Soil Use and Management (2002) 18, 61±67 DOI: 10.1079/SUM2001102

Parameterization of the MACRO model to representleaching of colloidally attached inorganic phosphorus

following slurry spreading

M.B. McGechan1*, N.J. Jarvis2, P.S. Hooda3 & A.J.A. Vinten1

Abstract. The dual porosity soil water and contaminant transport model MACRO was tested for its suit-ability to represent water ¯ows and leaching of phosphorus (P) through ®eld drains following spreading ofslurry. These ¯ows are characterized by very high loadings of P, including a high proportion in colloidallyattached form, for about one week following winter spreading of slurry, followed by quite a rapid decline tothe low background level. Use was made of the option in MACRO for representing colloid facilitated con-taminant transport. The model simulates transport through macropores and soil matrix pores (micropores)of contaminant carrying colloids, as well as trapping of colloids by straining and ®ltration using an adapta-tion of standard ®ltration equations. Calibration involved selecting soil hydraulic parameters, colloid ®ltra-tion coef®cients and P sorption characteristics for two soils from measured and literature values. Both P insolution and P attached to colloids were represented in simulated outputs. Reasonable agreement was foundbetween simulated and measured water and leached P ¯ows. Work with the model suggests that macropore¯ow through the soil to ®eld drains of colloidally transported P is an important component of water pollu-tion associated with slurry spreading

Keywords: Models, leaching, phosphorus, slurries, application to land

I N T R OD U C T I O N

A recent review of models which contain a representationof soil phosphorus (P) dynamics by Lewis & McGechan

(2002) highlighted the need for a P model which is not justan extension of a soil nitrogen (N) dynamics model with Ptreated as a soluble contaminant. Differences in the chemicalreactivity between N and P species mean that there aresigni®cant differences between the behaviour of N and P insoil, with P relying extensively upon particulate or colloidfacilitated transport. It is now apparent that sorption ontomobile suspended or colloidal soil particles is an importantmechanism leading to leaching of P. Slurry (liquid manure)contains large quantities of colloidal organic matter, ontowhich inorganic P compounds in the slurry tend to beattached by sorption. When slurry is spread on the soil,some of these P carrying colloids ®nd their way into water¯ows and to drains.

Particulate or colloidal material moves less freely thansolutes in moving soil water, since it can be subjected to

straining and ®ltration processes. However, restrictions onmovements are greater for larger particles and for ¯owsthrough smaller pores (McGechan & Lewis 2002a). Thelargest soil pores or `macropores' impose comparatively littlerestriction on movements of colloids, and when associatedwith fast water ¯ows this leads to potentially rapid transportof any associated pollutants. High P loads measured in ®elddrains immediately following winter spreading of slurry(Hooda et al. 1999), can really only be accounted for bymacropore ¯ow.

As well as arising in dry, cracking clay, macropores andmacropore ¯ow can also be found in very wet conditions inaggregated soils, when water-®lled inter-aggregate spacesprovide an unrestricted route. Colloidal particles also passwith almost no restriction in such ¯ows. Some simulationmodels of soil water movement provide representation ofmacropore ¯ows, but with varying levels of sophistication.Of all known models, the MACRO model (Jarvis 1994) hasthe most comprehensive treatment of macropore ¯ow; it hasrepresentation of distinct macropore and soil matrix poreregions (or `domains'), with different equations governingwater movement, and different solute concentrations in eachdomain. Recent developments of MACRO include a newfeature of colloid facilitated transport of reactive (sorbed)contaminants (Jarvis et al. 1999). The main application ofMACRO up to now has been concerned with movements of

+

1Land Management Department, Environment Division, SAC, BushEstate, Penicuik EH26 0PH, UK. 2Department of Soil Sciences, Divisionof Environmental Physics, SLU, Box 7014, 750 07 Uppsala, Sweden.3Centre for Earth and Environmental Science Research, KingstonUniversity, Kingston upon Thames, KT1 2EE, UK*Corresponding Author: Fax: 44 131 535 3031. Email: m.mcgechan@ed.sac.ac.uk

M.B. McGechan et al. 61

pesticides. However, some pesticides exhibit behavioursimilar to P, such as sorption onto surfaces both on mobilecolloidal particles and in the static soil matrix.Parameterization of the MACRO model to represent someof the important soil P processes, and testing simulatedoutput against experimental data from sites which havereceived slurry applications, are the subjects of this paper.

