Spatial and Temporal Variability in Yield Maps Can Localize Field Management—A Case Study with Corn and Soybean

Abstract

Yield maps represent crop production output and are essential for evaluating within-field spatial variability. Managing this yield variability is critical for precision and digital agriculture to facilitate optimized crop yield and reduced environmental impact. This work evaluated the spatial and temporal variability in corn and soybean yield data from three conventionally managed agricultural fields, with nine, three, and four seasons’ data. The data variability was measured through standard deviation (SD) and coefficient of variation (CV%). After separately normalizing each year of the yield data set, the temporal variability (TSD and TCV%) was calculated by grid cell for each field across years. A new index is proposed in this paper, the yield performance index (YPI, the ratio of mean normalized yield (${\overline{Y}}_N$) to the TSD), as an index with a lower value for lower yield and higher temporal variability. Two, three, and four zones were delineated using only YPI. These zones were valuable for identifying areas needing particular attention, with consistently (i) high yields and low variability or (ii) low yields and high variability.

1. Introduction

Issues related to the land are usually expressed with thematic maps (TMs). These employ graphical symbols where a specific geographically referenced phenomenon occurs. Data acquisition, investigation, interpretation, and representation are necessary to create TMs. The TMs facilitate the identification of similarities and enable the visualization of spatial correlations. TMs are usually generated based on measurements of crop, soil, and topography parameters to analyze the variability in these parameters and compare that variability to crop yield [1]. Choropleth maps are a specific case of TMs used in precision agriculture and can be built from categorical data (e.g., elevation) or relative data (e.g., density) [1]. Yield maps, a choropleth map, are an essential tool for evaluating spatial variability in agricultural fields.

Yield mapping delivers crucial information for evaluating crop variability within a field and highlights the importance of combining data from all sources of spatial variability with the farmer’s knowledge [2]. Several years of data collected under different weather conditions can identify problem areas, improve management, and increase yields [3], essential in characterizing spatial and temporal variability. Eghball and Varvel [4] found that corn had significantly less temporal yield variability than soybean (as concluded by [5]) or sorghum, and that the temporal variability was more critical than spatial variability. Jaynes and Colvin [5], using six years of corn and soybean data, also found that the yield structure and spatial pattern vary from year to year.

Yield data from the harvester’s monitoring device usually have considerable variability due to inherent measurement system noise and various operational and calibration conditions. Hence, before generating yield maps, it is essential to preprocess these noisy data using data-filtering techniques [6,7,8,9]. A standardized protocol is often used to analyze and map yield data and delineate management zones (MZs) and can include the generic steps shown in Figure 1 [1]. In each step of the delineation, the method must be decided. The steps selected in this case study are highlighted in blue.

Delineating MZs is critical in optimizing input use and maximizing crop yield in precision agriculture. Several data sources and analytical techniques can delineate sub-regions within a field with a relatively homogeneous combination of yield-limiting factors [10]. Two approaches commonly used for delineating MZs [11] are (i) empirical, which uses the yield frequency distribution and expert knowledge to define delineations [12,13,14,15,16], and (ii) cluster analysis, such as K-means (KM) and Fuzzy C-means (FCM) [11,17,18]. Cluster analysis enables greater differentiation among MZs or yield classes, typically employing stable attributes related to the target variable (e.g., yield); however, empirical methods are simpler and often utilize the target variable directly to delineate MZs [11].

Blackmore et al. [13], using yield from four fields over six years, separated temporal effects into two parts: the inter-year offset, characterized by the median of the yield, and the temporal variance map, showing the spatial changes over time, and concluded that homogenous MZs can be delineated with the spatial and temporal trend maps.

Maestrini and Basso [14] analyzed data from 338 corn, soybean, wheat, and cotton fields in the US Midwest and concluded that yield depended on the interaction between topography and rainfall patterns. They measured the yield spatial variability, the field yield variations within a single year, and the yield temporal variability, with each field variation observed across the years. Yield variability was significantly influenced by the hydrological dynamics associated with waterlogging during moist spring periods and drought conditions that prevail during the summer grain-filling phase. The authors advocated implementing strategic management approaches to stabilize yield zones and tactical management methods for unstable areas, leveraging within-season remote sensing observations.

