A quantitative model for integrating landscape evolution and soil formation

Authors

  • T. Vanwalleghem,

    Corresponding author
    1. Department of Agronomy, Campus de Rabanales, University of Cordoba, Cordoba, Spain
    • Corresponding author: T. Vanwalleghem, Department of Agronomy, Campus de Rabanales, University of Cordoba, 14010 Cordoba, Spain. (ag2vavat@uco.es)

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  • U. Stockmann,

    1. Department of Environmental Sciences, Faculty of Agriculture and Environment, University of Sydney, Eveleigh, New South Wales, Australia
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  • B. Minasny,

    1. Department of Environmental Sciences, Faculty of Agriculture and Environment, University of Sydney, Eveleigh, New South Wales, Australia
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  • Alex B. McBratney

    1. Department of Environmental Sciences, Faculty of Agriculture and Environment, University of Sydney, Eveleigh, New South Wales, Australia
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Abstract

[1] Landscape evolution is closely related to soil formation. Quantitative modeling of the dynamics of soils and landscapes should therefore be integrated. This paper presents a model, named Model for Integrated Landscape Evolution and Soil Development (MILESD), which describes the interaction between pedogenetic and geomorphic processes. This mechanistic model includes the most significant soil formation processes, ranging from weathering to clay translocation, and combines these with the lateral redistribution of soil particles through erosion and deposition. The model is spatially explicit and simulates the vertical variation in soil horizon depth as well as basic soil properties such as texture and organic matter content. In addition, sediment export and its properties are recorded. This model is applied to a 6.25 km2 area in the Werrikimbe National Park, Australia, simulating soil development over a period of 60,000 years. Comparison with field observations shows how the model accurately predicts trends in total soil thickness along a catena. Soil texture and bulk density are predicted reasonably well, with errors of the order of 10%, however, field observations show a much higher organic carbon content than predicted. At the landscape scale, different scenarios with varying erosion intensity result only in small changes of landscape-averaged soil thickness, while the response of the total organic carbon stored in the system is higher. Rates of sediment export show a highly nonlinear response to soil development stage and the presence of a threshold, corresponding to the depletion of the soil reservoir, beyond which sediment export drops significantly.

1 Introduction

[2] The interaction of pedogenetic and geomorphological processes fundamentally ties soils and landforms together at the landscape scale [Hall, 1983]. This notion has been conceptually present since the early soil-formation models [Jenny, 1941] and is explicitly formalized in the catena concept [Milne, 1936]. The catena concept implies that distinct soil types are associated with different landform elements and knowledge of one therefore allows prediction of the other [Gerrard, 1992]. Since these early studies, many others have convincingly corroborated and quantified the empirical relation between soil type and landform for different land uses and different geological or climatological settings [Odeh et al., 1992; Moore et al., 1993; Gessler et al., 2000]. In spite of the important interactions between soil formation and landform evolution, our quantitative understanding has remained largely limited to a statistical description of the system. The reason for this is that quantitative field research and mechanistic modeling efforts have largely evolved along separate lines. This resulted in two separate schools of mechanistic models: landscape evolution models and soil profile models [Minasny et al., 2008].

[3] The first school stems from a geomorphologic background [Ahnert, 1977; Kirkby, 1971; Willgoose et al., 1991] and operates at the landscape scale. Geomorphologic models recognize the difference between transport-limited and detachment-limited systems. However, even in the latter systems, erosion is only limited by the rate of the processes, not by the available sediment as detachment thresholds are often negligible [Tucker and Whipple, 2002]. Geomorphic models that do consider soil explicitly often limit it to a single layer of regolith. The main processes are production of regolith from bedrock through a weathering function and horizontal redistribution of this material through soil erosion and deposition processes [Ahnert, 1967; Dietrich et al., 1995; Minasny and McBratney, 1999, 2001, 2006]. Some advanced landscape evolution models, such as SIBERIA [Willgoose et al., 1991; Willgoose, 2004], CHILD [Tucker et al., 2001] or ARMOUR [Willgoose and Sharmeen, 2006], took into account sediment characteristics, but in spite of the long timescales on which some of these models operated, no explicit soil forming processes were taken into account. Textural differences could therefore only originate from sediment sorting by erosion and deposition processes.

[4] In soil profile models on the other hand, the main focus is on vertical redistribution within a single soil profile [Legros and Pedro, 1985; Salvador-Blanes et al., 2007; Finke and Huston, 2008]. This school of models comes from pedology and operates at the point or pedon scale. While some mechanistic models [Finke and Huston, 2008] included complex physical, chemical and biological processes, they failed to address one of the most important characteristics of soils, which is the spatial configuration and connection between individual points. Except for simple, flat areas, important lateral fluxes of water, solutes and soil particles exist at the landscape scale, which must be taken into account to accurately model the evolution of soils in a landscape context.

[5] Some recent models have bridged the gap between both schools to some extent. Sommer et al. [2008] proposed a detailed framework for such integrated modeling, although it is conceptual and yet to be filled in quantitatively. At present, no model exists that fully integrates soil formation and landscape evolution. The long-term model mARM [Cohen et al., 2009] focused on surface armoring and bedrock weathering. This allowed Cohen et al. [2009] to analyze the relative importance of both processes for the evolution of grain-size distribution in soils over time. In the subsequent, spatially explicit model, mARM3D, Cohen et al. [2010] included a full consideration of the vertical soil profile and spatial coupling. This model marked a great advance with respect to previous soil-landscape models as it accounted for bedrock weathering and physical weathering, although it did not yet account for other soil-forming processes, such as chemical weathering or bioturbation. The same applies for the interdisciplinary model proposed by Nicotina et al. [2011], who fully integrated surface hydrology into their model and obtained good results for predicting soil formation, but only considered a single layer of regolith. In turn, detailed geochemical soil formation models, such as LEACH-C [Finke and Huston, 2008], in theory allowed surface additions and removals of soil. In practice however, LEACH-C was point based and therefore used an independent input which needed to be derived from a different erosion model. Even with these additions or removals, this model would not result in a coupled soil-landscape evolution, unless the soil variables were also fed back into the erosion model.

[6] Given the complexity of the different processes and interactions that are involved, quantitative modeling is crucial to improve our understanding of the soil-landscape system. Such models could have a large impact on our understanding of feedbacks between climate change and ecosystems. Soil physical properties such as texture and soil depth are important inputs in vegetation models and hydrological models. Any long-term modeling effort of climate change therefore needs to take into account the effect of dynamic soils. For example, over the Holocene, the role of anthropogenic soil erosion on the carbon cycle is the subject of a controversial debate [Kuhn et al., 2009]. Apart from the direct effect through erosion and burial of carbon-rich sediment, this debate also needs to take into account the effect that changing soil properties, such as depth or stoniness, could have on the potential distribution of natural vegetation. Collins et al., 2010] showed how soil depth changes led to biome shifts in Mediterranean ecosystems. Another area of interest for quantitative modeling of soil formation is the spatial prediction of soil properties, through empirical soil-landscape regression models [e.g., Odeh et al., 1992] which relate landscape parameters to key soil properties. As such, these models are inherently linked to the conditions for which they have been developed and extrapolation is difficult. Also, in regions where limited data on soil properties is available to establish statistically meaningful relations, a mechanistic model of the underlying pedogenetic and geomorphological processes could provide a useful alternative to predict soil thickness and soil properties. Finally, the relation between geomorphological processes and environmental change cannot be fully understood without considering soils. In their review of sediment dynamics in the Eastern Mediterranean, an area with a long history of land use and anthropogenic soil erosion, Dusar et al. [2011] found a clear signal in the sediment record that soil profiles were depleted during the late Holocene. In the absence of field data on soils, they could have easily attributed the observed changes to apparent changes in climatic conditions.

