a quantitative model for integrating landscape evolution and soil formation

A quantitative model for integrating landscape evolutionand soil formation

T. Vanwalleghem,1 U. Stockmann,2 B. Minasny,2 and Alex B. McBratney2

Received 30 November 2011; revised 29 November 2012; accepted 3 December 2012; published 2 April 2013.

[1] Landscape evolution is closely related to soil formation. Quantitative modeling of thedynamics of soils and landscapes should therefore be integrated. This paper presents amodel, named Model for Integrated Landscape Evolution and Soil Development(MILESD), which describes the interaction between pedogenetic and geomorphicprocesses. This mechanistic model includes the most significant soil formation processes,ranging from weathering to clay translocation, and combines these with the lateralredistribution of soil particles through erosion and deposition. The model is spatiallyexplicit and simulates the vertical variation in soil horizon depth as well as basic soilproperties such as texture and organic matter content. In addition, sediment export and itsproperties are recorded. This model is applied to a 6.25 km2 area in the WerrikimbeNational Park, Australia, simulating soil development over a period of 60,000 years.Comparison with field observations shows how the model accurately predicts trends intotal soil thickness along a catena. Soil texture and bulk density are predicted reasonablywell, with errors of the order of 10%, however, field observations show a much higherorganic carbon content than predicted. At the landscape scale, different scenarios withvarying 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 ofsediment export show a highly nonlinear response to soil development stage and thepresence of a threshold, corresponding to the depletion of the soil reservoir, beyond whichsediment export drops significantly.

Citation: Vanwalleghem, T., U. Stockmann, B. Minasny, and A. B. McBratney (2013), A quantitative model forintegrating landscape evolution and soil formation, J. Geophys. Res. Earth Surf., 118, 331–347, doi:10.1029/2011JF002296.

1. Introduction

[2] The interaction of pedogenetic and geomorphologicalprocesses fundamentally ties soils and landforms togetherat the landscape scale [Hall, 1983]. This notion has beenconceptually present since the early soil-formation models[Jenny, 1941] and is explicitly formalized in the catena con-cept [Milne, 1936]. The catena concept implies that distinctsoil types are associated with different landform elementsand knowledge of one therefore allows prediction of theother [Gerrard, 1992]. Since these early studies, many othershave convincingly corroborated and quantified the empiricalrelation between soil type and landform for different landuses and different geological or climatological settings [Odehet al., 1992;Moore et al., 1993;Gessler et al., 2000]. In spiteof the important interactions between soil formation andlandform evolution, our quantitative understanding has

remained largely limited to a statistical description of thesystem. The reason for this is that quantitative field researchand mechanistic modeling efforts have largely evolved alongseparate lines. This resulted in two separate schools of mech-anistic models: landscape evolution models and soil profilemodels [Minasny et al., 2008].[3] The first school stems from a geomorphologic back-

ground [Ahnert, 1977; Kirkby, 1971; Willgoose et al., 1991]and operates at the landscape scale. Geomorphologic modelsrecognize the difference between transport-limited and de-tachment-limited systems. However, even in the latter sys-tems, erosion is only limited by the rate of the processes,not by the available sediment as detachment thresholds areoften negligible [Tucker and Whipple, 2002]. Geomorphicmodels that do consider soil explicitly often limit it to asingle layer of regolith. The main processes are productionof regolith from bedrock through a weathering functionand horizontal redistribution of this material through soilerosion and deposition processes [Ahnert, 1967; Dietrichet al., 1995; Minasny and McBratney, 1999, 2001, 2006].Some advanced landscape evolution models, such asSIBERIA [Willgoose et al., 1991; Willgoose, 2004], CHILD[Tucker et al., 2001] or ARMOUR [Willgoose and Sharmeen,2006], took into account sediment characteristics, but in spiteof the long timescales on which some of these models oper-ated, no explicit soil forming processes were taken into

1Department of Agronomy, Campus de Rabanales, University ofCordoba, Cordoba, Spain.

2Department of Environmental Sciences, Faculty of Agriculture andEnvironment, University of Sydney, Eveleigh, New South Wales, Australia.

Corresponding author: T. Vanwalleghem, Department of Agronomy,Campus de Rabanales, University of Cordoba, 14010 Cordoba, Spain.([email protected])

©2012. American Geophysical Union. All Rights Reserved.2169-9003/13/2011JF002296

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JOURNAL OF GEOPHYSICAL RESEARCH: EARTH SURFACE, VOL. 118, 331–347, doi:10.1029/2011JF002296, 2013

account. Textural differences could therefore only originatefrom 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 pro-file [Legros and Pedro, 1985; Salvador-Blanes et al., 2007;Finke and Huston, 2008]. This school of models comes frompedology and operates at the point or pedon scale. Whilesome mechanistic models [Finke and Huston, 2008] includedcomplex physical, chemical and biological processes, theyfailed to address one of the most important characteristicsof soils, which is the spatial configuration and connectionbetween individual points. Except for simple, flat areas,important lateral fluxes of water, solutes and soil particlesexist at the landscape scale, which must be taken into accountto accurately model the evolution of soils in a landscapecontext.[5] Some recent models have bridged the gap between

both schools to some extent. Sommer et al. [2008] pro-posed a detailed framework for such integrated modeling,although it is conceptual and yet to be filled in quantita-tively. At present, no model exists that fully integrates soilformation and landscape evolution. The long-term modelmARM [Cohen et al., 2009] focused on surface armoringand bedrock weathering. This allowed Cohen et al. [2009]to analyze the relative importance of both processes for theevolution of grain-size distribution in soils over time. In thesubsequent, spatially explicit model, mARM3D, Cohenet al. [2010] included a full consideration of the verticalsoil profile and spatial coupling. This model marked a greatadvance with respect to previous soil-landscape models asit accounted for bedrock weathering and physical weather-ing, although it did not yet account for other soil-formingprocesses, such as chemical weathering or bioturbation.The same applies for the interdisciplinary model proposedby Nicotina et al. [2011], who fully integrated surface hy-drology into their model and obtained good results for pre-dicting soil formation, but only considered a single layer ofregolith. In turn, detailed geochemical soil formation models,such as LEACH-C [Finke and Huston, 2008], in theoryallowed surface additions and removals of soil. In practicehowever, LEACH-C was point based and therefore used anindependent input which needed to be derived from a differ-ent erosion model. Even with these additions or removals,this model would not result in a coupled soil-landscape evo-lution, unless the soil variables were also fed back into theerosion model.[6] Given the complexity of the different processes and

interactions that are involved, quantitative modeling is cru-cial to improve our understanding of the soil-landscapesystem. Such models could have a large impact on ourunderstanding of feedbacks between climate change andecosystems. Soil physical properties such as texture and soildepth are important inputs in vegetation models and hydro-logical models. Any long-term modeling effort of climatechange therefore needs to take into account the effect ofdynamic soils. For example, over the Holocene, the roleof anthropogenic soil erosion on the carbon cycle is thesubject of a controversial debate [Kuhn et al., 2009]. Apartfrom the direct effect through erosion and burial of car-bon-rich sediment, this debate also needs to take into ac-count the effect that changing soil properties, such asdepth or stoniness, could have on the potential distribution

