JP2023034522A - Estimation method of soil water - Google Patents

Abstract

To provide an estimation method of soil water capable of acquiring a representative value of soil water in a farm field.SOLUTION: An estimation method comprises: a step for, in an experiment farm field, measuring soil water in the experiment farm field by a plurality of soil water sensors; a step for confirming a spatial distribution of the experiment farm field; a step for selecting the number of measured values, the number being obtained by subtracting, the number of sensors, from all measurement results of the plurality of soil water sensors; a step for calculating an empirical probability, from the measurement results of the soil water sensors in the experiment farm field, and the number of the measured values, the number being reduced; a step for selecting measurement accuracy according to, accuracy desired by a user, from contents of the calculated empirical probability; a step for determining the number of sensors to be used in an object farm field; a step for, in the object farm field, using the number of soil water sensors, the number being determined according to the measurement accuracy, measuring the soil water, then, on the basis of the measurement result, acquiring the representative value of the object farm field; and a step for confirming whether the object farm field indicates a uniform spatial distribution.SELECTED DRAWING: Figure 1

Description

The present invention relates to a method for estimating soil moisture. Specifically, based on the measurement information obtained from the experimental field, the soil moisture content of the target field was measured using an appropriate number of soil moisture sensors while ensuring the accuracy of the measurement. This relates to a method for estimating soil moisture that can obtain a representative value of

2. Description of the Related Art Conventionally, in fields where crops are cultivated, soil moisture is measured in order to carry out agriculture after watering at an appropriate timing and amount and controlling moisture.

Here, for example, for measuring soil moisture, a means for measuring soil moisture based on a change in capacitance between electrodes by providing electrodes on a probe of a soil moisture sensor is adopted (for example, patent Reference 1).

In addition, in many cases, a wide range of soil with a certain area or more is subject to measurement, and multiple soil moisture sensors are used to measure soil moisture. .

JP 2012-132794 A

Here, in the conventional method for measuring soil moisture in a field, it was difficult to appropriately obtain a representative value of the soil moisture in the target field, that is, the representative value of the field.

The reason for this is that the structure of the soil itself is complex, so even if the same target field is measured using a large number of soil moisture sensors, the obtained measured values will be different values. Things are mentioned.

In addition, even among the soil moisture sensors placed at short installation intervals, the measured values sometimes differed.

Therefore, even if a large number of soil moisture sensors are used, the conventional soil moisture measurement method cannot determine the representative value of the target field from the measured values of the individual sensors.

In addition, even within the same field section, the soil moisture and changes over time during drying may be completely different in some areas and other areas. may not be uniform.

Therefore, when determining the representative value of the soil moisture, it is necessary to consider the range in which the soil moisture is uniform. is good with one.

On the other hand, if there is no uniformity in soil moisture within the range of the target field, the range must be divided based on the soil moisture and changes over time during drying, and representative values derived from each range must be determined. , the soil moisture cannot be accurately determined.

Furthermore, in the conventional measurement method, when a plurality of soil moisture sensors are arranged in a field, it was unclear how many sensors should be used to obtain soil moisture with desired accuracy.

In addition, it was not realistic to increase the number of soil moisture sensors to be installed, so there was a need for an index to determine the appropriate number of soil moisture sensors according to the size of the target field and the measurement accuracy desired by the user. .

The present invention was invented in view of the above points, and based on the measurement information obtained from the experimental field, in measuring the soil moisture in the target field where it is desired to grasp the soil moisture, while ensuring the accuracy of the measurement. An object of the present invention is to provide a method for estimating soil moisture that can obtain a representative value of soil moisture in a target field using an appropriate number of soil moisture sensors.

In order to achieve the above object, the method for estimating soil moisture of the present invention calculates a representative value of soil moisture in a target field based on the information of the measurement results of soil moisture using a plurality of soil moisture measurement sensors in an experimental field. A method for estimating soil moisture for estimating the soil moisture in the experimental field using a plurality of the soil moisture sensors, and using a spatial statistical method to determine the soil moisture in the experimental field in a uniform space a first spatial distribution confirmation step of confirming whether or not the distribution is exhibited; Derived from measurement results for each measurement timing obtained by measuring the soil moisture in the experimental field at a predetermined measurement interval and a predetermined number of measurements using the first number of the soil moisture sensors that can be arranged according to the soil conditions. a total number derived value obtaining step of obtaining a total median value or a total average value; 2 of the measured values are selected, and for the selected measured values, the reduced median value or the reduced average value derived from the measurement results at each measurement timing is acquired in the second number of the plurality of patterns. a step of acquiring a value derived from the subtraction, setting an arbitrary predetermined width based on the value of the median value of all samples or the average value of all samples, and determining the median value of the subtraction or the average value of the subtraction from the standard at each measurement timing; It is determined whether or not it falls within the range of the arbitrary predetermined width viewed from the reference, and the same determination is performed for all measurement timings. an empirical probability calculating step of calculating an empirical probability of being within the range of the arbitrary predetermined width; and from the second number of the plurality of patterns based on the arbitrary predetermined width and the empirical probability , a sensor number selection step of selecting a third number, which is the number of said soil moisture sensors having a desired accuracy; said first number, said third number, and said number of said soil moisture sensors; The soil to be used in the target field based on the fourth number, which is the number that can be arranged according to the size of the target field, information on the area of the experimental field, and information on the area of the target field. Regarding the number _m2 of moisture sensors, when the first number and the fourth number are the same, the number _m2 is determined to be the same number as the third number, or If the number of 1s and the fourth number are different, the previous The first number is n ₁ , the third number is m ₁ , and the fourth number is n ₂ , and the number m ₂ is determined as an integer that satisfies the following formula (1): , a step of determining the number of sensors, measuring the soil moisture in the target field with the soil moisture sensors of the number _m2 , and using the median value or the average value of the measurement results as the representative value of the soil moisture in the target field. and a value estimation step.

・・・（１）

... (1)

Here, in the first spatial distribution confirmation step, the soil moisture in the experimental field is measured using a plurality of soil moisture sensors, and the spatial statistical method is used to determine whether the experimental field exhibits a uniform spatial distribution of the soil moisture. , it is possible to determine the required number of representative values of soil moisture in the target range of the experimental field. That is, it can be confirmed that if the entire range of the experimental field is a range in which the soil moisture is uniform, it is sufficient to determine one representative value. Moreover, if the entire range of the experimental field is a range that does not have uniformity in soil moisture, it can be divided into ranges that exhibit uniformity, and a representative value can be obtained for each range that exhibits uniformity.

Also, in the first spatial distribution confirmation step, when the experimental field exhibits a uniform spatial distribution of soil moisture, in the total number derived value acquisition step, it is the number that can be arranged according to the area size of the experimental field. Using the first number of soil moisture sensors, the soil moisture in the experimental field is measured at a predetermined measurement interval and at a predetermined number of times, and a total median value or total average value derived from the measurement results for each measurement timing is obtained. By doing so, it is possible to calculate a reference numerical value in the later empirical probability calculation process. In addition, the measurement result at each measurement timing here means that the first number of soil moisture sensors at that time at each measurement timing when measuring at a predetermined measurement interval and a predetermined number of measurements. It means to calculate from all measured values.

Further, in the subtrahend-derived value acquisition step, from among the measurement results using the first number, a second number, which is a number arbitrarily reduced from the first number, is selected, and For the selected measured value, the second number of reduced median values or reduced average values derived from the measurement results for each measurement timing are obtained, thereby obtaining the second number of measurement timings derived from the first number of soil moisture sensors. Calculation of numerical value for each individual number to obtain the empirical probability that a certain range based on the total median or total mean value for each number contains the measured values of a number less than the first number can do. It should be noted that here, "select a second number of measured values, which is a number arbitrarily reduced from the first number, and derive the selected measured value from the measurement results for each measurement timing. For example, if the measurement condition for the first number is 10 measurements at intervals of 1 minute, the reduced median value or reduced average value” is the “first measurement timing (for example, measurement at 0 minutes )” means the median value or average value of the measured values (measured values with a reduced number) selected from all the measured values of the first number of measurement results. Also, since it is calculated for each measurement timing, the first measurement timing (for example, measurement at 0 minutes), the second measurement timing (for example, measurement at 1 minute elapsed), the third measurement timing (for example, measurement at 2 minutes elapsed) ), the reduced median value or the reduced average value is calculated for each measurement timing.

Also, from the measurement results using the first number, select the measured value for the second number, which is the number arbitrarily reduced from the first number, and for the selected measured value, By acquiring the reduced median value or the reduced average value derived from the measurement results at each measurement timing with the second number of the plurality of patterns, the second number can be prepared in a plurality of patterns, and each For counts, a numerical value for each individual count can be calculated to determine the empirical probability. For example, if the first number is 90, the second number of the plurality of patterns is 45, 27, 14, 13, 9, 7, 90, 45, 27, 14, 13, 9, 7, 90, 90, 90, 90, 90, 45, 27, 14, 14, 13, 90, or 90. Set a plurality of numbers such as 1, 6, 5, 4, etc., and calculate the reduced median value or the reduced average value of the measured values selected for each second number at each measurement timing can do.

