SW—Soil and Water: Sorption of Phosphorus by Soil, Part 1: Principles, Equations and Models

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  • Biosystems Engineering (2002) 82 (1), 124w

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    information about sorption onto such colloids. Equations are considered for processes, column experiments

    1.

    muif&MptodethWthpsoinwsom

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    15and P dynamics systems studies. Isotherm equations representing fast reversible sorption have been identied.Instantaneous equilibrium can be assumed for most applications of the fast sorption equations, with theexception of surface erosion studies. Details of some very complex mechanistic models of the slow reactionand deposition processes are presented and discussed. Some simpler equations for these processes fromexisting eld-scale P dynamics models are also presented. It is concluded that, at least in the short term, themechanistic approach is too complex for incorporation into a systems model of the whole range of Pprocesses, and that further development should represent time-dependent processes by adaptation of thesimple equations. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved

    Introduction

    Plant nutrients from chemical fertilizer or animalanure are positive assets if retained in the soil forptake by plants, but become environmental pollutantsleached into watercourses or groundwater (McGechanWu, 1998; McGechan & Lewis, 1998, 2000; Lewis &cGechan, 1998). There has been much attention in theast devoted to nitrogen as a nutrient and pollutant, dueits high solubility and leachability through eld

    rains and to groundwater (McGechan et al., 1997; Wual., 1998), and its high potential for conversion to

    armful volatile or gaseous emissions (McGechan &u, 1998). Attention is currently moving more towardse less soluble and non-volatile contaminating nutrienthosphorus (P). The study of P as a plant nutrient and

    addresses sorption of P by soil components, and somefeatures of P sorption which make the process complexcompared to sorption of other reactive chemicals.Weather-driven simulation modelling has become an

    important component of studies of soil nutrients, bothfor crop growth and for their losses by leaching tobecome environmental pollutants. Such modellingstudies using the soil nitrogen dynamics model SOILN(Johnsson et al., 1987) and other models have beendescribed for nitrogen as a nutrient and pollutant by Wuand McGechan (1998a, 1998b) and Wu et al. (1998)The authors, Lewis and McGechan, have also reviewedthe eld-scale models GLEAMS, ANIMO andCENTURY, which are being used to study P (as welas nitrogen) cycling processes. Their review covers thewhole range of transformation and transport processesdoi:10.1006/bioe.2002.0054, available online at http://wwSW}Soil and Water

    REVIEW

    Sorption of Phosphorus by Soil, Part

    M. B. McGecha

    Environment Division, SAC, West Mains Road, Edinburgh EH9 3J

    (Received 26 January 2001; accepte

    The very extensive literature on phosphorus (P) sorptequations and parameter values for use in a soil P dysorption of P onto surface sites, and various slower pbelow surfaces of iron or aluminium oxide mineralsconsidered to take place both onto static soil componetransport in sediments moving in surface runo owsfacilitated through soil P pollution ows have only recil component is complicated by its long residence timethe ground due to sorption, and its tendency to moveith soil water in colloidal or particulate form. Unlike alute such as nitrate, there can be restrictions onovements of colloids in soil pores. This paper

    37-5110/02/$35.00 1.idealibrary.com on

    PAPER

    1: Principles, Equations and Models

    n; D. R. Lewis

    , UK; e-mail of corresponding author: m.mcgechan@ed.sac.ac.uk

    d in revised form 1 February 2002)

    ion studies is reviewed with the intention of selectingamics model. Processes considered are fast reversiblerocesses including reactions which deposit P at depthin soil or precipitate calcium phosphate. Sorption ists and onto mobile sediments or colloids. Phosphorushas been extensively studied, but problems of colloidently received attention. There is almost no publishedapplicable to P in the soil, including a short descriptionof sorption processes. However, due to the complexityof sorption processes for P and the extensive publishedliterature on it, this topic is the subject of a moredetailed review in the current paper, including models

    # 2002 Silsoe Research Institute. Published byElsevier Science Ltd. All rights reserved

  • M. B. MCGECHAN; D. R. LEWIS2Notation

    A coecient in Eqn (20) (Hansen et al.,1999)

    Aa coecient in Eqn (22) (Barrow, 1974b)Alox oxalate-extractable aluminium content,

    mmol kg1 or mg kg1

    [Alox+Feox] oxalate-extractable aluminium plus ironcontent, mmol kg1

    Ar coecient in the Arrhenius equation,Eqn (22) (Barrow & Shaw, 1975a)

    As specic surface area of soil particles inEqn (58) (Sharpley & Ahuja, 1983),cm2 g1

    a0a3 tted coecients in Eqn (40)ab proportion of P converted to an ineec-

    tive form [in Eqn (21), Barrow 1974a]ad coecient in diusivity function in Eqn

    (58) (Sharpley & Ahuja, 1983)ar coecient in Eqn (60) (Ahuja et al.,

    1982)as coecient in Eqn (34) (Sharpley, 1982)aw slope constant in Eqn (57) (Sharpley &

    Ahuja, 1982)B coecient in Eqn (20) (Hansen et al.,

    1999)B1, B2, B3 coecients in Eqn (23) (Barrow & Shaw,

    1975a)Bsat base saturation by ammonium acetate

    method in GLEAMS, %b1 exponent in the Freundlich sorption

    isotherm equation, Eqn (2)b2 exponent in time-dependent term of the

    Freundlich sorption isotherm equation,Eqn (5), and of desorption equation,Eqn (52)

    b3 third exponent in Eqn (52) (Barrow,1979)

    bk coecient in Eqn (7) (Kuo, 1988)br coecient in Eqn (60) (Ahuja et al.,

    1982)C concentration of P in solution, mg l1

    %CC average concentration of P in runowater [Eqn (60), Ahuja et al., 1982]

    Ce concentration of P at the interfacebetween oxide and phosphate [Eqn(41)], mg l1

    Cd,0 Limiting concentration of P in solu-tion for no desorption (Barrow, 1979),mg l1

    Ci, Ci1 concentrations of P in solution at times tiand ti1 [Eqn (37), Barrow, 1983a]

    C0 concentration of P in solution at timezero, mg l1

    C0,0 coecient representing limiting concen-tration of P in solution for zero deso-rption time (Barrow, 1979)

    Cd,0 composite coecient in desorption equa-tions, Eqns (50) and (52) (Barrow, 1979)

    Cro instantaneous concentration of desorbedP in runo water, Eqn (59) (Sharpleyet al., 1981a)

    Ct concentration of P in solution at time tin Eqn (23) (Barrow & Shaw, 1975a),mg l1

    CCaCO3 calcium carbonate concentration inGLEAMS

    CL clay content of soil, %cr coecient in Eqn (60) (Ahuja et al.,

    1982)D diusion coecient

    DSSP degree of saturation with P, %E energy of activation of chemical compo-

    nent [in Eqns (7) and (14), Kuo, 1988 andEqn (28), Barrow 1974a]

    Er kinetic energy of rainfall per unit areaper unit time in Eqn (60) (Ahuja et al.,1982)

    eT rate constant adjustment factor for soiltemperature in EPIC and GLEAMS

    es power coecient in Eqn (60) (Ahujaet al., 1982)

    ey rate constant adjustment factor for soilwater content in EPIC and GLEAMS

    F the FaradayFeox oxalate-extractable iron content,

    mmol kg1 or mg kg1

    f fraction of sorption sites that take partin the fast sorption process (Chen et al.,1996)

    fb parameter in Eqns (37) and (38) (Bar-row, 1983a)

    fl fraction of fertilizer P labile after 6months incubation period in EPIC

    fs diusion impedance factor (Nye &Staunton, 1994)

    I integral with respect to time of dier-ences in P concentration in solution andat the interface between oxide andphosphate within a particle, Eqn (40)

    Ir rainfall intensity, cm h1

    i index for summation in generalizedisotherm equation, Eqn (15) (Goldberg& Sposito, 1984)

    is coecient in Eqn (34) (Sharpley, 1982)j index for summation in Eqns (84) and (87)K coecient in Eqn (23) (Barrow & Shaw,

    1975a)K2,j, K3, j coecients in ANIMO, Eqn (84)

    (Schoumans, 1995)Ks constant in Eqn (56) (Sharpley et al.,

    1981b)

  • SORPTION OF PHOSPHORUS 3k1, k2, k3, k4 coecients in multiple-component sorp-tion and desorption equations

    kb the Langmuir coecient in Eqn (18)(Barrow, 1983a)

    kE1, kE2 coecients in the Elovich sorption iso-therm equation, Eqn (16)

    kF coecient in the Freundlich sorptionisotherm equation, Eqn (2)

    ki coecient in generalized sorption iso-therm equation, Eqn (15)

    kL coecient in the Langmuir sorptionisotherm equation, Eqn (6), lmg1 [P]

    kL1, kL2 coecients in two-component Langmuirsorption isotherm equation, Eqn (11),lmg1 [P]

    kT1, kT2 coecients in the Temkin sorption iso-therm equation, Eqn (1)

    kZ2, kZ3 coecients in kinetic form of Langmuirsorption isotherm equation, as presentedby Van der Zee et al. (1989a), Eqns (9)and (10)

    L length of slope in Eqn (60) (Ahuja et al.,1982)

    M mass of soil in interaction zone [Eqns(59) and (60)], kg

    m proportion of added P in solution attime zero in Eqn. (25) (Barrow & Shaw,1975a)

    md Power coecient in diusivityfunction in Eqn (58) (Sharpley &Ahuja, 1983)

    mr Power coecient in Eqn (60) (Ahujaet al., 1982)

    m1, m2 coecients in electrostatic potentialequations (Barrow, 1983a, 1983b)

    n number of components in generalizedisotherm equation, Eqn (15) (Goldberg& Sposito, 1984)

    nb power coecient in Eqns (21) and (29)(Barrow & Shaw, 1975b)

    nr power coecient in Eqn (60) (Ahujaet al., 1982)

