Soil erosion is a serious threat to agricultural productivity and the sustainable provision of food to a growing world population. No connection has hitherto been established between aerosols and rainfall-induced soil erosion on the ground. Here we use a cloud resolving model to simulate the effect of aerosols on rainfall erosivity (an indicator of the erosive potential of rain). Increased atmospheric aerosol concentrations tend to suppress precipitation in warm rain clouds, while in cold or mixed-phase systems, invigoration of surface rainfall can occur. We show that in both these cases, the response of erosivity to an increase in aerosol is in the same direction as, but amplified beyond the change in total rainfall. We also show that aerosols can impact erosivity through changes in raindrop size. Our results suggest that anthropogenic aerosol emissions affect erosivity and thus may have important consequences for agricultural productivity.
 Nearly 2 billion hectares of land, approximately 15% of the Earth's surface, suffers from soil degradation as a result of human activities, with over half of all soil erosion caused by water [Crosson, 1995; United Nations Environmental Programme, 2002]. Erosion directly affects food and water security [Pimentel et al., 1995] and reduces the capacity of land to act as a sink for the greenhouse gas carbon dioxide; up to 20% of carbon stored in eroded soils is released to the atmosphere as CO2 [Yang et al., 2003]. It is generally accepted that storms are responsible for the dominant share of erosion [Wischmeier and Smith, 1978; Boardman, 2006]. However, evidence suggests that light rainfall can also cause substantial erosion over long time scales [Kirkbride and Reeves, 1993; Marques et al., 2008; Baartman et al., 2012]. Both cases are explored in this study.
 Understanding the effects of aerosols on precipitation processes remains challenging, depending on a complex balance of microphysical and dynamic effects [Khain et al., 2005; Tao et al., 2012]. These may be simplified by classification into two broad categories which we study here [Tao et al., 2012]. Smaller cloud droplets in a polluted atmosphere inhibit the collision and coalescence processes that lead to raindrop formation, and may suppress surface rainfall [Squires and Twomey, 1960; Albrecht, 1989]. In warm rain clouds, this outcome usually prevails [Fan et al., 2012; Tao et al., 2012]. Conversely, in a mixed-phase system, these smaller droplets survive longer in the cloud, may be lifted to freezing level, and serve to invigorate cold rain formation processes (“aerosol invigoration effect”) [Rosenfeld and Woodley, 2000; Khain et al., 2005; Tao et al., 2012]. The associated latent heat release can intensify the whole system, resulting in a delayed enhancement of surface rainfall [Khain et al., 2005, 2008; Tao et al., 2012]. This process occurs mostly under conditions of low wind shear, high humidity, and atmospheric instability [Khain et al., 2008; Fan et al., 2009; Khain and Lynn, 2009]. The outcome ultimately depends on competing processes of condensate generation and loss, both of which are higher in polluted clouds and are affected by cloud type and environmental conditions. Some studies have found that a decrease in precipitation efficiency can offset the tendency of ice invigoration to increase precipitation [Khain et al., 2005; Khain, 2009; Khain and Lynn, 2009; Igel et al., 2013].
 We use a cloud resolving version of the Weather Research and Forecasting model (WRF version 3.1) [Skamarock et al., 2008] to simulate the erosivity response to increased aerosol loading in two idealised case studies, chosen to illustrate the two categories of behavior described above. This version includes the complete microphysics parameterizations of the full model but contains no radiation or land surface scheme and no Coriolis force.
 A two-dimensional moist flow over a bell-shaped hill with gentle orographic precipitation provides the warm rain example, where increasing aerosol concentrations cause a decrease in precipitation. A stationary supercell case study characterizes the response of a mixed-phase cloud, in which the aerosol invigoration effect dominates, resulting in a positive precipitation sensitivity overall. The background cloud condensation nuclei (CCN) number concentration was varied from 300 to 1200 cm−3 in both case studies.
 For the supercell, soundings provided initial profiles of potential temperature and water vapor mixing ratio [Weisman and Klemp, 1982], with water vapor increased by 7% throughout the column. The storm was initiated with a temperature perturbation of 3 K in the center of the domain, 1.5 km above the ground. The perturbation had a 10 km horizontal and 1.5 km vertical radius and approached zero at the domain boundaries. The domain was 42 × 42 km2 with a horizontal resolution of 1 km and 61 vertical levels. Total run time was 4 h with a time step of 6 s. For the two-dimensional hill case, tropical profiles of potential temperature and water vapor were used [Anderson et al., 1986] with a constant westerly 10 m s−1 wind. The hill was a bell shape, 2 km high with a half width of 30 km. The domain had 201 grids of 2 km horizontal resolution in the west-east direction and 41 vertical levels up to 30 km. Run time was 10 h with a 20 s time step. Model variables were extracted every 10 min for both case studies.
