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PA—Precision Agriculture
Biosystems Engineering (2002) 83(3), 299–306 doi:10.1016/S1537-5110(02)00201-5, available online at http://www.idealibrary.com on PA}Precision Agriculture
An Information Table for Yield Data Analysis and Management Q. Zhang1; S. Han2 1
Department of Agricultural Engineering, 338 Sc. Building, University of Illinois at Urbana-Champaign, 1304 W pennysywania Avenue, Urbana, IL 61801, USA; e-mail of corresponding author: [email protected] 2 John Deere Ag Management Solutions, Urbandale, IA 50322, USA; e-mail: [email protected] (Received 9 October 2001; accepted in revised form 16 August 2002)
The lack of standard methods for processing and managing yield data is an obstacle for farmers to utilise yield data effectively and efficiently. This paper presents a formal method of using an information table for analysing and managing raw yield data in a format of information subsets for a manageable block in the field. An ordinary procedure for developing such an information table was introduced. A case study was performed to demonstrate the use of this method to support decision-making in precision agricultural operations. This formal method provided a standard technique for yield data analysis and management in real-time, and can be easily programmed in a ‘transparent-to-farmer’ data management tool. The case study demonstrated the application of this model in managing the yield data obtained from an actual field in Central Illinois during a period of 5 yr. The results indicated that the model was capable of achieving its design goal. # 2002 Published by Elsevier Science Ltd. on behalf of Silsoe Research Institute
1. Introduction Recent advances in precision agriculture technology, such as site-specific management and variable-rate applications, have promised farmers a means of more efficient and more profitable production. For example, farmers are now capable of fertilising different zones of their fields at different rates to have the maximum yield (Yang et al., 1998). Yield mapping, a measure of the crop production integrated over space and time, provides the fundamental information to adjust the inputs to identified areas to optimise farming profitability. However, precision agriculture practices require special skills to deal with the enormous amount of yield data to obtain the necessary information to support optimising production efficiency and profitability. Lack of standard methods for yield data analysis and management is an obstacle for farmers utilising yield data effectively and efficiently to support their precision production. Numerous studies have been reported in the areas of yield monitoring, site-specific natural resources management, and geographical information system (GIS) based farming systems for storing site-specific production data in a map form (Graham et al., 1997; Payne et al., 1997; Plant, 2001; Robert et al., 1996; Walley et al., 2001). The 1537-5110/02/$35.00
challenge in utilising a yield map is how to convert the massive site-specific data into the knowledge to support the decision-making which often requires some special skills. Many researchers have put great effort into developing technologies to address this issue. Examples include the development of integrated information management system for agriculture (Thiel et al., 1999), finding a proper way of integrating multiple-year yield data into a single map (Panneton et al., 2001), developing a field-level geographic information system (FIS) for analysing agricultural data relevant to precision agriculture (Runquist et al., 2001), classifying yield levels using fuzzy logic (Stafford et al., 1998), and developing an automated and analytical procedure to delineate information management zones for variable application management based on the yield map (Fraisse et al., 1999). While technologies being developed can effectively collect, analyse and utilise the spatial and/or temporal data, more efforts are now focused on how to integrate those technologies and represent it in a standard way so that the integrated technology can be easily implemented in a ‘transparentto-farmer’ format. The focus of this paper is to develop a formal method of using an information table to represent the spatial and temporal yield data. The information table will 299
# 2002 Published by Elsevier Science Ltd. on behalf of Silsoe Research Institute
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Notation C D Ib Sb U X% M N P Q xi x% d yj
a measured yield level subset of U a block average yield subset of U information subset influential factor sub-subset a finite and non-empty set of yield data the average yield from the field of interest number of raw data within a block in the field number of raw data within an area of interest number of years of historic data being used number of blocks defined in a field a raw yield data element in set U the average yield from a block in the field a yield level in subset C, represented in natural language
provide a formal approach for raw data processing, massive yield data classification and site-specific yield class presentation. To present the developed method clearly, this paper is organized as follows. Section 2 provides the formal presentation of the information model, the detailed procedures for using the information table approach to represent the massive yield data, and the use of this information table to support decision-making. Section 3 uses an actual sample of 5 yr yield data to evaluate the effectiveness and accuracy of this developed information table method in sorting and representing the massive raw yield data. Finally, a brief summary is given based on the case study results.
2. Information table model
a myj ð Þ
an arbitrary valve for cut-off confidence level the confidence level of a yield level within a block in the field myj jUk ð Þ the confidence level of a yield level within a block in the field in year k the standard deviation of the yield from a sd block in the field the standard deviation of the yield within the sU field of interest Sup symbol of fuzzy union operation Subscripts A average level H High level L Low level
associated with a confidence factor between 0 and 1, where 0 means no confidence at all and 1 means completely confident. An information table presents the complete list of possible yield levels with an associated confidence factor for each block in a field, and prepares the massive raw yield data in a format suitable to support automated decision-making. To ensure the information table (Table 1) model containing adequate information, the following four properties should be held: 8x% d 2 D; 9 at least one yi 2 C; such that P D xi % % ½ xd ¼ yj ¼ ; myj ðxd Þ 2 0; 1 m n X
8x% d 2 D;
ð2Þ
j¼1
2.1. Formal presentation The information table model, consisting of a confidence measure of the yield levels, was developed for converting massive yield data into knowledge. The formal presentation of the information table model can be described as follows. Let U be a finite and non-empty set, called the universe of discourse, covering a definite range of yield data obtained from a field over a number of years. Let D be a subset of U containing the average yield from a specific block within the field, and C be another subset of U containing all the possible yield levels represented using natural language. Each element x% d in D can be mapped into at least one element yj in C
myj ðx% d Þ ¼ 1
ð1Þ
8x% di U1 ; 8x% di U2 ; y jjU1 U2
¼ sup myjjU x% di ; myjjU x% di 1
ð3Þ
2
where: sup indicates a logic operation of finding the maximum value, and myj ð Þ is a fuzzy membership used to describe the confidence level of an estimated yield level for an interested block in the field. The first property indicates that the average yield data obtained from each block in the field can be mapped into at least one fuzzy yield level, and its confidence level, described using a fuzzy membership, can be between 0 and 1. A confidence level of 0 means that the particular yield level does not reflect the average
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Table 1 General presentation of yield information table Block identity
Confidence level myi of a defined yield level
1 2 ... ... q
Yield level L
Yield level A
Yield level H
mL ðx% 1 Þ mL ðx% 2 Þ ... ... mL ðx% q Þ
mA ðx% 1 Þ mA ðx% 2 Þ ... ... mA ðx% q Þ
mH ðx% 1 Þ mH ðx% 2 Þ ... ... mL ðx% q Þ
x% , average yield of block.
