Soil Fertility & C

rop Nutrition

796 Agronomy Journa l • Volume 103 , I s sue 3 • 2011

Categorical Analysis of Spatial Variability in Economic Yield Response of Corn to Nitrogen Fertilization

P. M. Kyveryga,* T. M. Blackmer, and P. C. Caragea

Published in Agron. J. 103:796–804 (2011)Published online 17 Mar 2011doi:10.2134/agronj2010.0411Available freely online through the author-supported open access option.Copyright © 2011 by the American Society of Agronomy, 5585 Guilford Road, Madison, WI 53711. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

With the steady increase in economic and environmental pressures for increasing N fertilizer use

effi ciency in modern corn production, there is a growing inter-est in VRN fertilizer applications. Despite rapid technological advances (yield monitoring, remote sensing, guidance systems, and variable rate application technology) during the last two decades, we still lack the basic knowledge of how to identify areas that can profi t from VRN applications and to estimate potential YRs to N, potential fertilizer savings, and therefore, economic benefi ts.

Large spatial and temporal variability in YR to N and economic optimal nitrogen rates (EONR) within corn fi elds are well documented (Mamo et al., 2003; Scharf et al., 2005). However, many factors can potentially aff ect YR within fi elds. For example, the eff ect of soil moisture within fi elds dominates in some years (Kay et al., 2006; Schmidt et al., 2007) while the eff ect of the amount of N mineralized from soil organic matter dominates in others (Blackmer and White, 1998; Mulvaney et al., 2005; Ruff o et al., 2006). Establishing a predictable relation-ship between YR and soil organic matter or soil moisture within fi elds is oft en complicated by the eff ect of additional factors such as soil texture, slope, or water movement. Th ese factors oft en determine the degree of N losses from the soil (Balkcom et al., 2003; Kahabka et al., 2004). In general, the complex

interactions among the many variables that infl uence the loss and availability of N in the soil–plant system make the predic-tion of YR or EONR in space and time a formidable task.

Th e traditional procedure for on-farm experimentation presents numerous challenges to the study of the many interac-tions among factors as well as spatial dependence within fi elds. An ideal approach would be to apply a wide range of N fertil-izer rates over a large area of soils, estimate site-specifi c N yield response functions, and to calculate EONRs for many small areas within fi elds (Bullock and Lowenberg-DeBoer, 2007; Hur-ley et al., 2004; Schmidt et al., 2007). One practical challenge is that farmers are generally uncomfortable with yield losses from applying extremely low N rates or for residual fertilizer eff ects from applications of both extremely low and high N rates (Kyveryga et al., 2007). Second, conducting spatial analysis and testing for statistically signifi cant interactions between the eff ect of N and site-specifi c soil characteristics on corn yield have not yet become a mainstream procedure for practicing agronomists. Despite the intensive research done across the Midwest (Mamo et al., 2003; Massey et al., 2008; Scharf et al., 2005), there has been limited success for identifying site-specifi c factors that can be used for VRN applications in rainfed corn production in Iowa (Blackmer and White, 1998; Kyveryga et al., 2009).

A common approach is to create so-called N management zones based on spatial variables known to aff ect corn yields (Fridgen et al., 2004; Schepers et al., 2004). Because soils usually supply more than half of the N taken up by corn plants (Martens et al., 2006; Mulvaney et al., 2001), soil organic matter content, elevation, slope, ECa, and digital soil maps are oft en considered as factors guiding the classifi cation of fi elds into N management zones (Derby et al., 2007; Kitchen et al., 2003). While eff ects of topography on grain yields have been

ABSTRACTDespite growing interests in variable-rate nitrogen (VRN) fertilizer applications, we still lack basic knowledge and practical methodol-

ogy for identifying major factors that can be used to guide VRN application to corn (Zea mays L.). Th e objective was to develop a meth-

odology for identifying a predictable relationship between economic yield response (YR) to N and commonly measured soil and terrain

attributes in the presence of spatial dependence. Six 30-ha no-till fi elds in central Iowa were studied during 6 yr. Urea-ammonium

nitrate solution was sidedressed at 112 and 140 kg N ha−1 in alternating strips replicated from 10 to 22 times. Yield responses to the high

rate were calculated in a 20 by 25 m grid pattern and classifi ed into profi table and nonprofi table categories within each fi eld. Autolo-

gistic models were used to identify which (if any) of the following factors economically aff ected YR: elevation, apparent soil electrical

conductivity (ECa), slope, topographic wetness index (TWI), or digital soil map units. Signifi cant eff ects of some of the factors were

found within 8 of 15 site-years. Within fi ve of these site-years, well-drained areas with lower ECa and TWI, and higher elevation and

slope had the higher probability of profi table YR, but these eff ects were not stable over time. Within the proposed methodology, a high

spatial resolution of YR is used that increases the ability to identify areas profi table to N, and farmers can explore VRN possibilities by

applying a small fertilizer increment below or above a uniform optimal rate in many alternating strips across fi elds.

P.M. Kyveryga, T.M. Blackmer, On-Farm Network, Iowa Soybean Assoc., 1255 SW Prairie Trail Parkway, Ankeny, IA 50023; P.C. Caragea, Dep. of Statistics, Iowa State Univ., Ames, IA, 50011. Received 29 Sept. 2010. Corresponding author (pkyveryga@iasoybeans.com).

Abbreviations: ECa; apparent soil electrical conductivity; EONR, economic optimum nitrogen rate; Rel. Elev.; relative elevation; TWI, topographic wetness index; VRN, variable rate nitrogen; YR, yield response.

Published May, 2011

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extensively studied (Brock et al., 2005; Jaynes et al., 2003; Kravchenko and Bullock, 2000), there is little information about causal relationships between YR to N and site-specifi c factors (Schmidt et al., 2007). In fact, factors that aff ect yield levels within fi elds do not necessarily aff ect YR to N, which makes it diffi cult to develop a reliable decision support system that can help guide where to increase or decrease N fertilizer rates based on soil and terrain properties.