P A RA M E T E R I Z A T I O N O F T HE M A CR OM OD E L

Basic features of the modelThe main features of the MACRO model, including thebasic equations for water and solute transport in two`domains' of each of a number of layers in the pro®le, havebeen described in detail by Jarvis (1994), with a furtherevaluation by Larsson & Jarvis (1999). Standard hydro-logical equations are used in each domain, with commonvalues of the soil water content qb, hydraulic conductivityKb and soil water tension yb at the boundary (`break-point')between the two domains. For the current study, parametersof the soil water functions (McGechan 2001) were selectedbased on a previous calibration (McGechan et al. 1997) ofthe single domain (but layered) soil water model SOIL forthe same ®eld sites. Only features of MACRO important tothe current study, such as those concerning colloidfacilitated transport of contaminants (Jarvis et al. 1999),are described in detail here.

Procedure for simulating colloid facilitated transport ofcontaminantsTransport of soluble contaminants is represented inMACRO by a single simulation run in which theconvection-dispersion equation is solved at each timestepin each layer to estimate the solute concentration in both themacropores and soil matrix pores in that layer. Whensimulating colloid facilitated transport of a contaminant, twoconsecutive simulation runs are carried out. In the ®rst run,the `solute' is considered to be the colloids which carry thecontaminant. In the second, the `solute' is considered to bethe contaminant which is carried by sorption sites on thesurfaces of the colloids. The model includes the facility forgeneration of colloids by detachment of small soil particlesby rainfall impact on the surface, but this option is not themain source of colloids in this case. In the currentapplication, colloids are assumed to be a component ofslurry applied to the soil, and the `irrigation' routine inMACRO is used to represent the slurry application. Thesame quantity of `irrigation water' (in mm) is speci®ed forboth simulation runs, but in the ®rst run the concentrationof colloidal material is speci®ed, while in the second theconcentration of inorganic P is speci®ed.

SorptionSorption of reactive chemicals onto static soil components iscalculated in MACRO according to the Freundlich isothermequation (as discussed by McGechan & Lewis, 2002b),assuming instantaneous equilibrium between solution andsorbed phases

s = Kd cn (1)

where s is the sorbed phase concentration in eithermacropores or soil matrix pores, Kd is the sorptioncoef®cient, c is the concentration in solution and n is theFreundlich exponent. Sorption of chemicals onto mobilecolloidal particles is represented by a simpli®ed form ofEquation 1, with a colloid sorption coef®cient Kc, and theFreundlich exponent n always taking a value of unity.

For sorption onto static soil components, selected valuesof the sorption equation parameters Kd and n are listed inTable 1. For individual layers of the silty clay loam, thesewere based on measurements for a low P concentration rangereported by Hooda et al. (1999). A similar measurementprocedure was adopted for the clay loam, but as this soil hada history of regular ploughing, it was assumed that thesorption behaviour would be uniform and the same values

Table 1. Sorption equation parameters, and initial soil phosphorus contents (based on soil test P values) set at start of simulations, for soil layers.

Location Soil Layer depth,(m)

Sorption coef®cient Kd,ln mg1±n kg±1

Sorption exponentn

Sorbed P (Olsen test P)(mg P kg±1 soil)

Crichton Royal Silty clay 0-0.1 203 1.648 38Farm, Dumfries loam 0.1-0.2 307 1.648 28

0.2-0.3 350 1.648 270.3-0.4 4500 1.648 270.4-0.5 5500 1.648 270.5-1.5 6500 1.648 27

Bush, Edinburgh Clay loam 0-1.5 250 1.0 35

Table 2. Colloid and phosphorus transport parameters.

