JP7681303B2 - Nutrient supply amount estimation method, nutrient supply body utilization method, program, and estimation system - Google Patents

Description

Article 30, paragraph 2 of the Patent Act applies. Publication name: "Japanese Journal of Soil and Plant Nutrition Science, Vol. 91, No. 5, pp. 366-373" Publication date: October 5, 2020 Website address: https://www. jstage. jst. go. jp/article/dojo/91/5/91＿910503/＿article/-char/ja/ Publication date: October 10, 2020

The present invention relates to a method for estimating nutrient supply, a method for using a nutrient supplier, a program, and an estimation system.

In recent years, many agricultural support services, such as applications, have been developed. Among agricultural support services, in cultivation support services, understanding the amount of nutrients supplied to crops from nutrient suppliers such as soil, organic matter, and fertilizer is often important for promoting smart agriculture, which involves precise fertilization and prediction and control of crop growth. To date, technology for estimating the amount of nutrient supplied from nutrient suppliers has been researched.

As an example of such a technique, Non-Patent Document 1 describes an analytical method that uses the difference between two first-order reaction equations, based on a model in which the mineralization and organification of nitrogen in soil proceed in parallel.

Eiji Ishibashi, Hiroko Fujiwara (Shiba), Takenori Washio, Masaya Oya, "Proposal of a new analytical method for the reaction kinetics method in estimating the nitrogen mineralization rate from organic materials such as compost", Japanese Journal of Soil and Plant Nutrition Science, Vol. 85, No. 4, 2014, pp. 362-368

When the model for estimating the amount of nutrient supply from a nutrient supplier is made more complex and the number of parameters is increased, the estimated result of the nutrient supply matches the experimental measurement result well, but it tends to be difficult to set constant parameter values. The technology described in Non-Patent Document 1 is based on a model in which a maximum of seven parameters are set, so a lot of data is required to set the parameters for each nutrient supplier. In addition, because it is time-consuming to obtain that data, it has not been widely used in production sites. Therefore, there is a demand for a technology that can easily estimate the amount of nutrient supply from a nutrient supplier.

One aspect of the present invention has been made in consideration of the above problems, and its purpose is to provide a nutrient supply amount estimation method that easily estimates the amount of nutrients supplied from a nutrient supplier, and related techniques.

A nutrient supply estimation method according to one aspect of the present invention is a nutrient supply estimation method for estimating the amount of nutrients supplied from a nutrient supplier in a form that can be utilized by a plant, and includes a nutrient supply estimation step for estimating the nutrient supply amount at any time point by referring to a group of parameters for estimating the nutrient supply amount, the group of parameters including a first parameter indicating the nutrient supply amount at a reference time point, a second parameter indicating the maximum amount of change in the nutrient supply amount, a third parameter indicating the shape of an equation showing the progress of the nutrient supply amount, and a fourth parameter indicating a rate constant for the change in the nutrient supply amount.

A method for using a nutrient supplier according to one embodiment of the present invention includes estimating the state of the nutrient supplier by referring to at least one of (i) the nutrient supply amount estimated by the nutrient supply amount estimation method according to one embodiment of the present invention, and (ii) at least one parameter included in the parameter group used to estimate the nutrient supply amount.

A program according to one aspect of the present invention is a program for causing a computer to execute a nutrient supply amount estimation method according to one aspect of the present invention or a method for using a nutrient supplier according to one aspect of the present invention.

The estimation system according to one embodiment of the present invention includes a database that stores at least one of (i) a nutrient supply amount estimated by a nutrient supply amount estimation method according to one embodiment of the present invention, (ii) a state of a nutrient supplier estimated by a nutrient supplier utilization method according to one embodiment of the present invention, and (iii) any one of the values of parameters included in the parameter group used to estimate the nutrient supply amount, in association with the nutrient supplier, and an estimation device that estimates the nutrient supply amount of a test nutrient supplier by referring to the data stored in the database.

According to one aspect of the present invention, it is possible to provide a nutrient supply amount estimation method and related technology that can easily estimate the amount of nutrients supplied from a nutrient supplier.

FIG. 1 is a diagram showing the estimation results of the inorganic nitrogen content in an example.

The inventors have found that by using specific parameters set with reference to the state of the nutrient supplier, it is possible to easily estimate the amount of nutrient supply at any time. Furthermore, through extensive research, the inventors have further found that each of the specific parameters is strongly related to the state of the nutrient supplier, and that by referring to the similarity between the state of one nutrient supplier and the state of another nutrient supplier, it is possible to estimate the parameters of the other nutrient supplier, thus completing the present invention.

[Nutritional supply estimation method]
A nutrient supply estimation method according to one embodiment of the present invention is a nutrient supply estimation method for estimating the amount of nutrients supplied from a nutrient supplier and in a form that can be utilized by a plant, and includes a nutrient supply estimation step of estimating the nutrient supply amount at any point in time by referring to a group of parameters for estimating the nutrient supply amount, the group of parameters including a first parameter indicating the nutrient supply amount at a reference point in time, a second parameter indicating the maximum amount of change in the nutrient supply amount, a third parameter indicating the shape of an equation showing the progression of the nutrient supply amount, and a fourth parameter indicating a rate constant for the change in the nutrient supply amount.

[Nutrition]
As used herein, the term "nutrient" refers to a component that can be absorbed by a plant through the roots and can have a beneficial effect on the growth of the plant, or a precursor of the component, or a combination thereof. Examples of nutrients include, but are not limited to, nitrogen, potassium, calcium, magnesium, phosphorus, sulfur, chlorine, iron, boron, manganese, zinc, copper, nickel, and molybdenum, and any combination thereof. In addition, the nutrient may be one type alone or any combination of two or more types. The nutrient to be estimated may be appropriately selected from the desired types.

In one embodiment of the present invention, the nutrients to be estimated are in a form that can be used by plants. A form that can be used by plants means a form that can be absorbed by the plant through the roots. Even if a nutrient is present in an area outside the root zone of a plant that cannot be immediately absorbed by the plant, if the plant can absorb the nutrient when the plant's roots approach the nutrient, the nutrient is also a nutrient to be estimated. Examples of forms that can be used by plants include: nitrogen, such as inorganic exchangeable nitrogen such as ammonium nitrogen and nitrate nitrogen, and some organic nitrogen with small molecular weight such as amino acid form; potassium, such as exchangeable potassium containing potassium ions; and phosphorus, such as available phosphorus, such as soluble phosphorus containing phosphate ions.

