Journal of Hydrology 498 (2013) 132–143

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Journal of Hydrology

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Modelling soil erosion in a clayey, subsurface-drained agricultural fieldwith a three-dimensional FLUSH model

0022-1694/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.jhydrol.2013.06.020

⇑ Corresponding author. Tel.: +358 505416581.E-mail address: lassi@warsta.net (L. Warsta).

Lassi Warsta a,⇑, Antti Taskinen b, Harri Koivusalo c, Maija Paasonen-Kivekäs d, Tuomo Karvonen e

a Aalto University School of Engineering, Department of Civil and Environmental Engineering, P.O. Box 15300, FI-00076 Aalto, Finlandb Finnish Environment Institute, P.O. Box 140, FI-00251 Helsinki, Finlandc Aalto University School of Engineering, Department of Civil and Environmental Engineering, P.O. Box 15200, FI-00076 Aalto, Finlandd Sven Hallin Research Foundation, Simonkatu 12 A 11, FI-00100 Helsinki, Finlande Waterhope, Munkkiniemen Puistotie 20 A 6, FI-00330 Helsinki, Finland

a r t i c l e i n f o

Article history:Received 26 February 2013Received in revised form 30 May 2013Accepted 12 June 2013Available online 20 June 2013This manuscript was handled by GeoffSyme, Editor-in-Chief

Keywords:FLUSH modelClay soilSoil erosionSubsurface drainsSedimentPreferential transport

s u m m a r y

Soil erosion is an important environmental issue in agricultural areas of northern Europe where clayeysoils are prevalent. Clayey soils are routinely subsurface drained to accelerate drainage which createsan additional discharge route for suspended sediment. Previously, assessment of the sediment load fromclayey fields has been difficult, because process-based models were only able to simulate sediment loadsvia surface runoff. A new distributed, process-based erosion model was developed and incorporated intothe FLUSH modelling system to fulfil this void. The model facilitates simulation of spatially distributedsoil erosion on the field surface and sediment loads via surface runoff and subsurface drainflow. Soil ero-sion on the field surface is simulated with the two-dimensional sediment continuity equation coupledwith hydraulic and rain drop splash erosion, sediment settling, and transport capacity processes. Subsur-face sediment transport in macropores is described with the three-dimensional advection–dispersionequation. The model was applied to a clayey, subdrained field section (�3.6 ha) in southern Finland.The results demonstrated the capability of the model to simulate soil erosion and sediment transportin terms of the match between the measured (2669 kg ha�1) and modelled (2196 kg ha�1) sediment loadsvia surface runoff and the measured (2937 kg ha�1) and modelled (2245 kg ha�1) loads via drainflow dur-ing the validation period of 7 months. The model sensitivity analysis pointed out the importance of theflow model parameters in simulation of soil erosion through their control on the division of total runoffinto surface runoff and drainflow components. The key parameters in the erosion model were those thataffected hydraulic and splash erosion rates. The model application in the experimental field suggestedthat both hydraulic and splash erosion were the factors behind the sediment losses during the growingseason and early autumn, whereas high sediment loads in late autumn were caused by hydraulic erosiondue to overland flow in tilled soil.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

Soil erosion is defined as the loosening, dissolving, and removal ofearth or rock materials from any part of the surface (Aksoy and Kav-vas, 2005). The problems caused by erosion range from the loss offertile top soil for agriculture to increasing turbidity, sedimentationof eroded material, and eutrophication in surface waters. The mainproblem associated with soil erosion in northern Europe is usuallynot the actual soil loss itself, but the adverse effects of suspendedsediment, adsorbed nutrients, heavy metals, and pesticides inreceiving surface waters (Kirkby, 2006). In Finland, agriculture isconcentrated in the southern and western parts of the country dueto their milder weather and more cultivable soils. Clayey soil layers

are fertile but prone to erosion during peak runoff events. On aver-age, sediment loads vary between 0.03–3.3 t ha�1 a�1 in agriculturalcatchments while being considerably lower (0.02–0.2 t ha�1 a�1) inforested catchments (Tattari and Rekolainen, 2006).

Currently, about 75% of the cultivated fields in Finland are sub-surface-drained. Experimental studies conducted in Finland (e.g.Vakkilainen et al., 2010; Paasonen-Kivekäs et al., 2008; Turtolaet al., 2007; Uusitalo et al., 2001) and in other Nordic countries(e.g. Laubel et al., 1999; Øygarden et al., 1997; Ulén, 1995) haveindicated that a notable part (up to 95%) of the annual sedimentload from clayey fields is lost via subsurface drains. Initially, thesuspended sediment in the drain waters was considered a techni-cal problem of drain clogging, and the environmental aspects ofsediment in drain waters were overlooked (e.g. Øygarden et al.,1997). However, caesium-137 measurements on clayey fields(Uusitalo et al., 2001; Laubel et al., 1999) indicated that most of

L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143 133

the soil material in the subsurface drains originated from the soilsurface and tillage layer.

In Nordic conditions, infiltration excess overland flow can occurduring heavy summer rains, while both infiltration excess andsaturation excess type flows are common in the autumn and latespring when the soil layers are saturated with water and swollen.The main mechanisms for water-induced soil erosion are due to(1) hydraulic shear forces of the overland flow acting on the soilparticles, and (2) the impact of raindrops (e.g. Bradford et al.,1987a,b). Erosion with overland flow can be further partitionedinto rill and interrill components (e.g. Kavvas et al., 2006; Shardaand Singh, 1994; Meyer and Harmon, 1984).

Currently, only limited tools such as mathematical models areavailable to investigate the mechanisms of soil erosion and sedi-ment loss via surface runoff and especially via subsurface drain-flow in clayey soils. This study is motivated by the prospects ofmodel development and application to produce a holistic evalua-tion of sediment processes in a subsurface drained area.

Taskinen and Bruen (2007b) note that there are no widely ac-cepted theories for describing clay soil erosion in simulation mod-els. Due to electrostatic and van der Waals’ forces betweenindividual clay particles, erodibility of clayey soil can be lower thanexpected based on the particle size distribution (e.g. Klepsch et al.,2005). In addition, cohesive soils often erode in larger aggregatesrather than in elementary particles (e.g. Smith et al., 1999; Meyeret al., 1980), but mechanistic approaches (e.g. Nord and Esteves,2005; Sharda and Singh, 1994) describing aggregates as larger par-ticles may not function properly. Suspended sediment on the fieldsurface is apparently transported to the subsurface drains by pref-erential flow in soil macropores and drain trench backfill material(Jacobsen et al., 1997; Øygarden et al., 1997; McKay et al., 1993). Acertain amount of filtering may occur during transport through thesoil layers (Turtola et al., 2007; Jacobsen et al., 1997; Turtola andPaajanen, 1995). However, Paasonen-Kivekäs et al. (2008), Uusitaloet al. (2001), and Turtola and Paajanen (1995) found out in theirexperimental studies that the sediment concentrations in the sub-surface drainflow were approximately the same as the concentra-tions in surface runoff.

A large number of erosion models are available (e.g. Aksoy andKavvas, 2005) and they can be divided into (1) empirical modelsthat are based on crude process conceptualization and measure-ments of sediment concentrations and loads, and (2) distributed,process-based models that attempt to simulate actual erosive pro-cesses. Empirical models typically represent the field as a point-type entity with an area averaged parametrisation and they cannotbe used to assess spatial distribution of soil erosion within the fieldarea. Several field-scale applications of erosion modelling in claysoils have been conducted by empirical models including CREAMS(Kauppi, 1982; Knisel, 1980) or its derivatives GLEAMS (Knisel andTurtola, 2000; Leonard et al., 1987) and ICECREAM (e.g. Bärlundet al., 2009; Larsson et al., 2007; Paasonen-Kivekäs et al., 2006; Tat-tari et al., 2001; Rekolainen and Posch, 1993). All the CREAMSmodel variants are based on empirical regression equations de-rived from data measured in the USA. However, soils and climatein northern Europe are different, and this has affected the applica-bility of the models in the studied conditions, especially the simu-lation of the short-term dynamics of water flow and soil erosion(Paasonen-Kivekäs et al., 2006; Tattari et al., 2001; Knisel and Turt-ola, 2000; Kauppi, 1982). The most glaring issue with the CREAMS,GLEAMS, and ICECREAM models is the lack of an explicit descrip-tion for the subsurface drains.

Process-based erosion models can be further partitioned into(1) event-types and (2) continuous-types. Infiltration excess over-land flow initiation and coupled soil erosion are regularly simu-lated with event-type models, e.g. the model by Taskinen andBruen (2007a,b), CASC2D-SED (Johnson et al., 2000), and EROSION

3D (Werner, 1995). However, several authors (Smith et al., 1999;Wicks and Bathurst, 1996) reported problems in simulations withevent-type models due to the uncertainty in determining anteced-ent moisture conditions in soil. The continuous-type models aremore suitable for simulating the antecedent moisture conditionsas well as saturation excess flow initiation, which requires thatthe model keeps track of the moisture conditions in the underlyingsoil profile. Continuous-type process-based models (including LI-SEM (De Roo et al., 1996a,b), SHESED (Wicks and Bathurst, 1996),WEPP (USDA, 1995), and the model by Sharda and Singh (1994))apply integrated soil- and groundwater flow models to improvethe prediction of overland flow initiation. The presented reviewof model applications indicates that erosion processes are stronglybound with hydrological and hydraulic processes, and a properdescription of continuous soil moisture conditions and overlandflow generation is a prerequisite for successful simulation of over-land erosion.

