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Published in J. Environ. Qual. 33:210-231 (2004).
© ASA, CSSA, SSSA
677 S. Segoe Rd., Madison, WI 53711 USA

TECHNICAL REPORTS

Landscape and Watershed Processes

Mathematical Modeling of Phosphorus Losses from Land Application of Hog and Cattle Manure

R. F. Grant*,a, M. Amranib, D. J. Heaneyb, R. Wrightb and M. Zhangb

a Department of Renewable Resources, University of Alberta, Edmonton, AB, Canada T6G 2E3
b Plant Industry Division, Alberta Agriculture, Food and Rural Development, Edmonton, AB, Canada T6H 4P2

* Corresponding author (robert.grant{at}ualberta.ca).

Received for publication November 22, 2002.

   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MODEL DEVELOPMENT
 PHOSPHORUS RUNOFF EXPERIMENT
 MODEL APPLICATION
 RESULTS
 DISCUSSION
 REFERENCES
 
Mathematical models may provide a means to estimate phosphorus (P) losses from land application of manure. Phosphorus losses typically occur during brief episodes of runoff and erosion. Models must be able to simulate P losses during these episodes by representing the basic chemical, physical, and biological processes by which these losses occur. The mathematical model ecosys combines dynamic distributed flow of solutes and nonsolutes through runoff and erosion with convective–dispersive transport of solutes, and both biologically and thermodynamically driven transformations between solutes and nonsolutes. This model was tested against P lost in runoff, erosion, and leachate measured during 90 min of controlled rainfall at 65 mm h–1 on soils from six sites at which different rates of manure had been applied over the previous 3 to 6 yr. Transport and transformation kinetics in the model enabled it to simulate changes of dissolved inorganic phosphorus (DIP) in runoff from >1.0 to <0.05 mg L–1 and changes of total phosphorus (TP) in sediment from 15 to 3 mg L–1 measured during controlled rainfall on soils with diverse P contents. Results from 60-yr model runs using these kinetics with different application rates of cattle manure indicated that (i) a positive interaction exists between annual rainfall and application rate on P losses and (ii) rates greater than 30 Mg ha–1 yr–1 would cause TP concentrations in water leaving the site to rise above acceptable limits. The interaction between rainfall and rate suggests that P losses from manure application at any site should be assessed under the upper range of likely rainfall intensities.

Abbreviations: DIP, dissolved inorganic phosphorus in runoff • LP, organic + inorganic phosphorus in leachate • TP, total phosphorus in sediment


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MODEL DEVELOPMENT
 PHOSPHORUS RUNOFF EXPERIMENT
 MODEL APPLICATION
 RESULTS
 DISCUSSION
 REFERENCES
 
THE LAND APPLICATION of manure from expanding livestock production in Alberta has raised concerns about water quality. Many of these concerns focus on phosphorus (P) because ratios of P to N and C in manure are larger than those found in soils and taken up by plants. Phosphorus contents of surface water in areas of intensive manure application have been found to exceed water quality guidelines for the protection of aquatic life (Canada-Alberta Environmentally Sustainable Agriculture Council, 1998). There is a need therefore to establish application rates that enable disposal of livestock manure while avoiding P accumulation in surrounding waters.

Most P losses from land application of manure occur as dissolved organic and inorganic P in runoff, and as solid organic, adsorbed, or precipitated P in sediment. The concentration of dissolved P in runoff rises with repeated manure applications because the ability of soil to adsorb and precipitate added P declines as adsorption sites are occupied and coprecipitates are depleted. The concentration of solid P in sediment also rises with manure application because manure contributes to organic and inorganic P stocks at the soil surface. Attempts to relate the concentration of dissolved P in runoff to concentrations of P in soil are frequently based on P extracted according to existing soil test protocols (e.g., Daniel et al., 1993). However, P losses will also be affected by climatic, topographic, agronomic, and edaphic factors that determine runoff and erosion (Sharpley et al., 1996), requiring a broader approach to estimating these losses.

One emerging approach to estimating P losses from manure and other soil amendments is the use of mathematical models that simulate the key processes (adsorption, precipitation, mineralization, plant uptake, solute transport, runoff, and erosion) by which these losses are controlled. However, many such models function at temporal scales (typically daily) larger than those at which P losses occur (typically hourly or less), and are therefore forced to use simplifying assumptions to represent key processes. In some cases, key processes such as mineralization, adsorption, or leaching are omitted from the models (e.g., Zhang et al., 1995). Although these models have simulated P losses at monthly and annual time scales (e.g., Pierson et al., 2001; Yoon et al., 1994), they may have a limited ability to simulate events with temporal scales of minutes to hours during which most P loss occurs (Edwards et al., 1994). Some more detailed models simulate key processes explicitly at time scales better suited to modeling P loss events. However, these models often represent in detail only a subset of the key processes that control P losses, such as water, sediment, and solute transport (e.g., Walter et al., 2001; Wang et al., 1996). The modeling of P transfer between solid and soluble phases during these events is usually based on sorption isotherms that do not represent the mechanisms of P transformation in soil. Because these isotherms are fitted from soil-specific data, their parameters are not unique (Schoumans and Groenendijk, 2000) and hence are unlikely to be generally applicable (Mansell et al., 1985). These more detailed models are well adapted to simulating individual P loss events, but may not be well adapted to simulating long-term P loss under different land management practices unless all key processes affecting P losses are represented at similar levels of detail.

Because long-term P losses are the sum of several P loss events, models used to simulate long-term P losses must be capable of simulating individual P loss events over long periods of time. Such models must have three key attributes: (i) they must function at the time scales at which these events occur (minutes to hours), (ii) they must use basic theory to represent a comprehensive set of the processes by which P losses are controlled so that P loss events may be simulated accurately over several years, and (iii) all parameters used to model these processes should be evaluated from independent experiments to ensure generality of model application. We propose to combine these three attributes in the ecosystem model ecosys (Grant, 2001) by coupling P transport processes (runoff, erosion, solute movement, leaching), solved on a time step of 1 min, with P transformation processes, both biological (microbial mineralization–immobilization, root uptake) and geochemical (adsorption–desorption, precipitation–dissolution), solved on a time step of 1 h. We propose to model biological transformations from basic theory of microbial ecology and to model geochemical transformations from thermodynamic equilibria of specific P reactions. Values for all parameters used to model these processes are taken from published experiments conducted independently of the model.

The ability of this coupled model of P transport and transformation to simulate individual P loss events from manured soils was first tested against dissolved and total P in runoff, sediment, and leachate measured during controlled rainfall applied to several soils with different manure management histories. The ability of this same model to simulate long-term P losses as the total of individual P loss events was investigated by modeling P losses during 60 yr of different manure application rates on one of the soils tested under controlled rainfall. The model's ability to simulate longer-term P losses will be tested later against measurements of dissolved and total P from manured watersheds using this model in three-dimensional mode.


