HydroLorica is a raster-based model, where a digital elevation model (DEM) determines the shape of the terrain. Below each raster cell of the DEM there is a predetermined number of soil layers with layer thicknesses variable in space and time. Each layer can contain a specific mixture of gravel, sand, silt and clay and two types of organic matter (quickly and slowly decomposing, Yoo et al., 2006), depending on parent material and occurring pedogenic processes. Pedogenic and geomorphic processes affect the contents of the layers, leading to differences in soils in space and time. Changes in soil properties and contents modify layer thicknesses and surface elevation through a pedotransfer function (PTF) of bulk density. The use of a pedotransfer function allowed the model to calculate variations in layer thicknesses due to pedogenic and geomorphic processes. We used the same PTF for bulk density as the original Lorica model (Tranter et al., 2007). We refer to Temme and Vanwalleghem (2016) for more information about the spatial model architecture of Lorica, which we maintained in our adaptation HydroLorica. In this project, we worked with 25 soil layers, with an initial uniform thickness of 0.15 m. When a layer got very thick or very thin (55 % thicker or thinner than its initial value), the layer was split or combined with another layer.

The annual changes in texture classes tex (kg) and organic matter classes om (kg) in layer l at location xy and time t are governed following Eqs. (1) and (2) (for abbreviations of processes, see Table 1). The changes in mass of texture and organic matter are converted to a change in layer thickness (m) using a pedotransfer function (Tranter et al., 2007). We calculated the bulk density of the fine mineral fraction (kg m-3) with Eq. (3) using the sand and silt fraction (–) and the depth below the surface (m). HydroLorica includes a correction of bulk density taking into account the effects of the coarse fraction and the organic fraction using Eq. (4), using a density of 2700 kg m-3 for the coarse fraction (Temme and Vanwalleghem, 2016) and a density of 224 kg m-3 for the organic fraction (Tranter et al., 2007). In our study, there is no coarse soil material present. This pedotransfer function does not directly take into account changes in bulk density stemming from soil structuring, weathering or bioturbation. Instead, depth below the surface is used as a proxy for these factors. The used PTF has a relatively low fit with the data it was derived from (R2=0.41, Tranter et al., 2007). However, PTFs that yield a higher accuracy often require advanced calculation methods (Chen et al., 2018; Ramcharan et al., 2017) or soil properties that are not readily available in HydroLorica. As we discuss in Van der Meij et al. (2018), the estimation of such properties often gives biased or highly uncertain results, which would propagate into the calculation of bulk density. Rather than stacking pedotransfer functions, we decided to use a PTF that required input that is readily available in HydroLorica and could be calculated within the model itself.

The sum of changes in layer thickness of all layers L calculated through changes in bulk density and mass of the layers results in the annual change in elevation z (Eq. 5). Clay translocation and water erosion are directly driven by the total annual water flow, while occurrence of tree throw and rates of creep, bioturbation and organic matter accumulation are indirectly driven by water availability via vegetation controls. Infiltration I is the difference between precipitation P and spatially explicit actual evapotranspiration ETa, runon ROnn and runoff ROff (Eq. 6). HydroLorica works with dynamic time steps as suggested by Van der Meij et al. (2018) to capture process dynamics at their relevant scales while optimizing calculation time. Hydrologic processes are calculated with a daily, monthly, or yearly time step, with smaller time steps selected during wetter conditions for more accurate simulation. Annual sums of infiltration and overland flow are used to drive geomorphic, pedogenic and biotic processes. 1Δtexxy,l,t=ΔtexCR,xy,l,t+ΔtexWE,xy,l,t+ΔtexTT,xy,l,t+ΔtexTI,xy,l,t+ΔtexCT,xy,l,t+ΔtexBT,xy,l,t2Δomxy,l,t=ΔomCR,xy,l,t+ΔomWE,xy,l,t+ΔomTT,xy,l,t+ΔomTI,xy,l,t+ΔomCAB,xy,l,t+ΔomBT,xy,l,t3BDfine,xy,l,t=10001.35+0.452fsand+0.76fsilt+100fsand+0.76fsilt-44.652×-0.000614+0.06⋅log⁡10depth4BDsoil,xy,l,t=masstotal,xy,l,tmassfine,xy,l,tBDfine,xy,l,t+masscoarse,xy,l,t2700+massorganic,xy,l,t2245Δzxy,t=∑l=1LΔBDsoil∑texxy,l,t+∑omxy,l,t6Ixy,t=Pt-ETaxy,t+ROnnxy,t-ROffxy,t