of natural vegetation. Collins et al., 2010] showed how soildepth changes led to biome shifts in Mediterranean ecosys-tems. Another area of interest for quantitative modeling ofsoil 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 keysoil properties. As such, these models are inherently linkedto the conditions for which they have been developed andextrapolation is difficult. Also, in regions where limited dataon soil properties is available to establish statistically mean-ingful relations, a mechanistic model of the underlying ped-ogenetic and geomorphological processes could provide auseful alternative to predict soil thickness and soil properties.Finally, the relation between geomorphological processesand environmental change cannot be fully understood with-out considering soils. In their review of sediment dynamicsin the Eastern Mediterranean, an area with a long historyof land use and anthropogenic soil erosion, Dusar et al.[2011] found a clear signal in the sediment record that soilprofiles were depleted during the late Holocene. In theabsence of field data on soils, they could have easily attrib-uted the observed changes to apparent changes in climaticconditions.[7] In the light of this need for an integrated model, this

paper therefore aims to present a holistic soil-landscape evo-lution model that integrates a pedon-scale soil formationmodel with a regional-scale landscape evolution model.[8] The model capabilities are described in a landscape-

scale simulation including both vertical and horizontal redis-tribution processes. We show how soil erosion influencessoil profile depth and layering and to what extent the mainsoil properties, such as texture, stoniness and soil organiccarbon content are affected. The effect of soil developmenton sediment dynamics is also evaluated by comparing thesediment fluxes and properties generated under different ero-sion 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 mod-els for soil redistribution by Minasny and McBratney[1999, 2001] and the pedon-scale soil formation model bySalvador-Blanes et al. [2007].[10] However, MILESD differs from the previous models

as the soil is partitioned in four layers, three soil layers orhorizons and a bedrock layer. The subdivision of the regolithin three layers is justified from a pedological perspective.Johnson [1994] traced back the origin of this three-layer ap-proach to the early work of Dokuchaev and showed how itcan be applied to typical soils ranging from the mid latitudesto the tropics. The model is mass balance based and changesin soil thickness over time depend on (1) the production ofsoil material from bedrock through weathering; (2) changesin soil properties through soil formation processes as wellas (3) erosion and deposition. An overview of the modelstructure is shown in Figure 1.[11] Soil formation processes include physical and chemi-

cal weathering, neoformation of clays, clay translocationand biological mixing processes. By considering only thesolid phase, the complexity of soil formation processes is

VANWALLEGHEM ET AL.: MODELLING LANDSCAPE AND SOIL FORMATION

332

necessarily simplified in this model. While the explicit con-sideration of the liquid phase offers obvious advantages formodeling geochemical processes in detail [Samouëlian andCornu, 2008], the current state-of-the-art justifies our simpli-fied approach, as knowledge of many basic soil forming pro-cesses is absent [Yoo and Mudd, 2008].[12] Five size fraction classes are considered: coarse

(2� 10�3 – 10� 10�3m), sand (50� 10�6 – 2� 10�3m),silt (2� 10�6 – 50� 10�6), clay (1� 10�7 – 2� 10�6) andfine clay (<1� 10�7m). The limits are derived from theUSDA classification [Soil Survey Staff, 1993], with an addi-tional coarse fraction class and an additional class of fineclay. The latter is added because of its potential importancein clay translocation processes [e.g., Van Wambeke, 1976].The first size class (coarse fraction) is added so that each pri-mary mineral particle is first released into the coarse fractionsize class. This equates to the hypothesis that soil formationstarts from a layer of saprolite containing fractured rock.Soil-formation processes acting on these coarse particles willthen move them to the other size fraction classes.[13] To optimize computing efficiency, a matrix model

approach with dynamical transition matrices is used forcalculating the change in soil properties at each time step.Dynamical transition matrices have been used relativelylittle in soil science with respect to other disciplines such asecology [Lin et al., 1996]; examples in earth sciences aregiven by Shull [2001] for modeling bioturbation or by Cohenet al. [2009] for their armoring and weathering model. In thismatrix-model approach, the size class distribution of eachlayer j at time t is expressed by a vector Sjt and the transitionbetween states induced by the different soil formation pro-cesses 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 marginaltransition matrix Mjt.

Stþ1 ¼ AjtSt ¼ IþMjt

� �St (1)

with

Mjt ¼

aj1t bj2t ⋯ ⋯ ej5taj2t ⋯ ⋯ ⋯

aj3t ⋯ ⋯aj4t bj5t

aj5t

266664

377775:

[15] Each soil forming process will be characterized by acharacteristic transition matrix. The elements of this transi-tion matrix are continuously updated during the period ofsimulation 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 fromthe surface, due to the self-limiting nature of many pedogenicprocesses [Torrent and Nettleton, 1978;Muhs, 1984]. Exper-imental data from cosmogenic nuclide dating support eithera 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 [Humphreysand Wilkinson, 2007]. In this model, we adopted the expo-nential function as it provides the best fit to the majority ofpublicly available data [e.g., Heimsath et al., 2000, 2001,2006]. The conversion rate of bedrock material into soil reg-olith as a function of time (t) is then given by:

@h

@t¼ �p1e

�b1hð Þ (2)

where h is the total soil thickness, p1 is the potential bedrockweathering rate [L T�1] and b1 [L�1] is an empirical rateconstant. The bedrock weathering rate used in the model isderived from Heimsath et al. [2000] for a study area inAustralia.2.2.2. Physical Weathering[17] Physical weathering is the process by which minerals

or rock are disintegrated into smaller pieces by mechanicalprocesses such expansion and contraction due to temperaturevariation, wedging by ice, salt or plants. Field or laboratorystudies that quantify the change in particle size distributionover time during the fragmentation process are rare [Wellset al., 2007]. As in the Salvador-Blanes et al. [2007] model,fragmentation rates in MILESD are a simple function oftwo variables: particle size and depth below the surface.First, the rate of fragmentation will increase with particlesize, as the probability for occurrence of imperfections lead-ing to fragmentation increases. Secondly, fragmentation ismainly a temperature-driven process and therefore increaseswith increasing temperature amplitude. Soil depth is a goodproxy for this variable, since it is well known that the ampli-tude of temperature variations decreases exponentially withdepth [van Wijk, 1963]. However, whereas the Salvador-Blanes et al. [2007] model uses a detailed 1000 size classesapproach developed by Legros and Pedro [1985], MILESD

Chemical weathering

Physical weathering

Input parameters (Table1)

Bedrock lowering

Carbon cycle

Neoformation of clays

Clay translocation

Bioturbation

SOIL FORMATION MODULE(time step = 100 years)

Horizon 1 and 2 lowering

*

*

*

*

*

*

* recalculate bulkdensity, update layerthickness and DEM

Calculate selectivity

Correct for BAI and stoniness

Calculate total erosion

Redistribute soil

Export sediment onborders and where critical

threshold is exceeded

EROSION MODULE(time step = 10 years)

*

time = multiple of 100years?

NO: repeat erosion

module

YES: execute soil

formation module

*

Input conditions: DEM*, CTI,Upstream Area

Figure 1. Schematic representation of the model structure.


