Method for estimating runoff nutrient concentration based on equivalent exchange layer

Abstract

The application discloses a kind of based on equivalent exchange layer's runoff nutrient concentration estimation method, steps include: step 1: set up equivalent exchange layer theoretical framework, and based on equivalent exchange layer depth establishes nutrient loss prediction model;Step 2: perfect the related parameters of nutrient loss prediction model, establish estimation model;Step 3, in practical application, the estimation model three expressions of step 2 are substituted into formula (13) of step 1, then input the data collected in situ, calculate the change process of nutrient concentration using formula (13), namely, this application method greatly simplifies the calculation workload of nutrient loss process, combined with nutrient loss prediction model and estimation model, only need one rainfall data, determine rainfall intensity, initial soil moisture content, outlet flow, runoff time and initial soil nutrient concentration can simulate the nutrient loss process.

Description

Technical Field

[0001] This invention belongs to the technical field of soil nutrient loss assessment with surface runoff, and relates to a method for estimating runoff nutrient concentration based on an equivalent exchange layer. Background Technology

[0002] Under natural rainfall conditions, surface runoff from sloping farmland carries away a large amount of soil nutrients, leading to a series of environmental problems such as sloping farmland degradation and agricultural non-point source pollution. In fact, factors such as rainfall intensity, temperature, wind speed, and the spatiotemporal variability of soil structure during natural rainfall have a significant impact on the acquisition of measured data. In particular, the amount of chemical migration during natural rainfall is difficult to quantify on-site.

[0003] Existing studies have used artificial rainfall experiments and upstream water flushing experiments to simulate the characteristics of nutrient loss with runoff and to establish mathematical models to simulate the loss process. However, most of these mathematical models are based on the mixed layer theory and do not consider the contribution of raindrop splash to nutrient loss. Therefore, these models cannot be applied in the Loess Plateau region, which suffers from severe soil erosion.

[0004] To address this situation, it is essential to propose a more suitable theory of equivalent exchange layer depth for the Loess Plateau region and to establish an analytical model for predicting nutrient loss based on the equivalent exchange layer. Summary of the Invention

[0005] The purpose of this invention is to provide a method for estimating runoff nutrient concentration based on an equivalent exchange layer, which solves the problem that existing mathematical models are difficult to predict runoff nutrient concentration conveniently and accurately.

[0006] The technical solution adopted in this invention is a method for estimating runoff nutrient concentration based on an equivalent exchange layer, which is implemented according to the following steps:

[0007] Step 1: Establish the theoretical framework of the equivalent exchange layer and build a nutrient loss prediction model based on the depth of the equivalent exchange layer.

[0008] The specific process of establishing a nutrient loss prediction model is as follows:

[0009] 1.1) In the equivalent exchange layer, the expression for the nutrient mass conservation equation is:

[0010]

[0011] In equation (1), EED is the equivalent exchange layer depth, in cm; θ s This is the saturated moisture content, measured in cm³. 3 cm -3 ;ρ s This refers to soil bulk density, measured in grams per centimeter (g / cm³).-3 ;k a This is the soil adsorption coefficient, measured in cm. 3 g -1 t is the rainfall time in minutes; i(t) is the infiltration rate in centimeters per minute. -1 ;e r It is the rate of water transfer induced by raindrops, measured in cm / min. -1 C e (t) represents the nutrient concentration in the mixed layer, in mg·L⁻¹. -1 α is the ratio of the equivalent infiltration layer to the equivalent exchange layer;

[0012] 1.2) Assuming that the transfer of nutrients from soil to runoff is driven by raindrop splash, the expression for the nutrient transfer rate in runoff water is:

[0013] M r (t)=e r (1-α)C e (t), (2)

[0014] In equation (2), M r (t) is the rate at which nutrients are transferred from the mixed layer to runoff, expressed in mg / min. -1 ;

[0015] Similarly, another expression for the nutrient transfer rate in runoff water is:

[0016] M r (t)=q(t)C e (t), (3)

[0017] In equation (3), q(t) is the flow rate, and the unit is cm min. -1 ;

[0018] 1.3) The runoff generation process is represented by the approximate solution of slope runoff. The expression for the runoff generation process is as follows:

[0019]

[0020]