In our model we considered only the impact of physical and biological processes on soil properties. The current model architecture does not facilitate the simulation of soil chemical processes. The selected processes are described below. Drivers and impacts of each process are summarized in Table 1. We summarized the drivers per soil-forming factor. We mostly used the processes and parameters of Lorica as reported in Temme and Vanwalleghem (2016), which we summarize here. When we added a new process or changed its parameters, the adjustments are reported in this section. We provided a detailed overview of the equations and selected parameters in Supplement 1.

We aim to understand the functioning of general soil–landscape systems. Therefore, we parametrized and calibrated the model processes using regional data or process rates from the literature that are valid for larger regions. We did not calibrate the parameters on data from one specific study site to avoid the effect of any idiosyncrasies that can be present in those data. For other processes where there were no regional data available, we estimated the parameters so that the effects of those processes were on the same order of magnitude as processes with rates based on the literature. An overview of the process parameters is provided in Table S1 in the Supplement.

The hydrological module partitions spatially uniform rainfall (P) into three spatially explicit components: evapotranspiration (ET), infiltration (I) and surface flow (ROnn and ROff, Eq. 6). Potential ET is calculated from prescribed temperature using the Hargreaves–Samani equation (Hargreaves and Samani, 1985) and corrected for topographical position (Swift, 1976) and vegetation type (Allen et al., 1998). Surface flow is calculated on a daily basis, and only when rainfall intensity (amount / duration, mm h-1) exceeds the saturated hydraulic conductivity of the topsoil, which is a function of soil properties and slope (Morbidelli et al., 2018; Wösten et al., 2001), or precipitation in the form of snow is melting. The excess water is routed over the surface using the multiple flow algorithm (Holmgren, 1994) and can re-infiltrate in places with higher hydraulic conductivity, in local surface depressions, or can leave the catchment. HydroLorica can thus deal with DEMs that contain depressions and actively forms depression by simulating tree throw. The annual sum of daily surface flow is used to calculate annual water erosion and deposition using the stream power law. To account for seasonal differences, actual ET is calculated on a monthly basis from the potential ET and rainfall using the topsoil water budget model of Pistocchi et al. (2008). Infiltration is the sum of (re-)infiltrated surface water and the monthly difference between rainfall and actual ET (Eq. 6). The annual water balance is used as a driver of various geomorphic and pedogenic processes and to determine vegetation type. The hydrological module is described in detail in Appendix A of Van der Meij et al. (2018).

We considered two types of natural vegetation: grassland and forest. The vegetation type depends on the water availability; where rainfall plus re-infiltration exceeds potential evapotranspiration, there is no water stress and forests can grow. Otherwise, there is water stress and there will be grassland. This threshold is based on a hypothesis from Thompson et al. (2010), who used the Budyko curve (Budyko and Miller, 1974) to estimate vegetation type. By extending this relationship with re-infiltration, this relation can be used to assess local but spatially explicit vegetation type. Vegetation type thus has a climatic control and a topographic control in the form of hillslope aspect and local convergence of water flow in gullies and depressions (e.g., Metzen et al., 2019). This variation in moisture and vegetation can occur very locally, especially in semi-arid regions. Vegetation type influences evapotranspiration (Allen et al., 1998), bioturbation and creep rate (Gabet et al., 2003) and the occurrence of tree throw, and also controls organic matter input. Under intensive agricultural use, we convert the vegetation type to arable crops. We assume that soil and landscape processes are similar to landscapes under grassland vegetation. The differences are that arable crops have lower potential evapotranspiration and the process of tillage is introduced.

Our method of estimating vegetation type can lead to annual changes in vegetation type depending on water availability, because we do not consider ecological processes such as resilience or succession. The portion of years with grassland and forest vegetation aggregated over longer time spans (>100 yr) provides an estimate for the forest cover of that specific location (see the animations in Supplement 2). The vegetation distribution should thus be considered on an aggregated level rather than an annual level to yield meaningful results. This implementation suffices for our focus on long-term changes in soils and terrain, but should not be used to study systems on annual to decadal timescales.