333

uses a more simplified approach with only 5 size fractionsand does not consider mineralogy. Following the classifica-tion by Wells et al. [2008], our model is an asymmetricalmodel where the fragmented material is redistributed overtwo smaller size fraction classes of different size. Wellset al. [2008] found that the asymmetric fragmentation model,such as the one used here, provided a good fit of their exper-imental data, similar to that of symmetric models, althoughthey did not report any improvement when using variablefragmentation rates. Because MILESD builds on theSalvador-Blanes et al. [2007] model, the asymmetric modelwas chosen over the symmetric one. The proportion of eachof the daughter size classes is calculated as being directlyproportional to the size limits of each class. One mass unitof coarse fragments will thus break up into 0.975 units ofsand and 0.025 units silt. One mass unit of sand will breakup into 0.96 units of silt and 0.04 units of clay. Based onfield evidence, it is assumed that no fine clay is formedthrough physical weathering, so all fragmented silt is con-verted to clay. Smeck et al. [1981] and Chittleborough et al.[1984] indicated that the fine clay fraction is mainly formedby chemical weathering of clay and silt, rather than physicaldisintegration processes.[18] The diagonal elements of the marginal transition

matrix, ajit, defining the change in particle size distributionat each time step in a specific layer j, are then given by:

ajit ¼ �k1e�c1Djð Þ c2

Iog PDið ÞΔt (3)

where i is the particle size class (1 to 5), k1 the rate con-stant of physical weathering [T�1], Dj the depth below thesoil surface of layer j [L], c1 the depth rate constant forphysical 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-Blaneset al. [2007]. The latter used values between 0.6� 10�4

and 8� 10�4 yr�1, depending on the size class and the min-eralogy, where a single value of 10�4 yr�1 is used here(Table 1). Salvador-Blanes et al. [2007] explored the ef-fect of different physical and chemical rate constants onthe evolution of particle size in more detail. The valuesadopted here were selected so that the particle size evolu-tion corresponds to their “base scenario.”[20] For each soil layer, the physical fragmentation pro-

cess is depth-integrated between the top and the bottom ofthe layer.2.2.3. Chemical Weathering[21] Chemical weathering is the process by which min-

eral particles are dissolved, oxidized, or reduced. Chemicalweathering rates are complex functions of material proper-ties and site characteristics, such as runoff and lithology,temperature, vegetative cover, tectonics and therefore expo-sure and elevation [Gislason et al., 1996]. Commonly, dis-crepancies of up to 5 orders of magnitude between field andlaboratory rates of chemical weathering have been inferred.The discrepancy has been mostly attributed to the error inestimation of the surface area in the field, differences insolution chemistry, temperature differences, heterogeneousdistribution (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 var-iation of chemical weathering with depth is inherently complex.Gradients in solution parameters such as temperature, pH, dis-solved Al, and H2CO3 influence reaction kinetics, while gradi-ents in hydraulic conductivity, controlled by porosity, pore size,and water content, affect transport. On the other hand, the fluidis likely most reactive and the soil most permeable near the topof the reactor, while the minerals most prone to weathering areusually 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 fullcomplexity associated with chemical weathering. A simplemodel is proposed that relates chemical weathering intensitylinearly to surface area and exponentially to depth belowthe surface. Depth below the soil surface relates mainly tovariations in soil temperature and soil moisture. However,only the latter will result in vertical variations of chemicalweathering rates. De Vries [1963] showed how diurnal oryearly soil temperature variations are well represented bya sine wave. Therefore, while the amplitude of soil temper-ature variations declines with depth, average soil tempera-ture is constant with depth. This implies that chemical rateconstants, for example as determined using the Arrheniusequation, are higher near the surface than deeper in the soilduring warm periods. However, during subsequent coldperiods, reaction constants drop much more near the surfacethan deeper where these temperature variations are buffered.As a result, the long-term average reaction constants forchemical weathering processes at different depths should beequal. This is clearly in contradiction with field observationsof nonlinear weathering profiles with depth [Anderson et al.,2002;White et al., 2009].White et al. [2009] showed in theirstudy of marine terraces how weathering rates become trans-port-limited and dependent on the hydrological flux whenpore water approaches thermodynamic saturation. Therefore,we assume that the depth proxy we use in MILESD expressessoil moisture variations, which in turn control chemicalweathering fluxes. An exponential decline function withdepth is a good approximation of soil moisture variability[Amenu et al., 2005]. This variable depends on the balancebetween infiltration, percolation and evapotranspiration.The variability of evapotranspiration with depth is influencedby the plant root distribution, which is well approximated byan exponential decline function [Li et al., 1999]. In addition,Choi et al. [2007] proposed an exponential decline functionfor saturated hydraulic conductivity, which controls infiltrationand percolation, to express the effect of macropores near thesurface. As Jin et al. [2011] indicated, density of macroporesplays 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, ajit0, defining the mass loss for each particle sizeclass i due to chemical weathering at each time step, fora specific layer j, is then given by:

ajit0 ¼ �k2e

�c3Djð Þ c4SAið ÞΔt (4)

where k2 is the chemical weathering rate constant [ML�2 T�1],c3 the depth rate constant for chemical weathering [L�1], Dj


334

the depth below the soil surface of layer j [L], c4 the specificarea constant for chemical weathering and SAi the specific sur-face area of mineral particles within size class i of layer j[L2M�1]. Chemical weathering rates used in this model are inthe range of values used by Salvador-Blanes et al. [2007].

[25] Determining the specific area of a mineral is notstraightforward [Salvador-Blanes et al., 2007]. Therefore,the specific surface area of the different size fraction classesis defined (see Table 1), rather than calculated. This impliesthat additional complexity deriving from changing surface

Table 1. Input Parameter Values Used in the Simulations

Parameter Value Explanation Units Referencea Equation

Bedrock and Horizon Loweringp1 0.000053 potential bedrock weathering rate m yr�1 Heimsath et al. [2000] (2)b1 2 empirical bedrock weathering rate constant m�1 (2)kh10 0.00001 rate constant for lowering of layer 1 myr�1 (16)kh11 -0.01 constant relating lowering of

layer 1 with carbon content- (16)

kh20 0.00002 rate constant for lowering of layer 2 myr�1 (17)kh21 -0.01 constant relating lowering of

layer 2 with coarse fraction- (17)

Physical Weatheringk1 0.0001 physical weathering rate constant yr�1 Salvador-Blanes et al. [2007] (3)c1 -0.5 depth constant for physical weathering m�1 (3)c2 5 size constant for physical weathering m (3)Chemical Weatheringk2 70 chemical weathering rate constant kgm�2 mineral yr�1 Salvador-Blanes et al. [2007] (4)c3 -2.5 depth rate constant for chemical weathering m�1 (4)c4 1 specific surface area constant for

chemical weathering- (4)

SA1 10 specific surface area fraction 1 (coarse) m2 kg�1 (4)SA2 100 specific surface area fraction 2 (sand) m2 kg�1 (4)SA3 1000 specific surface area fraction 3 (silt) m2 kg�1 (4)SA4 50000 specific surface area fraction 4 (clay) m2 kg�1 (4)SA5 100000 specific surface area fraction 5 (fine clay) m2 kg�1 (4)Neoformationcnf 0.5 neoformation constant - (7)c5 1.2 constant for relation clay neoformation

with depthm�1 (7)

c6 20 constant for relation clay neoformationwith depth

m�1 (7)

