A tradeoff frontier for global nitrogen use and cereal production

Mueller et al [4] estimated Mitscherlich–Baule (M–B) nitrogen-yield curves and rainfed maximum yields for crop-specific climate zones (100 zones per crop). These curves were parameterized using global data on crop areas and yields [26], fertilizer application [4], irrigated area [27], and climate [28]. Additional bootstrap analyses are performed to provide a 95% CI on the M–B nitrogen response coefficients. We utilize 1000 bootstrap samples per climate zone per crop, and sampling of grid cells is performed in proportion to harvested area. We note that the bootstrapping does not account for spatial autocorrelation, and thus may underestimate uncertainty. Some crop-climate zone combinations in the Mueller et al [4] model lack a unique nitrogen response coefficient; this occurred when adding nitrogen as an explanatory variable did not minimize root-mean square error of the model fit (for example, nitrogen can have weak explanatory power in cases where yields are primarily limited by irrigation or other fertilizer nutrients). In these climate zones the model utilizes average M–B response coefficients across all climates (and upper and lower bound response coefficients from the bootstrapping results) in conjunction with climate-specific minimum and maximum yields to estimate an expected nitrogen-yield response.

Using the crop- and climate-specific nitrogen response curves, we build a tradeoff frontier relating total global production to total global nitrogen fertilizer use. To do this, for each crop we find levels of nitrogen application across all climate zones for each crop that give the same marginal yield response (dY/dN), which simulates maximum production for a total amount of nitrogen. We use 30 dY/dN values from 0.0001 to 2 Mg yield kg⁻¹ N. This exercise results in a series of crop-specific production and nitrogen application maps (simulated at 5 arc min × 5 arc min resolution) for every point on the tradeoff frontier, which are then summed across the globe (using fixed crop areas [26]) to determine total global production and nitrogen consumption per crop. Maximum yields differ between irrigated and rainfed systems, and expansion of irrigation may not be feasible in areas with limited water supplies. Thus, similar calculations are made for a scenario with no changes to irrigated areas, where nitrogen application rate increases stop on rainfed areas when yields reach the rainfed yield ceilings of Mueller et al [4]. These frontier calculations assume other inputs or management practices (e.g. phosphorus and potassium application, cultivar choice, etc) are not limiting yields. Organic and biologically-derived nitrogen sources are not included as drivers of production due to data limitations (see section 4.4), although they can be important sources of fertility.

To aggregate tradeoff frontiers across multiple crops, we keep the observed proportion of nitrogen allocation between crops (circa 2000) fixed, and then add up modeled production at different levels of total nitrogen use. Spline interpolation in MATLAB was used to interpolate between points on the crop-specific curves in order to construct the aggregate curve. Finally, we overlay 1997–2003 nitrogen consumption by crop [4] and 1997–2003 cereal production [26] to assess the current nitrogen use and production situation relative to the modeled frontier. All calculations are performed over the ∼95% of crop harvested area [26] encompassed by the crop-specific climate zones.

Nitrogen balance calculations are carried out using the approach of Foley et al [3], which builds on earlier nutrient balance work for both nitrogen [16, 29] and phosphorus [30]. This method tracks all of the nitrogen inputs (fertilizer [4], manure [31], atmospheric deposition [32], and legume fixation [3]) and outputs (removal of nitrogen in harvested material) spatially for each grid cell. We modify the approach of Foley et al [3] to assess crop-specific nitrogen balances by distributing manure nitrogen between the crops within each grid cell in proportion to the harvested area of each crop. Legume fixation rates are not included, as we only examine cereal crops in this study.

As we build the nitrogen consumption and production frontier, we generate a new nitrogen application rate map and a new yield map for each crop at each point on the curve. These maps are used as inputs to the nitrogen balance model to generate a map of excess nitrogen at every point, which is summed to create the excess nitrogen and production tradeoff frontier.

The tradeoff frontier for nitrogen use and cereal production potential quantifies the large potential for changes to global nitrogen management that both decrease excess nitrogen and increase crop production. While the analysis is not a prescription for any particular management change, it is a 'proof of concept' that changes in the spatial distribution of nitrogen intensity could lead to large production and environmental gains. Comparing spatial patterns of nitrogen application, nitrogen excess, and yield on the frontier relative to the current situation (figures 2–4) provides insight into the direction and magnitude of changes possible to both application rates and production. Pathways to achieve these changes involve a reallocation of nitrogen use intensity: decreases in areas where current nitrogen use is high, and increases in areas where nitrogen use is currently low. In addition, the whole system could and should improve by increasing the agronomic or technological efficiency of N use (see section: Moving the tradeoff frontier), as the models used to construct the tradeoff frontier are calibrated to circa 2000 data.