   MODEL DEVELOPMENT
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
PHOSPHORUS RUNOFF EXPERIMENT
 MODEL APPLICATION
 RESULTS
 DISCUSSION
 REFERENCES
 
Inorganic Transformations
Precipitation–Dissolution
Precipitation–dissolution of P is simulated by concurrently solving the equilibrium reactions listed in Eq. [A1] to [A9] in the Appendix below for each spatial element defined by its north–south, east–west, and vertical position within a landscape. Each of these reactions is solved by calculating a flux Q such that:

[1]
where A, B, and C are soluble products with stoichiometric coefficients a, b, and c and where D and E are soluble reactants with stoichiometric coefficients d and e, all expressed as solution concentrations (mol m–3). The {gamma} terms in Eq. [1] represent solution activity coefficients calculated from ionic strength using the Davies relationship (Stumm and Morgan, 1970). Solubility constants K for these reactions were taken from Lindsay (1979) and Aggarwal et al. (1986).

Cation Exchange
Cation exchange is simulated by concurrently solving the Gapon equilibria listed in Eq. [A10] to [A15] below to calculate a flux Q for each spatial element such that:

[2]
and such that:

[3]
where A and B in Eq. [2] are cation pairs with valences a and b in solution (mol m–3) and in adsorbed forms XA and XB (mol Mg–1), and where {gamma} terms represent solution activity coefficients. In Eq. [3], {theta} is the soil water content (m3 m–3), n the number of exchangeable cation species N from Eq. [A10] to [A15], {rho} the soil density (Mg m–3), and CEC the cation exchange capacity (molc Mg–1). Gapon selectivity coefficients g used in Eq. [A10] to [A15] were taken from Reuss (1983) and Robbins et al. (1980).

Anion Exchange
Anion exchange is simulated by concurrently solving the adsorption equilibria listed in Eq. [A16] to [A20] below to calculate a flux Q for each spatial element such that:

[4]
and such that:

[5]
where A and B in Eq. [4] are anion pairs in solution (mol m–3) and in adsorbed forms XA and XB (mol Mg–1), {gamma} terms represent solution activity coefficients, and ß terms represent surface activity coefficients calculated from surface potential according to Stumm et al. (1980). In Eq. [5], {theta} represents soil water content (m3 m–3), n the number of exchangeable anion species N from Eq. [A16] to [A20], {rho} the soil density (Mg m–3), and AEC the anion exchange capacity (molc Mg–1). Intrinsic equilibrium constants c for protonation of the anion exchange sites (Eq. [A16], [A17]) are taken from Goldberg and Sposito (1984a)( 1984b). Intrinsic equilibrium constants c for phosphate exchange at these sites are calculated from Goldberg and Sposito (1984a)( HREF="#BIB8">1984b) to conform to the reactions (Eq. [A18]–[A20]) proposed by Ryden and Syers (1975).

Ion Pairs
Soluble ion pairing is calculated by concurrently solving the equilibrium reactions listed in Eq. [A22] to [A55] as described in Eq. [1]. Equilibrium constants in Eq. [A1] to [A55] remain unchanged for all model applications. Further details concerning the solutions to Eq. [A1] to [A55] are given in Grant and Heaney (1997).

Organic Transformations
Organic Matter Hydrolysis
Organic transformations in ecosys are based on four organic matter–microbe complexes: plant litterfall, animal manure, particulate organic matter, and humus, each of which consists of six organic states: substrate, soluble, sorbed, acetate (for methanogenesis), microbial biomass, and microbial residues, among which C, N, and P are transformed. Plant litterfall and animal manure are partitioned into carbohydrate, protein, cellulose, and lignin components, each of which is of differing vulnerability to hydrolysis by heterotrophic decomposers. Particulate organic matter and humus are also of differing vulnerability to hydrolysis.

The rate at which each component is hydrolyzed (DSi,j,C) is a first-order function of the active biomass of obligately aerobic, facultatively anaerobic, and obligately anaerobic heterotrophic decomposers Mi,a,C associated in each organic matter–microbe complex (Eq. [A56], [A57]). These rates are affected by the temperatures and water contents of surface detritus and those of a spatially resolved soil profile (Grant and Rochette, 1994). Microbial biomass in ecosys is thus an active agent of organic matter transformation rather than a passive organic state as in models that use first-order kinetics. The rate at which each component is hydrolyzed is also a function of substrate concentration [Si,C] that approaches first order at low concentrations, and zero order at high concentrations (Eq. [A58], [A59]). These rates are controlled by soil temperature through an Arrhenius function (Eq. [A60]) and by soil water content through its effect on aqueous microbial concentrations [Mi,a,C] (Eq. [A58], [A59]). Soil temperatures and water contents are calculated from surface energy balances and from heat and water transfer schemes through canopy–snow–residue–soil profiles. Release of P from hydrolysis of each component in each complex is determined by its P concentration (Eq. [A61], [A62]). Hydrolysis products are adsorbed or desorbed according to a power function of their soluble concentrations (Eq. [A63]–[A65]).

Microbial Growth, Respiration, and Decomposition
The concentration of soluble hydrolysis products [Qi,C] drives C oxidation by each heterotrophic microbial population Rgi,C (Eq. [A66]), the total of which drives CO2 emission from the soil surface. Heterotrophic oxidation rates may be constrained by temperature (Eq. [A66]), nutrients (Eq. [A67]), and O2 (Eq. [A68]). Oxygen uptake RO2i,C is driven by C oxidation (Eq. [A69]) and constrained by O2 diffusivity (Eq. [A70]), so that C oxidation is coupled to O2 reduction by all aerobic populations according to O2 availability (Grant et al., 1993a, 1993b; Grant and Rochette, 1994). Carbon oxidation not coupled with O2 is coupled with the sequential reduction of NO–3, NO–2, and N2O by heterotrophic denitrifiers (Grant et al., 1993c, 1993d; Grant and Pattey, 1999) and with the reduction of organic C by fermenters and heterotrophic methanogens (Grant, 1998a; Grant and Roulet, 2002). In addition, autotrophic nitrifiers conduct NH+4 oxidation and NO–3 production (Grant, 1994) and N2O evolution (Grant, 1995), and autotrophic methanogens and methanotrophs conduct CH4 production (Grant, 1998a) and oxidation (Grant, 1999).

