Projecting future nitrogen inputs: are we making the right assumptions?

Global use of reactive nitrogen (N) has increased over the past century to meet growing food and biofuel demand, while contributing to substantial environmental impacts. Addressing continued N management challenges requires anticipating pathways of future N use. Several studies in the scientific literature have projected future N inputs for crop production under a business-as-usual scenario. However, it remains unclear how using yield response functions to characterize a given level of technology and management practices (TMP) will alter the projections when using a consistent dataset. In this study, to project N inputs to 2050, we developed and tested three approaches, namely ‘Same nitrogen use efficiency (NUE)’, ‘Same TMP’, and ‘Improving TMP’. We found the approach that considers diminishing returns in yield response functions (‘Same TMP’) resulted in 268 Tg N yr−1 of N inputs, which was 61 and 48 Tg N yr−1 higher than when keeping NUE at the current level with and without considering changes in crop mix, respectively. If TMP continue to evolve at the pace of past five decades, projected N inputs reduce to 204 Tg N yr−1, a value that is still 59 Tg N yr−1 higher than the inputs in the baseline year 2006. Overall, our results suggest that assuming a constant NUE may be too optimistic in projecting N inputs, and the full range of projection assumptions need to be carefully explored when investigating future N budgets.


Introduction
Global nitrogen (N) inputs to crop production have increased from 37 Tg N yr −1 in 1961 to 163 Tg N yr −1 in 2009 contributing to a 69 Tg N yr −1 increase in crop yield [1]. While this change increased crop yields, it has led to adverse environmental impacts for climate, water quality, and air quality from regional to global scales [2,3]. It has been proposed that global N inputs, mainly contributed by high-and midincome countries, have already exceeded the so-called 'planetary boundary' , which marks the safe operating space for humanity, by over 83%-142% [4]. In contrast, many regions of the world, such as sub-Saharan Africa (SSA), still have N inputs as one of the major limiting factors for crop yield [5][6][7][8][9]. To meet rising food demand, global crop production is projected to increase by 60%-110% by 2050 compared to 2005 baseline [10][11][12][13], suggesting a continuous increase in demand for N inputs worldwide. But the question of whether, where, and how much N inputs will continue to increase are critical for achieving future environmental sustainability and food security.
To project future N inputs and inform decision making related to N management, many studies have been conducted based on historical records of N inputs, nitrogen use efficiency (NUE; the fraction of applied nitrogen recovered in harvested crop), and food demand [12,[14][15][16][17][18]. Future N inputs can be calculated using projected food demand and NUE. The projection of food demand is usually based on the population and diet changes which have been described in shared socioeconomic pathways with a range of scenarios [19,20]. Meanwhile, NUE is often considered as representative of technologies and management practices for N.
Many studies assume NUE to be staying constant, or even increasing, under a reference scenario or 'business-as-usual' (BAU) scenario, which considers that the state of technology and other socioeconomic conditions do not have major changes [14,17,21,22]. However, considering the diminishing return of yield response to N inputs [23,24], NUE will decrease if yield increases rely solely on rising N inputs without any improvements in technology and management practice (TMP). The concept of diminishing return of yield means stagnating crop yield with increasing N inputs, and it has often been utilized at farm-scale agronomic research [24][25][26].
Even though several recent studies implemented the dynamic yield response to N inputs in national or global scale analyses and N inputs projection (e.g. Lassaletta et al [1,23]; Mogollon et al [18]; Mueller et al [27]; Billen et al [28][29][30]), most use aggregated N inputs or NUE of all crop classes and ignore the large variability in N inputs and NUE among crops and the impacts of changing crop mixes due to dietary shifts. At the global scale, NUE in 2010 varied from 0.14 to 0.80 among 11 major crop classes [31]. Such differences among crop classes are also evident on a national scale. For example, in China, average NUE (2011-2015) of different crops ranged from 0.08 to over 0.60 [32], while the aggregated NUE (i.e. NUE calculated for all crops) in China for year 2010 was 0.20-0.30 [1,31]. Hence, using aggregated NUE instead of crop specific NUE will likely introduce bias to the projection of future N inputs.
Therefore, it is imperative to investigate how the assumptions made when constructing N projections affect findings about the future of N inputs. As there is considerable variability among global N budget datasets [33], as well as datasets from different spatial scales [34], it is also critical to utilize a consistent dataset in a simple and transparent manner to reveal the importance of NUE and technology scenarios. Consequently, we update and use a database of N budgets by country and crop class for 115 countries or regions during 1961-2015; design and implement three approaches to project N inputs in 2050 considering different assumptions for NUE and yield response; compare our projections with existing literature; and discuss the implications of our findings for future N projections.

