Uncertainties, sensitivities and robustness of simulated water erosion in an EPIC-based global gridded crop model

Water erosion on arable land can reduce soil fertility and agricultural productivity. Despite the impact of water erosion on crops, it is typically neglected in global crop yield projections. Furthermore, previous efforts to quantify global water erosion have paid little attention to the effects of field management on the magnitude of water erosion. In this study, we analyse the robustness of simulated water erosion estimates in maize and wheat fields between the years 1980 and 2010 based on daily model outputs from a global gridded version of the Environmental Policy Integrated Climate (EPIC) crop model. By using the MUSS water erosion equation and country-specific and environmental indicators determining different intensities in tillage, residue handling and cover crops, we obtained the global median water erosion rates of 7 t ha−1 a−1 in maize fields and 5 t ha−1 a−1 in wheat fields. A comparison of our simulation results with field data demonstrates an overlap of simulated and measured water erosion values for the majority of global cropland. Slope inclination and daily precipitation are key factors in determining the agreement between simulated and measured erosion values and are the most critical input parameters controlling all water erosion equations included in EPIC. The many differences between field management methods worldwide, the varying water erosion estimates from different equations and the complex distribution of cropland in mountainous regions add uncertainty to the simulation results. To reduce the uncertainties in global water erosion estimates, it is necessary to gather more data on global farming techniques to reduce the uncertainty in global land-use maps and to collect more data on soil erosion rates representing the diversity of environmental conditions where crops are grown.

and harvest dates, tillage and plant residue management. Accordingly, neglecting the impact of seasonal changes 78 in vegetation cover and field management practices constitutes large uncertainty in global water erosion estimates.

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Crop models usually simulate crop growth on a daily timescale, which allows attached water erosion models to 80 account for daily changes in weather, soil properties and vegetation cover. However, uncertainty remains due to 81 the increasing requirement of input data for daily simulations, which is especially challenging at a global scale.

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In this study, we examine the uncertainties and sensitivities of water erosion estimates in an EPIC-based global-

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The simplified framework in Figure 1 illustrates the particular stages of the methodological procedure applied by 98 this study and their relationships to input data and model outputs. Both, input and output data are used twofold.

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We use input data i) to simulate daily wheat and maize growth and water erosion with EPIC, and ii) to analyse   Williams, 1990). Originally EPIC was named Erosion-Productivity Impact Calculator and 113 was developed to determine the relationship between erosion and soil productivity. Due to its origin, EPIC has 114 several options to calculate water erosion caused by precipitation, runoff and irrigation (Williams, 1990). available. This results in a total of 131,326 simulation units with a spatial resolution of 5' to 30' (about 9 km to 119 56 km near the equator). We run EPIC in each simulation unit upon a representative field with a defined slope 120 length and field size based on a set of rules for different slope classes (Table S1). The slope class for each 121 simulation unit is defined as the most common slope per simulation unit derived from a global terrain slope

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EPIC includes seven empirical equations to calculate water erosion (Wischmeier and Smith, 1978). The basic 129 equation is: where Y is soil erosion in Mg ha -1 (mass/area), R is the erosivity factor (erosivity unit/area), K is the soil erodibility 132 factor in Mg MJ -1 (mass/erosivity unit), LS is the slope length and steepness factor (dimensionless), C is the soil 133 cover and management factor (dimensionless) and P is the conservation practices factor (dimensionless).

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The main difference between the water erosion equations available in EPIC is their energy components used to

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The erosion energy component is calculated as a function of either runoff volume Q (mm), peak runoff rate qp

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(mm h -1 ) and watershed area WSA (ha), or via the rainfall erosivity index EI (MJ ha -1 ). The latter determines the deposition. If the sediment load exceeds the transport capacity, determined by a function of flow rate and slope 144 steepness, soil is deposited, which is calculated by a function of flow rate and particle size (USDA-ARC, 2013).

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The soil cover and management factor is updated for every day where runoff occurs using a function of crop 146 residues, biomass cover and surface roughness. The impact of soil erodibility on simulated water erosion is 147 calculated for the top-soil layer at the start of each simulation year as a function of sand, silt, clay and organic 148 carbon content. The topographic factor is calculated as a function of slope length and slope steepness. A detailed 149 description of the cover and management, soil erodibility and topographic factor is provided in the supporting 150 information (Text S1). The conservation practice factor is included in all equations as a static coefficient ranging 151 between 0 and 1, where 0 represents conservation practices that prevent any erosion and 1 represents no tillage and no-tillagewere designed by altering parameters related to water erosion to analyse the impact of field 162 management on simulated water erosion and to draw conclusions on its impact on the quality of simulation results.