 The model microphysics scheme is adapted from the standard parameterization in WRF [Morrison et al., 2009] to include a prognostic treatment of cloud droplet number [Morrison et al., 2005; Fan et al., 2012] (H. Morrison, personal communication, 2013). Droplet activation is based upon a power law CCN distribution [Pruppacher and Klett, 1997]: NCCN = cSk, where NCCN is the number of activated CCN (cm−3) and S is the supersaturation (%). NCCN is not prognostic: k was fixed at 0.308, while c (the CCN number with a supersaturation of 1%) was varied from 300 to 1200 cm−3. These values are consistent with other studies [Khain et al., 2005; Fan et al., 2012] and with observations [Pruppacher and Klett, 1997], and produced mean cloud droplet concentrations of about 200 to 740 cm−3 for the supercell and 130 to 430 cm−3 for the hill. An exponential raindrop size distribution is assumed.
 We adopt a formulation which expresses rainfall erosivity, R, as the product of rainfall kinetic energy flux and surface runoff [Kinnell et al., 1994]. Surface runoff is a fraction of intensity, and we assume here that this fraction, k, is constant:
where et is the kinetic energy flux (J m−2 h−1) and, it is the intensity (mm h−1) at time t of rain falling over a period ∆t. The widely used Universal Soil Loss Equation (USLE) [Wischmeier and Smith, 1978] and Revised-USLE (RUSLE) [Renard et al., 1997] adopt a different formulation for erosivity:
where ∑ tet. Δt is the total storm kinetic energy (J m−2), and I30 is the maximum 30 min rain intensity of the storm (mm h−1). Equation (1) is preferred because it incorporates runoff, an essential component required for erosion to take place, and because it better accounts for soil detachment and transport than equation (2) [Kinnell et al., 1994], but we include RU,R for comparison because this formulation remains widely used. The relationship between kinetic energy flux and intensity is approximately linear [Wischmeier and Smith, 1958; Brown and Foster, 1987; Salles et al., 2002; Nissan and Toumi, 2013]. Energy flux is typically parameterized from rain intensity, but here we model this dynamically within the bulk microphysics scheme based on the size distribution, N(D), and drop fall speed relation, V(D) [Nissan and Toumi, 2013]:
where ρw is the density of water, c = π/6, and D is the diameter of the raindrops. This captures the observed variability in energy for a given intensity and couples energy flux to raindrop size, an important advantage which is explored in further detail below.
 Rainfall kinetic energy flux modeled within the microphysics scheme is shown in Figure 1 for both case studies. Stronger updrafts in the supercell activate more cloud droplets and sustain larger, more energetic raindrops than in the gentler orographic rain case (hill) for similar intensities. The modeled relationships are approximately linear and fall mainly within the range of observed relationships reported in the literature [Salles et al., 2002; Nissan and Toumi, 2013]. The energy flux for a given intensity increases with aerosol loading in the hill case, but not in the supercell; this is discussed in further detail below.
 Figure 2 shows the relative change in accumulated rainfall, kinetic energy, and domain total erosivity for increases in CCN concentration of 900 cm−3 for both scenarios. In the supercell, rainfall increases with CCN loading between 300 and 700 CCN cm−3 (Figure 2a). A clear invigoration effect occurs in this range, with a 2% increase in updraft velocity (averaged over values greater than 2 m s−1) owing to rises in mean ice (+2%) and liquid (+31%) water content. A saturation effect above 700 CCN cm−3 can be explained by limited moisture availability, and/or by detrainment of smaller (lighter) cloud ice particles which dries the upper cloud levels and enhances evaporation and sublimation [Rosenfeld and Woodley, 2000]. In the following analysis, we present results for the supercell only for the CCN range which exhibits an invigoration effect on precipitation (300 to 700 cm−3). For this range, total rainfall and kinetic energy rise by +25% and +29%, respectively, while erosivity (R) increases by +36%. For comparison, the total RUSLE erosivity (RR, equation (2)) is calculated, with energy computed directly from rain intensity according to the energy-intensity parameterization used in the RUSLE model [Brown and Foster, 1987]. The change in RR is also amplified relative to the change in accumulated rainfall (+37%, Figure 2a). The USLE erosivity (RU), defined similarly to the RUSLE term with a different energy-intensity parameterization [Wischmeier and Smith, 1958] also shows an amplification (+37%, not shown). This gives confidence that the amplification signal is robust across different commonly used measures of erosivity.
 In the hill case, accumulated precipitation is suppressed by −71% and kinetic energy by −80%, while total erosivity (R) falls by −90% (Figure 2b). The change in RR is also amplified relative to the change in total rainfall (−89%) and the same is true for RU (−93%, not shown). In both cases, therefore, the change in erosivity exceeds the change in total rainfall.
