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Nitrogen Management with Abnormal Rainfall

Eseul Choi, Guilherme DePaula, Peter Kyveryga, and Suzanne Fey

Abnormally high rainfall may increase both the uncertainty about nitrogen fertilizer use in agriculture and the discharge of nitrate into water streams. Furthermore, changes in climate may lead to higher variability in rainfall with more frequent abnormal precipitation. In this study, we use experimental data from the Iowa Soybean Association (ISA) to investigate the effects of abnormal rainfall on farm nitrogen management, considering both farmer profitability and the potential for environmental damages.

Figure 1 shows the variation in rainfall in Iowa during 1950–2020. The rainfall variable is the average of total early-season precipitation (May to July) across Iowa fields in our data. Early-season rainfall is particularly relevant for both plant growth and nitrogen leaching. Figure 1 shows that both average rainfall and rainfall variability are increasing. We define abnormally high early-season precipitation as rainfall above the 80th percentile of a distribution for the last 25 years.

Figure 1
Figure 1. Rainfall variability in Iowa (1950–2020).
Note:The rainfall variable is the average of total early-season precipitation (May to July) across fields in the data. The two experiment periods are shaded.
Source: Daymet (2022) and IEM (2021) for data during 1980–2020 and 1950–1979.

We first study how abnormal rainfall changes the relationship between corn yields and nitrogen use. We estimate a corn production function using the target-input model, a quadratic function conveniently transformed to capture the uncertainty in nitrogen application (Foster and Rosenzweig 1995):

Yield = Max Yield - penalty × (optimal nitrogen - actual nitrogen)2

The observed quantity produced is a function of the maximum potential yield using the optimal nitrogen rate and a loss in productivity associated with suboptimal application of nitrogen. The target input model is useful when there is uncertainty about the optimal level of an input such as nitrogen. The penalty captures the yield loss for a deviation from the optimal (maximum-yielding) input level.

We find that the yield penalty doubles with abnormal rainfall. Figure 2 shows our estimates for corn production functions with normal and wet weather for a soybean-corn rotation. The penalty represents the curvature of the production function in the graph. A higher penalty in wet conditions means that an error in application of nitrogen could be more costly in terms of yield losses. The production function also tends to be steeper for lower levels of nitrogen use. This means that nitrogen tends to be more productive in wet conditions.

Figure 2
Figure 2. Corn production function with abnormal rainfall.
Note: We estimate the yield response to nitrogen application using field experimental data that examines 3–5 different levels of nitrogen rates across Iowa from 2017 to 2020. The previous crop is set to soybean. For each field, we define wet weather if May-to-July precipitation exceeded the 80th percentile of the empirical distribution of the previous 25 years.

Nitrogen is a critical input for food production. However, when leached to stream waters, it is also a pollutant; thus, we add the potential environmental damage of nitrate leaching into our analysis of nitrogen management. We use the inverse relation between nitrogen deficiency in cornstalks at the end of the season and nitrogen concentration in streams to approximate the probability of leaching (Balkcom et al. 2003). We estimate the marginal damage of nitrogen as the probability of leaching times the social cost of nitrogen, namely the monetized damage of one additional unit of nitrogen in water. We then combine this marginal environmental damage with the marginal cost of reducing nitrogen use, which we approximate by the lost net revenue of using one unit less of nitrogen for farming. An efficient level of nitrogen use would equate marginal costs and benefits of nitrogen abatement.

The key insight of the analysis is that abnormal rainfall tends to increase the productivity of nitrogen but also the likelihood of environmental damage because of more leaching. Farmers anticipating heavier rains may “insure” against potential yield loss by applying additional nitrogen upfront (Babcock 1992) but subsequently risk more leaching. In the case of wet weather, environmental protection tends to become more costly because the pollutant becomes more productive. Figure 3 illustrates the results for normal and wet weather (calculation summary is in the methods section). Note that excessive nitrogen application is not profitable because nitrogen is costly and has diminishing effects on yields. The marginal cost (profit losses) is steeper with wet weather because nitrogen is more productive. The marginal damage band is wide because of large uncertainty and heterogeneity in damages. However, damages tend to be higher in wet weather because of the higher likelihood of leaching.