Maestrini and Basso [15] also divided 571 fields planted with corn, cotton, soybean, and wheat in the US Midwest into stable and unstable zones and concluded that previous years’ yield maps best predicted spatial variability in the stable zones since the stable component of yield spatial distribution depended primarily on soil properties and landscape. Nevertheless, the yield spatial variability in the unstable zones was more related to the interaction between soil characteristics, landscape, and weather. In both studies, the temporal variability was defined as the standard deviation (SD) across years of the normalized yield. The yield was normalized for each field-year yield map to a zero-arithmetic mean and an SD of 1. Subsequently, for each pixel across all fields, we computed the SD of the normalized yield utilizing all available years pertinent to that specific field. Cells were categorized as unstable if their temporal variability exceeded one and conversely classified as stable if it did not. According to Kharel et al. [16], spatial and temporal variability should be considered when delineating MZs since both were uncorrelated after yield data were analyzed in 847 fields (six farms).

Along with analyzing the spatial and temporal behavior of field attributes, it is also important to locate field areas that require particular attention; various variables and methods are employed across different studies. These variables often involve visual interpretation, application of expert knowledge, and computational models to identify and prioritize areas of interest. Past reports in the literature use these various variables to de-lineate MZs [11,12,13,14,15,16,17,18]. However, this work looks to develop a new variable, the yield performance index (YPI), that captures crop performance by its yield and the variability by the temporal standard deviation, and that could be used to delineate more efficient MZs.

Given past research findings that spatial and temporal variability are important in defining MZs, this study (1) proposes a new method for analyzing within-field spatial and temporal yield variability using a yield performance index (YPI), (2) delineates homogenous MZs with two, three, and four classes, and (3) demonstrates the method using data from two fields in the US and one in Brazil.

2. Materials and Methods

2.1. Study Sites and Data Sets

Data from two agricultural fields (A and B) located in the United States and one (C) located in Brazil (Figure 2,

Table 1. Description of the three experimental fields (A, B, and C) used in the study.

Field	A	B	C
Latitude	39.2347	40.6659	−25.1092
Longitude	−92.1466	−104.9981	−53.8319
Area (ha)	13	4.7	15.6
Municipality	Centralia	Denver	Céu Azul
State	Missouri	Colorado	Paraná
Country	US	US	BR
Soil type	Claypan (Alfisol)	Kim Loam	Rhodic Ferralsol
Tillage	No tillage	No tillage	No tillage

) were used in the analysis. The equipment used to collect the yield in each experimental field is described in

Table 2. Equipment used to collect the yield in each experimental field.

Crop	Field A		Field B		Field C
	Year	Equipment	Year	Equipment	Year	Equipment
Corn Yield	97, 00, 02	Gleaner R42 combine harvester	11, 12, 13	Case IH 1660 combine harvester
Soybean Yield	96, 98, 99, 01, 03, 04				12, 13, 14, 16	Case IH 2388 combine harvester

Gleaner R42 combine harvester (AGCO, Inc., Duluth, GA, USA) with Ag Leader YM2000 yield monitor (AgLeader Technology, Ames, IA, USA); Case IH 1660 combine harvester (CNH Industrial, Basildon, UK) with AgLeader yield monitor; Case IH 2388 harvester with Case AFS PRO 600 yield monitor.

. The AgDataBox platform (http://adb.md.utfpr.edu.br/map/login, accessed on 10 June 2024) [19] was utilized for data normalization, interpolation, and the creation of yield maps. Data from Field A have been previously reported by Kitchen et al. [20].

