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The environmental stresses of existing US–China crop tradeIn the past, producing the volumes of crops demanded by China exacerbated US environmental pressures, but potentially relieved the environmental stresses on China and the world. In 2014–2016, on average, to produce the crops exported to China, the United States devoted an additional 12 Mha of harvested area, demanded 4 trillion litres (1 trillion = 1 × 1012) more blue water, and increased nitrogen and phosphorus surplus by 0.5 TgN (1 Tg = 1 × 109 kg) and 0.007 TgP (Fig. 2). In contrast, if China’s crop imports from the United States were produced in China domestically with its current technology and management practices, assuming adequate resources and suitable climates and soil conditions, it would require nearly 20 Mha harvested area and 9 trillion litres of blue water, and would lead to nitrogen and phosphorus surpluses of 1.7 TgN and 0.3 TgP. Such drastic shifts in the associated environmental stressors would consequently produce a net increased global burden of environmental stresses, including net additional exploitation of 8 Mha of harvested area and 5 trillion litres of blue water, and further losses of 1.2 TgN and 0.3 TgP to the environment.Fig. 2: Environmental stresses affecting crop substitution.a–d, Environmental stresses of producing the average 2014–2016 crop portfolio China imported from the United States at each region’s current RUE levels, given adequate resources and suitable climate and soil conditions: required harvested area (ha) (a), induced nitrogen surplus (kg) (b), phosphorus surplus (kg) (c) and blue water demand (litres) (d). Each coloured bar indicates the environmental stress of each crop type. Only the US bars show the environmental stressors that actually happened. Other regions’ bars are the potential environmental stressors that would have happened if those regions had grown the same crops to meet China’s demands. For example, in the nitrogen surplus graph (b), the US bar shows that the United States generated a 0.5 TgN surplus when producing the crops exported to China. China’s bar in panel b denotes that China would have generated a 1.8 TgN surplus if its entire imported crop portfolio from the United States had been produced domestically. Similarly, if those crops had been grown in Brazil, the potential burdens are shown by the bars for Brazil. SoAmer, South America (apart from Brazil).Source dataFull size imageIf China’s crop imports from the United States were entirely substituted by imports from other regions of the world, the environmental stressors of the production would vary among regions due to the different production efficiencies and available resources (Fig. 2). For example, to produce the same volume of crops demanded by China, Brazil would require an additional 2 Mha of harvested area and would induce an additional 0.5 TgN surplus and 0.22 TgP surplus, compared with the United States, but would substantially reduce blue water demands. Other South American countries would be a less-polluting alternative to the United States given the region’s more efficient nitrogen use and blue water demand, but higher costs and limited resource availability may impede them from replacing the crop supply from the United States entirely17. Overall, this comparison suggests that the current production reallocations from China to the United States achieved through international trade have relieved environmental burdens for China and the world due to China’s relatively low efficiencies in both water use and fertilizer use compared with the United States and the rest of the world. Admittedly, this comparison with Brazil and other South American countries demonstrates an extreme case of production reallocations from the United States to the rest of the world, and such reallocation is likely to be buffered by market-mediated responses and considerations of biophysical limits; however, it demonstrates the general direction of changes in environmental consequences in the context of weakening US–China crop trade.The national impacts of the weakening trade relationshipShifts in crop production portfoliosUnder the proposed December 2019 tariff scenario (Table 1), China’s retaliatory tariffs would potentially increase the prices of US agricultural products in China’s domestic market. This would lower China’s demands for US agricultural products, eventually lowering US farmers’ income and discouraging them from producing relevant crops3,4,5. Given the fact that over 70% of China’s crop imports from the United States are soybeans, domestic soybean prices in the United States are affected, depressing their production in the United States by about 3 Mha. Crops that are less traded with China would be less affected by China’s tariff increase. Hence, over the long term, US farmers would switch to these less-traded crops with China, such as other coarse grains (primarily corn), wheat and other agricultural products. Besides soybeans, non-soybean oilseeds are also among the major crops that China imports from the United States. Under the defined scenario, non-soybean oilseeds are also retaliated, and their production thus contracts in the United States by 0.6 Mha. As a result, the total harvested area in the United States would decline by 1.25 Mha.Table 1 China’s retaliatory tariff percentage increases for US agriculture as of May and December 2019Full size tableRelatively lower-priced soybeans from Brazil and other South American countries, due to the absence of tariffs, would incentivize China’s soybean imports from these countries. China’s rising demands would increase the income of soybean farmers and motivate soybean expansion in Brazil and other South American countries by 3 and 0.8 Mha, respectively, adding pressures to their cropland expansion19,20,21. China’s retaliation on US soybeans would spur China’s domestic oilseed production in general by 0.5 Mha. However, with intensified agricultural production and limited harvested area expansion capabilities, China would experience limited changes in its crop portfolio and harvested area. As soybean is the major protein source for livestock animals29, tariffs on meat could further disincentivize US soybean production. Since South America mainly competes with the United States in China’s domestic soybean market, the production of all non-soybean crops in South America would experience limited incentives.Changes in environmental stressesShifts in crop portfolios are accompanied by changes in environmental stressors such as nitrogen surplus, phosphorus surplus and blue water demand. Although the total harvested area in the United States would contract by 1.25 Mha, its total nitrogen surplus (expressed as kgN) would increase by 35 million kgN as soybean, a nitrogen-fixing crop with relatively high nitrogen-use efficiency (NUE) and low nitrogen surplus intensity (expressed as kgN ha−1), shifts to other crops (Fig. 3). The reduction of 105 million kgN surplus due to soybean contraction in the United States is less than the additional nitrogen surplus generated by the expansion of other crops, such as other coarse grains, with higher nitrogen surplus intensity. In contrast, Brazil and other South American countries would reduce their nitrogen surplus by 119 million kgN and 81.5 million kgN owing to substitutions of soybean for other non-soybean crops. Globally, the nitrogen surplus increase in the United States is offset by the nitrogen surplus decline in Brazil as a result of the soybean shifts from the United States to Brazil to meet demands of China. Overall, global nitrogen surplus would significantly decline by 154 million kgN due to the contractions of nitrogen-inefficient crops (for example, other coarse grains, wheat, sugar crops and other agricultural products) in South America, and their increase in the United States, where they can be grown more efficiently and with lower nitrogen surplus intensity.Fig. 3: Changes in environmental stresses.a–d, Changes in environmental stresses by region and crop type: harvested area (ha) (a), total nitrogen surplus (kg) (b), total phosphorus surplus (kg) (c) and total blue water demand (litres) (d). In each bar, total changes are denoted by black dots, which are further decomposed into contributions from changes in each crop type represented by coloured blocks. The leftmost bar summarizes total global changes and the contributions from each crop type.Source dataFull size imageThe contraction of the harvested area in the United States would not lead to any reduction in blue water demand. If soybean alone is subject to China’s retaliation, the US blue water demand would increase substantially by 1.6 billion litres (Supplementary Information, section 9 and Supplementary Fig. 7). In this case, the crops that are projected to increase production in the United States either replace soybean production with higher water demand per harvested area (for example, corn in the ‘other coarse grains’ category) or tend to