yield data in the block of interest, and 1 means the yield level strongly reflects the average yield data. A confidence level between, but not including, 0 and 1 indicates that this yield level partially reflects the average yield from the block of interest. The second property indicates that the yield from the block of interest can be classified into more than one yield level. However, the total membership, a measure of the confidence on those possible yield levels, should be 1. This property prevents the same information from being over-counted. The third property is used to handle multi-year data from the same block. When yields from multiple years are being considered, a separate universe of discourse should be used because the distribution of the yield data may be totally changed from year to year due to the influence of many factors, including many unknown ones. To solve this problem, the first and the second property should be held in preparing yield data for each year. Based on all single year results, this property provides the yield potential from each block.
Low yield
2.2. Model development procedure To develop an informative site-specific production information table based on massive yield data, the following six procedural steps should be followed for ensuring that all three properties are held. (1) Determine the average yield X% and its standard deviation sU based on the sample size n of the massive raw yield data obtained from the field of interest: X xi ð4Þ X% ¼ U
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn % 2 i¼1 xi X sU ¼ n 1
ð5Þ
(2) Define a manageable size of blocks for the field of interest. It is recommended to define 50–150 blocks ha 1 to keep the table within a manageable size
High yield
Average yield
Fuzzy membership
1.0 0.8 0.6 0.4 0.2 0
X−3σ U
X−2σ U
X−σ U
X
X + σU
X +2σ U
X +3σ U
Average block yield
Fig. 1. Definition of fuzzy membership functions for low, average and high yield from a block in field relation to the average yield from the entire field: X% ; average yield of the entire field; sU standard deviation of the yield.
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while still being capable of representing reasonable details of the yield distribution within a field. (3) Collect the raw data of sample size m from each block, and calculate its average yield x% d and standard deviation sd within that block: X xi ð6Þ x% d ¼ D
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pm % d Þ2 i¼1 ðxi x sd ¼ m 1
x% d 4X% X% 5x% d 4X% þ sU X% þ sU 5x% d 4X% þ 2sU x% d > X% þ 2sU
ð7Þ ð10Þ
(4) Define the yield level from the block of interest for a particular year by placing the average yield of the block related to the overall average yield of the field using the following fuzzy membership functions. It is recommended to represent the yield variation in the block of interest using three levels of low, average and high yield. To be able to restore the original average yield, some overlap of these yield levels were defined using fuzzy memberships. Three fuzzy membership functions were used to describe the degree of overlap. If a yield from a block was between plus/minus two standard deviations of the average yield from the field, it was defined as an average yield. If the yield was below or above the average yield of the field, it was defined as a low or high yield. Fig. 1 illustrates the domains of these fuzzy membership functions: mL ðx% d Þ ¼ 8 1; > > > > !2 > > > X% 2sU x% d > > ; 1
2 > < 2sU > > X% x% 2 > d > >2 ; > > 2sU > > > : 0;
mH ðx% d Þ ¼ 8 0; > > > > % 2 > > > > 2 X x% d ; > > < 2sU !2 > > X% þ 2sU x% d > > 1 2 ; > > 2sU > > > > : 1;
x% d 4X% 2sU X% 2sU 5x% d 4X% sU X% sU 5x% d 4X% x% d > X%
where mL , mA and mH are the confidence levels for the low, average and high yield levels, respectively. (5) Determine the yield potential for each block of interest based on p multiple-year data using the following fuzzy union operation equation. The fuzzy union operation screens the yield level with the highest fuzzy membership out from all applicable levels:
myjjU U U ¼ sup myjjU ðx% d Þ; myjjU ðx% d Þ; yjjUk ðx% d Þ 1
2
1
k
2
p
¼ [ myjjU ðx% d Þ i¼1
ð11Þ
l
(6) List the obtained block yield levels (both for multiple-year and for a particular year of interest) from the field in the information table. The information table can be extended by including other factors of influence, such as the soil type, field elevation and slope, as well as the amount of fertiliser being applied and the precipitation of the year of interest. The only requirement is that the influence of all factors should be represented in the form of fuzzy memberships using the method introduced in steps (1)–(5).
(8) 2.3. Application of the information table mA ðx% d Þ ¼ 8 0; > > > !2 > > > > X% 2sU x% d > > ; 2 > > > 2sU > > > > % 2 < X x% d ; 1
2 > 2sU > > > !2 > > > > > 2 X% þ 2sU x% d ; > > > > 2sU > > > : 0;
After the information table has been completed, the yield-related information for a block of interest is represented in a form of information subset Ib : The numerator of each element in the subset represents the yield level, and the denominator represents the confidence level for the obtained yield level: y yA yH yU L yU A yU H L Ib ¼ m ð12Þ myA myH myUL myU myUH yL
x% d 4X% 2sU X% 2sU 5x% d 4X% sU X% sU 5x% d 4X% þ sU X% þ sU 5x% d 4X% þ 2sU x% d > X% þ 2s
A
ð9Þ
To support decision-making effectively for optimising the production, it is important to retrieve only the information which influences the yield significantly. An
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a-cut method, which eliminates all the elements with associated fuzzy membership less than an arbitrary value of a from the subset (Passino & Yurkovich, 1998), is used to create a new sub-subset from the information subset by selecting only the influential factors using an appropriate threshold value for a. Normally, it is recommended to use a value greater than 0.5 to pick the influential factors from a subset. ( ) yi Sb ¼ ; m 5a Ib ð13Þ myi yi The influential factor sub-subset Sb of the information subset carries only a few selected influential factors based on the objective of optimisation in support of the decision-making. Therefore, this information table model can reduce a complicated and tedious massive yield data analysis and management into a standard and simple fuzzy mapping problem and prepare the data in a ‘ready-to-use’ format for further applications.