Field A is a claypan (silty clay loam) soil field, typically farmed in a corn–soybean rotation, except for the soybean following soybean sequence observed in 1998–1999 and 2003–2004. This soil features a subsoil argillic horizon with a clay content exceeding 500 g kg⁻¹, comprising clays with high shrink–swell properties, specifically, smectitic clay minerals. These clays impart a distinct hydrological attribute, characterized by slow water flow within the soil matrix of the clay layer during wet periods (such as winter and spring) but swift preferential flow through cracks once the profile dries out (during late summer and early fall) [20,21]. The field was managed with no tillage; the mean field slope is 1.8%.

Field B is a portion of a field under a pivot irrigation system. The soil type is a Kim Loam, classified as fine-loamy, mixed, active, mesic Ustic Torriorthents [22], and the texture is a sandy clay loam. The field slope is 0.9% in a single-plane gradient. This field has been managed in a conventional tillage continuous corn cropping system since 1990.

Field C has been cultivated in a no-tillage system since 2000, with a sequence of soybean, wheat, oats, and corn. The soil is classified as Rhodic Ferralsol [23]. The average field slope was 1.2%, ranging from 0.0 to 10.1%. Since this area features several curved contour lines, irregular sampling grids were employed, and the sampling points were positioned in locations that did not align with the curves. Thus, the sampling points were located on the imaginary central line between the elevation contour lines, and field operations were also conducted along these curves.

2.2. Protocol of Data Analysis

In this case study, the steps selected for data analysis, the creation of the TMs, and the delineation of MZs are highlighted in sky blue in Figure 1 (adapted from [1]). The reasons for the selections are described in Section 2.3.1, Section 2.3.3, and Section 2.3.4.

2.3. Exploratory Data Analysis

The exploratory data analysis calculated the mean, median, SD, coefficient of variation (CV%), and normality (the Kolmogorov–Smirnov test at 0.05 significance level). Outliers, or values outside the mean ± 3 SD, were removed [24]. The data variability was measured through SD and CV%. The weighted standard deviation (WSSD, Equation (A1)) was used to calculate the SD when comparing yield data with different numbers of measurements. The classification proposed by Pimentel-Gomes and Garcia [25] was used to classify CV% ≤ 10% as low, 10% < CV% ≤ 20% as medium, 20% < CV% ≤ 30% as high, and CV% > 30% as very high.

2.3.1. Data Normalization and Creation of Choropleth Maps

The yield values were normalized ($Y_N$) using the mean method (Equation (1)) [2,20,26] to stabilize these data, which are often heavily influenced by variations in climate and precipitation. Then, since there is more than one year of yield data for each field, the arithmetic mean of the normalized yield was calculated, generating a single variable corresponding to the mean normalized yield (${\overline{Y}}_N$). After that, yield choropleth maps (Figure 1 (step 3)) were created to evaluate the yield distribution visually.

$$Y_{Ni}={\displaystyle \frac{Y_i}{\overline{Y}}},$$

(1)

where $Y_{Ni}$—normalized yield at point i; $Y_i$—yield at point i; $\overline{Y}$—mean yield for the specific year.

2.3.2. Yield Performance Index

The yield performance index (YPI) (Equation (2)) was introduced to identify places in the field that may require particular management attention. If YPI is low, it indicates a low yield and high temporal variability; if YPI is high, it signifies a high yield and low temporal variability.

$${YPI}_i={\displaystyle \frac{{\overline{Y}}_{Ni}}{{TSD}_i}},$$

(2)

where ${\overline{Y}}_{Ni}$—mean normalized yield at the point i; ${TSD}_i$—temporal standard deviation at the point i.

2.3.3. Data Interpolation

The data of ${\overline{Y}}_N$, TSD, and YPI were interpolated to create continuous and smooth TMs and MZs. The Inverse Distance Weighted (IDW) interpolation was used, as the number of data pairs exceeded 300, the maximum allowed by ADB-Map for kriging. The choice of IDW should not be a problem because when dealing with large sample sizes (from 455 to 1585 data points), the choice between IDW interpolation and kriging becomes less critical [27]. Using the interpolation selection index (ISI, Equation (A2)) [19], the best exponent and number of neighbors for IDW were found. Grids of 4 × 4 m (Field B), 6 × 6 m (Field C), and 8 × 8 m (Field A) were created to increase the density of points and facilitate the delineation of smoother and more continuous TMs. The ADB-Map automatically sets the pixel size as 1/100 of the larger dimension in the eastern/western direction [19].