[Nutrient supply body]
In one embodiment of the present invention, the nutrients to be estimated are supplied from a nutrient supplier. As used herein, the term "nutrient supplier" refers to an object that can be a main body that supplies nutrients to plants. The supply of nutrients from the nutrient supplier to plants can be achieved by the components contained in the nutrient supplier being appropriately subjected to physical changes such as dissolution, and chemical changes such as decomposition or synthesis mediated by other substances, microorganisms, or heat, and then becoming in a form that can be used by the plant.

The "nutrients" supplied by the nutrient supplier include both "nutrients" in a form that can be used by plants, and "nutrients" that can become a form that can be used by plants. In other words, the form of nutrients supplied by the nutrient supplier may be (i) the form that can be used by plants, or (ii) a form that cannot be used by plants as it is, but can be converted into a form that can be used by plants through a change in state, such as decomposition.

Examples of nutrient suppliers include soil, organic matter, fertilizers and root zone supports, and any combinations of these. Nutrient suppliers may be solid or liquid.

Specific examples of soils include, but are not limited to: minerals such as rock, gravel, sand, silt and clay; soil and mud; organic matter contained in soil, i.e. soil organic matter; and complexes of organic matter and inorganic matter contained in soil, i.e. organic-inorganic complexes.

Examples of organic matter include, but are not limited to, feces, animal waste, plant waste and compost thereof.

Specific examples of fertilizers include, but are not limited to: inorganic fertilizers and organic fertilizers, when classified based on ingredients; nitrogen fertilizers, potassium fertilizers, phosphate fertilizers, magnesium fertilizers, and calcium fertilizers, when classified based on the nutrients they supply; and fast-release fertilizers and slow-release fertilizers, when classified based on the speed at which they supply nutrients (excluding coated urea fertilizers).

Root zone support means an object that supports the root zone of a plant. Specific examples of root zone supports include, but are not limited to, sponges, rock wool, coconut shells, and water.

As used herein, the term "nutrient supply amount" refers to the amount of nutrients supplied from a nutrient supplier. The amount may be, but is not limited to, an integrated amount over time, a differential amount over time, or a derivative amount. A desired type of amount may be selected as appropriate. In addition, depending on the type selected, the mathematical processing described below may be modified. Such modifications are known to those skilled in the art. Below, as a non-limiting example, a case where an integrated amount over time is selected as the nutrient supply amount will be described.

The nutrient supply amount estimation method according to one embodiment of the present invention may be a method for mathematically estimating the amount of nutrient supply by inputting a time value as a variable and optionally further inputting a temperature value as a variable into an equation including a group of parameters described below as constants. The number of types of parameters included in the group of parameters is small, at a minimum four. Furthermore, each of the multiple parameters is independently related to one or more of the characteristics possessed by the nutrient supplier. Therefore, in one embodiment of the present invention, the phenomenon in which when one of the multiple parameters changes, the estimated value finally calculated is maintained by changing the other parameters, i.e., interference between different parameters, is prevented or reduced. Therefore, in one embodiment of the present invention, it is possible to handle each parameter independently. Specifically, each parameter can be estimated independently by referring to the similarity between the states of the multiple nutrient suppliers. Therefore, even if it is difficult to set each parameter by an experimental method in all nutrient suppliers, each parameter can be set by estimation, and then the amount of nutrient supply can be estimated.

In this specification, when the term "parameter" is used, unless otherwise specified, the term means at least one of the following: "parameter," "parameter value," and "information representing the parameter value."

Below, non-limiting characteristics of each parameter included in the parameter group referenced in the nutrient supply amount estimation method according to one embodiment of the present invention are described. For simplicity of explanation, "nutrient supply amount" may be abbreviated to "supply amount." Similarly, "nutrient supplier" may be abbreviated to "supplier."

[First Parameter]
The first parameter n _i indicates the amount of nutrients supplied at a reference time point. In one embodiment of the present invention, the reference time point may be appropriately selected. Examples of the reference time point include, but are not limited to, the time point at which fertilizer is applied, and a specific period before or after the time point.

As an example, the first parameter n _i may be set using an experimental method involving collection of at least one of the feeder and the plant and chemical analysis of the components contained therein. If there are multiple types of feeders, chemical analysis of the components may be performed for each type. The experimental method may be a method known in the art. Examples of experimental methods include, but are not limited to, methods that can measure the amount of inorganic nitrogen or the amount of ammonium nitrogen. As another example, the first parameter n _i may be set using a representative value (such as an average value) for each type of nutrient feeder based on past knowledge. In addition, when applying fertilizer, the first parameter n _i may be considered to be the amount of nutrients in the fertilizer to be administered.

[Second parameter]
The second parameter N indicates the maximum change in the amount of nutrients supplied. The maximum change means the difference between the amount of nutrients supplied at a time when a sufficient amount of time has passed from the reference time and the amount of nutrients supplied at the reference time. In general, the amount of nutrients supplied may change due to chemical reactions and changes in physical conditions. However, in the absence of addition and reduction of components and changes in field conditions due to external factors, the amount of nutrients supplied may reach a steady state after a sufficient amount of time has passed. Therefore, the second parameter N may correspond to the amount of change in the amount of nutrients supplied from the reference time to the time when the steady state is reached.

As an example, the second parameter N can be set by determining the types and amounts of components contained in the feed using empirical methods known in the art. As another example, the second parameter N can be set by reference to the amount of feed applied.