In addition to overland erosion, suspended sediment transportto subsurface drains, as discussed above, is an important processin clayey soils. Only three previous empirical erosion models werefound that simulate both overland erosion and suspended sedi-ment transport to subsurface drains: PSYCHIC by Davison et al.(2008), the modified ICECREAM model by Larsson et al. (2007)and the USLE-based model called ERONOR developed for Norwe-gian conditions (Lundekvam, 2007). Knisel and Turtola (2000)made a rough approximation of sediment loads via subsurfacedrains by multiplying daily percolation results calculated byGLEAMS with average particulate concentration over all simulatedseasons and for all plots. No previous distributed, process-basedmodels were found that could simulate sediment transport to sub-surface drains. Such feature requires the model to simulate distrib-uted preferential water flow in macropores which is currently notsupported by the earlier models.

FLUSH is a three-dimensional hydrological model, which is ex-panded in this study to simulate erosion and sediment transport.The hydrological processes supported by the model were describedand tested in Warsta et al. (2013). The main objective in this studyis to build an erosion component in FLUSH by coupling a standardapproach for simulating two-dimensional (2-D) overland erosionin distributed, process-based models (e.g. Taskinen and Bruen,2007b; Johnson et al., 2000) with a three-dimensional (3-D) sub-surface suspended sediment transport component. A specific goalis to evaluate how this combined system simulates sediment loadsvia both surface runoff and drainflow in clayey, subsurface drainedagricultural fields. Previously, only simple empirical models wereable to accomplish this while process-based models only simulatederosion on the field surface and sediment load via surface runoff.The capabilities and performance of the model are demonstratedthrough an application to a field section, where measurements ofsoil properties and sediment concentrations and loads areavailable.

2. Methods

2.1. Hydrological model

FLUSH divides the investigated field section into separate 2-Doverland and 3-D subsurface domains. The 2-D overland domainis compatible with the existing approaches (e.g. Taskinen and Bru-en, 2007b) to simulate soil surface erosion processes in a distrib-uted manner. The hydrological part of FLUSH was earlierintroduced by Warsta et al. (2013) and is briefly summarised here.The surface and subsurface water movement is initiated by precip-itation. Water on the field surface infiltrates into the soil matrixand macropore systems. When the infiltration capacity of the soil

134 L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143

is exceeded or the groundwater table rises to the surface, overlandflow is initiated. Both unsaturated and saturated flow is supportedin matrix and macropore systems, which exchange water whenthere is a pressure-head difference between the pore systems. Dry-ing and wetting cause shrinkage and swelling of the clay soil. Thesechanges in soil structure increase or decrease the volumetric frac-tion of shrinkage cracks, which are part of the macropore system.The shrinkage and swelling model was derived from the SWAPmodel (Kroes et al., 2008), and the system was described in moredetail in Warsta et al. (2013).

Water is lost from the field via evapotranspiration, openditches, subsurface drains, and groundwater outflow. The bottomof the soil profile is handled as a no-flow boundary while ground-water flow is removed as a flux-type boundary condition from thegrid sides. The model is used here to simulate the growing seasonsand the following autumns. The hydrological part of FLUSH wasfurther tested by Turunen et al. (2013), who applied the modelto another clayey field in southern Finland to investigate the ef-fects of different subsurface drainage installation methods on thewater balance of the field. The hydrological model does not cur-rently support simulation of winter time processes, although theyare under development (Warsta et al., 2012). While the model istargeted to soil types with two distinct pore systems such as clay,it can be applied to homogenous soils with a single pore system bydeactivating the shrinkage and swelling model and setting themacropore system as impermeable.

2.2. Conceptual and mathematical representations of the erosionmodel

FLUSH is extended to simulate erosion according to a conceptu-alisation that defines the erosion processes in the overland andsubsurface domains (Fig. 1). Sediment is entrained by hydraulic(1 in Fig. 1) and raindrop splash erosion (2) in the overland domain.Only sheet-type hydraulic erosion, i.e. no rills, and one sedimentparticle size class are currently supported. Erosion due to leaf dripis not included. Tillage operations can change the erodibility of thesoil at user-specified points in time. Sediment suspended in over-land flow is transported by advective transport mechanism (3)and hydrodynamic dispersion is omitted. The amount of sedimentconveyed by water is controlled by the sediment transport capacityof the overland flow. When the sediment concentration exceedsthe transport capacity of the flow, excess sediment is depositedon the surface of the field (4). After rain, suspended sediment startsto settle due to gravity (4) while during rain, turbulent mixingcaused by rain drops cancels deposition. Suspended sediment inthe overland flow discharges into open ditches (5).

Fig. 1. Conceptualisation of erosion processes in the overland and subsurface d

Suspended sediment on the field surface enters the macroporeopenings with infiltrating water (6 in Fig. 1). Dimensions of thesuspended sediment particles are not considered in the infiltrationprocess and neither is sieving of sediment particles in macropores.In contrast to water exchange between the pore domains, sus-pended sediment cannot be transported into the soil matrix be-cause the voids in the clay soil matrix are considered to be toosmall for the particles to enter. Sediment erosion from the macro-pore walls is not considered either. However, infiltrated sedimentcan be deposited on macropore walls when water is lost throughtranspiration or water seeping from the macropore domain intothe soil matrix. Deposited sediment is flushed onwards again aftermore water enters the macropores, i.e. clogging of the macroporesby deposited sediment is disregarded. Sediment is transported inthe macropore domain by advection and dispersion mechanisms.Unsaturated transport occurs above the groundwater table andsaturated transport below the groundwater table. Transport of sed-iment is constrained to the macropore domain between the fieldsurface and the subsurface drains (7). In line with the findings ofPaasonen-Kivekäs et al. (2008) and Yli-Halla et al. (2000), it is as-sumed here that the pathways below the drains are too narrowfor sediment particle transport. Suspended sediment is dischargedvia drains (8) and seepage to open ditches. Part of the infiltratedsediment is transported horizontally with groundwater flow whenthe groundwater table rises above the drain level and when themacropore network is continuous along the slope.

An implicit finite volume method is used to solve the spatialcomponents of the governing partial differential equations, and abackwards difference approach is applied to discretise the tempo-ral differential terms. The overland domain is discretised into rect-angular cells, whereas the subsurface domain is divided intohexahedric control volumes. The numerical solution algorithmsare parallelised with OpenMP (OARB, 2008). The overland erosionmodel was derived from Taskinen and Bruen (2007b) by simplify-ing their model to support a single characteristic particle size. Themodel is built around the sediment continuity equation, wheresuspended sediment transport is purely advective, combined withsources and sinks:

@ðhW CÞ@t

þ @ðQ XCÞ@x

þ @ðQ Y CÞ@y

¼ gR þ gH �wSUSC � SS ð1Þ

where hW (m) is the overland water depth, C (kg m�3) is the sedi-ment concentration in the overland water, t (s) is the time, QX andQY (m2 s�1) are the overland unit flow rates, gR (kg m�2 s�1) is the po-tential rain drop splash erosion rate, gH (kg m�2 s�1) is the potentialhydraulic erosion rate, wS (–) is the coefficient for the particle set-tling, US (m s�1) is the particle settling velocity, and SS (kg m�2 s�1)

omains in FLUSH. The shaded areas depict saturated conditions in the soil.

L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143 135

is the overland sediment source/sink, e.g. open ditches. Potentialerosion rates gR and gH in this context signify the maximum amountof sediment produced by the erosion processes when the transportcapacity of the flow is not limiting sediment entrainment.

The transport of suspended sediment in the subsurface domainis simulated with the advection–dispersion equation (Eq. (2)),where sediment is treated as a non-reactive and conservative sol-ute. Only the macropore system transports sediment and the ex-change of sediment between the macropore and matrix domainsis disabled. While the matrix does not store sediment, it still re-serves a large, varying part of the total pore space due to soilshrinkage and swelling phenomena (see Warsta et al., 2013), whichhas to be taken into account in the numerical solution of

@ðhcÞ@t¼ @

@xhDXX

@c@x

� �þ @

@yhDYY

@c@y

� �þ @

@zhDZZ

@c@z

� �

� @

@xðqxcÞ � @

@yðqycÞ � @

@zðqzcÞ � SS ð2Þ

where h (m3 m�3) is the volumetric water content, c (kg m�3) is thesediment concentration, DXX, DYY and DZZ (m2 h�1) are the disper-sion coefficients, q (m h�1) is the unit (Darcian) water flux, and sS

(kg m�3 h�1) is the sediment source/sink. In the following sectionsthe numerical solution algorithms of Eqs. (1) and (2) are discussedin more detail. A thorough presentation of the solution approachesis available in Warsta (2011).

