sw—soil and water: a review of field scale phosphorus dynamics models

Biosystems Engineering (2002) 82 (4), 359–380doi:10.1006/bioe.2002.0102, available online at http://www.idealibrary.com onSW}Soil and Water

REVIEW PAPER

A Review of Field Scale Phosphorus Dynamics Models

D. R. Lewis; M. B. McGechan

Environment Division, SAC, West Mains Road, Edinburgh EH9 3JG, Scotland, UK; e-mail of corresponding author: [email protected]

(Received 3 July 2001; accepted in revised form 27 May 2002))

In order to ascertain the limitations of current soil phosphorus models, three dynamic models are reviewed andcompared, along with a more general contaminant transport model which has been applied to phosphorusdynamics. These models are ANIMO from the Netherlands, GLEAMS and DAYCENT from the USA, andMACRO from Sweden. The model concepts and constituent processes are analysed with particular reference tothe equations used. Processes considered are the transport of soluble and particulate phosphorus, surfaceapplication (as fertilizer, manure or slurry, atmospheric deposition, and deposition or incorporation of dead plantmaterial), mineralization/immobilization (between organic and inorganic forms), absorption/desorption, leaching,runoff and uptake by plants. All the models considered have a partial representation of these processes. In orderto improve our understanding and simulation of phosphorus in soils, further P modelling work is required, whichshould be focussed on constructing a new hybrid version of the four models described here. Such a model is likelyto include a description of both soluble and particulate P flow through micropores and macropores as in theMACRO model framework, combined with a full representation of the C/N/P cycle as described by GLEAMS,with manure and slurry components as described by ANIMO, and plant residue decay equations taken from theDAYCENT model. Finally, the overland flow and erosion losses should be represented by components from theGLEAMS model. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved

1. Introduction

Phosphorus (P) from non-point sources such asagricultural soils can have a major environmental effecton the water quality of receiving waters. The manage-ment of P in agricultural fields with hydrologicalpathways to sensitive surface waters is thus of funda-mental importance. As a management tool, simulationmodels of the P cycle within soils have been developedsince the late 1970s. In general, these models have tendedto be: physically based, driven by climate variables andcapable of assessing nutrient transport to ground andsurface waters. This paper is concerned with a review ofthree comprehensive P models which have been undercontinual development since the mid 1980s, plus a moregeneral model of contaminant transport that has onlyrecently been applied to soil phosphorus processes.

2. General characteristics of the models

2.1. Models considered for review

Here, three detailed field scale models of the processesinvolving in the P-cycle within soils are reviewed.

1537-5110/02/$35.00 35

ANIMO, set up by Winand Staring Centre forIntegrated Land Soil and Water Research, Wageningen,The Netherlands, is described by Groenendijk andKroes (1999) and Kroes and Rijtema (1998). GLEAMS(Groundwater Loading Effects on Agricultural Manage-ment Systems) was developed by the US Department ofAgriculture, Agricultural Research Service (Leonardet al., 1987; Knisel et al., 1993). The CENTURY model(Parton et al., 1987; Metherell et al., 1993a, 1993b) wasinitially funded by the US National Science Foundation,with the latest version (V5, 2000; the Century ModelInterface) funded in part by the US Geological Survey.In this review, DAYCENT is considered, this being thedaily version of the monthly output time-step CEN-TURY ecosystem model which incorporates all of theecosystem processes of its predecessor model. It shouldbe noted that DAYCENT is currently being modifiedwith respect to its phosphorus components (Parton,2000). This study concentrates on physically basedmodels driven by climatic variables, which are capableof assessing nutrient losses to groundwater andsurface waters following the application of agriculturalwaste.

9 # 2002 Silsoe Research Institute. Published by

Elsevier Science Ltd. All rights reserved

D. R. LEWIS; M. B. MCGECHAN360

Notation

a decomposition assimilation factorindicating fraction going to slowcycling humus pool

A, B, C, D empirical parameters in water contentexpression

[Alox +Feox] aluminium and iron content of soil,mmol kg�1

Bsat base saturation by ammonium acetatemethod, %

C dissolved contaminant concentration,kgm�3

Cav available dissolved contaminantconcentration in the surface soil layer,kg m�3

C CaCo3calcium concentration in calcerous soils,kgm�3

Ccrom carbon content of organic crop residue,g [C] g�1 dry wt.

Ceq dissolved contaminant concentration atwhich phosphorus precipitation occurs,kgm�3

CL soil clay content, %CNP function in crop residue decomposition

expressionCom,fn carbon content of organic matter

of fraction fn, g [C] g�1 dry wt.Com,fp carbon content of fresh organic matter

of fraction fp, g [C] g�1 dry wt.Csom carbon content of structural organic

matter, gC g�1 dry wt.(C:N)i C:N ratio of residue in soil layer i(C:P)fp C:P ratio of fraction fp(C:P)i C:P ratio of residue in soil layer iCS contaminant concentration sorbed

onto soil at equilibrium, kgm�3

Cw dissolved contaminant concentrationat equilibrium, kgm�3

ea soil aeration response functionepH pH response functioneT temperature response functioney soil water content response functionF empirical exponent in water content

functionfdecomp fraction of original residue remainingfh,fp degree of non-solubilization for fresh

organic fractionsfS fraction of lignin going to structural poolk rate coefficient for first-order rate processkcrl decomposition rate parameter for

structural pool, d�1

kcr decomposition rate parameter for cropresidue, d�1

kd partition coefficientkF Freundlich rate coefficient, kgm�3

kFdes kinetic-Freundlich rate coefficient fordesorption, d�1

kfp decomposition rate parameter for freshorganic fractions, d�1

kFsor kinetic-Freundlich rate coefficient forsorption, d�1

kL Langmuir rate coefficient, kgm�3

kL1, kL2 Langmuir rate coefficients for twodistinct sorption sites, kg m�3

kref optimum reference value for first-orderrate process, d�1

ksomin organic mineralization coefficient, d�1

Kms constant parameter in phosphorus flowsbetween sorbed pools, d�1

Ksm parameter in phosphorus flows betweensorbed pools, d�1

L lignin content of structural poolL/N lignin-N ratio of the residuen non-linear sorption coefficientpi constants in sorption equation, d�1

p1, p2, p3 constants in expression definingphosphorus transfers

Pact phosphorus content of active pool,g [P] g�1

PF function of matric potentialPfn phosphorus content of organic matter,

root exudent or dissolved organic pools,g [P] g�1 [dry wt.]

Pfresho phosphorus content in fresh organicpool, g [P] g�1

pH pH of the soilPhu phosphorus content of humus/biomass

material, g [P] g�1 [dry wt.]Plab phosphorus content of labile pool,

g [P] g�1

PLI labile P immobilization factorPpfr phosphorus content of fresh residue,

g [P] g�1

Psorb phosphorus content of sorbed pool,g [P] g�1

PSP phosphorus sorption coefficientPssorb phosphorus content of strongly sorbed

pool, g [P] g�1

Pstab phosphorus content of stable mineralpool, g [P] g�1

Ras phosphorus transfer rate betweenactive and stable mineral pools,kg [P] m�3 d�1

Rcr decomposition rate of crop residue,kg [C] m�3 d�1

Rcrl decomposition rate of surface andstructural pools, kg [C] m�3 d�1

Rdcr factor in decomposition rate for cropresidue, kg [C] m�3 d�1

PHOSPHORUS MODELS 361

RFom!Som formation rate of soluble organicphosphorus from fresh organicphosphorus kg [P] m�3 d�1

Rimmob immobilization rate, kg [P] m�3 d�1

Rla phosphorus transfer rate between labileand active mineral pools, kg [P] m�3 d�1

Rmin/imm net mineralization or immobilization rate,kg [P] m�3 d�1

Rso phosphorus transfer rate between sorbedand strongly sorbed pools, kg [P] m�3 d�1

S adsorbed contaminant concentration,kgm�3

Saff sorption affinitySD soil sand content, %Sfeq adsorbed contaminant concentration

determined by Freundlich isotherm,kgm�3

Smax maximum soil sorption capacity, kgm�3

Smax1,Smax2

maximum soil sorption capacities fortwo distinct sorption sites, kgm�3

t time, dT soil temperature, 8CTref base soil temperature at which eT=1, 8Ca composite parameter in temperature

response functionb extraction coefficienty soil water content, % [by volume]ybp water content at the ‘break-point0,

% [by volume]yfc soil water content at 33 kPa

(field capacity), % [by volume]yw wilting point, % [by volume]rd soil dry bulk density, kgm�3

o phosphorus flow coefficient betweenactive and stable pools

Subscriptsfn organic fractionfp fresh organic fraction

In passing, mention should be given to the EPIC(Erosion-Productivity Impact Calculator) model(Sharpley & Williams, 1990), which was originallydeveloped to simulate the impact of erosion oncrop productivity and has now evolved into a compre-hensive agricultural management, field scale, non-pointsource loading model. The P routines developed forEPIC (Jones et al., 1984a) were incorporated in theGLEAMS model, and so only the latter model isreviewed here. Another model CREAMS (model forChemicals, Runoff and Erosion from AgriculturalManagement Systems) as described by Knisel (1980),also incorporates the P routines from EPIC. However,CREAMS will not be considered further here as it is

Rapid cycling organSlow inorganic

Fertilizer Plants

Primary P minerals

Secondary P minerals

Occluded P Labile and moderately labile

inorganic P

Solution P

Fig. 1. The soil P cycle: its components and measurabl

really a precursor of GLEAMS with the same Proutines.

