A method for quantifying the migration of nutrients in an agricultural ecosystem by coupling carbon and nitrogen markers

Abstract

The present application relates to the field of farmland nutrient analysis, and particularly relates to a carbon-nitrogen labeled coupled analysis farmland ecosystem nutrient migration quantification method, which comprises the following steps: obtaining carbon-nitrogen concentration time series by collecting and preprocessing carbon-nitrogen isotope monitoring data; obtaining trajectory evolution optimization factors by performing two-dimensional collaborative trajectory evolution analysis on the carbon-nitrogen concentration time series; obtaining jump distortion optimization factors by performing real migration flux jump distortion feature analysis on the carbon-nitrogen concentration time series; obtaining nutrient migration mode division results by jointly modifying the trajectory evolution optimization factors and the jump distortion optimization factors on the basis of time series distance; and obtaining carbon-nitrogen nutrient migration evaluation results by performing quantification analysis on the nutrient migration mode division results, so as to solve the problem of migration mode division distortion caused by the forced alignment of secondary fluctuation misalignment and the confusion of deep background noise artifacts in the carbon-nitrogen isotope time series clustering of the farmland ecosystem by the existing multi-dimensional dynamic time warping algorithm.

Description

Technical Field

[0001] This invention relates to the field of farmland nutrient analysis technology, and in particular to a method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis. Background Technology

[0002] In farmland ecosystem research, the migration, transformation, and retention of carbon and nitrogen directly affect soil fertility evolution, nutrient use efficiency, and the effectiveness of agricultural non-point source pollution control. To accurately reveal the dynamic fate of nutrients applied to farmland in different soil layers and spatial locations, existing studies typically employ carbon and nitrogen isotope dual labeling technology to continuously monitor changes in carbon and nitrogen isotope abundance within the target farmland area, thereby obtaining multi-temporal data reflecting nutrient migration processes. Based on this monitoring data, further analysis of the response differences at different monitoring sites during nutrient migration can identify migration patterns under different soil microenvironments, providing data support for farmland fertilization regulation, soil improvement, and nutrient cycling mechanism research. When analyzing the aforementioned carbon and nitrogen isotope monitoring data, since each monitoring site simultaneously possesses both temporal and multivariate dimensions, existing techniques typically employ a multidimensional dynamic time warping algorithm to calculate the temporal similarity distance between different monitoring sites, and use the obtained distance results as input for cluster analysis to classify nutrient migration patterns in farmland ecosystems. This type of method can address the issue of inconsistent temporal response rates between different monitoring sites to some extent, and is therefore applied to classification and pattern recognition scenarios for multivariate time-series data. However, in real farmland ecosystems, influenced by factors such as differences in soil physicochemical properties, microbial absorption and release processes, and changes in local hydrothermal conditions, the carbon-nitrogen coupling transformation process within the same monitoring site is often accompanied by multiple secondary fluctuations, and these secondary fluctuations typically exhibit varying degrees of misalignment on the absolute time axis between different monitoring sites. Existing multidimensional dynamic time warping algorithms tend to forcibly align these temporally misaligned secondary fluctuations during global warping, resulting in redundant penalties during distance calculations. This leads to monitoring sites with similar nutrient migration mechanisms being misjudged as significantly different. On the other hand, existing technologies mainly focus on time stretching and numerical matching of data from different dimensions, lacking in-depth utilization of the co-evolutionary relationship of carbon and nitrogen concentrations within the same monitoring site. In particular, it is difficult to effectively distinguish the local morphological similarities between low-concentration background noise in deep soil and the true impulse response of shallow active migration zones, thus affecting the physical meaning of clustering results and the reliability of quantitative analysis.

[0003] Therefore, how to construct a quantitative method for nutrient migration in farmland ecosystems that can reduce secondary fluctuation misalignment interference, suppress deep background noise artifact confusion, and improve the accuracy of nutrient migration pattern classification, based on the coupled evolution characteristics of carbon and nitrogen isotope time series data, has become an urgent technical problem to be solved. Summary of the Invention

[0004] In view of this, the present invention aims to propose a method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis, in order to solve the problem of distorted migration pattern segmentation caused by secondary fluctuation misalignment forced alignment and deep background noise artifacts in the existing multidimensional dynamic time warping algorithm for carbon and nitrogen isotope time-series clustering of farmland ecosystems.

[0005] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0006] A method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis, the method comprising:

[0007] Step S1: Obtain the carbon and nitrogen concentration time series by collecting and preprocessing carbon and nitrogen isotope monitoring data;

[0008] Step S2: Obtain trajectory evolution optimization factors by performing two-dimensional cooperative trajectory evolution analysis on the carbon and nitrogen concentration time series;

[0009] Step S3: Obtain the jump distortion optimization factor by performing real migration flux jump distortion characteristic analysis on the carbon and nitrogen concentration time series;

[0010] Step S4: Obtain the nutrient migration pattern division results by jointly correcting the basic time series distance using trajectory evolution optimization factor and jump distortion optimization factor;

[0011] Step S5: Obtain carbon and nitrogen nutrient migration assessment results by quantitatively analyzing the nutrient migration pattern classification results.

[0012] Furthermore, the acquisition and preprocessing of carbon and nitrogen isotope monitoring data to obtain carbon and nitrogen concentration time series includes:

[0013] Within the selected farmland ecosystem monitoring area, multiple monitoring points are set up at different spatial locations and soil depths; fertilizers or organic materials containing dual carbon and nitrogen isotope labels are applied to the farmland ecosystem monitoring area at the set start time.

[0014] In-situ sensors are set up at each monitoring point, and continuous monitoring and data collection are carried out at each monitoring point according to a preset sampling frequency. The data collection time covers the preset total observation time period to obtain the carbon and nitrogen isotope monitoring data of each monitoring point in the entire observation time period. The carbon and nitrogen isotope monitoring data includes at least the carbon isotope concentration data and nitrogen isotope concentration data of each monitoring point at each time step.

[0015] The collected carbon and nitrogen isotope monitoring data are preprocessed. The preprocessing includes at least outlier detection using the three-standard-deviation principle to remove outliers caused by equipment failure or sampling contamination, and data completion for missing time points caused by sampling interruption using linear interpolation.

[0016] For each monitoring point after preprocessing, the corresponding carbon isotope concentration data sequence and nitrogen isotope concentration data sequence are extracted in chronological order, and the carbon isotope concentration data sequence and nitrogen isotope concentration data sequence corresponding to each monitoring point are used as carbon and nitrogen concentration time series.

[0017] Furthermore, the step of obtaining trajectory evolution optimization factors through two-dimensional cooperative trajectory evolution analysis of carbon and nitrogen concentration time series includes:

[0018] By constructing two-dimensional state trajectories at adjacent time points from carbon and nitrogen concentration time series data, dynamic trajectory area evolution characteristic data are obtained.

