The model LandscapeDNDC (LDNDC) was used to simulate maize production in circa 2015 conditions on a global grid of 0.5° (~50 km close to the equator). LDNDC is a process-based biogeochemical model that simulates major carbon and nitrogen flows, as well as plant growth and water cycling on a sub-daily timestep (Haas et al., 2013). It has been parameterized using a wide variety of site measurements across temperate (Molina-Herrera et al., 2016, 2017), tropical (Kraus et al., 2015, 2016) and savannah (Rahimi et al., 2021) ecosystems, and successfully used to study N₂O emissions and NO3- leaching (Kiese et al., 2011; Kraus et al., 2015, 2016; Dirnböck et al., 2016; Molina-Herrera et al., 2016, 2017; Houska et al., 2017; Kasper et al., 2019; Schroeck et al., 2019). It performs comparably to other state-of-the-art crop models when simulating maize yields on a global scale (Jägermeyr et al., 2021).

For this study, we used LDNDC version 1.32.3, including the soil-chemistry module MeTr^x (Kraus et al., 2015, 2016), the plant growth model PlaMo^x (Kraus et al., 2016), the hydrology module WatercycleDNDC (Kiese et al., 2011) and the microclimate module CanopyECM (Grote et al., 2009). The strengths of LDNDC include a detailed, process-based description of N cycling, which has been extensively calibrated against measured data for N₂O emissions and NO3- leaching. The weaknesses include an assumption of homogeneous conditions parallel to the soil surface (i.e., in this study homogeneity within each 0.5 degree grid cell).

Model inputs were largely based on those used in the Global Gridded Crop Model Intercomparison (GGCMI) project (Jägermeyr et al., 2021); the state of the art for global crop modeling. Soil data was taken from the harmonized world soil database (HWSD, 2012). The climate data was taken from the repository of the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP), and in particular the GSWP3-W5E5 product, which provides climate data for the years 1901–2016 (Dirmeyer et al., 2006; Lange, 2019; Cucchi et al., 2020). Air-chemistry data was also adapted from the ISIMIP repository. Monthly, grid-cell-dependent NH4+ and NO3- deposition rates for the year 2015 (Tian et al., 2018a) were scaled to daily values, while atmospheric CO₂ concentrations were set to the average 2015 value of 399.9 ppm.

Maize planting dates were fixed according to the gridded crop calendar developed for the GGCMI project (Jägermeyr et al., 2021). Field management was also set in accordance with the GGCMI project. Tilling was performed 1 day before planting and again 1 day after harvesting, to a depth of 20 cm. Fertilization was split between two applications, with 20% of the total on the planting day, and the remainder after reaching 25% of the growing degree days required for crop maturity. After harvesting, 70% of the crop residuals were removed from the field.

LDNDC is calibrated against field-scale measurement data for a wide range of different agro-ecosystems (Kraus et al., 2015, 2016; Molina-Herrera et al., 2016; Rahimi et al., 2021). Here, we used the crop calendar to additionally calibrate the cumulative growing degree days required for plants to reach maturity, with the aim of modeling the different maize cultivars grown in different regions. For each grid cell, the growing degree days required for maturity were set to the mean number of growing degree days between planting and harvesting dates in the period 1980–2010. The growing degree days required for other plant developmental stages were adjusted consistently. During the subsequent simulations, harvest was performed not on the date specified by the crop calendar, but at physiological maturity, whose date varied from year to year depending on the climatic conditions during the growing season.

We aimed to simulate agricultural conditions typical of 2015, assuming that similar conditions will prevail in the near future, and the input data was chosen accordingly. Nevertheless, we ran the model using climate data for the period 1986–2016, with the first 20 years treated as spin up, and model outputs averaged over the period 2006–2016. The reason for performing a 10-year average, rather than just using 2015 climate data, was to reduce the bias associated with the timing of specific weather events. For example, heavy rainfall shortly after fertilization that results in unusually high NO3- leaching.

Baseline simulations were run using gridded N-fertilizer-application-rates data for the year 2015, which was developed for the GGCMI project (Jägermeyr et al., 2021). For subsequent simulations, synthetic N-fertilizer inputs were set to 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 350, 400, 500, and 600 kg-N/ha, while manure supply was kept fixed at the 2015 level. The balance between urea and ammonium-nitrate synthetic fertilizer was set on a grid-cell basis according to the dataset reported in Nishina et al. (2017). Separate simulations were performed for rain-fed and irrigated water management. Irrigation was assumed to be sufficient to avoid stress associated with lack of water.