[7] In the light of this need for an integrated model, this paper therefore aims to present a holistic soil-landscape evolution model that integrates a pedon-scale soil formation model with a regional-scale landscape evolution model.

[8] The model capabilities are described in a landscape-scale simulation including both vertical and horizontal redistribution processes. We show how soil erosion influences soil profile depth and layering and to what extent the main soil properties, such as texture, stoniness and soil organic carbon content are affected. The effect of soil development on sediment dynamics is also evaluated by comparing the sediment fluxes and properties generated under different erosion rates and equal soil formation rates.

2 Model Description

2.1 Approach

[9] The presented landscape and soil evolution model, MILESD, builds conceptually on the landscape-scale models for soil redistribution by Minasny and McBratney [1999, 2001] and the pedon-scale soil formation model by Salvador-Blanes et al. [2007].

[10] However, MILESD differs from the previous models as the soil is partitioned in four layers, three soil layers or horizons and a bedrock layer. The subdivision of the regolith in three layers is justified from a pedological perspective. Johnson [1994] traced back the origin of this three-layer approach to the early work of Dokuchaev and showed how it can be applied to typical soils ranging from the mid latitudes to the tropics. The model is mass balance based and changes in soil thickness over time depend on (1) the production of soil material from bedrock through weathering; (2) changes in soil properties through soil formation processes as well as (3) erosion and deposition. An overview of the model structure is shown in Figure 1.

Figure 1.

Schematic representation of the model structure.

[11] Soil formation processes include physical and chemical weathering, neoformation of clays, clay translocation and biological mixing processes. By considering only the solid phase, the complexity of soil formation processes is necessarily simplified in this model. While the explicit consideration of the liquid phase offers obvious advantages for modeling geochemical processes in detail [Samouëlian and Cornu, 2008], the current state-of-the-art justifies our simplified approach, as knowledge of many basic soil forming processes is absent [Yoo and Mudd, 2008].

[12] Five size fraction classes are considered: coarse (2 × 10−3 – 10 × 10−3 m), sand (50 × 10−6 – 2 × 10−3 m), silt (2 × 10−6 – 50 × 10−6), clay (1 × 10−7 – 2 × 10−6) and fine clay (<1 × 10−7 m). The limits are derived from the USDA classification [Soil Survey Staff, 1993], with an additional coarse fraction class and an additional class of fine clay. The latter is added because of its potential importance in clay translocation processes [e.g., Van Wambeke, 1976]. The first size class (coarse fraction) is added so that each primary mineral particle is first released into the coarse fraction size class. This equates to the hypothesis that soil formation starts from a layer of saprolite containing fractured rock. Soil-formation processes acting on these coarse particles will then move them to the other size fraction classes.

[13] To optimize computing efficiency, a matrix model approach with dynamical transition matrices is used for calculating the change in soil properties at each time step. Dynamical transition matrices have been used relatively little in soil science with respect to other disciplines such as ecology [Lin et al., 1996]; examples in earth sciences are given by Shull [2001] for modeling bioturbation or by Cohen et al. [2009] for their armoring and weathering model. In this matrix-model approach, the size class distribution of each layer j at time t is expressed by a vector Sjt and the transition between states induced by the different soil formation processes by different matrices Ajt.

[14] In the following discussion, the transition matrix Ajt will be expressed as the sum of the identity matrix I, with all but the diagonal elements equal to zero, and the marginal transition matrix Mjt.

display math(1)

with

display math

[15] Each soil forming process will be characterized by a characteristic transition matrix. The elements of this transition matrix are continuously updated during the period of simulation in function of secondary variables.

2.2 Soil-Forming Processes

2.2.1 Bedrock Weathering

[16] As the regolith thickness increases, the pedogenic rate tends to decline as the weathering front moves farther from the surface, due to the self-limiting nature of many pedogenic processes [Torrent and Nettleton, 1978; Muhs, 1984]. Experimental data from cosmogenic nuclide dating support either a simple exponential dependency on total soil thickness (h) for the lowering of the bedrock surface [Heimsath et al., 1997] or a humped soil production function [Humphreys and Wilkinson, 2007]. In this model, we adopted the exponential function as it provides the best fit to the majority of publicly available data [e.g., Heimsath et al., 2000, 2001, 2006]. The conversion rate of bedrock material into soil regolith as a function of time (t) is then given by:

display math(2)

where h is the total soil thickness, p1 is the potential bedrock weathering rate [L T−1] and b1 [L−1] is an empirical rate constant. The bedrock weathering rate used in the model is derived from Heimsath et al. [2000] for a study area in Australia.

2.2.2 Physical Weathering

[17] Physical weathering is the process by which minerals or rock are disintegrated into smaller pieces by mechanical processes such expansion and contraction due to temperature variation, wedging by ice, salt or plants. Field or laboratory studies that quantify the change in particle size distribution over time during the fragmentation process are rare [Wells et al., 2007]. As in the Salvador-Blanes et al. [2007] model, fragmentation rates in MILESD are a simple function of two variables: particle size and depth below the surface. First, the rate of fragmentation will increase with particle size, as the probability for occurrence of imperfections leading to fragmentation increases. Secondly, fragmentation is mainly a temperature-driven process and therefore increases with increasing temperature amplitude. Soil depth is a good proxy for this variable, since it is well known that the amplitude of temperature variations decreases exponentially with depth [van Wijk, 1963]. However, whereas the Salvador-Blanes et al. [2007] model uses a detailed 1000 size classes approach developed by Legros and Pedro [1985], MILESD uses a more simplified approach with only 5 size fractions and does not consider mineralogy. Following the classification by Wells et al. [2008], our model is an asymmetrical model where the fragmented material is redistributed over two smaller size fraction classes of different size. Wells et al. [2008] found that the asymmetric fragmentation model, such as the one used here, provided a good fit of their experimental data, similar to that of symmetric models, although they did not report any improvement when using variable fragmentation rates. Because MILESD builds on the Salvador-Blanes et al. [2007] model, the asymmetric model was chosen over the symmetric one. The proportion of each of the daughter size classes is calculated as being directly proportional to the size limits of each class. One mass unit of coarse fragments will thus break up into 0.975 units of sand and 0.025 units silt. One mass unit of sand will break up into 0.96 units of silt and 0.04 units of clay. Based on field evidence, it is assumed that no fine clay is formed through physical weathering, so all fragmented silt is converted to clay. Smeck et al. [1981] and Chittleborough et al. [1984] indicated that the fine clay fraction is mainly formed by chemical weathering of clay and silt, rather than physical disintegration processes.

