A method for establishing a wheat root growth model by using water carbon flux for root-soil coupling

Abstract

The application relates to a wheat root growth model established by coupling root system, rhizosphere and soil by using water carbon flux and a method thereof, and is based on the response of wheat root parameters, root density and root activity to water, and establishes a wheat root growth model by coupling root system, rhizosphere and soil by using water carbon flux, so as to form a crop root growth model system with applicability. The wheat root growth model is further coupled with a rhizosphere model on the basis of CA and L-System, a root system-rhizosphere-soil model with water carbon flux as an internal link is constructed, and the wheat root growth model is fully applied and developed. Model results show that the root mean square error (RMSE) of the test value and the model value of the root length distribution under water stress treatment and sufficient water treatment is 0.0261 and 0.0396 respectively, the model accuracy R 2 is 0.9179 and 0.8758 respectively, the simulation accuracy is relatively close, and the accuracy is very high.

Description

Technical Field

[0001] This invention relates to a method for establishing a wheat root growth model using water and carbon flux through root-rhizosphere-soil coupling, and belongs to the technical field of vegetation root model simulation. Background Technology

[0002] The root system is a vital organ for plants to obtain water and nutrients from the soil during growth. The extent and degree of root growth in the soil are closely related to the soil environment, and the interaction between roots and soil directly affects the growth of the above-ground parts of the plant, thus influencing crop yield. Therefore, root growth models are one of the main directions of crop research and have practical guiding significance for future agricultural development. The root system of wheat (Triticum aestivum L.) consists of primary roots and secondary roots. Secondary roots are divided into primary and secondary lateral roots. Secondary roots are the main component of the wheat root system, and their development status is one of the indicators of seedling growth strength. Primary roots play a greater role in the early stages and their growth is more stable than that of secondary roots, continuing to play a role until the later stages of wheat growth. Secondary roots have a longer rooting time and a larger root mass, playing an important role in significantly increasing yield under suitable conditions. The main functions of wheat roots are absorption, metabolism, and support. Of the water and nutrients absorbed by the roots, some are retained for utilization, while the rest enters the vascular tissue in their original form or is transformed into other compounds. This latter part is then transported to all parts of the plant with the rising transpiration stream, meeting the needs of the leaves, stems, ears, and other organs for growth and development. The root system has both horizontal distribution and vertical growth, forming excellent support and tension, ensuring the plant remains upright. Therefore, strong roots are essential for strong seedlings, and deep roots lead to lush foliage; a robust root system is the foundation for strong seedlings, strong stems, and large ears. Generally, in clay soils, wheat roots are slender and branched; in sandy soils, wheat roots are thick and less branched. Appropriate soil drought promotes deeper root development; the number and mass of secondary roots per plant increase significantly with increased soil water and fertilizer, resulting in deeper and more evenly distributed roots. A well-developed root system is fundamental to high wheat yields, and with the development of wheat production, the relationship between root distribution in the soil and yield is receiving increasing attention. Most existing models of wheat root systems are derived by simulating the effects of wheat's own growth factors. However, many environmental factors have a significant impact on wheat growth. If only wheat's own growth factors are considered, the simulated models will differ from reality, resulting in suboptimal models with limited practical application. Summary of the Invention

[0003] This invention provides a method for establishing a wheat root growth model by using water and carbon flux to couple the root system, rhizosphere, and soil. The model results are verified by analyzing wheat root parameters. This invention establishes an applicable crop root growth model, which solves the problem that existing wheat models obtained by using wheat's own production factors or water as a single indicator are not ideal and have little practical application significance.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] A model for wheat root growth using root-rhizosphere-soil coupling based on water and carbon flux includes...

[0006] (1) Formula for the relationship between root weight density and root length density:

[0007] RLD = a + b * ln(RWD + c),

[0008] Wherein, RLD is root length density, cm cm⁻³; RWD is root weight density, g cm⁻³; a is the same unit as RLD, cm cm⁻³; b is the fitting parameter for calculating root length density by fitting the experimentally measured root weight density, cm g⁻¹; c is the same unit as RWD, g cm⁻³.

[0009] (2) Formula for the relationship between root length density and soil water suction:

[0010] RLD=m+n*ln(S+e l ),

[0011] Where RLD is root length density; S is soil water suction value, which has been normalized; m, n, and l are the fitting parameters representing the root-soil-water relationship during the fitting process of root length density and soil water suction.

[0012] (3) The dynamic root growth model of water absorption after root-soil coupling is as follows:

[0013]

[0014] Where t represents time, θ represents soil volumetric water content, d represents buffering capacity, and D l denoted by , f represents the resistance coefficient, and f(s) represents the water absorbed through the root system, which is based on the root length density distribution and soil hydraulic distribution.