2.3. Numerical solution of the overland sediment continuity equation

The five main processes governing soil erosion in the extendedFLUSH are presented briefly below and include (1) suspended sed-iment settling, (2) advective transport with water flow, (3) trans-port capacity of the flow, (4) hydraulic erosion, and (5) raindropsplash erosion. The particle settling velocity (US in Eq. (1)) is calcu-lated with the Stokes’ law. The advective transport is solved withan implicit upwind scheme. Both water depth and field surface ele-vation are considered in the solution. Transport capacity of theoverland flow is calculated with the Yalin’s equation (Yalin, 1963):

TC ¼0:635qwdSGDSUSH

URhw1� 1

aYdlnð1þ aYdÞ

� �ð3Þ

where SG (–) is the sediment specific gravity in water, i.e. the sedi-ment particle density qS (kg m�3) divided by the water density qW

(kg m�3), DS (m) is the mean particle diameter or aggregate size, USH

(m s�1) is the overland shear velocity, UR (m s�1) is the overlandresultant flow velocity, and aY (–) and d (–) are parameters (e.g.,Warsta, 2011; Taskinen, 2002). An option for setting a minimum va-lue for TC in standing water was included. The hydraulic erosion (gH

in Eq. (1)) was computed according to Taskinen and Bruen (2007b)and Taskinen (2002):

gH ¼ kHssC� 1

� �; s > sC

gH ¼ 0; s 6 sC

(ð4Þ

where kH (kg m�2 s�1) is the overland flow soil erodibility coeffi-cient, s (kg s�2 m�1) is the shear stress of the overland flow, andsC (kg s�2 m�1) is the critical shear stress, which is computed withthe modified Shields method for small particles proposed by Mantz(1977) and Yalin (1977). The method to compute gR is a simplifica-tion of the approach in the SHESED model (Wicks and Bathurst,1996):

gR ¼ kRFW MR ð5Þ

where kR (s2 kg�1 m�2) is the raindrop splash soil erodibility coeffi-cient, FW (–) is the overland water depth correction factor, and MR

(kg2 s�3) is the momentum squared for rain (see, e.g., Warsta,2011; Taskinen, 2002).

In the numerical solution, the spatial components in the sedi-ment continuity equation (Eq. (1)) are solved implicitly with itera-tion. The variables gH, gR, US and TC are pre-computed before theiteration stage with the results from the flow simulation. TC marksthe maximum sediment concentration in a cell, and excess sedi-ment is removed from the cell during the iteration. The sedimentflux into an open ditch is treated as a sink and is calculated by mul-tiplying the volumetric water flux to the ditch (see Warsta et al.,2013) with the sediment concentration in the cell. Sediment infil-tration is computed by the subsurface transport model. Sedimentmass is converted to concentration only within the solution algo-rithm to maintain mass balance.

The cropping and tillage effects submodel in FLUSH (Warstaet al., 2013; Warsta, 2011) can be used to change the propertiesof different subareas of the field over time to simulate crop growthand the effects of tillage operations on soil parameters. The valuesof kH and kR (Eqs. (4) and (5)) can be modified at the time of the till-age operations.

2.4. Numerical solution of the subsurface suspended sedimenttransport equation

The numerical solution of the advection–dispersion equationdepicting sediment transport in the macropore system (Eq. (2)) isbased on an implicit, iterative approach. The vertical sedimentfluxes are solved directly in a column of cells with the tridiagonalmatrix algorithm, and the horizontal fluxes are solved with itera-tion. Sediment concentration is converted to sediment mass out-side the solution algorithm to minimise the mass balance errorresulting from changes in water content and macropore volumescaused by tillage and soil shrinkage and swelling processes. Trans-port of sediment is restricted to the macropore domain betweenthe field surface and subsurface drains. This is ensured in the mod-el by calculating the solution only in the cells located above thedrains and forcing the sediment influxes and outfluxes at the do-main border to zero.

Similar to the numerical solution of the sediment continuityequation (Eq. (1)), an upwind scheme is used to compute advectivetransport between cells. Both advective and dispersive transportterms are implicitly solved to ensure the stability of the algorithm.Short time steps are still required during fast transport events tominimise numerical dispersion. On the other hand, suspended sed-iment is produced in the overland domain by erosive processes in adiffuse manner and not in sharp fronts, making the numerical dis-persion problem less critical. The directional components of thedispersion terms (DXX, DYY and DZZ) are computed according toZheng and Bennet (2002):

Di ¼ aLm2

i

jmj þ aTm2

j

jmj þ aTm2

k

jmj þ D� ð6Þ

where i, j, and k are the direction indices (XX, YY or ZZ in Eq. (2)), aL

and aT (m) are the longitudinal and transverse dispersivities,respectively, v (m h�1) is the subsurface flow velocity, |v| (m h�1)is the magnitude of the velocity vector, and D� (m2 h�1) is the effec-tive molecular diffusion. The cross terms (DFXY, DFYX, DFXZ. . .) are as-sumed to be zero.

Sediment sinks, sources, and boundary conditions in the sub-surface transport domain are bound to the corresponding pro-cesses in the subsurface flow domain (Warsta et al., 2013). Thesediment mass entering a grid cell of the macropore domain viainfiltration is calculated by multiplying the infiltration volumewith the sediment concentration in the corresponding overlanderosion cell. The sediment fluxes to ditches, subsurface drains,and groundwater flow are calculated by multiplying the

136 L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143

corresponding volumetric water flow with the grid cell sedimentconcentrations in the origin of the water flow.

3. Site description and data

The model was applied to the Sjökulla experimental field lo-cated in Kirkkonummi in southern Finland (60�1402800N24�230500E, Fig. 2). The region has a temperate climate, with a meanannual precipitation of 700 mm (uncorrected value) and a meanannual air temperature of +5 �C. Runoff generation and the trans-port of nutrients and eroded soil, as well as meteorological vari-ables (air temperature, relative humidity, precipitation, incomingshort-wave radiation, and wind speed), were monitored in the fieldduring intermittent periods during 1993–1999. The measurementsused in this study cover two frost-free periods: from May toNovember in 1996 and from May to October in 1998. The measure-ment site is briefly described here and more information about thesite, land use, soil characteristics, and measurement system can befound in Warsta et al. (2013), Warsta (2011), Alakukku et al.(2010), Paasonen-Kivekäs et al. (2008), and Peltovuori et al. (2002).

The simulated area is 3.6 ha within a larger field of arable land(Fig. 2). Topography of the field is undulating with a maximumslope of almost 5%. The field site is delimited in the southern sideby a paved road and in the western side by a gravel road, while theeastern and northern sides are connected to adjacent field sections.Shallow ditches separate the roads from the field area. A mainditch, which runs partly in a pipe, borders the northern side ofthe field. Subsurface drain pipes were installed in 1951 to a depthof 0.7–1.5 m and spaced 10–15 m apart. The tiles have gravel asenvelope material and the trench was back-filled with the originalsoil. The inner and outer diameters of the tiles are 0.04 m and0.06 m, respectively.

The soil is post-glacial clay and classified (Soil Survey Staff,1998) as very fine Aeric Cryaquept (Peltovuori et al., 2002). Miner-als of the surface horizons (0–0.20 m and 0.20–0.29 m) consist oftectosilicates and mica, and the deeper horizons (0.29–0.70 m)are dominated by illitic mica (Peltovuori et al., 2002). The soil isprone to cracking and swelling. During dry spells, large cracks ex-tended at least to a depth of 0.60 m from the soil surface (Alakukkuet al., 2010). Soil texture, bulk density, porosity, hydraulic conduc-tivity, and water retention characteristics were determined fromthree horizons in several locations within the field (Alakukku

Fig. 2. Location of Kirkkonummi in Finland and map of the Sjökulla experimental field. Tthe subsurface drains, and the open circles (P and S) are the surface runoff and subsurfa

et al., 2010). On average, the top soil (0–0.25 m) contains 47% clay(60.002 mm), 28% silt (0.002–0.02 mm), and 2.6% organic carbon.The content of clay fraction varies from 46% to 90% in the bottomsoil (0.25–0.80 m). The bottom soil silt content is 16–24% and or-ganic carbon 0.3–0.9%.

The cropping consisted of small grain production with mineralfertilizers. Autumn rye (Secale cereale) seeded in August 1995was grown in May–August 1996 and spring wheat (Triticumaestivum) in May–September 1998. Seedbed preparation (depth5 cm) was carried out before seeding on 6 May 1998. After theharvest, the field was ploughed (depth 23 cm) on 10 October1996 and partly ploughed and partly stubble-cultivated (depth15 cm) on 2–7 October 1998. The soil remained bare until thefollowing spring.