[18] The diagonal elements of the marginal transition matrix, ajit, defining the change in particle size distribution at each time step in a specific layer j, are then given by:

display math(3)

where i is the particle size class (1 to 5), k1 the rate constant of physical weathering [T−1], Dj the depth below the soil surface of layer j [L], c1 the depth rate constant for physical weathering [L−1], PDi the mean particle size [L], c2 the size rate constant for physical weathering [L] and Δt the model time step [T].

[19] The physical weathering rate constant used in this model is in the range of values used by Salvador-Blanes et al. [2007]. The latter used values between 0.6 × 10−4 and 8 × 10−4 yr−1, depending on the size class and the mineralogy, where a single value of 10−4 yr−1 is used here (Table 1). Salvador-Blanes et al. [2007] explored the effect of different physical and chemical rate constants on the evolution of particle size in more detail. The values adopted here were selected so that the particle size evolution corresponds to their “base scenario.”

Table 1. Input Parameter Values Used in the Simulations
ParameterValueExplanationUnitsReferenceaEquation
  1. a

    Please see text for details, in some cases the referenced sources served as a basis to derive the parameters cited.

  2. b

    These are the values for the “moderate” erosion scenario. Values for the high erosion scenario are 5 times higher.

Bedrock and Horizon Lowering
p10.000053potential bedrock weathering ratem yr−1Heimsath et al. [2000]((2))
b12empirical bedrock weathering rate constantm−1((2))
kh100.00001rate constant for lowering of layer 1m yr−1 ((16))
kh11-0.01constant relating lowering of layer 1 with carbon content- ((16))
kh200.00002rate constant for lowering of layer 2m yr−1 ((17))
kh21-0.01constant relating lowering of layer 2 with coarse fraction- ((17))
Physical Weathering
k10.0001physical weathering rate constantyr−1Salvador-Blanes et al. [2007]((3))
c1-0.5depth constant for physical weatheringm−1((3))
c25size constant for physical weatheringm((3))
Chemical Weathering
k270chemical weathering rate constantkg m−2 mineral yr−1Salvador-Blanes et al. [2007]((4))
c3-2.5depth rate constant for chemical weatheringm−1((4))
c41specific surface area constant for chemical weathering-((4))
SA110specific surface area fraction 1 (coarse)m2 kg−1 ((4))
SA2100specific surface area fraction 2 (sand)m2 kg−1 ((4))
SA31000specific surface area fraction 3 (silt)m2 kg−1 ((4))
SA450000specific surface area fraction 4 (clay)m2 kg−1 ((4))
SA5100000specific surface area fraction 5 (fine clay)m2 kg−1 ((4))
Neoformation
cnf0.5neoformation constant- ((7))
c51.2constant for relation clay neoformation with depthm−1((7))
c620constant for relation clay neoformation with depthm−1((7))
Clay Translocation
Cmax0.007base rate of clay translocationkg

Alexandrovskiy [2007]

((8))
kcl200constant for relation of clay translocation with depth-((8))
Bioturbation
BT016maximum bioturbation rate from layer 2 to 1kg yr−1

Muller-Leemans and Van Dorp [1996]

((10))
BT023maximum bioturbation rate from layer 1 to 2kg yr−1((10))
kbt12.5constant for relation of bioturbation with layer thicknessm−1((10))
kbt22.5constant for relation of bioturbation with BAI-((10))
kBAI2.5constant for relation of bioturbation with depthm−1((9))
Carbon Cycling
C′in1.5base rate carbon productionkg yr−1MODIS-derived (Atlas of Living Australia, 2012, online)((13))
kOC4constant for relation carbon production with depthm−1

Minasny et al. [2008]

((12))
kc10.01fast carbon decomposition rate constantyr−1((14))
kc20.00005slow carbon decomposition rate constantyr−1((14))
c70.1constant for relation carbon decomposition with wetness index-((15))
c82constant for relation carbon decomposition with depthm−1((15))
f0.8fraction fast-slow carbon decomposition pool-((14))
Bulk Density
BDrock2700bedrock bulk densitykg m−3 ((19))
Erosion
D0.1bdiffusivity constantm2 yr−1Prosser and Rustomji [2000]((20))
K0.2 × 10−8bconcentrated flow erodibility constantyr−1((21))
m1.67constant for relation concentrated flow - area-((21))
n1.3constant for relation concentrated flow - slope-((21))
kst0.032constant relating erosion and rock fragment content-((22))

[20] For each soil layer, the physical fragmentation process is depth-integrated between the top and the bottom of the layer.

2.2.3 Chemical Weathering

[21] Chemical weathering is the process by which mineral particles are dissolved, oxidized, or reduced. Chemical weathering rates are complex functions of material properties and site characteristics, such as runoff and lithology, temperature, vegetative cover, tectonics and therefore exposure and elevation [Gislason et al., 1996]. Commonly, discrepancies of up to 5 orders of magnitude between field and laboratory rates of chemical weathering have been inferred. The discrepancy has been mostly attributed to the error in estimation of the surface area in the field, differences in solution chemistry, temperature differences, heterogeneous distribution (or flow) of water in the field, and differences in the surface condition of minerals [White and Brantley, 2003; Maher, 2010].

[22] The chemical weathering rate in MILESD depends on the surface area of the soil particles and soil depth. Vertical variation of chemical weathering with depth is inherently complex. Gradients in solution parameters such as temperature, pH, dissolved Al, and H2CO3 influence reaction kinetics, while gradients in hydraulic conductivity, controlled by porosity, pore size, and water content, affect transport. On the other hand, the fluid is likely most reactive and the soil most permeable near the top of the reactor, while the minerals most prone to weathering are usually at the bottom of the profile [Anderson et al., 2007].

[23] As MILESD does not take into account the soil's liquid phase, the model cannot take into account the full complexity associated with chemical weathering. A simple model is proposed that relates chemical weathering intensity linearly to surface area and exponentially to depth below the surface. Depth below the soil surface relates mainly to variations in soil temperature and soil moisture. However, only the latter will result in vertical variations of chemical weathering rates. De Vries [1963] showed how diurnal or yearly soil temperature variations are well represented by a sine wave. Therefore, while the amplitude of soil temperature variations declines with depth, average soil temperature is constant with depth. This implies that chemical rate constants, for example as determined using the Arrhenius equation, are higher near the surface than deeper in the soil during warm periods. However, during subsequent cold periods, reaction constants drop much more near the surface than deeper where these temperature variations are buffered. As a result, the long-term average reaction constants for chemical weathering processes at different depths should be equal. This is clearly in contradiction with field observations of nonlinear weathering profiles with depth [Anderson et al., 2002; White et al., 2009]. White et al. [2009] showed in their study of marine terraces how weathering rates become transport-limited and dependent on the hydrological flux when pore water approaches thermodynamic saturation. Therefore, we assume that the depth proxy we use in MILESD expresses soil moisture variations, which in turn control chemical weathering fluxes. An exponential decline function with depth is a good approximation of soil moisture variability [Amenu et al., 2005]. This variable depends on the balance between infiltration, percolation and evapotranspiration. The variability of evapotranspiration with depth is influenced by the plant root distribution, which is well approximated by an exponential decline function [Li et al., 1999]. In addition, Choi et al. [2007] proposed an exponential decline function for saturated hydraulic conductivity, which controls infiltration and percolation, to express the effect of macropores near the surface. As Jin et al. [2011] indicated, density of macropores plays a major role in the flux of fresh water through the profile, which in turn will influence chemical weathering processes.

