Calculation method of soil mineral-bound organic carbon based on adsorption function

Abstract

The present invention provides a soil mineral-bound organic carbon calculation method based on an adsorption function, comprising: collecting soil parameters; modifying the Langmuir adsorption function to describe the relationship between the DOC concentration of dissolved organic carbon in an unsaturated soil solution and the MAOC density that can undergo an adsorption / desorption process; establishing a differential equation for the change of the DOC concentration of the soil solution and the MAOC density that undergoes the adsorption / desorption process in the soil over time; establishing a numerical difference equation for the differential equation of the DOC solution in a unit volume of soil and the MAOC that undergoes the adsorption / desorption process; solving the differential equation group simultaneously; and obtaining the DOC concentration of the soil solution and the MAOC density that undergoes the adsorption / desorption process in the soil and the total MAOC density. The present invention can ensure the mass balance of organic carbon in the calculation time step, and can be used in a soil organic carbon numerical model, thereby improving the simulation capability of the model for the decomposition rate of soil organic carbon and the size of the carbon pool.

Description

Technical Field

[0001] The invention relates to the technical field of soil organic carbon content calculation, and in particular to a method for calculating soil mineral-bound organic carbon based on an adsorption function. Background Art

[0002] The soil organic carbon pool is the largest carbon pool in terrestrial ecosystems. The dissolved organic carbon DOC in the soil solution is adsorbed by minerals to form soil mineral-bound organic carbon MAOC. Microorganisms in the soil can absorb and utilize DOC and release CO2 into the atmosphere, but cannot absorb and utilize MAOC. In this way, organic carbon can be stored in the soil in the form of MAOC, thereby reducing the decomposition of soil organic carbon and slowing down the increase in atmospheric CO2 concentration. Therefore, it is crucial for the soil organic carbon model to accurately calculate the size of the MAOC carbon pool in order to predict future climate change.

[0003] There are two opposite processes between soil solution DOC and soil MAOC, namely adsorption and desorption of DOC, which occur simultaneously. In the equilibrium state, the rates of adsorption and desorption are the same, and the relationship between the DOC concentration in the soil solution and the amount of soil MAOC can basically be described by the Langmuir adsorption function. In the time step of the soil organic carbon model (hourly scale), without considering the changes in temperature and water content, when there is DOC input and output in the soil solution, the adsorption and desorption rates change significantly, and imbalance occurs; they reach equilibrium from the imbalance state in a very short time (seconds to minutes), and the adsorption and desorption processes change nonlinearly. At present, the soil organic carbon models used for numerical calculation of soil carbon pool changes basically use the following calculation method: in the model time step (hourly scale), the adsorption and desorption coefficients are introduced, the soil MAOC, maximum MAOC and DOC concentration are used to calculate the adsorption and desorption process rates, and then the difference in adsorption and desorption rates is used to calculate the change in MAOC. This calculation method uses linear adsorption and desorption rates to describe the actually nonlinear adsorption and desorption process, and does not consider the equilibrium state, resulting in large errors in the MAOC calculation of the model.

[0004] Some models use the above method to calculate the adsorption and desorption rates, and then calculate the changed DOC concentration, and then use the Langmuir function relationship to calculate MAOC, but it cannot guarantee that the difference between the adsorption and desorption DOC calculated in the model time step is equal to the MAOC change. Therefore, this MAOC calculation method is still to use linear speed to describe the nonlinear adsorption and desorption process; compared with the previous method, it may reduce the error, but it cannot maintain the calculated organic carbon DOC and MAOC total mass balance. Summary of the invention

[0005] The purpose of the present invention is to provide a method for calculating soil mineral-bound organic carbon based on an adsorption function, which can ensure the mass balance of organic carbon in the calculation time step and can be used in a soil organic carbon numerical model.

