This paper describes the coupling of the State Space Soil Production and Assessment Model (SSSPAM) soilscape evolution model with a landform evolution model to integrate soil profile dynamics and landform evolution. SSSPAM is a computationally efficient soil evolution model which was formulated by generalising the mARM3D modelling framework to further explore the soil profile self-organisation in space and time, as well as its dynamic evolution. The landform evolution was integrated into SSSPAM by incorporating the processes of deposition and elevation changes resulting from erosion and deposition. The complexities of the physically based process equations were simplified by introducing a state-space matrix methodology that allows efficient simulation of mechanistically linked landscape and pedogenesis processes for catena spatial scales. SSSPAM explicitly describes the particle size grading of the entire soil profile at different soil depths, tracks the sediment grading of the flow, and calculates the elevation difference caused by erosion and deposition at every point in the soilscape at each time step. The landform evolution model allows the landform to change in response to (1) erosion and deposition and (2) spatial organisation of the co-evolving soils. This allows comprehensive analysis of soil landform interactions and soil self-organisation. SSSPAM simulates fluvial erosion, armouring, physical weathering, and sediment deposition. The modular nature of the SSSPAM framework allows the integration of other pedogenesis processes to be easily incorporated. This paper presents the initial results of soil profile evolution on a dynamic landform. These simulations were carried out on a simple linear hillslope to understand the relationships between soil characteristics and the geomorphic attributes (e.g. slope, area). Process interactions which lead to such relationships were also identified. The influence of the depth-dependent weathering function on soilscape and landform evolution was also explored. These simulations show that the balance between erosion rate and sediment load in the flow accounts for the variability in spatial soil characteristics while the depth-dependent weathering function has a major influence on soil formation and landform evolution. The results demonstrate the ability of SSSPAM to explore hillslope- and catchment-scale soil and landscape evolution in a coupled framework.
Soil is one of the most important substances found on planet Earth. As the uppermost layer of the Earth's surface, soil supports all the terrestrial organisms ranging from microbes to plants to humans and provides the substrate for terrestrial life (Lin, 2011). Soil provides a transport and a storage medium for water and gases (e.g. carbon dioxide which influences the global climate) (Strahler and Strahler, 2006). The nature of the soil heavily influences both geomorphological and hydrological processes (Bryan, 2000). In addition to the importance of soil from an environmental standpoint, it provides a basis for human civilisation and played an important role in its advancement through the means of agricultural development (Jenny, 1941). Understanding the formation and the global distribution of soil (and its functional properties) is imperative in the quest for sustainable use of this resource.
Characterisation of soil properties at a global scale by sampling and analysis is time-consuming and prohibitively expensive due to the dynamic nature of the soil system and its complexity (Hillel, 1982). However, over the years researchers have found strong links between different soil properties and the geomorphology of the landform on which they reside (Gessler et al., 2000, 1995). Working on this relationship several statistical methods have been developed to determine and map various soil properties depending on other soil properties and geomorphology such as pedotransfer functions, geostatistical approaches, and state-factor (e.g. clorpt) approaches (Behrens and Scholten, 2006). Pedotransfer functions (PTFs) use easily measurable soil attributes such as particle size distribution, amount of organic matter, and clay content to predict hard-to-measure soil properties such as soil water content. Although very useful, PTFs need a large database of spatially distributed soil property data and require site-specific calibration (Benites et al., 2007). Geostatistical methods use a finite number of field samples to interpolate the soil property distribution over a large area. Developing soil property maps using geostatistical methods is possible for smaller spatial scales; however, soil sampling and mapping soil attributes can be prohibitively expensive and time-consuming for larger spatial domains (Scull et al., 2003). State-factor methods, such as scorpan (developed by introducing existing soil types and geographical position to the clorpt framework), use digitised existing soil maps and easily measurable soil attribute data to generate spatially distributed soil property data using mathematical concepts such as fuzzy set theory, artificial neural network, or decision tree methods (McBratney et al., 2003). However, these techniques also suffer from scalability issues and the typical need for site-specific calibration.