Clay TranslocationCmax 0.007 base rate of clay translocation kg Alexandrovskiy [2007] (8)kcl 200 constant for relation of clay translocation

with depth- (8)

BioturbationBT01 6 maximum bioturbation rate from layer 2 to 1 kg yr�1 Muller-Leemans and

Van Dorp [1996](10)

BT02 3 maximum bioturbation rate from layer 1 to 2 kg yr�1 (10)kbt1 2.5 constant for relation of bioturbation with

layer thicknessm�1 (10)

kbt2 2.5 constant for relation of bioturbation with BAI - (10)kBAI 2.5 constant for relation of bioturbation with depth m�1 (9)Carbon CyclingC0

in 1.5 base rate carbon production kg yr�1 MODIS-derived (Atlas ofLiving Australia, 2012, online)

(13)

kOC 4 constant for relation carbon productionwith depth

m�1 Minasny et al. [2008] (12)

kc1 0.01 fast carbon decomposition rate constant yr�1 (14)kc2 0.00005 slow carbon decomposition rate constant yr�1 (14)c7 0.1 constant for relation carbon decomposition

with wetness index- (15)

c8 2 constant for relation carbon decompositionwith depth

m�1 (15)

f 0.8 fraction fast-slow carbon decomposition pool - (14)Bulk DensityBDrock 2700 bedrock bulk density kgm�3 (20)ErosionD 0.1b diffusivity constant m2 yr�1 Prosser and Rustomji [2000] (20)K 0.2� 10�8b concentrated flow erodibility constant yr�1 (21)m 1.67 constant for relation concentrated flow - area - (21)n 1.3 constant for relation concentrated flow - slope - (21)kst 0.032 constant relating erosion and rock

fragment content- (22)

aPlease see text for details, in some cases the referenced sources served as a basis to derive the parameters cited.bThese are the values for the “moderate” erosion scenario. Values for the high erosion scenario are 5 times higher.


335

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 reactivesites 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 mate-rial will form new minerals (see neoformation), but chemicalweathering will also affect particle size indirectly as masslosses result in smaller particles. To calculate the mass ofparticles falling into a finer size class due to this process,particles are again approximated by spheres. The dimension-less term F expressing this mass loss can then be calcu-lated as:

F ¼ R3iþ1

R3i � Riþ1

3(5)

with Ri the mean radius of the particles in the original sizeclass i and Ri+1 the mean radius of the particles in the finalsize class i + 1.[27] The final marginal transition matrix Mjt is then

obtained by correcting the previously calculated one (Mjt0)

with this additional loss term:

Mjt ¼ � Iþ Fð ÞMjt0

(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 than1� 10�6m. The total amount available to neoformation isassumed to be directly related to the amount of chemicalweathering in the entire soil profile. It is difficult to assessthe relative importance of clay eluviation/illuviation versusclay neoformation, but there is definitely field evidence that

shows the latter to be an important process in some environ-ments. White et al. [2009] showed that argillic horizonscould be explained by in situ clay formation in a series ofmarine terrace soils. To derive quantitative information onclay formation rates from the clay content in soil profiles isnot straightforward as the original clay content and claytranslocation processes need to be accounted for, as dis-cussed in detail by Barshad [1957]. Empirical evidence sug-gests that the rate of secondary clay formation is highest atsome depth below the surface, often assumed to be between0.05 and 0.25m [Barshad, 1957]. Therefore, neoformationof clay was modeled as a double exponential function ofdepth below the soil surface. The marginal transition matrixis therefore 0, except for the diagonal element correspondingto the fine clay fraction (size class 5), aj5:

aj5 ¼ cnf e �c5dð Þ � e �c6dð Þ� �h i

Mcw (7)

where cnf, c5, c6 are constants, d is the depth below soil sur-face [L] and Mcw is the total mass lost by chemical weather-ing in all soil layers [M].[29] Constant cnf will determine the potential or maximum

neoformation rate, while c5 and c6 control the shape of therelation with depth (see Figure 2).[30] Maher et al. [2009] used a multicomponent reactive

transport model to simulate the formation of secondary claysin marine terraces, taking into account the full complexity ofsoil chemistry. Their results confirmed that the neoformationrate is highest at some depth below the surface, as repre-sented by equation (7), but also evidenced that neoformationrates change over time as mineral composition changes. Atthis point, our simplified model does not include this time-dependent behavior.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 anddata on clay migration rates are scarce. Legros [1982]attempted to model illuviation and eluviation processesbased on a simple procedure whereby a given quantity ofclay is eluviated or illuviated at each time step. MILESDfollows a similar approach, where clay lessivage is expressedas a flux from the superficial layer 1 to the underlyinglayer 2, only that the rate of lessivage increases up to amaximum value in function of the fine clay content inlayer 1.

ΔC ¼ Cmax 1� e �kclPfcð Þh iΔt (8)

where ΔC is the amount of fine clay eluviated at each timestep [M], Cmax the maximum amount of clay that can beeluviated per time step [MT�1], kcl a constant and Pfcthe fine clay content in layer 1 (%). An estimate of claytranslocation was made based on data of Luvisol genesisby 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, numer-ous studies have followed and thanks to the attention fromvarious research areas, such as ecology, pedology, geologyand archaeology [Lee, 1985; Canti, 2003; Gabet et al.,

Figure 2. Relative rate of clay neoformation with depth, asa function of different coefficients selected in equation (7).Clay neoformation is calculated relative to the chemicallyweathered fraction.


336

2003], soil turnover rates by burrowing animals, plant root-ing and tree throw are now much better known [Roeringet al., 2002; Kaste et al., 2007]. Nevertheless, a lack of in-sight into the different controlling processes makes model-ing bioturbation processes still a difficult task.[33] A simple approach is proposed here because at

present, to our knowledge, there is no published quantita-tive model available for soil bioturbation. In MILESD,bioturbation causes mixing of each of the three layersrepresenting the soil column and results in fluxes betweenthe three layers. The mixing of the material within eachindividual soil layer supports the model assumption wheresoil 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 carbonfluxes were calculated between individual soil layers. How-ever, in the latter model mixing velocities were calculateddirectly based on the soil profile’s 210Pb inventory. InMILESD, the fluxes are calculated as being proportional tothe biological activity of the layer receiving the materialand inversely proportional to the distance between layers.[34] Biological activity is expressed here through a biolog-

ical activity index (BAI). This index is based on the soil pro-ductivity function as defined by Salvador-Blanes et al.[2007] andMinasny et al. [2008] and varies according to soilthickness, soil carbon content and depth in the profile:

BAI ¼ BAI0e�kBAI dð Þ (9)

where BAI0 is the potential or maximum biological activity =BAI0 = fs1(h)fs2(OC), htotal the total soil thickness, OC therelative carbon content of the soil layer (OC, %), fs1 andfs2 are sigmoid functions of the form c0

c0þ 1�c0ð Þ exp �c1Xð Þwith c0 and c1 constants and X either h or OC, kBAI is aproportionality constant, and d is the depth below the soilsurface [L].[35] The biological activity index of each layer j, BAIj, is

then calculated for each soil layer by integrating this func-tion between the upper and lower boundary of each layer.BAI0, the maximum biological activity, is reached at the sur-face. Biological activity then drops exponentially withdepth, which is supported by experimental data of earth-worm activity [Canti, 2003]. Depending on the soil climaticconditions however, other depth-dependent functions couldbe considered. Yoo et al. [2011] for example determinedfor a Delaware forest soil profile that the highest biologicalactivity did not occur at the surface but at some depth belowthe surface because of adverse surface conditions. Addition-ally, in the model, there is a feedback between depth andthickness of the different layers on its total biological activityindex. For example, as the superficial layer 1 grows, its bio-logical activity index increases. However, layers 2 and 3,even at a constant thickness, will be deeper below the surfaceand their biological activity index drops. At this moment, noexperimental data are available that allow a detailed quanti-fication of selectivity in bioturbation processes. Selectivityof the bioturbation process is therefore modeled as a binaryprocess: coarse fragments are not moved, while all other sizeclasses are moved in the same proportion by biota. Evidencefor 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 pro-duce a stone-free upper horizon. Later, many others reportedevidence for this selective transport in soils from widelydifferent areas [Webster, 1965; Soil Survey Staff, 1975;Johnson, 1989; Johnson et al., 2005], but that all show aclear separation between an upper, biologically active layerof fine material, also often called the biomantle, and anunderlying stone layer.[36] The movement of soil between two layers due to

bioturbation can then be expressed as:

ΔBTij ¼ BT0j 1� e �kbt1dijð Þh i1� e �kbt2BAIjð Þh i

Δt (10)

where ΔBTij is the soil material moved from layer i to j [M],BT0j the maximum bioturbation rate for layer j [MT�1], kbt1a distance constant [L�1], kbt2 a biological activity constant,dij the distance between center of layer i and j [L], BAIj thebiological 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 reviewfrom Muller-Leemans and van Dorp [1996]).2.2.7. Carbon Cycle[38] The carbon component of the model includes pro-

duction (Ij), decomposition (kcCj), mixing (qm,j) and losses(qc,j), similar to the model by Yoo et al. [2006] andMinasny et al. [2008]. The evolution of the organic carboncontent (Cj, [M]) for each layer j through time can there-fore be expressed as:

@Cj

@t¼ Ij � kcCj þ qm;j � qc;j (11)

[39] The mixing term, qm, is handled explicitly by the bio-turbation component of the model (see previous paragraph).Carbon can be transferred from one layer to the other by bio-turbation. The carbon loss term, qc, is explicitly accountedfor through the erosion component of the model (see below).After calculating the amount of soil moved by both biotur-bation and erosion, carbon is then moved together with thesoil. Soil carbon is assumed to be associated with thefine fraction of the soil (sand to fine clay). In this way,the erosion and bioturbation processes are also selectivewith 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 soillayer, Ij, is determined by the base rate of carbon productionCin [MT�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 onthe 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 foran infinitesimal layer of thickness @z equals:

@Iz ¼ Cine�kOCdð Þ@z (12)

Cin ¼ C0infs1 thickð Þfs2 OCð Þ (13)

where fs1 and fs2 are two sigmoid functions. C’in is the baserate or potential carbon production [MT�1], which can bederived from measurements of Net Primary Productivity.


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[41] To obtain the total carbon production for each layer j,Iz, equation (12) is integrated between the top and bottomboundary of that layer.[42] The carbon production at the soil surface is made

spatially variable through a sigmoid function of total soilthickness and organic carbon content present in the soil,suggesting a feedback of both variables on carbon produc-tion rates [Minasny et al., 2008]. The value for C0

in inequation (13) is taken as the MODIS-derived mean annualnet 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]. Inthis two-pool system, the decomposition constant kc fromequation (11) can therefore be defined as:

k0c ¼ fkc1 þ 1� fð Þkc2 (14)

where f is the fraction of the first pool, kc1 and kc2 are thedecomposition rates of each of the pools. Both slow andfast decomposition are made horizontally and verticallyvariable, based on differences in soil depth and wetness in-dex, reflecting decreasing decomposition rates with depthand increasing wetness.

kc ¼ k0c e c7CTIð Þe c8dð Þh i

(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 timestep.[45] Parameters for carbon cycling are derived from

Minasny et al. [2008] who calibrated their model with localsoil 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 controlthe lowering of the boundaries between the first three layers.In the absence of experimental data, it is assumed in themodel that the self-limiting nature of pedogenic processesresults in rates of boundary lowering that are variable overtime and depend on certain soil properties, in a similar wayas the weathering front is controlled by the overlying totalsoil depth. The set of rules that was selected is related to thethree-layer concept that is common in pedology [Johnson,1994]. The first layer or A horizon represents a organic-richlayer. The second layer or B horizon is a transitional zoneto the C material, the parent rock. Therefore, the criteria weselected for horizon growth are organic carbon content andcoarse fragment content, respectively. The evolution of theboundary between the surface layer, layer 1, and the underly-ing layer 2, is set as a negative exponential function of thedifference in organic carbon content between both layers(ΔOC).

@h1@t

¼ �kh10ekh11ΔOCð Þ (16)

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

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

@h2@t

¼ �kh20ekh21ΔCð Þ (17)

where h2 is the thickness of layer 2 [L], kh20 and kh21 arerate constants.[48] Equations (16) and (17) imply that the rate of growth

of each layer will depend on the relative difference in organiccarbon or coarse fragment content with the layer below. Aslong as layer properties are significantly different, growthwill be slow. When layer properties are similar, growth willbe faster. The process is self limiting in the sense that horizongrowth implies addition of material from the underlyinglayer. As the intensity of weathering, biological processesand carbon production decrease with depth, increasingly dif-ferent material will be added at each step, hereby increasingthe difference in organic carbon content and coarse frag-ments 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, thatis, to avoid that any given layer disappears.2.2.9. Evolution of Bulk Density and Strain[50] To link soil profile development with landscape devel-

opment, it is crucial to convert the mass changes in soil prop-erties through soil-forming processes, especially size-classdistribution, to volumetric changes as elevation is a keydriver of erosion and deposition processes. It is well-knownthat bedrock and soil material undergoes strain through itsweathering phase [Brimhall and Dietrich, 1987]. Here, apedotransfer function, derived from experimental data byTranter et al. [2007], is used to calculate the bulk densityof each layer j (BD0

j):

BD0j ¼ 1:35þ 0:452 sand þ 0:76siltð Þ

þ �0:0000614 sand þ 0:76siltð Þ � 44:65ð Þ½ � (18)

[51] Note that with respect to the original pedotransferfunction used by Tranter et al. [2007], no depth factor isincluded in equation (19) to simplify and accelerate calcu-lations. This introduces a small error for thin layers closeto the surface, but generally does not affect the results sig-nificantly. More important is the effect of rock fragmentson bulk density calculation. Therefore, bulk density iscorrected for coarse fragment content (rock) according toVincent and Chadwick [1994]. The bulk density of layer j,corrected for rock fragments is then:

BDj ¼ Msoil

Mfine

BD0j

þ MrockBDrock

� � ð19Þ

with Mfine and Mrock the mass of fine (<2� 10�3m) and

coarse material (>2� 10�3m), respectively. Msoil is thesum of both and BDrock is the bulk density of the rock frag-ments in the soil matrix.