[0015] This section demonstrates the coupling between L-System root growth and the soil model, for the sake of simplification:

[0016]

[0017] Among them, F m K represents the maximum flow rate into the root system. m This represents the Michaelis-Menten constant;

[0018] (4) Root growth function;

[0019] Assuming initial value: t = 0, root topological stage i, the root growth function of i at t = 0 is:

[0020]

[0021] Among them, K i Maximum root length, R i The initial growth rate of the i-th root, interpolated (age), describes the age of the most recent root surface.

[0022] (5) A root fractal model was established by combining cellular automata (CA) and Lindenmayer-System (L-System), and the simulation was performed using Matlab R2016a. At the beginning of the simulation (t=0), the boundary conditions of all root surfaces were set to zero flow.

[0023] The coupling in soil is illustrated using the following code: Iterate over i, where i is the current time step, from 0 to N-1, where N is the total number of time steps. In this loop, first calculate the soil water suction S. Based on S, simulate root growth and calculate the xylem water pressure Sr of the root. Calculate the root water absorption rate based on the root structure, xylem pressure, and soil saturation (soil water suction calculation).

[0024] This invention also provides a method for establishing a wheat root growth model using root-rhizosphere-soil coupling based on water and carbon flux, comprising the following steps:

[0025] (1) Collect and analyze local data on the actual growth of wheat;

[0026] (2) Based on the data obtained in step (1), the model of claim 1 is used to construct a wheat root growth model;

[0027] (3) To analyze the accuracy of the fit between the model values ​​and the experimental values, two statistical standards are used: mean squared error (RMSE) and coefficient of determination (R²), as shown in the following formula:

[0028]

[0029] In the formula, Mi and Pi are the measured value and the model value, respectively, where i = 1, 2, 3, ..., n. is the mean of Mi, and n is the number of observations in the validation dataset. The R² value ranges from 0 (least accurate) to 1.0 (most accurate), and 0 ≤ RMSE value is not less than zero.

[0030] Furthermore, preferably, the local data for wheat includes soil moisture, wheat root density, water content in wheat plants, carbon flux, and nitrogen flux.

[0031] The wheat root growth model of the present invention is used to calculate the energy of various organs of the plant.

[0032] The beneficial effects of this invention are:

[0033] Based on the response of wheat root parameters, root density, and root activity to water, this invention establishes a wheat root growth model by coupling root system, rhizosphere, and soil using water and carbon flux, thereby forming an applicable crop root growth model system.

[0034] The application of crop root growth models, using biochar as a soil environmental factor, to study the root growth of wheat under water-regulated conditions of sufficient and stressful soil moisture. The study shows that secondary lateral root growth is more vigorous under sufficient soil moisture, while water stress inhibits the formation of new roots. Under sufficient water treatment, wheat roots grow in a balanced horizontal and vertical direction, primarily absorbing surface water, resulting in a slightly larger root angle. Under water stress treatment, the root angle is smaller, with roots primarily growing downwards. Rhizosphere enzyme analysis shows that enzyme activity in the surface soil of water stress treatment is significantly lower than that of sufficient water treatment, but the depth of the subsoil is significantly greater. This indicates that water stress forces roots to grow deeper, resulting in a deep and long root system. Based on the CA and L-System models, the wheat root growth model further couples with a rhizosphere model, constructing a root-rhizosphere-soil model with water and carbon flux as the intrinsic link, thus enabling the full application and development of wheat root growth models. The model results show that the root mean square error (RMSE) of the root length distribution under water stress and adequate water treatments is 0.0261 and 0.0396 respectively, with model accuracy R² of 0.9179 and 0.8758 respectively. The simulation accuracy is relatively close and very high. This model can simulate the flow of water and carbon within a complete crop root system, forming a suitable crop root growth model. By simulating the aboveground parts of wheat root growth and extrapolating the processes of various aboveground wheat organs, the digital characteristics and structure of crop root architecture and crop growth are revealed, thus forming a suitable crop root growth model system and providing theoretical support for the development of crop growth models. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a diagram illustrating the experimental setup and process of the present invention;

[0037] Figure 2 A graph showing the growth rate of wheat primary roots;

[0038] Figure 3 A diagram showing the root length density of wheat at different soil depths;

[0039] Figure 4 A schematic diagram of water and carbon flux in a wheat model;

[0040] Figure 5 Flowchart of root system simulation analysis;

[0041] Figure 6 A diagram describing the model process;

[0042] Figure 7 This is a simulation of the dissolved carbon content under steady-state conditions.

[0043] Figure 8 A simulation diagram of dissolved carbon in symbiotic and oligotrophic organisms in soil under stable conditions;

[0044] Figure 9 Simulation results of wheat root length under water stress treatment;

[0045] Figure 10 The results of the simulation of wheat root length under full water treatment;

[0046] Figure 11 The results of the simulation of the growth of various organs of wheat plants;

[0047] Figure 12 The results represent the total structural carbon content of wheat plants. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] Example 1

[0050] A model for wheat root growth using water and carbon flux coupling between the root system and rhizosphere-soil is described.

