Large-scale deployment of in-rotation grass cultivation as a multifunctional soil climate mitigation strategy

The agricultural sector can contribute to climate change mitigation by reducing its own greenhouse gas (GHG) emissions and sequestering atmospheric carbon in vegetation and soils, and by providing biomass for substituting fossil fuels and other GHG intensive products in the energy, industry and transport sectors. New policies at EU level provide incentives for more sustainable land use practices, for example, cultivation systems using perennial plants that provide biomass for food, bioenergy and other biobased products along with land carbon sequestration and other environmental benefits. Based on spatial modelling across more than 81,000 landscapes in Europe, we find that introduction of grass-clover leys into rotations with annual crops could result in soil organic carbon sequestration corresponding to 5-10% of total current GHG emissions from agriculture in EU27+UK, annually until 2050. The combined annual GHG savings from soil carbon sequestration and use of biogas produced in connection to grass-based biorefineries equals 13-48% of current GHG emissions from agriculture. The assessed environmental co-benefits (reduced wind and water erosion, reduced nitrogen emissions to water, and mitigation of impacts associated with flooding) are considerable. Besides policy instruments, new markets for grass biomass, e.g., as feedstock for producing biofuels and protein concentrate, can incentivize widespread deployment of in-rotation grass cultivation.


Introduction
The recently published IPCC WG1 AR6 report 1 concluded that global warming of 1.5C and 2C will be exceeded during the 21st century unless substantial reductions in greenhouse gas (GHG) emissions occur in the coming decades. The majority of climate scenarios limiting warming below 1.5C and 2C (with no or limited overshoot) deploy carbon dioxide removal (CDR) from the atmosphere 2,3 . The agricultural sector can contribute to climate change mitigation through greenhouse gas (GHG) emissions reductions and CDR via carbon sequestration in vegetation and soils, and by providing biomass for mitigation in the energy, industry and transport sectors through substitution of fossil fuels and other GHG-intensive products 4 . At the same time, the agriculture sector needs to address water, soil, and biodiversity impacts caused by historic and current practices 5,6 and adapt to climate change, which is expected to cause new stresses on agricultural systems and exacerbate risks to livelihoods, human and ecosystem health, and food systems 4 .
The European Union (EU) Common Agricultural Policy (CAP) for the period 2021-2027 includes regulations and incentives to promote climate change mitigation, environmental protection, and preservation of biodiversity 7 . Other EU policies that are likely to influence agricultural practices include the Renewable Energy Directive 8 , the European Green Deal 9 , the Biodiversity Strategy for 2030 10 , and the Farm to Fork Strategy 11 . Changes in agricultural practices towards increased cultivation of perennial plants in intensively cultivated agricultural landscapes, can contribute to many of the objectives underlying these policies by providing biomass for food, bioenergy and other biobased products while reducing environmental impacts from agriculture [12][13][14][15][16][17] . The strategic design, localization and management of cultivation systems using grasses and leguminous plants (from here on referred to as "grass") is one example of such beneficial land use change. For example, biomass production in species-rich mixtures of perennial grasses on marginal land have shown potential for enhancing biodiversity and carbon sequestration into soils 18 , and increased grass cultivation in cereal-dominated crop rotations can increase the soil organic carbon (SOC) content and enhance crop yields in the longer term 19 .