[Third Parameter]
The third parameter d indicates the shape of the formula expressing the transition of the nutrient supply amount. In one embodiment of the present invention, the formula used to estimate the supply amount expresses the transition of the supply amount with the value of time as a variable. In one embodiment of the present invention, the shape of this formula is not limited to one specific type, and may have the characteristics of multiple types of mathematical formulas in combination. The third parameter d is related to the determination of the shape of the formula. As a typical example, the shape of the formula is an integral first-order reaction rate formula, a sigmoid formula, or a formula obtained by transforming these. In addition, examples of the transformation style include both an equation that interpolates between an integral first-order reaction rate formula and a sigmoid formula, and an equation that extrapolates these. In addition, an equation that interpolates between these two formulas refers to the fact that at least one parameter included in the formula takes a predetermined value, and when the shape of the formula approximates each of the shapes of these two formulas, the parameter can be set to a value included between two predetermined values corresponding to each of the shapes of these two formulas. In addition, the expression "an equation that extrapolates these two equations" refers to the fact that, when at least one of the parameters included in the equation takes a predetermined value, and the shape of the equation approximates each of the shapes of these two equations, the parameter can be set to a value that is not included between the two predetermined values corresponding to each of the shapes of these two equations. The third parameter d can determine the type and degree of the deformation.

In one embodiment of the present invention, the formula used to mathematically estimate the supply amount is an integral first-order reaction rate equation, a sigmoid equation, or an equation obtained by a modification of these. The difference in the formula used is considered to be due to the complexity of the reaction system of the reaction (such as dissolution and decomposition) in which the supplier supplies nutrients. For example, the type of supplier is not limited to one type, but may be two or more types. In general, the fewer the types of supplier, the simpler the reaction system becomes, and the reaction rate equation of the reaction becomes closer to a first-order reaction rate equation. For this reason, the formula expressing the transition of the supply amount shows a higher similarity to an integral first-order reaction rate equation with the time value as a variable. Conversely, the more the types of supplier, the more complex the reaction system becomes, and the reaction rate equation of the reaction becomes closer to a higher-order reaction rate equation. For this reason, the formula expressing the transition of the supply amount shows a higher similarity to a sigmoid equation with the time value as a variable.

In one embodiment of the present invention, the equation used to mathematically estimate the supply amount includes a third parameter d, so that the equation reflects the complexity of the reaction system. Therefore, by using this equation, the nutrient supply amount estimation method according to one embodiment of the present invention can estimate the supply amount for a comprehensive and diverse range of nutrients and supplies, regardless of the type and combination of supplies.

[Fourth parameter]
The fourth parameter k indicates the rate constant in the change of the nutrient supply amount. The rate constant in the change of the supply amount means the rate constant of the reaction in which the supplier supplies the nutrient. Typically, the faster the reaction in which the supplier supplies the nutrient, the larger the fourth parameter k can be.

The fourth parameter k may be a parameter that changes depending on the temperature of the supply body. When the temperature of the supply body may change, the fourth parameter k may be calculated by referring to the fifth parameter k _s and the sixth parameter E. In this way, the nutrient supply amount estimation method according to one embodiment of the present invention can estimate the nutrient supply amount according to the temperature change by calculating the fourth parameter k.

That is, in the nutrient supply amount estimation method according to one embodiment of the present invention, the fourth parameter k may be calculated by referring to the fifth parameter k _s indicating the rate constant of the change in the nutrient supply amount at the reference temperature, and the sixth parameter E indicating the temperature dependency of the rate constant.

In one embodiment of the present invention, the temperature of the supply body can be set as appropriate and may be variable during the period including the time when the estimation is performed. The temperature of the supply body is preferably 5°C to 40°C. In this way, by including a lower temperature range in the temperature range, the sixth parameter E described below will more strongly indicate the state of the supply body, making it easier to estimate the sixth parameter E and improving the accuracy of estimating the supply amount.

[Fifth parameter]
The fifth parameter k _s represents the rate constant of the change in the amount of nutrient supply at a reference temperature. In one embodiment of the present invention, the reference temperature may be appropriately selected. The reference temperature may be, but is not limited to, 5° C., 10° C., 15° C., 20° C., 25° C., 30° C., or 40° C.

[Sixth parameter]
The sixth parameter E indicates the temperature dependence of the rate constant. In one embodiment of the present invention, the sixth parameter E is considered to be a value corresponding to the activation energy of the rate-determining reaction in the reaction system in which the supplier supplies nutrients. When there are many types of suppliers, or when the reaction in which the supplier supplies nutrients is a multi-step reaction, the reaction system becomes more complicated. However, in the reaction system, the reaction rate of the rate-determining reaction is dominant in the overall reaction rate, so the temperature dependence of the reaction rate of the overall reaction is considered to be dominated by the temperature dependence of the rate-determining reaction, i.e., the activation energy of the rate-determining reaction.

[Alternative parameters]
In one embodiment of the present invention, the parameters included in the parameter set are not limited to the above-mentioned set of the first, second, third, and fourth parameters, and the additional fifth and sixth parameters. The parameter set may include a parameter obtained by converting at least one of the above-mentioned parameters using a mathematical conversion formula as a substitute for the at least one parameter.

That is, the parameter group may include a parameter obtained by converting at least one parameter included in the parameter group using a mathematical conversion formula as a substitute for at least one parameter included in the parameter group. A user who implements the nutrient supply amount estimation method according to one embodiment of the present invention can appropriately convert or add characteristics indicated by the obtained substitute parameter by appropriately selecting a mathematical conversion formula. This allows the user to easily understand or intuitively perceive the outline of the state and characteristics of the supply body. This makes it easy to transmit information indicating the characteristics of the supply body, for example, between the sender of information about the supply body and the user, and such information can be used as an indicator for the distribution of the supply body. An example of a mathematical conversion formula for obtaining such a substitute parameter will be described later.

Below, we explain a non-limiting configuration of each step that may be included in the nutrient supply estimation method according to one embodiment of the present invention.

[Parameter setting process]
The nutrient supply amount estimation method according to one embodiment of the present invention may further include a parameter setting step prior to a nutrient supply amount estimation step described later. The parameter setting step may be a step of setting at least one parameter included in a parameter group.

Examples of methods for setting at least one parameter include, but are not limited to: (i) a method in which a user sets a parameter by referring to a measured supply amount; and (ii) a method in which a user sets a parameter by referring to parameters stored in any database. Each of the parameters may be set by the same method or by different methods.

Among the methods for setting parameters, (i) a method in which the user sets parameters by referring to the measured supply amount will be described. Hereinafter, this method may be abbreviated as "method (i)."

