Wheat nitrogen response conditional on past yield and rainfall: A step in improving optimal nitrogen applications

Abstract

Making precision nitrogen (N) application clearly profitable will likely require incorporating multiple sources of information. Low-cost sources of information include rainfall and the previous year's yield. This paper uses data from a long-term experiment on the response of winter wheat (Triticum aestivum L.) to N fertilizer, as well as rainfall data from the University of Oklahoma's Mesonet weather station. The goal was to determine optimal topdress levels of N. A regression was used to determine the previous year's yield and rainfall on the marginal product of farmer-applied N. Information from lagged yield and rainfall increases profit by $2.79 ha^–1. Therefore, lagged yield and rainfall could be a low-cost information source to add to other sources of information to achieve the goal of widespread adoption of precision N application.

Core Ideas

•  An alternative to precision sensing is needed to determine optimal N rates for grain crops.
•  A Bayesian analytical approach using yield monitor and rainfall data is suggested.
•  Lagged yield and measures of rainfall improve the estimation of economically optimal N rates.

1 INTRODUCTION

Grain crops such as wheat (Triticum aestivum L.) utilize nitrogen (N) from three primary sources: N that is applied by the farmer, N released throughout the growing season from decomposing residues from previous crops, and soil N carryover from the previous year. Due to uncertainty about available N from sources other than the amount applied, producers do not apply the amount of N that would be optimal if they had complete information.

Precision farming technologies have been developed to reduce this uncertainty and allow applying additional N only when it is needed. Unfortunately, precision N techniques are not typically profitable, such as in precision soil sampling (Hurley et al., 2001; Swinton & Lowenberg-DeBoer, 1998) and precision sensing of the plant (Biermacher et al., 2009; Boyer et al., 2011). Multiple sources of information may be needed to make precision N application profitable.

Yield monitor data were intended to help producers identify areas of low yields within a field and to apply less N to these areas. Yield monitor data alone, however, offer little predictability. In a year with above-average rainfall, low areas of the field can become oversaturated with water or can have N leaching problems, lowering yields. Conversely, in a year with below-average rainfall, these low areas of the field will have higher yields.

There are differing hypotheses on the interaction between yield and N response because of the uncertainty about the amount of N released from organic matter. When wheat yield is high, N removal from the soil will also be high, so more N would be needed in the following year. But high yields also produce more crop residue. As residue decomposes, N is released back into the soil. Soil microorganisms that are breaking down this straw, however, may tie up some N fertilizer, leading to the need for more N (Turley et al., 2003). Furthermore, if mineralization is incomplete, then the N is not released during the growing season and an even greater amount of additional N would be needed (Singh et al., 2004). Since the decomposition is affected by many different factors, such as rainfall and temperature, it can be difficult to accurately predict optimal N rates.

There are also competing hypotheses regarding the effect of rainfall on plant N needs. Rainfall could create greater need for additional N due to the greater yields expected from the rainfall. Also, when N is applied before a heavy rainfall, the rain could cause leaching of N and thus increase the need for additional N. Alternatively, more rainfall could speed the decomposition of organic matter and thus make more N available. Soils have considerable N in the form of organic matter that is normally not available, and decomposition of only a small portion of this organic matter could meet plant needs.

Nitrogen carryover from the previous year is also a source of N in the current year but is often difficult to measure directly. Nitrogen soil tests have proven unreliable. Other studies use simulation routines such as the Environmental Policy Integrated Climate (EPIC) model to estimate N carryover (Stoecker & Onken, 1989), which have not yet been demonstrated to be accurate.

As an alternative (or as an addition) to expensive precision sensing technology, yield data from yield monitors as well as local rainfall data are used to improve estimates of the optimal amount of N that should be applied. Specifically, rainfall is used as a proxy for decomposition of crop residues, and lagged grain yield in year t − 1 is a proxy for N carryover in year t. Note that the model lets the response to N be a function of rainfall rather than just the yield being a function of rainfall. Also, yield monitor data and rainfall data are available at relatively little cost since they are already being collected.