To develop a practical methodology for testing the feasibility of VRN applications, studies should have suffi cient data and spatial resolution of N fertilizer treatments to identify factors that can predict YRs. With the advent of on-the-go sensors, it becomes less expensive to collect data on soil and terrain attributes. Moreover, new technologies such as light detection and ranging (LIDAR) can help create low-cost, high spatial resolution, and highly accu-rate digital elevation models. Terrain attributes derived from such data are becoming freely available to the general public in several states. Th ere is a great potential for using these data in site-specifi c N management (Moiling et al., 2005).

Temporal variability in YR to N fertilizer is also diffi cult to study. Th e experimental design should consider conducting on-farm experiments over several growing seasons to account for large temporal variation in weather. Few studies have attempted to study simultaneously the spatial and temporal variability in YR and the eff ects of site-specifi c soil character-istics on YR (Kahabka et al., 2004; Liu et al., 2006). As fi elds and farm implements grow larger and many fi elds show marked spatial variability in soil properties and previous management history, the ultimate goal is to establish relationships between YRs and soil and terrain characteristics. Currently, Iowa farm-ers have the ability and are well trained to conduct their own on-farm fi eld-scale evaluations by applying various fertilizer treatments, measuring YR to these treatments, and collecting site-specifi c information at a relatively low cost (Blackmer and Kyveryga, 2010). Th e practical question is oft en focused on whether farmers can explore VRN application possibilities by applying a small fertilizer increment below or above a uniform optimal rate in many alternating strips across their fi elds.

Th e objective of this study was to implement a method that can identify a predictable relationship between economic YR to N and commonly measured soil and terrain attributes in the presence of spatial dependence when N fertilizer was applied to corn at two near-optimal rates.

MATERIALS AND METHODSTh is study included 15 site-years within six 25- to 32-ha no-till

fi elds that were located in central Iowa and planted to corn aft er soybean [Glycine max (L). Merr.] during a 6-yr period, from 2004 to 2009. Th e fi elds received two N fertilizer rates (112 and 140 kg N ha−1) applied in alternating strips and replicated from 10 to 22 times, covering nearly all of each fi eld (Fig. 1A). All strips were 12-row wide going the full length of each fi eld, and were fertilized with urea-ammonium nitrate solution injected into the soil when corn was at V3 to V5 growth stage (Ritchie et al., 1993). Th e corn was planted in rows 76-cm apart in mid- or late April during each year. Th e fi elds were managed by the same farmer, with all management practices within the fi elds and over the years relatively constant, except the corn hybrids planted. Th e majority of the hybrids were Pioneer with LibertyLink traits.

Th e fertilizer strips were harvested using a six-row com-bine equipped with a GPS and a yield monitor that recorded yields at 1-s intervals. Th e time for grain fl ow delay within the combine was set as 12 or 14 s when exporting yield data using Ag Leader SMS 7.0–8.5 soft ware (Ag Leader Technol., Ames, IA). Yield data were cleaned by removing all points that were located <30 or 50 m from the beginning and the end of the fi elds. Additional observations were removed around waterways, grass buff ers or fl ooded areas based on late-season digital color and near-infrared aerial imagery taken in late August or early September (Kyveryga et al., 2010). Yield observations associated with extreme grain moisture and combine speed that were two standard deviations below and above the means were considered as outliers and were also eliminated from further calculation.

Individual yield observations were grouped within each fertilizer rate (12 corn rows) into 20 m wide and 25 m long grid cells (Fig. 1C). Th e fi elds had from 276 to 609 grid cells. On average, each grid cell had from 30 to 35 individual yield observations for each N rate. Grid cells with <15 observations (about 1–2% from the total) were removed from the analysis. Th e average aggregated yield was calculated for each cell, sepa-rately, for each of the fertilizer rates. Yield responses to the high N rate in each grid cell were calculated as diff erences between the aggregated yield values at the high (140 kg N ha−1) and low (112 kg N ha−1) fertilizer rates (Fig. 1B and 1C). Th e X and Y coordinates for the aggregated YR were assigned at the center between the two fertilizer strips within each grid cell (Fig. 1C).

We used the long-term average corn and fertilizer prices at which 0.20 Mg of corn grain was considered enough to cover the cost of the additional 28 kg N ha−1 to classify YR to the higher N rate in each cell as profi table and nonprofi table. Expressing YR as two categories was consistent with the com-mon practice that farmers use to make their VRN decisions: applying or not applying a small fertilizer increment above or below a given uniform reference or normal N rate. We selected the 140 kg ha−1 N rate as a reference value because past obser-vations conducted on the same farm have shown that a uniform

Fig. 1. (A) An example of a 30-ha corn field with replicated N fertilizer strips applied at 112 kg N ha–1 (gray) and 140 kg N ha–1 (black); (B) calculated yield responses (YR) to the high N rate expressed as profitable (black) and nonprofitable (gray) categories; (C) a 20 by 25 m grid cell with individual yield monitor observations.

798 Agronomy Journa l • Volume 103, Issue 3 • 2011

EONR for these fi elds for corn aft er soybean was in a range from 112 to 168 kg N ha−1 (Kyveryga et al., 2009).

Classifying YR into two economic categories has the advan-tage to eliminate possible problems related to the cell aggregation procedure described above. Such problems may occur due to diff erences in corn plant density, weed and insect pressure, soil compaction, combine speed, yield monitor malfunctions, etc. In addition, studying only two near-optimal N rates and calculating YR in each grid cell reduced the need to test for possible statistical interactions between the treatment eff ect (i.e., N rates) and eff ects of soil and terrain attributes on corn yield. Th e disadvantage of using the binary YR was that more accurate estimations of YR within fi elds could be useful when quantifying the amount of N that is supplied or lost from the soil in any given year.

Spatially interpolated (4-km grids) monthly rainfall data for each site-year were received from the Iowa Environmen-tal Mesonet, Agronomy Department, Iowa State University (http://mesonet.agron.iastate.edu/rainfall). Because of the close proximity (<10 km in radius) and the relatively small variation among the fi elds, the rainfall data were analyzed as means for the fi elds studied in each year.

