Global warming intensity of biofuel derived from switchgrass grown on marginal land in Michigan

Energy crops for biofuel production, especially switchgrass (Panicum virgatum), are of interest from a climate change perspective. Here, we use outputs from a crop growth model and life cycle assessment (LCA) to examine the global warming intensity (GWI; g CO2 MJ−1) and greenhouse gas (GHG) mitigation potential (Mg CO2 year−1) of biofuel systems based on a spatially explicit analysis of switchgrass grown on marginal land (abandoned former cropland) in Michigan, USA. We find that marginal lands in Michigan can annually produce over 0.57 hm3 of liquid biofuel derived from nitrogen‐fertilized switchgrass, mitigating 1.2–1.5 Tg of CO2 year−1. About 96% of these biofuels can meet the Renewable Fuel Standard (60% reduction in lifecycle GHG emissions compared with conventional gasoline; GWI ≤37.2 g CO2 MJ−1). Furthermore, 73%–75% of these biofuels are carbon‐negative (GWI less than zero) due to enhanced soil organic carbon (SOC) sequestration. However, simulations indicate that SOC levels would fail to increase and even decrease on the 11% of lands where SOC stocks >>200 Mg C ha−1, leading to carbon intensities greater than gasoline. Results highlight the strong climate mitigation potential of switchgrass grown on marginal lands as well as the needs to avoid carbon rich soils such as histosols and wetlands and to ensure that productivity will be sufficient to provide net mitigation.


| INTRODUCTION
Maintaining a global temperature increase below 1.5°C relies significantly on the large scale deployment of negative CO 2 emissions (carbon dioxide removal) technologies Intergovernmental Panel on Climate Change, 2018;Minx et al., 2018;Nemet et al., 2018). Negative emission technologies particularly applicable to the cellulosic biofuel production system are soil organic carbon (SOC) sequestration and carbon capture and storage (CCS). Combining these two technologies can mitigate greenhouse gas (GHG) emissions more efficiently than can any single technology alone (Gelfand et al., 2020;Kim et al., 2020).
Marginal lands such as those abandoned from agriculture due to low soil fertility or other environmental factors (Emery et al., 2017;Gelfand et al., 2013;Khanna et al., 2021) can be attractive locations to grow bioenergy crops in order to minimize or avoid food-fuel conflicts, indirect land use change effects, and debilitating carbon debts . Switchgrass (Panicum virgatum L.), a native perennial warm-season grass, is considered a promising feedstock for cellulosic biofuel production due to its high productivity, ability to grow on low fertility soils, low input requirements, and potential for SOC sequestration (Follett et al., 2012;Jin et al., 2019;Liebig et al., 2008;Martinez-Feria et al., 2022;McLaughlin & Kszos, 2005;Tilman et al., 2006;U.S. Department of Energy, 2016;Wright & Turhollow, 2010).
Soil organic carbon increase by switchgrass ranges from −0.6 to 4.3 Mg C ha −1 year −1 , depending on climate, soil properties, land use history and so on (Agostini et al., 2015;Dheri et al., 2022;Follett et al., 2012;Jin et al., 2019;Lee et al., 2007;Lemus & Lal, 2005;Liebig et al., 2008;Slessarev et al., 2020;Valdez et al., 2017). According to Liebig et al. (2008), switchgrass decreases SOC at two of ten experimental sites due to a significant decrease in soil bulk density near the surface depth, which contributes to decreased SOC, whereas switchgrass increases SOC at the remaining experimental sites. Dheri et al. (2022) show that switchgrass grown in Ohio could increase SOC in the 0-20 cm depth by 8.22 Mg C ha −1 within the first 8 years of their study. Switchgrass production on marginally productive croplands can also increase SOC by 0.9-1.3 Mg C ha −1 year −1 for 0-30 cm depth and over 2 Mg C ha −1 year −1 for the 0-150 cm depth (Follett et al., 2012;Jin et al., 2019). In addition, switchgrass has the potential to support increased biodiversity and resulting ecosystem services in agricultural landscapes (Werling et al., 2014). Biofuels derived from switchgrass can be carbon negative due to SOC sequestration during switchgrass production (Dwivedi et al., 2015;Schmer et al., 2014) or due to CCS during its biorefining (Gelfand et al., 2020).