expand in the regions with high blue water demand (for example, ‘other oilseeds’). However, when non-soybean oilseeds are also retaliated, the increase in US water demands would be only 0.1 billion litres, much lower than that of the soybean-only tariff scenario, as these water-demanding crops also decline in production. Although it is unlikely that farmers will invest significantly for irrigation equipment given a short-term policy or market shock5,30, it is possible for farmers to increase irrigation water use on land already equipped with irrigation infrastructure, to shift crop type (for example, from soybean–corn rotation to continuous corn) and perhaps even to invest in new equipment as the trade tension becomes a norm in the context of growing tensions between the United States and China. Therefore, the reduction of blue water demand for soybean in the United States could be outweighed by the increase in water demand for other crops (Fig. 3d). Under both scenarios, similar patterns are observed on the global scale: global blue water demand would increase because the benefits of blue water savings from shifts in soybeans production (that is, shifts from the United States to Brazil and other South American countries) would be offset by the increasing blue water demand in non-soybean oilseed expansion in water-scarce regions.Trade-offs and synergies also exist within each region across different environmental stressors. The expansion of soybean, a nitrogen-fixing plant that is relatively more efficient than many other crops, would reduce Brazilian nitrogen surplus by 120 million kgN but increase its phosphorus surplus by 23.5 million kgP. Brazilian soybean is intensively produced in areas with highly weathered, naturally acidic soils that render much of the native and applied phosphorus unavailable to the crop. Brazilian soybean production thus requires higher phosphorus fertilizer and lime inputs than soybeans produced in most temperate regions31. With similar PUE levels, the phosphorus surplus increase due to soybean expansion is higher than the phosphorus surplus decline driven by the contraction of other crops—resulting in a net 23.5 million kgP surplus increase in Brazil. Although most of this phosphorus surplus is currently retained in Brazilian soils, the accumulated phosphorus could eventually reach saturation and pollute water bodies32. In addition, the increased demand for phosphorus fertilizer and lime in Brazil may exceed domestic supplies of rock phosphorus reserves and lime. In contrast to Brazil, the United States would suffer from an increase in both phosphorus and nitrogen surplus by 34.7 million kgP and 10.3 million kgN, respectively, as the production shifts from soybean to more fertilizer-intensive crop types, while other South American countries would experience alleviation in both phosphorus and nitrogen surplus by 81.5 million kgP and 5 million kgN, respectively, due to the shifts opposite to those in the United States. Global phosphorus surplus would be further aggravated by 30 million kgP as soybeans are expanded in Brazil where phosphorus use is more inefficient.Overall, the weakening US–China agricultural trade relationship would worsen the US environmental stressors of both nutrient surpluses and water resource depletion. Such patterns of environmental consequences are primarily driven by China’s retaliation on US soybeans. Additional environmental stresses imposed on the United States could also be affected by the extent of China’s retaliation on non-soybean oilseeds (Supplementary Fig. 7). Brazil would reduce its nitrogen surplus and blue water demand through crop mix changes but face an aggravated phosphorus surplus issue. China would experience limited environmental improvements. Globally, trade-offs exist among nitrogen surplus reduction, increases in phosphorus surplus, increases in blue water demand and increased harvested area.Sensitivity analysesWhile the environmental stressor evaluation in this study adopts standard Global Trade Analysis Project (GTAP) parameters and uses crop-specific environmental stressor intensity databases from reliable sources13,33,34, uncertainties in these parameters and data could affect the outcomes of the evaluation. To test the robustness of the evaluation outcomes, we designed the following sensitivity analyses focusing on these two major sources of uncertainties.Regarding the uncertainties associated with the GTAP-BIO model, we first identified parameters to which the production portfolios are most sensitive, varied these parameters by 50% following an independent triangular distribution and obtained the consequent crop portfolio variations35. We then evaluated the resulting variations in global and regional environmental stressors by assuming that crop-specific environmental stressor intensity in each region remained unchanged (see Supplementary Information, section 7 for the rationale for the selection of parameters and the 50% variation). We found that even with 50% variations, parameter uncertainties did not alter the direction of changes in environmental stressors. The environmental consequences in the United States and Brazil are most sensitive to soybean’s trade elasticity and cropland transformation, while China is mostly affected by its protein preferences for animal feed (Supplementary Table 9).Concerning the uncertainties in crop-specific environmental stressor intensity, we varied each major crop’s intensity of nitrogen surplus, phosphorus surplus and blue water demand following independent triangular distribution. We then assessed the corresponding variations in global and regional environmental stressors by assuming constant average harvested area changes (changes reported in Fig. 3a). We found that the coefficient of variation for each environmental stressor is linearly related to the intensity variation level (Supplementary Table 10). Regional nitrogen surplus changes are more sensitive to the accuracy of the nitrogen surplus intensity estimate for soybean and other coarse grains, and the United States is most sensitive to its estimate of blue water demand intensity for soybeans, other coarse grains and sugar crops (Supplementary Table 10). Hence, potential variations in the data could also moderately weaken or amplify the conclusions made in this analysis but would not change the direction of patterns.Local hotspots with additional environmental stressesHeterogeneous distributions of crops and varying crop mixes and RUEs in crop production at subnational scales cause divergence of the local environmental stress changes from the aggregate national changes (Fig. 4). Unique crop portfolios in each grid cell could lead to spatial trade-offs and synergies within each environmental stressor and across different environmental stressors. To investigate the heterogeneous consequences on a subnational scale, we downscaled the modelling results from GTAP for each AEZ to 30 × 30 arcminute grids, following the approach that has been applied in multiple studies34,36,37. The downscaled results represent one of the plausible changes in crop distribution and subsequent changes in intensities of nitrogen surplus, phosphorus surplus and blue water demand on a subnational scale under the trade tension and based on the model structure and assumptions.Fig. 4: Changes in nitrogen surplus, phosphorus surplus and blue water demand intensity across different regions in China, the contiguous United States and South America.a–c, Changes in environmental stressors due to China’s potential trade policy on US agricultural products: gridded nitrogen surplus (kgN ha−1) (a), phosphorus surplus (kgP ha−1) (b) and blue water demand (l ha−1) (c). d, Combining the three environmental stressors shows the hotspots of increased environmental degradation. The transparency of each grid cell denotes the logarithmic form of the total harvested area in ha where high transparency corresponds to high quantities of harvested area, and low transparency corresponds to low quantities of harvested area. For example, the Brazilian Amazon has low harvested area and thus is less transparent.Source dataFull size imageChina’s retaliation on US agriculture would lead to the contraction of soybean production mainly in the US soybean/corn belt where the production of other coarse grains expands—resulting in a reduction in total nitrogen surplus (Supplementary Fig. 6b) but an increase in nitrogen surplus intensity for this region (Fig. 4a). The expansion of other coarse grains is much less than the reduction in soybean production, leading to the decline of harvested area for the region. However, because other coarse grain has a higher nitrogen surplus intensity than soybean, the intensity of nitrogen loss increases on the remaining cropland (Fig. 4a). The expansion of wheat would focus on the northern and western regions of the midwestern United States, accompanied by increasing phosphorus surplus intensity. Such phosphorus surplus intensity increase is aggravated by further expansion