Efficacy and Economics of Different Soil Sampling Grid Sizes for Site-Specific Nutrient Management in Southeastern USA

Abstract

Precision soil sampling on larger grid sizes (≥2.0 ha) is a common practice to reduce the number of soil samples and associated sampling costs. A study was conducted to evaluate the influence of different grid sizes on the depiction of spatial nutrient variability and their influence on the accuracy of variable-rate fertilizer application and total application costs. Soil sampling was conducted in nine agricultural fields using grid sizes of 0.4, 1.0, 2.0, 3.0, and 4.0 ha, and the resulting variable-rate prescription maps for lime, P, and K were spatially analyzed and compared with a reference map (generated from high-density soil sampling; approximately 2.5 samples per hectare) to determine the amount of under-, on-target, and over-application that would occur within each field. An economic analysis was conducted including the soil sampling costs, soil analysis costs, and nutrient costs to determine the effect of grid size on total application costs. Soil sampling on a 0.4 ha grid size had the best performance in depicting the spatial variability of soil pH, P, and K within the fields, and exhibited the highest application accuracy for the variable-rate prescription maps. The general trend was that the application accuracy decreased with an increase in grid size, with the potential for the under- and over-application of nutrients significantly increasing at the larger grid sizes of ≥2.0 ha. The total application cost varied among the fields as it was largely influenced by the amount of under- and over-application associated with each grid size. In most fields, the total application costs for a 0.4 ha grid size were lower or comparable to other grid sizes. In some fields, the larger grid sizes exhibited lower application costs but at the expense of reduced application accuracy. Overall, the results suggest that the smaller grid sizes of ≤1.0 ha are optimal for soil sampling in agricultural fields to ensure accurate and cost-effective variable-rate applications for site-specific nutrient management.

1. Introduction

Highly inherent spatial variability within agricultural fields poses a significant challenge in row crop production, particularly in the southeastern United States. This variability can be related to many factors, including topographical features, soil properties, and historical field management [1]. This within-field spatial variability also leads to crop variability, which can be observed in stand establishment, crop health, maturity, and yield. Since both soil and crop variability make crop management challenging, one of the main ways to accurately detect and address this variability is by using various precision agriculture practices and technologies [2]. The site-specific management of crop inputs such as fertilizer, seed, and water is one of the primary mechanisms used to address within-field spatial variability and improve productivity [3]. With recent advancements in sensing and application technologies, new and improved methods of site-specific crop input management have been developed and adopted in the US. These precision practices enable growers to be more efficient and sustainable while improving productivity to meet the needs of the growing population [4], which is expected to reach 9.8 billion globally by 2050 [5].

Among various site-specific management strategies, the variable-rate (VR) application of fertilizer is a widely adopted practice in agriculture in the United States, where different rates are applied within a field to address nutrient spatial variability [6]. One of the key aspects of site-specific nutrient management is proper soil sampling to determine varying nutrient levels within the fields. Over the years, soil sampling approaches have evolved from composite soil sampling [7] to precision soil sampling techniques, such as collecting samples based on grids or pre-defined zones within a field [8]. In contrast to composite sampling, where only a single or a few samples represent the entire field, a grid soil sampling approach involves placing uniformly sized grids within a field, ranging from 1.0 to 5.0 ha in size, and then collecting soil samples within each grid [9]. Zone-based soil sampling involves utilizing various soil and crop features, such as the soil type and texture, elevation, aerial imagery, yield, historical management, and other spatial data [10,11,12] to delineate homogenous areas within the field, and then collecting samples from each area, which is representative of a management zone within the field. While grid soil sampling is easier to implement, the accurate representation of the spatial nutrient variability in the field depends largely on the selected grid size [2]. In contrast, zone-based sampling can be challenging to implement because of the need for more advanced knowledge and experience in analyzing spatial data layers. While both are effective soil sampling methods, grid sampling remains one of the most widely used approaches by growers and consultants in the southeastern US, mainly due to its ease of implementation and non-reliance on any other data or historical field information.

Several researchers have evaluated the appropriateness of different grid soil sampling methods in effectively representing the spatial distribution of soil nutrients and reported varied findings depending on the geographic location and other environmental factors associated with agricultural production [7,10,13,14,15]. Wollenhaupt and Wolkowski [9] reported that a grid size of 61 × 61 m (approximately 0.4 ha) should be used during the first year to determine soil nutrient variability, along with additional sampling in field areas with very low or high nutrient values. Mallarino and Wittry [14] suggested that a 0.2 ha grid can produce a very detailed map of soil nutrients; however, this approach is not practical due to the high cost and increased time required for collecting a large number of soil samples. Stepień [15] reported that a 2.0 ha grid sampling method depicted more variability in soil pH, P, and K than sampling on 4.0 ha grids. Contrary to the previous studies, Brouder et al. [13] stated that soil sampling on 1.0 ha grids is only 10% better than whole-field composite sampling. Most of these previous studies were conducted in different regions across the US, and the results likely vary due to the different soil types and crop management practices prevalent in each region. Sabbe and Marx [16] stated that the goal of soil sampling should be to increase the precision and accuracy of the depiction of nutrient variability with the least number of samples. Failure to accurately depict nutrient variability in agricultural fields is suggested to be one of the main reasons for VR applications not being profitable [2]. While precision soil sampling using grids can be costly due to the number of samples needed to produce accurate prescription maps [17,18], data quality is an important consideration for VR applications to be accurate and effective [19].