Thus, as grass is introduced in crop rotations, the decrease in area under annual crops used for food and feed, can be counterbalanced by improved soil fertility and higher crop yields. The food/feed crop displacement effect is further reduced when grass biomass is used in biorefineries producing food and feed, along with bioenergy and other biobased products 20,21 . For example, lactic acid bacteria can facilitate the use of grass biomass to produce a protein concentrate suitable for feeding monogastric animals as well as ruminants, and also other products for material or energy use 22 . Such solutions, using alternatives to high-input and high-emission annual grain and seed crops as feedstock, can enable sustainable intensification of the agricultural systems with reduced environmental impacts 23 . To illustrate, grass production on one hectare of cropland in EU (assuming 10 tonne dry matter (DM) annual yield) can support protein concentrate production in a biorefinery equivalent to soy meal from 0.8 hectare of soybean cultivation in EU (2.8 t y -1 ) or 0.6-0.8 ha of soybean cultivation in Brazil (2.8-3.5 t y -1 ). This reduces the cropland displacement effect with 60-80%. Higher crop yields from improved soil fertility would reduce the cropland displacement effect even further. When factoring in also other biorefinery outputs, such as biogas and biobased products, the deployment of in-rotation grass cultivation may in some regions even result in net cropland savings.
Here, we estimate the effects of widespread deployment of in-rotation grass cultivation, aimed to remediate SOC losses from historic land-use while providing biomass and additional environmental benefits. We model the introduction of perennial grasses into annual crop rotations in more than 81 000 sub-watersheds across Europe (EU27+UK). We then quantify expected increases in SOC and grass biomass production, in terms of dry matter (DM), extractable protein, energy content, and biogas output, and the corresponding GHG emissions savings. Finally, we quantify and indicate multiple environmental co-benefits.
The results show that widespread deployment of in-rotation grass production would result in significant carbon sequestration in agricultural soils. The annual carbon sequestration until 2050 in two illustrative deployment scenarios corresponds to some 5-10% of current GHG emissions from agriculture in EU27+UK. The combined annual GHG savings from soil carbon sequestration and biogas use amounts to 20-50% of current GHG emissions from agriculture. In addition, environmental co-benefits can be substantial, including avoided soil loss by wind and water erosion, reduced nitrogen emissions to water, and mitigation of flooding events. Some European farmers may consider soil quality improvements sufficient motivation for in-rotation grass cultivation. Grass cultivation may also be an attractive option where intensive annual crop cultivation becomes restricted to protect the environment. In other places, incentives such as payments for soil carbon sequestration and other environmental benefits may be needed 16 . Investors need to be confident in the long-term economic viability of grass-based biorefineries 24 , which is likely to be influenced by the outcome of the current process following the European Commission's proposal 25 to revise the Renewable Energy Directive (RED). For example, treatment of biogas from biorefineries in the revised RED will depend on whether biogas is considered a main product or co-product of the biorefinery process.

Results
Perennial grass was introduced into crop-rotations on 115 million hectares (Mha) of arable land, in 24 363  landscapes (see Methods), including about 80% of all arable land in Europe currently used for annual crop cultivation. Most of these landscapes (76%) are classified as subject to "high" accumulated SOC losses, while 17% and 7% are classified as subject to "medium" and "very high" accumulated SOC losses, respectively. Adding two years of grass cultivation to a four-year crop rotation (2y system) in all these landscapes results in 30 Mha of land being used for cultivation of grass instead of annual crops, on average over time. Adding one or two additional years of grass cultivation in the crop rotation (3y system and 4y system) increases the grass area to 39 Mha and 46 Mha, respectively. The corresponding grass production on these areas is about 210, 300, and 370 Mt DM y -1 , for the 2y, 3y, and 4y systems, respectively. In a "low estimate" deployment scenario -in which the 2y system is implemented on all agricultural land where the accumulated SOC loss is classified as "very high", on 50% of the lands where it is classified as "high", and on 25% of the lands where it is classified as "medium" -the total area under grass production amounts to 15 Mha, corresponding to 16% of the area under annual crops in the affected landscapes and 13% of the total area under annual crops in Europe. The corresponding grass biomass production is 100 Mt DM y -1 , equivalent to about 1.9 EJ. Biogas output is about 1 EJ. Extractable crude-and true protein amounts to about 20 Mt and 10 Mt, respectively. The SOC increase amounts to about 140Mt C by 2050, and 190 Mt by 2080. (Table 1) In a "high estimate" deployment scenario -in which the 2y system is implemented on all land currently under annual crop production where the accumulated SOC loss is classified as "medium", the 3y system is implemented where it is classified as "high", and the 4y system is implemented where it is classified as "very high"-the total area under grass production amounts to 38 Mha, corresponding to 41% of the area under annual crops in the affected landscapes and 35% of the total area under annual crops in Europe.  Effects on SOC vary substantially between the different systems and deployment scenarios, as well as between different regions and individual landscapes. Naturally, areas subject to the largest accumulated SOC losses also show the greatest potential for SOC increase. Since the calculations were made on a landscape scale, the density of annual crop production in each landscape also affects SOC increases. Higher densities result in larger areas of grass production in rotations, causing larger SOC increases compared with landscapes with lower densities. In the deployment scenarios, higher implementation results in larger areas under grass production in rotations, and consequently larger SOC increases.
