A method for predicting leaf area index

Abstract

The application provides a leaf area index prediction method, which comprises the following steps: calculating the length of a growth season of vegetation by using a GSI model, solving an annual total leaf area index based on meteorological variables, and predicting a seasonal daily maximum leaf area index LAI SM , simulating a steady-state leaf area index LAI s , satisfying LAI s ≤LAI SM , based on LAI s , predicting a leaf area index time series LAI TS by using a restrictive growth process model, and constraining a LAI time series to be simulated by the predicted LAI SM , wherein the prediction of LAI SM only uses meteorological variables, vegetation phenology under future climate change can be predicted, and then the spatiotemporal distribution of leaf area index related indexes at a local to global scale can be evaluated and analyzed; the prediction method provided by the application can be embedded into an existing land surface model, and the dynamic change of the leaf area index LAI of global biomes can be more stably and accurately predicted.

Description

Technical Field

[0001] This invention belongs to the field of vegetation phenology prediction, and in particular relates to a method for predicting leaf area index. Background Technology

[0002] Establishing ecosystem process models is a scientific foundation for addressing climate change. Terrestrial biosphere models provide insights into how vegetation responds to changing climate. Vegetation phenology, generally reflected by leaf area index (LAI) or key phenological periods, is a sensitive indicator of ecosystem response to climate change, and its changes affect ecosystem processes such as evapotranspiration and carbon balance. While current vegetation phenology models can predict the timing of phenological events, such as budding and leaf fall, many models do not explicitly predict the seasonally maximum LAI, thus failing to simulate LAI time series. Current methods for obtaining LAI include field measurements, satellite-based inversion, and model simulations.

[0003] Field measurements are difficult to obtain on a large scale, have limited coverage, and are greatly affected by measuring instruments and vegetation characteristics. Satellite-based inversion often uses remote sensing data, but satellite observations are easily affected by factors such as clouds and shadows, reducing data quality and affecting the accuracy of vegetation index estimation. Furthermore, due to the time scale and timeliness of remote sensing images, satellite-based prediction models can only simulate historical and current ecosystem phenological processes, often leading to errors in predictions under future climate change. Simulations based on numerical phenology models combine multiple empirical equations, simulating the phenology of only a few vegetation types at a coarse spatial resolution. Their high empirical nature results in insufficient simulation accuracy.

[0004] In vegetation phenology predictions under future climate change, the seasonal maximum LAI is a crucial determining parameter. Besides using prescribed values ​​or satellite remote sensing data, existing dynamic vegetation and land surface models mostly obtain the seasonal maximum LAI by simulating the average LAI at the individual plant level, primarily based on vegetation traits such as stem diameter and root mass. Some of these attribute variables are difficult to obtain, and significant uncertainties remain on a large scale or globally. Furthermore, the seasonal maximum LAI used in existing prediction models cannot be directly obtained from meteorological variables. Summary of the Invention

[0005] Based on this, the present invention proposes a leaf area index (LAI) prediction method, which predicts LAI by constraining meteorological variables. SM And then by LAI SM Constrained steady-state LAI, used to simulate LAI over a future period of time. TS This is to overcome the shortcomings of existing prediction models.

[0006] This invention provides a leaf area index prediction method, comprising:

[0007] The length of the growing season for vegetation was calculated using the GSI model.

[0008] Calculating the annual total leaf area index based on meteorological variables;

[0009] LAI is predicted based on annual total leaf area index and vegetation growing season length. SM LAI SM Indicates the seasonal maximum daily leaf area index;

[0010] Simulated daily steady-state leaf area index (LAI) s To meet LAI s ≤LAI SM ;

[0011] Based on LAI s Using a limiting growth process model to predict the time series leaf area index (LAI) TS .

[0012] Furthermore, LAI was predicted based on leaf area index and vegetation growing season length. SM As shown in the following formula

[0013]

[0014] LAI AS denoted by Total Leaf Area Index, GSL represents the number of growing days from greening to dormancy, and s represents the slope of the linear coefficient.

[0015] Furthermore, the calculation of the growing season length of vegetation using the GSI model includes:

[0016] Using the expression iGSI=iTMIN×iVPD×iPHO, the instantaneous growth season index iGSI is calculated based on the normalized daily minimum temperature, daily vapor pressure deficit, and sunshine duration. iTMIN represents the normalized daily minimum temperature, iVPD represents the normalized vapor pressure deficit, and iPHO represents the normalized sunshine duration.