4.1 Amplification of the Erosivity Response
 Defined as the product of two positively correlated variables (equations (1) and (2) and Figure 1), the change in erosivity can mostly be expected to be amplified beyond the change in total rainfall. However, referring to the same definition, erosivity changes are also dominated more by the upper end of the rainfall intensity/energy distribution than are changes in accumulated rain. The top 10% of rain intensity values constitute 69% of domain total erosivity in the supercell and 89% in the hill case. As a result, when extreme rain intensity changes more or less than the average, this amplification may either be enhanced further or dampened. In extreme cases, changes in erosivity could even oppose changes in mean rain intensity, when these are decoupled from changes to the upper end of the precipitation distribution. These results indicate that there is a complex erosivity response to increasing aerosol that differs from the precipitation signal.
4.2 Raindrop Size Effect
 Changes in raindrop size can either amplify or mitigate the sensitivity of erosivity to aerosol. Large raindrops have been shown to contribute disproportionately to rainfall kinetic energy flux compared with their mass and number and therefore constitute a greater fraction of total erosivity than surface precipitation [Nissan and Toumi, 2013]. Drop size changes can therefore differentially affect the sensitivities of erosivity and precipitation to aerosol. In the supercell, raindrop diameter increases (+27%) owing to the rise in mean precipitation intensity (+23%). Drop size distribution measurements show that raindrop size is positively correlated with intensity [Laws and Parsons, 1943], but in the model microphysics scheme, this is only achieved for low intensities [Nissan and Toumi, 2013]. This suggests that the amplification of erosivity (R) in the supercell case may be underestimated by this scheme, as the energy-intensity relationship would be steeper with a more realistic treatment of drop size. This is consistent with a larger increase in RR than R in the supercell case (Figure 2a).
 In the hill case, there is an overall decrease in average raindrop diameter (−24%) with increasing aerosol concentrations, leading to the reduction in mean precipitation intensity (−70%). Figure 3a indicates fewer drops of all sizes with a disproportionate decrease in the number of large drops. This corresponds to a shift along the kinetic energy-intensity curve in Figure 1. Despite this reduction in rainfall we find, surprisingly, that drops are actually larger for a given rain intensity. As CCN increases, rain of a given intensity consists of fewer small drops and more large drops, shown by a cross over in the relative size distributions at about 0.4 mm in Figure 3b. Overall, less rain falls in the polluted scenario, but erosivity for a given intensity of rain is greater. This is illustrated by an upward shift in the kinetic energy-intensity curve for the hill case (Figure 1), which mitigates the decrease in erosivity. The overall outcome is a reduction in mean rainfall brought about by smaller cloud droplets, but a subtle invigoration effect also occurs. Instantaneous saturation adjustment in the model is independent of particle size, but the diffusional growth stage of droplets in the polluted cloud is prolonged by the decrease in collision efficiency of the smaller droplets, increasing the total mass of condensate (20% rise in mean liquid water content) [Khain et al., 2005]. This releases extra latent heat, driving an intensification of airflow in the cloud. Stronger vertical velocities can support heavier raindrops, which grow to a larger size for a given intensity.
 The supercell case does not exhibit a similar drop size effect for a given intensity, despite a clear invigoration effect. Instead, the kinetic energy-intensity relationship is relatively well constrained and insensitive to aerosol loading (Figure 1). This can partly be explained by the problem of raindrop size simulation in the model microphysics described above.
 Rainfall erosivity, an indicator of the potential of rain to cause soil erosion, was simulated in two idealized case studies using a simple cloud resolving model. A mixed-phase stationary supercell storm exhibited invigoration of ice processes and an enhancement of precipitation with increased aerosol loading. A warm rain cloud generated by moist flow over a two-dimensional hill demonstrated a reduction in precipitation.
 We find that in both these cases, the change in erosivity with increasing aerosol concentrations is in the same direction as, but amplified beyond the change in surface rainfall. The effect of aerosols on raindrop size has a disproportionate impact on erosivity compared with surface precipitation and can either enhance or mitigate the overall amplification signal. We show that despite a reduction in precipitation in the hill case, raindrops are actually larger for a given intensity of rain.
 These results suggest that anthropogenic aerosol emissions affect rainfall erosivity in a manner which is not obvious from the precipitation response. The complexities of many competing cloud processes can result in different outcomes, and other cases may involve subtle combinations of the examples discussed here.
 There are several intriguing implications of these results. Heavy rain dominates erosion [Boardman, 2006], so the drive for reducing urban aerosol emissions could benefit regional agricultural productivity. Agricultural practices like biomass burning could decrease productivity through erosion. Finally, in regions where precipitation correlates positively with dust loading [Zender, 2005], there is the possibility of a positive dust-aerosol-erosion feedback.
 This study was supported by the Natural Environment Research Council and the BP Environmental Technology Program. We would like to thank Hugh Morrison for providing the updated microphysics scheme used for this study and for helpful advice relating to this.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.