Moving towards more efficient spatial allocation of nitrogen would likely require substantial changes to infrastructure and markets. For example, many regions in Sub-Saharan Africa with low nutrient use suffer from a combination of high fertilizer prices due to overland transport costs and low per-capita income. In addition, inadequate storage facilities may prevent marketing of increased crop production, further discouraging management for higher productivity [33]. Likewise, reducing nitrogen use in areas of currently high nitrogen use may be politically and economically challenging unless reductions can be done in a way that doesn't hurt farm profits and productivity.

Reallocating nitrogen intensity to both increase production and decrease global excess nitrogen should tend to increase human well-being through several pathways. However, such changes will depend strongly on local conditions and the direction and magnitude of local changes to nitrogen use, and areas with increases in excess nitrogen could see negative impacts.

Increasing crop production in areas with currently low yields could enhance food security and promote economic development. However, while food availability (i.e. crop production) is necessary for access to healthy, safe, and nutritious food, it is not sufficient to ensure food security. Chronic poverty—not food availability—is the primary cause of food insecurity [34]. Income inequality, markets, infrastructure, and institutions also play a major role [35].

Efforts to reallocate nitrogen fertilizer application intensity would decrease N₂O emissions disproportionately to any reduction in nitrogen use, leading to large benefits for climate and stratospheric ozone. This result is due to nonlinear increases in N₂O emissions at high nitrogen application rates, particularly when there are large imbalances between applied and removed nitrogen [36, 37].

Potential human health benefits from decreasing excess nitrogen include decreases in nitrate-contaminated water and improved air quality [5, 7, 8, 19]. Ecosystem recreation value, fishing, and food provision could also benefit from improved water quality and climate change mitigation [8, 38]. Biodiversity, which is important for underpinning myriad ecosystem services, could benefit from improved air and water quality, less severe climate change, and reductions in reactive nitrogen deposition [5, 8]. In contrast, areas where nitrogen use and excess nitrogen increases (such as Eastern Europe, Russia, and Sub-Saharan Africa in the scenario presented by figures 2–4) could experience declines in human well-being through negative impacts on water and air quality.

Though not explicitly modeled here, we expect that efficient spatial allocation of nitrogen use would increase aggregate human well-being by coupling relatively large excess nitrogen reductions in areas of currently high nitrogen use with small to moderate excess nitrogen increases in areas with currently low nitrogen use. However, more information on the relationships between nitrogen-driven ecosystem impacts and human well-being in different regions would substantially aid these analyses. For example, population density in an area, the relationship between nitrogen pollution and fishing productivity, marginal benefits of a reduction in air pollution, and other factors all influence the complex relationships between nitrogen and human well-being in a given region [8]. If future research is able to systematically quantify the costs and benefits (social and private) of agricultural nitrogen use across the globe [e.g. 5, 7, 19], this information would allow greater insight into nitrogen management scenarios that maximize well-being.

The tradeoff frontier presented here should be viewed as a first estimate of potential efficiency gains at a snapshot in time, characterizing production possibilities and tradeoffs with circa 2000 technology and average agronomic efficiencies. Substantial changes to the frontier are possible with improved practices and technologies.

A variety of management techniques could increase on-field nitrogen use efficiency and decrease excess nitrogen. Such strategies are characterized under the '4R Nutrient Stewardship' paradigm, which promotes use of the right fertilizer source with the right application rate, timing of application, and fertilizer placement in order to increase agronomic efficiency [39, 40]. Integrated management systems that incorporate these factors have provided dramatic experimental evidence that substantial increases to agronomic efficiencies are possible [18, 41]. For example, Chen et al [42] were able to double maize yields in the People's Republic of China while completely eliminating mass balance excess nitrogen by applying nitrogen in five split doses with soil testing guiding application rates. While such practices may represent a substitution of labor and technology for nitrogen, increasing adoption of these sophisticated agronomic practices could dramatically push up the tradeoff frontier as illustrated in figure 1.

However, despite the large potential for improving agronomic efficiency, broad trends in observed nitrogen recovery efficiency (a large-scale measure of agronomic efficiency) are relatively flat over time in both developed and developing countries [43]. Developed country efficiencies remain higher than developing country efficiencies. So while there is considerable potential for progress, achieving gains in practice will require overcoming system inertia as well as infrastructure, political, and economic obstacles.

Increasing biologically-derived nitrogen inputs can decrease dependency on chemical nitrogen for fertility, although may not necessarily lead to decreases in excess nitrogen [14]. However, organic inputs are especially critical for replenishing soil carbon [44] and ensuring responsive soils [20]. Appropriate crop rotations, mixed cropping systems, and agroforestry with leguminous trees can replenish soil fertility [33].

Other agronomic improvements, such as appropriate plant population, protection from pests and diseases, and improved seed can also improve field-scale agronomic efficiency and production [14]. Such improvements, and the continued development of crop varieties with higher yield potentials, would contribute to future shifts in the frontier. In addition, landscape management with perennial vegetation can capture runoff, and winter cover crops can reduce reactive nitrogen losses [40].

