1 Introduction

Fertilizer-intensive agriculture boosts crop yields to support population growth. However, the overuse of nitrogen fertilizers damages air quality, human health, and climate as the leading source of reactive nitrogen (Nr) emissions (Aneja et al. 2009; Ribaudo et al. 2011; SAB, 2011). Despite their importance, agricultural emissions receive far less attention in environmental management than sources such as industry and transportation (Bachmann 2007; Kanter et al. 2017; National Research Council 2004). Due to excess input and inefficient management, roughly a quarter of the nitrogen added to soils is lost to the atmosphere as Nr emissions (Luo et al. 2022). Those emissions come in the form of ammonia (NH3) and nitric oxide (NO), which react in the atmosphere to form particulate matter (PM) and ozone air pollution (Geddes et al. 2022; Guo et al. 2020; Lu et al. 2021; Paulot and Jacob 2014; Sha et al. 2021; Wang et al. 2021), as well as nitrous oxide (N2O), which is a potent greenhouse gas and contributor to stratospheric ozone depletion (Ravishankara et al. 2009; Tian et al. 2020). Emission rates depend on climate, soil properties, and farming practices, with spatial and temporal patterns that differ by species (Cao et al. 2020; Guo et al. 2020; Rasool et al. 2019, 2016; Sha et al. 2021; Venterea et al. 2012). Whereas long-lived N2O influences climate globally, other gases are short-lived and highly variable in their propensity to form PM and ozone and impact health downwind (Luo et al. 2022). Incomplete understanding of those variations complicates efforts to mitigate emissions while maintaining crop yields at high and sustainable levels.

Biochar is a solid composed mainly of carbon and ash that is produced from biomass under oxygen-limited conditions, typically via pyrolysis (International Biochar Initiative 2015). Applying biochar as a soil amendment has gained attention because of its potential to mitigate nitrogen emissions and increase crop yields while providing long-term storage of carbon in soils (Kroeger et al. 2021; Lehmann et al. 2021; Liu et al. 2019; Luo et al. 2023; Pourhashem et al. 2017). Biochar could also enhance soil’s ability to retain nutrients, and moisture (Ippolito et al. 2015; Lehmann et al. 2021; Novak et al. 2012). However, the impacts of biochar on Nr emissions remain highly uncertain, with positive, negative, and neutral impacts observed in the studies that applied various types and amounts of biochar in various regions (Borchard et al. 2019; Cayuela et al. 2014; Gao et al. 2020; He et al. 2017; Liu et al. 2019, 2018; Schmidt et al. 2021; Sha et al. 2019; Verhoeven et al. 2017; Zhang et al. 2021).

Pyrolysis of light hydrocarbons (e.g., methane) has been proposed (Dagle et al. 2017; Muradov 1993; Pasquali and Mesters 2021) as a way to produce hydrogen without the carbon dioxide emissions that accompany steam methane reforming, the dominant source of hydrogen today(Sun et al. 2019). The process would produce a carbon solid byproduct, which we term zero-valent carbon (ZVC). However, the emission impacts of ZVC as a soil amendment have not been studied.

The impacts of biochar or other soil amendments on nitrogen cycling depend on the properties of the material and its interaction with soil properties, crop types, farming practices, and meteorological conditions (Borchard et al. 2019; Cayuela et al. 2014; Sha et al. 2019). The chemical and physical properties of soil amendments vary with feedstock and pyrolysis conditions (Gul and Whalen 2016). For NH3, a meta-analysis found that applying biochar with high pH may stimulate emissions in acidic soils, but applying wood-based biochar combined with urea or manure may mitigate emissions (Sha et al. 2019). For NO and N2O, net impacts depend on how the amendments influence nitrification and denitrification (Cayuela et al. 2014; Sánchez-García et al. 2014). Biochar is more likely to increase NO and N2O emissions from nitrification but decrease emissions from denitrification (Sánchez-García et al. 2014). Irrigation and fertilizer management practices also influence net impacts (Ramlow et al. 2019; Thomazini et al. 2015).

Previous studies have characterized the influence of biochar on N cycling based on incubation experiments (Baechle et al. 2018; Spokas et al. 2009; Thomazini et al. 2015), field studies (Abagandura et al. 2022; Angst et al. 2014; Deng et al. 2015; Duan et al. 2022; Edwards et al. 2018; Fidel et al. 2019; Gao et al. 2022, 2020; Lu et al. 2020; Ramlow et al. 2019; Shaukat et al. 2019; Sistani et al. 2019; Suddick et al. 2011; Verhoeven and Six 2014), or modeling (Archontoulis et al. 2016; Liu et al. 2019; Lychuk et al. 2015, 2017, 2021). While field studies enable observations in real-world settings, too few have been conducted to characterize how the impacts of biochar vary with location, soil properties, farming practices, and meteorological conditions. Modeling is needed to predict the impacts of biochar across a broad spectrum of conditions. Process-based agroecosystem models have been extended to simulate biochar applications and their interactions with soil nitrogen and carbon cycling. For instance, Lychuk et al., (2015, 2017, 2021) added algorithms into the Environmental Policy Integrated Climate (EPIC) model to study how biochar amendments influence nitrogen leaching and crop yield in ten farms. Archontoulis et al. (2016) developed a biochar module within the Agricultural Production Systems sIMulator (APSIM) to analyze the trade-off effects of biochar additions on N2O emissions and crop yield in two farms. However, these models have not previously been used to predict how the impacts of amendments vary with the properties of the amendments and by region. Such modeling is needed to inform the planning of field studies to test how amendments should be designed and where they should be applied to mitigate emissions.

