The method of estimating the parameters of the linear plus platform fertilizer effect function equation

Abstract

The invention discloses a method for calculating the parameters of a linear plus platform type fertilizer effect function equation, which relates to a method for calculating the parameters of a linear plus platform type fertilizer effect function equation, and belongs to the field of soil fertilizer science. The invention aims to solve the technical problems that the existing method for determining the parameters of the fertilizer effect function equation is time-consuming and the experiment is prone to failure. The method for calculating the parameters of the linear plus platform type fertilizer effect function equation is as follows: Y = 0.75m (X + X s ), X <X′ max (1) Y = Y′ max , X ≥ X′ max (2) Where Y is crop yield, unit: kg·hm ‑2 , X is the amount of nutrient applied; m( is the yield formed by the crop absorbing 1kg of nutrients, i.e., nutrient production efficiency, unit: kg·hm ‑2 , X s The actual available nutrient content of soil, unit: kg·hm ‑2 , Y max (kg·hm ‑2 ) is the target output, unit: kg·hm ‑2 The present invention is based on crop nutrient physiological utilization rate (m), target yield (Y max ) Actual soil available nutrient content (X s ) is used as the basis to solve the problems of time-consuming method and easy experiment failure in determining the parameters of the linear plus platform fertilizer effect function equation, and the parameters of the linear plus platform fertilizer effect function equation are quickly deduced.

Description

Technical Field

[0001] The invention relates to a method for calculating parameters of a linear plus platform fertilizer effect function equation, and belongs to the field of soil fertilizer science. Background Art

[0002] There is a very significant linear plus plateau functional relationship between crop yield and fertilizer application amount, namely the fertilizer effect function. The amount of fertilizer can be determined based on the fertilizer effect function. The conventional method for determining the parameters of the fertilizer effect function equation requires field experiments, which is time-consuming (at least one growing season) and is easily affected by unreasonable fertilizer application settings, resulting in unsatisfactory experiments or experimental failures. How to determine the parameters of the fertilizer effect function equation based on crop nutrient requirements has always been a key issue that has not been resolved in related research. Summary of the invention

[0003] The purpose of the present invention is to solve the technical problems that the existing method for determining the parameters of the fertilizer effect function equation is time-consuming and the experiment is prone to failure, and a method for estimating the parameters of a linear plus platform fertilizer effect function equation is provided.

[0004] The calculation method of the parameters of the linear plus platform fertilizer effect function equation is as follows:

[0005] Y=0.75m(X+X s ), X <X′ max (1)

[0006] Y=Y′ max , X ≥ X′ max (2)

[0007]

[0008] Where Y is crop yield, unit: kg·hm -2 , X is the amount of nutrient applied; m is the yield formed by the crop absorbing 1 kg of nutrients, i.e., nutrient production efficiency, unit: kg·hm -2 , X s The actual available nutrient content of soil, unit: kg·hm -2 , Y max is the target output, unit: kg·hm -2 .

[0009] The present invention is based on the crop nutrient production efficiency (m), target yield (Y max ) and the measured available nutrient content in soil (X s ) is used as the basis to solve the problems of time-consuming method and easy experiment failure in determining the parameters of the linear plus platform fertilizer effect function equation, and the parameters of the linear plus platform fertilizer effect function equation are quickly deduced. DETAILED DESCRIPTION

[0010] The technical solution of the present invention is not limited to the specific implementation modes listed below, but also includes any combination of the specific implementation modes.

[0011] Specific implementation method 1: The method for calculating the parameters of the linear plus platform fertilizer effect function equation in this implementation method is as follows:

[0012] Y=0.75m(X+X s ), X <X′ max (1)

[0013] Y=Y′ max , X ≥ X′ max (2)

[0014]

[0015] Where Y is crop yield, unit: kg·hm -2 , X is the amount of nutrient applied; m is the yield formed by the crop absorbing 1 kg of nutrients, i.e., nutrient production efficiency, unit: kg·hm -2 , X s The actual available nutrient content of soil, unit: kg·hm -2 , Y max is the target output, unit: kg·hm -2 .

[0016] The derivation process of equation (1) is:

[0017] The form of the quadratic fertilizer effect equation is:

[0018] Y=aX 2 +mX+c (4)

[0019] In the formula, a<0, m>0, c>0.