Most bioenergy modeling efforts are implicitly based on a static approach, which is based on average (or timeindependent) values for foreground and background systems (Adler et al., 2007;Dwivedi et al., 2015;Kim & Dale, 2015;Kim et al., 2019Kim et al., , 2020Schmer et al., 2008Schmer et al., , 2014Wang et al., 2012). Unlike static life cycle assessments (LCAs), dynamic LCAs use time-dependent values for the foreground system, dynamic inventory data, and dynamic characterization factors to reduce uncertainty (International Organization for Standardization, 2006). Dynamic LCAs in the bioenergy system can capture annual fluctuations in biomass yields and subsequent SOC changes due to weather, as well as changes in electricity fuel mixes that affect GHG avoidance benefits. Relatively few studies, however (Albers et al., 2020;Almeida et al., 2015;Daystar et al., 2017;Levasseur et al., 2010;Yang & Chen, 2014), have used dynamic modeling. Yang and Chen (2014) estimated timedependent GHG emissions associated with electricity based on historical data in their crop residue gasification study. Levasseur et al. (2010) developed time-dependent dynamic global warming potentials (GWPs) for CO 2 and other GHGs based on the cumulative radiative forcing concept. Daystar et al. (2017) showed that dynamic GHG accounting is a more robust method than the static GHG accounting method because of temporal boundaries.
Here, we estimate the global warming intensity (GWI; g CO 2 MJ −1 ) of biofuel produced from switchgrass grown on marginal lands in Michigan and its GHG mitigation potential (Mg CO 2 year −1 ) with SOC changes and biomass yields estimated by the system approach to land use sustainability (SALUS) model (Basso & Ritchie, 2015). We use results to populate both a static (time-independent) and dynamic LCA to calculate GWI and GHG mitigation. The time-independent GWPs are considered under both to avoid carbon rich soils such as histosols and wetlands and to ensure that productivity will be sufficient to provide net mitigation.

K E Y W O R D S
γvalerolactone (GVL), cellulosic biofuel, dynamic LCA, global warming intensity, marginal land, static LCA, switchgrass the static and dynamic approaches to compare with the GWI of gasoline (93.08 g CO 2 MJ −1 ; U.S. Environmental Protection Agency, 2010), with a time horizon of 100 years.

| Area of study and marginal lands identification
We conducted this analysis for the state of Michigan USA (see Figure S1), which is in the northern portion of the US Corn Belt. The region has a humid continental climate (Köppen climate classification Dfb), with warm, short summers and cold, icy winters, and precipitation well distributed throughout the year. On average, the region receives 795 mm of annual precipitation, and the average daily temperature is 7.9°C (Liu & Basso, 2017). Land cover is dominated by cropland in the south, and deciduous and boreal woodlands in the north. Michigan also features a significant amount of lands that have been abandoned from annual crop production for varying periods (Lark et al., 2020), which means that such lands could be attractive for growing biomass crops because of their low opportunity cost (Kells & Swinton, 2014).
We identify marginal lands using land capability classes (LCC) as defined by the US Department of Agriculture in the SSURGO database (https://sdmda taacc ess.sc.egov. usda.gov). Following Gelfand et al. (2013), we consider soils with LCCs I-IV to be productive agricultural land excluded from the analysis. From the remaining soils (LCCs V-VIII), we further exclude those classified as urban as well as carbon dense habitats such as forests and wetlands as identified in the Cropland Data Layer (Boryan et al., 2011).

| Crop growth modeling
We used the SALUS model to estimate the potential yield and SOC changes in the identified marginal land sites. SALUS is a biogeochemical cropping systems simulation platform that contains process-based models to simulate crop growth and development, and carbon, water, and nutrient cycling on a daily time step basis. Model inputs are daily values of incoming solar radiation (MJ m −2 ), maximum and minimum air temperature (°C), and rainfall (mm), as well as information on soil characteristics and management. The SALUS model has been validated for several crops and management practices (Basso & Ritchie, 2015) and was previously used to spatially simulate switchgrass yields across Michigan (Liu & Basso, 2017) and to evaluate soil carbon sequestration from switchgrass across the US Midwest (Martinez-Feria & Basso, 2020). The SALUS switchgrass model has been validated under conditions of both loss and gains of SOC (Martinez-Feria & Basso, 2020). Martinez-Feria et al. (2022) used data from 28 experimental sites across eight Midwestern states to satisfactorily estimate observed yields and SOC change.
We used the SALUS model (Basso & Ritchie, 2015;Martinez-Feria & Basso, 2020) to simulate the yield of a switchgrass crop planted on marginal land following a conventional tillage event at 30 cm depth which allowed for the incorporation of the previous vegetation (mixed annual and perennial plants). The procedure of tilling and incorporating the previous vegetation was chosen to represent a realistic scenario. The large first-year losses of SOC from the conversion of marginal land to switchgrass is considered conservative rather than choosing a scenario with conditions which would produce results more favorable to growing bioenergy crops in terms of reduced SOC losses (e.g., no tillage).