[0006] The purpose of the present invention can be achieved by the following technical measures: a soil mineral bound organic carbon calculation method based on an adsorption function, the soil mineral bound organic carbon calculation method based on an adsorption function comprises:

[0007] Step 1, collect soil parameters and data;

[0008] Step 2, modify the Langmuir adsorption function to describe the relationship between the DOC concentration of unsaturated soil solution and the MAOC density where adsorption / desorption processes can occur;

[0009] Step 3, when the soil water content remains unchanged, differential equations for the time-varying DOC concentration in the soil solution and the MAOC density in the soil adsorption / desorption process are established to describe the mass balance of the respective carbon pools;

[0010] Step 4, establishing numerical difference equations of the solution DOC and the MAOC differential equations for the adsorption / desorption process occurring in a unit volume of soil;

[0011] Step 5, solving the difference equations simultaneously;

[0012] Step 6, calculate the soil solution DOC concentration at the new moment, the MAOC density of the soil adsorption / desorption process, and the total MAOC density.

[0013] The purpose of the present invention can also be achieved by the following technical measures:

[0014] In step 1, soil parameters including soil bulk density are collected. , Porosity , soil binding affinity parameters , Maximum soil MAOC per unit mass These parameters, It represents the intensity of interaction between minerals and DOC in unit mass of soil.

[0015] In step 2, at a volumetric water content of The saturated soil is in equilibrium, and the DOC in the soil solution can undergo adsorption / desorption with all MAOC. The Langmuir adsorption function describes the DOC concentration in the saturated soil solution. and total soil MAOC density per unit volume The relationship between:

[0016] (1)

[0017] The Langmuir adsorption function is a regression equation based on experimental observation data of saturated soil. Since the adsorption / desorption process of DOC by soil minerals can only occur in soil solution, when the soil has a volumetric water content of Under unsaturated conditions, the MAOC density of the soil undergoing adsorption / desorption process Total MAOC density The relationship is linearly dependent on soil moisture , modify the Langmuir adsorption function to:

[0018] (2).

[0019] In step 2, the MAOC density at which adsorption / desorption cannot occur when the soil volumetric water content remains unchanged It does not change with time and can be calculated as follows:

[0020] (3).

[0021] In step 3, the change of soil solution DOC concentration mainly comes from the input or output of DOC and the change of mineral adsorption of soil solution DOC; the mass balance equation of the change of solution DOC concentration per unit volume of soil over time can be written as:

[0022] (4)

[0023] in, It is the sum of the amount of DOC adsorbed on the mineral surface in the solution per unit time and per unit soil (-) and the amount of MAOC desorbed into the solution (+); is the input or output rate of DOC per unit volume of soil solution, t represents the time in hours, is the DOC concentration of soil solution, is the volumetric water content of the soil.

[0024] In step 3, the change in MAOC density per unit volume of soil undergoing adsorption / desorption is mainly caused by the difference between the adsorption and desorption amounts, and its mass balance equation over time can be written as:

[0025] (5)

[0026] In the formula, is the MAOC density of the soil where adsorption / desorption process occurs.

[0027] In step 4, the difference equations of equations (4) and (5) in step 3 are written as:

[0028] (6)

[0029] (7)

[0030] in is the time step of the numerical calculation, which is the length between two moments; and is the value at the nth moment, and is the value at the n+1th moment; and

[0031] They are respectively their values ​​in the n+1th time step, that is, the step between the nth and n+1th moments.

[0032] In step 4, the numerical difference equation for the MAOC density where the adsorption / desorption process occurs is rewritten using the modified Langmuir adsorption function; Equation (7) is rewritten as:

[0033] (8).

[0034] In step 5, if the soil solution DOC concentration at the nth time, the MAOC density of the soil adsorption / desorption process, and the solution DOC input or output rate in the n+1th time step are known variables, equations (6) and (8) in step 4 can be solved simultaneously to obtain the solution formula for the unknown soil solution DOC concentration at the n+1th time step;

[0035] That is, according to the known soil solution DOC concentration at the nth moment, the MAOC density of the soil adsorption / desorption process, and the soil solution DOC input or output in the n+1th time step, the differential equations are solved simultaneously;

[0036] Adding equations (6) and (8) together gives:

[0037] (9)

[0038] make (10)

[0039] (11)

[0040] (12)

[0041] Equation (9) can be rewritten as

[0042] (13)

[0043] According to the solution formula of the two-variable linear equation (13), the solution at the n+1th moment is obtained:

[0044] (14).