[0017]

[0018]

[0019]

[0020] Where TMIN, VPD, and PHO represent the daily minimum temperature, daily vapor pressure deficit, and sunshine duration, respectively. min and TMIN max VPD represents the lower and upper limits of the daily minimum temperature that restricts vegetation growth. min and VPD maxPHO represents the lower and upper limits of daily vapor pressure deficit that restrict vegetation growth, respectively. min and PHO max These represent the lower and upper limits of sunlight duration that restrict vegetation growth, respectively. The above parameters are calibrated to TMIN. min = -0.76℃, TMIN max =6.65℃, VPD min =0.70kPa, VPD max =1.74kPa, PHO min =8h, PHO max =11h;

[0021] The daily GSI time series was calculated using a 21-day moving average. The number of days within the seasonal circle where the daily GSI exceeded the amplitude by 10% was used as the annual growing season length (GSL) of the vegetation, expressed by the following expression.

[0022]

[0023] iGSI represents the daily growth seasonal index calculated using a 21-day moving average. max and iGSI min These represent the maximum and minimum values ​​in the daily GSI time series, respectively.

[0024] Furthermore, solving for the leaf area index based on meteorological variables includes:

[0025] Based on the Budyko curve equation, the annual total leaf area index (LAI) was established. AS The relationship with meteorological variables is as follows:

[0026]

[0027] f(Rg)=0.95·PAR·ε max PAR = Rg·0.45

[0028] f(Prec) = P·θ max ,

[0029]

[0030] Where f(Rg) and f(Prec) represent the maximum assimilation rate constrained by radiation and precipitation, respectively, represents the parameters of the bottom surface, which vary with plant functional type and external environmental factors, PAR represents annual photosynthetically active radiation, and ε max θ represents the maximum light energy utilization rate, P represents the annual precipitation, and θ represents the annual precipitation. max Indicates the maximum rainwater utilization rate. The function represents the daily GSI annual average, ΔT represents the temperature difference of the annual average temperature in a year, Elev represents the altitude of each station or each pixel, and a, b, c and d are calibration parameters.

[0031] Furthermore, the leaf area index time series LAI TS The prediction is expressed by the following formula.

[0032]

[0033] LAI represents the actual leaf area index at a diurnal scale, k leaf This represents the time constant, indicating the lag response of vegetation to climate change when allocating biomass to its leaves.

[0034] Furthermore, the daily steady-state leaf area index (LAI) s Prediction is performed using the following closed-ended equation.

[0035] LAI s =m×GPP s ,

[0036] GPP s =ε max ×PAR×f(TMIN)×f(VPD)×(1-exp(-kLAI s )),

[0037] m represents the ratio of leaf area index to total primary productivity (GPP) under canopy closure conditions. s Indicates the steady-state leaf area index (LAI) s The corresponding total primary productivity, ε max PAR represents the maximum light energy utilization rate, f(TMIN) and f(VPD) represent scalar functions, respectively illustrating the limiting effects of daily minimum temperature and daily vapor pressure deficit on vegetation canopy photosynthesis, and k represents the canopy extinction coefficient, with a value of 0.5.

[0038] Furthermore, the Newton-Raphson method is used to find approximate solutions for the closed-form equations.

[0039] Furthermore, the scalar functions f(TMIN) and f(VPD) are calculated using the MOD17 model as follows:

[0040]

[0041]

[0042] Where TMIN and VPD represent the daily minimum temperature and daily vapor pressure deficit, respectively. min and TMIN maxVPD represents the lower and upper limits of the daily minimum temperature that restricts canopy photosynthesis, respectively. min and VPD max These represent the lower and upper limits of the daily vapor pressure deficit that restricts canopy photosynthesis, respectively.

[0043] Furthermore, LAI is obtained based on the Lambert W function. s The analytical solution is obtained through the following process:

[0044] Let μ = m × ε max ×PAR×f(TMIN)×f(VPD), then the steady-state leaf area index (LAI) is calculated. s It can be represented as LAI s =μ×(1-exp(-kLAI) s ));

[0045] Let y = kμ - kLAI s Then we have y·exp(-y)=kμ·exp(-kμ);

[0046] Using the Lambert W function to solve for y·exp(-y)=kμ·exp(-kμ), we have y=W0·(-kμ·exp(-kμ)), where W0 represents the Lambert W function operator, i.e., the function f(z=ze z The inverse relation, e z Let z denote an exponential function, and z denote a complex number. The range of -kμ·exp(-kμ) is (-e^(-kμ) / k). -1 ,0];

[0047] The analytical solution for the steady-state leaf area index is expressed as:

[0048] The present invention also provides an electronic device, including a memory and a processor, the memory being used to store a program that supports the processor in executing the above-described leaf area index prediction method, and the processor being configured to execute the program stored in the memory.

