Soil organic carbon density and reserve estimation method

Abstract

The invention relates to the technical field of soil measurement, in particular to a soil organic carbon density and reserve estimation method which comprises the following steps: S1, collecting basic information of multi-region and multi-type soil samples; s2, constructing a basic nonlinear regression model according to the basic information; s3, introducing a multi-source correction factor based on the basic nonlinear regression model; s4, dynamically adjusting the weight of the multi-source correction factor according to the basic information through an adaptive algorithm to form a transferable model; and S5, by utilizing a model transfer learning method, when the method is used, correction factors can be adaptively adjusted according to different geographical and soil characteristics through a dynamic weight mechanism, so that the accuracy of the transferable model in remote prediction can be improved, the dynamic adjustment of the weight and sensitivity coefficient does not depend on manual setting, and the accuracy of the transferable model in remote prediction can be improved. And the transferable model is automatically adjusted according to a statistical rule, so that subjective intervention is reduced, and the generalization ability is further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of soil measurement, and particularly relates to a method for estimating soil organic carbon density and reserves. Background Art

[0002] The estimation of soil organic carbon density and reserves is an important basis for evaluating soil carbon sequestration capacity, monitoring the impact of land use change on climate change, and formulating corresponding environmental protection measures. Soil organic carbon density refers to the mass of organic carbon in the soil within a certain depth range per unit area, usually expressed in kg / m 2 and the soil organic carbon reserve refers to the total amount of organic carbon in all soil layers within a certain area, generally in tons or thousands of tons.

[0003] The patent with the publication number CN112782385A discloses in its specification that "the present invention discloses a method for estimating soil organic carbon density and reserves, belonging to the technical field of metrological pedology, and comprising the following steps: setting the positions of soil sampling points, collecting profile samples of the soil body, and simultaneously measuring the thickness of each soil layer; testing the organic carbon content, the volume percentage of gravel larger than 2 mm, and the bulk density index of each soil layer; calculating the soil organic carbon density per unit centimeter depth of each soil layer sample, and establishing a linear regression model between the soil organic carbon density per unit centimeter depth and the soil organic carbon content; based on the established linear regression model, respectively establishing the functional relationships between soil organic carbon density and organic carbon content, and between soil organic carbon reserve and organic carbon content. The present invention directly, quickly, and accurately estimates soil carbon density and carbon reserve through organic carbon content, improving the accessibility of soil organic carbon reserve data". Although the above technology reduces the dependence on difficult-to-measure data by establishing a linear regression model between the soil organic carbon density per unit centimeter depth and the organic carbon content, and realizes the rapid and accurate estimation of soil carbon density and carbon reserve, achieving the effect of significantly shortening the detection time, the above technology relies on establishing a linear regression model between organic carbon content and SOCD. However, the soil types vary greatly in different regions, and the gravel composition and bulk density have a wide range of changes, resulting in the regionality of model parameters. Therefore, the linear regression model of the above technology has high accuracy locally, but a new model needs to be established for cross-regional use, and its universality is still limited.

[0004] In summary, developing a method for estimating soil organic carbon density and reserves is still a key problem urgently to be solved in the technical field of soil measurement. Summary of the Invention

[0005] The object of the present invention is to solve the problem that although the above-mentioned technology reduces the dependence on difficult-to-measure data by establishing a linear regression model between the soil organic carbon density per centimeter depth and the organic carbon content, realizes the rapid and accurate estimation of soil carbon density and carbon storage, and achieves the effect of significantly shortening the detection time, the above-mentioned technology depends on establishing a linear regression model between the organic carbon content and SOCD. However, due to the large differences in soil types in different regions, the gravel composition and bulk density vary widely, resulting in the regionality of model parameters. As a result, the linear regression model of the above-mentioned technology has high accuracy locally, but the model needs to be re-established when used across regions, and the universality is still limited.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention provides a method for estimating soil organic carbon density and storage, including the following steps: S1. Collect the basic information of soil samples in multiple regions and of multiple types;

[0008] S2. Construct a basic non-linear regression model according to the basic information;

[0009] S3. Introduce multi-source correction factors based on the basic non-linear regression model;

[0010] S4. Dynamically adjust the weights of the multi-source correction factors according to the basic information through an adaptive algorithm to form a transferable model;

[0011] S5. Use the model transfer learning method to dynamically adjust the parameters of the transferable model according to the soil sample data input in the new region.

[0012] Further, in step S1, the method for collecting the basic information of soil samples in multiple regions and of multiple types is:

[0013] The basic information includes the organic carbon content C soc , the organic carbon density ρ soc , the bulk density ρ bk , the gravel content and the geographic coordinate information x i , y i , z i . Select the regional range for collecting soil samples through a geographic information system and obtain the geographic coordinate information of the sampling points. Use a standardized soil sampling technique to collect soil samples from the depth levels of 0 - 10 cm, 10 - 20 cm, and 20 - 30 cm. Conduct the organic carbon content test and the organic carbon density test according to the soil samples. The expression formula: ρ soc = C soc ·ρ bk ·q, where ρ soc is the organic carbon density in the soil sample, C socis the organic carbon content in the soil sample, ρ bk is the bulk density of the soil sample, q is the sampling depth of the soil sample, the bulk density is measured by the dry weight method, and the mass ratio of the gravel in the soil sample is obtained by screening and weighting. The expression formula is: where is the gravel content in the soil sample, m gl is the mass of the gravel in the soil sample, m se is the total mass of the soil sample. The information of the collected soil sample is summarized and preprocessed to obtain the basic information set of the soil sample. The expression formula is: , where Sme i is the basic information set of the soil sample, C soc,nm,i is the normalized organic carbon content of the i-th sample, ρ bk,i is the bulk density of the i-th sample, is the gravel content of the i-th sample, (x i , y i , z i ) is the geographical coordinate of the i-th sample. After data cleaning and outlier detection, it is stored using MongoDB.