Parameter Site Date Parametervalue

Reference ®lter coef®cient formacropores, fref (m±1)

0.5

Reference ¯ow velocity (macropores)vref (m h±1)

50

Filtering exponent (macropores) nf

(dimensionless)1.8

Filter coef®cient (micropores) fc (m±1) 40

Freundlich sorption coef®cient Dumfries 1 Oct 94 1.7(linear) for P sorption on colloids, 1 Oct 95 2.7Kc (m3 g±1) Bush, arable 1 Jan 99 1.2

Bush, grass 1 Jan 99 10

Parameterization of the MACRO model to represent leaching of phosphorus62

were assumed for all layers. No direct measurements wereavailable for the coef®cient for sorption of P onto slurrycolloids Kc. An initial value was selected on the basis of thatassumed for colloid transport of pesticide in the studies ofJarvis et al. (1999) and Villholth et al. (2000) to give a similarratio Kc/Kd of around 400 (representing the quantity of Psorbed per unit mass of sorbing material for the mobilecolloid compared to static soil material). This ratio takesaccount of the much larger surface area in the very smallcolloidal particles compared to the static soil matrix (whichcontains particles with a wide range of sizes from ®ne clay tocoarse sand). The value of Kc was later adjusted (Table 2)from its initial assumed value to improve ®ts of simulated tomeasured P losses.

Slow phosphorus deposition represented as degradationThere are a large number of published papers (reviewed byMcGechan & Lewis, 2002b) describing how inorganic Pundergoes, in addition to and in parallel with sorption ontosurface sites, a slow, time-dependent deep sorption reactionleading to deposition of P at a depth below surfaces withinsoil mineral particles. Phosphorus which has undergone thisprocess is no longer immediately available as a nutrient forplant growth (Sharpley 1982). Barrow (1983) presented acomplex mechanistic model of the process, but also showedthat the behaviour was closely mimicked by a much simplerrepresentation based on an adaptation of the Freundlichisotherm equation:

s = Kd cntb (2)

where S is the sum of rapidly sorbed P (to surface sites) andP deposited by the slow reaction, t is time and b is a secondexponent.

Use was made of a facility in MACRO for describingdegradation of contaminants (to harmless substances) as a®rst order exponential decay equation characterized by asingle rate constant (or half life) parameter. Strictly, P doesnot undergo degradation, but the time-dependent depositionprocess does remove it from the system into an isolatedrelatively inaccessible pool, which can be thought of (overshort time periods after a P application) as being similar todegradation. The simple ®rst order degradation (exponentialdecay) equation does not give an exact representation of theprocess described by Equation 2, but it could beapproximated using a further facility in MACRO formaking changes to any model parameter values at a speci®eddate and time. By making periodic changes to the selected

degradation rate parameter, a good approximation to therelationship given by Equation 2 with b=0.264 (based onBarrow 1983) could be obtained (Figure 1). Adjustmentswere made to each of these degradation rate values for eachparticular slurry application, to take account of the quantityof P already present in the soil prior to the application, asEquation (2) applies only to P newly applied to the soil.

FiltrationRepresentation by MACRO of ®ltration in macropores, asdescribed in detail by Jarvis et al. (1999), is given by thefollowing adaptation of standard ®ltration equations:

F = fref vrefnfv1±nfcq (3)

where F is the ®ltration sink term (g m±3 h±1), fref is areference ®lter coef®cient (m±1), nf is an empirical exponent,v is the pore water velocity (m h±1) and vref is the pore watervelocity at which fref is measured. For ®ltration inmicropores, Equation 3 is simpli®ed to:

F = fc vcq (4)

where fc is the constant micropore ®ltration coef®cient(m±1). Trapping of colloids by ®ltration is considered to beirreversible.

No measurements were available for the parameters in the®ltration equations. There had been similarly no direct

Figure 1. Degradation with periodic changes in degradation rates torepresent slow deposition process for newly applied P. Ð, Equation 2;- - - , MACRO approximation with degradation rate (day±1) indicatedbelow curve.

Table 3. Slurry applications at drained plot ®eld sites.

Location Crop Date Total P in slurry,(kg ha±1)

Available P in slurry,(kg ha±1)

Available P in slurry(liquid, g m±3)

Colloid in slurry(liquid, gm±3)

Crichton Royal Grass 14 February 1994a 23.0 12.0 240 5000Farm, Dumfries 25 May 1994 8.4 4.4 88 1825

21 November 1994 17.0 8.9 178 370031 May 1995 12.7 6.6 132 27607 July 1995 4.1 2.1 41 900

31 January 1996 23.9 12.5 250 5200Bush, Edinburgh Arable and grass 9 March 1999 6.7 3.5 700 6000

aBefore commencement of drain ¯ow monitoring.