The main (bio-)geomorphic processes affecting topography in loess areas are soil creep, tree throw, water erosion and tillage erosion. Soil creep is a bio-geomorphic process that causes a diffuse movement of soil material on a hillslope, driven by various factors such as (micro)climate, organisms and terrain (Pawlik and Šamonil, 2018; Regmi et al., 2019; Roering et al., 2002). The potential creep rate is a function of vegetation type and slope (Gabet et al., 2003). We adopt higher creep rates in forested areas, because of the deeper rooting depth and higher root abundance. We divided the potential creep rate at a certain location over all soil layers, with exponentially decreasing rates deeper in the soil. The transport of soil material from a layer to layers in its lower-lying neighboring cells is proportional to the surface slope and shared layer boundaries.

Tree throw is a bio-geomorphic process that has a distinct effect on the terrain and water routing; the created pit can act as a hotspot for soil formation by the increased infiltration of water (Šamonil et al., 2018). We simulated tree throw as a random process, with on average 0.2 trees falling per hectare per year. This rate is lower than other rates found in natural forests around the world (0.3–1.5 trees ha-1 yr-1, Finke et al., 2013; Gallaway et al., 2009; Phillips et al., 2017), because some factors controlling tree uprooting like shallow rooting depths due to impermeable layers or steep slopes are not present in our spatial setting. The dimensions of the root clump that is transported by tree throw were scaled with the age of the falling tree, which was also randomly selected. We assumed that tree growth occurs in the first 150 years of a tree's existence, after which size remains stable until a maximum age of 300 years. These numbers and trends are loosely based on Rozas (2003). A pit and mound topography is only formed when the dimensions of the root clump exceed the size of the raster cell (1.5 m in our case) and that material is transported to a cell downslope. When the root clump is smaller than the cell size or when the slope of the terrain does not lead to downward transport of the material, tree throw will only cause a (partial) turbation of the upper layers in the affected raster cells.

Water erosion and deposition are calculated using the same approach as the original Lorica model (Temme and Vanwalleghem, 2016). Sediment uptake and deposition are calculated as a function of discharge and surface gradients (Schoorl et al., 2002). Sediment uptake is simulated as a selective process, where smaller particles are easier to erode and more difficult to deposit. Organic matter behaves the same as clay under erosion, because we assumed that organic matter occurs in associations with clay particles. Water erosion is limited by the occurrence of coarse soil particles (surface armoring) and vegetation. The role of water erosion in forested loess catchments is limited (Vanwalleghem et al., 2010); the vegetation protects the soil below from erosion. However, disturbances such as forest fires can temporarily increase erodibility of the soil. Therefore, we did simulate water erosion in forested landscapes, but with lower rates than in grassland. We simulated this by including a high vegetation protection constant (value of 1) in forested sites. In grasslands we used the aridity index between 0 and 1 as the vegetation protection constant.

Tillage erosion was simulated as a diffusive process, similar to creep, with some differences: tillage homogenized the soil over the reach of the plough depth, erosion only occurred from the top layer contrary to the whole soil profile as with creep, and the erosion rates were much higher due to the intensive land management.

We simulated three dominant (bio-)pedogenic processes that change texture and organic matter properties in loess landscapes. These are clay translocation, bioturbation and soil organic matter accumulation and breakdown.

We adapted a new way of simulating clay translocation, using the advection equation of Jagercikova et al. (2017). The diffusive part of clay translocation as described by Jagercikova et al. (2017) is separately modeled by bioturbation. We scaled the parameters of clay translocation with local infiltration to develop an infiltration-dependent equation. Not all clay in the soil is available for translocation. Part of it is not available to the percolating water, because it is bonded to other minerals and organic matter. We used the equations of Brubaker et al. (1992) to estimate the part of the clay that is water-dispersible, i.e., that is available for translocation by water. We estimated the required cation exchange capacity (CEC) with a pedotransfer function from Ellis and Foth (1996), as a function of clay content and organic matter content. Following from these equations, the fraction of non-dispersible (remaining) clay is 5.9 % in soils without soil organic matter (SOM) and increases with 1.2 % for every extra percent of SOM. This approach is similar to the one used in soil profile model SoilGen2 (Finke, 2012).