The fourth model reviewed here MACRO is a ‘two-domain’ soil water and contaminant transport model withseparate representation of processes in ‘macropores’ andsoil matrix ‘micropores’. This model, developed in the SoilSciences Department of the Swedish University ofAgricultural Sciences, is described in detail by Jarvis(1994). In earlier versions of the model, only solublecontaminants were considered, and applications con-cerned mainly water contamination by pesticides. How-ever, a recent new feature of MACRO (Jarvis et al., 1999)is the representation of colloid facilitated contaminanttransport, a process particularly relevant to phosphorus

Microbial P

Slow organicic and inorganic

Animal waste

Labile and moderately labile

organic P

Chemically and physically

protected organic P

e fractions (adapted from Stewart & Sharpley, 1997)


pollution. An attempt to use this feature of MACRO forP transport has been described by McGechan et al. (2002).

2.2. Overview of soil phosphorus dynamics

Phosphorus is distributed within soils, betweeninorganic and organic forms, with relative proportionsin the top 20 cm varying from 20 to 80% depending onthe soil type (Brady & Weil, 1996). Figure 1 identifies themajor soil P cycle components and measurable frac-tions, along with an indication of the relative residencetime for P in each component.

Since the solubility of naturally occurring P com-pounds is low, and soil/particle absorption of P is high,the concentration of P in soil solution is limited.Generally, leaching losses of dissolved P range from0�01 kg P ha�1 yr�1 in very infertile drained soils, to0�2 kg Pha�1 yr�1 in heavily fertilized drained soils.Phosphorus losses via surface runoff include dissolvedP and particulate P, with total losses ranging from0�1 kg Pha�1 yr�1 for grasslands to 5 kg P ha�1 yr�1 forsloping tilled arable land (Brady & Weil, 1996). Otherlosses such as the movement of particulate P throughmacropores may also be important in some drainedsoils. These loss processes and all the processes shown inFig. 1 require some representation in a model of the Psoil cycle.

The three P models considered here both haverepresentation of surface application (as fertilizer,manure or slurry, atmospheric deposition, weatheringand deposition or incorporation of dead plant material),

DepositionP

FertilizerP

MineralP

A

Precipitatedinorganic

soil P

Adsorbedinorganic

soil P(kinetic)

Adsorbedinorganic

soilP(equilibrium)

Dissolvedinorganic

soil P

P runP lea

Fig. 2. Pools and flows of phosp

mineralization/immobilization (between organic andinorganic forms), P-soil sorption and desorption pro-cesses, uptake by plants and P leaching. Surfacemovement of dissolved P is considered in both theANIMO and GLEAMS models but the movement of Pbound to particulate material is only considered in theGLEAMS model. The DAYCENT model considerssorbed soil-P in equilibrium with a labile soil-P fromwhich leaching occurs, and includes representation of Ploss through soil erosion. Neither of the P modelsconsiders the important process of the movement‘through-the-soil’ of P bound to particulate material,hence the interest in applying the MACRO model whichhas the capability to represent this.

The main flows and states for the soil P dynamicprocesses represented in the models are shown diagra-matically in Figs 2–4, with pools and flows arranged asfar as possible to a common layout, and the relativecycling rates for the pools also indicated. It should benoted that all soil P pools and transformations occurwithin in each defined soil layer, and for simplicity, thefollowing description of the models are given in terms ofonly one layer. There is some variation between modelsin the definition and subdivision of pools, and in thenames given to the flows. Both organic matter andinorganic matter are divided into several sub-pools,generally according to the rate at which material flowsout of each sub-pool. Flows from fast cycling pools tothe main slow cycling pool of organic matter arevariously described as ‘decomposition’, ‘humification’and ‘decay’. Soil sorption of inorganic or labile P

Shoots P

Root P

nimal wasteP

Freshorganic

P

Freshorganicsoil P

Stableorganicsoil P

Exudatessoil P

Dissolvedorganicsoil P

offching

horus in the ANIMO P model

P runoffP sedimentP leaching

Stalk P

Grain P

Root PFertilizer

P

Freshorganicsoil P Stable

organicsoil P

Labileinorganic

soil P

Stableinorganic

soil P

OrganicP

(animalwaste)

Activeinorganic

soil P

Fig. 3. Pools and flows of phosphorus in the GLEAMS P model

P runoffP leachingP erosion

PlantP

FertilizerP

WeatheringP

OrganicwasteP

Structuralorganic

P

Sloworganicsoil P

Metabolicorganic

P

Activeorganicsoil P

Stronglysorbed

inorganicsoil P

Occludedinorganic

soil P

Sorbedinorganic

soil P

Passiveorganicsoil P

Labileinorganic

soil P

Fig. 4. Pools and flows of phosphorus in the DAYCENT P model


(i.e. that available for plant use) occurs through a rapidprocess, but desorption involves both a rapid and a slowprocess. Some of the compartments delineated in thesefigures are for surface only (grain, stover, atmosphericP), some are for both surface and subsurface computa-tional soil layers (fresh organic P in crop residue androots, organic P in animal waste, fertilizer and dissolvedforms of P), whereas adsorbed and stable soil P occursonly in the soil.

2.3. Other related processes

2.3.1. Soil water

Many of the soil P dynamic processes such asmineralization and immobilization are dependent on

soil water content. Phosphorus transport, via overlandflow or through the soil profile and out into fielddrains, is controlled by water movement. Any model ofsoil P dynamics is therefore very dependent on anaccurate description of soil water content and soil watermovement. ANIMO is designed to operate in conjunc-tion with either of the Dutch soil water simulationmodels, the multilayer model SWATRE (Feddes et al.,1978) or the two-layer model WATBAL (Berghuijs vanDijk, 1990). GLEAMS uses the same basic methods asthe CREAMS model (Williams & Nicks, 1982), andlinks surface runoff curve number techniques withevapotranspiration and multilayer storage-routing mod-els. The DAYCENT land surface submodel (Partonet al., 1998) was developed from multilayer daily water


flow models (Parton, 1978; Parton & Jackson,1989; Sala et al., 1992) simulating variably saturatedwater contents and flows. SWATRE, WATBAL allinclude representation of water flow to field drains aswell as downwards through the soil layers, whereasGLEAMS and DAYCENT only consider verticalpercolation. MACRO has multilayer representationof soil water movement in macropores and soilmatrix pores, including vertical drainage to deepgroundwater and horizontal drainage to the nearestfield drain.

2.3.2. Soil evapotranspiration and heat

Evaporation links the soil water and soil heatprocesses. GLEAMS, SWATRE and MACRO allcalculate evapotranspiration using the physically basedPenman–Monteith equation, and GLEAMS has theoption of using the Priestly Taylor method (Jensen et al.,1990). Transpiration rates in DAYCENT are simulatedusing the Penman potential evapotranspiration equa-tion, adjusted according to soil water potential and rootbiomass (Parton, 1978). All the transformations con-cerned with soil P dynamics are very temperaturedependent, so it is important to have an accuratedescription of soil heat processes. ANIMO, GLEAMS,DAYCENT (Parton, 1984) and MACRO all calculatedaily soil temperatures at depth, from estimates of soilsurface or air temperature values and soil watercontents, together with thermal conductivities for eachlayer.

2.3.3. Soil erosion and particulates

Erosion and sediment yield from fields is estimated inGLEAMS through calculation of soil particledetachment and the subsequent transportation of thissediment (Foster et al., 1980; Leonard et al., 1987).Particle detachment is assumed to be a function of soilproperties, management, and rainfall and runoff char-acteristics. Sediment is considered to consist of amixture of five mineral classes which are composed ofprimary particles and aggregates, and an organic class,whose distributions are either input by the user(calibration) or assumed for given soil types. Whenoverland flow occurs the sediment load is assumed to belimited by either the amount of sediment made availableby detachment or by the transport capacity (Yallin,1963). In the latter case, deposition takes place, withusually the coarse and dense particles deposited first,leaving a finer sediment mixture. GLEAMS splits atypical field into segments of given slope, soil type, etc.,with detachment–deposition processes calculated onprogression down a single segment. Nutrient transportassociated with the sediment movement, is estimatedthrough knowledge of the surface layer soil nutrient

concentration and the ‘enrichment ratio’: the ratio of thetotal specific surface area for the sediment to that of theoriginal soil.