Method (i) may be an experimental method in which the amount of supply is measured by collecting the supply and analyzing the components contained in the supply. The collection and analysis may be appropriately selected from methods known in the art.

In method (i), the parameters can be set by inputting the measured supply amount into an equation that includes the group of parameters as constants and fitting the parameters. The fitting can be achieved by a method known in the art. In the fitting, if all of the parameters included in the group of parameters are unknown, all of these parameters may be fitted. In the fitting, if any one or more of the parameters included in the group of parameters are known, the values of the known parameters may be fixed and only the remaining unknown parameters may be fitted.

The fitting conditions can be set to conditions known to those skilled in the art. For example, if the fitting results diverge, or if multiple fitting results exist or none exist, fitting can be performed with the initial value of one of the parameters set to a predetermined constant, for example, 0 or 1.

Among the methods for setting parameters, (ii) a method in which a user sets parameters by referencing parameters stored in an arbitrary database will be described. Hereinafter, this method may be abbreviated as "method (ii)."

Method (ii) may be a method in which a user selects parameters stored in any database and sets the parameters as is or by appropriate mathematical transformation. Examples of databases include computer-readable storage media and publicly accessible media such as the Internet.

Alternatively, in method (ii), information for selecting a stored parameter may be input by a user, and then a parameter automatically selected based on the input information may be set as the parameter. As an example, a user may input information about the field state as information for selecting a stored parameter, and then the corresponding parameter may be automatically called up with reference to the input information.

[Parameter Estimation Process]
In addition to the method of setting the parameters as described above, the parameters may be estimated as described below. That is, the nutrient supply amount estimation method according to one embodiment of the present invention may further include, before the nutrient supply amount estimation step, a parameter estimation step of estimating at least one parameter included in the parameter group in at least one of the other nutrient suppliers by referring to the similarity between a state of one nutrient supplier and at least one state of the other nutrient supplier and at least one parameter included in the parameter group in the one nutrient supplier.

Each of the parameters included in the parameter group is strongly related to the state of the nutrient supplier. Therefore, when another nutrient supplier is the subject of the nutrient supply amount estimation method, by referring to the similarity between the state of one nutrient supplier and the state of the other nutrient supplier that is the subject, and the known parameters set in the one nutrient supplier, the parameters in the other nutrient supplier can be set by estimation without involving experimental methods.

In the parameter estimation process, a total of three or more nutrient suppliers may be used as references. For example, two or more nutrient suppliers with known parameters and one nutrient supplier with unknown parameters may be used as references to estimate the unknown parameters.

In the parameter estimation process, the user can use any method to obtain known parameters set in a nutrient supplier. As an example, the user can obtain known parameters stored in a computer-readable storage medium or described in a publicly viewable medium such as the Internet.

In the parameter estimation process, examples of the state of the nutrient supplier referred to include: the type of nutrient supplier; the components and amount or content rate contained in the nutrient supplier; the components other than the nutrient supplier contained in the field containing the nutrient supplier; the type of soil in the field; the moisture conditions in the field; and the activity of microorganisms present in the field. The user may obtain information on the state of one nutrient supplier and the state of other nutrient suppliers using a method known in the art. As an example, a representative value (such as an average value) for each type of similar nutrient supplier based on past knowledge can be set as the first parameter n _i .

In the parameter estimation step, the estimation of the parameters may be performed based on the assumption that the greater the similarity between the state of one nutrient supplier and the state of at least one of the other nutrient suppliers, the greater the similarity of the parameters. As an example, the state of one nutrient supplier may be compared with the other nutrient supplier in terms of the type of nutrient supplier, and if there is a high similarity, at least one of the sixth parameter E and the third parameter d among the parameters of the other nutrient supplier may be set to a value similar to a known parameter set in the one nutrient supplier.

In the parameter estimation process, the parameters that can be estimated are not limited to the first to sixth parameters. For example, the above-mentioned alternative parameters may be estimated. That is, in the parameter estimation process, an alternative parameter included in the parameter group of one nutrient supplier may be referenced to estimate an alternative parameter included in the parameter group of at least one of the other nutrient supplier.

[Acquisition process]
The nutrient supply amount estimation method according to one embodiment of the present invention may further include an acquisition step before the nutrient supply amount estimation step. The acquisition step may be a step of acquiring values to be input as variables to an equation including parameters as constants.

The values entered as variables include a time value indicating any point in time desired by the user, and optionally further include a supply temperature value.

[Nutrient supply amount estimation process]
A nutrient supply estimation method according to one embodiment of the present invention includes a nutrient supply estimation step of estimating a nutrient supply amount at any point in time by referring to a group of parameters for estimating a nutrient supply amount.

In one embodiment of the present invention, referencing the set of parameters can be accomplished by using a formula that includes the set of parameters as constants. The formula can include a time value as a variable that indicates any point in time desired by the user, and by inputting the variable, can output an estimated supply amount at any desired point in time.

The formula used in the nutrient supply amount estimation step can be appropriately set by the user, taking into consideration the state of the supplier indicated by the parameters included in the above-mentioned parameter group. As an example, the formula used may be a formula with the first parameter n _i as an intercept, and a value obtained by multiplying the second parameter N by a value calculated by an equation including the third parameter d, the fourth parameter k, and the variable t is added to the intercept. A non-limiting example of a formula (i) used in one embodiment of the present invention is shown below.

n=N・[1+d・exp{exp(d+1)−1−k・t}] ^−1/d +n _i Formula (i)
In formula (i), n (unit: mg/100 mg nutrient supplier) indicates the amount of nutrient supplied (unit: mg) from 100 mg of nutrient supplier at time t (unit: day). _{n i} (unit: mg/100 mg nutrient supplier) is the first parameter and indicates the amount of nutrient supplied from 100 mg of nutrient supplier at t=0. N (unit: mg/100 g) is the second parameter. d (unit: -) is the third parameter. k (unit: day ^-1 ) is the fourth parameter.

Equation (i) is an equation that has a first parameter n _i as an intercept, and n is calculated by adding a value obtained by multiplying the second parameter N by a value calculated by a term (iA) including a third parameter d, a fourth parameter k, and a variable t to the intercept.