[0014] Furthermore, in step S2, the method for constructing the basic non-linear regression model is:

[0015] Establish a preliminary association between the organic carbon content C i in the basic information set Sme soc and the organic carbon density ρ soc . The basic non-linear regression model includes non-linear functions of polynomial terms and exponential terms. Set the organic carbon content C soc and the organic carbon density ρ soc , which is described by the basic non-linear regression model. The expression formula is:

[0016] where ρ soc,i is the organic carbon density of the i-th soil sample, C soc,i is the organic carbon content of the i-th soil sample, exp(·) refers to the natural exponential function, ∈ i represents the random error between the prediction and the true observed value. α0 is the constant term parameter of the regression model, α1 is the regression coefficient related to the first-order term of the organic carbon content, α2 is the regression coefficient related to the second-order term of the organic carbon content, α3 is the regression coefficient related to the exponential function part, and α4 is the coefficient in the exponential function that adjusts the influence rate of the organic carbon content in the exponential function.

[0017] Furthermore, in step S2, the method is:

[0018] In the basic non - linear regression model, the optimal regression parameters are found by minimizing the sum of squared errors, and the expression formula is:

[0019] where n is the total number of samples, represents solving for the optimal values of the five parameters α0, α1, α2, α3, α4 in the form of minimizing the sum of squared errors, is the symbol for cumulative overall error, and the gradient descent method is used for parameter update, and the expression formula is: where is the updated value of the k - th parameter, is the original value of the k - th parameter in the old model, β is the learning rate, is the gradient of the loss function L with respect to the k - th parameter α k After training the basic non - linear regression model, regression evaluation metrics are used to evaluate the performance of the basic non - linear regression model.

[0020] Furthermore, in step S3, the method is as follows:

[0021] The multi - source correction factors include soil type factor, bulk density change factor, gravel correction factor, and geographical block factor. A dynamic correction system is constructed based on the four major factors of soil type, bulk density change, gravel content, and geographical block. The soil type factor introduces the influence coefficient matrix corresponding to different categories according to soil classification, and the expression formula is: where F st (i) represents the soil type correction factor of the i - th sample, m st is the total number of soil types, χ j,i indicates whether the i - th sample belongs to the j - th soil type (1 if it belongs, 0 otherwise), and δ st,j is the correction coefficient of the j - th soil type. The expression formula for the bulk density change factor is: where F bd (i) is the bulk density correction factor of the i - th sample, BD i is the soil bulk density of the i - th sample, BD is the average soil bulk density within the sample set, ε bd is the logarithmic term adjustment coefficient for bulk density correction to control the deviation correction degree, φ bd is the hyperbolic cosine term adjustment coefficient for bulk density correction to enhance non - linear correction, ln(·) is the natural logarithm function to reflect the relative deviation, and cosh(·) is the hyperbolic cosine function to increase the amplification effect of the bulk density extreme value on the result. The gravel correction factor represents the dilution effect of gravel content on organic carbon density through a hyper - exponential function, and the expression formula is: where F gr (i) is the gravel correction factor of the i - th sample, GR i is the gravel content of the i - th sample, is the coefficient controlling the decay rate of the gravel index, γ gr is the power coefficient of the gravel exponential function to adjust the nonlinear strength, ι gr is the coefficient of the sine adjustment term in the gravel correction factor to reflect the periodic disturbance, exp(·) is the exponential function representing the decay trend of gravel on the organic carbon density, and sin(·) is the sine function to introduce the correction of the weak periodic disturbance of the gravel content.

[0022] Furthermore, in step S3, the method is as follows:

[0023] The influence of the geographical block factor on the soil carbon storage is obtained through high-dimensional embedding mapping, and the expression formula is: where F go (i) is the geographical block correction factor of the i-th sample, Uat i , Uon i are the latitude and longitude of the i-th sample, λ p (·), λ w (·) are high-order polynomial basis functions for nonlinearly mapping the geographical location into high-dimensional features, y p,w is the element of the geographical mapping weight matrix representing the interaction influence weight of the p-th order of latitude and the w-th order of longitude, and P, W are the expansion orders of the high-order basis functions during the latitude and longitude mapping. Multiply and couple the above factors to form the comprehensive multi-source correction coefficient F crr , and the expression formula is: F crr (i) = F st (i) · F bd (i) · F gr (i) · F go (i), where F crr (i) is the comprehensive multi-source correction coefficient of the i-th sample, F st (i) is the soil type correction factor (usually modeled based on different soil types and regional empirical factors), F bd (i), F gr (i), F go (i) are the bulk density correction factor, gravel correction factor, and geographical block factor respectively, so that the basic nonlinear regression model is solved by the nonlinear least squares method after multi-source correction, and a regularization term is introduced at the same time. The expression formula is: where ρ soc,ped (i) is the predicted value of the soil organic carbon density of the i-th sample, C soc,i is the soil organic carbon content of the i-th sample, α0, α1, α2, α3, α4 are the regression parameters of the basic nonlinear regression model, and F crr (i) is the comprehensive multi-source correction coefficient of the i-th sample. is the sum of squared errors between the true soil organic carbon density of the sample and the predicted soil organic carbon density, and μ is the regularization coefficient that controls the intensity of the penalty term. is the square of the L2 norm of the geographical mapping weight matrix. is the square of the L2 norm of the soil type weight coefficient, and α, δ, ε, φ, γ, ι, λ are the entire set of model parameters to be solved by fitting.

[0024] Furthermore, in step S4, the method for... is:

[0025] The transferable model needs to dynamically weight the correction factors, couple them with the basic non - linear regression model, introduce the dynamic weight coefficient vector, and the expression formula is: I = {h st , h bd , h gr , h go}, where I represents a vector containing the weights of multiple correction factors, and h st is the weight of the soil type factor, h bd is the weight of the bulk density change factor, h gr is the weight of the gravel correction factor, h go is the weight of the geographical block factor, and it satisfies the constraint condition, and the expression formula is: h st + h bd + h gr + h go = 1. Define the multi - source factor weighting function, and the expression formula is:

[0026] where F ttl (i) is the soil organic carbon density factor after comprehensive correction, represents the correction value of the soil type factor under the sample, represents the correction value of the bulk density factor weighted in the sample to the soil organic carbon density, represents the correction value of the gravel factor weighted in the sample to the soil organic carbon density, represents the correction value of the geographical block factor weighted in the sample to the soil organic carbon density.

