SW—Soil and Water

Biosystems Engineering (2002) 82 (4), 359–380 doi:10.1006/bioe.2002.0102, available online at http://www.idealibrary.com on SW}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 and compared, along with a more general contaminant transport model which has been applied to phosphorus dynamics. These models are ANIMO from the Netherlands, GLEAMS and DAYCENT from the USA, and MACRO from Sweden. The model concepts and constituent processes are analysed with particular reference to the equations used. Processes considered are the transport of soluble and particulate phosphorus, surface application (as fertilizer, manure or slurry, atmospheric deposition, and deposition or incorporation of dead plant material), 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 order to improve our understanding and simulation of phosphorus in soils, further P modelling work is required, which should be focussed on constructing a new hybrid version of the four models described here. Such a model is likely to include a description of both soluble and particulate P flow through micropores and macropores as in the MACRO 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 the DAYCENT model. Finally, the overland flow and erosion losses should be represented by components from the GLEAMS model. # 2002 Silsoe Research Institute. Published by Elsevier Science Ltd. All rights reserved 1. Introduction Phosphorus (P) from non-point sources such as agricultural soils can have a major environmental effect on the water quality of receiving waters. The management of P in agricultural fields with hydrological pathways to sensitive surface waters is thus of fundamental importance. As a management tool, simulation models of the P cycle within soils have been developed since the late 1970s. In general, these models have tended to be: physically based, driven by climate variables and capable of assessing nutrient transport to ground and surface waters. This paper is concerned with a review of three comprehensive P models which have been under continual development since the mid 1980s, plus a more general model of contaminant transport that has only recently 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 processes involving in the P-cycle within soils are reviewed. 1537-5110/02/$35.00

ANIMO, set up by Winand Staring Centre for Integrated Land Soil and Water Research, Wageningen, The Netherlands, is described by Groenendijk and Kroes (1999) and Kroes and Rijtema (1998). GLEAMS (Groundwater Loading Effects on Agricultural Management Systems) was developed by the US Department of Agriculture, Agricultural Research Service (Leonard et al., 1987; Knisel et al., 1993). The CENTURY model (Parton et al., 1987; Metherell et al., 1993a, 1993b) was initially funded by the US National Science Foundation, with the latest version (V5, 2000; the Century Model Interface) funded in part by the US Geological Survey. In this review, DAYCENT is considered, this being the daily version of the monthly output time-step CENTURY ecosystem model which incorporates all of the ecosystem processes of its predecessor model. It should be noted that DAYCENT is currently being modified with respect to its phosphorus components (Parton, 2000). This study concentrates on physically based models driven by climatic variables, which are capable of assessing nutrient losses to groundwater and surface waters following the application of agricultural waste.

359

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

360

D. R. LEWIS; M. B. MCGECHAN

Notation a

decomposition assimilation factor indicating fraction going to slow cycling humus pool A, B, C, D empirical parameters in water content expression [Alox +Feox] aluminium and iron content of soil, mmol kg
1 Bsat base saturation by ammonium acetate method, % C dissolved contaminant concentration, kg m
3 Cav available dissolved contaminant concentration in the surface soil layer, kg m
3 C CaCo3 calcium concentration in calcerous soils, kg m
3 Ccrom carbon content of organic crop residue, g [C] g
1 dry wt. dissolved contaminant concentration at Ceq which phosphorus precipitation occurs, kg m
3 CL soil clay content, % function in crop residue decomposition CNP expression carbon content of organic matter Com,fn of fraction fn, g [C] g
1 dry wt. carbon content of fresh organic matter Com,fp of fraction fp, g [C] g
1 dry wt. carbon content of structural organic Csom matter, g C g
1 dry wt. C:N ratio of residue in soil layer i (C:N)i C:P ratio of fraction fp (C:P)fp C:P ratio of residue in soil layer i (C:P)i contaminant concentration sorbed CS onto soil at equilibrium, kg m
3 Cw dissolved contaminant concentration at equilibrium, kg m
3 ea soil aeration response function pH response function epH temperature response function eT soil water content response function ey F empirical exponent in water content function fraction of original residue remaining fdecomp degree of non-solubilization for fresh fh,fp organic fractions fraction of lignin going to structural pool fS k rate coefficient for first-order rate process decomposition rate parameter for kcrl structural pool, d
1 kcr decomposition rate parameter for crop residue, d
1 kd partition coefficient Freundlich rate coefficient, kg m
3 kF

kFdes kfp kFsor kL kL1, kL2 kref ksomin Kms Ksm L L/N n pi p 1, p 2, p 3 Pact PF Pfn Pfresho pH Phu Plab PLI Ppfr Psorb PSP Pssorb Pstab Ras Rcr Rcrl Rdcr

kinetic-Freundlich rate coefficient for desorption, d
1 decomposition rate parameter for fresh organic fractions, d
1 kinetic-Freundlich rate coefficient for sorption, d
1 Langmuir rate coefficient, kg m
3 Langmuir rate coefficients for two distinct sorption sites, kg m
3 optimum reference value for first-order rate process, d
1 organic mineralization coefficient, d
1 constant parameter in phosphorus flows between sorbed pools, d
1 parameter in phosphorus flows between sorbed pools, d
1 lignin content of structural pool lignin-N ratio of the residue non-linear sorption coefficient constants in sorption equation, d
1 constants in expression defining phosphorus transfers phosphorus content of active pool, g [P] g
1 function of matric potential phosphorus content of organic matter, root exudent or dissolved organic pools, g [P] g
1 [dry wt.] phosphorus content in fresh organic pool, g [P] g
1 pH of the soil phosphorus content of humus/biomass material, g [P] g
1 [dry wt.] phosphorus content of labile pool, g [P] g
1 labile P immobilization factor phosphorus content of fresh residue, g [P] g
1 phosphorus content of sorbed pool, g [P] g
1 phosphorus sorption coefficient phosphorus content of strongly sorbed pool, g [P] g
1 phosphorus content of stable mineral pool, g [P] g
1 phosphorus transfer rate between active and stable mineral pools, kg [P] m
3 d
1 decomposition rate of crop residue, kg [C] m
3 d
1 decomposition rate of surface and structural pools, kg [C] m
3 d
1 factor in decomposition rate for crop residue, kg [C] m
3 d
1

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PHOSPHORUS MODELS

RFom ! Som formation rate of soluble organic phosphorus from fresh organic phosphorus kg [P] m
3 d
1 Rimmob immobilization rate, kg [P] m
3 d
1 Rla phosphorus transfer rate between labile and 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 sorbed and strongly sorbed pools, kg [P] m
3 d
1 S adsorbed contaminant concentration, kg m
3 Saff sorption affinity soil sand content, % SD adsorbed contaminant concentration Sfeq determined by Freundlich isotherm, kg m
3 Smax maximum soil sorption capacity, kg m
3 Smax1, maximum soil sorption capacities for Smax2 two distinct sorption sites, kg m
3 In passing, mention should be given to the EPIC (Erosion-Productivity Impact Calculator) model (Sharpley & Williams, 1990), which was originally developed to simulate the impact of erosion on crop productivity and has now evolved into a comprehensive agricultural management, field scale, non-point source loading model. The P routines developed for EPIC (Jones et al., 1984a) were incorporated in the GLEAMS model, and so only the latter model is reviewed here. Another model CREAMS (model for Chemicals, Runoff and Erosion from Agricultural Management Systems) as described by Knisel (1980), also incorporates the P routines from EPIC. However, CREAMS will not be considered further here as it is

Slow inorganic

t T Tref a b y ybp yfc yw rd o Subscripts fn fp

time, d soil temperature, 8C base soil temperature at which eT=1, 8C composite parameter in temperature response function extraction coefficient soil water content, % [by volume] water content at the ‘break-point0 , % [by volume] soil water content at 33 kPa (field capacity), % [by volume] wilting point, % [by volume] soil dry bulk density, kg m
3 phosphorus flow coefficient between active and stable pools organic fraction fresh organic fraction

really a precursor of GLEAMS with the same P routines. The fourth model reviewed here MACRO is a ‘twodomain’ soil water and contaminant transport model with separate representation of processes in ‘macropores’ and soil matrix ‘micropores’. This model, developed in the Soil Sciences Department of the Swedish University of Agricultural Sciences, is described in detail by Jarvis (1994). In earlier versions of the model, only soluble contaminants were considered, and applications concerned mainly water contamination by pesticides. However, a recent new feature of MACRO (Jarvis et al., 1999) is the representation of colloid facilitated contaminant transport, a process particularly relevant to phosphorus