Surface runoff and subsurface drainflow were measured in thelocations marked with P and S, respectively, on the map (P1, P2,and S1 in Fig. 2). Embankments were used to convey overlandwaters to the measurement weirs P1 and P2. Data from the obser-vation points P1 and S1 were used in this study. The subcatchmentof P1 covered 0.63 ha. The outlet of the subsurface drainage system(S1) integrated a field area of 3.14 ha. Both surface runoff and sub-surface drainage outflow was measured using a v-notch weir and apressure sensor with a measurement frequency of 15–30 min.Hourly runoff values were calculated from the measurements. Amicrometeorological station recorded the above mentioned mete-orological variables at the site. Precipitation was measured by acollector bucket installed on a scale. The weight of the bucketwas recorded every 15–30 min, and hourly rainfall was calculatedfrom these data. The measured rainfall was corrected with a con-stant multiplier of 1.05.

Grab samples were manually collected from surface runoff atthe weir outlet in 1996 and 1998. Subsurface drainage outflowwas manually sampled throughout May–November 1996. An auto-sampler (EPIC 1011 Portable Water Sampler) with a 4-h samplinginterval was installed at the drainflow measurement weir inMay–October 1998. The water samples were analysed for total sus-pended solids (TSS). The concentration of TSS was determined in1996 by using the mass of dried (105 �C) matter retained on the1 lm fibreglass filter. In 1998, the concentration was determinedby weighing the evaporation residue of a subsample. The hourlyvalues of TSS loads were calculated by multiplying the hourly run-off volumes with the measured or estimated (interpolated from

hin lines inside the field borders are the elevation contours (m), the thicker lines arece drainflow measurement points (Warsta et al., 2013).

L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143 137

measurements) concentrations. The hourly data includingsediment loads and rainfall measurements are shown in Section 4in conjunction with the simulation results.

4. Simulation results

The model was tested by calibrating the model with one-half ofthe data set, and then applying the calibrated model to the otherhalf of the data for validation. Data from 1998 (May–October)was used for calibration and 1996 (May–November) for validation.The runoff events were more uniformly distributed during 1998,making the data more suitable for the model calibration than1996, which had an exceptionally dry August and September butheavy rain events in November. A sensitivity analysis was con-ducted to identify the parameters that had a high impact on thesimulated sediment loads. Calibration, validation, and sensitivityanalysis were manually done due to the high computational loadassociated with the model.

4.1. Model parametrisation

The resolution of the computational grid (144 � 104 � 16 cellsin x-, y-, and z-directions) was identical to the water flow simula-tion grid in Warsta et al. (2013). The horizontal cell dimensionswere 2 � 2 m2, and the depth of the profile was 2.4 m. The simula-tion time step varied between 1.0 h and 3.5 s. The time step wasdecreased during precipitation events and when the iterative solu-tion algorithm did not numerically converge (Warsta et al., 2013;Warsta, 2011). The number of parameters required in the erosionmodel is notably lower than in the corresponding flow model; theirvalues are presented in Table 1. The Nash–Sutcliffe model effi-ciency coefficient (NSME) (Nash and Sutcliffe, 1970) was used toevaluate the simulation results against the sediment load measure-ments. NSME values were calculated between the hourly modelledload and the occasionally measured loads (at the water samplingtimes).

DS was set here to approximately tenfold of a single clay soilparticle to represent the presence of aggregates (1.5 � 10�5 m),while qS was set to 2650.0 kg m�3. kH and kR were calibrated di-rectly against the measured sediment loads. It was obvious fromthe results that kH increased after tillage (Table 1). On the otherhand, it was difficult to interpret from the results if tillage had ef-fects on kR because hydraulic erosion produced large amounts ofsuspended sediment, which masked the effect of raindrop splasherosion during autumn rain events. In addition, it was found outin the calibration that a minimum value had to be defined for TC.A high value of 5.0 kg m�3 was used as a minimum TC (TC,MIN in Ta-ble 1) in the simulations to depict transport of suspended clay soilparticles. Suspended sediment settling due to gravity (Eq. (1)) wasnot required and it was switched off in this application. This is

Table 1Model parameter values applied in the simulations. The symbols ! and # depicterodibility values before and after tillage, respectively. The parameter names arepresented next to Eqs. (3)–(6).

Parameter Value Unit

aL 0.1 (m)aT 0.01 (m)qS 2650.0 (kg m�3)qW 1000.0 (kg m�3)D� 3.6 � 10�6 (m2 h�1)DS 1.5 � 10�5 (m)kH ! 1.0 � 10�7 (kg m�2 s�1)kH # 2.2 � 10�6 (kg m�2 s�1)kR 1.2 (s�2 kg�1 m�2)TC,MIN 5.0 (kg m�3)

likely to be connected to the small particle size and the corre-sponding slow settling speed.

The values of aL and aT could not be calibrated properly with theavailable data because the effect of dispersion was masked by non-uniform soil erosion on the field surface, transport in the soil pro-file, and mixing in the subsurface drains. The method presented bySpitz and Moreno (1996) was applied here to derive the values foraL and aT. The transport distance from the surface to the drains(1.0 m) was divided by 10.0 to estimate the aL value of 0.1 m, whilethe value of aT was set to 10% of the value of aL., i.e. to 0.01 m. Thevalue of D� was set to a value of 3.6 � 10�6 m2 h�1 (e.g. Ray et al.,1997).

4.2. Model calibration

The modelled amount of entrained sediment at the end of thecalibration period in 1998 was 4353 kg ha�1. The modelled sedi-ment load was lost from the field via surface runoff to open ditches(44%), via subsurface drains (30%), by seepage to open ditches(17%), and through groundwater flow (9%). Transport with ground-water flow was only possible when the groundwater table levelrose above the subsurface drains. Measured and simulated cumu-lative sediment loads via surface runoff and drainflow during thecalibration year are presented in Fig. 3. In the simulations, raindrop splash erosion was responsible for the sediment load beforethe autumn tillage operations from May to September, whereasthe sharp increases in the sediment loads after the tillage opera-tions in October were produced by hydraulic erosion. The suscep-tibility of soil to hydraulic erosion was increased twenty-fold aftertillage (see values of kH in Table 1). NSME values between mea-sured and modelled sediment loads via surface runoff and drain-flow in 1998 were 0.107 and 0.750, while the bias values were�0.10 and +0.0019 kg ha�1 h�1, respectively. The average hourlysediment loads via surface runoff and drainflow were 0.54 and0.29 kg ha�1 h�1, respectively.

Fig. 4 presents hourly modelled and measured sediment loads.The time series are presented for October 1998, when most ofthe surface runoff and overland sediment load was observed. Thedynamics of the simulated overland sediment load (Fig. 4) visuallyresembled the earlier results of simulated surface runoff (see Fig. 9in Warsta et al., 2013). The NSME value, calculated with the mea-sured and simulated overland sediment load, gained a low value of0.107, which is due to the pronounced underprediction of peaks(Fig. 4). This comes from the model’s tendency to underestimateflow concentrations during peak surface runoff events and overes-timate the low flow concentrations. Overland flow over ploughedfield does not actually occur as the sheet-type flow assumed inthe model but as concentrated flow in rills, which can lead tounderestimation of peak overland flow velocities.

Similarly to the overland sediment load, the modelled drainsediment load dynamics (Fig. 5) closely resembled simulateddrainflow patterns (see Fig. 10 in Warsta et al., 2013). Ploughingand stubble cultivation were conducted from 2 October to 7 Octo-ber (Fig. 5). Soil erodibility, and as a result sediment transport, in-creased in response to the tillage, which was taken into account byincreasing the value of kH (Table 1). In terms of NSME, the sedimentload via drains (0.750) was modelled more accurately than the sed-iment load via surface runoff (0.107).

4.3. Model validation

During the validation year 1996, the modelled amount of en-trained sediment was 6489 kg ha�1, which is almost 50% morethan in 1998. The amount of sediment lost via overland flow toditches decreased to 34% from the total sediment load (44% in1998), while the sediment load via subsurface drains rose to 35%.

0

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(b) (a) Fig. 3. Measured and simulated cumulative sediment loads via (a) surface runoff and (b) drainflow in May–October 1998 (calibration).

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Fig. 4. Hourly measured and simulated sediment loads via surface runoff in October 1998 (calibration).

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Tilla

ge

Fig. 5. Hourly measured and simulated sediment loads via drainflow in May–October 1998 (calibration). Autumn tillage date is illustrated with an arrow.

138 L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143

The relative sediment loads via seepage to ditches and groundwa-ter flow rose 3 and 2 percentage points to 20% and 11%, respec-tively, of the total sediment load. Contrary to 1998, the measuredsediment load via surface runoff and drainflow in May–October1996 was minor (Fig. 6). The simulated sediment load via subsur-face drains was over three times as high as the measured load inMay–October. However, the absolute amounts were relativelysmall during the period (simulated 225 kg ha�1 vs. measured69 kg ha�1). The heavy rains in November 1996 (234 mm) pro-duced more suspended sediment (Fig. 6) than was lost duringMay–October 1998 (Fig. 3), although the precipitation sums duringthe whole simulated periods were similar (584 mm in 1996 and603 mm in 1998). As in October 1998, high erosion occurring inNovember 1996 was due to hydraulic erosion caused by overlandflow.