Data
This study used the Global Database of Nitrogen Budget in Crop Production, a country-and crop-specific N budget database, and updated it for the period of 1961-2015 based on the methodologies developed by Zhang et al [31]. The total N inputs to cropland included N-fertilization, N-manure, N-fixation and N-deposition in kg N ha −1 yr −1 , while the output included crop yield (i.e. grains or editable parts of the crop only; straw and residues are not included) representing N in harvested crop (kg N ha −1 yr −1 ). The N-manure represents the amount of manure collected and applied to cropland. The analysis was performed with a focus on the crop production system, and was carried out for 115 countries or regions based on the list of major crop producing countries used in Zhang et al [33] for statistical assessment, and 11 crop classes following International Fertilizer Association's (IFA) guidelines [35] (see SI tables S1 and S2 available online at stacks.iop.org/ERL/17/054035/mmedia). Projections of crop yield and harvested area for year 2050 were from Food and Agricultural Organization of the United Nations (FAO) 2012 report [20] with baseline year of 2006 (averaged 2005-2007), which was derived based on food demands and is in line with historical trajectories of N yield for major regions (figure S17). The projected crop yield is expressed in kg N ha −1 yr −1 .

Assumptions and approaches for projection
To project N inputs in 2050, we designed three approaches using the same projected crop demand but different assumptions for NUE (table 1 and SI text S3).

'Same NUE' approach
The first approach, named 'Same NUE' , assumes that NUE stays the same as the current level (i.e. averaged NUE for 2011-2015). We first estimated the NUE for each country (k) and crop class (c) for the 2011-2015 period (t), then calculated N input rates in 2050 using projected crop yields in 2050 [20] divided by the estimated NUE assuming that NUE stays the same in 2050 (SI equation (1)). We then calculate total N input quantity in 2050 using the harvested area from the same report [20] (SI equation (2)). In order to investigate the impacts of changes in crop mixes on the projection of N inputs, we also tested the projection with the aggregated NUE of all 11 crop classes in a country instead of the crop-specific NUE (see SI text 3.1 for details).

'Same TMP' approach
The second approach, 'Same TMP,' considers the TMP (represented by the yield response function derived from the observations during 2006-2015) stay the same as the current level. Under the same TMP and ecological conditions, yield response to N inputs levels off as N inputs increases, and consequently NUE decreases. Yield response functions have been developed to characterize such relationship between N inputs and yield [23,[36][37][38]. The yield response function could be changed due to the adoption of new TMP, such as precision farming, controlled release fertilizer, nitrification inhibitors and polymer-coated fertilizer [24]. The yield response function keeps evolving following the pace and trajectory observed in the past decades  a This approach was tested in two cases: one considers the changes in crop mixes and the other does not.  (5)). The shaded area around lines is the 95% confidence interval estimated using 1000× bootstrap resampling. The blue horizontal line is the 2050 yield target obtained from FAO 2012 report.
Based on the N inputs and yield records for the most recent ten years (i.e. t = 2006-2015), we first estimated a yield response function for each country and crop class (SI equation (5); figure 1(a)). Then, we used these yield response functions to estimate N input rates when yield changes to 2050 level (SI equation (6)). Similar to several published studies [18,23,27], we adopted one-parameter hyperbolic function as yield response function; meanwhile, we also carried out uncertainty test to investigate the impact of using different function forms (e.g. quadratic plateau function) on projection results.