2.3. Landscape Evolution

[52] After the soil-formation model has acted on all pedonsin the landscape, the soil is redistributed by erosion and


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deposition (see Figure 1). It has to be noted that this is asimplification, as material produced by weathering and soilformation is in reality immediately available for erosion. Inthis model, the newly produced soil goes through a seriesof soil-forming processes during which its properties areadapted, before it becomes available for transport (seeTable 1). Phillips [1995] discussed the potential implica-tions of such a time lag. The model is topography-drivenand a local cellular automata approach is used, whereby eachcell is visited randomly. To avoid a full depletion of the soilcolumn, the deepest soil layer, layer 3, is not subject to ero-sion. Once the erosion amount and direction of flow has beencalculated for each cell, all deposited sediments are addedto 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 processesare modeled as the sum of diffusive and concentrated flowprocesses. Only erosion processes that have an effect onsurface elevation are considered here.[53] The first is commonly termed the diffusion equation

and represents a series of processes such as mass wastingor nonconcentrated water erosion:

qd ¼ DS (20)

where qd is the erosion flux per unit width by diffusivetransport [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:

qc ¼ KAmSn (21)

where qc is the erosion flux per unit width by concentratedflow [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]. Theerodibility constant encompasses both effects of erodibilityand effects relating drainage area with discharge. Erosionparameters are based on a review by Prosser and Rustomji[2000] and are summarized in Table 1. Feedbacks to thesoil erosion model are introduced with respect to vegeta-tion growth and stoniness. The protection by superficialplant cover and subsurface roots is well known. Thiseffect is expressed through a linear coupling with thebiological activity index at the soil surface, BAI0. Experi-mental data linking of stone cover with erosion suggestsa negative exponential relation between both [Poesenet al., 1994, 1999]. The corrected erosion fluxes (qcorr)are then:

qcorr ¼ 1� 0:5BAI0ð Þe�kstRCqt (22)

where kst is a constant, RC is the rock content (%) andqt = 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 Poesenet al. [1994]. The approach to distribute the generated sedi-ment over the landscape is similar to the approach by

Willgoose et al. [1991]. The soil eroded by diffusive pro-cesses is distributed to downslope cells proportional to theheight differences between the eroding cell and the differ-ent downslope cells. The soil eroded by concentrated flowerosion on the other hand is transported and depositedonly in the steepest flow direction. However, in MILESD,a fraction of the eroded soil is also subject to direct ex-port. For each cell, a random number is generated andcompared with a critical threshold to decide whether ornot to export the generated sediment from the system.As sediment transport capacity is directly proportional tostream power, this threshold is made proportional tostream power, so that areas located along stream lines willbe characterized by low sedimentation rates.[57] Additionally, in MILESD, a component is added to

the landscape evolution model to take into account selectiv-ity. The size selectivity of the erosion process will varydepending on (1) the intensity of the erosion event, (2) thesize distribution of the eroded material itself, and (3) the rel-ative availability of each size class. High-intensity erosionevents with high transport capacity will be less selectiveand remove nearly all size classes, whereas low-intensityevents will mostly remove fine material that is more mobile.Selectivity effects are expressed through a transformationmatrix that, multiplied with the original eroded mass fractionvector, results in the final eroded or deposited mass fractionsthat are corrected for selectivity.[58] The effect of the event intensity (1) is obtained by re-

lating the overall selectivity coefficient ks to the total erosionquantity through a simple negative exponential relation:

ks ¼ cs1e1�cs2qtð Þ (23)

with ks the selectivity coefficient for total erosion, cs1 and cs2are constants and qt is the total erosion flux per unit width[L2 T�1].[59] The effect of particle size (2) is expressed by calculat-

ing individual selectivity coefficients for each of the five sizeclasses that are considered in the model (k0se,i) as a functionof the total selectivity coefficient. These form the diagonalmatrix elements for erosion that are then, respectively, calcu-lated as:

k0se;i ¼

ks2iþ 0; 2� 3

2ks

� �(24)

[60] Equation (24) expresses that in the absence of se-lectivity (ks = 0), all size classes are eroded equally ask0se,i = 0.2. Under conditions of maximum selectivity, ks = cs1,size class 5 (coarse material) is eroded much faster than sizeclass 1 (fine material).[61] The final erosion of each size class will also depend

on the amount of material that is actually available in eachclass (3). Therefore, for the final matrix, the selectivity coef-ficients (k0se,i) are corrected for the relative proportions ofthe five size classes in the soil (PSi). This correction isexpressed as:

kse;i ¼PSi1=ni * k

0se;iX PSi

1=ni* k

0se;i

� �i

(25)


339

with PSi = the actual proportion of each size class i in thesoil and ni the number of size classes considered in themodel (= 5).[62] From equation (25) it can easily be seen that if a

certain size class is not present in the soil, the respectiveselectivity coefficient will be set to 0. Figure 3 illustratesthe process of calculating the elements of the selectivitytransformation matrix. Lower erosion, corresponding tohigher ks values, will result in higher selectivity. It is alsoshown how the actual size class distribution of the soil affectsthe final, corrected selectivity values (kse,i). In Figure 3, anexample is shown with the final selectivity coefficients cal-culated for c = 0.19 and a soil with a particle size distributionof 0.4 (coarse), 0.3 (sand), 0.1 (silt), 0.1 (clay) and 0.1 (fineclay).[63] Finally, the model not only tracks the evolution of

soil properties but also allows explicit tracking of exportedsediment quantity and properties over time.

2.4. Model Application and Validation

[64] The soil formation and landscape evolution modelhas been run on a test area within the Werrikimbe NationalPark in NSW, Australia, to illustrate its capabilities. Theobjective is to evaluate the model results at the point andlandscape scale. At the point or pedon scale, the modeled soilprofile depth, layering and properties were compared withfield data [Stockmann, 2010]. Three points in contrastinggeomorphological settings, ranging from stable or steady-state(point 1), over erosive (point 2) to depositional (point 3), wereselected to compare the model results with a similar catenafrom 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 weredelineated. The steady-state area or stable area is defined hereby a change in surface elevation below 0.05m. The erodingand depositional areas are then defined by a higher surfacelowering or raising, respectively. At the landscape scale, weshow how regional soil patterns can be modeled and howthese change under changing erosion intensity. The modelwas also used to assess the effect of soil properties on geo-morphological processes, by analyzing the sediment export.The digital elevation model of the selected area of 6.25 km2

has a 25m resolution (Figure 4). The area was selectedbecause it has a wide topographic variability, with altitudesranging between 707 and 1147m. At the same time, the areais small enough to ensure that the overall climate and geologyis similar. The model was run for an elapsed time of60,000 years. The soil-formation model was executed withtime steps of 100 years, while smaller time steps of 10 yearswere used for the landscape evolution model to obtain realis-tic soil redistribution patterns and avoid artificial accumula-tion of large sediment bodies. The values given to severalmodel parameters are given in Table 1. These values were,where possible derived from existing literature as discussedin the previous paragraph.

