Nitrous oxide emission reductions from cutting excessive nitrogen fertilizer applications


Farmers may choose to apply nitrogen fertilizer at a rate that exceeds the average ex post agronomically optimal rate when the yield response to nitrogen varies across growing seasons. Negative environmental consequences such as nitrous oxide (N2O) emissions and/or water pollution can result when all the applied nitrogen is not needed by the crop. Here we consider a nonlinear market instrument targeting farmers’ nitrogen use, and by solving for the optimal nitrogen reduction using a model of expected utility of farm profits, we evaluate the induced N2O emission reductions that are consistent with the instrument introduced. The market instrument is nonlinear because of the expected nonlinear relationship between N2O and nitrogen application rates. Our simulations show that, in cases where farmers apply N at rates which exceed recommendations and the N2O response is likely to be non-linear, payments will induce participation in the program and will have a significant impact on both expected and actual N2O emissions without significantly harming expected or actual yields. Failure to consider this nonlinearity would deviate the attention away from N2O pollution because it would require large N reductions (and crop yields) to achieve equivalent N2O abatement.

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Fig. 1


  1. 1.

    The value of 298 is the direct GWP for one molecule of N2O on a mass basis for a 100-year time horizon, relative to one molecule of CO2, which is ascribed a value of 1 by convention.

  2. 2.

    While the majority of the previous and recent evidence points towards a nonlinear curve, there is also evidence that for irrigated corn in Colorado N2O response is highly linear up to 230 kg N/ha (Halvorson et al. 2009, 2014), and that N2O emission factors decrease as N rate increases (Pelster et al. 2011). Kim et al. (2013) in a meta-analysis of 26 published datasets found exponential or hyperbolic responses in 18 datasets, linear in 4, and no response in the rest. Furthermore, Shcherbak et al. (2014) on a global meta-analysis comprising datasets of 78 published studies performed for various crops, soil types, and countries found that the response tends to deviate little from linearity at rates below about 200 kg N/ha.

  3. 3.

    Conditioning on θ implies that optimal N rate, the solution to problem (1), is different if θ changes, making the problem potentially firm-specific. Therefore, the model is general enough and contemplates as a special case the situation observed in practice where implementation of these type of schemes rely on protocols using a regional N2O-N response curve (Millar et al. 2012, 2013; and CAR 2013).

  4. 4.

    Other inputs apart from N are not included in the profit function as they remain constant in the optimization problem. While some substitution between inputs is likely to occur in practice, the objective of this analysis is to focus on N optimal application decision.

  5. 5.

    In the next section we remove the linearity and independence assumptions and solve the expected utility problem under risk aversion and correlated random deviates of yield and prices.

  6. 6.


  7. 7.

    Indirect emissions consist of indirect N2O emissions produced from atmospheric deposition of N volatilized, as well as N2O emissions produced from leaching and runoff of N, both as a result of N applications at the project site.

  8. 8.

    Offset payments computed based on ϕ underestimate price signals to farmers because the damage function and payment structure do not include abatement of other externalities caused by N application reductions such as the contribution to water pollution of runoff and leached N as well as other indirect effects on human health.

  9. 9.

    Sensitivity analysis on parameter θ is cumbersome because it requires knowing each curve’s direction of change. Many situations may occur, but for example, N applications (and N2O emissions) will decrease if  ϕ′(N; θ) curve shifts up and the marginal value product curve shifts down.

  10. 10.

    In the previous section, for exposition, we assumed a farmer who maximizes under a linear utility. In what follows, we assume a utility that can accommodate different degrees of risk aversion. However results are very similar for different risk aversion levels.

  11. 11.

    Conditioning parameters of f(y|N; θ) and ϕ(N; θ) are omitted in the rest of the paper to save notation.

  12. 12.

    Similarly, to save notation we omit the conditioning parameter θ in ϕ(N; θ).

  13. 13.