Rapid cycling organic and inorganic

Fertilizer

Plants

Slow organic

Animal waste

Primary P minerals

Secondary P minerals

Solution P

Occluded P

Labile and moderately labile inorganic P

Microbial P

Chemically and physically protected organic P

Labile and moderately labile organic P

Fig. 1. The soil P cycle: its components and measurable fractions (adapted from Stewart & Sharpley, 1997)

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D. R. LEWIS; M. B. MCGECHAN

pollution. An attempt to use this feature of MACRO for P transport has been described by McGechan et al. (2002). 2.2. Overview of soil phosphorus dynamics Phosphorus is distributed within soils, between inorganic and organic forms, with relative proportions in the top 20 cm varying from 20 to 80% depending on the soil type (Brady & Weil, 1996). Figure 1 identifies the major soil P cycle components and measurable fractions, along with an indication of the relative residence time for P in each component. Since the solubility of naturally occurring P compounds 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 from 001 kg P ha
1 yr
1 in very infertile drained soils, to 02 kg P ha
1 yr
1 in heavily fertilized drained soils. Phosphorus losses via surface runoff include dissolved P and particulate P, with total losses ranging from 01 kg P ha
1 yr
1 for grasslands to 5 kg P ha
1 yr
1 for sloping tilled arable land (Brady & Weil, 1996). Other losses such as the movement of particulate P through macropores may also be important in some drained soils. These loss processes and all the processes shown in Fig. 1 require some representation in a model of the P soil cycle. The three P models considered here both have representation of surface application (as fertilizer, manure or slurry, atmospheric deposition, weathering and deposition or incorporation of dead plant material),

Deposition P

Fertilizer P

Mineral P

Precipitated inorganic soil P

Adsorbed inorganic soil P (kinetic)

mineralization/immobilization (between organic and inorganic forms), P-soil sorption and desorption processes, uptake by plants and P leaching. Surface movement of dissolved P is considered in both the ANIMO and GLEAMS models but the movement of P bound to particulate material is only considered in the GLEAMS model. The DAYCENT model considers sorbed soil-P in equilibrium with a labile soil-P from which leaching occurs, and includes representation of P loss through soil erosion. Neither of the P models considers the important process of the movement ‘through-the-soil’ of P bound to particulate material, hence the interest in applying the MACRO model which has the capability to represent this. The main flows and states for the soil P dynamic processes represented in the models are shown diagramatically in Figs 2–4, with pools and flows arranged as far as possible to a common layout, and the relative cycling rates for the pools also indicated. It should be noted that all soil P pools and transformations occur within in each defined soil layer, and for simplicity, the following description of the models are given in terms of only one layer. There is some variation between models in the definition and subdivision of pools, and in the names given to the flows. Both organic matter and inorganic matter are divided into several sub-pools, generally according to the rate at which material flows out of each sub-pool. Flows from fast cycling pools to the main slow cycling pool of organic matter are variously described as ‘decomposition’, ‘humification’ and ‘decay’. Soil sorption of inorganic or labile P

Animal waste P

Shoots P Root P

Fresh organic P

Exudates soil P

Fresh organic soil P

Stable organic soil P

Dissolved inorganic soil P

Adsorbed inorganic soilP (equilibrium)

Dissolved organic soil P

P runoff P leaching

Fig. 2. Pools and flows of phosphorus in the ANIMO P model

363

PHOSPHORUS MODELS

Grain P Organic P (animal waste)

Stalk P

Stable inorganic soil P

Fertilizer P

Root P

Active inorganic soil P

Labile inorganic soil P

Fresh organic soil P

Stable organic soil P

P runoff P sediment P leaching

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

Weathering P

Organicwaste P

Fertilizer P Plant P

Metabolic organic P

Strongly sorbed inorganic soil P

Occluded inorganic soil P

Sorbed inorganic soil P

Labile inorganic soil P

P runoff P leaching P erosion

Active organic soil P

Structural organic P

Slow organic soil P

Passive organic soil P

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

(i.e. that available for plant use) occurs through a rapid process, but desorption involves both a rapid and a slow process. Some of the compartments delineated in these figures are for surface only (grain, stover, atmospheric P), some are for both surface and subsurface computational soil layers (fresh organic P in crop residue and roots, organic P in animal waste, fertilizer and dissolved forms of P), whereas adsorbed and stable soil P occurs only in the soil. 2.3. Other related processes 2.3.1. Soil water Many of the soil P dynamic processes such as mineralization and immobilization are dependent on

soil water content. Phosphorus transport, via overland flow or through the soil profile and out into field drains, is controlled by water movement. Any model of soil P dynamics is therefore very dependent on an accurate description of soil water content and soil water movement. ANIMO is designed to operate in conjunction with either of the Dutch soil water simulation models, the multilayer model SWATRE (Feddes et al., 1978) or the two-layer model WATBAL (Berghuijs van Dijk, 1990). GLEAMS uses the same basic methods as the CREAMS model (Williams & Nicks, 1982), and links surface runoff curve number techniques with evapotranspiration and multilayer storage-routing models. The DAYCENT land surface submodel (Parton et al., 1998) was developed from multilayer daily water

364

D. R. LEWIS; M. B. MCGECHAN

flow models (Parton, 1978; Parton & Jackson, 1989; Sala et al., 1992) simulating variably saturated water contents and flows. SWATRE, WATBAL all include representation of water flow to field drains as well as downwards through the soil layers, whereas GLEAMS and DAYCENT only consider vertical percolation. MACRO has multilayer representation of soil water movement in macropores and soil matrix pores, including vertical drainage to deep groundwater and horizontal drainage to the nearest field drain. 2.3.2. Soil evapotranspiration and heat Evaporation links the soil water and soil heat processes. GLEAMS, SWATRE and MACRO all calculate evapotranspiration using the physically based Penman–Monteith equation, and GLEAMS has the option of using the Priestly Taylor method (Jensen et al., 1990). Transpiration rates in DAYCENT are simulated using the Penman potential evapotranspiration equation, adjusted according to soil water potential and root biomass (Parton, 1978). All the transformations concerned with soil P dynamics are very temperature dependent, so it is important to have an accurate description of soil heat processes. ANIMO, GLEAMS, DAYCENT (Parton, 1984) and MACRO all calculate daily soil temperatures at depth, from estimates of soil surface or air temperature values and soil water contents, together with thermal conductivities for each layer. 2.3.3. Soil erosion and particulates Erosion and sediment yield from fields is estimated in GLEAMS through calculation of soil particle detachment and the subsequent transportation of this sediment (Foster et al., 1980; Leonard et al., 1987). Particle detachment is assumed to be a function of soil properties, management, and rainfall and runoff characteristics. Sediment is considered to consist of a mixture of five mineral classes which are composed of primary particles and aggregates, and an organic class, whose distributions are either input by the user (calibration) or assumed for given soil types. When overland flow occurs the sediment load is assumed to be limited by either the amount of sediment made available by detachment or by the transport capacity (Yallin, 1963). In the latter case, deposition takes place, with usually the coarse and dense particles deposited first, leaving a finer sediment mixture. GLEAMS splits a typical field into segments of given slope, soil type, etc., with detachment–deposition processes calculated on progression down a single segment. Nutrient transport associated with the sediment movement, is estimated through knowledge of the surface layer soil nutrient