In this study, we incorporate the Lychuk biochar algorithms into an agroecosystem model to simulate how soil amendments may influence Nr emissions from fertilized soils across the contiguous United States (CONUS). We model how Nr emissions and crop yields would be expected to vary with the application of two types of carbon amendments, biochar and ZVC. Building upon our recent study (Luo et al. 2022) of how soil emission rates and per-ton health impacts of NO and NH3 vary by location, this modeling can help identify potential sites for field studies to test where carbon amendments may be most beneficial.

2 Method and materials

The Fertilizer Emission Scenario Tool for CMAQ (FEST-C) (Cooter et al. 2012; Ran et al. 2019) served as our base agroecosystem model (Fig. 1). Our previous work (Luo et al. 2022) enhanced the representation of nitrogen schemes in FEST-C to simulate Nr emissions from the US. fertilized soils in a consistent and mechanistic manner. Here, we added biochar algorithms developed by Lychuk et al. (2015) to simulate the impacts of soil amendments. The following sections describe FEST-C and the carbon amendment algorithms, along with our simulation configurations and other methods.

Fig. 1
figure 1

Carbon and nitrogen dynamics modeled in FEST-C

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2.1 FEST-C with enhanced nitrogen schemes

FEST-C is adapted from the widely-used agroecosystem model EPIC (Wang et al. 2012), which simulates crop growth and the fate and transport of nitrogen, carbon, and other nutrients (Cooter et al. 2012; Ran et al. 2019). Unlike conventional field-scale models, FEST-C can simulate 42 types of rainfed or irrigated croplands and managed grasslands (Additional file 1: Table S1) across CONUS with 12-km resolution on a daily basis. FEST-C features built-in databases representing farming practices (e.g., fertilizer type, timing, placement, and rates; tillage; irrigation), soil properties, and meteorological conditions. FEST-C has been linked with atmospheric and hydrological models to track nitrogen loss to the environment (Pleim et al. 2019; Ran et al. 2019; Yuan et al. 2018).

The original FEST-C (Cooter et al. 2012; Ran et al. 2019) and the underlying EPIC (Wang et al. 2012) model employ only simplified schemes to estimate NH3 emissions from volatilization and N2O from denitrification on a daily time-step. They neglect NO and N2O emissions from nitrification and NO emissions from denitrification, and thus likely underestimate emissions (Gaillard et al. 2018). Our previous work (Luo et al. 2022) enhanced FEST-C by introducing nitrification and denitrification mechanisms from another structurally similar agroecosystem model, DayCent (Del Grosso et al. 2000; Parton et al. 2001), to include these overlooked emission pathways. Briefly, volatilization and nitrification processes were simulated together as a first-order reaction. Then, 5% of the combined rates were allocated to volatilization while the rest to nitrification (\({R}_{nit}\)). Emissions from those processes varied with soil ammonium levels (NH4+), wind speed, temperature, water content, pH, cation exchange capacity, and depth of simulated layer. NO and N2O emissions from denitrification depended mostly on the nitrate levels (NO3−), porosity, respiration rate, water, and clay content of the soil.

Besides, we also considered the influence of pulsing effects after long dry period and canopy reduction effects on NO emissions. Detailed algorithms of nitrogen schemes were described in Supplementary Information and Luo et al. (2022).

The original FEST-C and EPIC models compute fertilizer application rates based on theoretical crop needs, neglecting overuse by farmers (Cooter et al. 2012; Ran et al. 2019). We addressed this by integrating fertilizer sales data from the United States Geological Survey to reflect actual fertilizer use (Falcone 2021) as described by Luo et al. (2022).

2.2 Carbon amendment algorithms

The Lychuk biochar module in EPIC has demonstrated good performance in predicting how biochar applications influence soil properties and crop yields in field studies (Lychuk et al. 2015), and has been applied to simulate influences on leaching, runoff, and crop yield (Lychuk et al. 2017, 2021). Since FEST-C is derived from EPIC, adapting the module for FEST-C was relatively straightforward. This paper is the first to extend the module to ZVC.