    OM organic matter, %Pact active P pool in EPIC and GLEAMSPacto previous value of Pact in Eqn (86)Pd quantity of P desorbed, g [P] kg

    1 [soil]Pfe fertilizer P added, g [P] kg

    1 [soil]Pilf labile P after fertilization and incubation

    in EPIC and GLEAMSPili initial labile P (prior to fertilization)Plab labile P pool in EPIC and GLEAMSPom minimum quantity of desorbable P in

    Eqn (57) (Sharpley & Ahuja, 1982)Pox oxalate-extractable P content,

    mmol kg1 or mg kg1

    Psp proportion of added P which remainslabile after incubation in EPIC andGLEAMS

    Pspcl clay content related proportion of addedP which remains labile after incubationin ICECREAM

    Pspph soil pH related proportion of added Pwhich remains labile after incubation inICECREAM

    Pstab stable deposited P poolP0 initial quantity of desorbable P in Eqn

    (56) (Sharpley et al., 1981a, 1981b)pH pH in GLEAMSQ quantity of P sorbed on surface sorption

    sites, including that sorbed by fast time-dependent processes, mg [P] kg1 [soil]

    Qe equilibrium value of quantity of P sorbedon surface sorption sites, mg [P]kg1 [soil][Eqn (43), Raats et al., 1982]

    Qmax maximum P sorption capacity for sur-face sorption sites, including that sorbedby fast time-dependent processes, mg[P] kg1 [soil]

    Qmax,1,Qmax,2

    maximum P sorption capacity for sur-face sorption sites in two-componentLangmuir sorption isotherm equation,Eqn (11), mg [P] kg1 [soil]

    Q0 surface-sorbed P in soil prior to the startof a soil P test, Eqn (3)

    Qr runo rate per unit area in Eqn (60)(Ahuja et al., 1982)

    q coecient in Eqns (31) and (32) (Bar-row, 1983b)

    R universal gas constantRas ow rate for slow P adsorption in EPIC

    and GLEAMS, kg ha1 day1

    Rla ow rate for rapid P adsorption in EPICand GLEAMS, kg ha1 day1

    S quantity of P deposited below sorptionsurfaces by slow reaction, or quantitysorbed by time-dependent processeswhich include slow deposition, g[P] kg1 [soil]

    S1, S2, S3 three components of S (for j=1, 2 and 3)given by Eqn (87) (Schoumans, 1995)

    Sl angle of slope in Eqn (60) (Ahuja et al.,1982), %

    Smax maximum quantity of P deposited belowsorption surfaces by slow reaction, ormaximum quantity sorbed by time-de-pendent processes which includes slowdeposition, g [P] kg1 [soil]

    Stot quantity of P sorbed on surface sorptionsites plus that deposited below sorptionsurfaces by slow reaction, g [P] kg1

    [soil]s coecient in Eqn (34) (Sharpley, 1982)T absolute temperature, K

    T1, T2 temperatures in Eqn (32) (Barrow 1983c)Tc soil temperature, 8Ct time, day

  • 2

    M. B. MCGECHAN; D. R. LEWIS4of sorption processes applied to laboratory experiments.The availability and usefulness of data for estimatingparameters of equations which may be incorporated intoeld-scale models is later assessed in a follow-on Part 2of this paper (McGechan, 2002).

    2. General principles of phosphorus sorption

    Sorption is the process by which reactive chemicalsbecome attached to surfaces, sometimes of otherwiserelatively harmless solids. Small particles have a largespecic surface area, so tend physically to have a highsorption capacity (but this is further modied by theirchemistry). In addition to those on immobile particles inthe soil matrix, there are competing sorption sites onotherwise non-polluting sediments and colloids whichmove relatively freely in water ows along the surface orthrough the soil. Small soil particles readily becomedetached to become mobile sediments or colloids, andland-spread manures and wastes contain additionalcolloidal material. However, attention in the extensiveliterature has been directed mainly to sorption onto

    immobile soil components, with a few references tosorption onto sediments moving in surface runoows.In common with other reactive chemicals, the extent

    to which P is adsorbed relative to that in solution ishighly non-linear, as energy levels vary between dierentbinding sites on the solid surfaces, high-energy sitesbecoming occupied before low-energy sites. This non-linearity is commonly represented mathematically by anumber of alternative equations (isotherms), withlogarithmic or other transformations to make linearapproximations.For P (which may dier from some other reactive

    chemicals), the sorption process is complicated for onemain reason. Apparent sorption of P can be thought ofas being a combination of several processes, including afast (almost instantaneous) reversible true sorptionprocess on soil particle surfaces, plus various slowertime-dependent processes, some of which lead todeposition of P at a depth below the surface of particles.These slower processes can be further subdivided intorelatively faster and very slow components, and aredescribed by various authors as slow adsorption, the

    HPO4 (Barrow, 1983a)as power constant in Eqn (56) (Sharpley

    et al., 1981a, 1981b)b rate constant in kinematic sorption

    isotherm equations, and also in Eqn(45) (Raats et al., 1982)

    1993)rd dry bulk density of soil, gm

    3

    s standard deviation of electrostaticpotential (Barrow, 1983a)t1, t2 time periods in Eqn (32) (Barrow &Shaw, 1983b)

    td desorption time, h (Barrow, 1979)tL lag time which elapses before the slow

    deposition process becomes establishedin Eqn (20) (Hansen et al., 1999)

    t0 start of time period, dayV constant relating quantity of desorbable

    P to eective concentration in Eqn (58)(Sharpley & Ahuja, 1983)

    Vr total rain volume in the rainfall event perunit area in Eqn (60) (Ahuja et al., 1982)

    v water velocity in convection/dispersionequation

    W water:soil ratio in Eqn (56) (Sharpleyet al., 1981a, 1981b)

    Wk interaction energy in Eqn (14) (Kuo,1988)

    z depth in soil in convection/dispersionequation

    zi valency, including sign (2 for HPO42)

    zk number of nearest neighbour surround-ing a central phosphate species in Eqn(14) (Kuo, 1988)

    a proportion of phosphate present asbas rate constant for slow adsorption inEPIC, day1

    bb rate constant in Eqn (21) (Barrow 1974a)be rate variable [Eqns (43) and (45), Raats

    et al., 1982]bs power constant in Eqn (56) (Sharpley

    et al., 1981a, 1981b)g activity coecient of ions in solutionja electrostatic potential in Eqns (18), (19)

    and (40) (Barrow, 1983a)jao initial value of electrostatic potential in

    Eqns (19) and (40) (Barrow, 1983a)y volumetric water content of soil, fraction

    y003 volumetric soil water content at a ten-sion of 30 kPa

    yd proportion of sites occupied (Barrow,1983a)

    yfc volumetric soil water content ateld capacity in GLEAMS model (as-sumed to be at a tension of 33 kPa inNorth America) (Knisel, 1993)

    yk replaces Q/Qmax in Eqn (7) (Kuo, 1988)yw volumetric soil water content at the

    wilting point (assumed to be at1500 kPa) in GLEAMS model (Knisel,

  • SORPTION OF PHOSPHORUS 5slow reaction, deposition, xation, precipitation orsolid-state diusion; opinions dier about the extent towhich such processes are reversible. A description of theslow deposition process, and the role of soil mineralssuch as iron (Fe), aluminium (Al) and calcium (Ca)compounds (including the somewhat dierent precipita-tion process in calcareous soils compared to that onmetal oxides in acid soils), is presented by Hemwall(1957). The distinction between fast and slow sorptionprocesses, and that between sorption on the surface andat depth below surfaces, are in both cases indistinct;Addiscott and Thomas (2000) have suggested that theseprocesses could better be regarded as belonging to acontinuum. The multiple sorption processes complicatewhat happens when desorption is induced by dilution ofthe soil solution, since the extent to which slowdeposition has progressed inuences the quantity ofsorbed material available for fast desorption from thesurface (rapid) sorption sites. This complication isillustrated by the observations of Barrow (1979) andothers that curves representing the reverse process ofdesorption do not retrace the paths of the sorptioncurves. In particular, they observed that dilution of thedissolved P occurs after long incubation periods withhigh P concentrations (or alternatively after shorterincubation periods at raised temperatures), a muchlower quantity of P was desorbed than the quantityoriginally adsorbed. Also, where dilution occurred afteronly short incubation periods, desorption more nearlyfollowed the path of adsorption, but this was followedby a period of re-adsorption.Soil P can be considered as being contained in a

    number of pools, including (amongst others) dissolvedinorganic P, inorganic P sorbed onto surface sites,inorganic P sorbed or deposited by various slow time-dependent processes and various organic P pools(including unbound precipitates). The quantity of P ineach pool at a given time depends on the history of Pfertilizer application, including the lapsed time since themost recent applications. The term labile P iscommonly used to represent mobile P which is available(or rapidly becomes available by reactions with fastkinetics) as a nutrient for plant growth, includingsoluble P and that which is sorbed onto surfacesites, but not that which has been deposited by theslow reaction (which is not readily available). Also,the buering capacity is commonly used as anindication of the quantity of P sorbed on surfacesites which will rapidly desorb when dilution occurs,and again P deposited by the slow reaction isexcluded from this. The multiple sorption processesare further complicated if competing sorption sites in thestatic soil matrix and on mobile particles are bothconsidered.The concept of saturation is mentioned by manyauthors (e.g. Beauchemin & Simard, 1999), togetherwith the degree of saturation with P (DSSP). However,the quantity of P deposited below the surface by theslow reaction in soil saturated with P is not clearlydened. A change point soil P content (not related tosaturation but generally much lower than the saturationP content) has been discussed by some researchers,including Heckrath et al. (1995). If the P content isabove the change point there is a tendency for P to beleached to eld drains at a much higher level than if thecontent is below the change point.