The SD and CV% were calculated for the mean normalized yield (${\overline{Y}}_N$) of each data set, corresponding to the spatial variability (SSD, Equation (3) and SCV%, Equation (4)):

$$SSD=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left({\overline{Y}}_{Ni}-\overline{{\overline{Y}}_N}\right)}^2}{n-1}}},$$

(3)

$$SCV\%=100{\displaystyle \frac{SSD}{\overline{{\overline{Y}}_N}}} ,$$

(4)

where SSD—yield spatial standard deviation; SCV—yield spatial coefficient of variation; ${\overline{Y}}_{Ni}$—mean normalized yield at point i; $\overline{{\overline{Y}}_N}$—mean of mean normalized yield (${\overline{Y}}_N$).

The temporal variability (TSD, Equation (5) and TCV%, Equation (6)) was calculated across each grid cell of interpolated normalized yield ($Y_N)$ of each year and for each field [16].

$${TSD}_i=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{\left(Y_{Nij}-{\overline{Y}}_{Ni}\right)}^2}{n-1}}}$$

(5)

$${TCV\%}_i=100{\displaystyle \frac{{TSD}_i}{{\overline{Y}}_{Ni}}},$$

(6)

where TSD_i—yield temporal standard deviation of yield i; ${TCV\%}_i$—yield temporal coefficient of variation i; $Y_{Nij}$—mean normalized yield at point i; ${\overline{Y}}_{Ni}$—mean normalized yield at point i

2.3.4. Data Clustering, Rectification, and Evaluation of the Management Zones

To account for spatial and temporal variability when delineating MZs [16], we selected YPI as the input variable. Cluster analysis was chosen because it is superior to empirical classification. The FCM clustering algorithm was selected because it is powerful and flexible, but it may not always be the best choice for every situation. Its most notable feature is the adaptability of its membership, which can result in more refined clustering outcomes in contrast to rigid clustering techniques such as K-means, where each data point is assigned to only a single cluster [28]. The FCM algorithm delineated two, three, and four zones, building upon previously interpolated YPI. The rectification of the MZs was performed using the algorithms proposed by Betzek et al. [19] to remove isolated pixels and small regions. The median method, square kernel format, and 5 × 5 kernel sizes were used.

The delineated MZs were evaluated (see Appendix A for details and equations) using:

(i)

Analysis of variance (ANOVA) using the Tukey test at 0.05% significance to identify whether sub-regions within the MZs designed show significant differences in the mean value of the variable of interest;

(ii)

Variance Reduction (VR%) [19]: measures the reduction in the sum of the MZs data variances;

(iii)

Fuzziness Performance Index (FPI) [29]: evaluates the degree of fuzziness in a classification;

(iv)

Modified Partition Entropy (MPE) [29]: evaluates the uncertainty in cluster assignments;

(v)

Improved Cluster Validation Index (ICVI) [19]: a combination of the FPI, MPE, and VR%;

(vi)

Smoothness Index (SI%) [19]: characterizes the smoothness of the boundary curves of MZs;

(vii)

Fragmentation index (FI%) [19]: characterizes the division of land into smaller, often irregularly shaped parcels, which can impact land management strategies;

(viii)

Global Quality Index (GQI) [1]: it looks to find the optimum number of classes during MZ delineation, considering all indices together.

The definition of the number of MZs was conducted in two stages:

(i)

ANOVA: This procedure was performed to verify if the mean values of the YPI (target variable) in each class were statistically distinct [19] using Tukey’s range test (0.05 level).

(ii)

Choosing the best GQI (the lowest), which contains all the remaining ones (FPI, MPE, VR%, ICVI, SI%, and FI%).

