A method for simulating broadleaf tree wood formation and radial growth using climate data

Abstract

The application discloses a method for simulating wood formation and radial growth of broad-leaved trees by using climate data and belongs to the technical field of tree growth prediction. In order to solve the problem of accurate simulation of wood formation and radial growth of broad-leaved trees, the application comprises the following steps: collecting input data including latitude data of a target region and long-term daily meteorological data of the target region; establishing cambium activation conditions of the broad-leaved trees; calculating relative growth rates of cell expansion, cell wall deposition and cambium cells, and calculating expansion rates of the cambium cells; establishing a cambium cell division model and a vessel cell differentiation cycle model; establishing a cell expansion model and a cell wall thickening model, simulating the growth process of the cells in the xylem until the cell wall lignification process is completed, and then the cells enter a mature cell stage; and based on the mature cell stage, calculating annual ring width and anatomical characteristics, and completing the simulation process of simulating the wood formation and radial growth of the broad-leaved trees by using the climate data.

Description

Technical Field

[0001] This invention belongs to the field of tree growth prediction technology, specifically relating to a method for simulating the formation and radial growth of broadleaf tree timber using climate data. Background Technology

[0002] In existing technologies, the Vaganov-Shashkin model, a tree growth process model, simulates tree growth on a daily time step. Its core principle is based on Liebig's minimum factor law, which states that the daily radial growth rate is limited by the minimum of temperature, moisture, and light intensity. The model constructs a nonlinear climate response function to convert meteorological data into daily relative growth rates, and then accumulates these rates throughout the growing season to obtain the simulated tree ring width. This model, to a certain extent, integrates statistical correlation with physiological mechanisms, and can identify the dominant limiting factors at different stages of the growing season, making it particularly suitable for tree ring-climate reconstruction studies in regions with complex climate responses.

[0003] However, existing mainstream tree growth models are mainly based on coniferous tree growth theories and experimental data. The wood of coniferous trees is primarily composed of tracheids, while the wood of broadleaf trees contains various cell types, including vessels and wood fibers. Existing models lack descriptions of cell differentiation processes, making it difficult to accurately simulate the formation and radial growth of broadleaf tree wood. Summary of the Invention

[0004] The problem this invention aims to solve is to achieve accurate simulation of the formation and radial growth of broadleaf tree timber, and proposes a method for simulating the formation and radial growth of broadleaf tree timber using climate data.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for simulating broadleaf tree wood formation and radial growth using climate data includes the following steps:

[0007] S1. The input data collected includes the latitude data of the target area and the long-term daily meteorological data of the target area, including the daily average temperature, daily precipitation, daily average atmospheric humidity, daily average saturated water vapor pressure difference, soil moisture and day length;

[0008] S2. Establish the cambium activation conditions for broad-leaved trees. When the effective accumulated temperature and day length exceed the set thresholds, proceed to the next step.

[0009] S3. Convert the climate-driven growth response into dimensionless climate-driven relative cell growth rates, then calculate the relative growth rate of cell expansion egR, the relative growth rate of cell wall deposition wgR, and the relative growth rate of cambium cells czgR, and calculate the expansion rate of cambium cells. ;

[0010] S4. Based on the expansion rate of cambium cells obtained in step S3, establish a cambium cell division model and a vessel cell differentiation cycle model to realize the entry of cells from the cambium into the xylem;

[0011] S5. Establish models of cell expansion and cell wall thickening to simulate the cell growth process in the xylem until the cell wall lignification process is completed, at which point the cell enters the mature cell stage.

[0012] S6. Based on the mature cell stage, calculate the annual ring width and anatomical features to complete the simulation process of broad-leaved tree wood formation and radial growth using climate data.

[0013] Furthermore, the formula for calculating the effective accumulated temperature in step S2 is as follows:

[0014]

[0015] in, T represents the daily average temperature. min The lowest temperature for tree growth. For effective accumulated temperature.