of wheat production. With the increasing tariffs imposed on all crops, the northwestern United States would experience a reduction in nitrogen surplus reduction as other coarse grains produced in the midwest substitute those produced in this region. Meanwhile, the contraction of nitrogen-efficient non-soybean oilseeds in southern regions would aggravate local nitrogen surplus intensity but relieve local demands for blue water. However, if the non-soybean oilseeds are not retaliated, soybean reduction could potentially incentivize their production in southern regions, reducing local nitrogen surplus intensity (Fig. 4a) but demanding more blue water (Fig. 4c).In contrast to the contraction in the United States, soybean would expand in South America mainly in the central-west and southern regions of Brazil and the northeastern regions of Argentina. While adding pressures on land use changes in these areas, the expansion of soybean production may relieve nitrogen surplus intensity and blue water demand intensity by replacing wheat, other coarse grains, sugar crops and other agricultural products. Consistent with national-scale analysis, the Brazilian soybean production area may experience aggravated phosphorus surplus intensity but other South American countries would benefit from lower phosphorus surplus intensity due to their different soil types (Fig. 4b).Considering all three environmental stressors together, China’s retaliatory tariffs would lead to the worsening of one or more environmental stresses in most regions (Fig. 4d). The region with reduced environmental stresses is mainly concentrated in southeast and northeast China, where soybeans and rapeseeds expand at the cost of other resource-intensive crops, and Argentina, where soybean production is incentivized. The rest of China is dominated by intensified blue water demand, while some regions would face increased nitrogen surplus (green areas in Fig. 4d for China) and phosphorus surplus intensity as well (purple areas in Fig. 4d for China). It is notable that 8.3% of the regions in China where crop production is incentivized would face challenges from aggregations of all three environmental stressors (brown areas in Fig. 4d for China). Most regions in the midwestern, southern and northeastern United States are dominated by increases in nitrogen surplus and blue water demand intensity (green areas in Fig. 4d for United States), as part of soybean production shifts to other crops with more intensive nitrogen surplus and/or blue water demand. Northern parts of the western United States show modest intensifying nutrient surpluses, and southern areas of the western United States have slight intensification in nitrogen surplus but intensified blue water demand if non-soybean oilseeds would not be retaliated (Supplementary Fig. 8). The Brazilian Amazon region faces the situation of intensified nutrient losses and blue water demands of existing agricultural practices as a result of a reduction in resource use efficient crops in crop mixes. Since total harvested area devoted to crop production in the Brazilian Amazon is relatively low (less transparent brown areas in Fig. 4d for Brazil), changes in the environmental stressors analysed here may be less of a concern, although any cropland expansion in the Amazon region would probably be important regarding other conservation issues. The rest of Brazil, where the crop production is more active, is dominated by intensified phosphorus fertilizer use and phosphorus losses in soybean-intensive areas. More

This section describes how we used freely-available data to compile Classic driver input files for the VIC model. First, we created parameter files for VIC-5 Classic, then we converted them to NetCDF format for VIC-5 Image. VIC-5 Classic requires three parameter files: a soil parameter file, a vegetation parameter file, and a vegetation library file. An optional elevation band file can be provided to resolve sub-grid variability in elevation, which is important in regions with complex topography. The parameters are arranged as a relational database: each grid cell has a unique identifier, called a grid cell number, in the soil parameter file, that VIC uses to find the corresponding rows of data in the vegetation parameter and elevation band files. The Image driver uses a different setup, with all parameters stored in a single NetCDF file.Soil parametersThe soil parameter file for VIC-5 Classic is an ASCII text file that includes soil parameters such as hydraulic conductivity and porosity, but also other kinds of static parameters, such as average precipitation and time zone offset from GMT. Each row of the soil parameter file represents one grid cell, and each column represents a different variable. We compiled the soil parameter file using MERIT20 elevation data, soil texture data from the FAO HWSD, pedotransfer tables relating soil texture to other soil properties, and interpolated weather station data (WorldClim21). Any remaining parameters were set to suggested values from the VIC model’s documentation2. The following sections describe the estimation of each variable in the soil parameter file, summarized in Table 1.Table 1 VIC model parameters for the soil parameter file.Full size tableElevation and land maskThe VICGlobal soil parameter file uses the Multi-Error-Removed Improved-Terrain (MERIT20) digital elevation model (DEM) to define the elevations, latitudes, and longitudes of each land grid cell. The MERIT DEM is an error-corrected and extended version of the SRTM DEM, with 3 arc-second resolution and coverage from 60°S to 85°N and 180°W to 180°E. Specifically, MERIT is a combination of the SRTM, AW3D, and Viewfinder Panoramas’ DEMs, corrected for striping, speckle, absolute bias, and tree height bias. We used bilinear interpolation to aggregate MERIT to 1/16° resolution and derive a 1/16° MERIT-based land mask and DEM (Figure S1).Soil texture dataSoil texture (percent sand, silt, and clay) and bulk density were obtained from the FAO HWSD, a gridded soil parameter dataset derived from in-situ measurements of the soil column. We used a 0.05° resolution NetCDF dataset converted from the original HWSD Microsoft Access database by Wieder et al.22. We resampled the HWSD soil data from 0.05° to 1/16° resolution using bilinear interpolation with the MATLAB® function griddedInterpolant. While HWSD has near global coverage, there are missing data in some places around the world, notably Greenland and northern Africa. We filled in these missing data using inpainting, a gap-filling method from the field of image processing. We used the MATLAB® function inpaintnans23, which uses a partial differential equation method to fill in missing data, to fill gaps in the HWSD data over the MERIT land mask. Figure 1 shows the HWSD bulk density data before and after inpainting.Fig. 1Bulk density data from the Harmonized World Soils Database (HWSD). The top panel shows HWSD bulk density data resampled to 1/16° resolution, the middle panel shows bulk density after infilling holes, and the bottom panel shows the difference.Full size imageThe HWSD data are divided into “topsoil” and “subsoil” parameters. The first 30 cm of the soil column are considered topsoil and the lower 70 cm subsoil. VIC is typically run with three soil layers, so we created a three-layer soil parameter file by breaking up the 30 cm HWSD topsoil layer into two soil layers: one of 10 cm and one of 20 cm, so the final soil parameter file has three layers, with thicknesses of 10 cm, 20 cm and 70 cm, from top to bottom of the soil column. Ten centimeters has been a common choice for the uppermost layer soil depth in VIC modeling applications since its use by Liang et al.24. Soil layer depths are typically used as calibration parameters. VICGlobal values should be considered a starting estimate.Calculating soil parameter values based on soil texturesPedotransfer functions (e.g. Cosby et al.25) relate readily available soil properties, such as soil texture, to less easily-observed properties, such as hydraulic conductivity. After resampling the HWSD data from 1/4° to 1/16° resolution, we estimated soil parameters by classifying each grid cell’s USDA soil texture class and assigning physical soil properties based on a lookup table included with the VIC documentation2,26. The lookup table (Table 2) relates the 12 USDA soil texture classes to bulk density, field capacity, wilting point, porosity, saturated hydraulic conductivity, and slope of the soil water retention curve in Campbell’s equation. We classified soil textures using the USDA soil texture triangle, as implemented by the MATLAB® function soil_classification27. Figure 2 shows the derived USDA soil texture map. We used these along with the lookup table to estimate saturated hydraulic conductivity (Ksat), the exponent in Campbell’s equation for hydraulic conductivity (expt), fractional soil moisture at the critical point (wcrfract), where the critical point is about 70% of field capacity, fractional soil moisture at the wilting point (wpwpfract), quartz content, and porosity for each soil layer. The lookup table26 did not include quartz content, so we supplemented it with the soil texture-quartz content lookup table from Peters-Lidard et al.28.Table 2 USDA soil texture class lookup table.Full size tableFig. 2USDA soil texture classifications based on HWSD. Topsoil is soil from 0–30 cm below the surface, and subsoil is soil between 30–100 cm deep.Full size imageWe set the variable infiltration capacity parameter ({b}_{infilt}=0.2), the maximum baseflow fraction threshold ({d}_{s}=0.001), and maximum soil moisture threshold ({w}_{s}=0.9), their suggested values from the VIC documentation. These parameters, along with maximum baseflow velocity (dsmax) and soil depth, are typically calibrated. We set the baseflow curve exponent c = 2, the soil thermal damping depth dp = 4 m, soil density = 2685 kg/m3, surface roughness = 0.001 m, and snow roughness = 0.0005 m, also based on guidance from the VIC documentation. The soil moisture diffusion parameter phis is not used in the current version of VIC, so we set it to the no-data value (−999). The final few soil parameters — dsmax, initial soil moisture (initm), and bubbling pressure (bubble)— were calculated using the following equations, based on guidance from the VIC documentation.$$dsmax=slopeast {bar{K}}_{sat}$$
