Site-specific production functions for variable rate corn nitrogen fertilization
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- Ruffo, M.L., Bollero, G.A., Bullock, D.S. et al. Precision Agric (2006) 7: 327. doi:10.1007/s11119-006-9016-7
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Specific recommendations for variable rate nitrogen (VRN) fertilization in corn (Zea mays L.) are required to realize the potential environmental and economic benefits of this technology. However, recommendations based on algorithms that consider the processes controlling crop response to nitrogen fertilizer (NF) within fields have not yet been developed. The objectives of this study were to develop site-specific corn yield production functions for VRN fertilization and to determine the site-specific variables controlling corn response to NF. The experiments were conducted on eight commercial production fields. Fields were divided into 13–20 sections composed of five plots. Each plot received one NF rate. Site-specific variables included primary and secondary terrain attributes, and the Illinois Soil Nitrogen Test (ISNT). Nitrogen fertilizer significantly increased corn yield and it interacted with at least one site-specific variable. The ISNT was the site-specific variable that interacted with NF in most fields where the CV of ISNT was larger than 10%. The parameter estimates indicate that ISNT had a positive effect on corn yield and that it reduced the response to NF. Terrain attributes also affected corn yield and its response to NF. In general, parameter estimates indicated that well drained areas (i.e. small specific catchment area, moderate slopes) had higher yields and responded less to NF than areas where water is expected to accumulate. These results indicate that terrain attributes as surrogates for soil water content and the ISNT as a measure of soil mineralizable nitrogen are site-specific characteristics that affect corn yield and its response to NF.
KeywordsIllinois soil nitrogen testProduction functionManagement zones
Variable rate nitrogen application is a technology that affords corn producers the opportunity to site-specifically apply the economically optimal nitrogen fertilizer rate (EONR) at locations within a field, which potentially may realize both environmental benefits for society and economic benefits for the farmer. The potential environmental benefits consist primarily of a reduction in the soil residual NO3-N concentration at the end of the growing season and consequently in reductions in leaching of NO3-N (Dinnes et al. 2002). It should be noted that the EONR for a whole field is not necessarily equivalent to the mean of the EONR for subsections of fields (Bullock et al. 2002). Thus, at times VRN affords the opportunity to reduce the total amount of NF applied while increasing crop yield. Where the increased revenue and NF savings exceed the costs of the VRN technology, producers will see an increase in profit.
The use of VRN for EONR application requires a producer to know the production functions at the scale at which VRN is used. It is well documented that corn yield varies widely within fields (Jaynes and Colvin 1997; Sadler et al. 1998). The EONR for corn has also been shown to be very different between fields and highly variable within fields (Mamo et al. 2003; Anselin et al. 2004; Scharf et al. 2005). Scharf et al. (2005) suggested that there is a need for further research on the measurable factors which affect the within-field variability of the EONR in order to develop systems for within-field VRN recommendation.
Compared to variable rate application of phosphorus or potassium fertilizers, the adoption of VRN has been extremely limited (Bullock et al. 2002; Robert 2002). There are agronomic and economic reasons for this limited adoption of VRN. The agronomic reasons include the spatial and temporal variability of the different soil processes that determine soil N supply and crop response to NF and the lack of a robust and simple N diagnostic test (Pan et al. 1997; Power et al. 2000). However, it can be argued that VRN adoption will increase once NF recommendations are specifically developed for VRN application.
Initially, the algorithms proposed to determine NF applications for VRN were based on regional recommendations, yield potential and expected yield differences of management zones (Ferguson et al. 2002; Redulla et al. 1996; Kitchen et al. 1995). However, the use of these algorithms did not increase corn yield or reduce applied NF compared to the uniform NF application.
Response models specifically developed for VRN management must consider the processes controlling crop response to NF within fields (Bullock et al. 2002; Ferguson et al. 2002). Bullock and Bullock (2000) proposed a theoretical framework to analyze site-specific production functions. They considered yield as a function of site-specific non-manageable but fixed characteristics, manageable inputs and stochastic variables. Therefore, it is critical to determine which site-specific characteristics affect corn response to NF and to quantify the relationship between these variables and corn response to NF. Furthermore, the estimation of site-specific response functions will allow the estimation of the economically optimal NF rate site-specifically at a management scale and detail required for VRN application. Unfortunately, very little research has attempted to explain the causes of this variability or to develop site-specific response functions (Bullock and Bullock 2000; Bullock et al. 2002).