[0027] Furthermore, in step S4, the method for... is:

[0028] Based on the basic non - linear regression model, after introducing the dynamically weighted correction factors, the transferable model is obtained, and the expression formula is: ρ soc,tnsr (i)=ρ soc,be (i)·F ttl (i), where ρ soc,tnsr (i) represents the soil organic carbon density value of the target area obtained after transfer learning, and ρ soc,be(i) represents the soil organic carbon density value of the reference area, F ttl (i) is the soil organic carbon density factor after comprehensive correction. An adaptive algorithm is introduced to dynamically adjust the weight according to the sample statistics of different regions. The expression formula is: where j′ ∈ {st, bd, gr, go}, θ j′ is the adjustment sensitivity coefficient, Δ j′ is the sensitivity of factor j′ to the error of the transferable model, V j′ represents the weight of the specific correction factor j′, θ k′ represents the exponential coefficient of the correction factor k′, Δ k′ represents the specific change corresponding to the correction factor k′, is the exponential function value of the correction factor k′, represents the exponential term corresponding to the correction factor j′. In the construction of the transferable model, the parameters and weight coefficients of the transferable model are simultaneously fitted through the objective function.

[0029] Furthermore, in step S5, the method is:

[0030] Obtain the outermost input data of the soil sample data in the new area, normalize the input data, and construct a new area sample matrix. The expression formula is: where represents the organic carbon content in the soil sample of the new area, represents the soil bulk density in the soil sample of the new area, represents the gravel content in the soil sample of the new area, represents the geographical coordinates of the soil sample in the new area, represents the soil type of the soil sample in the new area, represents the sampling depth of the soil sample in the new area, is a vector containing the characteristics of the soil sample in the new area. Based on the transferable model, a parameter adjustment variable set is introduced. The expression formula is: Θ = {ζ, ψ}, where Θ represents the parameter set of the transferable model, ζ represents the regression coefficient in the transferable model, and ψ represents the weight matrix in the transferable model. The model transfer learning method defines a new area loss function. The expression formula is:

[0031] where represents Δψ = ψ - ψ pre

[0032] The new loss function, A′ is the total number of samples, and i represents the index of the i-th sample. represents the actual observed value of the i-th sample, ρ soc,tnsr (i; Θ) represents the predicted value of the i-th sample obtained through transfer learning, Hyperparameters representing regularization terms, is the Euclidean distance, Hyperparameters representing another regularization, ||Δψ||1 represents the norm of the change in the weights of the transferable model, Δψ is the weight adjustment increment, ψ is the multi-source correction factor weight matrix calculated in the current iteration, ψ pre is the multi-source correction factor weight matrix of the previous iteration, and is updated adaptively based on the small-sample fine-tuning strategy, with the expression formula: where Θ (t″) represents the set of transferable model parameters at time step t″, Θ (t″+1) represents the updated set of transferable model parameters at time step t″, is a hyperparameter that controls the magnitude of the update of the transferable model parameters, represents the loss function with respect to the current transferable model parameters Θ (t″) gradient.

[0033] Furthermore, in step S5, the method is:

[0034] Introduce Bayesian optimization, with the expression formula:

[0035] where Θ (t″) represents the set of transferable model parameters at time step t″, Θ (t″+1) represents the updated set of transferable model parameters at time step t″, is a hyperparameter that controls the magnitude of the update of the transferable model parameters, represents the loss function with respect to the current transferable model parameters Θ (t″) gradient, represents the random noise term added during parameter update, represents the variance of the noise term, and the convergence condition expression formula: and terminate the iteration when, where represents the change in the loss function between the (t″ + 1)-th iteration and the t″-th iteration of the model, Ω is a threshold, and t″ represents the current iteration number, represents the maximum number of iterations, and the adjusted transferable model is applied to the full-range prediction of the new area, with the expression formula: where represents the predicted value of soil organic carbon density at the spatial coordinates (x′, y′) and depth layer z′, ρ tnsr (·) is a function, represents the predicted soil organic carbon content at the spatial coordinates (x′, y′) and depth layer z′, Denotes the predicted soil bulk density at the spatial coordinates (x′, y′) and depth layer z′. Denotes the predicted gravel content at the spatial coordinates (x′, y′) and depth layer z′. Denotes the soil type mapping at the spatial coordinates (x′, y′). Denotes the geographical block information at the spatial coordinates (x′, y′), and the profile distribution is as follows: Where Denotes the depth range, forms a multi-level carbon density curve output diagram, and defines the expression formula for the total carbon storage in the new area: Where (TC) denotes the estimated result of the total carbon storage in the new area. Is for the new area Performs a double integral operation on the (x′, y′) range in the plane coordinate system. Is to sum according to the different depth layers z′ of the soil profile. Is the soil organic carbon density at the z′ depth layer at the position (x′, y′), and Δz′ is the increment of the soil depth layer thickness. Is the predicted value of the gravel content under the z′ depth layer at the position (x′, y′). Denotes the integration of the infinitesimal area element of the regional area, and the discrete calculation expression formula: Where (TC) denotes the estimated result of the total carbon storage in the new area. Denotes the predicted value of the soil organic carbon density at the spatial coordinates (x′ m′ , y′ n′ ) and depth layer z′, and Δz′ denotes the depth increment of the soil. Denotes the predicted value of the gravel content at the spatial coordinates (x′ m′ , y′ n′ ) and depth layer z′, and Δx′, Δy′ respectively denote the spatial increments in the x″ and y′ directions. Denotes the summation in the x″ direction. Denotes the summation in the y′ direction. Denotes the summation over the depth layer z′. Is the total number of depth layers, and the final output results include the organic carbon density distribution curves at multiple depth layers, the estimated table of the organic carbon storage in the new area, and the spatial distribution heat map.

[0036] Beneficial effects

[0037] Adopting the technical solution provided by the present invention, compared with the known public technology, has the following beneficial effects:

[0038] When the present invention is in use, through the dynamic weight mechanism, the correction factor can be adaptively adjusted according to different geographical and soil characteristics, which is convenient for improving the accuracy of the transferable model in off-site prediction. The dynamic adjustment of the weight and sensitivity coefficient does not depend on manual setting, but is automatically adjusted by the transferable model according to statistical laws, reducing subjective intervention and being beneficial to further improving the generalization ability. The transferable model not only retains the stability of the basic model but also has adjustability, and can quickly establish a highly adaptable prediction model in a new area, which is beneficial for applying to the soil carbon storage estimation work in a large range and multiple regions. Utilizing the model transfer ability of the existing area, reliable carbon storage estimation can be achieved only through a small number of new area samples, which is beneficial for saving sampling and testing costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a flowchart of a method for estimating soil organic carbon density and storage of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0040] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0041] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products, or devices.