All microbial populations in the model undergo maintenance respiration RMi,j,C (Eq. [A71], [A72]) and decomposition DMi,j,C (Eq. [A76], [A77]). Heterotrophic respiration in excess of maintenance requirements is used as growth respiration Rgi,C (Eq. [A73), the energy yield {Delta}G of which determines heterotrophic and autotrophic growth yields, and hence substrate consumption (Eq. [A74]) and P uptake (Eq. [A75]). Changes in microbial biomass arise from differences between substrate consumption and maintenance + growth respiration + decomposition (Eq. [A78]). During these changes, microbial populations seek to maintain equilibrium ratios of biomass C to N to P by mineralizing or immobilizing NH+4, NO–3, and H2PO–4 (Ii,j,P in Eq. [A79]), thereby controlling solution concentrations of inorganic N and P. Changes in microbial P arise from differences in organic P uptake plus inorganic P immobilization and microbial P decomposition (Eq. [A80]). Labile and resistant components of microbial biomass are used to calculate active microbial biomass Mi,a,C (Eq. [A81]), which then drives C oxidation (Eq. [A56], [A57]).

Humification of Products from Residue Hydrolysis and Microbial Decomposition
Carbon and P products of litterfall and manure hydrolysis DSi,j (Eq. [A56], [A61]) are transferred to the particulate organic matter complex at a rate HSi,j that depends upon lignin hydrolysis and soil clay concentration (Eq. [A82]–[A85]) according to stoichiometry proposed by Shulten and Schnitzer (1997). Carbon and P products of microbial decomposition DMi,j (Eq. [A76], [A77]) are transferred to the humus complex at a rate HMi,j that depends on soil clay content (Eq. [A86], [A87]; Grant et al., 1993a, 1993b).

Plant Uptake
Phosphorus uptake is calculated for each plant species in a complex biome by solving for the aqueous concentrations of H2PO–4 at both root and mycorrhizal surfaces in each rooted soil layer at which radial convective–dispersive transport from the soil solution equals active uptake by these surfaces. Active uptake is calculated from length densities and surface areas (Itoh and Barber, 1983) given by a root and mycorrhizal growth submodel (Grant, 1998b; Grant and Robertson, 1997). The products of P uptake are added to root and mycorrhizal storage pools from which they are combined with storage C when driven by growth respiration to form new plant biomass. The modeling of plant P uptake is described in more detail elsewhere (Grant, 1998b; Grant and Robertson, 1997).

Water Transport
Surface Flow
Surface flow is calculated as the product of runoff velocity v, depth of mobile surface water d, and width of flow paths L in west to east x and north to south y directions for each landscape position x,y (Eq. [A88]). Changes in the depth of surface water dw arise from differences in surface flows among adjacent landscape positions. Runoff velocity is calculated in x and y directions for each x,y from the hydraulic radius R, from slope s, and from Manning's roughness coefficient zr calculated from microtopographic roughness and particle size according to Morgan et al. (1998b). Slopes with easterly and southerly aspects have positive values (Eq. [A89a, A89b]), and those with westerly or northerly aspects have negative values (Eq. [A89c, A89d]). The depth of mobile surface water d in Eq. [A88] is the positive difference between depth of surface water dw + ice di and the maximum depth of surface storage ds, calculated from microtopographic roughness and slope according to Shaffer and Larson (1987). The value of dw arises from the difference between rates of precipitation and infiltration (described in the next paragraph). The calculation of R in Eq. [A89] assumes overland flow through triangular channels (Schwab et al., 1996) (Eq. [A91]). The slopes sx and sy in Eq. [A89] are the elevational gradients of water surfaces calculated in x and y directions for each x,y from the sum of ground surface elevation E, ds, and d (Eq. [A92]). Equations [A88] to [A92] thus implement the kinematic wave theory of overland water flow in which changes in horizontal flow plus changes in surface water depth equal the difference between rainfall and infiltration.

Subsurface Flow
Water fluxes (Qw in Eq. [A93]) are the product of hydraulic conductances K' and water potential {psi} differences in west to east x, north to south y, and vertical z directions for each landscape position x,y,z. Water potentials are the sum of matric, osmotic (multiplied by a reflection coefficient), and gravitational components. Conductances are calculated from the geometric means of the hydraulic conductivities K (Green and Corey, 1971) of adjacent landscape positions in x, y, and z directions (Eq. [A94a], [A95a], and [A96a]) unless {psi} of one of the positions exceeds its air entry potential {psi}e. In these cases conductance is calculated from hydraulic conductivity of the saturated position only (Eq. [A94b, A94c], [A95b, A95c], and [A96b, A96c]), and {psi} of the unsaturated position is calculated from a water content that excludes water added while {psi} of the first position of >{psi}e, thereby simulating a wetting front. Water movement between adjacent positions thus alternates between Richard's and Green–Ampt flow depending upon {psi} vs. {psi}e in each position. Water may also move through macropores driven by gravitational gradients and conductances calculated from Poiseuille–Hagen theory using set numbers and radii of macropore channels.

Solute Transport
Solute transport Qr{gamma} in x and y directions across the soil surface (Eq. [A97]) is calculated for each solute {gamma} in Eq. [A1] to [A55] from surface water flow Qr (Eq. [A88]) and surface solute concentration (Eq. [A98]). Solute transport Qs{gamma} in x, y, and z directions through the soil (Eq. [A99]) is calculated for each solute {gamma} as the sum of convective (from subsurface water flow Qw in Eq. [A93]) and dispersive–diffusive (Eq. [A100]) components. The concentrations of each solute by which transport is driven are generated from precipitation, ion exchange, and ion pairing reactions (Eq. [A1]–[A55]), and from production and consumption by roots, mycorrhizae (Grant, 1998b), and microbial communities (Eq. [A56]–[A87]).

Sediment Transport
Soil Detachment by Rainfall
The modeling of sediment transport in ecosys is based on that of Morgan et al. (1998a). Soil may be detached by kinetic energy of rainfall impact {kappa}, calculated from intensity of direct rainfall (Eq. [A101]) and from effective height of indirect rainfall (Eq. [A102]). Direct and indirect rainfall are calculated from interception and storage of precipitation by leaf and stem surfaces based on their area indices. Kinetic energy of direct plus indirect rainfall is reduced by surface water depth dw (Eq. [A90]). This energy is multiplied by soil detachability k, estimated from soil surface texture according to guide values in Morgan et al. (1998b), to calculate rate of soil detachment by rainfall Dr (Eq. [A103]).

Soil Detachment by Surface Flow
Soil detachment by surface flow Df (Eq. [A104]) is modeled in x and y directions as the difference between current sediment concentration in surface water [S] and that at transport capacity [Sc], where positive differences indicate detachment and negative differences deposition. Detachment is constrained by soil cohesion J (Eq. [A105]) estimated from soil texture and organic C content according to guide values in Morgan et al. (1998b). Sediment concentration at transport capacity (Eq. [A106]) is calculated from unit stream power {omega}, which is the product of slope and flow velocity (Eq. [A107]), and its critical value {omega}cr, using parameters based on median soil particle size according to Morgan et al. (1998a).