Most of the yield variation is associated with water availability and its dynamics (Mulla and Schepers 1997), which not only affect crop yield directly, but also indirectly through the N cycle. Soil organic N mineralization, denitrification and leaching are processes of the soil N cycle affected by soil water content and their balance determines soil mineral N availability for crop uptake and also affects corn response to NF.
At a field scale, soil water spatial distribution and consequently corn yield are largely determined by topography (Moore et al. 1993; Western et al. 1999; Kravchenko and Bullock 2000; Kaspar et al. 2004). Slope and curvature largely determine the flow and accumulation of soil water in different positions of the landscape, as well as the redistribution of soil mineral particles and organic matter through erosion (Pachepsky et al. 2001). It is expected that corn response to NF will be largely explained by topographic attributes, especially those that are surrogates for soil water availability.
The Illinois Soil Nitrogen Test (ISNT) (Khan et al. 2001) has shown a promising ability to discriminate fields where corn is responsive to NF from non-responsive fields. Soils where corn was non-responsive to N fertilization had ISNT values larger than 235 mg kg−1, whereas where corn was responsive to N the ISNT was lower than 225 mg kg−1. The ISNT estimates the aminosugar-N fraction of the soil organic N, a labile pool of N that mineralizes during the growing season and thus it can be considered as an approximation of the N which will be available to the crop during the growing season (Hoeft et al. 2002). Ruffo et al. (2005) reported a strong spatial structure for the ISNT, a desirable characteristic for VRN. It is expected that areas or fields with high values of ISNT will show less response to NF than areas where the ISNT values are low.
We hypothesize that corn yield response to NF can be modeled using production functions that include topographic attributes and ISNT as arguments. The objectives of this study were: (i) to develop site-specific corn yield production functions for VRN fertilization and (ii) to determine the site-specific variables controlling corn response to NF.
Materials and methods
Location and soil series association of each field included in the study
Field size (ha)
Ipava SiL-Sable SiCL-Tama SiL
Ipava SiL-Sable SiCL-Tama SiL
Dana SiL- Flanagan SiL-Drummer SiCL
Flanagan SiL-Drummer SiCL- Elburn SiL
Ipava SiL-Sable SiCL-Tama SiL
Ipava SiL-Sable SiCL-Tama SiL
Dana SiL- Flanagan SiL
Flanagan SiL-Drummer SiCL- Catlin SiL- Elburn SiL- Dana SiL
Experimental design and treatments application
The fields were subdivided into 13–20 sections, depending on field shape and size. Each section was composed of five plots (i.e. experimental units). Plot dimensions varied slightly among fields, depending on field shape, size and farming equipment, but were at least 70 m long and 24 m wide. At each field, plots were wide enough to accommodate two passes of the commercial fertilizer applicator and four passes of the combine used to harvest the experimental units.
University of Illinois recommended nitrogen fertilizer rate, nitrogen source and time of nitrogen fertilizer application for each field in the study
Time of application
160 kg N ha−1
190 kg N ha−1
170 kg N ha−1
170 kg N ha−1
190 kg N ha−1
160 kg N ha−1
195 kg N ha−1
180 kg N ha−1
The yield goal (Mg ha−1) was calculated by averaging the previous 5 years corn yields as provided by the producer. A 45 kg N ha−1 rotation credit was used because corn was planted after soybean in every field. The incidental N considered the N applied with starter fertilizer and herbicides.
The GIS spatial design of the experiments (i.e. the plot plan) was developed with the EFRA extension (www.farmresearch.com/efra) of ArcView GIS (Environmental System Research Institute Inc. (ESRI), Redlands, CA, USA). The randomization of the allocation of the NF rates to each experimental unit was performed with the PLAN procedure of SAS (SAS Institute 2003). At least 20 m were left as buffer between the field headlands and the start of the experiment in order to improve fertilizer application and yield monitor performance.
The digital plot plan of each field was transferred to each producer and the NF rates were applied with commercial variable rate applicators equipped with differential global positioning system (DGPS). Applied NF rate was recorded at two-second intervals. Specific NF source and time of application for each field are presented in Table 2.