Further, in the empirical probability calculation step, an arbitrary predetermined width is set based on the value of the total median value or the total average value, and at each measurement timing, the reduced median value or the reduced average value is an arbitrary value in terms of the reference Determine whether or not it falls within the range of a predetermined width, make determinations for all measurement timings, and determine whether the median or average value of the second number is within any predetermined width when viewed from the reference By calculating the empirical probability that the , it becomes possible to acquire information on the accuracy of measurement that can be guaranteed by the second number of the selected measurement values. In other words, when the number of soil moisture sensors is reduced in the experimental field, the numerical value to what extent the accuracy of the measurement with the reduced number is within the original measurement result of the first number. You can check the information. The arbitrary predetermined width referred to here is a numerical value width that can be set according to the accuracy desired by the user, and both a numerical value width of a single numerical value and a numerical value width of a plurality of numerical values can be set. In addition, the arbitrary predetermined width can be set to a numerical width with arbitrary measurement accuracy desired by the user, such as ±5%, ±3%, ±1%, and the like.

Further, in the sensor number selection step, a third number, which is the number of soil moisture sensors having a desired accuracy, is selected from the second numbers of the plurality of patterns based on an arbitrary predetermined width and empirical probability. This determines the accuracy of the soil moisture sensor measurement desired by the user. For example, through the empirical probability calculation process, the first number is 90 and the third number (one of the second numbers) is selected as 14, and the 14 sensors are used In the case, if the empirical probability of falling within ±3% is 87% based on the total median value of 90 sensors, the user can say, "Based on the total median value of 90 sensors , the empirical probability of falling within ±3% is set as the accuracy of soil moisture measurement. In this manner, the user can set the accuracy of measurement for each third number. Also, by setting the second number of the plurality of patterns, it is possible to prepare a plurality of types of measurement accuracy that can be selected by the user.

In addition, the first number, the third number, and the number of soil moisture sensors, the fourth number which is the number that can be arranged according to the area of the target field, information on the area of the experimental field, Then, based on the information on the area of the target field, regarding the number m ₂ of the soil moisture sensors used in the target field, in the sensor number determination step, if the first number and the fourth number are the same, the number m ₂ is the same number as the third number, the number of soil moisture sensors actually used in the target field is reduced while maintaining the user-selectable accuracy of measurement set in the experimental field. , to a third number. Further, here, the size of the experimental field and the size of the target field are the same, that is, the first number, which is the number that can be arranged according to the size of the experimental field, and the arrangement according to the size of the target field The number _m2 can be the same number as the third number because the fourth possible number can be considered the same.

In addition, the first number, the third number, and the number of soil moisture sensors, the fourth number which is the number that can be arranged according to the area of the target field, information on the area of the experimental field, And, based on the information on the area of the target field, regarding the number m ₂ of sensors used in the target field, in the sensor number determination step, if the first number and the fourth number are different, the first number n ₁ , the third number m ₁ , and the fourth number n ₂ , the number m ₂ was determined as an integer that satisfies the above formula (1), and was set up in the experimental field, In practice, the number of soil moisture sensors used in a given field can be determined while maintaining a user-selectable accuracy of measurement. Further, here, the size of the experimental field and the size of the target field are different. Since it can be considered that the fourth number, which is the number that can be arranged, is different, the first number is n ₁ , the third number is m ₁ , and the fourth number is n ₂ , and the number is m _{2 .} by determining the number of soil moisture sensors to be used in the target field in practice while maintaining the user-selectable accuracy of measurement set in the experimental field. number can be determined.

Here, the above formula (1) is derived based on the following content.
First, regarding the number of soil moisture sensors, if the original total number is n, and there are m, which is the number obtained by subtracting the number from n, the "small average" of the measured values of m out of n and n Theoretically, the expected value (the center of the distribution) is 0 and the standard deviation (spread of the distribution) is derived from the following formula (2).

・・・（２）但し、σは測定値の標準偏差。

(2) where σ is the standard deviation of the measured values.

Based on the above formula (2), for example, when the total number of _n1s is 90 and the number of _m1s is 7, the standard deviation is given by the following formula (3). Also, when _n2 is 30 and _m2 is 6, the standard deviation is given by the following equation (4).

・・・（３）

... (3)

・・・（４）

... (4)

Thus, if the values of the standard deviation coefficients (formula (5) below) in formula (1) above are approximately equal, the standard deviations are also substantially equal as in formulas (3) and (4) above. .

・・・（５）

... (5)

This is a similar distribution of the difference between the "small mean" of m1 out of _n1 measurements and the "whole mean" of _n1 measurements, i.e., ( _n1 , _{m1 )} = (90, 7) and (n ₂ , m ₂ ) = (30, 6), the distribution of the difference between the "small average" of the measured values and the "overall average" of the measured values is similar. represent.

In general, the above equation (1) is obtained by solving the following equation (6).

・・・（６）

... (6)

Here, when using the "average value" of n and m measured values, the number _m2 of soil moisture sensors used in the target field can be calculated based on the above equation (1). Also, even when using the "median" of n and m measured values, the distribution of the difference between the "small median" and the "all median" is approximated using the average value, that is, the small median Similarly, the above Based on the formula (1), the number m ₂ of soil moisture sensors used in the target field can be calculated.

Regarding the relationship between the number n ₁ and the number n ₂ of the soil moisture sensors, regardless of whether n ₁ >n ₂ or n ₁ <n ₂ , the above equation (1) is used. , the number m ₂ of soil moisture sensors used in the target field can be calculated. Also, here, the experimental field is wider, that is, n ₁ > n ₂ , or the target field is wider, that is, n ₁ < n ₂ , the above formula (1 ), the number m ₂ of soil moisture sensors to be used in the target field can be calculated.

Further, in the representative value estimation step, by measuring the soil moisture in the target field with the soil moisture sensors of the number m ₂ and using the median value or the average value of the measurement results as the representative value of the soil moisture in the target field, A representative value of the soil moisture in the target field can be estimated from the results of measurement by the soil moisture sensors of the number m ₂ . The representative value of the soil water content in the target field is a value determined from the measurement of the experimental field and the accuracy of the measurement is guaranteed. In addition, the measurement can be performed using an appropriate number of soil moisture sensors that can ensure measurement accuracy.

In addition, when the soil moisture measurement result of the soil moisture measurement sensor employs only the measured values within a predetermined range, it is possible to improve the accuracy of the obtained measured values. Moreover, as a result, it is possible to improve the accuracy of the representative value of the soil moisture in the target field. That is, for example, for the soil moisture sensor to be used, by setting a predetermined range based on the range of the upper limit and the lower limit of the measured value that maintains good measurement accuracy, only the measured value within the same range is adopted. , and the accuracy of the measured values can be improved.

In addition, the measured value of the soil moisture measured by the soil moisture measurement sensor falls within the predetermined range so that the measured value that is not within the predetermined range is included within the predetermined range. The accuracy of the obtained measurements can be increased if they are treated as lower bound values, or if measured values that exceed a given range are treated as upper bound values of a given range. Moreover, as a result, it is possible to improve the accuracy of the representative value of the soil moisture in the target field. That is, for example, for the soil moisture sensor to be used, a predetermined range is set based on the range of the upper and lower limits of the measured value that maintains good measurement accuracy, and the measured value that is less than the set range or the set range is treated as the lower limit value or the upper limit value of the range, it becomes possible to collect the measured value within the set range, and the accuracy of the measured value can be improved.

In addition, when measuring the soil moisture with the soil moisture measurement sensor multiple times at a certain measurement interval, the measurement result is the division median value or the division average value of the multiple measurement values included in the fixed range division in the series of measurements. is adopted, the influence of fluctuating errors that can occur in each measured value is reduced, and the accuracy of the representative value of the soil moisture in the target field can be improved. For example, when measuring at 1-minute intervals for several hours, by adopting the median value or average value for each soil moisture measurement sensor for each 30-minute range as the measurement result, the measurement at 1-minute intervals Measurement results can be obtained that are less affected by possible measurement errors. In other words, even if some values considered to be measurement errors are included in the 30 measurements, the influence of values considered to be measurement errors can be reduced by using the median or average value for 30 measurements. can be done.

In addition, when measuring the soil moisture with the soil moisture measuring sensor a plurality of times at constant measurement intervals, the measurement result is a moving range in which the number of measurements is fixed and the timing of measurement is shifted in a series of measurements. If a moving median value or a moving average value for each soil moisture measurement sensor of a plurality of measurements included in the division is employed, the effects of measurement errors that may occur in measurements at one-minute intervals can be reduced in real time. That is, for example, when the measurement at 1-minute intervals is continued for several hours, and the median value or average value for each soil moisture measurement sensor in each 30-minute range is adopted as the measurement result, from 0 minutes to 30 minutes By adopting the median or average value for each 30-minute range in different ranges from 1 minute to 31 minutes instead of adopting only the same range (30-minute range), the influence of fluctuating errors can be corrected in real time. It is possible to improve the accuracy of the representative value of the soil moisture in the target field in real time.

In addition, in the process of creating a sample semivariogram using the spatial statistics method, the distance between the sensors is calculated for all combinations of selecting any two of the n soil moisture sensors placed in the experimental field, In addition to dividing into distance group groups, which are groups according to the distance between sensors, a sample semivariogram is created based on the data group of the difference in the measured value of soil moisture for each group in the distance group group, and in the semivariogram estimation step , a curve is fitted to the distance between the sensors and the scatter plot of the sample semivariogram to create a semivariogram model. It is possible to obtain a semivariogram value for the distance between arbitrary points, including points other than the coordinates of the location of the moisture sensor. In addition, by creating a semivariogram model, the presence or absence of spatial similarity, the strength of spatial similarity, and the spatial similarity can be determined by the relational expression (relational expression with covariogram) derived from random field theory. You can check the distance. The semivariogram means spatial similarity, and the sample semivariogram means spatial similarity calculated from measured values.