While spatial mapping of soil properties is important, understanding the
evolution of these soil properties and processes responsible for observed
spatial variability of soil properties is also important. In order to
quantify these processes and predict the soil characteristics evolution
through time, dynamic process-based models are required
(Hoosbeek and Bryant, 1992). These mechanistic process models
predict soil properties using both geomorphological attributes and various
physical processes such as weathering, erosion, and bioturbation
(Minasny and McBratney, 1999). ARMOUR, developed by
Sharmeen and Willgoose (2006), is one of the earliest
process-based pedogenesis models. ARMOUR simulated surface armouring based
on erosion and size-selective entrainment of sediments driven by rainfall
events and overland flow, as well as physical weathering of the soil particles
which break down the surface armour layer. However, very high computational
resource requirements and long run times prevented ARMOUR from performing
simulations beyond short hillslopes. Subsequently Cohen et al. (2009)
developed mARM by implementing a state-space matrix methodology to simplify
the process-based equations and calibrated its process parameters using the
results from ARMOUR. Its high computational efficiency allowed mARM to
explore soil evolution characteristics on spatially distributed landforms.
Through their simulations, Cohen et al. (2009) found a strong relationship
between the geomorphic quantities contributing area, slope, and soil surface
grading
The first attempt to integrate soilscape evolution with landform evolution was done by Minasny and McBratney (1999, 2001). They used a single layer to model the influence of soil and weathering processes on landform evolution. In addition to Minasny and McBratney (1999, 2001) there are a number of conceptual frameworks found in the literature for developing coupled soil-profile–landform evolution models (Yoo and Mudd, 2008; Sommer et al., 2008). MILESD (Vanwalleghem et al., 2013) is a model which can simulate soil profile evolution coupled with landform evolution. MILESD is built upon the conceptual framework of landscape-scale models for soil redistribution by Minasny and McBratney (1999, 2001) and the pedon-scale soil formation model developed by Salvador-Blanes et al. (2007). In MILESD the soil profile is divided into four layers containing the bottommost bedrock layer and three soil layers above it representing the A, B, and C soil horizons. MILESD was used to model soil development over 60 000 years for a field site in Werrikimbe National Park, Australia (Vanwalleghem et al., 2013). They matched trends observed in the field such as the spatial variation of soil thickness, soil texture, and organic carbon content. A limitation of MILESD is that it only uses three layers to represent the soil profile. Recently the soil evolution module used in MILESD has been modified to incorporate additional layers and has been combined with the landform evolution model LAPSUS to develop a new coupled soilscape–landform evolution model, LORICA (Temme and Vanwalleghem, 2015). They found similar results for soil–landform interaction and evolution similar to MILESD simulation results.
Since only three layers were used in MILESD, the representation of the particle size distribution down the soil profile was limited. Although LORICA incorporated additional soil layers into the MILESD modelling framework, detailed exploration of soil profile evolution or interactions between landform evolution and soil profile evolution has not yet been done with this model. Importantly, particle size distribution of the soil can be used as a proxy for various soil attributes such as the soil moisture content (Arya and Paris, 1981; Schaap et al., 2001). The main objective of this paper is to present a new soilscape evolution model capable of predicting the particle size distribution of the entire soil profile by integrating a previously developed soil grading evolution model into a landscape evolution model.
Here we present the methodology for incorporating sediment transport, deposition, and elevation changes of the landform into the SSSPAM modelling framework to create a coupled soilscape–landform evolution model. Detailed information regarding the development and testing of the SSSPAM soil grading evolution model is provided in previous papers by the authors (Cohen et al., 2010; Welivitiya et al., 2016). The main focus of this paper is to incorporate landform evolution into the SSSPAM framework. In addition to the model development we also present the initial results of coupled soilscape–landform evolution exemplified on a linear hillslope.
The introduction of a landform into the SSSPAM framework is done using a digital elevation model. The structure of the landform evolution model follows that for transport-limited erosion (Willgoose et al., 1991) but modified so as to facilitate its coupling with the soilscape soil grading evolution model SSSPAM described in Welivitiya et al. (2016). Here a regular square grid digital elevation model was used and converted into a two-dimensional array which can be easily processed and analysed in the Python/Cython programming language. Using the steepest-slope criterion (Tarboton, 1997) the flow direction and the slope value of each pixel was determined. Then using the created flow direction matrix, the contributing area of each pixel was determined using the D8 method (O'Callaghan and Mark, 1984) with a recursive algorithm.