2.2.1 Overview of biochar module

The module treats biochar similarly to organic matter such as manure and crop residue but with a higher proportion of recalcitrant carbon that is resistant to decomposition in soils. Biochar applications thus influence soil carbon pools and bulk density. The alkaline nature of biochar, along with its high surface area and charge density, tends to increase soil pH and CEC (Cation Exchange Capacity). Those changes alter nitrogen cycling and associated emissions.

2.2.2 Impacts of biochar amendments on soil organic carbon

FEST-C simulates carbon cycling and its interactions with nitrogen cycling using a soil organic matter model, adapted from the CENTURY agroecosystem model (Fig. 1) (Izaurralde et al. 2006; Parton 1996). Organic inputs in FEST-C were from crop residues or manure applications. FEST-C first split organic inputs into two litter pools, structural and metabolic, according to their lignin and nitrogen content, and then stimulated their transformation to organic matter. FEST-C then partitioned organic matter into three pools: microbial biomass, slow humus, and passive humus. Microbial biomass had the most rapid decomposition rates of organic carbon and nitrogen (~ days to weeks), while slow humus contained relatively recalcitrant organics with turnover times up to decades. Passive humus was adsorbed to mineral surfaces and needed hundreds of years to decompose. FEST-C stimulated carbon and nitrogen flows in litter and organic carbon pools in layers from the surface to the root zone via a daily mass balance approach.

Mineralization converts organic N into plant-available inorganic N. In the reverse process, immobilization, soil microbes took up inorganic N, making it unavailable to plants. Net mineralization is gross mineralization minus immobilization. In FEST-C, if net mineralization is above zero, organic N will be mineralized to inorganic N, with 90% of the net mineralized N allocated to ammonia and 10% to nitrate. Otherwise, inorganic N will be immobilized from nitrate to organic N. FEST-C also considers the loss of organic matter in sediments, leaching or runoff, or released into the atmosphere as CO2 via respiration.

Unlike organic inputs from plant residue and manure, most of the organic carbon in biochar is recalcitrant. Nevertheless, the decomposition rates of biochar remain unclear and depend on the feedstock, pyrolysis temperature, and soil clay content (Wang et al. 2016). A recent meta-analysis based on 128 observations found that only around 3% of the carbon in biochar was labile with a mean residence time (MRT) of 108 days, while the rest was recalcitrant with an MRT as long as 556 years (Wang et al. 2016). We treat biochar as an organic carbon input, allocating 2% to metabolic litter, 38% to passive humus, and 60% to slow humus (Lychuk et al. 2015), and track subsequent transport and fate in the same way as other organic carbon. Lychuk et al. (2015) demonstrated that this approach effectively simulated observed changes in soil organic carbon after application of a woody biochar.

2.2.3 Impacts of biochar amendments on soil bulk density

FEST-C estimates soil bulk density (BD, ton m−3) as a function of soil organic matter content (SOM, %), bulk density of organic matter (BDOM), and bulk density of minerals (BDM), adapted from the classical Adams equations (ADAMS, 1973).

$$BD=\frac{100}{\frac{SOM}{{BD}_{OM}}+\frac{100-SOM}{{BD}_{M}}}$$
(1)

BDOM is set to 0.244 ton m−3 in FEST-C, while BDM is estimated based on BDOM and soil organic carbon content.

Soil BD is inversely related to soil organic matter. Therefore, biochar applications can decrease the BD by introducing additional organic matter into the soil. The increased bulk density upon biochar additions (\({BD}_{NEW}\), ton m−3) is calculated in a similar way to the original bulk density algorithm in FEST-C by introducing the bulk density of biochar (BDBC, ton m−3) and weight percentage of biochar applied in soil (BC, %).

$${BD}_{NEW}=\frac{100}{\frac{SOM}{{BD}_{SOM}}+\frac{100-SOM-BC}{{BD}_{M}}+\frac{BC}{{BD}_{BC}}}$$
(2)

BC is determined by the biochar application rate (BCapp, ton ha−1) and the weight of soil mass (Msoil, ton ha−1) across the application depth.

$$BC=\frac{{BC}_{app}}{{M}_{soil}}\times 100$$
(3)

2.2.4 Impacts of biochar amendments on soil CEC

Due to its high surface area and negative surface charges, biochar typically increases soil CEC (Hailegnaw et al. 2019; Singh et al. 2022), although it can reduce soil CEC if the biochar has a lower CEC than the soil (Hailegnaw et al. 2019). Our biochar model assumed that the soil CEC (CECnew, cmolc kg−1) after biochar application was a function of soil CEC (CECsoil), BC, and biochar CEC (CECBC), consistent with previous findings (Hailegnaw et al. 2019; Singh et al. 2022).

$${CEC}_{new}=\frac{{CEC}_{soil}+\frac{BC}{100}\times {CEC}_{BC}}{1+\frac{BC}{100}}$$
(4)