In addition, in the spatial statistics method, in the arbitrary point moisture value estimation process, the soil at an arbitrary point in the experimental field using an extended weighted average based on the measured values of soil moisture by n soil moisture sensors In the case of estimating moisture, it is possible to obtain information on the measured value of soil moisture at an arbitrary point other than the position where the soil moisture sensor is arranged. The weighting factor in the extended weighted average here reflects the semivariogram γ(h) with respect to the distance h between an arbitrary point and the sensor.

In addition, by the spatial statistics method, from the soil moisture measured by n soil moisture sensors and the soil moisture at an arbitrary point estimated from the arbitrary point moisture value estimation process, at each measurement time, in the experimental field Visualize the soil moisture and if you have a spatial distribution comprehension step to confirm the uniformity of the spatial distribution of the experimental field, visualize the state of the soil moisture in the experimental field at each measurement time and change it over time By tracking , it is possible to confirm whether a uniform spatial distribution is exhibited within the range of the experimental field. Here, for example, the spatial distribution of the measured or estimated soil moisture at each point in the experimental field at each measurement point is graphed using a contour map, etc., and changes over time in the graph are plotted. By checking, the uniformity or non-uniformity (tendency or deviation) of the spatial distribution can be visualized.

In addition, the soil moisture in the target field is measured using m ₂ of soil moisture sensors, and a second spatial distribution for confirming whether the target field exhibits a uniform spatial distribution of soil moisture by a spatial statistical method. When a confirmation process is provided, it is possible to confirm the validity of using one value, the median value or the average value of the measurement results of the soil moisture sensors of the number m ₂ , as the representative value of the soil moisture in the target field. can.

In order to achieve the above object, the method for estimating soil moisture of the present invention is based on the information of the measurement results of the soil moisture using a plurality of soil moisture measuring sensors in the experimental field. A method of estimating soil moisture for estimating a a spatial distribution confirmation step for confirming whether a uniform spatial distribution is shown; , a first measurement result of measuring the soil moisture in the experimental field with the first number of the soil moisture sensors, and the first measurement result, the number of which is arbitrarily reduced from the first number. A second measurement result obtained by selecting a second number of measurement values, which is the number of An arbitrary predetermined width is set based on the value of the value, and the reduced median value or the reduced average value obtained at each measurement timing of the second measurement result is within the arbitrary predetermined width range with respect to the reference. an empirical probability calculation step of calculating an empirical probability of falling within the second number of the plurality of patterns based on the arbitrary predetermined width and the empirical probability, the second number of the plurality of patterns having a desired accuracy A sensor number selection step of selecting a third number that is the number of soil moisture sensors; a number-of-sensors determination step of determining the number of the soil moisture sensors to be used in the target field using approximation by values; and a representative value estimating step of measuring and using the median value or average value of the measurement results as the representative value of the soil moisture in the target field.

Here, in the spatial distribution confirmation step, when the experimental field exhibits a uniform spatial distribution of soil moisture, in the empirical probability calculation step, at a predetermined measurement interval and a predetermined number of measurements, the first number of soils A first measurement result obtained by measuring soil moisture in an experimental field with a moisture sensor, and measurements for a second number, which is a number arbitrarily subtracted from the first number, from the first measurement result. A second measurement result with selected values is obtained in a plurality of patterns, and an arbitrary predetermined width is obtained based on the value of the total median value or the total average value obtained at each measurement timing of the first measurement result. By calculating the empirical probability that the reduced median value or the reduced average value obtained at each measurement timing of the second measurement result falls within an arbitrary predetermined width range as viewed from the reference, the first For the measurement results of the soil moisture sensors of the number, a second number of measurement values obtained by reducing the number from the first number of measurement results are selected, and the selected measurement values are obtained by the second number. , it becomes possible to obtain information on the accuracy of measurements that can be guaranteed. In other words, when the number of soil moisture sensors is reduced in the experimental field, the numerical value to what extent the accuracy of the measurement with the reduced number is within the original measurement result of the first number. You can check the information.

Further, in the representative value estimation step, the soil moisture in the target field is measured with the number of soil moisture sensors determined in the sensor number determination step, and the median or average value of the measurement results is used as the representative value of the soil moisture in the target field. By doing so, the representative value of the soil moisture in the target field can be estimated from the results measured by the determined number of soil moisture sensors. The representative value of the soil water content in the target field is a value determined from the measurement of the experimental field and the accuracy of the measurement is guaranteed. In addition, the measurement can be performed using an appropriate number of soil moisture sensors that can ensure measurement accuracy.

The method for estimating soil moisture according to the present invention uses an appropriate number of soil moisture sensors while ensuring the accuracy of measurement in a target field where it is desired to grasp the soil moisture based on the measurement information obtained from the experimental field. It is possible to obtain the representative value of the soil moisture in the target field.

FIG. 2 is a flow chart showing an outline of the overall flow in an example of a method for estimating soil moisture to which the present invention is applied; FIG. 10 is a graph for explaining the work of fitting a curve to the distance h and the scatter diagram of the sample semivariogram; FIG. 4 is a graph showing the relationship between a semivariogram and a covariogram. It is an explanatory diagram showing that a field is divided into squares with a size of 0.5 m containing the coordinates of the soil moisture sensor. It is explanatory drawing which shows color-coding for every square division of the size of 0.5 m based on the value of a soil moisture. FIG. 10 is an explanatory diagram showing an example in which a field is divided into squares each having a size of 0.1 m including the coordinates of the soil moisture sensor, and each square division is color-coded based on the value of the soil moisture. FIG. 7 is an explanatory diagram showing a state in which contour lines are superimposed on the explanatory diagram of FIG. 6; FIG. 8 is an explanatory diagram showing a state in which colors corresponding to soil moisture values are added again along the contour lines in the explanatory diagram of FIG. 7 ; It is explanatory drawing which visualized the state of the soil moisture including the arbitrary point using 90 soil moisture sensors in the experimental field. FIG. 9 is an explanatory diagram that visualizes the state of soil moisture in the experimental field at different time points of measurement, following FIG. FIG. 10 is an explanatory diagram visualizing the state of soil moisture in an experimental field at different time points of measurement, following FIGS. 9 and 10. FIG.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described with reference to the drawings for understanding of the present invention.
The content shown below is an example of a method for estimating soil moisture to which the present invention is applied, and the content of the present invention is not limited to the content shown below, and settings can be changed as appropriate.

An estimation method, which is an example of a method for estimating soil moisture to which the present invention is applied, is based on the information of the measurement result of a soil moisture measurement sensor in an experimental field of a certain size, and the soil moisture in a target field smaller than the experimental field. This is a method of estimating a representative value.

First, with reference to FIG. 1, the overall outline of the flow of the method for estimating soil moisture according to the present invention will be described.

As shown in FIG. 1, in the present invention, first, in an experimental field, soil moisture is measured using the number of soil moisture measuring sensors that can be arranged in the area of the experimental field (n: ₁ ). (STEP 1 in the figure). In the following description, 90 pieces will be described as an example of the number _n1 . Also, the number _n1 may be referred to as the "total number" as necessary.

Next, the spatial distribution of the experimental field is confirmed from the measurement results of the number n ₁ (total number) of soil moisture measuring sensors (STEP 2 in FIG. 1).

In this step of confirming the spatial distribution of the experimental fields, a spatial statistical method is used to confirm whether the experimental fields exhibit a uniform spatial distribution.

In addition, it can be confirmed that one representative value of soil moisture in the experimental field is enough if the entire range shows a uniform spatial distribution in the experimental field. That is, in this step, the validity of the representative value of the experimental field can be verified.

Moreover, the spatial distribution of the target field can be visualized by the process of confirming whether the experimental field exhibits a uniform spatial distribution. In addition, in this step, it is possible to obtain information on the distance (range) to which the spatial similarity of the soil moisture sensor extends in the experimental field. Details of confirmation of the soil moisture measurement sensor and the spatial distribution of the experimental field will be described later.

In addition, in the process of confirming the spatial distribution of the experimental field, if the experimental field shows a uniform spatial distribution, from the measurement results (all measured values) of the number n ₁ (90) soil moisture measurement sensors, The number of measured values is selected by reducing the number from the number n _{of 1} (STEP 3 in FIG. 1).

Here, in the step of selecting the measurement accuracy to be described later, the number n is reduced from ₁ so that the user can select the desired accuracy from the measurement accuracy of a plurality of patterns. ₄₅ , 27, 14, 13, 9, 7, 6, 5, 4 Multiple patterns are used to select measurements.

When the number of soil moisture sensors was reduced from n ₁ , the number was selected so that the distance between the sensors would be the same and the shape of the outer edge of the sensor would be rectangular.

Here, the number of soil moisture sensors (n ₁ ) used in confirming the spatial distribution of the experimental field does not necessarily need to be set to 90, and can be set as appropriate. However, this number must be arranged and set as a number that can be arranged according to the size of the experimental field.

In addition, the number of patterns with a reduced number of soil moisture sensors is necessarily limited to 45, 27, 14, 13, 9, 7, 6, 5, and 4. Instead, it is possible to select the contents that have changed the number. However, in order to provide a wide range of variations in measurement accuracy that can be selected by the user in the later process of selecting measurement accuracy, the variation in the number of pieces to be reduced should be set widely, from a large number to a small number. is preferred.

Further, when reducing the number of soil moisture sensors, it is not always necessary to reduce the number so that the distance between the sensors is the same and the shape of the outer edge of the sensor is rectangular. Any condition can be selected to reduce the number.

Subsequently, the empirical probability is calculated from the measurement results of the soil moisture sensor number n ₁ in the experimental field and the measurement values of the number n ₁ minus the number selected (STEP 4 in FIG. 1).