At the landscape scale, the average SOC increase in the 2y system at 100% implementation is 3 t ha -1 by 2050, and 4.1 t ha -1 by 2080. For the 4y system, the corresponding increases are 4.6 t ha -1 and 6.2 t ha -1 . In most landscapes (80%), SOC increases by 2080 are between 2.1-7.3 t/ha for the 2y system and 3.1-11 t ha -1 for the 4y system. In the low estimate deployment scenario, the average SOC increase is 1.4 t ha -1 by 2050 and 1.9 t ha -1 by 2080. In the high estimate deployment scenario, the corresponding increases are 3.7 t ha -1 and 5. Total average annual SOC sequestration in the high-and low estimate deployment scenarios amounts to 12.1 and 4.7 Mt C y -1 , respectively, by 2050, relative a business as usual scenario with continued land use. This is equivalent to 4.0-10.3 % of total current GHG emissions from agriculture in EU27+UK 26 . Comparing with 2020 levels instead of BAU results in slightly higher values. The combined GHG savings from SOC increase and biogas use is equivalent to 13-48% of current GHG emissions from agriculture. The range depends on the deployment scenario, whether biogas displaces natural gas in power plants or is upgraded to vehicle fuel displacing petrol and diesel in cars, and whether SOC increases is calculated relative BAU or 2020 levels. (Table  1)

Co-benefits
The degree of other environmental impacts differs spatially across Europe (Supplementary Figure 1; see also Englund et al. 15,17 ). For example, N emissions to water are high in the northwest and central parts of Europe, whereas water erosion is primarily a problem in southern and central parts. Wind erosion is a problem primarily in coastal areas in northern and eastern Europe, whereas recurring floods are problematic all over Europe, primarily around major rivers. While all these impacts could be mitigated by increased grass production in the agricultural landscape, the mitigation potential is, naturally, determined by the location and degree of the impact. (Figure 2).
N emissions to water are decreased by a total of 119 kt N y -1 in the low estimate and 324 kt N y -1 in the high estimate deployment scenario (Table 1). In the low estimate scenario, grass rotations contribute with 34% of the reductions necessary to achieve a "low" impact level (median for all individual landscapes). In the high estimate scenario, the contribution surpasses 100% in the median landscape.
A substantial mitigation potential can be seen also for soil loss by water erosion, which is reduced by 37 and 95 Mt annually in the low and high impact scenarios, respectively (Table 1). At the landscape scale, an average of 33% of the reduction necessary to achieve a "low" impact is achieved, and in the high estimate scenario, the reduction amounts to 85%.
Soil loss by wind erosion is generally a lesser problem, but the mitigation potential is nevertheless substantial in areas where it is severe. The total reduction potential is 9 Mt and 22 Mt y -1 in the low and high impact scenarios, respectively (Table 1). At the landscape scale, an average of 48% of the reduction necessary to achieve a "low" impact is achieved, and in the high estimate scenario, the reduction surpasses 100%.