3. Case study of information table development and application To demonstrate the development and application of this information table model without loss of generality, a yield information table for a small portion of a field in Central Illinois was created based on a 5-yr yield data. The field of interest covers an area of 475 m by 800 m. The crop follows a rotation of maize and soya bean. Due to the influence of numerous factors, the yield variation is very large from year to year. Table 2 lists the yields from the blocks of interest, the average yield of the entire field, the standard deviation of the yield, and the total number of yield points collected from the field
of interest from 1996 to 2000. All the yield points were collected using a commercial yield monitor. Yield data were recorded at a 1 s time interval from 1996 to 1999, and at a 3 s interval in 2000. One important step in developing an efficient information table is the definition of a manageable and informative base information block. To demonstrate the technique without loss of generality, a small portion of a 35 56 m by 35 56 m area (a square of three-header widths of the combine harvester used on this farm) was randomly selected from the field. Therefore, the square area of one header width (9 14 m by 9 14 m) was defined as the base block in this case study with a total number of nine blocks. Due to the uneven distribution of sampling points in the field, the results indicate that the number of yield samples obtained from those blocks vary from 1 to 17. Figure 2 shows the distribution of yield data samples collected from the nine base blocks in the portion being studied within the 5-yr period. To handle the variation in sampling size within a block, it is strongly recommended to use the average yield data from a particular block as the base information. By applying the fuzzy membership functions defined in the previous section based on the overall average yield, the overall standard deviation, and the block average yield data, Table 3 gives the annual yield levels from the study blocks for year 2000 and the potential yield levels estimated based on yields of 1996– 2000. Each line in Table 3 defines an information subset regarding the particular block in the field of interest. For example, the content in the first line and the sixth line of Table 3 defined information sublets for blocks 1 and 6. Table 2 indicates that the yields from blocks 1 and 6
Table 2 Yield from blocks of interest, average yield of the entire field, standard deviation of the yield, and the number of sampling points obtained from the field of interest in a 5-yr period Variables
Maize
1
Yield of block 1, kg ha Yield of block 2, kg ha 1 Yield of block 3, kg ha 1 Yield of block 4, kg ha 1 Yield of block 5, kg ha 1 Yield of block 6, kg ha 1 Yield of block 7, kg ha 1 Yield of block 8, kg ha 1 Yield of block 9, kg ha 1 Average yield, kg ha 1 Standard deviation, kg ha 1 Total number of yield points
Soya bean
1997
1999
1996
1998
2000
11223 10910 13162 10599 11058 8754 11372 11056 11089 10425 1193 27466
7348 6774 6573 9685 9624 6289 8665 9392 6985 11430 1382 26975
3028 1470 2428 2837 3027 1792 2708 2563 2612 3042 505 21768
2824 2624 3167 2896 2867 1858 2639 2881 3582 3372 545 23670
2879 1864 2530 2734 3044 1807 2575 2865 2562 2726 505 7667
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12
Number of blocks
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
11 12
13 14
15 16
17
Number of samples obtained from one block
Fig. 2. Frequency of yield data samples collected inside a base block from a portion of the study field located in Central Illinois between years 1996 and 2000.
Table 3 Fuzzy yield levels from individual base information blocks for the year 2000 and for the period 1996-2000 (the numbers in the table are confidence levels for the corresponding yield levels) Block identity
1 2 3 4 5 6 7 8 9
Year 2000 yield
Past 5 yr yield
Low
Average
High
Low
Average
High
0 0 96 0 07 0 0 0 98 0 04 0 0 05
0 95 0 04 0 93 1 00 0 80 0 02 0 96 0 96 0 95
0 05 0 0 0 0 20 0 0 0 04 0
1 00 1 00 1 00 0 72 0 75 1 00 1 00 0 86 1 00
1 00 0 92 0 93 1 00 1 00 0 15 0 96 0 96 0 95
0 22 0 08 1 00 0 01 0 20 0 0 31 0 13 0 15
were 2879 and 1807 kg ha 1, respectively, while the average yield for the field was 2726 kg ha 1 with a standard deviation of 505 kg ha 1 for year 2000. Substitute these values to Eqns. (8)–(10); it results in confidence levels of 0 95 and 0 05 for average and high yield levels, respectively. Similarly, substitute the block yields, the field average yields and the standard deviations for years from 1996 to 1999 to appropriate equations, and then apply Eqn. (11) to determine the highest confidence levels for different yield levels from these blocks; it results in the following information subsets: ny yA yH yU L yU A yU H o L Ib1 ¼ ð14Þ 0 0 95 0 05 1 0 1 0 0 22 n y yA yH yU L yU A yU H o L Ib6 ¼ ð15Þ 0 98 0 02 0 1 0 0 15 0
As defined in Eqn (12), the first three information agents indicate the fuzzy yield level of the most recent year (year 2000 in this case), and the second three information agents indicate the fuzzy levels of potential yield based on historic data (5 yr data in this case). The total fuzzy membership of 1 for the first three information agents provides yield distribution information based on the most recent year’s production condition. The total fuzzy memberships of the second three information agents are always greater than 1, which provides a measure on the consistency of the yield from the block of interest under various production conditions. As an example, the first three elements in subset Ib1 represented that the confidence levels for low, average, and high yield levels of the most recent year in block 1 were 0, 0 95 and 0 05, respectively. The second three elements indicated that the confidence levels for
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150 100
Error in yield, kg-1 ha
50 0 -50 -100 -150 -200 -250 0
5
10
15
20
25
Ordinal number of the evaluated block
Fig. 3. Error distribution of yield data back-calculated from the fuzzy yield levels in the evaluated blocks; the base values were the raw yield data obtained from those blocks (year 2000 data)