[0045] In step 6, based on the known soil solution DOC concentration and total MAOC density at the nth moment and the soil solution DOC input or output rate in the n+1th time step, the MAOC density of the adsorption / desorption process and the MAOC density of the non-adsorption / desorption process at the nth moment are calculated using formulas (2) and (3) in step 2, and then the unknown soil solution DOC concentration at the n+1th moment is calculated using formula (14) in step 5, and then the MAOC density of the soil adsorption / desorption process and the total MAOC density at the n+1th moment are calculated using formulas (2) and (3) in step 2;

[0046] That is, according to the known soil solution DOC concentration and total MAOC density at the nth moment and soil volumetric water content The value of and the soil solution DOC input or output rate in the n+1th time step These values ​​are used to calculate the MAOC density per unit volume of soil undergoing adsorption / desorption processes at this moment based on the modified Langmuir adsorption function formula (2). Based on formula (3), the MAOC density at which adsorption / desorption cannot occur is calculated: ;

[0047] Substitute the above calculated variables into equations (11), (12) and (13) to obtain variables A, P and B. Then substitute these three variables into the differential equation system to solve equation (14) to obtain the DOC concentration of the solution at time n+1: ;Will Substituting into formula (2) we can solve ; Use formula (3) to obtain the total MAOC density at the n+1th moment.

[0048] The method for calculating soil mineral-bound organic carbon based on the Langmuir adsorption function of the present invention uses the difference (unknown quantity) in the amount of DOC adsorbed and desorbed by soil minerals to respectively establish differential equations for the change of soil solution DOC concentration and MAOC density with time during the adsorption / desorption process; improves the Langmuir adsorption function describing the relationship between saturated soil solution DOC concentration and MAOC so that it can describe the relationship between unsaturated soil solution DOC concentration and soil MAOC density during adsorption / desorption; based on the modified Langmuir adsorption function, the difference format of the two differential equations is solved simultaneously; the solution DOC concentration at a new moment is obtained, and then the soil MAOC density and the total MAOC density during the adsorption / desorption process at the new moment are obtained using the Langmuir adsorption function. This method avoids introducing adsorption and desorption coefficients and directly solving the nonlinear adsorption and desorption rates. The principle of this method for calculating soil mineral-bound organic carbon based on the Langmuir adsorption function is simple, and it can ensure the mass balance of organic carbon in the calculation time step. It can be used in the soil organic carbon numerical model, thereby improving the model's simulation ability of the soil organic carbon decomposition rate and carbon pool size. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] FIG1 is a flow chart of an implementation method of a method for calculating soil mineral-bound organic carbon based on an adsorption function of the present invention;

[0050] FIG. 2 is a flowchart of the calculation implementation of the change in MAOC density caused by the reduction of DOC in the soil solution in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0051] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0052] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations and / or combinations thereof.

[0053] As shown in FIG1 , FIG1 is a flow chart of a method for calculating soil mineral-bound organic carbon based on an adsorption function of the present invention. The method for calculating soil mineral-bound organic carbon based on an adsorption function includes:

[0054] Step 1: Collect soil parameters, including soil bulk density (kg m -3 ), porosity (m 3 m -3 ), soil binding affinity parameters (m 3 g -1 )、Maximum soil MAOC per unit mass (g C kg -1 soil) and other parameters, It represents the intensity of interaction between minerals and DOC in unit mass of soil.

[0055] Step 2, modify the Langmuir adsorption function to describe the relationship between the DOC concentration in the unsaturated soil solution and the density of MAOC at which adsorption / desorption processes can occur.