[0016] Furthermore, the specific implementation method of step S3 includes the following steps:

[0017] S3.1. Convert climate-driven growth response into dimensionless climate-driven relative cell growth rate;

[0018] The formula for calculating the relative rate of cell growth, gE, driven by day length is:

[0019]

[0020] Where Q represents atmospheric radiation. This refers to the annual average atmospheric radiation.

[0021] The formula for calculating the temperature-driven relative rate of cell growth, gT, is as follows:

[0022]

[0023] Where T is temperature. Let R be the activation enthalpy, R be the gas constant, and A be the normalization coefficient. and These are the enthalpy and entropy that affect the reversible denaturation of enzymes, respectively; T min The lowest temperature for tree growth, T max This is the highest temperature for tree growth;

[0024] gM represents the relative cell growth rate driven by soil moisture, and gV represents the relative cell growth rate driven by VPD. Both are calculated in a piecewise manner.

[0025] S3.2. Calculate the relative growth rate of cell expansion at time t, egR t The relative growth rate of cell wall deposition, wgR t The relative growth rate of cambium cells czgR t The calculation formula is:

[0026]

[0027]

[0028]

[0029] in, The growth rate of the initial region of the cambium. The growth rate is affected by the cambium width. The width of the forming layer;

[0030] S3.3. Calculate the expansion rate of cambium cells at time t. The calculation formula is:

[0031]

[0032] in, It is the theoretical maximum expansion rate of cambium cells, Trend cz The potential impact of age on cambium activity;

[0033]

[0034] in, The normalization coefficient is... This represents the rate of change in cell expansion rate with age. The age of the tree.

[0035] Furthermore, the specific implementation method of step S4 includes the following steps:

[0036] S4.1. Based on the expansion rate of cambium cells obtained in step S3, the cambium cell division process is established as follows:

[0037]

[0038] in, Let be the area of ​​the outermost cell of the cambium at time t. The initial area of ​​the cambium cells;

[0039] S4.2. The number of cambium divisions required from each duct differentiation to the next duct differentiation is called the duct differentiation cycle. When the number of divisions reaches or exceeds the duct differentiation cycle, the cell layer differentiates into duct cells, and the counting process restarts.

[0040] The number of cell layers D since the last ductal differentiation t The calculation formula is as follows:

[0041] ;

[0042] The formula for judging ductal differentiation is:

[0043]

[0044] Wherein, Div is an indicator variable for duct differentiation. A Div of 1 indicates that one duct differentiates during the division of the cambium cells in that subdivision, while a Div of 0 indicates that no duct differentiates during the division of the cambium cells in that subdivision. The ductal differentiation cycle at time t is calculated using the following formula:

[0045]

[0046] in, For potential ductal differentiation cycles, α is the minimum ductal differentiation cycle, and L is the minimum ductal differentiation cycle. div For the correction rate of ductal differentiation cycle, Trend ca β represents the potential maximum ductal area affected by age, and β is the ductal differentiation rate correction coefficient when the potential maximum ductal area changes.

[0047] Furthermore, the specific implementation method of step S5 includes the following steps:

[0048] S5.1. Establish a model for cell expansion, expressed as:

[0049]

[0050] Where CA represents the cell area. CA represents the current cell expansion rate. max WT represents the maximum surface area of ​​the cell, and WT represents the cell wall thickness. The threshold thickness at which cell expansion stops;

[0051] S5.2. Establish a model for cell wall thickening. Assuming that cells are rectangular due to their mutual interaction, the formula for calculating WT is:

[0052]

[0053] Where CTD is the tangential dimension of the cell, CRD is the radial dimension of the cell, and WA is the cell wall area;

[0054] The formula for calculating the rate of cell wall expansion is:

[0055]

[0056] in, WA represents the current cell wall deposition rate. max m is the maximum potential surface area of ​​the cell wall. w For the first calibration parameter, s w For the second calibration parameter, Death is a Boolean variable;

[0057] Cell death is defined when the cell wall becomes completely lignified. The "Death" parameter is a function related to the Wake-Up Call (WA) mechanism, as shown below:

[0058]

[0059] Where LWA is the area of ​​the lignified wall;

[0060] The formula for calculating cell wall lignification is:

[0061]

[0062] in, m represents the current cell wall lignification rate. l and s l These are the third calibration parameter and the fourth calibration parameter, respectively.