In the process of calculating this empirical probability, based on the "total median value" at each measurement timing derived from the measurement results of 90 soil moisture sensors, within a predetermined numerical range from this total median value , select the measured values obtained by reducing the number of soil moisture sensors, and calculate the probability (empirical probability) that the selected measured values include the measured median value (reduced median value) at each measurement timing. .

This empirical probability becomes It is an index that indicates how much measurement accuracy can be guaranteed.

Here, in calculating the empirical probability, it is not necessary to adopt the median value (the total median value, the reduced median value) of the measurement results at each measurement timing, and the average value at each measurement timing is adopted. , an empirical probability may be calculated. However, the median value of the measurement results is adopted because it is easy to obtain highly accurate values by excluding outliers derived from obvious measurement errors, etc., and because it is robust against outliers. is more preferable.

Next, in the measurement accuracy selection step, one is selected from a plurality of patterns selected to reduce the number of soil moisture sensors according to the accuracy desired by the user from the content of the calculated empirical probability. (STEP 5 in FIG. 1).

That is, the number of 90 soil moisture sensors obtained in the process of calculating the empirical probability is 45, 27, 14, 13, 9, 7, 6, 5, 4 The number of sensors (m _{= 1} ) is selected according to the accuracy desired by the user from among the measurement accuracies for each number when decreasing.

Accuracy here means that, for example, when 13 soil moisture sensors are selected, the empirical probability of being included in the total median ±5% of the measurement results of 90 sensors is 99.3% (0 .993).

In other words, if we reduce the number of soil moisture sensors from 90 to 13, the median (small median) of the 13 sensor results is 99.3% likely to be It means that the accuracy of the measurement results in the "total median ± 5%" range is guaranteed.

Therefore, in the measurement accuracy selection step, the user selects a reduced number of sensors, thereby selecting the measurement accuracy required by the user.

Next, in the process of determining the number of sensors to be used in the target field, the reduced number of sensors in the experimental field (m ₁ sensor) selected in the measurement accuracy selection process and the The number of soil moisture sensors that can be placed in each area, the number of soil moisture sensors before reducing the number (n ₁ = 90), and the number of soil moisture sensors that can be placed in the area of the target field (n ₂ and The number of sensors ( ₂ m) to be used in the target field is determined from the information of (STEP 6 in FIG. 1).

In this process, the number of soil moisture sensors is determined so that the level of measurement accuracy corresponding to the number of soil moisture sensors selected to reduce the number in the experimental field can be maintained in the target field. . In other words, this is a step of determining the number of soil moisture sensors ( ₂ per square meter) that can guarantee the measurement accuracy required by the user based on the size of the target field.

Through the steps up to this point, it is possible to set the soil moisture measurement accuracy required by the user and the number of soil moisture sensors (m ₂ ) required to obtain the accuracy in the target field.

Subsequently, in the target field, soil moisture is measured using 2 m ₂ soil moisture sensors, and a representative value of the target field is obtained based on the measurement results (STEP 7 in FIG. 1). In this step, the soil moisture is measured under predetermined measurement conditions via m ₂ soil moisture sensors, and in principle, the median value is calculated from the measured values at each measurement timing. This median value can be estimated as the representative value of soil moisture in the target field.

In addition, as a further step, a step of confirming whether the target field exhibits a uniform spatial distribution using a spatial statistical method from the measurement results of the target field measured using _m2 soil moisture sensors. (STEP 8 in FIG. 1).

In this target field, if the entire range shows a uniform spatial distribution, it can be confirmed that only one representative value of the soil moisture content of the target field is sufficient. That is, in this step, the validity of the representative value of the target field can be verified.

Further, although the details will be described later, the spatial distribution of the target field can be visualized by the process of confirming whether the target field exhibits a uniform spatial distribution.

The above is an outline of the method for estimating the representative value of the soil moisture in the target field according to the estimation method A, which is an example of the method for estimating the soil moisture to which the present invention is applied. Subsequently, the details of the estimation method A will be described below.

[Soil moisture sensor]
First, the soil moisture sensor will be explained. In the present invention, as a soil moisture sensor for measuring soil moisture, a capacitance type non-contact soil moisture sensor (manufactured by DFROBOT, model number: Capacitive Soil Moisture Sensor v1.2) is used.

This soil moisture sensor can measure the volumetric moisture content (θ: ratio of water volume to total soil volume, m ³ /m ³ ), which is one index of soil moisture, in real time without contact. can. Therefore, the measured value of soil moisture in the present embodiment is the value of volumetric water content (θ).

Here, the volumetric water content does not necessarily have to be adopted as the soil moisture measurement value in the present invention. For example, a mode using a water content ratio (w) or a dry density (ρ _b ), which is an index of soil moisture, may be used. Also, in the present invention, it is possible to employ other known measuring means as a soil moisture sensor.

[Confirmation of spatial distribution by spatial statistical method]
Next, the confirmation of the spatial distribution in the experimental field by the spatial statistical technique will be described in detail. In addition, the same method can be adopted for the confirmation of the spatial distribution by the spatial statistical method in the target field for the following contents.

[Arrangement of the soil moisture sensor in the experimental field]
First, 90 (n ₁ ) soil moisture sensors were used in the spatial distribution by the spatial statistical technique in the experimental field. In this embodiment, the experimental field is a rectangular field with a width of 6 m and a length of 18 m.

In this experimental field, 90 soil moisture sensors were arranged in a grid pattern, with 5 sensors arranged horizontally and 18 sensors vertically, with a distance of 1m between the sensors both vertically and horizontally. .

With this arrangement, most of the experimental field is occupied by evenly distributed soil moisture sensors, and 90 sensors can be arranged over the expansive area of the experimental field. can be regarded as a number

In addition, the sensor used in this embodiment has a measuring portion within a range of about 7 cm in the main body. The sensor was placed in the soil so that it was located in range. All 90 sensors were similarly installed in the range of 2 cm to 9 cm in depth from the ground surface.

In addition, the measurement of the soil moisture sensor varies depending on the depth of the soil where the measuring portion of the sensor main body is installed, even if the measurement target is a substantially flat field. Therefore, when a substantially flat field is to be measured, it is necessary to align the installation depths of the sensors.

In the above description, the sensors were installed at a depth of 2 to 9 cm from the ground surface, but if the measurement is to be made at a deeper position in the soil, the insertion depth of the sensors should be the same. Further, for example, in the case of soil with ridges provided in a field and including height differences, it is divided into a range with ridges and a range without ridges, and the method for estimating soil moisture to which the present invention is applied is applied to each range. can do.

Here, in the present invention, it is not always necessary to arrange the 90 soil moisture sensors in a lattice pattern with a distance of 1 m between the sensors both vertically and horizontally, and the distance between the sensors can be calculated. If there is, the installation interval and the shape of the arrangement of the sensors are not limited. However, by arranging the sensors in a lattice pattern at intervals of 1 m, it becomes easy to install a large number of sensors and to easily calculate the distance between the sensors in each combination of two sensors.

90 soil moisture sensors were arranged as described above, and the soil moisture in the experimental field was measured under the following measurement conditions. First, for the entire range of the experimental field, the soil was watered from a dry state to the maximum water capacity of the soil, and then naturally dried and the soil was no longer dried, and measured over time. did

After watering the soil, there was a period of 3 weeks until the soil was no longer dry. In addition, the measurement with the 90 soil moisture sensors was started from the initial dry state, and after watering, the measurement was performed at intervals of 1 minute until the soil dried again. That is, with one sensor, for example, 30 measured values were obtained in 30 minutes, and these were measured over time for 3 weeks to acquire data.

Subsequently, the spatial distribution of soil moisture in the experimental field was confirmed using a spatial statistical method for the measurement results for 3 weeks using 90 soil moisture sensors in the experimental field.

[Specimen semivariogram preparation process]
First, in the spatial statistical method, a sample semivariogram creation step is performed for the measured values at each measurement timing. The sample semivariogram preparation process is the following procedure.

Here, from 90 sensors, for a combination of arbitrarily selecting two, there are 90 × (90-1) / 2 combinations, that is, 4005 combinations. Grouping was performed according to the distance h between the two sensors. For example, the sensors are classified into groups in which the distances between sensors are the same, such as a group with a distance of 1 m, a group with a distance of 2 m, a group with a distance of 2, and the like.

Then, for each group (section) in the distance h between the two sensors, the average value of the squares of the differences in each measurement value (z _i , z _j ) of the combination of the two sensors included in the group is 2. A sample semivariogram, which is the divided value, is calculated. A sample semivariogram is represented by the following equation (7). That is, a sample semivariogram is calculated for each distance h.

・・・（７）

... (7)

[Semivariogram estimation step]
A curve is then fitted to the scatterplot of the distance h and the sample semivariogram. In spatial statistics (random field theory), this curve is called a semivariogram model. This semivariogram model is used to estimate the semivariogram value γ(h) for any distance h.

Here, the semivariogram has multiple models in spatial statistics (random field theory). One of them is a model combining a nugget effect model and a spherical model, which is defined by the following equation (8).

・・・（８）
ここで、θ₀、θ₁、θ₂はパラメータで、これらの値により、このモデルの曲線の形が決まる。また、セミバリオグラムは、２つのセンサー間の距離ｈの関数である。

... (8)
where θ ₀ , θ ₁ , θ ₂ are parameters whose values determine the shape of the curve of this model. Also, the semivariogram is a function of the distance h between the two sensors.

Also, the work of fitting a curve to the scatter diagram of the distance h and the sample semivariogram will be described with reference to FIG. FIG. 2 is a scatter diagram with the distance h between sensors on the horizontal axis and the sample semivariogram on the vertical axis, and the circles in the graph indicate the sample semivariogram at each distance h.