Corn grain yield was measured and recorded using calibrated commercial yield monitors mounted on combines equipped with DGPS. Corn yield data were recorded every second and were corrected to 15.5% grain moisture. Applied NF and corn yield were imported into ArcView GIS using the EFRA extension. Only the two central passes of the combine and the applicator pass closest to these passes were retained for further analysis. Yield and applied NF points at a distance shorter than 7.5 m from the start and end of the plot were discarded. Mean corn yield and mean applied NF were calculated with EFRA for each experimental unit.
A digital elevation map was made for each field. Latitude, longitude and elevation (m) data were collected with a 12-channel Leica SR530 real time kinematic DGPS receiver. The rover GPS receiver was mounted on a Polaris 500 all terrain vehicle (ATV) traveling at 20–25 km h−1. The rover GPS unit recorded horizontal coordinates and elevation every 3 m. The ATV was driven in transects oriented in the row direction and separated by 10 m. A light bar was used to maintain a straight transect and to determine the transect separation distance. Elevation data was interpolated to a regular 3-m grid digital elevation model (DEM) using the TOPOGRID command in Arc-Info (ArcInfo ver. 8.3, 2002, ESRI, Redlands, CA, USA).
The mean value of each terrain attribute for each plot was calculated with EFRA using the same buffer area used for corn yield.
ISNT sampling and analysis
All fields were sampled for ISNT either during early spring or fall. Three-core composite soil samples separated by 300 mm were taken from the center of each experimental unit in every field, resulting in an approximately 24 m by 70 m rectangular grid. Soil samples were taken to a depth of 0.3 m with a 17.5-mm diameter probe. In some fields (A02, S02, A03, J03), 40 additional samples were taken in cells of five samples arranged as squares of 10 m per side with samples at the corners and at the geometric center. The mean number of samples per field was 110. Soil samples were dried and ground to pass a 2-mm sieve, then analyzed for ISNT following the method described by Khan et al (2001).
Omnidirectional variograms were estimated using GSLIB (Deutsch and Journel 1998), up to a distance equal to half the maximum lag distance for each data set. Ordinary kriging to a square 5 m grid was performed with GSLIB. The ISNT value per plot was calculated by averaging the points within the buffer area used for yield with EFRA. In summary, the data set consisted of the following variables per plot: mean corn yield, mean applied NF rate, mean ISNT, mean elevation, slope, aspect, LSCA, plan curvature, profile curvature, CTI and SPI.
Site-specific production functions were estimated by multiple regression, using the site-specific characteristics and applied NF as independent variables and corn yield as the dependent variable. The models were estimated by maximum likelihood (ML) with the MIXED procedure of SAS (Littell et al. 1996).
Model development started with a second-degree polynomial for NF rate, and then the site-specific variables were added starting with the variable that had the largest correlation with yield. Once a variable entered the model, the interaction of this variable and the linear term for NF rate was tested. If significant, the interaction between the variable and the quadratic term for NF was also tested. The criteria for a term to enter the model were that the significance level of the approximate t-test for the parameter was less than 0.1, and that the small sample Aikaike’s information criteria (AICC) for the full model was lower than for the reduced one. The AICC reduces the risk of over-fitting a model and has been recommended for model building (Burnham and Anderson 1998).
The spatial structure of the regression model was tested with a likelihood-ratio test between the spatial covariance model and an independent error model, with the same variables included in the fixed effects (Littell et al. 1996). The type of spatial covariance structure was selected based on the AICC (Littell et al. 1996). Zimmermann and Harville (1991) and Lark (2000) concluded that the fixed effects tests are relatively robust to the specification of the covariance function and that the critical step is to model the spatial structure of the errors. Normality and homoskedasticity of the errors were assessed by analyzing the residuals with the Shapiro–Wilk’s test (Shapiro and Wilk 1965), with normal probability plots using the UNIVARIATE procedure in SAS (SAS Institute 2003), and by visual inspection of the plots of the residuals against NF rate and the dependent variable.