concentration and the ‘enrichment ratio’: the ratio of the total specific surface area for the sediment to that of the original soil. ANIMO does not have any representation of particulate movement and consequently soil erosion is not considered. Surface runoff in ANIMO is assumed to contain only the soluble inorganic and organic nutrient fractions of the surface layer. Similarly, DAYCENT considers surface losses from the labile inorganic and active organic P pools. The model also considers soil erosion effects in addition to surface runoff losses. The new colloid facilitated transport version of MACRO (Jarvis et al., 1999) includes representation of detachment of colloidal soil particles from the soil surface by rainfall impact. However, once detachment has taken place, transport of such colloidal particles (carrying a contaminant such as P) is represented according to the ‘through-the-soil’ route only. 2.3.4. Crop growth ANIMO assumes that dissolved inorganic P uptake can be described by interacting soil and plant compartments, in which uptake is calculated by balancing the demand of the crop and the supply of the soil. Separate supply potentials are calculated for each compartment and the actual crop growth rates are adjusted if these are limiting factors. Both grassland and arable land are described, using different rates for each supply potential. Grassland growth or demand is assumed to be dependent on date and sunshine factors using an empirical equation (de Wit, 1965), and arable crop growth is defined using optimal cumulative uptake and transpiration curves input by the user. Phosphorus uptake in GLEAMS follows that of the EPIC model (Sharpley & Williams, 1990), in which the uptake of labile P is estimated for each layer where transpiration occurs, with the total uptake from all layers equal to the plant P demand. Plant growth and plant P demand is taken to be a function of the optimum leaf area index, which is tabulated for a large number of crops over a growing season. This potential plant growth is moderated by soil temperature, water and P stress factors on a daily basis. In DAYCENT, potential crop biomass growth (for both roots and shoots) is moderated by soil temperature, water moisture, nutrient status and seedling growth. The plant growth response curve to soil temperature follows a sigmoidal function up to an optimum temperature, with a band of approximately 108C of high growth rates, followed by a rapid decline at higher temperatures. Plant P uptake is controlled by the size of the labile P pool, with the fraction of labile P that is available varying with the size of the mineral N pool

PHOSPHORUS MODELS

(higher P fractions for higher mineral N levels). This uptake is also constrained by upper and lower limits for nutrient content in the shoots and roots, which in turn are taken as a function of plant biomass. MACRO has the ability to represent crop growth only in relation to water uptake and evapotranspiration, plus interception of surface applied contaminants (in water) by plant leaves before reaching the soil surface. MACRO also includes the representation of the degradation of a contaminant, a process which strictly does not take place for phosphorus, but this feature can be used to provide a crude representation of the removal of P from the soil, by plant uptake. 2.3.5. Soil carbon Some soil P dynamic processes depend on a supply of carbon and so are closely linked with the dynamics of carbon in soil organic matter. Only the ANIMO and DAYCENT models include representations of soil carbon dynamics in parallel with soil N and P dynamics. 2.3.6. Soil nitrogen Nitrogen (N) is another nutrient taken up by plants from the soil which, like P, becomes a serious pollutant if it escapes into watercourses or deep groundwater. ANIMO, GLEAMS and DAYCENT have a representation of soil N, in the form of nitrate (NO3) and ammonium (NH4). They consider movement of N from applied fertilizer or slurry by solute transport, uptake of N by plants, mineralization/immobilization (between organic and inorganic forms), nitrification/denitrification, and volatilization of NH4. The review paper by Wu and McGechan (1998) gives a useful description of the characteristics of several soil nitrogen dynamic models. Similarly a range of soil nitrogen models simulating N2O emissions are compared in the paper by Frolking et al. (1998). 2.3.7. Application of animal manure and slurry Both ANIMO and GLEAMS make provision for application of animal manure or slurry. ANIMO allows for applications of cattle slurry, specified as mineral P, plus three categories of organic material each with its own P content. These P inputs are initially added to the appropriate pools in the upper layer of the profile, but after ploughing (at a date also specified in the input), the material is distributed throughout the profile down to the ploughing depth. GLEAMS represents land application of animal waste through the use of an animal waste organic phosphorus pool, from which P mineralizes to the inorganic pool at a faster rate than from the stable organic pool. A portion of the animal waste (25%) also

365

mineralizes to the active soil mineralizable P pool (stable organic pool). DAYCENT has a limited treatment of organic waste, allowing the partition of such material into a surface labile inorganic P pool, a surface labile organic P litter component and a surface structural organic P pool resistant to decomposition. MACRO includes an option for the representation of surface application of irrigation water containing a contaminant at a specified concentration, and this can be used to represent P applied in slurry or manure. Also, in the new version of MACRO with colloid facilitated contaminant transport, the concentration of the carrier colloid material in slurry can be specified. Animal slurry contains substantial quantities of colloidal material (mainly finely divided organic matter), and much of the inorganic P in slurry is sorbed onto such colloidal material rather than being in dissolved form.

2.4. Spatial and temporal discretization The P models divide the soil profile into layers to simulate vertical movement of P, carbon and water between layers, as well as transformation within each layer and uptake by plants from each layer at various rates. Similarly, MACRO divides the profile into layers for water and contaminant movements. The ANIMO, GLEAMS, DAYCENT and MACRO models can divide the profile into up to 50, 12, 10 and 15 layers, respectively, for soil nutrient processes. Dynamic model simulations are driven by weather variables. ANIMO does not use weather data directly, instead it uses output from previously run weather driven simulations with the associated soil water model, and operates at the same time-step as the soil water simulations (daily or weekly). GLEAMS operates on a daily time-step, using weather data to drive the hydrology, erosion and temperature sub-models. An optional climate generator can be used for daily rainfall, temperature and radiation data, similar to that used in the EPIC model (Richardson & Nicks, 1990). There is some loss of realism and accuracy of model representation when operating with a weekly rather than a daily time-step, particularly regarding processes influenced by rainfall such as high soil wetness, drainflows and P runoff and leaching, since rainfall occurs in distinct events rather than having an average intensity over a weekly period. DAYCENT requires daily time-step weather data to drive the hydrology, temperature and nutrient sub-models, constructing average weekly values for some components of the model, such as atmospheric deposition. The CENTURY model, requires monthly averages of precipitation and minimum and maximum

366

D. R. LEWIS; M. B. MCGECHAN

air temperature. MACRO operates with weather data on a daily, hourly or shorter time-step. 3. Mathematical description of transformation processes Generally, the P models consider transformations between pools to be represented by ‘first-order rate processes’, such that the flow out of the first pool to the second is proportional to the quantity of material remaining in the first pool. Similarly, in MACRO the degradation of a contaminant (a flow from a pool to nowhere) is represented by a first-order rate process. Solution of the resultant first-order differential equation, requires specification of an initial value at the beginning of the time period. To take account of the sensitivity of such transformations to environmental factors such as temperature eT , soil aeration ea , soil wetness ey and pH epH , transformation rate coefficients k may incorporate multiplicative response functions for each of the factors. ANIMO uses expression such as k ¼ eT ea ey epH kref

ð1Þ

where the multiplicative factors will be defined later and kref is the reference value of the first order transformation rate constant under optimum conditions. For the rate of degradation in the DAYCENT and MACRO models, a response function for temperature and water content of similar form to Eqn (1) is assumed. GLEAMS uses expression such as k ¼ ðeT ey Þ1=2 kref

ð2Þ

and so transformation rates vary according to a powerlaw expression for these environmental factors. 3.1. Temperature response 3.1.1. ANIMO On the basis of literature sources, the authors of ANIMO concluded that temperature has the greatest effect on organic matter decomposition processes. Other processes follow a similar pattern but the influence of temperature is less important. It is assumed that a reaction rate increases with soil temperature in a layer T measured in 8C in a manner described by an Arrhenius equation, a commonly used function for chemical reactions. The correction factor for temperature is then 
 1 1 eT ¼ exp
9000
ð3Þ T þ 273 Tref þ 273 where: Tref is a reference temperature usually taken as the average annual soil surface temperature, and if T is below zero, eT is set to zero.