Here, the curve in FIG. 2 is the semivariogram model. This curve is calculated by the above formula (9) so that the sum of the squares of the error between the curve and the sample semivariogram at each distance h (indicated by the vertical dotted line in FIG. 2) is minimized. It can be generated by obtaining the values of parameters θ ₀ , θ ₁ , and θ ₂ in . Note that FIG. 2 is a typical curve shape used for ease of explanation.

Thus, a curve is fitted to the scatterplot of the distance h and the sample semivariogram to generate a semivariogram model, which is used to estimate the semivariogram value γ(h) for any distance h. . That is, by giving an arbitrary distance h to the curve, the semivariogram value γ(h) for the distance h can be obtained.

Note that the semivariogram γ(h) is also called spatial dissimilarity. The sample semivariogram is also called the average spatial similarity.

Further, according to random field theory, the theorem represented by the following equation (9) holds for the semivariogram (spatial dissimilarity) γ(h).

・・・（９）
特にγ（０）＝０のとき、Ｃ=Ｃ（０）よりＣ（ｈ）＝Ｃ（０）－γ（ｈ）が成り立つ。

... (9)
In particular, when γ(0)=0, C(h)=C(0)−γ(h) holds from C=C(0).

where the function C(h) represents the covariogram (spatial similarity) and C represents a constant. In addition, from the theory of random fields, the semivariogram and the covariogram are two sides of the same coin (see Fig. 3).

That is, FIG. 3 shows a covariogram curve (indicated by symbol C) for the semivariogram model shown in FIG. In addition, from the relationship between the semivariogram (spatial dissimilarity) and the covariogram (spatial similarity), the strength of the spatial similarity (indicated by symbol Y in FIG. 3) and the distance to which the spatial similarity extends ( The location indicated by the symbol X) becomes clear.

The distance over which the spatial similarity extends can also be confirmed from the distance (h) at which the sample semivariogram peaks out on the curve of the semivariogram model.

Here, the distance (range) covered by the spatial similarity is a numerical value indicating the range covered by the measured value of the soil moisture sensor. In this embodiment, the distance (range) covered by the spatial similarity was 0.55 m. Therefore, in the experimental field, the spatial similarity of the distance between the soil moisture sensors did not extend to the adjacent soil moisture sensors, and it was confirmed that it is meaningful to measure with each sensor.

In addition, from the semivariogram model shown in FIGS. 2 and 3, the distance (h) is 0 with the position of the distance (h) (about 1.9 m) where the specimen semivariogram peaks as a boundary. In the range of ~1.9 m, there is a proportional relationship between the distance (h) and the sample semivariogram, and in the range where the distance (h) is 1.9 m or more, there is a proportional relationship between the distance (h) and the sample semivariogram It turns out that there is no relationship. Thus, the semivariogram model also reveals spatial similarity relationships.

[Optional point moisture value estimation step]
The value of soil moisture at any point in the experimental field is then estimated using an "extended weighted average", taking into account all 90 soil moisture sensor readings collectively. That is, the soil moisture value is estimated at points where no sensor is placed in the experimental field.

Here, the expanded weighted average is represented by the following equation (10), and the condition of the weighting factor wi is only the following equation (11).

・・・（１０）

(10)

・・・（１１）

(11)

First, when the soil moisture value at an arbitrary point is obtained as a normal _average value from the measured values z ₁ , z ₂ . Therefore, it is not possible to know the difference in values (spatial distribution) for each point.

Therefore, we consider a "weighted average" that is an extension of the normal average. A typical average value can be regarded as the sum of all soil moisture sensor measurements z ₁ , z ₂ . . . z _n multiplied by a weighting factor (1/n). A weighted average is obtained by setting this weighting coefficient to a more general w _i , and setting 0≦w _i ≦1 as a condition for w _i and a value that satisfies the above equation (11). This weighted average is represented by Equation (10) above.

Here, further, as described above, excluding the condition of 0≦w _i ≦1 in the weighted average and using only the above equation (11) as the condition of _wi is the “extended weight "Average with". This is also called a linear combination. Further, in spatial statistics (stochastic field theory), a more general one in which only the above equation (11) is used as a condition for _wi is adopted.

Estimation of soil moisture values using extended weighted averages for arbitrary points is further described below.

First, when considering soil moisture sensors at two points, the x-coordinate is x ₁ , the y-coordinate is y ₁ , and the measured value is z ₁ for the first sensor, and the x-coordinate is x ₂ for the second sensor. , the y-coordinate is y ₂ and the measured value is z ₂ . The extended weighted average at this time is given by the following equation (12). Also, the weighting factors w ₁ and w ₂ satisfy w ₁ +w ₂ =1.

・・・（１２）

(12)

Further, according to the random field theory, the weighting coefficients _w1 and _w2 are determined according to the distance from each soil moisture sensor at an arbitrary point as shown in the following formulas (13) and (14). In addition, h ₀₁ is the distance between an arbitrary point and the first sensor, h ₀₂ is the distance between an arbitrary point and the second sensor, and h ₁₂ is the first sensor and the first sensor is the distance of γ(h) is a semivariogram. Thus, the weighting factor reflects the semivariogram γ(h) for an arbitrary point and the sensor distance h.

・・・（１３）

(13)

・・・（１４）

(14)

Consider the following three cases for an arbitrary point and distances h ₀₁ and h ₀₂ .
(Case 1) Any point is equidistant from two soil moisture sensors (h ₀₁ =h ₀₂ ).
(Case 2) An arbitrary point is close to the first soil moisture sensor (h ₀₁ <h ₀₂ ).
(Case 3) Any point is close to the second soil moisture sensor (h ₀₁ >h ₀₂ ).

First, in case 1, h ₀₁ =h ₀₂ and the semivariograms have the same value (γ(h ₀₁ )=γ(h ₀₂ )), and the weighting factors w ₁ and w ₂ are given by the above equation From (13) and (14), the same 1/2 value is obtained. Then, from equation (12), the extended weighted average is (z ₁ +z ₂ )/2, which is the normal average.

In addition, in the case of “Case 2”, h ₀₁ <h ₀₂ , the semivariogram is γ(h ₀₁ )≦γ(h ₀₂ ), and the weighting factors w ₁ and w ₂ are the above equations (13) and From (14), w ₁ ≧w ₂ . Then, if the weighting factor _w1 is larger than the weighting factor _w2 , the expanded weighted average becomes a value closer to _z1 than the normal average value, according to equation (12).

Further, in case 3, h ₀₁ >h ₀₂ , the semivariogram is γ(h ₀₁ )≧γ(h ₀₂ ), and the weighting factors w ₁ and w ₂ are the above equations (13) and From (14), w ₁ ≤ w ₂ . Then, if the weighting factor _w2 is larger than the weighting factor _w1 , the expanded weighted average becomes a value closer to _z2 than the normal average value, according to equation (12).

In this way, at an arbitrary point in the experimental field, using the extended weighted average from the relationship between the distance from the coordinates of the two soil moisture sensors and the measured value of each sensor, of soil moisture can be estimated.

In order to simplify the explanation, the above contents were explained in relation to soil moisture sensors at two points. Consider the relationship between the distance from each coordinate and the measured value of each sensor. That is, if 90 sensors are deployed, an estimate of the soil moisture value for any one point is computed in relation to the 90 sensors.

[Spatial distribution grasping process]
Next, the details of the visualization of the spatial distribution of soil moisture in the experimental field will be described.
Here, the soil moisture value at an arbitrary point estimated from the measured values of the soil moisture sensor at each measurement timing and the measured values of all the soil moisture sensors using the above-mentioned extended weighted average is used. Visualize the soil moisture in the experimental field at each measurement timing.

First, it demonstrates using FIG.4 and FIG.5. In this part, for convenience of explanation, an example using 12 soil moisture sensors will be explained. Here, the vertical and horizontal ranges surrounded by the 12 sensors placed in the field are divided into squares of 0.5 m in size, and the soil moisture in each square range is indicated. The horizontal axis in FIG. 4 is the x-coordinate, and the vertical axis is the y-coordinate. Also, the scale bar on the right indicates the magnitude of the soil moisture value by color coding.

Also, the black circles in FIG. 4 indicate the positions of the 12 soil moisture sensors. A square of size 0.5m is segmented so that the sensor is located in the middle. In FIG. 4, the squares corresponding to each sensor are colored to indicate the soil moisture according to the respective sensor readings.

Also, the dashed square indicated by symbol A in FIG. 4 is a diagram showing one range of arbitrary points where there are no soil moisture sensors. In order to make the content easier to understand in FIG. 4, one arbitrary point is shown, but in reality, 0.5 m A square of size is set.

Then, for the coordinates of the central position of the square at an arbitrary point, the above-mentioned extended weighted average is used from the relationship between the distance (h) to the 12 soil moisture sensors and the measured values of all sensors. to estimate the value of soil moisture at an arbitrary point. That is, the calculated extended weighted average value is taken as the soil moisture value at that arbitrary point.

Such work is performed for all squares at arbitrary points in the field where there is no soil moisture sensor, and the value of soil moisture at each point is calculated. As a result, as shown in FIG. 5, the measured values of the 12 soil moisture sensors and the estimated values of an arbitrary point without sensors are colored according to the soil moisture. It is possible to visualize the state of soil moisture in the field.

Moreover, although FIGS. 4 and 5 show an example of a square with a size of 0.5 m, by reducing the size of the square, it is possible to show the condition of the soil moisture in the field in more detail. As an example, in FIG. 6, the field is divided into squares with a size of 0.1 m with respect to 12 soil moisture sensors, and the state of soil moisture in the field is visualized.