[0063] Furthermore, in step S6, the width of the tree rings is determined by the ratio of the total cell area to the width of the simulated region, and the change in the width of the tree rings over time is given by the formula:

[0064]

[0065] Where RW is the width of the annual rings, and CA is the width of the annual rings. i Let T be the area of ​​the i-th cell within the simulation region, and n be the number of cells within the simulation region. width This represents the tangential width of the simulated region.

[0066] The beneficial effects of this invention are:

[0067] This invention discloses a method for simulating broadleaf tree wood formation and radial growth using climate data. This method effectively simulates the interannual variation of tree ring width and the dynamic formation process of vessels and fiber cells within the year, quantifying the impact of climate factors on these processes. Based on this, the invention correlates microscale xylem cell growth with macroscale trunk radial growth, achieving cross-scale simulation of tree growth processes. This model has significant application value in the study of climate-growth relationships in broadleaf trees and in predicting tree growth changes under different future climate scenarios. This invention provides an effective tool for studying the wood formation process of broadleaf trees, contributing to a deeper understanding of the wood formation mechanisms of different tree species and the impact of climate change on them. Attached Figure Description

[0068] Figure 1 This is a flowchart illustrating a method for simulating the formation and radial growth of broadleaf tree wood using climate data, as described in this invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0070] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0071] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 Detailed explanation is as follows:

[0072] Example 1:

[0073] A method for simulating broadleaf tree wood formation and radial growth using climate data includes the following steps:

[0074] S1. The input data collected includes the latitude data of the target area and the long-term daily meteorological data of the target area, including the daily average temperature, daily precipitation, daily average atmospheric humidity, daily average saturated water vapor pressure difference, soil moisture and day length;

[0075] Furthermore, meteorological data is obtained from regional meteorological stations or in combination with remote sensing satellite data or reanalysis datasets (such as ERA5). The collected meteorological data undergoes preprocessing to ensure data continuity and standardization.

[0076] S2. Establish the cambium activation conditions for broad-leaved trees. When the effective accumulated temperature and day length exceed the set thresholds, proceed to the next step.

[0077] Furthermore, the formula for calculating the effective accumulated temperature in step S2 is as follows:

[0078]

[0079] in, T represents the daily average temperature. min The lowest temperature for tree growth. For effective accumulated temperature.

[0080] Furthermore, when With day length Exceeding preset thresholds and At that time, the cambium activity is activated, and the cambium activity rate is calculated.

[0081] S3. Convert the climate-driven growth response into dimensionless climate-driven relative cell growth rates, then calculate the relative growth rate of cell expansion egR, the relative growth rate of cell wall deposition wgR, and the relative growth rate of cambium cells czgR, and calculate the expansion rate of cambium cells. ;

[0082] Furthermore, the specific implementation method of step S3 includes the following steps:

[0083] S3.1. Convert climate-driven growth response into dimensionless climate-driven relative cell growth rate;

[0084] The formula for calculating the relative rate of cell growth, gE, driven by day length is:

[0085]

[0086] Where Q represents atmospheric radiation. This refers to the annual average atmospheric radiation.

[0087] The formula for calculating the temperature-driven relative rate of cell growth, gT, is as follows:

[0088]

[0089] Where T is temperature. Let R be the activation enthalpy, R be the gas constant, and A be the normalization coefficient. and These are the enthalpy and entropy that affect the reversible denaturation of enzymes, respectively; T min The lowest temperature for tree growth, T max This is the highest temperature for tree growth;

[0090] gM represents the relative cell growth rate driven by soil moisture, and gV represents the relative cell growth rate driven by VPD. Both are calculated in a piecewise manner.