having low, average and high yield levels were 1 0, 1 0, and 0 22 based on the 5-yr historic yield data. It means that the yield level from this block is more likely to be of low–average range than to be high. The inconsistency in the confidence factors for low yield between the most recent year data and the five-yr average data indicated that there might be some unusual factors contributing to the yield variation during the most recent year. All these could provide important information for determining fertilising rate in the block. Similarly, the elements in subset Ib6 indicated confidence levels of 0 98, 0 02, and 0 for low, average, and high yield for the most recent year, and 1 0, 0 15, 0 for low, average and high yield potential from this block. The consistency in the confidence levels between the most recent year’s yield and the yield potential provided additional useful information that this block was located in a low-yield area compared to the rest of the field. One advantage of applying fuzzy mapping approach to classify the yield levels related to the average yield is its capability of back-calculating the real-valued yield based on the fuzzy memberships. Fig. 3 shows the error between the real-valued yield back-calculated from the fuzzy yield levels and the original raw yield data sampled from the evaluated blocks. It indicated that the maximum error was 211 kg ha 1, and the root mean square (RMS) error was 13 kg ha 1. Further analysis found that such an error was mainly caused by the uneven readings of the raw yield data within a block since the fuzzy yield levels were defined based on the mean yield from the block.
More elements can be included in the information subset if more related information becomes available. Some of the elements recommended to be included are the field topography, the soil type, and the fertilising rate for the block for the most recent year. The more elements included in this information subset, the more informative this subset will become. However, the information subset will become more complicated if dealing with a large number of information agents, especially when it needs only part of the processed information to make an optimal production decision. To solve this problem, an information-reduction method is introduced to eliminate the irrelevant information agents using an a-cut method. This approach would create a sub-subset which contains only the most relevant attributes to the decision-making. For example, when the optimisation goal in a particular decision-making process is to apply less fertiliser in consistently high-yield blocks, average amounts of fertiliser in average-yield areas, and more fertiliser in the consistently low-yield zones, a threshold value a of 0 5 can be used to eliminate the irrelevant agents to this optimisation. Based on this method, the new sub-subsets for blocks 1 and 6 will be represented as follows: n y yU L yU A o A Sb1 ¼ ð16Þ Ib1 0 95 1 0 1 0 n y yU L o L Sb6 ¼ ð17Þ Ib6 0 98 1 0 The first sub-subset indicates that block 1 in this field had an average yield for the most recent year.
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Historically, the yield level from this block is between low and average. Based on the defined optimisation criterion, the available information suggests an average to high fertilising rate to this particular block. Similarly, the remaining information agents in the sub-subset of block 6 indicate that yield from this block is always low, and a high fertilising rate should be applied to block 6 to bring the yield in this block up to a higher level. By this information table approach, the yield variation in a field and its consistency over the years in the field could be represented using 322 information subsets instead of over 100,000 raw data points for a 5-yr period. It not only reduced the size of the base information units by 99 7%, but more importantly organized the processed data in an ‘easy-to-understand’ and ‘ready-to-use’ format. As the number of years increased in the yield distribution database, this feature of the information table approach would be more attractive. 4. Conclusions This paper presents a method of using an information table model to process and manage yield data in a format of information subset based on a manageable number of blocks within a field. This model provides a formal method to treat the unevenly distributed and widely variable yield data, converts the massive raw yield data into informative and manageable fuzzy levels, and represents the resulting fuzzy levels in such a way that it can be easily connected with other relevant production information to support site-specific decisionmaking. This formal method can be easily programmed so that it can be used to process the yield information automatically and lead to the development of a ‘transparent-to-farmer’ precision farming informationsupporting tool. The case study demonstrates the application of this model in managing the yield data obtained from an actual field in Central Illinois during a period of 5 yr. It could reduce over 99 7% data points and provide more informative yield distribution information. The results indicate that the model is capable of achieving its design goal. Acknowledgements This research was supported by the Strategic Research Initiative in Information Systems and Technology of the Illinois Council on Food and Agricultural
Research (CFAR-SRI-IT) and the United States Department of Agriculture (Hatch Project 10-306 AE). All mentioned supports are gratefully acknowledged. References Fraisse C W; Sudduth K A; Kitchen N R; Fridgen J J (1999). Use of unsupervised clustering algorithms for delineating within-field management zones. ASAE Paper No. 99–3043 Graham G I; Wolff D W; Stuber C W (1997). Characterization of a yield quantitative trait locus on chromosome five of maize by fine mapping. Crop Science, 37, 1601–1610 Panneton B; Brouillard M; Piekutowski T (2001). Integration of yield data from several years into a single map. In: Proceedings of the Third European Conference on Precision Agriculture (Blackmore S; Grenier G, eds), pp 73–78, Agro Montpellier, France Passino K M; Yurkovich S (1998). Fuzzy Control. Addison Wesley Longman, Inc., Menlo Park, CA, USA Payne R W; Potts J M; Verrier P J (1997). The description of experimental designs in information systems. Computers and Electronics in Agriculture, 19(1), 69–86 Plant R E (2001). Site-specific management: the application of information technology to crop production. Computers and Electronics in Agriculture, 30(1–3), 9–29 Robert M; LeQuintrec A; Boisgontier D; Grenier G (1996). Determination of field and cereal crop characteristics for spatially selective applications of nitrogen fertilizers. In: Proceedings of the Third International Conference on Precision Agriculture, pp 303–314, American Society of Agronomy, MN, USA Runquist S; Zhang N; Taylor R K (2001). Development of a field-level geographic information system. Computers and Electronics in Agriculture, 31(2), 201–209 Stafford J V; Lark R M; Bolam H C (1998). Using yield