[24] The diagonal elements of the marginal transition matrix, ajit′, defining the mass loss for each particle size class i due to chemical weathering at each time step, for a specific layer j, is then given by:

display math(4)

where k2 is the chemical weathering rate constant [M L−2 T−1], c3 the depth rate constant for chemical weathering [L−1], Dj the depth below the soil surface of layer j [L], c4 the specific area constant for chemical weathering and SAi the specific surface area of mineral particles within size class i of layer j [L2 M−1]. Chemical weathering rates used in this model are in the range of values used by Salvador-Blanes et al. [2007].

[25] Determining the specific area of a mineral is not straightforward [Salvador-Blanes et al., 2007]. Therefore, the specific surface area of the different size fraction classes is defined (see Table 1), rather than calculated. This implies that additional complexity deriving from changing surface reactivity with time throughout the weathering process [White and Brantley, 2003] or from changes in the pore-space configuration that can affect the availability of reactive sites is not considered here [Maher, 2010].

[26] Chemical weathering causes direct mass losses of solid soil particles to the soil solution. Part of this lost material will form new minerals (see neoformation), but chemical weathering will also affect particle size indirectly as mass losses result in smaller particles. To calculate the mass of particles falling into a finer size class due to this process, particles are again approximated by spheres. The dimensionless term F expressing this mass loss can then be calculated as:

display math(5)

with Ri the mean radius of the particles in the original size class i and Ri+1 the mean radius of the particles in the final size class i + 1.

[27] The final marginal transition matrix Mjt is then obtained by correcting the previously calculated one (Mjt) with this additional loss term:

display math(6)

2.2.4 Neoformation of Clays

[28] A portion of the primary minerals that are lost by chemical weathering will form new secondary minerals. These newly formed minerals are assumed to be smaller than 1 × 10−6 m. The total amount available to neoformation is assumed to be directly related to the amount of chemical weathering in the entire soil profile. It is difficult to assess the relative importance of clay eluviation/illuviation versus clay neoformation, but there is definitely field evidence that shows the latter to be an important process in some environments. White et al. [2009] showed that argillic horizons could be explained by in situ clay formation in a series of marine terrace soils. To derive quantitative information on clay formation rates from the clay content in soil profiles is not straightforward as the original clay content and clay translocation processes need to be accounted for, as discussed in detail by Barshad [1957]. Empirical evidence suggests that the rate of secondary clay formation is highest at some depth below the surface, often assumed to be between 0.05 and 0.25 m [Barshad, 1957]. Therefore, neoformation of clay was modeled as a double exponential function of depth below the soil surface. The marginal transition matrix is therefore 0, except for the diagonal element corresponding to the fine clay fraction (size class 5), aj5:

display math(7)

where cnf, c5, c6 are constants, d is the depth below soil surface [L] and Mcw is the total mass lost by chemical weathering in all soil layers [M].

[29] Constant cnf will determine the potential or maximum neoformation rate, while c5 and c6 control the shape of the relation with depth (see Figure 2).

[30] Maher et al. [2009] used a multicomponent reactive transport model to simulate the formation of secondary clays in marine terraces, taking into account the full complexity of soil chemistry. Their results confirmed that the neoformation rate is highest at some depth below the surface, as represented by equation ((7)), but also evidenced that neoformation rates change over time as mineral composition changes. At this point, our simplified model does not include this time-dependent behavior.

Figure 2.

Relative rate of clay neoformation with depth, as a function of different coefficients selected in equation ((7)). Clay neoformation is calculated relative to the chemically weathered fraction.

2.2.5 Clay Lessivage

[31] The vertical migration of clay is possibly one of the most important processes in soil formation. In spite of this, existing clay migration models are mostly conceptual and data on clay migration rates are scarce. Legros [1982] attempted to model illuviation and eluviation processes based on a simple procedure whereby a given quantity of clay is eluviated or illuviated at each time step. MILESD follows a similar approach, where clay lessivage is expressed as a flux from the superficial layer 1 to the underlying layer 2, only that the rate of lessivage increases up to a maximum value in function of the fine clay content in layer 1.

display math(8)

where ΔC is the amount of fine clay eluviated at each time step [M], Cmax the maximum amount of clay that can be eluviated per time step [M T−1], kcl a constant and Pfc the fine clay content in layer 1 (%). An estimate of clay translocation was made based on data of Luvisol genesis by Alexandrovskiy [2007].

2.2.6 Bioturbation

[32] Animals and plants can cause significant movement of soil material within a soil profile. Since Darwin [1840] first published his observations on earthworm casts, numerous studies have followed and thanks to the attention from various research areas, such as ecology, pedology, geology and archaeology [Lee, 1985; Canti, 2003; Gabet et al., 2003], soil turnover rates by burrowing animals, plant rooting and tree throw are now much better known [Roering et al., 2002; Kaste et al., 2007]. Nevertheless, a lack of insight into the different controlling processes makes modeling bioturbation processes still a difficult task.

[33] A simple approach is proposed here because at present, to our knowledge, there is no published quantitative model available for soil bioturbation. In MILESD, bioturbation causes mixing of each of the three layers representing the soil column and results in fluxes between the three layers. The mixing of the material within each individual soil layer supports the model assumption where soil properties of each layer are considered homogeneous. This approach is similar to the model published by Yoo et al. [2011] where rates of soil mixing and associated carbon fluxes were calculated between individual soil layers. However, in the latter model mixing velocities were calculated directly based on the soil profile's 210Pb inventory. In MILESD, the fluxes are calculated as being proportional to the biological activity of the layer receiving the material and inversely proportional to the distance between layers.

[34] Biological activity is expressed here through a biological activity index (BAI). This index is based on the soil productivity function as defined by Salvador-Blanes et al. [2007] and Minasny et al. [2008] and varies according to soil thickness, soil carbon content and depth in the profile:

display math(9)

where BAI0 is the potential or maximum biological activity = BAI0 = fs1(h)fs2(OC), htotal the total soil thickness, OC the relative carbon content of the soil layer (OC, %), fs1 and fs2 are sigmoid functions of the form math formula with c0 and c1 constants and X either h or OC, kBAI is a proportionality constant, and d is the depth below the soil surface [L].

[35] The biological activity index of each layer j, BAIj, is then calculated for each soil layer by integrating this function between the upper and lower boundary of each layer. BAI0, the maximum biological activity, is reached at the surface. Biological activity then drops exponentially with depth, which is supported by experimental data of earthworm activity [Canti, 2003]. Depending on the soil climatic conditions however, other depth-dependent functions could be considered. Yoo et al. [2011] for example determined for a Delaware forest soil profile that the highest biological activity did not occur at the surface but at some depth below the surface because of adverse surface conditions. Additionally, in the model, there is a feedback between depth and thickness of the different layers on its total biological activity index. For example, as the superficial layer 1 grows, its biological activity index increases. However, layers 2 and 3, even at a constant thickness, will be deeper below the surface and their biological activity index drops. At this moment, no experimental data are available that allow a detailed quantification of selectivity in bioturbation processes. Selectivity of the bioturbation process is therefore modeled as a binary process: coarse fragments are not moved, while all other size classes are moved in the same proportion by biota. Evidence for such a process of biosorting is well documented in nature [e.g., Horwath and Johnson, 2006]. Darwin [1840], for example, described how in gravelly soils earthworms produce a stone-free upper horizon. Later, many others reported evidence for this selective transport in soils from widely different areas [Webster, 1965; Soil Survey Staff, 1975; Johnson, 1989; Johnson et al., 2005], but that all show a clear separation between an upper, biologically active layer of fine material, also often called the biomantle, and an underlying stone layer.