[0051] (1) Formula for the relationship between root weight density and root length density:

[0052] RLD = a + b * ln(RWD + c),

[0053] Where RLD is root length density, cm cm-3; RWD is root weight density, g cm-3; a, b, and c are the fitting parameters for calculating root length density by fitting the root weight density measured in the experiment.

[0054] (2) Formula for the relationship between root length density and soil water suction:

[0055] RLD=m+n*ln(S+e l ),

[0056] Where RLD is root length density; S is soil water suction value, which has been normalized; m, n, and l are the fitting parameters representing the root-soil-water relationship during the fitting process of root length density and soil water suction.

[0057] (3) The dynamic root growth model of water absorption after root-soil coupling is as follows:

[0058]

[0059] Where t represents time, θ represents soil volumetric water content, d represents buffering capacity, and D l denoted by , f represents the resistance coefficient, and f(s) represents the water absorbed through the root system, which is based on the root length density distribution and soil hydraulic distribution.

[0060] This section demonstrates the coupling between L-System root growth and the soil model, for the sake of simplification:

[0061]

[0062] Among them, F m K represents the maximum flow rate into the root system. m This represents the Michaelis-Menten constant;

[0063] (4) Root growth function;

[0064] Assuming initial value: t = 0, root topological stage i, the root growth function of i at t = 0 is:

[0065]

[0066] Among them, K i Maximum root length, R i The initial growth rate of the i-th root, interpolated (age), describes the age of the most recent root surface.

[0067] (5) A root fractal model was established by combining cellular automata (CA) and Lindenmayer-System (L-System). At the start of the simulation (t=0), the boundary conditions of all root surfaces were set to zero flow.

[0068] The coupling in soil is illustrated using the following code: Iterate over i, where i is the current time step, from 0 to N-1, where N is the total number of time steps. In this loop, first calculate the soil water suction S. Based on S, simulate root growth and calculate the xylem water pressure Sr of the root. Calculate the root water absorption rate based on the root structure, xylem pressure, and soil saturation (soil water suction calculation).

[0069] for i in range(N):

[0070] Si+1 = soil_model(S,i)

[0071] root_architecturei+1=root_system_growth(S,i+1)

[0072] Sr,i+1=model(root_architecture,ps,i+1)

[0073] Si+1=root_water_uptake(root_architecturei+1,Sr,i+1,S,i+1).

[0074] This invention also provides a method for establishing a wheat root growth model using root-rhizosphere-soil coupling based on water and carbon flux, comprising the following steps:

[0075] (1) Collect and analyze local data on the actual growth of wheat;

[0076] (2) Based on the data obtained in step (1), the model of claim 1 is used to construct a wheat root growth model;

[0077] (3) To analyze the accuracy of the fit between the model values ​​and the experimental values, two statistical standards are used: mean squared error (RMSE) and coefficient of determination (R²), as shown in the following formula:

[0078]

[0079] In the formula, Mi and Pi are the measured value and the model value, respectively, where i = 1, 2, 3, ..., n. is the mean of Mi, and n is the number of observations in the validation dataset. The R² value ranges from 0 (least accurate) to 1.0 (most accurate), and 0 ≤ RMSE value is not less than zero.

[0080] The specific process is as follows:

[0081] 1. Experiment Introduction

[0082] 1.1 Overview of the Experimental Area

[0083] The wheat experiment was conducted in a greenhouse from May to August 2021. The experimental area has a temperate maritime climate with an average annual temperature of 8.8℃ and an average annual precipitation of 809.3 mm. The soil texture is sandy loam, with 24.8% sand, 55.1% silt, and 20.1% clay, and a soil bulk density of 1.29 g / cm³. 3 The soil had a carbon content of 14.1 g / kg, a microbial carbon content of 73 μg / g, a nitrogen content of 0.8 g / kg, and an average pH of 6.5. Wheat was planted within soil columns, each measuring 20 cm × 10 cm × 60 cm (length × width × height). The soil was sieved through a 5 mm sieve before being placed into the soil columns.

[0084] 1.2 Experimental Design

[0085] The wheat experiment primarily used water as the control factor to study root-soil interactions and the flow of water and carbon in the root-soil environment. The experimental treatments included two types: Non-drought (65%-75% WHC) and Drought (30%-40% WHC), with three replicates for each treatment. An additional unplanted soil column was also included, for a total of seven soil columns.

[0086] Once the wheat plant has grown large enough, it will undergo... 13 Marked by C, the process diagram is shown in Figure 1. After the wheat planting soil column was dried for 7 days, it was placed in a closed transparent chamber (length × width × height: 1.0m × 1.0m × 1.5m). Circulating fans were installed on the sides and top, and detection sensors were installed to measure the indoor CO2 concentration and indoor temperature in real time.