Terrain and Soil Attributes

Apparent soil electrical conductivity was collected by using a Geonics EM-38 unit (Geonics Ltd, Mississauga, ON, Canada). Elevation data were collected by using a kinematic DGPS receiver (Magellan Corp, Santa Clara, CA). Both ECa and elevation data were collected by driving 7-m wide transects within each fi eld in early spring of 2004 before planting. To calculate slope values, the elevation data were interpolated using the inverse-distance algorithm of ArcViev 3.3 soft ware (Environ. Syst. Res. Inst., Redlands, CA). Topographic wetness index (TWI) values were calculated using Terrain Analysis extension of ArcView. Topographic wetness index shows the spatial distribution of soil moisture within fi elds, potential surface runoff , ponding water, or water saturation aft er heavy rainfalls (Beven and Kirkby, 1979).

Digital soil maps were downloaded from the Iowa Depart-ment of Natural Recourses. Th e soils in these fi elds were from two common soil associations of central Iowa: Clarion–Nicol-let–Webster association (Clarion: fi ne-loamy, mixed, superac-tive, mesic Typic Hapludolls; Nicollet: fi ne-loamy, mixed, superactive, mesic Aquic Hapludolls; Webster: fi ne-loamy, mixed, superactive, mesic Typic Endoaquolls) and Canisteo–Nicollet–Webster association (Canisteo: fi ne-loamy, mixed, superactive, calcareous, mesic Typic Endoaquolls). All soil and terrain attributes were aggregated at the same grid cell size (20 by 25 m) as the yield observations. Elevation data within a fi eld were expressed as the relative elevation (Rel. Elev.) by subtract-ing the minimum elevation from each elevation point.

Categorical Spatial Statistical Analysis

Autologistic statistical regressions were used to model the spatial structure in corn YR expressed as a georeferenced binary response variable (a value of 1 is assigned if a cell is deemed profi table and 0 otherwise) and to identify the eff ects of spatial covariates such as Rel. Elev., ECa, slope, TWI, digital soil map units, as well as the yield of previous corn crop. Autologistic models belong to a family of logistic models that are used to predict the probability of occurrence of binary categorical

events while simultaneously modeling spatial dependence in the categorical response variable. Th e autologistic models in our study predicted the probability of obtaining a profi table YR to the additional fertilizer. Th e prefi x “auto” indicates that these logistic models address statistical dependence by esti-mating how much the categorical response in one grid cell is aff ected by the response situated at the surrounding, neigh-borhood grid cells. For a given location Si = (Ui, Vi) with U indicating the horizontal position and V indicating the vertical position, the general unidirectional autologistic model with covariates as stated by Caragea and Kaiser (2009) is of the form

e[x( ) ][y( ),x( )] x( ) ( )

1 e[x( ) ]j i

TjT

i i i i i j j Tjs N

sA N s s y ssÎ

ì üï= + h - ýí +ï þîå β

ββ

[1]

Here Ai is a natural parameter function, Ni is a set of neighbors, x(Si) is a spatial covariate, ηij are statistical dependence parameters, and β is a vector of parameters or coeffi cients of the logistic regres-sion relating spatial covariates to the binary economic YR. Because preliminary visual observations of economic YR showed larger spatial dependence (correlation) along corn rows than across them (Fig. 1), spatial dependence parameters were estimated for two directions: along and across (perpendicular to) rows.

Th e autologistic model used in this study permitted to match the large-scale (a spatial trend) model structure with the mar-ginal structure (small scale controlled by variance or covariance) in the observed data (Caragea and Kaiser, 2009). Th is feature made interpolation of model parameters consistent over a wide range of spatial dependencies observed in data. Th e model, by its construction, accounts for the eff ect of the various covariates while leaving all other structures that cannot be explained by the covariates to be modeled as spatial dependence. Th e general idea behind the autologistic model is that it places the systematic large-scale structure in the marginal mean, while the small-scale structure is modeled via spatial dependence.

Four nearest neighbors, two grid cells along the rows and two grid cells across the rows, were used to account for spatial depen-dence in the binary YR observations. Neighborhood matrices were calculated based on a distance of 35 m from the center of each cell. Estimation of model parameters was performed using the maxi-mum pseudo-likelihood procedure proposed by Besag (1974).

Eff ects of covariates on economic YR in autologistic models were evaluated by testing the eff ect of one covariate at a time or testing the eff ects of three or four covariates simultaneously. Covariates that had signifi cant eff ects on binary economic YR were preliminarily selected based on the largest t ratios (i.e., ratios between estimated model parameters and the corresponding standard errors) and based on the lowest mean square diff erence between the observed and the predicted probabilities. Because standard errors calculated from the pseudo-likelihood function are not accurate, we used the parametric bootstrap approach to obtain more appropriate standard error estimates for model parameters. Total 2000 datasets based on estimated autologistic model param-eters were simulated using a Gibbs sampler algorithm, separated by two iterations to avoid serial correlations, and a burn-in period of 100. Th e statistical signifi cance of the model parameters was determined based on 90 and 95% percentile confi dence intervals from the simulated datasets. Th e criteria for selecting signifi cant covariates were the same for each fi eld in each year.

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Th e predictive accuracy of autologistic models was assessed by calculating the percentage of correctly predicted binary eco-nomic YR [i.e., the percentage of grid cells correctly predicted as profi table (diagnostic sensitivity), and the percentage of grid cells correctly predicted as nonprofi table (diagnostic specifi c-ity)]. A cut point for the probability that separates a profi table from a nonprofi table YR was selected as 0.51. Th e predictive accuracy was calculated by constructing two-way contingency tables for the observed and predicted events. Th e Cohen Kappa Index (Cohen, 1960) was calculated to make adjustments for the random chance in the agreement between the observed and predicted binary economic YR. Th e Cohen Kappa Index compares the agreement against what might be expected by a random chance. All calculations in this study were done using the statistical soft ware R (R Development Core Team, 2004). Distances for the neighborhood matrices were calculated using Spatstat (Baddleley and Turner, 2005) and Cohen Kappa Index using Concord (Lemon and Fellows, 2009) packages of the R.