(1)
$$initm=wc{r}_{fract}ast porosityast {t}_{l}$$
(2)
$$bubble=0.32ast expt+4.3$$
(3)
Equation (1) estimates dsmax for each grid cell as the product of soil-column average Ksat and land surface slope, which was calculated from the elevation data using the MATLAB® function gradientm29g. Equation (2), where tl is the thickness of soil layer l, assumes that initial soil moisture is equal to the fractional soil moisture content at the critical point. Equation (3) calculates bubbling pressure as a function of expt, based on linear regression of bubbling pressure vs. expt30. Figures S2–S9 in the Supplementary Information show maps of each soil parameter. We assumed residual soil moisture, the amount of soil moisture that cannot be removed from the soil by drainage or evapotranspiration, was zero.Elevation bandsVIC uses an elevation band file (also called a snow band file) to account for subgrid heterogeneity in grid cell elevations. The assumption of uniform elevation over an entire grid cell can lead to modeling errors in mountainous regions, where higher topography is associated with cooler temperatures and higher precipitation rates. The elevation band file accounts for subgrid variability in topography by dividing each grid cell into a number of elevation bands, each of which is simulated separately. VIC adjusts temperature, pressure, and precipitation depending on the elevation in each band. We prepared an elevation band file with five elevation bands by comparing the 1/16° DEM used for the soil parameter file with a 30 arc-second DEM. Both DEMs were derived by aggregating MERIT data. For simplicity, we assumed precipitation was evenly distributed among elevation bands within a grid cell. The elevation band file is provided with the caveat that using elevation bands requires more computing power; users may wish to turn elevation bands on or off (via the VIC global parameter file) depending on their needs.Vegetation parametersVIC-5 Classic uses a vegetation parameter file to define the fractional cover of different vegetation types within each grid cell and some of their physical properties. Other vegetation parameters are stored in the “vegetation library” file. (VIC-5 Image simply stores all parameters in a single “parameter” file.) The VIC-5 Classic vegetation parameter file consists of information about fractional cover of each land cover type in each grid cell, and their corresponding root zone depths and root fractions within each root zone. The vegetation parameter file can optionally include time-varying LAI, fractional canopy cover, and albedo data, but it is simpler to specify these in the vegetation library (at the cost of not representing some spatial heterogeneity).We used MODIS land cover data from the 0.05° MODIS MCD12C1 Collection 6 data product31 to assign fractional land cover values to each grid cell by calculating the average land cover for MCD12C1 observations over the 2017 calendar year. We chose 2017 because it was the most recent year with data in all the MODIS-based datasets used for this study, and there is very low interannual variability of land cover32 in MCD12C1 Collection 6. Figure 3 shows majority land cover types from the 2017 MCD12C1 observations.Fig. 3MODIS MCD12C1 majority land cover types (IGBP classifications). .Full size imageLike all global land cover data products, MCD12C1 makes classification errors. Sulla-Menashe et al.32 reported 67% overall IGBP classification accuracy for 2001 land cover. Classification errors are more common in the “mixed” land covers, such as cropland/natural vegetation mosaic, shrublands, grasslands, and savannas. Fortunately for our purposes, the vegetation parameters for commonly-confused land covers tend to be fairly similar themselves, which reduces the impact of misclassification on land surface modelling results. For example, the LAI of open shrubland is not too different from the LAI of closed shrubland.We calculated root fraction as a function of land cover class following the method of Zeng33, who defined the following formula (Eq. 4) for use in parameterizing land surface models:$$Y=1-frac{1}{2}left({e}^{-ad}+{e}^{-bd}right)$$
(4)
where Y = cumulative root fraction, d = depth, and a and b are empirical parameters defined by Zeng33 for each International Geosphere–Biosphere Programme (IGBP) land cover type, based on a rooting depth database compiled from more than 200 field surveys. We used this formula with depths of 0.1 m, 0.7 m, and dr, corresponding to three root zones. The value of dr, the maximum rooting depth for each IGBP land cover type, was taken from Zeng33. This method assumes that the depth and distribution of roots depends only on the land cover type; we assume that land cover type is the primary control on root characteristics. Table 3 shows root fractions and root zone depths for each IGBP land cover type.Table 3 Root zone depths (m) and fraction of roots in each zone for IGBP land cover classes.Full size tableLike previous large-scale VIC vegetation cover datasets, our vegetation parameter file neglects land cover change over time. However, it does have a few other advantages over past vegetation parameter datasets. The land cover classification used in the N2001 and L2013 VIC parameter sets is referred to as “UMD-NLDAS” because it is a modified version of the AVHRR-based University of Maryland (UMD) land cover product34. The UMD-NLDAS classification was modified for the North American Land Data Assimilation project (NLDAS35) to exclude open water, urban, and snow and ice land cover classes (see BV2019). VICGlobal uses 17 IGBP land cover classes, including urban, barren, perennial snow and ice, and inland water bodies, permitting better description of land cover variability than the 11 UMD-NLDAS classification.Vegetation library fileThe vegetation library maps each land cover type to a set of vegetation parameters (Table 4). We adapted the LDAS vegetation library36 for use with the 17 IGBP land cover classes, taking monthly average LAI, fractional canopy cover (fcanopy), and albedo values obtained from recent MODIS data products. We set architectural resistance (r0) and minimum stomatal resistance (rmin) to values from literature (described below). The rest of the parameters, which are described in the N2001 paper, were left to their original LDAS vegetation library values. This section describes how we estimated LAI, fcanopy, albedo, r0, and rmin, and how we transferred the remaining parameters from the 11 UMD-NLDAS land cover classes to the 17 IGBP land cover classes.Table 4 VIC model parameters for the vegetation library file.Full size tableWe used MODIS observations from the year 2017 to calculate monthly average LAI, fcanopy, and albedo for each IGBP land cover type. We calculated LAI and albedo from the MODIS-based Global LAnd Surface Satellite dataset (GLASS37,38,39) and fcanopy from NDVI observations (MCD13C140) The expression used for fcanopy follows BV2019:$$fcanopy={left(frac{NDVI-NDV{I}_{min}}{NDV{I}_{max}-NDV{I}_{min}}right)}^{2}$$
(5)