As stated earlier, soil sampling results can vary depending on the geographic location and other soil and crop management practices specific to the region. Most previous studies focused on precision soil sampling were conducted in the midwestern US and some in other countries, with minimal to no published information available for the southeastern US. Additionally, these studies did not consider the effect of grid size on economics, i.e., the total application costs related to the VR application of nutrients. Data quality is becoming increasingly important in every aspect of agriculture due to the growing adoption of technology among growers and the rising interest in the more efficient use of crop inputs. With rising input costs and narrow profit margins, growers are motivated to make more informed, data-driven decisions to improve efficiency and productivity in their farming operations. Due to the diverse cropping systems and production practices in the southeastern US, the suitability and efficacy of different grid sizes for precision soil sampling must be investigated, along with a better understanding of how grid size affects the application accuracy and economics of site-specific nutrient management. Therefore, the main objectives of this study were as follows: (1) to compare and evaluate the effectiveness of different grid sizes in depicting soil nutrient variability and their influence on fertilizer application accuracy, and (2) to perform an economic analysis among different soil sampling grid sizes to determine how grid size affects total application costs related to site-specific nutrient management.

2. Materials and Methods

Nine different agricultural fields, primarily planted in prevalent row crops in the southeastern US (cotton, corn, or peanuts), were selected for this study. The selected fields ranged from 8.3 to 37.6 ha in size. All of the fields were located in the Coastal Plain physiographic region of the southeastern United States and had two or more soil types (predominantly Ultisols) present within each field. Detailed information on the location, size, and soil types within each field is presented in

Table 1. The location and size of all fields used in this soil sampling grid size study.

Field	Latitude	Longitude	Size (ha)	Soil Type(s)
1	32.880897	−82.20426	9.1	Tifton, Dothan, Carnegie, Grady
2	31.307355	−83.914703	37.6	Tifton, Carnegie, Leefield, Borrow
3	31.077626	−83.694082	9.1	Dothan, Tifton
4	33.209401	−82.503499	36.9	Faceville, Tifton, Orangeburg, Nankin
5	32.045822	−84.377226	12.4	Greenville, Tifton, Ochlockonee
6	32.043561	−84.365362	8.3	Greenville, Tifton, Ochlockonee
7	31.729895	−84.463742	25.5	Greenville, Grady
8	31.473537	−83.407591	22.4	Ocilla, Clarendon, Alapaha, Tifton
9	31.535035	−83.659815	12.7	Tifton, Carnegie

. These fields were selected by local county extension agents and growers with the criteria that the field be representative of the local geographic area. The soil sampling methods and other procedures were kept consistent among all field sites and were conducted in 2022 and 2023.

2.1. Grid Soil Sampling

For each field, soil sampling maps were created for grid sizes of 0.4, 1.0, 2.0, 3.0, and 4.0 hectares (example maps shown in Figure 1 for Field 2), using the SMS Advanced software version 22.5 (AgLeader Technology, Ames, IA, USA). Each sampling grid was independent of the others (i.e., no sample was used for multiple grid sizes). Sampling points were placed at the center of each grid for ease of navigation to the center of the grid during soil sampling. The soil sampling maps were uploaded on a handheld Trimble GPS unit, Nomad 1050 (Trimble Inc., Sunnyvale, CA, USA), and were used to navigate to different grids within each field. For each grid size, soil samples were collected using the point sampling method, which involved collecting 12 to 15 or 15.2 cm deep cores in an approximately 6.1 to 9.1 m radius around each point and mixing all the cores together to make a composite sample representing that grid. During soil sampling, soil from each grid was placed in a pre-labeled paper bag with the field and sample number. Once all the samples were collected, they were sent to the University of Georgia’s Agricultural and Environmental Services Laboratories (AESL) in Athens, GA, for soil nutrient analysis. In the lab, the soil pH was determined with a 1:1 volume of 0.01 M CaCl₂ solution, and the lime buffering capacity was calculated after incubation with saturated Ca(OH)₂ [20]. Plant available phosphorus (P), potassium (K), calcium (Ca), magnesium (Mg), and manganese (Mn) were measured using the Mehlich 1 extraction (0.025 N H₂SO₄ + 0.05 N HCl) method. The cation exchange capacity (CEC) was estimated by summing the milliequivalents of exchangeable cations (Ca, Mg, K, and H) from the Mehlich 1 extraction, pH, and lime buffering capacity determination. Since this study focused on determining the spatial variability of soil pH, P, and K, soil test results for these nutrients only were used for further mapping and analysis.