Figure 3
Figure 3. Balancing net returns and environmental damages in nitrogen management.
Note:An abatement of zero corresponds to 250 pounds of nitrogen application. The solid line is the marginal cost of abatement, which is forgone net revenue due to additional reduction of nitrogen application. The dashed lines are the lowest and highest marginal benefit of abatement. The marginal benefit of abatement is the environmental damage avoided by reducing one unit of nitrogen application.

The analysis in figure 3 does not account for alternative strategies to manage Nitrogen such as the use of cover crops. It also does not differentiate the timing and form of nitrogen application. These are important topics of continuing research. Particularly because as both nitrogen productivity and potential environmental damages increase with abnormal rainfall, so does the value of alternative adaptation strategies for managing nitrogen.

Summary and methods

We estimate a production function and a probability of nitrogen deficiency function using data from two ISA experiments. The first experiment randomly assigns 3–5 levels of nitrogen in 30 fields from 2017 to 2020. The second experiment randomly adds and removes 50 pounds/acre from the farmer nitrogen rate in 107 fields from 2007 to 2010. ISA records yields and a nitrogen concentration in cornstalks at the end of the season. We estimate the production function using a block fixed-effects model and we estimate the probability of nitrogen deficiency in the cornstalk using a probit model. We use our estimates for the production function and the probability of nitrogen deficiency function to approximate the marginal costs and benefits of nitrogen abatement in the farm. The marginal cost of abatement is the forgone net revenue in the farm due to a unit reduction of nitrogen application. We calculate the net revenue by subtracting the nitrogen cost from total revenue.

The marginal benefit of abatement is the social cost of nitrogen multiplied by the probability of occurrence of nitrogen loss. Table 1 shows the values for each parameter used in the analysis presented in figure 3. We use historical averages for corn and nitrogen prices and estimates for the social cost of nitrogen from the Environmental Protection Agency (2015). The data sources for rainfall are Thornton et. al. (2020) and IEM (2021).

Table 1. Parameter Values Used in Figure 3
Parameter Value
Corn price4
Nitrogen fertilizer price0.4 ($/lb)
Social cost of nitrogen0.15~5.45 ($/lb)
Probability of nitrogen loss0.45 (normal) and 0.57 (wet)
Previous crop in the rotationSoybean
Range of nitrogen rate in the data90–250 lbs


Babcock, B.A. 1992. “The Effects of Uncertainty on Optimal Nitrogen Applications.” Applied Economic Perspectives and Policy 14(2):271–280.

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.” Journal of Environmental Quality 32(3):1015–1024.

Daymet. 2022. “Daily Surface Weather and Climatological Summaries.”

Foster, A.D. and M.R. Rosenzweig. 1995. “Learning by Doing and Learning from Others: Human Capital and Technical Change in Agriculture.” Journal of Political Economy 103(6):1176–1209.

US Environmental Protection Agency (EPA). 2015. “A Compilation of Cost Data Associated with the Impacts and Control of Nutrient Pollution.” Technical Report EPA 820-F-15-096.

Iowa Environmental Mesonet (IEM) of Iowa State University. 2021. IEM Rainfall.

Thornton, M.M., R. Shrestha, Y. Wei, P.E. Thornton, S. Kao, and B.E. Wilson. 2020. Daymet: Daily Surface Weather Data on a 1-km Grid for North America, Version 4. ORNL DAAC, Oak Ridge, Tennessee, USA.

Suggested citation:

Choi, E., G. DePaula, P. Kyveryga, and S. Fey. 2022. "Nitrogen Management with Abnormal Rainfall." Agricultural Policy Review, Spring 2022. Center for Agricultural and Rural Development, Iowa State University. Available at