maps to regionalize fields into potential management units. In: Proceedings of the Fouth International Conference on Precision Agriculture (Robert PC; Rust RH; Larson WE eds) pp 225–237, American Society of Agronomy; Crop Science Society of America; Soil Science Society of America, Madison, USA Thiel S; Helbig R; Schiefer G (1999). Executive control center, integrated information management in agriculture. ASAE Paper No. 99–3185 Walley F; Fu G; Van Groenigen J W; Van Kessel C (2001). Nitrogen fixation and precision agriculture: constraints to predicting variability. In: Proceedings of the Third European Conference on Precision Agriculture (Blackmore S; Grenier G, eds), pp 965–970, Agro Montpellier, France Yang C; Anderson G L; King J H; Chandler E K (1998). Comparison of uniform and variable rate fertilization strategies using grid soil sampling, variable rate technology, and yield monitoring. In: Proceedings of the Fourth International Conference on Precision Agriculture (Robert PC; Rust RH; Larson WE eds) pp 479–486, American Society of Agronomy; Crop Science Society of America; Soil Science Society of America, Madison, USA
An Information Table for Yield Data Analysis and Management Q. Zhang1; S. Han2 1
Department of Agricultural Engineering, 338 Sc. Building, University of Illinois at Urbana-Champaign, 1304 W pennysywania Avenue, Urbana, IL 61801, USA; e-mail of corresponding author: [email protected] 2 John Deere Ag Management Solutions, Urbandale, IA 50322, USA; e-mail: [email protected] (Received 9 October 2001; accepted in revised form 16 August 2002)
The lack of standard methods for processing and managing yield data is an obstacle for farmers to utilise yield data effectively and efficiently. This paper presents a formal method of using an information table for analysing and managing raw yield data in a format of information subsets for a manageable block in the field. An ordinary procedure for developing such an information table was introduced. A case study was performed to demonstrate the use of this method to support decision-making in precision agricultural operations. This formal method provided a standard technique for yield data analysis and management in real-time, and can be easily programmed in a ‘transparent-to-farmer’ data management tool. The case study demonstrated the application of this model in managing the yield data obtained from an actual field in Central Illinois during a period of 5 yr. The results indicated that the model was capable of achieving its design goal. # 2002 Published by Elsevier Science Ltd. on behalf of Silsoe Research Institute
1. Introduction Recent advances in precision agriculture technology, such as site-specific management and variable-rate applications, have promised farmers a means of more efficient and more profitable production. For example, farmers are now capable of fertilising different zones of their fields at different rates to have the maximum yield (Yang et al., 1998). Yield mapping, a measure of the crop production integrated over space and time, provides the fundamental information to adjust the inputs to identified areas to optimise farming profitability. However, precision agriculture practices require special skills to deal with the enormous amount of yield data to obtain the necessary information to support optimising production efficiency and profitability. Lack of standard methods for yield data analysis and management is an obstacle for farmers utilising yield data effectively and efficiently to support their precision production. Numerous studies have been reported in the areas of yield monitoring, site-specific natural resources management, and geographical information system (GIS) based farming systems for storing site-specific production data in a map form (Graham et al., 1997; Payne et al., 1997; Plant, 2001; Robert et al., 1996; Walley et al., 2001). The 1537-5110/02/$35.00
challenge in utilising a yield map is how to convert the massive site-specific data into the knowledge to support the decision-making which often requires some special skills. Many researchers have put great effort into developing technologies to address this issue. Examples include the development of integrated information management system for agriculture (Thiel et al., 1999), finding a proper way of integrating multiple-year yield data into a single map (Panneton et al., 2001), developing a field-level geographic information system (FIS) for analysing agricultural data relevant to precision agriculture (Runquist et al., 2001), classifying yield levels using fuzzy logic (Stafford et al., 1998), and developing an automated and analytical procedure to delineate information management zones for variable application management based on the yield map (Fraisse et al., 1999). While technologies being developed can effectively collect, analyse and utilise the spatial and/or temporal data, more efforts are now focused on how to integrate those technologies and represent it in a standard way so that the integrated technology can be easily implemented in a ‘transparentto-farmer’ format. The focus of this paper is to develop a formal method of using an information table to represent the spatial and temporal yield data. The information table will 299
# 2002 Published by Elsevier Science Ltd. on behalf of Silsoe Research Institute
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Notation C D Ib Sb U X% M N P Q xi x% d yj
a measured yield level subset of U a block average yield subset of U information subset influential factor sub-subset a finite and non-empty set of yield data the average yield from the field of interest number of raw data within a block in the field number of raw data within an area of interest number of years of historic data being used number of blocks defined in a field a raw yield data element in set U the average yield from a block in the field a yield level in subset C, represented in natural language
provide a formal approach for raw data processing, massive yield data classification and site-specific yield class presentation. To present the developed method clearly, this paper is organized as follows. Section 2 provides the formal presentation of the information model, the detailed procedures for using the information table approach to represent the massive yield data, and the use of this information table to support decision-making. Section 3 uses an actual sample of 5 yr yield data to evaluate the effectiveness and accuracy of this developed information table method in sorting and representing the massive raw yield data. Finally, a brief summary is given based on the case study results.