NSME of sediment load via surface runoff in the calibration per-iod of 1998 (0.107) increased in validation to a value of 0.693 in1996, while NSME of sediment load via drains rose to an excep-tional value of 0.953 in 1996. Bias values for sediment loads via

surface runoff and drainflow increased to �0.27 and�0.13 kg ha�1 h�1, respectively, in 1996 from 1998 results(�0.10 and +0.0019 kg ha�1 h�1). The average sediment load viasurface runoff in 1996 was 0.57 kg ha�1 h�1, which is similar tothe 1998 result (0.54 kg ha�1 h�1), while the average drain sedi-ment load almost doubled from 0.29 kg ha�1 h�1 in 1998 to0.57 kg ha�1 h�1 in 1996.

The hourly dynamics of sediment load via surface runoff in1996 is again presented for the month with the highest events(Fig. 7). The simulated sediment load peaks via surface runoff(Fig. 7) were lower with longer falling limbs than the load peaksestimated from the measurements. The NSME value (0.693) be-tween the measured and modelled overland sediment loads duringthe validation period was clearly higher than the correspondingNSME value (0.107) during the calibration year.

The large rainstorm event in the beginning of July (22 mm h�1)produced a sediment peak via drainflow (Fig. 8) but only a minimalsediment load via surface runoff. Tillage occurring on 10 October1996 increased the late autumn sediment peaks compared to the

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(b) (a) Fig. 6. Measured and simulated cumulative sediment loads via (a) surface runoff and (b) drainflow in May–November 1996 (validation).

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Fig. 7. Hourly measured and simulated sediment loads via surface runoff in November 1996 (validation).

Fig. 8. Hourly measured and simulated sediment loads via drainflow in May–July and October–November 1996 (validation). Autumn tillage date is illustrated with an arrow.

L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143 139

growing season peaks, although the runoff peaks (Warsta et al.,2013) were on the same level in the summer and autumn. Theparameterisation change characterising the tillage effect on soilerodibility was the same in both years. It should be noted that till-age made in 1998 was a mixture of stubble cultivation and plough-ing, whereas the tillage in the validation year of 1996 wascomplete ploughing of the field.

4.4. Sensitivity analysis

A sensitivity analysis was performed with 1998 data to inspecthow sensitive the simulation results were to perturbations in themodel parameter values. The test was conducted with a low reso-lution grid (18 � 13 � 16 cells in x-, y-, and z-directions) due to thelong simulation times associated with the high resolution grid usedin the model calibration and validation stages. The test was con-ducted by offsetting the parameter values in the model one byone by �10 and +10% of the calibrated value, running the simula-tion, and saving the corresponding sediment load results via

surface runoff and drainflow. The computed total sediment loadsfor the simulated period were then compared to the results pro-duced with the calibrated parameter values and the percentagechanges of the sediment loads were summarised in Table 2. Theparameters in Table 2 were ranked in descending order of thecriterion, which is an indicator of the absolute change in the com-puted sediment loads in surface runoff and drainflow:

EC;p ¼ ðLSr1 � LSr2Þ2 þ ðLDr1 � LDr2Þ2 ð7Þ

where EC,p is the criterion for the parameter p, LSr1 is the load withsurface runoff using the +10% change of the parameter, LSr2 is theload with surface runoff using the �10% change of the parameter,LDr1 is the load with drainflow using the +10% change of the param-eter, and LDr2 is the load with drainflow using the �10% change ofthe parameter. The parameters of the flow model were includedin Table 2 because they had a large impact on the sediment load re-sults, which is due to the fact that the erosion model is coupled tothe flow model. The parameters related to the flow model are pre-sented in Appendix A.

Table 2Parameter sensitivity analysis results (%). Abbreviations used: LSr = sediment load(kg ha�1) via surface runoff, LDr = sediment load (kg ha�1) via drainflow, G.w.depth = initial groundwater table depth and Dit. w. depth = ditch water depth. Rootdepth parameter refers to the maximum root depth value. Parameters marked with �are parameters of the erosion model. The erosion model parameter names arepresented next to Eqs. (3)–(6). The flow model parameters are described in moredetail in Appendix A.

Rank Offset -> Depth +10% �10% +10% �10%Parameter p (m) LSr1 (%) LSr2 (%) LDr1 (%) LDr2 (%)

1 nMVG,M 0.25–2.4 79.2 112.9 94.5 99.52 Drain depth – 95.8 107.7 110.2 803 nMVG,M 0.0–0.25 99.6 95.6 89.6 113.34 hS 0.25–2.4 91.2 107.1 101.9 98.15 hW,THR Surface 101.5 99.4 106.1 92.46 hS 0.0–0.25 94.4 104.8 98.7 99.97 KFS,MUL 0.0–2.4 97.2 105.7 102.3 978 w 0.45–1.05 97.8 102.7 103.1 96.29 kH� Surface 103.1 97.3 101.6 97.4

10 Root depth – 97.6 102.3 102.8 98.611 cK 0.25–2.4 96.5 102 101.9 99.512 kR� Surface 100.6 99.7 103.4 97.513 cK 0.0–0.25 97.8 103.1 100.1 10014 aMVG,M 0.25–2.4 97.9 102 100.6 99.515 w 0.0–0.25 98 102 100 99.916 KSM 0.0–0.25 98.9 101.9 98.8 100.717 n Surface 101.6 98.7 100.6 99.118 Ditch depth – 98.8 101.7 99.5 100.619 G.w. depth – 98.3 101.3 100.4 100.120 aMVG,F 0.0–2.4 100.6 100.2 101.6 98.721 nMVG,F 0.0–2.4 99.6 101.8 99.2 100.522 w 1.05–2.4 99.5 101.7 99.8 99.323 aMVG,M 0.0–0.25 99.1 100.9 99.9 99.824 aK 0.0–0.25 101 99.5 100.8 100.425 aT� 0.0–2.4 100.3 100 99.2 100.626 Dit. w. depth – 100.6 99.6 100.6 99.627 aK 0.25–2.4 99.6 98.4 100.5 10128 KSM 0.25–2.4 99.7 99.3 99.5 100.529 w 0.25–0.45 100.6 100.2 99.1 100.130 hR 0.0–0.25 100.1 99.2 100.3 100.431 bK 0.0–0.25 99.8 99.8 100.2 100.932 d 0.0–2.4 99.9 100.3 100 100.433 aL� 0.0–2.4 99.9 100.2 100.1 10034 DS� Surface 99.8 99.5 100.5 100.435 bK 0.25–2.4 99.3 99.5 100.9 101

140 L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143

It is obvious from Table 2 that the erosion results are more sen-sitive to some of the flow model parameters than to the parame-ters in the erosion model. The flow model parameters primarilyaffected the erosion through their impact on the distribution of to-tal runoff to surface runoff and drainflow. In the erosion model, thesensitive parameters were those that controlled hydraulic andsplash erosion.

Both the erosion model and the flow model were sensitive tonMVG in the soil matrix (Ranks 1 and 3), hS (Ranks 4 and 6), anddrain depth from the surface (Rank 2). On Rank 5 is hW,THR, whicheffectively controls overland depression storage and thus initiationof overland flow. kH and kR have relatively high ranks (Ranks 9 and12, respectively) because they dictate how much suspended sedi-ment is generated via hydraulic and raindrop splash erosion pro-cesses. The effect of DS is small (Rank 34) because it is onlyassociated with the calculation of TC and a large minimum valuewas used for the parameter (5.0 kg m�3) in the simulations (seeSection 4.1). Since soil parameters are on the highest ranks the sed-iment load via subsurface drains is more sensitive to the studiedparameter perturbations than the sediment load via surface runoff.

5. Discussion

The simulated total sediment load through all pathways (sur-face runoff, drainflow, and groundwater seepage) in the Sjökulla

experimental field was high (4353 and 6489 kg ha�1 in 1998 and1996, respectively) compared with the reported regional levels of30–3300 kg ha�1 a�1 (Tattari and Rekolainen, 2006) although thesimulations included only the growing seasons and the followingautumns. The loads estimated from the measurements in surfacerunoff and tile drain outflow were also prominent for the respec-tive periods (3648 kg ha�1 in 1998 and 5678 kg ha�1 in 1996) com-pared to other Finnish clayey fields. Vakkilainen et al. (2010)reported average annual sediment loads of 320–2663 kg ha�1 viasurface runoff and drainflow from five field sections in southernand southwestern Finland during a measurement period of twoyears. The highest load was observed from a clayey field with aslope of 5%. According to Vakkilainen et al. (2010), 60–95% of theannual sediment loads were discharged via subsurface drains. Ina 10-year study by Turtola et al. (2007) in clayey field sections(average slope of 2%) in southwestern Finland, the total sedimentloads via surface runoff and drainflow were 407–1700 kg ha�1 a�1

under autumnal ploughing and stubble cultivation and 51–94% ofthe loads were transported via drainflow. In our simulations, 41%and 51% of the total sediment load via surface runoff and drainflowwas discharged via subsurface drains in May–October 1998 andMay–November 1996, respectively. The modelled proportions arein accordance with the measured ranges in other clayey field sitesin Finland. The measurements support the model assumption thaterosion primarily occurs in the tillage layer, and sediment is trans-ported to subsurface drains through the macropore domain. Theadded value of the model comes through the holistic quantificationof sediment transport through different pathways. The results re-veal that there are other transport pathways, such as groundwaterseepage, in addition to surface runoff and drainflow.