Total N-fertilizer input, circa 2015, was 25.5 Tg-N, consisting of 22.3 Tg-N of synthetic fertilizer and 3.2 Tg-N of manure. In addition, there was 2.0 Tg-N of atmospheric deposition. This corresponds to an average N-input of 146 kg-N/ha (135 kg-N/ha of synthetic and organic fertilizer). However, there were large regional differences in N-fertilizer usage, as can be seen in Table 1. Using these N-inputs, we simulated a total global maize production of 954 Tg, giving a global average yield of 5.1 Mg/ha, and corresponding to yield-scaled synthetic N-fertilizer usage of 23.4 kgN/Mg.

In conditions of global N sufficiency, we found that production would increase to 1,291 Tg, resulting in an average global yield of 6.9 Mg/ha. Actual production is thus 74% of potential production (i.e., the average global fractional yield is 0.74). Equivalently, maize production could be increased by 35% without increasing the harvested area. However, fractional yields differ significantly between grid cells, as can be seen in Figure 1A. This remains the case at regional scale, where North America (0.97) and East Asia (0.96) have fractional yields close to the maximum, while Sub-Saharan Africa (0.37) and Eurasia (0.30) are far below their potential. Europe (0.66) is split between a higher fractional yield west and lower fractional yield east. Yield-scaled synthetic N-fertilizer usage also shows large differences between grid cells, as shown in Figure 1B. At regional scale it varies from 3.1 kgN/Mg in Eurasia to 48.4 kgN/Mg in the Middle East and North Africa (see Table 2).

We calculated global direct N₂O emissions of 315 Gg-N, corresponding to an average of 1.67 kg-N/ha, or, on a yield-scaled basis, 0.33 kg-N/Mg. Direct N₂O emissions thus account for 1.2% of the N contained in synthetic and organic fertilizer inputs to the soil. We determined indirect N₂O emissions of 101 Gg-N, corresponding to an average of 0.54 kg-N/ha or 0.11 kg-N/Mg. Summing the direct and indirect emissions results in N₂O emissions of 416 Gg-N, corresponding to an average of 2.21 kg-N/ha or 0.44 kg-N/Mg. Figure 1C shows the global distribution of yield-scaled N₂O emissions across grid cells, with high values in Western Europe and across Asia. On a regional scale, yield-scaled-emission rates range from 0.15 kgN/Mg in Eurasia to 1.17 kgN/Mg in the Middle East and North Africa (see Table 2).

We simulated total NO3- leaching of 5.9 Tg-N, with an average of 31.3 kg-N/ha, or, on a yield-scaled basis, 6.2 kg-N/Mg. Figure 1D shows the distribution of yield-scaled leaching rates across grid cells, and it can be seen that rates are particularly high across South and East Asia. Regional values range from 1.0 kgN/Mg in Eurasia to 11.9 kgN/Mg in South Asia, with East Asia (10.8 kg-N/Mg) and South-East Asia (11.0 kg-N/Mg) also close to the top of the range (see Table 2).

To determine where yield gaps could be closed at the lowest cost in harmful N losses, it is necessary to quantify the additional N-fertilizer requirements and N losses (ΔN) associated with yield increases (ΔY). Figure 2A shows the additional N fertilizer required to increase yields (i.e., ΔN/ΔY), and Figures 2C,D show the ΔN/ΔY's for N₂O emissions and NO3- leaching. Grid cells with high fractional yields typically require large amounts of additional N fertilizer to drive yield increases, as can be seen by comparing Figures 2A,C,D with Figure 1A. This relationship is quantified in Figure 2B, which shows the dependence of ΔN/ΔY on fractional yield. For fractional yields >0.7–0.8 there is a steep rise in the additional N fertilizer required to increase yields. A similar pattern is seen for N₂O emissions and NO3- leaching (see Supplementary Figure 4).

Figure 3 shows the effect of following the “minimum fractional yield” scenario for yield-gap closing. Setting a minimum fractional yield of 0.5 results in production increasing to 1.06 times its current value, N-fertilizer requirements to 1.07, direct and indirect N₂O emissions to 1.04 and NO3- leaching to 1.05. Since the relative increase in production is almost identical to the increase in N-fertilizer requirements and N-losses, there is very little change in the yield-scaled values, as can be seen in Table 2. Further increasing the minimum fractional yield to 0.8 results in production of 1.20 times the current value, N-fertilizer requirements of 1.47, direct and indirect N₂O emissions of 1.30 and NO3- leaching of 1.58. As a result, there is an increase in yield-scaled N-fertilizer requirements and N-losses, as can be seen in Table 2. Beyond a fractional yield of 0.8, increases in the N-fertilizer requirements and N-losses significantly decouple from production increases, resulting in a rapid acceleration of yield-scaled N-losses.