[0049] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program, which, when run by a processor, executes the steps of the above-described leaf area index prediction method.

[0050] As can be seen from the above technical solutions, the present invention has the following beneficial effects:

[0051] This invention proposes a leaf area index (LAI) prediction method. It constrains the simulated LAI time series by predicting the seasonal maximum LAI, where the prediction of the seasonal maximum LAI uses only meteorological variables such as temperature, vapor pressure, sunshine duration, photosynthetic radiation, and precipitation. This method can predict vegetation phenology under future climate change, and further evaluate and analyze the spatiotemporal distribution of LAI-related indicators at local to global scales. The prediction method proposed in this invention can be embedded into existing land surface models, providing a more robust and accurate prediction of the dynamic changes in LAI across various biological communities worldwide. Attached Figure Description

[0052] 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 embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0053] Figure 1 A flowchart of a leaf area index prediction method provided in an embodiment of the present invention;

[0054] Figure 2 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0055] 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.

[0056] Example 1

[0057] According to an embodiment of the present invention, an embodiment of a leaf area index prediction method is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0058] See Figure 1 The method includes:

[0059] The length of the growing season for vegetation was calculated using the GSI model.

[0060] Calculating the annual total leaf area index based on meteorological variables;

[0061] LAI is predicted based on annual total leaf area index and vegetation growing season length. SM LAI SM Indicates the seasonal maximum daily leaf area index;

[0062] Simulated daily steady-state leaf area index (LAI) s To meet LAI s ≤LAI SM ;

[0063] Based on steady-state leaf area index (LAI) s Using a limiting growth process model to predict the time series leaf area index (LAI) TS .

[0064] Specifically, calculating the growing season length of vegetation using the GSI model includes:

[0065] Using the expression iGSI=iTMIN×iVPD×iPHO, the instantaneous growth season index iGSI is calculated based on the normalized daily minimum temperature, daily vapor pressure deficit, and sunshine duration. iTMIN represents the normalized daily minimum temperature, iVPD represents the normalized vapor pressure deficit, and iPHO represents the normalized sunshine duration.

[0066]

[0067]

[0068]

[0069] Where TMIN, VPD, and PHO represent the daily minimum temperature, daily vapor pressure deficit, and sunshine duration, respectively. MIN and TMIN MAX VPD represents the lower and upper limits of the daily minimum temperature that restricts vegetation growth. MIN and VPD MAX PHO represents the lower and upper limits of daily vapor pressure deficit that restrict vegetation growth, respectively. MIN and PHO MAX These represent the lower and upper limits of sunlight duration that restrict vegetation growth, respectively.

[0070] The daily GSI time series was calculated using a 21-day moving average. The number of days within the seasonal circle where the daily GSI exceeded the amplitude by 10% was used as the annual growing season length (GSL) of the vegetation, expressed by the following expression.

[0071]

[0072] iGSI represents the daily growth seasonal index calculated using a 21-day moving average.max and iGSI min These represent the maximum and minimum values ​​in the daily GSI time series, respectively.

[0073] Specifically, solving the leaf area index based on meteorological variables includes:

[0074] Based on the Budyko curve equation, the annual total leaf area index (LAI) was established. AS The relationship with meteorological variables is as follows:

[0075]

[0076] f(Rg)=0.95·PAR·ε max PAR = Rg·0.45

[0077] f(Prec) = P·θ max ,

[0078]

[0079] Where f(Rg) and f(Prec) represent the maximum assimilation rate constrained by radiation and precipitation, respectively, represents the parameters of the bottom surface, which vary with plant functional type and external environmental factors, PAR represents annual photosynthetically active radiation, and ε max The maximum light energy utilization efficiency is represented by P, and the annual precipitation is represented by θ. max Indicates the maximum rainwater utilization rate. The function represents the daily GSI annual average, ΔT represents the temperature difference of the annual average temperature in a year, Elev represents the altitude of each station or each pixel, and a, b, c and d are calibration parameters.

[0080] After obtaining the annual total leaf area index and vegetation growing season length using meteorological variables, the predicted LAI is constrained by a linear function relationship expressed by the following formula. SM ,

[0081]

[0082] LAI AS denoted by Total Leaf Area Index, GSL represents the number of growing days from greening to dormancy, and s represents the slope of the linear coefficient.

[0083] Specifically, the daily steady-state leaf area index (LAI) s Prediction is performed using the following closed-ended equation.