[0087] Carbon is produced by injecting CO2 (99 atom%) 13 C) Then wheat plants are placed in a rich... 13The plants were cultured in a C-CO2 environment for 2 hours to allow for the absorption and incorporation of carbon isotopes. The total CO2 concentration in the indoor chamber was increased to 1000 ppm, and then reduced to 700 ppm in the transparent chamber over 2 hours (MG811, CO2 gas module, DFRobot, Shanghai, China). After CO2 pulse labeling, the plants were given 2 days to allow for photosynthesis. 13 C-CO2 is transported to the ground. Then, samples are taken from the leaves and stems, followed by the collection of a soil column with a diameter of 50 mm. The soil sample is then immediately passed through a 2 mm sieve to separate the living roots from the soil. Finally, the soil column is transported to the laboratory for decomposition and sampling of the soil and root system. 13 The trajectory of C-labeled molecules is: photosynthesis. 13 C(Photosynthetic 13 C) → In the plant's leaves and stems 13 C( 13 C in plant) → root system 13 C( 13 C in roots) → root zone 13 C( 13 C in rhizodeposits) → in the soil 13 C( 13 C in soil). The ultimate goal is biological processes. 13 C decomposition refers to the process by which C flows from photosynthesis to plant roots or plant residues and then to soil microorganisms, as well as from soil organic matter to CO2. This paper uses... 13 The purpose of C labeling is to study plant root growth in soil, track the distribution and transport of labeled carbon in plant roots, and understand the soil depth and type chosen by plant roots when absorbing nutrients, so as to calculate the carbon flux in root-soil interaction processes.

[0088] 2. Test Items and Methods

[0089] 2.1 Wheat plant analysis

[0090] To determine the water, carbon, and nitrogen fluxes in different parts of the wheat plant, after the wheat experiment, the wheat was cut from the soil layer, and the total weight of the wheat plant was weighed. After removing yellow and withered leaves, each organ (stem, ear, and leaf) of the wheat plant was taken and weighed fresh. Finally, each organ was placed in a kraft paper bag and dried in an oven at 75℃ for 72 hours. After the oven was closed and the temperature was kept constant, the dry weight of each part was weighed. The dried wheat plant samples were ground or chopped to ensure homogeneity, placed in glass bottles, and prepared for subsequent weighing. Using an electronic balance with an accuracy of 0.001 mg, 3 mg of each plant sample and 25 mg of soil sample were weighed and placed in tin containers for TC, TN, and other measurements. 13 C and 15 Measurement of N. One standard (1 mg glutamic acid) is required for every 10 samples. In addition, three tin sachets containing standard soil are weighed for standard comparison.

[0091] 2.2 Analysis of wheat root morphological parameters

[0092] WinRhizo Pro 2020a was used to analyze the morphological parameters of wheat roots. After obtaining wheat root samples, root samples were taken from different locations and depths in three replicates of the two treatments for root analysis.

[0093] 2.3 Data Statistics and Analysis

[0094] Image processing and analysis in this paper were performed using the open-source software imageJ. SPSS 22.0, Origin 2022b, and Excel 2016 were used for statistical analysis, graphing, and other data processing. Matlab R2016a was used for simulation and model validation.

[0095] To analyze the accuracy of the fit between model values ​​and experimental values, two statistical standards are used: mean squared error (RMSE) and coefficient of determination (R²). 2 The formula is as follows:

[0096]

[0097] In the formula, M i and P i These are the measured values ​​and the model values, respectively, where i = 1, 2, 3, ..., n. It is M i The average value of R is given by , where n is the number of observations in the validation dataset. 2 The value ranges from 0 (least accurate) to 1.0 (most accurate), and 0 ≤ RMSE value is not less than zero.

[0098] 3. Analysis of Experimental Results

[0099] 3.1 Root System Structure Parameter Analysis

[0100] The wheat experiment results were mainly analyzed using wheat root parameters, specifically primary roots, first-order lateral roots, and second-order lateral roots. Root parameters for the adequate water treatment and water stress treatment are shown in Table 1. Regarding total root length, the primary roots, first-order lateral roots, and second-order lateral roots in the water stress treatment were all greater than those in the adequate water treatment. The total length of the first-order lateral roots in the water stress treatment was 72.22 cm, significantly greater than the 47.00 cm in the non-drought treatment; the total length of the second-order lateral roots was 104.13 cm, also significantly greater than the 65.42 cm in the adequate water treatment.

[0101] For the water stress treatment, the average and median lateral distances of primary roots were 0.43 cm and 0.44 cm, respectively. However, the adequate water treatment showed that both the average and median lateral distances of primary roots were greater than those under the water stress treatment, at 0.55 cm and 0.53 cm, respectively. This indicates that the adequate water treatment resulted in higher lateral distances of primary roots, suggesting that root growth tends towards horizontal extension rather than vertical growth. However, the average (0.44 cm) and median (0.44 cm) lateral distances of primary lateral roots under the water stress treatment were slightly greater than those under the adequate water treatment (0.39 cm and 0.41 cm), indicating no significant difference in lateral root distances.