3.1.2. GLEAMS The temperature effect in GLEAMS on decomposition rates is expressed as an exponential equation T ð4Þ eT ¼ T þ exp½993
0312T

and if T is below zero, eT is set to zero. 3.1.3. DAYCENT Using a non-linear data-fitting procedure, parameter values were determined for a generalized Poisson function that represented the effect of soil temperature on decomposition of labelled cellulose at several temperatures (Parton et al., 1987). This produced a temperature response function of the form: eT ¼
006 þ 013 exp½007T

ð5Þ

and if T is below zero, eT is set to zero, otherwise T is set to one. 3.1.4. MACRO The temperature response function in MACRO is given by a numerical approximation of the Arrhenius equation (Boesten & van der Linden, 1991) modified for low soil temperatures: 8   T > 58
Tref Þ ; > < exp ðaðT   eT ¼ 02T exp að5
Tref Þ ; 04T458C ð6Þ > : 0; T508C where: a is a composite parameter dependent on all of T, the reference temperature Tref, the gas constant and the molar activation energy. These response functions produce the curves shown in Fig. 5 in which Tref has a value of 35 for the ANIMO and MACRO expressions. ANIMO and MACRO consider the temperature effect relative to that at the value of Tref, at which point eT = 1 and this makes it more difficult to compare with the GLEAMS and DAYCENT models which maintains that eT 41. Overall, however, there is reasonable similarity between the functions. 3.2. Soil aeration and water response

3.2.1. ANIMO Since aeration has a major influence on transformation rates, detailed sub-models describing oxygen diffusion in the soil gas and in soil aggregates are implemented (Groendendijk & Kroes, 1999). When ea ¼ 1, organic transformations and nitrification processes are optimal, otherwise there is an oxygen requirement which the diffusive capacity of the unsaturated zone cannot fulfil. Soil atmospheric oxygen

367

PHOSPHORUS MODELS

1.0

Temperature response function

0.8

0.6

0.4

0.2

0 0

5

10

20 25 15 Soil temperature, ˚C

Fig. 5. Soil temperature response functions for the four models considered: , MACRO

concentration is determined by solving the vertical diffuse transport equation for oxygen in the air-filled pores of the soil system with expressions for atmospheric oxygen demand caused by microbial based transformations. Under partial anaerobiosis conditions, the fraction ea is determined through the solution of a radial diffusion equation for aqueous oxygen concentration in soil water around a pore, and an estimate of the average radius of air-filled pores determined from the air entry and current matric potential of the soil layer. The reduction in the transformation rate coefficients due to lack of atmospheric oxygen is treated through ea , whereas water stress for the microorganisms are described by the response factor ey . This factor is reduced from unity, below the wilting point, and is dependent on matric potential (expressed as pF; log10 of the soil water potential in cm water) in the rootzone through the empirical relationships: 8 1; pF 532 > < ey 1
08ðpF
32Þ; 324pF 4 42 ð7Þ > : 02; pF > 42

30

35

, ANIMO; .

40

, GLEAMS;

, DAYCENT;

response factor:

8 > < y
yw ; ey ¼ yfc
yw > : 0;

y4yfc

ð8Þ

y > yfc

where: yw is the volumetric soil water content at the wilting point of 1500 kPa, and yfc is the volumetric soil water content at 33 kPa tension (described as field capacity for a North American soil). 3.2.3. DAYCENT Using the daily soil water budget model, the following function of the volumetric water content is employed in DAYCENT:

 y
B DðB
A=A
CÞ y
C D ey ¼ ð9Þ A
B A
C

with no modifications considered below the rootzone.

where the empirical parameters A, B, C, D are defined for coarse, medium and fine soils. The anaerobic dependence of the decomposition, rates, etc. is defined through the use of an empirical equation involving the precipitation and potential evapotranspiration rates.

3.2.2. GLEAMS Aeration is not described in GLEAMS, instead transformations are assumed to be linearly reduced from saturation and to be dependent upon the volumetric soil water content y as a % through the

3.2.4. MACRO In MACRO, the water content function is given by 8
F > < y ; y4ybp ybp ey ¼ ð10Þ > : 0; y > ybp

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D. R. LEWIS; M. B. MCGECHAN

1.0

Water response function

0.8

0.6

0.4

0.2

0 0

0.1

0.2

0.3 0.4 Soil water content, v/v

0.5

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

where: ybp is the water content at the ‘break-point’ (when the soil matrix pores are full but the macropores are empty), and F is an empirical exponent. In order to compare the functions, a clay loam soil is assumed with a typical water release curve (indicating the relationship between potential and water content). Figure 6 then illustrates the relatively similar behaviour of the ANIMO and DAYCENT water stress responses without their respective anaerobic dependencies, and the GLEAMS and MACRO water stress factors which includes some representation of anaerobic effects. Decomposition is generally assumed to take place at the maximum rate (ey ¼ 1) in the middle of the water

0.6

, ANIMO;

, GLEAMS;

,

content range, declining at low water contents, and also declining at high water contents. Table 1 gives typical values for the parameters involved in the water response functions. 3.3. pH response In ANIMO only the organic transformations are influenced by soilwater pH, with the response function given as 1 epH ¼ ð11Þ 1 þ exp½
25ð pH
5Þ

Table 1 Typical parameters in soil water response functions Parameter

Suggested coefficient Sand

yw the volumetric soil water content at wilting point (GLEAMS) yfc the volumetric soil water content at field capacity (GLEAMS) A an empirical factor (DAYCENT) B an empirical factor (DAYCENT) C an empirical factor (DAYCENT) D an empirical factor (DAYCENT) ybp the volumetric soil water content at break-point (MACRO)

Silt

References

Data source*

Clay

003

013

028

Knisel et al. (1993)

a

016

027

039

Knisel et al. (1993)

a

055 170
0007 322 035

060 127 00012 284 042

060 127 00012 284 050

Metherell et al. Metherell et al. Metherell et al. Metherell et al. Jarvis (1994)

(1993b) (1993b) (1993b) (1993b)

a a a a a

McGechan et al. (2002)

a

All soils F an empirical exponent (MACRO) *a}data cited by author of reference.

01

369

PHOSPHORUS MODELS Fast cycling pools

Slow cycling pool

Mineralization

Manure/slurry

Decomposition Decomposition

Soil organic matter/ biomass/humus

Mineralization Immobilization

Inorganic soil P

Stable inorganic soil P

Litter Mineralization

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

where each soil horizon is assigned a pH value pH by the user. It is assumed that under optimal agricultural practises this pH value will not change over a year and so seasonal fluctuations can be ignored. GLEAMS also assumes that an annual pH for each horizon is input by the user. The P sorption capacity of the soil for sorption of P from the active to the stable P pool is defined as a function of pH. DAYCENT is dependent upon pH for the P sorption processes, which are discussed in greater depth in Section 3.5.3. MACRO has no such dependence.

3.4. Decomposition, mineralization and immobilization Generally, mineralization and immobilization of P are controlled by associated carbon and N processes. In Fig. 7, organic matter is divided into several pools, roughly categorized as fast cycling pools, such as fresh organic consisting of plant litter or manure, and slow cycling pools, mainly of soil humus. These pools are also distinguished by different C:N:P ratios, with fresh organic pools having a ratio range of 1:12–25:>200, respectively, and the longer term stable organic pools having ratios of 1:512:125–200, respectively. Transformation flows important for P dynamics models consist of those from the fast cycling pools to the slow cycling pool and also mineralization (or the reverse process}immobilization) from each organic pool to a labile or inorganic P pool. Carbon and associated N transformation processes described as ‘decomposition’ or ‘humification’, control these P transformations. An important quantity which determines the direction of flow of P is the ‘assimilation factor’ which is the proportion of carbon going from the fast organic cycling pool to the slow organic cycling one, with the remaining carbon lost as CO2. As soil microbes multiply in response to the input of fresh organic material, there is an increase both in the biomass and correspondingly in

the slow cycling organic pool due to organic matter dissimulation, which is sustainable only if there are sufficient N and P reserves. Thus, another important quantity which determines the direction of flow of P is the C:N:P ratio, both at the source and at the destination pool. In the transfer from fast to slow cycling pools the fast cycling material generally has a higher C:P ratio than slow cycling material, so (unless most of the carbon in the fast cycling pool is lost as CO2 due to a low assimilation factor) soluble inorganic P has to be converted back to organic form or ‘immobilized’ to satisfy the higher P requirement of the slow cycling pool. The slow cycling humus pool is the final destination for organic carbon, so decomposition of carbon in this pool generally produces CO2 alone. However, some of the models also allow for a decomposition process in one or more organic pool which recycles some material back to the same pool with some carbon loss as CO2. Decomposition from each carbon pool is usually treated in these models as a first-order rate process with adjustment to the rate coefficient K for environmental factors. Conversion of rates in terms of C to P are usually obtained by dividing the C rate process by the appropriate C:P ratio. 3.4.1. ANIMO In the ANIMO model, organic matter is divided into four categories: organic plant parts and manure (sometimes also called fresh organic material), root exudates, soil organic matter/biomass and soluble organic material (Fig. 2). The fast cycling fresh organic material pool consists of the litter and manure/slurry pools in Fig. 7, where litter is composed of root and other crop residues after harvesting. Root exudates, is an additional fast cycling pool which consists of organic products excreted by living roots plus dead root cells discarded by the plant. The slow cycling soil organic matter/biomass pool contains material formed from part of the available