[0021] In equations (4) and (5), Q(t) is the runoff volume, and the unit is cm. 3 min -1 ; SC is the slope topographic factor, k is the water surface morphology factor, t p 'r' is the initial runoff time in minutes; 'r' is the rainfall intensity in centimeters per minute. -1 ;

[0022] 1.4) The expression for the infiltration process under rainfall conditions is:

[0023]

[0024] In equation (6), S is the soil infiltration rate, and the unit is cm min. -0.5 t0 is the time difference between water infiltration and rainfall infiltration, measured in minutes (min), t0 = s. 2 / (4p 2 );

[0025] 1.5) Combining equations (1) and (6), the nutrient concentration in the equivalent exchange layer is obtained, as expressed below:

[0026]

[0027] In equation (7), C m It is t p Nutrient concentration in the equivalent exchange layer at any given time, expressed in mg·L⁻¹. -1 ;

[0028] in,

[0029]

[0030] β=k a ρ s +θ s (9)

[0031] In equation (8), C s This refers to the initial nutrient content of the soil, measured in mg / g. -1 ;

[0032] 1.6) Combining equations (2), (3), (5), (6), and (7), the nutrient concentration in the runoff is obtained, as shown in the following expression:

[0033]

[0034] In equation (10), C r (t) represents the nutrient concentration in the runoff, in mg·L⁻¹. -1 ;

[0035] 1.7) Assuming the equivalent infiltration layer depth decreases exponentially, the ratio of the equivalent infiltration layer to the equivalent exchange layer is expressed as follows:

[0036] α=α0exp(-m(t-t0)), (11)

[0037] In equation (11), α0 is the initial ratio of the equivalent infiltration layer to the equivalent exchange layer, and m is a coefficient;

[0038] Combining equations (1), (6), and (11), the expression for the nutrient concentration in the equivalent exchange layer is:

[0039]

[0040] in,

[0041]

[0042] 1.8) The expressions for the nutrient concentration and total loss in runoff are:

[0043]

[0044]

[0045] In equation (14), TN is the total amount of nutrient loss, and the unit is mg; a nutrient loss prediction model is established;

[0046] Step 2: Improve the relevant parameters of the nutrient loss prediction model and establish an estimation model;

[0047] Step 3: In practical applications, substitute the three expressions of the estimation model established in Step 2 into Equation (13) in Step 1, input the data collected on site, and use Equation (13) to calculate the nutrient concentration change process.

[0048] The beneficial effects of this invention are that, based on the equivalent exchange layer theory, a nutrient loss prediction model is established, and model parameters are obtained through 36 measured nutrient loss data points; furthermore, an estimation model based on rainfall intensity, initial soil moisture content, and slope is established. This method significantly simplifies the computational workload of the nutrient loss process. Combining the nutrient loss prediction model and the estimation model, only one rainfall data point is needed, measuring rainfall intensity, initial soil moisture content, outlet flow rate, runoff time, and initial soil nutrient concentration, to simulate the nutrient loss process. Attached Figure Description

[0049] Figure 1 This is a simulated soil layer profile used in the method of this invention;

[0050] Figure 2 This is a simulation diagram of the potassium ion loss process in an embodiment of the method of the present invention;

[0051] Figure 3 This is a simulation diagram of the rapid phosphorus ion loss process in an embodiment of the method of the present invention;

[0052] Figure 4 This is a simulation diagram of the nitrate nitrogen loss process in an embodiment of the method of the present invention. Detailed Implementation

[0053] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0054] Reference Figure 1 The method for estimating runoff nutrient concentration of the present invention is implemented according to the following steps:

[0055] Step 1: Establish the theoretical framework of the equivalent exchange layer and build a nutrient loss prediction model based on the depth of the equivalent exchange layer.

[0056] Based on the exchange layer theory of Gao et al. (2004), without considering diffusion, an equivalent exchange layer theory is established, mainly including the following three points: 1) It is assumed that raindrop splashing is the only way nutrients migrate from the upper soil layer to the runoff; 2) It is assumed that only nutrients in the surface "very thin" soil layer have the ability to exchange into the runoff and the lower soil, and this "very thin" soil layer is defined as the "equivalent exchange layer"; 3) Furthermore, it is assumed that the nutrients entering the runoff through raindrop splashing and the nutrients entering the lower soil layer through infiltration are equivalent to the changes in nutrients in two independent spaces, that is: the equivalent mixed layer is divided into upper and lower nutrient layers, and it is assumed that the decrease in nutrients in the upper layer is equivalent to the nutrient content entering the runoff layer through raindrop splashing; similarly, the decrease in nutrients in the lower layer is equivalent to the nutrient content entering the lower soil layer through infiltration. Therefore, the upper and lower nutrient layers are defined as the "equivalent runoff layer" and the "equivalent infiltration layer" respectively.