[0084] LAI s =m×GPP s ,

[0085] GPP s =εmax ×PAR×f(TMIN)×f(VPD)×(1-exp(-kLAI s )),

[0086] m represents the ratio of leaf area index to total primary productivity (GPP) under canopy closure conditions. s Indicates the steady-state leaf area index (LAI) s The corresponding total primary productivity, ε max PAR represents the maximum light energy utilization rate, f(TMIN) and f(VPD) represent scalar functions, respectively illustrating the limiting effects of daily minimum temperature and daily vapor pressure deficit on vegetation canopy photosynthesis, and k represents the canopy extinction coefficient, with a value of 0.5.

[0087] For the closed equation above, the Newton-Raphson method can be used to find an approximate solution.

[0088] Based on the MOD17 model, the scalar functions f(TMIN) and f(VPD) are calculated as follows:

[0089]

[0090]

[0091] Where TMIN and VPD represent the daily minimum temperature and daily vapor pressure deficit, respectively. min and TMIN max VPD represents the lower and upper limits of the daily minimum temperature that restricts canopy photosynthesis, respectively. min and VPD max These represent the lower and upper limits of the daily vapor pressure deficit that restricts canopy photosynthesis, respectively.

[0092] Given that the MOD17 model has a simple expression, the LAI can be obtained based on the Lambert W function. s The analytical solution is obtained through the following process:

[0093] Let μ = m × ε max ×PAR×f(TMIN)×f(VPD), then the steady-state leaf area index (LAI) is calculated. s It can be represented as LAI s =μ×(1-exp(-kLAI) s ));

[0094] Let y = kμ - kLAI s Then we have y·exp(-y)=kμ·exp(-kμ);

[0095] Using the Lambert W function to solve for y·exp(-y)=kμ·exp(-kμ), we have y=W0·(-kμ·exp(-kμ)), where W0 represents the Lambert W function operator, i.e., the function f(z=ze z The inverse relation, e z Let z denote an exponential function, and z denote a complex number. The range of -kμ·exp(-kμ) is (-e^(-kμ) / k). -1 ,0];

[0096] The analytical solution for the steady-state leaf area index is expressed as:

[0097] Example 2

[0098] This embodiment describes the leaf area index prediction method provided by the present invention from the perspective of model building.

[0099] 1. Seasonal maximum leaf area index (LAI) SM Prediction

[0100] Previous studies have shown that changes in annual terrestrial gross primary productivity (GPP) can be explained by a robust index: plant physiological and phenological characteristics. Similar to the method used to derive GPP, to illustrate the impact of plant phenology and physiological activity on land area index (LAI), this invention proposes a prediction method that constrains potential LAI using a linear function of the interannual LAI capacity of the vegetation canopy and the length of the growing season. SM As shown below, this linear relationship is robust.

[0101]

[0102] Among them, LAI here SM (Unit: leaf area m²) 2 / ground area (m²) 2 () represents the seasonal maximum day LAI for a given year; LAI AS represents the total leaf area index for the year, which is the sum of the daily LAI for a given year; the growing season length (GSL) of vegetation represents the number of growing days from the greening-up date to the dormant date, and s represents the slope of the linear coefficient.

[0103] In order to predict LAI SM The purpose is to solve LAI using meteorological variables. AS And GSL.

[0104] (1) Vegetation growing season length LAI AS Acquisition

[0105] There are generally two ways to obtain the length of the growing season. One method is to calculate the timing of key phenological periods in vegetation growth using modeling methods. For example, the budding and leaf fall GDD (CDD) model, which corresponds to the beginning and end of the growing season, is widely used to predict greening (withering). This model was developed for temperate biomes, where key phenological periods are easily defined. However, because vegetation phenology is influenced by various environmental factors, the limitation of a single temperature is empirical and insufficient for calculating the length of the growing season in multi-biome communities. Alternatively, the length of the growing season can be obtained by extracting key nodes (i.e., the beginning and end of the season) from the time series of vegetation indices using existing rule-based algorithms.

[0106] Another widely used method, the Growing Season Index (GSI) model developed by Jolly et al., is capable of simulating time series of growing season indices from field to global scales based on existing climate factors. Its results are consistent with the trends of the Normalized Difference Vegetation Index (NDVI) and the LAI. Therefore, the method of this invention draws on the GSI model to obtain the length of the growing season of vegetation.