Weather conditions during 2002 and 2003 growing seasons
Monthly rainfall and mean temperature during the 2002 and 2003 growing seasons and for the 30-year average
30-year avg. (mm)
30-year avg. (mm)
30-year avg. (°C)
30-year avg. (°C)
Corn production functions for nitrogen fertilization
Mean corn yield by field ranged from 9 Mg ha−1 to 10 Mg ha−1 in 2002 (Table 6). In contrast, in 2003 yields were greater than 12 Mg ha−1 at all fields, with a maximum yield of 14 Mg ha−1 for S03 (Table 7).
Parameter estimates and standard errors (in parentheses) of fixed effects, covariance parameter estimates and goodness of fit criteria for the 2002 fields
NF × Plan curvature
NF2 × Plan curvature
NF × CTI
NF × LSCA
NF2 × LSCA
NF × ISNT
NF2 × ISNT
NF × Slope
Slope × LSCA
Sill (g m−2)2
−2 log likelihood
Parameter estimates and standard errors (in parentheses) of fixed effects, covariance parameter estimates and goodness of fit criteria for the 2003 fields
NF × LSCA
NF × ISNT
NF2 × ISNT
Nugget (g m−2)2
Sill (g m−2)2
−2 log likelihood
In six out of eight fields corn yield were significantly affected by the main effect of ISNT. For the 2002 fields (Table 4), the main effect of ISNT was significant in A02 and M02. In addition, at M02 there were significant ISNT × NF and ISNT × NF2 interactions. In 2003, the main effect of ISNT was significant in all the fields (Table 5) and it interacted significantly with NF in A03, SY03 and J03. The estimates of the ISNT parameter had a positive sign in every field except for S03, indicating that ISNT had a positive effect on corn yield. The estimate of the ISNT parameter in S03 was an order of magnitude smaller than the estimate for the other 2003 fields where ISNT was significant and positive (Table 5). In all the fields where ISNT interacted with NF, the estimates of the parameters were negative for the linear NF terms and positive for the quadratic NF term (NF2), indicating that the marginal yield response to NF decreased as ISNT increased (Tables 4, 5).
Among the topographic attributes, LSCA was the site-specific characteristic that was significant in most fields (two). In M02, the main effect of LSCA was significant and negative (Table 4). In addition, there were significant LSCA × NF and LSCA × NF2 interactions. In MH02, LSCA interacted negatively with slope. As occurred in M02, in S03 the main effect of LSCA was also negative and LSCA increased the response to NF.
In A02, S02, MH02 and A03, the main effects of the primary topographic attributes slope, profile curvature and plan curvature were significant and positive (Tables 4, 5). In MH02, there were significant slope × NF and slope × LSCA interactions. In A02, there were significant plan curvature × NF and plan curvature × NF2 interactions (Table 4).
The secondary topographic attributes SPI and CTI were significant in some cases. In S02, the main effect of CTI and the CTI × NF interaction were significant, whereas the main effect of SPI was significant in SY03. In both fields, these secondary terrain attributes had a negative effect on corn yield.
The parameter estimates of the spatial covariance model are reported in Tables 4 and 5. In 2002, none of the models included a nugget, and the best model was spherical for A02, S02 and M02 and exponential for MH02. In 2003, the best model was spherical with a nugget for A03, S03 and SY03 and exponential without a nugget for J03. The total sill was largest for M02 and smallest for A02, whereas the shortest range was 90 m for J03 and the longest was 443 m for S03.
The significant interactions between NF and site-specific characteristics indicate that the response of corn to NF was not homogeneous across the fields, but instead was affected by the site-specific characteristics and varied accordingly. This is a critical and necessary condition for VRN to be of any value. If there were no significant interactions then the response of corn to NF would be the same everywhere within the field. Consequently, one NF rate would be economically optimal for the whole field. Other authors have reported different responses for crops within fields that were subdivided based upon landscape position or other variables. Pennock et al. (2001) reported different response functions of canola to NF for convex, linear and concave landform positions but they failed to report statistics to compare the parameters among landforms. Similarly, Schmidt et al. (2002) found that in three site-years out of five, corn response to NF varied between sections of fields that had different soil organic matter content. Based on one year of data on a single field, Anselin et al. (2004) also found that corn response to NF varied among landscape positions (hilltop, east and west slopes, valley) within a field. However, these publications did not report site-specific production functions.
