81 4 Basic Approaches to Modeling Phosphorus Leaching Nathan O. Nelson Kansas State University, Manhattan, KS John E. Parsons* North Carolina State University, Raleigh, NC CONTENTS 4.1 Introduction 81 4.2 Functional Definition of P Leaching 83 4.3 Model Components Affecting P Leaching 83 4.3.1 Hydrology 83 4.3.1.1 Vertical Flow 83 4.3.1.2 Nonequilibrium and Preferential Flow 86 4.3.1.3 Lateral Flow 89 4.3.2 Phosphorus Chemistry 90 4.3.2.1 Inorganic P Leaching 90 4.3.2.2 Dissolved Organic P Leaching 96 4.3.2.3 Preferential and Subsurface Particulate P Transport 96 4.4 Model Evaluation 97 4.5 Conclusions 98 References 99 4.1 INTRODUCTION Leaching is an active process in the phosphorus (P) cycle, thereby affecting P transport in agroecosystems. Although subsurface P transport is not the predominant loss path- way in most regions (Hansen et al. 2002; Lemunyon and Daniel 2002; Osborne and Kovacic 1993; Peterjohn and Corell 1984), there is increasing evidence of vertical P movement in soils when P applications exceed crop P removal over extended periods of time. For example, many studies have documented elevated subsoil P concentrations * Deceased © 2007 by Taylor & Francis Group, LLC 82 Modeling Phosphorus in the Environment resulting from repeated waste applications (King et al. 1990; Maguire et al. 2000; Mozaffari and Sims 1994; Nelson et al. 2005; Novak et al. 2002; Sharpley et al. 1984a). Leaching processes affect P distribution within the soil, removing P from surface horizons where it would be available for crop uptake or loss through runoff and erosion. In soils with low P sorption capacities, leaching can potentially remove more P from the root zone than crop uptake (Nelson et al. 2005). P can also be lost to surface waters through leaching and subsurface transport in soils where P loading exceeds crop P removal (resulting in a high soil test P), P sorption capacities are low (sandy or organic soils), and subsurface transport is expedited by artificial drainage systems. Sims et al. (1998) reviewed past research and found evidence indicating that subsurface P losses from tile-drained lands can be an environmentally significant component of the total P exported from agricul- tural watersheds, where 4 of 21 studies had tile drainage P concentrations > 0.3 mg L −1 . Culley and Bolton (1983) estimated that tile drainage contributed 25% of total P and 50% of dissolved P exported from a 51-km 2 watershed in Ontario, Canada. An adequate description of P leaching is an important component of modeling the fate and transport of P in the environment. As with other model processes, an adequate model for describing P leaching is dependent on the characteristics of the agroecosystem being modeled and the modeling objectives. Because most soils have strong P sorption characteristics, P has historically been considered immobile within soils; therefore, most watershed- and field-scale models tend to underestimate ver- tical and subsurface P transport. However, accurately representing P leaching pro- cesses is important in long-term simulations with excessive P applications (e.g., with animal waste). In these cases, underestimation of P leaching can result in unrealis- tically high estimates of P accumulation in surface soils, potentially overestimating P loss through erosion and overland flow (Knisel 1993; Stone et al. 2001). It is important to consider subsurface pathways in artificially drained soils because subsurface drainage can be an order of magnitude greater than surface runoff; therefore, relatively low P concentrations in subsurface drainage can pro- duce greater P losses than from surface runoff (Deal et al. 1986). Excessive accumulation of P in soils buffers soil solution P concentrations to changes in management. Therefore, P leaching losses from artificially drained soils can con- tinue for many years after initial detection of increased P concentrations in drain- age waters, despite changes in management practices (Breeuwsma and Silva 1992; Schoumans and Groenendijk 2000). Unremediable circumstances could eventually result if traditional models, which focus on P loss through surface pathways and underestimate P leaching losses, are used to decide issues with long-term conse- quences, such as siting of confined animal feeding operations. Computer models, with accurate P leaching subroutines, are therefore a primary tool in the prevention of P leaching losses from tile-drained soils and the protection of ecologically sensitive water bodies in regions dominated by sandy soils, such as the eastern U.S. coastal plain. The objective of this chapter is to develop a framework for evaluating a model with respect to its capabilities to describe, in part or entirety, P transport from field to surface waters through leaching processes and subsurface flow pathways. © 2007 by Taylor & Francis Group, LLC Basic Approaches to Modeling Phosphorus Leaching 83 4.2 FUNCTIONAL DEFINITION OF P LEACHING A complete