Bioturbation works as a diffusive processes, homogenizing the soil vertically (Yoo et al., 2011). We used the same rates for bioturbation as for creep, because these processes are driven by the same organisms reworking the soil. The potential bioturbation rate was divided over each soil layer by integrating the exponential depth function over the layer thickness and then dividing by the integration of the function over the entire soil profile. Every layer exchanges a certain fraction of its contents, based on initial bioturbation rate and depth, with all other layers. The amount of exchange between two layers decreases with increasing distance.

SOM accumulation and breakdown were simulated as in earlier soil–landscape evolution models (Minasny et al., 2008; Temme and Vanwalleghem, 2016; Vanwalleghem et al., 2013; Yoo et al., 2006). Accumulation of SOM is controlled by the potential input and depth in the soil. The accumulation is divided over a young and old SOM pool using a fractionation factor. These pools differ in their rate of decomposition. We calibrated the SOM cycle in agricultural settings with the average depth distribution of organic carbon in agricultural soils on the Chinese loess plateaus (Liu et al., 2011). We simulated 5000 years of soil development using different process parameters. We selected the parameter set that simulated an organic matter distribution most similar to the reference distributions from Liu et al. (2011). The reported depth distributions for pasture and forest soils by Liu et al. (2011) were not useful for this project. Soils under these vegetation types on the Chinese loess plateau generally contain lower SOM stocks than natural landscapes, because these positions often have recently been replanted to combat soil erosion or because they occur in topographic positions which are not favorable for plant growth and agriculture. Instead, we calculated reference carbon stocks for forest and grassland soils by adjusting the agricultural carbon stocks of Liu et al. (2011) with changes in carbon stocks after conversion from forest to crop and from forest to pasture (Guo and Gifford, 2002). With the resulting reference carbon stocks for natural vegetation we ran additional calibrations to calculate the potential SOM input for forest and grassland.

Soils have been affected by humans for over 1000s of years, either directly by agricultural use or indirectly by adjusting factors that form the soil, such as vegetation or climate (Amundson et al., 2015; Bajard et al., 2017; Dotterweich, 2008; Stephens et al., 2019). Therefore it is difficult, if not impossible, to find locations where truly natural soils can be observed and compared to agricultural soils in similar settings. Model simulations enable this comparison, as we show in this study. Unfortunately, there are limited field data to calibrate and validate the model. To our knowledge, the dataset from Vanwalleghem et al. (2010) is the only dataset that enables quantification of the spatial distribution of natural soils and links it to terrain properties at a local to regional scale, similar to the setting we simulated. In this section, we rely mainly on this dataset to discuss and evaluate the patterns of natural soils we simulated with our model. For the agricultural soil patterns, we use an extensive dataset from an intensively managed agricultural field in northeastern Germany (CarboZALF-D, Van der Meij et al., 2017). In our model simulations, we simplified the agricultural conversion by assuming a single vegetation type in the entire catchment and direct intensive management with tillage. This enabled us to isolate the role of tillage erosion in the development of agricultural soil and landscape patterns. We did not consider a slow historical development of the agricultural system with increasing management intensity and upscaling of agricultural field sizes. The results of our simulations should be considered to be within-field variation in soil and landscape properties. In smaller-scale farming, the within-field soil–landscape relations will also be present, but they are probably secondary to variation between fields caused by different management (history), vegetation type or anthropogenic structures such as hedges, banks and roads (e.g., Follain et al., 2006; Peukert et al., 2016; Yemefack et al., 2005).

We used semivariograms to illustrate the spatial autocorrelation of soil and landscape properties (Fig. 6). Semivariograms are very case-study-specific, because the range, sill and nugget are affected by the scale of topographic and lithogenic variation, different rates of pedogenic and geomorphic processes and different types of human disturbances in the landscape. Therefore, we only compare the trends in the semivariograms from model and field results to evaluate the type of spatial autocorrelation of soil properties in such settings.