[0102] The results of the root growth rate experiment on primary roots within 12 days showed that the root growth rate of primary roots under water stress treatment was 2.91 cm / day, while the root growth rate of primary roots under adequate water treatment was 3.81 cm / day. The results of observation and experimental simulation of primary root growth rate are as follows... Figure 2As shown in the figure, under water stress treatment, the primary root growth rate was 2.9 cm / day within 11.3 days; after 11.3 days, the total primary root length was 39.0 cm. Under adequate water treatment, the primary root growth rate was 3.8 cm / day within 8.6 days, and the primary root length thereafter was 40.4 cm. The experimental observations and simulation results are similar, indicating that after a certain period, primary roots cease to grow, and root growth is dominated by lateral root growth. It also shows that the adequate water treatment resulted in more roots in the surface soil, while the water stress treatment resulted in roots growing deeper into the soil, requiring more water. The average (0.26 cm / day) and median (0.28 cm / day) growth rates of secondary lateral roots under adequate water treatment were significantly faster than those under water stress treatment (0.10 cm / day), with the rate being nearly three times that of the water stress treatment. This indicates that sufficient water leads to more vigorous growth of secondary lateral roots, while insufficient water also suggests that water stress inhibits the formation of new roots.

[0103] Regarding the root angle, the root angle under water stress treatment was smaller at 34.8°, indicating that water primarily promotes downward growth. Under sufficient water treatment, the primary root angle was 37.1°, indicating that in a sufficiently moist soil environment, wheat roots grow in a balanced manner in both horizontal and vertical directions, and the roots mainly absorb surface water, hence the slightly larger root angle.

[0104] Table 1. Root parameters of wheat under different moisture distributions

[0105]

[0106]

[0107] Note: * indicates the mean calculated from the transformed data; ±sd indicates the standard deviation; NA indicates not applicable.

[0108] 3.2 Analysis of wheat root morphological parameters

[0109] Table 2 shows the morphological parameters of wheat roots at different soil depths under different treatments. The table shows significant differences in root morphological parameters between the adequate water treatment and the water stress treatment.

[0110] Table 2. Wheat root indexes at different soil depths under different treatments.

[0111]

[0112] For the adequate water treatment, the total root length was greater at all soil depths than that under the water stress treatment, especially at the 0-30cm depth. For the water stress treatment, the root length was relatively shorter at 0-30cm, but increased significantly at 30-60cm depth, particularly at 50-60cm, where it was nearly three times that of the 0-10cm treatment. This indicates that under water stress, wheat roots extend deeper, with longitudinal growth exceeding lateral growth. In contrast, the total root length at the 0-10cm depth (1113.237cm) for the adequate water treatment was approximately twice that of the water stress treatment (638.723cm), and the total root length remained relatively stable at all soil depths. This suggests that with adequate water, root growth is more balanced both longitudinally and laterally. Meanwhile, the total root length at a soil depth of 50-60cm was similar for the water stress treatment (1818.935cm) and the fully watered treatment (1860.998cm). This suggests that the root growth in deep soil may be due to the absence of water infiltration in the deep soil column test, resulting in a similar soil moisture environment. This also reflects that the roots under water stress treatment grew more vigorously in deep soil.

[0113] Table 3-6 analyzes and compares the total root length, root surface area, expected area, and root volume of wheat under the two treatments, dividing them into 10 levels. The analysis covers the root coverage at different lengths, different surface area ranges, different area ranges, and different volume ranges. Table 3 shows that in both the sufficient water and water stress treatments, only the root distribution in the 0-10cm topsoil layer is relatively wide, while the root length in the 10-60cm soil depth is entirely concentrated in the range of 0 < L <= 0.500cm. For the sufficient water treatment, analysis of the root length across the ten length levels reveals that the surface root system's water absorption and growth capacity is greater than that in the water stress treatment. However, under water stress, the root lengths in the ranges of 2.000 < L <= 2.500 cm, 2.500 < L <= 3.000 cm, 3.000 < L <= 3.500 cm, and 3.500 < L <= 4.000 cm were 3.421 cm, 3.942 cm, 4.097 cm, and 2.691 cm, respectively, which were greater than those under the adequate water treatment (1.058 cm, 2.134 cm, 1.650 cm, and 2.334 cm, respectively). Regarding wheat root surface area, Table 4 shows that, similar to root length, only the root surface area in the 0-10 cm soil layer was distributed across all levels under both adequate and water stress treatments. However, the root surface area in the 10-60 cm soil depth was mainly concentrated in the 0 < L <= 0.500 cm layer. 2 And 0.500 < SA <= 1.000 cm 2 Range. The root surface area ranges from 2.000 < SA <= 2.500 cm². 22.500 < SA <= 3.000 cm 2 3.000 < SA <= 3.500 cm 2 3.500 < SA <= 4.000 cm 2 The root surface area under water stress was 2.398 cm². 2 3.409cm 2 4.098cm 2 3.136cm 2 Moisture content was fully treated (its values ​​were 0.742 cm). 2 1.812cm 2 1.674cm 2 2.778cm 2 This result is consistent with the root length result. Tables 5 and 6 show that the distribution range of the expected root area and root volume is the same as that of the root surface area, with distribution in all grades within the 0-10cm topsoil layer. The two values ​​in the 10-60cm soil depth are mainly concentrated between 0 < PA < 0.500cm. 2 And 0.500 < PA <= 1.000 cm 2 Range, 0 < SA <= 0.500cm 3 And 0.500 < SA <= 1.000 cm 3 scope.