RESULTS AND DISCUSSIONMean monthly rainfalls for each year of the study and mean

monthly rainfalls for the last 30-yr are shown in Fig. 2. Rainfall amounts observed in May, right before N fertilizer applications, and in June, right aft er N applications, are the most interest. Because urea-ammonium nitrate solution (UAN) has 25% of nitrate-N and 50% of urea-N and the urea form rapidly converts to ammonium and then to nitrate in the soil, above average rainfall aft er UAN is sidedressed can cause substantial nitrate losses through leaching or dentrifi cation. Except in 2008 and 2005, rainfall in June was below or at the 30-yr averages. Rainfall amounts in May, June, and July in 2008 were twice of the 30-yr mean monthly rainfall. However, rainfalls in May and June in 2006 were only about one-fourth of the long-term averages.

Th e fi elds included in this study had a typical range in varia-tion for soil and terrain properties for central Iowa. Table 1 shows means, standard deviations, and ranges for elevation, ECa, slope, and TWI values. Th e diff erence between the maxi-mum and minimum values in the fi elds was 5.1 to 11.1 m for elevation, 22.5 to 39.8 of mS m–1 for ECa, 10.4 to 26.6% for slope, and 2.6 to 6.4 ln ratios for TWI. Each fi eld had at least one spatial variable that had a relatively large range or standard deviation for the measured soil and terrain properties.

Th e high N rate increased corn grain yield in 14 of 15 fi elds when considering mean YR, and in 13 fi elds when considering median YR (Fig. 3). Both statistics were calculated using from 276 to 609 grid cells within each fi eld. Although on average the high N rate was not profi table to apply within fi ve fi elds where means were <0.20 Mg ha−1, a preliminary analysis showed that some areas within these fi elds had YR large enough to justify application of the additional N. Interquartile ranges in YR (i.e., ranges between 25th and 75th percentiles) also indicated large spatial variability.

Th e mean and median YR varied among the fi elds within each year (Fig. 3), but they varied less among the years of the study. Only one fi eld in 2004 and two fi elds in 2008 had a mean YR>0.5 Mg ha−1. Both 2004 and 2008 growing seasons had above-average amount of rainfall (Fig. 2) that could have increased N losses from the soil. Th ese observations also sug-gest that rainfall had some eff ects on YR, however, temporal variability in YR was relatively smaller than spatial variability.

Applying fertilizer treatments just before the time plants began intensively taking up fertilizer N probably reduced potential N losses, and therefore, helped to focus this study on the spatial variability in YR attributed to the supply of N from the soil.

Spatial Variability in Economic Yield Response

Some variability in YR observed in Fig. 3 could be due to potential eff ects of other factors on YR, other than N supply, when comparing aggregated yield values of the two N fertilizer rates applied within each grid cell. Th us, a YR<0.20 Mg ha−1 was classifi ed as nonprofi table and a YR>0.20 Mg ha−1 was classi-fi ed as profi table by considering the long-term average corn grain price ($112 Mg−1) and fertilizer price ($0.80 kg−1 of N).

Fig. 2. Average monthly rainfall for each year of the study and 30-yr average rainfall.

Table 1. Summary statistics for soil and terrain attributes measured within six fi elds.

Field Statistics Elevation ECa† Slope TWI‡m mS m–1 % ln ratio

N Mean 307 31.4 3.7 7.7SD 1.2 5.8 1.8 0.6

Range 5.1 30.0 12.7 3.5

S Mean 307 32.3 3.3 7.7SD 2.0 7.3 1.9 0.7

Range 7.2 37.3 10.5 4.7

R Mean 315 34.5 5.0 7.4SD 1.7 7.1 2.5 0.52

Range 8.0 34.5 11.9 2.6

RT Mean 291 23.5 3.6 7.7SD 1.9 5.09 1.7 0.50

Range 8.1 28.6 10.4 6.4

G Mean 308 29.1 4.5 7.6SD 1.1 9.3 2.6 0.92

Range 5.6 39.8 12.5 5.2

B Mean 305 23.5 4.3 7.6SD 1.5 4.0 3.0 0.76

Range 11.1 22.5 26.6 4.4† ECa, apparent soil electrical conductivity.‡ TWI, topographic wetness index.

800 Agronomy Journa l • Volume 103, Issue 3 • 2011

Large spatial variability in YR expressed as profi table and non-profi table within 15 fi elds is shown in Fig. 4. Because of the strong spatial dependence in directions at which the fi elds were planted and harvested, we used autologistic models that had spatial param-eters calculated for two directions: along and across (perpendicular to) corn rows. Table 2 shows parameter estimates for the autologis-tic models of the eight fi elds at which we identifi ed statistically sig-nifi cant covariates. Th e magnitude of spatial dependence along the

rows was from three to six times larger than that across the rows. Th e larger spatial dependence along the rows could be partially attributed to the delay in grain movement within the combine when harvesting fi eld strips (Arslan and Colvin, 2002).

Th e estimated parameters of the autologistic model (Table 2) show how the increase in values of covariates by one unit changes the probability of getting a profi table YR at a given location. Positive model parameters indicate the increased probability in economic YR while negative model param-eters indicate the decreased probability in economic YR. For example, TWI was a signifi cant factor within the fi eld 2004-S and 2005-RT. Because of the negative model parameter, areas having lower TWI values within both fi elds were more likely to have profi table YR. In the 2004-S fi eld, with each unit increase of TWI the probability of profi table YR decreased by 0.48 times [i.e., e (−0.72) = 0.48]. Th e low TWI areas are usually well drained, with higher slope and higher Rel. Elev, and with shallow soils having lower water holding capacity and with plants developing shallow root systems.