[0042] The present invention will be further described in detail below with reference to the accompanying drawings:

[0043] Embodiment:

[0044] As Figure 1 shown, the present invention provides a method for estimating soil organic carbon density and storage, including the following steps: S1. Collect the basic information of soil samples in multiple regions and of multiple types;

[0045] Further, in step S1, the method for collecting the basic information of multi-region and multi-type soil samples is as follows:

[0046] The basic information includes the organic carbon content C soc , the organic carbon density ρ soc , the bulk density ρ bk , the gravel content and the geographic coordinate information x i , y i , z i . The area range for collecting soil samples is selected through the Geographic Information System and the geographic coordinate information of the sampling points is obtained. Soil samples are collected from the depth levels of 0-10 cm, 10-20 cm, and 20-30 cm using standardized soil sampling techniques. The organic carbon content test and the organic carbon density test are performed based on the soil samples. The expression formula: ρ soc = C soc ·ρ bk ·q, where ρ soc is the organic carbon density in the soil sample, C soc is the organic carbon content in the soil sample, ρ bk is the bulk density in the soil sample, q is the sampling depth of the soil sample. The bulk density is measured by the dry weight method. The mass ratio of the gravel in the soil sample is obtained through screening and weighting. The expression formula: where is the gravel content in the soil sample, m gl is the mass of the gravel in the soil sample, m se is the total mass of the soil sample. The information of the collected soil samples is summarized and preprocessed to obtain the basic information set of the soil samples. The expression formula: , where Sme i is the basic information set of the soil samples, C soc,nm,i is the normalized organic carbon content of the i-th sample, ρ bk,i is the bulk density of the i-th sample, is the gravel content of the i-th sample, (x i , y i , z i ) is the geographic coordinate of the i-th sample. After data cleaning and outlier detection, it is stored using MongoDB.

[0047] In this embodiment, in step S1, the richness and coverage of the sample library data are ensured by collecting soil samples in different regions, at different depths, and of different types. By adopting a unified and standardized sampling and detection method, the accuracy and comparability of experimental data are improved, providing a reliable basis for constructing a basic non-linear regression model. Systematic data cleaning and outlier processing ensure the high quality and stability of the subsequent modeling data. The use of the MongoDB database enhances the efficiency and flexibility of data retrieval and processing.

[0048] S2. Construct a basic non-linear regression model according to the basic information;

[0049] Further, in step S2, the method for constructing a basic non-linear regression model according to the basic information is as follows:

[0050] Establish a preliminary association between the organic carbon content C i in the basic information set Sme soc and the organic carbon density ρ soc . The basic non-linear regression model includes a non-linear function of polynomial terms and exponential terms. Set the organic carbon content C soc and the organic carbon density ρ soc , and describe them through the basic non-linear regression model. The expression formula is:

[0051] where ρ soc,i is the organic carbon density of the i-th soil sample, C soc,i is the organic carbon content of the i-th soil sample, exp(·) refers to the natural exponential function, ∈ i represents the random error between the prediction and the true observed value, α0 is the constant term parameter of the regression model, α1 is the regression coefficient related to the first-order term of the organic carbon content, α2 is the regression coefficient related to the second-order term of the organic carbon content, α3 is the regression coefficient related to the exponential function part, and α4 is the coefficient in the exponential function that adjusts the influence rate of the organic carbon content in the exponential function.

[0052] Further, in step S2, the method is as follows:

[0053] In the basic non-linear regression model, find the optimal regression parameters by minimizing the sum of squared errors. The expression formula is:

[0054] where n is the total number of samples, represents solving for the optimal values of the five parameters α0, α1, α2, α3, α4 in the form of minimizing the sum of squared errors, is the symbol for accumulating the total error, and the gradient descent method is used for parameter update. The expression formula is: where is the updated k-th parameter value, is the original value of the k-th parameter in the old model, β is the learning rate, is the gradient of the loss function L with respect to the k-th parameter α k After training the basic non-linear regression model, use regression evaluation metrics to evaluate the performance of the basic non-linear regression model.

[0055] In this embodiment, through a polynomial and exponential mixed model, the non-linear relationship between organic carbon content and carbon density is established in an interpretable form, providing a mathematical basis for subsequent introduction of multi-source factor correction. The model parameters of the basic non-linear regression model are automatically optimized through gradient descent and error minimization, and can better adapt to the basic relationships under different regions and different soil types. After the exponential term is introduced, the sensitivity of the model to high carbon content or extreme value samples can be enhanced, and the asymmetric growth trend in the real scenario can be captured.

[0056] S3. Introduce multi-source correction factors based on the basic non-linear regression model;

[0057] In step S3, the method is as follows:

[0058] The multi-source correction factors include soil type factor, bulk density change factor, gravel correction factor and geographical block factor. A dynamic correction system is constructed based on the four factors of soil type, bulk density change, gravel content and geographical block. The soil type factor introduces the influence coefficient matrix corresponding to different categories according to soil classification, and the expression formula is: where F st (i) represents the soil type correction factor of the i-th sample, m st is the total number of soil types, χ j,i represents whether the i-th sample belongs to the j-th type of soil. If it belongs, it is 1, otherwise it is 0, and δ st,j is the correction coefficient of the j-th type of soil. The expression formula of the bulk density change factor is: where F bd (i) is the bulk density correction factor of the i-th sample, BD i is the soil bulk density of the i-th sample, is the average value of the soil bulk density within the sample set, ε bd is the logarithmic term adjustment coefficient of bulk density correction to control the deviation correction degree, φ bd is the hyperbolic cosine term adjustment coefficient of bulk density correction to enhance non-linear correction. ln(·) is the natural logarithm function to reflect the relative deviation, and cosh(·) is the hyperbolic cosine function to increase the amplification effect of bulk density extreme values on the result. The gravel correction factor represents the dilution effect of gravel content on organic carbon density through a hyper-exponential function, and the expression formula is: where F gr(i) is the gravel correction factor of the i-th sample, GR i is the gravel content of the i-th sample, is the coefficient controlling the decay rate of the gravel index, γ gr is the power coefficient of the gravel index function to adjust the nonlinear strength, ι gr is the coefficient of the sine adjustment term in the gravel correction factor, reflecting the periodic disturbance. exp(·) is the exponential function representing the decay trend of gravel on the organic carbon density, and sin(·) is the sine function introducing the weak periodic disturbance correction of the gravel content.