ANIMO does not have any representation ofparticulate movement and consequently soil erosion isnot considered. Surface runoff in ANIMO is assumedto contain only the soluble inorganic and organicnutrient fractions of the surface layer. Similarly,DAYCENT considers surface losses from the labileinorganic and active organic P pools. The model alsoconsiders soil erosion effects in addition to surfacerunoff losses.

The new colloid facilitated transport version ofMACRO (Jarvis et al., 1999) includes representationof detachment of colloidal soil particles from the soilsurface by rainfall impact. However, once detachmenthas taken place, transport of such colloidal particles(carrying a contaminant such as P) is representedaccording to the ‘through-the-soil’ route only.

2.3.4. Crop growth

ANIMO assumes that dissolved inorganic P uptakecan be described by interacting soil and plant compart-ments, in which uptake is calculated by balancing thedemand of the crop and the supply of the soil. Separatesupply potentials are calculated for each compartmentand the actual crop growth rates are adjusted if these arelimiting factors. Both grassland and arable land aredescribed, using different rates for each supply potential.Grassland growth or demand is assumed to bedependent on date and sunshine factors using anempirical equation (de Wit, 1965), and arable cropgrowth is defined using optimal cumulative uptake andtranspiration curves input by the user.

Phosphorus uptake in GLEAMS follows that of theEPIC model (Sharpley & Williams, 1990), in which theuptake of labile P is estimated for each layer wheretranspiration occurs, with the total uptake from alllayers equal to the plant P demand. Plant growth andplant P demand is taken to be a function of the optimumleaf area index, which is tabulated for a large number ofcrops over a growing season. This potential plantgrowth is moderated by soil temperature, water and Pstress factors on a daily basis.

In DAYCENT, potential crop biomass growth (forboth roots and shoots) is moderated by soil tempera-ture, water moisture, nutrient status and seedlinggrowth. The plant growth response curve to soiltemperature follows a sigmoidal function up to anoptimum temperature, with a band of approximately108C of high growth rates, followed by a rapid decline athigher temperatures. Plant P uptake is controlled by thesize of the labile P pool, with the fraction of labile P thatis available varying with the size of the mineral N pool


(higher P fractions for higher mineral N levels). Thisuptake is also constrained by upper and lower limits fornutrient content in the shoots and roots, which in turnare taken as a function of plant biomass.

MACRO has the ability to represent crop growthonly in relation to water uptake and evapotranspiration,plus interception of surface applied contaminants (inwater) by plant leaves before reaching the soil surface.MACRO also includes the representation of thedegradation of a contaminant, a process which strictlydoes not take place for phosphorus, but this feature canbe used to provide a crude representation of the removalof P from the soil, by plant uptake.

2.3.5. Soil carbon

Some soil P dynamic processes depend on a supply ofcarbon and so are closely linked with the dynamicsof carbon in soil organic matter. Only the ANIMOand DAYCENT models include representations ofsoil carbon dynamics in parallel with soil N and Pdynamics.

2.3.6. Soil nitrogen

Nitrogen (N) is another nutrient taken up by plantsfrom the soil which, like P, becomes a serious pollutantif it escapes into watercourses or deep groundwater.ANIMO, GLEAMS and DAYCENT have a represen-tation of soil N, in the form of nitrate (NO3) andammonium (NH4). They consider movement of N fromapplied fertilizer or slurry by solute transport, uptake ofN by plants, mineralization/immobilization (betweenorganic and inorganic forms), nitrification/denitrifica-tion, and volatilization of NH4. The review paper by Wuand McGechan (1998) gives a useful description of thecharacteristics of several soil nitrogen dynamic models.Similarly a range of soil nitrogen models simulatingN2O emissions are compared in the paper by Frolkinget al. (1998).

2.3.7. Application of animal manure and slurry

Both ANIMO and GLEAMS make provision forapplication of animal manure or slurry. ANIMO allowsfor applications of cattle slurry, specified as mineral P,plus three categories of organic material each with itsown P content. These P inputs are initially added to theappropriate pools in the upper layer of the profile, butafter ploughing (at a date also specified in the input), thematerial is distributed throughout the profile down tothe ploughing depth. GLEAMS represents land applica-tion of animal waste through the use of an animal wasteorganic phosphorus pool, from which P mineralizes tothe inorganic pool at a faster rate than from the stableorganic pool. A portion of the animal waste (25%) also

mineralizes to the active soil mineralizable P pool (stableorganic pool).

DAYCENT has a limited treatment of organic waste,allowing the partition of such material into a surfacelabile inorganic P pool, a surface labile organic P littercomponent and a surface structural organic P poolresistant to decomposition. MACRO includes an optionfor the representation of surface application of irrigationwater containing a contaminant at a specified concen-tration, and this can be used to represent P applied inslurry or manure. Also, in the new version of MACROwith colloid facilitated contaminant transport, theconcentration of the carrier colloid material in slurrycan be specified. Animal slurry contains substantialquantities of colloidal material (mainly finely dividedorganic matter), and much of the inorganic P in slurry issorbed onto such colloidal material rather than being indissolved form.

2.4. Spatial and temporal discretization

The P models divide the soil profile into layers tosimulate vertical movement of P, carbon and waterbetween layers, as well as transformation within eachlayer and uptake by plants from each layer at variousrates. Similarly, MACRO divides the profile into layersfor water and contaminant movements. The ANIMO,GLEAMS, DAYCENT and MACRO models candivide the profile into up to 50, 12, 10 and 15 layers,respectively, for soil nutrient processes.

Dynamic model simulations are driven by weathervariables. ANIMO does not use weather data directly,instead it uses output from previously run weatherdriven simulations with the associated soil water model,and operates at the same time-step as the soil watersimulations (daily or weekly). GLEAMS operates on adaily time-step, using weather data to drive thehydrology, erosion and temperature sub-models. Anoptional climate generator can be used for daily rainfall,temperature and radiation data, similar to that used inthe EPIC model (Richardson & Nicks, 1990). There issome loss of realism and accuracy of model representa-tion when operating with a weekly rather than a dailytime-step, particularly regarding processes influenced byrainfall such as high soil wetness, drainflows and Prunoff and leaching, since rainfall occurs in distinctevents rather than having an average intensity over aweekly period. DAYCENT requires daily time-stepweather data to drive the hydrology, temperature andnutrient sub-models, constructing average weekly valuesfor some components of the model, such as atmosphericdeposition. The CENTURY model, requires monthlyaverages of precipitation and minimum and maximum


air temperature. MACRO operates with weather dataon a daily, hourly or shorter time-step.

3. Mathematical description of transformation processes

Generally, the P models consider transformationsbetween pools to be represented by ‘first-order rateprocesses’, such that the flow out of the first pool to thesecond is proportional to the quantity of materialremaining in the first pool. Similarly, in MACRO thedegradation of a contaminant (a flow from a pool tonowhere) is represented by a first-order rate process.Solution of the resultant first-order differential equation,requires specification of an initial value at the beginningof the time period.

To take account of the sensitivity of such transforma-tions to environmental factors such as temperature eT ,soil aeration ea, soil wetness ey and pH epH , transforma-tion rate coefficients k may incorporate multiplicativeresponse functions for each of the factors. ANIMO usesexpression such as

k ¼ eT ea ey epH kref ð1Þ

where the multiplicative factors will be defined later andkref is the reference value of the first order transforma-tion rate constant under optimum conditions. For therate of degradation in the DAYCENT and MACROmodels, a response function for temperature and watercontent of similar form to Eqn (1) is assumed.GLEAMS uses expression such as

k ¼ ðeT eyÞ1=2 kref ð2Þ

and so transformation rates vary according to a power-law expression for these environmental factors.

3.1. Temperature response

3.1.1. ANIMO

On the basis of literature sources, the authors ofANIMO concluded that temperature has the greatesteffect on organic matter decomposition processes. Otherprocesses follow a similar pattern but the influence oftemperature is less important.

It is assumed that a reaction rate increases with soiltemperature in a layer T measured in 8C in a mannerdescribed by an Arrhenius equation, a commonly usedfunction for chemical reactions. The correction factorfor temperature is then

eT ¼ exp �90001

T þ 273�

1

Tref þ 273

� �� ð3Þ

where: Tref is a reference temperature usually taken asthe average annual soil surface temperature, and if T isbelow zero, eT is set to zero.

3.1.2. GLEAMS

The temperature effect in GLEAMS on decomposi-tion rates is expressed as an exponential equation

eT ¼T

T þ exp½9�93� 0�312T ð4Þ

and if T is below zero, eT is set to zero.

3.1.3. DAYCENT

Using a non-linear data-fitting procedure, parametervalues were determined for a generalized Poissonfunction that represented the effect of soil temperatureon decomposition of labelled cellulose at severaltemperatures (Parton et al., 1987). This produced atemperature response function of the form:

eT ¼ �0�06þ 0�13 exp½0�07T ð5Þ

and if T is below zero, eT is set to zero, otherwise T is setto one.