The ISNT is considered a measure of the potentially mineralizable soil organic N pool (Hoeft et al. 2002) and, as such, it is a site-specific characteristic to consider. Since ISNT is related to soil N supply, higher levels of ISNT are indication of increased soil N availability to corn. Thus, corn yield should increase as ISNT increases and corn response to NF should be reduced. The positive sign of the main effect for ISNT (Tables 4, 5) indicates a positive effect on corn yield. In addition, the combination of the negative sign of the ISNT × NF and the positive sign of the ISNT × NF2 interactions support the hypothesis that ISNT reduces corn response to NF. In addition, we cannot speculate on the reasons for the ISNT negative sign in S03. However, the agronomic significance of this effect is limited since the parameter for ISNT in S03 was an order of magnitude smaller than the positive parameters of ISNT for the other 2003 fields.
The ISNT × NF interaction can be understood by examining the variability of ISNT in each field. Three out of four fields with significant ISNT × NF interaction had CVs greater than 10% (M02 = 10.1%, J03 = 12.1%, and SY03 = 12.8%). In A03, although the CV was 5.7%, 75% of the ISNT values were classified as non-responsive or inconclusive according to Khan et al. (2001), who classified soils with ISNT values of 237–435 mg kg−1 as non-responsive to NF and soils with ISNT values of 72–223 mg kg−1 as responsive.
The significance of several primary and secondary topographic attributes indicates that topography affected corn yield and, in many cases, the response to NF. The topographic attributes that were significant in each field varied, showing a degree of field-specificity. Other authors also have reported that significant topographic variables differed among the fields under analysis when used in models to explain corn or soybean yields (Kravchenko and Bullock 2000; Cox et al. 2003).
In this study, LSCA was the topographic attribute that was significant in some fields. Western et al. (1999) found that LSCA was related to soil water content. Under Central Illinois growing conditions in 2002 and 2003, where rainfall was close to normal, areas with high values of LSCA may have suffered from soil water saturation that stressed the crop and reduced corn yield. Kravchenko and Bullock (2000) reported that corn yield was negatively affected by excessive spring rainfall on locations that had large flow accumulation. In agreement, Kaspar et al. (2004) separated dry and wet years and found that lower landscape positions (i.e. large LSCA values) had a negative effect on corn yield in wet years.
There was a significant interaction between LSCA and NF in S03 and between LSCA and NF and NF2 in M02. In both cases, the signs of the interactions (positive for NF and negative for NF2) indicate that the response to NF increased in areas with high LSCA. We speculate that this is due to lower N availability from soil organic N sources, probably due to a combination of losses through denitrification and lower N mineralization rates during the growing season. Farrell et al. (1996) found that denitrification was greatest in areas that received runoff from the surrounding areas, which also had large soil water content. Excessive soil water content increases denitrification (Pennock et al. 1992) and leaching (Campbell et al. 1984), and reduces mineralization (Drury et al. 2003), resulting in less N available for crop growth.
Profile curvature was significant and had a positive effect on corn yields in S02. Sinai et al. (1981) found a strong positive correlation between profile curvature and soil water content which explained the large and positive correlation that they observed between this topographic attribute and wheat yield. Timlin et al. (1998) reported that corn grain yields in dry to normal years were significantly higher in areas of high profile curvature (positive effect of curvature), but they found no significant correlation in wet years. The beneficial effect of profile curvature on corn yield observed in this study is probably due to a combination of water availability and soil material that accumulated on the toe-slopes as a consequence of erosion.