[0091] Furthermore, the effects of soil moisture and VPD were calculated using a piecewise model. The formula is:

[0092]

[0093]

[0094] Wherein, gM is the relative rate of cell growth driven by soil moisture; M1 is the minimum soil moisture (relative to saturated soil) that limits tree growth, M2 is the lower limit of the optimal soil moisture range, M3 is the upper limit, and M4 is the maximum limiting value; gV is the relative rate of cell growth driven by VPD; VPD1 is the minimum VPD that limits tree growth, VPD2 is the lower limit of the optimal VPD range, VPD3 is the upper limit, and VPD4 is the maximum limiting value.

[0095] S3.2. Calculate the relative growth rate of cell expansion at time t, egR t The relative growth rate of cell wall deposition, wgR t The relative growth rate of cambium cells czgR t The calculation formula is:

[0096]

[0097]

[0098]

[0099] in, The growth rate of the initial region of the cambium. The growth rate is affected by the cambium width. The width of the forming layer;

[0100] Furthermore, to ensure that the activity rate in the cambium region does not exceed the limitations imposed by environmental factors, the czgR is constrained using the following formula:

[0101] ;

[0102] S3.3. Calculate the expansion rate of cambium cells at time t. The calculation formula is:

[0103]

[0104] in, It is the theoretical maximum expansion rate of cambium cells, Trend cz The potential impact of age on cambium activity;

[0105]

[0106] in, The normalization coefficient is... This represents the rate of change in cell expansion rate with age. The age of the tree.

[0107] S4. Based on the expansion rate of cambium cells obtained in step S3, establish a cambium cell division model and a vessel cell differentiation cycle model to realize the entry of cells from the cambium into the xylem;

[0108] Furthermore, the specific implementation method of step S4 includes the following steps:

[0109] S4.1. Based on the expansion rate of cambium cells obtained in step S3, the cambium cell division process is established as follows:

[0110]

[0111] in, Let be the area of ​​the outermost cell of the cambium at time t. The initial area of ​​the cambium cells;

[0112] The model must determine whether the cells entering the xylem differentiate into vessel cells. The model tracks the timing of cell division as the cambium begins to divide each year. After the cambium completes its first division, the cell layer entering the xylem begins to differentiate, forming the initial vessel cells.

[0113] S4.2. The number of cambium divisions required from each duct differentiation to the next duct differentiation is called the duct differentiation cycle. When the number of divisions reaches or exceeds the duct differentiation cycle, the cell layer differentiates into duct cells, and the counting process restarts.

[0114] The number of cell layers D since the last ductal differentiation t The calculation formula is as follows:

[0115] ;

[0116] The formula for judging ductal differentiation is:

[0117]

[0118] Wherein, Div is an indicator variable for duct differentiation. A Div of 1 indicates that one duct differentiates during the division of the cambium cells in that subdivision, while a Div of 0 indicates that no duct differentiates during the division of the cambium cells in that subdivision. The ductal differentiation cycle at time t is calculated using the following formula:

[0119]

[0120] in, For potential ductal differentiation cycles, α is the minimum ductal differentiation cycle, and L is the minimum ductal differentiation cycle. div For the correction rate of ductal differentiation cycle, Trend ca β represents the potential maximum ductal area affected by age, and β is the ductal differentiation rate correction coefficient when the potential maximum ductal area changes.