[0114] Table 3. Range of wheat root length at different soil depths under different treatments.

[0115]

[0116]

[0117] Note: L represents the root length within the range of 10 levels.

[0118] Table 4. Range of wheat root surface area at different soil depths under different treatments.

[0119]

[0120]

[0121] Note: SA represents the root surface area within a range of 10 levels.

[0122] Note:SAis root surface area in the range of ten class by class.

[0123] Table 5. Expected range of wheat root area at different soil depths under different treatments.

[0124]

[0125] Note: PA represents the projected root area within a 10-level range.

[0126] Table 6. Range of wheat root volume at different soil depths under different treatments.

[0127]

[0128] Note: V represents the root volume within a range of 10 levels.

[0129] This indicates that, in addition to physiological factors affecting root growth, water stress causes roots to compete for soil resources within a certain range, and appropriate water stress promotes root growth. It also demonstrates that wheat roots can grow deep under moderate drought without wilting, and that crops can enhance root growth capacity through root hair absorption under water-scarce conditions.

[0130] 3.3 Analysis of wheat root density

[0131] Figure 3 The root density at different soil layers was calculated based on Table 2 for both water-sufficient and water-stress treatments. The figure shows that the root density at all soil depths was greater in the water-sufficient treatment than in the water-stress treatment. However, root volume decreased in the 20-30 cm soil layer. This may be due to the physiological characteristics of root growth stages, where root diameter increases primarily rather than root length increases; or, during the wheat growth stage, root growth is hindered at this depth due to lack of water in the lower soil layers. This issue requires further investigation. However, at the bottom soil depth of 50-60 cm, the root densities of the two treatments gradually approached each other, with the water-sufficient treatment showing a root density 0.021 cm higher than the water-stress treatment. -3 This indicates that deep soil growth is greater than surface soil growth under water stress. Furthermore, this root density study also validates conclusion 5.1.3 above, demonstrating that surface soil roots primarily stabilize crop seedlings in the early stages of growth, exhibiting larger root diameters but slower length increases; while deep soil roots are mainly fine roots, with root hairs primarily used for resource searching.

[0132] 4. Construction of a wheat root growth model

[0133] The model used is based on CA and L-System, with carbon flux added as a validation medium for the wheat root system model. Root system simulation analysis was performed using the above simulation method. Figure 4This describes the state of the water and carbon flux model during wheat root system simulation. As shown in the figure, firstly, a plant structure composed of connected nodes is constructed, resembling a directed graph. Secondly, water flow in the roots (xylem) and the plant's photosynthetic rate are calculated. The soil water model uses the uptake rate as the source term, providing the average soil water potential for each soil voxel. New carbon flows and sinks are calculated based on xylem water potential and carbon input. This yields the carbon required for the growth of each organ, which is used in the next time step to simulate the expansion or creation of plant parts and is incorporated into the rhizosphere model within the soil-plant framework. For each root segment, radial root flux provides the internal boundary conditions of the rhizosphere model, while the soil module provides the external boundary conditions.

[0134] At the same time, from Figure 4 It can be seen that aboveground plant growth is mainly driven by photosynthesis, plant water flow, carbon flow, and utilization. In the underground soil, the main process is soil water flow, accompanied by root water absorption and rhizosphere and soil exudates. The analysis of the water and carbon flow processes utilized in wheat root system simulation is as follows: Figure 5 As shown in the figure, the plant growth process is as follows: plant water flow and photosynthesis are the basis of soil water flow, while plant carbon flow is circulated, and soil resources are circulated through root water absorption and soil matrix potential.

[0135] Figure 6 This diagram illustrates the process of establishing a rhizosphere model, specifically the connection between the root system and the rhizosphere. The diagram depicts the spatial distribution of dissolved carbon content and microbial biomass within the rhizosphere. The model divides carbon content into two parts: dissolved carbon in the soil solution and insoluble carbon. The insoluble carbon region consists of macromolecular carbon, such as lignin, selenides, and plant residues, belonging to oligotrophs—organisms capable of living in environments with very low nutrient levels. Dissolved carbon consists of small molecules, which foster the growth of copiotrophs in the microbial community—organisms that thrive in nutrient-rich environments, particularly carbon-rich ones. Copiotrophic bacteria are a key component of the soil carbon cycle and exude large amounts of carbon compounds.