[0059] Furthermore, in step S3, the method for is:

[0060] The influence of the geographical block factor on the soil carbon storage is obtained through high-dimensional embedding mapping, and the expression formula is: where F go (i) is the geographical block correction factor of the i-th sample, Uat i , Uon i are the latitude and longitude of the i-th sample, λ p (·), λ w (·) is the high-order polynomial basis function for nonlinearly mapping the geographical location into high-dimensional features, y p,w is the element of the geographical mapping weight matrix, representing the interaction influence weight of the p-th order of latitude and the w-th order of longitude. P and W are the expansion orders of the high-order basis functions during latitude and longitude mapping. Multiply and couple the above factors to form the comprehensive multi-source correction coefficient F crr , and the expression formula is: F crr (i) = F st (i) · F bd (i) · F gr (i) · F go (i), where F crr (i) is the comprehensive multi-source correction coefficient of the i-th sample, F st (i) is the soil type correction factor (usually modeled based on different soil types and regional empirical factors), F bd (i), F gr (i), F go (i) are the bulk density correction factor, gravel correction factor, and geographical block factor respectively, so that the basic nonlinear regression model is solved by the nonlinear least squares method after multi-source correction, and a regularization term is introduced at the same time. The expression formula is: where ρ soc,ped (i) is the predicted value of the soil organic carbon density of the i-th sample, C soc,i is the soil organic carbon content of the i-th sample, α0, α1, α2, α3, α4 are the regression parameters of the basic nonlinear regression model, F crr(i) is the comprehensive multi-source correction coefficient of the th sample, is the sum of squared errors between the true soil organic carbon density and the predicted soil organic carbon density of the sample, μ is the regularization coefficient to control the intensity of the penalty term, is the square of the L2 norm of the geographical mapping weight matrix, is the square of the L2 norm of the soil type weight coefficient, α, δ, ε, φ, γ, ι, λ are the set of all model parameters to be solved by fitting.

[0061] In this embodiment, in this step, by incorporating four typical influencing factors into the model, the comprehensive correction coefficient significantly improves the adaptability of the model in different regions and different soil types. Through mathematical tools such as logarithmic functions, hyper-exponential functions, hyperbolic cosine, and sine perturbation terms, more non-linear relationships and extreme value effects in real scenarios can be captured. The high-dimensional geographical mapping method not only considers the influence of longitude and latitude but also introduces higher-order interactions, which can effectively characterize spatial continuity and boundary changes. Introducing a regularization term prevents overfitting of the basic non-linear regression model, enabling good fitting on samples and good generalization ability.

[0062] S4. Dynamically adjust the weights of the multi-source correction factors according to the basic information through an adaptive algorithm to form a transferable model;

[0063] Furthermore, in step S4, the method for is:

[0064] The transferable model needs to dynamically weight the correction factors, couple them with the basic non-linear regression model, and introduce a dynamic weight coefficient vector. The expression formula is: I = {h st , h bd , h gr , h go}, where I represents a vector containing the weights of multiple correction factors, h st is the weight of the soil type factor, h bd is the weight of the bulk density change factor, h gr is the weight of the gravel correction factor, h go is the weight of the geographical block factor, and satisfies the constraint condition. The expression formula is: h st + h bd + h gr + h go = 1. Define the multi-source factor weighting function. The expression formula is:

[0065] where F ttl (i) is the soil organic carbon density factor after comprehensive correction, represents the correction value of the soil type factor under the sample, It represents the corrected value of the bulk density factor weighted in the sample for soil organic carbon density. It represents the corrected value of the gravel factor weighted in the sample for soil organic carbon density. It represents the corrected value of the geographical block factor weighted in the sample for soil organic carbon density.

[0066] Furthermore, in step S4, the method is as follows:

[0067] Based on the basic non - linear regression model, a transferable model is obtained by introducing a dynamic weighted correction factor. The expression formula is: ρ soc,tnsr (i) = ρ soc,be (i)·F ttl (i), where ρ soc,tnsr (i) represents the soil organic carbon density value of the target area obtained after transfer learning, ρ soc,be (i) represents the soil organic carbon density value of the reference area, F ttl (i) is the soil organic carbon density factor after comprehensive correction. An adaptive algorithm is introduced to dynamically adjust the weight according to the sample statistics of different regions. The expression formula is: where j′ ∈ {st, bd, gr, go}, θ j′ is the adjustment sensitivity coefficient, Δ j′ is the error sensitivity of factor j′ to the transferable model, V j′ represents the weight of the specific correction factor j′, θ k′ represents the exponential coefficient of the correction factor k′, Δ k′ represents the specific change amount corresponding to the correction factor k′, is the exponential function value of the correction factor k′, represents the exponential term corresponding to the correction factor j′. In the construction of the transferable model, the parameters and weight coefficients of the transferable model are simultaneously fitted through the objective function.

[0068] In this embodiment, in this step, through the dynamic weight mechanism, the correction factors can be adaptively adjusted according to different geographical and soil characteristics, which is convenient for improving the accuracy of the transferable model in predicting in different places. The dynamic adjustment of the weight and the sensitivity coefficient does not depend on manual setting, but is automatically adjusted by the transferable model according to statistical laws, reducing subjective intervention, which is beneficial to further improving the generalization ability. The transferable model not only retains the stability of the basic model but also has adjustability, and can quickly establish a highly adaptable prediction model in the new area, which is beneficial to be applied to the soil carbon storage estimation work in a large range and multiple regions.