3.1.4. MACRO

The temperature response function in MACRO isgiven by a numerical approximation of the Arrheniusequation (Boesten & van der Linden, 1991) modified forlow soil temperatures:

eT ¼

exp ðaðT � Tref Þ� �

; T > 58

0�2T exp að5� Tref Þ� �

; 04T458C

0; T508C

8><>: ð6Þ

where: a is a composite parameter dependent on all of T,the reference temperature Tref, the gas constant and themolar activation energy.

These response functions produce the curves shown inFig. 5 in which Tref has a value of 35 for the ANIMOand MACRO expressions. ANIMO and MACROconsider the temperature effect relative to that at thevalue of Tref, at which point eT = 1 and this makes itmore difficult to compare with the GLEAMS andDAYCENT models which maintains that eT41. Over-all, however, there is reasonable similarity between thefunctions.

3.2. Soil aeration and water response

3.2.1. ANIMO

Since aeration has a major influence on transforma-tion rates, detailed sub-models describing oxygen diffu-sion in the soil gas and in soil aggregates areimplemented (Groendendijk & Kroes, 1999). Whenea ¼ 1, organic transformations and nitrification pro-cesses are optimal, otherwise there is an oxygenrequirement which the diffusive capacity of the unsatu-rated zone cannot fulfil. Soil atmospheric oxygen

0

1.0

0 5 10 15 20 25 30 35 40

Tem

pera

ture

res

pons

e fu

nctio

n

Soil temperature, ˚C

0.2

0.4

0.6

0.8

Fig. 5. Soil temperature response functions for the four models considered: , ANIMO; . , GLEAMS; , DAYCENT;, MACRO


concentration is determined by solving the verticaldiffuse transport equation for oxygen in the air-filledpores of the soil system with expressions for atmosphericoxygen demand caused by microbial based transforma-tions. Under partial anaerobiosis conditions, the frac-tion ea is determined through the solution of a radialdiffusion equation for aqueous oxygen concentration insoil water around a pore, and an estimate of the averageradius of air-filled pores determined from the air entryand current matric potential of the soil layer.

The reduction in the transformation rate coefficientsdue to lack of atmospheric oxygen is treated through ea,whereas water stress for the microorganisms aredescribed by the response factor ey. This factor isreduced from unity, below the wilting point, and isdependent on matric potential (expressed as pF; log10 ofthe soil water potential in cm water) in the rootzonethrough the empirical relationships:

ey

1; pF53�2

1� 0�8ðpF � 3�2Þ; 3�24pF4

0�2; pF > 4�2

8><>: 4�2 ð7Þ

with no modifications considered below the rootzone.

3.2.2. GLEAMS

Aeration is not described in GLEAMS, insteadtransformations are assumed to be linearly reducedfrom saturation and to be dependent upon thevolumetric soil water content y as a % through the

response factor:

ey ¼

y� yw

yfc � yw

; y4yfc

0; y > yfc

8><>: ð8Þ

where: yw is the volumetric soil water content at thewilting point of 1500 kPa, and yfc is the volumetric soilwater content at 33 kPa tension (described as fieldcapacity for a North American soil).

3.2.3. DAYCENT

Using the daily soil water budget model, the followingfunction of the volumetric water content is employed inDAYCENT:

ey ¼y� B

A � B

� �DðB�A=A�CÞ y� C

A � C

� �D

ð9Þ

where the empirical parameters A, B, C, D aredefined for coarse, medium and fine soils. Theanaerobic dependence of the decomposition, rates, etc.is defined through the use of an empirical equationinvolving the precipitation and potential evapotran-spiration rates.

3.2.4. MACRO

In MACRO, the water content function is given by

ey ¼yybp

� �F

; y4ybp

0; y > ybp

8><>: ð10Þ

00

1.0

Wat

er r

espo

nse

func

tion

0.2

0.4

0.6

0.8

0.1 0.2 0.3 0.4 0.5 0.6Soil water content, v/v

Fig. 6. Soil water response functions for the four models considered for a clay soil: , ANIMO; , GLEAMS; ,DAYCENT; , MACRO


where: ybp is the water content at the ‘break-point’(when the soil matrix pores are full but the macroporesare empty), and F is an empirical exponent.

In order to compare the functions, a clay loam soil isassumed with a typical water release curve (indicatingthe relationship between potential and water content).Figure 6 then illustrates the relatively similar behaviourof the ANIMO and DAYCENT water stress responseswithout their respective anaerobic dependencies, and theGLEAMS and MACRO water stress factors whichincludes some representation of anaerobic effects.Decomposition is generally assumed to take place atthe maximum rate (ey ¼ 1) in the middle of the water

TabTypical parameters in soil

Parameter Suggeste

Sand

yw the volumetric soil water content at wiltingpoint (GLEAMS)

0�03

yfc the volumetric soil water content at fieldcapacity (GLEAMS)

0�16

A an empirical factor (DAYCENT) 0�55B an empirical factor (DAYCENT) 1�70C an empirical factor (DAYCENT) �0�007 0D an empirical factor (DAYCENT) 3�22ybp the volumetric soil water content at

break-point (MACRO)0�35

A

F an empirical exponent (MACRO)

*a}data cited by author of reference.

content range, declining at low water contents, and alsodeclining at high water contents. Table 1 gives typicalvalues for the parameters involved in the water responsefunctions.

3.3. pH response

In ANIMO only the organic transformations areinfluenced by soilwater pH, with the response functiongiven as

epH ¼1

1þ exp½ � 2�5ð pH � 5Þð11Þ

le 1water response functions

d coefficient References Data source*

Silt Clay

0�13 0�28 Knisel et al. (1993) a

0�27 0�39 Knisel et al. (1993) a

0�60 0�60 Metherell et al. (1993b) a1�27 1�27 Metherell et al. (1993b) a�0012 0�0012 Metherell et al. (1993b) a2�84 2�84 Metherell et al. (1993b) a0�42 0�50 Jarvis (1994) a

ll soils

0�1 McGechan et al. (2002) a

Decomposition

Mineralization

Mineralization

Decomposition

Mineralization

Immobilization

Inorganicsoil P

Manure/slurry

Litter

Stableinorganic

soil P

Soil organic matter/biomass/humus

Fast cycling pools Slow cycling pool

Fig. 7. General representation of decomposition, mineralization and immobilization processes


where each soil horizon is assigned a pH value pH by theuser. It is assumed that under optimal agriculturalpractises this pH value will not change over a year andso seasonal fluctuations can be ignored.

GLEAMS also assumes that an annual pH for eachhorizon is input by the user. The P sorption capacity ofthe soil for sorption of P from the active to the stable Ppool is defined as a function of pH. DAYCENT isdependent upon pH for the P sorption processes, whichare discussed in greater depth in Section 3.5.3. MACROhas no such dependence.

3.4. Decomposition, mineralization and immobilization

Generally, mineralization and immobilization of P arecontrolled by associated carbon and N processes. InFig. 7, organic matter is divided into several pools,roughly categorized as fast cycling pools, such as freshorganic consisting of plant litter or manure, and slowcycling pools, mainly of soil humus. These pools are alsodistinguished by different C:N:P ratios, with freshorganic pools having a ratio range of 1:12–25:>200,respectively, and the longer term stable organic poolshaving ratios of 1:512:125–200, respectively. Transfor-mation flows important for P dynamics models consistof those from the fast cycling pools to the slow cyclingpool and also mineralization (or the reverse proces-s}immobilization) from each organic pool to a labile orinorganic P pool. Carbon and associated N transforma-tion processes described as ‘decomposition’ or‘humification’, control these P transformations. Animportant quantity which determines the direction offlow of P is the ‘assimilation factor’ which is theproportion of carbon going from the fast organic cyclingpool to the slow organic cycling one, with the remainingcarbon lost as CO2. As soil microbes multiply inresponse to the input of fresh organic material, there isan increase both in the biomass and correspondingly in

the slow cycling organic pool due to organic matterdissimulation, which is sustainable only if there aresufficient N and P reserves. Thus, another importantquantity which determines the direction of flow of P isthe C:N:P ratio, both at the source and at thedestination pool. In the transfer from fast to slowcycling pools the fast cycling material generally has ahigher C:P ratio than slow cycling material, so (unlessmost of the carbon in the fast cycling pool is lost as CO2

due to a low assimilation factor) soluble inorganic P hasto be converted back to organic form or ‘immobilized’to satisfy the higher P requirement of the slow cyclingpool.