[1+d・exp{exp(d+1)−1−k・t}] ^−1/d term (iA)

Equation (i) is an integral first-order reaction rate equation, a sigmoid equation, or an equation obtained by modifying these, and the equation selected and the degree of modification depend on the value of d.

As an example, in formula (i), when the third parameter d satisfies d = -1, the change in the supply amount represented by n is an integral first-order reaction rate equation including the variable t. In this case, it is inferred that there are few types of supplier, and the reaction system in which the supplier supplies nutrients is simple. As another example, in formula (i), when the third parameter d satisfies d = 1, the change in the supply amount represented by n is a logistic equation (a special form of the sigmoid equation) including the variable t. In this case, it is inferred that there are many types of supplier, and the reaction system in which the supplier supplies nutrients is complex.

As another example, in formula (i), when the third parameter d satisfies -1<d<1, the smaller the third parameter d, the higher the similarity of the change in the supply amount to the integral first-order reaction rate equation, and the simpler the reaction system is inferred to be. Also, the larger the third parameter d, the higher the similarity of the change in the supply amount to the logistic equation, and the more complex the reaction system is inferred to be.

In formula (i), the range of values that the third parameter d can take is not limited to the range of -1≦d≦1, and may be in the range of d<-1, 1<d. From the viewpoint of the complexity of the reaction system, it is conventionally common to set parameters 1, 2, 4, 5, and 6 for each of the reactions that make up the reaction system. However, according to one aspect of the present invention, the range of values that the third parameter d can take is wide, specifically, it can take the range of d<-1, 1<d, so that a complex reaction system can be easily handled using a small number of parameters.

In addition, when d = 0, the value of term (iA) in formula (i) cannot be mathematically calculated. However, since the value of term (iA) coincides in the limit where d approaches 0 from a positive or negative value, the value of term (iA) when d = 0 may be treated as being equal to the value in that limit. In addition, when the base (iB) below of term (iA) is a negative value, the value of term (iA) may not be a real number. In this case, the value of base (iB) may be treated as 0 and formula (i) including term (iA) may be calculated, or the value of base (iB) may first be multiplied by -1 to make it a positive value, the value of term (iA) may be calculated, and then formula (i) may be calculated by multiplying the value of term (iA) by -1.

[1+d・exp{exp(d+1)−1−k・t}] Bottom (iB)

In one embodiment of the present invention, the fourth parameter k may be calculated by referring to the fifth parameter k _s and the sixth parameter E. In this way, the fourth parameter k is calculated, and the nutrient supply amount estimation method according to one embodiment of the present invention can estimate the supply amount according to the temperature change. Referring to the fifth parameter k _s and the sixth parameter E can be achieved by using an equation including these parameters as constants. The equation includes a value indicating the supplier temperature as a variable, and by inputting the variable, the fourth parameter k at the input supplier temperature can be output. An example of the non-limiting Arrhenius equation used to calculate the fourth parameter k in one embodiment of the present invention is shown in the following equation (ii).

k = k _s · exp {E / R · (1 / T _s - 1 / T)} Equation (ii)
In formula (ii), k _s (unit: day ⁻¹ ) is the fifth parameter and indicates the rate constant for the change in the supply amount at a reference temperature of 25° C.; E (unit: kJ·mol ⁻¹ ) is the sixth parameter; R (8.31 kJ·mol ⁻¹ ·K (absolute temperature)) indicates the gas constant; _{T s} (unit: K (absolute temperature)) indicates the absolute temperature corresponding to the reference temperature of 25° C.; T (unit: K (absolute temperature)) indicates the supply temperature.

In addition, in the nutrient supply amount estimation process, the supply amount may be estimated by referring to an alternative parameter instead of at least one of the parameters included in the parameter group. Here, the alternative parameter is a parameter obtained by converting at least one parameter included in the parameter group using a mathematical conversion formula.

As an example of mathematical conversion to obtain alternative parameters, a condition where the temperature is 25° C. as the reference temperature, that is, k=ks _, is taken as an example. In this case, when n=0.25N+ _ni is input into formula (i), the following formula (iii) is obtained.

0.25N+n _i =N・[1+d・exp {exp(d+1)−1−k _s・t _25% }] ^−1/d +n _i Formula (iii)

Formula (iii) is a conversion formula for obtaining the alternative parameter t25 _% from the third parameter d and the fifth parameter _k2s . The alternative parameter t25 _% indicates the time at which the ratio of the change in the supply amount to the maximum change in the supply amount reaches 25%. Therefore, by referring to the alternative parameter t25 _% , the user can easily understand the time at which the nutrient supplied from the supplier reaches 25% of the maximum change.

Similarly, when n=0.5N+n _i and n=0.75N+n _i are input into formula (i), the alternative parameters t _50% and t 75 _{%, which indicate the time when the nutrient supplied from the supplier reaches 50% and 75} % of the maximum change, are obtained. By obtaining t _25% , t _50% , and t _75% , respectively, the user can understand the time when the nutrient supplied from the supplier reaches 25%, 50%, and 75% of the maximum change, and can easily understand the characteristics of nutrient supply to the plant.

Furthermore, the third parameter d and the fifth parameter k _s can be calculated by performing mathematical conversion using at least two of t _25% , t _50% , and t _75% . In other words, the alternative parameters that facilitate the user's understanding can also function as parameters included in the formula used in the nutrient supply estimation process.

The alternative parameters are not limited to the above examples and can be set by any mathematical transformation. As another example, the median (t _{50% )} and the quartile deviation {(t _75% -t _25% )/2} can be calculated from t _25% , t _50% , and t 75 _% . Using these, the user can understand that half of the nutrients are supplied during the period of the median ± the quartile deviation, and can roughly understand the timing of nutrient supply. The third parameter d and the fifth parameter k _s can also be calculated reversibly from these two parameters.

[Method of using nutrient suppliers]
One aspect of the present invention relates to a method for using a nutrient supplier. The method for using a nutrient supplier according to one embodiment of the present invention includes estimating a state of the nutrient supplier by referring to at least one of (i) a nutrient supply amount estimated by a nutrient supply amount estimation method according to one embodiment of the present invention, and (ii) at least one parameter included in a parameter group used to estimate the nutrient supply amount.