where NDVImin and NDVImax are the minimum and maximum values of NDVI observed for that month. Monthly LAI, fcanopy, and albedo values were calculated by averaging over all grid cells of the same land cover type, counting only cells that were at least 90% homogenous, to avoid noise from grid cells with multiple land covers. Excepting perennial snow and ice land cover, the vegetation parameters in the VIC vegetation library should describe snow-free vegetation. Therefore, before calculating LAI, fcanopy, and albedo for each land cover class, we used fractional snow cover data from MOD10CM41, a global 0.05 degree monthly snow cover dataset, to exclude grid cells with more than 90% snow cover. Additionally, we set albedo to 0.05 for open water, and we set LAI and fcanopy to 0 for open water and perennial snow and ice.The resistances rmin and r0 play a role in determining how much plant transpiration occurs. Higher resistance means less transpiration. Stomatal resistance is resistance to the release of water through the plant stomata, and architectural resistance is the aerodynamic resistance between the leaves and the canopy top42. Two sets of resistance parameters have been used in past large-scale VIC implementations. N2001 ran VIC over the entire globe using rmin values adapted from Dorman and Sellers’ global database of rmin values43 computed using the Simple Biosphere Model44 (SiB). The Nijssen et al.45 r0 values were taken from Ducoudre et al.’s SECHIBA land surface parameterization42. The other set of rmin and r0 parameters are those used in the LDAS vegetation library and in studies such as Livneh et al.12. This set of rmin values comes from Mao et al.46 and Mao and Cherkauer47. We used the rmin values from SiB44 and the r0 values from SECHIBA42 for VICGlobal as they appeared to be the better documented values.For the other parameters in the vegetation library file (displacement height, roughness length, etc.), we assigned values using the existing LDAS vegetation library. Since there are 17 IGBP land cover classes, and only 11 UMD-NLDAS land cover classes in the LDAS vegetation library, we re-assigned some IGBP land cover classes to take the parameters of UMD-NLDAS land cover classes. We remapped barren land, permanent wetlands, snow and ice, urban land, and water bodies to take the parameters of “grasslands” from the LDAS vegetation parameter file. While the characteristics of the barren, snow and ice, urban, and water land cover types clearly differ from those of grasslands, their low LAI and fcanopy values, corresponding to sparse vegetation, essentially “turns off” the other vegetation parameters in the VIC model, as pointed out by BV2019. The other remappings were more straightforward. Croplands and croplands/natural vegetation mosaics inherited values from “croplands,” savannas became “wooded grasslands,” and woody savannas became “woodlands.” We were thus able to assign vegetation parameter values to the each of the 17 IGBP land cover classes.To calculate global average time series of seasonally-varying vegetation parameters would be of limited interest as the seasonal cycle would average out across the equator. Therefore, we calculated average monthly fcanopy, LAI, and albedo for each vegetation type in each hemisphere, and we developed two separate vegetation library files: one for the northern hemisphere and one for the southern hemisphere. Maps of January and July LAI, fcanopy, and albedo are shown in Fig. 4. For illustrative purposes, the parameter values in this figure have been averaged over the 17 IGBP land cover classes using area-based weighting. Figures S14–S19 show maps of the remaining vegetation parameters. Figures S20–S22 show the cycle of LAI, fractional canopy cover, and albedo for each vegetation type, averaged separately over each hemisphere.Fig. 4Maps of leaf-area index, albedo, and fractional canopy cover values. Parameter values have been averaged over the 17 IGBP land cover classes using area-based weighting.Full size image More

Description of scenarios used in this studyTo assess future urban water scarcity, we used the scenario framework from the Scenario Model Intercomparison Project (ScenarioMIP), part of the International Coupled Model Intercomparison Project Phase 6 (CMIP6)38. The scenarios have been developed to better link the Shared Socioeconomic Pathways (SSPs) and Representative Concentration Pathways (RCPs) to support comprehensive research in different fields to better understand global climatic and socioeconomic interactions38,39. We selected the four ScenarioMIP Tier 1 scenarios (i.e., SSP1&RCP2.6, SSP2&RCP4.5, SSP3&RCP7.0, and SSP5&RCP8.5) to evaluate future urban water scarcity. SSP1&RCP2.6 represents the sustainable development pathway of low radiative forcing level, low climate change mitigation challenges, and low social vulnerability. SSP2&RCP4.5 represents the business-as-usual pathway of moderate radiative forcing and social vulnerability. SSP3&RCP7.0 represents a higher level of radiative forcing and high social vulnerability. SSP5&RCP8.5 represents a rapid development pathway and very high radiative forcing38.Estimation of urban water scarcityTo estimate urban water scarcity, we quantified the total urban population living in water-scarce areas2,3,7,19. Specifically, we first corrected the spatial distribution of the global urban population, then identified water-scarce areas around the world, and finally quantified the urban population in water-scarce areas at different scales (Supplementary Fig. 1).Correcting the spatial distribution of global urban populationThe existing global urban population data from the History Database of the Global Environment (HYDE) provided consistent information on historical and future population, but it has a coarse spatial resolution of 10 km (Supplementary Table 1)40,41. In addition, it was estimated using total population, urbanization levels, and urban population density, and does not align well with the actual distribution of urban land42. Hence, we allocated the HYDE global urban population data to high-resolution urban land data. We first obtained global urban land in 2016 from He et al.42. Since the scenarios used in existing urban land forecasts are now dated43,44, we simulated the spatial distribution of global urban land in 2050 under each SSP at a grid-cell resolution of 1km2 using the zoned Land Use Scenario Dynamics-urban (LUSD-urban) model45,46,47 (Supplementary Methods 1). The simulated urban expansion area in this study was significantly correlated with that in existing datasets (Supplementary Table 6). We then converted the global urban land raster layers for 2016 and 2050 into vector format to characterize the spatial extent of each city. The total population within each city was then summed and the remaining HYDE urban population cells located outside urban areas were allocated to the nearest city. Assuming that the population density within an urban area was homogeneous, we calculated the total population per square kilometer for all urban areas and converted this back to raster format at a spatial resolution of 1 km2. The new urban population data had much lower error than the original HYDE data (Supplementary Table 7).Identification of global water-scarce areasAnnual and monthly WSI values were calculated at the catchment level in 2014 and 2050 as the ratio of water withdrawals (TWW) to availability (AWR)33. Due to limited data availability, we combined water-scarce areas in 2014 and the urban population in 2016 to estimate current urban water scarcity. WSI for catchment i for time t as:$${{{{{mathrm{WS{I}}}}}}}_{t,i}=frac{{{{{mathrm{TW{W}}}}}}_{t,i}}{{{{{mathrm{AW{R}}}}}}_{t,i}}$$
(1)
For each catchment defined by Masutomi et al.48, the total water withdrawal (TWWt,i) equalled the sum of water withdrawals (WWt,n,i) for each sector n (irrigation, livestock, industrial, or domestic), while the water availability equalled the sum of available water resources for catchment i (Rt,i), inflows/outflows of water resources due to interbasin water transfer ((varDelta {{{{mathrm{W{R}}}}}}_{t,i})), and water resources from each upstream catchment j (WRt,i,j):$${{{{{mathrm{TW{W}}}}}}}_{t,i}={{sum }_{n}{{{{mathrm{WW}}}}}}_{t,n,i}$$
(2)
$${{{{{mathrm{AW{R}}}}}}}_{t,i}={R}_{t,i}+varDelta {{{{mathrm{W{R}}}}}}_{t,i}+mathop{sum}limits_{j}{{{{mathrm{W{R}}}}}}_{t,i,j}$$
(3)
The changes of water resources due to interbasin water transfer were calculated based on City Water Map produced by McDonald et al.3. The number of water resources from upstream catchment j was calculated based on its water availability (AWRt,i,j) and water consumption for each sector n (WCt,n,i,j)49:$${{{{{mathrm{W{R}}}}}}}_{t,i,j}=,max (0,{{{{mathrm{AW{R}}}}}}_{t,i,j}-{{sum }_{n}{{{{mathrm{WC}}}}}}_{t,n,i,j})$$
(4)
For areas without upstream catchments, the number of available water resources was equal to the runoff. Following Mekonnen and Hoekstra36, and Hofste et al.33, we did not consider environmental flow requirements in calculating water availability.Annual and monthly WSI for 2014 were calculated directly based on water withdrawal, water consumption, and runoff data from AQUEDUCT3.0 (Supplementary Table 1). The data from AQUEDUCT3.0 were selected because they are publicly available and the PCRaster Global Water Balance (PCRGLOBWB 2) model used in the AQUADUCT 3.0 can better represent groundwater flow and available water resources in comparison with other global hydrologic models (e.g., the Water Global Assessment and Prognosis (WaterGAP) model)33. The annual and monthly WSI for 2050 were calculated by combining the global water withdrawal data from 2000 to 2050 provided by the National Institute of Environmental Research of Japan (NIER)34 and global runoff data from 2005 to 2050 from CMIP6 (Supplementary Table 1). Water withdrawal ({{{{{mathrm{W{W}}}}}}}_{s,m,n,i}^{2050}) in 2050 for each sector n (irrigation, industrial, or domestic), catchment i, and month m under scenario s was calculated based on water withdrawal in 2014 (({{{{{mathrm{W{W}}}}}}}_{m,n,i}^{2014})):$${{{{{mathrm{W{W}}}}}}}_{s,m,n,i}^{2050}={{{{mathrm{W{W}}}}}}_{m,n,i}^{2014}cdot [1+{{{{mathrm{WW{R}}}}}}_{s,m,n,i}cdot (2050-2014)]$$