M.B. McGechan et al. 63

measurements of this group of parameters available for theprevious study of colloid facilitated pesticide transportreported by Villholth et al. (2000); values had been selectedbased on a combination of literature sources and adjustmentof parameter values at the model testing stage to givesimulated losses similar to those in measured data. In thecurrent study, the same approach was adopted of adjustingthe parameters from their initial assumed values to give good®ts of simulated to measured P losses. Parameter valuesselected by this approach are listed in Table 2.

Sites and soils as data sourcesField data were available from two sites on which slurryapplications had been made. The ®rst site was grasslandon a silty clay loam at the Crichton Royal Farm,Dumfries. The second site was a clay loam at BushEstate near Edinburgh, with a history of arable cropping,but two of the four plots have recently been sown withgrass. Soil details and layouts of hydrologically isolatedplots with equipment for measurement of drain ¯owquantities and solute concentrations, are described byVinten et al. (1991, 1992 & 1994), McGechan et al.(1997) and Hooda et al. (1998 & 1999).

Slurry applicationsDetails of slurry (always at a rate of approximately50 m3 ha±1) applied at the ®eld sites are listed in Table 3.No mineral P was applied during the experimental period.Slurry was analysed for total P concentration and dry mattercontent. Of the total P, it was assumed that approximatelyhalf would be inorganic (`available') P (Dyson 1992), fromwhich the concentration of P in `irrigation water' wasestimated for the second sequential simulation run. For the

®rst sequential simulation run, it was necessary to make anassumption about the quantity of colloidal material (ontowhich P would be heavily sorbed) in the applied slurry.Based on very little available information from Matthews etal. (1998) and Douglas (pers. comm.), this was estimated as10% of the slurry dry matter. `Irrigation' was assumed totake place over a 0.0003 h (1.0 s) period commencing at 1000 h on each of the days listed in Table 3.

At the Dumfries grassland site, the plots were closed offfor silage cuts during the spring and summer of 1994, 1995and 1996, but during the autumn of each year the aftermathgrowth was grazed by dairy cows. Some P would have beendeposited on the soil surface in faeces by these grazinganimals.

Initial phosphorus levelsInitial values of soil P, set at the start of the second(contaminant) run of MACRO (Table 1) are based oninformation from the `Olsen P' test, as measured for theDumfries soil by Hooda et al. (1999 & 2000).

Figure 2. Comparison between measured and simulated cumulative phos-phorus ¯ows to ®eld drains at the Dumfries grassland site. Periods beforeand after two winter slurry applications (on (a) 21 November 1994 , and(b) 31 January 1996) with cumulation from the start of each simulationperiod (1 October) and from slurry application date. d, measured totalinorganic P; Ð, simulated total inorganic P; - . - . -, simulated colloid-sorbed inorganic P; - - - , simulated dissolved inorganic P.

Figure 3. Comparison between measured and simulated cumulative phos-phorus ¯ows to ®eld drains at Bush clay loam site. Period before andafter one winter slurry application onto (a) grass and (b) arable plots (on9 March 1999). d , m, measured total inorganic P (for two grass and twoarable plots respectively); Ð, simulated total inorganic P; - . - . -, simulatedcolloid-sorbed inorganic P; - - - , simulated dissolved inorganic P.

Parameterization of the MACRO model to represent leaching of phosphorus64

TE S TI N G M O D E L R E P R E S E N TA TI O N O FP HO S P H OR U S T RA NS P OR T

Phosphorus leaching dataCumulative losses of total inorganic P at roughly weeklyintervals (measured as un®ltered molybdenum-reactive,MRP in drainage water) are shown in Figure 2, forperiods before and after winter slurry applications at theDumfries grassland site. These data, as presentedpreviously by Hooda et al. (1999), show very largecontaminant loads of all classes of P during the ®rstweek or two following the winter slurry application on 21November 1994. A similar short lasting large loadfollowed the winter slurry application on 31 January1996, but this was delayed somewhat by a period ofextreme low temperatures with deep penetrating frostand a fall of snow, when ¯ows of water through thedrains fell to a low level. It appeared that a highproportion of inorganic P in these large losses was incolloidally attached rather than soluble form, although itwas not possible to accurately determine this subdivisionsince other drain ¯ow P concentration measurements(TP, TDP) included some organic P forms. After theseshort periods, inorganic P concentrations fell quiterapidly to a low background level, which appeared tobe mainly in soluble form. The ®rst signi®cant autumndrain ¯ows following slurry applications in May and July(when drains were not ¯owing) had low P concentrationsrather than raised levels which might have beenattributed to the slurry applications. During late autumn1994 and 1995 there was a small rise in the rate ofleaching of P to drains above the low background levelwhich may be attributable (amongst other possiblecauses) to deposition of P in faeces by grazing animals.