Sediment Transport
Sediment transport Qe (Eq. [A108]) is the product of sediment concentration in surface water [S] (Eq. [A109]) and surface water flow Qr in x and y directions (Eq. [A88]). Changes in surface sediment arise from soil detachment by rainfall plus soil detachment or deposition from surface flow, and from net sediment transport in x and y directions (Eq. [A110]). The transport of material in sediment (Eq. [A111]) is the product of sediment transport (Eq. [A108]) and the concentrations of precipitated plus exchangeable forms in the surface soil (Eq. [A1]–[A20]).


   PHOSPHORUS RUNOFF EXPERIMENT
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 PHOSPHORUS RUNOFF EXPERIMENT
MODEL APPLICATION
 RESULTS
 DISCUSSION
 REFERENCES
 
Composite 200-L soil samples were gathered during fall 2000 from the upper 10 cm of all replicate plots in each treatment of manure application trials conducted at six locations in central Alberta (Table 1). The soil was stored in waterproof, aerated containers until February 2001 when the soil was passed through a 1-cm sieve, mixed, sampled for extractable P content, and placed in a 50- x 95-cm stainless steel frames to a depth of 10 cm. These frames were designed to collect runoff and leachate during controlled rainfall events imposed by a rainfall simulator that consisted of two chambers each using a nozzle (Fulljet 1/2-HH-50WSQ; Spraying Systems, Wheaton, IL) operating 2.9 m above the target area. This nozzle, operating at 28 kPa at 3.0 m above a soil surface, produces rainfall-sized drops that fall within 2% of terminal velocity. Recent work has shown that this simulator produced raindrop distributions and velocities similar to those of natural rainfall. The average kinetic energy produced by this simulator (24.6 J m–2 mm–1) was about 85% of that measured in natural storms. Within each chamber, two frames were situated below the nozzle on tables with adjustable slopes, permitting up to four treatments to be rained on simultaneously. The nozzles were calibrated such that rainfall intensity was 65 mm h–1 and coefficient of uniformity was 95% in each frame. Further information about the rainfall simulator is given in Wright et al. (2002).


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  		Table 1. Locations and treatments of manure trials conducted in central Alberta from which soil P losses were measured.

 
The soil in each frame was first wetted by maintaining a water table 1 cm above the bottom of the frame for 18 h and then draining for 1 h. The frames were then tilted at a slope of 7% and rainfall was applied for 1.5 h. After the start of runoff, samples of runoff and sediment were collected from each frame for a period of 1 min, or until 300 mL of sample had been obtained, at time intervals that increased from 6 to 20 min as the rainfall event progressed. Leachate was collected from each frame for a period of 10 min every 30 min after the start of rainfall. Dissolved inorganic phosphorus (DIP) in each runoff and leachate sample was measured by the ascorbic acid reduction method (American Public Health Association, 1992) on a Technicon (Tarrytown, NY) II Automated Analyzer after passing the sample through a 0.45-µm paper filter. Total phosphorus (TP) in each runoff, sediment, and leachate sample was measured by digesting 50 mL of unfiltered sample in 2 mL of concentrated HCl for 15 min, and then decanting and measuring P concentration with inductively coupled plasma (ICP).


   MODEL APPLICATION
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 PHOSPHORUS RUNOFF EXPERIMENT
 MODEL APPLICATION
RESULTS
 DISCUSSION
 REFERENCES
 
The model experiment consisted of three stages: (i) the management history of each manure treatment at each field site was simulated so that the state of each soil sample could be modeled at the time of the controlled rainfall event; (ii) the controlled rainfall event was simulated for a modeled soil sample from each manure treatment at each field site and model results for P losses in runoff, sediment, and leachate were tested with measurements; and (iii) the tested model was then used to predict long-term P losses from different rates of manure application at one of the field sites.

Stage 1: Simulation of Management History
Ecosys was provided with the soil (Table 2) and manure (Table 3) properties and with the crop rotations (Table 1) at each of the six sites included in the P runoff experiment described above. To simulate management history, the model was run from 1 Jan. 1995 (Calmar, Devon, Lacombe, Ponoka) or 1 Jan. 1998 (Ellerslie, Cooking Lake) to 31 Oct. 2000 for each manure treatment (Table 1) on a time step of 3 min, assuming constant surface boundary conditions during each hour. Surface boundary conditions for these runs were taken from daily climate data (maximum and minimum temperatures, solar radiation, relative humidity, windspeed, and precipitation) compiled for the ecodistrict within which each site was located as part of the Alberta Drought Program, and resolved into hourly values by ecosys. During the 3 yr (Ellerslie, Cooking Lake) or 6 yr (Calmar, Devon, Lacombe, Ponoka) that the model was run to simulate management history, P was added to the soils listed in Table 2 according to the manure application rates and schedules shown in Table 1 and the compositions in Table 3. Phosphorus was also removed from the soil during the model runs through plant uptake according to aqueous H2PO–4 concentrations and root activity (Grant and Robertson, 1997), and through runoff, erosion, and leaching according to aqueous and total soil P concentrations.


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  		Table 2. Key properties of the upper 10 cm of soils at six locations in central Alberta from which P losses were measured.

 

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  		Table 3. Composition of hog and cattle manure used in the P loss study.

 
To simulate soil sampling and storage after completion of the field experiments but before the start of the P runoff experiment described above, each model run was continued from 1 Nov. 2000 to 31 Mar. 2001 on a time step of 1 min under controlled climate (20°C, no radiation, 99% relative humidity, no wind, no precipitation). These runs used only the upper 10 cm of each soil profile following a simulated tillage event of a 10-cm depth with full mixing on 1 Nov. 2000.