Figure 6b and c show experimental semivariograms of depths to Bt horizons in model and field data. In both panels, the agricultural settings show higher spatial autocorrelation compared to the natural settings, expressed by the higher sill and range. This indicates that in agricultural fields the depths to Bt horizons are more spatially organized (higher large-scale variability), with larger differences between different landscape positions. In natural areas, the spatial differences in depth to Bt horizon are lower and there is less spatial organization of the depth distributions. The model and field results show different magnitudes in nugget, range and sill. This can be explained by (1) the high density of data points in the model results which enabled us to calculate the semivariance over very short distances, reducing the nugget, and (2) the fact that we used a very condensed DEM with high local variation in topographic properties as input for the model results, which led to high local variation in soil properties too. Nonetheless, the similar trends in the field and model semivariograms indicate that the general soil patterns from model and field results agree. Also, the correlations between soil and landscape properties are similar for field and model results. Vanwalleghem et al. (2010) found correlations between different horizon depths and topographic properties with R2s ranging between 0.02 and 0.1, which are the same order as most correlations we calculated in Fig. 7. These similarities indicate that our model HydroLorica simulated the essential processes that form these natural soil patterns.

Our simulations show a large diversity of natural soil patterns, influenced by the amount of rainfall and associated vegetation type. The available water leads to a regionally higher rate of soil development, for example in the form of deeper clay eluviation (Fig. 3), and also to a greater lateral redistribution of soil material by water erosion and tree throw (Fig. 5) and spatially varying infiltration rates. With more rainfall, the higher rates and interactions between these processes lead to a spatially more heterogeneous soil pattern, as expressed in higher ranges and sills in the semivariograms (Fig. 6). This local variation in pedogenesis due to different water input has been recognized and partly accounted for in other modeling studies (Finke et al., 2013; Saco et al., 2006; Shepard et al., 2017), but had not emerged from soil–landscape evolution studies. Also, the terrain, summarized by slope, TPI and TWI, becomes more heterogeneous with higher rainfall. Water flow thus affects soil and terrain patterns in a similar way.

Intensively managed agricultural soils display entirely different patterns compared to natural soils. There is lower small-scale variability due to the absence of tree throw and local homogenization by tillage, while the semivariograms of soil properties suggest higher sills, i.e., higher large-scale variability and spatial autocorrelation of soil properties compared to natural soil properties. This is due to the slope-dependent intensity of tillage erosion (Phillips et al., 1999). This erosion leads to truncation of soils at convex positions, while concave positions have a net accumulation of material (De Alba et al., 2004). This truncation is visible in many agricultural landscapes, because subsurface horizons with different colors get exposed at the surface in heavily eroded locations (e.g., Smetanová, 2009; Van der Meij et al., 2017). In contrast, terrain properties seem to display lower spatial variation in agricultural landscapes. The smoothing effect of tillage on the terrain removed local pits and rills created in the natural phase. We hypothesized earlier that a smoother terrain would have higher hillslope connectivity, leading to increased water erosion (Van der Meij et al., 2017). However, we observed the contrary in our model results (Fig. 5). The export of sediments from the catchment might be higher, but the uptake and local redistribution of sediments on the hillslope is lower, because local steep gradients are removed. Tillage is thus the dominant process forming agricultural soil patterns. The effect of anthropogenic soil erosion on soil heterogeneity far exceeds effects of changes in for example rainfall, which shows the huge impact we have as humans on soil–landscape development.

The rates of the simulated processes were difficult to calibrate and validate. This is mainly due to a lack of field data that cover a range of climatic, topographic, chronologic and geographic settings (Van der Meij et al., 2018). Such data are essential for formulating pedogenic functions that are applicable in a wide range of settings instead of only in case studies, or for verifying model results. The chronosequence collection of Shepard et al. (2017) is a global dataset of soils in various settings covering different time steps. This dataset could be a good starting point for developing such functions owing to its large coverage. But as chronosequences are generally situated in relatively flat, stable landscapes, they often do not contain information about variations of soil properties at small distances, as a function of local terrain (Harden, 1988; Sauer, 2015) – with the exception of some pro-glacial soil chronosequences whose use is limited because of their extreme climate and parent material (Egli et al., 2006; Temme and Lange, 2014). Such more complete information is essential for understanding the formation of soil patterns, as illustrated in the previous section. Therefore, we suggest including topographic variation in future chronosequence studies (Temme, 2019). A dataset covering different geographies could also raise the comparison of model and field results beyond the case-study level.

In this study, we worked with an artificial landscape to avoid effects of uncertainties and local variations in initial and boundary conditions that are often present in data from field settings (e.g., Van der Meij et al., 2017). This allowed us to investigate the universal effects of changes in rainfall and land use on the model results, as a function of terrain morphology. Although uncertainties in boundary conditions appear to have a limited effect on the outcomes of soil evolution models, uncertainties in initial conditions can strongly influence the results (Keyvanshokouhi et al., 2016).