In FIG. 6, as an example, division is made into 875 squares with a size of 0.1 m. In this way, by changing the setting of the size of the square, it is possible to visualize the state of the soil moisture in the field with higher accuracy.

Also, in the visualization of the spatial distribution of soil moisture, contour lines can be overlaid and displayed based on the results of measured and estimated values of soil moisture (see FIG. 7). Note that FIG. 7 is a diagram in which contour lines are superimposed on the results of FIG. Further, from the state of FIG. 7, if colors are reapplied according to the soil moisture value along the contour lines, the overhanging color disappears, and the soil moisture state in the field can be more naturally visualized ( See Figure 8).

With the flow described above, it is possible to visualize the spatial distribution of soil moisture in the experimental field at a certain measurement timing. In the present embodiment, 90 soil moisture sensors were actually used to visualize the state of soil moisture in the experimental field at each measurement timing in a similar manner.

In addition, visualization of the spatial distribution of soil moisture in this experimental field was carried out at each measurement at 1-minute intervals using 90 sensors. As a result, for example, it is possible to obtain information on the state of soil moisture in the experimental field at each time of measurement, as shown in FIGS. 9 to 11. FIG.

In addition, in the present invention, as a step of confirming the spatial distribution of the experimental field (STEP 2 in FIG. 1), the contents are verified using a diagram of the state of the soil moisture in the experimental field at each measurement time point. Confirm whether the experimental field exhibits a uniform spatial distribution of soil moisture.

More specifically, if the diagrams of the soil moisture conditions in the experimental field are observed in order, and if the same soil moisture value is observed for the entire surface of the experimental field at multiple measurement timings. , it can be determined that the observed field area has uniformity (shows a uniform spatial distribution).

Here, for example, in FIGS. 9 to 11, one black dot indicates the position of one soil moisture sensor. In addition, the rectangle surrounding all the sensors corresponds to the entire surface of the field area, and since this entire surface (rectangle) shows the same color, that is, the same soil moisture value, the observed field area can be judged to be uniform.

A portion without a black dot indicates that there is no measured value of the soil moisture sensor at the time of measurement due to deviation of measurement timing or the like. Also, since there is variation in the measured values of each sensor, the range centered on each sensor shows a different color.

In this case, the total measurement timing is 46,519, and there are 46,519 spatial distribution images for all the measurement timings. Then, except for only 10 images (approximately 2/10,000) in all the images, the entire surface (rectangle) of the field area has the same color, that is, the same soil moisture value, in all the remaining images. The result was shown.

On the other hand, if the entire surface (rectangle) of the field area does not have the same color, and an image that includes multiple boundary ranges with different colors in the entire surface is an image of the spatial distribution for all the measurement timings. An area of the observed field is considered nonuniform (does not exhibit a uniform spatial distribution) if it is observed in large numbers.

In this way, by grasping the soil moisture conditions in the experimental field at each time point of measurement as the "surface" of the entire experimental field, it is possible to determine whether the entire area exhibits a uniform spatial distribution of soil moisture. can decide.

In this embodiment, as shown in FIGS. 9 to 11, the results showing the same soil moisture value (same color) for the entire surface (rectangle) of the field area were obtained at most of the measurement points. Therefore, the experimental field showed a uniform spatial distribution. In addition, from this, it was clarified that one representative value of soil moisture is sufficient in the experimental field, since the soil exhibits a uniform spatial distribution.

On the other hand, if the area of the experimental field does not have the same color, and multiple border areas with different colors are included in the entire surface, the image is observed at multiple measurement timings, showing a uniform spatial distribution. If there is no clear boundary, it can be handled separately from the range with a clear boundary and the range without it.

In other words, for example, targeting only a range with a clear boundary, using the same method from the measurement results of multiple soil moisture sensors, if it shows a uniform spatial distribution, for a range with a clear boundary, It can be treated as if only one representative value is sufficient.

In addition, depending on the location of the experimental field, even if it is the same land, due to differences in drainage and ease of drying, for example, 20% of one end side and the remaining 80% of a rectangular land may have a soil moisture content. Cases with different behavior are also assumed. In such a case, it is possible to divide 20% of the land and 80% of the land and obtain the representative value of the soil moisture in each of the lands.

In this way, in the process of confirming the spatial distribution of the experimental field, it is possible to confirm whether or not the experimental field exhibits a uniform spatial distribution of soil moisture using a spatial statistical method. Validity can be verified that one value is acceptable. Furthermore, in this step, the distance (range) spanned by the spatial similarity of the soil moisture sensor can be obtained.

[Measurement with reduced number of soil moisture sensors]
As described above, next, from the measurement results (all measured values) of the soil moisture sensor, the number of measured values reduced from _n1 is selected (STEP 3 in FIG. 1).

In this process, the 90 (n ₁ ) soil moisture sensors used to confirm the spatial distribution of the experimental field were reduced to 45, 27, 14, 13, 9, 7, and 6 sensors. , 5 and 4 were selected.

[Step of calculating empirical probability]
Subsequently, the empirical probability was calculated from the measurement results of the number _n1 of the soil moisture sensors in the experimental field and the results of selecting the measurement values of the number _n1 less than the number n1 (STEP 4 in FIG. 1).

In this process, based on the "median value of total number" at each measurement timing derived from the measurement results of 90 soil moisture sensors, within a predetermined numerical range from the median value of all values at each measurement timing The number of measured values obtained by reducing the number of soil moisture sensors is selected, and the probability (empirical probability) that the selected measured values include the measurement median value (reduced median value) at each measurement timing is calculated.

In more detail, the procedure is as follows. First, let d be the width of a predetermined numerical range. Any value can be set for d. In addition, the total number of time points (total number of measurements) under the measurement conditions is n (measurement was performed a total of n times at 1-minute intervals).

Also, the median value (the total median value) is calculated from the measured values at each measurement timing with the 90 soil moisture sensors.

In addition, the median value of the measured values of the 45 sensors at a certain measurement timing (once in n) in the measurements of the soil moisture sensors selected to reduce the number, for example, 45 sensors (reduced median value ) falls within the range from “total median −d” to “total median +d” at the same measurement timing. Note that this part is mathematically synonymous with "|reduced median−full median|≦d" (the symbol "|" is an absolute value).

Then, this determination is made for the measured values of all the measurement timings of the 45 soil moisture sensors. Also, let x be the number of times that the value of the reduced median value of the 45 sensors falls within the range from “all median value −d” to “all median value +d”.

Subsequently, a value is calculated by dividing the number of times x of times of entry by the total number of time points n. This value is the empirical probability. Empirical probabilities are calculated for each of 27, 14, 13, 9, 7, 6, 5, and 4 as well as 45.

In the empirical probability, d, which is the width of the predetermined numerical range, can be set according to the accuracy desired by the user. For example, d can be set to values such as 5, 3, and 1. Table 1 shows the results of empirical probabilities calculated in this embodiment.

[Process of selecting measurement accuracy]
Next, in the step of selecting the measurement accuracy, one is selected from a plurality of patterns with a reduced number of soil moisture sensors according to the accuracy desired by the user based on the content of the empirical probability (Fig. 1). STEP5).

Here, based on Table 1, when the number of 90 soil moisture sensors is reduced to 45, 27, 14, 13, 9, 7, 6, 5, and 4 , the number of sensors (m ₁ ) is selected according to the accuracy desired by the user from among the measurement accuracies for each number.

For example, when the number of soil moisture sensors "13" is selected, the empirical probability that the measurement results of 90 sensors are included in the total median ±5% is 99.3% (0.993).

In other words, the median (small median) of the measurement results with 13 sensors has a probability of 99.3%, and the accuracy that falls within the range of "total median ± 5%" of the measurement results with 90 sensors. will be guaranteed.

Therefore, the user selects the measurement accuracy required by himself/herself by selecting the reduced number of sensors.

[Step of determining the number of sensors to be used in the target field]
Subsequently, the number of sensors to be used in the target field is determined (STEP 6 in FIG. 1).

In this step, the number of the reduced number in the experimental field (m ₁ piece) selected in the selection step of the measurement accuracy described above, and the number that can be arranged in the area in the experimental field. From the information _on the number of soil moisture sensors (n ₁ = 90) before reducing Determine the number of sensors to be used (m _{= 2} ).

First, in this example, it is assumed that the number _n2 of the soil moisture sensors that can be arranged according to the size of the target field is "30". That is, if the soil moisture sensors are arranged in a lattice pattern with a distance of 1 m between each sensor in the vertical and horizontal directions, the target field corresponds to 30 sensors that can be arranged. In addition, the target field shall be smaller in area than the experimental field.

Equation (1) is derived from the contents of Equations (2) to (6) described above. Also, regarding formula (1), the small median corresponds to the small mean, and the total median corresponds to the total mean. As a replacement, the number of soil moisture sensors _m2 used in the target field is calculated.

For example, in the measurement accuracy selection process, when the user selects "7" as the number of soil moisture sensors m ₁ from the accuracy desired by the user, the integer that satisfies the above formula (1) is: The number _m2 of soil moisture sensors used in the target field can be calculated as "6".

That is, it is found that 6 sensors are used when measuring in the target field while maintaining the level of measurement accuracy using 7 soil moisture sensors secured in the experimental field. , can determine the appropriate number of sensors to use in the target field.

[Measurement of soil moisture in target fields and acquisition of representative values]
Then, in the target field, soil moisture is measured using six soil moisture sensors, and a representative value of the target field is obtained based on the measurement results (STEP 7 in FIG. 1).