The slow cycling humus pool is the final destinationfor organic carbon, so decomposition of carbon in thispool generally produces CO2 alone. However, some ofthe models also allow for a decomposition process inone or more organic pool which recycles some materialback to the same pool with some carbon loss as CO2.Decomposition from each carbon pool is usually treatedin these models as a first-order rate process withadjustment to the rate coefficient K for environmentalfactors. Conversion of rates in terms of C to P areusually obtained by dividing the C rate process by theappropriate C:P ratio.

3.4.1. ANIMO

In the ANIMO model, organic matter is divided intofour categories: organic plant parts and manure (some-times also called fresh organic material), root exudates,soil organic matter/biomass and soluble organic materi-al (Fig. 2). The fast cycling fresh organic material poolconsists of the litter and manure/slurry pools in Fig. 7,where litter is composed of root and other crop residuesafter harvesting. Root exudates, is an additional fastcycling pool which consists of organic products excretedby living roots plus dead root cells discarded by theplant. The slow cycling soil organic matter/biomass poolcontains material formed from part of the available


fresh organic material and root exudates, and consists ofboth dead organic soil material and living biomass. Thefourth pool, soluble organic matter, is part of soilorganic matter from other pools which has beenrendered soluble. ANIMO also considers manure orslurry to contain a soluble organic component, and thisis added to the dissolved organic matter pool whenapplied.

The four fresh organic fractions have varying degreesof non-solubilization fh,fp, with the total formation rateRFom!Som of soluble organic matter from fresh organicmaterial represented in the model by summing all thesoluble fractions with different first-order rate coeffi-cients, i.e.:

RFom!Som ¼X

fp

ð1� fh;fpÞ kfp rd Com;fp

ðC : PÞfpð12Þ

where: rd is the dry bulk density, Com,fp is the mass offresh organic matter of fraction fp, (C:P)fp is thecarbon:P ratio of the fraction fp and kfp is thedecomposition rate parameter which includes soilmoisture and temperature factors, etc. Decompositionof the non-soluble fraction to stable organic matter isalso described by first-order kinetics. Root exudateproduction is assumed to be proportional to the rate ofroot biomass production. Decomposition of the rootexudate pool and also the soluble organic matter pool isrepresented by first-order rate processes, both with thesame assimilation factor a, to indicate the fraction goingto the slow cycling humus pool. The remainder of thesedecomposing pools goes to CO2. The separate solubleorganic material pool in ANIMO (which receives inputsboth as components of added slurry and by decomposi-tion of solid components of added slurry, plant parts(mainly roots) and root exudates) moves with water inthe soil and so is subject to losses by leaching.

Mineralization of P from the fast cycling organicpools is calculated from the assimilation factor and theC:P ratios of the source and destination pools. The flowsof carbon (to CO2) and of P (mineralization) from theslow cycling pool are first-order rate processes both withthe same specified rate coefficient. The general form ofthe equations describing net mineralization or immobi-lization rate (Rmin/imm) is given by

Rmin=imm ¼X

fn

ðPfn � aPhuÞkfnrdCom;fn ð13Þ

where: Pfn is the phosphorus content of the organicmatter class, root exudent pool or dissolved organicpool, Phu is the phosphorus content of the humus/biomass material, Com,fn is the organic matter content ofclass fn and kfn is the mineralization rate parameterwhich includes soil moisture and temperature factors,etc. These combined transformations will result in a net

mineralization or immobilization of mineral P, depen-dent upon the sign of the equation.

Net immobilization is most likely after harvest orafter ploughing when there is a large input of litter withhigh C:P ratio to the pool. At other times the pool willtend to be dominated by recycled microbial biomass(C:P ratio 125) to give a combined C:P ratio below 200,so net mineralization will occur. Rate coefficients for allthe first-order rate decomposition processes are multi-plied by the same environmental factors for tempera-ture, soil water content and pH of the soil as mentionedin previous sections.

3.4.2. GLEAMS

In the GLEAMS model, three categories of organicmatter are used which consist of the fast cycling freshorganic and animal waste organic pools and a slowcycling organic humus pool. The fast cycling freshorganic material pool consists of surface crop residuesafter harvesting and sub-surface root residues, with theslow cycling soil organic matter/biomass pool consistingof both dead organic soil material and living biomass.The treatment of the decomposition of the organicmatter pools follows that of the ANIMO model, withappropriate soil water and temperature terms, andremoval of the solubilization terms in Eqn (12).

Decomposition of crop residue in the soil is treated asa single-step first-order process (Jones et al., 1984a),with the crop residue decomposition rate Rcr linearlydependent on a rate constant kcr (a function of cropresidue composition) and the function CNP:

Rcr ¼ 0�4 RdcrrdCcrom ð14Þ

With the decomposition rate factor Rdcr given by

Rdcr ¼ CNPkcrðeT eyÞ1=2 ð15Þ

where: Ccrom is the carbon content of the crop residue,and the function CNP is given by

CNP ¼ min

exp½�0�693ððC : NÞi � 25Þ=25

exp½�0�693ððC : PÞi � 200Þ=200

1�0

8><>: ð16Þ

where: (C:N)i and (C:P)i are the C:N and C:P ratios,respectively, of the residue in a particular soil layer i. Inthe calculation of these ratio’s the total residue (cropand animal), nitrate, ammonia and phosphorus massesin a layer are used, as it is difficult experimentally todetermine the relative amounts of each crop residue,animal waste residue and soluble components.

The value of the residue composition factor kcr isdetermined by the stage of residue decomposition fdecomp

defined as the fraction of the original residue remaining.Carbohydrate-like material is considered to decomposefirst causing up to a 20% reduction, with the next


20-90% reduction caused by decomposition of cellulose-like material, and the final 10% by lignin (Sharpley &Williams, 1990). Values of kcr for these stages are givenby

kcr ¼

0�8; fdecomp420%

0�05; fdecomp490%

0�0095; fdecomp > 90%

8><>: ð17Þ

The temperature and water content multiplicationfactors defined earlier are used to modify the miner-alization rate. As in the EPIC model (Sharpley &Williams, 1990), 75% of the mineralized fresh organic Pis added to the labile P pool and 25% is added to theorganic humus P pool (Jones et al., 1984b). In order tobe consistent for the organic mineralization processes,the same type of relationships are used for animal wastemineralization within the soil, with similar proportionsgoing to labile and humic pools.

Phosphorus in surface residue (crop and animalwaste), is mineralized to labile P, and is calculated bythe same processes as for soil mineralization. The soilwater conditions for the top 1 cm and the daily airtemperature are used in Eqn (2) to modify this rate.

Mineralization, from the slow cycling organic humusP pool, is treated as a first-order reaction, with amineralization coefficient ksomin. The ratio of active andstable soil P pool is used to partition soil organic humusP into the mineralization fraction. This rate is thenmodified by the water and temperature factors definedearlier.

Immobilization calculations in GLEAMS follow thatof the PAPRAN model (Seligman & van Keulin, 1981).The immobilized rate Rimmob is given by

Rimmob ¼ RdcrrdPfresho½0�16PLI � ðPpfrÞ ð18Þ

where: Pfrsho is the amount of P in the fresh organicpool, the coefficient 0�16 results from assuming thatcarbon is 40% of fresh residue, and that 40% of thecarbon is assimilated by soil microorganisms. Theconcentration of P in the fresh residue is Ppfr, and PLI

is known as the labile phosphorus immobilizationfactor;

PLI ¼0�01þ 0�001Plab; Plab410

0�02; Plab > 10

(ð19Þ

where: Plab is the concentration of labile P. If Rimmob

exceeds 95% of Plab, then a new decomposition rate iscalculated which reduces the immobilization rate to thislimit. Immobilized P in this model is subtracted fromPlab and added to the fresh organic pool. Surfaceimmobilization of P follows the same procedure as in thesoil, with the appropriate value subtracted from labile Pand added to P in the surface residue.

3.4.3. DAYCENT

In the DAYCENT model, plant residue is decom-posed by microbes, with the resulting microbial pro-ducts becoming the substrates for humus formation. Soilorganic matter is divided into three fractions; an activecomponent consisting of live microbes and microbialproducts into which plant residue, manure, etc. passes, aprotected slow component (through physical or chemi-cal means), and a passive component that is resistantwith a long turnover time. Decomposition of the organicmatter pools follows the treatment of the ANIMO andGLEAMS models, with appropriate soil water andtemperature response terms.

Plant residue (shoot and root plant biomass) isdivided into structural and metabolic pools. Thelignin-to-N plant residue ratio, controls the divisioninto each pool, with a large ratio leading to a substantialfraction of the residue going to the structural pool, withthe fraction fs going to the structural pool given by

fs ¼ 0�15þ 0�018L=N ð20Þ

where: L/N is the lignin-N ratio of the residue.All of the plant residual lignin will flow into the

structural pool. This fast cycling pool subsequentlydecays with a rate Rcrl dependent upon the lignincontent, which is released as microbes decompose themore labile components of the structural material (e.g.cellulose). The decomposition rate of the surface andsoil structural organic pools is given by an equation ofthe form

Rcrl ¼ Csomrdkcrl exp �3�0Lð Þ ð21Þ

where: kcrl is a rate parameter dependent upon thestructural pool, and contains appropriate soil moistureand temperature terms, with Csom the structural organicmatter concentration. A high lignin content L reducesthe ability of microbes to decompose the substrate, withthe lignin fraction of the structural pool passing into theslow soil organic pool, and the non-lignin fractionpassing to the active organic pool. The fast cyclingmetabolic or microbial biomass pool is incorporatedonly into the active organic pool.