[0019] By accumulating and normalizing the cross-point differences in dynamic trajectory area evolution characteristic data, trajectory evolution optimization factors are obtained.

[0020] Furthermore, the process of constructing two-dimensional state trajectories at adjacent time points from carbon and nitrogen concentration time series data to obtain dynamic trajectory area evolution characteristic data includes:

[0021] For any target monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data of the target monitoring point at each time step from the carbon and nitrogen concentration time series; for any target time step, combine the carbon isotope concentration data and nitrogen isotope concentration data of the target monitoring point at the target time step as the two-dimensional state vector at the current time, and combine the carbon isotope concentration data and nitrogen isotope concentration data of the target monitoring point at the next time step as the two-dimensional state vector at the next time step;

[0022] For any target monitoring point, the product of the carbon isotope concentration data in the current two-dimensional state vector and the nitrogen isotope concentration data in the next two-dimensional state vector is used as the first cross-product evaluation, the product of the nitrogen isotope concentration data in the current two-dimensional state vector and the carbon isotope concentration data in the next two-dimensional state vector is used as the second cross-product evaluation, and the difference between the first cross-product evaluation and the second cross-product evaluation is used as the single-step trajectory area evolution evaluation of the target monitoring point at the target time step.

[0023] For each target monitoring point, the single-step trajectory area evolution evaluation corresponding to each time step is arranged in chronological order to obtain the dynamic trajectory area evolution characteristic data corresponding to each monitoring point.

[0024] Furthermore, the step of obtaining trajectory evolution optimization factors by performing cross-point difference accumulation and normalization processing on the dynamic trajectory area evolution feature data includes:

[0025] For any target monitoring point and any comparison monitoring point, extract the single-step trajectory area evolution assessment of the target monitoring point at each time step and the single-step trajectory area evolution assessment of the comparison monitoring point at each time step from the dynamic trajectory area evolution feature data; for any target time step, use the absolute value of the difference between the single-step trajectory area evolution assessment of the target monitoring point at the target time step and the single-step trajectory area evolution assessment of the comparison monitoring point at the target time step as the trajectory evolution difference assessment for the target time step;

[0026] For any target monitoring point and any comparison monitoring point, the trajectory evolution difference assessments corresponding to each target time step are accumulated to obtain the cumulative value of the trajectory evolution difference between the target monitoring point and the comparison monitoring point.

[0027] For any target monitoring point and any comparative monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the carbon and nitrogen concentration time series. Also extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the comparative monitoring point. For any target time step, use the product of the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the target time step as the first concentration product evaluation for the target monitoring point. Use the product of the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the comparative monitoring point as the second concentration product evaluation for the comparative monitoring point. The sum of the first and second concentration product evaluations is used as the concentration evaluation for the target time step.

[0028] For any target monitoring point and any comparison monitoring point, the concentration assessments corresponding to each target time step are accumulated to obtain the cumulative concentration value corresponding to the target monitoring point and the comparison monitoring point; the cumulative value of trajectory evolution difference is used as the numerator, the cumulative concentration value is used as the denominator, and the corresponding fraction is used as the trajectory evolution optimization factor corresponding to the target monitoring point and the comparison monitoring point.

[0029] Furthermore, the step of obtaining the jump distortion optimization factor by performing real migration flux jump distortion characteristic analysis on the carbon and nitrogen concentration time series includes:

[0030] By extracting the cumulative concentration and maximum jump gradient from the carbon and nitrogen concentration time series data, flux-structure ratio feature data were obtained.

[0031] By performing cross-site difference analysis on flux structure ratio characteristic data, flux jump distortion assessment data can be obtained.

[0032] By performing average modulus smoothing and multiplication mapping on the flux jump distortion assessment data, the jump distortion optimization factor is obtained.

[0033] Furthermore, the step of extracting flux-structure ratio feature data by performing cumulative concentration and maximum gradient abrupt change processing on carbon and nitrogen concentration time series data includes:

[0034] For any target monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the carbon and nitrogen concentration time series; add the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step to obtain the single-step cumulative concentration assessment for each time step; sum the single-step cumulative concentration assessments corresponding to each time step to obtain the total cumulative concentration data corresponding to the target monitoring point.

[0035] For any target monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to adjacent time steps from the carbon and nitrogen concentration time series. For any target time step, use the absolute value of the difference between the carbon isotope concentration data corresponding to the target monitoring point in the next time step and the carbon isotope concentration data corresponding to the target time step as the carbon isotope transition gradient assessment corresponding to the target time step, use the absolute value of the difference between the nitrogen isotope concentration data corresponding to the target monitoring point in the next time step and the nitrogen isotope concentration data corresponding to the target time step as the nitrogen isotope transition gradient assessment corresponding to the target time step, and use the calculation result of adding the carbon isotope transition gradient assessment and the nitrogen isotope transition gradient assessment as the joint transition gradient assessment corresponding to the target time step.

[0036] For any target monitoring point, the maximum value in the joint jump gradient assessment corresponding to each target time step is taken as the maximum jump gradient data corresponding to the target monitoring point; the total cumulative concentration data corresponding to the target monitoring point is taken as the numerator, the maximum jump gradient data corresponding to the target monitoring point is taken as the denominator, and the corresponding fraction is taken as the flux-structure ratio characteristic data corresponding to the target monitoring point.

[0037] Furthermore, the step of obtaining flux jump distortion assessment data by performing cross-site difference analysis on flux structure ratio characteristic data includes:

[0038] For any target monitoring point and any comparison monitoring point, extract the flux structure ratio feature data corresponding to the target monitoring point and the flux structure ratio feature data corresponding to the comparison monitoring point from the flux structure ratio feature data; use the absolute value of the difference between the flux structure ratio feature data corresponding to the target monitoring point and the flux structure ratio feature data corresponding to the comparison monitoring point as the flux jump distortion assessment data corresponding to the target monitoring point and the comparison monitoring point.

[0039] Furthermore, the step of obtaining the jump distortion optimization factor by performing average modulus smoothing and multiplicative mapping on the flux jump distortion assessment data includes:

[0040] For any target monitoring point and any comparative monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the carbon and nitrogen concentration time series. Also extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the comparative monitoring point. For any target time step, take the square root of the sum of the squares of the carbon isotope concentration data and the nitrogen isotope concentration data corresponding to the target time step as the first modulus assessment of the target monitoring point at the target time step. Take the square root of the sum of the squares of the carbon isotope concentration data and the nitrogen isotope concentration data corresponding to the comparative monitoring point at the target time step as the second modulus assessment of the comparative monitoring point at the target time step. Take the sum of the first modulus assessment and the second modulus assessment as the joint modulus assessment of the target time step.