Th e eff ect of soil ECa on economic YR was not consistent among fi elds. For example, it was profi table to increase N rate within areas with higher ECa values within one fi eld (2007-B) and with lower ECa values within the other fi eld (2006-R) (Table 2). Th e higher ECa values usually correspond to the higher clay, higher soil moisture or higher soil organic matter content. A previ-ous study in Iowa showed that the most important single factor aff ecting ECa values was soil moisture content among soil clay content, soluble salt concentration, and soil temperature (Brevik

Fig. 3. Distributions of corn yield responses (YR) received from an additional 28 kg N ha–1 applied within 15 site-years. Wishker caps of the box plots show fifth and 95th percentiles and means are shown as dash lines inside the boxes (25th and 75th percentiles).

Fig. 4. Profitable (black) and nonprofitable (gray) yield responses (YR) to the high N fertilizer rate within 15 site-years. Identical letters indicate the same fields studied in different years. Row directions were changed from North–South to West–East in eight fields. The maps were plotted without a defined scale.

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et al., 2006). During dry years, corn plants can deplete available water within high sloping and high elevation areas. Th is was unlikely in our study because the fi elds studied were under no-till system for the past 17 yr, and one of the common benefi ts of no-till is to conserve water and improve soil moisture regime.

Th e eff ect of Rel. Elev. was signifi cant within two fi elds. Th e additional N was profi table within areas with higher Rel. Elev. in the 2004-R and with lower Rel. Elev. in the 2009-RT (Table 2).

Digital soil map units were found to have no signifi cant eff ects on economic YR in all fi elds (data not shown). However, using the existing digital soil maps is attractive because they are readily available without the additional cost for collecting this informa-tion. Th e accuracy of soil maps is oft en questionable. For exam-ple, ECa maps matched well digital soil map units in some fi elds but they matched poorly in other (data not shown). Th e fi nding that the soil map units had little eff ect on YR is consistent with the previous study conducted in Iowa (Karlen et al., 2005).

While diff erent factors tended to control spatial variability in economic YRs within eight fi elds, some general relationships could be observed. For example, the higher probability of eco-nomic YR was observed in well-drained areas that do not tend to fl ood or pond (lower TWI values) because the signs of the model parameters for TWI were negative. It is oft en observed that these areas and areas with higher Rel. Elev. tend to have higher yield levels in years with above-average rainfall (Kaspar et al., 2004). Including corn grain yield from the previous growing seasons as a covariate in the autologistic models provided no improvements in predicting economic YR in all fi elds (data not shown). It is likely that the larger YR within higher elevation and well-drained areas was more attributed to higher leaching potential, smaller supply of soil-derived N, and smaller plant root depth rather than to the corn yield potentials or corn N uptake. A

study in Illinois, for example, reported higher yields but smaller YRs in well-drained areas within corn fi elds (Ruff o et al., 2006).

Th e partial eff ect of soil and terrain covariates on economic YR may be attributed to the eff ect of soil organic matter on sup-ply of N to the plants. Including densely measured soil organic matter and total soil N content as covariates in the autologistic model for the 2007-G fi eld did not improve the prediction of economic YR (data not shown). Measuring soil organic matter content would be desirable within the remaining fi elds. How-ever, soil maps in central Iowa usually capture the majority of variability in soil organic matter because soil map units had been mapped using the topography features and historical aerial imag-ery of the soil surface (Iowa Cooperating Soil Survey, 2003)

Predicting Probability of Economic Yield Response

Predictive accuracy of autologistic models that detected signifi cant soil and terrain covariates within eight site-years is shown in Table 3, and predicted economic YR based on the autologistic models described in Table 2 are shown in Fig. 5. Observed probabilities were compared with predicted probabili-ties in each grid cell. If the predicted probability was >0.51, then the grid cells were assigned the value 1, meaning that the high N rate was profi table. Th e predictive accuracy ranged from 68 to 81%, which was relatively good for considering that the percent-age of correct classifi cation equal or <50% would be due to the random chance rather than the eff ects of the covariates.

Th e percentage agreement between the observed and pre-dicted categories measured by the Cohen Kappa Index ranged from a moderate agreement (<0.60) to a substantial agreement (>0.60) (Table 3). Th is suggests that one spatial factor could be suffi cient to model spatial variability in economic YR within fi elds that showed signifi cant eff ects of terrain and soil proper-

Table 2. Parameter estimates and their corresponding parametric bootstrap standard deviations for autologistic models that were used to identify the probability of receiving profi table yield response (YR) to an additional 28 kg N ha–1 applied within eight fi elds based on soil and terrain attributes.

Year-site Intercept Covariate Spatial dependence parameter

Rel. Elev.† ECa‡ Slope TWI§ Along rows Across rows2004-S 7.94** –0.72** 3.10** –0.72

(1.83)¶ (0.24) (0.56) (0.61)2004-R –0.64** 0.19* 2.21** –0.58

(0.31) (0.082) (0.47) (0.53)2005-RT 4.99** –0.59* 2.67** –0.36

(2.64) (0.32) (0.45) (0.48)2006-N 1.39** –0.55* 2.77** 0.54

(0.46) (0.30) (0.39) (0.40)2006-R –1.05** –0.050** 1.90** 0.22

(0.50) (0.018) (0.45) (0.56)2007-B –4.41** 0.18** 3.24** 1.17**

(1.56) (0.065) (0.38) (0.35)2008-S –2.18** 0.41** 3.33** 0.69*

(0.56) (0.12) (0.42) (0.39)2009-RT 1.28** –2.0* 2.74** –1.23

(0.33) (0.70) (0.42) (0.76)* Signifi cant at P < 0.10 based on the simulated 90 percentile bootstrap confi dence intervals.** Signifi cant at P < 0.05 based on the simulated 95 percentile bootstrap confi dence intervals.† Rel. Elev., relative elevation.‡ EC, apparent soil electrical conductivity.§TWI, topographic wetness index.¶ Data in parentheses are standard deviations computed using parametric bootstrap.