[0056] The volumetric water content is The saturated soil is in equilibrium, and the soil solution DOC can undergo adsorption / desorption with all MAOC. The Langmuir adsorption function describes the concentration of DOC in the saturated soil solution. (g Cm -3 water) and total MAOC density per unit volume of soil (g C m -3 soil):

[0057] (1)

[0058] Since the Langmuir adsorption function is a regression equation based on experimental observation data of saturated soil, the algorithm of the present invention believes that since the process of soil mineral adsorption / desorption of DOC can only occur in the soil solution, when the soil is at a volumetric water content of (m 3 m -3 ) under unsaturated conditions, the MAOC density of the soil undergoing adsorption / desorption process (gC m -3 soil) and total MAOC density The relationship is linearly dependent on soil moisture , modify the Langmuir adsorption function to:

[0059] (2)

[0060] The MAOC density at which adsorption / desorption cannot occur when the soil volumetric water content remains unchanged (g C m -3 soil) does not change with time and can be calculated as follows:

[0061] (3)

[0062] Step 3: Under the condition that the soil moisture content remains unchanged, differential equations for the time-varying DOC concentration in the soil solution and the MAOC density during the adsorption / desorption process in the soil are established to describe the mass balance of each carbon pool.

[0063] The change of soil solution DOC concentration mainly comes from the input or output of DOC and the change of mineral adsorption of soil solution DOC. The mass balance equation of the change of solution DOC concentration in unit volume of soil over time can be written as:

[0064] (4)

[0065] in, It is the sum of the amount of DOC adsorbed on the mineral surface (-) and the amount of MAOC desorbed into the solution (+) per unit time and per unit soil (g C m -3 soil -1 ); is the input or output rate of DOC per unit volume of soil solution per unit time (g C m -3 soil -1 ), t represents the time in hours (h).

[0066] The change in MAOC density per unit volume of soil undergoing adsorption / desorption is mainly caused by the difference between the adsorption and desorption amounts, and its mass balance equation over time can be written as:

[0067] (5)

[0068] Step 4, establish the numerical difference equations of the solution DOC and the MAOC differential equations for the adsorption / desorption process occurring in the unit volume of soil.

[0069] The difference equations of equations (4) and (5) are written as:

[0070] (6)

[0071] (7)

[0072] in is the time step of the numerical calculation, which is the length between two moments; and is the value at the nth moment, and is the value at the n+1th moment; and

[0073] are their respective values ​​in the n+1th time step (the step between the nth and n+1th moments).

[0074] Then, the modified Langmuir adsorption function is used to rewrite the numerical difference equation of the MAOC density where the adsorption / desorption process occurs. Equation (7) is rewritten as:

[0075] (8)

[0076] Step 5: If the variable values ​​at the nth time and the soil solution DOC input or output in the n+1th time step are known, the differential equations can be solved simultaneously.

[0077] Adding equations (6) and (8) together gives:

[0078] (9)

[0079] make (10)

[0080] (11)

[0081] (12)

[0082] Equation (9) can be rewritten as

[0083] (13)

[0084] According to the solution formula of the two-variable linear equation (13), the solution at the n+1th moment is obtained:

[0085] (14)

[0086] Step 6, substitute the known variables at the nth moment into the solution formula in step 5 to obtain the unknown variables at the n+1th moment.

[0087] Get the known soil solution DOC concentration at time n (g C m -3 water), total MAOC density and soil volumetric water content The value of and the soil solution DOC input or output in the n+1th time step The MAOC density of the adsorption / desorption process per unit volume of soil at this moment is calculated based on the modified Langmuir adsorption function formula (2). (g C m -3soil); Based on formula (3), the MAOC density where adsorption / desorption process cannot occur is calculated .

[0088] Substitute the above calculated variables into equations (11), (12) and (13) to obtain variables A, P and B. Then substitute these three variables into the differential equation system to solve equation (14) to obtain the DOC concentration of the solution at time n+1: ;Will Substituting into formula (2) we can solve ; Use formula (3) to obtain the total MAOC density at the n+1th moment.

[0089] The above calculation method avoids directly solving the variables The solution of the difference equation can ensure that the modified Langmuir adsorption function is satisfied between organic carbon DOC and MAOC, and can ensure the total mass balance of the two carbon pools.

[0090] In a specific embodiment of the present invention, as shown in FIG. 2 , the embodiment provides a calculation implementation process of the change in MAOC density caused by the reduction of DOC in the soil solution.