2.2. Spatial Nutrient Mapping and Analysis

For each field, the soil nutrient results for different grid sizes were used to generate spatial maps for soil pH, P, and K using an inverse distance weighting (IDW) interpolation method [21] in the SMS Advanced software. The interpolation procedure consisted of creating a 9.14 × 9.14 m raster map for all grid sizes, where each cell (9.14 × 9.14 m) was georeferenced and represented soil nutrient (pH, P, and K) values. The soil analysis results for all sampling methods, i.e., grid sizes of 0.4, 1.0, 2.0, 3.0, and 4.0 ha, were combined to create a high-density sampling method (approximately 2.5 samples per hectare), which was assumed to represent the existing spatial variability within each field and was used as a reference layer for comparison among the maps based on different grid sizes. This high-density map served as the reference map for each nutrient. The VR lime, phosphorus (P), and potassium (K) prescription maps were created for each grid size strategy to fertilize cotton, aiming for a yield of 1345 kg ha⁻¹, using UGA lime and fertilization recommendations for agronomic crops [22]. All prescription maps were converted to a raster format to enable direct comparison to the reference prescription map for each nutrient. By performing spatial analysis in ArcGIS using the reference map and different prescription maps (based on varying grid sizes), a ‘difference’ map was generated, depicting the spatial location and the amount of under-, on-target, and over-application in different areas within the field. Figure 2 illustrates an example of this process for Field 2, where Figure 2a is the reference P map depicting the assumed existing nutrient variability within the field, Figure 2b is the prescription map generated from the soil sampling results from a 1.0 ha grid size, and Figure 2c is the difference map which represents the areas of on-target (green), under- (red), and over-application (blue) within the field. The on-target application computed for each grid size was used to determine the application accuracy associated with soil sampling at that grid size. It should be noted that the term ‘application accuracy’, referred to here and in the results and discussion, was computed by comparing different prescription maps (based on grid sizes) against the reference map. The term only refers to the effectiveness of the soil sampling grid size and does not include any misapplications or errors that could occur due to the application equipment when implementing VR lime/fertilizer applications.

2.3. Economic Analysis

An economic analysis was conducted for each field to determine the total cost per hectare for the sampling strategy based on different grid sizes. The total amount of recommended lime and fertilizer for each grid size was computed from the VR prescription maps for lime, P, and K. The lime and fertilizer costs (USD kg⁻¹) were obtained from the UGA Enterprise Row Crop Budgets [23]. The prices used for this analysis were as follows: lime—0.055 USD per kg⁻¹, phosphorus—1.47 USD kg⁻¹, and potassium—1.50 USD kg⁻¹. The soil sampling costs were calculated based on the nominal sampling fees charged by consultants in the southeastern US. This cost was determined to be USD 20 per hectare for a 0.4 ha grid size, USD 15 per hectare for a 1.0 ha grid size, and USD 10 per hectare for the remaining larger grid sizes of 2.0 to 4.0 ha. A soil analysis cost of USD 6 per sample was used, which again represented the nominal soil sample analysis fees charged by most private and public soil testing laboratories in the southeastern US.

Table 2. Example computation of total cost (USD ha⁻¹) for VR lime application based on different grid sizes for Field 2 (37.6 ha).

Grid Size	Number of Soil Samples	Sampling Cost	Analysis Cost	Total Lime Rec.	Total Lime Cost	Total Cost
(ha)		(USD ha−1)	(USD ha−1)	(kg)	(USD ha−1)	(USD ha−1)
0.4	90	20	14	55,690	37	71
1.0	35	15	6	48,050	32	53
2.0	17	10	3	43,344	29	42
3.0	13	10	2	47,020	31	43
4.0	8	10	1	62,164	41	52

below illustrates an example of the total cost calculation (USD ha⁻¹) for VR lime application based on different grid sizes for one of the fields (Field 2) used in this study. The total cost per hectare for each grid size strategy is the sum of the soil sampling cost, the analysis cost (which varied based on the grid size and the number of soil samples), and the lime/fertilizer costs (which depended on the total amount of lime/fertilizer prescribed by each grid size strategy). Additionally, the total cost per hectare for fertilizing the field was computed by combining the per-hectare costs associated with each nutrient (lime, P, and K). All costs listed above and in Table 2 are in US dollars.

3. Results and Discussion

3.1. Effectiveness of Different Grid Sizes

The application accuracy results for soil sampling at different grid sizes are presented separately for each nutrient (lime, P, and K) in the following sections. The data presented in tablesin the following sections present the percentage of under-application, on-target, and over-application associated with soil sampling at different grid sizes (0.4, 1.0, 2.0, 3.0, and 4.0 ha) in each field. It should be noted that the application data presented in these tables were computed by performing comparisons to the reference application map, which was based on the high-density soil sampling (2.5 samples per hectare) and assumed to represent the existing spatial variability within each field. Additionally, as visual representation helps in better illustrating the differences among the maps, the reference prescription map and prescription maps generated using soil sampling at different grid sizes are also presented within each section for one of the fields (Field 2) used in this study.