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In the reduced and no-tillage scenarios, we decrease soil disturbance by reducing cultivation operations, tillage 164 depth and surface roughness, and we increase plant residues left in the field after harvest. In addition, we reduce  We estimate the rate of water erosion globally by combining these six tillage and cover crop scenarios in different 173 regions of the world, using climatic and country-specific assumptions and indicators (Table 3). We chose maize 174 and wheat as two contrasting crop types for analysing water erosion in different cultivation systems. Maize is a 175 row crop with relatively large areas of bare and unprotected soil between the crop rows. The plant density in wheat 176 fields is much higher, which improves the protection of soils against water erosion.

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We consider conventional and reduced tillage systems globally while considering no-tillage only for countries in 178 which the share of conservation agriculture is at least 5 %. In tropical regions, we simulate water erosion with a 179 grass cover in between maize and wheat seasons to account for soil cover from a year-round growing season. In 180 temperate and snow regions, we simulate water erosion affected by both soil cover throughout the year and bare 181 soil in winter seasons. In arid regions, we do not simulate grass cover in between growing seasons due to the 182 limited water supply.

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On slopes steeper than 5 %, we consider only rainfed agriculture, as hilly cropland is irrigated predominantly on 184 terraces that prevent water runoff. To account for erosion control measures on steep slopes we use a conservation between simulated and measured water erosion as discussed below. Table 3 summarises the field management 191 assumptions used in the baseline scenario.

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We use a sensitivity analysis to identify the most essential input parameters to the factors in the seven water 202 erosion equations. We use the Sobol method (Sobol, 1990), which is a variance-based sensitivity analysis that is

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We test 30 parameters directly connected to the water erosion equations in EPIC. In total, we assign 126,976 208 random values to all input parameters along a pre-defined triangular distribution or a range of discrete values 209 (Table S2). Water erosion is simulated with EPIC using the seven available equations for each random input

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We compared our simulated water erosion rates with 473 soil erosion measurements from 39 countries; 314 218 records were derived by the 137 Cs method and 159 records from erosion plots. An overview of the field data is 219 presented in Fig. S5-S8, and the full dataset is available in Table S5. points, which can provide valuable information on the spatial distribution of erosion.

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To expand the field data records for evaluation, we use also erosion rate measurements from erosion plots conditions. Therefore, only field measurements with recorded slope steepness and annual precipitation are used.

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Where annual precipitation amounts are not recorded, they are taken from the WorldClim2 dataset (Fick and

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Hijmans, 2017). Due to the non-normal distribution of the simulated and measured data, the median deviation

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(MD) is used as a measure to compare the agreement between simulated and measured water erosion values.

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We estimate global annual average and median water erosion rates in wheat and maize fields of 19 t ha -1 and 6 t

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The first-order sensitivity indices do not include interactions between input parameters, which leads to the sum of 284 all first-order sensitivity indices being lower than 1. The total-order sensitivity indices sum all first-order effects 285 and interactions between parameters, which leads to overlaps in case of interactions and a sum greater than 1. The

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differences between the first-order and the total-order indices can be used as a measure to determine the impact 287 of the interactions between a specific parameter with other parameters. The total-order sensitivity indices show 288 that slope steepness, including interactions to other parameters, contributes 63-75 % of the output variance from 289 which 18-21 % are due to interactive effects with other parameters (Table 5). The total-order sensitivity indices 290 from precipitation range from 21-36 %, from which 10-18 % is due to interactions with other parameters.

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The high sensitivity of slope and precipitation is similar for all equations, but the most sensitive parameters after  (Table S4).

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Furthermore, the relations between kinetic energy and rainfall energy in the American Great Plains differ from 364 other regions in the world (Roose, 1996). Similarly, the runoff curve number method, which is the key

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The evaluation against field measurements in this study provided a first indication of the robustness of results

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under specific topographic and climatic conditions. However, the reported data does not enable us to further           fields. Dark areas illustrate grids where slopes are steeper than 8 % and annual precipitation is above 1000 mm.

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Correspondingly, blue, red, and grey pixels are below one or both thresholds.     • Mix of off-season cover with and without cover crops in temperate and cold zones. • Weighted average of water erosion under wheat and maize cultivation where both crops are grown.
• Weighted average of irrigated and rainfed cropland based on MIRCA2000.

METHOD MUSS water erosion equation.
716 Table 4: First-order sensitivity indices (SI) ranking for the five most sensitive input parameters (PARM) for each  Table S3.