[0069] S5. Using the model transfer learning method, dynamically adjust the parameters of the transferable model according to the soil sample data input in the new area;

[0070] Further, in step S5, the method is as follows:

[0071] Obtain the outermost input data of the soil sample data in the new area, perform normalization processing on the input data, and construct a new area sample matrix. The expression formula is: where represents the organic carbon content in the soil sample of the new area, represents the soil bulk density in the soil sample of the new area, represents the gravel content in the soil sample of the new area, represents the geographical coordinates of the soil sample in the new area, represents the soil type of the soil sample in the new area, represents the sampling depth of the soil sample in the new area, is a vector containing the characteristics of the soil sample in the new area. Based on the transferable model, introduce a set of parameter adjustment variables. The expression formula is: Θ = {ζ, ψ}, where Θ represents the parameter set of the transferable model, ζ represents the regression coefficient in the transferable model, and ψ represents the weight matrix in the transferable model. The model transfer learning method defines the loss function of the new area. The expression formula is:

[0072] where represents Δψ = ψ - ψ pre

[0073] The new loss function, A′ is the total number of samples, i represents the index of the i-th sample, represents the actual observed value of the i-th sample, ρ soc,tnsr (i; Θ) represents the predicted value of the i-th sample obtained through transfer learning, represents the hyperparameter of the regularization term, is the Euclidean distance, represents another hyperparameter of regularization, ||Δψ||1 represents the norm of the change in the weights of the transferable model, Δψ is the weight adjustment increment, ψ is the multi-source correction factor weight matrix calculated in the current iteration, and ψ pre is the multi-source correction factor weight matrix of the previous iteration. Update using an adaptive increment based on the small sample fine-tuning strategy. The expression formula is: where Θ (t″) represents the set of transferable model parameters at time step t″, and Θ (t″+1) represents the updated set of transferable model parameters at time step t″, is a hyperparameter that controls the magnitude of the update of the transferable model parameters, represents the loss function with respect to the current transferable model parameters Θ (t″) gradient.

[0074] Further, in step S5, the method is as follows:

[0075] Introduce Bayesian optimization, and the expression formula is:

[0076] where Θ (t″) represents the set of transferable model parameters at time step t″, and Θ (t″+1) represents the updated set of transferable model parameters at time step t″. is a hyperparameter that controls the amplitude of the update of the transferable model parameters. represents the loss function with respect to the current transferable model parameters Θ (t″) gradient, represents the random noise term added during parameter update, represents the variance of the noise term, and the convergence condition expression formula is: and terminate the iteration when, where represents the change in the loss function between the (t″ + 1)-th iteration and the t″-th iteration of the model, Ω is a threshold, and t″ represents the current iteration number. represents the maximum number of iterations. The adjusted transferable model is applied to the full-range prediction of the new area, and the expression formula is: where represents the predicted value of soil organic carbon density at the spatial coordinates (x′, y′) and the depth layer z′, and ρ tnsr (·) is a function, represents the predicted soil organic carbon content at the spatial coordinates (x′, y′) and the depth layer z′, represents the predicted soil bulk density at the spatial coordinates (x′, y′) and the depth layer z′, represents the predicted gravel content at the spatial coordinates (x′, y′) and the depth layer z′, represents the soil type mapping at the spatial coordinates (x′, y′), represents the geographical block information at the spatial coordinates (x′, y′). The obtained profile distribution is: where represents the depth level range, forming a multi-level carbon density curve output graph. Define the expression formula for the total carbon storage in the new area: where (TC) represents the estimation result of the total carbon storage in the new area. is the double integral operation on the (x′, y′) range of the new area in the plane coordinate system, is the summation according to the different depth layers z′ of the soil profile, is the soil organic carbon density of the z'-th depth layer at the position (x′, y′), and Δz′ is the increment of the soil depth layer thickness. is the predicted gravel content under the z'-th depth layer at the position (x′, y′). denotes the integration over the infinitesimal area element of the regional area, and the discrete calculation expression formula is: where (TC) represents the estimated result of the total carbon storage in the new area. denotes the predicted value of the soil organic carbon density at the spatial coordinates (x′ m′ , y′ n′ ) and the depth layer z′, and Δz′ represents the increment of the soil depth. denotes the predicted value of the gravel content at the spatial coordinates (x′ m′ , y′ n′ ) and the depth layer z′, and Δx′ and Δy′ respectively represent the spatial increments in the x″ and y′ directions. denotes the summation in the x″ direction. denotes the summation in the y′ direction. denotes the summation over the depth layer z′. is the total number of depth layers, and the final output results include the organic carbon density distribution curves of multiple depth layers, the estimated table of the organic carbon storage in the new area, and the spatial distribution heat map.

[0077] In this embodiment, in this step, through transfer learning, Bayesian optimization, and incremental fine-tuning, the transferable model can quickly adapt to the new area with limited data, accurately predict the carbon density distribution, and at the same time consider factors such as geographical blocks, soil types, and gravel content to achieve high-dimensional and multi-variable-driven spatial prediction. Using the model transfer ability of the existing area, reliable carbon storage estimation can be achieved only through a small number of new area samples, which is beneficial to saving sampling and testing costs. At the same time, the output stratified curve graph and the carbon storage spatial heat map help policymakers and developers of farmland carbon sink projects intuitively grasp the regional carbon storage distribution status, facilitating the guidance of land use and carbon trading strategies.

[0078] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements will not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating soil organic carbon density and reserves, characterized in that: The following steps are involved: S1. Collect basic information of soil samples from multiple regions and types; S2. constructing a basic nonlinear regression model based on the basic information; S3, introducing a multi-source correction factor based on the basic nonlinear regression model; S4, dynamically adjust the weights of multi-source correction factors according to basic information through an adaptive algorithm to form a transferable model; S5. Use the model transfer learning method to dynamically adjust the parameters of the transferable model based on the soil sample data input from the new area.

2. A soil organic carbon density and reserve estimation method according to claim 1, characterized in that: In step S1, the method for collecting basic information of multi-region and multi-type soil samples is: The basic information includes organic carbon content C soc , organic carbon density ρ soc , bulk density ρ bk , gravel content and geographic coordinate information x i ,y i ,z i , select the area for collecting soil samples through the geographic information system and obtain the geographic coordinate information of the sampling points, use standardized soil sampling technology to collect soil samples from 0-10cm, 10-20cm and 20-30cm depth levels, and perform the organic carbon content test and the organic carbon density test based on the soil samples, expressed as: ρ soc =C soc ·ρ bk q, where ρ soc is the organic carbon density in the soil sample, C soc is the organic carbon content in the soil sample, ρ bk is the bulk density in the soil sample, q is the sampling depth of the soil sample, the bulk density is measured by dry weight method, and the mass ratio of the gravel in the soil sample is obtained by sieving and weighting, and the expression formula is: in is the gravel content in the soil sample, m gl is the mass of gravel in the soil sample, m se is the total mass of the soil sample. The information of the collected soil samples is summarized and preprocessed to obtain the basic information set of the soil samples. The expression formula is: Among them, Sme i is the basic information set of soil samples, C soc,nm,i is the normalized organic carbon content of the ith sample, ρ bk,i is the volumetric density of the ith sample, is the gravel content of the ith sample, (x i ,y i ,z i ) is the geographic coordinate of the i-th sample, and then MongoDB is used to store it after data cleaning and outlier detection.