2. Information table model
a myj ð Þ
an arbitrary valve for cut-off confidence level the confidence level of a yield level within a block in the field myj jUk ð Þ the confidence level of a yield level within a block in the field in year k the standard deviation of the yield from a sd block in the field the standard deviation of the yield within the sU field of interest Sup symbol of fuzzy union operation Subscripts A average level H High level L Low level
associated with a confidence factor between 0 and 1, where 0 means no confidence at all and 1 means completely confident. An information table presents the complete list of possible yield levels with an associated confidence factor for each block in a field, and prepares the massive raw yield data in a format suitable to support automated decision-making. To ensure the information table (Table 1) model containing adequate information, the following four properties should be held: 8x% d 2 D; 9 at least one yi 2 C; such that P D xi % % ½ xd ¼ yj ¼ ; myj ðxd Þ 2 0; 1 m n X
8x% d 2 D;
ð2Þ
j¼1
2.1. Formal presentation The information table model, consisting of a confidence measure of the yield levels, was developed for converting massive yield data into knowledge. The formal presentation of the information table model can be described as follows. Let U be a finite and non-empty set, called the universe of discourse, covering a definite range of yield data obtained from a field over a number of years. Let D be a subset of U containing the average yield from a specific block within the field, and C be another subset of U containing all the possible yield levels represented using natural language. Each element x% d in D can be mapped into at least one element yj in C
myj ðx% d Þ ¼ 1
ð1Þ
8x% di U1 ; 8x% di U2 ; y jjU1 U2
¼ sup myjjU x% di ; myjjU x% di 1
ð3Þ
2
where: sup indicates a logic operation of finding the maximum value, and myj ð Þ is a fuzzy membership used to describe the confidence level of an estimated yield level for an interested block in the field. The first property indicates that the average yield data obtained from each block in the field can be mapped into at least one fuzzy yield level, and its confidence level, described using a fuzzy membership, can be between 0 and 1. A confidence level of 0 means that the particular yield level does not reflect the average
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Table 1 General presentation of yield information table Block identity
Confidence level myi of a defined yield level
1 2 ... ... q
Yield level L
Yield level A
Yield level H
mL ðx% 1 Þ mL ðx% 2 Þ ... ... mL ðx% q Þ
mA ðx% 1 Þ mA ðx% 2 Þ ... ... mA ðx% q Þ
mH ðx% 1 Þ mH ðx% 2 Þ ... ... mL ðx% q Þ
x% , average yield of block.
yield data in the block of interest, and 1 means the yield level strongly reflects the average yield data. A confidence level between, but not including, 0 and 1 indicates that this yield level partially reflects the average yield from the block of interest. The second property indicates that the yield from the block of interest can be classified into more than one yield level. However, the total membership, a measure of the confidence on those possible yield levels, should be 1. This property prevents the same information from being over-counted. The third property is used to handle multi-year data from the same block. When yields from multiple years are being considered, a separate universe of discourse should be used because the distribution of the yield data may be totally changed from year to year due to the influence of many factors, including many unknown ones. To solve this problem, the first and the second property should be held in preparing yield data for each year. Based on all single year results, this property provides the yield potential from each block.
Low yield
2.2. Model development procedure To develop an informative site-specific production information table based on massive yield data, the following six procedural steps should be followed for ensuring that all three properties are held. (1) Determine the average yield X% and its standard deviation sU based on the sample size n of the massive raw yield data obtained from the field of interest: X xi ð4Þ X% ¼ U
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn % 2 i¼1 xi X sU ¼ n 1
ð5Þ
(2) Define a manageable size of blocks for the field of interest. It is recommended to define 50–150 blocks ha 1 to keep the table within a manageable size
High yield
Average yield
Fuzzy membership
1.0 0.8 0.6 0.4 0.2 0
X−3σ U
X−2σ U
X−σ U
X
X + σU
X +2σ U
X +3σ U
Average block yield
Fig. 1. Definition of fuzzy membership functions for low, average and high yield from a block in field relation to the average yield from the entire field: X% ; average yield of the entire field; sU standard deviation of the yield.
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while still being capable of representing reasonable details of the yield distribution within a field. (3) Collect the raw data of sample size m from each block, and calculate its average yield x% d and standard deviation sd within that block: X xi ð6Þ x% d ¼ D
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pm % d Þ2 i¼1 ðxi x sd ¼ m 1
x% d 4X% X% 5x% d 4X% þ sU X% þ sU 5x% d 4X% þ 2sU x% d > X% þ 2sU
ð7Þ ð10Þ
(4) Define the yield level from the block of interest for a particular year by placing the average yield of the block related to the overall average yield of the field using the following fuzzy membership functions. It is recommended to represent the yield variation in the block of interest using three levels of low, average and high yield. To be able to restore the original average yield, some overlap of these yield levels were defined using fuzzy memberships. Three fuzzy membership functions were used to describe the degree of overlap. If a yield from a block was between plus/minus two standard deviations of the average yield from the field, it was defined as an average yield. If the yield was below or above the average yield of the field, it was defined as a low or high yield. Fig. 1 illustrates the domains of these fuzzy membership functions: mL ðx% d Þ ¼ 8 1; > > > > !2 > > > X% 2sU x% d > > ; 1
2 > < 2sU > > X% x% 2 > d > >2 ; > > 2sU > > > : 0;
mH ðx% d Þ ¼ 8 0; > > > > % 2 > > > > 2 X x% d ; > > < 2sU !2 > > X% þ 2sU x% d > > 1 2 ; > > 2sU > > > > : 1;
x% d 4X% 2sU X% 2sU 5x% d 4X% sU X% sU 5x% d 4X% x% d > X%
where mL , mA and mH are the confidence levels for the low, average and high yield levels, respectively. (5) Determine the yield potential for each block of interest based on p multiple-year data using the following fuzzy union operation equation. The fuzzy union operation screens the yield level with the highest fuzzy membership out from all applicable levels:
myjjU U U ¼ sup myjjU ðx% d Þ; myjjU ðx% d Þ; yjjUk ðx% d Þ 1
2
1
k
2
p
¼ [ myjjU ðx% d Þ i¼1
ð11Þ
l
(6) List the obtained block yield levels (both for multiple-year and for a particular year of interest) from the field in the information table. The information table can be extended by including other factors of influence, such as the soil type, field elevation and slope, as well as the amount of fertiliser being applied and the precipitation of the year of interest. The only requirement is that the influence of all factors should be represented in the form of fuzzy memberships using the method introduced in steps (1)–(5).