The environmental cost of yield-gap closing varies considerably between regions (see Tables 1, 2). For example, in South Asia we predict significant additional NO3- leaching as yield gaps are closed, resulting in yield-scaled losses of 22.2 kgN/Mg at a minimum fractional yield of 0.8 (compared to a global average of 8.2 kgN/Mg). On the other hand, increasing yields in Eurasia results in relatively little additional N₂O emissions or NO3- leaching, with yield-scaled losses significantly below the global average even after more than doubling yields.

Figure 4 shows the effect of following the “optimal” yield-gap closing scenario, and how this compares to the “minimum fractional yield” scenario. By focusing additional N-fertilizer on areas with the largest resultant production gains, production can be increased by ~20% (to ~1,150 Tg) without increasing yield-scaled N losses. Increasing production beyond this value results in rapidly accelerating N-fertilizer requirements, N₂O emissions and NO3- leaching.

The FAO estimates that global maize production has increased from 592 Tg in 2000 (4.3 Mg/ha) to 1,053 Tg in 2015 (5.5 Mg/ha) (FAO, 2021). Our simulated value of 954 Tg (5.1 Mg/ha) thus matches well to the FAO values. It is worth stressing that LDNDC is not calibrated to reproduce crop yields on a global scale. Instead global crop yields are an emergent feature of a model whose underlying processes are calibrated using field-scale data (see Section Model Calibration). Furthermore, LDNDC has taken part in the Global Gridded Crop Model Intercomparison (GGCMI) project, which compared the performance of 12 global crop models with observed FAO data (Jägermeyr et al., 2021). It was found that LDNDC performs similarly to other state-of-the-art crop models in simulating yield anomalies (i.e., interannual, climate-driven yield variation) for maize at both a global and country level.

There is also good agreement between the potential yield modeled by LDNDC (6.9 Mg/ha on a global scale) and that determined by other studies. Mueller et al. (2012) constructed yield vs. N-fertilizer curves for different climatic zones, and then projected the results across global croplands to find a potential yield for maize of 7.4 Mg/ha under abundant nutrient supply. Similarly, Neumann et al. (2010) used a stochastic method to determine a maximum achievable maize yield of 6.9 Mg/ha. On the other hand, the Global Agro-ecological Zones (GAEZ) project estimates a considerably higher potential yield of 9.6 Mg/ha under optimal management conditions (GAEZ, 2012).

Despite the difference in potential yields between LDNDC and the GAEZ project, we find good agreement in the spatial distribution of fractional yields. Comparing fractional yields at a grid cell level results in a coefficient of determination of r² = 0.88 (see Supplementary Figure 5). This shows that the two approaches agree as to which regions have the highest agro-climatic potential to increase yields.

Our finding that direct N₂O emissions equate to 1.2% of synthetic and organic N-fertilizer inputs can also be compared to previous studies. Del Grosso et al. (2009) found a value of 0.81% for maize using the biogeochemical model DAYCENT, while Gerber et al. (2016) found 0.91% using a non-linear emission factor approach. It should be noted that, unlike in our analysis, these studies corrected for background emissions (i.e., soil N₂O emissions under conditions of zero synthetic or organic fertilizer application). More recent results averaged across upland crops have found higher emission rates. For example, Wang et al. (2019) found 1.05% using a non-linear emission factor approach, while Tian et al. (2018b) found 1.8% and Xu et al. (2020) 2.2% using process based models. The LDNDC value lies roughly in the middle of these previous results, suggesting that it provides a reasonable estimate of N₂O emissions.

For NO3- leaching, the simulated average global loss of 31.3 kgN/ha corresponds to 23% of the synthetic and organic N-fertilizer input. This is very similar to the IPCC tier 1 guideline of 24% (IPCC, 2019). It also matches well with a meta-analysis of global maize cultivation that found 22% (Zhou and Butterbach-Bahl, 2014) and to a previous modeling result of 19% averaged across all crops (Lin et al., 2001).

There is thus close agreement between LDNDC simulations and either data or previous modeling results for actual yields, potential yields, current N₂O emissions and current NO3- leaching on a global scale. This suggests that LDNDC is able to make robust predictions for yields, N₂O emissions and NO3- leaching in the case of increased N fertilizer inputs. For N₂O emissions and NO3- leaching, we are not aware of any previous work that has made such predictions on a global scale.

To develop realistic and practical recommendations for how yield gaps could be closed most effectively, our scenarios would also need to take into account economic and political factors, such as the affordability of additional N-inputs or the development of regional food demand. This would clearly make an interesting area for further study, but would require coupling our biogeochemical model to one or more socio-economic models. Other areas that should be addressed in further studies include the effects of climate-change scenarios on yield-gap closing, exploring how far it is possible to balance decreases of N-inputs in N-surfeit regions against increases in N-deficit regions and determining to what extent yield gaps could be closed via non-synthetic N-inputs, such as organic soil amendments or biological nitrogen fixation.