802 Agronomy Journa l • Volume 103, Issue 3 • 2011

ties. Th is is desirable because of high multi-collinearity among some covariates within some fi elds.

Temporal Variability in Economic Yield Response

Fields coded as N, S, R, and RT were studied during three corn growing seasons to evaluate temporal variability in economic YR and the eff ects of covariates (Fig. 4). Field B was studied during two growing seasons, in 2007 and 2009. Unfortunately, none of the fi elds had the same signifi cant factors aff ecting economic YR over time (Table 2). However, the signifi cant covariates were interre-lated within two of the eight fi elds (Table 2). Within Field S, it was profi table to apply the extra N within areas with lower TWI values in 2004 while it was profi table to apply the extra N within higher sloping areas in 2006 (Table 2). Visual observations of TWI and slope maps showed that the high sloping areas matched lower TWI areas within Field S (data not shown). However, it is not always reasonable to expect that low TWI areas would correspond to high ground or relatively high elevation areas. Within some fi elds, fl ooding oft en occurs within high relief areas, where small or closed depressions are formed due to low permeability of subsoil layers.

For Field R, profi table YRs were more likely within areas with higher Rel. Elev. values in 2004 and within areas with lower ECa values in 2006 (Fig. 4). Within this fi eld, ECa values were negatively correlated with Rel. Elev. values (r = –0.79). But, the size of the area predicted as profi table for Fields S and R were not the same during the 2 yr (Fig. 5).

For Field RT, the eff ect of TWI in 2005 and the eff ect of Rel. Elev. in 2009 on profi table YR was negative (Table 2). But the areas with lower TWI values usually correspond to areas with higher, not lower, Rel. Elev. values. Fields N and B showed no evidence that the observed eff ects of the covariates were stable over time.

Th e lack of consistency in the eff ects of soil and terrain attributes on economic YR over time is an important problem that needs to be studied and discussed more (Kahabka et al., 2004; Liu et al., 2006). Compared with small-plot N response studies, the proposed methodology enables to study temporal variability in YR more eff ectively by increasing the resolution of N fertilizer treatments in both space and time.

Economic Benefi ts and Fertilizer Saving

Table 4 shows potential economic benefi ts and fertilizer savings if the additional 28 kg N ha−1 would be applied only to areas that

were predicted as profi table by the autologistic models in Table 3. Partial marginal analysis was done to compare two hypotheti-cal scenarios when the additional N was applied uniformly and variably within the eight site-years. Th e marginal returns were calculated by subtracting the cost of extra N from the value of additional grain produced, and by assuming that the value of 0.2 Mg grain covers the cost of the extra N (28 kg ha−1). Th e largest diff erences between the uniform and variable N rates were found in 2006-N and 2008-S fi elds, $42.23 and $ 52.13 ha−1, respec-tively. Th e uniform application in 2004-R and 2008-S fi elds would produce negative marginal returns of $8.89 and $23.46, respectively. Nitrogen fertilizer saving (Table 4) was inversely related to the percentage area that had economic YR (Table 4). Th e data in Table 4 should be interpreted with caution because we did not consider the cost of collecting elevation and ECa data, although this cost can be considered as fi xed over several years.

An additional analysis showed no substantial changes (compared with Tables 2 and 3) in eff ects of the covariates on economic YR when using various grain and N fertilizer prices (data not shown). For example, a 25% change in the corn/fertil-izer price ratio only slightly decreased or increased the size of the areas with profi table and nonprofi table YRs within the fi elds.

It is noteworthy that the economic benefi ts calculated in Table 4 were not aff ected by the shape of N yield response curves, which are oft en estimated for a wide range of N rates applied in small-plot experiments (Kyveryga et al., 2007). It has been proven that discontinuous N yield response curves (with yield plateaus) will likely show lower potential economic benefi ts from VRN applications than those without yield pla-teaus (Brennan et al., 2007). We think that when identifying EONR in experiments with a wide range of N rates applied, a N response curve that predicts yields is not always suffi cient because it does not consider the eff ects of other factors on YR at diff erent ranges of N fertilization.

While most soil and terrain properties are more or less stable over time, N supply from the soil varies from year to year. Th erefore, on-farm methodology and spatial categorical analy-sis described in this study provide three practical advantages by (i) reducing the risk from extreme over- or underapplications of N fertilizer that enables farmers to implement this meth-odology (ii) increasing spatial and temporal resolution of N fertilizer treatments, and therefore, (iii) increasing the ability

Table 3. Predictive accuracy of autologistic models for predicting economic yield responses (YR) within eight fi elds that showed statistically signifi cant effects of soil and terrain attributes.

Year-site Covariate Correct prediction Sensitivity† Specifi city‡ Area with predicted profi table YR Cohen Kappa Index%

2004-S TWI § 81 90 51 78 0.532004-R Rel. Elev.¶ 68 57 75 40 0.602005-RT TWI 74 84 50 70 0.512006-N Slope 65 87 53 52 0.522006-R ECa # 69 77 54 63 0.482007-B ECa 73 78 66 57 0.622008-S Slope 78 64 78 36 0.722009-RT Rel. Elev. 74 82 58 65 0.55† Sensitivity, the percentage of grid cells correctly predicted as profi table.‡ Specifi city, the percentage of grid cells correctly predicted nonprofi table.§ TWI, topographic wetness index.¶ Rel. Elev., relative elevation.# ECa, apparent soil electrical conductivity.

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to identify areas within fi elds that can be potentially fertilized with two near-optimal N rates. Th e proposed methodology should advance the current eff ort in Iowa that is based on estimating multi-year fi eld average EONR for corn without considering spatial variability in YR to N (Sawyer et al., 2006).

CONCLUSIONSResponsiveness of corn to N fertilizer is profoundly aff ected

by the supply of N from the soil, but this supply is regulated by many complex biological processes and weather. Th is study attempted to develop a practical on-farm methodology for

Fig. 5. Predicted profitable (black) and nonprofitable (gray) yield responses (YR) to the high N fertilizer rate within eight site-years. Identical letters indicate the same fields studied in different years. Row directions were changed from North–South to West–East in three fields. The maps were plotted without a defined scale.