Stage 2: Simulation of Controlled Rainfall Event
Comparisons of modeled vs. measured P after 3 or 6 yr of manure applications (Table 4) provided an indirect test of model performance, but better-constrained tests at smaller temporal scales were necessary to test model algorithms described above. To accomplish such tests, the upper 0.10 m of the soil modeled for each manure treatment at each site (Table 2) was used to simulate P losses during short-term controlled rainfall events. Subsurface irrigation was applied on 1 Apr. 2001 of each model run at 1 mm h–1 for 18 h, after which the surface slope was set to 4° (7%) and rainfall was applied at 65 mm h–1 for 2 h with both surface runoff and subsurface drainage fully enabled. Because soil was sieved and packed into the runoff frames used in the physical experiment, macroporosity was set to zero in the model. Model output for DIP and TP losses in runoff, sediment, and leachate from each manure treatment were compared with values measured during the controlled rainfall events described above. In the model, DIP in runoff and leachate was calculated as: DIP = + + + (soluble P from Eq. [A5]–[A9], [A18]–[A20], and [A47]–[A55]). The TP in runoff + sediment was calculated as: TP = DIP in runoff + AlPO4(p) + FePO4(p) + Ca(H2PO4)2(p) + CaHPO4(p) + Ca5(PO4)3OH(p) (precipitated P from Eq. [A5]–[A9]) + X-H2PO4 + X-HPO–4 (exchangeable P from Eq. [A18]–[A20]) + {sum}Ii=1 [Qi,P + {sum}Jj=1 (Si,j,P + Zi,j,P + Mi,j,P)] (dissolved + solid organic P from Eq. [A56]–[A81]) in sediment. The term X denotes surface exchange site for cation or anion adsorption, while the term (p) is precipitated. The organic + inorganic phosphorus in leachate (LP) was calculated as: LP = DIP in leachate + {sum}Ii=1 Qi,P (dissolved organic P) in leachate.


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  		Table 4. Exchangeable P measured (M) and simulated (S) in 0.10-m soil columns after 3 yr (Ellerslie, Cooking Lake) or 6 yr (Calmar, Devon, Lacombe, Ponoka) of different manure treatments.

 
Lengths Lx, Ly, and Lz for each row, column, and layer in ecosys are set by the model user to best represent spatial variability and to best resolve model processes at the site being simulated. For these simulations, Lx and Ly were set to 0.50 and 0.95 m, respectively, to simulate the size of the soil frames used in the P runoff experiment. The term Lz was set to 0.005, 0.020, 0.025, 0.050, 0.050, 0.15, 0.30, 0.30, and 0.30 m for z = 1 to 9 so as to resolve surface processes (energy exchange, surface flow of water, solutes, and sediment) and subsurface processes (soil heat, water, and solute transfers) during the simulated management history in Stage 1 above. Only z = 1 to 4 were mixed and used in the simulated P runoff experiment described in Stage 2.

Stage 3: Predicting Long-Term Phosphorus Losses from Manure Application
To demonstrate model application, ecosys was then used to examine the long-term impact of manure applications on water quality by running the model for 60 yr under repeated sequences of 1995–2000 daily climate data with the manure treatments and cropping systems at Lacombe (Table 1). A key assumption used by ecosys to convert these data to hourly values was that daily rainfall occurred uniformly from 1500 to 1700 h. Model output for P loss was compared with current water quality guidelines to determine environmentally acceptable manure application rates for this site.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 PHOSPHORUS RUNOFF EXPERIMENT
 MODEL APPLICATION
 RESULTS
DISCUSSION
 REFERENCES
 
Stage 1: Phosphorus Accumulation in Soil during Manure Application Trials
At the end of each 3- or 6-yr simulation of management history, exchangeable P in the model (X-H2PO4 + X-HPO–4 from Eq. [A18]–[A20]) was compared with exchangeable P estimated from modified Kelowna extractions conducted on soil from each manure treatment according to a relationship established by McKenzie et al. (1995) (Table 4). Three to six years of hog and cattle manure applications raised exchangeable P above control values, especially the large annual applications of cattle manure at Lacombe and Ponoka. These large applications caused exchangeable P modeled and measured at both Lacombe and Ponoka to exceed 0.25 of anion exchange capacity (Table 2). Ratios above this value were found by Breeuwsma and Silva (1992) to cause potentially unacceptable P movement into surface and ground waters. Rises in exchangeable P modeled for a given manure treatment were larger than those measured at Calmar, and smaller than those at Devon. Rises in exchangeable P modeled for manure treatments at Ellerslie, Cooking Lake, Lacombe, and Ponoka were close to those measured.

Stage 2: Phosphorus Loss in Runoff and Sediment during Controlled Rainfall
Model results from the controlled rainfall events on the soils at each site are presented below.

Calmar
In the model, simulated runoff (Eq. [A88]) began 5 min after the start of controlled rainfall and rose rapidly to near the rate of rainfall after 10 min. The time course of modeled runoff was similar to that of measured runoff during controlled rainfall in the hog and cattle manure treatments (Fig. 1a) , although the time course of runoff measured from the unmanured soil was atypically slower. Sediment loss in the model (Eq. [A108]) rose to 0.4 kg m–2 h–1 between 5 and 10 min after the start of rainfall, and stabilized thereafter as sediment concentrations equilibrated (Fig. 1b). Slightly lower sediment losses were modeled at higher manure application rates because resulting increases in organic C concentrations raised soil cohesion (Eq. [A105]). Concentrations of DIP modeled and measured in runoff remained <0.1 mg L–1 during controlled rainfall on the unmanured soil, and <0.2 mg L–1 on the manured soils (Fig. 1c). Higher DIP concentrations modeled in runoff from manured soils was caused by higher exchangeable P concentrations (Table 4) with which DIP was in equilibrium (Eq. [A18]–[A20]). Concentrations of TP in runoff (Eq. [A97]) and sediment (Eq. [A111]) were 12 to 15 mg L–1 at the start of runoff but equilibrated at approximately 7.5 mg L–1 after 5 min of runoff (Fig. 1d) once sediment flux had stabilized (Fig. 1b). Higher TP concentrations were modeled early in the rainfall event because soil detachment by rainfall impact (Eq. [A103]) contributed to surface sediment as soon as surface water appeared and before runoff began. This previously detached sediment caused higher sediment and hence TP concentrations to be modeled during the first few minutes of runoff. As surface water deepened with continued rainfall, soil detachment by rainfall impact declined and that by surface flow rose (Eq. [A104]). Higher TP concentrations modeled from the manured soils were attributed to higher exchangeable (Table 4), precipitated, and organic P concentrations. Differences between modeled and measured concentrations of DIP and TP were close to the standard errors of measured values during most of the rainfall event.



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  		Fig. 1. (a) Runoff, (b) sediment loss, (c) dissolved inorganic phosphorus (DIP) concentration in runoff, and (d) total phosphorus (TP) loss in runoff and sediment, measured (symbols with vertical bars showing standard error) and modeled (lines) during 90 min of controlled rainfall on soils after 6 yr of different manure treatments (H, hog; C, cattle) at Calmar (see Table 1).