For weather inputs we used the Gridded Surface Meteorological dataset (gridMET; http://www.clima tolog ylab.org/gridm et.html; Abatzoglou, 2013), a highresolution (~4 km, daily) weather dataset ideal for land surface modeling. For every 30 × 30 m grid point within our study area, we used daily weather values for the period of 1980-2019. Data on soil characteristics at every site are retrieved from the gridded SSURGO dataset (30 m resolution) and used to configure the soil component of the model following the methodology described by Liu and Basso (2017). The model is run for each 30 m grid cell for each combination of soil and weather inputs, resulting in 750,000 unique simulations.
We ran each simulation for 30 years and assumed each stand is replanted on each 11th year of the simulation following harvest and tillage events. This means that each simulation encompasses three planting cycles. To avoid confounding the effect of weather year and renewal of the perennial stand, the year to start the simulation for each grid cell was chosen at random from the first 10 years in the gridMET dataset (1980)(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989). Plantings were simulated to occur in mid-May, and annual harvests in mid-October. The simulation considered both unfertilized (N0) and fertilized (N50) scenarios, with the fertilized scenarios receiving 50 kg N ha −1 top-dressed in late May every year. Based on evidence from long-term experiments in the region, we assume a 65% harvest efficiency, that is, that 35% of total above ground net primary productivity is returned to the soil as plant residues prior to or during harvest operations (Martinez-Feria & Basso, 2020). Outputs from the simulation are annual dry biomass yields (Mg ha −1 ), hereafter referred to as switchgrass production, and annual SOC contents (Mg C ha −1 ; 0-15, 15-40, 40-90 cm and entire soil profile). The grid cells are aggregated based on proximity to ~40,000 individual parcels, considered as farm units supplying switchgrass to the biorefinery. The median size of individual parcels is 1.76 ha, and ranges from 0.01 to over 100 ha.

| Biofuel production system
We include in our analysis only those land parcels capable of producing one biomass bale (541 dry kg, Hess et al., 2009) at least 9 of 10 years to avoid excessive logistics costs. Baled switchgrass is assumed to be transported from these marginal land parcels to a centralized biorefinery by truck and then processed to produce biofuel.
The centralized biorefinery consists of facilities for feedstock handling, pretreatment (if applicable), enzyme production (if applicable), hydrolysis, fermentation, cogeneration and wastewater treatment. Biofuel yield from switchgrass is assumed to be equal to that from corn stover (Argonne National Laboratory, 2020). Two different hydrolysis technologies are considered in the analysis: (1) chemical hydrolysis and (2) enzymatic hydrolysis. The chemical hydrolysis technology uses a mixture of γvalerolactone (GVL), water, and toluene plus dilute sulfuric acid as a catalyst to hydrolyze cellulose and hemicellulose into fermentable sugars (Won et al., 2017). In the enzymatic hydrolysis technology, dilute acid pretreatment is performed prior to the enzymatic hydrolysis (Tao, Schell, et al., 2014). Process data for the biorefinery are obtained from the literature: one process data set for the biorefinery with chemical hydrolysis technology (referred to as "CHEM", Won et al., 2017) and two process data sets for the biorefinery with enzymatic hydrolysis technology (referred to as "ACID", Tao, Schell, et al., 2014 and "GREET", Argonne National Laboratory, 2020, respectively). The assumptions and parameters relevant to the biorefinery are summarized in Tables S1 and S2.

| Static GHG emissions
The GWI of biofuel includes GHG emissions associated with switchgrass production, transportation of baled switchgrass to a biorefinery, storage, biorefinery operations, transportation/distribution of biofuel, avoided grid electricity, biofuel combustion, and upstream processes (e.g., materials and fuels). GHG emissions of switchgrass production per hectare on each marginal land parcel are calculated based on average values over 30 years. GHG emissions of switchgrass production derive from agronomic inputs (i.e., seed, fertilizers, and herbicides), fuel for field operations, CO 2 emissions from SOC change, and N 2 O emissions. The agronomic inputs and fuel use are obtained from field experiment data at the Great Lakes Bioenergy Research Center (GLBRC) biofuel cropping system experimental site and marginal land experimental sites in Michigan (https://data.susta inabi lity.glbrc.org/ datat ables). Although little phosphorus and potassium fertilizers have been applied in the two experimental sites, we conservatively assume that phosphorus and potassium fertilizers are applied annually at rates of 2 kg P 2 O 5 and 7 kg K 2 O dry Mg −1 of switchgrass harvested regardless of nitrogen application rate (U.S. Department of Energy, 2016). Fuel use per hectare is assumed to be constant regardless of the size of the marginal land parcel. CO 2 emissions from SOC change are calculated based on results from the SALUS simulations. N 2 O emissions are estimated by the IPCC Tier 1 methodologies (Intergovernmental Panel on Climate Change, 2019). Both direct and indirect N 2 O emissions are included in the calculations.