The C:P ratio of active, slow and passive soil organicpools varies approximately linearly as a function oflabile P (defined as orthophosphate which is isotropi-cally exchangeable or extractable with anion exchangeresin), with low labile concentrations resulting in highratios. Experiments have shown (McGill & Cole, 1981)that under low levels of labile P, phosphatase enzymesare capable of directly mineralizing P from the system.Hence, any new soil organic matter additions will haveC:P ratios which also vary as a function of labile P.

Decomposition of both plant residues and soil organicmatter has an associated loss of CO2 as a result of

Table 2Decomposition rate coefficients

Model Material/pool Suggested coefficient, d�1 References Source of data*

Fast cyclingANIMO Slurry Fraction 1 (soluble) and

soluble part of Fraction 28�2� 10�2 See Section 3.4.1 b

Slurry Fraction 2 (rapidly decomposing)‘fresh’ part

2�7� 10�3 See Section 3.4.1 b

Slurry Fraction 3 (slowly decomposing) 3�3� 10�4 See Section 3.4.1 bCrop residues (mainly roots) See Section 3.4.1 b

rapidly decomposing part (0�9 of total) 5�5� 10�3

slowly decomposing part (0�1 of total) 6�0� 10�4 See Section 3.4.1 bRoot exudates 1�0 See Section 3.4.1 b

GLEAMS Crop and surface residue (dependantupon decomposition stage)

9�5, 50, or 800� 10�3 See Section 3.4.2 b

Animal waste (dependant upondecomposition stage)

9�5, 50, or 800� 10�3 See Section 3.4.2 b

DAYCENT Active 1�8–5�1� 10�2 See Section 3.4.3 bPlant residue}structural 1�1–1�3� 10�2 See Section 3.4.3 b

SAC Litter Vinten et al. (1996) aClay loam soil (topsoil) 2�4� 10�2

Sandy loam soil (topsoil) 2�6� 10�2

experiments a

Intermediate cycling

DAYCENT Slow physically or chemically protected 55� 10�4 See Section 3.4.3 a

Slow cyclingANIMO 4�1–5�5� 10�5 Wu and McGechan (1998) bGLEAMS 1�0–30� 10�5 See Section 3.4.2 bDAYCENT Passive pool 1�8� 10�5 See Section 3.4.3 b

SAC Vinten et al. (1996) aexperiments Clay loam soil (topsoil) 1�0� 10�5 a

Sandy loam soil (topsoil) 3�3� 10�5

*a}reference author’s experimental data; b}data cited by author of reference.


microbial respiration, with a definite fraction of thecarbon flow from one organic pool to another, lost tothe soil atmosphere. For the active pool this loss of CO2

on decomposition, increases with increasing soil sandcontent. The P attached to carbon lost as microbialrespiration (typically 30–80% of the carbon flow) isassumed to be mineralized, so that decomposition ofmetabolic plant material, active, slow and passive soilorganic matter (with low C:P ratio) generally results inmineralization of labile P. Decomposition of structuralplant material which has a high C:P ratio requiresimmobilization from labile P. Mineralization or im-mobilization of P occurs as is necessary to maintain theC:P ratios within their defined limits in the variousorganic pools.

3.4.4. Rate coefficients for decomposition

Rate coefficients for the first-order rate processes offlows out of each organic matter pool, and C:N:P ratios

assumed in these models are listed in Tables 2 and 3.Incubation experiments (Tiessen et al., 1983, 1984;Andr!een & Paustian, et al., 1987; Lind et al., 1990;Vinten et al., 1996) can be used as source data fordecomposition rates of litter and humus. Experimentaldata for material added to the soil is mainly for plantparts (litter), with little data for manure or slurry. Thegeneral assumption made is that the faeces componentof manure and slurry consists of plant parts similar tothose in litter, and that the same decomposition ratevalues can be assumed. Only the authors of ANIMOhave attempted to estimate values specific to slurry,showing generally slightly slower decomposition ratesthan for litter. ANIMO considers slurry to consist of anumber of components, with the organic part sub-divided into several fractions with different decomposi-tion rates and associations with the ‘fresh’ organic pooland the dissolved organic pool. Details of the propor-tions allocated to each of the fractions for several types

Table 3Typical C/N/P ratios

Model Material/pool Suggested C/N ratio Suggested C/P ratio

Fast cyclingANIMO Slurry Fraction 1 (soluble) and soluble part of Fraction 2 8�3 150

Slurry Fraction 2 (rapidly decomposing) ‘fresh’ part 11�6 150Slurry Fraction 3 (slowly decomposing) 58 150Arable crop residues (mainly roots) 58 150

rapidly decomposing part(0�9 of tot)slowly decomposing part (0�1 of total) 39 150

Grassland crop residues (mainly roots)rapidly decomposing part(0�9 of tot) 58 150slowly decomposing part(0�1 of total) 58 150

Root exudates 23 150GLEAMS Crop and surface residue 12–25 >200

Animal waste e.g.dairy slurry 15 235dairy solid 20 105

DAYCENT Active 3–15 30–80Plant residue}structural 20 500

Intermediate cyclingDAYCENT Slow physically or chemically protected pool 12–20 20–200

Slow cyclingANIMO Soil organic matter (humus) alone 11 150

Humus plus microbial biomass 14 150GLEAMS Soil organic humus pool 7–13 125–200

Stable inorganic soil pool 7–13 125–200DAYCENT Passive pool 7–10 90–200


of animal slurry are listed in the paper by Wu andMcGechan (1998), which also contains a more detaileddiscussion of the issues of how decomposition ismodelled and rate coefficients used in several models.

3.5. Sorption and desorption of inorganic phosphorus

The rate at which P added to soil is absorbed by soilmaterial has been much studied, generally through ananalysis of the amount of P added to soil solutions andthe quantity remaining over time (Barrow, 1974, 1978,1980a, 1980b; Barrow & Carter, 1978; Barrow & Shaw,1979). Much effort has been expended on determiningrelationships between the rate and extent of P adsorp-tion and the chemical and physical properties of soils.However, such relationships have still not been attainedfor a wide range of soils.

These experiments have shown that following solubleP application, inorganic or labile P concentrationsdecrease rapidly with time, and that this ‘fast’ reactionis then followed by a slower decrease which maycontinue for several years (Barrow & Shaw, 1975a,1975b). Models take this behaviour into account byassuming that when e.g. fertilizer P is applied, both

rapid equilibrium processes and slow reaction processesare simulated.

Experimentally, the determination of P that can bereleased from a soil sample has been carried out usingseveral chemical extractants. The strength of these vary,with dilute CaCl2 solution (Barrow, 1980b), a weak soilextractant, used to determine very rapid responsedesorption P fractions, or anion exchange resin (Sibbe-sen, 1977), used to determine P adsorbed on the surfacesof more crystalline compounds. Stronger extractants arenormally used to provide soil P fertility values, such asdilute NaHCO3 solutions (Olsen et al., 1954), NH4F/HCl (Bray & Kurtz, 1945), or the Mehlich-3 soil Pmethod (Mehlich, 1984). The inorganic labile P poolused in GLEAMS and DAYCENT are defined throughthe use of several of these extractants, and so are subtlydifferent to the dissolved inorganic P pool used inANIMO.

Chemical sorption from a solute onto the porousmatrix surface can be described by an equilibriumreaction when flow velocities are low enough to allow anequilibrium state to be reached. Soil matrix solutereactions then usually follow either non-linear Langmuiror Freundlich isotherms (Ibaraki & Sudicky, 1995).However, when flow velocities for the solute are


relatively large, or if absorption is strong, sorption maybe described more correctly by a kinetic-type Langmuiror Freundlich reaction (Selim & Amacher, 1988). Forkinetic reactions, when the sorbed phase concentrationattains its equilibrium values, the sorbed phase concen-tration will not change unless the aqueous phaseconcentration changes.

The use of a Freundlich-type reaction implies that thematrix has an infinite capacity to absorb, whereas aLangmuir reaction implies that there is a maximumquantity of P which can be absorbed (‘saturation’).Sorption data for many soils do not give good fits to theLangmuir equation, whereas the Freundlich equation(without a defined sorption maximum) gives good fitsfor nearly all soils. Holford et al. (1974) showed that forsoils where only the Freundlich equation gave good fitsto sorption data, an alternative was to fit a ‘doubleLangmuir equation’. This has two terms similar to theright-hand side of Eqn (22), with four parameters Smax1,kL1, Smax2 and kL2, and implies that there are twodistinct sorption sites each with its own sorptionmaximum Smax1 and Smax2. However, in many instancesthe quantity of P in the soil is small relative tosaturation, so the simple, single term Langmuir equationcan give a good fit over the narrow concentration rangewhich is relevant, although the fitted sorption maximumis not a true indication of saturation.