2.2.5 Impacts of biochar amendments on soil pH

Previous observations found that a substantial increase of soil pH occurred when biochar with high CEC was added to acidic soils with relatively low CEC (Xu et al. 2012; Yuan and Xu 2011). However, for alkaline soils with high CEC, soil pH changes little after biochar application (Dai et al. 2017). Such phenomena can be attributed to the alkaline nature of biochar (Fidel et al. 2017) and the pH buffering capacity of soils (Magdoff and Bartlett 1985). Soil pH changes after applying biochar are similar to adding base amendments to soils such as agriculture lime. Classical relationships between soil pH and the quantity of exchangeable cations from base additions can thus estimate the changes in soil following biochar amendments (Nelson and Su 2010). We assumed the increase in soil CEC upon biochar amendments corresponded to the quantity of base additions in terms of exchangeable cations.

Specifically, our biochar module employed a classical S-shape pH buffering curve, adapted from Magdoff and Bartlett (1985), to estimate soil pH upon biochar addition. Although soils vary widely in their pH buffering capacity, Magdoff and Bartlett (1985) found that when acid or base additions are expressed based on soil organic matter mass, different soils exhibit similar capacity curves. This curve can be described using a sigmoid function where pH is related to the upper (UpH) and lower (LpH) levels of pH of agricultural soils and the soil organic matter-based amendment rate (X, mmolc g−1 OM).

$$pH=\frac{UpH-LpH}{1+0.652{e}^{-1.16X}}+LpH$$
(5)

Our biochar module converted this logistic function to another sigmoidal form for consistency with other S-curve algorithms in FEST-C via curve fitting of data from Magdoff and Bartlett (1985). Also, we adjusted UpH and LpH to 8.5 and 3.5 respectively to reflect the conditions observed in U.S. agricultural soils (Archontoulis et al. 2016).

$$pH=\frac{UpH-LpH}{1+{e}^{-0.76(X-7.21)}}+LpH$$
(6)

We first estimated the initial soil equivalent amendment (Xsoil, mmolc g−1 OM) at the original pH (pHsoil) using the reverse form of the pH buffering curve.

$${X}_{soil}=7.21-\frac{1}{0.76}\mathrm{ln}\left(\frac{UpH-LpH}{{pH}_{soil}-LpH}-1\right)$$
(7)

The equivalent base increases to \({X}_{new}\) (mmolc g−1 OM) upon biochar addition. \({X}_{new}\) is computed based on the variations in CEC, noting that total organic matter fraction (g OM g−1 soil) after biochar addition is related to the sum of \(SOM\) and \(BC\).

$${X}_{new}={X}_{soil}+\left(\frac{{CEC}_{new}-{CEC}_{soil}}{\frac{SOM}{100}+\frac{BC}{100}}\right)\times \text{unit conversion} (0.01,\mathrm{ from\, cmolc\, {kg}^{-1}}\,\mathrm{ to\, mmolc \,{g}}^{-1})$$
(8)

Finally, the new pH is calculated by substituting \({X}_{new}\) in the buffering curve.

2.2.6 ZVC algorithms

ZVC is a pyrolysis product of light hydrocarbons (primarily methane) and has a more stable organic carbon component and lower decomposition rate than biochar. Therefore, we allocated 100% of the organic carbon in ZVC to the passive humus pool while assuming the responses of soil pH, CEC, and BD to ZVC were the same as to biochar, as shown in Table 1.

Table 1 Field studies for model performance evaluation and biochar and ZVC properties for default model simulations
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2.3 FEST-C biochar model evaluation

2.3.1 Performance evaluation

Previous studies have evaluated FEST-C for estimating Nr emissions from U.S. soils (Luo et al. 2022; Ran et al. 2019) and EPIC for predicting how biochar additions influence crop yields (Lychuk et al. 2015; Ran et al. 2019). To evaluate the performance of our enhanced FEST-C in predicting the influence of biochar on Nr emissions, we compiled field studies conducted in the US. agricultural areas. We found five relevant studies (10 cases) published from 2009 to 2020 using the Web of Science and Google Scholar databases that provided sufficient information (site location, fertilizer source, timing, amounts, tillage level, planting, and harvesting dates) to enable us to simulate a similar scenario for comparisons (Table 1) (Deng et al. 2015; Edwards et al. 2018; Gao et al. 2022; Ramlow et al. 2019; Verhoeven and Six 2014). Despite their limited number, the field studies covered a range of soil, climate, crop, and biochar conditions. For studies lacking information on biochar properties, we assumed the missing physical and chemical biochar properties were the same as the ones used in Lychuk et al. (2015). The model’s default biochar CEC and BD values (Table 1) were higher than those of biochar used in field measurements. Other essential information such as climate conditions and soil properties for each observation was derived from the FEST-C database, modifying the soil properties for consistency with each field study.