[36] The movement of soil between two layers due to bioturbation can then be expressed as:

display math(10)

where ΔBTij is the soil material moved from layer i to j [M], BT0j the maximum bioturbation rate for layer j [M T−1], kbt1 a distance constant [L−1], kbt2 a biological activity constant, dij the distance between center of layer i and j [L], BAIj the biological activity index of layer j and Δt the time step [T].

[37] The rates for bioturbation are chosen to match reported soil movement caused by bioturbation (see review from Muller-Leemans and van Dorp [1996]).

2.2.7 Carbon Cycle

[38] The carbon component of the model includes production (Ij), decomposition (kcCj), mixing (qm,j) and losses (qc,j), similar to the model by Yoo et al. [2006] and Minasny et al. [2008]. The evolution of the organic carbon content (Cj, [M]) for each layer j through time can therefore be expressed as:

display math(11)

[39] The mixing term, qm, is handled explicitly by the bioturbation component of the model (see previous paragraph). Carbon can be transferred from one layer to the other by bioturbation. The carbon loss term, qc, is explicitly accounted for through the erosion component of the model (see below). After calculating the amount of soil moved by both bioturbation and erosion, carbon is then moved together with the soil. Soil carbon is assumed to be associated with the fine fraction of the soil (sand to fine clay). In this way, the erosion and bioturbation processes are also selective with respect to carbon movement in the landscape.

[40] The first two terms are calculated in a similar way as in previous models. The production of carbon in each soil layer, Ij, is determined by the base rate of carbon production Cin [M T−1] and varies with the depth below the soil surface (d, [L]) [Baisden et al., 2002a, 2002b; Ewing et al., 2006; Yoo et al., 2006]. The carbon production Cin depends on the thickness of the biologically active layers 1 and 2 (thick, [L]) and the relative carbon content of the soil layer (OC, %) through a sigmoid function. The carbon production ∂Iz for an infinitesimal layer of thickness ∂z equals:

display math(12)
display math(13)

where fs1 and fs2 are two sigmoid functions. C’in is the base rate or potential carbon production [M T−1], which can be derived from measurements of Net Primary Productivity.

[41] To obtain the total carbon production for each layer j, Iz, equation ((12)) is integrated between the top and bottom boundary of that layer.

[42] The carbon production at the soil surface is made spatially variable through a sigmoid function of total soil thickness and organic carbon content present in the soil, suggesting a feedback of both variables on carbon production rates [Minasny et al., 2008]. The value for C′in in equation ((13)) is taken as the MODIS-derived mean annual net primary productivity (Atlas of Living Australia, 2012, available at http://www.ala.org.au).

[43] The soil carbon is assumed to be in either a fast and slow pool for decomposition [Hénin and Dupuis, 1945]. In this two-pool system, the decomposition constant kc from equation ((11)) can therefore be defined as:

display math(14)

where f is the fraction of the first pool, kc1 and kc2 are the decomposition rates of each of the pools. Both slow and fast decomposition are made horizontally and vertically variable, based on differences in soil depth and wetness index, reflecting decreasing decomposition rates with depth and increasing wetness.

display math(15)

where d is depth [L], CTI is the topographic wetness index [Beven and Kirkby, 1979] and c7 and c8 are constants.

[44] The total decomposition of carbon for each layer is obtained by integrating over its entire thickness at each time step.

[45] Parameters for carbon cycling are derived from Minasny et al. [2008] who calibrated their model with local soil profile data.

2.2.8 Lowering of Soil Layer Boundaries

[46] To obtain a dynamical evolution of the soil profile boundaries over time, a set of rules is defined that control the lowering of the boundaries between the first three layers. In the absence of experimental data, it is assumed in the model that the self-limiting nature of pedogenic processes results in rates of boundary lowering that are variable over time and depend on certain soil properties, in a similar way as the weathering front is controlled by the overlying total soil depth. The set of rules that was selected is related to the three-layer concept that is common in pedology [Johnson, 1994]. The first layer or A horizon represents a organic-rich layer. The second layer or B horizon is a transitional zone to the C material, the parent rock. Therefore, the criteria we selected for horizon growth are organic carbon content and coarse fragment content, respectively. The evolution of the boundary between the surface layer, layer 1, and the underlying layer 2, is set as a negative exponential function of the difference in organic carbon content between both layers (ΔOC).

display math(16)

where h1 is the thickness of layer 1 [L], kh10 and kh11 are rate constants.

[47] The evolution of the boundary between the second and third soil layer is set as a function of the difference in coarse fragment content between both layers (ΔC).

display math(17)

where h2 is the thickness of layer 2 [L], kh20 and kh21 are rate constants.

[48] Equations ((16)) and ((17)) imply that the rate of growth of each layer will depend on the relative difference in organic carbon or coarse fragment content with the layer below. As long as layer properties are significantly different, growth will be slow. When layer properties are similar, growth will be faster. The process is self limiting in the sense that horizon growth implies addition of material from the underlying layer. As the intensity of weathering, biological processes and carbon production decrease with depth, increasingly different material will be added at each step, hereby increasing the difference in organic carbon content and coarse fragments and pushing back the boundary growth rates.

[49] The downward growth of each layer is limited by the growth of the underlying layer to assure model stability, that is, to avoid that any given layer disappears.

2.2.9 Evolution of Bulk Density and Strain

[50] To link soil profile development with landscape development, it is crucial to convert the mass changes in soil properties through soil-forming processes, especially size-class distribution, to volumetric changes as elevation is a key driver of erosion and deposition processes. It is well-known that bedrock and soil material undergoes strain through its weathering phase [Brimhall and Dietrich, 1987]. Here, a pedotransfer function, derived from experimental data by Tranter et al. [2007], is used to calculate the bulk density of each layer j (BD′j):

display math(18)

[51] Note that with respect to the original pedotransfer function used by Tranter et al. [2007], no depth factor is included in equation ((18)) to simplify and accelerate calculations. This introduces a small error for thin layers close to the surface, but generally does not affect the results significantly. More important is the effect of rock fragments on bulk density calculation. Therefore, bulk density is corrected for coarse fragment content (rock) according to Vincent and Chadwick [1994]. The bulk density of layer j, corrected for rock fragments is then:

display math(19)

with Mfine and Mrock the mass of fine (<2 × 10−3 m) and coarse material (>2 × 10−3 m), respectively. Msoil is the sum of both and BDrock is the bulk density of the rock fragments in the soil matrix.