McGechan and Lewis (2002) and McGechan (2002)have reviewed the extensive range of published literature

Tab

Parameters in so

Model Process Sugges

ANIMO Langmuir rate coefficientKL m3kg�1,

Maximum soil sorptioncapacity Smax kgm�3,

5�167� 10�

Freundlich rate coefficientkF kgm�3,

11�87� 10�

Kinetic-Freundlich ratecoefficient sorption kFsor d

�1,Non-linear sorption coefficient, n

DAYCENT Sorption affinity Saff 1Sorption maximum Smax kgm�3, 0Constant sorption parameter

Kms d�1,

Constant sorption parameterp1, p2, p3 d�1,

0�0008

Silty clay loam

MACRO Freundlich rate coefficientkF kgm�3,

203–6500

Non-linear sorption exponent, n 1�65

*a}reference author’s experimental data; b}data cited by aNote: rd , dry bulk density, kgm�3, [Alox þ Feox], aluminium

desorption parameters are the same as for sorption.

on the subject of P sorption by soil (includingexperimental data for fitting isotherm relationships forsome soils), in more detail. However, Table 4 givestypical values associated to the sorption parametersdescribed here.

3.5.1. ANIMO

ANIMO uses the Langmuir isotherm for situationswhere equilibrium is rapidly achieved, with the instan-taneous sorption of P described by

S ¼ Smax

kL Cn

1þ kL Cn

� �ð22Þ

where: kL is the Langmuir rate coefficient, n is a non-linear coefficient and the quantities S represents themass of contaminant adsorbed from the dissolvedconcentration C, and Smax corresponds to the maximumsorption capacity of the soil. Schoumans (1995) hasestablished a set of parameters for the Langmuir-isotherm describing fast P sorption in sandy soils andshowed that the maximum sorption capacity is depen-dent upon the aluminium and iron content of the soil.

For non-equilibrium conditions ANIMO describessorption and desorption in terms of a kinetic-Freundlichreaction, and the following first-order equations aresolved,

@S

@t¼

kFsorðkF Cn � SÞ; Sfeq > S

kFdesðkF Cn � SÞ; Sfeq5S

(ð23Þ

le 4

rption functions

ted coefficient References Source of data*

1129 Schoumans (1995) a

6 rd ½Alox þ Feox Schoumans (1995) a

6 rd ½Alox þ Feox Schoumans (1995) a

1�1755 Schoumans (1995) a

0�5357 Schoumans (1995) a�00–2.00 Metherell et al. (1993) b�10–0.20 Metherell et al. (1993) b2�00 Metherell et al. (1993) b

,0�015, 0�004 Metherell et al. (1993) b

soil Clay loam soil

250 McGechan et al. (2002) b

1�0

uthor of reference.and iron content, mmol kg�1, and for the ANIMO model


where: kFsor and kFdes are the kinetic rate coefficient forsorption and desorption respectively and Sfeq is theadsorbed concentration determined by the equilibriumFreundlich isotherm, defined by

S ¼ kF Cn ð24Þ

where: kF is the equilibrium rate coefficient for adsorb-tion. Schoumans (1995) derived rate-dependent P

PSP ¼

0�58� 0�0061CCaCO3calcerous soils

0�0054Bsat þ 0�116 pH � 0�73 slightly weathered non-calcerous soils

0�46� 0�0916 lnðCLÞ highly weathered non-calcerous soils

8><>:

with 0�054PSP40�75

ð27Þ

sorption parameters for a wide range of Dutch sandysoils, but noted that data for the desorption ratecoefficient has not yet been determined.

Precipitation of P takes place immediately when theconcentration of the solution exceeds a defined equili-brium buffer concentration Ceq. This precipitatedmineral dissolves immediately when the concentrationdrops below this limit. For establishing this equilibriumconcentration ANIMO uses the following relation basedon the soil pH:

Ceq ¼ 0�135� 3ð Þ5�pH ð25Þ

3.5.2. GLEAMS

In the GLEAMS model, flows between active andstable mineral phosphorus pools, and between activemineral P and labile P pools (Fig. 3) are defined, with therelative P pool sizes dependent upon soil classification,texture and chemical properties. A long-term stablesystem is maintained between the mineral P pools withthe stable pool four times the size of the active mineralpool at equilibrium. Rapid immobilization of labile P bysorption to the active P pool occurs when the labile Ppool gets large from fertilizer or manure application, orby mineralization. A slow adsorption of inorganic Pfrom the active P pool to the stable P pool is simulated.Movements of P by sorption processes are treated as afunction of soil characteristics.

The flow rates Rla between the labile and activemineral P pools are given by

Rla ¼ 0�1ey exp ð0�115T � 2�88Þ½

Plab � Pact

PSP

1� PSP

� �� rd ð26Þ

where a positive value for this rate indicates the sorptionof P from labile to the active pool and a negative rateindicates a desorption rate from the active pool. Thisexpression includes a temperature-dependence factor,and differs slightly from the original EPIC model

definition. Here, Pact is the amount in the active P pool,ey is defined from Eqn (8), T is soil temperature in 8C,and PSP is the phosphorus sorption coefficient defined asthe fraction of added P remaining in the labile pool afterthe initial rapid sorption phase is complete. Thecoefficient PSP is a function of chemical and physicalsoil properties as shown in the following expressions(Sharpley & Williams, 1990)

where: CCaCO3is the calcium carbonate concentration,

Bsat is base saturation determined as a percentage by theammonium acetate method, pH is the soil acidity, andCL is the percentage clay content.

Flow Ras between the active mineral P pool and thestable mineral P pool occurs until the stable pool Pstab isassumed to be four times the active mineral pool(Sharpley & Williams, 1990) and is expressed as

Ras ¼ oð4Pact � PstabÞrd ð28Þ

with a positive flow indicating that P moves from theactive to the stable pool and vice versa for a negativeflow. The factor o is a flow coefficient which is afunction of PSP, given by

o ¼0�00076 calcareous soils

exp ð�1�77PSP �7�05Þ½ non-calcareous soils

(ð29Þ

3.5.3. DAYCENT

In DAYCENT the inorganic labile P pool is assumedto be in equilibrium with the inorganic sorbed pool. Thisequilibrium relationship is defined in terms of aquadratic equation with two parameters, the sorptionaffinity Saff and the sorption maximum Smax, and thesolution of the equation provides the labile P concen-tration. Essentially, this is a representation of theLangmuir isotherm, Eqn (22), with n=1, and kL given by

kL ¼2

Smaxð2� Saff Þ

� �ð30Þ

The sorption affinity parameter controls the fractionof the mineral P (labile plus sorbed pools) which is in thelabile pool at low levels of P in these pools. Correspond-ingly, the sorption maximum parameter is the maximumamount of P in the sorbed pool, and controls thecurvature of the relationship between labile P andmineral P. Equilibrium between the labile and sorbedpools is recalculated after any P additions or removalsfrom the soil.


Sorbed P is in dynamic equilibrium with a morestrongly sorbed P pool Rso, with the flow rates betweenthe two pools given by

Rso ¼ ½KmsPsorb � KsmPssorbrd ð31Þ

where the rates are also multiplied by the temperatureand moisture factors mentioned earlier, Psorb and Pssorb

are the P pool concentrations, Kms is a constantparameter. The parameter Ksm is a function of soil pHand soil texture through an equation of the form:

Ksm ¼ 12½ p1pH þ p2 þ p3SD ð32Þ

with pi constants and SD the sand content as a % of thesoil. In turn, the strongly sorbed P may be lost to anoccluded P pool with flow rates comparable to the firstcomponent of Eqn (31).

3.5.4. MACRO

MACRO assumes the Freundlich isotherm equationfor sorption of a contaminant onto static sorption sitesin the soil [Eqn (24)]. Only instantaneous equilibriumcan be considered. The Freundlich isotherm is alsoassumed for sorption of a contaminant onto sites on amobile colloid, but in this case the exponent n must takea value of unity (implying a linear isotherm).

When used as a P model, the sorption processdescribed by the Freundlich isotherm represents fast,reversible sorption of P onto sites on the surface of soilparticles. As MACRO is not intended primarily as a Pmodel, no direct provision is made for representation ofthe slow reaction which P undergoes following attain-ment of equilibrium for fast sorption. However (asalready mentioned in relation to crop uptake of P),provision is made in MACRO for representation ofdegradation, and this facility can also be used to providea simplistic representation of the slow reaction. The slowreaction is reversible only at a very slow rate (someresearchers regard it as totally irreversible), so, overrelatively short periods after manure or fertilizerspreading, degradation is an appropriate representationof the slow reaction which effectively removes P fromthe active, labile pools.