The co-benefits are thus considerable; in the high estimate deployment scenario, no further measures are needed to reduce either N emissions to water or soil loss by wind erosion in most landscapes where in-rotation grass production is established with the purpose of enhancing SOC. In addition to the co-benefits described above, there are multiple other co-benefits that are possible, and even likely, but that have not been quantified, such as reduced need for pesticides and mitigation of recurring floods. Concerning the latter, an indicative assessment suggests that most of the landscapes where in-rotation grass is established has a "very low" (46%) or low (26%) likelihood of mitigated flooding events, but in 12 % of the landscapes it is classified as "medium", in 13% as "high", and in 3% as "very high" (Figure 3). This illustrates that more efforts should be directed towards better understanding and quantifying other potential co-benefits than what has been done here, to get a more complete picture of the positive effects of large-scale deployment of in-rotation grass production. : Co-benefits of introducing grass production in crop rotations with the primary objective to enhance soil organic carbon. The figure shows the relative contribution towards achieving a "low" impact at the landscape scale for N emissions to water, soil loss by water erosion, and soil loss by wind erosion, respectively, in the low estimate (left) and high estimate (right) deployment scenarios. Landscapes already having a "low" or lower impact are excluded.

Discussion
In line with previous research 27 the results show that there is a substantial SOC sequestration potential on European cropland, possibly exceeding 10% of total annual GHG emissions from agriculture in EU27+UK, when grass-clover leys are introduced into rotations with annual crops at a large scale. The results also show that this potential can be realized with multiple environmental co-benefits, including reduced wind and water erosion, reduced N emissions to water, and, possibly, mitigated flooding events.
Average annual SOC-sequestration rates for the base rotations (2y, 3y, and 4y) are in the range of 0.11 -0.16 t C ha -1 yr -1 in a 30 year perspective, and 0.07 -0.11 t C ha -1 yr -1 in a 60-year perspective (Supplementary Table 1). This illustrates that a larger share of leys (longer leys) in the total crop rotation is positive for SOC sequestration 28,29 It also confirms that SOC sequestration tends to be larger in the years following deployment of measures, and then decline towards a new equilibrium level; so-called carbon sink saturation 30 .
Grass/legume leys are commonly included in crop rotations in mixed farming systems in cold or humid climate 28 , thus primarily in northern Europe. To validate modelled SOC sequestration, measurements from long term agricultural field trials are valuable, albeit scarce. In England, SOC changes have been measured since 1938, when an arable 5-year rotation with cereals and root crops were changed into a ley-arable rotation with three years of ley and two years of cereal crops (i.e., a 0.6 share of ley in the overall rotation, cf. Supplementary Table 1 There is an on-going rapid decline in biodiversity 33 Insecticides and fungicides have consistent negative effects on biodiversity, including negative impact of insecticides on the potential for biological pest control 34 . The need for pesticides, especially fungicides and insecticides, is very low (or zero) in leys 35 . A change from annual crop rotations into more diversified ley-arable rotations would thus reduce the overall need for pesticides and reduce the biodiversity impacts of agriculture 36 . Increased crop diversity is also an important measure to increase biodiversity at landscape level 37 Biomass cultivation systems are connected to, and interact with, surrounding and supporting systems, e.g., the soil system and adjacent landscapes. Such interactions are not well captured in environmental assessments conducted based on life cycle assessment (LCA). Partly because the product-based approach followed by this method focuses on the output of specific provisioning services, and partly because key aspects of sustainable agriculture, e.g., better soil health, lower biodiversity impacts, and lower pesticide-use impacts, are generally ignored 38 . Spatial modelling, such as in this study, can provide complementary information about biomass cultivation systems, including their output in terms of provisioning as well as maintaining and even cultural, ecosystem services. In particular, spatial modelling support assessment of multiple environmental effects from different land-use scenarios at a large scale, quantifying effects at different aggregation levels, while providing spatially explicit details at local to continental scales. However, the large scale also comes with a loss of precision, as local conditions cannot be fully considered. To understand how to optimize conditions for biodiversity and multiple ecosystem services, more detailed landscape level analyses are necessary 15,39,40 .