3. Results

3.1. Summary Statistics

Descriptive statistics of the original yield data for nine (Field A), three (Field B), or four years (Field C) are shown in Table 3. Among all three fields, we observed (Table 3) that:

• The 2003 soybean in Field A, 2002 corn in Field A, 2012 corn in Field B, and 2012 soybean in Field C presented very high SCV% (>30%);
• Notably, low minimum yield values were seen for the 1999 soybean in Field A, the 2003 soybean in Field A, and the 2002 corn in Field B;
• The highest weighted spatial variability (WSCV%) was found for corn in Field A (26.3%) and the lowest for soybeans in Field A (17.5%).

Table 3. Summary of descriptive statistics calculated for the original yield data without outliers for each year and field under consideration.

Field	Year/Crop	Original Yield (Sampling Data) (t ha−1)					SSD	SCV%	WSSD		WSCV%
									Soybean or Corn	Mean	Soybean or Corn	Mean
		No.S	Min.	Mean	Median	Max.	(t ha−1)	(%)	(t ha−1)		(%)
A	1996 Soybean	1209	1.80	3.07	3.10	4.32	0.41	13.3	0.41	0.87	17.5	24.0
	1998 Soybean	1207	1.59	2.53	2.57	3.25	0.30	12.0
	1999 Soybean	1213	0.29	1.39	1.36	2.66	0.42	29.9
	2001 Soybean	1202	1.28	2.49	2.50	3.67	0.38	15.3
	2003 Soybean *	1216	0.26	1.55	1.57	2.95	0.49	31.6
	2004 Soybean	1192	1.46	2.94	2.99	4.09	0.43	14.6
	1997 Corn	1216	1.17	6.41	6.56	11.85	1.90	29.6	1.40		26.3
	2000 Corn	1191	6.31	9.27	9.39	11.42	0.85	9.2
	2002 Corn	1212	0.06	3.06	3.11	6.73	1.23	40.2
B	2011 Corn	455	6.59	9.28	9.44	11.42	0.90	9.7	1.60		19.7
	2012 Corn	455	0.86	6.33	6.67	10.78	2.07	32.7
	2013 Corn	454	4.63	8.85	9.35	11.72	1.61	18.2
C	2012 Soybean	1585	0.63	2.58	2.46	4.82	0.96	37.1	0.67		18.1
	2013 Soybean	1575	2.12	4.15	4.14	6.13	0.66	15.9
	2015 Soybean *	1572	3.24	4.72	4.71	6.13	0.47	10.0
	2016 Soybean	1566	2.00	3.45	3.41	5.02	0.49	14.1

No.S: number of samples; Min.: minimum; Max.: maximum; SSD: spatial standard deviation; WSSD: weighted SSD; SCV%: spatial coefficient of variation; WSCV%: weighted SCV%. * normally distributed by the Kolmogorov–Smirnov test at a 0.05 significance level.

Table 3. Summary of descriptive statistics calculated for the original yield data without outliers for each year and field under consideration.

Field	Year/Crop	Original Yield (Sampling Data) (t ha−1)					SSD	SCV%	WSSD		WSCV%
									Soybean or Corn	Mean	Soybean or Corn	Mean
		No.S	Min.	Mean	Median	Max.	(t ha−1)	(%)	(t ha−1)		(%)
A	1996 Soybean	1209	1.80	3.07	3.10	4.32	0.41	13.3	0.41	0.87	17.5	24.0
	1998 Soybean	1207	1.59	2.53	2.57	3.25	0.30	12.0
	1999 Soybean	1213	0.29	1.39	1.36	2.66	0.42	29.9
	2001 Soybean	1202	1.28	2.49	2.50	3.67	0.38	15.3
	2003 Soybean *	1216	0.26	1.55	1.57	2.95	0.49	31.6
	2004 Soybean	1192	1.46	2.94	2.99	4.09	0.43	14.6
	1997 Corn	1216	1.17	6.41	6.56	11.85	1.90	29.6	1.40		26.3
	2000 Corn	1191	6.31	9.27	9.39	11.42	0.85	9.2
	2002 Corn	1212	0.06	3.06	3.11	6.73	1.23	40.2
B	2011 Corn	455	6.59	9.28	9.44	11.42	0.90	9.7	1.60		19.7
	2012 Corn	455	0.86	6.33	6.67	10.78	2.07	32.7
	2013 Corn	454	4.63	8.85	9.35	11.72	1.61	18.2
C	2012 Soybean	1585	0.63	2.58	2.46	4.82	0.96	37.1	0.67		18.1
	2013 Soybean	1575	2.12	4.15	4.14	6.13	0.66	15.9
	2015 Soybean *	1572	3.24	4.72	4.71	6.13	0.47	10.0
	2016 Soybean	1566	2.00	3.45	3.41	5.02	0.49	14.1