[0020] The marginal output equation is derived from equation (4), that is,

[0021]

[0022] In the formula, is the marginal yield, i.e. the yield increase caused by the application of unit nutrients, therefore, And a<0. So, The maximum value of is m. Theoretically, The maximum value is when the nutrients applied to the soil are completely absorbed by the crop. At this time, m is the yield value formed by the crop absorbing a unit amount of nutrients, that is, the nutrient production efficiency, which is related to the nutrient coefficient n (the amount of nutrients absorbed by the crop to form a unit yield, kg kg -1 ) are reciprocals of each other, that is

[0023] m×n=1 (6)

[0024] The general form of the linear plus plateau fertilizer effect equation is:

[0025] Y=KX+c(X <X′ max ) (7)

[0026] Y=Y′ max (X≥X′ max ) (8)

[0027] Assuming X = -(m / 4a), the outputs of equation (4) and equation (7) are equal, then

[0028]

[0029] Solving equation (9) yields

[0030] K=0.75m (10)

[0031] Combining equation (7) and equation (10) we get:

[0032] Y=0.75mX+c(X <X′ max ) (11)

[0033] The formula for calculating fertilizer nutrient utilization (f) rate is:

[0034]

[0035] Combining equations (11), (12), and (6), we obtain:

[0036] f=0.75(X <X′ max ) (13)

[0037] In equation (7), parameter c is the basic yield, that is, the crop yield when no fertilizer is applied. c is determined by the amount of available nutrients absorbed by the crop from the soil. The available nutrient content of the soil is Xs, and the ratio of the amount that can be absorbed by the crop to Xs is called the soil available nutrient correction coefficient, which is equal to the fertilizer utilization rate f, that is, 0.75. Therefore, the amount of available nutrients absorbed by the crop from the soil is 0.75Xs, and the product of this and m is the crop yield when no fertilizer is applied to the soil, that is:

[0038] c=0.75X s m (14).

[0039] Combining equations (11) and (14), we get:

[0040] Y=0.75m(X+X s )(X <X′ max ) (1)

[0041] Equation (1) is the linear part of the linear plus platform fertilizer effect function equation. The platform part is the constant yield, that is, Y is a fixed value. Therefore, the target yield is Y max When , the platform part is expressed as:

[0042] Y=Y′ max (X≥X′ max ) (2)

[0043] Combining equations (1) and (2), we can obtain

[0044]

[0045] The following experiments were used to verify the effect of the present invention:

[0046] Nitrogen fertilizer test:

[0047] The target yield of cotton seed is set at 6800 kg·hm2 -2 The m values ​​corresponding to the final N absorption of the plant are approximately 24kgkg -1 The available nitrogen content of the tillage layer (0-20cm) is about 150kg·hm -2 The N application rates were 0, 150, 225, 300, and 375 kg·hm -2 , P2O5 and K2O application rates were 108 kg·hm -2 and 300kg·hm -2 The harvest yield is 2750kg·hm -2 、5578kg·hm -2 、6167kg·hm -2 、6709kg·hm -2 、6531kg·hm -2 The linear plus platform fertilizer effect function equation fitted according to the measured data is:

[0048] Y=18.25×(X+150) X≤221 (3)

[0049] Y=6800 X>221 (4)

[0050] The linear plus platform fertilizer effect function equation calculated according to the method of the present invention is:

[0051] Y=18×(X+150) X≤228 (5)

[0052] Y=6804 X≤228 (6)

[0053] P2O5 fertilizer efficiency experiment:

[0054] The target yield of cotton seed is set at 6800 kg·hm2-2 The m values ​​corresponding to the final absorption of P2O5 by the plants are approximately 70kgkg -1 The available phosphorus (P2O5) content in the tillage layer (0-20cm) is about 52kg·hm -2 The P2O5 application rates were 0, 36, 72, 108, and 144 kg·hm -2 , N and K2O application rates were both 300 kg·hm -2 The harvest yield was 2742kg·hm -2 4634kg·hm -2 、6768kg·hm -2 、6822kg·hm -2 、6698kg·hm -2 The linear plus platform P2O5 fertilizer efficiency equation is:

[0055] Y=52.7(X+52)(X<77.5) (7)

[0056] Y=6825(X≥77.5) (8)

[0057] The linear plus platform fertilizer effect function equation calculated according to the method of the present invention is:

[0058] Y=52.5(X+52)(X<78) (9)

[0059] Y=6825(X≥78) (10)