[0041] For any target monitoring point and any comparison monitoring point, the joint modulus evaluation corresponding to each target time step is accumulated and then divided by the total number of time steps to obtain the average modulus smoothing data corresponding to the target monitoring point and the comparison monitoring point.

[0042] For any target monitoring point and any comparison monitoring point, the flux jump distortion assessment data is used as the numerator, the average modulus smoothing data is used as the denominator, and the calculation result of adding the corresponding fraction to the constant 1 is used as the jump distortion optimization factor for the target monitoring point and the comparison monitoring point.

[0043] Furthermore, the step of obtaining the nutrient migration pattern segmentation result by jointly correcting the basic temporal distance using trajectory evolution optimization factors and jump distortion optimization factors includes:

[0044] For any target monitoring point and any comparison monitoring point, the basic time series distance between the target monitoring point and the comparison monitoring point is calculated using a multidimensional dynamic time warping algorithm based on the carbon and nitrogen concentration time series corresponding to the target monitoring point and the comparison monitoring point.

[0045] For any target monitoring point and any comparison monitoring point, the trajectory evolution optimization factor corresponding to the target monitoring point and the comparison monitoring point is extracted from the trajectory evolution optimization factor, and the jump distortion optimization factor corresponding to the target monitoring point and the comparison monitoring point is extracted from the jump distortion optimization factor; the calculation result of adding the trajectory evolution optimization factor to the constant 1 is used as the first joint correction coefficient, and the product of the basic time series distance, the first joint correction coefficient and the jump distortion optimization factor is used as the comprehensive time series distance corresponding to the target monitoring point and the comparison monitoring point.

[0046] A comprehensive distance matrix is ​​constructed based on the pairwise temporal distances between all monitoring points, and multiple nutrient migration pattern cluster centers are initialized based on the comprehensive distance matrix. For any target monitoring point, the comprehensive temporal distance between the target monitoring point and each nutrient migration pattern cluster center is calculated, and the nutrient migration pattern cluster center with the smallest comprehensive temporal distance is taken as the cluster center to which the target monitoring point belongs. After completing one monitoring point allocation, the corresponding nutrient migration pattern cluster centers are updated according to the monitoring points contained in each cluster. The monitoring point allocation and cluster center update are repeated until the change in cluster centers is lower than a preset threshold or the preset number of iterations is reached. The cluster number corresponding to each monitoring point is taken as the nutrient migration pattern category label, and the set of nutrient migration pattern category labels corresponding to all monitoring points is taken as the nutrient migration pattern partitioning result.

[0047] Compared with the prior art, the present invention has the following advantages:

[0048] This invention presents a method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupling analysis. Addressing the real-world monitoring scenarios in farmland ecosystems where carbon and nitrogen isotope dual-label data exhibit significant coupling, frequent secondary fluctuations, and temporal misalignments in responses across different soil layers, this method departs from existing multidimensional dynamic time warping algorithms that independently stretch and align the carbon and nitrogen dimensions. Instead, it introduces a mechanism for identifying the co-evolutionary trajectories of carbon and nitrogen within the same monitoring point, incorporating the coupling changes in carbon and nitrogen concentrations over continuous time intervals into the similarity determination process. This distance correction method, oriented towards internal co-evolutionary mechanisms, effectively reduces the interference of secondary fluctuations caused by microbial absorption-release processes on clustering results. This allows monitoring points with similar carbon and nitrogen metabolic transformation patterns but slightly different response times to be accurately classified into the same migration pattern, thereby improving the accuracy and stability of nutrient migration pattern identification at different spatial locations and soil depths in farmland. Meanwhile, this invention further combines the characteristics of actual migration flux with the relationship of local jump distortion to suppress the pseudo-similarity phenomenon that may occur between low-concentration background noise in deep soil and active migration zones in shallow soil, avoiding the misjudgment of random fluctuations in the instrument background as real migration pulses in local morphology. Through this comprehensive discrimination mechanism that takes into account both cooperative trajectory characteristics and physical flux constraints, the final nutrient migration pattern can better conform to the actual physical processes of carbon and nitrogen migration, fixation, transformation, and leaching in farmland ecosystems. This improves the reliability of quantitative results such as total carbon and nitrogen isotope accumulation, vertical transport attenuation characteristics, and metabolic turnover lag characteristics, providing more reliable data support for farmland nutrient use efficiency assessment, soil microenvironment difference analysis, and fertilization regulation strategy formulation. Attached Figure Description

[0049] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0050] Figure 1 This is a flowchart illustrating a method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis, as described in an embodiment of the present invention. Detailed Implementation

[0051] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0052] See Figure 1 This is a flowchart of a method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis, as provided in Embodiment 1 of the present invention. Figure 1 As shown, a method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis may include:

[0053] Step S1: Obtain the carbon and nitrogen concentration time series by collecting and preprocessing carbon and nitrogen isotope monitoring data.

[0054] First, within the selected farmland ecosystem monitoring area, multiple monitoring points are established at different spatial locations and soil depths. At a predetermined start time, fertilizer or organic material containing dual carbon and nitrogen isotope labels is applied to the farmland ecosystem monitoring area. It should be noted that in this embodiment, monitoring points are established at soil depths of 10cm, 20cm, 40cm, and 80cm. In-situ sensors are installed at each monitoring point, and continuous monitoring data is collected at a preset sampling frequency, covering a preset total observation period. This obtains carbon and nitrogen isotope monitoring data for each monitoring point throughout the entire observation period. The carbon and nitrogen isotope monitoring data includes at least the carbon and nitrogen isotope concentrations at each monitoring point at each time step. In this embodiment, data is collected at a sampling frequency of once per day for a total observation period of 90 days.

[0055] The collected carbon and nitrogen isotope monitoring data are preprocessed. The preprocessing includes at least outlier detection using the three-standard-deviation principle to remove outliers caused by equipment failure or sampling contamination, and data completion for missing time points caused by sampling interruption using linear interpolation.

[0056] For each monitoring point after preprocessing, the corresponding carbon isotope concentration data sequence and nitrogen isotope concentration data sequence are extracted in chronological order, and the carbon isotope concentration data sequence and nitrogen isotope concentration data sequence corresponding to each monitoring point are used as carbon and nitrogen concentration time series. In this embodiment of the invention, a continuous time series of length 90 is extracted for each monitoring point.

[0057] This completes the acquisition and preprocessing of carbon and nitrogen isotope monitoring data to obtain the time series of carbon and nitrogen concentrations.

[0058] Step S2: Obtain trajectory evolution optimization factors by performing two-dimensional collaborative trajectory evolution analysis on the carbon and nitrogen concentration time series.