4. Solute and particulate phosphorus transport

The removal of P from the soil/water system byleaching of solutes (organic and inorganic) and bysurface-runoff (dissolved and particulate) is an impor-tant consideration in modelling the P cycle in soils.Export of P through runoff as particulate P (associatedwith soil particles and eroded organic matter) isconsidered to be the major constituent of P transportfrom cultivated land (Sharpley et al., 1992). However,export of particulate P by the ‘through-the-soil’ route is

not considered. Runoff from grassland or forestscontains little sediment and so dissolved P forms thedominant loss. Leaching losses of P are controlled bymore complex factors than surface losses, with percola-tion to groundwater, and soil micropore and fractureflow to drainage systems forming important P lossmechanisms in some soils. The loss of dissolved Pthrough leaching is generally related to the degree of Psaturation of soils (Heckrath et al., 1998; Brookes et al.,1997), whereas particulate P losses through subsoilmovement are dependent upon the degree of macroporeor bypass flow. A significant proportion (up to 50%) ofthe total P from deep drains under clayey non-calcerousgrassland, has been reported to be in the form ofinorganic particulate P (Haygarth et al., 1998), forwhich macropore flow must be an important transportmechanism.

At the larger farm or catchment scale, effort is nowbeing expended in determining the mass balances andflows of phosphorus in agricultural systems (Cassellet al., 1998). Modelling tools which predict the environ-mental consequences of the application of fertilizers, andanimal waste and their transport and transformationsare seen as an important means of controlling thispollution (Daniel et al., 1998).

Representation of solute and colloid transport, andalso surface runoff, are dependent on the associated soilwater model or subroutine (see Sections 2.3.1 and 2.3.4).ANIMO, GLEAMS, DAYCENT and MACRO can allrepresent vertical leaching of dissolved or labile P todeep groundwater, with ANIMO and MACRO alsosimulating movement to field drains.

Solute transport in ANIMO is treated through anumerical solution of the convection–dispersion masstransport equation with sink/source terms representingsorption and transformations. Physical dispersion isrepresented in the model by numerical dispersionobtained through a judicious choice of the layerspacings. ANIMO adds all inputs of animal manureand fertilizer into an imaginary surface reservoir whosevolume and decay properties are determined by anappropriate thickness of the reservoir. These materialinputs are not released to the soil until a rainfall eventoccurs. The fraction of material released is dependentupon the ratio of volume of rainfall and the reservoirvolume, with the store of nutrients evaluated after eachtime step through a mass balance exercise, and beingtotally depleted when the precipitation volume equalsthe reservoir volume. Surface runoff occurs throughinfiltration excess or saturation excess, and in both casesthis runoff may contain solute from precipitation, theupper part of the soil and the surface reservoir.

Within GLEAMS the hydrology component describessoil water movement through a storage-routing


technique (Knisel, 1980) which calculates the outflowfrom each soil layer to its neighbour. Percolation is thendetermined from the layers soil moisture and saturatedhydraulic conductivities, whenever the volume of waterin each layer is above field capacity. Solute transport istreated in GLEAMS through an advective process witha percolation mass of solute determined for each layeroutflow. Since P is sorbed onto soil surfaces, the amountin solution is determined through a partition coefficientkd between the solid phase and the water phaseaccording to the linear adsorption isotherm:

kd ¼Cs

Cw

ð33Þ

where: Cs and Cw are the equilibrium concentrations insoil and water, respectively. This partition coefficient istaken to be dependent upon the soil clay fractionthrough the empirical expression:

kd ¼ 1�00þ 0�025CL ð34Þ

where: CL is the percent clay in the soil layer. Researchis currently being carried out to relate this coefficient tosoil P status and the nature of the soil. The concentra-tion of labile P is then determined through a massbalance approach for each layer taking into account theuptake by plants and the various transformations thatoccur.

Phosphorus is extracted from the soil surface whenoverland flow occurs and by mixing of the soil materialwith this runoff water. GLEAMS assumes that the top1 cm of soil is the active layer that interacts with therunoff water, and that the extraction of P is incomplete.In this case we can describe the soil and waterconcentrations of the surface layer by

Cs ¼Cavkdb1þ kdb

Cw ¼Cavb

1þ kdb

ð35Þ

where: Cav is the available concentration in the surfacesoil layer and b is the extraction coefficient which hasvalues of (Leonard et al., 1987)

b ¼

0�5; kd41�0

0�598 exp½�0�179kd ; 1�05kd510�0

0�1; kd410�0

8><>: ð36Þ

It can thus be seen that when kd ¼ 0 then Cs=0 andCw=Cav b, and that when kd gets very large Cs

approaches Cav. The rate of change of P in the surfacelayer is defined in GLEAMS as being proportional toCw and the water flux, and at saturation this equationcan be integrated to give an approximation for theavailable concentration Cav.

The movement of particulate P through runoff isrepresented in the GLEAMS model (Section 2.3.3), onthe basis of the enrichment ratio (the ratio of the surfacearea of the sediment leaving the field and the surfacearea of the matrix soil), which is given as a function ofthe sizes and composition of the sediment particles. TheP mass transported with the sediment is then theproduct of the sediment mass, enrichment ratio and Cs.

In DAYCENT, P losses from the system can occur asa result of leaching of labile P, with P losses accumulat-ing in the soil layer below the last layer, eventuallypercolating out of the defined profile. Leaching of labilemineral P occurs when there is saturated water flowbetween the soil layers. The fraction of the mineral poolthat flows from the upper layer to the lower layerincreases as a linear function of the sand content, up to amaximum set value. A fraction of the products from thedecomposition of the active organic P pool is lost asleached organic matter. Leaching of this organic matteris a function of the decay rate for active soil organicmatter, and the clay content of the soil (with lower lossesfor clay soils). This leaching only occurs if the water flowis sufficiently high, with a minimum flow required fordrainage of water below the 30 cm soil depth. Themovement of particulate P through soil erosion iscalculated in a similar fashion to that of the GLEAMSmodel.

The MACRO model can provide the most sophisti-cated representation of transport of P through the soil(as opposed to by the surface route) in both dissolvedand particulate forms. Important features which distin-guish MACRO from the other models are representa-tion of colloid facilitated transport of sorbed P, and thedual porosity representation of water movement, asmacropore flow of colloid-bound P through the soilappears to be a very significant polluting loss process inmany circumstances.

5. Conclusions

A comprehensive description of all processes relevantto P in soil would consider transport of both soluble andparticulate P, and of both inorganic and organic P, bythree routes}overland (surface runoff ), through the soilto field drains, and vertically through the soil down todeep groundwater, as well as transformations from oneform of P to another following applications of bothmineral fertilizer and manure P. None of the modelsconsider all these processes, but some consider a sub-setappropriate to a particular situation. GLEAMS con-siders everything except transport to field drains so isappropriate to many North American situations wherethere are no field drains and most P is applied as mineral


fertilizer. However, it is less appropriate to parts of theUS farm belt which have field drains installed to drainformer swamps, and drain water quality is a major issuein these regions. DAYCENT also only considers verticaltransport, but some of its parameters are more appro-priate to long-time scale processes. It is, however, theonly model to consider plant residue decomposition interms of the lignin-N ratio. ANIMO has the mostcomprehensive treatment of manure and slurry, andincludes a rigorous description of soluble forms ofphosphorus, but lacks consideration of particulatetransport. MACRO has the most comprehensive treat-ment of through-the-soil transport processes, includingmicropore and macropore domains (although not sur-face runoff ) and particulate transport, but currently hasonly simplistic representation of P transformations.

Modelling of temperature and soil wetness effects ontransformation rates is broadly similar between all fourmodels. The general approach to modelling decomposi-tion and mineralization (or immobilization) is similarbetween ANIMO, GLEAMS and DAYCENT (assumedto be based on N and C processes), but details of theequations differ. MACRO, however, does not have adescription of soil N and C transformation, butconcentrates on soil solute transport characteristics.

Detailed P loss experiments in field drained soils andtheir simulation using simplified P cycle models (McGe-chan et al., 2002), has identified that there is a furtherrequirement for model P development. Further Pmodelling work is likely to be focussed on constructinga new hybrid version of the four models described here,with full representation of the missing processes. Such amodel is likely to include a description of both solubleand particulate P flow through micropores and macro-pores as in the MACRO model. This would becombined with a full representation of the C/N/P cycleas described by GLEAMS, with manure and slurrycomponents as described by ANIMO, and plant residuedecay equations taken from the DAYCENT model.Finally, the overland flow and erosion losses could berepresented by components from the GLEAMS model.

Acknowledgements

Funds to carry out this work were provided by theScottish Executive Environment and Rural AffairsDepartment.

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