent specific growth stages, including the tillering stage, jointing stage, heading stage, heading stage, and grain-filling stage.

3. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 2, characterized in that, The comprehensive nitrogen nutrition index model is as follows: ,in, This indicates a deviation from the nitrogen allocation penalty term. This represents the corresponding penalty intensity coefficient.

4. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 3, characterized in that, Nitrogen allocation deviation penalty term Represented using a piecewise function: ,in, Indicates the deviation index of nitrogen allocation in leaves and stems. For the first When the nitrogen allocation in the leaf-stem region deviates from the penalty tolerance threshold at each growth stage node, when At that time, it was considered that the deviation in nitrogen allocation from leaf and stem distribution was within the tolerable range. 0, no penalty is imposed on the plant's nitrogen nutrient index; when At that time, only the deviation exceeding the tolerance threshold is subject to a squared penalty; the leaf-stem nitrogen allocation deviation index Represented as: ,in, Indicates the first Reference ratio of leaf and stem nitrogen allocation for high-yielding samples at each growth stage ; Indicates the first Leaf nitrogen accumulation at each growth stage; Indicates the first Stalk nitrogen accumulation at each growth stage; To preset the high-yield screening threshold, This indicates that high-yield samples that meet the preset high-yield screening criteria are selected. This represents the median of the ratio of nitrogen accumulation in leaves and stems among the selected high-yield samples.

5. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 1, characterized in that, The integral nitrogen nutrition index and the comprehensive nitrogen nutrition index The unified representation is: ;in, These correspond to four adjacent growth stages: tillering-jointing, jointing-booting, booting-heading, and heading-filling. and The first The relative growth days corresponding to the start and end points of adjacent reproductive stages; ,when hour, Recorded as ;when hour, Recorded as The relative growth rate daily model is as follows: , ,in, For relative growth days; To accumulate growth over time; The total growth during the entire reproductive period; This refers to the number of days within this sampling phase. The first The highest and lowest temperatures of the day, Base temperature.

6. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 1, characterized in that, The linear-plus-plateau model is represented as follows: , In the formula, Indicates the first Nitrogen-like nutritional index , respectively corresponding , and ; The first Intercept, slope, and plateau value of a linear plus plateau model; This corresponds to the critical value under the nitrogen nutrient index; when hour, Follow Increases linearly; when hour, Reaching the platform level.

7. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 1, characterized in that, The sampling of key growth periods shall cover at least three growth stages before flowering, including tillering, jointing, and heading; and heading and grain-filling stages, to form no fewer than five growth period nodes. Dynamic data.

8. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 4, characterized in that, No. Reference ratio of leaf and stem nitrogen allocation for high-yielding samples at each growth stage Determined from high-yield samples with a relative yield of not less than 0.90; The preferred range is the 25th percentile to the 75th percentile of the ratio of leaf-stem nitrogen accumulation in high-yield samples at the corresponding growth stage.

9. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 4, characterized in that, The first Leaf and stem nitrogen allocation at each growth stage deviates from the penalty tolerance threshold and penalty intensity coefficient From the corresponding adjacent reproductive stages and Assigning value to the first Nodes of adjacent reproductive stages ,make = , = In determining the first When combining corrective parameters for adjacent reproductive stages The candidate range is 0-0.

35. The candidate range is 0-12, and candidate parameter combinations are generated through grid search. Leave-one-out cross-validation is used to evaluate the yield estimation error, and the candidate parameter combination with the smallest leave-one-out cross-validation error is taken as the optimal correction parameter combination for the corresponding interval.

10. The rice yield prediction method based on the accumulated temperature-constrained allometric growth framework according to claim 1, characterized in that, Rice samples were sampled in at least three replicates, and the leaves, stems and panicles were separated. The samples were blanched at 105℃ for 30 min, dried at 80℃ to constant weight, and then weighed to obtain plant biomass. Finally, the dried samples were ground into powder and sieved. The total nitrogen content of each organ was determined by semi-micro Kjeldahl nitrogen determination method using an AA3 type continuous flow analyzer.

Images