2.3.2 Sensitivity analysis

To identify which biochar properties have the most significant impact on Nr emissions, we ran multiple sensitivity analyses across corn-growing regions by varying biochar properties, including CEC, organic carbon content (OrgC, %), BD, and application rates. The UC Davis biochar database (https://biochar.ucdavis.edu/) was used as a reference for setting simulation ranges for each biochar property, ranging from 10 to 80 for OrgC (%), 10 to 400 for CEC (cmolc kg−1), 0.05 to 0.8 for BD (ton m−3), and 2.5 to 40 for application rates (ton ha−1). For each simulation, only one of the biochar properties was altered, while others remained at default values (Table 1) (Lychuk et al. 2015). We only performed the sensitivity analysis for corn-growing areas because corn is one of the most important crops in the U.S. and has the largest acreage spanning numerous regions. Also, sensitivity analysis for all crops will significantly increase the computational burden as FEST-C considers 42 types in the U.S. with 12-km spatial resolution.

2.4 Scenario analysis

We used enhanced FEST-C to estimate Nr emissions across CONUS fertilized soils for 2011 with the same configurations as Luo et al. (2022). We chose 2011 as the base year because the FEST-C built-in databases can best represent the farming practices, soil properties, site information, and crop information in that year. Those databases were developed by combining cropping practice surveys, agricultural census data, satellite data, and expert opinions. An update of the input information to a more recent year on such fine scale is too costly and beyond the scope of this study. Details of the input information are described in Cooter et al. (2012) and Ran et al. (2019).

Scenario analyses were performed with biochar application rates of 5 and 20 ton ha−1 using the same type of biochar from Lychuk et al. (2015) (Table 1). Biochar or ZVC was assumed to be applied concurrently with the first fertilizer application of the year, with an application depth of 15 cm and 100% mixing efficiency. For ZVC, we modeled only a 20 ton ha−1 application rate, with ZVC properties shown in Table 1. Since ZVC is a novel substance whose properties could be modified in future applications, we set the CEC and BD values to match default biochar. Sensitivity analysis showed that 20–40% changes in BD and CEC would not have significantly changed ZVC’s impacts on Nr emissions (Additional file 1: Fig. S1).

2.5 Environmental impacts of carbon amendments

We examined FEST-C results to assess other changes associated with carbon amendments, including crop yield and nitrogen fluxes to water and sediments. Furthermore, we compared the radiative forcing of changes in N2O emissions (based a 100-year global warming potential of 273) (Forster et al. 2021) with estimates from Woolf et al. (2021) of the sequestration of CO2 by the biochar itself. Details were provided in the Supplementary Information.

3 Results and discussion

3.1 Comparisons to observations

The model matched the sign of the observed responses of N2O and NH3 emissions to biochar amendments at each field study location, demonstrating an ability to distinguish conditions under which biochar mitigates or stimulates emissions of each gas (Fig. 2). That is crucial to the model’s applicability to this study, as we aim to identify locations where soil carbon amendments would be expected to mitigate rather than stimulate emissions. However, the model tended to predict smaller changes than were observed, especially for the stimulation effects of N2O emissions reported by Verhoeven and Six (2014) in California. The linear regression results (R2) showed the model could explain 43% of the variance in the impacts of biochar amendments, a similar performance to a study that used a Random Forest regression model (R2 = 0.47 for NH3 and 0.24 for N2O) (Liu et al. 2019).

Fig. 2
figure 2

Simulated and observed impacts of biochar application on emissions of N2O (circles) and NH3 (triangles) at sites in California (CA, red) (Deng et al. 2015; Gao et al. 2022; Verhoeven and Six 2014), Colorado (CO, green) (Ramlow et al. 2019), and Illinois (IL, blue) (Edwards et al. 2018)

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Discrepancies may have arisen in part because the biochar module (Lychuk et al. 2015) assumed a hardwood-derived biochar, whereas the field measurements (Deng et al. 2015; Edwards et al. 2018; Gao et al. 2022; Ramlow et al. 2019; Verhoeven and Six 2014) applied different kinds of biochar (Table 1), such as ones derived from pine chips and walnut shells. Feedstock type can influence the interaction of biochar and nitrogen cycling (Liu et al. 2018; Sha et al. 2019; Zhang et al. 2021). Also, the field studies did not report some of the parameters that can be set in the biochar module, leading us to use the model’s default values for those parameters. For example, most studies did not report the CEC and BD values of the biochar. Furthermore, the module did not explicitly simulate bacterial processes and neglected the adsorption and desorption of inorganic nitrogen in soils.

3.2 Responses of soil properties to carbon amendments

Soil physical and chemical properties significantly influence nitrogen cycling and emission rates. FEST-C simulated that the responses of soil properties to carbon amendments vary widely spatially (Fig. 3), mainly depending on the original value of each soil property and the application rates of the amendment. Specifically, for CEC, FEST-C simulated that the lower the original soil CEC value, the greater the increase upon carbon amendment application.