[0059] After acquiring time-series data on carbon and nitrogen isotope concentrations at various monitoring points, existing multidimensional dynamic time warping algorithms typically align multidimensional variables by nonlinearly stretching the time axis when calculating the temporal distance between points. However, during nutrient migration in farmland ecosystems, influenced by soil microbial turnover mechanisms and local environmental factors, the time-series curves of carbon and nitrogen concentrations are often accompanied by multiple secondary fluctuations caused by microbial absorption and re-release. Due to objective differences in the physicochemical environments of different spatial points, these secondary fluctuations often exhibit asynchronous misalignment on the absolute time axis. The global optimization mechanism of multidimensional dynamic time warping algorithms tends to forcibly align these temporally misaligned secondary fluctuations in different point sequences, thereby accumulating redundant distance penalty costs on the time warping path. This results in monitoring points with the same carbon and nitrogen metabolic evolution mechanism but with slight differences in response cycles being judged as dissimilar.

[0060] To address the computational bias in basic distance metrics caused by forced alignment of secondary fluctuations, this method departs from the conventional approach of treating carbon and nitrogen as independent dimensions for cross-sample comparison. Instead, it delves into the synergistic evolution of carbon and nitrogen concentrations within a single measurement point. By constructing a synergistic vector in a two-dimensional state space from the carbon and nitrogen isotope concentrations at the same point at the same instant, and extracting the dynamic trajectory area evolution rate between adjacent states during the temporal evolution of this synergistic vector, the underlying carbon and nitrogen metabolic synergistic ratio at that point is characterized. Based on this, by evaluating the structural differences in the dynamic trajectory area evolution rate among different measurement points, a metric correction mechanism unaffected by significant temporal shifts is constructed, thereby suppressing the artificially inflated clustering distance caused by forced alignment due to secondary fluctuations.

[0061] In summary, this invention first constructs two-dimensional state trajectories for adjacent time steps from carbon and nitrogen concentration time series data to obtain dynamic trajectory area evolution characteristic data. Specifically, for any target monitoring point, carbon and nitrogen isotope concentration data at each time step are extracted from the carbon and nitrogen concentration time series. For any target time step, the carbon and nitrogen isotope concentration data at the target monitoring point at the target time step are combined to form the two-dimensional state vector at the current time step, and the carbon and nitrogen isotope concentration data at the target monitoring point at the next time step are combined to form the two-dimensional state vector at the next time step.

[0062] For any target monitoring point, the product of the carbon isotope concentration data in the current two-dimensional state vector and the nitrogen isotope concentration data in the next two-dimensional state vector is used as the first cross-product evaluation. The product of the nitrogen isotope concentration data in the current two-dimensional state vector and the carbon isotope concentration data in the next two-dimensional state vector is used as the second cross-product evaluation. The difference between the first and second cross-product evaluations is used as the single-step trajectory area evolution evaluation for the target monitoring point at the target time step. For each target monitoring point, the single-step trajectory area evolution evaluations corresponding to each time step are arranged in chronological order to obtain the dynamic trajectory area evolution characteristic data for each monitoring point.

[0063] After obtaining the dynamic trajectory area evolution characteristic data corresponding to each monitoring point, the trajectory evolution optimization factor is obtained by further processing the cross-point difference accumulation and normalization of the dynamic trajectory area evolution characteristic data. Specifically, for any target monitoring point and any comparison monitoring point, the single-step trajectory area evolution evaluation of the target monitoring point at each time step and the single-step trajectory area evolution evaluation of the comparison monitoring point at each time step are extracted from the dynamic trajectory area evolution characteristic data. For any target time step, the absolute value of the difference between the single-step trajectory area evolution evaluation of the target monitoring point and the single-step trajectory area evolution evaluation of the comparison monitoring point at the target time step is taken as the trajectory evolution difference evaluation for the target time step. For any target monitoring point and any comparison monitoring point, the trajectory evolution difference evaluations for each target time step are accumulated to obtain the cumulative value of the trajectory evolution difference between the target monitoring point and the comparison monitoring point.

[0064] For any target monitoring point and any comparative monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the carbon and nitrogen concentration time series. Also extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the comparative monitoring point. For any target time step, use the product of the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the target time step as the first concentration product assessment for the target monitoring point. Use the product of the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the comparative monitoring point as the second concentration product assessment for the comparative monitoring point. The sum of the first and second concentration product assessments is used as the concentration assessment for the target time step. For any target monitoring point and any comparison monitoring point, the concentration assessments corresponding to each target time step are accumulated to obtain the cumulative concentration value corresponding to the target monitoring point and the comparison monitoring point; the cumulative value of trajectory evolution difference is used as the numerator, the cumulative concentration value is used as the denominator, and the corresponding fraction is used as the trajectory evolution optimization factor corresponding to the target monitoring point and the comparison monitoring point.

[0065] In one implementation, assume the first The monitoring points are at the [number]th The carbon isotope concentration data at each time point are: ;No. The monitoring points are at the [number]th The nitrogen isotope concentration data at each time point are: ;No. The monitoring points are at the [number]th The carbon isotope concentration data at each time point are: ;No. The monitoring points are at the [number]th The nitrogen isotope concentration data at each time point are: ;No. The monitoring points are at the [number]th The carbon isotope concentration data at each time point are: ;No. The monitoring points are at the [number]th The nitrogen isotope concentration data at each time point are: ;No. The monitoring points are at the [number]th The carbon isotope concentration data at each time point are: ;No. The monitoring points are at the [number]th The nitrogen isotope concentration data at each time point are: Then the first The monitoring point and the first The calculation expression for the trajectory evolution optimization factor of each monitoring point is as follows:

[0066]

[0067] in, Indicates the first The monitoring point and the first Trajectory evolution optimization factors for each monitoring point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; This indicates absolute value calculation; This indicates the total time step of the isotope concentration time series collected at the monitoring points.