370

D. R. LEWIS; M. B. MCGECHAN

fresh organic material and root exudates, and consists of both dead organic soil material and living biomass. The fourth pool, soluble organic matter, is part of soil organic matter from other pools which has been rendered soluble. ANIMO also considers manure or slurry to contain a soluble organic component, and this is added to the dissolved organic matter pool when applied. The four fresh organic fractions have varying degrees of non-solubilization fh,fp, with the total formation rate RFom ! Som of soluble organic matter from fresh organic material represented in the model by summing all the soluble fractions with different first-order rate coefficients, i.e.: X ð1
fh;fp Þ kfp r Com;fp d RFom!Som ¼ ð12Þ ðC : PÞ fp fp where: rd is the dry bulk density, Com,fp is the mass of fresh organic matter of fraction fp, (C:P)fp is the carbon:P ratio of the fraction fp and kfp is the decomposition rate parameter which includes soil moisture and temperature factors, etc. Decomposition of the non-soluble fraction to stable organic matter is also described by first-order kinetics. Root exudate production is assumed to be proportional to the rate of root biomass production. Decomposition of the root exudate pool and also the soluble organic matter pool is represented by first-order rate processes, both with the same assimilation factor a, to indicate the fraction going to the slow cycling humus pool. The remainder of these decomposing pools goes to CO2. The separate soluble organic material pool in ANIMO (which receives inputs both as components of added slurry and by decomposition of solid components of added slurry, plant parts (mainly roots) and root exudates) moves with water in the soil and so is subject to losses by leaching. Mineralization of P from the fast cycling organic pools is calculated from the assimilation factor and the C:P ratios of the source and destination pools. The flows of carbon (to CO2) and of P (mineralization) from the slow cycling pool are first-order rate processes both with the same specified rate coefficient. The general form of the equations describing net mineralization or immobilization rate (Rmin/imm) is given by X Rmin=imm ¼ ðPfn
aPhu Þkfn rd Com;fn ð13Þ fn

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

mineralization or immobilization of mineral P, dependent upon the sign of the equation. Net immobilization is most likely after harvest or after ploughing when there is a large input of litter with high C:P ratio to the pool. At other times the pool will tend 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 all the first-order rate decomposition processes are multiplied by the same environmental factors for temperature, soil water content and pH of the soil as mentioned in previous sections. 3.4.2. GLEAMS In the GLEAMS model, three categories of organic matter are used which consist of the fast cycling fresh organic and animal waste organic pools and a slow cycling organic humus pool. The fast cycling fresh organic material pool consists of surface crop residues after harvesting and sub-surface root residues, with the slow cycling soil organic matter/biomass pool consisting of both dead organic soil material and living biomass. The treatment of the decomposition of the organic matter pools follows that of the ANIMO model, with appropriate soil water and temperature terms, and removal of the solubilization terms in Eqn (12). Decomposition of crop residue in the soil is treated as a single-step first-order process (Jones et al., 1984a), with the crop residue decomposition rate Rcr linearly dependent on a rate constant kcr (a function of crop residue composition) and the function CNP: Rcr ¼ 04 Rdcr rd Ccrom

ð14Þ

With the decomposition rate factor Rdcr given by Rdcr ¼ CNP kcr ðeT ey Þ1=2

ð15Þ

where: Ccrom is the carbon content of the crop residue, and the function CNP is given by 8 > < exp½
0693ððC : NÞi
25Þ=25

CNP ¼ min exp½
0693ððC : PÞi
200Þ=200

ð16Þ > : 10 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. In the calculation of these ratio’s the total residue (crop and animal), nitrate, ammonia and phosphorus masses in a layer are used, as it is difficult experimentally to determine the relative amounts of each crop residue, animal waste residue and soluble components. The value of the residue composition factor kcr is determined by the stage of residue decomposition fdecomp defined as the fraction of the original residue remaining. Carbohydrate-like material is considered to decompose first causing up to a 20% reduction, with the next

371

PHOSPHORUS MODELS

20-90% reduction caused by decomposition of celluloselike material, and the final 10% by lignin (Sharpley & Williams, 1990). Values of kcr for these stages are given by 8 fdecomp 420% > < 08; 005; fdecomp 490% kcr ¼ ð17Þ > : 00095; fdecomp > 90% The temperature and water content multiplication factors defined earlier are used to modify the mineralization rate. As in the EPIC model (Sharpley & Williams, 1990), 75% of the mineralized fresh organic P is added to the labile P pool and 25% is added to the organic humus P pool (Jones et al., 1984b). In order to be consistent for the organic mineralization processes, the same type of relationships are used for animal waste mineralization within the soil, with similar proportions going to labile and humic pools. Phosphorus in surface residue (crop and animal waste), is mineralized to labile P, and is calculated by the same processes as for soil mineralization. The soil water conditions for the top 1 cm and the daily air temperature are used in Eqn (2) to modify this rate. Mineralization, from the slow cycling organic humus P pool, is treated as a first-order reaction, with a mineralization coefficient ksomin. The ratio of active and stable soil P pool is used to partition soil organic humus P into the mineralization fraction. This rate is then modified by the water and temperature factors defined earlier. Immobilization calculations in GLEAMS follow that of the PAPRAN model (Seligman & van Keulin, 1981). The immobilized rate Rimmob is given by Rimmob ¼ Rdcr rd Pfresho ½016PLI
ðPpfr Þ

ð18Þ

where: Pfrsho is the amount of P in the fresh organic pool, the coefficient 016 results from assuming that carbon is 40% of fresh residue, and that 40% of the carbon is assimilated by soil microorganisms. The concentration of P in the fresh residue is Ppfr, and PLI is known as the labile phosphorus immobilization factor; ( 001 þ 0001Plab ; Plab 410 PLI ¼ ð19Þ 002; Plab > 10 where: Plab is the concentration of labile P. If Rimmob exceeds 95% of Plab, then a new decomposition rate is calculated which reduces the immobilization rate to this limit. Immobilized P in this model is subtracted from Plab and added to the fresh organic pool. Surface immobilization of P follows the same procedure as in the soil, with the appropriate value subtracted from labile P and added to P in the surface residue.

3.4.3. DAYCENT In the DAYCENT model, plant residue is decomposed by microbes, with the resulting microbial products becoming the substrates for humus formation. Soil organic matter is divided into three fractions; an active component consisting of live microbes and microbial products into which plant residue, manure, etc. passes, a protected slow component (through physical or chemical means), and a passive component that is resistant with a long turnover time. Decomposition of the organic matter pools follows the treatment of the ANIMO and GLEAMS models, with appropriate soil water and temperature response terms. Plant residue (shoot and root plant biomass) is divided into structural and metabolic pools. The lignin-to-N plant residue ratio, controls the division into each pool, with a large ratio leading to a substantial fraction of the residue going to the structural pool, with the fraction fs going to the structural pool given by fs ¼ 015 þ 0018L=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 subsequently decays with a rate Rcrl dependent upon the lignin content, which is released as microbes decompose the more labile components of the structural material (e.g. cellulose). The decomposition rate of the surface and soil structural organic pools is given by an equation of the form Rcrl ¼ Csom rd kcrl expð
30LÞ