3.1.1. Application Accuracy—Lime

The 0.4 ha grid size exhibited the greatest application accuracy (>85%) for lime in most fields, while the under- and over-application, on average, increased with the grid size (

Table 3. The computed application accuracy for lime based on prescription maps generated from soil sampling at different grid sizes. The data represent the over-application (%), on-target (%), and under-application (%) associated with each grid size.

Field	Application	0.4 ha	1.0 ha	2.0 ha	3.0 ha	4.0 ha
		%
1	Over	4	1	0	6	5
	Target	95	92	75	94	65
	Under	2	8	25	0	30
2	Over	10	3	1	12	47
	Target	87	66	51	46	45
	Under	3	31	48	42	9
3	Over	2	1	11	2	65
	Target	95	93	87	92	30
	Under	3	6	3	6	2
4	Over	8	13	29	8	4
	Target	90	70	65	70	48
	Under	3	17	6	22	48
5	Over	11	9	13	25	25
	Target	75	82	80	75	75
	Under	14	9	8	0	0
6	Over	7	3	12	2	2
	Target	91	41	68	41	41
	Under	1	56	20	57	57
7	Over	6	9	7	0	4
	Target	90	78	81	89	54
	Under	4	13	13	11	42
8	Over	6	3	9	29	41
	Target	89	85	75	66	34
	Under	5	13	16	5	24
9	Over	5	13	22	8	24
	Target	91	76	77	81	76
	Under	4	9	1	10	0

). This trend of decreased lime application accuracy with increasing grid size was observed across all nine fields and can be attributed to the fact that as the grid size increases, the distance between adjacent sampling points also increases, which makes the interpolation procedure (IDW) predict across the field with fewer known points. The 1.0 ha grid size resulted in lime applications that were ≥80% accurate in only four fields, whereas the accuracy ranged between 66% and 78% in the other fields. This was most likely due to the high level of soil pH variability in these fields. These data also suggest that the application accuracy in these fields was considerably lower, even when using a grid size of 0.4 ha to 1.0 ha. For grid sizes of 2.0 ha and greater, the lime application accuracy was mostly inconsistent, ranging between 19% and 82%. However, in one of the fields (Field 3), the application accuracy was greater than 85%, even at the larger grid sizes of 2.0 and 3.0 ha, likely due to the low soil pH variability (the soil pH ranged between 6.0 and 6.4) within this field. While a general trend regarding on-target lime application existed across the fields (Table 3), no specific trend related to over- or under-application was observed. In general, the inaccuracy of lime application increased with grid size, with an under- or over-application rate of less than 20% for grid sizes of 1.0 ha and lower. For grid sizes of 2.0 ha and greater, the under- or over-application rate was as large as 50% or more in some fields.

The VR prescription maps presented in Figure 3 for Field 2 illustrate the trends observed in the lime application data (Table 3). The prescription map based on the 0.4 ha grid size (Figure 3b) is most closely associated with the reference lime prescription map (Figure 3a). In contrast, the association between the prescription maps decreases thereafter for grid sizes ≥1.0 ha (Figure 3c–f). The corresponding under- and over-application associated with each grid can also be observed by examining the change in area for each recommended lime application rate. For example, Figure 3a (reference map) shows that 18.8 and 17.1 ha within the field would receive the recommended lime application rate of 1120 and 1680 kg ha⁻¹, respectively. Now observing the prescription map based on the 0.4 ha grid size (Figure 3b), the areas within the field receiving the lime application rates of 1120 and 1680 kg ha⁻¹ are 16.5 and 19.5 ha, respectively, which means that approximately 2.3 ha in this field will be over-applied based on soil sampling at 0.4 ha grid size. Similarly, the areas within the field for the 1.0 ha grid sizes (Figure 3c) receiving application rates of 1120 and 1680 kg ha⁻¹ are 9.0 and 27.2 ha, respectively, which indicates that 8.4 ha in this field will be under-applied based on soil sampling at the 1.0 ha grid size.

3.1.2. Application Accuracy—Phosphorus (P)

The application accuracy for P at the 0.4 ha grid size was greater than 80% for most fields, except for Field 7, which fell below 75% (

Table 4. Computed application accuracy for phosphorus (P) based on prescription maps generated from soil sampling at different grid sizes. The data represent the over-application (%), on-target (%), and under-application (%) associated with each grid size.