    3. Factors inuencing extent of sorption

    The physical and chemical mechanisms of P sorptionin soil are described in a number of textbooks, e.g. Wild(1988). The extent to which a soil adsorbs P (bueringcapacity or sorption capacity) diers widely betweendierent soils. It tends to be high in soils with a highproportion of small-size particles (and hence a highspecic surface area) such as clay. Manure or slurryadded to the soil have large contents of both P andcolloidal material on which P is sorbed (as discussed byDe Willigen et al., 1982), and such colloids provideadditional sorption sites when distributed by ploughing.The eect of manure applications on the sorptioncapacity of soil has been studied by Eghball et al.(1996). Chemical considerations mean that clay soilscontaining high proportions of Fe or Al oxide mineralshave particularly high buering capacities, as discussedby Bowden et al. (1977). Another important environ-mental factor is pH (e.g. Barrow, 1984), which has amajor inuence on ionic mechanisms of sorption (asdiscussed in Section 4.2.2). This results in a distinctsorption behaviour for alkaline calcareous soils whichdiers from that of more acid soils.

    4. Equations and models representing sorption processes

    4.1. Isotherm equations

    There are a number of standard isotherm equationswhich are commonly used to t experimental data foradsorption of P and other reactive solutes, taking intoaccount the non-linearity of these relationships. Theseinclude the Temkin equation, the Freundlich equationthe Langmuir equation, the two-surface Langmuirequation and the Elovich equation. They are describedin various textbooks and papers, including Barrow(1978), Travis and Etnier (1981), Mead (1981), Chienand Clayton (1980) and Kinniburgh (1986). In their

  • simplest form, these equations are dened to assumeinstantaneous approach to equilibrium, but they canalso be modied to represent a time-dependent(kinematic) approach to equilibrium.

    4.1.1. Temkin equationThe Temkin equation is described by Barrow (1978)

    and Mead (1981) as follows:

    Q kT1 lnkT2C 1

    where Q is the quantity of P sorbed in g [P] kg1 [soil], Cis the concentration of P in solution in mg l1 and kT1and kT2 are coecients.

    4.1.2. Freundlich equationThe equilibrium Freundlich equation has the general

    formb1

    Incorporating the kinetic component into the Freun-dlich equation requires a solution to the following rst-order dierential equation:

    @Q

    @t bkFCb1 Q 4

    where b in day1 is the kinetic rate constant for thereaction. An alternative form of the Freundlich equationincorporating time dependence is presented by Barrow(1983a):

    Stot kFCb1 tb2 5

    where Stot is the sum of instantaneous and time-dependent sorption and b2 is a second exponent fortime t.

    4.1.3. Langmuir equationThe equilibrium Langmuir equation is usually written

    st

    M. B. MCGECHAN; D. R. LEWIS6Q kFC 2

    where non-linearity is introduced by the exponent b1and kF is a coecient [other symbols dened as for Eqn(1)]. The form of the Freundlich equation (Fig. 1) is suchthat good ts can be obtained to sorption data fornearly all soils. However, the equation has the dis-advantage that it does not dene a maximum (satura-tion) value. Barrow (1978) discusses the need to considerP already present in the soil when tting Eqn (2) toexperimental sorption data, suggesting an extra term inthe isotherm:

    QQo kFCb1 3

    where Qo is the surface-sorbed P in the soil prior to thestart of the test andQ is the P sorbed during the test. Chenet al. (1999) discuss units and conversion transformationsfor kF , so values of kF can be compared between dierentsorbents where the value of the exponent b1 varies.

    Fig. 1. Langmuir and Freundlich isotherms for some English soilisotherms, from Holford et al. (1974) and from Holford and Main the form

    Q QmaxkLC

    1 kLC

    6

    where Qmax in g [P] kg1 [soil] corresponds to the

    maximum sorption capacity (saturation) and kL is acoecient.An alternative form of the Langmuir equation has

    been presented by Kuo (1988) as follows:

    yk1 yk bkCE=RT 7

    In this form compared to the standard form, yk hasreplaced Q=Qmax and bkE=RT has replaced kL, where Eis the energy derived from the chemical component, T isthe absolute temperature and R is the universal gasconstant.The kinetic version of the Langmuir equation can be

    represented by the following rst-order dierential

    eries (for parameter values see Table 1). , double Langmuirtingley (1995); , Freundlich isotherm, from Barrow (1978)

  • SORPTION OF PHOSPHORUS 7equation:

    Q QmaxkLC 1=b@Q=@t

    1 kLC

    8

    An alternative form of equation to represent the kineticsof approach to equilibrium for a Langmuir isotherm ispresented by Van der Zee et al. (1989a):

    dQ

    dt kZ2CQmax Q kZ3Q 9

    where

    kL kZ2=kZ3 10

    4.1.4. Two-surface Langmuir equationHolford et al. (1974) and Holford and Mattingly

    (1975, 1976) present a two-surface modication to theLangmuir equation, for the situation where the simpleLangmuir equation tends to give poor ts to sorptiondata. Equation (6) is extended to include two terms eachwith dierent coecient values:

    Q Qmax;1kL1C

    1 kL1C

    Qmax;2

    kL2C

    1 kL2C

    11

    In this case, there are two sorption maxima Qmax,1 andQmax,2 so saturation can be dened as Qmax,1+Qmax,2.This represents sorption by a solid or soil whichcontains two distinct populations of sorption sites, oneof high bonding strength, the other with much lowerbonding strength (typically around one hundredth of thestrength, i.e. kL1 100 kL2, but with a populationthree times that of the high bonding strength sites, i.e.Qmax;2 3Qmax;1). Holford et al. (1997) postulatethat no leaching should occur before a quantity of P hasbeen applied equivalent to the high-strength sorptioncapacity Qmax,1 (although this is not the case in practiceas leaching always occurs to some degree). The high-strength sorption capacity may correspond roughly tothe change point as discussed by Heckrath et al. (1995)(Section 2), although this is more loosely dened basedon a simple P extraction procedure as used for advisorypurposes. The shape of the two-surface Langmuirisotherm can be similar to the Freundlich isotherm(Fig. 1), but (unlike with Freundlich) it still has denedsorption maxima.Holford and Mattingly (1976) dene buering capa-

    city as being the change in the quantity of adsorbed Pper unit change in concentration of dissolved P, whichfollows from Eqn (11) as being

    dQ

    dC Qmax;1

    kL1C

    1 kL1C2

    Qmax;2

    kL2C

    1 kL2C2

    12

    Also, the maximum value of the buering capacityoccurs at very low concentrations, i.e.

    dQ=dC

    c!0 Qmax;1kL1 Qmax;2kL2 13Selim et al. (1976) describe a kinetic version of a two-siteequation, with rst-order approach to equilibrium, butwithout any non-linearity.

    4.1.5. Modied Langmuir equationKuo (1988) has described a modied Langmuir

    equation as follows:

    yk=1 yk bkC exp E zkWkyk=RT

    14

    where Wk is the interaction energy from which the netcontribution to the total energy of sorption can increaseor decrease depending on the number of the nearest-neighbour zk surrounding a central phosphate speciesand on the fraction of the sites occupied, and the othersymbols are as for Eqn (7).

    4.1.6. Generalized isotherm equationGoldberg and Sposito (1984) present a generalized

    form of equilibrium isotherm:

    Q Xni1

    Qmax;ikiCbi

    1 kiCbi

    15

    They demonstrate that this generalized form converts tothe standard equation forms, n=1 and b1=1 for theLangmuir equation, n=2 and b1=b2=1 for the two-surface Langmuir equation and n=1, 05b151 andki51 for the Freundlich equation.

    4.1.7. Elovich equationThe Elovich equation describes P reaction kinetics,

    although it can be thought of as taking the placeof a kinematic sorption isotherm. It is generallyexpressed as

    Q 1=kE2lnkE1kE2 1=kE2lnt t0 16

    where kE1 and kE2 are constants and t0 is the start of thetime period in days. Chien and Clayton (1980) present asimplied form of the Elovich equation, by assumingkE1kE2t41:

    Q 1=kE2ln1 kE1kE2t 17

    4.2. The fast sorption process

    4.2.1. Application of isotherm equations to representfast sorption processThe term model is used widely in literature on P

    sorption to describe tting of experimental data toequilibrium isotherm equations, or the kinetics ofapproach to such an equilibrium. Barrow (1978) andother authors have discussed the application of thealternative standard isotherm equations to the adsorp-tion of P in soils.

  • M. B. MCGECHAN; D. R. LEWIS8There have been a number of attempts to t Langmuirisotherms, as discussed by Van der Zee et al. (1989a). Insome cases, this concerns tting data on sorption of P tospecic metal oxide minerals (e.g. McLaughlin et al.,1977; Bowden et al., 1980), where there is a clear valueof Qmax, so good ts can be obtained with thisequation form. However, other researchers such asVan der Zee and Gjaltema (1992) have used thisequation for sorption by soil. Barrow (1978)compared the standard isotherm equations for ttingto P sorption to soils data, concluding that Freundlichwas superior to Langmuir but even this was satisfactoryfor limited concentration ranges only. Shayan andDavey (1978) and Sibbesen (1981) both found that tscould be improved by modications to the Freundlichequation.

    4.2.2. Ionic mechanismsPartt et al. (1975) discuss the mechanism of

    phosphate xation by Fe oxides in terms of molecularstructures and the electrical charges on the ions. Bowdenet al. (1977, 1980) and Barrow et al. (1980, 1981a,1981b) have worked with an equation representing theelectrochemical energy levels of the process of binding tosurface sites for particular clay minerals. Sposito (1980)showed how the Freundlich isotherm could be generatedfrom a distribution of these binding parameters (eachrepresented by the Langmuir equation) for a series ofminerals. Based on this approach, Barrow (1983a)developed a mechanistic model consisting of thefollowing equations:

    yd kbagC expziFja=RT

    1 kbagC expziFja=RT 18

    ja ja0 m1yd 19

    where yd is the proportion of sites occupied, ja is theelectrostatic potential in the plane of adsorption, andthe initial value of the potential ja0 is considered tobe a normal distribution (of 30 elements with widths/3) with mean ja0 and standard deviation s (leadingto yd being the weighted mean of the 30 elements).Also, a is the proportion of phosphate presentas HPO4

    2, g is the activity coecient of those ionsin solution, zi is the valency, with sign (2 for HPO4

    2),T is the absolute temperature, F is the Faraday, R isthe universal gas constant and kb is a coecient(similar to kL in the Langmuir isotherm equation).Posner and Bowden (1980) discuss a model withthree Langmuir isotherm terms of form similar to0Eqn (18).