Field mean, minimum and maximum (in parenthesis) values of site-specific characteristics and grain yield for the 2002 fields
ISNT (mg kg−1)
Profile curvature (km−1)
Plan curvature (km−1)
LSCA log (m)
Yield (g m−2)
Field mean, minimum and maximum (in parenthesis) values of site-specific characteristics and grain yield for the 2003 fields
ISNT (mg kg−1)
Profile curvature (km−1)
Plan curvature (km−1)
LSCA log (m)
Yield (g m−2)
Both CTI and SPI are secondary topographic attributes related to soil water saturation. Each of these attributes was significant in one field (CTI in S02 and SPI in SY0) and both had a negative effect on corn yield. Furthermore, in S02, CTI interacted positively with N. Both attributes take into account the specific catchment area (SCA) and slope, and in both cases large values for SCA in turn yielded large values for these indices. Chaplot et al. (2000) found that CTI was a good predictor of hydromorphic soils and Moore et al. (1988) reported that CTI was the topographic variable that best explained soil water content. The negative effect of both indices on corn yield agrees with the negative effect of LSCA and suggests that excess water availability decreased corn yield. As occurred with LSCA in M02 and S03, CTI increased corn response to NF (positive CTI × NF interaction), suggesting that areas with large CTI probably have lower soil N supply either due to increased losses or lower soil organic N mineralization. In addition, SPI is used as a measure of the erosive power of runoff and has been used to predict the location of ephemeral gullies (Moore et al. 1988; Lentz et al. 1993). Areas where SPI was high probably suffered from erosion and negatively impacted corn yield. The significant and negative LSCA × slope interaction in MH02 is mathematically and functionally similar to the SPI (Eq. 3). Areas with large LSCA and high slopes probably suffered from erosive processes that reduced soil fertility, degraded soil physical properties and ultimately decreased corn yield.
The relatively different values of the covariance model parameters (nugget, sill and range) are not surprising when they are compared to variograms of corn yield reported in the literature. Jaynes and Colvin (1997) reported ranges of corn yield from 52 m to 135 m for the same field in three different growing seasons and they did not observe a significant nugget effect in any year. Similarly, Schepers et al. (2004) showed variograms for 5 years of a single 51 ha field with ranges of exponential variograms that varied from 16 m to 85 m. Sadler et al. (1998) studied the spatial structure of corn yield in 5 years on one field and found that the range was as short as 60 m in 1 year but reached 156 m in another year. Their variograms included significant nugget effects with nugget/sill ratios that ranged from 0.007 to 0.416. The interaction between the site-specific terrain attributes and the weather conditions prevailing at each field probably had a singular effect on the spatial distribution of soil water content. Soil water content affects the rates of soil organic N cycle which, in turn, determines the spatial variability of soil mineral N. Thus, the direct effect of soil water content on corn yield combined with the indirect effect through the availability of mineral N probably determined the different spatial structure found in each field.
Future research should include a larger data set of response studies conducted on the same fields over several growing seasons in order to quantify the effect of weather on the production functions and the interactions between weather, site specific characteristics and NF on corn yield. In addition, it would be relevant to analyze and quantify the effect of terrain attributes or relative position in the landscape on soil organic N mineralization, mineral N denitrification and leaching because these processes ultimately determine N availability to crops. If such future research showed that denitrification or leaching occurred at higher rates in areas with large SCA or curvature, then it would be relevant to analyze the potential economic and environmental benefit of applying nitrification inhibitors based on these terrain characteristics.
Production functions for corn N fertilization were developed for all of the fields under study using site-specific characteristics and NF as independent variables. In all of the fields, corn responded to NF, and NF significantly interacted with site-specific characteristics. This is a critical and necessary condition for VRN to be economically profitable because it indicates that corn response to NF varies within any given field. A lack of interaction would indicate that the response to NF would be uniform across fields and thus that a single NF rate would be economically optimal.
The site-specific characteristics that affected corn yield and corn response to NF varied among fields but some trends were consistent. For example, the ISNT was the single most consistent site-specific characteristic that showed a significant interaction with NF in fields where the ISNT CVs were greater than 10%. The sign of the ISNT × NF interaction indicates that as ISNT increased, the marginal response of corn to NF decreased, supporting the claim that the ISNT can be considered a surrogate for potential soil N mineralization. Terrain attributes (i.e. LSCA and slope) that have been shown by other studies to be related to soil water content also were significant site-specific variables in the production functions that interacted with NF in some fields. These results indicate that primary terrain attributes, as surrogates for soil water content and the ISNT as a surrogate for soil N mineralization are site-specific characteristics that help to explain corn yield and its response to NF.
The development of maps of terrain attributes and ISNT is critical to any potential application of these production functions for corn VRN. Studies conducted in these and other fields indicate that ISNT has a spatial structure that will allow mapping with a relatively sparse grid (approximately a 1 ha grid). Furthermore, other ongoing studies indicate that the soil samples for ISNT would not need to be collected every year but rather every 4 or 5 years. These characteristics make the ISNT a suitable soil test for VRN. In addition, several commercial and public sources of DEMs are available or can be contracted to estimate terrain attributes.