Average GHG emissions associated with one metric ton of switchgrass are estimated by dividing the average GHG emissions of switchgrass production per hectare by an average switchgrass yield. Since no biorefinery sites are specified in this analysis, the transport distance from marginal land parcels to a biorefinery is arbitrarily assumed to be 80.5 km (50 miles). GHG emissions associated with storage and transportation/distribution of biofuel are estimated using data from the literature (Argonne National Laboratory, 2020; Brownell, 2009). Surplus electricity from the biorefinery is exported to the grid and is assumed to displace the U.S. grid electricity. Biogenic CO 2 emissions from combusting biofuel are offset by carbon uptake of switchgrass and are not taken into account in these GHG calculations. Thus, the GHG emissions of combusting biofuel include only CH 4 and N 2 O emissions from tailpipe combustion (U.S. Environmental Protection Agency, 2010).
The GHG emissions of materials and energy production are calculated based on the unit process data obtained from the US Life Cycle Inventory Database (https://www. nrel.gov/lci/), the Ecoinvent database version 3.4 (https:// www.ecoin vent.org/datab ase/datab ase.html), and the GREET model (Argonne National Laboratory, 2020). Matrix inversion (Frischknecht et al., 2007) is used to calculate the cumulative GHG emissions associated with materials and energy productions. The GHG emissions associated with a product (or an energy flow) can be split into two categories: off-process and in-situ process (gateto-gate) GHG emissions. The off-process emissions are the GHG emissions associated with other products (or energy) involved in the product system of interest (e.g., upstream and downstream processes-raw materials and input fuels production, transportation, waste management, etc.). The in-situ process emissions are the GHG emissions released from the unit process that generates the product (or energy flow) of interest. Thus, the cumulative GHG emissions associated with the mth product, e m , can be expressed as: where p m is the in-situ process GHG emissions of the mth product production process, and u m is the off-process GHG emissions of the mth product production process. The GHGs in this analysis include CO 2 , CH 4 and N 2 O. The off-process GHG emissions, u m , can be calculated as where a is the economic entity defined by Heijungs (1994). For example, a l,m denotes the quantity of the lth product (or energy) involved in the mth product production process. The economic entity is obtained from the unit process data. Note that the economic entities for multi-functional processes in Equation (2a) are allocated entities via proper methods (e.g., physical or economic properties, etc.), which are provided by the databases. The GHG emissions of a product (an energy) can be written in a matrix form.
Solving Equation (3c) if A is a nonsingular matrix, the off-process emission matrix, U, is where I is the identity matrix. The cumulative GHG emissions, E, therefore become The 2016 electricity fuel mix (U.S. Energy Information Administration, 2018) is used to calculate the cumulative GHG emissions of materials and energy in the static approach. The transmission and distribution loss for electricity (4.5%; U.S. Environmental Protection Agency, 2018) is also included in the calculations. The cumulative GHG emissions for materials and energy are shown in Figure S2.
GHG emissions associated with transportation of materials and energy (US Department of Transportation, 2015) are included in the cumulative GHG emissions.
Greenhouse gas mitigation by biofuel is categorized into two types: carbon removal and GHG avoidance. The carbon removal is the net sum of carbon absorbed by SOC sequestration and GHG emissions released from the biofuel system (including switchgrass production, transportation, storage, biorefinery, distribution and combustion). The GHG avoidance is avoided life cycle GHG emissions associated with alternative systems (i.e., grid electricity and gasoline) displaced by the biofuel system.

| Dynamic (time-dependent) approach
In the dynamic approach, annual GHG emissions of materials and fuels are projected based on the electricity fuel mixes from 2016 to 2045 (see Figure S3). No evolution of technologies (e.g., "technological advances", "technological shift", etc.) in the material and fuel productions are assumed in the dynamic approach due to lack of data. Two electricity fuel-mix projections are considered in the dynamic approach. The electricity fuel mix projections by the U.S. Energy Information Administration (2019) are used in the first projection (referred to as "P_EIA", see Figure S3a). The second projection ("P_COAL", see Figure S3b) assumes that after 2023 (arbitrarily chosen), fossil fuels except for natural gas decline faster than in the first projection, using maximum annual decrease rates in the first projection. In contrast to coal and petroleum, the projections for natural gas and nuclear in the second projection are the same as in the first projection. The differences are therefore assigned to renewable energy sources. As seen in Figure S3b, coal is projected to be totally phased out in 2035 in the second projection.