(5)
adjusted by the mean annual change in water withdrawal from 2000 to 2050 (WWRs, m, n, i), calculated using the global water withdrawal for 2000 (({{{{{mathrm{W{W}}}}}}}_{{{{{mathrm{NIER}}}}},m,n,i}^{2000})) and 2050 (({{{{{mathrm{W{W}}}}}}}_{{{{{mathrm{NIER}}}}},s,m,n,i}^{2050})) provided by the NIER34:$${{{{{mathrm{WW{R}}}}}}}_{s,m,n,i}=frac{({{{{mathrm{W{W}}}}}}_{{{{{mathrm{NIER}}}}},s,m,n,i}^{2050}/{{{{mathrm{W{W}}}}}}_{{{{{mathrm{NIER}}}}},m,n,i}^{2000})-1}{2050-2000}$$
(6)
Based on the assumption of a constant ratio of water consumption to water withdrawal in each catchment, water consumption in 2050 (({{{{{mathrm{W{C}}}}}}}_{s,m,n,i}^{2050})) was calculated as:$${{{{{mathrm{W{C}}}}}}}_{s,m,n,i}^{2050}={{{{mathrm{W{W}}}}}}_{s,m,n,i}^{2050}cdot frac{{{{{mathrm{W{C}}}}}}_{m,n,i}^{2014}}{{{{{mathrm{W{W}}}}}}_{m,n,i}^{2014}}$$
(7)
where ({{{{{mathrm{W{C}}}}}}}_{m,n,i}^{2014}) denotes water consumption in 2014. Due to a lack of data, we specified that water withdrawal for livestock remained constant between 2014 and 2050, and used water withdrawal simulation under SSP3&RCP6.0 provided by the National Institute of Environmental Research in Japan to approximate SSP3&RCP7.0.To estimate water availability, we calculated available water resources (({R}_{s,m,i}^{2041-2050})) for each catchment i and month m under scenario s for the period of 2041–2050 as:$${R}_{s,m,i}^{2041-2050}={R}_{m,i}^{{{{{mathrm{ols}}}}},2005-2014}cdot frac{{bar{R}}_{s,m,i}^{2041-2050}}{{bar{R}}_{m,i}^{2005-2014}}$$
(8)
based on the amount of available water resources with 10-year ordinary least square regression from 2005 to 2014 (({R}_{m,i}^{{{{{mathrm{ols}}}}},,2005-2014})) from AQUEDUCT3.0 (Supplementary Table 1). ({overline{R}}_{m,i}^{2005-2014}) and ({overline{R}}_{s,m,i}^{2041-2050}) denote the multi-year average of runoff (i.e., surface and subsurface) from 2005 to 2014, and from 2041 to 2050, respectively, calculated using the average values of simulation results from 10 global climate models (GCMs) (Supplementary Table 2).We then identified water-scarce catchments based on the WSI. Two thresholds of 0.4 and 1.0 have been used to identify water-scarce areas from WSI (Supplementary Table 4). While the 0.4 threshold indicates high water stress49, the threshold of 1.0 has a clearer physical meaning, i.e., that water demand is equal to the available water supply and environmental flow requirements are not met36,37. We adopted the value of 1.0 as a threshold representing extreme water stress to identify water-scarce areas. The catchments with annual WSI >1.0 were identified as perennial water-scarce catchments; the catchments with annual WSI equal to or 1.0 were identified as seasonal water-scarce catchments.Estimation of global urban water scarcityBased on the corrected global urban population data and the identified water-scarce areas, we evaluated urban water scarcity at the global and national scales via a spatial overlay analysis. The urban population exposed to water scarcity in a region (e.g., the whole world or a single country) is equal to the sum of the urban population in perennial water-scarce areas and that in seasonal water-scarce areas. Limited by data availability, we used water-scarce areas in 2014 and the urban population in 2016 to estimate current urban water scarcity. Projected water-scarce areas and urban population in 2050 under four scenarios were then used to estimate future urban water scarcity. In addition, we obtained the location information of large cities (with population >1 million in 2016) from the United Nations’ World Urbanization Prospects1 (Supplementary Table 1) and identified those in perennial and seasonal water-scarce areas.Uncertainty analysisTo evaluate the uncertainty across the 10 GCMs used in this study (Supplementary Table 2), we identified water-scarce areas and estimated urban water scarcity using the simulated runoff from each GCM under four scenarios. To perform the uncertainty analysis, the runoff in 2050 for each GCM was calculated using the following equation:$${R}_{s,g,m,i}^{2050}={R}_{m,i}^{2014}cdot frac{{R}_{s,g,m,i}^{2041-2050}}{{R}_{g,m,i}^{2005-2014}}$$
(9)
where ({R}_{s,g,m,i}^{2050}) denotes the runoff of catchment i in month m in 2050 for GCM g under scenario s. ({R}_{g,m,i}^{2005-2014}) and ({R}_{s,g,m,i}^{2041-2050}) denote the multi-year average runoff from 2005 to 2014, and from 2041 to 2050, respectively, calculated using the simulation results from GCM g. Using the runoff for each GCM, the WSI in 2050 for each catchment was recalculated, water-scarce areas were identified, and the urban population exposed to water scarcity was estimated.Contribution analysisBased on the approach used by McDonald et al.2 and Munia et al.50, we quantified the contribution of socioeconomic factors (i.e., water demand and urban population) and climatic factors (i.e., water availability) to the changes in global urban water scarcity from 2016 to 2050. To assess the contribution of socioeconomic factors (({{{{{mathrm{Co{n}}}}}}}_{s,{{{{mathrm{SE}}}}}})), we calculated global urban water scarcity in 2050 while varying demand and population and holding catchment runoff constant (({{{{{mathrm{UW{S}}}}}}}_{s,{{{{mathrm{SE}}}}}}^{2050})). Conversely, to assess the contribution of climate change ((Co{n}_{s,CC})), we calculated scarcity while varying runoff and holding urban population and water demand constant (({{{{{mathrm{UW{S}}}}}}}_{s,{{{{mathrm{CC}}}}}}^{2050})). Socioeconomic and climatic contributions were then calculated as:$${{{{{mathrm{Co{n}}}}}}}_{s,SE}=frac{{{{{mathrm{UW{S}}}}}}_{s,{{{{mathrm{SE}}}}}}^{2050}-{{{{mathrm{UW{S}}}}}}^{2016}}{{{{{mathrm{UW{S}}}}}}_{s}^{2050}-{{{{mathrm{UW{S}}}}}}^{2016}}times 100 %$$
(10)
$${{{{{mathrm{Co{n}}}}}}}_{s,CC}=frac{{{{{mathrm{UW{S}}}}}}_{s,{{{{mathrm{CC}}}}}}^{2050}-{{{{mathrm{UW{S}}}}}}^{2016}}{{{{{mathrm{UW{S}}}}}}_{s}^{2050}-{{{{mathrm{UW{S}}}}}}^{2016}}times 100 %$$
(11)
Feasibility analysis of potential solutions to urban water scarcityPotential solutions to urban water scarcity involve two aspects: increasing water availability and reducing water demand2. Approaches to increasing water availability include groundwater exploitation, seawater desalination, reservoir construction, and inter-basin water transfer; while approaches to reduce water demand include water-use efficiency measures (e.g., new cultivars for improving agricultural water productivity, sprinkler or drip irrigation for improving water-use efficiency, water-recycling facilities for improving domestic and industrial water-use intensity), limiting population growth, and virtual water trade2,3,18,32. To find the best ways to address urban water scarcity, we assessed the feasibility of these potential solutions for each large city (Supplementary Fig. 2).First, we divided these solutions into seven groups according to scenario settings and the scale of implementation of each solution (Supplementary Fig. 2). Among the solutions assessed, water-use efficiency improvement, limiting population growth, and climate change mitigation were included in the simulation of water demand and water availability under the ScenarioMIP SSPs&RCPs simulations34. Here, we considered the measures within SSP1&RCP2.6 which included the lowest growth in population, irrigated area, crop intensity, and greenhouse gas emissions; and the largest improvements in irrigation, industrial, and municipal water-use efficiency34.We then evaluated the feasibility of the seven groups of solutions according to the characteristics of water-scarce cities (Supplementary Fig. 2). Of the 526 large cities (with population >1 million in 2016 according to the United Nations’ World Urbanization Prospects), we identified those facing perennial or seasonal water scarcity under at least one scenario by 2050. We then selected the cities that no longer faced water scarcity under SSP1&RCP2.6 where the internal scenario assumptions around water-use efficiency, population growth, and climate change were sufficient to mitigate water scarcity. Following McDonald et al.2,3 and Wada et al.18, we assumed that desalination can be a potential solution for coastal cities (distance from coastline More