Fig. 3
figure 3

Soil pH (top), CEC (center), and bulk density (bottom) under base case conditions (left) and their differences with 5 ton ha−1 (middle) and 20 ton ha−1 application of carbon amendments (right)

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For pH, the soil was acidic (pH < 5.8) in the Southeast, moderately acidic (< 6.5) in near the Pacific Northwest coast, close to neutral (pH ~ 7) in the Midwest, and alkaline in most western and Plains regions (Fig. 3). Carbon amendments tended to make soil pH more alkaline, especially in acidic areas.

Compared with soil pH and CEC, soil BD was less variable across regions, ranging from 1.24 to 1.46 ton m−3 with higher values in the western regions (Fig. 3). Application of carbon amendments slightly decreased BD, with less spatial variability than soil CEC and pH.

Carbon amendments were also modeled to slightly increase soil temperature, soil moisture, field capacity, and permanent wilting point via its influence on BD, consistent with previous observations (Edeh et al. 2020).

3.3 Responses of soil Nr emissions to carbon amendments

FEST-C estimated that soil emissions peak after fertilizer application (April–June and October) (Additional file 1: Figs. S2 and S3) and vary by region (Fig. 4), with the highest values in intensely fertilized regions such as the Midwest and California. The responses of emissions to carbon amendments also varied with application rate (Fig. 4). Low-dose biochar application (5 ton ha−1) stimulated emissions of all three nitrogen species in 75% of simulated agricultural areas, while high-dose applications (20 ton ha−1) mitigated emissions in 76% of simulated areas.

Fig. 4
figure 4

Spatial distributions of annual emissions of NO (top), NH3 (middle), and N2O (bottom), and the percent change in emissions under carbon amendment applications

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The low-dose biochar scenario was modeled to stimulate emissions most strongly in central and western states where soils are alkaline and inorganic nitrogen and organic carbon levels are high (Fig. 5). Mitigation effects mostly occurred in the Southeast and along the Pacific Northwest coast, where soils are acidic and have low levels of inorganic nitrogen and organic carbon (Fig. 5). By contrast, the high-dose scenario was modeled to mitigate emissions in most regions, with strongest mitigation where the low-dose scenario mitigated emissions (Fig. 5). Stimulation occurred soon after fertilizer input, while mitigation occurred later in the year (Additional file 1: Fig. S2).

Fig. 5
figure 5

Soil pH (left), soil inorganic nitrogen (center), and soil organic nitrogen (right) in areas where 5 ton ha−1 biochar application is modeled to mitigate (left box-and-whiskers) or stimulate emissions (right box-and-whiskers)

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Spatial patterns were similar across the three nitrogen species (Fig. 4), as the nitrogen cycling processes that generate them are closely connected and influenced by similar soil properties. For NO and N2O, the net effects of carbon amendments largely depended on how nitrification was affected (Additional file 1: Figs. S4 and S5). FEST-C modeled nitrification as the primary source (~ 80%) of NO and N2O emissions, especially during the growing season (April-July) (Additional file 1: Fig. S6), consistent with DayCent simulations but with a larger share from nitrification (Parton et al. 2001). Generally, nitrification is the dominant pathway for NO and N2O emissions in aerobic conditions with water-filled pore space (WFPS) lower than ~ 53%, while denitrification is the primary source under anaerobic conditions with higher WFPS (Congreves et al. 2019). In 2011, the severe drought in agricultural regions could explain why nitrification played a larger role than in some other studies.

3.4 Underlying mechanisms that drive the impacts of carbon amendments

Our simulations showed that the net change in nitrification rate is the key factor that determines the responses of emissions to carbon amendments. Mitigation occurs mainly in acidic soils with low substrate (inorganic nitrogen and organic carbon) levels and during the non-growing months. By linking those soil properties with nitrification rates, we further investigated the underlying mechanisms that drove disparate impacts using biochar as example.

Impacts of biochar amendments on emissions vary with soil properties as discussed above. We divided sites into three groups based on their initial soil pH, inorganic nitrogen levels, and organic carbon content, using the first and third quartiles as the thresholds for categorization. We defined a Low Substrate group to be acidic soils (pH < 5.84) with low organic carbon (< 55.9 kg C ha−1) and low inorganic nitrogen (< 101.5 kg N ha−1). Our High Substrate group has more alkaline soils (pH > 6.49) with high organic carbon (> 66.7 kg C ha−1) and high inorganic nitrogen (> 177 kg N ha−1). All other areas were assigned to a Moderate Substrate group.

Biochar applications tended to mitigate emissions from Low Substrate sites and stimulate emissions from High Substrate sites (Fig. 6). Impacts on Moderate group sites varied widely in sign and magnitude (Fig. 6). A strong correlation was found between the changes in Rnit with the variations of net mineralization rates (Rnmn) for areas in all three groups (Fig. 7).