    The Climate Action Reserve (CAR) is currently evaluating its adoption.

  14. 14.


  15. 15.


  16. 16.

    This curve is representative of the North-Central region of the United States, which includes the State of Iowa. Therefore, the value of θ in e(N, θ), omitted to ease notation, is set at the average over the firms’ values in the mentioned region.

  17. 17.

    The Intergovernmental Panel on Climate Change (IPCC) assumes that N2O emissions are a constant proportion of 1.00 +/− 1 % of N applications (IPCC 2006).

  18. 18.

    The rationale of this assumption is that if we average a farmer’s emission reductions over several years, they will be consistent with the incentive payment received in each year.

  19. 19.

    Conclusions are conditional on the representativeness of this dataset of Iowa agronomic and weather conditions.

  20. 20.

    Nitrogen application rates were not updated because average Iowa N rates remained relatively the same in the period (only 6 % increase) and do not have a clear pattern of behavior, as compared to the 51 % increase of yields around a linear trend.

  21. 21.

    We selected two levels of correlation; one negative based on historical observed correlation between corn yields and prices, and one positive for sensitivity analysis purposes. Negative correlation would exist because when corn prices increase, farmers have the incentive to plant more corn, substituting land away from other uses. If that new corn land is of lower productivity, we can expect a yield decrease. However, positive correlation might occur if higher prices induce changes in management practices with the objective of obtaining higher yields (using high-yielding seeds, higher seed density, different type of fertilizers and/or herbicides).

  22. 22.

    The risk premium (RP) is the dollar amount an individual is willing to pay to avoid a risky bet and receive a certain profit. For our utility function, the risk premium is found to be \( RP=E\left(\tilde{\pi}\right)+\frac{1}{ra} \log \left[E\left({e}^{-ra\tilde{\pi}}\right.\Big)\right.\Big] \).

  23. 23.

    Throughout the estimation we assumed a nitrogen price of $722/ton N, equivalent to $0.44/lb N suggested by Iowa State University Extension Services for continuous corn (Duffy 2014). A higher price of N fertilizer relative to corn price induces the participating farmer to optimally make larger N application reductions because the savings from the N not applied are relatively bigger.

  24. 24.

    Emissions trading systems with various degrees of development, linkages between them, and a wide range of carbon prices are active in EU, Switzerland, United States (California and the Regional Greenhouse Gas Initiative involving nine Northeast and Mid-Atlantic states), Canada (Alberta and Québec), Kazakhstan, Australia, New Zealand, Japan, and pilots in six regions of China. As of March 2014 this range goes from 4.0 to 12.4 $/ton of CO2 and as high as 168 $/ton of CO2 if carbon taxes are considered (World Bank 2014).

  25. 25.

    Iowa State University Extension Services using the MRTN-based Corn Nitrogen Rate Calculator recommends, for Iowa and for corn and N prices used in this analysis, N application rates between 202 and 231 kg/ha (ISU Extension 2014).

  26. 26.

    The standard error of the emissions curve is: σ e(N) = 0.058 × exp[0.01 × N] (Millar et al. 2010).

  27. 27.

    We solved the model with a positive correlation (ρ = 0.30), and results were very similar.

  28. 28.

    Because end of the cropping season N2O emissions are affected by weather, a distribution of emissions reductions can be simulated by using an emissions curve affected by correlated random draws of temperature and rainfall. This is left for future work.


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The authors thank the David and Lucile Packard Foundation for project funding, and Sergio Lence, Alicia Rosburg, Juan Dubra, and Marcelo Caffera for useful suggestions.

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Correspondence to Francisco Rosas.

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Rosas, F., Babcock, B.A. & Hayes, D.J. Nitrous oxide emission reductions from cutting excessive nitrogen fertilizer applications. Climatic Change 132, 353–367 (2015).

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  • Emission Reduction
  • Risk Premium
  • Output Price
  • Incentive Payment
  • Continuous Corn