[0136] 5. Validation results of the wheat root system model

[0137] 5.1 Results of the root zone model

[0138] Figure 7 and 8 The figures shown are the rhizosphere simulation results for two treatments, with the figures obtained under steady-state conditions. Figure 7In the image, the dissolved carbon concentration (mg / cm³) in the soil solution at a distance of 0-1 cm from the root surface can be observed. -3 Due to root exudates, the concentration of dissolved carbon is higher near the roots, reaching 0.20 mg / cm³. -3 When it is far from the root surface, it decreases slightly to approximately 0.19 mg / cm³. -3 .from Figure 8 As can be seen, the spatial distribution of the two functional groups is plotted in the same graph. Due to the high carbon content, the concentration of copitotrophs near the roots is very high, with values ​​greater than 0.30 mg / cm³. -3 The concentration of symbiotic biomass decreases continuously from the root center to the soil, reaching approximately 0 mg / cm³ at a distance of 1 cm from the root system. -3 Oligotrophs, on the other hand, exhibit the opposite trend, with lower dissolved carbon concentrations near the roots, reaching 0.07-0.08 mg / cm³ at a distance of 1 cm from the root surface. -3 Both have one thing in common: their concentrations tend to stabilize at the root surface. This may be due to the amount of substrate supplied near the roots and the decrease in substrate concentration in the soil direction.

[0139] Wheat root-rhizosphere models are models of the wheat root system and the surrounding soil microbial community. These models typically involve factors such as soil physical, chemical, and biological properties, and utilize mathematical and computer simulation methods to analyze and predict the ecosystem functions of the wheat rhizosphere. These functions include nutrient cycling, carbon and nitrogen metabolism, soil carbon sequestration and nitrogen capture, and plant-microbe interactions. Research on wheat root-rhizosphere models is a future research direction, providing valuable information for understanding wheat growth and development and ecosystem functions, and offering guidance for optimizing wheat production.

[0140] 5.2 Model Result Analysis

[0141] Root model results of water and carbon flows in the root system, rhizosphere, and soil under conditions of sufficient and water stress in wheat showed significant differences in root growth. In the water stress treatment, lateral root growth was dominant, while in the sufficient water treatment, horizontal root growth was dominant. Under water control, the initial root response to water stress was characterized by reduced swelling pressure at the root tip, decreased root elongation, and accelerated root tip elongation. The root length distribution fractions in the model and experiments at different soil depths are shown below. Figure 9 and 10As shown in the figure, the model with sufficient water performed better, with the model values ​​for root length distribution more closely matching the experimental values, while the water stress treatment was slightly less effective. Furthermore, the comparison between measured and model values ​​showed that both treatments exhibited larger measured values ​​in the upper soil layer (0-30 cm) and larger model values ​​in the deeper soil layer (30-60 cm). Regression analysis was used to calculate RMSE and R0. 2 Analysis of the simulation results revealed model errors. The root mean square error (RMSE) between the experimental and model values ​​of root length distribution under water stress and adequate water treatments was 0.0261 and 0.0396, respectively, indicating that the model accuracy R0 was [not specified]. 2 The simulation accuracy is relatively close, with values ​​of 0.9179 and 0.8758 respectively. This is in contrast to the measured and model RMSE range of 0.0016-0.0259 for tobacco root length distribution and the model accuracy R0. 2 The simulation results for wheat were better, ranging from 0.5969 to 0.9044, indicating that the model with soil moisture as a single factor control had higher accuracy. Simulating crop root growth is a complex process involving multiple fields such as soil mechanics, plant physiology, and biomechanics; therefore, accurately simulating root growth is extremely challenging. The simulation method used in this study achieved a root growth model with significantly higher accuracy than the root simulations of other crops, demonstrating the greater applicability of the proposed method.

[0142] Meanwhile, the model results are similar to those obtained from wheat experiments, specifically regarding wheat root growth under water stress and adequate water treatments. Specifically, compared to the adequate water treatment, wheat roots under water stress extended deeper into the soil to seek more resources. This indicates that under water scarcity, plants tend to extend their roots to find water and nutrients. Furthermore, under adequate water treatment, wheat roots grew faster horizontally and relatively less vertically, especially below 40 cm in soil depth. This suggests that under sufficient water, plants prefer to utilize horizontal water and nutrient resources, enabling rapid root growth and expansion. Additionally, the angle between the root system and the vertical direction was slightly larger for the more balanced root system. This implies a more balanced growth pattern, allowing for sufficient horizontal water and nutrient access while also reaching deeper into the soil for more nutrients. These results reveal the adaptive strategies of wheat roots under different water conditions and can provide a reference for better understanding the growth patterns of plant roots.

[0143] 5.3 Plant Analysis Using Wheat Simulation Application

[0144] Based on the wheat root growth model, further simulation analysis of wheat plants was conducted. Figure 11 To simulate wheat plants in13 Under C-labeled conditions, the growth process of simulated wheat plant organs from day 30 to day 33 was extracted after simulating 100 days of plant organ growth. The sucrose concentrations of each plant organ were simulated under photosynthetic conditions, affecting wheat grains, roots, stems, and leaves. 13 Growth under C labeling. The graph shows that the leaves have the highest sucrose content, increasing during the day due to photosynthesis; followed by the stems, where sucrose is first transported after photosynthesis in the leaves, and finally to the roots. The main reason for this is that plant organs accumulate carbon at night for plant maintenance, growth, or root exudation. This also indicates that carbon has a high velocity, reaching the root-soil environment quickly and accumulating fastest in the roots. This is consistent with the conclusion that carbon reaches the roots in a shorter time under pulsed isotope labeling. In the plant organ growth simulation, the plant reaches its maximum relative length on day 33, while the amount of sucrose used for growth decreases, and the maximum sucrose concentration obtained in each organ increases.