[0068] It should be noted that, regarding the distance penalty redundancy problem arising from the multidimensional dynamic time warping algorithm when handling misaligned secondary fluctuations, this invention addresses this issue by constructing the aforementioned preliminary optimization factor formula. In existing time series alignment mechanisms, the algorithm primarily relies on single-dimensional absolute numerical fitting, which leads to a sharp increase in the base difference once the peaks are misaligned in time. To overcome this deficiency, the numerator of this formula does not employ conventional time series differencing or statistical variance calculations, but instead uses… The cross-product form was used to extract the location. The geometrical evolution area swept across the phase plane by the two-dimensional carbon and nitrogen state vectors within adjacent time steps. This geometrical evolution area reflects the relative metabolic rate of carbon-nitrogen interconversion and consumption at the same spatial location, and is a unique evolutionary property within the measuring point. This is achieved by calculating the point location. with point By summing the absolute values ​​of the differences in evolutionary areas over the same time step and accumulating them over the entire time period, the formula transforms the direct comparison of waveforms across samples into a structural comparison of differences in the co-evolutionary mechanisms within the measurement points. Under this design, even if there is a delay of several days in the carbon and nitrogen secondary fluctuations of two points on the time axis, as long as their underlying carbon and nitrogen co-conversion mechanisms are similar, the cumulative difference in their dynamic trajectory evolutionary areas will remain at a low level, thus objectively reflecting the similarity of the two in their physical evolutionary patterns. Meanwhile, considering that differences in initial farmland water content or basic fertility at different monitoring points can lead to significant differences in the absolute magnitude of the collected isotope concentrations, using only the absolute area difference in the numerator would result in points with higher concentration bases having an excessively strong dominant effect on the optimization factor, making it impossible to form a universal dimensionless correction coefficient. To ensure the comparability of the extracted co-evolutionary difference features across points, this formula constructs a measurement point-based... and The sum of the cross-products of carbon and nitrogen concentrations at the same time. The denominator is accumulated using concentration products with the same dimensions as the numerator's area, providing a smooth benchmark for the dynamic trajectory area evolution differences that can adaptively change with the original data size. The trajectory evolution optimization factor can accurately quantify the true differences in the carbon and nitrogen synergistic characteristics within two points without being directly affected by the absolute concentration base or temporal misalignment. This factor is then used as a correction to reduce the artificially high distance output by the multidimensional DTW algorithm, ensuring the reliability of the temporal distance measurement.

[0069] Thus, the acquisition of trajectory evolution optimization factors through two-dimensional collaborative trajectory evolution analysis of carbon and nitrogen concentration time series has been completed.

[0070] Step S3: Obtain the jump distortion optimization factor by performing real migration flux jump distortion feature analysis on the carbon and nitrogen concentration time series.

[0071] After introducing a trajectory evolution optimization factor to correct the basic temporal distance of the multidimensional dynamic time warping algorithm, the similarity criterion is transformed into a purely relative geometric trajectory area evolution rate through denominator normalization in the formula design. This leads to a detailed misidentification problem exposed in real observations of farmland ecosystem soil profiles. In deep soil regions, effective migration of isotopic markers is usually not received, and the data collected by sensors are mostly extremely low-concentration instrument background random noise. However, such small-amplitude random fluctuations may occasionally exhibit geometric area evolution characteristics highly similar to those of shallow, truly active migration areas in the local trajectory evolution of the two-dimensional state space. This purely morphological artifact overlap can cause the initial optimization factor to incorrectly classify shallow high-concentration strong migration areas and deep low-concentration background noise areas, which have completely different physical mechanisms, as similar patterns, thus narrowing their clustering distance and causing confusion.

[0072] To overcome the deep noise artifacts caused by normalized morphological features, it is necessary to introduce physical constraints that reflect the distortion of true nutrient transport flux. True isotopic pulse migration exhibits significant single-step jump characteristics in time, with a relatively stable flux-structure ratio between the total accumulated retention of the sequence and the maximum positive jump gradient. In contrast, the maximum single-step jump of pure random noise is extremely small, and its corresponding flux-structure ratio differs fundamentally from that of the true migration region. By extracting and comparing this difference in flux-pulse ratio characteristics between locations, a refined penalty-multiplication correction mechanism can be constructed, effectively identifying and eliminating clustering distance misjudgments caused by local morphological similarities.

[0073] In summary, this invention first extracts flux-structure ratio characteristic data by processing the carbon and nitrogen concentration time series data for cumulative concentration and maximum jump gradient extraction. Specifically, for any target monitoring point, carbon and nitrogen isotope concentration data for each time step are extracted from the carbon and nitrogen concentration time series. The sum of the carbon and nitrogen isotope concentration data for each time step is used as the single-step cumulative concentration assessment for each time step. The single-step cumulative concentration assessments for each time step are accumulated to obtain the total cumulative concentration data for the target monitoring point. For any target monitoring point, carbon and nitrogen isotope concentration data for adjacent time steps are extracted from the carbon and nitrogen concentration time series. For any target time step, the absolute value of the difference between the carbon isotope concentration data of the target monitoring point at the next time step and the carbon isotope concentration data of the target time step is used as the carbon isotope transition gradient assessment for the target time step. The absolute value of the difference between the nitrogen isotope concentration data of the target monitoring point at the next time step and the nitrogen isotope concentration data of the target time step is used as the nitrogen isotope transition gradient assessment for the target time step. The result of adding the carbon isotope transition gradient assessment and the nitrogen isotope transition gradient assessment is used as the joint transition gradient assessment for the target time step. For any target monitoring point, the maximum value among the joint transition gradient assessments for each target time step is used as the maximum transition gradient data for the target monitoring point. The total cumulative concentration data for the target monitoring point is used as the numerator, the maximum transition gradient data for the target monitoring point is used as the denominator, and the resulting fraction is used as the flux-structure ratio characteristic data for the target monitoring point.

[0074] After obtaining the flux structure ratio characteristic data corresponding to the monitoring points, the flux structure ratio characteristic data is further processed by cross-point difference analysis to obtain flux jump distortion assessment data. Specifically, for any target monitoring point and any comparison monitoring point, the flux structure ratio characteristic data corresponding to the target monitoring point and the flux structure ratio characteristic data corresponding to the comparison monitoring point are extracted from the flux structure ratio characteristic data. The absolute value of the difference between the flux structure ratio characteristic data corresponding to the target monitoring point and the flux structure ratio characteristic data corresponding to the comparison monitoring point is used as the flux jump distortion assessment data corresponding to the target monitoring point and the comparison monitoring point.

[0075] After obtaining the flux jump distortion assessment data between monitoring points, the final step is to perform average modulus smoothing and multiplicative mapping on the flux jump distortion assessment data to obtain the jump distortion optimization factor. Specifically, for any target monitoring point and any comparison monitoring point, the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step of the target monitoring point are extracted from the carbon and nitrogen concentration time series, and the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step of the comparison monitoring point are also extracted. For any target time step, the target monitoring... The square root of the sum of the squares of the carbon isotope concentration data and the nitrogen isotope concentration data at the target time step is used as the first modulus assessment for the target monitoring point at the target time step. The square root of the sum of the squares of the carbon isotope concentration data and the nitrogen isotope concentration data at the comparative monitoring point at the target time step is used as the second modulus assessment for the comparative monitoring point at the target time step. The sum of the first and second modulus assessments is used as the joint modulus assessment for the target time step. For any target monitoring point and any comparative monitoring point, the joint modulus assessments for each target time step are accumulated and divided by the total number of time steps to obtain the smoothed average modulus data for the target and comparative monitoring points. For any target and any comparative monitoring point, the flux jump distortion assessment data is used as the numerator, the smoothed average modulus data is used as the denominator, and the result of adding the corresponding fraction to a constant 1 is used as the jump distortion optimization factor for the target and comparative monitoring points.