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Overview of the SWE Retrieval methodThe SWE processing system relies on Bayesian assimilation which combines ground-based data with satellite-borne observations2. The method applies two vertically polarized satellite-based brightness temperature observations at 19 and 37 GHz and a scene brightness temperature model (the HUT snow emission model4). First, snow microstructure described by an ‘effective snow grain size’ is estimated for grid cells with a coincident weather station SD observation. Effective snow grain size is used in the HUT model as a scalable model input parameter to optimize agreement with the satellite measurements. These values of grain size are used to interpolate a background map of the effective grain size, including an estimate of the effective grain size error. This spatially continuous map of grain size is then used as an input for a second HUT model inversion to provide an estimate of SWE. In the inversion process, the effective grain size in each grid cell is weighed with its respective error estimate and a constant value of snow density is applied. The spatially continuous SWE map obtained from the second run of the HUT snow model described above is fused with a background SD field (converted to SWE using 0.24 g cm−3) to obtain a final estimate of SWE using a Bayesian non-linear iterative assimilation approach (which weights the information sources with their estimated variances). The background SD field is generated from the same weather station SD observations used to estimate the effective snow grain size using kriging interpolation methods.The microwave scattering response to SWE saturates under deep snow conditions ( >150 mm) and model inversion of SD/SWE over areas of wet snow is not feasible because the microwave signal is absorbed rather than scattered. For these reasons, the method decreases the weight of satellite data for deep dry snowpacks and wet snow by assessing the modeled sensitivity of brightness temperature to SWE within the data assimilation procedure2,3.Before SWE retrieval, dry snow is identified from brightness temperature data7. For the autumn snow accumulation season (August to December), the dry snow detection is used to construct a cumulative snow presence mask to track the advance of snow extent (SWE estimates are restricted to the domain indicated by the cumulative snow presence mask). During spring the overall mapped snow extent is determined from the cumulative mask, which (as the melt season proceeds) is reduced using a satellite passive microwave derived estimate for the end of snow melt season for each grid cell8.The snow part of the applied scene brightness temperature model is based on the semi-empirical HUT snow emission model which describes the brightness temperature from a multi-layer snowpack covering frozen ground in the frequency range of 11 to 94 GHz4,5. Input parameters to the model include snowpack depth, density, effective grain size, snow volumetric moisture and temperature. Separate modules account for ground emission and the effect of vegetation and atmosphere. Comparisons of HUT model simulations to airborne and tower-based observations, reported elsewhere (e.g.9,10), demonstrate the ability of the model to simulate different snow conditions and land cover regimes. Intercomparisons with other emission models show comparable performance when driven by in situ data11,12 or physical model outputs13, although the HUT model has the tendency to underestimate brightness temperatures for deep snowpacks12.Basic underlying assumptionsPassive microwave sensitivity to SWE is based on the attenuating effect of snow cover on the naturally emitted brightness temperature from the ground surface. The ground brightness temperature is scattered and absorbed by the overlying snow medium, typically resulting in a decreasing brightness temperature with increasing (dry) snow mass. The scattering intensity increases as the wavelength approaches the size of the scattering particles. Considering that individual snow particles tend to range from 0.5 to 4 mm in the long axis direction, high microwave frequencies (short wavelengths) will be scattered more than low frequencies (long wavelengths). The intensity of absorption can be related to the dielectric properties of snow, with snow density largely defining the permittivity for dry snow. Absorption at microwave frequencies increases dramatically with the inclusion of free water (moisture) in snow, resulting in distinct differences of microwave signatures from dry and wet snowpacks.Initial investigations pointed out the sensitivity of microwave emission from snowpacks to the total snow water equivalent14. This led to the development of various retrieval approaches of SWE from the earliest passive microwave instruments in space (e.g.15,16). From the available set of observed frequencies, most SWE algorithms employ the ~37 GHz and ~19 GHz channels in combination. These two frequencies are available continuously since 1979. The scattering from snow at 19 GHz is smaller when compared to 37 GHz, while the emissivity of frozen soil and snow is estimated to be largely similar at both frequencies. The brightness temperature difference of the two channels can be related to snow depth (or SWE), with the additional benefit that the effect of variations in physical temperature on the measured brightness temperature are reduced (relative to the analysis of single frequencies). Similarly, observing a channel difference reduces or even cancels out systematic errors of the observation, provided that the errors in the two observations are similar (e.g. due to using common calibration targets on a space-borne sensor). Typically, the vertically polarized channel at 19 and 37 GHz is preferred due to the inherent decreased sensitivity to snow layering (e.g.17).A basic assumption in the data assimilation procedure that combines spaceborne passive microwave observations and synoptic weather station data to estimate snow depth is that the background snow depth field, interpolated from weather station data, provides meaningful information on the spatial patterns of snow depth. A limitation of the methodology is that this assumption does not hold for complex terrain (mountains). Further, the methodology is not suitable for snow cover on top of ice sheets, sea ice or glaciers.Input dataThe main input data are synoptic snow depth (SD) observations and spaceborne passive microwave brightness temperatures from the Scanning Multichannel Microwave Radiometer (SMMR), Special Sensor Microwave/Imager (SSM/I) and Special Sensor Microwave Imager/Sounder (SSMIS) data from Nimbus-7 and DMSP F-series satellites. The most important frequencies for SWE retrieval and snow detection are 19 GHz (reference measurement with very little scattering from the snow volume) and 37 GHz (sensitive to volume scattering by dry snow), which are available in all instruments. The satellite datasets are described in detail in Data Records section.Ground-based SD data were acquired from the Finnish Meteorological Institute (FMI) weather station observation database, augmented from several archive sources, including the European Centre for Medium-Range Weather Forecasts (ECMWF), The United States National Climatic Data Centre (NCDC), The All-Russia Research Institute of Hydrometeorological Information-World Data Centre (RIHMI-WDC) and The Meteorological Service of Canada (MSC) archives, as described in the Data Records section.In the assimilation of SD values with space-borne estimates, a density value of 0.24 g cm−3 is assumed in estimating SWE. In the assimilation procedure the spatial small-scale variability of SD is considered by assigning a variance of 150 cm2 to the weather station observations over forested areas, and a variance of 400 cm2 for open areas. These variance estimates describe how well a single-point SD observation describes the snow depth over a larger area surrounding the measurement site, and were determined from available FMI, Finnish Environment Institute (SYKE) and Environment and Climate Change Canada (ECCC) snow transect measurements, as well as experimental field campaign data from across Finland and Canada.Daily SD background fields were generated from observations at synoptic weather station locations acquired from multiple archives for the years 1979–2018. For each measurement, the exact location, date of measurement, and SD are required. The long-term weather station data is pre-processed before utilization in the SWE retrieval to remove outliers and improve the overall consistency of the data, as described in the Methods section.Land use and, most importantly, forest cover fraction are derived from ESA GlobCover 2009 300 m data18. Stem volume is required as an input parameter to the emission model to compensate for forest cover effects4,19; average stem volumes are estimated by the ESA BIOMASAR20 data records as described in the Methods section.The following auxiliary datasets are used to mask out water and complex terrain (mountain) pixels:

ESA CCI Land Cover from 2000: water fraction is aggregated to the 25 km grid cell spacing of the SWE product, pixels with a water fraction >50% are masked as water.

ETOPO521: if the standard deviation of the elevation within a 25 km grid cell is above 200 m it is masked as complex terrain.