The absolute sediment loads in the Sjökulla field were muchhigher than the annual loads in the other comparable fields (Vak-kilainen et al., 2010; Turtola et al., 2007). During the calibrationyear 1998, the clay soil was wet and swollen in October whenthe 2-week long rainy period (129 mm) occurred and over 80% ofthe 1998 sediment load was generated. In the validation year1996, a dry period from August to September preceded the autumnrains. In October, 58 mm of precipitation was measured and inNovember a record breaking 234 mm (the average November rain-fall at the site is about 90 mm). Both 1996 and 1998 had extraordi-nary rainfall patterns and high amounts of surface runoff, whichcaused the high erosion and sediment loads during the simulationperiods. Even though the absolute amounts of simulated surfacerunoff were similar in 1996 (67 mm) and 1998 (61 mm), the pro-portions of sediment load via surface runoff were different (34%in 1996 and 44% in 1998). As shown in the sensitivity analysis ofthe model, the hydrological parameters have a large impact on sed-iment load generation and therefore, it is crucial to have a realisticrepresentation of runoff generation in the erosion model to be ableto reproduce sediment transport (Smith et al., 1999; Wicks andBathurst, 1996). The successful results of runoff generation in ear-lier FLUSH applications (Warsta et al., 2013; Turunen et al., 2013)support the use of the model as a basis for erosion modelling.

Knisel and Turtola (2000) simulated soil erosion in the Kotkano-ja field in Finland with GLEAMS combined with an approximationof suspended sediment transport via preferential flow pathwaysinto subsurface drains (see Section 1). The simulated cumulativesediment load via drains (3255 kg ha�1) during the 7-year studyperiod was approximately half of the sediment load via surfacerunoff (7911 kg ha�1) (Knisel and Turtola, 2000). Larsson et al.(2007) applied a modified ICECREAM model to a silty clay field sitein Sweden. According to their results for the calibration period1994–1995, the cumulative sediment loads via drains were similarto the measurements (simulated 231 kg ha�1 vs. measured261 kg ha�1). Lundekvam (2007) measured and simulated soil ero-sion in five sites in southern Norway and assessed their results in

Table 3Flow model parameters in the sensitivity analysis. Abbreviations used: G.w.depth = initial groundwater table depth and Dit. w. depth = ditch water depth.

Parameter p Unit Explanation

aMVG (m�1) Water retention curve parameteraK (–) Shrinkage curve parameterbK (–) Shrinkage curve parametercK (–) Shrinkage curve parameterhR (m3 m�3) Residual volumetric water contenthS (m3 m�3) Saturated volumetric water contentDrain depth (m) Installation depth of subsurface drainsDitch depth (m) Open ditch depthDit. w. depth (m) Water depth in open ditchesd (m) Radius or half width of matrix structureG.w. depth (m) Initial groundwater depth from surfacehW,THR (m) Overland flow threshold depthKFS,MUL (m h�1) Macropore hydraulic conductivity multiplierKS (m h�1) Saturated hydraulic conductivityn (–) Manning’s roughness coefficientnMVG (–) Water retention curve parameterRoot depth (m) Maximum root depthw (m3 m�3) Macropore fraction of total porosity

L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143 141

terms of annual sediment loads during 1992–2000. The sites hadslopes of 12–13%, and the soil types were silty clay loam, clay,and loam with the average sediment loads of 2700–6350, 1043,and 158 kg ha�1 a�1, respectively. In all the aforementioned modelapplications, the simulated sediment loads were assessed only interms of annual values even though daily time steps were usedin the simulations. Lundekvam (2007) notes that their model,which can be regarded as an example of an empirical erosion mod-el, easily overestimates or underestimates erosion for years when afew runoff episodes dominate the annual sediment transport. Suc-cessful simulation of short-term sediment transport episodes callsfor the use of process-based models, such as FLUSH operating withsub-hour time steps. The distributed nature of FLUSH supportsdetection of erosion prone areas in the field area and testing of buf-fer zone effects on sediment loads.

Since the erosion model embedded in FLUSH evolved fromearlier process-based models (Taskinen and Bruen, 2007b; Wicksand Bathurst, 1996), the calibrated parameter values can bereflected against the values suggested in earlier modelling studies.The values of kH and kR, which were found out to be among themost sensitive erosion model parameters, were set in this studyto 1.0 � 10�7 (2.2 � 10�6 after tilling) kg m�2 s�1 and 1.2 s�2 kg�1

m�2, respectively. The range of previously reported kH values isnotably high (5.0 � 10�3 kg m�2 s�1–18.0 � 10�8 kg m�2 s�1) (e.g.Taskinen, 2002; Wicks and Bathurst, 1996; Ariathurai and Arulan-andan, 1978) which reflects the uncertainty related to the determi-nation of its value, while kR values varied between 82 and19 s�2 kg�1 m�2 (e.g. Wicks and Bathurst, 1996; Bradford et al.,1987a,b; Meyer and Harmon, 1984). Our calibrated kH values fallwell within this range. The calibrated value of kR was clearly smal-ler than in previous studies. It is noteworthy that the value of kR

was calibrated against the conditions preceding the tillage in1998 and the value was not increased for the period followingthe tillage because the hydraulic erosion (parameter kH) dominatedthe erosion process and masked the effect of increasing kR on sed-iment transport. Therefore the value was likely to be underesti-mated for the conditions after tillage.

FLUSH was constructed by including the assumed key processesthat control sediment load generation and ignoring some pro-cesses, such as sieving, rill and interrill erosion, and simulation ofmultiple particle size classes. The simulated sediment load resultswere comparable to the measurements although there was no sed-iment sieving process description in the model. Sieving was notlikely to occur to a large extent due to the small size of clay

aggregates and direct preferential flow routes from the surface tothe subsurface drains. Larsson et al. (2007) had to include sedimentsieving in the macropore system to decrease the simulated sedi-ment load via drains. Interrill and rill erosion were not simulatedseparately by FLUSH because no data were available to paramete-rise the processes. Similar to FLUSH, interrill and rill erosion arelumped as sheet erosion in several earlier models (e.g. Taskinenand Bruen, 2007b; Wicks and Bathurst, 1996). Inclusion of interrilland rill erosion schemes in FLUSH might be one option to improvethe prediction of sediment load peaks (Figs. 4 and 7) by adjustingflow velocities and related transport capacity. FLUSH simulatesonly a single particle size class, which is a common assumptionin erosion models (e.g. Nord and Esteves, 2005; Sharda and Singh,1994). Simulation of several sediment particle size classes was rec-ommended by Beuselinck et al. (2002) and Heilig et al. (2001).However, in our field the sediment loads were composed mostlyof suspended, fine clay aggregates, and the use of several particlesize classes would have unnecessarily complicated the overlanderosion and subsurface transport models. Additionally, accordingto the sensitivity analysis (Table 2), the simulation results werenot sensitive to changes in the particle diameter.

The following problems were encountered in the hydraulic ero-sion and transport capacity descriptions in the overland erosionmodel. Because hydraulic erosion was estimated as a function ofthe overland flow shear stress (s) and not flow velocity, soil erosionactually increased when the Manning roughness coefficient n wasincreased. When n is increased, flow velocity decreases, but flowdepth increases. The value of s in Eq. (4) was calculated as a func-tion of flow depth. The flow depth effect on erosion through its ef-fect on shear stress is visible, albeit faintly, in the sensitivityanalysis (Table 2), i.e. when n is increased, sediment loads via sur-face runoff and drainflow increase. The same effect was reportedpreviously by Nord and Esteves (2005) and Sharda et al. (1994).Several authors (e.g. Taskinen and Bruen, 2007b; Julien and Si-mons, 1985) recommended Yalin’s transport capacity equation(Yalin, 1963) for overland erosion simulation. The application ofYalin’s equation was problematic in this study because it is as-sumed in the formulation that the value of TC drops to zero whenwater is not moving, which is unrealistic for suspended clay parti-cles. There are areas in the centre of the northern part of the field(Fig. 2) that are almost flat and where water can remain practicallystill. Previously, Wicks and Bathurst (1996) encountered similarproblems in their simulations. The method by Engelund and Han-sen (1967) was also tried in FLUSH, but the simulation results werenot improved (not shown). In the end, a minimum value of5.0 kg m�3 was applied for TC, even for standing water, althoughthis practically dampened the effect of transport capacity on over-land sediment transport in the simulations.