ð21Þ

where: kcrl is a rate parameter dependent upon the structural pool, and contains appropriate soil moisture and temperature terms, with Csom the structural organic matter concentration. A high lignin content L reduces the ability of microbes to decompose the substrate, with the lignin fraction of the structural pool passing into the slow soil organic pool, and the non-lignin fraction passing to the active organic pool. The fast cycling metabolic or microbial biomass pool is incorporated only into the active organic pool. The C:P ratio of active, slow and passive soil organic pools varies approximately linearly as a function of labile P (defined as orthophosphate which is isotropically exchangeable or extractable with anion exchange resin), with low labile concentrations resulting in high ratios. Experiments have shown (McGill & Cole, 1981) that under low levels of labile P, phosphatase enzymes are capable of directly mineralizing P from the system. Hence, any new soil organic matter additions will have C:P ratios which also vary as a function of labile P. Decomposition of both plant residues and soil organic matter has an associated loss of CO2 as a result of

372

D. R. LEWIS; M. B. MCGECHAN

Table 2 Decomposition rate coefficients Model

Material/pool

Fast cycling Slurry Fraction 1 (soluble) and soluble part of Fraction 2 Slurry Fraction 2 (rapidly decomposing) ‘fresh’ part Slurry Fraction 3 (slowly decomposing) Crop residues (mainly roots) rapidly decomposing part (09 of total) slowly decomposing part (01 of total) Root exudates GLEAMS Crop and surface residue (dependant upon decomposition stage) Animal waste (dependant upon decomposition stage) DAYCENT Active Plant residue}structural

Suggested coefficient, d
1

References

Source of data*

82  10
2

See Section 3.4.1

b

27  10
3

See Section 3.4.1

b

33  10
4

See Section 3.4.1 See Section 3.4.1

b b

See Section 3.4.1 See Section 3.4.1 See Section 3.4.2

b b b

95, 50, or 800  10
3

See Section 3.4.2

b

18–51  10
2 11–13  10
2

See Section 3.4.3 See Section 3.4.3

b b

Vinten et al. (1996)

a

ANIMO

SAC

55  10
3 60  10
4 10 95, 50, or 800  10
3

Litter Clay loam soil (topsoil) Sandy loam soil (topsoil)

24  10
2 26  10
2

experiments

a Intermediate cycling

DAYCENT Slow physically or chemically protected Slow cycling ANIMO GLEAMS DAYCENT Passive pool SAC experiments

Clay loam soil (topsoil) Sandy loam soil (topsoil)

55  10
4

See Section 3.4.3

a

41–55  10
5 10–30  10
5 18  10
5

Wu and McGechan (1998) See Section 3.4.2 See Section 3.4.3

b b b

Vinten et al. (1996)

a a

10  10
5 33  10
5

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

microbial respiration, with a definite fraction of the carbon flow from one organic pool to another, lost to the soil atmosphere. For the active pool this loss of CO2 on decomposition, increases with increasing soil sand content. The P attached to carbon lost as microbial respiration (typically 30–80% of the carbon flow) is assumed to be mineralized, so that decomposition of metabolic plant material, active, slow and passive soil organic matter (with low C:P ratio) generally results in mineralization of labile P. Decomposition of structural plant material which has a high C:P ratio requires immobilization from labile P. Mineralization or immobilization of P occurs as is necessary to maintain the C:P ratios within their defined limits in the various organic pools. 3.4.4. Rate coefficients for decomposition Rate coefficients for the first-order rate processes of flows 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!en & Paustian, et al., 1987; Lind et al., 1990; Vinten et al., 1996) can be used as source data for decomposition rates of litter and humus. Experimental data for material added to the soil is mainly for plant parts (litter), with little data for manure or slurry. The general assumption made is that the faeces component of manure and slurry consists of plant parts similar to those in litter, and that the same decomposition rate values can be assumed. Only the authors of ANIMO have attempted to estimate values specific to slurry, showing generally slightly slower decomposition rates than for litter. ANIMO considers slurry to consist of a number of components, with the organic part subdivided into several fractions with different decomposition rates and associations with the ‘fresh’ organic pool and the dissolved organic pool. Details of the proportions allocated to each of the fractions for several types

373

PHOSPHORUS MODELS

Table 3 Typical C/N/P ratios Model ANIMO

GLEAMS

DAYCENT

DAYCENT ANIMO GLEAMS DAYCENT

Material/pool

Suggested C/N ratio

Fast cycling Slurry Fraction 1 (soluble) and soluble part of Fraction 2 Slurry Fraction 2 (rapidly decomposing) ‘fresh’ part Slurry Fraction 3 (slowly decomposing) Arable crop residues (mainly roots) rapidly decomposing part(09 of tot) slowly decomposing part (01 of total) Grassland crop residues (mainly roots) rapidly decomposing part(09 of tot) slowly decomposing part(01 of total) Root exudates Crop and surface residue Animal waste e.g. dairy slurry dairy solid Active Plant residue}structural Intermediate cycling Slow physically or chemically protected pool Slow cycling Soil organic matter (humus) alone Humus plus microbial biomass Soil organic humus pool Stable inorganic soil pool Passive pool

of animal slurry are listed in the paper by Wu and McGechan (1998), which also contains a more detailed discussion of the issues of how decomposition is modelled 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 soil material has been much studied, generally through an analysis of the amount of P added to soil solutions and the quantity remaining over time (Barrow, 1974, 1978, 1980a, 1980b; Barrow & Carter, 1978; Barrow & Shaw, 1979). Much effort has been expended on determining relationships between the rate and extent of P adsorption and the chemical and physical properties of soils. However, such relationships have still not been attained for a wide range of soils. These experiments have shown that following soluble P application, inorganic or labile P concentrations decrease rapidly with time, and that this ‘fast’ reaction is then followed by a slower decrease which may continue for several years (Barrow & Shaw, 1975a, 1975b). Models take this behaviour into account by assuming that when e.g. fertilizer P is applied, both

Suggested C/P ratio

83 116 58 58

150 150 150 150

39

150

58 58 23 12–25

150 150 150 >200

15 20

235 105

3–15 20

30–80 500

12–20

20–200

11 14 7–13 7–13 7–10

150 150 125–200 125–200 90–200

rapid equilibrium processes and slow reaction processes are simulated. Experimentally, the determination of P that can be released from a soil sample has been carried out using several chemical extractants. The strength of these vary, with dilute CaCl2 solution (Barrow, 1980b), a weak soil extractant, used to determine very rapid response desorption P fractions, or anion exchange resin (Sibbesen, 1977), used to determine P adsorbed on the surfaces of more crystalline compounds. Stronger extractants are normally used to provide soil P fertility values, such as dilute NaHCO3 solutions (Olsen et al., 1954), NH4F/ HCl (Bray & Kurtz, 1945), or the Mehlich-3 soil P method (Mehlich, 1984). The inorganic labile P pool used in GLEAMS and DAYCENT are defined through the use of several of these extractants, and so are subtly different to the dissolved inorganic P pool used in ANIMO. Chemical sorption from a solute onto the porous matrix surface can be described by an equilibrium reaction when flow velocities are low enough to allow an equilibrium state to be reached. Soil matrix solute reactions then usually follow either non-linear Langmuir or Freundlich isotherms (Ibaraki & Sudicky, 1995). However, when flow velocities for the solute are