    4.2.3. Kinetics of fast sorptionFast sorption has been described by Van der Zee and

    Van Riemsdijk (1991) in Eqn (9) as a dynamic processwith a forward and reverse reaction term. Onceequilibrium has been reached dQ/dt=0, rearrangementof Eqn (9) gives the Langmuir isotherm. In practice,sorption of P onto surface sites happens so fast that formost purposes it can be considered to be instantaneous.For instance, the ANIMO weather-driven systemssimulation model (Groenendijk & Kroes, 1999) assumesa Langmuir isotherm based on Eqn (9) from Van derZee and Van Riemsdijk (1991) reaching instantaneousequilibrium.A few authors have presented equations for the

    kinetics of reaching equilibrium for the fast sorptionprocess, as the faster component of time-dependentsorption (as distinct from the slower components whichrepresent slow deposition as discussed in Section 4.3).Staunton and Nye (1989a) postulate that any delay inreaching equilibrium for fast sorption arises not becauseof slow exchange at the solid/liquid interface butbecause of the time taken for dissolved P to move intocontact with sorption sites within soil aggregates aslimited by diusion transport. Staunton and Nye(1989b) present three approaches to modelling thisdiusion process, one of which is selected and testedagainst P sorption data for aggregated soils by Nye andStaunton (1994). Parameter values (including adiusion impedance factor fs) are chosen for theselected model, which has diusion processes repre-sented according to cylindrical rather than sphericalaggregate geometry, and reasonable ts are found todata for a 10 day contact time. Over a longer period(57 day) ts are improved if representation of the slowdeposition reaction is included in addition to fastsorption. Hansen et al. (1999) present an empiricalequation for the kinetics of phosphate sorption inmacropores of aggregated subsoils, which they foundto be a better t to their experimental data than kineticversions of any of the standard isotherm equations:

    lnC A; 05t4tL

    A B lnt 1tL 1

    ; t > tL

    8>: 20

    where tL is the lag-time which elapses before the slowdeposition process becomes established (although forsome subsoils a simplied form of the equation with tLset to zero was found to be adequate), and A and B arecoecients.

    4.3. Slow reaction processes

    Earlier studies assumed P sorption to be a simple butnon-linear process which could be represented by one ofthe standard equilibrium isotherm equations (as pre-sented in Section 4.1), with parameters estimated by a

  • SORPTION OF PHOSPHORUS 9range of standard techniques as discussed in Part 2(McGechan, 2002). The most common technique forestimating isotherm parameters involved measurementsafter a xed period of contact between P and theabsorbant, usually 24 h. However, parameters wereobserved to vary with variation in the contact timeand temperature. This had the eect of giving areduction in dissolved P (and of P in a form readilyavailable as a plant nutrient) with increase in time sinceinitial contact (or since fertilizer application to soil). Linet al. (1983a, 1983b) represented this simply by adding atime-dependent term to the isotherm equations [as Eqn(4), (5) or (8)]. However, this approach was generallyfound not to adequately describe the process ofdesorption which occurs when the soil solution isdiluted.

    4.3.1. Empirical equations for slow reaction from BarrowBarrow (1974a) described the slow reaction eect by

    an empirical rate equation

    dab

    dt bb 1 ab

    nb 21

    where ab is the proportion of added P fertilizer Pfeconverted to an ineective form and nb is an exponent.The eect of temperature T in K on the rate constant bbwas represented by a form of the Arrhenius equation:

    bb Ar exp E=RT

    22

    where E is analogous to the energy of activation, R isthe gas constant and Ar is a coecient. Barrow andShaw (1975a) then combined these equations with theFreundlich isotherm [Eqn (2)] to give a general empiricaltime- and temperature-dependent equation for theconcentration of P in solution Ct at time t:

    lnCt K B1 lnPa B2 lnt B3=T 23

    where

    K 1=b1lnm=k1 b2=b1lnA=b2 24

    m C0=Pa 25

    B1 1=b1 26

    B2 b2=b1 27

    B3 b2E=Rb1 28

    b2 1=nb 1 29

    and B1, B2 and B3 are constants arising from logarithmictransformations of equations with the power coecientsb1 and b2; C0 is the concentration of P in solution at timezero and Eqn (29) is a simplication of the integral ofEqn (21) between the limits 0 and ab. Barrow and Shaw(1975a) also present a version of Eqn (23) for constanttemperature, with a dierent value for the constant term(equal to K+B3/T). The constant temperature version isin eect a logarithmic transformation and rearrange-ment of Eqn (5) from Barrow (1983a) where

    K B3=T 1=b1lnkF 30

    As presented here, the subscripts for b1 and b2 have beenreversed compared to those used by Barrow and Shaw(1975a), in order to correspond to those used by Barrow(1983a). The time course following fertilizer spreading ofsurface-sorbed P and P which has undergone the slowreaction, as given by Eqn (5) or (23) with coecients forone soil at 258C from Barrow and Shaw (1975a), isillustrated in Fig. 2. Barrow (1983b) later presents aslightly dierent form of Eqn (30) without the logarith-mic transformation and including another coecient q:

    Ct Pa=kF 1=b1ft expqb2=b1Tg

    b2=b1 31

    He used this to compare the results of incubationexperiments at dierent temperatures, equating timeperiod t1 at temperature T1 to corresponding period t2 atanother temperature T2, since it follows from Eqn (31)that

    t1

    t2expqb1=b2T2expqb1=b2T1

    32

    4.3.2. Empirical equations based on the work of SharpleySharpley (1982) measured the decline in water

    extractable P Psp during a period following fertilizerspreading. This decline represents in eect the quantityof P removed from the surface (water-extractable)sorbed pool by the slow reaction. He tted the followingequations to his data:

    Psp Pili sPfe 33

    s is as log t 34

    as 0232 000301CL 35

    is 0722 000679CL 36

    where Pili is the water-extractable P before spreading,Pfe is the P added, CL is the soil clay content in % and s,is and as are coecients. The time course of Pspfollowing fertilizer spreading as given by Eqns (33)and (34) is illustrated in Fig. 2. Sharpley et al. (1984)determined parameter values for Eqn (33) for a numberof soils at a xed incubation time of 6 months, as acomponent of a eld-scale model [Eqn (77), see Section4.7].

    4.3.3. Extension of Barrows ionic mechanism equationBarrow (1979) found that the empirical Eqns (23)

    (29) could not adequately explain his and others obser-vations that desorption does not retrace the path of

  • M. B. MCGECHAN; D. R. LEWIS10Fig. 2. Time course variation in phosphorus pools indicated bytemperatures: (a) 158C; EPIC, labile; EPIC, active;previously occurring sorption but tends to occur a lesserextent than adsorption. After initially developingempirical equations to represent desorption [Barrow(1979), as discussed in Section 4.5], Barrow (1983a) laterdeveloped a mechanistic model that assumed thatreversible fast sorption to sites on the surface of theadsorbant material is accompanied by a parallel slowreaction by which P is deposited at a depth below thesurface. The mechanism for this slow process is assumedto be solid-state diusion, represented by modicationof a standard diusion equation (which includes thediusion coecient D, based on Ficks Law) presentedby Crank (1964):

    S 2=p

    pC0

    Dfbt

    p

    Xi0

    Ci Ci1Dfbt ti

    p 37

    where the parameter fb is given by

    fb 1=1 yd 1 for small values of yd 38

    and where S is the quantity of P deposited by the slowreaction, C0 is the initial concentration of P in solution,Ci is the concentration of P in solution at time ti andCi1 is the concentration of P at the previous timestep.

    ANIMO, S3. (b) 258C EPIC, labile; EPIC, active;Barrow, deposited. Results are shown at both temperatures for EP

    S1;S2 and S3 are three components of S (fBarrow (1983a) and by EPIC and ANIMO models, at twoEPIC, slow; ANIMO, surf; ANIMO, S1 S2;The concept of electrical charge described by Eqn (18) isretained (Section 4.2.2), including a distribution ofLangmuir isotherm equations together with an exten-sion of Eqn (19):

    ja ja0 m1yd m2S=Smax 39

    where Smax is the maximum quantity of P deposited bythe slow reaction, and m1 and m2 are coecients. Oneimplication of Eqn (39) is that P transferred from surfacesites to a depth below the surface partially (but notentirely) frees up surface sites for further fast sorption.