In the method for using a nutrient supplier according to one embodiment of the present invention, the state of the supplier can be estimated by referring to at least one of the supply amount and the parameters described above. Examples of the state of the supplier include, but are not limited to, an excess or deficiency in the supply amount and a delay in the supply timing. Therefore, according to the method for using a nutrient supplier according to one embodiment of the present invention, the user can select an optimal supplier based on the estimated state of the supplier, and set the application amount, application timing, application period, etc. of the supplier. As an example, the user can set a plan based on the estimated state of the supplier, such as whether to use the supplier contained in the field as it is, or to add a supplier to the field.

In a method of using a nutrient supplier according to one embodiment of the present invention, the estimated nutrient supply amount and at least one parameter included in the parameter group used for the estimation may be referenced to a nutrient supply amount and parameters written or stored in any medium. Examples of media include, but are not limited to, the packaging of the nutrient supplier and instructions. In addition, the any medium may be referenced by writing or storing a method of accessing the medium that allows the nutrient supply amount and parameters to be viewed, such as a homepage address or a QR code (registered trademark), rather than the nutrient supply amount and parameters themselves.

In the method for using a nutrient supplier according to one embodiment of the present invention, in the estimation step, the state of the nutrient supplier may be estimated by referring to the time until an arbitrary amount of nutrients is obtained from the nutrient supplier, which is calculated from at least one parameter included in the parameter group. According to one embodiment of the present invention, by referring to the time until an arbitrary amount of nutrients is obtained, the state of the nutrient supplier can be estimated taking into account the time required for a desired amount of nutrients to be supplied to the plant. This allows the user to set a more appropriate plan.

[Software implementation example]
The scope of the present invention also includes an apparatus for executing each step of the nutrient supply amount estimation method according to one embodiment of the present invention or the method for using a nutrient supply body according to one embodiment of the present invention. The functions of the apparatus can be realized by a program for making a computer function as the apparatus, and a program for making a computer function as each control block of the apparatus. In other words, the scope of the present invention also includes a program for making a computer execute the nutrient supply amount estimation method according to one embodiment of the present invention or the method for using a nutrient supply body according to one embodiment of the present invention.

In this case, the device includes a computer having at least one control device (e.g., a processor) and at least one storage device (e.g., a memory) as hardware for executing the program. By executing the program with this control device and storage device, each step of the nutrient supply amount estimation method or nutrient supply body utilization method described above is realized.

The program may be recorded on one or more computer-readable recording media, not on a temporary basis. The recording media may or may not be included in the device. In the latter case, the program may be provided to the device via any wired or wireless transmission medium.

In addition, some or all of the functions of each of the above control blocks can be realized by a logic circuit. For example, an integrated circuit in which a logic circuit that functions as each of the above control blocks is formed is also included in the scope of the present invention. In addition, it is also possible to realize the functions of each of the above control blocks by, for example, a quantum computer.

Furthermore, each step of the above-mentioned nutrient supply amount estimation method or nutrient supplier utilization method may be executed by AI (Artificial Intelligence). In this case, the AI may be one that operates on the above-mentioned control device, or may be one that operates on another device (e.g., an edge computer or a cloud server, etc.).

[Estimation system]
Furthermore, the present invention also includes an estimation system comprising a database that stores the above-mentioned data in association with a nutrient supply body, and an estimation device that estimates the amount of nutrient supply. That is, the estimation system according to one embodiment of the present invention comprises a database that stores at least one of (i) the amount of nutrient supply estimated by the nutrient supply amount estimation method according to one embodiment of the present invention, (ii) the state of the nutrient supply body estimated by the method for using the nutrient supply body according to one embodiment of the present invention, and (iii) any of the values of the parameters included in the parameter group used to estimate the amount of nutrient supply, in association with the nutrient supply body, and an estimation device that refers to the data stored in the database and estimates the amount of nutrient supply of the test nutrient supply body.

In an estimation system according to one embodiment of the present invention, the database can be accessed by a user, and at least one of (i) the amount of nutrient supply, (ii) the state of the nutrient supplier, and (iii) any of the parameter values can be written and/or read. Thus, a user can estimate the amount of nutrient supply of a desired test nutrient supplier by referring to data and parameter values based on estimations performed by the user or other users.

The estimation system according to one embodiment of the present invention may include a means for modifying the formula used to mathematically estimate the supply amount by referring to a user's operation or by referring to the result of an estimation performed by the user. As an example, the database may include a means for storing the result of the estimation of the supply amount performed by the user and the corresponding actual result of the supply amount, and for appropriately modifying the formula used so as to reduce the difference between the estimated result and the actual result. With such a configuration, the estimation system according to one embodiment of the present invention can further improve the accuracy of the estimation.

[Modifications]
The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention.

For example, the formula used to mathematically estimate the supply amount can be set appropriately depending on the desired format of the information on the nutrient supply amount. As an example, the formula (iv) shown below may be used.

n=N・[1+d・exp{exp(d+1)−1−k・t}] ^−1/d formula (iv)
Formula (iv) is a formula when n _i = 0 in formula (i), and n represents the difference in the amount of nutrient supply over time. In other words, it is within the scope of one aspect of the present invention to estimate the difference over time by appropriately setting the value of n _i .

As another example, formula (v) or formula (vi) shown below may be used.

n/N=[1+d・exp{exp(d+1)−1−k・t}] ^−1/d +n _i /N Formula (v)
n/N=[1+d・exp{exp(d+1)−1−k・t}] ^−1/d formula (vi)
Formula (v) is a formula for calculating the ratio n/N of the supplied nutrients. Formula (vi) is a formula when n _i =0 is set in formula (v), and n/N indicates the ratio of the difference in the amount of nutrients supplied over time. In formulas (v) and (vi), N=1 may be set, and each formula may be set so that n corresponds to the ratio. In other words, it is also within the scope of one aspect of the present invention to estimate the ratio of the amount of nutrients supplied per nutrient supplier by appropriately modifying the formula.

As another example, in the formulas used, the values entered as variables may include, in addition to the time value, corrections for conditions that may affect nutrient supply, such as field water potential and pH.

One embodiment of the present invention is described below.