[0076] In one embodiment, the first The monitoring point and the first The calculation expression for the jump distortion optimization factor corresponding to each monitoring point is as follows:

[0077]

[0078] in, Indicates the first The monitoring point and the first The jump distortion optimization factor corresponding to each monitoring point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Carbon isotope concentration data at each time point; Indicates the first The monitoring points are at the [number]th Nitrogen isotope concentration data at each time point; This represents the maximum value function.

[0079] It should be noted that, regarding the clustering confusion caused by the similarity of local trajectories in deep low-concentration background noise after the introduction of preliminary optimization factors, this invention corrects and distinguishes these issues by constructing the aforementioned refined optimization factor formula. When identifying true migration responses and random noise, relying solely on conventional statistical measures such as mean or variance is easily affected by different soil background values ​​and becomes ineffective. To overcome this limitation, the formula's numerator contains a structural ratio of the total cumulative flux to the maximum single-step gradient within the curly braces. For surface or shallow active areas experiencing true isotopic migration, the data characteristics are characterized by significant pulse injections and extremely significant maximum adjacent concentration differences (i.e., a large single-step maximum gradient), keeping this structural ratio within a specific range. However, for instrument noise in deep stagnant water areas, although the total cumulative flux exists, the maximum single-step gradient consists only of a small random range, causing the denominator to tend towards a minimum, thus leading to an order-of-magnitude distortion in the flux structural ratio. This is achieved by calculating the values ​​at different points. and points The flux-structure ratio is calculated, and the absolute value of the difference is taken to capture the essential difference between the two states. When morphological artifacts are misjudged, i.e., when the real active region is paired with the deep noise region for calculation, the absolute difference in the numerator will increase sharply. At the same time, in order to avoid the distortion penalty term from diverging out of control due to local concentration singularities, this formula extracts the point value in the denominator. and points The sum of the average magnitudes of the time-series vectors is used as a basic smoothing reference. The denominator uses the Euclidean norm of the absolute carbon and nitrogen concentrations at each time point and performs time averaging to provide a stable data scale baseline for the ratio differences in the numerator. Based on this overall structure, the jump distortion optimization factor, as a multiplicative coefficient superimposed on the base value of 1, has a penalty term close to zero when the two points being compared are both true migration regions of equal degree, keeping the distance after the initial correction unchanged; however, when artifacts of deep noise and true pulses are detected to overlap, the penalty term increases significantly, directly widening the spatial distance between two points that were misjudged as similar, thereby eliminating the interference of deep background noise on the clustering of farmland nutrient migration patterns and further ensuring the objectivity and accuracy of the quantification method.

[0080] Thus, the optimization factor for jump distortion was obtained by analyzing the characteristics of real migration flux jump distortion in the carbon and nitrogen concentration time series.

[0081] Step S4: Obtain the nutrient migration pattern division result by jointly correcting the basic time series distance using trajectory evolution optimization factor and jump distortion optimization factor.

[0082] After obtaining the trajectory evolution optimization factor reflecting the differences in internal carbon-nitrogen synergy mechanisms and the jump distortion optimization factor reflecting the distortion of real physical flux, the existing multidimensional dynamic time warping algorithm is used to perform basic global nonlinear alignment calculations on the carbon-nitrogen concentration time series between monitoring points, obtaining the basic time series distance based solely on one-dimensional independent stretching. Subsequently, the constructed trajectory evolution optimization factor and jump distortion optimization factor are used to perform layer-by-layer multiplication and combination correction on this basic time series distance to obtain the final comprehensive similarity distance. Finally, a global distance matrix is ​​constructed based on the comprehensive similarity distances calculated pairwise between all monitoring points, and this distance matrix is ​​used as input to the existing K-means clustering algorithm. Through iterative optimization, monitoring points with similar carbon-nitrogen evolution characteristics in space are divided into multiple different nutrient migration pattern clusters.

[0083] Specifically, for any target monitoring point and any comparison monitoring point, based on the carbon and nitrogen concentration time series corresponding to the target monitoring point and the comparison monitoring point, a multidimensional dynamic time warping algorithm is used to calculate the basic temporal distance between the target monitoring point and the comparison monitoring point. For any target monitoring point and any comparison monitoring point, trajectory evolution optimization factors corresponding to the target monitoring point and the comparison monitoring point are extracted from the trajectory evolution optimization factors, and jump distortion optimization factors corresponding to the target monitoring point and the comparison monitoring point are extracted from the jump distortion optimization factors. The result of adding the trajectory evolution optimization factors to a constant 1 is used as the first joint correction coefficient, and the product of the basic temporal distance, the first joint correction coefficient, and the jump distortion optimization factor is used as the comprehensive temporal distance between the target monitoring point and the comparison monitoring point.

[0084] A comprehensive distance matrix is ​​constructed based on the pairwise temporal distances between all monitoring points, and multiple nutrient migration pattern cluster centers are initialized based on this matrix. For any target monitoring point, the comprehensive temporal distance between the target monitoring point and each nutrient migration pattern cluster center is calculated, and the nutrient migration pattern cluster center with the smallest comprehensive temporal distance is selected as the cluster center to which the target monitoring point belongs. After completing one monitoring point allocation, the corresponding nutrient migration pattern cluster centers are updated according to the monitoring points included in each cluster. This process of monitoring point allocation and cluster center update is repeated until the change in cluster centers is lower than a preset threshold or a preset number of iterations is reached. The cluster number corresponding to each monitoring point is used as the nutrient migration pattern category label, and the set of nutrient migration pattern category labels corresponding to all monitoring points is taken as the nutrient migration pattern partitioning result.

[0085] It should be noted that the basic temporal distance is first increased by the relative increment of the trajectory evolution optimization factor, thereby incorporating the differences in the two-dimensional evolution mechanism of carbon-nitrogen co-trajectories within the measurement points into the distance evaluation system, weakening the artificially high distance penalty caused by simply relying on time stretching to align secondary peaks. Subsequently, it is further multiplied by the jump distortion optimization factor. When there is deep background noise and real migration active areas that overlap due to local morphology artifacts, a sudden increase in the multiplicative penalty coefficient is used for correction, re-stretching the distance of points that were misjudged as similar. Through this comprehensive correction, the final distance not only encompasses the absolute temporal misalignment under the same physical mechanism, but also strictly limits the mismatch in the underlying transport flux. Finally, the existing K-means clustering algorithm is used to iteratively calculate the cluster centers based on the distance matrix composed of the comprehensive temporal distance, outputting the category label of each monitoring point. For the clustering algorithm, the number of clusters is determined by the elbow method in this embodiment of the invention.