Also, the six soil moisture sensors are arranged with a distance between them in the target field.

Then, the measurement is performed under predetermined measurement conditions, and in principle, the median value is calculated from the measured values at each measurement timing. This median value can be estimated as the representative value of soil moisture in the target field.

For example, it is possible to grasp the information of the soil moisture in the target field during drying by performing the measurement at the timing before watering the target field and obtaining the representative value of the measurement. In addition, when growing crops in the target field, the soil moisture sensor monitors the soil moisture over time and confirms the soil moisture at the desired timing, thereby setting the appropriate watering timing and watering time. be able to.

In addition, it is also possible to confirm whether the target field exhibits a uniform spatial distribution using a spatial statistical method from the measurement results of the target field measured using six soil moisture sensors (STEP 8 in FIG. 1 ).

In this target field, if the entire range shows a uniform spatial distribution, it can be confirmed that only one representative value of the soil moisture content of the target field is sufficient. Also, the spatial distribution of soil moisture in the target field can be visualized.

In addition, in estimation method A, which is an example of a method for estimating soil moisture to which the present invention is applied, it is also possible to adopt only measured values within a predetermined numerical range for the measured values of the soil moisture sensor as measurement results. is. Here, the predetermined numerical range is, for example, a measured value range defined by the sensor used and whose accuracy is ensured. That is, before the sensor measurement values are adopted as measurement results, preprocessing is performed to filter the data values so as not to include measurement values that are considered to be abnormal in terms of sensor performance. By doing so, the accuracy of measurement is improved, and as a result, the accuracy of the representative value of soil moisture can be improved.

Further, in estimation method A, which is an example of a method for estimating soil moisture to which the present invention is applied, a measured value that is not within a predetermined range is included within a predetermined range with respect to the measured value of the soil moisture sensor. Thus, a measured value below the predetermined range can be treated as the lower limit value of the predetermined range, or a measured value exceeding the predetermined range can be treated as the upper limit value of the predetermined range. Here, the predetermined numerical range is, for example, a measured value range defined by the sensor used and whose accuracy is ensured. That is, before adopting the measured value of the sensor as the measurement result, a predetermined range is set based on the upper and lower limits of the measured value that maintains good measurement accuracy, and the measured value that is less than the set range Also, the values that exceed the set range are filtered by preprocessing so that they are treated as the lower or upper limit of the range, and the measured values that are considered abnormal from the sensor performance are also included in the specified range. By processing in this manner, the accuracy of measurement is increased, and as a result, the accuracy of the representative value of soil moisture can be improved.

Further, in the estimation method A, which is an example of the method for estimating the soil moisture to which the present invention is applied, the measured values of the soil moisture sensor are measured at 1-minute intervals. It is not necessary to use each measured value as it is. For example, when measuring at intervals of 1 minute, the median value or average value can be calculated for each soil moisture sensor from each measurement value of 30 times with 30 minutes as one segment, and this can be used.

This can be adopted in each process such as the process of confirming the spatial distribution in the experimental field, the process of calculating the empirical probability, the process of obtaining the representative value in the target field, and the like. In this way, by obtaining the median value or average value for each soil moisture sensor within a certain time range, it is possible to obtain measurement results that reduce the influence of measurement errors that may occur in individual measurements. As a result, the accuracy of the representative value of soil moisture can be improved.

Further, in the estimation method A, which is an example of the method for estimating the soil moisture to which the present invention is applied, when taking the median value or the average value in a certain time range, for example, the timing of measurement is shifted, and the soil moisture It is also possible to set the median or mean value for each sensor. That is, for example, when monitoring soil moisture for a long time, instead of calculating the average value of 30 minutes from each measurement value of 0 minutes to 30 minutes as a certain time range, 1 minute to From each measurement value of 31 minutes, the timing of measurement is shifted so that the median value or average value of 30 minutes is calculated. You can also This also makes it possible to obtain measurement results in which the influence of measurement errors that may occur in individual measurements is reduced, and to improve the accuracy of the representative value of soil moisture.

In the estimation method, which is an example of the method for estimating soil moisture to which the present invention is applied, a spatial statistical method is used based on the measurement information obtained from the experimental field, and the spatial distribution of the experimental field is uniform. In addition to confirming that , the spatial distribution can be visualized. Moreover, the validity of the representative value of the experimental field can be verified.

In addition, in the estimation method of the present invention, in the experimental field, measurements are performed with a reduced number of soil moisture sensors, the empirical probability is calculated from the measurement results of each number, and the average value is used to approximate the target field. By determining the number of sensors to be selected, the number of sensors necessary for the accuracy desired by the user can be determined.

In addition, in the estimation method of the present invention, the representative value of the soil moisture in the entire surface of the field can be estimated using the number of soil moisture sensors corresponding to the accuracy required by the user in the target field.

As described above, the method for estimating soil moisture of the present invention is based on the measurement information obtained from the experimental field. Using the soil moisture sensor, it is possible to obtain a representative value of the soil moisture in the target field.

In order to achieve the above object, the method for estimating soil moisture of the present invention estimates a representative value of soil moisture in a target field based on information obtained from measurement results of soil moisture using a plurality of soil moisture sensors in an experimental field. A method for estimating soil moisture for the purpose of measuring the soil moisture in the experimental field using a plurality of the soil moisture sensors, and using a spatial statistical method to estimate the soil moisture in the experimental field with a uniform spatial distribution and in the first spatial distribution confirmation step, when the experimental field exhibits a uniform spatial distribution of soil moisture, the area of the experimental field The first number of the soil moisture sensors that can be arranged according to the measurement results of measuring the soil moisture in the experimental field at a predetermined measurement interval and a predetermined number of measurements at each measurement timing. , a total number derived value obtaining step of obtaining a total median value or a total average value; number of measured values are selected, and for each of the selected measured values, a reduced median value or a reduced average value derived from the measurement results at each measurement timing is acquired with the second number of patterns A derived value acquisition step, setting an arbitrary predetermined width based on the value of the all-number median value or the all-number average value, and at each measurement timing, the reduced median value or the reduced average value is determined from the reference. It is determined whether or not it falls within the range of the arbitrary predetermined width, and the same determination is performed for all measurement timings, and the subtrahend median value or the subtrahend average value in the second number is the above when viewed from the reference. An empirical probability calculation step of calculating an empirical probability of falling within any predetermined width, and based on the arbitrary predetermined width and the empirical probability, out of the second number of the plurality of patterns, a sensor number selection step of selecting a third number that is the number of the soil moisture sensors having a desired accuracy; The soil moisture used in the target field based on the fourth number, which is the number that can be arranged according to the size of the target field, information on the area of the experimental field, and information on the area of the target field. Regarding the number _m2 of sensors, when the first number and the fourth number are the same, the number _m2 is determined to be the same number as the third number, or the first number When the number of and the fourth number are different, the The number of 1's is n ₁ , the third number is m ₁ , and the fourth number is n ₂ , and the number of the number m ₂ is determined as an integer satisfying the following formula (1): a number determining step, measuring the soil moisture in the target field with the soil moisture sensors of the number _m2 , and estimating the representative value using the median value or the average value of the measurement results as the representative value of the soil moisture in the target field. and a step.

In addition, when the soil moisture measurement result of the soil moisture sensor employs only the measured values within a predetermined range, it is possible to improve the accuracy of the obtained measured values. Moreover, as a result, it is possible to improve the accuracy of the representative value of the soil moisture in the target field. That is, for example, for the soil moisture sensor to be used, by setting a predetermined range based on the range of the upper limit and the lower limit of the measured value that maintains good measurement accuracy, only the measured value within the same range is adopted. , and the accuracy of the measured values can be improved.

In addition, the measurement result of the soil moisture sensor, so that the measured value that is not included in the predetermined range is included in the predetermined range, the measured value that is less than the predetermined range is the lower limit of the predetermined range or treating a measured value exceeding the predetermined range as the upper limit value of the predetermined range, the accuracy of the obtained measured value can be improved. Moreover, as a result, it is possible to improve the accuracy of the representative value of the soil moisture in the target field. That is, for example, for the soil moisture sensor to be used, a predetermined range is set based on the range of the upper and lower limits of the measured value that maintains good measurement accuracy, and the measured value that is less than the set range or the set range is treated as the lower limit value or the upper limit value of the range, it becomes possible to collect the measured value within the set range, and the accuracy of the measured value can be improved.

Also, when measuring the soil moisture with the soil moisture sensor multiple times at regular measurement intervals, the measurement result is the division median value or the division average value of the multiple measurement values included in the fixed range division in the series of measurements. When adopted, the influence of fluctuating errors that may occur in each measured value is reduced, and the accuracy of the representative value of the soil moisture in the target field can be increased. For example, when the measurement at 1-minute intervals continues for several hours, by adopting the median value or average value for each soil moisture sensor in each 30-minute range for the measurement results, It is possible to obtain a measurement result in which the influence of possible measurement errors is reduced. In other words, even if some values considered to be measurement errors are included in the 30 measurements, the influence of values considered to be measurement errors can be reduced by using the median or average value for 30 measurements. can be done.

In addition, when the soil moisture sensor measures the soil moisture a plurality of times at regular measurement intervals, the measurement result is a movement range classification in which the number of measurements is fixed and the measurement timing is staggered in a series of measurements. If a running median or average value for each soil moisture sensor of the multiple measurements contained in is employed, the effect of possible measurement errors in measurements at one-minute intervals can be reduced in real time. That is, for example, when the measurement at 1-minute intervals is continued for several hours and the median value or average value for each soil moisture sensor in each 30-minute range is adopted as the measurement result, the same By adopting the median value or average value for each 30-minute range in different ranges from 1 minute to 31 minutes instead of adopting only the range (30-minute range), the influence of fluctuating errors is reduced in real time. As a result, the accuracy of the representative value of the soil moisture in the target field can be improved in real time.