The Forward model applied in SWE retrievalCalculation of brightness temperature for a satellite sceneFor a satellite scene consisting of a mixture of non-forested terrain, forests, and snow-covered lake ice, the bottom-of-atmosphere brightness temperature TB,BOA is calculated so that:$${T}_{B,BOA}=left(1-FF-LFright){T}_{B,snow}+FFcdot {T}_{B,forest}+LFcdot {T}_{B,lake}$$
(1)
where FF is the forest fraction and LF the lake fraction of a given grid cell. ({T}_{B,snow}), ({T}_{B,forest}), and ({T}_{B,lake}) are the brightness temperatures emitted from non-forested terrain (ground/snow), forested terrain, and lake ice, respectively. Land cover fractions FF and LF are determined from ESA GlobCover data resampled to the 25 km EASE grid. A statistical approach is used to calculate top-of-atmosphere brightness temperatures from TB,BOA, statistics are based on studies covering the Northern Hemisphere4,22,23.Brightness temperature from snow-covered groundThe brightness temperature ({T}_{B,snow}) for snow-covered, non-forested terrain is calculated using the HUT snow emission model4. The model is a radiative transfer-based, semi-empirical model which calculates the emission from a single homogenous snowpack. The current approach utilizes multi-layer modification which allows the simulation of brightness temperature from a stacked system of snow or ice layers5.The absorption coefficient in the HUT model is determined from the complex dielectric constant of dry snow, applying the Polder-van Santen mixing model for the imaginary part24. The calculation of the dielectric constant for dry snow as well as effects of possible liquid water and salinity inclusions, are described through empirical formulae25. Emission from the snow layer is considered as both up- and down-welling emission. These are, in turn, reflected from interfaces between layers (air-snow, snow-ground). The transmission and multiple reflections between layer interfaces are calculated using the incoherent power transfer approach.Applying the delta-Eddington approximation to the radiative transfer equation, the HUT model assumes that most of the scattered radiation in a snowpack is concentrated in the forward direction (of propagation) due to multiple scattering within the snow media, based on26, which assumes that losses due to scattering are approximately equal to generation of incoherent intensity by scattering. However the omission of the backward scattering component as well as omission of trapped radiation will lead to underestimation of brightness temperature for deep snowpacks12. In the HUT model, the rough bare soil reflectivity model27 is applied to simulate the upwelling brightness temperature of the soil medium.Brightness temperature from forest vegetationThe brightness temperature over forested portions of the grid cell ({T}_{B,forest}) is derived from ({T}_{B,snow}) using a simple approximation so that:$${T}_{B,forest}={t}_{veg}cdot {T}_{B,snow}+left(1-{t}_{veg}right)cdot {T}_{veg}+left(1-{t}_{veg}right)cdot left(1-{e}_{snow}right)cdot {t}_{veg}cdot {T}_{veg}$$
(2)
where ({t}_{veg}) is the one-way transmissivity of the forest vegetation layer, ({T}_{veg}) the physical temperature of the vegetation (considered to be equal to air, snow and ground temperatures, ({T}_{veg}={T}_{air}={T}_{snow}={T}_{gnd}=-,{5}^{^circ }{rm{C}})) and ({e}_{snow}) the emissivity of the snow covered ground system. The choice of −5 °C is based on experimental data28 and follows the previous publications2,3,4. Moreover the impact of physical temperature is minimal on the simulated brightness temperature difference of two frequencies applied in the retrieval (typically More

The development of the proposed decision-support system requires the undertaking of interdisciplinary research brought about by a diverse team. It is in this context that researchers from the chemical engineering department and the geomatics sciences department at Laval University, in Quebec, Canada, have developed a nutrient stakeholder platform (NutriPlatform-QC), i.e. a regrouping of actors from research institutions, industry, governmental authorities, municipalities, and agricultural organizations, among others, that are active in the field of organic waste management. Since 2017, regular meetings have been organized with the members of the platform in order to frame the objectives and methodology of such interdisciplinary research, as well as to adapt the scope of the research to the stakeholder needs.As such, the authors initiated the design and development of a decision-support software tool that allows setting up optimal organic waste value chains for the province of Quebec, with Primodal Inc. and Chamard Environmental Strategies as industrial partners. The system, named optim-O (www.optim-o.com), applies a holistic modelling approach that focuses on minimization of costs and greenhouse gas emissions throughout the entire value chain. The scope (Fig. 1) includes the generation and collection of organic waste across the province (including urban, suburban, peri-urban and rural areas), the treatment of the waste through biomethanation, composting, and/or nutrient recovery, and the distribution of the end-products such as biogas, digestate, compost, and recovered mineral fertilizers. All of these items are geolocated in order to account for transport distances and potential traffic nuisance. Regulatory and market restrictions for product distribution are also taken into account.Fig. 1: Scope and four use cases of the optim-O decision-support system.Scope and use cases.Full size imageThe software tool integrates three key components: (1) a multidimensional spatiotemporal database system (including georeferenced and non-georeferenced data), (2) a model-based decision module (for simulation and optimization) and (3) a user-friendly interface (to facilitate knowledge transfer and interpretation). Table 1 provides an overview of the data included in the system. Generally speaking, georeferenced data includes data that is location-specific, such as population, commerce, services and industry (position and size), road networks, hydrographic networks, existing infrastructure (wastewater treatment plants, biogas and composting facilities), agricultural parcels (location, size, crop, nutrient saturation index) and associated regulatory and market constraints (fertilizer application limitations). Non-georeferenced data includes costs and other factors used for economic assessments, greenhouse gas emission factors, technical process-related factors (used for the mathematical process models), and social factors (odour emissions, population density, the latter also being part of the georeferenced data). Default values are provided for the non-georeferenced data, but the user can modify these if case-specific data would be available. A prototype of the developed tool is currently being validated using two major biomethanation plants in Quebec. The tool also has the flexibility for extension with other resource recovery processes.Table 1 Georeferenced and non-georeferenced data included in the optim-O decision-support software tool.Full size tableFigure 1 presents the four use cases for which the tool can be used. It concerns decision problems related to (1) the collection of organic waste, (2) the treatment process operation, (3) the end-product distribution and (4) the integration of the three previous use cases as one global optimization problem. In each case, the tool can be used to either simulate and evaluate various scenarios defined by the user, or to solve the optimization problem taking into account optimization criteria defined by the user, as described in the examples below.In the first use case, i.e. the collection of organic waste, the tool allows for the estimation of organic waste generation based on data from households, services, businesses and industries, with associated organic matter generation rates for each, either based on the number of members in a household, employees or clients, as well as the type of service, business or industry. As presented in Table 1, all of this information is geolocated, allowing users to locate sources of organic waste across a territory, as presented in Fig. 2. From here, using the treatment plant location and road networks, various waste collection routes can be simulated. The user can also select specific modelling objectives, for example: maximising organic waste collection, evaluating the potential to collect a certain waste type, assessing long-distance travel (for example, through transfer stations), as well as associated optimization objectives, for example, reducing GHG emissions, reducing costs or reducing both at the same time.Fig. 2: Geolocated organic waste generation throughout the southern area of the province of Quebec, as estimated by the decision-support system.Geolocated organic waste generation Southern Quebec.Full size imageIn the second use case, i.e. treatment process operation, the system can evaluate processing outcomes through a mathematical model library developed for this tool. It includes models for anaerobic digestion, composting and processes to recover nutrients as mineral fertilizers from digestate, and allows easy extension with other process models in the future. The models are numerically simple, requiring basic data inputs (e.g., key physico-chemical waste characteristics), and are coded directly in the database. By selecting this approach, a balance was sought between model complexity and simulation times, with the aim to minimize computational efforts, while maximizing usability. Using the models, one can aim at evaluating the impact of varying substrates on the process performance, seeking to optimize certain parameters (e.g., minimizing GHG emissions, maximizing product quality or minimizing process duration/size). Moreover, different treatment process combinations can be evaluated and compared, for example the implementation of anaerobic digestion as sole technology vs the implementation of anaerobic digestion with nitrogen recovery from the liquid fraction of digestate and composting of the solid fraction of digestate.In the third use case, users can simulate and optimize locations for end-product distribution. In this case, an estimation of quantity and quality factors for the end-products (biogas, digestate, compost, recovered mineral fertilizers), either provided as model outputs or entered by the user, are considered as data inputs. From here, agricultural lands can be evaluated regarding their receptivity for the product. This receptivity is based on the quality of the product, size of the plot, the phosphorus saturation status of the soil, the nitrogen pollution status of the surrounding water bodies and the nitrogen requirements for crop production, which all determine how much product can be accepted on the land under study. Distribution networks can then be set up and optimized using spatial analysis, identifying the nearest receptive lands.Finally, a fourth use case concerns the integrated assessment of the above three use cases. Indeed, the outputs of one module can serve as the inputs to another module. As such, the outputs of the waste collection module can be used as inputs to the treatment process module, providing a certain quantity and quality of substrate(s). The process models can then be run to determine the optimal treatment process chain, as well as quantity and quality factors for the end-products. The latter can then be used to search for an optimal agricultural site for end-product distribution. This process can be undertaken iteratively by the system seeking to meet desired criteria and/or propose a few scenarios of interest to decision makers. The fourth use case can also be applied to select the optimal position of a new treatment plant, taking into account the organic waste availability and the access to agricultural land for end-product distribution. Moreover, such integrated approach can allow users to understand the impact of changing waste collection strategies on existing treatment process chains, or to evaluate how a change in process conditions can affect end-product distribution. More