3. A soil organic carbon density and reserve estimation method according to claim 2, characterized in that: In step S2, according to the basic information, the method of constructing a basic nonlinear regression model is: The basic information set Sme i The organic carbon content C soc and organic carbon density ρ soc Establish a preliminary correlation, the basic nonlinear regression model includes a nonlinear function of polynomial terms and exponential terms, and set the organic carbon content C soc and organic carbon density ρ soc , described by the basic nonlinear regression model, the expression formula is: where ρ soc,i is the organic carbon density of the ith soil sample, C soc,i is the organic carbon content of the ith soil sample, exp(·) refers to the natural exponential function, ∈ i represents the random error between the prediction and the actual observation value, α0 is the constant term parameter of the regression model, α1 is the regression coefficient related to the linear term of organic carbon content, α2 is the regression coefficient related to the quadratic term of organic carbon content, α3 is the regression coefficient related to the exponential function part, and α4 is the coefficient in the exponential function that regulates the influence rate of organic carbon content in the exponential function.

4. A soil organic carbon density and reserve estimation method according to claim 3, characterized in that: In step S2, the method is: In the basic nonlinear regression model, the optimal regression parameters are found by minimizing the sum of squared errors, expressed as: Where n is the total number of samples, It means that the optimal values ​​of the five parameters α0, α1, α2, α3, and α4 are solved by minimizing the sum of squared errors. Is the symbol of total error accumulation, and the gradient descent method is used to update the parameters, and the expression formula is: in is the updated kth parameter value, is the original value of the kth parameter in the old model, β is the learning rate, is the loss function L for the kth parameter α k After training the basic nonlinear regression model, the performance of the basic nonlinear regression model is evaluated using a regression evaluation index.

5. A soil organic carbon density and reserve estimation method according to claim 4, characterized in that: In step S3, the method is: The multi-source correction factors include soil type factor, bulk density change factor, gravel correction factor and geographical block factor. A dynamic correction system is constructed based on the four factors of soil type, bulk density change, gravel content and geographical block. The soil type factor introduces the influence coefficient matrix corresponding to different categories according to soil classification, and the expression formula is: where F st (i) represents the soil type correction factor of the i-th sample, m st is the total number of soil types, χ j,i Indicates whether the i-th sample belongs to the j-th soil type. If yes, it is 1, otherwise it is 0. st,j is the correction coefficient for the jth type of soil, and the bulk density change factor is expressed as: where F bd (i) is the bulk density correction factor for the i-th sample, BD i is the soil bulk density of the ith sample, is the average soil bulk density in the sample set, ε bd is the logarithmic adjustment coefficient of bulk density correction to control the degree of deviation correction, φ bd is the hyperbolic cosine adjustment coefficient of bulk density correction to enhance nonlinear correction, ln(·) is the natural logarithmic function reflecting the relative deviation, cosh(·) is the amplification effect of the hyperbolic cosine function on the result by increasing the bulk density extreme value, and the gravel correction factor represents the dilution effect of gravel content on organic carbon density through a super exponential function, expressed as follows: where F gr (i) is the gravel correction factor of the i-th sample, GR i is the gravel content of the ith sample, is the coefficient controlling the exponential decay rate of gravel, γ gr is the power coefficient of the gravel exponential function regulating the nonlinear intensity, ι gr is the coefficient of the sinusoidal adjustment term in the gravel correction factor, reflecting the periodic disturbance. exp(·) is an exponential function that represents the attenuation trend of gravel on organic carbon density. sin(·) is a sinusoidal function that introduces a correction for the weak periodic disturbance of gravel content.

6. A soil organic carbon density and reserve estimation method according to claim 5, characterized in that: In step S3, the method is: The effect of the geographic block factor on soil carbon storage is obtained through high-dimensional embedding mapping, expressed as: where F go (i) is the geographic block correction factor of the i-th sample, Uat i , Uon i is the latitude and longitude of the ith sample, λ p (·),λ w (·) is a high-order polynomial basis function used to nonlinearly map geographic location to high-dimensional features, y p,w The geographical mapping weight matrix element represents the interaction weight of the p-th latitude and w-th longitude terms. P and W are the expansion orders of the high-order basis functions when mapping latitude and longitude. The above factors are multiplied and coupled to form a comprehensive multi-source correction coefficient F. crr , expression formula: F crr (i) = F st (i) F bd (i) F gr (i) F go (i), where F crr (i) is the comprehensive multi-source correction coefficient of the i-th sample, F st (i) is the soil type correction factor (usually based on modeling of different soil types and regional empirical factors), F bd (i),F gr (i),F go (i) are the bulk density correction factor, gravel correction factor and geographic block factor, respectively, so that the basic nonlinear regression model is corrected by multiple sources and solved by the nonlinear least squares method. At the same time, the regularization term is introduced, and the expression formula is: where ρ soc,ped (i) is the predicted value of soil organic carbon density of the i-th sample, C soc,i is the soil organic carbon content of the ith sample, α0, α1, α2, α3, α4 are the regression parameters of the basic nonlinear regression model, and F crr (i) is the comprehensive multi-source correction coefficient of the sample, is the sum of squares of the errors between the true soil organic carbon density of the sample and the predicted soil organic carbon density, μ is the regularization coefficient controlling the intensity of the penalty term, is the L2 norm squared of the geographic mapping weight matrix, is the L2 norm square of the soil type weight coefficient, α, δ, ε, φ, γ, ι, λ are the set of all model parameters that need to be solved through fitting.