[0060] K2O fertilizer efficiency experiment:

[0061] The target yield of cotton seed is set at 6800 kg·hm2 -2 The m values ​​corresponding to the final K2O absorption of the plant are approximately 25kgkg -1 The available potassium (K2O) content in the tillage layer (0-20cm) is about 164kg·hm -2 The K2O application rates were 0, 100, 200, 300, and 400 kg·hm -2 , P2O5 and N application rates were 108 kg·hm -2 and 300kg·hm -2 The harvest yield was 3052kg·hm -2 、4980kg·hm -2 、6838kg·hm -2 、6804kg·hm -2 、6717kg·hm -2 The linear plus platform K2O fertilizer efficiency equation is:

[0062] Y=18.6(X+164)(X<204) (11)

[0063] Y=6845(X≥204) (12)

[0064] The linear plus platform fertilizer effect function equation calculated according to the method of the present invention is:

[0065] Y=18.75(X+164)(X<200) (13)

[0066] Y=6825(X≥200) (14)

[0067] The slopes of the linear platform equations of N, P2O5 and K2O calculated by the method of the present invention are 18.0, 52.5 and 18.75 respectively, and the slopes of the linear platform equations of N, P2O5 and K2O fitted according to the measured data are 18.2, 52.7 and 18.6 respectively. The calculated results of the present invention are very close to the actual results, which proves that the method of the present invention is correct. In addition, the maximum yield fertilizer application amount of N, P2O5 and K2O calculated by the method of the present invention is 228kg·hm -2 、78kg·hm -2 and 200kg·hm -2 The economic optimum fertilizer application rate of N, P2O5 and K2O calculated by the linear plus platform fertilizer efficiency equation is 221 kg·hm -2 、77.5kg·hm -2 and 204kg·hm -2 The calculation results of the present invention are almost the same as those of the conventional method, which also proves that the method of the present invention is correct.

Claims

1. A method for calculating the parameters of a linear plus platform fertilizer effect function equation, characterized in that: The method for calculating the parameters of the linear plus platform fertilizer effect function equation is as follows: Y=0.75m(X+X s ), X<X′ max (1) Y=Y′ max ,X≥X′ max (2) Where Y is crop yield, unit: kg·hm -2 , X is the amount of nutrient applied; m is the yield formed by the crop absorbing 1 kg of nutrients, i.e., nutrient production efficiency, unit: kg·hm -2 , X s The actual available nutrient content of soil, unit: kg·hm -2 , Y max is the target output, unit: kg·hm -2 ; The derivation process of equation (1) is: The form of the quadratic fertilizer effect equation is: Y=aX 2 +mX+c(4) Wherein, a<0, m>0, c>0; The marginal output equation is derived from equation (4), that is, In the formula, is the marginal output, in kg·hm -2 , that is, the yield increase caused by the application of unit nutrients, therefore, And a<0, so, The maximum value of is m; theoretically, The maximum value is when the nutrients applied to the soil are completely absorbed by the crop. At this time, the value m is the yield value formed by the crop absorbing a unit amount of nutrients, that is, the nutrient production efficiency, which is the reciprocal of the nutrient coefficient n, that is, m×n=1 (6) The general form of the linear plus plateau fertilizer effect equation is: Y=KX+c(X<X′ max )(7) Y=Y′ max (X≥X′ max ) (8) Assuming X = -(m / 4a), the outputs of equation (4) and equation (7) are equal, then Solving equation (9) yields: K = 0.75m(10); Combining equation (7) and equation (10) we get: Y=0.75mX+c(X<X′ max ) (11) The formula for calculating fertilizer nutrient utilization (f) rate is: Combining equations (11), (12), and (6), we obtain: f=0.75(X<X′ max )(13) The amount of available nutrients absorbed by crops from the soil is 0.75Xs, and the product of s and m is the crop yield when no fertilizer is applied to the soil, that is: c = 0.75 × sm (14); Combining equations (11) and (14), we get: Y=0.75m(X+X s ), X<X′ max (1) Equation (1) is the linear part of the linear plus platform fertilizer effect function equation. The platform part is the constant yield, that is, Y is a fixed value. Therefore, when the target yield is Ymax, the expression form of the platform part is: Y=Y′ max ,X≥X′ max (2) Combining equations (1) and (2), we can obtain The maximum fertilizer application amount was calculated using the linear plus platform fertilizer effect function equation.

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