The soil profile evolution of each pixel is determined using the interactions between the soil profile and the flowing water at the surface. Figure 1 shows these layers and their potential interactions. This is similar to the schematic for the stand-alone soil grading evolution model but is different in that the erosion/deposition at the surface is a result of the imbalance between upslope and downslope sediment transport. The water layer acts as the medium in which soil particle entrainment or deposition occurs depending on the transport capacity of the water at that pixel. The water provides the lateral coupling across the landform, by the sediment transport process. The soil profile is modelled as several layers to reflect the fact that the soil grading changes with soil depth depending on the weathering characteristics of soil. Erosion of soil and/or sediment deposition occurs at the surface soil layer (surface armour layer).
Schematic diagram of the SSSPAM model.
SSSPAM uses the state-space matrix approach to evolve the soil grading through the soil profile. The state-space matrix methodology used for soilscape evolution is presented in detail elsewhere (Cohen et al., 2009, 2010; Welivitiya et al., 2016) and will not be discussed in detail here. Using this method a range of processes (e.g. erosion, weathering, deposition) can be represented and applied so that the total change in soil layers and their properties can be determined (Cohen et al., 2009, 2010). Once the erosion and deposition mass is determined, elevation changes are calculated and the digital elevation model is modified accordingly. Once the algorithm completes modifying the digital elevation model matrix, the calculation of flow direction and contributing area is done and the process is repeated until a given number of iterations (evolution time) is reached.
As described in Welivitiya et al. (2016), the SSSPAM
soil grading evolution model used a detachment-limited erosion model to
calculate the amount of erosion. In order to simulate deposition and to
differentiate between erosion and deposition, a transport-limited model is
incorporated into the soil grading evolution model SSSPAM. Before
calculating the erosion or deposition at a pixel (i.e. grid cell/node), we
determine the transport capacity of the flow at that particular pixel. The
transport capacity determines if the pixel is being subjected to erosion or
deposition. The calculation of the transport capacity at each pixel is done
according to the empirical equation presented by Zhang et al. (2011),
which was determined by flume-scale sediment detachment experiments. The
transport capacity at a pixel (node)
Determination of erosion and deposition.
The calculation of potential erosion
Erosion, deposition, and the restructuring of the soil profile:
As described by the above equations, mass is removed from the surface armour layer into the water flowing above. In SSSPAM, mass conservation of the surface armour layer is achieved by adding a portion of soil from the first subsurface layer to the surface armour layer equal to the mass entrained into the water flow. It is important to note that the materials resupplied to the surface armour have the same soil grading as the subsurface layer. So both small particles and large particles are resupplied to the armour layer. Most of the time the net effect of this material resupply and the size-selective erosion will be enrichment of larger particles and armour strengthening. Depending on the depth-dependent weathering function, the relative coarseness of the subsurface layers can be less compared to armour layer. But once the armour layer is reconfigured with the added material from below and removal of small particles through erosion, again the net effect is armour strengthening. More detailed description of this process can be found in Cohen et al. (2009) and Welivitiya et al. (2016)
This material resupply propagates down the soil profile (one soil layer supplying material to the layer above and receiving material from the layer below) all the way to the bedrock layer, which is semi-infinite in thickness. Since the soil gradings of different layers are different to each other, this flux of material through the soil profile changes the soil grading of all the subsurface layers. Conceptually the position of the modelled soil column moves downward since all vertical distances for the soil layers are relative to the soil surface. In the case of deposition the model space would move upwards (discussed in detail later). This movement of the soil model space during erosion is illustrated in Fig. 2.
Note that erosion is limited by the imbalance between sediment transport
capacity and the amount of the sediment load in the flow as well as the
threshold diameter of the particle which can be entrained (Shields shear
threshold; see Cohen et al., 2009, for details) by the water flow. These
factors limit the potential erosion rate at a pixel. During the test
simulations presented later in this paper, the depth of erosion
If the total mass of incoming sediment
Consider the example values given in Table 2. The total mass of the incoming
sediments is 75 kg and the sediments are distributed in four size classes.
Here the size class one is the largest and has the highest potential for
deposition (with
Example calculation of adjustment vector
The deposition of material from the incoming sediment flow reduces the total
mass of the sediment load in the flow and changes its distribution due to
this size-selective deposition (particles with higher settling velocity
deposit faster). The outflow sediment mass vector
The following section describes the methodology for deriving the deposition transition matrix.
The deposition transition matrix is derived by considering the particle
trajectories at the pixel level. Assuming all the sediments flowing into the
pixel are homogeneously distributed throughout the water column, we define
the critical immersion depth
Determination of the critical immersion depth of a sediment particle.