Fig. 6
figure 6

Changes in emissions for areas allocated to Low, Moderate, and High Substrate groups under biochar application rates of a 5 ton ha−1 and b 20 ton ha−1. Low and High Substrate groups and b Moderate Substrate. Low Substrate is defined to be acidic soils (pH < 5.84) with low organic carbon (< 55.9 kg C ha−1) and inorganic nitrogen (< 101.5 kg N ha−1), while High Substrate refers to more alkaline soils (pH > 6.49) with high organic carbon (> 66.7 kg C ha−1) and inorganic nitrogen (> 177 kg N ha−1). All other sites are categorized as Moderate

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Fig. 7
figure 7

Relationships between changes in net mineralization rates (Rnit) and nitrification rates (Rnmn) under 5 ton ha−1 biochar applications for sites in (a) Low and High Substrate groups and (b) Moderate Substrate. Low Substrate is defined to be acidic soils (pH < 5.84) with low organic carbon (< 55.9 kg C ha−1) and inorganic nitrogen (< 101.5 kg N ha−1), while High Substrate refers to more alkaline soils (pH > 6.49) with high organic carbon (> 66.7 kg C ha−1) and inorganic nitrogen (> 177 kg N ha−1). All other sites are categorized as Moderate

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In FEST-C, Rnit are especially sensitive to the soil \(N{H}_{4}^{+}\) (R2 > 0.6), while other regulators as indicated in eq in Sect. 2.1 have relatively minor impacts. FEST-C treats \(N{H}_{4}^{+}\) as an intermediate variable that is influenced dynamically by net mineralization on a daily basis. In FEST-C, Rnmn are inversely affected mainly by organic carbon content (\({f}_{OC}\)) and inorganic N/C ratios (\({f}_\frac{N}{C}\)) for each carbon pool, and the impacts of those two variables on the net rates are comparable. Specifically, \({f}_{OC}\) correlates linearly with organic carbon while \({f}_\frac{N}{C}\) depends on inorganic nitrogen levels, corresponding to the key soil properties identified to distinguish mitigation or stimulation effects (Fig. 8).

Fig. 8
figure 8

Relationships between soil organic carbon factor (fOC) and inorganic nitrogen factor (fN/C) with net mineralization rates for areas in a Low Substrate group and b High Substrate group. Arrows indicate the changes in factors during fertilizer applications, after biochar applications, and in the non-growing season compared with the base case without biochar amendments. The red color refers to an increase in substrate levels and associated factors, while the blue color refers to a decrease in substrate levels and associated factors. The changes in net mineralization rates caused by the changes in fOC and fN/C are shown above each sub-figure. Low Substrate sites are defined to be acidic soils (pH < 5.84) with low organic carbon (< 55.9 kg C ha−1) and inorganic nitrogen (< 101.5 kg N ha−1), while the High Substrate group has more alkaline soils (pH > 6.49) with high organic carbon (> 66.7 kg C ha−1) and inorganic nitrogen (> 177 kg N ha−1). Remaining sites are assigned to the Moderate Substrate group with more moderate pH, organic carbon, and inorganic nitrogen

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Upon application of biochar, Rnmn immediately declines as the organic carbon and \({f}_{OC}\) increase, resulting in a decrease in \(N{H}_{4}^{+}\). Consequently, the associated decrease in soil inorganic nitrogen causes \({f}_\frac{N}{C}\) to decline. Assuming the biochar is applied concurrently with the fertilizer, the reduction in \({f}_\frac{N}{C}\) under high inorganic nitrogen levels outweighs the effects from the increase in \({f}_{OC}\), resulting in an increase in Rnmn and emissions (Fig. 8).

In non-growing seasons without fertilizer input, the changes in Rnmn diversify among three groups, depending on the relative magnitude of changes in \({f}_{OC}\) and \({f}_\frac{N}{C}\). Due to the increase in emissions during fertilizer application periods after applying biochar amendments, the amount of inorganic nitrogen remaining in soils in non-growing season declines, resulting in the \({f}_\frac{N}{C}\) decrease. For Low Substrate sites, the change in \({f}_\frac{N}{C}\) can be smaller than the change in \({f}_{OC}\), leading to the decrease in Rnmn. However, at High Substrate sites, the change in \({f}_\frac{N}{C}\) is more pronounced, leading to increases in Rnmn and emissions, as shown in conceptualized schematic (Fig. 8).

Conditions in the Moderate substrate group fell in between those of the High Substrate and Low Substrate groups. However, biochar tended to mitigate emissions at some Moderate sites where soil pH, organic carbon, and inorganic nitrogen are low, but stimulate emissions at most other Moderate sites (Additional file 1: Fig. S7).

As biochar application rates increased, the increases in \({f}_{OC}\) became more significant and tended to be larger than \({f}_\frac{N}{C}\), favoring mitigation of emissions. Therefore, the high application scenario (20 ton ha−1) generated more favorable impacts.