No.S: number of samples; Min.: minimum; Max.: maximum; SSD: spatial standard deviation; WSSD: weighted SSD; SCV%: spatial coefficient of variation; WSCV%: weighted SCV%. * normally distributed by the Kolmogorov–Smirnov test at a 0.05 significance level.

3.2. Yield, Temporal Variability, and Yield Performance Index Maps

Figure 3 shows the thematic maps of (i) the mean normalized yields (${\overline{Y}}_N$), (ii) the temporal standard deviation (TSD), and (iii) the yield performance index (YPI) for each field. To improve readability, the maps of ${\overline{Y}}_N$ and TSD were classified by manual intervals and YPI by quantiles because the data range was similar for the first two variables and not for the third. Planting and other farm operations were conducted in the east–west direction for Fields A and B, whereas operations in Field C were performed along level curves (i.e., contour farming). A headland yield reduction was observed for Fields A and B, as shown by the red regions of YPI (Figure 3). This reduction was absent in Field C because a 15 m strip was discarded in the east and west parts. The yield pattern in Field C was concordant with the elevation contour lines. The data normalization enabled a 37% reduction in spatial data variability (Table 3 and

Table 4. Summary of descriptive statistics calculated for the mean normalized yield for each field.

		Number Of Crop-Years		Mean Normalized Yield $\left({\overline{\mathit{Y}}}_{\mathit{N}}\right)$					SSD	SCV%	TSV	Relation TSV/SSD
				(Dimensionless)
Field	No.S	Corn	Soybean	Min.	Mean	Median	Max.	Range		(%)	(%)
A	1216	3	6	0.49	1.00	1.01	1.39	0.89	0.15	14.8	19.7	1.33
B	455	3	-	0.64	1.00	1.02	1.31	0.67	0.13	12.7	20.2	1.59
C	1585	-	4	0.69	1.00	1.00	1.29	0.60	0.12	11.5	20.4	1.77
Mean									0.13	13.0	20.1	1.57

No.S: number of samples; Min.: minimum; Max.: maximum; SSD: spatial standard deviation; SCV%: spatial coefficient of variation.

).

The ${\overline{Y}}_N$ distribution shows a yield increase from the border to the center for Fields A and B and from the south to the north of Field C. For the data variability measured by the TSD, it increased like ${\overline{Y}}_N$, i.e., from the border to the center for Field A and inversely for Fields B and C. And finally, the YPI (${\overline{Y}}_N/TSD$) increased from the border to the center for Fields B and C, and it is almost uniformly distributed across Field A. In summary, all three variables (${\overline{Y}}_N$, TSD, and YPI) have distinct behaviors.

The mean normalized yield spatial variability (SCV%, Figure 3, Table 4) of Field A was the highest (15%), and of Field C, the lowest (12%). Furthermore, all fields’ mean normalized yield temporal variability (TCV%) was about 20%.

3.3. Management Zones

Although the thematic maps of YPI can show their spatial variability, visualization of the MZs is also helpful because this makes it possible to delineate statistically distinct classes [19]. Using the YPI of each field (A, B, and C), MZs were delineated (

Table 5. Evaluation of management zones delineated with yield performance index (YPI) for each field (A, B, and C) using two, three, and four classes. NC: number of classes.