2 MATERIALS AND METHODS

2.1 Experimental databases

This analysis uses data from 1971 to 2015 from a long-term experiment on winter wheat response to N fertilizer. The experiment was conducted at Lahoma, OK, using a randomized complete block design with five N application rates and four replications. Nitrogen rates of 0, 22.42, 44.83, 89.66, and 112.09 kg ha^–1 were applied. Ammonium nitrate (34–0–0) was used as the N source and was applied in October before planting. When the long-term trial was developed, grain producers commonly applied N at the time of planting, in many cases in the form of anhydrous ammonia (82–0–0). Over time, N application recommendations have changed to apply N as a topdress after plant emergence. All N applications in our experiment are preplant; therefore, to make predictions regarding economically optimal topdress N requires assuming a relationship between preplant and topdress N. Boyer et al. (2012) reported a 17% gain in N use efficiency from topdress applications compared with preplant applications.

Core Ideas

•  An alternative to precision sensing is needed to determine optimal N rates for grain crops.
•  A Bayesian analytical approach using yield monitor and rainfall data is suggested.
•  Lagged yield and measures of rainfall improve the estimation of economically optimal N rates.

Wheat was planted in 25.4-cm rows at a seeding rate of 67.25 kg ha^–1. Conventional tillage practices were used, so these results cannot be extrapolated to minimum or zero tillage systems. Further details on this experiment can be seen in OSU (2018).

Rainfall data since 1995 were from the Oklahoma Mesonet weather station at Lahoma, OK, with earlier data from Enid, OK. Rainfall is the cumulative precipitation in millimeters from October to January for each year (averaged 179 mm with measurable precipitation on 20% of days and lows below freezing about half of the time). Note that rainfall data are available to adjust application rates in February for the dual-purpose (grazing and grain) wheat system common to the U.S. southern Great Plains.

2.2 Model

There is no consensus as to which functional form is the best to predict yield (Makowski et al., 1999). Here, a linear stochastic plateau model (Tembo et al. 2008) was estimated using Bayesian methods similar to Brorsen (2013) and Ouedraogo and Brorsen (2018). The model allows the intercept, slope, and plateau to shift due to changes in rainfall and lagged yields. Bayesian methods converge better than maximum likelihood methods with such a nonlinear model. The model estimated was

$$\begin{equation}{Y_{it}} = \min \left( \def\eqcellsep{&}\begin{array}{l} {\beta _0} + {\beta _1}{N_i} + {\beta _2}{Y_{it - 1}} + {\beta _3}{R_t} + {\rm{\ }}{\beta _4}{N_i}{R_t}\\ + {\;\beta _5}{N_i}{Y_{it - 1}},P + {\rho _1}{Y_{it - 1}} + {\rho _2}{R_t} + {v_t} \end{array} \right) + {u_t} + {\varepsilon _{it}}\end{equation}$$(1)

where Y_it is the yield in year t on the ith plot, N_i is the N applied on the ith plot, Y_it-1 is the yield of the previous year, R_t is the cumulative precipitation from October to January of year t, N_iR_t is the interaction between N and rainfall in year t, N_iY_it-1 is the interaction between N applied and the previous year's yield, P is the plateau intercept, v_t ∼ N(0, σ_v²) is the plateau year random effect, u_t ∼ N(0, σ_u²) is the year random effect, and ε_it ∼ N(0, σ_ε²) is a random error term.

In Tembo et al. (2008), the optimal level of N was found by maximizing expected profit:

$$\begin{equation}\mathop {{\rm{max}}}\limits_{N \ge 0} \ \smallint E\pi \left( {N{\rm{|}}{{\theta }}} \right)p\left( {{{\theta }}{\rm{|}}{{X}}} \right){\rm{d}}{{\theta }}\end{equation}$$(2)

where Eπ(N|θ) is the expected profit function with the stochastic plateau, θ = (β₀, ..., β₅, P, ρ₁, ρ₂, σ_v²) is the vector of relevant parameters, and p(θ|X) is the posterior distribution for θ. In this study, the optimum was found by approximating the integral in Equation (2) using Monte Carlo integration:

$$\begin{eqnarray}\mathop {{\rm{max}}}\limits_{N \ge 0} \ \left( {\frac{1}{n}} \right)\ \mathop \sum \limits_{i = 1}^n E\pi (N|{{{\tilde{\bf{\theta }}}}_{{i}}})\end{eqnarray}$$(3)

where $${{ {\tilde{\bf{\theta }}}}_{{i}}}$$= (β_i0, ..., β_i5, P_i, ρ_i1, ρ_i2, σ_v²) is a random vector of the parameters drawn from the posterior distribution.

