Management practices for each RWS buffer zone were retrieved from local EMBRAPA agronomists and other experts. Requested information include: dominant crop rotations and proportion of each of them to the total harvested area, sowing window, dominant cultivar name and maturity, and optimal plant population density (CONAB, 2019). The provided data were subsequently corroborated by other local and national experts. Table 1. Average (2015-2019) total production, harvested area, and average yield of soybean, maize, sugarcane and rice in Brazil. Source: CONAB. Heinemann, A. B., Ramirez-Villegas, J., Rebolledo, M. C., Neto, G. M. F. C., & Castro, A. P., 2019. Upland rice breeding led to increased drought sensitivity in Brazil. Field Crops Research 231, 57-67.

For each crop-RWS combination, each crop sequence x soil type combination was simulated, and then weighted by their relative proportion to retrieve an average Yw at the level of the RWS buffer zone (or Yp in the case of irrigated rice). Simulations assumed no limitations to crop growth by nutrients and no incidence of biotic stresses such as weeds, insect pests, and pathogens. Jones, J.W., Hoogenboom, G., Porter, C.H., Boote, K.J., Batchelor, W.D., Hunt, L.A., Wilkens, P.W., Singh, U., Gijsman, A.J., Ritchie, J.T., 2003. The DSSAT Cropping System Model. Eur. J. Agron. 18, 235–265. Most typical maize and soybean crop systems were: 2-y soybean-maize (with one crop per year) and 1-y soybean-maize (‘safrinha'). In the latter, soybean is planted with the onset of rains in October and matures in January. Maize is planted after soybean harvest. The rainy season ends before maize maturity, leading to terminal drought in most years. For maize, we simulated both safra and safrinha when both accounted for >30% of maize area within each buffer; if not, only the most dominant maize system was simulated in each buffer.While only one crop per year is grown in the eastern part of the country, most producers grow two crops (1-year soybean-maize sequence called ‘safrinha') in the western region (Mato Grosso, Mato Grosso do Sul, Tocantins, Goiás, and Parana). Duarte, Y.C.N., Sentelhas, P.C., 2019. NASA / POWER and DailyGridded weather datasets — how good they are for estimating maize yields in Brazil ? Int. J. Biometeorol. doi: 10.1007/s00484-019-01810-1 For the simulations, rooting depth was set at 2 m (sugarcane), 0.8 m (soybean and maize), and 0.4 m (upland rice) to reflect the limitation to root growth in deep horizons due to low pH and differences among crop species in rooting patterns and/or tolerance to low pH (Pivetta et al., 2011, Battisti et al., 2017; Franchini et al., 2017). Calibrated pedo-transference functions for tropical soils were used to derive soil water limits (Tomasella et al., 2000). Field capacity was set at -10 kPa following the observations for tropical soils by Reichardt (1998) and Tomasella and Hodnett (2004). Soil properties were not considered for simulation of yield potential for irrigated rice. A weighted average yield was calculated based on the average yield reported for the municipalities located within the buffer zone and the relative contribution of each department to the total crop harvested area in the buffer zone. Reported Yw (or Yp for irrigated rice) in the Atlas are long-term averages. Yield gap (Yg) was calculated as the difference between long-term average Yw (rainfed crops) or Yp (irrigated crops) and average (2012-2017) farmer yield. Including more years before 2012 in the calculation of average actual yield would have led to a biased estimate of average actual yield due to a strong technology trend in Brazil. In the case of buffers where both safra and safrinha were common maize, average maize yield was estimated by averaging their respective average yields, weighting by the proportion of maize area under each crop system.

Bouman, B.A.M.; Kropff, M.J.; Tuong, T.P.; Wopereis, M.C.S.; Ten Berge, H.F.M.; Laar van, H.H, 2004. Van. Oryza 2000: modeling lowland rice. Manila, Philippines: International Rice Research Institute (IRRI). 245 pp.Marin, F. R. Jones, J. W. Royce, F. 2011. Parameterization and Evaluation of Predictions of DSSAT/CANEGRO for Brazilian Sugarcane. Agron. J. 103, 297-303. To portray most dominant practices in sugarcane farms, 3 main cycles of ratoon crops of 12-month duration each were simulated at each location: early (April-15), mid (Aug-15), and late planting (Nov 15). Tomasella, J, Hodnett, MG, Rossato, L, 2000. Pedotransfer functions for the estimation of soil water retention in Brazilian soils. Soil Sci Soc Am J 69, 649-652.

Van Wart, J., Grassini, P., Yang, H.S., Claessens, L., Jarvis, A., Cassman, K.G., 2015 Creating long-term weather data from the thin air for crop simulation modelling. Agric. For. Meteoro. 209-210, 45-58. Monteiro, L.A., Sentelhas, C., Pedra, G.U., 2018. Assessment of NASA / POWER satellite-based weather system for Brazilian conditions and its impact on sugarcane yield simulation. Int. J. Climatol. 38, 1571–1581. There are two dominant rice systems: irrigated lowland rice (southern brazil) and rainfed upland rice (north-central and western Brazil). Rice is grown as a single crop per year; in southern Brazil rice is sown from late September to early December and with the onset of rainfall (typically between early November and early December) in north-central Brazil rice is planted. In all cases, rice is direct seeded. Figure 1. Comparison of simulated and observed phenology (left) and grain yields (right) for rice (top), soybean (middle), and maize (bottom).The solid red line represents y = x and the dashed red lines represents ± 20% deviation from the y -x line.RMSE = mean square root of error.The phenological stages of rice, soybean and maize were based on the scales ofCounce et al.(2000), Fehr and Caviness (1977), and Ritchie et al. (1993), respectively . Franchini, J.C., Antonio, A., Junior, B., Debiasi, H., Nepomuceno, A.L., 2017. Root growth of soybean cultivars under different water availability conditions Crescimento radicular de cultivares de soja em campo em diferentes disponibilidades hídricas. Ciências Agrárias, Londrina, 38, 715–724.Marin, FR, Jones, JW, Singles, A., Royce, F., Assad, E.D., Pellegrino, G.Q., Justino, F., 2012. Climate change impacts on sugarcane attainable yield in southern Brazil. Climatic Change 117, 227-239. Inman-Bamber, N.G., 1991. A growth model for sugarcane based on a simple carbon balance and the CERES-Maize water balance. S. Afr. J. Plant Soil 8, 93–99.