Field (Area)	NC		Tukey’s Test				FPI	MPE	VR%	ICVI	SIr%	MZs	FIr%	GQI
			C1	C2	C3	C4
	2	YPI	5.38 a	9.37 b			0.086	0.103	30.7	0.73	94.7	7	250	2.71
		Area (ha)	10.39	2.61
		%Area	79.9%	20.1%
A	3	YPI	4.23 a	7.12 b	10.6 c		0.080	0.081	37.4	0.58	90.8	12	300	2.56
(13.0 ha)		Area (ha)	5.13	7.12	0.75
		%Area	39.5%	54.8%	5.8%
	4	YPI	4.01 a	6.77 b	10.1 c	***	0.078	0.069	38.3	0.53	89.9	16	300	2.34
		Area (ha)	4.27	7.52	1.22
		%Area	32.8%	57.8%	9.4%
	2	YPI	9.14 a	110 b			0.011	0.013	29.8	0.30	99.6	2	0	0.30
		Area (ha)	4.70	0.042
		%Area	99.1%	0.9%
B	3	YPI	6.14 a	23.4 b	129 c		0.046	0.047	48.4	0.66	95.7	6	100	1.37
(4.7 ha)		Area (ha)	3.86	0.84	0.031
		%Area	81.5%	17.8%	0.7%
	4	YPI	5.17 a	16.9 b	41.1 c	153 d	0.048	0.043	49.0	0.64	94.5	6	50	1.01
		Area (ha)	3.34	1.22	0.16	0.021
		%Area	70.5%	25.7%	3.3%	0.4%
	2	YPI	5.17 a	9.53 b			0.065	0.079	17.8	0.66 ¥	95.3	10	400	3.46
		Area (ha)	12.43	3.18
		%Area	79.6%	20.4%
C	3	YPI	4.79 a	7.47 b	12.8 c		0.075	0.075	20.1	0.65 ¥	92.1	13	333	3.06
(15.6 ha)		Area (ha)	9.47	5.51	0.63
		%Area	60.7%	35.3%	4.0%
	4	YPI	4.55 a	6.69 b	9.48 c	11.6 d	0.074	0.066	17.8	0.65 ¥	90.0	13	225	2.33
		Area (ha)	7.56	6.06	1.62	0.37
		%Area	48.5%	38.8%	10.3%	2.4%

NC: Number of classes; C1…C4: class 1 to 4; Sym: Symbology; MZ_A_2: management zones of Field A with 2 zones; FPI: Fuzziness Performance Index; MPE: Modified Partition Entropy; VR%: Variance Reduction; ICVI: Improved Cluster Validation Index; SIr%: Smoothness index rectified; FIr%: Fragmentation index rectified; GQI: Global Quality Index; means followed by the same letter in the same row do not differ statistically among themselves by Tukey’s test (p < 0.05); the best index for each normalization method is highlighted in blue (simple index) and pink (composite index); ¥: indices not statistically different; ***: After the rectification, this class disappeared. The YPI increases from the left (C1) to the right (C4).

, Figure 4) with two, three, and four classes. The similarity between the MZs with four zones and the YPI quantile classification (Figure 3) was remarkable. Evaluation of the quality of the MZs was conducted in two stages, conforming to item 2.3.4: First, it was found that all delineated classes were statistically different. Second, after analysis of the GQI index (the lower, the better), it was found that four, two, and four classes were the optimum number of classes (NC) in Fields A, B, and C, respectively.

We highlight that the choice of the best NC using only one of the MZ quality indices FPI, MPE, VR%, ICVI, SI%, and FI% (the lower the FPI, MPE, ICVI, and FI%, the better; however, the opposite occurs with VR% and SI%) (Appendix A) could lead to controversial results; let us examine the case of Field C: (i) the indices FPI, ICVI, and SI%, and FI% would indicate two classes; (ii) the VR%, three, and (iii) the MPE, ICVI, and FI%, four. These discrepancies highlight the importance of using the combined GQI index.