Field	Application	0.4 ha	1.0 ha	2.0 ha	3.0 ha	4.0 ha
		%
1	Over	5	45	81	50	12
	Target	82	40	19	32	42
	Under	13	16	0	18	47
2	Over	10	12	26	21	22
	Target	84	58	49	42	42
	Under	6	30	26	36	35
3	Over	7	3	33	12	1
	Target	88	82	51	64	37
	Under	5	15	16	24	63
4	Over	6	6	5	6	7
	Target	92	82	81	82	72
	Under	2	13	13	12	21
5	Over	10	20	45	12	4
	Target	81	57	46	55	55
	Under	9	22	10	33	41
6	Over	7	12	22	18	28
	Target	91	60	65	60	64
	Under	2	28	14	23	8
7	Over	1	58	35	54	77
	Target	75	36	53	32	20
	Under	23	5	12	14	3
8	Over	2	12	20	17	7
	Target	92	82	70	74	77
	Under	6	6	10	9	15
9	Over	3	19	27	21	36
	Target	91	68	63	67	57
	Under	6	14	10	12	8

). Similar to the trend observed for the lime application, the application accuracy of P decreased with an increase in grid size. The application accuracy for the 1.0 ha grid size was ≥80% for only three of the nine fields, while it ranged between 36% and 68% for other fields. For grid sizes ranging from 2.0 to 4.0 ha, the application accuracy varied considerably among fields, with values ranging from 19% to 82%. These data demonstrate the inconsistency in the effectiveness of larger grid sizes, particularly those exceeding 2.0 ha, and their ability to accurately depict P variability within agricultural fields. While there was one field (Field 4) with an on-target application rate of >80% for the larger sizes of 2.0 and 3.0 ha, this is likely due to the low P variability in this field. Similar to lime application, the amount of under- and over-application for P did not follow a particular trend and increased with grid size. For grid sizes of 1.0 ha and lower, the amount of under-application was ≤30% for all fields, whereas the over-application was <20%, except for two fields (Fields 1 and 7), where it exceeded 45%.

The prescription maps for P, shown in Figure 4 for one of the fields (Field 2), show a general trend observed in the data presented in Table 4. The areas for different P application rates in the prescription map for the 0.4 ha grid size (Figure 4b) closely resemble the application areas in the reference prescription map (Figure 4a); however, these similarities among the prescription maps diminish quickly as the grid size increases. Figure 4 shows that while the total area under different P application rates does not vary considerably between the maps, under- and over-application in the field is still noticeable as the grid size increases. This can be attributed to the difference in spatial accuracy of P among these maps, which indicates that in some cases, the total area within the field receiving a particular application rate may not change between grid sizes; however, the spatial accuracy of nutrient application reduces with an increase in the grid size. Therefore, assessing the spatial locations of under- and over-applications within each field, along with the total amount, is important to accurately understand the effectiveness of different soil sampling strategies.

3.1.3. Application Accuracy—Potassium (K)

The application accuracy results for K for the 0.4 ha grid size were similar to those for lime and P, with an application accuracy of ≥84% for all fields except Field 5, which was 73%. The results for Field 5 suggest that spatial nutrient variability can be difficult to capture in some fields, even with a grid sampling size of 0.4 ha. For the 1.0 ha grid size, none of the fields had a K application accuracy above 80%, indicating that most of these fields had high amounts of K variability that cannot be accurately depicted with soil sampling at grid sizes of 1.0 ha or greater. The application accuracy for larger grid sizes (2.0–4.0 ha) across all fields ranged from 26% to 68%, exhibiting poor performance compared to the 0.4 ha grid size. The low application accuracy associated with larger grid sizes also suggests that relying long-term (especially every year) on these grid sizes to create K prescription maps could be detrimental to the areas of the fields that receive an over-application of K year after year. As observed for lime and P, no specific trend in under- or over-application existed for K with respect to grid size. For grid sizes of 1.0 ha and greater, the under-application ranged between 1% and 66%, whereas the over-application varied between 2% and 54% across all the fields (

Table 5. The computed application accuracy for potassium (K) based on prescription maps generated from soil sampling at different grid sizes. The data represent the over-application (%), on-target (%), and under-application (%) associated with each grid size.

Field	Application	0.4 ha	1.0 ha	2.0 ha	3.0 ha	4.0 ha
		%
1	Over	7	20	1	16	23
	Target	86	64	59	63	53
	Under	8	16	40	20	23
2	Over	9	20	16	7	32
	Target	85	57	52	49	44
	Under	6	22	32	45	24
3	Over	6	12	27	24	31
	Target	84	61	48	45	60
	Under	10	26	25	31	9
4	Over	4	26	24	25	16
	Target	84	64	61	57	54
	Under	12	10	15	18	30
5	Over	19	20	23	19	21
	Target	73	42	30	27	26
	Under	8	38	47	54	53
6	Over	8	32	32	33	19
	Target	84	57	55	54	64
	Under	8	12	12	14	16
7	Over	1	35	19	51	66
	Target	89	59	68	38	32
	Under	10	6	13	11	2
8	Over	5	13	10	30	28
	Target	88	72	66	49	54
	Under	6	14	23	21	18
9	Over	11	27	32	25	15
	Target	87	61	39	51	58
	Under	2	12	29	24	27

).