Future work should quantify how the adoption of practices that improve agronomic efficiency would change the tradeoff frontier and the current nitrogen-production status (i.e. changes to figure 1). Such efforts would benefit from consistent assessments of how global fertilizer use is allocated between different crops over both time and space, detailed records of which are currently very limited.

All models are simplifications of reality, and agricultural management is a complex reality to simulate. Thus, there are a number of limitations and caveats that should be considered when interpreting this work.

The nitrogen-yield response curves utilized in this study estimate the minimum amount of nitrogen needed to determine a given yield circa 2000, and do not represent theoretically optimal agronomic efficiency [e.g. 45]. While the curves were parameterized taking into account possible yield limitation by irrigation, phosphorus, and potassium, frontier nitrogen use as estimated here assumes these inputs (and other management practices, including cultivar choice) are not limiting yields. The curves represent a general yield response for a given range of growing conditions, and are not appropriate for quantifying yield response for specific fields under specific management regimes. Given the scale at which the curves were parameterized, the curves do not capture variability in agronomic efficiency and yield that can occur at fine spatial and temporal scales in response to field-specific management and soil conditions [46, 47]. Likewise, this model only captures yield as a function of applied fertilizer nitrogen, not plant-available soil nitrogen, so it does not simulate indigenous nitrogen supply or how that stock may change between years or with specific cropping systems or soil conditions. Furthermore, we ignore the impact of biologically derived (i.e. organic) nitrogen on yield, focusing on inorganic fertilizer in this initial study (further discussion below regarding manure).

The bootstrapping analysis provides an estimate of uncertainty in the nitrogen-yield responses (specifically, the M–B response coefficients), but it does not capture all of the model or data uncertainties. A comparison of median bootstrap parameter estimates and mean estimates is presented in figure S4. Yield y-intercepts and asymptotes were set in the model using the upper and lower tails of the yield distribution in each climate zone [4]. We note that if high-yielding areas were not observed within a climate zone, the asymptote for the yield response could be artificially low, which would tend to make our estimate of the tradeoff frontier conservative.

The soil surface nitrogen balance model used utilizes detailed spatial data on nitrogen inputs and outputs to estimate excess nitrogen. However, we stress that mass balance excess nitrogen as calculated here is only a useful proxy for nitrogen pollution. Even locations with little to no mass balance excess may still experience reactive nitrogen loss throughout a growing season.

We also note that we modified the nitrogen balance model of Foley et al [3] by generating crop-specific nitrogen balances. These crop-specific calculations required apportioning manure inputs between crops proportionally to the area in each crop. The resulting manure use estimates are likely the most uncertain aspect of the spatial nitrogen balance approach, given the relatively rough estimates about the proportion of manure generated that is applied [see 3, 16, 30] and how the manure is divided between crops (this study). Given the lower confidence in the manure application data, manure was left out of the yield response model, but included in the nitrogen balance model. This allows us to roughly characterize the important influence of manure in determining excess nitrogen in areas with high livestock densities without introducing data artifacts into the yield model.

When building the cereal production frontier (figure 1), we aggregate across the crop-specific frontiers (online figures S1–S3) by keeping a fixed proportion of nitrogen consumption between the crops. One could also aggregate using fixed production proportions, i.e. aggregating along the y-axis instead of the x-axis. However, even without using fixed production proportions, the crop production mix varies only slightly under our method of aggregation (figure S5). More generally, we note that the aggregate (multi-crop) production frontier could shift in the future with changes towards or away more nitrogen-responsive crops.

All of the global datasets utilized for this study capture the state of agriculture circa 2000, and we do not capture changes in yield potential and crop area that have occurred in the recent past. Updates to the crop area, yield, fertilizer, and irrigation data would enable better understanding of global agricultural management and production. In addition to greater temporal resolution, different methodological approaches could be useful as well. Future work could generate global production frontiers using process-based models that may be more sensitive to fine-scale weather and soil variations, and such an analysis would be a useful complement to our study.

This analysis quantifies how substantial improvements are possible in crop production and reduction of both applied and excess nitrogen. Our results suggest global benefit from reductions in nitrogen intensity in some regions and increases in nitrogen intensity in others, along with wholesale increases in agronomic efficiency across the entire system. While such changes may be difficult to achieve, they would be important steps towards meeting projected increases in food demand while improving environmental quality [48].

Lastly, we suggest that the methodology adopted here—a crop production and environmental outcome tradeoff frontier—be utilized more widely to help determine production possibilities in agricultural systems that maximize human well-being. These analyses could and should be carried out at many different scales and over time, with the potential to improve land-use and agricultural land management decision-making.