3. Results and Discussion

3.1. Pedon Scale Soil Profile Variability

[65] The evolution of soil layer thickness with time isshown in Figure 5, for three representative landscape points:a point from a steady-state area, an eroding area and a depo-sitional area. The position of these three points is shown inFigure 4. Finally, observations from soil profiles along a sim-ilar, nearby catena are shown to the right. Total soil thicknessin the three landscape positions is markedly different. Thefirst point is representative of soil development in the entirearea under the absence of erosion. At this steady-state point,the soil profile formed at the end of the simulation period of

Figure 3. Grain-size selectivity of soil erosion for differentvalues of parameter ks (larger ks values representing lowererosion rates) and correction for the actual grain-size dis-tribution in the soil. k’se,i are the uncorrected selectivity coef-ficients. The final, corrected selectivity coefficients (kse,i) areshown for a soil with a grain-size distribution for size classes1 through 5 of (.4,.3,.1,.1,.1) and ks =0.19.

Figure 4. Digital elevation model of the study area inWerrikimbe National Park, New South Wales, Australia.Three points are indicated that represent a typical steady-state, erosive and deposition environment. The selection ofthese points was based on several model runs with differenterosion intensity to identify zones where the surface remainedstable (<0.05m change), lowered or raised.


340

60,000 years is nearly stable and changes in profile thick-ness are slow. However, in contrast with previous models[Minasny and McBratney, 2006], total soil thickness isnot entirely stable at the end of the simulation. Previousmodels only took into account soil conversion from bed-rock. Here, chemical weathering processes act in the soilprofile. This results in a maximum total soil thickness be-tween 30,000 and 40,000 years (Figure 5a.1). However, asthe soil material still becomes finer in the course of the sim-ulation due to physical weathering, chemical weatheringlosses will increase as well resulting in a slight decreaseof soil thickness over time.[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: between20,000 and 30,000 years. Toward the end of the simulationit can be seen how the upper soil horizon, layer 1, is almostcompletely eroded. The main reason for this behavior is thatsoil particles become finer with time, i.e., they are moreeasily detached and transported.[67] As expected, the thickest soils are found in the de-

positional area. Total soil thickness here is almost doublethe value of the eroded areas. As the model adds the de-posited sediment to the upper horizon, layer 1, this layersubsequently grows the most. However, it can be seenhow surface deposition also affects the growth dynamicsof the underlying layers.[68] When compared to the field observations, the model

performs well in reproducing the overall trend in total soilthickness along the catena with the shallowest profile onthe eroding hillslope (Figure 5b.2) and the deepest soil pro-file in the valley bottom (Figure 5c.2). The comparison be-tween individual soil layers is more difficult. This is partlydue to the limitations of the model approach, but also dueto the difficulties to translate the field observations to thethree-layer approach of the model. In the field, often morehorizons 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 prop-

erties within the different layers. First of all, it can be seenfrom Figure 6 that the simplified approach used in thismodel, where only 5 size class fractions are used, yields a soiltexture evolution that is similar to more complex modelsusing 1000 size classes (“1000 box model”) [Pedro andLegros, 1984; Salvador-Blanes et al., 2007]. The textural

Figure 5. Evolution of the soil profile thickness over60,000 years under moderate erosion (K = 0.2� 10�8 yr�1,D = 0. 1m2 yr�1) at the three representative points shownin Figure 3: (a.1) steady-state, (b.1) erosive and (c.1) deposi-tion, and comparison with observed soil profiles in similarlandscape positions (a.2, b.2, c.2).

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.


341

evolution of the three landscape situations (steady-state,erosion and deposition) again shows significant differences.The deposition point shows the finest soil texture, becausefine sediment is constantly added. The erosion point showsthe coarsest texture of the three. Here, finer soil particlesare constantly removed by soil erosion. Additionally, aslayer 1 almost disappears toward the end of the simulation,texture changes become much more erratic toward the endof the simulation.[70] The soil profile evolution shown in Figure 7, for the

steady-state landscape point, illustrates the evolution of soilproperties with more detail. Whilst the thickness of the soillayers does not change much after 30,000 years, it can beseen that the soil properties still evolve. In particular, theclay and fine clay fractions are increasing, with the forma-tion of a second horizon that becomes enriched in clay. Alsothe organic carbon content increases, especially in the firstlayer.[71] In Figure 7 field observations are shown, for the pur-

pose of comparison, on the right hand side. It has to be notedthat stone content was not explicitly measured in the field,but was derived from visual observations. The mass fractionof the other size classes was recalculated taking into accountthe stone fraction of the soil. Also, no fine clay was mea-sured. Overall, the texture of the modeled profile after60,000 years compares well with the observations. The stonecontent near the surface is higher than observed, but com-pares well within the rest of the profile. The predicted in-crease of coarse fragments in the lower part of the profileis also present in the field data. The model overpredicts sandcontent and underpredicts silt content, but only by around10%. Modeled clay content is almost the same as the ob-served clay content, and the layer of clay illuviation that isobserved 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 modelpredicts clay loam whereas the observations show clay. Asbulk density depends on soil texture through the pedotrans-fer function, the predicted trend compares well with the ob-served trend, with errors between 8 and 12%. Soil organiccarbon however is problematic. The high values of almost6% that were observed in the surface horizon in the fieldare not predicted by the model. Although the lower part ofthe profile is closer to the observations, future research,based on a more extensive field dataset, will have to focuson calibrating the carbon cycle model or perhaps replace itby 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 propertiesare shown in Figures 8 and 9. Figure 8 shows the total soilthickness after 10,000, 20,000, 30,000, 40,000, 50,000,and 60,000 years. It can be seen how the convex hillslopepositions are characterized by shallow, eroded soils. Deposi-tional soils occur in the concave valley bottoms. The maxi-mum soil depth in the upslope areas again occurs around20,000–30,000 years, as can be seen from Figure 5b.1. How-ever, the overall soil variability is largest at the end of thesimulation since the eroded soils are shallower while the de-positional areas have gained soil thickness. Figure 9 showsthe total carbon content in the soil after 60,000 years. Theerosion-deposition pattern marks the regional patterns ofcarbon distribution. Important storage of carbon takes placein the depositional soils, where carbon is buried at severalmeters depth. This example shows that the simulated pat-terns of soil formation follow the general soil–landscape re-lationship in eroding landscapes [Doetterl et al., 2012].Dlugoß et al. [2010] found very similar differences in aneroding agricultural landscape in Germany. They found that

Figure 7. Evolution of the soil profile and its properties over 60,000 years at a steady-state landscapeposition and comparison with an observed soil profile in a similar landscape setting. SOC is soil organiccarbon content and BD is apparent soil bulk density.


342

valley bottom positions were characterized by much higherorganic carbon stocks than eroding or stable sites. At thesevalley bottom sites, the organic carbon content in the surfacelayers was up to two times that of eroding sites and the dif-ference even amounted up to 20 times in subsurface layers.