 
Devon
The time course of modeled runoff was similar to that measured, and was not affected by manure treatment (Fig. 2a) . Modeled sediment loss rose rapidly to 0.3 kg m–2 h–1 after the start of runoff (Fig. 2b), less than that at Calmar because mean particle size was larger and hence sediment transport capacity was smaller (Table 2; Eq. [A106]). Sediment loss in the model was consistent with that measured from the check and the triennial hog manure treatment, but was less than that measured in the other manure treatments. The DIP concentrations modeled and measured in runoff (Fig. 2c) were larger than those for the same manure treatments at Calmar (Fig. 1c) because exchangeable P at Devon was higher (Table 4) and anion exchange capacity was lower (Table 2). Modeled DIP concentrations were only approximately two-thirds of those measured for all treatments, which was consistent with the lower exchangeable P modeled vs. measured at this site (Table 4). Modeled TP concentrations in runoff and sediment declined during early runoff from 14 to 5 mg L–1, above those measured from the check and hog manure treatments, but lower than those from the cattle manure treatments (Fig. 2d). Modeled TP concentrations were lower than those at Calmar because sediment loss was less. These differences could not be corroborated because of variation in the measured losses.



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  		Fig. 2. (a) Runoff, (b) sediment loss, (c) dissolved inorganic phosphorus (DIP) concentration in runoff, and (d) total phosphorus (TP) loss in runoff and sediment, measured (symbols with vertical bars showing standard error) and modeled (lines) during 90 min of controlled rainfall on soils after 6 yr of different manure treatments (H, hog; C, cattle) at Devon (see Table 1).

 
Ellerslie
The time course of runoff modeled at this site was more rapid than that measured (Fig. 3a) , although sediment loss of 0.25 kg m–2 h–1 was within the SE of measured values (Fig. 3b). Sediment loss modeled at Ellerslie was less than that modeled at Calmar because higher organic C concentrations (Table 2) raised soil cohesion (Eq. [A105b]). Both modeled and measured DIP concentrations in runoff were <0.2 mg L–1 for all treatments (Fig. 3c) because the soil at this site had comparatively low exchangeable P and high anion exchange capacity (Table 2). Effects of manure application on DIP concentrations were small because total manure P application was low (Table 1). The TP concentrations modeled from this soil declined from 10 to <5 mg L–1, lower than those at Calmar and Devon because exchangeable P concentrations (Table 4) and sediment losses (Fig. 3b vs. Fig. 1b and 2b) were lower.



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  		Fig. 3. (a) Runoff, (b) sediment loss, (c) dissolved inorganic phosphorus (DIP) concentration in runoff, and (d) total phosphorus (TP) loss in runoff and sediment, measured (symbols with vertical bars showing standard error) and modeled (lines) during 90 min of controlled rainfall on soils after 3 yr of different manure treatments (H, hog; C, cattle) at Ellerslie (see Table 1).

 
Cooking Lake
As at Ellerslie, the time course of modeled runoff was more rapid than that measured (Fig. 4a) , although sediment loss was within the SE of measured values (Fig. 4b). Sediment loss modeled at Cooking Lake (0.35 kg m–2 h–1 in Fig. 4b) was more rapid than that at Ellerslie (0.25 kg m–2 h–1 in Fig. 3b) because organic C (Table 2) and hence soil cohesion (Eq. [A105b]) were lower, even though mean particle size was larger. Both modeled and measured DIP concentrations in runoff were slightly higher than those for the same treatments at Ellerslie because exchangeable P at Cooking Lake was higher (Table 4) and anion exchange capacity was lower (Table 2). The TP concentrations modeled and measured from this soil were <5 mg L–1 (Fig. 4d), similar to those at Ellerslie (Fig. 3d).



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  		Fig. 4. (a) Runoff, (b) sediment loss, (c) dissolved inorganic phosphorus (DIP) concentration in runoff, and (d) total phosphorus (TP) loss in runoff and sediment, measured (symbols with vertical bars showing standard error) and modeled (lines) during 90 min of controlled rainfall on soils after 3 yr of different manure treatments (H, hog; C, cattle) at Cooking Lake (see Table 1).

 
Lacombe
The time course of modeled runoff was more rapid than that measured (Fig. 5a) and modeled sediment loss was lower (Fig. 5b), although similar to sediment losses modeled and measured at other sites (Fig. 1a, 2a, 3a, and 4a). The large amount of organic C applied in the manure treatments at this site (Table 2) raised soil cohesion (Eq. [A105b]) and reduced modeled sediment loss below that from the unmanured soil. Corresponding reductions were apparent in the measured sediment losses. The large amount of organic P applied at this site (Table 2) caused large rises in exchangeable P (Table 4) and hence in DIP concentrations (>1.0 mg L–1) modeled and measured in runoff (Eq. [A16]–[A21]) (Fig. 5c). These large applications also caused increases in modeled TP concentrations (Eq. [A111]), especially during early runoff because of soil detachment by rainfall (Fig. 5d; Eq. [A103]), although differences in measured TP concentrations were not clear.



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  		Fig. 5. (a) Runoff, (b) sediment loss, (c) dissolved inorganic phosphorus (DIP) concentration in runoff, and (d) total phosphorus (TP) loss in runoff and sediment, measured (symbols with vertical bars showing standard error) and modeled (lines) during 90 min of controlled rainfall on soils after 6 yr of different manure treatments (H, hog; C, cattle) at Lacombe (see Table 1).

 
Ponoka
As at Lacombe, the time course of modeled runoff was more rapid than that measured (Fig. 6a) and modeled sediment loss was lower (Fig. 6b). Large manure P applications at this site (Table 1) raised exchangeable P (Table 4) and hence raised DIP (Fig. 6c) and TP (Fig. 6d) concentrations in runoff. There was some evidence that TP concentrations measured early in the rainfall event also rose with manure application.



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  		Fig. 6. (a) Runoff, (b) sediment loss, (c) dissolved inorganic phosphorus (DIP) concentration in runoff, and (d) total phosphorus (TP) loss in runoff and sediment, measured (symbols with vertical bars showing standard error) and modeled (lines) during 90 min of controlled rainfall on soils after 6 yr of different manure treatments (H, hog; C, cattle) at Ponoka (see Table 1).

 
Stage 2: Phosphorus Loss in Leachate during Controlled Rainfall
The comparatively small amounts of P added as hog and cattle manure at Calmar and Devon (Table 1) caused modeled LP (Eq. [A99] at lower boundary) to be raised by only 2 to 4 mg m–2 h–1 from nonmanure rates (Table 5). The LP modeled at Calmar was similar to that measured. However, LP modeled at Devon was less than that measured, which was consistent with lower modeled vs. measured exchangeable P before the controlled rainfall experiment (Table 4) and lower modeled vs. measured runoff DIP during the experiment (Fig. 2c). These lower values indicated that the model did not simulate the full amount of P that accumulated in the soil from the manure applications reported at Devon (Table 1). However, ecosys may have simulated P losses from the modeled accumulation accurately. Both modeled and measured LP at Ellerslie and Cooking Lake were raised by only 1 to 3 mg m–2 h–1 from nonmanure rates (Table 5). The low LP modeled at Ellerslie was caused by low exchangeable P (Table 4) and high anion exchange capacity (Table 2) that caused low (Eq. [A16]–[A21]). The large amounts of P added as cattle manure at Lacombe and Ponoka (Table 1) caused increases from 10 to 100 mg m–2 h–1 in both modeled and measured LP due to high concentrations of exchangeable and soluble P (Table 4). The amount and timing of LP in the model was affected by the assumed absence of soil macropores.