[0107] The principle of this method is to first use the product of normalized daily minimum temperature, vapor pressure deficit, and light duration as the instantaneous GSI, and then calculate the time series of daily GSI using a 21-day moving average. Based on this, the method of this invention uses the amplitude threshold method to define the number of days in the entire seasonal cycle where the daily GSI exceeds 10% of its amplitude as the length of the annual growing season for vegetation. The specific calculation formula is as follows:

[0108] iGSI=iTMIN×iVPD×iPHO (2)

[0109]

[0110] Among them, iGSI represents the instantaneous growth index, iTMIN represents the normalized daily minimum temperature, iVPD represents the normalized vapor pressure deficit, and iPHO represents the normalized sunshine duration. These are the limiting factors for vegetation canopy development. The daily GSI is calculated from the 21-day moving average of the instantaneous GSI; iGSI max and iGSI min These represent the maximum and minimum values ​​in the daily GSI time series, respectively.

[0111] The three climate indicators are determined as follows:

[0112]

[0113]

[0114]

[0115] Where TMIN, VPD, and PHO represent the daily minimum temperature, daily vapor pressure deficit, and sunshine duration, respectively. MIN and TMIN MAX VPD represents the lower and upper limits of the daily minimum temperature that restricts vegetation growth. MIN and VPD MAX PHO represents the lower and upper limits of daily vapor pressure deficit that restrict vegetation growth, respectively. MIN and PHO MAX These represent the lower and upper limits of sunlight duration that restrict vegetation growth, respectively. In this embodiment, the above parameters are calibrated to TMIN. MIN = -0.76℃, TMIN MAX =6.65℃, VPD MIN =0.70kPa, VPD MAX =1.74kPa, PHO MIN =8h, PHO MAX =11h.

[0116] (2) Annual Total Leaf Area Index (LAI) AS Analysis

[0117] Climate conditions have a decisive influence on natural processes on the Earth's surface and are a primary concern in terrestrial ecosystem models regarding how to regulate carbon balance. The Budyko hydroclimatology model (also known as the "Budyko curve"), first proposed by Budyko, effectively describes the relationship between surface water cycle and energy balance, and successfully provides an important theoretical tool for assessing the sensitivity between climate and other environmental factors. With the increasing influence of the Budyko curve on the hydrological and climatological communities, international scholars have constructed different forms of the Budyko equation through improvement, derivation, and simplification, and these have been widely applied in various research fields. Considering the close relationship between the carbon cycle and the hydro-energy cycle, Y. Yang, Donohue, McVicar, and Roderick (2015) have demonstrated that carbon cycle modeling can be represented by a generalized, Budyko-like rate-limiting framework, indicating that canopy photosynthesis is partially constrained by surface energy and water supply. Based on this core idea, the prediction method of this invention also uses a Budyko-like curve framework to represent the annual total leaf area index (LAI). AS :

[0118]

[0119] Where f(Rg) and f(Prec) represent the maximum assimilation rate constrained by radiation and precipitation, respectively, and represent the parameters of the bottom surface, which vary with plant functional type and external environmental factors.

[0120] f(Rg)=0.95·PAR·ε max PAR=Rg·0.45 (8)

[0121] f(Prec) = P·θ max (9)

[0122]

[0123] Wherein, PAR (unit: MJ / m 2 ) represents annual photosynthetically active radiation; ε max (Unit: gC / MJ) represents maximum light energy utilization efficiency; P (unit: mm / year) represents annual precipitation; θ max (Unit: m) 2 / m 2 ( / mm) represents the maximum rainwater utilization rate, affected by LAI. AS (Unit: m) 2 / m 2 The constraint of the ratio of annual precipitation (in mm) to total annual precipitation; the coefficient 0.95 indicates f PAR The maximum possible amount of incident PAR absorbed by the canopy; The function represents the daily GSI annual average, ΔT represents the temperature difference of the annual average temperature in a year; Elev represents the altitude of each station or each pixel; a, b, c and d are calibration parameters.

[0124] 2. Establishment of vegetation phenology prediction model

[0125] A linear relationship was established between vegetation productivity (i.e., light utilization efficiency in the MOD17 model) and steady-state LAI, and the steady-state LAI was simulated using analytical solutions based on the Lambert-W equation, with the previously predicted LAI... SM To constrain the simulated steady-state LAI, a simple restricted growth process model is used to obtain the predicted LAI time series. TS .

[0126] Taking into account daily weather conditions, the steady-state LAI for a day is simulated using the following closed-form equation:

[0127] LAI s =m×GPP s (11)

[0128] GPP s =ε max ×PAR× f(TMIN)×f(VPD)×(1-exp(-kLAI s (12)

[0129] Among them, LAI sRepresents steady-state LAI; m represents the ratio of leaf area index to total primary productivity under canopy closure conditions; GPP s Indicates the steady-state leaf area index (LAI) s Corresponding total primary productivity; ε max PAR represents the maximum light energy utilization rate; f(TMIN) and f(VPD) represent scalar functions, respectively illustrating the limiting effects of daily minimum temperature and daily vapor pressure deficit on vegetation canopy photosynthesis; k represents the canopy extinction coefficient, with a value of 0.5.