    4.3.4. Unreacted shrinking core modelVan Riemsdijk et al. (1984a) also describe a model of

    the slow reaction of P with soil based on diusionaccording to Ficks Law. However, they assume areaction with the bulk of metal oxides with diusiontowards the reaction zone being rate limiting, and anemphasis on the sizes and geometry of particles, ratherthan diusion according to penetration and electricalcharge theories assumed by Barrow (1983a). This is laterdescribed by Van der Zee et al. (1989b) and Van der Zeeand Van Riemsdijk (1991) as being an example of anunreacted shrinking core (USC) model, as mentionedin chemical engineering literature (Wen, 1968). Van

    EPIC, slow; Sharpley, labile; Barrow, surface;IC as this is the only model to include temperature dependence;

    or j 123) given by Eqn (87) in ANIMO

  • SORPTION OF PHOSPHORUS 11Riemsdijk et al. (1984a) developed the USC model byconsidering a sphere of metal oxide which is graduallyconverted (starting at the surface of the sphere) to metalphosphate. At each point in time, there is a distinctinterface between the inner sphere of unconverted metaloxide and the outer shell of metal phosphate. Solid-statediusion limits the rate of transfer of new P through theever-increasing thickness of the metal phosphate shell.Complex equations relating diusion to the square rootof solute concentration, similar to Eqn (37), arepresented for dierent geometric shapes (a cylinderand a platelet as well as a sphere). A set of equations forthe spherical case of this shrinking core model ispresented by Van der Zee et al. (1989a). However, VanRiemsdijk et al. (1984b) considered such idealisticequations to be of little practical use for real soils withvarious shapes and sizes of particles. For application ofthe model to a real soil with varying quantities ofdierent metal oxides, and a range of sizes of particleswith dierent and largely irregular shapes, they showedthat the diusion equations are equivalent to

    S a0 a1 lnI a2lnI2 a3lnI

    3 40

    I Z t0

    C Ce dt 41

    where C is the variable P concentration in solution, Ce isthe concentration at the interface between oxide andphosphate (a tted parameter), I is the integral withrespect to time of the concentration dierences and a0a3 are tted coecients of a third-order polynomial for aparticular soil.Van der Zee and Van Riemsdijk (1986) and Van der

    Zee et al. (1989a) reduce Eqn (40) to a second-orderpolynomial, while Van der Zee and Van Riemsdijk(1988) further reduce it to a rst-order polynomial anddrop the constant term. Freese et al. (1995) replace thepolynomial in Eqn (40) by an expression similar to theLangmuir isotherm equation to give the followingequation for total sorption:

    Q S SmaxkLI

    b1

    1 kLIb1

    42

    where I is given by Eqn (41).

    4.3.5. Other equations for time-dependent sorptionand slow reaction processesThe slow reaction between P and soil is discussed in

    other papers. Munns and Fox (1976) call it slowreaction or slow xation, describing the kinetics by asimple rst-order reaction. Raats et al. (1982) use theterms xation or chemisorption (regarding it astotally irreversible), representing the process by a rst-order reaction equation with a rate constant modied bythe extent of fast sorption, as follows:

    @S

    @t beQQe if Q > Qe 43

    0 if Q5Qe 44

    where (QQe) is the excess mobile solute (i.e. solubleplus surface-sorbed P) above the equilibrium value Qe sothat be=b when Q=0, and be is the rate variabledetermined from the rate constant b by

    be 1 S=Smax

    b 45

    Eneld et al. (1976) tested a model consisting of a fastreversible sorption process (according to either aLangmuir or Freundlich isotherm) plus a solid-statediusion process, showing better ts to data (represent-ing high P loadings associated with wastewater treat-ment by soil) than either a simple rst-order kineticequation or a kinematic Freundlich isotherm equation.Eneld et al. (1981b) developed this model further usingvarious summation expressions to generate an integralof the form given in Eqn (41). Chien and Clayton (1980)found that their modication to the Elovich equation[Eqn (17)] gave better ts to data on sorption overvarious time periods than either an equilibrium isothermequation or a simple rst-order kinetic equation.Aharoni et al. (1991) concluded that a diusion-basedmodel is valid over a longer time period than a modelbased on rst-order kinetics or the Elovich equation.Similarly, Polyzopoulos et al. (1986) had found that theElovich equation has limited applicability, particularlyduring initial fast sorption and also much later when thesorption rate drops to a very low value. In contrast,Agbenin and Tiessen (1995) concluded that the Elovichequation was most satisfactory out of a number ofmodels including one based on diusion.The slow rate transfer of P between dierent P

    minerals pools accounts for reductions over time inboth soil solution P and P available for plant growth, asobserved by Barrow (1974a, 1974b) and Barrow andShaw (1975a, 1975b). This description can also explaintime-dependent sorption/desorption isotherms pre-sented by Sawhney (1977).

    4.4. Degree of saturation with phosphorus

    The concept of degree of saturation of soil with P hasrecently become widely used as an indication of thesusceptibility of a site to exporting polluting losses of Pto the environment. Beauchemin and Simard (1999)have reviewed papers describing P sorption indicesdetermined by various test procedures, as a measure ofsoil P saturation degree. These include a single-point Psorption index described by Bache and Williams (1971),estimated as Q/logC in Eqn (1) following the addition of

  • M. B. MCGECHAN; D. R. LEWIS1215 g [P] kg1 [soil], which they considered to be a usefulreference index to characterize the sorption properties ofsoils. Use of the sorption index concept is heavilydependent on a satisfactory denition of what is meantby soil saturated with P, i.e. the maximum or limitingsorption capacity of the soil. A common denition ofthe limiting sorption capacity is Qmax in the Langmuirisotherm, Eqn (6), but this represents the maximum forfast, reversible sorption and opinions dier aboutwhether any or all of the pools into which P is adsorbedor deposited by a time-dependent process should also besaturated. Van der Zee and Van Riemsdijk (1988)related the sorption coecient a1 in Eqn (40) (with rst-order term only) to the oxalate-extractable Fe and Alcontents [Feox+Alox] of the soil. Borggaard et al. (1990)suggest that the Fe component should be subdividedbetween crystalline and non-crystalline forms, withdierent coecients for one aluminium and two ironcomponents. Freese et al. (1992) after tting a largebody of experimental data (including that for soilsheavily contaminated by animal slurry and industrialwastes) concluded that separating Feox into twocomponents was unnecessary, but the quantity of Ppreviously adsorbed (Pox, also determined by oxalateextraction) had to be considered. Also, the limits of bothfast adsorption and the slow reaction were related to[Feox+Alox]. Overall, there appear to be two distinctapproaches to dening saturation in terms of the variouspools, each with an associated procedure for determin-ing the degree of saturation.The rst approach, described by Mozaari and Sims

    (1994), Sharpley (1995) and Maguire (1996), is to denesaturation (for the fast reversible surface-sorbed P poolonly) as being equal to Qmax in the Langmuir isotherm[Eqn (6)], determined by shaking soil samples withvarious quantities of P for 24 h as described in Part 2(McGechan, 2002). With this approach, the degree ofsaturation is determined by a soil P test such as Mehlich-3 (Mehlich, 1984, see Part 2; McGechan, 2002), whichindicates the quantity of labile or plant-available P heldin the reversible surface-sorbed pool. Beauchemin andSimard (1999) note that there is some confusion aboutwhether the quantity of P already absorbed is taken intoaccount when determining the Langmuir sorptionisotherm and Qmax as the basis for estimating the degreeof saturation.The second approach is to determine a saturation

    index (sometimes referred to as the Dutch P saturationindex) using ammonium oxalate extraction methods,also described in Part 2 (McGechan, 2002). Thisprocedure extracts all the P associated with Al and Feoxides and hydroxides in the soil. Saturation is alsodetermined by using ammonium oxalate, to determinethe quantities of Al and Fe which can be extracted usingthis reagent. Schoumans (1995) describes the chemicalprocesses by which P becomes associated with Al and Fe(hydr)oxides, showing that the theoretical maximumquantity of Pox which can be sorbed in all the pools (fastreversible sorption to the surface sites plus diusion-limited time-dependent sorption or deposition belowsurfaces) is equal to [Alox+Feox], where Pox, Alox andFeox are expressed on a molar basis. This leads to onedenition of the Dutch saturation index as

    DSSP Pox=Alox Feox 46

    Schoumans (1995) and Schoumans and Groenendijk(2000) found experimentally that in practice the max-imum sorbed P determined by oxalate extraction isequal to roughly 05[Alox+Feox], consisting of a max-imum for fast reversible surface sorption (Qmax in theLangmuir isotherm) of roughly 1/6[Alox+Feox], and themaximum for time-dependent sorption of roughly1/3[Alox+Feox]. This leads to the more commonly useddenition of the Dutch saturation index as

    DSSP Pox=f05Alox Feoxg 47

    4.5. Desorption process

    4.5.1. Quantity of phosphorus desorbedBarrow (1979) studied the process of desorption

    which occurs following the dilution of soil water aftera period of incubation of P with soil. At that time, hedeveloped a set of empirical equations to represent thedesorption process (and how it diers from sorption) forone particular soil, using a linearizing procedure similarto the standard Freundlich isotherm equation. For avarying quantity of added P (Pfe g [P] kg

    1 [soil]) but axed incubation period and temperature (22 day at258C), the quantity of P desorbed Pd after dilution tovarious degrees was given by an equation which includesa term of the Freundlich form

    Pd k2 k1Cb1 48

    where coecient k1=415, index b1=04 and coecientk2 is given by

    k2 0227Pfe 716 49

    For a xed quantity of added P (15 g [P] kg1 [soil]) butvarying incubation periods and temperatures, Eqn (48)was modied to

    Pd k1Cb1d;0 C

    b1 50

    where

    k1 k3tb2d 51

    and

    Cb1d;0 Cb10;01 k4td

    b3 52

  • SORPTION OF PHOSPHORUS 13For the desorption time td (and b1 retaining the value04), values of the coecients k1, k3, k4 and C0,0 plus theindices b2 and b3 were tted for each set of incubationperiod and temperature, to give the composite coe-cient Cd,0. These equations illustrated his observationsthat: rstly, dilution of the dissolved P after longincubation periods with high P concentrations (oralternatively after shorter incubation periods at raisedtemperatures), a much lower quantity of P is desorbedthan the quantity originally adsorbed, and secondly,where dilution occurred after only short incubationperiods, desorption more nearly followed the path ofadsorption, but this was followed by a period of re-adsorption. Later, Barrow (1983a) found that hismechanistic models of the parallel fast sorption andslow reaction processes [Eqns (18), (19) and (37)(39)]gave an equally good t to the experimental data fordesorption, along with a more satisfactory mechanisticexplanation of the processes. By assuming the parallelslow reaction to be irreversible (or reversible at a veryslow rate), desorption as the reverse of the fast truesorption process could be assumed to be reversiblefollowing the same isotherm equation as for sorption,but allowing for the portion of P no longer available fordesorption due to progress of the slow precipitation ordiusion reaction.Raven and Hossner (1993) also studied the process of

    desorption which occurs on dilution of soil water afterincubation (for 31 day at 248C) of P with soil. Theytted the following relationship to their data:

    Pd k1C01 k2 lnC 1 k3 53

    They also found that Eqn (48) (from Barrow, 1979) gaveequally good ts, and both Eqns (48) and (53) gavemuch better ts than the following equation fromBrewster et al. (1975):

    Pd k2 lnC k3 54

    Hooda et al. (2000) tted desorption data to a linearisedFreundlich model:

    log Pd log k1 1=b1 logC 55

    4.5.2. Rate of phosphorus desorptionSharpley et al. (1981b) studied the kinetics of P

    desorption over short time periods (as the reverse of thefast sorption process), as an indication of the release ofP from agricultural soils in surface runo arising duringheavy rainfall. In a review of previous similar studies,they note that Amer et al. (1955), Li et al. (1972), Kuoand Lotse (1972, 1973), Grin and Jurinak (1973) andEvans and Jurinak (1976) all found poor ts of data to arst-order kinetic reaction equation. Most used a higherorder kinetic equation, while Kuo and Lotse (1973) andBarrow (1979) favoured an adaptation of the Freundlichisotherm equation. Sharpley et al. (1981b) also adaptedthe Freundlich isotherm, nding that their experimentaldesorption data (obtained by shaking soil samples withvarious soil-to-water ratios for periods up to 3 h) couldbe described by the equation

    Pd KsP0tasWbs 56

    where Pd is the quantity of P desorbed in time t at awater-to-soil ratio of W ; Ks, as and bs are constants fora particular soil; and P0 is described as the initialquantity of desorbable P after incubation for 3 day at258C. Sharpley and Ahuja (1982) investigated the eectsof varying the time period, temperature and soil watercontent during incubation prior to desorption, on theparameters in Eqn (56). They found that the ttedvalues of Ks, as and bs remained almost unchanged for aparticular soil, but there was a very large eect of thesefactors on P0. The eect of time and temperature couldbe described by Eqn (23) from Barrow and Shaw(1975a), while the eect of soil water content y (fraction)could be described by the following equation:

    P0 Pom aw25 100y 57

    where Pom is the minimum quantity of desorbable P (aty=025 for the particular soil tested) and aw is the slopeconstant. Sharpley and Ahuja (1983) later describe adiusion interpretation of desorption. They suggestthat (for the fast sorption process from surface sites)reaction times are limited by diusion of desorbed Pthrough static lms of water surrounding particles andwithin aggregates. They present a dierential equationfor desorption consisting of multiplicative area, diu-sivity and concentration gradient terms, as follows:

    dPd

    dt Asad

    P0 PdP0

    md:P0 Pd

    VPd

    W

    58

    where dPd/dt is the rate of desorption, As is the specicsurface area in cm2 g1 of the soil particles and P0 andW are dened as for Eqn (56). The expression ad P0 Pd =P0md with parameters ad and md is thevariable diusivity function in cm s1, and (P0Pd)/V isthe eective concentration of desorbable P at any time t.The constant V , which relates the quantity of desorbableP P0Pd to the eective concentration, is interpreted asthe volume of the diusion layer on the surface or insideparticles which contains the P in the soil. Presentation ofEqn (58) is followed by a number of steps ofmathematical manipulation to produce Eqn (56).Sharpley et al. (1981a) developed Eqn (56) into

    further equations representing the release of P in runoevents following heavy rainfall, which they test experi-mentally (see McGechan, 2002, Part 2). They noted thatthe instantaneous concentration of desorbed P in runo

  • M. B. MCGECHAN; D. R. LEWIS14water (and also in inltration water) Cro would be equalto the rate of P desorption dPd/dt [given by dierentiat-ing Eqn (56) with respect to time] divided by the rainfallrate Ir:

    Cro KsP0Mtas1Wbs =Ir 59

    where M is the mass of soil in the interaction zone.Ahuja et al. (1982) present a series of equations based onEqns (56) and (57) (not given here), representing runodown a slope of length L, leading ultimately to anequation for the average concentration of P in runo %CCin relation to rainfall, runo and soil characteristics:

    %CC KsP0 arSl br Er crLmrSesl Q

    nrr

    1bsIr 05LQr

    bs=Iasr V1asr 60

    where Ir is the rainfall intensity in cmh1, Sl is the angle

    of slope in %, L is the length of slope, Er is the kineticenergy of rainfall per unit area per unit time, Qr is theruno rate per unit area, Vr is the total rain volume (inthe whole rainfall event) per unit area and ar, br, cr, es,mr and nr are constants for a given soil.Lookman et al. (1995) describe an equation for

    desorption kinetics with two rst-order terms fordesorption from two pools Q (fast, P sorbed ontosurface sites) and S (slow, P which has undergone theslow reaction)

    Pd Q 1 exp k1t f g S 1 exp k2t f g 61

    Q S Pox 62

    where Pox is the oxalate-extractable P content of the soil.The fast pool Q is described as P sorbed onto surfacesites, but the time constant (around 05 day1, muchslower than that measured by Sharpley et al., 1981b)suggests that this might represent the faster componentof the diusion-limited reaction described by otherauthors.Kirk (1999) and Geelhoed et al. (1999) describe

    simulation models of another process, by which someplants exude organic anions or acids from their roots togain access to P in the deposited or precipitated poolwhich is not normally available to plants. Thisprocess appears to be conned to a few particular plantspecies (such as white lupin and rape), and also toconditions of low soil P fertility, so will not beconsidered further here.

    4.6. Models for analysis of column experiment data

    Models of the sorption processes described in Sections4.14.5 have been developed into simulation modelsrepresenting the sorption kinetics and transport of P foruse in analysis of results of laboratory column experi-ments. For such simulations, equations representing thesorption processes have to be combined with represen-tation of the transport processes by the convection/dispersion equation:

    @C

    @t D

    @2C

    @z2 v

    @C

    @z63

    where z is the depth below the soil surface and v is thewater velocity.Raats et al. (1982) in the rst of a series of three

    papers (each with a dierent rst author), link theconvection/dispersion equation to their sorption equa-tions [Eqns (43)(45)], then explore analytically solu-tions of limiting cases based on specic initial andboundary conditions as well as xation capacities. In thesecond paper in the series, De Willigen et al. (1982)develop the equations into a computer simulation modelfor a column 1m long divided into 20 equal layers.Simulations start with an application of P of 140 kg ha1

    (corresponding to a heavy dose of pig slurry), and theeects of a range of scenarios regarding precipitation,evaporation, initial levels of sorbed and xed P andsorption equation parameters (isotherms for fast sorp-tion and xation rate for the slow reaction) are tested.Results indicated that the xed P pool created by theslow reaction would go on rising for 30 yr or morebefore becoming saturated. In the third paper in theseries, Gerritse et al. (1982) compared simulation resultswith experimental data for scenarios with a range ofhigh P application rates.Van der Zee et al. (1989a) t the second-order version

    of Eqn (40) to data from column experiments. Van derZee and Gjaltema (1992), in the rst of two papers onsimulating P transport in column experiments, add aterm for total sorption (fast reversible sorption plusxation by the slow reaction) to the convection/dispersion equation:

    r@Stot@t

    y@C

    @t yD

    @2C

    @z2 yv

    @C

    @z64

    where y is the volumetric water content, r is the dry bulkdensity of the soil and

    Stot Q S 65

    They also discuss extensively alternative assumptionsabout boundary conditions and whether or not there is aneed for daily interaction between the sorption andtransport processes. In the second paper, Van der Zeeet al. (1992) test assumptions and options are tested bysimulation (but not by comparison with experiments).Eneld and Shew (1975), Eneld et al. (1976, 1981a)

    and Stuanes and Eneld (1984) also use Eqn (64) (withor without the dispersion term), with various versions ofthe equations for rapid sorption and the slow reaction,to represent P movement in laboratory soil samples (in

  • SORPTION OF PHOSPHORUS 15tests carried out with a view to develop of a system forwaste water treatment by soil). Similar sets of equationswere used in column experiments relating to applicationof wastes to soil by Shah et al. (1975) and Mansell et al.(1977, 1985), and in other applications of columnexperiments by Murali and Aylmore (1981), Aylmoreand Murali (1981), Lin et al. (1983a, 1983b), Cho (1991)and Akinremi and Cho (1991). Beauchemin et al. (1996)use Eqn (53) (from Raven & Hossner, 1993) as a bulkmodel of a column experiment, to t data on phosphateconcentration in water passing out of the bottom of thecolumn during desorption. For analysis of columnexperiments in which sorbed and solution P concentra-tions were measured at various depths after surfaceapplications of phosphate solution, Chen et al. (1996)assume two identical kinetic Freundlich equation forms(with dierent coecient values) to represent the twoparallel fast and slow sorption processes:

    @Q

    @tyrk1C

    n k2Q 66

    @S

    @tyrk3C

    n k4S 67

    where the total sorption Stot is given by Eqn (64), and

    Q fStot 68

    S 1 f Stot 69

    where a fraction f of the sorption sites which take partin the fast sorption process.

    4.7. Weather-driven soil phosphorus dynamics models

    Representation of sorption processes has also beenincorporated into sub-models which are components ofmore wide-ranging weather-driven simulation models ofsoil P dynamics. Such models include pools represent-ing categories of P, as well as processes of transforma-tion and transfer between pools. The relevant pools forP sorption as discussed in this paper are described asdissolved inorganic P, surface-sorbed inorganic P(resulting from the fast, reversible sorption process)and various categories of inorganic P which has under-gone time-dependent sorption (including that depositedat a depth below sorption surfaces due to the slowreaction). The models also include pools for organic Pfor which sorption processes are of less importance.