In this example, the amount of inorganic nitrogen supplied from the soil and compost was estimated as the nutrient supply. A group of parameters was set with reference to the amount of inorganic nitrogen contained in the soil and compost measured by an experimental method described in Non-Patent Document 1 above. The amount of inorganic nitrogen was then estimated using the set group of parameters, and the estimated amount of inorganic nitrogen (estimated value) and the referenced amount of inorganic nitrogen (experimental value) were plotted in the graph shown in Figure 1 for comparison. Figure 1 shows the estimation results of the amount of inorganic nitrogen in the example.

Example 1
The first, second, third, fifth, and sixth parameters were set so as to minimize the residual sum of squares of the difference between the inorganic nitrogen amount values contained in the soil and the soil to which compost was applied at each temperature listed in "Table 1" of Non-Patent Document 1 and the estimated value by formula (i) and formula (ii). In this example, the inorganic nitrogen amount refers to the total amount of the ammonium nitrogen amount and the nitrate nitrogen amount.

n=N・[1+d・exp{exp(d+1)−1−k・t}] ^−1/d +n _i Formula (i)
In formula (i), n indicates the estimated amount of inorganic nitrogen contained in the soil at time t. _{n i} is a first parameter and indicates the amount of inorganic nitrogen contained in the soil at t = 0. N is a second parameter and indicates the maximum amount of change in the amount of inorganic nitrogen, that is, the amount of change in the amount of inorganic nitrogen at a point when sufficient time has passed. d is a third parameter and indicates the shape of formula (i) representing the transition of the amount of inorganic nitrogen. k is a fourth parameter and indicates the rate constant for the change in the amount of inorganic nitrogen at soil temperature T (unit: K (absolute temperature)).

k = k _s · exp {E / R · (1 / T _s - 1 / T)} Equation (ii)
In formula (ii), k _s is the fifth parameter and indicates the rate constant for the change in the amount of inorganic nitrogen at 25°C. E is the sixth parameter and indicates the temperature dependence of the rate constant. _{T s} indicates the reference temperature, i.e., the absolute temperature corresponding to 25°C. R is the gas constant (8.31 kJ·mol ^-1 ·K (absolute temperature)).

The parameters were set for condition (1) only soil with no fertilizer applied, (2) soil with cow, pig and chicken manure compost applied, (3) soil with cow manure compost applied, and (4) soil with chicken manure applied. In order to understand the effect of compost, the parameters were also set for the difference between the inorganic nitrogen amount value in (1) and the inorganic nitrogen amount value in (4) using conditions (1) and (4) where the difference in the effect of compost was large, i.e., condition (5) only chicken manure compost excluding the effect of soil. For each of conditions (1) to (5), the soil temperature was set to 10°C, 20°C, and 30°C.

The following Table 1 shows the inorganic nitrogen content by temperature (in duplicate) used to set each parameter in this example, as described in "Table 1" of Non-Patent Document 1.

The estimated values obtained by referencing the set parameters were close to the experimental values. In addition, the sixth parameter was close under conditions (1) to (5), regardless of the type of soil or compost.

Example 2
Therefore, further, under the condition that the value of the sixth parameter is the same under all conditions (1) to (5), the first parameter, the second parameter, the third parameter, the fifth parameter, and the sixth parameter were set so that the residual sum of squares of the difference between the estimated value according to formula (i) and formula (ii) and the experimental value was minimized.

Table 2 shows the results of each parameter set in Example 2.

Figure 1 shows the experimental value of the amount of inorganic nitrogen and the estimated value according to formula (i) including each parameter set in Example 2. In Figure 1, the points show the experimental value data, and the curve shows the estimated value according to formula (i). However, under condition (5), the experimental value shown is the value obtained by subtracting the estimated value under condition (1) from the estimated value under condition (4).

Example 3
Furthermore, alternative parameters indicating the times t25%, t50% and t75% at which the ratio of the change in the amount of inorganic nitrogen to the maximum change reaches _25% , _50% and _75% , respectively, were calculated using the third parameter d and the fourth parameter. Specifically, the alternative parameters _t25% , _t50% and _t75% were calculated from the following formula (iii), formula (vii) and formula (viii), respectively.

0.25N+n _i =N・[1+d・exp {exp(d+1)−1−k _s・t _25% }] ^−1/d +n _i Formula (iii)
0.50N+n _i =N・[1+d・exp {exp(d+1)−1−k _s・t _50% }] ^−1/d +n _i Formula (vii)
0.75N+n _i =N・[1+d・exp{exp(d+1)−1−k _s・t _75% }] ^−1/d +n _i Formula (viii)

Table 3 shows the alternative parameters calculated in Example 3.

Comparative Example 1
The parameters included in model formula 2 were set so that the residual sum of squares of the difference between the inorganic nitrogen amount value in the soil for each temperature listed in "Table 1" of Non-Patent Document 1 and the estimated value by "Model Formula 2" of Non-Patent Document 1 was minimized. Each of the set parameters was the same as the results listed in "Table 2" of Non-Patent Document 1. Each of the parameters listed in "Table 2" of Non-Patent Document 1 is shown in Table 4 below. Please refer to Non-Patent Document 1 for detailed meanings of each parameter.
N=N ₀ [1-exp(-k·t)]-N _0im [1-exp(-k _im ·t)]+b ("Model Formula 2" in Non-Patent Document 1)

In the "Model Formula 2" of Non-Patent Document 1, k _im , k, and t are calculated as follows.
k _im =Bexp(-E _aim /RT)
k=Cexp(-E _a /RT)

In accordance with "Table 2" or "Table 4" in Non-Patent Document 1, N ₀ and N _0im in Table 4 are expressed as the amount (unit: mg) relative to 50 g of soil for conditions (1) to (4), and are expressed as the weight percentage of the applied chicken manure compost for condition (5).

[Discussion]
As shown in Table 2, in Example 1, the sixth parameter E, which indicates the temperature dependency of the rate constant, was close to each other under each of the conditions (1) to (5), so that the same value could be set. This suggests that in a reaction system thought to be mediated by microorganisms contained in soil, the rate-limiting reaction for the production of inorganic nitrogen is the same regardless of the type of compost, so the sixth parameter corresponding to the activation energy of the rate-limiting reaction also has the same value. In contrast, as shown in Table 4, in Comparative Example 1, the variation of E _a and E _aim , which indicate the temperature dependency, was large under each of the conditions (1) to (5). This indicates that in a model formula containing multiple parameters with similar meanings, interference occurs between the parameters, so that even if the value of the estimated value N finally calculated is accurate, it may be difficult to assign meaning to the value of each parameter itself.