[0130] According to the MOD17 model, the scalar functions represented by f(TMIN) and f(VPD) are calculated by the following expressions:

[0131]

[0132]

[0133] Where TMIN and VPD represent the daily minimum temperature and daily vapor pressure deficit, respectively. min and TMIN max VPD represents the lower and upper limits of the daily minimum temperature that restricts canopy photosynthesis, respectively. min and VPD max These represent the lower and upper limits of the daily vapor pressure deficit that restricts canopy photosynthesis, respectively.

[0134] Since equations (11) and (12) are closed-form equations, the Newton-Raphson method can be used to obtain approximate solutions. Furthermore, since the MOD17 model represented by equations (12), (13), and (14) has a simplified form, the analytical solution can be obtained using the following method:

[0135] Let μ be an intermediate variable, as shown below:

[0136]

[0137] Substituting μ into equations (11) and (12), we get:

[0138] LAI s =μ×(1-exp(-kLAI) s (16)

[0139] Let y be another intermediate variable, as follows:

[0140] y = kμ - kLAI s (17)

[0141] Substituting y into equation (16), we get:

[0142] y·exp(-y)=kμ·exp(-kμ) (18)

[0143] Equation (18) can be solved directly using the Lambert W function, as shown below:

[0144] y=W0·(-kμ·exp(-kμ)) (19)

[0145] Where W0 represents the Lambert W function operator, i.e., the function f(z) = ze z The inverse relation, e z Let z denote an exponential function, and z denote a complex number. Since kμ ≥ 0, the range of -kμ·exp(-kμ) is (-e^(-kμ) / kμ). -1 ,0]

[0146] Substituting equation (19) into equation (17), we obtain the analytical solution as follows:

[0147]

[0148] Among them, the LAI solution s LAI must be met s ≤LAI SM The conditions, LAI SM The seasonal daily maximum canopy leaf area index is obtained by the previous equation (1).

[0149] Due to the dramatic fluctuations in diurnal meteorological conditions, the steady-state LAI varies significantly across different time periods. To illustrate the lagged effects of vegetation phenology on changes in meteorological conditions, a simple limiting growth process model can be used to simulate the time series of actual LAI, as shown below:

[0150]

[0151] Where LAI represents leaf area index, k leaf This represents the time constant, indicating the lag response of vegetation to climate change when allocating biomass to its leaves.

[0152] 3. Model calibration and evaluation

[0153] For different plant functional types (PFTs), the model was parameterized at the site scale using 80% of the flux tower sites and at the global scale using 36,000 pixels (4,000 pixels randomly selected for each PFT). First, LAI derived from reprocessed satellite products was used. SM LAI ASThe parameter s in formula (1) is calibrated using GSL (the sum of the number of days in which the daily LAI exceeds 20% of the seasonal amplitude). Due to the large differences in the number of sites among different PFTs, a uniform parameter s is calibrated for all PFTs at the site scale to avoid overfitting at the site scale.

[0154] Secondly, regarding LAI AS In the equations, multi-year average meteorological variables from 2001 to 2010 are used for global-scale model parameterization. Due to the insufficient proportion of the CSH category, it is merged into the OSH category for unified calibration. For different PFTs, the model in this embodiment adopts the latest maximum light energy utilization (LUE) parameter scheme in the MOD17 algorithm. Rainwater utilization (RUE) can be obtained by considering the LAI of the study location or pixel. AS The value is obtained by dividing the corresponding annual precipitation, and then the 95th percentile value of RUE is determined as θ for different PFTs. max To optimize model parameters, this embodiment implements the Shuffled Complex Evolution (SCE-UA) algorithm during the model calibration process. This is an effective and robust global optimization method that minimizes the root mean square error (RMSE) between the model and the observed data.

[0155] Table 1. Model parameters for different plant functional types (PFT) at the site scale.

[0156]

[0157]

[0158] ENF, Evergreen coniferous forest; EBF, Evergreen broad-leaved forest; DBF, Deciduous broad-leaved forest; MIF, Mixed forest; CSH, Closed shrubland; OSH, Open shrubland; WSA, Woody savanna; SAV, Savanna; GRA, Grassland.

[0159] Table 2 Model parameters for different plant functional types (PFT) at a global scale

[0160]

[0161] DNF represents deciduous coniferous forest.