Greenhouse gas emissions of switchgrass production per hectare on each marginal land parcel for each year are calculated, and then are divided by switchgrass yield in a given year to calculate GHG emissions of one metric ton of switchgrass. When no switchgrass is harvested from a particular parcel in a given year, the GHG emissions of switchgrass production are assigned to the next harvest year. GHG emissions of agronomic inputs, fuels and materials used in the biofuel system during each year are calculated based on the electricity fuel mix of the harvest year through Equations (3-5). We assume that the GHG avoidance from the surplus electricity is calculated based on the electricity fuel mix of the year following harvest, implying that the surplus electricity from switchgrass-based biofuel system displaces electricity in the year following harvest. However, the GHG avoidance from the surplus electricity is assigned to the switchgrass production year for consistency and ease of understanding. More information on methods and background data can be found in Kim et al. (2023).

| GHG emissions of switchgrass in the static approach
The total potentially available marginal land in Michigan is 324,000 ha. However, not all of these lands are suitable for biofuel production: The GWI of biofuels derived from switchgrass grown on about 11% of available marginal lands (35-36,000 ha) is greater than that of gasoline due to high SOC loss (see Figures S5 and S7). We thus exclude these lands from further analysis, leaving 288,000 ha available for further analysis. Results from the SALUS model show that switchgrass yield with no nitrogen fertilizer added (0N) is 30% lower on average compared to 50N (see Figure S6), very close to field experiment results from the GLBRC marginal land experimental sites in Michigan (https://data.susta inabi lity.glbrc.org/datat ables). Mean switchgrass yield is 5.35 (±2.18) Mg ha −1 year −1 for 0N and 7.65 (±2.87) Mg ha −1 year −1 for 50N, and the total annual switchgrass production is 1.5 Tg of biomass for 0N and 2.2 Tg of biomass for 50N. The area-weighted simulated average SOC sequestration rates are 0.09 (±0.14) and 0.39 (±0.23) Mg C ha −1 year −1 for 0N and 50N, respectively. However, switchgrass production and harvesting on about 22% of the marginal land of 288,000 ha for a fertilizer application rate of 0N and on about 6% of 288,000 ha for an application rate of 50N reduces SOC levels by 0.13 (±0.14) and 0.19 (±0.18) Mg C ha −1 year −1 , respectively (see Figure S7). Results from the SALUS model show that switchgrass production on marginal lands with low initial SOC stock increases SOC levels. In contrast, switchgrass production on marginal lands with high initial SOC stocks (>200 Mg C ha −1 ) reduces SOC regardless of the nitrogen fertilizer application (see Figure S8). Several field studies (Goidts et al., 2009;Kampf et al., 2016;Mann, 1986;Minasny et al., 2017;Saby et al., 2008;Sollins et al., 1996;Zhao et al., 2013) also show that soils with low initial SOC stock increased SOC, but soils with high initial SOC stock lose SOC.
Mass-weighted average GHG emissions of switchgrass grown on suitable marginal lands in Michigan are 15.3 (±99.6) kg CO 2 Mg −1 for 0N and −62.8 (±117.1) kg CO 2 Mg −1 for 50N. Approximately 60% of unfertilized switchgrass grown on marginal lands (0.9 Tg of biomass) has negative GHG emissions (see Figure S10) and can remove 0.11 Tg of CO 2 year −1 directly from the atmosphere and sequester the atmospheric carbon in soil, resulting in net GHG mitigation of 0.05 Tg of CO 2 year −1 . About 76% of fertilized switchgrass (1.7 Tg of switchgrass biomass) has negative GHG emissions (see Figure S10) and can sequester 0.41 Tg of atmospheric CO 2 year −1 in soil. The net GHG mitigation by fertilized switchgrass with negative GHG emissions amounts to 0.20 Tg of CO 2 year −1 . SOC sequestration is the major source of negative emissions, and the mass-weighted average SOC sequestration is 58.9 (±96.4) kg CO 2 Mg −1 for 0N and 188.1 (±113.9) kg CO 2 Mg −1 for 50N (see Figure 1). N 2 O emissions from fertilized switchgrass are greater than those from unfertilized switchgrass production because of N 2 O resulting from nitrogen fertilizer application.