The following discussion briefly describes the methodology used to calculate
the above variables. The average settling velocity of all the particle size
classes can be calculated for typical sediment sizes using Stoke's law
(Lerman, 1979).
Deposition of sediment on the soil surface moves the soil surface upwards
(soil model space moves upwards). As mentioned earlier the deposition height
Figure 2b2 and c2 show the movement of the model space for three soil layers. In the restructured soil column (Fig. 2c2) the new third layer consists of a portion of the original layer one (surface armour layer) and the first original subsurface layer. Because of the upward movement of the model space, a portion of the second original soil layer and the entire third soil layer has been incorporated into the new bedrock layer. However, the grading of the new bedrock layer remains unchanged although the material from the original soil layers two and three is added to the bedrock layer. At the first glance it may seem that this process would drastically alter the soilscape evolution dynamics by introducing a sharp contrast in soil grading at the soil–bedrock interface. In SSSPAM a large number of soil layers (50 to 100) are used to ensure smooth soil grading transition from soil to bedrock.
Figure 4 shows three different cases that can occur during the deposition
process. In Case 1 (Fig. 4b) the deposition height
Different deposition scenarios.
The methodology used for simulating weathering within the soil profile is
detailed by Welivitiya et al. (2016). It uses a physical
fragmentation mechanism where a parent particle disintegrates into
The weathering rate of each soil layer is simulated using a depth-dependent weathering function. It defines the weathering rate as a function of the soil depth relative to the soil surface depending on the mode of weathering of that particular material. SSSPAM can use different depth-dependent weathering functions to simulate the soil profile weathering rate. For the initial simulations presented in this paper we used the exponential (Humphreys and Wilkinson, 2007) and humped exponential (Ahnert, 1977; Minasny and McBratney, 2006) depth-dependent weathering functions. A detailed explanation and the rationale of these weathering functions are presented in Welivitiya et al. (2016) and extended by Willgoose (2018).
It is important to note that SSSPAM can assign different weathering
mechanisms (using different values of
The objective of the simulations below was to explore the capabilities and implications of the SSSPAM coupled soilscape–landform evolution model. Although the model is capable of simulating soilscape and landform evolution for a three-dimensional catchment-scale landform, a synthetic two-dimensional linear hillslope (length and depth) landform was used here. Because it is two-dimensional, the landform always discharges in a single direction. In this way the complexities of multidirectional discharge were avoided so we can focus on the soilscape–landform coupling.
The simulated landform starts from an almost flat 1 km long plateau (almost flat area at the top of the hillslope) with a very small gradient of 0.001 % (Fig. 5). A hillslope with a gradient of 2.1 % starts at the edge of the plateau and continues 1.5 km horizontally while dropping 31.5 m vertically and terminates at a valley. The valley (another almost flat area at the bottom of the hillslope) itself has the same gradient as the upslope plateau (0.001 %) and continues for another 1 km. The valley (the bottom section of the landform) is designed to facilitate sediment deposition so the effect of sediment deposition on soilscape development can be analysed. The simulated hillslope has a constant width of 10 m (one pixel wide) and is divided into 350 10 m long pixels along slope. At each pixel the soil profile is defined by a maximum of 102 soil layers. The soil surface armour layer is the topmost soil layer and it has a thickness of 50 mm. The 100 layers below the surface layer are subsurface soil layers with a thickness of 100 mm each. The bottommost layer (102nd layer) is a permanent non-weathering layer and it is the limit of the hillslope modelling depth. In this way SSSPAM is capable of modelling a soil profile with a maximum thickness of 10.05 m. By changing the number of soil layers used in the simulation SSSPAM is able to simulate a soil profile with any thickness. However, as the number of model layers increases, the time required for the each simulation also increases. During our initial testing, we found that the soil depth rarely increased beyond 10 m and decided to set 10.05 m as the maximum soil depth for this scenario.
The simulated landform and the definition of nodes.