4. Discussion

It was found that the weighted spatial yield variability (WSCV%) for corn in rainfed Field A was 26%, considerably higher than in irrigated Field B (20%) (Table 3). The WSCV% in Field A and Field B for soybeans was approximately 18%, lower than that of the corn fields, corroborating the results from Jaynes and Colvin [5].

Concerning (i) the mean normalized yields (${\overline{Y}}_N$), (ii) the temporal standard deviation (TSD), and (iii) the yield performance index (YPI) of each field (Figure 3), it could be observed that:

• The highest yields (${\overline{Y}}_N, \mathrm{d}\mathrm{a}\mathrm{r}\mathrm{k} \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{v}\mathrm{e}\mathrm{r}\mathrm{y} \mathrm{d}\mathrm{a}\mathrm{r}\mathrm{k} \mathrm{g}\mathrm{r}\mathrm{e}\mathrm{e}\mathrm{n}$) correspond to regions that could benefit from a differentiated treatment that takes advantage of their high productive potential. However, these regions do not always correspond to low TSD (blue maps in Figure 3), so temporal yield stability must be considered before implementing a treatment plan.
• The large part of the area with higher TSD coincides with low ${\overline{Y}}_N$. Although corn and soybean were planted in these fields in rotation, the time-dependent variations in normalized yield may be due to plant growth response to heat, precipitation, soil water, and plant nitrogen availability. Reducing TSD is a challenge that can be effectively achieved through precision agriculture, soil conservation practices, crop rotation, and advanced data analysis techniques, as remarked by Yost et al. [30].
• The information presented in the YPI shows the ratio of mean normalized yield (${\overline{Y}}_N$) to the TSD, having two particular cases: (i) the black areas correspond to consistently high yields with low variability; (ii) the red areas have low yields with high variability. This information is more visible than when presented separately as ${\overline{Y}}_N$ and TSD and can help define parts of the field that should receive particular attention.

The descriptive statistics of the mean normalized yield (${\overline{Y}}_N$, Table 4) for each field showed that the temporal variability (20%) was larger than the spatial within-field variability (13%) in all fields (Table 4), with a mean of 57%, corroborating what Eghbal and Varvel [4] and Maestrini and Basso [14] observed.

During the MZ delineation, the ideal number of classes was found to be four, two, and four for Fields A, B, and C, respectively. It has been demonstrated that the YPI spatial dependence is sufficiently large to delineate MZs, allowing for the implementation of differential management practices. This implementation of MZs in the field holds significant potential for optimizing economic returns while minimizing environmental impacts. However, dividing the field into four classes may introduce complications for management operations. Therefore, it may be more practical to adopt two classes in all fields.

It is essential to recognize that many factors that have not been considered might have contributed to the observed ${\overline{Y}}_N$, TSD, and YPI patterns, like geomorphology, soil chemical and physical attributes, and crop coverage [31]. Nonetheless, the variable YPI has the advantage of presenting temporal integration, multi-crop capability, and a more straightforward interpretation.

A more detailed comparison with previous studies was impossible because the YPI index was initially proposed in this work.

5. Conclusions

The spatial and temporal variability in yield data from three conventional agriculture fields were analyzed. The mean normalized yield spatial variability (SCV) varied from 12 to 15%, and the mean normalized yield temporal variability (TCV) was about 20% for all fields. Typically, crop harvests with a high SCV were associated with low yields. That reinforces the potential of precision agriculture to improve yield averages by reducing field variability with site-specific management. Furthermore, the yield performance index (YPI) delineated four, two, and four management zones (MZs) in Fields A, B, and C, respectively, proving helpful in identifying areas that require particular attention, characterized by consistently high yields and low variability, or low yields and high variability. Furthermore, these MZs help enable variable-rate fertilizer application.

Further research is needed with more years of data, testing YPI in diverse environments and integrating specific soil/climate data layers. Studying the influence of climatic and management factors, as well as topographic, soil, and plant properties, on the spatial and temporal variability in yield maps would also be beneficial.