'Improving TMP' approach
The third approach 'Improving TMP,' assumes that TMP keeps evolving following the pace and trajectory observed in the past decades . Therefore, for each country and crop class, we first estimated yield response functions based on the N inputs and yield records for each of the six time periods between 1961 and 2015 ( figure 1(b)). As the coefficient of the hyperbolic yield response function (M k,c,t ) represents maximum achievable yield, it serves as an indicator of the TMP level represented by the yield response function [23]. Larger values of the coefficient demonstrate improvement in TMP, and viceversa [18]. Consequently, we used M k,c,t for the past six time periods to extrapolate to 2050 and estimate a new yield response curve, which is then used to estimate N input in 2050.

Uncertainty tests
We examined three potential sources of uncertainties for projected N inputs: (a) the uncertainty associated with estimated parameters in the yield response function, (b) the effect of using different yield response functions, and (c) the effect of yield response to nonfertilizer N inputs (see text S6 for details).

Projection of global N inputs
While all approaches projected significant increase in global N inputs by 2050, the range of projected Projecting N inputs without considering the shifts in crop mix leads to biases in the projection. Taking the 'Same NUE' approach as an example, using the aggregated NUE for all crops instead of crop specific NUE results in an overestimation of 13 Tg N yr −1 (or 6%) for future N inputs globally (table 2), and such overestimation is larger in regions with strong shifts towards N efficient crops (e.g. soybean). However, this difference is lower than the difference between the 'Same NUE' and the 'Same TMP' approaches.
The projected N inputs are not significantly affected by the potential different yield response to fertilizer and non-fertilizer inputs (SI text S6.3 and table S5). When N-fixation is assumed to be constant and stay at the current level until 2050, the projections are around 7 Tg N yr −1 (or 3%) lower than the N inputs projected from the 'Same TMP' approach that uses all N inputs in the yield response curve. In contrast, when only N-fixation followed the yield response curve and the remaining N-inputs are assumed to stay at the current level until 2050, the projections are 36 Tg N yr −1 (or 13%) lower than the 'Same TMP' approach.

Regional N input differences
Most countries around the world project increase in N inputs from baseline year to 2050 across all approaches used in this study (figure 2). India and Brazil may increase N inputs by 14-26 (the lower and upper bounds of projection results from different approaches) and 8-12 Tg N yr −1 respectively, the top two countries with the largest increase in all tested approaches. But these additional N inputs will be utilized at a very different NUE level, namely 0.23-0.30 in India and 0.45-0.57 in Brazil (figure S7). The USA, China, and Argentina are among the top five countries considering the projection with the 'Same TMP' or 'Same NUE' approach only; but N input may reduce from the baseline level in China following the 'Improving TMP' projection. Despite the projection methods, the NUE in China and India are consistently lower than USA, Argentina and Brazil (figure S7), suggesting the critical role of improving NUE for reducing global N inputs and the urgency of accelerating the development and adoption of nitrogenefficient agricultural practices (i.e. improved TMP) in these two countries. We further note the critical situation in India, where NUE is projected to decline even in the 'Improving TMP' approach, suggesting the pace of TMP improvement in the past decades is not even sufficient to keep the NUE constant.
Among the nine world regions [39], Asia accounts for the largest fraction of global N input for the baseline year (about 52%) and is also the region projected to experience the largest increase in N inputs regardless of the projection methodology ( figure 3). About 57% of the increase is contributed by India. In comparison, SSA accounts for 3% of global N input for the baseline year, but its projected increase is 8-22 Tg N yr −1 , about 174%-502% of the current level. SSA has the largest variation in projected NUEs among all world regions, suggesting how TMP will be adopted in SSA is critical in determining the future N inputs in this region [40] ( figure S8).
Almost all countries and regions project the largest increase in N inputs with the 'Same TMP' approach, higher than both 'Same NUE' and 'Improving TMP' approaches. This observation confirms that ignoring the diminishing return in yield response (i.e. the 'Same NUE' approach) may underestimates future N inputs on a national scale. Almost half of countries (about 43%, e.g. China and USA) show higher projection with 'Same NUE' than with 'Improving TMP' approach. It indicates that these countries may improve NUE while reaching the target yield, if the TMP keep the pace of improvement as the past five decades. But there are countries (e.g. India and Pakistan) show the opposite pattern, indicating the improvement in TMP need to be accelerated in order to increase NUE and achieve the target yield.