| GWI in the static approach
The total annual biofuel production on the suitable marginal lands in Michigan is 0.40-0.49 hm 3 for 0N and 0.57-0.71 hm 3 for 50N, depending on the biorefinery model F I G U R E 1 Breakdown of GHG emissions of switchgrass in the static approach. "Agronomic inputs" include GHG emissions of fertilizers (N, P, K), seed and herbicides. "Fuel" is GHG emissions associated with diesel used in field operations. "SOC" is GHG emissions of SOC sequestration. "N 2 O" is N 2 O emissions. GHG, greenhouse gas; IQR, interquartile range; SOC, soil organic carbon employed. Volume-weighted average GWI of biofuel derived from unfertilized switchgrass (0N) is from 5.0 to 7.6 g CO 2 MJ −1 , while volume-weighted average GWI of biofuel derived from fertilized switchgrass (50N) is negative, ranging from −9.4 to −4.8 g CO 2 MJ −1 (see Table 1). More than 93% of biofuels derived from switchgrass grown on marginal lands (equivalent to 85%-87% of the total available marginal lands) meet the 60% GHG reduction requirement of the U.S. Energy Independence and Security Act (U.S. Environmental Protection Agency, 2010), regardless of nitrogen fertilizer application. About 41%-51% of biofuels derived from unfertilized switchgrass (0.17-0.20 hm 3 year −1 ) and 73%-75% of biofuels derived from fertilized switchgrass (0.43-0.52 hm 3 year −1 ) are carbon negative (see Figures S11-S13).
Marginal lands for switchgrass production resulting in carbon-negative biofuels have low initial carbon stock (See Figures S14-S16). The initial carbon stock in over 70% of Michigan marginal lands for switchgrass production for carbon-negative biofuels is less than 100 Mg C ha −1 . The initial SOC stock could be one of the key indicators of (spatially) differentiated GWI. As seen in Figures S17-S19, the GWI of biofuels derived from switchgrass grown on marginal lands tends to increase with initial SOC stock due to large SOC losses in carbon-rich marginal lands. The GHG tradeoff between SOC loss and biomass yield is insignificant. Carbon-rich soils can achieve high biomass yield (see Figure S9), but GHG emissions from SOC loss are so large that the positive effect of high biomass yield is negligible.
The CHEM model (biorefinery with chemical hydrolysis technology) has the lowest average GWI among other models regardless of nitrogen fertilizer application. The primary reason that the CHEM model achieved the lowest average GWI is that it provides the greatest GHG avoidance from the surplus electricity compared to the other models (−25 g CO 2 MJ −1 ). The GHG avoided by the surplus electricity is −19 g CO 2 MJ −1 for the ACID model and −17 g CO 2 MJ −1 for the GREET model. Volumeweighted average GHG emissions associated with unfertilized switchgrass in the GWI of biofuel are from 2.7 to 2.8 g CO 2 MJ −1 , while volume-weighted average GHG emissions of fertilized switchgrass range from −11.5 to −9.0 g CO 2 MJ −1 , depending on the biorefinery models, especially as these models determine biofuel yields (see Figures S20-S22). GHG emissions associated with the biorefinery are 16-18 g CO 2 MJ −1 .

| GHG mitigation in the static approach
The total GHG emissions from the biofuel production system based on switchgrass grown on marginal lands in Michigan (including CO 2 released from SOC loss, N 2 O, GHG emissions of materials and fuels, etc., not including GHG avoidance from the surplus electricity) are 0.33-0.37 Tg CO 2 year −1 for 0N and 0.56-0.61 Tg CO 2 year −1 for 50N. Over 37% of the total GHG emissions in the biofuel production system come from biorefinery processes (see Figure S23).
In the biofuel production system based on fertilized switchgrass, GHG emissions from agronomic inputs and N 2 O emissions account for 41%-45% of the total GHG emissions released, while in the biofuel production system based on unfertilized switchgrass, these emissions only account for 24%-27% of total GHG emissions. CO 2 released from SOC loss contributes 2%-9% of the total GHG emissions released. As mentioned previously, switchgrass production on some marginal lands (22% for unfertilized switchgrass production and 6% for fertilized switchgrass production) reduces the SOC level, thereby releasing CO 2 to the atmosphere. SOC sequestration is 0.12 Tg CO 2 year −1 for the biofuel system based on unfertilized switchgrass and 0.43 Tg CO 2 year −1 for the biofuel system based on fertilized switchgrass.