[0086] Thus, the nutrient migration pattern classification results were obtained by jointly correcting the basic time series distance using trajectory evolution optimization factors and jump distortion optimization factors.

[0087] Step S5: Obtain carbon and nitrogen nutrient migration assessment results by quantitatively analyzing the nutrient migration pattern classification results.

[0088] After accurately clustering the nutrient migration patterns of all monitoring sites, independent quantitative assessments were conducted for each cluster. Based on the data set of monitoring sites included in each cluster, existing statistical and numerical integration methods were used to calculate three key quantitative indicators for the corresponding migration patterns: the total cumulative residence of carbon and nitrogen isotopes, the maximum concentration decay coefficient of vertical downward transport, and the lag days of carbon and nitrogen metabolic turnover (i.e., the time interval from the application of the marker to the appearance of the main concentration peak).

[0089] By comparing and analyzing the numerical differences and spatial profile distribution characteristics of different migration pattern clusters on the above three specific indicators, the distribution pattern and dynamic destination ratio of carbon and nitrogen markers applied to farmland ecosystems in different soil microenvironments are accurately quantified. Because this invention effectively eliminates the segmentation errors caused by secondary microbial fluctuations and deep instrument noise artifacts in the early temporal clustering distance measurement stage, the final extracted quantitative indicators can objectively reflect the true coupling mechanism of isotope-labeled fertilizers being fixed, transformed, and leached downwards by microorganisms within the farmland ecosystem, thereby improving the reliability and guiding value of the overall nutrient migration quantitative assessment.

[0090] This concludes the assessment of carbon and nitrogen nutrient migration by quantitatively analyzing the nutrient migration pattern classification results.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis, characterized in that, The method includes: Step S1: Obtain the carbon and nitrogen concentration time series by collecting and preprocessing carbon and nitrogen isotope monitoring data; Step S2: Obtain trajectory evolution optimization factors by performing two-dimensional cooperative trajectory evolution analysis on the carbon and nitrogen concentration time series; Step S3: Obtain the jump distortion optimization factor by performing real migration flux jump distortion characteristic analysis on the carbon and nitrogen concentration time series; Step S4: Obtain the nutrient migration pattern division results by jointly correcting the basic time series distance using trajectory evolution optimization factor and jump distortion optimization factor; Step S5: Obtain carbon and nitrogen nutrient migration assessment results by quantitatively analyzing the nutrient migration pattern classification results; The method of obtaining trajectory evolution optimization factors by performing two-dimensional collaborative trajectory evolution analysis on carbon and nitrogen concentration time series includes: obtaining dynamic trajectory area evolution feature data by constructing two-dimensional state trajectories at adjacent time points on carbon and nitrogen concentration time series data; and obtaining trajectory evolution optimization factors by accumulating and normalizing cross-point differences in dynamic trajectory area evolution feature data. The process of constructing two-dimensional state trajectories for adjacent time steps on carbon and nitrogen concentration time series data to obtain dynamic trajectory area evolution characteristic data includes: for any target monitoring point, extracting the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the target monitoring point at each time step from the carbon and nitrogen concentration time series; for any target time step, combining the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the target monitoring point at the target time step as the current two-dimensional state vector, and combining the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the target monitoring point at the next time step as the next two-dimensional state vector; for any target monitoring point... The product of the carbon isotope concentration data in the current two-dimensional state vector and the nitrogen isotope concentration data in the next two-dimensional state vector is used as the first cross-product evaluation. The product of the nitrogen isotope concentration data in the current two-dimensional state vector and the carbon isotope concentration data in the next two-dimensional state vector is used as the second cross-product evaluation. The difference between the first cross-product evaluation and the second cross-product evaluation is used as the single-step trajectory area evolution evaluation of the target monitoring point at the target time step. For each target monitoring point, the single-step trajectory area evolution evaluations corresponding to each time step are arranged in chronological order to obtain the dynamic trajectory area evolution feature data corresponding to each monitoring point. The step of obtaining jump distortion optimization factors by analyzing the real migration flux jump distortion characteristics of carbon and nitrogen concentration time series includes: obtaining flux structure ratio feature data by extracting cumulative concentration and maximum jump gradient from carbon and nitrogen concentration time series data; obtaining flux jump distortion evaluation data by performing cross-site difference analysis on flux structure ratio feature data; and obtaining jump distortion optimization factors by performing average modulus smoothing and multiplicative mapping on flux jump distortion evaluation data. The process of extracting flux-structure ratio characteristic data by performing cumulative concentration and maximum gradient extraction on carbon and nitrogen concentration time series data includes: for any target monitoring point, extracting carbon and nitrogen isotope concentration data corresponding to each time step from the carbon and nitrogen concentration time series; adding the carbon and nitrogen isotope concentration data corresponding to each time step as the single-step cumulative concentration assessment for each time step; accumulating the single-step cumulative concentration assessments for each time step to obtain the total cumulative concentration data corresponding to the target monitoring point; for any target monitoring point, extracting carbon and nitrogen isotope concentration data corresponding to adjacent time steps from the carbon and nitrogen concentration time series; for any target time step, extracting the carbon isotope concentration data corresponding to the target monitoring point in the next time step. The absolute value of the difference between the carbon isotope concentration data corresponding to the target time step and the nitrogen isotope concentration data corresponding to the target time step is used as the carbon isotope transition gradient assessment corresponding to the target time step. The absolute value of the difference between the nitrogen isotope concentration data corresponding to the target monitoring point at the next time step and the nitrogen isotope concentration data corresponding to the target time step is used as the nitrogen isotope transition gradient assessment corresponding to the target time step. The result of adding the carbon isotope transition gradient assessment and the nitrogen isotope transition gradient assessment is used as the joint transition gradient assessment corresponding to the target time step. For any target monitoring point, the maximum value in the joint transition gradient assessment corresponding to each target time step is used as the maximum transition gradient data corresponding to the target monitoring point. The total cumulative concentration data corresponding to the target monitoring point is used as the numerator, the maximum transition gradient data corresponding to the target monitoring point is used as the denominator, and the resulting fraction is used as the flux-structure ratio characteristic data corresponding to the target monitoring point.