Two soil grading data sets (Table 3) were used for the initial surface soil grading and the bedrock. The first soil grading was from Ranger Uranium Mine (Northern Territory, Australia) spoil site. This soil grading was first used by Willgoose and Riley (1998) for their landform simulations. It was also subsequently used by Sharmeen and Willgoose (2007) for their work with ARMOUR simulations and Cohen et al. (2009) for mARM simulation work. The soil grading consisted of stony metamorphic rocks produced by mechanical weathering with a body fracture mechanism (Wells et al., 2008). It had a median diameter of 3.5 mm and a maximum diameter of 19 mm (Table 3 – Ranger1a). The second grading was created to represent the bedrock of the previous soil grading. It contained 100 % of its mass in the largest particle size class that is 19 mm (Table 3 – Ranger1b). These soil gradings are the same soil gradings used in the SSSPAM parametric study of Welivitiya et al. (2016). At the start of the simulation the surface armour layer was set to the soil grading (Table 3 – Ranger1a) and all the subsurface layers were set to bedrock grading (Table 3 – Ranger1b). The discharge (runoff excess generation) rate of water is derived from averaging the 30-year rainfall data collected by Willgoose and Riley (1998). Using the simulation setup described above, simulations were carried out using the yearly averaged discharge rate. For this simulation we set the time step to 10 years and the model was run for 10 000 time steps (simulating 100 000 years of evolution).
Soil grading distribution data used for SSSPAM simulation.
Figure 6 shows six outputs at different times during hillslope and soil profile evolution.
Evolution of the soilscape with the exponential depth-dependent weathering function.
The upper section in each of the panels in Fig. 6 is the cross-section
median diameter (
If we initially consider the landform evolution alone, the erosion-dominated
regions and the deposition-dominated regions can be clearly identified.
Initially erosion is highest on top of the hillslope where the plateau
transitions to the hillslope (plateau–hillslope boundary) and erosion
gradually reduces down the hillslope. Also, there is a sharp increase in
surface
Turning to the evolution of the soil profile, the upslope plateau retains the initial surface soil layer without any armouring due to the very low erosion, and it develops a relatively thick soil profile as a result of bedrock weathering. The high erosion rate at the plateau–hillslope boundary removes all the fine particles from the initial soil layer as well as fine particles produced by the weathering process, creating a very coarse surface armour layer. This high erosion rate also leads to a relatively shallow soil profile. The erosion rate reduces down the slope due to saturation of the flow with sediments from upstream. Low erosion leads to a weak armouring, and the fine particles produced from surface weathering remain on the surface. These processes lead to the fining of the surface soil layer and thickening of the soil profile down the hillslope.
With time the location of the high erosion region shifts upstream onto the
plateau cutting into it. The
Deposition of material occurs on either side of the hillslope–valley boundary. The valley at the foot of the hillslope has a very low initial slope gradient. At the hillslope–valley boundary (toe slope) the slope gradient reduces suddenly. This sudden slope gradient reduction reduces the transport capacity of the water flow and initiates deposition. Initially deposition occurs only at the hillslope–valley boundary node and increases its elevation. This deposition and slope reduction propagates upslope until equilibrium is reached with erosion. Deposition propagates across the valley and produces the deposits in Fig. 6.
There is a change in surface
Near the erosion–deposition boundary, only a small amount of sediment is
deposited. Since the larger particles have the highest probability of
deposition, a small amount of coarse material deposits there. Downslope into
the deposition region the slope further decreases, the difference between
the transport capacity and the sediment load increases, and the rate of
deposition steadily increases. Since larger particles have a higher
probability of depositing first, coarse material preferentially deposits.
Mixing of these coarse particles with pre-existing weathered fine particles
produces the observed coarsening of the surface
With time the deposition region moves upslope. The gradient of
The simulation produced a landform morphology which resembles the five-unit model proposed by Ruhe and Walker (1968). At the conclusion of the simulation the plateau area resembles a flat summit, the plateau–hillslope boundary resembles the convex shoulder, the transition region from the plateau–hillslope boundary to the deposition region resembles the backslope with a uniform slope, and the deposition region resembles the concave base divided into upper footslope and lower toeslope. Generally the soil grading distribution is fine at the summit and coarsens from the summit to the shoulder and backslope followed by fining from the backslope to the base (Birkeland, 1984). Furthermore, the soil depth is typically high in the summit area, low in the shoulder and backslope, and high in the upper footslope and lower toeslope (Brunner et al., 2004). The soil grading and the soil depth variations of our simulations produce similar trends.