The introduction of grass into annual crop rotations reduces the harvested area of cereal crops where grass is introduced. Displacement of soy meal with protein concentrate from grass-based biorefineries reduces this cropland displacement effect by an estimated 60-80%. But the effects of introducing grass cultivation in existing 10  Changes to more diversified crop rotations are well known to enhance the yield of grain crops, such as wheat.
The principal mechanisms behind these yield gains include enhanced disease control and improved supply of nitrogen and water. There are, however, other "rotation effects" that are not yet fully understood 41 . Wheat yields preceded by a break crop instead of wheat increase between 0.5 t ha -1 (pre-crop: oats) to 1.2 t ha -1 (pre-crop: grain legumes). There are also yield increases in the second wheat harvest after a break crop, corresponding to 20-60% of the effect in the first year 42 . Understanding overall rotation effects on yields requires, as for SOC sequestration rates, data from long-term agricultural field experiments. Based on data from seven such experiments across Europe, Marini et al. 43 show that diversified crop rotations (e.g., including temporary leys) provided higher yields for both winter and spring cereals (average +0.86 and +0.39 t ha -1 yr -1 , respectively), compared with a continuous monoculture of cereals. Yield gains were higher in years with high temperatures and limited precipitation, i.e., conditions expected to become more frequent in the future climate, up to around 1 t ha -1 yr -1 compared to monocultures 43 . Angus et al. 42 estimate that on a global level, 40% of the wheat area is not preceded by an effective break crop, forage, or fallow, indicating a substantial potential for yield increases.
In the EU, cereals (primarily wheat) are the dominating crops on arable land and estimates of potential yield increases from diversified crop rotations are lacking. These yield effects are however important to consider when assessing effects of crop rotation diversification on the agricultural system and associated food production. Here, research is urgently needed to build a stronger empirical, as well as theoretical, foundation.
A prerequisite for widespread deployment of in-rotation grass cultivation is a demand for products that can be produced from the grass biomass. There is an increasing interest in biorefineries, processing grass-clover mixes into protein concentrate and a multitude of other products, e.g., feed, fibers, heat, power, and biofuels 24 . Pig feeding trials in Denmark show that extracted grass protein with a high protein content (47% DM) can substitute soymeal without any adverse effects on animal performance and meat quality 44 . Beyond the mitigation of cropland displacement discussed above, protein feed production in Europe can substitute imported plant protein, mostly soymeal, which is a major import commodity to the EU food sector, both in terms of volume and use of agricultural land abroad 45 . Since this import is associated with substantial environmental concerns (deforestation, biodiversity loss, extensive pesticide use, etc.), the motives for developing a substitute feed protein source are strong 44 . This is highlighted by recent efforts by the European Commission to support EU-grown plant-based protein use, via support schemes in the new CAP and by boosting innovation and technology development 7 . Furthermore, the increased target goal in the recent proposal for a revision of the EU Renewable Energy Directive 25 , where the share of renewable energy should amount to 40% in 2030, is likely to be a strong driver for increased production of biogas for heat, power and transportation fuel. Here, the outcome of the current process following the European Commission's proposal 25 to revise the Renewable Energy Directive (RED) will likely influence how investors consider biorefineries. For example, treatment of biogas from biorefineries in the revised RED will depend on whether biogas is considered a main product or co-product of the biorefinery process.