[0057] The specific process of establishing a nutrient loss prediction model is as follows:

[0058] 1.1) In the equivalent exchange layer, the expression for the nutrient mass conservation equation is:

[0059]

[0060] In equation (1), EED is the equivalent exchange layer depth, in cm; θ s This is the saturated moisture content, measured in cm³. 3 cm -3 ;ρ s This refers to soil bulk density, measured in grams per centimeter (g / cm³). -3 ;k a This is the soil adsorption coefficient, measured in cm. 3 g -1 ,K + ,PO4 3- -P,NO3 - k in -N a The values ​​are 0.026, 0.160, and 0.030 respectively; t is the rainfall time in minutes; i(t) is the infiltration rate in cm / min. -1 ;e rIt is the rate of water transfer induced by raindrops, measured in cm / min. -1 C e (t) represents the nutrient concentration in the mixed layer, in mg·L⁻¹. -1 α is the ratio of the equivalent infiltration layer to the equivalent exchange layer;

[0061] 1.2) There are many ways in which nutrients are transferred from the mixed layer to surface runoff, any of which can be summarized as a mass transfer process. In this step, we assume that the transfer of nutrients from the soil to the runoff is driven by raindrop splash, then the expression for the nutrient transfer rate in the runoff water is:

[0062] M r (t)=e r (1-α)C e (t), (2)

[0063] In equation (2), M r (t) is the rate at which nutrients are transferred from the mixed layer to runoff, expressed in mg / min. -1 ;

[0064] Similarly, another expression for the nutrient transfer rate in runoff water is:

[0065] M r (t)=q(t)C e (t), (3)

[0066] In equation (3), q(t) is the flow rate, and the unit is cm min. -1 ;

[0067] 1.3) The runoff generation process is represented by the slope runoff approximation solution (the slope runoff approximation solution is existing technology, established by Tao et al. in 2018). The expression for the runoff generation process is as follows:

[0068]

[0069]

[0070] In equations (4) and (5), Q(t) is the runoff volume, and the unit is cm. 3 min -1 ; SC is the slope topographic factor, k is the water surface morphology factor, t p 'r' is the initial runoff time in minutes; 'r' is the rainfall intensity in centimeters per minute. -1 ;

[0071] 1.4) The expression for the infiltration process under rainfall conditions is:

[0072]

[0073] In equation (6), S is the soil infiltration rate, and the unit is cm min. -0.5 t0 is the time difference between water infiltration and rainfall infiltration, measured in minutes (min), t0 = s. 2 / (4p 2 );

[0074] 1.5) Combining equations (1) and (6), the nutrient concentration in the equivalent exchange layer is obtained, as expressed below:

[0075]

[0076] In equation (7), C m It is t p Nutrient concentration in the equivalent exchange layer at any given time, expressed in mg·L⁻¹. -1 ;

[0077] in,

[0078] β=k a ρ s +θ s (9)

[0079] In equation (8), C s This refers to the initial nutrient content of the soil, measured in mg / g. -1 ;

[0080] 1.6) Combining equations (2), (3), (5), (6), and (7), the nutrient concentration in the runoff is obtained, as shown in the following expression:

[0081]

[0082] In equation (10), C r (t) represents the nutrient concentration in the runoff, in mg·L⁻¹. -1 ;

[0083] 1.7) Existing research indicates that as runoff progresses, runoff scouring intensifies, increasing the depth of soil layers involved in runoff exchange, leading to a continuous decrease in the nutrient carrying capacity of infiltrated water; that is, as the duration of runoff increases, the equivalent infiltration layer decreases, while the equivalent runoff layer increases. Assuming the equivalent infiltration layer depth decreases exponentially, the ratio of the equivalent infiltration layer to the equivalent exchange layer is expressed as:

[0084] α=α0exp(-m(t-t0)), (11)

[0085] In equation (11), α0 is the initial ratio of the equivalent infiltration layer to the equivalent exchange layer, and m is a coefficient;

[0086] Combining equations (1), (6), and (11), the expression for the nutrient concentration in the equivalent exchange layer is:

[0087]

[0088] in,

[0089]

[0090] 1.8) Further, the expressions for the nutrient concentration and total loss in runoff are:

[0091]

[0092]

[0093] In equation (14), TN is the total amount of nutrient loss, and the unit is mg; a nutrient loss prediction model is established.