Crop specific N input differences
Across all the approaches used for projection, N inputs for each of the 11 crop groups are projected to increase. However, the level of projected increase varies largely, attributing not only to the different increases in production levels but also to the different projection approaches (figure 4). For example, with the 'Same NUE' approach, soybean is projected to increase N inputs by 13 Tg N yr −1 , the highest among all crop groups, and it is mainly contributed by 80% expansion in production level globally. In contrast, with the 'Same TMP' approach, maize projects the highest increase in N inputs at the level of 26 Tg N yr −1 , about 98% higher than the projection by the 'Same NUE' approach. In contrast to the large variation in projected N inputs, the differences in NUE caused by projection approaches are smaller than the differences among crop classes (figure S9): across all projection approaches, soybean has the highest NUE at 0.73-0.81 (the lower and upper bounds of projection results from different approaches) in 2050; the NUEs for rice, wheat and maize range from 0.35 to 0.53; and fruits and vegetables and sugar crops showed the lowest NUEs at 0.14-0.20.
The projected increase by the 'Same TMP' approach is consistently higher than the other two approaches indicating the impact of diminishing return in yield to N inputs in projection. Meanwhile, the 'Improving TMP' approach projects the lowest increase in N inputs for most crop classes except fruits and vegetables, other crops and sugar crops. It suggests that, for these three crop classes, improving TMP at the pace of past five decades will not be sufficient to maintain NUE with the intensifying production. Considering their current NUEs are already the lowest among all crop classes, this result highlights the urgency for accelerating the improvement in N management for these crops.

Are we being optimistic to assume constant NUE with increased crop production?
The much higher projected N inputs from the 'Same TMP' than the 'Same NUE' approach suggest that we have been optimistic about the future NUE by assuming it stays the same as we increase the crop production under the BAU scenario. On a farm scale, it has been widely recognized that the yield response to N inputs gradually levels off as N inputs and yield increase for a given farm and TMP level [24]. Applying this theory of diminishing return to a broader spatial scale [23,27] suggests that achieving the higher production level (i.e. higher yield) without expansion in cropland area and TMP improvement results in decline in NUE. Besides increasing yield on the existing cropland, crop production could be increased by expanding the existing cropland at the expense of other land including natural habitat; however, when the expansion is on marginal land, it is unlikely to achieve the same NUE and yield as the current level. The shifts in crop mix towards more N-efficient crops (e.g. soybean) reduce total N inputs, but the reduction is relatively small when comparing to the difference in N inputs caused by different TMP assumptions. Based on the crop production portfolio projected by FAO [20], soybean production (with world average NUE of 0.80; Zhang et al [31]) will increase by 80%, requiring less N inputs per unit of crop product than other crops. But the NUE increases due to the expanding soybean is compromised by the continuous expansion of fruits and vegetables production (with world average NUE at 0.14; Zhang et al [31]), which is projected to increase more than 80% [41]. In addition, the current increase in soybean production is mostly used for animal feed, only a small fraction of which will be converted to food products [42], therefore, it is important to recognize that improving NUE for the whole food supply chain is critical in addition to improving the NUE for crop production [2,43,44].