One soil property for which there are plenty of data on the spatiotemporal variation is soil organic matter or carbon, due to the current interest in its potential to store atmospheric carbon (Minasny et al., 2017). We used a regional dataset from the loess plateau to calibrate our SOM cycle in agricultural landscapes, and we used carbon sequestration rates for adjusting the SOM balances for forest and grassland areas. The modeled SOM stocks for agricultural sites match the field data fairly well (Table 2), but stocks for natural areas are estimated higher than often observed. For example, in Bavaria, Germany, carbon stocks in the first meter, including the optional litter layer, are 9.8–11.8 kg m-2 (Wiesmeier et al., 2012), where we simulated 15.7–17.1 kg m-2 in our natural settings without consideration of a litter layer. Also, the depth distributions are different. De Vos et al. (2015) found that 50 % of the carbon stock occurs in the top 20 cm in European forests on various parent materials. In our results this is around 20 %. This implies that agriculturally derived SOM depth functions are not suitable for calibrating natural SOM depth functions, probably because input, vertical redistribution, litter quality and decay of SOM behave differently in natural and agricultural sites. To calibrate these parameters, data from agricultural and natural sites in close vicinity are needed to avoid effects of geographic and climatic differences. We are currently not able to simulate and calibrate these processes properly.

Different soil-forming factors dominate the variance in soil properties in natural and agricultural systems (Table 3). In natural systems, rainfall is the dominant factor explaining the variance. In scenarios with greater rainfall, rates of soil and landscape change are larger, leading to more complex patterns. Although we did not simulate a changing climate, the results suggest that we can expect more stable conditions with similar pedogenesis rates throughout the landscape in periods with lower rainfall, while periods with greater rainfall may induce landscape change and spatially varying rates of pedogenesis. The major driver of this increased landscape change is the higher occurrence of tree throw. The higher water availability increases forest cover, leading to more tree throws (see the animations in Supplements 2 and 3).

Although our vegetation module is very simple, it was able to simulate the climatic and topographic control on vegetation patterns which affect geomorphic and pedogenic processes. We would expect similar results to be obtained if a more complex vegetation module that does justice to ecological complexity (i.e., resilience, succession) would be incorporated.

In intensive agricultural systems with large fields, landform is the dominant factor explaining the variance (Table 3). This shift from external factors in natural systems to internal factors in agricultural systems marks the importance of geomophic processes in agricultural soil patterns. Although relief controls rates and directions of geomorphic processes, the type of process is human-controlled. Humans have a massive impact on soil development (Amundson and Jenny, 1991; Dudal, 2005). Direct effects include agricultural use, excavations, introduction of organisms and creation of new parent materials (Richter et al., 2015), while indirectly anthropogenic changes in climate can have severe effects on soil properties (Nearing et al., 2004; Schuur et al., 2015). We have focussed on the main of these anthropogenic changes in loess landscapes: removal of forest and complete introduction of tillage, even though intermediate forms with incomplete clearing, smaller fields and forested borders may have historically existed. Humans as soil-forming factors form new catenae (anthroposequences) and soil patterns, where the ultimate pattern only depends little on the initial variation (Fig. 6). In our model results, we observe four of the six anthropogenic changes to soils, as described by Dudal (2005): human-made soil horizons, deep soil disturbance, topsoil changes and changes in landforms. These changes substantially affect soil functions, such as biodiversity and food security. Our simulations thus support the view that humans are the dominant factor in forming soils in agricultural landscapes.

The development of soils and landscapes is not merely a collection of individual processes, but also of interactions between different processes. When processes interact, and when changes to soils and landscapes are on the same order of magnitude, soil–landscape co-evolution can occur. This co-evolution can amplify or diminish certain processes or can completely change the direction of soil and landscape evolution (Van der Meij et al., 2018). Often, co-evolution is used to describe soil and landscape processes with similar rates but that do not necessarily interact (e.g., Willgoose, 2018). This would imply that these processes would co-occur rather than co-evolve. In this section we evaluate some co-occurring processes in HydroLorica to see whether co-evolution occurred. There are different co-occurring processes in the natural phase of slow landscape change compared to the agricultural phase of intense landscape change.