3.3. Effect of Erosion Intensity on Soil Properties

[73] The model allows comparing the influence of vari-ous erosion scenarios on soil properties. Figure 10 com-pares three situations with the same soil formation rates,but in the absence of soil erosion (Figure 10a), underconstant, moderate erosion where D = 0.1m2 yr�1 andK= 0.2� 10�8 yr�1 (Figure 10b), and finally, in a situa-tion where a period of moderate erosion is followed by afinal period of 10,000 years with erosion rates five timeshigher (Figure 10c). This third scenario mimics the transi-tion of the global climate and the associated change of ero-sion rates experienced during the Holocene.[74] On a regional scale, the overall soil thickness is

not too different between the three cases, resulting fromthe deposition of most of the eroded soil material inside thestudy area. The effect of erosion (Figures 10a and 10b),is mainly expressed in the mean carbon content. In thepresence of soil erosion, the carbon content is lower in up-land soils, while it is much higher in the depositional areasbecause of the burial of carbon-rich sediments. Finally, ifthe same moderate erosion scenario is followed by a periodof higher erosion during the last 10,000 years, the soilresponds rapidly (Figure 10c). In upland areas, the firsttwo layers of the soil are eroded. However, in the deposi-tional areas, part of this material is deposited again intothe upper layer. This caused an increase in the thicknessof layer 1, while the thickness of layer 2 decreases. Themain effect however is on the carbon stored in the systemwhich nearly doubles in this short time span: from ca.

12.7 kgm�2 to 19.7 kgm�2. This corresponds to a carbonsequestration rate of 0.7 gm�2 yr�1 averaged over the entirestudy area. This value is at the lower end of the rangereported in the literature. For example, Mcleod et al.,2011] found carbon burial rates between 0.7 and 13.1 g Cm�2 yr�1 for temperate forested areas. A carbon sequestra-tion rate of 2.2 gm�2 yr�1 is obtained considering the depo-sitional areas only, which occupy about 30% of the area.Corresponding Holocene carbon sequestration rates fromliterature are in the same order of magnitude. For example,Hoffmann et al. [2007] reported Holocene carbon seques-tration rates for the Rhine floodplain of 3.4 gm�2 yr�1.

3.4. Effect of Soil Formation on Erosion Processes

[75] A comparison of sediment export from the modeledarea under different erosion scenarios shows the importantimpact of soil formation on the erosion cycle (Figure 11).Under moderate erosion (Figure 11a) the production ofnew soil keeps up with erosion. The result is a stable meansediment export rate after about 30,000 years. This resultsin a linear increase of the cumulative sediment export. Notethe peak in the annually exported sediment at around8,000 years, which is probably an artifact of the drainagebasin connectivity in combination with the cellular automataapproach. Figure 11a also shows how the properties of theexported sediment change throughout the simulation, fol-lowing important changes in soil profile properties. Suchinformation could become useful for the interpretation oflong-term stratigraphic records.[76] Figure 11b then shows the sediment export under

high erosion rates that are five times higher compared tothe moderate erosion scenario. The yearly sediment exportvalues clearly show how a breakpoint occurs between15,000 and 20,000 years. After an initial nearly exponentialincrease in the produced sediment, the system has been de-pleted of soil. After this threshold has been crossed, yearlysediment export rates drop drastically. As a result, overallsediment export rates are actually lower than in the previousscenario (Figure 11a).[77] Such sudden changes have been observed in envir-

onments with long-lasting human impact and associated

Figure 8. Evolution of total soil thickness in the study areaover 60,000 years.

Figure 9. Total soil organic carbon content in the studyarea after 60,000 years.


343

anthropogenic soil erosion. Dusar et al. [2011] reportedon sediment archives in the Eastern Mediterranean wherechanges could be linked to a depletion of the soil reservoir.This has also been observed in other regions. Anselmettiet al. [2007] observed an important increase in sediment

influx during the Maya period in a 6000 year long recordof lake sediments. However, despite a growing populationdensity, they observed a decrease in erosion intensity afterthe initial land-use phase, which they attributed to decreas-ing erodibility of subsurface soil.

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

Figure 11. Cumulative (above) and yearly (below) export of sediment per size fraction and carbon fromthe study area under constant weathering intensity and two erosion scenarios: (a) moderate and (b) high.


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3.5. Directions for Future Research

[78] Clearly, the model has limitations, which future workwill need to address. A first main concern is that the currentversion of the model “forces” soil horizon growth. Thisshould be replaced by spontaneous development, possiblyeven a variable number of horizons. Replacing the cellular-automata based landscape evolution model by more complexerosion and sediment routing processes is another importantissue. Alternatively, the model could be coupled with exist-ing state-of-the-art landscape evolution models. Futuremodels should also take into account heat and water fluxesexplicitly. Only by doing so, can we incorporate the depen-dence of all soil forming processes on landscape position.For example, aspect will affect soil temperature and soilwater content and therefore influence leaching processes.Finally, accounting for the geological and climatologicalvariability will be necessary before this model can be takenfrom a conceptual form to practical application.

4. Conclusions

[79] In this paper, we presented a mechanistic soil for-mation model, MILESD, which provides a first attemptto couple and explore the relation between soil-formingprocesses and soil redistribution. The model allows the de-velopment of soil profiles that are both vertically differen-tiated and spatially variable. Comparison of model resultswith field observations along a catena shows that the modelaccurately predicts the trends in change of soil profile thick-ness from stable soils on the hill top, over eroding hillslopesoils to depositing valley bottom soils. Modeled soil textureand bulk density values are acceptable, although fieldobservations show a much higher organic carbon contentthan modeled.[80] At the landscape scale, this model uses an open sys-

tem approach, allowing export of sediment from the stud-ied area through rivers, which eliminates the limitation ofever-growing soils in previous closed system approaches[Minasny and McBratney, 2006]. When scenarios with vary-ing erosion intensity are compared, the changes in landscape-averaged soil thickness are small. However, the total organiccarbon stored in the system responds much more to varia-tions in soil erosion intensity, mainly due to deep burialof organic carbon. It must be noted that this result is condi-tioned by the depth functions used for carbon productionand mineralization. Model calibration with more field data,not only from upland soils but also from deep sedimentdeposits, is likely to modify these conclusions.[81] Finally, the model also contributes to our understand-

ing of the interaction between geomorphic systems and exter-nally forcing factors. The consideration of sediment exportin MILESD allows exploring the effect of soil formationon sediment that is exported from the system and its proper-ties. It is shown that scenarios with different erosion inten-sity, representing changing climatic or human forcing, resultin a different response depending on the stage of soil de-velopment. Of particular interest is the threshold that isassociated with soil depth in the study area. When the soilreservoir becomes exhausted, a drastic reduction in sedimentexport was observed. This illustrates that apart from thetraditional climatic and anthropogenic land-use changedrivers, it is also important to consider the stage of soil

development or degradation. In such situations, the modelMILESD could be used to help with the interpretation ofcomplex sediment records.

[82] Acknowledgments. The first author thanks the University ofSydney International Visiting Researcher Fellowship programme and theRamon and Cajal Fellowship programme of the Ministry of Science andInnovation for making this study possible. The data presented in this paperis funded by the ARC Discovery project How soil grows. Budiman Minasnyacknowledges the funding of ARC QEII Fellowship. Alex McBratneyacknowledges the support of ARC project Global space-time carbonassessment.We also acknowledge the support of the Australian ResearchCouncil. Finally, we thank Alex Densmore, Simon Mudd, Garry Will-goose, and one anonymous reviewer for their helpful comments on anearlier version of this manuscript.

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