Uncertainties in the projection
Three major sources of uncertainties were examined in this study. The first uncertainty was associated with the parameters in the yield response function, and was quantified and reported along with the main result. The second uncertainty was associated with the choice of the yield response function format, and was evaluated by testing additional function forms. The use of quadratic plateau function resulted in higher N inputs projection than hyperbolic yield response function (see SI table S4). It leads to even larger Figure 5. Projections of N input from different studies along with the projection estimates from this study. Each symbol shows different studies, while their fill color shows the estimates corresponding to the approaches. If a symbol is filled entirely (half-filled), then the projections are for total N (N fertilizer), respectively. Projections only for cereal crops are indicated by arrows, while estimates which include all crop classes are not. The horizontal pink stripe demonstrate the planetary boundary (62-82 Tg N yr −1 ) of anthropogenic N inputs from fertilizer and biological N fixation introduced into the earth system adopted from Steffen et al [4]. The red and blue line show historical records of total N and N fertilization from 1961 to 2015, respectively. The details of the projections from these studies are in SI table S6. difference between the 'Same TMP' and 'Same NUE' approaches, supporting our conclusions regarding the impacts of considering diminishing returns on N input projection. Indeed, yield increases are not only limited by N inputs and N management, but also affected by factors such as the availability of other macronutrients (e.g. phosphorus), micronutrients, and water. Although our approaches do not explicitly express these factors as parameters in the yield response function, they are implicitly reflected in our yield response functions since changes in these factors can shift the yield response curves (i.e. changes in TMP). The third uncertainty was about the potential difference in yield response to fertilizer and non-fertilizer inputs and was assessed by varying the use of fertilizer and non-fertilizer inputs in the yield response function. However, no significant differences were found in the global as well as the crop specific projections (SI table S5).
A survey of existing projections for crop N inputs reveals large variations among studies (figure 5), which could be attributed to a range of causes, such as projection methods and assumptions, the coverage of N inputs (total N vs fertilizer only), the baseline year, the projection year, and the coverage of crop classes considered (See SI table S6). Among all studies, Mogollón et al [18] and Lassaletta et al [1] are the only two studies to consider the diminishing return in yield response. Their projection approaches correspond to 'Same TMP' and 'Improving TMP' approaches in this study respectively, and the projection results are about 12 Tg N yr −1 and 3 Tg N yr −1 higher than our results, respectively. The differences are mainly caused by their approach to project yield response function (M) to 2050. The Mogollón et al [18] projected M based on the relationship between M and gross domestic product for each world region in their study, whereas we performed linear extrapolation of M to project future yield response curve and N inputs. In contrast, Lassaletta et al [1] used the past three decades (1980-2009) for extrapolation of yield response curve, while we used the past five decades . Additionally, they projected N inputs by considering aggregated crop production of 12 regions of the world, while we projected it for each country and crop mixes combination. Other studies within the 'Improving TMP' approach, such as Wood et al [22] and Erisman et al [14], assume an increase in NUE by 30% and 50% by 2050 relative to the baseline (1997 and 1995-97) resulting in 107 and 100 Tg N yr −1 N fertilizer inputs for cropland, respectively. Despite using different approaches, their projections estimates are similar to our N fertilizer projection in the 'Same NUE' approach which is around 114 Tg N yr −1 (assuming fraction of fertilizer in total N stay the same as in baseline year). Cassman et al [21]and Wood et al [22] assumed constant NUE in their projection, but Cassman et al [21] was projecting for an earlier year 2025. Accounting for N fertilizer inputs only, our projection in the 'Same TMP' approach is about 15% higher than Cassman et al [21] and 6% lower than Wood et al [22]. Despite the difference, almost all projections are outside the N planetary boundaries [4,45], and most of the predictions are surpassing the upper bound of the uncertainty range for the planetary boundaries. Overall, this study presents projections comparable to values in literature, and it is among the first to systematically evaluate the impacts of yield responses under different TMP assumptions and crop mix on N input projection.
In addition to these causes, discrepancies in projections could arise due to the uncertainties associated with the data sources. Our analysis relied on the dataset complied by Food and Agricultural Organization of the United Nations Statistical Database (FAOSTAT [46]), but recent studies have demonstrated that large discrepancies exist among different datasets for N budget estimates such as N in harvested crop [33,34]. We chose FAOSTAT as the primary data source for this study because it has good spatio-temporal coverage, which is critical for the global scale analysis in this study. Using the same database for the projection under different scenarios will minimize the impact of different input data. However, further investigation on the discrepancies among various data sources developed from different spatial scales is needed to address these discrepancies and their impacts on the N input projection.

