Supplement content: S1 Supplementary information to methods and data S1.1 General model functions in LPJmL5.0-tillage-cc S1.2 Model input data S1.3 Overview simulation setup for cover crop and tillage scenarios 10 S1.4 Conservation Agriculture cropland area time series data S2 Supplementary information to management results S2.1 Simulated responses to cover crop and tillage practices in comparison to values found in the literature S2.2 Soil N immobilization rate and gross N mineralization rate

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... ith management duration S2.3 Spatial pattern of changes in soil C and N leaching rate due to cover crop management 15 S2.4 Boxplots of changes for rainfed and irrigated crop productivity due to altered management S2.5 Spatial pattern of productivity changes due to cover crop practices combined with no-tillage S1 Supplementary information to methods and data S1.1 General model functions in LPJmL5.0-tillage-cc 20 In the model three litter layers and five hydrologically active soil layers of differing thickness to a total depth of three meter are distinguished. Each soil layer has its specific temperature and moisture levels, affecting the decomposition rates of soil organic matter, represented in the model by fast and slow decomposing (30 and 1000 years turnover time, respectively) C and N pools (Lutz et al., 2019; Schaphoff et al., 2018). Carbon and N pools of represented vegetation, litter, and soil layers are updated daily. Biomass formation is represented by a 25 simplified version of photosynthesis according to Farquhar et al. (1980). The phenology of tree and grass plant functional types (PFTs) of the represented natural vegetation are based on Jolly et al. (2005) with modification of the growing season index as described in Forkel et al. (2014). Crop functional types (CFTs, see Table S1 .1) representing the vegetation on managed land are parameterized with specific temperature and phenological heat unit requirements for growth (Müller et al., 2017). Cropland irrigation was mechanistically simulated by either 30 surface flooding, sprinkler, or drip irrigation, here setting one type per country (Jägermeyr et al., 2015; Rohwer et al., 2007). We used the potential irrigation setting to simulate irrigated cropping systems (for cropland areas equipped for irrigation as informed by the input data, see Sect. S1.2) to account for missing representation of ground water sourcing, when this model version only considers surface water withdrawal amounts, in the case of alternatively setting to limited irrigation. 35 During simulated main crop growing seasons, manure (C to N ratio of applied manure was assumed to be 14.5 to 1) was applied at the first scheduled mineral N fertilization event of a growing crop (CFT). Half of the N contained in the manure was assumed as ammonium (NH 4 ) and added to the pool of the upper soil layer, whereas the entire C and the remaining N (assumed as organic share), were transferred to the respective litter pools. Conventional tillage was assumed as the default soil management on all cropland, applied when 40 converting land to cropland, as well as at main crop seeding and harvest events. The tillage routine submerges and transfers 95 % of the surface biomass remaining on-site, to the incorporated soil litter pools. In the model, tillage mostly affects processes in the first soil layer up to 20 cm depth (Lutz et al., 2019). In the case of notillage, the remaining aboveground biomass of the main crops' residues left on the field after harvest are added to the surface soil litter pools, representing mulching practices. 45 Table S1.1 Crop functional types (CFTs) in LPJml5.0-tillage-cc and included in the study CFT Simulated as temperate cereals wheat rice rice tropical cereals millet pulses field peas temperate roots sugar beet tropical roots cassava maize maize sunflower sunflower soybean soybean groundnuts groundnuts CFT Simulated as rapeseed rapeseed sugarcane sugarcane others maize in tropical and wheat in temperate regions managed grass managed temperate C3, polar C3, and tropical C4 grass (outputs not considered here) bioenergy grass not simulated here bioenergy trees not simulated here cover crop temperate C3, polar C3, and tropical C4 grass with daily allocation S1.2 Model input data For the simulations of this study, the model was driven with monthly mean temperature input data from the Climate Research Unit (CRU TS version 3.23, University of East Anglia Climate Research Unit, 2015; Harris et al. (2014)). Monthly precipitation and number of wet days data was from the Global Precipitation Climatology 50 Centre (GPCC Full Data Reanalysis version 7.0; Becker et al. (2013)). The monthly radiation data (shortwave and net longwave downward) was taken from the ERA-Interim data set (Dee et al., 2011). Soil texture classes remained static over the simulation period and were based on the Harmonized World Soil Database (Nachtergaele et al., 2009) and soil-pH was taken from the WISE data set (Batjes, 2006). Annual atmospheric CO 2 -concentration input data were based on the NOAA/ESRL Mauna Loa station (Tans and Keeling, 2015) 55 reports, and natural N deposition data on the ACCMIP database (Lamarque et al., 2013). Model input data on historical land use, distinguishing shares of irrigated and rainfed crop-group specific physical cropland (years 850-2015), as well as mineral N fertilizer application rates (years 1900-2015), were based on LUH2v2 data by Hurtt et al. (2020). The original data per crop group were (dis-)aggregated and remapped, using the MADRaT tool (Dietrich et al., 2020), to match the CFTs of LPJmL (Table S1 .1) and the 60 here targeted simulation unit of 0.5 degree grid cell resolution (~50 km x 50 km at the equator). In the year 2010 there were 1,502,674,969 ha total physical cropland ( Fig. S1 .2 for maps of physical cropland and mineral N fertilizer application rates). Figure S1.2 Maps depict the spatial pattern of the model input data used in the process based simulations and for 65 post-processing model outputs: (a) Physical cropland in 1000 hectares per grid cell and (b) Mineral N fertilizer application rate in kg N ha -1 for the year 2010, based on LUH2v2 (Hurtt et al., 2020) physical cropland distribution data.