[0121] Furthermore, the correction rate for vessel differentiation cycle was calculated using the daily water limitation factor and the specific conductance (Ks) in the daily tree rings. Growth rates (gM and gV) under current water limitation quantify the severity of the drought. Trees under drought stress produce more vessels. Specific conductance is the balance between wood water transport and mechanical stability. The model assumes that under favorable climatic conditions, trees have a fixed growth equilibrium to achieve optimal carbon use efficiency. div Calculated using the following formula:

[0122]

[0123]

[0124]

[0125] Among them, Water div The correction rate for the vascular differentiation cycle under water limitation is given by a1, where a1 is the calibration parameter under water limitation, gM is the relative cell growth rate driven by soil moisture, gV is the relative cell growth rate driven by VPD, a2 is the calibration parameter affected by specific conductivity, and Ks is the calibration parameter. div Ks represents the correction rate of the ductal differentiation cycle affected by specific conductivity. s Ks is the optimal specific derivative at the current time. t This represents the actual specific derivative at the current time.

[0126] Due to the differences in hydraulic properties between earlywood and latewood regions, tree growth was calculated using the relative growth rate effect driven by day length. As the amount of carbon allocated to cell wall growth increases, the optimal specific conductivity (Ks) gradually decreases and remains constant at a low threshold, as calculated by the following formula:

[0127]

[0128] Among them, Ks max A represents the maximum value of the optimal catheter ratio throughout the year. ks L is the normalization coefficient. i Ks represents the growth relative rate effect driven by day length. min This represents the minimum optimal catheter ratio for the year.

[0129] S5. Establish models of cell expansion and cell wall thickening to simulate the cell growth process in the xylem until the cell wall lignification process is completed, at which point the cell enters the mature cell stage.

[0130] Furthermore, after cells enter the xylem from the cambium, fiber cells and vessel cells follow the same growth process, but are simulated using different growth parameters. This embodiment uses a set of allometric models of cell expansion and cell wall thickening to simulate the cell growth process. Specifically, in the initial growth stage, the cell area (CA) and lumen area (LA) expand rapidly. As the lumen area increases, the rate of cell wall thickening and lignification also gradually increases. However, when the cell wall thickness increases to a certain extent, the cell expansion rate begins to slow down until a critical point is reached, at which point cell expansion activity completely ceases. But the process of cell wall thickening and lignification continues, leading to a further reduction in the lumen area (LA), which in turn limits the rate of cell wall thickening and lignification. Finally, when the lignification process of the cell wall is complete (LWA=WA), the cell enters the programmed cell death phase.

[0131] Furthermore, the specific implementation method of step S5 includes the following steps:

[0132] S5.1. Establish a model for cell expansion, expressed as:

[0133]

[0134] Where CA represents the cell area. CA represents the current cell expansion rate. max WT represents the maximum surface area of ​​the cell, and WT represents the cell wall thickness. The threshold thickness at which cell expansion stops;

[0135] Furthermore, the age trend of tree growth is reflected in the maximum vessel surface area. The CA (cathode area) is calculated annually using a formula in the simulated vessel system. max :

[0136]

[0137] in, The maximum potential area of ​​the cell surface, Trend ca The largest cell area affected by age;

[0138] S5.2. Establish a model for cell wall thickening. Assuming that cells are rectangular due to their mutual interaction, the formula for calculating WT is:

[0139]

[0140] Where CTD is the tangential dimension of the cell, CRD is the radial dimension of the cell, and WA is the cell wall area; for fibroblasts, CTD remains constant during morphogenesis, while CRD is calculated at each time step (CRD = CA / CTD). For ductal cells, both CTD and CRD are calculated at each time step (CTD = CRD = CA). 0.5 ).

[0141] The formula for calculating the rate of cell wall expansion is:

[0142]

[0143] in, WA represents the current cell wall deposition rate. max m is the maximum potential surface area of ​​the cell wall. w For the first calibration parameter, s w For the second calibration parameter, Death is a Boolean variable;

[0144] Cell death is defined when the cell wall becomes completely lignified. The "Death" parameter is a function related to the Wake-Up Call (WA) mechanism, as shown below:

[0145]

[0146] Where LWA is the area of ​​the lignified wall;

[0147] The formula for calculating cell wall lignification is:

[0148]

[0149] in, m represents the current cell wall lignification rate. l and s l These are the third calibration parameter and the fourth calibration parameter, respectively.