[0094] Step 2: Improve the relevant parameters of the nutrient loss prediction model and establish an estimation model. The specific process is as follows:

[0095] 2.1) A parameter iteration calculation program based on the Markov chain Monte Carlo (MCMC) architecture was written in Python. Then, the calculation equation (13) was added to the parameter iteration calculation program. The 36 sets of measured nutrient loss data shown in Table 1 were then input to solve the four parameters involved in equation (13), namely EED, e r ,α0,m;

[0096] 2.2) Establish parameters EED,e r α0 is an empirical function relating rainfall intensity, initial moisture content, and slope, expressed as follows:

[0097] EED = 2.305r 0.2465 θ0 0.1251 slp -0.086 R 2 =0.917 (15)

[0098] e r =0.0578r 1.481 exp(4.6835θ0)slp -0.486 R 2 =0.995 (16)

[0099] α0 = 3.4216r 0.5407 θ0 0.3124 slp -0.215 R 2 =0.962 (17)

[0100] Table 1. Basic parameters of the measured nutrient loss prediction model

[0101]

[0102] The estimation model is now complete.

[0103] Step 3: In practical applications, substitute the equations (15), (16), and (17) established in Step 2 into equation (13), and then input the data of rainfall intensity, slope, initial moisture content, rainfall duration, and initial nutrient concentration collected on site. Calculate the nutrient concentration change process using equation (13), and the result is obtained.

[0104] Experimental verification:

[0105] Substitute equations (15), (16), and (17) obtained in step 2 into equation (13) to establish a new nutrient loss prediction model; then substitute the initial nutrient loss concentration of the measured nutrient loss data into equation (13) to verify the accuracy of the nutrient loss prediction model.

[0106] The verification results are shown in Tables 2, 3, and 4, demonstrating that the combination of the nutrient loss prediction model established in step 1 and the parameter estimation model established in step 2 of the method of the present invention can accurately predict the nutrient loss process.

[0107] Table 2. Validation results of potassium ion loss

[0108]

[0109] Table 3. Validation results of phosphorus ion loss

[0110]

[0111] Table 4. Verification results of nitrate nitrogen ion loss

[0112]