Greenhouse gas avoidance by displacing grid electricity ranges from 0.16 to 0.26 Tg CO 2 year −1 , and the GHG avoidance by displacing gasoline range between about 0.79 and 1.40 Tg CO 2 year −1 . The net GHG mitigation by biofuel is therefore 0.74-0.91 Tg CO 2 year −1 for the biofuel system based on unfertilized switchgrass and 1.24-1.47 Tg CO 2 year −1 for the biofuel system based on fertilized switchgrass (see Figure 2). Applying nitrogen fertilizer can increase the GHG mitigation by biofuel due to larger biofuel volume produced and lower GWI. The biofuel system based on the GREET model exhibits the greatest GHG mitigation regardless of nitrogen fertilizer application simply because of greater biofuel yield.

| Dynamic approach
We analyzed with the dynamic approach only the 50N case with the chemical hydrolysis technology. As seen in Figure 3 (also Table S3), the dynamic GWIs in each year range from −415 to 442 g CO 2 MJ −1 , reflecting GHG emissions associated with each year's activities in the biofuel production system (e.g., switchgrass production, biorefinery, combustion, etc.), with a volume-weighted average of −7.2 (±21.4) g CO 2 MJ −1 in the P_EIA projection and of −3.0 (±21.4) g CO 2 MJ −1 in the P_COAL projection. The average dynamic GWI is higher than the average static GWI (−9.4 (±21.5) g CO 2 MJ −1 ). The decline of coal used in the electricity fuel mix plays a major role in increasing GWI in the dynamic approach and reduces the GHG avoidance due to supplying surplus electricity to the grid by 12% and 35% in the P_EIA and the P_COAL projections, respectively. Changes in the electricity fuel mix reduce GHG emissions of materials and fuels by only 1%-3%. The GWI in the first year is much higher than GWIs in other years because of GHG emissions from CO 2 released from SOC loss. The SOC sequestration rates in the first 3 years are negative (see Figures  As seen in the dynamic GWI pattern in Figure 3, the GWIs in the final year of any planting cycle (11th and 22nd years) rapidly decline compared to the GWI in the previous year. The primary reason for the rapid GWI declines is dead biomass at the end of the cycle, which is incorporated into the soil and increases SOC level, resulting in a high SOC sequestration rate, particularly SOC sequestration rate at a soil depth of 15 cm (see Figures S24 and S25). The GWIs in the establishment year of the second and third planting cycles (12th and 23rd years) decline more rapidly and are much lower than those in other years, less than −310 g CO 2 MJ −1 due to higher SOC sequestration rates and lower switchgrass yields in the establishment year (see Figures S24  and S25). The SOC sequestration rates in the second and third years after planting switchgrass (except for the first planting cycle) decrease compared to the SOC sequestration rate in the establishment year; hence GWIs increase greatly in those 2 years. After the third year, GWIs are relatively stable until the final year of a given planting cycle.
F I G U R E 2 GHG mitigation for 288,000 ha of marginal land in Michigan for biofuel production using the static approach. CO 2 released includes GHG emissions of materials and fuels, CO 2 released from SOC loss and N 2 O. CO 2 absorbed is atmospheric carbon absorbed by SOC sequestration. Avoided electricity is the GHG avoidance from the surplus electricity. Avoided gasoline is the GHG avoidance by displacing gasoline. GHG, greenhouse gas; SOC, soil organic carbon F I G U R E 3 GWI in the dynamic approach. "Inputs/fuels" includes GHG emissions of fertilizers (N, P, K), seed, herbicides and fuels. "N 2 O" is N 2 O emissions. "GHG from SOC change" is GHG emissions from SOC loss. "C absorbed by SOC change" is atmospheric carbon absorbed by SOC sequestration. "Electricity" is GHG avoidance from the surplus electricity. "Biorefinery" is GHG emissions of biorefinery, transportation, storage, distribution and combustion. GHG, greenhouse gas; GWI, global warming intensity; SOC, soil organic carbon As seen in the spatial and temporal GWIs for each parcel (see Figures S26 and S27), the GWIs of some parcels are significantly higher than those of other parcels in most years (except the final year of each planting cycle). Higher GWIs in those parcels are caused by lower SOC sequestration rates in those years compared to SOC sequestration rates in other parcels. Due to low SOC sequestration rates and higher N 2 O emissions, the GWIs of approximately 42% of total parcels in Wayne County (southeast Michigan) in the establishment year of the second and third planting cycles (12th and 23rd years) are greater than the GWI of gasoline.
In the first year after converting marginal lands to switchgrass production, GHGs released from the biofuel production system are much larger than the sum of carbon absorbed and GHG avoidances due to SOC loss; hence about 1.1 Tg of CO 2 is released (see Figure 4). After the first year, biofuel derived from switchgrass can mitigate GHG emissions by between 0.03-2.6 Tg CO 2 year −1 . The biofuel volume in the establishment year of the second and third planting cycles is 12%-20% lower than the biofuel volume in the final year of the previous planting cycle, resulting in less GHG avoidance (see Figure 4).