Finally, European farmers may consider soil quality improvements sufficient motivation for in-rotation grass cultivation. Grass cultivation may also be an attractive option where intensive annual crop cultivation becomes restricted to protect the environment. In other places, incentives such as payments for soil carbon sequestration and other environmental benefits may be needed 16

Methods
In this study, a model was constructed to identify individual landscapes where the introduction of ley in annual crop rotations would increase SOC. To illustrate the effects of different management alternatives, different rotation systems were tested as well as two scenarios for large-scale deployment, a high-and a low estimate. In each case, the model identifies the total area under ley production in each landscape and the corresponding grass biomass production, in terms of dry matter (DM), energy (J), and protein (tonnes of extractable crude-and true protein, respectively). Furthermore, the model estimates corresponding SOC increases by 2030, 2050, and 2080, both relative 2020 and relative a business as usual scenario with a continuation of current land use. Finally, the model quantifies a number of co-benefits, i.e., environmental benefits other than SOC increases, for which there are no dedicated incentives in the model, including avoided soil loss by water and wind erosion, respectively, avoided nitrogen emissions to water, and mitigated flooding events.
Unless otherwise specified, "landscapes" refer here to polygons in a dataset containing over 81 000 subwatersheds across EU28 15,17 . This dataset is an important basis for the modelling approach, as each landscape is profiled with information regarding, e.g., the area under annual crop production, degree of current environmental impact (N emissions to water, soil loss by water-and wind erosion, respectively, recurring floods, and accumulated losses of SOC), and the estimated effectiveness of strategic perennialization in mitigating these impacts, in general terms, for each individual landscape.
The term landscape is here defined as an intermediate integration level between the field and the physiographic region and is used synonymous to sub-watershed 46 . The unit is considered appropriate for this purpose since the anthropogenic processes (agricultural land use) within a sub-watershed, combined with hydrological processes that are constrained by a sub-watershed, determines (changes in) nutrient, water, and mass flows 17 . Using the term landscape also clarifies that implementation and impact mitigation is enabled by measures taken by multiple stakeholders at a greater scale than the individual field, thus applying a "landscape perspective" 47 .
All GIS operations, including all database aggregation queries, were done in GRASS GIS 48 with projection EPSG:3035. All modelling, apart from input data preparation, was conducted using a python script with a dedicated GUI, facilitating execution of selected modules. Cartography was done in QGIS 49 .

Basic production systems and scenarios for widespread deployment
The model introduces grass rotations into landscapes where the effectiveness of strategic perennialization was classified by Englund et al. 15 as medium or higher, based on accumulated losses of SOC in combination with the density of annual crops (Supplementary Figure 2). To illustrate the effects of different management alternatives, three rotation systems were modelled: two, three, and four years of ley, respectively, added to a 4-year rotation with the most dominant crops in the area, following the SOC simulations described below (Supplementary Figure 2). These systems are henceforth referred to as 2y, 3y, and 4y systems. Two scenarios for widespread deployment were then constructed: In the "low estimate" scenario, a 2y system was implemented on 100% of all agricultural fields where the accumulated losses of SOC is classified as "very high", on 50% of all fields where it is classified as "high", and on 25% of all fields where it is classified as "medium". In the "high estimate" deployment scenario, a 2y system was instead implemented on all land currently under annual crop production where the impact is classified as "medium", a 3y system where it is "high" and a 4y system where it is "very high". Based on this, areas, effects on SOC, biomass production and selected co-benefits were modelled for the three rotation systems and the two deployment scenarios, as follows.

Grassland area and corresponding biomass and protein production
Area with grassland was calculated as the product of annual crop area 15 and the share of grass relative to annual crops over time in the different systems, i.e., 1/3 for the 2y system, 3/7 for 3y, and ½ for 4y, at 100% implementation.
The corresponding biomass production was estimated for each individual landscape by multiplying the grassland area with simulated grass yields from a pan-European dataset at NUTS3 level 50 . The average yield for miscanthus, switchgrass, and reed canary grass, using a "medium" yield-input management level was calculated in each NUTS-3 region and identified for each landscape by first spatially joining landscapes to NUTS-3 regions, and then joining the database tables. The yields were then adjusted for each system assuming that the yield in the establishment year is 50% of the yield thereafter 51 . Yields for the different systems were thus adjusted as follows: 2y = (0.5 + 1) / 2 = 3/4; 3y = (0.5 + 2) / 3 = 5/6; and 4y = (0.5 + 3) / 4 = 7/8. Yields are expressed as t DM ha y -1 (Supplementary Figure 2). The energy output was calculated as the product of biomass production and energy content of the harvested biomass, 18.7 MJ/kg DM 17,52 .