Implications for crop N management
Crop N management is facing tremendous challenges in the next three decades. The projections in this study suggest that N inputs will continue to increase by 59 Tg N yr −1 (115 Tg N yr −1 for N surplus and 0.49 for NUE) globally, even if TMP keeps improving at the pace of past decades. To meet the food demand and bring N surplus back to planetary boundary, Zhang et al [31] proposed a set of NUE goals for countries and crops. Comparing to those goals, most of our projected NUEs are still much lower even with the 'Improving TMP' approach (assuming the TMP improves at the pace of past decades) (SI text S9). For instance, NUE of China (0.43), Brazil (0.57) and India (0.29) in the 'Improving TMP' approach are significantly lower than the NUE goals of 0.60, 0.70, and 0.60, respectively (see SI figure S7). Among the 11 crop classes, fruits and vegetables and sugar crops are those require the largest NUE improvement to meet the NUE goals. Even the major cereal crops (i.e. wheat, rice, and maize) have NUE (0.50, 0.44, and 0.53, respectively) in the 'Improving TMP' approach lower than the NUE goals (0.70, 0.60, and 0.70, respectively). The comparison indicates the priority regions as well as crop classes that require accelerated improvement in TMP development and adaptation.
However, even keeping the pace of TMP improvement is challenging in most countries. For example, significant progress has been made in developing and adopting TMP in many developed countries. USA and European Union (EU) have managed to increase NUE from 44% in 1980s to 62% in 2010s while maintaining and increasing yield through adopting TMP such as '4Rs' principles [47] and improved crop cultivars [48]. However, such improvement has been heavily relying on market incentives (e.g. fertilizer tax, subsidy for enhanced efficiency fertilizer) in the USA and strong regulations at EU, and it is not clear whether those mechanisms will continue to be effective in the coming decades given the volatile crop and energy markets. In contrast, SSA countries are still at the early intensification stage, with low N inputs and high NUE. With projected increase in crop production, more N inputs and lower NUE are expected based on the development trajectories exhibited by most developed and developing countries around the world [31]. Changing such trajectories for crop intensification in SSA would require yield increase relying more on TMP improvement than input increase, which is challenging for least developed countries with very limited resources [2,44]. Continuously improving and implementing TMP is also facing challenges in developing countries such as China and India, where inefficient use of fertilizer has already led to various N pollution issues. Heavily subsidized fertilizer provides limited incentives for farmers to adopt more N-efficient TMP, although phasing out subsidies need to be balanced with food security and social well-being concerns for rural communities.
In addition to the challenges in maintaining or even accelerating the momentum of TMP improvement in countries, challenges also exist in the changing ecological conditions for cropland around the world. Besides TMP, the changes in climate and soil conditions can affect yield response to N inputs. For example, increasing heat stress caused by global warming might stagnate the yield of major cereal crops even after implementing management practices [49][50][51]. These impacts need to be assessed and addressed in future studies. These challenges for crop N management are also accompanied by opportunities. There have been a wide range of TMP available for improving N management on farms, and many of them are associated with low implementation cost. In addition, governments and international communities have increasingly recognized the adverse impacts of inefficient N use not only on ecosystem health but also on human health and the economy [52], and consequently, an increasing number of countries have put forward policies and targets to curtail N inputs in agricultural production (e.g. the 'Zero growth' goal for fertilizer consumption set by the Chinese government [53];. Finally, despite the recent set-back by the COVID-19 pandemic and the rise of deglobalization movements, international collaboration and open science-sharing will continue to help accelerating the TMP improvement across countries.

Conclusions
The approach for projecting N inputs under the BAU or reference scenario by assuming NUE staying at the current level results in a much lower projection in N inputs than the projection considering the diminishing return of yield to N inputs under the same TMP. The optimistic projection by the constant NUE approach can be potentially achieved by keep improving TMP at the pace of past decades, but sustaining the improvement faces multiple challenges such as climate change. In addition, even with the optimistic projection of keeping NUE constant or steadily improving TMP, N inputs and N surplus are projected to increase by 2050, and projected NUE is lower than the NUE goal set for meeting the dual challenges of food demand and N pollution by 2020, further highlighting the urgent need for accelerating the development and implementation of TMP around the world. The comparison among N inputs projected with different approaches in this study demonstrates the importance of assumptions made in BAU scenarios, and also highlights countries (e.g. India, Brazil, and Pakistan) and crop classes (e.g. fruits and vegetables, and sugar Crops) that need to be prioritized for improving NUE and TMP.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.