(8) 2.3. Application of the information table mA ðx% d Þ ¼ 8 0; > > > !2 > > > > X% 2sU x% d > > ; 2 > > > 2sU > > > > % 2 < X x% d ; 1
2 > 2sU > > > !2 > > > > > 2 X% þ 2sU x% d ; > > > > 2sU > > > : 0;
After the information table has been completed, the yield-related information for a block of interest is represented in a form of information subset Ib : The numerator of each element in the subset represents the yield level, and the denominator represents the confidence level for the obtained yield level: y yA yH yU L yU A yU H L Ib ¼ m ð12Þ myA myH myUL myU myUH yL
x% d 4X% 2sU X% 2sU 5x% d 4X% sU X% sU 5x% d 4X% þ sU X% þ sU 5x% d 4X% þ 2sU x% d > X% þ 2s
A
ð9Þ
To support decision-making effectively for optimising the production, it is important to retrieve only the information which influences the yield significantly. An
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a-cut method, which eliminates all the elements with associated fuzzy membership less than an arbitrary value of a from the subset (Passino & Yurkovich, 1998), is used to create a new sub-subset from the information subset by selecting only the influential factors using an appropriate threshold value for a. Normally, it is recommended to use a value greater than 0.5 to pick the influential factors from a subset. ( ) yi Sb ¼ ; m 5a Ib ð13Þ myi yi The influential factor sub-subset Sb of the information subset carries only a few selected influential factors based on the objective of optimisation in support of the decision-making. Therefore, this information table model can reduce a complicated and tedious massive yield data analysis and management into a standard and simple fuzzy mapping problem and prepare the data in a ‘ready-to-use’ format for further applications.
3. Case study of information table development and application To demonstrate the development and application of this information table model without loss of generality, a yield information table for a small portion of a field in Central Illinois was created based on a 5-yr yield data. The field of interest covers an area of 475 m by 800 m. The crop follows a rotation of maize and soya bean. Due to the influence of numerous factors, the yield variation is very large from year to year. Table 2 lists the yields from the blocks of interest, the average yield of the entire field, the standard deviation of the yield, and the total number of yield points collected from the field
of interest from 1996 to 2000. All the yield points were collected using a commercial yield monitor. Yield data were recorded at a 1 s time interval from 1996 to 1999, and at a 3 s interval in 2000. One important step in developing an efficient information table is the definition of a manageable and informative base information block. To demonstrate the technique without loss of generality, a small portion of a 35 56 m by 35 56 m area (a square of three-header widths of the combine harvester used on this farm) was randomly selected from the field. Therefore, the square area of one header width (9 14 m by 9 14 m) was defined as the base block in this case study with a total number of nine blocks. Due to the uneven distribution of sampling points in the field, the results indicate that the number of yield samples obtained from those blocks vary from 1 to 17. Figure 2 shows the distribution of yield data samples collected from the nine base blocks in the portion being studied within the 5-yr period. To handle the variation in sampling size within a block, it is strongly recommended to use the average yield data from a particular block as the base information. By applying the fuzzy membership functions defined in the previous section based on the overall average yield, the overall standard deviation, and the block average yield data, Table 3 gives the annual yield levels from the study blocks for year 2000 and the potential yield levels estimated based on yields of 1996– 2000. Each line in Table 3 defines an information subset regarding the particular block in the field of interest. For example, the content in the first line and the sixth line of Table 3 defined information sublets for blocks 1 and 6. Table 2 indicates that the yields from blocks 1 and 6
Table 2 Yield from blocks of interest, average yield of the entire field, standard deviation of the yield, and the number of sampling points obtained from the field of interest in a 5-yr period Variables
Maize
1
Yield of block 1, kg ha Yield of block 2, kg ha 1 Yield of block 3, kg ha 1 Yield of block 4, kg ha 1 Yield of block 5, kg ha 1 Yield of block 6, kg ha 1 Yield of block 7, kg ha 1 Yield of block 8, kg ha 1 Yield of block 9, kg ha 1 Average yield, kg ha 1 Standard deviation, kg ha 1 Total number of yield points
Soya bean
1997
1999
1996
1998
2000
11223 10910 13162 10599 11058 8754 11372 11056 11089 10425 1193 27466
7348 6774 6573 9685 9624 6289 8665 9392 6985 11430 1382 26975
3028 1470 2428 2837 3027 1792 2708 2563 2612 3042 505 21768
2824 2624 3167 2896 2867 1858 2639 2881 3582 3372 545 23670
2879 1864 2530 2734 3044 1807 2575 2865 2562 2726 505 7667
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12
Number of blocks
10
8
6
4
2
0
1
2
3
4
5
6
7
8
9
10
11 12
13 14
15 16
17
Number of samples obtained from one block
Fig. 2. Frequency of yield data samples collected inside a base block from a portion of the study field located in Central Illinois between years 1996 and 2000.