2. The method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis according to claim 1, characterized in that, The process of acquiring and preprocessing carbon and nitrogen isotope monitoring data to obtain carbon and nitrogen concentration time series includes: Within the selected farmland ecosystem monitoring area, multiple monitoring points are set up at different spatial locations and soil depths; fertilizers or organic materials containing dual carbon and nitrogen isotope labels are applied to the farmland ecosystem monitoring area at the set start time. In-situ sensors are set up at each monitoring point, and continuous monitoring and data collection are carried out at each monitoring point according to a preset sampling frequency. The data collection time covers the preset total observation time period to obtain the carbon and nitrogen isotope monitoring data of each monitoring point in the entire observation time period. The carbon and nitrogen isotope monitoring data includes at least the carbon isotope concentration data and nitrogen isotope concentration data of each monitoring point at each time step. The collected carbon and nitrogen isotope monitoring data are preprocessed. The preprocessing includes at least outlier detection using the three-standard-deviation principle to remove outliers caused by equipment failure or sampling contamination, and data completion for missing time points caused by sampling interruption using linear interpolation. For each monitoring point after preprocessing, the corresponding carbon isotope concentration data sequence and nitrogen isotope concentration data sequence are extracted in chronological order, and the carbon isotope concentration data sequence and nitrogen isotope concentration data sequence corresponding to each monitoring point are used as carbon and nitrogen concentration time series.

3. The method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis according to claim 1, characterized in that, The process of obtaining trajectory evolution optimization factors by accumulating and normalizing cross-point differences in dynamic trajectory area evolution characteristic data includes: For any target monitoring point and any comparison monitoring point, extract the single-step trajectory area evolution assessment of the target monitoring point at each time step and the single-step trajectory area evolution assessment of the comparison monitoring point at each time step from the dynamic trajectory area evolution feature data; for any target time step, use the absolute value of the difference between the single-step trajectory area evolution assessment of the target monitoring point at the target time step and the single-step trajectory area evolution assessment of the comparison monitoring point at the target time step as the trajectory evolution difference assessment for the target time step; For any target monitoring point and any comparison monitoring point, the trajectory evolution difference assessments corresponding to each target time step are accumulated to obtain the cumulative value of the trajectory evolution difference between the target monitoring point and the comparison monitoring point. For any target monitoring point and any comparative monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the carbon and nitrogen concentration time series. Also extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the comparative monitoring point. For any target time step, use the product of the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the target time step as the first concentration product evaluation for the target monitoring point. Use the product of the carbon isotope concentration data and nitrogen isotope concentration data corresponding to the comparative monitoring point as the second concentration product evaluation for the comparative monitoring point. The sum of the first and second concentration product evaluations is used as the concentration evaluation for the target time step. For any target monitoring point and any comparison monitoring point, the concentration assessments corresponding to each target time step are accumulated to obtain the cumulative concentration value corresponding to the target monitoring point and the comparison monitoring point; the cumulative value of trajectory evolution difference is used as the numerator, the cumulative concentration value is used as the denominator, and the corresponding fraction is used as the trajectory evolution optimization factor corresponding to the target monitoring point and the comparison monitoring point.

4. The method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis according to claim 1, characterized in that, The process of obtaining flux jump distortion assessment data by performing cross-site difference analysis on flux structure ratio characteristic data includes: For any target monitoring point and any comparison monitoring point, extract the flux structure ratio feature data corresponding to the target monitoring point and the flux structure ratio feature data corresponding to the comparison monitoring point from the flux structure ratio feature data; use the absolute value of the difference between the flux structure ratio feature data corresponding to the target monitoring point and the flux structure ratio feature data corresponding to the comparison monitoring point as the flux jump distortion assessment data corresponding to the target monitoring point and the comparison monitoring point.

5. The method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis according to claim 1, characterized in that, The step involves performing average modulus smoothing and multiplication mapping on the flux jump distortion assessment data to obtain the jump distortion optimization factor, including: For any target monitoring point and any comparative monitoring point, extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the carbon and nitrogen concentration time series. Also extract the carbon isotope concentration data and nitrogen isotope concentration data corresponding to each time step from the comparative monitoring point. For any target time step, take the square root of the sum of the squares of the carbon isotope concentration data and the nitrogen isotope concentration data corresponding to the target time step as the first modulus assessment of the target monitoring point at the target time step. Take the square root of the sum of the squares of the carbon isotope concentration data and the nitrogen isotope concentration data corresponding to the comparative monitoring point at the target time step as the second modulus assessment of the comparative monitoring point at the target time step. Take the sum of the first modulus assessment and the second modulus assessment as the joint modulus assessment of the target time step. For any target monitoring point and any comparison monitoring point, the joint modulus evaluation corresponding to each target time step is accumulated and then divided by the total number of time steps to obtain the average modulus smoothing data corresponding to the target monitoring point and the comparison monitoring point. For any target monitoring point and any comparison monitoring point, the flux jump distortion assessment data is used as the numerator, the average modulus smoothing data is used as the denominator, and the calculation result of adding the corresponding fraction to the constant 1 is used as the jump distortion optimization factor for the target monitoring point and the comparison monitoring point.

6. The method for quantifying nutrient migration in farmland ecosystems using carbon and nitrogen labeling coupled analysis according to claim 1, characterized in that, The method of obtaining nutrient migration pattern segmentation results by jointly correcting the basic temporal distance using trajectory evolution optimization factors and abrupt distortion optimization factors includes: For any target monitoring point and any comparison monitoring point, the basic time series distance between the target monitoring point and the comparison monitoring point is calculated using a multidimensional dynamic time warping algorithm based on the carbon and nitrogen concentration time series corresponding to the target monitoring point and the comparison monitoring point. For any target monitoring point and any comparison monitoring point, the trajectory evolution optimization factor corresponding to the target monitoring point and the comparison monitoring point is extracted from the trajectory evolution optimization factor, and the jump distortion optimization factor corresponding to the target monitoring point and the comparison monitoring point is extracted from the jump distortion optimization factor; the calculation result of adding the trajectory evolution optimization factor to the constant 1 is used as the first joint correction coefficient, and the product of the basic time series distance, the first joint correction coefficient and the jump distortion optimization factor is used as the comprehensive time series distance corresponding to the target monitoring point and the comparison monitoring point. A comprehensive distance matrix is ​​constructed based on the pairwise temporal distances between all monitoring points, and multiple nutrient migration pattern cluster centers are initialized based on the comprehensive distance matrix. For any target monitoring point, the comprehensive temporal distance between the target monitoring point and each nutrient migration pattern cluster center is calculated, and the nutrient migration pattern cluster center with the smallest comprehensive temporal distance is taken as the cluster center to which the target monitoring point belongs. After completing one monitoring point allocation, the corresponding nutrient migration pattern cluster centers are updated according to the monitoring points contained in each cluster. The monitoring point allocation and cluster center update are repeated until the change in cluster centers is lower than a preset threshold or the preset number of iterations is reached. The cluster number corresponding to each monitoring point is taken as the nutrient migration pattern category label, and the set of nutrient migration pattern category labels corresponding to all monitoring points is taken as the nutrient migration pattern partitioning result.

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