    4.7.1. EPIC and related modelsFor one such model, Erosion/Productivity Impact

    Calculator EPIC (Jones et al., 1984a, 1984b; Sharpleyet al., 1984), separate equations are included for whatare called rapid adsorption and slow adsorption ofinorganic P. However, no soluble P is considered in themodel, so the processes described are not sorption out ofsolution in the manner in which the term sorption isused in other studies discussed in this paper. In fact, therapid process represents a ow from the labile pool Plab(consisting of soluble plus surface-sorbed inorganic P) toan active inorganic pool Pact. The active pool resemblesa component of P which has undergone time-dependentsorption or deposition (as described in other studies), towhich the ow is relatively fast and also reversible. Slowadsorption represents an irreversible ow from theactive pool to a stable deposited pool Psta at a muchslower rate. The ow rate for rapid adsorption Rla isgiven by

    Rla 01eyeT Plab PactPsp

    1 Psp

    70

    The initial value of Pact is given by

    Pact Plab 1 Psp

    =Psp 71

    The proportion of added P which remains labile afterincubation Psp is given by

    Psp Pilf Pili

    =Pfe 72

    where Pili is the initial labile P (prior to fertilization), Pfeis the fertilizer P added and Pilf is the labile P afterfertilization and incubation. The temperature andmoisture content adjustment factors eT and ey (both inthe range 01) are given by

    eT exp0115Tc 288 73

    ey y=y003 74

    where Tc is the soil temperature in 8C, y is thevolumetric soil water content and y003 is the volumetricsoil water content at a tension of 30 kPa. The ow ratefor slow adsorption Ras is

    Ras bas4Pact Psta 75

    where the rate constant bas takes a value of000076 day1 for calcareous soils, and for non-calcar-eous soils is given by the equation

    bas exp177Psp 705 76

    The CREAMS (Knissel, 1988) and GLEAMS (Knis-sel, 1993) weather-driven systems simulation models aredevelopments of the EPIC model and use similarequations. For the proportion of added P remainingafter incubation, Psp, alternative equations are providedfor dierent categories of soils. For non-calcareous soilsthey also dier between the original EPIC paper(Sharpley et al., 1984), the EPIC Model Documentation(Sharpley & Williams, 1990) and the GLEAMS ModelDocumentation (Knissel, 1993) which quotes Sharpley

  • and Williams (1990). They are presented here as inGLEAMS, as follows:

    with 0054Psp4075 where CCaCO3 is the calciumcarbonate concentration, Bsat is the base saturation bythe ammonium acetate method in %, pH is the soil pH

    Agricultural Nitrogen Model before the P routines wereadded) from the Netherlands (Kroes & Rijtema, 1998;

    Groenendijk & Kroes, 1999). For fast, reversible sorption,ANIMO works with an equation based on the equili-brium Langmuir isotherm, Eqn (6). Parameter values in

    Psp

    058 00061CCaCO3 calcareous soils00054Bsat 0116pH 073 slightly weathered non-calcareous soils

    046 00916 ln CL highly weathered non-calcareous soils

    8>: 77

    lParameter values in Eqn (85) for slow-deposition process in ANIMO model (Groenendijk & Kroes, 1999)

    2 00334

    nd

    M. B. MCGECHAN; D. R. LEWIS163 00014382

    Note: rd , dry bulk density, kgm3; Alox Feox, aluminium aSorption class, j Coecients Exponent b1

    K2,j, day1 K3,j, kgm

    3 kg m3b1

    1 11755 1187 106 rd Alox Feox 053576and CL is the clay content in %.Compared to the original EPIC (Jones et al., 1984a),

    the soil moisture content adjustment factor ey inGLEAMS (Knissel, 1993) is modied to

    ey

    y ywyfc yw

    ; y4yfc

    0; y > yfc

    8>: 78

    where yw is the volumetric soil water content at thewilting point of 1500 kPa and yfc is the volumetric soilwater content at eld capacity (assumed to be at atension of 33 kPa, a larger tension value than commonlyassumed for eld capacity in Europe).The ICECREAM model (Simes et al., 1998) is a

    development of GLEAMS for Finnish soils. It retainsthe same equation forms, but the coecients in Eqn (77)for Psp required dierent values, reecting higher Pretention by Finnish soils compared to that for NorthAmerican soils:

    Psp Pspph 00054Bsat 0116pH 073

    if pH 073CL42 79

    Psp Pspcl 046 00916 lnCL if OM410% 80

    Psp 00025CL 065Pspcl 035 00025CLPspphfor other soils 81

    where organic matter is abbreviated as OM.

    4.7.2. ANIMOAnother weather-driven simulation model of soil P

    dynamics is ANIMO (formerly known as the

    Tab4667 10 rd Alox Feox 019959711 106 rd Alox Feox 02604

    iron content, mmol kg1.m3kg1 [P], estimated by Schoumans (1995), are

    kL 1129 82

    Qmax 5167 106rAlox Feox 83

    where [Alox+Feox] is the Al plus Fe content of the soil inmmol kg1.For the time-dependent processes including the slow

    diusion-limited reaction, the authors of ANIMOconsidered using the shrinking core model (as describedby Van Riemsdijk et al., 1984a, see Section 4.3.3),but found it to be impractical as a component of a eld-scale model. Instead, they estimated a reaction rate asthe sum of three widely diering rates for three distinctsorption (or deposition) sub-pools (designated j=13),according to the following equation:

    @S

    @tP3j1

    K2;jK3;jCb1 S; K3;jCb1 > S 84

    Coecients K2,j and K3,j listed in Table 1, tted bySchoumans (1995) to data reported by Schoumans et al.(1986), were found to be suitable for a wide range ofsandy soils in the Netherlands for sorption. Therelationships represented by these equations werealso checked against those for column experimentspresented by Van der Zee et al. [1989a, with thesecond-order version of Eqn (40) tted to columnexperiment data] and Van der Zee and Gjaltema(1992). As the equations were simply empirical ts todata, the authors do not state which processes arerepresented; however, the fastest component (indexj=1) may represent the kinetic component of

    e 1

  • SORPTION OF PHOSPHORUS 17fast sorption as described in Section 4.2.3, while theslower components (index j=2, 3) may represent theslow deposition reaction. An equation of similar form toEqn (84) is suggested for desorption, but the samecoecient values as for sorption have to be assumed asdierent values have not been determined experimen-tally.

    4.7.3. Comparison of kinetic transfer ratesbetween modelsA comparison of time series solutions of Eqns (70),

    (75) and (84) representing the pools simulated by EPIC(at two alternative temperatures) and ANIMO is shownin Fig. 2, alongside results from equations presented byBarrow (1983a) and Sharpley (1982). The comparison at158C (the temperature of the experiments on whichANIMO is based) suggests that the labile pool in EPICdeclines in a manner roughly similar to the surface-sorbed P pool in ANIMO. At 258C, the decline in thelabile pool in EPIC is similar to that for Psp (water-extractable P) in the equations from Sharpley (1982) andsurface-sorbed P in the work of Barrow (1983a). Also,the active pool in EPIC corresponds roughly to thesum of the rst two (index j=1, 2) time-dependentsorption subpools in ANIMO. Similarly at 158C, thestable pool in EPIC corresponds roughly to thethird (index j=3) time-dependent sorption subpoolin ANIMO. These time series were obtained bysolving the rst-order decay processes represented byEqns (70), (75) and (84), as follows. For the decline inthe labile pool (due to transfer to the active pool) inEPIC:

    Plab Pili PspPfe Pfe 1 Psp

    exp 01eyeTt 85

    for the active pool in EPIC:

    Pact Pacto 4 3 exp bast

    PspPfe Pfe 1 Psp

    exp 01eyeTt 86

    where Pacto is the initial value of Pact; for ANIMO (aspresented by Schoumans, 1995):

    S X3j1

    K3;jCb1 1 exp K2;j t

    87

    4.7.4. Other soil phosphorus dynamics modelsTwo other soil models with P dynamics routines are

    CENTURY and ecosys. CENTURY (Parton et al.,1987; Metherell et al., 1993) diers from the othermodels in that it operates with a monthly timestep as itis designed to indicate long-term trends, but there is arecent version DAYCENT operating on a daily time-step which has been reviewed by the authors, McGechanand Lewis (2001). It operates with a number of soil Ppools, dynamic ow rates between pools and fastsorption of inorganic P following the Langmuirisotherm. The ecosys model (Grant & Heaney, 1997)has a very complex treatment of individual reactions(including those representing sorption) between P and arange of Al, Fe, Ca and other soil mineral compounds.Equilibrium associations are listed for over 50 sets of ionpairs. The model was initially tested to represent Ptransformations and transport in laboratory columnexperiments, then linked to a P uptake routine(comprising a further 19 equations) to represent Puptake by root systems (Grant & Robertson, 1997).

    4.7.5. Further developments of sorption equationsin phosphorus dynamics modelsThe two existing weather-driven soil P dynamics

    models, GLEAMS (with the associated models EPIC,CREAMS and ICECREAM) and ANIMO, use rela-tively simplistic equations to represent the parallel fastsorption, slower sorption and very slow depositionprocesses. Some of the sources on which these equationsare based are either old or represent preliminaryinvestigations. Also, equation parameters may applyonly to specic soils in the countries where measure-ments were made. Meanwhile, there has been extensiveresearch into the mechanisms of sorption processes(including the slow, diusion-limited depositionreaction), leading to more mechanistic and generallyapplicable equations. A logical next step would be toincorporate such mechanistic equations into eld-scalemodels, and to determine values of coecients andparameters applicable to a wide range of soils.