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  		Table 5. Average fluxes of total P in leachate measured (M ± standard error) and simulated (S) from 0.10-m soil columns with different manure treatments during 90 minute controlled rainfall events.

 
Stage 3: Long-Term Rates of Phosphorus Loss from Field Applications of Manure
The large amounts of P lost in surface and subsurface water flows during controlled rainfall events on the manure-treated soils at Lacombe and Ponoka (Fig. 5c and 6c, Table 5) caused concern about the long-term environmental impacts of the manure applications at these sites. To simulate these impacts, the model of short-term P loss dynamics tested above was used as part of ecosys in 60-yr model runs under repeated sequences of 1995–2000 climate data and cropping practices for the Lacombe ecodistrict. Results from these runs indicated that large increases in the mass and concentration of P in runoff and sediment from manured soils occurred with higher application rates, especially during years with higher rainfall as occurred in 1996 and every 6 yr thereafter in the model run (Fig. 7) . There was an underlying trend toward greater P losses over time in all the manure treatments that became more pronounced at higher application rates. This trend accelerated after 30 yr of manure applications of >60 Mg ha–1 yr–1 as the capacity of the modeled soil profile to retain additional P through adsorption (Eq. [A18]–[A20]), precipitation (Eq. [A5]–[A9], and immobilization (Eq. [A79b]) was exceeded. When this occurred, P losses rose above 1 g m–2 yr–1 (Fig. 7a) and TP concentrations in runoff and sediment exceeded 5 mg L–1 (Fig. 7b). The trend toward greater P losses over time was not apparent in the unmanured soil where P losses remained <0.1 g m–2 yr–1 (TP concentrations of approximately 0.5 mg L–1) and gradually declined with continued removal of P by crops. This model result is consistent with the finding of Heckrath et al. (1995) that P concentrations in water drained from field plots under long-term manure application rose with higher soil P concentrations once a threshold soil P concentration was exceeded. The time course of rises in modeled P losses depended upon values for anion exchange capacity estimated for lower soil layers, and on assumptions about macropore volume used in macropore flow calculations.



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  		Fig. 7. (a) Mass and (b) concentration of total P in runoff and sediment modeled with annual applications of 0, 30, 60, 90, and 120 Mg ha–1 of cattle manure (Table 3) during 60 yr under repeated sequences of 1995–2000 climate data for the Lacombe ecodistrict (annual precipitation in 1995 = 435 mm, 1996 = 604 mm, 1997 = 534 mm, 1998 = 466 mm, 1999 = 450 mm, 2000 = 461 mm). Note logarithmic scale on vertical axis.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MODEL DEVELOPMENT
 PHOSPHORUS RUNOFF EXPERIMENT
 MODEL APPLICATION
 RESULTS
 DISCUSSION
REFERENCES
 
The detailed nature of the algorithms in this model enabled a wide range of site, soil, management, and climate conditions to be represented in the modeling of P losses, allowing versatility in model use. Although the model appears complex, it is well constrained because its parameters are defined and evaluated independently of the model at spatial and temporal scales smaller than those of prediction. Consequently, model parameterization does not require calibration with measured P losses that may be controlled by site-specific conditions not accounted for in the model. However, the model does require more detailed information about site conditions (e.g., soil properties) than do simpler models that may limit its application at sites about which little is known. The application of this model to such sites will depend upon ongoing development of pedotransfer functions for key hydrologic properties (e.g., field capacity, wilting point, saturated conductivity) and erosional properties (e.g., soil detachability, cohesion, mean particle size) derived from more readily available soil properties such as texture and organic C content.

The use of algorithms for thermodynamic equilibria to simulate geochemical P transformations (Eq. [A1]–[A55] using Eq. [1]–[ 5]) is a key difference between ecosys and other detailed models of P loss events. These algorithms were subjected to detailed testing during the controlled rainfall events in Stage 2 of the model experiment. Dynamic solutions to these thermodynamic equilibria allowed the model to simulate the declines from initial to equilibrium concentrations of DIP in runoff water that were measured during controlled rainfall events (Fig. 1c, 2c, 3c, 4c, 5c, and 6c). These equilibrium concentrations occurred in the model when rates of DIP loss in runoff (Eq. [A97]) equaled rates of P desorption (Eq. [A18]–[A20]) plus dissolution (Eq. [A5]–[A9]) in the surface soil layer (the upper 5 mm of the soil profile) plus rates of upward P solute transport (Eq. [A99]) from the soil layers below, sustained by rates of P desorption and dissolution in the lower layers. Modeled vs. measured equilibrium DIP concentrations during controlled rainfall were thus a test of the combined kinetics of transport and transformation in the model. These equilibrium concentrations rose with manure application rates because thermodynamic equilibria in the model allowed higher and to be maintained through transport and transformation processes in soils to which more manure had been applied (Table 4). During a series of controlled rainfall events, Sharpley (1995) also found that DIP concentrations in runoff declined toward equilibrium values that rose with manure P application rates similarly to those reported here.

Modeled DIP losses in runoff, calculated as the product of runoff rate (Fig. 1a, 2a, 3a, 4a, 5a, and 6a) and DIP concentrations (Fig. 1c, 2c, 3c, 4c, 5c, and 6c) approximated those measured at all sites except Devon where they were underestimated (Fig. 2). The DIP concentrations modeled from thermodynamic equilibria also contributed to modeled LP (Table 5), which rose only slightly with the lower manure application rates at Calmar, Devon, Cooking Lake, and Ellerslie, but rose sharply with the higher application rates at Lacombe and Ponoka. The higher DIP concentrations in runoff and leachate at Lacombe and Ponoka were modeled when the ratio of exchangeable P (Table 4) to anion exchange capacity (Table 2) exceeded 0.25, a ratio above which Breeuwsma and Silva (1992) found that P losses may cause adverse environmental impacts. The relationship between this ratio and DIP in runoff modeled and measured here was very similar to that found for several diverse soils by Sharpley (1995). For example, the ratios of approximately 0.1, approximately 0.3, and approximately 0.5 modeled and measured for the 0, 60, and 120 Mg ha–1 yr–1 treatments, respectively, at Lacombe and Ponoka (Table 4 vs. Table 2) were found by Sharpley (1995) to correspond to DIP concentrations in runoff of 0.25, 0.83, and 1.4 mg L–1, respectively, close to those modeled and measured for these treatments early in the rainfall event (Fig. 5c and 6c). Changes in DIP concentrations modeled and measured during controlled rainfall indicate that the relationship between DIP concentrations and the ratio of exchangeable P to anion exchange capacity will vary with the intensity and duration of rainfall. Therefore the thermodynamic equilibria used in this model of P loss would benefit from testing under rainfall intensities and durations more typical of natural events.