Crude protein yield was calculated by multiplying DM yield with the average concentration (g kg −1 DM) of crude protein (i.e., sum of average fractions A, B1, B2, and B3) in seven lucerne harvests during field experiments 53 . True protein was similarly calculated by multiplying DM yield with the average concentration of true protein (i.e., sum of average fractions B1, B2, and B3) from the same data source.

Biogas production and GHG savings from fossil fuel substitution
The greenhouse gas (GHG) emissions from biogas production based on ley crops has been estimated at 33 and 30 g CO2 eq MJ -1 biogas, respectively, with and without upgrading of the biogas to natural gas quality 54 , based on the methodology in the EU RED 8,55 but excluding changes in soil carbon content from grass cultivation and crediting for feed output. When upgraded biogas replaces petrol and diesel as transportation fuels in vehicles, GHG savings are about 61 g CO2 eq MJ -1 biogas (65% reduction). The reference fuel-cycle GHG emissions for petrol and diesel 8 are 94 g CO2 eq MJ -1 . When biogas (not upgraded) replaces natural gas for electricity production, GHG savings are about 38 g CO2 eq MJ -1 biogas (56% reduction). Here, the reference fuel-cycle GHG emissions from natural gas 56 are 68 g CO2 eq MJ -1 . The average methane yield per tonne DM grass-based feedstock 54 is 9.2 GJ. Thus, the GHG saving is approximately 560 and 350 kg CO2-eq t -1 DM grass when the feedstock is used for biogas production replacing petrol and diesel as vehicle fuel, and natural gas for electricity production, respectively.

Effects on soil organic carbon
The effects on SOC from the introduction of the different production systems were based on SOC simulations of 2-year ley systems and permanent grassland, respectively, in relation to SOC levels in 2020 as well as a business as usual (BAU) SOC scenario 27  "SOCinc" values are expressed in relation to 2010. They were therefore re-estimated with 2020 as base year, to be able to represent SOC changes from current levels while maintaining 2050, 2080, and 2100 as points in time for assessment. "SOCbau" did not require re-estimation as it represents a continuation of BAU land-use. "SOCbau_2020" was thus considered representative for current SOC. "SOCinc_ley" and "SOCinc_permgrass", however, needed to be re-estimated to represent a 10-year shorter time period than in the original simulations.
At this point, SOC changes by 2050/2080/2100 relative BAU, with base year 2020, has been identified for the 2y system ("SOCinc_BAU_2y_2050/2080/2100"). To estimate SOC changes for the other systems, we assumed a linear correlation between SOC changes and the share of total area under annual crops that are used for grass production, on average over time. SOCinc_BAU_2y_lim50 and _lim25 are therefore estimated by multiplying SOCinc_BAU_2y with 0.5 and 0.25, respectively. Similarly, SOCinc_BAU_3y and _4y was estimated by multiplying SOCinc_BAU_2y by 9/7 and 3/2, respectively.
Total SOC changes were then calculated as the product of SOC changes per hectare and the total area under annual crops, for each system and in each landscape. Finally, the relative difference between "SOCinc_BAU" and "SOCbau" was calculated for the different assessment years. The same calculations (t C ha -1 , t C, and %) were also made relative 2020 instead of BAU. The first was done by adding the difference in BAU SOC between 2020 and the assessment year to the SOC increase relative BAU for the assessment year, e.g.: "SOCinc_2020_3y_2080" = "SOCinc_BAU_3y_2080" + ("SOCbau_2080" -"SOCbau_2020"). The latter two were calculated as described above. Finally, absolute SOC values for all assessment years and ley systems were calculated as the sum of SOC in 2020 and SOC change relative 2020. Finally, for each production system and assessment year, the share of maximum attainable SOC increase was estimated as the quotient of SOC increase relative 2020 in the different ley systems and in permanent grasslands.