2.3 Landscape Evolution

[52] After the soil-formation model has acted on all pedons in the landscape, the soil is redistributed by erosion and deposition (see Figure 1). It has to be noted that this is a simplification, as material produced by weathering and soil formation is in reality immediately available for erosion. In this model, the newly produced soil goes through a series of soil-forming processes during which its properties are adapted, before it becomes available for transport (see Table 1). Phillips [1995] discussed the potential implications of such a time lag. The model is topography-driven and a local cellular automata approach is used, whereby each cell is visited randomly. To avoid a full depletion of the soil column, the deepest soil layer, layer 3, is not subject to erosion. Once the erosion amount and direction of flow has been calculated for each cell, all deposited sediments are added to the top layer, layer 1, of their respective downslope cells. Following the approach used in numerous hillslope models [Smith and Bretherton, 1972; Simpson and Schlunegger, 2003; Willgoose, 2005; Minasny and McBratney, 2006; Follain et al., 2006; Minasny et al., 2008], erosion processes are modeled as the sum of diffusive and concentrated flow processes. Only erosion processes that have an effect on surface elevation are considered here.

[53] The first is commonly termed the diffusion equation and represents a series of processes such as mass wasting or nonconcentrated water erosion:

display math(20)

where qd is the erosion flux per unit width by diffusive transport [L2 T−1], D the diffusivity constant [L2 T−1] and S the local slope gradient [L L−1].

[54] The second encompasses fluvial transport by Hortonian overland flow and can be generally expressed as:

display math(21)

where qc is the erosion flux per unit width by concentrated flow [L2 T−1], K is the concentrated flow erodibility constant [T−1], A the drainage area [L2], S the local slope gradient [L L−1] and m and n are constants.

[55] The latter is a common simplification of the widely used Yalin [1972] equation [Dietrich et al., 2003]. The erodibility constant encompasses both effects of erodibility and effects relating drainage area with discharge. Erosion parameters are based on a review by Prosser and Rustomji [2000] and are summarized in Table 1. Feedbacks to the soil erosion model are introduced with respect to vegetation growth and stoniness. The protection by superficial plant cover and subsurface roots is well known. This effect is expressed through a linear coupling with the biological activity index at the soil surface, BAI0. Experimental data linking of stone cover with erosion suggests a negative exponential relation between both [Poesen et al., 1994, 1999]. The corrected erosion fluxes (qcorr) are then:

display math(22)

where kst is a constant, RC is the rock content (%) and qt = qd + qc = the total erosion flux [L2 T−1].

[56] The reported feedback relations between erosion and stone cover used in this model are derived from Poesen et al. [1994]. The approach to distribute the generated sediment over the landscape is similar to the approach by Willgoose et al. [1991]. The soil eroded by diffusive processes is distributed to downslope cells proportional to the height differences between the eroding cell and the different downslope cells. The soil eroded by concentrated flow erosion on the other hand is transported and deposited only in the steepest flow direction. However, in MILESD, a fraction of the eroded soil is also subject to direct export. For each cell, a random number is generated and compared with a critical threshold to decide whether or not to export the generated sediment from the system. As sediment transport capacity is directly proportional to stream power, this threshold is made proportional to stream power, so that areas located along stream lines will be characterized by low sedimentation rates.

[57] Additionally, in MILESD, a component is added to the landscape evolution model to take into account selectivity. The size selectivity of the erosion process will vary depending on (1) the intensity of the erosion event, (2) the size distribution of the eroded material itself, and (3) the relative availability of each size class. High-intensity erosion events with high transport capacity will be less selective and remove nearly all size classes, whereas low-intensity events will mostly remove fine material that is more mobile. Selectivity effects are expressed through a transformation matrix that, multiplied with the original eroded mass fraction vector, results in the final eroded or deposited mass fractions that are corrected for selectivity.

[58] The effect of the event intensity (1) is obtained by relating the overall selectivity coefficient ks to the total erosion quantity through a simple negative exponential relation:

display math(23)

with ks the selectivity coefficient for total erosion, cs1 and cs2 are constants and qt is the total erosion flux per unit width [L2 T−1].

[59] The effect of particle size (2) is expressed by calculating individual selectivity coefficients for each of the five size classes that are considered in the model (k′se,i) as a function of the total selectivity coefficient. These form the diagonal matrix elements for erosion that are then, respectively, calculated as:

display math(24)

[60] Equation ((24)) expresses that in the absence of selectivity (ks = 0), all size classes are eroded equally as k′se,i = 0.2. Under conditions of maximum selectivity, ks = cs1, size class 5 (coarse material) is eroded much faster than size class 1 (fine material).

[61] The final erosion of each size class will also depend on the amount of material that is actually available in each class (3). Therefore, for the final matrix, the selectivity coefficients (k′se,i) are corrected for the relative proportions of the five size classes in the soil (PSi). This correction is expressed as:

display math(25)

with PSi = the actual proportion of each size class i in the soil and ni the number of size classes considered in the model (= 5).

[62] From equation ((25)) it can easily be seen that if a certain size class is not present in the soil, the respective selectivity coefficient will be set to 0. Figure 3 illustrates the process of calculating the elements of the selectivity transformation matrix. Lower erosion, corresponding to higher ks values, will result in higher selectivity. It is also shown how the actual size class distribution of the soil affects the final, corrected selectivity values (kse,i). In Figure 3, an example is shown with the final selectivity coefficients calculated for c = 0.19 and a soil with a particle size distribution of 0.4 (coarse), 0.3 (sand), 0.1 (silt), 0.1 (clay) and 0.1 (fine clay).

Figure 3.

Grain-size selectivity of soil erosion for different values of parameter ks (larger ks values representing lower erosion rates) and correction for the actual grain-size distribution in the soil. k'se,i are the uncorrected selectivity coefficients. The final, corrected selectivity coefficients (kse,i) are shown for a soil with a grain-size distribution for size classes 1 through 5 of (.4,.3,.1,.1,.1) and ks =0.19.

[63] Finally, the model not only tracks the evolution of soil properties but also allows explicit tracking of exported sediment quantity and properties over time.

2.4 Model Application and Validation

[64] The soil formation and landscape evolution model has been run on a test area within the Werrikimbe National Park in NSW, Australia, to illustrate its capabilities. The objective is to evaluate the model results at the point and landscape scale. At the point or pedon scale, the modeled soil profile depth, layering and properties were compared with field data [Stockmann, 2010]. Three points in contrasting geomorphological settings, ranging from stable or steady-state (point 1), over erosive (point 2) to depositional (point 3), were selected to compare the model results with a similar catena from a nearby area, called Plateau Beech [Stockmann, 2010]. The selection of these points was based on several model runs with different erosion intensity. Three different zones were delineated. The steady-state area or stable area is defined here by a change in surface elevation below 0.05 m. The eroding and depositional areas are then defined by a higher surface lowering or raising, respectively. At the landscape scale, we show how regional soil patterns can be modeled and how these change under changing erosion intensity. The model was also used to assess the effect of soil properties on geomorphological processes, by analyzing the sediment export. The digital elevation model of the selected area of 6.25 km2 has a 25 m resolution (Figure 4). The area was selected because it has a wide topographic variability, with altitudes ranging between 707 and 1147 m. At the same time, the area is small enough to ensure that the overall climate and geology is similar. The model was run for an elapsed time of 60,000 years. The soil-formation model was executed with time steps of 100 years, while smaller time steps of 10 years were used for the landscape evolution model to obtain realistic soil redistribution patterns and avoid artificial accumulation of large sediment bodies. The values given to several model parameters are given in Table 1. These values were, where possible derived from existing literature as discussed in the previous paragraph.