Further, in order to achieve the above object, the method for estimating soil moisture of the present invention provides a representative soil moisture value The soil moisture estimation method for estimating the a spatial distribution confirmation step of confirming whether or not the spatial distribution is exhibited, and in the spatial distribution confirmation step, when the experimental field exhibits a uniform spatial distribution of the soil moisture, at a predetermined measurement interval and a predetermined number of measurements, A first measurement result obtained by measuring the soil moisture in the experimental field with the first number of soil moisture sensors, and the first measurement result, the number of which is arbitrarily reduced from the first number. A second measurement result obtained by selecting a second number of measurement values, which is a number, in a plurality of patterns, and a total median value or a total average value obtained for each measurement timing of the first measurement result An arbitrary predetermined width is set based on the value of the second measurement result, and the reduced median value or the reduced average value obtained at each measurement timing of the second measurement result is within the arbitrary predetermined width as viewed from the reference. an empirical probability calculation step of calculating an empirical probability of entering the soil having a desired accuracy from among the second number of the plurality of patterns based on the arbitrary predetermined width and the empirical probability A sensor number selection step of selecting a third number that is the number of moisture sensors, an average value for the information on the area of the experimental field, the information on the area of the target field, and the information on the third number a number of sensors determining step of determining the number of the soil moisture sensors to be used in the target field, using the approximation by , and measuring the soil moisture of the target field with the number of the soil moisture sensors determined in the number of sensors determining step. and a representative value estimating step of determining the median value or average value of the measurement results as the representative value of the soil moisture in the target field.

The estimation method, which is an example of the method for estimating soil moisture to which the present invention is applied, is based on the information of the measurement result of the soil moisture sensor in the experimental field of a certain size, and represents the soil moisture in the target field smaller than the experimental field. It is a method of estimating the value.

As shown in FIG. 1, in the present invention, first, in an experimental field, soil moisture is measured using the number of soil moisture sensors (n ₌₁ ) that can be arranged in the area of the experimental field ( STEP 1) in the figure. In the following description, 90 pieces will be described as an example of the number _n1 . Also, the number _n1 may be referred to as the "total number" as necessary.

Next, the spatial distribution of the experimental field is confirmed from the measurement results of the number n ₁ (total number) of soil moisture sensors (STEP 2 in FIG. 1).

Moreover, the spatial distribution of the target field can be visualized by the process of confirming whether the experimental field exhibits a uniform spatial distribution. In addition, in this step, it is possible to obtain information on the distance (range) to which the spatial similarity of the soil moisture sensor extends in the experimental field. The details of confirmation of the soil moisture sensor and the spatial distribution of the experimental field will be described later.

In addition, in the process of confirming the spatial distribution of the experimental field, if the experimental field shows a uniform spatial distribution, the measurement results (total measured values) of n ₁ (90) soil moisture sensors The number n of measured values is selected by decreasing the number from ₁ (STEP 3 in FIG. 1).

Claims (8)

A method for estimating soil moisture for estimating a representative value of soil moisture in a target field based on information on the results of measuring soil moisture using a plurality of soil moisture measurement sensors in an experimental field, comprising:
A first spatial distribution confirmation of measuring the soil moisture in the experimental field using a plurality of the soil moisture sensors and confirming whether the experimental field exhibits a uniform spatial distribution of the soil moisture by a spatial statistical method. process and
In the first spatial distribution confirming step, when the experimental field exhibits a uniform spatial distribution of soil moisture, the first number, which is the number that can be arranged according to the area size of the experimental field. The soil moisture sensor measures the soil moisture in the experimental field at a predetermined measurement interval and a predetermined number of measurements, and obtains the total median value or the total average value derived from the measurement results for each measurement timing. process and
From the measurement results using the first number, select a second number of measurements, which is a number arbitrarily reduced from the first number, and for the selected measurement value, a subtraction-derived value acquisition step of acquiring the subtraction median value or the subtraction average value derived from the measurement result for each measurement timing, in the second number of a plurality of patterns;
An arbitrary predetermined width is set based on the value of the all-number median value or the all-number average value, and at each measurement timing, the reduced median value or the reduced average value changes to the arbitrary predetermined width as viewed from the reference. The same determination is made for all measurement timings, and the median value or average value of the second number is within the arbitrary predetermined width range viewed from the reference an empirical probability calculation step of calculating an empirical probability of falling within
sensor number selection for selecting a third number, which is the number of the soil moisture sensors having a desired accuracy, from the second number of the plurality of patterns based on the arbitrary predetermined width and the empirical probability; process and
The first number, the third number, and the number of the soil moisture sensors, and the fourth number, which is the number that can be arranged according to the area size of the target field, and the area of the experimental field. and information on the area of the target field, the number m ₂ of the soil moisture sensors used in the target field,
if the first number and the fourth number are the same, the number _m2 is determined to be the same number as the third number;
or,
When the first number and the fourth number are different, the first number is n ₁ , the third number is m ₁ , and the fourth number is n ₂ . A sensor number determination step of determining the number of _m2 as an integer that satisfies the following formula (1);
a representative value estimating step of measuring the soil moisture in the target field with the _m2 soil moisture sensors, and using the median value or average value of the measurement results as the representative value of the soil moisture in the target field. A method for estimating soil moisture.

... (1) The measurement result of the soil moisture in the soil moisture measurement sensor is
The method for estimating soil moisture according to claim 1, wherein only measurements falling within a predetermined range are employed. The measurement result of the soil moisture in the soil moisture measurement sensor is
So that the measured value not included in the predetermined range is included in the predetermined range,
The measured value less than the predetermined range is treated as the lower limit value of the predetermined range, or the measured value exceeding the predetermined range is treated as the upper limit value of the predetermined range. A method for estimating soil moisture. When the soil moisture measurement sensor measures the soil moisture a plurality of times at constant measurement intervals, the measurement result is the division median value or the division average value of the plurality of measured values included in the fixed range division in the series of measurements. The method for estimating soil moisture according to claim 1, claim 2 or claim 3. When measuring the soil moisture by the soil moisture measuring sensor a plurality of times at a constant measurement interval, the measurement result is divided into movement ranges in which the number of measurements is fixed and the timing of measurement is shifted in a series of measurements. The method for estimating soil moisture according to claim 4, wherein a moving median value or a moving average value of a plurality of measured values included in the soil moisture measurement sensor is adopted. The spatial statistics method includes:
A distance group group, which is a group corresponding to the distance between the sensors, by calculating the distance between the sensors for all combinations of selecting any two sensors from the n soil moisture sensors arranged in the experimental field. a sample semivariogram creating step of creating a sample semivariogram based on a data group of differences in measured values of soil moisture for each group in the distance group group;
Semivariogram estimation, wherein a curve is fitted to the inter-sensor distances and a scatter plot of the sample semivariogram to create a semivariogram model, and the semivariogram model is used to estimate the value of the semivariogram for any given distance. process and
an arbitrary point moisture value estimation step of estimating the soil moisture at an arbitrary point in the experimental field using an expanded weighted average based on the soil moisture values measured by the n soil moisture sensors;
Visualization of the soil moisture in the experimental field at each measurement time based on the soil moisture measured by the n soil moisture sensors and the soil moisture at the arbitrary point estimated by the arbitrary point moisture value estimation step. and a spatial distribution grasping step of confirming the uniformity of the spatial distribution of the experimental field. . A second step of measuring the soil moisture in the target field using the number m ₂ of the soil moisture sensors, and confirming whether the target field exhibits a uniform spatial distribution of soil moisture by the spatial statistical method. and a spatial distribution confirmation step of . A method for estimating soil moisture for estimating a representative value of soil moisture in a target field based on information on the results of measuring soil moisture using a plurality of soil moisture measurement sensors in an experimental field, comprising:
a spatial distribution confirmation step of measuring the soil moisture in the experimental field using a plurality of the soil moisture sensors and confirming whether the experimental field exhibits a uniform spatial distribution of the soil moisture by a spatial statistical technique;
In the spatial distribution confirmation step, when the experimental field exhibits a uniform spatial distribution of the soil moisture, the first number of the soil moisture sensors are used at a predetermined measurement interval and a predetermined number of times to measure the experimental field. and the first measurement result of measuring the soil moisture, and from the first measurement result, the measurement value for the second number, which is the number arbitrarily reduced from the first number, was selected. , obtaining the second measurement result in a plurality of patterns, and setting an arbitrary predetermined width based on the value of the total median value or the total average value obtained at each measurement timing of the first measurement result, An empirical probability calculation step of calculating an empirical probability that the reduced median value or the reduced average value obtained at each measurement timing of the second measurement result falls within the arbitrary predetermined range with respect to the reference. and,
sensor number selection for selecting a third number, which is the number of the soil moisture sensors having a desired accuracy, from the second number of the plurality of patterns based on the arbitrary predetermined width and the empirical probability; process and
The number of the soil moisture sensors to be used in the target field is calculated using approximation by an average value for the information on the area of the experimental field, the information on the area of the target field, and the information on the third number. a step of determining the number of sensors to be determined;
Measure the soil moisture in the target field with the number of soil moisture sensors determined in the number of sensors determining step, and estimate the representative value using the median or average value of the measurement results as the representative value of the soil moisture in the target field. and a method for estimating soil moisture.

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