Table 3 Fuzzy yield levels from individual base information blocks for the year 2000 and for the period 1996-2000 (the numbers in the table are confidence levels for the corresponding yield levels) Block identity
1 2 3 4 5 6 7 8 9
Year 2000 yield
Past 5 yr yield
Low
Average
High
Low
Average
High
0 0 96 0 07 0 0 0 98 0 04 0 0 05
0 95 0 04 0 93 1 00 0 80 0 02 0 96 0 96 0 95
0 05 0 0 0 0 20 0 0 0 04 0
1 00 1 00 1 00 0 72 0 75 1 00 1 00 0 86 1 00
1 00 0 92 0 93 1 00 1 00 0 15 0 96 0 96 0 95
0 22 0 08 1 00 0 01 0 20 0 0 31 0 13 0 15
were 2879 and 1807 kg ha 1, respectively, while the average yield for the field was 2726 kg ha 1 with a standard deviation of 505 kg ha 1 for year 2000. Substitute these values to Eqns. (8)–(10); it results in confidence levels of 0 95 and 0 05 for average and high yield levels, respectively. Similarly, substitute the block yields, the field average yields and the standard deviations for years from 1996 to 1999 to appropriate equations, and then apply Eqn. (11) to determine the highest confidence levels for different yield levels from these blocks; it results in the following information subsets: ny yA yH yU L yU A yU H o L Ib1 ¼ ð14Þ 0 0 95 0 05 1 0 1 0 0 22 n y yA yH yU L yU A yU H o L Ib6 ¼ ð15Þ 0 98 0 02 0 1 0 0 15 0
As defined in Eqn (12), the first three information agents indicate the fuzzy yield level of the most recent year (year 2000 in this case), and the second three information agents indicate the fuzzy levels of potential yield based on historic data (5 yr data in this case). The total fuzzy membership of 1 for the first three information agents provides yield distribution information based on the most recent year’s production condition. The total fuzzy memberships of the second three information agents are always greater than 1, which provides a measure on the consistency of the yield from the block of interest under various production conditions. As an example, the first three elements in subset Ib1 represented that the confidence levels for low, average, and high yield levels of the most recent year in block 1 were 0, 0 95 and 0 05, respectively. The second three elements indicated that the confidence levels for
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150 100
Error in yield, kg-1 ha
50 0 -50 -100 -150 -200 -250 0
5
10
15
20
25
Ordinal number of the evaluated block
Fig. 3. Error distribution of yield data back-calculated from the fuzzy yield levels in the evaluated blocks; the base values were the raw yield data obtained from those blocks (year 2000 data)
having low, average and high yield levels were 1 0, 1 0, and 0 22 based on the 5-yr historic yield data. It means that the yield level from this block is more likely to be of low–average range than to be high. The inconsistency in the confidence factors for low yield between the most recent year data and the five-yr average data indicated that there might be some unusual factors contributing to the yield variation during the most recent year. All these could provide important information for determining fertilising rate in the block. Similarly, the elements in subset Ib6 indicated confidence levels of 0 98, 0 02, and 0 for low, average, and high yield for the most recent year, and 1 0, 0 15, 0 for low, average and high yield potential from this block. The consistency in the confidence levels between the most recent year’s yield and the yield potential provided additional useful information that this block was located in a low-yield area compared to the rest of the field. One advantage of applying fuzzy mapping approach to classify the yield levels related to the average yield is its capability of back-calculating the real-valued yield based on the fuzzy memberships. Fig. 3 shows the error between the real-valued yield back-calculated from the fuzzy yield levels and the original raw yield data sampled from the evaluated blocks. It indicated that the maximum error was 211 kg ha 1, and the root mean square (RMS) error was 13 kg ha 1. Further analysis found that such an error was mainly caused by the uneven readings of the raw yield data within a block since the fuzzy yield levels were defined based on the mean yield from the block.
More elements can be included in the information subset if more related information becomes available. Some of the elements recommended to be included are the field topography, the soil type, and the fertilising rate for the block for the most recent year. The more elements included in this information subset, the more informative this subset will become. However, the information subset will become more complicated if dealing with a large number of information agents, especially when it needs only part of the processed information to make an optimal production decision. To solve this problem, an information-reduction method is introduced to eliminate the irrelevant information agents using an a-cut method. This approach would create a sub-subset which contains only the most relevant attributes to the decision-making. For example, when the optimisation goal in a particular decision-making process is to apply less fertiliser in consistently high-yield blocks, average amounts of fertiliser in average-yield areas, and more fertiliser in the consistently low-yield zones, a threshold value a of 0 5 can be used to eliminate the irrelevant agents to this optimisation. Based on this method, the new sub-subsets for blocks 1 and 6 will be represented as follows: n y yU L yU A o A Sb1 ¼ ð16Þ Ib1 0 95 1 0 1 0 n y yU L o L Sb6 ¼ ð17Þ Ib6 0 98 1 0 The first sub-subset indicates that block 1 in this field had an average yield for the most recent year.
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Historically, the yield level from this block is between low and average. Based on the defined optimisation criterion, the available information suggests an average to high fertilising rate to this particular block. Similarly, the remaining information agents in the sub-subset of block 6 indicate that yield from this block is always low, and a high fertilising rate should be applied to block 6 to bring the yield in this block up to a higher level. By this information table approach, the yield variation in a field and its consistency over the years in the field could be represented using 322 information subsets instead of over 100,000 raw data points for a 5-yr period. It not only reduced the size of the base information units by 99 7%, but more importantly organized the processed data in an ‘easy-to-understand’ and ‘ready-to-use’ format. As the number of years increased in the yield distribution database, this feature of the information table approach would be more attractive. 4. Conclusions This paper presents a method of using an information table model to process and manage yield data in a format of information subset based on a manageable number of blocks within a field. This model provides a formal method to treat the unevenly distributed and widely variable yield data, converts the massive raw yield data into informative and manageable fuzzy levels, and represents the resulting fuzzy levels in such a way that it can be easily connected with other relevant production information to support site-specific decisionmaking. This formal method can be easily programmed so that it can be used to process the yield information automatically and lead to the development of a ‘transparent-to-farmer’ precision farming informationsupporting tool. The case study demonstrates the application of this model in managing the yield data obtained from an actual field in Central Illinois during a period of 5 yr. It could reduce over 99 7% data points and provide more informative yield distribution information. The results indicate that the model is capable of achieving its design goal. Acknowledgements This research was supported by the Strategic Research Initiative in Information Systems and Technology of the Illinois Council on Food and Agricultural
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