The prescription maps for K (Figure 5) also showed a similar trend as observed for lime and P (Figure 3 and Figure 4, respectively), where the prescription K map based on the 0.4 ha grid size (Figure 5b) was comparable to the reference K map (Figure 5a). However, this association between the reference map and other prescription maps (Figure 5c–f) decreases rapidly as the grid size increases. Referring to the prescription maps in Figure 5a,b, the areas within the field receiving different K rates are very similar, with only about 1.0 ha of the field being over-applied. The areas receiving the same K application rates in Figure 5c–f vary considerably from the reference K map, indicating a high level of under- and over-application associated with grid sizes of 1.0 ha and greater. Unlike the P maps (Figure 4a–f), where the total area within each P application rate remained relatively similar, the maps for K highlight the differences in both the magnitude and spatial resolution of application accuracy associated with soil sampling at different grid sizes.

Collectively observing the data for all three nutrients (presented in Table 3, Table 4 and Table 5) highlights an issue that may arise for a grower when choosing a grid size for their farm due to the variation in accuracy among different nutrients. For example, a grower may choose to collect samples using a 2.0 ha grid for Field 7, which exhibited an on-target lime application rate of >80%, but it was only 53% for P and 68% for K at the same grid size. Similar observations can also be made for other fields where a certain grid size provides a high application accuracy for lime, P, or K, but may not be suitable for all of them. These results suggest that the optimal grid size may vary for each field and nutrient; however, it is not feasible for a grower to collect soil samples at different grid sizes within the same field to target different nutrients. For this reason, it may be reasonable to determine a limiting nutrient based on the crop to be grown or consider the economics of different grid sizes to determine the optimal soil sampling grid size for each field. However, as the farm’s size grows, the need to be efficient with various operations, including soil sampling, also increases. Thus, while conducting soil sampling on different grid sizes across the farm may be feasible for a few growers, it is not practical for most growers in the southeastern US.

Table 6. The computed mean application accuracy for lime, phosphorus, and potassium based on different soil sampling grid sizes. The data presented are averaged across nine fields for lime, P, and K.

Grid Size (ha)	Lime		P		K
	Accuracy	CV	Accuracy	CV	Accuracy	CV
	(%)	(%)	(%)	(%)	(%)	(%)
0.4	89	7	86	7	84	6
1.0	69	38	63	28	60	14
2.0	73	15	55	32	53	24
3.0	64	42	56	32	48	22
4.0	52	32	52	35	49	26

presents the application accuracy averaged across all nine fields for lime, P, and K, along with CV values representing the amount of variability across the fields for each nutrient. When averaged across all fields, the overall results again exhibit a similar trend for lime, P and K, where the application accuracy is greatest from 84% to 89% at a grid size of 0.4 ha. In contrast, it decreased considerably for grid sizes of 1.0 ha, greater to below 73% for lime, and to below 63% and 60% for P and K, respectively. As indicated by the low CV values (6–7%), the results for the 0.4 ha grid size were also consistent across all the fields, whereas the relatively higher CV values for grid sizes of ≥1.0 ha indicate that the application accuracy depicted using larger grid sizes can vary among the fields depending on the existing nutrient variability within the field and previous management history. Previous studies have published similar reports on the accuracy of nutrient applications at different soil sampling grid sizes. Wollenhaupt and Wolkowski [9] recommended that a 0.4 ha grid sampling method is the most appropriate in the first year to determine the amount of nutrient variability within the field. After the first year, the authors speculate that a thorough nutrient budget, maintaining accurate records of fertilizer applications and crop removals, will be sufficient to inform fertilizer applications in subsequent years. Stępień et al. [15] chose 1.0 ha as their densest sampling area but suggested that more variability may be present within the fields for certain nutrients that were not captured by the 1 ha grid size. The authors recommend a sampling size of 1.0 ha, with the option to collect samples on a coarser grid size (2.0 or 4.0 ha) in the following two years. Mallarino and Witty [14] found that a 1.2 to 1.6 ha grid sampling method had an accuracy of 54% and 66% for P and K, respectively. These findings were similar to the accuracy values attained in the present study, where a 1.0 ha grid size exhibited an application accuracy of 63% and 60% for P and K, respectively. It can be concluded based on these findings that soil sampling using a grid size of 0.40 ha captures the greatest nutrient spatial variability within the fields and results in the highest application accuracy compared to larger grid sizes (≥1.0 ha).

3.2. Economics of Different Grid Sizes—Material Costs

Besides assessing application accuracy, it is also important to evaluate the economics of different soil sampling grid sizes to identify an optimal soil sampling method that is both accurate and cost-effective. The data in

Table 7. Total material cost per hectare computed for lime, P, and K application based on soil sampling on different grid sizes.