[0150] Furthermore, the relative growth response to climate modulates the annual variation in cell growth rate. Therefore, the cell growth rate at time t is calculated using the following formula:

[0151]

[0152]

[0153]

[0154] in, This represents the theoretical maximum rate of cell expansion. This represents the theoretical maximum rate of cell wall thickening. This represents the theoretical maximum rate of cell wall lignification.

[0155] Furthermore, the change in day length is used to distinguish cell wall growth changes at the beginning and end of the growing season, as shown in the following formula:

[0156]

[0157]

[0158] in, The growth relative rate effect is driven by day length. Ls is the change in sunshine duration at time t. t Let Ls be the duration of sunshine at time t. t - 1 Let t be the duration of sunshine the day before.

[0159] S6. Based on the mature cell stage, calculate the annual ring width and anatomical features to complete the simulation process of broad-leaved tree wood formation and radial growth using climate data.

[0160] Furthermore, in step S6, the width of the tree rings is determined by the ratio of the total cell area to the width of the simulated region, and the change in the width of the tree rings over time is given by the formula:

[0161]

[0162] Where RW is the width of the annual rings, and CA is the width of the annual rings. i Let T be the area of ​​the i-th cell within the simulation region, and n be the number of cells within the simulation region. width This represents the tangential width of the simulated region.

[0163] Furthermore, anatomical features, including xylem anatomical parameters such as vessel density, vessel lumen area sequence, fiber lumen area sequence, and cell wall thickness sequence, enable the complete reconstruction of the microstructure of annual rings.

[0164] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0165] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A method for simulating the formation and radial growth of broadleaf tree timber using climate data, characterized in that, The steps include the following: S1. The input data collected includes the latitude data of the target area and the long-term daily meteorological data of the target area, including the daily average temperature, daily precipitation, daily average atmospheric humidity, daily average saturated water vapor pressure difference, soil moisture and day length; S2. Establish the cambium activation conditions for broad-leaved trees. When the effective accumulated temperature and day length exceed the set thresholds, proceed to the next step. S3. Convert the climate-driven growth response into dimensionless climate-driven relative cell growth rates, then calculate the relative growth rate of cell expansion egR, the relative growth rate of cell wall deposition wgR, and the relative growth rate of cambium cells czgR, and calculate the expansion rate of cambium cells. ; S4. Based on the expansion rate of cambium cells obtained in step S3, establish a cambium cell division model and a vessel cell differentiation cycle model to realize the entry of cells from the cambium into the xylem; S5. Establish models of cell expansion and cell wall thickening to simulate the cell growth process in the xylem until the cell wall lignification process is completed, at which point the cell enters the mature cell stage; S6. Based on the mature cell stage, calculate the annual ring width and anatomical features to complete the simulation process of broad-leaved tree wood formation and radial growth using climate data.

2. The method for simulating broadleaf tree wood formation and radial growth using climate data according to claim 1, characterized in that, The formula for calculating the effective accumulated temperature in step S2 is: ； Where T is the daily average temperature, T min AT represents the minimum temperature required for tree growth, and AT represents the effective accumulated temperature.

3. The method for simulating broadleaf tree wood formation and radial growth using climate data according to claim 2, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. Convert climate-driven growth response into dimensionless climate-driven relative cell growth rate; The formula for calculating the relative rate of cell growth, gE, driven by day length is: ； Where Q represents atmospheric radiation. This refers to the annual average atmospheric radiation. The formula for calculating the temperature-driven relative rate of cell growth, gT, is as follows: ； Where T is temperature. Let R be the activation enthalpy, R be the gas constant, and A be the normalization coefficient. and These are the enthalpy and entropy that affect the reversible denaturation of enzymes, respectively; T min The lowest temperature for tree growth, T max This is the highest temperature for tree growth; gM represents the relative cell growth rate driven by soil moisture, and gV represents the relative cell growth rate driven by VPD. Both are calculated in a piecewise manner. S3.