6. Conclusions

The FLUSH model was supplied with a process-based erosioncomponent to simulate overland erosion and sediment transportvia preferential flow pathways to the subsurface drains. The mostprominent difference between the new model and the existingconceptual models describing both overland and subsurface sedi-ment transport processes is the possibility to simulate the spatialdistribution of soil erosion and sediment loads with short-termdynamics. FLUSH incorporates descriptions for the most importantprocesses and pathways of sediment transport. The model was ableto reproduce the measured sediment loads via surface runoff anddrainflow during periods with highly variable sediment load gen-eration. The data and simulations demonstrate that the sedimentloads via subsurface drains can be a major part of the annual loadin the clayey soils of northern Europe. Overland flow and the

142 L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143

resulting hydraulic erosion were found to be the culprit for thehigh sediment loads generated in tilled soils during heavy rains,while raindrop splash erosion was causing the erosion in crop orstubble covered soils. Tillage in the autumn increased soil erodibil-ity and exposed the soil to the effects of hydraulic erosion. Our out-comes confirmed the results from many earlier studies and therecommendations to leave the soils without tilling in the autumnbecause long-term rainy periods or heavy rain storms in tilled soilscan lead to high sediment losses also in Nordic conditions. It isobvious from the conducted sensitivity analysis that the erosionresults are more sensitive to some of the flow model parametersthan to the parameters in the erosion model. The flow modelparameters primarily affected the erosion through their impacton the distribution of total runoff to surface runoff and drainflow.In the erosion model, the sensitive parameters were those thatcontrolled hydraulic and splash erosion rates. The measurementsand model simulations suggested that the clay soil aggregatescan stay suspended for prolonged times, even in stagnant flow con-ditions. This was described in FLUSH by introducing a minimumvalue for sediment transport capacity that is independent of over-land flow velocity.

Acknowledgements

The data sets were provided by several organisations, includingAalto University, University of Helsinki, MTT Agrifood ResearchFinland, and the Finnish Meteorological Institute. The authorswould like to express their gratitude to Prof. Pertti Vakkilainenfor his contribution to this study. We are also grateful to Prof. Nich-olas Jarvis, Prof. Jirí Šimunek, and Prof. Eila Turtola for their valu-able feedback and advice. We would like to thank Prof. HafzullahAksoy and the anonymous reviewer for their constructive com-ments. The study was funded by Maa- ja vesitekniikan tuki ry.,the ENARCH Doctoral Programme of Aalto University, Salaojituk-sen tukisäätiö (Finnish Drainage Foundation), Sven Hallinin tut-kimussäätiö (Sven Hallin Research Foundation), the DoctoralProgramme of the Built Environment (RYM-TK), and the Aalto Uni-versity School of Engineering. We acknowledge CSC – IT Center forScience Ltd. for the allocation of computational resources.

Appendix A

Explanations of the flow model parameters investigated in thesensitivity analysis are presented in Table 3. Parameters are dis-cussed more in depth in Warsta et al. (2013). Subscripts M and Frefer to the soil matrix and macropore versions of the parameterin Table 2 in Section 4.4.

References

Aksoy, H., Kavvas, M., 2005. Review of hillslope and watershed scale erosion andsediment transport models. Catena 64, 247–271.

Alakukku, L., Nuutinen, V., Ketoja, E., Koivusalo, H., Paasonen-Kivekäs, M., 2010. Soilmacroporosity in relation to subsurface drain location on a sloping clay field inhumid conditions. Soil Till. Res. 106, 275–284.

Ariathurai, R., Arulanandan, K., 1978. Erosion rates of cohesive soils. Proc. Am. Soc.Civ. Eng., J. Hydraul. Div. 104, 279–283.

Bärlund, I., Tattari, S., Puustinen, M., Koskiaho, J., Yli-Halla, M., Posch, M., 2009. Soilparameter variability affecting simulated field-scale water balance, erosion andphosphorus losses. Agric. Food Sci. 18, 402–416.

Beuselinck, L., Hairsine, P.-B., Govers, G., Poesen, J., 2002. Evaluating a single-classnet deposition equation in overland flow conditions. Water Resour. Res. 38,1110. http://dx.doi.org/10.1029/2001WR000248.

Bradford, J.M., Ferris, J.E., Remley, P.A., 1987a. Interrill soil erosion processes: I.Effects of surface sealing on infiltration, runoff, and soil splash detachment. SoilSci. Soc. Am. J. 51, 1566–1571.

Bradford, J.M., Ferris, J.E., Remley, P.A., 1987b. Interrill soil erosion processes: II.Relationship of splash detachment to soil properties. Soil Sci. Soc. Am. J. 51,1571–1575.

Davison, P.S., Withers, P.J.A., Lord, E.I., Betson, M.J., Strömqvist, J., 2008. PSYCHIC – aprocess based model of phosphorus and sediment mobilisation and deliverywithin agricultural catchments. Part 1: model description andparameterisation. J. Hydrol. 350, 290–302.

De Roo, A.P.J., Wesseling, C.G., Jetten, V.G., Ritsema, C.J., 1996a. LISEM: a single-event physically based hydrological and soil erosion model for drainage basins.I: theory, input and output. Hydrol. Proc. 10, 1107–1117.

De Roo, A.P.J., Wesseling, C.G., Jetten, V.G., Ritsema, C.J., 1996b. LISEM: a physically-based hydrological and soil erosion model incorporated in a GIS. In: HydroGIS96: Application of Geographic Information Systems in Hydrology and WaterResources Management. Proceedings of the Vienna Conference, April 1996,IAHS Publ. No. 235, pp. 395–403.

Engelund, F., Hansen, E., 1967. A Monograph on Sediment Transport in AlluvialStreams. Teknisk Forlag, Copenhagen.

Heilig, A., DeBruyn, D., Walter, M., Rose, C., Parlange, J., Steenhuis, T., Sander, G.,Hairsine, P., Hogarth, W., Walker, L., 2001. Testing a mechanistic soil erosionmodel with a simple experiment. J. Hydrol. 224, 9–16.

Jacobsen, O., Moldrup, P., Larsen, C., Konnerup, L., Petersen, L., 1997. Particletransport in macropores of undisturbed soil columns. J. Hydrol. 196,185–203.

Johnson, B.E., Julien, P.Y., Molnar, D.K., Watson, C.C., 2000. The two-dimensionalupland erosion model CASC2D-SED. J. Am. Water Res. Assoc. 36, 31–42.

Julien, P.Y., Simons, D.B., 1985. Sediment transport capacity of overland flow. Trans.ASAE 28, 755–762.

Kauppi, L., 1982. Testing the Applicability of the CREAMS Model to Estimation ofAgricultural Nutrient Losses in Finland. Publications of the Water ResearchInstitute, National Board of Waters, Finland, No. 49, 30–39.

Kavvas, M.L., Yoon, J., Chen, Z.Q., Liang, L., Dogrul, E.C., Ohara, N., Aksoy, H.,Anderson, M.L., Reuter, J., Hackley, S., 2006. Watershed environmentalhydrology model: environmental module and its application to a Californiawatershed. J. Hydrol. Eng. 11, 261–272.

Kirkby, M., 2006. Impacts of environmental changes on soil erosion across Europe.In: Boardman, J., Poesen, J. (Eds.), Soil Erosion in Europe. John Wiley & Sons, pp.729–742.

Klepsch, S., Gerzabek, M.H., Loiskandl, W., Bossew, P., 2005. Water and solutemovement in soils – concepts and models for migration phenomena apart fromclassical convection–dispersion equation. OICMS, 249–261.

Knisel, W.G. (Ed.), 1980. CREAMS – A Field Scale Model for Chemicals, Runoff, andErosion from Agricultural Management Systems. USDA, Conservation ReportNO. 26, US Department of Agriculture, Washington, DC.

Knisel, W.G., Turtola, E., 2000. Gleams model application on a heavy clay soil inFinland. Agric. Water Manage. 43, 285–309.

Kroes, Van Dam, Groenendijk, P., Hendriks, R.F.A., Jacobs, C.M.J., 2008. SWAPVersion 3.2 Theory Description and User Manual. Alterra-Report, Wageningen,262 pp.

Larsson, M.H., Persson, K., Ulén, B., Lindsjö, A., Jarvis, N.J., 2007. A dual porositymodel to quantify phosphorus losses from macroporous soils. Ecol. Mod. 205,123–134.

Laubel, A., Jacobsen, O.H., Kronvang, B., Grant, R., Andersen, H.E., 1999. Subsurfacedrainage loss of particles and phosphorous from field plot experiments and atile-drained catchment. J. Environ. Qual. 28, 576–584.