In order to better understand the dynamics of soilscape evolution we also
plotted the elevation, slope, rate of erosion (and/or deposition), surface
For site 1 (Fig. 7 – solid line plots) the erosion and surface
Evolution characteristics of sites 1 and 2:
When the erosion front crosses site 1, the gradient increases as does the
erosion rate (at around 20 000 years). During this phase of increasing
erosion the surface
Both soil depth and profile
For site 2 (Fig. 7 – dashed line plots) the evolution is simpler than site 1. The initial transport capacity and discharge energy at site 2 is very
high while the sediment inflow from upstream is low because of low erosion
from the plateau. The resulting higher erosion rate produces a very coarse
surface layer and exposes the bedrock in the subsurface. This effect causes
both the surface
Although the surface
For site 3 (Fig. 8 – solid line plots) the elevation increases due to
deposition. The initial increase in surface
Evolution (near the hillslope–valley boundary) of sites 3 and 4:
The subsequent decrease in the surface
For site 4 (Fig. 8 – dashed line plots), while the initial evolution is
different, in the latter stages (beyond year 15 000) the evolution
characteristics of the soil properties are similar to those of site 3. Since
the valley initially has a low slope, the initial erosion is negligible and
the elevation, slope, and erosion remain close to 0. With the growth of the
deposition region, a deposition front moves across the valley. Before
the deposition front reaches site 4, the elevation, slope, and
erosion/deposition remain unchanged. Because the initial erosion rate at
site 4 is low, there is no armouring so that weathering dominates and the
surface
To test the sensitivity of the conclusions in the previous section to changes in the depth-dependent weathering functions, in this section we explore the effect of weathering using the humped exponential weathering function. The key difference is that the humped function has a low weathering rate at the surface with the peak weathering rate occurring mid-profile.
Superficially, both the humped and exponential weathering functions produce
similar trends; however, there are some differences in the particle size
distribution, soil depth, and the evolution of the landform (Fig. 9). At
identical times the surface
Evolution of the soilscape with the humped exponential depth-dependent weathering function.
These differences in landform evolution are explained by the near surface
weathering rates. For the exponential weathering function the weathering
rate is highest at the surface and declines exponentially with depth. For
the humped exponential weathering function the highest weathering rate is at
a finite depth below the surface and exponentially decreases below and above
this depth. Because of the lower surface weathering rate for humped, the
surface
Currently the coupled soilscape–landform evolution model SSSPAM presented here is limited in its scientific scope. The model is based on physical fragmentation of parent soil particles, and it does not model chemical transformations. Also at the current time SSSPAM does not account for soil organic carbon (SOC) and its influence in the soil formation and evolution processes. The modelling approach used here is complimentary to the chemical weathering modelling work done by Kirkby (Kirkby, 1977, 1985, 2018). However, we will be incorporating a physically based chemical weathering model described by Willgoose (2018) into SSSPAM in the future. All available evidence suggests that, in order to effectively model SOC, it will require an extremely complicated coupled model which requires soil grading, soil moisture, and vegetation and decomposition rates. Although formulating such a model is very desirable (and would be an important endeavour by itself) for the entire scientific community, it is well beyond the scope of this current research work.
The deposition model of SSSPAM is designed in such a way that the difference between the transport capacity and the sediment load of the flow is always deposited regardless of the settling velocities. This is done to prevent the flow from being over the transport capacity. Depending on the material grading distribution and the concentration in the profile of the flow, the theoretical amount of the material that can be deposited can be different. In this model formulation we assume that the sediment grading is uniform and the sediment concentration is also uniform within the flow. The reality may not be as simple as that. There is some literature such as Agrawal et al. (2012) which argues that the sediment concentration profile has an exponential distribution (i.e. most of the sediments are concentrated near the bottom of the flow) and that the grading distribution profile in the flow is also a function of the settling velocity of different particles (i.e. larger particles are concentrated near the bottom of the flow). So in practice the amount of material deposited at each pixel according to the critical immersion depth might be higher. Although the approach used in SSSPAM may not perfectly mimic the natural behaviour of sediment deposition, we believe that this is an effective way to numerically represent this process in the model at this time.