Claims

1. A method for estimating runoff nutrient concentration based on an equivalent exchange layer, characterized in that, Follow these steps to implement the procedure: Step 1: Establish the theoretical framework of the equivalent exchange layer and build a nutrient loss prediction model based on the depth of the equivalent exchange layer. First, without considering diffusion effects, we establish the theory of equivalent exchange layers, which includes the following three points: 1) Assume that raindrop splashing is the only way nutrients are transferred from the upper soil layer to runoff; 2) Assuming that only the nutrients in the surface "very thin" soil layer have the ability to enter runoff and exchange into the underlying soil, this "very thin" soil layer is defined as the "equivalent exchange layer"; 3) Assume that the nutrients entering the runoff through raindrop splash and the nutrients entering the lower soil layer through infiltration are equivalent to the changes in nutrients in two independent spaces. That is, the equivalent mixed layer is divided into upper and lower nutrient layers. It is assumed that the decrease in nutrients in the upper layer is equivalent to the nutrient content entering the runoff layer through raindrop splash; similarly, the decrease in nutrients in the lower layer is equivalent to the nutrient content entering the lower soil layer through infiltration. Therefore, the upper and lower nutrient layers are defined as the "equivalent runoff layer" and the "equivalent infiltration layer", respectively. Then, the specific process of establishing a nutrient loss prediction model is as follows: 1.1) In the equivalent exchange layer, the expression for the nutrient mass conservation equation is: ，(1) In equation (1), EED It is the equivalent exchange layer depth, in cm; θ s This is the saturated moisture content, measured in cm³. 3 cm -3 ; ρ s This refers to soil bulk density, measured in grams per centimeter (g / cm³). -3 ; k a This is the soil adsorption coefficient, measured in cm. 3 g -1 ; t This refers to the duration of rainfall, measured in minutes. i ( t () is the infiltration rate, measured in cm / min. -1 ; e r It is the rate of water transfer induced by raindrops, measured in cm / min. -1 ; C e ( t () represents the nutrient concentration in the mixed layer, in mg·L⁻¹. -1 ; α It is the ratio of the equivalent infiltration layer to the equivalent exchange layer; 1.2) Assuming that the transfer of nutrients from soil to runoff is driven by raindrop splash, the expression for the nutrient transfer rate in runoff water is: ，(2) In equation (2), M r ( t () is the rate at which nutrients are transferred from the mixed layer to runoff, measured in mg / min. -1 ; Similarly, another expression for the nutrient transfer rate in runoff water is: ，(3) In equation (3), q ( t () is the flow rate, in cm / min. -1 ; 1.3) The runoff generation process is represented by the approximate solution of slope runoff. The expression for the runoff generation process is as follows: ，(4) ，(5) In equations (4) and (5), Q ( t () is runoff, the unit is cm. 3 min -1 ; SC It is a comprehensive topographic factor of the slope. k It is a water surface morphology factor. t p This is the initial abortion time, in minutes; r It refers to rainfall intensity, measured in cm / min. -1 ; 1.4) The expression for the infiltration process under rainfall conditions is: ，(6) In equation (6), S It refers to soil infiltration rate, measured in cm / min. -0.5 ; t 0 represents the time difference between water infiltration and rainfall infiltration, measured in minutes. t 0= S 2 / (4 p 2 ); 1.5) Combining equations (1) and (6), the nutrient concentration in the equivalent exchange layer is obtained, as shown in the following expression: ，(7) In equation (7), C m yes t p Nutrient concentration in the equivalent exchange layer at any given time, expressed in mg·L⁻¹. -1 ; in, ，(8) ，(9) In equation (8), C s This refers to the initial nutrient content of the soil, measured in mg / g. -1 ; 1.6) Combining equations (2), (3), (5), (6), and (7), the nutrient concentration in the runoff is obtained, as shown in the following expression: ，(10) In equation (10), C r ( t () represents the nutrient concentration in runoff, measured in mg·L⁻¹. -1 ; 1.7) Assuming the equivalent infiltration layer depth decreases exponentially, the ratio of the equivalent infiltration layer to the equivalent exchange layer is expressed as follows: ，(11) In equation (11), α 0 is the initial ratio of the equivalent infiltration layer to the equivalent exchange layer. m It is a coefficient; Combining equations (1), (6), and (11), the expression for the nutrient concentration in the equivalent exchange layer is: ，(12A) in, (12B) ，(12C) 1.8) The expressions for the nutrient concentration and total loss in runoff are: ，(13) ，(14) In equation (14), TN This is the total amount of nutrients lost, expressed in mg. From this point on, a nutrient loss prediction model was established; Step 2: Improve the relevant parameters of the nutrient loss prediction model and establish an estimation model. The specific process is as follows: 2.1) A parameter iteration calculation program based on a Markov chain Monte Carlo architecture is written in Python. Then, the calculation equation (13) is added to this parameter iteration calculation program. Then, the measured nutrient loss data is input, and the four parameters involved in equation (13) are solved. EED, e r , α 0 ,m ; 2.2) Establish parameters EED, e r , α 0 , The empirical function relating rainfall intensity, initial moisture content, and slope is expressed as follows: ，R 2 =0.917(15) ，R 2 =0.995(16) ，R 2 =0.962(17) The estimation model is now complete. Step 3: In practical applications, substitute the three expressions of the estimation model established in Step 2 into Equation (13) in Step 1, input the data collected on site, and use Equation (13) to calculate the nutrient concentration change process.

2. The method for estimating runoff nutrient concentration based on an equivalent exchange layer according to claim 1, characterized in that: In step 1, K + ,PO4 3- -P,NO3 - -N k a The values ​​are 0.026, 0.160, and 0.030, respectively.

3. The method for estimating runoff nutrient concentration based on an equivalent exchange layer according to claim 1, characterized in that: In step 3, the data collected on-site includes rainfall intensity, slope, initial moisture content, rainfall duration, and initial nutrient concentration.

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