374

D. R. LEWIS; M. B. MCGECHAN

relatively large, or if absorption is strong, sorption may be described more correctly by a kinetic-type Langmuir or Freundlich reaction (Selim & Amacher, 1988). For kinetic reactions, when the sorbed phase concentration attains its equilibrium values, the sorbed phase concentration will not change unless the aqueous phase concentration changes. The use of a Freundlich-type reaction implies that the matrix has an infinite capacity to absorb, whereas a Langmuir reaction implies that there is a maximum quantity of P which can be absorbed (‘saturation’). Sorption data for many soils do not give good fits to the Langmuir equation, whereas the Freundlich equation (without a defined sorption maximum) gives good fits for nearly all soils. Holford et al. (1974) showed that for soils where only the Freundlich equation gave good fits to sorption data, an alternative was to fit a ‘double Langmuir equation’. This has two terms similar to the right-hand side of Eqn (22), with four parameters Smax1, kL1, Smax2 and kL2, and implies that there are two distinct sorption sites each with its own sorption maximum Smax1 and Smax2. However, in many instances the quantity of P in the soil is small relative to saturation, so the simple, single term Langmuir equation can give a good fit over the narrow concentration range which is relevant, although the fitted sorption maximum is not a true indication of saturation. McGechan and Lewis (2002) and McGechan (2002) have reviewed the extensive range of published literature

on the subject of P sorption by soil (including experimental data for fitting isotherm relationships for some soils), in more detail. However, Table 4 gives typical values associated to the sorption parameters described here. 3.5.1. ANIMO ANIMO uses the Langmuir isotherm for situations where equilibrium is rapidly achieved, with the instantaneous sorption of P described by   kL C n S ¼ Smax ð22Þ 1 þ kL C n where: kL is the Langmuir rate coefficient, n is a nonlinear coefficient and the quantities S represents the mass of contaminant adsorbed from the dissolved concentration C, and Smax corresponds to the maximum sorption capacity of the soil. Schoumans (1995) has established a set of parameters for the Langmuirisotherm describing fast P sorption in sandy soils and showed that the maximum sorption capacity is dependent upon the aluminium and iron content of the soil. For non-equilibrium conditions ANIMO describes sorption and desorption in terms of a kinetic-Freundlich reaction, and the following first-order equations are solved, ( kFsor ðkF C n
SÞ; Sfeq > S @S ¼ ð23Þ @t kFdes ðkF C n
SÞ; Sfeq 5S

Table 4 Parameters in sorption functions Model ANIMO

DAYCENT

Process

Suggested coefficient

References

Source of data*

Langmuir rate coefficient KL m3 kg
1, Maximum soil sorption capacity Smax kg m
3, Freundlich rate coefficient kF kg m
3, Kinetic-Freundlich rate coefficient sorption kFsor d
1, Non-linear sorption coefficient, n Sorption affinity Saff Sorption maximum Smax kg m
3, Constant sorption parameter Kms d
1, Constant sorption parameter p1, p2, p3 d
1,

1129

Schoumans (1995)

a

5167  10
6 rd ½Alox þ Feox

Schoumans (1995)

a

1187  10
6 rd ½Alox þ Feox

Schoumans (1995)

a

11755

Schoumans (1995)

a

05357 100–2.00 010–0.20 200

Schoumans (1995) Metherell et al. (1993) Metherell et al. (1993) Metherell et al. (1993)

a b b b

00008,0015, 0004

Metherell et al. (1993)

b

McGechan et al. (2002)

b

Silty clay loam soil MACRO

Freundlich rate coefficient kF kg m
3, Non-linear sorption exponent, n

203–6500 165

Clay loam soil 250 10

*a}reference author’s experimental data; b}data cited by author of reference. Note: rd , dry bulk density, kg m
3, [Alox þ Feox ], aluminium and iron content, mmol kg
1, and for the ANIMO model desorption parameters are the same as for sorption.

375

PHOSPHORUS MODELS

where: kFsor and kFdes are the kinetic rate coefficient for sorption and desorption respectively and Sfeq is the adsorbed concentration determined by the equilibrium Freundlich isotherm, defined by S ¼ kF C n

ð24Þ

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 as the fraction of added P remaining in the labile pool after the initial rapid sorption phase is complete. The coefficient PSP is a function of chemical and physical soil properties as shown in the following expressions (Sharpley & Williams, 1990)

where: kF is the equilibrium rate coefficient for adsorbtion. Schoumans (1995) derived rate-dependent P 8 calcerous soils 058
00061CCaCO3 > < PSP ¼ 00054Bsat þ 0116 pH
073 slightly weathered non-calcerous soils > : 046
00916 lnðCL Þ highly weathered non-calcerous soils with

ð27Þ

0054PSP4075

sorption parameters for a wide range of Dutch sandy soils, but noted that data for the desorption rate coefficient has not yet been determined. Precipitation of P takes place immediately when the concentration of the solution exceeds a defined equilibrium buffer concentration Ceq. This precipitated mineral dissolves immediately when the concentration drops below this limit. For establishing this equilibrium concentration ANIMO uses the following relation based on the soil pH:

where: CCaCO3 is the calcium carbonate concentration, Bsat is base saturation determined as a percentage by the ammonium acetate method, pH is the soil acidity, and CL is the percentage clay content. Flow Ras between the active mineral P pool and the stable mineral P pool occurs until the stable pool Pstab is assumed to be four times the active mineral pool (Sharpley & Williams, 1990) and is expressed as

Ceq ¼ 0135  ð3Þ5
pH

with a positive flow indicating that P moves from the active to the stable pool and vice versa for a negative flow. The factor o is a flow coefficient which is a function of PSP, given by ( 000076 calcareous soils o¼ ð29Þ exp½ð
177PSP
705Þ non-calcareous soils

ð25Þ

3.5.2. GLEAMS In the GLEAMS model, flows between active and stable mineral phosphorus pools, and between active mineral P and labile P pools (Fig. 3) are defined, with the relative P pool sizes dependent upon soil classification, texture and chemical properties. A long-term stable system is maintained between the mineral P pools with the stable pool four times the size of the active mineral pool at equilibrium. Rapid immobilization of labile P by sorption to the active P pool occurs when the labile P pool gets large from fertilizer or manure application, or by mineralization. A slow adsorption of inorganic P from the active P pool to the stable P pool is simulated. Movements of P by sorption processes are treated as a function of soil characteristics. The flow rates Rla between the labile and active mineral P pools are given by Rla ¼ 01ey exp½ð0115T
288Þ


 PSP Plab
Pact rd 1
PSP

ð26Þ

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

Ras ¼ oð4Pact
Pstab Þrd

ð28Þ

3.5.3. DAYCENT In DAYCENT the inorganic labile P pool is assumed to be in equilibrium with the inorganic sorbed pool. This equilibrium relationship is defined in terms of a quadratic equation with two parameters, the sorption affinity Saff and the sorption maximum Smax, and the solution of the equation provides the labile P concentration. Essentially, this is a representation of the Langmuir isotherm, Eqn (22), with n=1, and kL given by   2 kL ¼ ð30Þ Smax ð2
Saff Þ The sorption affinity parameter controls the fraction of the mineral P (labile plus sorbed pools) which is in the labile pool at low levels of P in these pools. Correspondingly, the sorption maximum parameter is the maximum amount of P in the sorbed pool, and controls the curvature of the relationship between labile P and mineral P. Equilibrium between the labile and sorbed pools is recalculated after any P additions or removals from the soil.

376

D. R. LEWIS; M. B. MCGECHAN

Sorbed P is in dynamic equilibrium with a more strongly sorbed P pool Rso, with the flow rates between the two pools given by Rso ¼ ½Kms Psorb
Ksm Pssorb rd

ð31Þ

where the rates are also multiplied by the temperature and moisture factors mentioned earlier, Psorb and Pssorb are the P pool concentrations, Kms is a constant parameter. The parameter Ksm is a function of soil pH and soil texture through an equation of the form: Ksm ¼ 12½ p1 pH þ p2 þ p3 SD

ð32Þ

with pi constants and SD the sand content as a % of the soil. In turn, the strongly sorbed P may be lost to an occluded P pool with flow rates comparable to the first component of Eqn (31). 3.5.4. MACRO MACRO assumes the Freundlich isotherm equation for sorption of a contaminant onto static sorption sites in the soil [Eqn (24)]. Only instantaneous equilibrium can be considered. The Freundlich isotherm is also assumed for sorption of a contaminant onto sites on a mobile colloid, but in this case the exponent n must take a value of unity (implying a linear isotherm). When used as a P model, the sorption process described by the Freundlich isotherm represents fast, reversible sorption of P onto sites on the surface of soil particles. As MACRO is not intended primarily as a P model, no direct provision is made for representation of the slow reaction which P undergoes following attainment of equilibrium for fast sorption. However (as already mentioned in relation to crop uptake of P), provision is made in MACRO for representation of degradation, and this facility can also be used to provide a simplistic representation of the slow reaction. The slow reaction is reversible only at a very slow rate (some researchers regard it as totally irreversible), so, over relatively short periods after manure or fertilizer spreading, degradation is an appropriate representation of the slow reaction which effectively removes P from the active, labile pools.