7. A soil organic carbon density and reserve estimation method according to claim 6, characterized in that: In step S4, the method is: The transferable model needs to dynamically weight the correction factor, couple it with the basic nonlinear regression model, and introduce a dynamic weight coefficient vector, expressed as: I = {h st ,h bd ,h gr ,h go }, where I represents a vector containing multiple correction factor weights, h st is the weight of the soil type factor, h bd is the weight of the bulk density change factor, h gr is the weight of the gravel correction factor, h go is the weight of the geographic block factor and satisfies the constraints, expressed as: st +h bd +h gr +h go =1, define the multi-source factor weighting function, the expression formula is: where F ttl (i) is the soil organic carbon density factor after comprehensive correction, represents the correction value of the soil type factor under the sample, It represents the correction value of soil organic carbon density by weighted bulk density factor in the sample. It represents the correction value of soil organic carbon density by the weighted gravel factor in the sample. It represents the correction value of soil organic carbon density by the weighted geographical block factor in the sample.

8. A soil organic carbon density and reserve estimation method according to claim 7, characterized in that: In step S4, the method is: On the basis of the basic nonlinear regression model, the dynamic weighted correction factor is introduced to obtain a transferable model, which is expressed as: soc,tnsr (i) = ρ soc,be (i) F ttl (i), where ρ soc,tnsr (i) represents the soil organic carbon density value of the target area obtained after transfer learning, ρ soc,be (i) represents the soil organic carbon density value of the reference area, F ttl (i) is the soil organic carbon density factor after comprehensive correction. The adaptive algorithm is introduced to dynamically adjust the weight according to the sample statistics of different regions. The expression formula is: where j′∈{st,bd,gr,go},θ j′ To adjust the sensitivity coefficient, Δ j′ is the sensitivity of factor j′ to the transferable model error, V j′ represents the weight of a specific correction factor j′, θ k′ represents the exponential coefficient of the correction factor k′, Δ k′ represents the specific change corresponding to the correction factor k′, is the exponential function value of the correction factor k′, It represents the exponential term corresponding to the correction factor j′. In the construction of the transferable model, the parameters and weight coefficients of the transferable model are fitted simultaneously through the objective function.

9. A soil organic carbon density and reserve estimation method according to claim 8, characterized in that: In step S5, the method is: The outermost input data of the soil sample data of the new area is obtained, the input data is normalized, and a new area sample matrix is ​​constructed, which is expressed as: in represents the organic carbon content in the soil samples of the new area, represents the soil bulk density in the soil sample of the new area, Indicates the gravel content in the soil sample of the new area, represents the geographic coordinates of the soil samples in the new area, Indicates the soil type of the soil sample in the new area, represents the sampling depth of soil samples in the new area, is a vector containing the characteristics of soil samples in the new area. Based on the transferable model, a set of parameter adjustment variables is introduced, expressed as: Θ={ζ,ψ}, where Θ represents the parameter set of the transferable model, ζ represents the regression coefficient in the transferable model, and ψ represents the weight matrix in the transferable model. The model transfer learning method defines a new regional loss function, which is expressed as: in It means Δψ=ψ-ψ pre New loss function, A′ is the total number of samples, i represents the index of the i-th sample, represents the actual observed value of the i-th sample, ρ soc,tnsr (i; Θ) represents the predicted value of the i-th sample obtained through transfer learning, represents the hyperparameter of the regularization term, is the Euclidean distance, represents another regularized hyperparameter, ||Δψ||1 represents the norm of the change in the weight of the transferable model, Δψ is the weight adjustment increment, ψ is the multi-source correction factor weight matrix calculated in the current iteration, and ψ pre It is the weight matrix of the multi-source correction factor in the previous iteration, which is updated by adaptive increments based on the small sample fine-tuning strategy. The expression formula is: where Θ (t″) represents the set of transferable model parameters at time step t″, Θ (t″+1) represents the set of updated transferable model parameters at time step t″, is a hyperparameter that controls the magnitude of the transferable model parameter update. Represents the loss function About the current transferable model parameters Θ (t″) gradient.

10. A soil organic carbon density and reserve estimation method according to claim 8, characterized in that: In step S5, the method is: Introduce Bayesian optimization and express the formula: where Θ (t″) represents the set of transferable model parameters at time step t″, Θ (t″+1) represents the set of updated transferable model parameters at time step t″, is a hyperparameter that controls the magnitude of the transferable model parameter update. Represents the loss function About the current transferable model parameters Θ (t″) The gradient of represents the random noise term added when the parameters are updated, Represents the variance of the noise term, and the convergence condition is expressed as: and The iteration is terminated when It represents the change in the loss function between the t″+1th iteration and the t″th iteration. Ω is a threshold, and t″ represents the current number of iterations. Represents the maximum number of iterations. The adjusted transferable model is applied to the full range prediction of the new area. The expression formula is: in represents the predicted value of soil organic carbon density at spatial coordinates (x′, y′) and depth layer z′, ρ tnsr (·) is a function, represents the predicted soil organic carbon content at spatial coordinates (x′, y′) and depth layer z′, represents the predicted soil bulk density at spatial coordinates (x′, y′) and depth layer z′, represents the predicted gravel content at spatial coordinates (x′, y′) and depth layer z′, Represents the soil type mapping on the spatial coordinates (x′, y′), Representing the geographic block information on the spatial coordinates (x′, y′), the profile distribution is: in Indicates the depth level range, forms a multi-level carbon density curve output map, and defines the expression formula for the total carbon storage of the new area: Where (TC) represents the total carbon stock estimation result of the new area, For new areas Perform double integral operation in the range (x′, y′) in the plane coordinate system. It is summed according to the different depth layers z′ of the soil profile. is the soil organic carbon density of the z′th depth layer at position (x′, y′), Δz′ is the thickness increment of the soil depth layer, is the predicted value of gravel content in the depth layer z′ at position (x′, y′), It means integrating the small area elements of the area, and the discrete calculation expression formula is: Where (TC) represents the total carbon stock estimation result of the new area, Indicates that in the space coordinate (x′ m′ ,y′ n′ ) and the predicted value of soil organic carbon density at depth layer z′, Δz′ represents the depth increment of soil, Indicates that in the space coordinate (x′ m′ ,y′ n′ ) and the predicted gravel content at depth layer z′, Δx′ and Δy′ represent the spatial increments in the x″ and y′ directions, respectively. represents the sum in the x″ direction, represents the sum of y′ with respect to the direction, represents the sum of the depth layer z′, is the total number of depth layers. The final output results include the organic carbon density distribution curves of multiple depth layers, the organic carbon stock estimation table of the new area, and the spatial distribution heat map.

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