    5. Sorption onto mobile particulate and colloidal material

    5.1. Sorption onto sediments in surface runo

    Phosphorus sorption as described up to now in thispaper, and as described in nearly all published papers onthe subject, generally refers to sorption onto static soilcomponents. However, some desorption studies fromNorth America refer to sediment material that hasbecome detached from the main body of soil and movein surface runo water (overland ow) leading to Ppollution of receiving water bodies. Models of theprocess have been described in Section 4.5.2, andexperimental data are discussed in Part 2 (McGechan,2002).

    5.2. Sorption onto colloidal particles moving through thesoil

    The concept that, in addition to surface ow Ptransport, there is also a substantial ow of P to water

  • bodies through soil movement of P-laden particulatematerial, has only recently been proposed. Particulatematerial passing through the soil (mainly by macroporeow) tends to be very nely divided colloids (derivedfrom animal manures, soil organic matter or the clayfraction of soil minerals) with a very high specicsurface area and extensive sorption surfaces. There are afew recent studies from Europe reporting substantialthrough-soil losses of P. Stamm et al. (1998) observedraised concentrations of P during large rainfall/drainage

    manures, particularly slurry (liquid manure), containlarge quantities of both colloid-sized particles and P, soland application of manures provides an additionalimportant source of P-laden colloids. The only knownmodel of colloid-facilitated transport of contaminantsthrough soil is an adaptation of MACRO (Jarvis, 1994)as described by Jarvis et al. (1999). This model focusseson macropore ow, in view of its importance fortransport of colloids. It also includes representation ofprocesses by which colloids become trapped by straining

    n

    M. B. MCGECHAN; D. R. LEWIS18events in grassland soils. This suggests mobilization ofcolloid material, since if this did not occur a lowerconcentration due to dilution of the soil solution byincoming rain would be expected. Similar raised Pconcentrations during rainfall events have been ob-served in through-soil leaching from grassland byHawkins and Scholeeld (1996) and by Haygarth et al.(1998). These studies also support the hypothesis thatcolloid-facilitated transport plays an important role inthrough-soil leaching of P to receiving waters. Addiscottet al. (2000) observed high P losses on arable croppedland, which they attribute to colloid transport; theysuggest that colloidal clay particles are initially mobi-lized in surface runo ows until they reach amacropore through-the-soil pathway leading to a moledrain channel. All these results tend to refute a widelyheld misconception that where all incident rainwaterinltrates through the soil surface (so overland ow isabsent) nearly all phosphorus present is sorbed ontostatic soil components and removed from leaching ows.This mobile solid represents a third phase for thecontaminant (Fig. 3), in addition to that in solution andthat sorbed onto the static soil matrix, as described byMcCarthy and Zachara (1989).Modelling of colloid-facilitated pollutant transport

    processes is dependent on an accurate model descriptionof the dynamics of the carrier colloids. It is commonlyassumed that colloids can be generated by detachmentof soil particles from the static body of soil. Jarvis et al.(1999) reviewed literature on this subject, and concludedthat detachment occurs mainly by rainfall impact atthe soil surface rather than due to scouring bywater passing through sub-surface soil pores. Animal

    Fig. 3. Simplied schematic representatioand ltration. Separate ltration equations are denedfor micropores (where most trapping of colloids occurs)and for macropores. While developed mainly torepresent transport of sorbed pesticides (Villholth et al.,2000), McGechan et al (2002) have recently applied thisadaptation of MACRO to describe this process asapplied to P transport. With this model, it is necessaryto specify sorption parameters for both sorption ontostatic soil material and onto the mobile colloid particles(according to the Freundlich equation for MACRO).The limited available information about parametervalues for sorption of P onto colloidal material isdiscussed in Part 2 (McGechan, 2002).

    5.3. Sorption onto organic material

    While there is evidence supporting the concept oftransport of inorganic P in association with organiccolloids (mainly in manure or slurry but perhaps alsothose derived from plant residues/litter or soil organicmatter), the mechanism by which P is sorbed on suchmaterial is less clear. There is a clear ionic mechanismfor P sorption onto metal oxides (which are oppositelycharged), but this will not apply for sorption ontoorganic material since phosphate anions will not beattracted to organic colloids which also tend to have anegative charge. Cation bridging involving othersubstances may have a part to play. Gerke andHermann (1992) studied this bridging process in theadsorption of orthophosphate onto humic-FE-com-plexes, observing a large increase in the extent ofsorption in relation to the quantity of iron present.

    of main inorganic soil phosphorus pools

  • SORPTION OF PHOSPHORUS 196. Conclusions

    6.1. General comments regarding phosphorus sorptionrelationships

    The processes of sorption of P in soil are verycomplex, and the very extensive literature on the subjectcan present a very confusing picture regardingthe mechanisms of sorption. Nevertheless, there aresome broad trends and some general comments canbe made.In some of the earlier works, attempts at tting

    simple, single mathematical equations (isotherms) toexperimental sorption data were confused by the timedependence factor. In early studies on desorption,empirical relationships were tted to measured datawith no explanation of why desorption did not retracethe path of sorption. Later work claried that thereappear to be at least two distinct processes, a fastreversible sorption onto solid surfaces, plus a slowalmost irreversible process consisting of diusionthrough the sorbing layer followed by precipitation ordeposition below the sorption surfaces. The sorbingsurfaces consist mainly of iron and aluminium oxides (inthe clay components) in acid soils, or calcium carbonatein calcareous soils for which the process diers some-what from that in acid soils. Simple Langmuir isothermscan represent sorption onto individual minerals, but forreal soils either the two-surface Langmuir or theFreundlich isotherm equation (which can be consideredto be in eect an integration of several Langmuirisotherms) has sometimes been found to be moresatisfactory. Equilibrium sorption represented by suchan isotherm equation is reached within about 1 day offertilizer or manure application, but following this there isa gradual reduction (over several months) of dissolved Pin the soil solution (available for plant growth) due tovarious ongoing slow time-dependent diusion or pre-cipitation processes. The distinction between almostinstantaneous sorption on surface sites and the slowprocess of deposition below surfaces is not clear-cut.Some researchers have described an intermediatetime-dependent process, faster than slow deposition,where there is some time dependence due to diusionthrough the soil water to sites within the soil matrix;others suggest that all the processes should be regarded asa continuum.

    6.2. Applications of sorption relationships in simulationmodels and other studies

    Weather-driven simulation models of soil P dyna-mics require mathematical equations to describe Ptransformation processes such as reversible sorptionon particle surfaces and the slow deposition processbelow surface sites. Identifying such relationships formodels on the basis of literature sources was the reasonfor carrying out this review.

    6.2.1. Sorption phases and pollutant transport modelsA simplied representation of the phases and compo-

    nents of sorption by P in soil is shown in Fig. 3, makingthe distinction between P sorbed onto static componentsof the soil matrix and that sorbed onto mobile sedimentsor colloids. This also shows the over-simplistic repre-sentation with distinct compartments for instantaneoussurface sorption and slow deposition (when in fact theremight also be some intermediate faster time-dependentpools or else representation as a continuum). The mobilesorbed components consist of both P associated withsediments transported in surface runo and that sorbedonto ner colloidal material transported through the soilby macropore ow. The ideal model will consider allthese components and all possible pollutant transportroutes. Currently, EPIC ignores the solute phasecompletely, so cannot indicate leaching of soluble Pvia eld drains or to deep groundwater. In contrast,soluble P leaching to eld drains is the main loss routeconsidered in ANIMO. Transport in mobile sedimentsin surface runo ows is the main loss processconsidered in EPIC. No models currently considerlosses of P attached to mobile colloidal material movingthrough the soil by macropore ow, but a modicationto the MACRO model to represent this is currentlybeing undertaken.

    6.2.2. Selection of timestep in models in relationto sorptionFor many purposes, models can operate on a daily

    timestep, assuming instantaneous equilibrium for fastreversible sorption on surface sites represented either bythe Freundlich, single Langmuir or double Langmuirisotherm equations. Surface runo, and the associatedprocesses of sediment erosion and pollutant transport of Pas well as components of surface spread manure or slurry,tend to happen during short-lasting high-intensity rainfallevents where fast-acting processes are important. Unlikewhere other transport processes are represented by themodels, it may not be adequate to assume instantaneousequilibrium for fast, reversible sorption on surface sites.Also, model simulations need to be carried out overa timestep of minutes rather than days. The equationsand approach adopted by Sharpley are appropriatein this situation, including representation of timedependence particularly for desorption of P from surfacesites.

  • M. B. MCGECHAN; D. R. LEWIS206.2.3. Required complexity for representation ofsorption in modelsFor fast reversible sorption on surface sites, repre-

    sentation by isotherm equations (either Freundlich,single Langmuir or double Langmuir) is satisfactoryfor most modelling processes. The more complexmechanistic model of Barrow is in eect an extensionof the Langmuir equation. The main debate aboutcomplexity concerns the slow, time-dependent sorptionor deposition processes. For these slower processes, theequations in mechanistic models may be unnecessarilycomplex for their representation alongside other trans-formations, as well as having parameters which areunknown for many soils. More practical is to assume asimple time-dependent relationship such as Eqn (5) or(84) to represent transfer from labile (readily availablefor plant uptake) pools to the less-available depositedpool. To this should be added the constraint of amaximum total P content for all time-dependent pools,based on oxalate-extracted Al plus Fe. This was theapproach adopted in the Dutch ANIMO model, inpreference to the equations from the USC model whichwas considered to be too complex.

    Acknowledgements

    Funds to carry out this work were provided by the Sco-ttish Executive Environment and Rural Aairs Department.

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    M. B. MCGECHAN; D. R. LEWIS24

    Notation1. Introduction2. General principles of phosphorus sorption3. Factors influencing extent of sorption4. Equations and models representing sorption processesFigure 1Figure 2Table 1

    5. Sorption onto mobile particulate and colloidal materialFigure 3

    6. ConclusionsAcknowledgementsReferences

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