The main objective of this paper was to introduce the new coupled soilscape–landform evolution model. Here some applications of the model simulations albeit simple were presented to show how the model performed in reality and to highlight some of the geomorphic signatures emerging from the modelling results itself. The simulation setup may not be a reasonable application that necessarily reflects the total environment. However, we are inspired by the early work on hillslope geomorphology by authors such as Kirkby (1971) and Carson and Kirkby (1972) which was very useful in understanding hillslope evolution processes. So as a first step we used a one-dimensional hillslope to run our simulations because understanding dynamics of 1-D hillslope evolution is simpler and we can better illustrate possible implications for different processes. Further, only limited comparison with field data was possible because of a dearth of any experimental work done by other researchers using setups comparable with our simulations. However, a subsequent paper will deal with implications of model results in terms of one-dimensional and three-dimensional alluvial fans. In this paper, we compare and contrast the model results with experimental work done by authors like Seal et al. (1997) and Toro-Escobar et al. (2000), as well as general observations on naturally occurring alluvial fans and their formation dynamics.
This study presents a methodology for incorporating landform evolution into the SSSPAM soil grading evolution model. This was achieved by incorporating elevation changes produced by erosion and deposition. Previous published work with SSSPAM assumed that the landform, slope gradients, and contributing areas remained constant during the simulation. This did not preclude the landform from evolving, only that the soil reached equilibrium faster (i.e. had a shorter response time) than the landform evolved (i.e. a “fast” soil, Willgoose, 2018). In the new version of SSSPAM discussed here, the elevations, contributing area, slope gradient, and slope directions at each node dynamically evolve. This new model explicitly models co-evolution of the soil and the landform, where the response times for soil and landform are similar.
By defining the critical immersion depth, a novel and simple methodology for size-selective deposition was introduced to formulate the deposition transition matrix. This deposition transition matrix characterises the size selectivity of sediment deposition depending on the settling velocity of the sediment particle, with faster settling velocity particles settling first.
The results demonstrated SSSPAM's ability to simulate erosion, deposition, and weathering processes which govern soil formation and its evolution coupled with an evolving landform. The simulation results qualitatively agree with general trends in soil catena observed in the field. The model predicts the development of a thin and coarse-grained soil profile on the upper eroding hillslope and a thick and fine-grained soil profile at the bottom valley. Considering the dominant process acting upon the soilscape, the hillslope can be divided into weathering-dominated, erosion-dominated, and deposition-dominated sections. The plateau (summit) was mainly weathering-dominated due to its very low slope gradient and low erosion rate. The upper part of the hillslope was erosion-dominated owing to its high slope gradient and high contributing area. The lower part of the hillslope and the valley was deposition-dominated. The position and the size of these sections change with time due to the evolution of the landform and the soil profile. During the simulation, the weathering-dominated region shrinks due to the erosional region dominating it. The erosion-dominated region expands upslope into the previously weathering-dominated region, and the downstream boundary retreats upslope away from the deposition-dominated region but shows a net expansion in area. The deposition-dominated region expands upslope into the previously erosion-dominated region with a net expansion.
The simulation results also show how the interaction of different processes can have unexpected outcomes in terms of soilscape evolution. The best example is the fining of the surface grading despite an increasing transport capacity and potential erosion rate. This occurs due to saturation of the flow with sediment eroded from upstream nodes. Further, the comparison of results produced by the exponential and humped exponential weathering functions showed how the distribution of weathering rate down the soil profile changes the overall properties of the soilscape. For instance, the humped exponential simulation produced a thinner soil profile and coarser soil surface armour compared with simulation results of exponential weathering function because of the reduced weathering rate at the soil surface. This led to a longer-lived surface armour for the humped function.
The synthetic landform simulations demonstrated SSSPAM's ability to qualitatively simulate erosion, deposition, and weathering processes and to generate familiar soilscapes observed in the field. Comparison of results obtained from two different depth functions demonstrates how the soilscape dynamic evolution is influenced by the weathering mechanisms. This in turn links to the geology of the soil parent materials and their preferred weathering mechanism, which leads to the heterogeneity of soilscape properties in a region. A future paper will discuss how this work can be extended to include the impact of chemical weathering into soilscape evolution.
The SSSPAM model (computer code, parameters) and data (soil grading and elevation data) used in this paper are available on request from the authors.
The authors declare that they have no conflict of interest.
The authors would like to acknowledge Peter Finke and Arnaud Temme for their review comments which greatly assisted in strengthening this paper. The research work presented in this paper were performed while the lead author was on a post graduate scholarship from The University of Newcastle, Australia.
This research has been supported by the Australian Research Council (grant no. DP110101216).
This paper was edited by Andreas Baas and reviewed by Arnaud Temme and Peter Finke.