As shown in this example, the sixth parameter E can sometimes be a constant value among multiple reaction systems. Because the sixth parameter E is a parameter that corresponds to the activation energy of the rate-limiting reaction, it is presumed that the sixth parameter E can be treated as a constant value when dealing with similar reaction systems. Therefore, by expressing temperature dependence using only the sixth parameter in this way and eliminating the effects of temperature using the sixth parameter, it is possible to easily estimate the amount of nutrient supply, as if it were under constant temperature conditions with no temperature effects.

Next, the value of the first parameter n _i or the value of "second parameter N+first parameter n _i " shown in Table 2 tended to be close to the nitrogen supply amount at t=0 or the nitrogen supply amount after a sufficient amount of time has passed, as shown in Fig. 1. This shows that information on the supply amount can be roughly grasped by the first parameter n _i and the second parameter N.

Further, a comparison of conditions (1), (4) and (5) will be discussed. As shown in Table 2, in Example 1, the value obtained by subtracting the value of the parameter set in condition (1) from the value of the first parameter n _i and the second parameter N set in condition (4) tended to be close to the value of the parameter set in condition (5). This indicates that the first parameter n _i corresponds favorably to the amount of inorganic nitrogen contained in the soil or compost at t=0, and the second parameter N corresponds favorably to the maximum change in the amount of inorganic nitrogen. This further indicates that it is possible to estimate unknown parameters corresponding to one nutrient supplier from known parameters corresponding to another nutrient supplier.

In Table 4 showing the results of Comparative Example 1, b, N ₀ , and N _0im are expressed as amounts per 50 g of soil (however, in condition (5), they are expressed as weight percentages of chicken manure compost, so condition (5) is excluded from the subject of discussion here), and it should be noted that the values in Table 4 must be doubled to compare with Table 2 and FIG. 1, which are expressed as amounts per 100 g of soil. Parameter b in Table 4, like the corresponding first parameter n _i , tended to indicate the amount of nitrogen supplied at t=0. However, the value of "parameter b + parameter N _{0 ,} " calculated using the second parameter N and the corresponding parameter N ₀ in Table 4, had an unclear relationship with the amount of nitrogen supplied after a sufficient amount of time had passed. Therefore, even if parameter b and parameter N ₀ were used, it was difficult to roughly grasp information regarding the amount of supply.

Also, it was possible to set the alternative parameter to indicate the time at which the ratio of the amount of change in inorganic nitrogen to the maximum amount of change reaches a specified value. As an example, as shown in Table 3, in condition (5) where only chicken manure compost is used without soil, it can be intuitively understood that at 25°C, the ratio of inorganic nitrogen that changes from chicken manure compost reaches 50% 60 days after application.

This invention can be used to support agricultural operations.

Claims (7)

A method for estimating a nutrient supply amount, the method comprising: estimating an amount of inorganic nitrogen , the nutrient being supplied from a nutrient supplier selected from soil, organic matter, and organic fertilizer;
The method includes a nutrient supply amount estimation step of estimating the nutrient supply amount at any time point by referring to the following formula (i) including a group of parameters for estimating the nutrient supply amount, or an equation obtained by mathematically converting the formula (i) ,
n=N・[1+d・exp{exp(d+1)−1−k・t}] ^−1/d +n _i Formula (i)
The parameter group includes:
A first parameter n _i indicating the amount of nutrient supply at a reference time point;
A second parameter N indicating the maximum change in the nutrient supply rate;
A third parameter d indicating the shape of the equation representing the transition of the nutrient supply amount;
A fourth parameter k indicating a rate constant for the change in the nutrient supply rate;
Includes :
In formula (i),
n represents the amount of nutrients supplied;
t indicates the elapsed time from the reference point,
Nutrient supply estimation method. The fourth parameter k is
A fifth parameter k _s indicating a rate constant for the change in the nutrient supply amount at a reference temperature;
A sixth parameter E indicating the temperature dependence of the rate constant;
It is calculated with reference to the following formula (ii) including :
k = k _s · exp {E / R · (1 / T _s - 1 / T)} Equation (ii)
In formula (ii),
R is the gas constant,
Ts represents the reference temperature _,
T denotes the temperature of the nutrient supply;
The method for estimating nutrient supply according to claim 1. 3. The nutrient supply amount estimation method according to claim 1 or 2, wherein in the nutrient supply amount estimation step, a desired nutrient supply amount is input into the nutrient supply amount n in the formula (i) to estimate a time t required to reach the desired nutrient supply amount instead of the nutrient supply amount n at any time point . (i) the nutrient supply amount n estimated by the nutrient supply amount estimation method according to claim 1 or 2 , and (ii) at least one parameter included in the parameter group used to estimate the nutrient supply amount n , to estimate the state of the nutrient supplier;
The state of the nutrient supplier is selected from an excess or deficiency of the nutrient supply amount n and a slow or fast supply time of the nutrient.
How to use nutrient providers. In the estimating step,
A method for using a nutrient supplier as described in claim 4, wherein the state of the nutrient supplier is estimated by referring to the time it takes for a desired amount of nutrients to be supplied from the nutrient supplier to a plant to be obtained, which is calculated from at least one parameter included in the group of parameters. A program for causing a computer to execute the nutrient supply amount estimation method according to any one of claims 1 to 3 , or the nutrient supply body utilization method according to claim 4 or 5 . A database that stores at least one of (i) a nutrient supply amount n estimated by the nutrient supply amount estimation method according to claim 1 or 2 , (ii) a state of the nutrient supply body estimated by the nutrient supply body utilization method according to claim 4 or 5 , and (iii) any one of the values of the parameters included in the parameter group used to estimate the nutrient supply amount n , in association with the nutrient supply body;
An estimation device that estimates the nutrient supply amount n of a test nutrient supply body by referring to the data stored in the database;
An estimation system comprising:

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