2.3 Empirical application

Equation (1) was estimated with the MCMC Procedure in SAS V. 9.4 (SAS Institute). The priors were given a large variance and so are noninformative. Using the NLP Procedure in SAS V. 9.4, Equation (3) was solved to find the economically optimum levels of N using a wheat price of $0.184 kg^–1 and a N price of $0.218 kg^–1. An example SAS program can be found in Brorsen (2013).

3 RESULTS AND DISCUSSION

The mean posterior parameter estimates of the model are in Table 1. All of the posterior means for rainfall and N are positive and thus they increase the intercept, slope, and plateau. For lagged yields, the effects that are large relative to posterior standard deviations are on the intercept and plateau. Rainfall, however, has its strongest effect on the slope, indicating that N use efficiency increases with rainfall.

TABLE 1. Posterior parameter estimates for the regression of wheat grain yield (kg ha^-1)

Parameter	Posterior mean	Posterior SD
Intercept	1,510.19	217.15
Nitrogen (kg ha^–1)	5.46	2.10
Lagged yield (kg ha^-1)	0.11	0.04
Rainfall (mm)	0.18	1.08
Rainfall–nitrogen interaction	0.12	0.01
Lagged yield–nitrogen interaction	0.0009	0.0006
Plateau (kg ha^-1)	2,298.31	289.05
Lagged yield plateau shifter	0.23	0.02
Rainfall plateau shifter	0.10	1.52

For rainfall, the intercept increases more than the plateau and the effect on the slope is positive, so increased rainfall will result in lower optimal levels of N. For lagged yield, the plateau increases more than the intercept and the effect on the slope is small, so optimal N would increase with greater lagged yield.

Table 2 shows the value of information gained from using rainfall and lagged yield. Using rainfall and lagged yield increases expected profit by nearly $3 ha^–1 and the amount of N applied goes up by almost 3 kg ha^–1. Thus, small gains can be made using low-cost data that many producers are already collecting.

TABLE 2. Value of information gained from using rainfall and lagged yield

Information scenario	Profit	N rate
	$ ha^−1	kg ha^−1
Using rainfall and lagged yield	439.21	67.17
Without using rainfall and lagged yield	436.42	64.22
Difference	2.79	2.95

4 CONCLUSIONS

Profitable precision N application will likely require multiple sources of information. The economic value from using lagged yields and rainfall is only around $3 ha^–1, but the costs of obtaining this information on a large scale could be low. The long-term goal is to combine the value of this information with other sources such as precision sensing and on-farm experiments (Bullock et al., 2019). Lastly, the data used here were from only one field in Oklahoma, so parameters will need to be estimated for other sites and crops to develop models that are more widely applicable.

ACKNOWLEDGMENTS

Funding was provided by Oklahoma Agricultural Experiment Station and National Institute of Food and Agriculture Hatch Project OKL03170 as well as the A.J. and Susan Jacques chair. The research would also not be possible without the numerous individuals over the years who collected and maintained these data and made them publicly available.

AUTHOR CONTRIBUTIONS

Brian E. Mills: Formal analysis; Methodology; Validation; Writing – original draft. B. Wade Brorsen: Conceptualization; Data curation; Formal analysis; Funding acquisition; Methodology; Project administration; Resources; Supervision; Validation; Writing – review & editing. Emilio Tostão: Conceptualization; Formal analysis; Investigation; Methodology; Validation; Writing – original draft; Writing – review & editing. Jon T. Biermacher: Conceptualization; Writing – review & editing.

CONFLICT OF INTEREST

Authors declare no conflict of interest.