[0145] Figure 12 Indicates in Figure 11 Based on the description of sucrose concentrations in various organs of wheat plants, the total structural carbon content of wheat plants was analyzed. As shown in the figure, the total structural carbon content increased by nearly 0.20 mol from day 30 to day 33, indicating that the total structural carbon content continuously increased during the simulation process as the plant grew. The largest increase was on day 30 (0.08 mol), while the increase slowed down to less than 0.05 mol by day 33. This is closely related to the carbon concentration. The rate of increase is consistent with the increase in concentration in various plant organs, i.e., a rapid increase during the day and a slow increase at night. Under photosynthesis, plant leaves absorb carbon dioxide and react with it, which flows through the carbon flow to the stem and finally to the roots. This is of great significance for the overall plant model study. Both figures simultaneously verify the plant simulation results. The model of this invention can simulate the flow of water and carbon in a complete plant root system and can also be extrapolated to the leaves to simulate aboveground plant growth. By inverting the simulation process of wheat root architecture, the growth process of plant structural carbon is simulated in reverse, further reflecting the simulation of local ecology to regional carbon sink, thereby studying the dynamic response of plants to climate environment.

[0146] Furthermore, by using wheat root systems to simulate wheat plant growth, we can further explore the impact of carbon distribution in various plant organs on plant growth and development. Since carbon is a crucial substance for photosynthesis, future research aims to link plant growth functions with local soil carbon levels, thereby exploring the feedback relationships between plants, soil, and the environment. The applicability of the crop root model established in this invention also provides feasible theoretical support for research on the root systems of other crops.

[0147] 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 model for establishing wheat root growth using root-rhizosphere-soil coupling via water and carbon flux, characterized in that, include (1) Formula for the relationship between root weight density and root length density: RLD = a + b * ln(RWD + c), Where RLD is the root length density, in cm·cm -3 RWD is the root weight density, g·cm³. -3 ;a has the same unit as RLD, cm·cm -3 b represents the fitting parameters for calculating root length density using experimentally measured root weight density, in cm·g. -1 c has the same unit as RWD, g·cm³ -3 ; (2) Formula for the relationship between root length density and soil water suction: RLD=m+n*ln(S+e l ), Where RLD is root length density; S is soil water suction value, which has been normalized; m, n, and l are the fitting parameters representing the root-soil-water relationship during the fitting process of root length density and soil water suction. (3) The dynamic root growth model of water absorption after root-soil coupling is as follows: Where t represents time, θ represents soil volumetric water content, d represents buffering capacity, and D l denoted by , f represents the resistance coefficient, and f(s) represents the water absorbed through the root system, which is based on the root length density distribution and soil hydraulic distribution. This section demonstrates the coupling between L-System root growth and the soil model, for the sake of simplification: Among them, F m K represents the maximum flow rate into the root system. m This represents the Michaelis-Menten constant; (4) Root growth function; Assuming initial value: t = 0, root topological stage i, the root growth function of i at t = 0 is: Among them, K i Maximum root length, r i The initial growth rate of the i-th root; (5) A root fractal model was established by combining cellular automata and L-system, and Matlab R2016a was used for simulation. At the beginning of the simulation, t=0 and the boundary conditions of all root surfaces were set to no flow. The i-th iteration was performed, where i is the current time step, from 0 to N-1, where N is the total number of time steps. In this loop, the soil water suction S was calculated first. Based on S, the root growth was simulated and the xylem water pressure Sr of the root was calculated. The root water absorption rate was calculated based on the root structure, xylem water pressure and soil saturation calculated using soil water suction.

2. A method for establishing a wheat root growth model using water and carbon flux through root-rhizosphere-soil coupling, characterized in that, Includes the following steps: (1) Collect and analyze data on the actual growth of wheat; (2) Based on the data obtained in step (1), the model of claim 1 is used to construct a wheat root growth model; (3) To analyze the accuracy of the fit between the model values ​​and the experimental values, two statistical standards are used: the root mean square error (RMSE) and the coefficient of determination (R²). 2 The formula is as follows: In the formula, M i and P i These are the measured values ​​and the model values, respectively, where i = 1, 2, 3, ..., n. It is M i The average value, where n is the number of observations in the validation dataset, R0 2 The value ranges from 0 to 1.

0.

3. The method according to claim 2, characterized in that: The data includes soil moisture, wheat root density, water content in wheat plants, carbon flux, and nitrogen flux.

4. The use of the wheat root growth model of claim 1 in calculating the energy of various organs of the plant.

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