[0162] Tables 1 and 2 list the specific parameter settings for model calibration at the site and global scales, respectively, and apply them to predict vegetation LAI. SM It was then used to predict LAI at two scales. TS The parameters of the model are shown in Table 3.

[0163] Table 3 Model parameters for different plant functional types (PFT) simulating vegetation dynamics

[0164]

[0165]

[0166] To evaluate the performance of the model in this embodiment, four commonly used metrics were employed, targeting different simulation results: Pearson correlation coefficient (r), Nash efficiency coefficient (NSE), root mean square error (RMSE), and mean bias error (Bias). LAI data was derived from the reprocessed remote sensing dataset. SM and LAI TS It is used as reference data to evaluate the accuracy of the model. Generally, a more accurate model achieves higher r or NSE, and lower RMSE and bias error compared to the reference data.

[0167] By comparing the LAI obtained from global PVPM, GFDL-CM4, CESM2 simulations and satellite inversions in 2008 SM The spatial distributions of the Nash-Sutcliffe efficiency index (NSE), root mean square error (RMSE), and mean bias error (Bias) among the models illustrate the performance of each model in acquiring LAI from remote sensing products. SM Performance regarding intra-annual variation. In most parts of the world, the NSE between the modeling results (represented by PVPM) and the observed results of the prediction model established in this embodiment is close to 1, and the corresponding RMSE is less than 0.5m. 2 / m 2 The absolute deviation is less than 1m 2 / m 2 This verifies the robustness and reliability of the model. In high-latitude regions, considering the differences in shrub species, PVPM's LAI (Location Indication Level)... SM Slightly larger than observed values. Compared to PVPM, the NSE between simulated and observed results from the comparative model GFDL-CM4 and CESM2 shows similar results in Shanghai and most other regions, both close to 1. However, the GFDL-CM4 model generally overestimates LAI in high-latitude regions. SM The predicted values, compared to satellite data, underestimate LAI in the tropics. SM .

[0168] By comparing model results and satellite data, LAI (Laser Artificial Intelligence) was obtained from global PVPM, GFDL-CM4, and CESM2 simulations and satellite inversions from 2001 to 2017. TSThe spatial distribution of the correlation coefficient (r), root mean square error (RMSE), and mean bias error (Bias) between the models illustrates their performance in capturing interannual LAI variations. PVPM performs well in most regions, with low RMSEs and bias, except for slightly higher estimates in Central Africa. In contrast, the r-value between the LAI simulated by the contrastive model GFDL-CM4 and the LAI retrieved from satellites is not high. GFDL-CM4 tends to overestimate LAI on a pixel-by-pixel scale, as evidenced by its positive bias in most regions, similar to its LAI distribution. SM CESM2 captures the LAI variation in Central Africa and Central South America, which is dominated by EBF, very well, although it overestimates the LAI in North America and Southwest China.

[0169] Example 3

[0170] refer to Figure 2 The present invention also provides an electronic device, including a memory and a processor. The memory is used to store a program that supports the processor in executing the methods described in Embodiments 1 and 2 above. The processor is configured to execute the program stored in the memory.

[0171] The electronic device may include: at least one processor 1, at least one communication interface 2, at least one memory 3, and at least one communication bus 4.

[0172] In this embodiment of the application, the number of processor 1, communication interface 2, memory 3, and communication bus 4 is at least one, and processor 1, communication interface 2, and memory 3 communicate with each other through communication bus 4;

[0173] Processor 1 may be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method can be completed by the integrated logic circuitry in the hardware of processor 1 or by instructions in software form. Processor 1 can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; it can also be a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this invention. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this invention can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software module can reside in a mature storage medium in the field, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory 3. Processor 1 reads the information from memory 3 and, in conjunction with its hardware, completes the steps of the above method.

[0174] Memory 3 may include high-speed RAM, or non-volatile memory, such as at least one disk drive. Communication between this system network element and at least one other network element is achieved through at least one communication interface 2 (which can be wired or wireless), such as the Internet, wide area network, local area network, metropolitan area network, etc.

[0175] Bus 4 can be an ISA bus, PCI bus, or EISA bus, etc., and this bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 2 The symbol is represented by a single double-headed arrow, but this does not mean that there is only one bus or one type of bus.

[0176] The memory stores a program, which the processor can call to implement the leaf area index prediction method in the example above.

[0177] Example 4

[0178] This invention also provides a computer-readable storage medium storing a computer program, which, when run by a processor, executes the steps of the methods described in Embodiments 1 and 2 above.