[0091] Step 21, at the initial time (n=0), the soil solution DOC concentration (g C m -3 ), total MAOC density per unit volume of soil (g C m -3 ); the reduction rate of soil solution DOC 50% of the total DOC (g Cm -3 h -1 ). Soil volume water content 0.2 (m 3 m -3 ), the numerical calculation time step is half an hour (h) Collect the soil parameter data required for the calculation of this embodiment (see Table 1).

[0092] Table 1 Soil parameter data table

[0093]

[0094] Step 22: Substitute the soil bulk density in Table 1 (kg m -3 ), porosity (m 3 m -3 ), soil binding affinity parameters (m 3 g -1 )、Maximum soil MAOC per unit mass (g C kg -1 The parameters such as soil, soil solution DOC concentration and soil volume water content at the known time (n = 0) are substituted into the modified Langmuir adsorption formula (2) to calculate the MAOC density (g C m -3 ):

[0095]

[0096] Using the known total soil MAOC density at the initial time, calculate (g C m -3 ):

[0097]

[0098] Using the reduction rate of soil solution DOC , to calculate the DOC output (g C m -3 ):

[0099]

[0100] Step 23, the parameters in Table 1, soil volume water content , soil solution DOC concentration at time 0 , MAOC density during adsorption / desorption process And the soil solution DOC output in the first time step is known Substituting into equations (10)-(12), we can obtain the variables A, B and P:

[0101]

[0102]

[0103]

[0104] Substituting A, B and P into the differential equations to solve formula (14), we can obtain the soil solution DOC concentration at the first moment: (g Cm -3 ):

[0105]

[0106] Will Substitute into the modified Langmuir adsorption formula (2) to calculate the MAOC density during the adsorption / desorption process: (g C m -3 ):

[0107]

[0108] Will Substituting into equation (3) to calculate the total MAOC density (g C m -3 ):

[0109]

[0110] Deviation of the total mass balance of soil MAOC and DOC per unit volume per unit time step is calculated as:

[0111]

[0112] Relative deviation:

[0113] .

[0114] The soil mineral-bound organic carbon calculation method based on adsorption function of the present invention describes the physical and chemical mechanism of soil mineral adsorption of DOC between soil DOC and MAOC. The method requires DOC and MAOC data at a certain moment, and then according to the input and output of DOC in the time step and other data, the values ​​of DOC and MAOC at the next moment can be simulated and predicted. The present invention adopts a calculation method based on physical and chemical mechanism, which greatly improves the prediction accuracy of MAOC value and avoids the generation of prediction system error as much as possible.

[0115] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions recorded in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0116] Except for the technical features described in the specification, all other technical features are known technologies to those skilled in the art.

Claims

1. A method for calculating soil mineral-bound organic carbon based on adsorption function, characterized in that: The soil mineral-bound organic carbon calculation method based on adsorption function includes: Step 1, collect soil parameters and data; Step 2, modify the Langmuir adsorption function to describe the relationship between the DOC concentration of unsaturated soil solution and the MAOC density where adsorption / desorption processes can occur; Step 3, when the soil water content remains unchanged, differential equations for the time-varying DOC concentration in the soil solution and the MAOC density in the soil adsorption / desorption process are established to describe the mass balance of the respective carbon pools; Step 4, establishing numerical difference equations of the solution DOC and the MAOC differential equations for the adsorption / desorption process occurring in a unit volume of soil; Step 5, solving the difference equations simultaneously; Step 6, calculating the soil solution DOC concentration at the new moment, the MAOC density of the soil adsorption / desorption process, and the total MAOC density; In step 2, at a volumetric water content of The saturated soil is in equilibrium, and the DOC in the soil solution can undergo adsorption / desorption with all MAOC. The Langmuir adsorption function describes the DOC concentration in the saturated soil solution. and total soil MAOC density per unit volume The relationship between: （1） The Langmuir adsorption function is a regression equation based on experimental observation data of saturated soil. Since the adsorption / desorption process of DOC by soil minerals can only occur in soil solution, when the soil has a volumetric water content of Under unsaturated conditions, the MAOC density of the soil undergoing adsorption / desorption process Total MAOC density The relationship is linearly dependent on soil moisture , modify the Langmuir adsorption function to: （2）。 2. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 1, characterized in that: In step 1, soil parameters including soil bulk density are collected. , Porosity , soil binding affinity parameters , Maximum soil MAOC per unit mass These parameters, It represents the intensity of interaction between minerals and DOC in unit mass of soil.

3. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 1, characterized in that: In step 2, the MAOC density at which adsorption / desorption cannot occur when the soil volumetric water content remains unchanged It does not change with time and can be calculated as follows: （3）。 4. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 3, characterized in that: In step 3, the change of soil solution DOC concentration mainly comes from the input or output of DOC and the change of mineral adsorption of soil solution DOC; the mass balance equation of the change of solution DOC concentration per unit volume of soil over time can be written as: （4） in, It is the sum of the amount of DOC adsorbed on the mineral surface in the soil per unit time and per unit volume (-) and the amount of MAOC desorbed into the solution (+); is the input or output rate of DOC per unit volume of soil solution, t represents the time in hours, is the DOC concentration of soil solution, is the volumetric water content of the soil.

5. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 4, characterized in that: In step 3, the change in MAOC density per unit volume of soil undergoing adsorption / desorption is mainly caused by the difference between the adsorption and desorption amounts, and its mass balance equation over time can be written as: （5） In the formula, is the MAOC density of the soil where adsorption / desorption process occurs.

6. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 5, characterized in that: In step 4, the difference equations of equations (4) and (5) in step 3 are written as: （6） （7） in is the time step of the numerical calculation, which is the length between two moments; and is the value at the nth moment, and is the value at the n+1th moment; and They are respectively their values ​​in the n+1th time step, that is, the step between the nth and n+1th moments.

7. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 6, characterized in that: In step 4, the numerical difference equation of the MAOC density where the adsorption / desorption process occurs is rewritten using the modified Langmuir adsorption function; Equation (7) can be rewritten as: （8）。 8. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 7, characterized in that: In step 5, if the soil solution DOC concentration at the nth time, the MAOC density of the soil adsorption / desorption process, and the solution DOC input or output rate in the n+1th time step are known variables, equations (6) and (8) in step 4 can be solved simultaneously to obtain the solution formula for the unknown soil solution DOC concentration at the n+1th time step; That is, according to the known soil solution DOC concentration at the nth moment, the MAOC density of the soil adsorption / desorption process, and the soil solution DOC input or output in the n+1th time step, the differential equations are solved simultaneously; Adding equations (6) and (8) together gives: （9） make (10) （11） （12) Equation (9) can be rewritten as (13) According to the solution formula of the two-variable linear equation (13), the solution at the n+1th moment is obtained: (14)。 9. The method for calculating soil mineral-bound organic carbon based on adsorption function according to claim 8, characterized in that: In step 6, based on the known soil solution DOC concentration and total MAOC density at the nth time and the soil solution DOC input or output rate in the n+1th time step, the MAOC density of the adsorption / desorption process and the MAOC density of the non-adsorption / desorption process at the nth time are calculated using formulas (2) and (3) in step 2, and then the unknown soil solution DOC concentration at the n+1th time is calculated using formula (14) in step 5, and then the MAOC density of the soil adsorption / desorption process and the total MAOC density at the n+1th time are calculated using formulas (2) and (3) in step 2; That is, according to the known soil solution DOC concentration and total MAOC density at the nth moment and soil volumetric water content The value of and the soil solution DOC input or output rate in the n+1th time step These values ​​are used to calculate the MAOC density per unit volume of soil undergoing adsorption / desorption processes at this moment based on the modified Langmuir adsorption function formula (2). ; Based on formula (3), the MAOC density at which adsorption / desorption cannot occur is calculated: ; Substitute the above calculated variables into equations (11), (12) and (13) to obtain variables A, P and B. Then substitute these three variables into the differential equation system to solve equation (14) to obtain the DOC concentration of the solution at time n+1: ;Will Substituting into formula (2) we can solve ; Use formula (3) to obtain the total MAOC density at the n+1th moment.

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