We will first consider vertical and lateral soil transport processes. Soils and hillslopes can be considered a series of transport ways or conveyor belts (Román-Sánchez et al., 2019). Vertical transport or mixing occurs by bioturbation including tree throw and clay translocation, whereas lateral transport occurs by creep, tree throw, water erosion and tillage erosion. Interactions between processes can occur where transport ways affect the same material. Two examples we will discuss here are the vertical and lateral transport of clay and the interaction between creep and water erosion in the valley bottom.

The vertical translocation of clay is simulated in our model by an advection–diffusion equation, where the advective part is the downward transport by water flow and the diffusive part a homogenization by bioturbation (Jagercikova et al., 2017). When the rates of advection and diffusion are equal, the upward transport of clay by bioturbation equals the amount of downward translocation by water; the clay-depth profile of the soil occurs in steady state and will not change substantially. Steady-state circumstances are however rare in natural soil systems (Phillips, 2010). Our simulations do not show steady-state circumstances, because in our simulations there is always lateral transport of soil material that continuously changes slope and terrain properties and affects the soil's clay balance, complicating the achievement of a steady state. Periodic water erosion can remove substantial amounts of clay that have been transported to the surface by bioturbation. This is clearly visible in the results of the wet scenario (P=900 mm), where only 62 % of the soils developed a Bt horizon. The other 38 % had insufficient clay left to be classified as Bt according to our criteria. These results are quite extreme for such a small catchment as ours, probably due to too high simulated rates of water erosion, but they do show how pedogenic and geomorphic processes can interact in sloping terrain. In the natural phase the rates of clay translocation are similar to those of geomorphic processes. The recovery of the clay-depth profiles after disturbance of, e.g., tree throw takes similar times (∼1000s of years) to the re-occurrence of a sequential tree throw event in the vicinity (Fig. 3). Tree throw also temporarily changes rates of clay translocation by concentrating infiltration in the created pits. In the agricultural phase the rates of geomorphic processes far exceed the rates of clay translocation. This causes truncation of the soils, exposing the Bt horizons at the surface and burying these horizons elsewhere in the landscape. The clay profiles at eroded sites do not have time to react to the geomorphic disturbances. However, clay illuviation can start as a new pedogenic process in older depositional areas (Supplement of Leopold and Völkel, 2007; Van der Meij et al., 2019; Zádorová and Pení žek, 2018).

Another interaction that emerged from the simulations occurred at the valley bottom. Soil creep transported hillslope material downslope, whence the concentrated water flow in the valley removed it from the catchment, creating a v-shaped valley bottom (Fig. 2). This constant removal of material maintained the gradients that were used by soil creep to deliver new material. This interaction can be observed in various small hillslope catchments, which display typical v-shaped gulleys in the valley bottoms (e.g., Swanson and Swanston, 1977; West et al., 2013). Although this is not an interaction between pedogenic and geomorphic processes, it determines to a large extent how soil material gets redistributed along a hillslope and eventually gets exported from the catchment. In the agricultural phase, diffusive transport in the form of tillage erosion dominates over advective transport by water. As a consequence, the typical v shapes fill up and are replaced by u-shaped valleys. These valley fillings consist of coarse material from which most clay was eroded (Fig. 2). In agricultural areas, such infillings can temporarily remove erosion gulleys, but due to local water availability, they remain weak spots for future water erosion (Poesen, 2011).

Rates of SOM accumulation and decomposition far exceed rates of clay translocation. SOM stocks recover quickly after a disturbance by tree throw and can keep up with intense landscape change by tillage (Fig. 3). Freshly exposed, reactive soil material at eroding sites quickly accumulates new SOM, whereas SOM gets buried at depositional positions. Meanwhile, SOM decomposition increases during transport (Doetterl et al., 2012). In our simulations, the SOM stocks decrease substantially in the agricultural phase, mainly due to lower SOM input (Fig. 3). Carbon stocks show relatively homogeneous distributions throughout the catchment (Fig. 4), despite large spatial differences in erosion and deposition. This indicates that landscape change in both natural and agricultural systems did not induce substantial heterogeneity in SOM stocks. The small differences in SOM stocks in agricultural settings depend on landform (Table 3). These differences mainly emerge from differences in soil thickness at erosion and deposition positions. Deposition positions show a slight increase in SOM stocks after cultivation, while erosion positions show continually decreasing SOM stocks (Fig. 3). The differences in SOM stocks in the model results are thus related to burial of colluvium in the valley bottom. SOM cycling is heavily influenced by erosion processes, but erosion rates do not depend on the SOM cycling. In tillage-dominated systems, erosion rates do not depend on SOM content or SOM dynamics in the soil. The co-occurrence of SOM cycling and tillage erosion in agricultural settings thus does not lead to co-evolution.