4. Solute and particulate phosphorus transport The removal of P from the soil/water system by leaching of solutes (organic and inorganic) and by surface-runoff (dissolved and particulate) is an important consideration in modelling the P cycle in soils. Export of P through runoff as particulate P (associated with soil particles and eroded organic matter) is considered to be the major constituent of P transport from cultivated land (Sharpley et al., 1992). However, export of particulate P by the ‘through-the-soil’ route is

not considered. Runoff from grassland or forests contains little sediment and so dissolved P forms the dominant loss. Leaching losses of P are controlled by more complex factors than surface losses, with percolation to groundwater, and soil micropore and fracture flow to drainage systems forming important P loss mechanisms in some soils. The loss of dissolved P through leaching is generally related to the degree of P saturation of soils (Heckrath et al., 1998; Brookes et al., 1997), whereas particulate P losses through subsoil movement are dependent upon the degree of macropore or bypass flow. A significant proportion (up to 50%) of the total P from deep drains under clayey non-calcerous grassland, has been reported to be in the form of inorganic particulate P (Haygarth et al., 1998), for which macropore flow must be an important transport mechanism. At the larger farm or catchment scale, effort is now being expended in determining the mass balances and flows of phosphorus in agricultural systems (Cassell et al., 1998). Modelling tools which predict the environmental consequences of the application of fertilizers, and animal waste and their transport and transformations are seen as an important means of controlling this pollution (Daniel et al., 1998). Representation of solute and colloid transport, and also surface runoff, are dependent on the associated soil water model or subroutine (see Sections 2.3.1 and 2.3.4). ANIMO, GLEAMS, DAYCENT and MACRO can all represent vertical leaching of dissolved or labile P to deep groundwater, with ANIMO and MACRO also simulating movement to field drains. Solute transport in ANIMO is treated through a numerical solution of the convection–dispersion mass transport equation with sink/source terms representing sorption and transformations. Physical dispersion is represented in the model by numerical dispersion obtained through a judicious choice of the layer spacings. ANIMO adds all inputs of animal manure and fertilizer into an imaginary surface reservoir whose volume and decay properties are determined by an appropriate thickness of the reservoir. These material inputs are not released to the soil until a rainfall event occurs. The fraction of material released is dependent upon the ratio of volume of rainfall and the reservoir volume, with the store of nutrients evaluated after each time step through a mass balance exercise, and being totally depleted when the precipitation volume equals the reservoir volume. Surface runoff occurs through infiltration excess or saturation excess, and in both cases this runoff may contain solute from precipitation, the upper part of the soil and the surface reservoir. Within GLEAMS the hydrology component describes soil water movement through a storage-routing

PHOSPHORUS MODELS

technique (Knisel, 1980) which calculates the outflow from each soil layer to its neighbour. Percolation is then determined from the layers soil moisture and saturated hydraulic conductivities, whenever the volume of water in each layer is above field capacity. Solute transport is treated in GLEAMS through an advective process with a percolation mass of solute determined for each layer outflow. Since P is sorbed onto soil surfaces, the amount in solution is determined through a partition coefficient kd between the solid phase and the water phase according to the linear adsorption isotherm: kd ¼

Cs Cw

ð33Þ

where: Cs and Cw are the equilibrium concentrations in soil and water, respectively. This partition coefficient is taken to be dependent upon the soil clay fraction through the empirical expression: kd ¼ 100 þ 0025CL

ð34Þ

where: CL is the percent clay in the soil layer. Research is currently being carried out to relate this coefficient to soil P status and the nature of the soil. The concentration of labile P is then determined through a mass balance approach for each layer taking into account the uptake by plants and the various transformations that occur. Phosphorus is extracted from the soil surface when overland flow occurs and by mixing of the soil material with this runoff water. GLEAMS assumes that the top 1 cm of soil is the active layer that interacts with the runoff water, and that the extraction of P is incomplete. In this case we can describe the soil and water concentrations of the surface layer by Cav kd b 1 þ kd b Cav b Cw ¼ 1 þ kd b Cs ¼

ð35Þ

where: Cav is the available concentration in the surface soil layer and b is the extraction coefficient which has values of (Leonard et al., 1987) 8 05; kd 410 > < b ¼ 0598 exp½
0179kd ; 105kd 5100 ð36Þ > : 01; kd 4100 It can thus be seen that when kd ¼ 0 then Cs=0 and Cw=Cav b, and that when kd gets very large Cs approaches Cav. The rate of change of P in the surface layer is defined in GLEAMS as being proportional to Cw and the water flux, and at saturation this equation can be integrated to give an approximation for the available concentration Cav.

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The movement of particulate P through runoff is represented in the GLEAMS model (Section 2.3.3), on the basis of the enrichment ratio (the ratio of the surface area of the sediment leaving the field and the surface area of the matrix soil), which is given as a function of the sizes and composition of the sediment particles. The P mass transported with the sediment is then the product of the sediment mass, enrichment ratio and Cs. In DAYCENT, P losses from the system can occur as a result of leaching of labile P, with P losses accumulating in the soil layer below the last layer, eventually percolating out of the defined profile. Leaching of labile mineral P occurs when there is saturated water flow between the soil layers. The fraction of the mineral pool that flows from the upper layer to the lower layer increases as a linear function of the sand content, up to a maximum set value. A fraction of the products from the decomposition of the active organic P pool is lost as leached organic matter. Leaching of this organic matter is a function of the decay rate for active soil organic matter, and the clay content of the soil (with lower losses for clay soils). This leaching only occurs if the water flow is sufficiently high, with a minimum flow required for drainage of water below the 30 cm soil depth. The movement of particulate P through soil erosion is calculated in a similar fashion to that of the GLEAMS model. The MACRO model can provide the most sophisticated representation of transport of P through the soil (as opposed to by the surface route) in both dissolved and particulate forms. Important features which distinguish MACRO from the other models are representation of colloid facilitated transport of sorbed P, and the dual porosity representation of water movement, as macropore flow of colloid-bound P through the soil appears to be a very significant polluting loss process in many circumstances.

5. Conclusions A comprehensive description of all processes relevant to P in soil would consider transport of both soluble and particulate P, and of both inorganic and organic P, by three routes}overland (surface runoff ), through the soil to field drains, and vertically through the soil down to deep groundwater, as well as transformations from one form of P to another following applications of both mineral fertilizer and manure P. None of the models consider all these processes, but some consider a sub-set appropriate to a particular situation. GLEAMS considers everything except transport to field drains so is appropriate to many North American situations where there are no field drains and most P is applied as mineral

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fertilizer. However, it is less appropriate to parts of the US farm belt which have field drains installed to drain former swamps, and drain water quality is a major issue in these regions. DAYCENT also only considers vertical transport, but some of its parameters are more appropriate to long-time scale processes. It is, however, the only model to consider plant residue decomposition in terms of the lignin-N ratio. ANIMO has the most comprehensive treatment of manure and slurry, and includes a rigorous description of soluble forms of phosphorus, but lacks consideration of particulate transport. MACRO has the most comprehensive treatment of through-the-soil transport processes, including micropore and macropore domains (although not surface runoff ) and particulate transport, but currently has only simplistic representation of P transformations. Modelling of temperature and soil wetness effects on transformation rates is broadly similar between all four models. The general approach to modelling decomposition and mineralization (or immobilization) is similar between ANIMO, GLEAMS and DAYCENT (assumed to be based on N and C processes), but details of the equations differ. MACRO, however, does not have a description of soil N and C transformation, but concentrates on soil solute transport characteristics. Detailed P loss experiments in field drained soils and their simulation using simplified P cycle models (McGechan et al., 2002), has identified that there is a further requirement for model P development. Further P modelling work is likely to be focussed on constructing a new hybrid version of the four models described here, with full representation of the missing processes. Such a model is likely to include a description of both soluble and particulate P flow through micropores and macropores as in the MACRO model. This would be 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 the DAYCENT model. Finally, the overland flow and erosion losses could be represented by components from the GLEAMS model.

Acknowledgements Funds to carry out this work were provided by the Scottish Executive Environment and Rural Affairs Department.

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