Finally, annual C sequestration relative total GHG emissions from agriculture was estimated by first dividing total SOC increase by 2050, relative both 2020 levels and BAU, with 30 years and then dividing the quotients with total GHG emissions from agriculture in 2018 26 .

Environmental co-benefits
Four co-benefits were modelled: avoided (1) soil loss by water erosion, (2) soil loss by wind erosion, (3) nitrogen emissions to water, and (4) flooding events. 4. Recurring floods, indicated by "share of landscape area subject to 10-year flooding". Data on 10-year flooding events were retrieved from a published flood hazard dataset with 100 m resolution. The data were derived using a cascading model simulation approach 61 . The share of the total area in each landscape subject to 10-year flooding events was then calculated for each landscape.
The four impacts were then classified on a five-step scale from "very low" to "very high". See Englund et al. 15 for more details on methods, thresholds, and underlying data. For impacts 1 and 2, an assumption was made that the impact is marginal on grassland 62 . This implies that replacing, e.g., 10% of annual crop production with grass would reduce the impact with 10%. The potential impact mitigation in each individual landscape was therefore calculated as the product of current impact and the share of grassland relative current area under annual crops, for the five system designs and the two deployment scenarios. For impact 3, an assumption was made that N emissions to water from grass production is 75% lower than current N emissions to water. This assumption was based on field experiments showing that perennial grasses reduce N leaching with 70-80% compared to traditional systems 63 . The potential impact mitigation was then calculated in each landscape as the product of current impact, the share of grassland relative current annual crop area, and the mitigation factor of 0.75, for the five system designs and the two deployment scenarios. It was also estimated to what extent inrotation grass production could contribute to reducing impact 1-3 down to a "low" impact level. This was done by dividing potential impact mitigation by the difference between the upper threshold of the class "low impact", as defined by Englund et al. 15 , and the current impact.
Flood mitigation could not be estimated using the same approach. There is strong support for claiming that increased grass production in agricultural landscapes can mitigate flooding events 64 . However, the magnitude of this benefit depends on more landscape-specific characteristics and can thus not be generalized in the same way as for the other impacts. An attempt was instead made to indicate the likelihood of mitigated or avoided flooding events as a result of increased grass production in the landscape 17 . This was done by assuming that the likelihood is directly correlated with the previously estimated effectiveness of strategic perennialization in mitigating recurring floods 15 . A "medium" effectiveness thus corresponds to a "medium" likelihood, etc. The effectiveness of strategic perennialization in mitigating recurring floods was therefore identified for each landscape where the model introduces in-rotation grass systems.

Uncertainties and limitations
Where, and to what extent, implementation takes place, both in the base scenarios and in the high-and low estimates, is determined by the thresholds used for classification of impacts and impact mitigation effectiveness 15,17 . Different thresholds would thus yield different results. General spatial patterns would, however, be similar 15 . The use of average simulated yields for miscanthus, switchgrass, and reed canary grass to estimate ley yields, is justified by the lack of spatially explicit pan-European yield estimates specifically for ley crops. Visual assessment of the simulated yields across the study area suggests that reed canary grass yields are the most similar to ley yields, in spatial terms. In absolute numbers, however, miscanthus yields are more similar to what can be expected from ley crops. Using the average value for these three species provides both reasonable spatial patterns and reasonable yield levels. This approach can be further justified by the fact that selection of ley species will vary across Europe, given different biophysical conditions. It is therefore not reasonable to use simulated yields (if they existed) for one single species, or a specific combination of species, in all landscapes across Europe. See previous studies for additional general uncertainties related to the model, including cobenefits 15