Modeled and measured TP losses from sediment transport (Eq. [A108]) (Fig. 1d, 2d, 3d, 4d, 5d, and 6d) were an order of magnitude greater than those from DIP in runoff (Fig. 1c, 2c, 3c, 4c, 5c, and 6c), indicating that the accurate simulation of sediment loss (Fig. 1b, 2b, 3b, 4b, 5b, and 6b) is vital to that of P loss. Sediment loss in the model was sometimes lower than that measured, notably at Lacombe and Ponoka (Fig. 5b and 6b), but was frequently within standard errors of measured values at the other sites (Fig. 1b, 2b, 3b, and 4b). The underestimation at Lacombe and Ponoka could have been corrected by using the lower values of soil cohesion (Eq. [A105b]) for uncompacted soils given in Morgan et al. (1998b). High rates of manure application reduced sediment loss in the model by raising soil cohesion, although corresponding reductions in measured sediment loss were apparent only at Lacombe and Ponoka where manure C additions were largest (Fig. 5b and 6b). Phosphorus loss through sediment transport in the model (Eq. [A111]) also depended on sediment TP concentrations, which rose with manure application rates (Fig. 1d, 2d, 3d, 4d, 5d, and 6d). These concentrations caused modeled P losses through sediment transport to rise with manure application rate even though sediment transport declined (Fig. 1b, 2b, 3b, 4b, 5b, and 6b). These modeled rises were small except at Lacombe and Ponoka where manure application rates were highest. The effect of manure application on measured TP losses was variable. Soil transformations during several months of storage in 200-L containers (depth = 1 m) could have affected measured results.

Results from Stage 2 of the model experiment showed that DIP and TP losses were caused by short-term runoff and sediment transport events that particularly occur during intense rainfall events when soil infiltration rates are exceeded. Annual P losses modeled in Stage 3 were the sum of several short-term P losses driven by such events. These losses therefore rose sharply when high manure application rates coincided with high rainfall (Fig. 7). These rises suggest that estimates of long-term manure application rates designed to avoid adverse environmental impacts should be made under highest likely rates of rainfall rather than under long-term average rainfall. For example, if TP concentrations of <1 mg L–1 need to be maintained in surface and subsurface water leaving the Lacombe site, then application of cattle manure with the composition given in Table 3 would have to be limited to 30 Mg ha–1 yr–1. Applications of 60 Mg ha–1 yr–1 would cause this concentration to be consistently exceeded within 10 yr, while higher applications would cause this concentration to be exceeded immediately. Applications of 60 Mg ha–1 yr–1 at Lacombe would cause P losses during high rainfall years to exceed 0.87 g P m–2 yr–1 (the target for P loss in the Netherlands by 2010) after 30 yr. The impacts of these P losses on surface and subsurface water quality could be assessed by testing and then using ecosys in three-dimensional mode to simulate P loading rates at a watershed scale. Such assessments are currently in progress.

The use of detailed ecosystem models such as ecosys to estimate P losses from manure applications addresses the need identified by Sharpley (1995) for a comprehensive approach that integrates soil P levels with variability in runoff and erosion caused by climatic, topographic, edaphic, and agronomic factors. Such models can also be used concurrently to assess other adverse environmental impacts of manure application, such as emissions of N2O (Grant and Pattey, 1999, 2003) and CH4 (Grant, 1998a, 1999; Grant and Roulet, 2002), needed in comprehensive studies of manure in agricultural ecosystems.

APPENDIX

Inorganic Transformations

Transformation
 Notes
 Value
 Equation
Precipitation–dissolution
Al(OH)3(p) {leftrightarrow} (Al3+) + 3(OH–) amorphous Al(OH)3 –33.0 [A1]
Fe(OH)3(p) {leftrightarrow} (Fe3+) + 3(OH–) soil Fe –39.3 [A2]
CaCO3(p) {leftrightarrow} (Ca2+) + calcite –9.28 [A3]
CaSO4(p) {leftrightarrow} (Ca2+) + gypsum –4.64 [A4]
AlPO4(p) {leftrightarrow} (Al3+) + variscite –22.1 [A5]
FePO4(p) {leftrightarrow} (Fe3+) + strengite –26.4 [A6]
Ca(H2PO4)2(p) {leftrightarrow} (Ca2+) + 2 monocalcium phosphate –1.15 [A7]
CaHPO4(p) {leftrightarrow} (Ca2+) + monetite –6.92 [A8]
Ca5(PO4)3OH(p) {leftrightarrow} 5(Ca2+) + 3 + (OH–) hydroxyapatite –58.2 [A9]
Cation exchange
X-Ca + 2 {leftrightarrow} 2X-NH4 + (Ca2+) 1.00 [A10]
3X-Ca + 2(Al3+) {leftrightarrow} 2X-Al + 3(Ca2+) 1.00 [A11]
X-Ca + (Mg2+) {leftrightarrow} X-Mg + (Ca2+) 0.60 [A12]
X-Ca + 2(Na+) {leftrightarrow} 2X-Na + (Ca2+) 0.16 [A13]
X-Ca + 2(K+) {leftrightarrow} 2X-K + (Ca2+) 3.00 [A14]
X-Ca + 2(H+) {leftrightarrow} 2X-H + (Ca2+) 1.00 [A15]
Anion exchange
X-OH+2 {leftrightarrow} X-OH + (H+) –7.35 [A16]
X-OH {leftrightarrow} X-O– + (H+) –8.95 [A17]
X-H2PO4 + H2O {leftrightarrow} X-OH+2 + –2.80 [A18]
X-H2PO4 + (OH–) {leftrightarrow} X-OH + 4.20 [A19]
X-HPO–4+ (OH–) {leftrightarrow} X-OH + 2.60 [A20]
X-COOH {leftrightarrow} X-COO– + (H+) –5.00 [A21]
Ion pairs
{leftrightarrow} (NH3)g + (H+) –9.24 [A22]
H2O {leftrightarrow} (H+) + (OH–) –14.3 [A23]
(CO2)g + H2O {leftrightarrow} (H+) + –6.42 [A24]
{leftrightarrow} (H+) +