At the Bush site, the single slurry application on 9 March1999 was followed by a period of slightly raised Pconcentrations in the drains (Figure 3), less high but longerlasting (about 3 weeks) compared to the Dumfries site.

Simulated P leaching following slurry spreading at theDumfries grassland siteIn order to validate the model, weather driven simulationswere carried out to produce results to compare with themeasured leaching data, concentrating in the ®rst instanceon representing the large loads following slurry spreading.Some ®ne-tuning was carried out at this stage, initiallyadjusting the values of the ®ltration parameters, and thenthat of the coef®cient for sorption of P onto slurry colloidsKc (none of which could be measured experimentally).Results were found to be particularly sensitive to the balancebetween ®ltration in micropores (determined by fc) and®ltration in macropores (determined by fref and vref),requiring a substantial reduction in fc (compared to theinitial value from Jarvis et al. 1999) to obtain the correcttiming of the large peak in P leaching.

Simulated results for total inorganic P losses are good®ts to the experimental data (Figure 2), showing thelarge contaminant load immediately after spreading,dropping to a much lower level (almost as low as thebackground level prior to spreading) after the ®rst week.

Also, the large peak load can be seen to arise almostentirely as colloidally attached P, whereas in lossesbeyond the ®rst week there is a split between colloidaland soluble P. Examination of simulated colloid ¯ows,given by the ®rst of the sequential simulations, notshown here, show the same pattern with a peak ¯ow todrains following winter slurry spreading as illustrated forP in Figure 2. However, following spreading on dry soilin summer, all the colloids become trapped in the soilmatrix pores from which they never move again.Phosphorus attached to these trapped colloids is graduallymobilized by desorption, leading to a slow rate ofleaching of soluble P at low concentrations.

Representation of phosphorus leaching before slurry spreadingat the Dumfries grassland siteSimulations representing the period prior to slurry applica-tions, with initial soil P settings based on soil P test values,were found to give good ®ts to measured leaching duringautumn 1995 (Figure 2b). However, they indicated leachingat a substantially lower level than in the experimental dataduring autumn 1994. To give the somewhat higher levels ofleaching seen during this period, P applications in faecesfrom grazing animals was represented as a weekly `irrigation'application of 0.154 mm of liquid with composition524 g m±3 inorganic P. This composition for dairy cowsproducing 0.37 m3 week±1 of excretia was estimated fromtypical values for slurry from Dyson (1992), for a stockingdensity of 4.2 cows ha±1. The grazing period was set to 27September±7 November 1994, corresponding to ratherinadequate recorded information about actual grazing atthe site, to give simulated P leaching similar to the measuredvalues (Figure 2a).

Representation of phosphorus leaching before and after slurryspreading at the Bush siteAt the Bush site, ®ltration parameters were set to the samevalues as for Dumfries, and different values of theFreundlich sorption coef®cient for P sorption on colloidsKc were chosen for arable and grass plots, to give simulatedleaching similar to that measured experimentally (Figure 3).However, ®ts to the experimental data could not be made asgood as those for the Dumfries site, partly because of largedifferences in the experimental data between each of theBush plots. Higher loss levels in grass than arable plots(and in one grass plot in particular) may have arisen dueto grazing by sheep the previous autumn on the grassplots (which may have left more faeces and otherresidues in one plot than in the other). At this site,much of the leached P was derived from the initial soil Pat the start of the simulations (based on soil test P). Therelatively small increase in loss, compared to that atDumfries, following slurry spreading appeared to arisebecause the slurry application had been made following asequence of almost rain-free days so the soil wasrelatively dry. In this case, examination of output fromthe ®rst (colloid) sequential simulation indicated thatmost P carrying colloids became trapped in soilmicropores, as happened at the Dumfries site whenslurry was applied in summer.