Table 4. Potential economic benefi t and fertilizer saving from using soil and terrain attributes to guide the application of an addi-tional 28 kg N ha –1 uniformly and variably within eight fi elds.

Year-site CovariateNet return

Uniform rate†‡ Variable rate§ Difference (variable minus uniform) Fertilizer saving from 28 kg of N$ ha–1 kg N ha–1

2004-S TWI¶ 52 57 5 62004-R Rel. Elev.# –9 12 21 172005-RT TWI 20 51 32 92006-N Slope 19 60 42 92006-R ECa†† 5 19 15 102007-B ECa 16 33 18 122008-S Slope –23 29 52 182009-RT Rel. Elev. 15 35 20 10

Mean 12 37 26 11† Median yield at 112 kg N ha–1 was used as the baseline for calculations.‡ Based on a median YR received from applying 28 kg N ha–1 uniformly.§ Based on a median YR received from applying 28 kg N ha–1 variably. ¶ TWI, topographic wetness index.# Rel. Elev., relative elevation.†† ECa, apparent soil electrical conductivity.

804 Agronomy Journa l • Volume 103, Issue 3 • 2011

identifying factors aff ecting binary economic (profi table and nonprofi table) YR to N within spatially variable corn fi elds in central Iowa. Th e experimental design was intentionally focused on the near-optimal range of N fertilization to detect the direct eff ects of measured soil and terrain factors on economic YR. Th e use of autologistic models was shown to be eff ective for estimating the probability of economic YR within 15 site-years. We observed strong spatial dependence in economic YR in the direction of corn rows, but signifi cant eff ects of soil and terrain covariates were found only within eight site-years. Within fi ve of these site-years, well-drained areas with lower TWI and ECa, or higher Rel. Elev. and slopes were more likely to have profi table YR. However, the eff ects of these factors were not consistent over time. Th e potential economic benefi ts were moderate from applying the additional N in variable rates based on selected spatial factors within the eight site-years.

ACKNOWLEDGMENTS

The study was funded by the Iowa Soybean Association with soybean checkoff dollars. We are very thankful to James Andrew, a grower, from Jefferson, IA for his participation and long-term commitment to this study. The staff members of the On-Farm Network provided logistics support and collected data. We appreciate valuable comments to the ear-lier versions of this manuscript from Dr. Jun Zhang, Ohio Medi-Medi Statistician, AdvanceMed Corporation, Grove City, OH. We also thank Dr. Brad Van De Woestyne and Dr. Gaylia Ostermeier, currently at John Deere, Agricultural Management Solution, Urbandale, IA for oversee-ing the study during the 2004 and 2005 growing seasons.

REFERENCESArslan, S., and T.S. Colvin. 2002. Grain yield mapping: Yield sensing, yield

reconstruction, and errors. Precis. Agric. 3:135–154.Baddleley, A., and R. Turner. 2005. Spatstat: An R package for analzying sta-

tial point patterns. J. Stat. Soft war. 12:1–42.Balkcom, K.S., A.M. Blackmer, D.J. Hansen, T.F. Morris, and A.P. Mallarino.

2003. Testing soils and cornstalks to evaluate nitrogen management on the watershed scale. J. Environ. Qual. 32:1015–1024.

Besag, J. 1974. Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. Ser. B. Methodol. 36:192–236.

Beven, K.J., and M.J. Kirkby. 1979. A physically based, variable contributing area model of basin hydrology. Hydrol. Sci. Bull. 24:43–69.

Blackmer, A.M., and S.E. White. 1998. Using precision farming technologies to improve management of soil and fertilizer nitrogen. Aust. J. Agric. Res. 49:555–564.

Blackmer, T.M., and P.M. Kyveryga. 2010. A systematic approach for using precision agriculture tools for on-farm evaluations in Iowa. CDROM 135. In R. Khosla (ed.) Proc. 10th Int. Conf. on Precision Agriculture, Denver, CO. 18–21 July. ASA, SSSA, and CSSA, Madison, WI.

Brennan, L.E., M.J. Robertson, N.P. Dalgliesh, and S. Brown. 2007. Pay-off s to zone management in a variable climate: An example of nitrogen fertiliser on wheat. Aust. J. Agric. Res. 58:1046–1058.

Brevik, E., T. Fenton, and A. Lazari. 2006. Soil electrical conductivity as a function of soil water content and implications for soil mapping. Precis. Agric. 7:393–404.

Brock, A., S.M. Brouder, G. Blumhoff , and B.S. Hofmann. 2005. Defi ning yield-based management zones for corn-soybean rotations. Agron. J. 97:1115–1128.

Bullock, D.S., and J. Lowenberg-DeBoer. 2007. Using spatial analysis to study the values of variable rate technology and information. J. Agric. Econ. 58:517–535.

Caragea, P.C., and M.S. Kaiser. 2009. Autogistic models with interpretable parameters. J. Agric. Biol. Environ. Stat. 14:281–300.

Cohen, J. 1960. A coeffi cient of agreement for nominal scales. Educ. Psychol. Meas. 20:37–46.

Derby, N.E., F.X.M. Casey, and D.W. Franzen. 2007. Comparison of nitrogen man-agement zone delineation methods for corn grain yield. Agron. J. 99:405–414.

Fridgen, J.J., N.R. Kitchen, K.A. Sudduth, S.T. Drummond, W.J. Wiebold, and C.W. Fraisse. 2004. Management zone analyst (MZA): Soft ware for subfi eld management zone delineation. Agron. J. 96:100–108.

Hurley, T.M., G.L. Malzer, and B. Kilian. 2004. Estimating site-specifi c nitro-gen crop response functions: A conceptual framework and geostatistical model. Agron. J. 96:1331–1343.

Iowa Cooperating Soil Survey. 2003. Iowa State Univ. Extension and Iowa Dep. of Land Stewardship, and USDA/NRCS. Available at http://icss.agron.iastate.edu/ (accessed 11 Nov. 2010, verifi ed 8 Feb. 2011]. Iowa State Univ., Ames.