| DISCUSSION
Biofuel volume produced annually varied greatly across the study region. Based on switchgrass availability, Northern Michigan, and northern regions of Central and Western Michigan are likely the best candidate locations for a biorefinery when switchgrass grown on marginal lands is the sole feedstock for biofuel production (see Figure S28). Approximately 74% of switchgrass grown on marginal lands in Michigan could be transported to a biorefinery less than 137 km distant (see Figure S29), and from a logistics perspective, a bale-based logistics system would be preferred.
In contrast, a pellet-based logistics system is favored for about 26% of switchgrass grown in Michigan. Considering the cost of pelletization and transportation, the breakeven distance between bale-and pellet-based logistics systems is about 137 km (Sokhansanj et al., 2010). Most of switchgrass produced in the upper peninsula of Michigan would be transported over 137 km, and a depot (pellet)based biorefinery system would be needed for biofuel production from switchgrass. Chen et al. (2021) used the DayCent biogeochemical model to estimate the GWI of biofuel derived from switchgrass grown on Conservation Reserve Program (CRP) land in the eastern United States and found that the GWI of switchgrass-based biofuel is 1.69 g CO 2 MJ −1 , which is slightly higher than the GWIs in this study (see Table S4). The main difference between two studies is the change in SOC caused by biofuel yield, climate, biogeochemical model, time horizon (30-year vs. 14-year), simulation resolution (30 × 30 m vs. county), spatial boundary (Michigan vs. eastern region of the U.S.), and so on. However, both studies show that switchgrass production can raise SOC level.
The differences in the total GHG mitigation by biofuel between the static and dynamic approaches are small: only 2%-6%. GHG avoidance from the surplus electricity, which depends greatly on the electricity fuel mix, especially the fraction of coal in the mix, plays a major role in the differences between two approaches. The dynamic approach clearly reflects the effect of annual biomass yield fluctuations and the effect of future changes in the electricity fuel mix on GWI and GHG mitigation by biofuel. Therefore, the dynamic approach would be more F I G U R E 4 GHG mitigation in the dynamic approach. CO 2 released includes GHG emissions of materials and fuels, CO 2 released from SOC loss and N 2 O. CO 2 absorbed is atmospheric carbon absorbed by SOC sequestration. Avoided electricity is the GHG avoidance from the surplus electricity. Avoided gasoline is the GHG avoidance by displacing gasoline. GHG, greenhouse gas; SOC, soil organic carbon appropriate for the biofuel production system. However, results from the static approach are also important from a legislative and policy point of view because they are less uncertain.
The dynamic approach used in this study is incompletely realized, and there is room for improvement such as by utilizing or developing full dynamic inventory data (including "technological advances", "technological shift", etc.), time-dependent characterization factors, and so on (Levasseur et al., 2010;Lueddeckens et al., 2020;Sohn et al., 2020). Evolution of technologies would be forecasted by expert surveys, policies, extrapolation from historical data, discount rate method, and other methods (Lueddeckens et al., 2020;Tiruta-Barna et al., 2016;Yuan et al., 2015). Since modeling full dynamic inventory data is time-consuming (Beloin- Saint-Pierre et al., 2017;Hu, 2018), major GHG source processes in the biofuel production system (e.g., grid electricity, biorefinery, fertilizers, etc.) would be the best candidates for building dynamic inventory data.
As they are defined in our study, marginal lands clearly can produce crops for biofuel production to mitigate GHG emissions. This finding is consistent with the existing literature and suggests carbon-negative biofuels derived from switchgrass grown on marginal land could contribute to keeping the global temperature increase below 1.5°C (Intergovernmental Panel on Climate Change, 2018; Robertson et al., 2022). Furthermore, concentrating this energy crop production on marginal lands can reduce potential food-versus-fuel conflicts, further improving the environmental and societal benefits of such systems.
However, not all marginal lands are suitable for biofuel production. In Michigan, the GWI of biofuel derived from switchgrass grown on about 11% of the total available marginal lands is greater than that of gasoline due to high SOC loss. The initial carbon stock in those 11% of marginal lands is very high (>>200 Mg C ha −1 ) compared to marginal lands with negative GWI (see Figures S14-S16). This strongly implies that marginal lands with low initial SOC stock would be more favorable for producing switchgrass than carbon-rich lands. This result highlights the importance of site-specific assessment and using soil data, modeling, and other means to determine site-specific suitability of marginal lands for biofuel production prior to planting energy crops on such lands.