Figure 4.

Digital elevation model of the study area in Werrikimbe National Park, New South Wales, Australia. Three points are indicated that represent a typical steady-state, erosive and deposition environment. The selection of these points was based on several model runs with different erosion intensity to identify zones where the surface remained stable (<0.05 m change), lowered or raised.

3 Results and Discussion

3.1 Pedon Scale Soil Profile Variability

[65] The evolution of soil layer thickness with time is shown in Figure 5, for three representative landscape points: a point from a steady-state area, an eroding area and a depositional area. The position of these three points is shown in Figure 4. Finally, observations from soil profiles along a similar, nearby catena are shown to the right. Total soil thickness in the three landscape positions is markedly different. The first point is representative of soil development in the entire area under the absence of erosion. At this steady-state point, the soil profile formed at the end of the simulation period of 60,000 years is nearly stable and changes in profile thickness are slow. However, in contrast with previous models [Minasny and McBratney, 2006], total soil thickness is not entirely stable at the end of the simulation. Previous models only took into account soil conversion from bedrock. Here, chemical weathering processes act in the soil profile. This results in a maximum total soil thickness between 30,000 and 40,000 years (Figure 5a.1). However, as the soil material still becomes finer in the course of the simulation due to physical weathering, chemical weathering losses will increase as well resulting in a slight decrease of soil thickness over time.

Figure 5.

Evolution of the soil profile thickness over 60,000 years under moderate erosion (K = 0.2 × 10−8 yr−1, D = 0. 1 m2 yr−1) at the three representative points shown in Figure 3: (a.1) steady-state, (b.1) erosive and (c.1) deposition, and comparison with observed soil profiles in similar landscape positions (a.2, b.2, c.2).

[66] In the eroding areas, soils are thinner than those in the stable areas and layer thickness is generally more variable. Maximum soil thickness occurs somewhat earlier: between 20,000 and 30,000 years. Toward the end of the simulation it can be seen how the upper soil horizon, layer 1, is almost completely eroded. The main reason for this behavior is that soil particles become finer with time, i.e., they are more easily detached and transported.

[67] As expected, the thickest soils are found in the depositional area. Total soil thickness here is almost double the value of the eroded areas. As the model adds the deposited sediment to the upper horizon, layer 1, this layer subsequently grows the most. However, it can be seen how surface deposition also affects the growth dynamics of the underlying layers.

[68] When compared to the field observations, the model performs well in reproducing the overall trend in total soil thickness along the catena with the shallowest profile on the eroding hillslope (Figure 5b.2) and the deepest soil profile in the valley bottom (Figure 5c.2). The comparison between individual soil layers is more difficult. This is partly due to the limitations of the model approach, but also due to the difficulties to translate the field observations to the three-layer approach of the model. In the field, often more horizons can be distinguished based on color or structure, properties which are not considered in the model.

[69] Figures 6 and 7 show the evolution of the soil properties within the different layers. First of all, it can be seen from Figure 6 that the simplified approach used in this model, where only 5 size class fractions are used, yields a soil texture evolution that is similar to more complex models using 1000 size classes (“1000 box model”) [Pedro and Legros, 1984; Salvador-Blanes et al., 2007]. The textural evolution of the three landscape situations (steady-state, erosion and deposition) again shows significant differences. The deposition point shows the finest soil texture, because fine sediment is constantly added. The erosion point shows the coarsest texture of the three. Here, finer soil particles are constantly removed by soil erosion. Additionally, as layer 1 almost disappears toward the end of the simulation, texture changes become much more erratic toward the end of the simulation.

Figure 6.

Evolution of texture in the three soil layers at the three representative points shown in Figure 3: (a) steady-state, (b) erosive, and (c) deposition. The white diamonds indicate intervals of 10,000 years. The arrow indicates the direction of particle size evolution over time.

Figure 7.

Evolution of the soil profile and its properties over 60,000 years at a steady-state landscape position and comparison with an observed soil profile in a similar landscape setting. SOC is soil organic carbon content and BD is apparent soil bulk density.

[70] The soil profile evolution shown in Figure 7, for the steady-state landscape point, illustrates the evolution of soil properties with more detail. Whilst the thickness of the soil layers does not change much after 30,000 years, it can be seen that the soil properties still evolve. In particular, the clay and fine clay fractions are increasing, with the formation of a second horizon that becomes enriched in clay. Also the organic carbon content increases, especially in the first layer.

[71] In Figure 7 field observations are shown, for the purpose of comparison, on the right hand side. It has to be noted that stone content was not explicitly measured in the field, but was derived from visual observations. The mass fraction of the other size classes was recalculated taking into account the stone fraction of the soil. Also, no fine clay was measured. Overall, the texture of the modeled profile after 60,000 years compares well with the observations. The stone content near the surface is higher than observed, but compares well within the rest of the profile. The predicted increase of coarse fragments in the lower part of the profile is also present in the field data. The model overpredicts sand content and underpredicts silt content, but only by around 10%. Modeled clay content is almost the same as the observed clay content, and the layer of clay illuviation that is observed can also be seen in the modeled profile. Overall, the texture class of the modeled and predicted soil layers is the same, except for the lowermost layer where the model predicts clay loam whereas the observations show clay. As bulk density depends on soil texture through the pedotransfer function, the predicted trend compares well with the observed trend, with errors between 8 and 12%. Soil organic carbon however is problematic. The high values of almost 6% that were observed in the surface horizon in the field are not predicted by the model. Although the lower part of the profile is closer to the observations, future research, based on a more extensive field dataset, will have to focus on calibrating the carbon cycle model or perhaps replace it by a more advanced carbon cycle model such as CENTURY [Parton et al., 1994].

3.2 Regional Scale Soil Profile Variability

[72] The spatial patterns of soil thickness and properties are shown in Figures 8 and 9. Figure 8 shows the total soil thickness after 10,000, 20,000, 30,000, 40,000, 50,000, and 60,000 years. It can be seen how the convex hillslope positions are characterized by shallow, eroded soils. Depositional soils occur in the concave valley bottoms. The maximum soil depth in the upslope areas again occurs around 20,000–30,000 years, as can be seen from Figure 5b.1. However, the overall soil variability is largest at the end of the simulation since the eroded soils are shallower while the depositional areas have gained soil thickness. Figure 9 shows the total carbon content in the soil after 60,000 years. The erosion-deposition pattern marks the regional patterns of carbon distribution. Important storage of carbon takes place in the depositional soils, where carbon is buried at several meters depth. This example shows that the simulated patterns of soil formation follow the general soil–landscape relationship in eroding landscapes [Doetterl et al., 2012]. Dlugoß et al. [2010] found very similar differences in an eroding agricultural landscape in Germany. They found that valley bottom positions were characterized by much higher organic carbon stocks than eroding or stable sites. At these valley bottom sites, the organic carbon content in the surface layers was up to two times that of eroding sites and the difference even amounted up to 20 times in subsurface layers.

Figure 8.

Evolution of total soil thickness in the study area over 60,000 years.

Figure 9.

Total soil organic carbon content in the study area after 60,000 years.