Leonard, R.A., Knisel, W.G., Still, D.A., 1987. GLEAMS: groundwater loading effects ofagricultural management systems. Trans. Am. Soc. Agric. Eng. 30, 1403–1418.

Lundekvam, H.E., 2007. Plot studies and modelling of hydrology and erosion insoutheast Norway. Catena 71, 200–209.

Mantz, P.A., 1977. Incipient transport of fine grains and flakes by fluids-extendedShields diagram. Proc. Am. Soc. Civ. Eng, J. Hydraul. Div. 103, 601–615.

McKay, L.D., Gillham, R.W., Cherry, J.A., 1993. Field experiments in a fractured claytill 2. Solute and colloid transport. Water Resour. Res. 29, 3879–3890.

Meyer, L.D., Harmon, W.C., 1984. Susceptibility of agricultural soils to interrillerosion. Soil Sci. Soc. Am. J. 48, 1152–1157.

Meyer, L.D., Harmon, W.C., McDowell, L.L., 1980. Sediment sizes eroded from croprow sideslopes. Trans. ASAE 23, 891–898.

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models.Part I—a discussion of principles. J. Hydrol. 10, 282–290.

Nord, G., Esteves, M., 2005. PSEM_2D: a physically based model of erosion processesat the plot scale. Water Resour. Res. 41, 1–14.

OpenMP Architecture Review Board (OARB), 2008. OpenMP Application ProgramInterface Version 3.0. <http://www.openmp.org/mp-documents/spec30.pdf>.

Øygarden, L., Kværner, J., Jenssen, P.D., 1997. Soil erosion via preferential flow todrainage systems in clay soils. Geoderma 76, 65–86.

Paasonen-Kivekäs, M., Koivusalo, H., Bärlund, I., Tattari, S., Alakukku, L., 2006.Modelling runoff and erosion in agricultural soil: application of ICECREAMmodel to a field site in southern Finland. In: Proceedings of NJF Seminar No. 373Transport and Retention of Pollutants from Different Production Systems –With Respect to Implementation of the Water Framework Directive, 11–14 June2006, Tartu, Estonia.

Paasonen-Kivekäs, M., Vakkilainen, P., Karvonen, T., 2008. Nutrient transportthrough tile drains on a clayey field. In: 10th International DrainageWorkshop of ICID Working Group on Drainage, Helsinki-Tallinn, Finland-Estonia, 6–11 July 2008, Conference Proceedings, pp. 142–152.

Peltovuori, T., Uusitalo, R., Kauppila, T., 2002. Phosphorus reserves and apparentphosphorus saturation in four weakly developed cultivated pedons. Geoderma110, 35–47.

Ray, C., Ellsworth, T.R., Valocchi, A.J., Boast, C.W., 1997. An improved dual porositymodel for chemical transport in macroporous soils. J. Hydrol. 193, 270–292.

L. Warsta et al. / Journal of Hydrology 498 (2013) 132–143 143

Rekolainen, S., Posch, M., 1993. Adapting the CREAMS model for Finnish conditions.Nord. Hydrol. 24, 309–322.

Sharda, V.N., Singh, S.R., 1994. A finite element model for simulating runoff and soilerosion from mechanically treated agricultural lands 1. Governing equationsand solutions. Water Resour. Res. 30, 2287–2298.

Sharda, V.N., Singh, S.R., Sastry, G., Dhruvanarayana, V.V., 1994. A finite elementmodel for simulating runoff and soil erosion from mechanically treatedagricultural lands 2. Field validation and applications. Water Resour. Res. 30,2299–2310.

Smith, R.E., Goodrich, D.C., Unkrich, C.L., 1999. Simulation of selected events on theCatsop catchment by KINEROS2: a report for the GCTE conference on catchmentscale erosion models. Catena 37, 457–475.

Spitz, K., Moreno, J., 1996. A Practical Guide to Groundwater and Solute TransportModelling. John Wiley & Sons, 461 pp.

Soil Survey Staff, 1998. Keys to Soil Taxonomy, 8th Edition. US Department ofAgriculture Natural Resource Conservation Service, Washington, DC, 326 pp.

Taskinen, A., 2002. Mathematical Modelling of Overland Flow, Erosion andTransport of Phosphorus. PhD Thesis, University College Dublin.

Taskinen, A., Bruen, M., 2007a. Incremental distributed modelling investigation in asmall agricultural catchment: 1. Overland flow with comparison with the unithydrograph model. Hydrol. Proc. 21, 80–91.

Taskinen, A., Bruen, M., 2007b. Incremental distributed modelling investigation in asmall agricultural catchment: 2. Erosion and phosphorus transport. Hydrol.Proc. 21, 92–102.

Tattari, S., Rekolainen, S., 2006. Finland. In: Boardman, J., Poesen, J. (Eds.), SoilErosion in Europe. John Wiley & Sons, pp. 27–32.

Tattari, S., Bärlund, I., Rekolainen, S., Posch, M., Siimes, K., Tuhkanen, H.-R., Yli-Halla,M., 2001. Modeling sediment yield and phosphorus transport in Finnish clayeysoils. Trans. ASAE 44, 297–307.

Turtola, E., Paajanen, A., 1995. Influence of improved subsurface drainage onphosphorus losses and nitrogen leaching from a heavy clay soil. Agric. WaterManage. 28, 295–310.

Turtola, E., Alakukku, L., Uusitalo, R., 2007. Surface runoff, subsurface drainflow andsoil erosion as affected by tillage in a clayey Finnish soil. Agric. Food Sci. 16,332–351.

Turunen, M., Warsta, L., Paasonen-Kivekäs, M., Nurminen, J., Myllys, M., Alakukku,L., Äijö, H., Puustinen, M., Koivusalo, H., 2013. Modeling water balance andeffects of different subsurface drainage methods on water outflow componentsin a clayey agricultural field in boreal conditions. Agric. Water Manage. 121,135–148. http://dx.doi.org/10.1016/j.agwat.2013.01.012.

Ulén, B., 1995. Episodic precipitation and discharge events and their influence onlosses of phosphorus and nitrogen from tile drained arable fields. Swed. J. Agric.Res. 25, 25–31.

USDA, 1995. WEPP User Summary. NSERL Report No. 11, National Soil ErosionResearch Laboratory, USDA, 141 pp.

Uusitalo, R., Turtola, E., Kauppila, T., Lilja, T., 2001. Particulate phosphorus andsediment in surface runoff and drainflow from clayey soils. J. Environ. Qual. 30,589–595.

Vakkilainen, P., Alakukku, L., Koskiaho, J., Myllys, M., Nurminen, J., Paasonen-Kivekäs, M., Peltomaa, R., Puustinen, M., Äijö, H., 2010. Pellon vesitaloudenoptimointi, Loppuraportti 2010. Salaojituksen tutkimusyhdistys ry:n tiedote 30,Helsinki 2010, Salaojituksen tutkimusyhdistys ry, 114 pp (in Finnish).

Warsta, L., 2011. Modelling Water Flow and Soil Erosion in Clayey, SubsurfaceDrained Agricultural Fields. Doctoral Dissertation. 82, Aalto University, 209 pp.<http://lib.tkk.fi/Diss/2011/isbn9789526042893/>.

Warsta, L., Turunen, M., Koivusalo, H., Paasonen-Kivekäs, M., Karvonen, T., Taskinen,A., 2012. Modelling heat transport and freezing and thawing processes in aclayey, subsurface drained agricultural field. In: 11th ICID Int. DrainageWorkshop on Agricultural Drainage Needs and Future Priorities. Cairo 23–27.9.2012, Egypt. Proceedings. 10 pp.

Warsta, L., Karvonen, T., Koivusalo, H., Paasonen-Kivekäs, M., Taskinen, A., 2013.Simulation of water balance in a clayey, subsurface drained agricultural fieldwith three-dimensional FLUSH model. J. Hydrol. 476, 395–409. http://dx.doi.org/10.1016/j.jhydrol.2012.10.053.

Werner, M.V., 1995. GIS-orientierte Methoden der digitalen Reliefanalyse zurModellierung von Bodenerosion in kleinen Einzugsgebieten. DoctoralDissertation, Freie Universität, Berlin.

Wicks, J.M., Bathurst, J.C., 1996. SHESED: a physically based, distributed erosion andsediment yield component for the SHE hydrological modelling systems. J.Hydrol. 175, 213–238.

Yalin, M.S., 1963. An expression for bed-load transportation. Proc. Am. Civ. Eng., J.Hydraul. Div. 89, 221–250.

Yalin, M.S., 1977. Mechanics of Sediment Transport. Pergamon Press, Toronto, 298pp.

Yli-Halla, M., Mokma, L. Peltovuori, T., Sippola, J., 2000. Suomalaisia maaprofiileja,Agricultural soil profiles in Finland and their classification. Publications ofAgricultural Research Centre of Finland, Series A 78, 104 pp.

Zheng, C., Bennet, G.D., 2002. Applied Contaminant Transport Modelling, second ed.Wiley, 621 pp.