2. Calculate the relative growth rate of cell expansion at time t, egR t The relative growth rate of cell wall deposition, wgR t The relative growth rate of cambium cells czgR t The calculation formula is: ； ； ； in, The growth rate of the initial region of the cambium. The growth rate is affected by the cambium width. The width of the forming layer; S3.

3. Calculate the expansion rate of cambium cells at time t. The calculation formula is: ； in, It is the theoretical maximum expansion rate of cambium cells, Trend cz The potential impact of age on cambium activity; ； in, The normalization coefficient is... This represents the rate of change in cell expansion rate with age. The age of the tree.

4. The method for simulating broadleaf tree wood formation and radial growth using climate data according to claim 3, characterized in that, The specific implementation method of step S4 includes the following steps: S4.

1. Based on the expansion rate of cambium cells obtained in step S3, the cambium cell division process is established as follows: ； in, Let be the area of ​​the outermost cell of the cambium at time t. The initial area of ​​the cambium cells; S4.

2. The number of cambium divisions required from each duct differentiation to the next duct differentiation is called the duct differentiation cycle. When the number of divisions reaches or exceeds the duct differentiation cycle, the cell layer differentiates into duct cells, and the counting process restarts. The number of cell layers D since the last ductal differentiation t The calculation formula is as follows: ； The formula for judging ductal differentiation is: ； Wherein, Div is an indicator variable for duct differentiation. A Div of 1 indicates that one duct differentiates during the division of the cambium cells in that subdivision, while a Div of 0 indicates that no duct differentiates during the division of the cambium cells in that subdivision. The ductal differentiation cycle at time t is calculated using the following formula: ； in, For potential ductal differentiation cycles, α is the minimum ductal differentiation cycle, and L is the minimum ductal differentiation cycle. div For the correction rate of ductal differentiation cycle, Trend ca β represents the potential maximum ductal area affected by age, and β is the ductal differentiation rate correction coefficient when the potential maximum ductal area changes.

5. The method for simulating broadleaf tree wood formation and radial growth using climate data according to claim 4, characterized in that, The specific implementation method of step S5 includes the following steps: S5.

1. Establish a model for cell expansion, expressed as: ； Where CA represents the cell area. CA represents the current cell expansion rate. max WT represents the maximum surface area of ​​the cell, and WT represents the cell wall thickness. The threshold thickness at which cell expansion stops; S5.

2. Establish a model for cell wall thickening. Assuming that cells are rectangular due to their mutual interaction, the formula for calculating WT is: ； Where CTD is the tangential dimension of the cell, CRD is the radial dimension of the cell, and WA is the cell wall area; The formula for calculating the rate of cell wall expansion is: ； in, WA represents the current cell wall deposition rate. max m is the maximum potential surface area of ​​the cell wall. w For the first calibration parameter, s w For the second calibration parameter, Death is a Boolean variable; Cell death is defined when the cell wall becomes completely lignified. The "Death" parameter is a function related to the Wake-Up Call (WA) mechanism, as shown below: ； Where LWA is the area of ​​the lignified wall; The formula for calculating cell wall lignification is: ； in, m represents the current cell wall lignification rate. l and s l These are the third calibration parameter and the fourth calibration parameter, respectively.

6. The method for simulating broadleaf tree wood formation and radial growth using climate data according to claim 5, characterized in that, In step S6, the width of the tree rings is determined by the ratio of the total cell area to the width of the simulated region. The change in tree ring width over time is given by the formula: ； Where RW is the width of the annual rings, and CA is the width of the annual rings. i Let T be the area of ​​the i-th cell within the simulation region, and n be the number of cells within the simulation region. width This represents the tangential width of the simulated region.

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