3.3 Effect of Erosion Intensity on Soil Properties

[73] The model allows comparing the influence of various erosion scenarios on soil properties. Figure 10 compares three situations with the same soil formation rates, but in the absence of soil erosion (Figure 10a), under constant, moderate erosion where D = 0.1 m2 yr−1 and K = 0.2 × 10−8 yr−1 (Figure 10b), and finally, in a situation where a period of moderate erosion is followed by a final period of 10,000 years with erosion rates five times higher (Figure 10c). This third scenario mimics the transition of the global climate and the associated change of erosion rates experienced during the Holocene.

Figure 10.

Evolution of regionally averaged soil horizon thickness, total soil thickness and carbon content under constant weathering intensity and (a) no erosion, (b) constant moderate erosion, and (c) variable erosion rate over time with higher erosion intensity during the last 10,000 years of the simulation.

[74] On a regional scale, the overall soil thickness is not too different between the three cases, resulting from the deposition of most of the eroded soil material inside the study area. The effect of erosion (Figures 10a and 10b), is mainly expressed in the mean carbon content. In the presence of soil erosion, the carbon content is lower in upland soils, while it is much higher in the depositional areas because of the burial of carbon-rich sediments. Finally, if the same moderate erosion scenario is followed by a period of higher erosion during the last 10,000 years, the soil responds rapidly (Figure 10c). In upland areas, the first two layers of the soil are eroded. However, in the depositional areas, part of this material is deposited again into the upper layer. This caused an increase in the thickness of layer 1, while the thickness of layer 2 decreases. The main effect however is on the carbon stored in the system which nearly doubles in this short time span: from ca. 12.7 kg m−2 to 19.7 kg m−2. This corresponds to a carbon sequestration rate of 0.7 g m−2 yr−1 averaged over the entire study area. This value is at the lower end of the range reported in the literature. For example, Mcleod et al., 2011] found carbon burial rates between 0.7 and 13.1 g C m−2 yr−1 for temperate forested areas. A carbon sequestration rate of 2.2 g m−2 yr−1 is obtained considering the depositional areas only, which occupy about 30% of the area. Corresponding Holocene carbon sequestration rates from literature are in the same order of magnitude. For example, Hoffmann et al. [2007] reported Holocene carbon sequestration rates for the Rhine floodplain of 3.4 g m−2 yr−1.

3.4 Effect of Soil Formation on Erosion Processes

[75] A comparison of sediment export from the modeled area under different erosion scenarios shows the important impact of soil formation on the erosion cycle (Figure 11). Under moderate erosion (Figure 11a) the production of new soil keeps up with erosion. The result is a stable mean sediment export rate after about 30,000 years. This results in a linear increase of the cumulative sediment export. Note the peak in the annually exported sediment at around 8,000 years, which is probably an artifact of the drainage basin connectivity in combination with the cellular automata approach. Figure 11a also shows how the properties of the exported sediment change throughout the simulation, following important changes in soil profile properties. Such information could become useful for the interpretation of long-term stratigraphic records.

Figure 11.

Cumulative (above) and yearly (below) export of sediment per size fraction and carbon from the study area under constant weathering intensity and two erosion scenarios: (a) moderate and (b) high.

[76] Figure 11b then shows the sediment export under high erosion rates that are five times higher compared to the moderate erosion scenario. The yearly sediment export values clearly show how a breakpoint occurs between 15,000 and 20,000 years. After an initial nearly exponential increase in the produced sediment, the system has been depleted of soil. After this threshold has been crossed, yearly sediment export rates drop drastically. As a result, overall sediment export rates are actually lower than in the previous scenario (Figure 11a).

[77] Such sudden changes have been observed in environments with long-lasting human impact and associated anthropogenic soil erosion. Dusar et al. [2011] reported on sediment archives in the Eastern Mediterranean where changes could be linked to a depletion of the soil reservoir. This has also been observed in other regions. Anselmetti et al. [2007] observed an important increase in sediment influx during the Maya period in a 6000 year long record of lake sediments. However, despite a growing population density, they observed a decrease in erosion intensity after the initial land-use phase, which they attributed to decreasing erodibility of subsurface soil.

3.5 Directions for Future Research

[78] Clearly, the model has limitations, which future work will need to address. A first main concern is that the current version of the model “forces” soil horizon growth. This should be replaced by spontaneous development, possibly even a variable number of horizons. Replacing the cellular-automata based landscape evolution model by more complex erosion and sediment routing processes is another important issue. Alternatively, the model could be coupled with existing state-of-the-art landscape evolution models. Future models should also take into account heat and water fluxes explicitly. Only by doing so, can we incorporate the dependence of all soil forming processes on landscape position. For example, aspect will affect soil temperature and soil water content and therefore influence leaching processes. Finally, accounting for the geological and climatological variability will be necessary before this model can be taken from a conceptual form to practical application.

4 Conclusions

[79] In this paper, we presented a mechanistic soil formation model, MILESD, which provides a first attempt to couple and explore the relation between soil-forming processes and soil redistribution. The model allows the development of soil profiles that are both vertically differentiated and spatially variable. Comparison of model results with field observations along a catena shows that the model accurately predicts the trends in change of soil profile thickness from stable soils on the hill top, over eroding hillslope soils to depositing valley bottom soils. Modeled soil texture and bulk density values are acceptable, although field observations show a much higher organic carbon content than modeled.

[80] At the landscape scale, this model uses an open system approach, allowing export of sediment from the studied area through rivers, which eliminates the limitation of ever-growing soils in previous closed system approaches [Minasny and McBratney, 2006]. When scenarios with varying erosion intensity are compared, the changes in landscape-averaged soil thickness are small. However, the total organic carbon stored in the system responds much more to variations in soil erosion intensity, mainly due to deep burial of organic carbon. It must be noted that this result is conditioned by the depth functions used for carbon production and mineralization. Model calibration with more field data, not only from upland soils but also from deep sediment deposits, is likely to modify these conclusions.

[81] Finally, the model also contributes to our understanding of the interaction between geomorphic systems and externally forcing factors. The consideration of sediment export in MILESD allows exploring the effect of soil formation on sediment that is exported from the system and its properties. It is shown that scenarios with different erosion intensity, representing changing climatic or human forcing, result in a different response depending on the stage of soil development. Of particular interest is the threshold that is associated with soil depth in the study area. When the soil reservoir becomes exhausted, a drastic reduction in sediment export was observed. This illustrates that apart from the traditional climatic and anthropogenic land-use change drivers, it is also important to consider the stage of soil development or degradation. In such situations, the model MILESD could be used to help with the interpretation of complex sediment records.

Acknowledgments

[82] The first author thanks the University of Sydney International Visiting Researcher Fellowship programme and the Ramon and Cajal Fellowship programme of the Ministry of Science and Innovation for making this study possible. The data presented in this paper is funded by the ARC Discovery project How soil grows. Budiman Minasny acknowledges the funding of ARC QEII Fellowship. Alex McBratney acknowledges the support of ARC project Global space-time carbon assessment.We also acknowledge the support of the Australian Research Council. Finally, we thank Alex Densmore, Simon Mudd, Garry Willgoose, and one anonymous reviewer for their helpful comments on an earlier version of this manuscript.

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