		0.4 ha	1.0 ha	2.0 ha	3.0 ha	4.0 ha
	Field	USD ha−1
Lime	1	59	55	45	62	44
	2	81	70	63	69	91
	3	60	58	66	62	84
	4	69	68	77	66	43
	5	84	85	88	92	92
	6	74	62	73	62	62
	7	57	51	52	0	33
	8	26	19	24	37	31
	9	114	142	122	114	123
P	1	93	123	182	136	78
	2	67	51	65	48	46
	3	35	31	44	22	5
	4	13	7	8	7	2
	5	173	167	188	166	157
	6	46	33	58	51	67
	7	42	100	77	96	127
	8	16	22	19	22	14
	9	87	93	107	102	113
K	1	93	98	42	85	94
	2	114	119	105	90	125
	3	152	152	160	155	168
	4	30	42	47	39	27
	5	139	128	122	97	108
	6	56	61	60	59	42
	7	16	32	22	42	55
	8	196	195	191	200	200
	9	189	194	194	190	184

illustrate how the material cost per hectare changes with grid size. It should be noted that the material cost is directly related to the amount of over- and under-application associated with each grid size. Thus, the trend observed for lime, P, and K costs per hectare was analogous to the application accuracy results discussed in the previous sections. Hence, the material cost was higher where the lime or fertilizer was over-applied and lower where the lime or fertilizer was under-applied. For instance, Field 2 in Table 7 reports the cost of lime as USD 81, USD 70, USD 63, USD 69, and USD 91 per hectare for grid sizes of 0.4, 1.0, 2.0, 3.0, and 4.0 ha, respectively. There is a decrease in the cost of lime per hectare for the 1.0, 2.0, and 3.0 ha grid sizes and an increase in the cost of lime per hectare for the 4.0 ha grid size. Observing the application accuracy for different grid sizes in the same field, as shown in Table 3, reveals an increase in the under-application of lime for the 1.0, 2.0, and 3.0 ha grid sizes, and an increase in the over-application of lime for the 4.0 ha grid size compared to the 0.4 ha grid size. Although the smallest grid size of 0.4 ha recommends more lime per hectare (higher costs per hectare) when compared to the larger grid sizes, the application accuracy at this smaller grid size is also high (87%) for this field as opposed to a low accuracy (<66%) for the larger grid sizes. A practical implication of these results is that a grower would incur higher application costs due to the higher fertilizer costs, but they would also be more confident in the accuracy of site-specific fertilizer application (placement) by selecting a grid size of 0.4 ha. There is also an expectation that increased yields will be realized through the correct placement of nutrients, further increasing profit margins.

As discussed in the previous example, precision fertilizer application through soil sampling on a smaller grid size does not necessarily always correlate with high application costs; however, it can also help reduce total application costs in some cases. For example, the 0.4 ha grid size recommends the lowest material (lime and fertilizer) cost per hectare for Fields 7, 8, and 9, compared to the 1.0, 2.0, 3.0, and 4.0 ha grid sizes. In this case, it can be attributed to the fact that a 0.4 ha grid size has the highest application accuracy, which means a lower amount of under- and over-application (Table 4). It can again be noticed in these fields where the application accuracy decreases (an increase in over- or under-application), and the cost of material follows the same trend as the amount of over- and under-application. Similar observations are seen for the other fields for lime, P, and K in the present study, as shown in Table 7.

3.3. Economics of Different Grid Sizes—Application Costs

The total application cost per hectare, based on different grid sizes for all fields, is presented in

Table 8. The total application cost per hectare for soil sampling on different grid sizes. The data are averaged across lime, P, and K for each field.

	0.4	1.0	2.0	3.0	4.0
Field	USD ha−1
1	279	297	282	295	226
2	296	261	246	219	273
3	282	263	283	251	268
4	146	137	145	124	84
5	429	401	410	367	369
6	210	176	203	183	181
7	149	204	165	151	225
8	271	257	247	272	256
9	424	450	436	418	431

. This application cost includes the cost per hectare of each material (lime, P, and K), the labor cost per hectare for collecting soil samples, and the cost per hectare for analyzing the soil samples. It is challenging to identify a specific trend in data across the fields and between different grid sizes, as numerous factors can influence the total application cost per hectare, including the application accuracy associated with each grid, the cost of fertilizer, and the cost of the soil sampling method.

For most fields, the 0.4 ha grid sampling method results in the highest cost per hectare, which is expected due to the higher costs associated with sampling and analysis for the smaller grid size. Interestingly, the change in the total application cost per hectare from a 1.0 ha to 0.4 ha grid size is, on average, an increase of less than 2.5% of the total cost per hectare. However, this change in soil sampling grid size also increases the application accuracy, on average, by more than 20% for lime, P, and K. While changing soil sampling from a 2.0 ha to a 0.4 ha grid size will cost on average 3% more per hectare in sampling costs, lab analysis, and materials, the increase in application accuracy is greater than 30% for both P and K. Understanding that producers may not be willing to make such a significant shift to 0.4 ha grids, changing from a 2.0 ha grid size to a 1.0 ha grids increases the total cost by 1.6%, with an increase in application accuracy of 4%, on average.