Jaynes, D.B., T.C. Kaspar, T.S. Colvin, and D.E. James. 2003. Cluster analysis of spatiotemporal corn yield patterns in an Iowa fi eld. Agron. J. 95:574–586.

Kahabka, J.E., H.M. Van Es, E.J. McCleanahan, and W.J. Cox. 2004. Spatial analysis of maize response to nitrogen fertilizer in central New York. Pre-cis. Agric. 5:463–476.

Karlen, D.L., D.L. Dinnes, D.B. Jaynes, C.R. Hurburgh, C.A. Cambardella, T.S. Colvin, and G.R. Rippke. 2005. Corn response to late-spring nitrogen management in the Walnut Creek Watershed. Agron. J. 97:1054–1061.

Kaspar, T.C., D.J. Pulido, T.E. Fenton, T.S. Colvin, D.L. Karlen, D.B. Jaynes, and D.W. Meek. 2004. Relationship of corn and soybean yield to soil and terrain properties. Agron. J. 96:700–709.

Kay, B.D., A.A. Mahboubi, E.G. Beauchamp, and R.S. Dharmakeerthi. 2006. Integrating soil and weather data to describe variability in plant available nitrogen. Soil Sci. Soc. Am. J. 70:1210–1221.

Kitchen, N.R., S.T. Drummond, E.D. Lund, K.A. Sudduth, and G.W. Buchleiter. 2003. Soil electrical conductivity and topography related to yield for three contrasting soil-crop systems. Agron. J. 95:483–495.

Kravchenko, A.N., and D.G. Bullock. 2000. Correlation of corn and soybean grain yield with topography and soil properties. Agron. J. 92:75–83.

Kyveryga, P.M., A.M. Blackmer, and T.F. Morris. 2007. Disaggregating model bias and variability when calculating economic optimum rates of nitro-gen fertilization for corn. Agron. J. 99:1048–1056.

Kyveryga, P.M., A.M. Blackmer, and J. Zhang. 2009. Characterizing and clas-sifying variability in corn yield response to nitrogen fertilization on sub-fi eld and fi eld scales. Agron. J. 101:269–277.

Kyveryga, P.M., H. Tao, T.F. Morris, and T.M. Blackmer. 2010. Identifi cation of nitrogen management categories by corn stalk nitrate sampling guided by aerial imagery. Agron. J. 102:858–866.

Lemon, J., and I. Fellows. 2009. Concord: Concordance and reliability. R pack-age version 1.4-9. Available at http://cran.r-project.org/web/packages/concord/concord.pdf (verifi ed 9 Feb. 2011). R Development Core Team.

Liu, Y., S.M. Swinton, and N.R. Miller. 2006. Is site-specifi c yield response consistent over time? Does it pay? Am. J. Agric. Econ. 88:471–483.

Mamo, M., G.L. Malzer, D.J. Mulla, D.R. Huggins, and J. Strock. 2003. Spa-tial and temporal variation in economically optimum nitrogen rate for corn. Agron. J. 95:958–964.

Martens, D.A., D.B. Jaynes, T.S. Colvin, T.C. Kaspar, and D.L. Karlen. 2006. Soil organic nitrogen enrichment following soybean in an Iowa corn-soybean rotation. Soil Sci. Soc. Am. J. 70:382–392.

Massey, R.E., D.B. Myers, N.R. Kitchen, and K.A. Sudduth. 2008. Profi tability maps as an input for site-specifi c management decision making. Agron. J. 100:52–59.

Moiling, C.C., J.C. Strikwerda, J.M. Norman, C.A. Rodgers, R. Wayne, C.L.S. Morgan, G.R. Diak, and J.R. Mecikalski. 2005. Distributed run-off formulation designed for a precision agricultural landscape modeling system. J. Am. Water Resour. Assoc. 41:1289–1313.

Mulvaney, R.L., S.A. Khan, and T.R. Ellsworth. 2005. Need for a soil-based approach in managing nitrogen fertilizers for profi table corn production. Soil Sci. Soc. Am. J. 70:172–182.

Mulvaney, R.L., S.A. Khan, R.G. Hoeft , and H.M. Brown. 2001. A soil organic nitrogen fraction that reduces the need for nitrogen fertilization. Soil Sci. Soc. Am. J. 65:1164–1172.

R Development Core Team. 2004. R: A language and environment for statisti-cal computing.

Ritchie, S.W., J.J. Hanway, and G.O. Benson. 1993. How a corn plant develops. Iowa State Ext. Serv. Spec. Rep. 48. Iowa State Univ., Ames.

Ruff o, M., G. Bollero, D. Bullock, and D. Bullock. 2006. Site-specifi c production functions for variable rate corn nitrogen fertilization. Precis. Agric. 7:327–342.

Sawyer, J., E. Nafziger, G. Randall, L. Bundy, G. Rehm, and B. Joern. 2006. Concept and rationale for regional nitrogen rate guidelines for corn. Available at www.extension.iastate.edu/Publications/Pm2015.pdf (veri-fi ed 9 Feb. 2011). Iowa State Univ. Ext., Ames.

Scharf, P.C., N.R. Kitchen, K.A. Sudduth, J.G. Davis, V.C. Hubbard, and J.A. Lory. 2005. Field-scale variability in optimal nitrogen fertilizer rate for corn. Agron. J. 97:452–461.

Schepers, A.R., J.F. Shanahan, M.A. Liebig, J.S. Schepers, S.H. Johnson, and A. Luchiari, Jr. 2004. Appropriateness of management zones for char-acterizing spatial variability of soil properties and irrigated corn yields across years. Agron. J. 96:195–203.

Schmidt, J.P., N. Hong, A. Dellinger, D.B. Beegle, and H. Lin. 2007. Hillslope variability in corn response to nitrogen linked to in-season soil moisture redistribution. Agron. J. 99:229–237.