Overall, biochar amendment increases net mineralization, providing more soil ammonium for nitrification, resulting in increased emissions in most areas. However, as the application rates increased, the net mineralization tends to decline, resulting in less soil ammonium available for nitrification and lower emissions. Therefore, the net effects of carbon amendments depend most on how the nitrification process is affected, which is consistent with field measurements (Edwards et al. 2018; Sánchez-García et al. 2014).

Biochar properties also influence their impacts on nitrogen emissions. Our sensitivity analysis showed that the organic carbon content and the application rates were the two properties most affecting mitigation effects (Additional file 1: Fig. S8). Other biochar properties considered here had only minor influences on emissions, though biochar with lower BD was more likely to decrease NO emissions.

3.5 Co-benefits and trade-offs associated with biochar amendments

Beyond the emissions discussed above, nitrogen is also lost to the environment with water flow or sediments, harvested with crops, or accumulates in the soil. FEST-C modeled that 5 ton ha−1 application of biochar would reduce nitrogen loss via runoff, percolation, and denitrification by 4%, 5%, and 2%, respectively, while increasing nitrogen accumulation in soils by 6% nationwide and having a negligible effect on harvests. For the 20 ton ha−1 case, nitrogen loss to runoff and percolation was modeled to sharply decrease (~ 20%), and harvested nitrogen was modeled to decline 5%. That raised concern that high doses of biochar could reduce crop yield.

The influence of biochar amendments on the fate and transport of nitrogen depends on how biochar amendments influence net mineralization. FEST-C estimated that half of the inorganic nitrogen used by crops comes from net mineralization, consistent with field measurements (Sullivan et al. 2020). At low application rates, the minor changes in nitrogen budgets were attributed to the slight increase in net mineralization (3%). However, at high application rates, the considerable decrease in net mineralization (25%) resulted in a noticeable reduction of nitrogen input, reducing nitrogen losses in runoff and percolation but also reducing crop yield as noted above.

Our results are consistent with previous modeling studies that found that biochar application reduced nitrogen losses and could slightly reduce crop yields (Aller et al. 2018; Lychuk et al. 2015), and with field studies in the U.S. Midwest that found biochar slightly reduced crop yields (Holt et al. 2022) and only significantly increased yields in low-nutrient soils in the tropics.

Soil carbon amendments also sequester carbon in soils. For biochar, that carbon has been recently photosynthesized from the atmosphere by plants, whereas ZVC is derived from fossil fuels and thus is not a net sink of carbon from the atmosphere. On a 100-year global warming potential basis (Forster et al. 2021), we found that the climate impacts of biochar via carbon sequestration are two orders of magnitude larger than the impacts via N2O emissions in the first year.

3.6 Insights for further research

Given the numerous uncertainties in modeling highly complex biogeochemical systems, field studies will ultimately be needed to test the impacts of applying biochar and ZVC. The modeling presented here can inform the selection of sites and application rates. Our results suggested that the mitigation of emissions is most likely to be achieved if biochar is applied at sites with acidic soils and low levels of organic carbon and inorganic nitrogen. Our modeling predicted more favorable impacts for high-dose applications than for low-dose ones and for biochar rather than ZVC—results that would need to be tested in field studies. Impacts on crop yields remain highly uncertain.

Future modeling should examine alternate types of biochar and the roles of adsorption and desorption of inorganic nitrogen to refine the algorithms, and should compare results against additional field studies as they become available.

4 Conclusions

Applying carbon amendments to soils is a promising mitigation strategy to reduce reactive nitrogen emissions and mitigate their associated adverse impacts on air quality, climate, and human health. However, large-scale applications of carbon amendments require a spatially explicit assessment as their impacts on nitrogen emissions vary widely, ranging from positive, negative, to neutral. Our study is the first attempt to utilize a regional-scale agroecosystem model to simulate the applications of two types of carbon amendments, biochar, and ZVC, to the US. fertilized soils on a fine scale to identify the regions that could benefit most from this management. Our simulations indicated that the high-dose application (20 ton ha−1) of biochar amendments is most likely to mitigate emissions in acidic soils with low organic carbon (< 55.9 kg C ha−1) and inorganic nitrogen (< 101.5 kg N ha−1) content. The net effects of carbon amendment on nitrogen emissions depend most on how the nitrification process is affected. Under the favorable soil conditions mentioned earlier, high application rates of biochar amendments are likely to shift the conversion between inorganic nitrogen to organic nitrogen in favor of producing less ammonium. This slows nitrification, the process that dominates overall emissions under the drought conditions simulated in this study. Besides nitrogen emissions, biochar amendments at high application rates could also generate co-benefits in reducing other nitrogen losses via runoff, percolation, and denitrification. Our spatially explicit assessment of soil carbon amendments could inform policymakers and farmers where and how to apply these materials to generate benefits in reducing Nr emissions to improve air quality and mitigate climate change.