Overall, when considering both the application accuracy and total application costs associated with different soil sampling grid sizes, the results obtained in this study are valuable for producers in the southeastern U.S. as they highlight the strengths and weaknesses of different soil sampling grid sizes, as well as the importance of selecting a proper grid size as it impacts both accuracy and costs. If the nine fields used in this study were to represent a sub-sample of a grower’s farm, the data suggest an optimal grid size would vary on a field-by-field basis. However, when considering the overall results across all fields, it is also evident that the 0.4 ha grid size performs better than all other grid sizes, albeit at the expense of increased costs in some fields. However, an argument can also be made that some growers are more willing to spend extra money in areas or fields with high-yield potential, as precision soil sampling on a smaller grid size, such as 0.4 ha, gives them more confidence in their nutrient management decisions by ensuring fertilizer application at the correct rate and place. It is essential to note that the common grid size currently used for precision soil sampling across the southeastern United States is 2.0 ha, which exhibited application accuracy of only 50% to 70% across the nine fields used in this study. Interestingly, the larger grid sizes of 3.0 and 4.0 ha are also used by some consultants and growers in the southeastern US. The results suggest significant under- or over-application of nutrients associated with those grid sizes. While reducing soil sampling costs is one of the main reasons behind larger grid sizes, the authors believe that this effort to save money upfront is costing growers more in fertilizer misapplications and, consequently, in reduced crop yields. In some cases, these inaccurate fertilizer applications could also be causing more nutrient variability issues than initially present in the field. Therefore, growers who have traditionally sampled fields on larger grid sizes over the years need to be cautious about inadvertently causing these nutrient variations in their fields.

Based on the findings of this study, the authors recommend that most agricultural fields be soil sampled at a 0.4 ha grid size at least once to understand the nutrient variability within each field and to make informed decisions about soil sampling in subsequent years. While most fields have some inherent variability due to the soil type, texture, or management, the authors believe that some uniform fields can be soil sampled on larger grid sizes (1.0 or 2.0 ha) to manage soil sampling costs. This also presents a relatively different, yet novel approach to soil sampling, where, in contrast to soil sampling using a fixed grid size across the entire farm, growers can be more efficient with nutrient management and costs by adopting varied grid sizes for fields across their farm. Although grid soil sampling will remain prevalent in the southeastern US, the authors expect an increase in the adoption of zone-based soil sampling strategies as interest in precision nutrient management and increased crop yields rises among growers.

4. Conclusions

Site-specific nutrient management through the variable-rate application of lime and fertilizer is one of the most widely adopted practices in the US, including in the southeastern region. The rising costs of fertilizers and increased interest among growers in precision nutrient management have recently raised concerns and questions about the efficacy of the different grid sizes used for precision soil sampling across the southeastern US. Thus, this study was aimed at evaluating the effectiveness of different soil sampling grid sizes (0.4, 1.0, 2.0, 3.0, and 4.0 ha) in depicting the spatial nutrient (soil pH, P, and K) variability within nine agricultural fields and their influence on the accuracy of variable-rate fertilizer prescription maps. The results from this study showed that the smallest grid size of 0.4 ha was the best at representing the most spatial variability for soil pH, P, and K, while the ability to depict spatial variability decreased significantly with an increase in the grid size. The resulting VR prescription maps generated from soil sampling at different grid sizes indicated a similar trend, where the potential for under- or over-application was lower at the smaller grid sizes and higher at the larger grid sizes. In general, it was observed across all nutrients that application accuracy was greatest for grid sizes of 0.4 ha (over 80%), whereas it varied considerably (20% to 90%) among the fields for grid sizes of 1.0 ha or greater. Lower CV values (6–7%) for the application accuracy of lime, P, and K also indicated that the findings for the 0.4 ha grid size were consistent across the fields used in this study.

Over the years, one of the major drivers behind the push towards larger soil sampling grid sizes has been the increasing costs of soil sampling; however, this approach fails to consider the effect of grid size on fertilizer costs per hectare. The results from the economic analysis suggested that the material costs (lime and fertilizer) were directly correlated with the amount of under- and over-application associated with different grid sizes within each field. This also influenced the total application costs, as a greater amount of over-application results in high material costs and vice versa. Overall, these data suggest that while the larger grid sizes of ≥2.0 ha may help lower soil sampling costs upfront, the total application costs (including fertilizer costs) can be higher in some fields than the total cost associated with soil sampling on smaller grid sizes (0.4 or 1.0 ha). While the direct impact of accurate nutrient inputs on crop yield or long-term nutrient management is beyond the scope of this study, higher nutrient use efficiency would likely also translate to improved yields. In some cases, the 0.4 ha grid size may incur higher application costs than other grid sizes; however, it also yields the greatest application accuracy, ensuring precise and effective nutrient applications. In conclusion, the results of this study suggested that the smaller grid sizes of 0.4 or 1.0 ha are most optimal when considering both the efficacy and economics of VR fertilizer applications.