M.B. McGechan et al. 65

DI S C U SS I ON A N D CO NC L U S I O NS

General description of processesThe parameterization of the MACRO model described herehas given a plausible explanation of some of the processes,and hence a valuable insight into how the presence ofcolloids can aggravate pollution by heavily sorbed reactivesolutes.

Results showing large contaminant ¯ows following slurryspreading in wet conditions, but not when the soil was fairlydry, support the concept of rapid colloid movements bymacropore ¯ow in water ®lled inter-aggregate pore spaces.Also important is the concept of three contaminant phases;soluble, sorbed onto colloids and sorbed onto static soilcomponents (both fast, reversible sorption and slowdeposition represented simplistically in MACRO as degra-dation). When slurry is applied, a large quantity of P isinitially held sorbed onto colloidal material in the slurry. Aproportion of these colloids (all of them if the soil is fairlydry) become trapped or pulled into the soil matrix pores bycapillary forces. In wet soil, a proportion of the appliedcolloids pass rapidly through the macropores carryingsorbed P, leading to a high contaminant load in the drainsfor a short period. Once the initial rapid ¯ow of colloidsthrough macropores has passed, nearly all remaining colloidsare located in micropores. Any movement of colloids inmicropores leads to a high proportion becoming trapped by®ltration, since the ®ltration coef®cient in micropores ismuch higher than that for macropores. During the weeksfollowing slurry spreading, P continues to be leached outthrough the drains during rainfall/drainage events at arelatively low rate, with a roughly equal split between that insoluble form (P desorbed from sorption sites in the soilmatrix) and that in colloidally attached form. Deposition ofP in faeces by grazing animals can lead to accelerated Pleaching with rapid transfer of colloid attached P (similar tobut less compared with slurry spreading) from wet soil butnot from dry soil.

Parameter selection and availabilityParameters of the MACRO model, with the option forrepresenting colloid facilitated contaminant transport, wereselected using independently measured data where available.These included the hydrolological equation parameters, socalibration of the hydrological routines to represent soilwater content and drain ¯ow data was straightforward(McGechan et al. 1997). Information about colloid trapping(straining and ®ltration) parameters was limited, but thesewere adjusted from those in a previous study to representthe main features of P leaching data with high colloid ¯owsthrough drains following slurry spreading onto wet soil.Directly measured parameters of sorption equations wereavailable for sorption of P onto static soil components butnot for sorption onto colloids, although a clue to P sorptiononto colloids was obtained from the ratio (Jarvis et al. 1999 )of sorption onto colloids to sorption onto static soil forpesticides, since pesticides are reactive, sorbed contaminantsexhibiting similar behaviour to P. A ®nal further adjustmentto the colloid sorption coef®cient gave simulated resultswhich were very good ®ts to the measured data. That this

was possible implies that the simulated ¯ow of colloids mustalso have been close to reality. A further justi®cation formaking this ®nal adjustment to the colloid sorptioncoef®cient is that this parameter is very dependent on theproportion of slurry dry matter in the colloidal size range,for which an assumption had to be made based on limitedinformation.

Importance of colloids for P transportThis calibration of MACRO supports the supposition thatcolloid facilitated transport of P, with P carrying colloidspassing rapidly through soil macropores, is an importantmechanism leading to P leaching through soil to ®eld drains.It gives a plausible explanation for the occurrence of veryhigh losses of particulate and soluble inorganic P in drain¯ows for a short period (such as one week) followingspreading of slurry on wet soil, as observed in theexperimental data described here. This indicates that thereare opportunities for making large reductions in P leachingby avoiding spreading slurry on very wet soil, or converselyby selecting slurry spreading days with relatively dry soil.

A CK N O W L E D G E M E N TS

The authors are grateful to Mark Moynagh and colleagues atthe SAC Crichton Royal Farm for collecting informationabout drain¯ows, P contents, soils, crops and slurryapplications. Similar information from the SAC BushEstate Site was collected by Rab Howard, Colin Crawfordand Robert Ritchie. The Scottish Executive Rural AffairsDepartment provided funds to carry out the work.

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# British Society of Soil Science 2002

M.B. McGechan et al. 67