[0179] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method of predicting leaf area index, characterized by, Comprising: calculating the length of the growing season of the vegetation using a GSI model; Based on the Budyko curve equation, the annual total leaf area index The relationship with meteorological variables is as follows ， ， ， ， ， where, and respectively represent the maximum assimilation rate constrained by radiation and precipitation, and represent the parameters of the bottom surface, which vary with plant functional types and external environmental factors, represents the annual photosynthetically active radiation, represents the maximum light use efficiency, represents the annual precipitation, represents the maximum rainwater use efficiency, represents the function of the annual average of daily GSI, represents the temperature difference of the annual average temperature in a year, represents the elevation of each site or each pixel, and is a calibration parameter; According to the annual total leaf area index and vegetation growing season length prediction , denotes the seasonal maximum daily leaf area index, which is the The prediction of the seasonal maximum daily leaf area index is given by the following equation: ， represents the total leaf area index per year, the length of the growing season of the vegetation represents the number of days of growth of the vegetation from the day of green-up to the day of dormancy, represents the linear coefficient slope; Simulating a single day of steady-state leaf area index , satisfying ; Based on , the leaf area index time series is predicted using a restrictive growth process model .

2. The leaf area index prediction method according to claim 1, characterized in that, the calculating the length of the growing season of the vegetation using a GSI model comprises: Using the expression , the instantaneous growing season index is calculated from the normalized daily minimum temperature, daily vapor pressure deficit, and daily sunshine time , denotes the normalized daily minimum temperature, denotes the normalized daily vapor pressure deficit, denotes the normalized daily sunshine time; ， ， ， wherein, , , and respectively represent daily minimum temperature, daily vapor pressure deficit, and daily sunlight time, and respectively represent lower and upper limits of daily minimum temperature that restricts growth of vegetation, and respectively represent lower and upper limits of daily vapor pressure deficit that restricts growth of vegetation, and respectively represent lower and upper limits of daily sunlight time that restricts growth of vegetation, the above parameters are calibrated as = -0.76°C, = 6.65°C, = 0.70 kPa, = 1.74 kPa, = 8 h, = 11 h; The daily GSI time series is calculated by 21-day moving average, and the length of growing season is calculated by the days that the daily GSI exceeds 10% of the amplitude in the seasonal cycle using the amplitude threshold method is expressed by the following expression ， denotes the daily growing season index calculated by a 21-day moving average, and denotes the maximum and minimum, respectively, in the daily GSI time series.

3. The leaf area index prediction method according to claim 1, characterized in that, The leaf area index time series The prediction of the leaf area index time series is represented by the following calculation ， represents the leaf area index, represents the time constant, representing the lagged response of vegetation to climate change in allocating biomass to leaves.

4. The leaf area index prediction method according to claim 1 or 3, characterized by, the single-day steady-state leaf area index predicted by the following closed equation ， ， represents the ratio of leaf area index to total primary productivity under the condition of closed vegetation canopy, represents the single-day steady-state leaf area index corresponding to the total primary productivity, represents the maximum light use efficiency, represents the annual photosynthetically active radiation, and represents the scalar function, respectively, illustrating the restrictive effects of daily minimum temperature and daily vapor pressure deficit on the photosynthesis of vegetation canopy, represents the canopy extinction coefficient, taking the value of 0.

5.

5. The leaf area index prediction method according to claim 4, characterized in that, The MOD17 model was used to calculate the and As follows ， ， wherein, and Tmin and ETo represent the daily minimum temperature and the daily evapotranspiration deficit, respectively, and Tminlow and Tminup represent the lower and upper limits of the daily minimum temperature that limits the photosynthesis of the tree crown, respectively, and ETo low and ETo up represent the lower and upper limits of the daily evapotranspiration deficit that limits the photosynthesis of the tree crown, respectively.

6. The leaf area index prediction method according to claim 5, characterized in that, The analytical solution of the Lambert W function is used to determine the analytical solution, in particular as follows: Let , then the single-day steady-state leaf area index is expressed as ; Let then ; Solving with Lambert W function Then we have , denotes the Lambert W function operator, i.e. the inverse relation of the function , denotes an exponential function, denotes a complex number, the range of values of ; Then The analytical solution of the analysis is expressed as .

7. An electronic device, comprising: a memory for storing a program supporting the processor to perform the leaf area index prediction method of any one of claims 1-6, and a processor configured to execute the program stored in the memory.

8. A computer-readable storage medium, characterized in that, A computer readable storage medium has stored thereon a computer program which, when executed by a processor, performs the steps of the leaf area index prediction method of any one of claims 1-6.

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