The interactions between erosion and the SOM cycle are currently under debate, especially whether agricultural redistribution provides a carbon source or sink by affecting biogeochemical cycles and exporting carbon from fields and catchments (Berhe et al., 2018; Chappell et al., 2015; Doetterl et al., 2016; Harden et al., 1999; Lal, 2019; Lugato et al., 2018; Van Oost et al., 2007; Wang et al., 2017), which shows the importance of considering landscape processes in pedogenic studies and vice versa. Moreover, intensive agriculture has been practiced for over 1000s of years in parts of the world (Stephens et al., 2019), emphasizing the need to consider centennial to millennial time periods in studies on anthropogenic forcing on soil systems.

The co-occurrence of processes does not necessarily imply co-evolution. The analysis in this section showed that soil and landscape processes co-occurred in both natural and agricultural settings, but that interactions between processes only occurred in natural settings. Rates of soil and landscape change are controlled by drivers such as water availability and vegetation type, and these drivers are influenced by soil, landscape and climate properties. Changes in one domain in the landscape have effects on the formation of all other domains. These interactions, or co-evolution, occur on both short and long timescales in the natural system. There are already considerable differences between the soil patterns from each scenario after 500 years of natural soil formation, due to the role of water and vegetation in soil–landscape co-evolution. These differences become more pronounced over time, due to progressive soil and landscape formation (Supplement 2).

In comparison, the differences between the patterns of each scenario after 500 years of agricultural land use are much smaller (Supplement 2). This is because anthropogenic processes such as tillage erosion occur at such high rates that most natural processes cannot keep up and lead to more similar soil landscapes. In settings with uniform parent material such as we simulated, anthropogenic processes do not show co-evolution, because the rates of for example tillage erosion far exceed any rates of natural soil and landscape change (Fig. 5), and the rates of the anthropogenic processes are not influenced by soil properties. Tillage can introduce new processes or accelerate other processes, e.g., by breaking up aggregates. However, these processes do not affect the rate at which a plough transports sediments through a landscape. If interactions between processes do not occur on shorter timescales, they will also not emerge over longer timescales, as is the case with natural processes as described before. The occurrence of possible co-evolution of soils and landscapes thus depends on the type of processes that affect the system, not on the duration over which these processes change soils and landscapes. In other words, co-evolution is not time-dependent, but process-dependent.

Co-evolution of soils and landscapes can also occur via intrinsic thresholds which do not depend on changes in external drivers such as rainfall and land use. An example is the development of stagnating layers in the soil, which change the subsurface partitioning of water and can introduce reducing conditions. But, as we explain in Van der Meij et al. (2018), such intrinsic thresholds can currently not be modeled, because we lack the methods for estimating accurate soil hydraulic properties which drive this threshold behavior. Ideally, a model shows such threshold behavior without explicitly incorporating these thresholds into the model code as such imposed hard thresholds can cause problems when calibrating the model by creating sharp discontinuities in the model results as a response to slight variations in parameters (Barnhart et al., 2019). For these reasons we focused on heterogeneity and (co-)evolution related to external drivers in this research.

The soil and landscape interactions in natural settings emphasize the need to study natural soil formation in a landscape context rather than a pedon context. Only when landscapes are stable, flat and free of trees are changes in soil properties not influenced by changes in terrain. In such settings, a 1D soil profile evolution model would suffice to simulate soil development in different landscape positions (Finke, 2012; Minasny et al., 2015). When rates of geomorphic processes far exceed those of pedogenic processes, for example in tillage-dominated systems, a landscape evolution model would suffice (e.g., Temme et al., 2017). In undulating landscapes where various hillslope processes occur, soils should be considered 3D bodies, and soil–landscape evolution models are essential to simulate spatial drivers of soil and landscape evolution (Willgoose, 2018).