description of P leaching processes requires continuity and conservation of mass to describe P movement from the soil surface through the profile with eventual delivery to surface water — through tile drainage or interflow — or deep ground water. Because this is a complex process, mostly occurring on a time scale of decades or more, P leaching is often either ignored or simplified as one of the following partial descriptions: Vertical movement of P past a given depth, such as the bottom of a specific soil layer: surface horizon, root zone, or soil pedon Delivery of P to surface water through subsurface flow by means of a user-supplied or management-dependent P concentration in interflow and tile drainage Furthermore, a single model may use both partial descriptions but may lack the continuity and conservation of mass linking them in an actual setting. 4.3 MODEL COMPONENTS AFFECTING P LEACHING Incorporating complete or partial descriptions of P leaching into a simulation model requires coupling models that describe system hydrology and P transformations (Figure 4.1). Although a watershed model may handle hydrology separately from P transformations, the methods used to describe the hydrology will affect the output from the P reaction/transport submodel. For example, simplifications in model hydrology may preclude more complex descriptions of P transformation and trans- port since some of the water fluxes and content distributions may not be simulated. 4.3.1 H YDROLOGY A wide range of techniques is used for modeling water movement through soils with a correspondingly wide range of complexities. This chapter is not meant to be a complete review of these techniques but rather a brief review of the techniques as they affect the model capabilities to simulate P leaching, with a focus on methods employed by models described in subsequent chapters. Modeling the complete leaching process requires, at minimum, a hydrological model with two-dimensional water flow. In the unsaturated soil, lateral water fluxes can be assumed to be negli- gible and vertical flow dominates; however, lateral flow in the saturated portion of the soil is necessary for describing flow to surface waters. 4.3.1.1 Vertical Flow The one-dimensional Richards equation offers the most complete description of vertical water movement in soils and is (4.1)Ch h tz Kh h z Kh z () () ()∂ ∂ = ∂ ∂ ∂ ∂       − ∂ ∂ © 2007 by Taylor & Francis Group, LLC 84 Modeling Phosphorus in the Environment where h is the matric potential (cm), K(h) is the unsaturated hydraulic conductivity (cm h −1 ) expressed as a function of matric potential, z is the depth (cm), t is time (h), and C(h) is the capacitance function or d/dh (cm 3 cm −3 cm −1 ) where θ is the volu- metric water content (cm 3 cm −3 ). This is referred to as the h-based formulation and is more easily applied in situations with the presence of a water table. The Richards equation is frequently used for modeling water flow in laboratory column leaching studies (Porro et al. 1993), occasionally used in field-scale water quality models such as SWATRE and Root Zone Water Quality Model (RZWQM) (Jacques et al. 2002; Johnsen et al. 1995) but is seldom used for watershed-scale models. The Richards equation allows simulation of unsaturated water flow and typically uses relatively small temporal and spatial increments, thus facilitating the use of the advection-dispersion equation (ADE), also known as the advection- dispersion-reactive equation or convection-dispersion equation (Leij and van Genu- chten 2002; Parsons 1999; Wierenga 1995). Drawbacks to the Richards equation are that (1) boundary conditions can be difficult to define especially for continuous models; (2) it requires computationally intensive numerical solutions that tend to be susceptible to numerical instabilities and may not converge to a solution; and (3) generally it requires labor-intensive inputs to describe the relationship among soil moisture tension, water content, and hydraulic conductivity. These drawbacks, com- bined with the high spatial variability of soil properties, prohibit routine implemen- tation of the Richards equation at field and watershed scales. However, inputs may be adequately estimated from soil texture alone (Starks et al. 2003), potentially removing the requirement for intensive soil characterization. A much simpler approach for estimating percolation uses a simplified field capacity-water balance (FCWB) method — also referred to as the cascade method, or plate theory method — in which soil water in excess of a measured or user- defined field capacity flows to the underlying soil horizon (Diekkruger et al. 1995; FIGURE 4.1 General soil P transformations and subsurface transport pathways in cross- sectional views of naturally drained and artificially drained landscapes. Base Flow Interflow Tile Drainage Vertical Flow Stream Soil Surface Drain Tile Ver tical Flow Soil Surface Adsorbed P Mineral P adsorption desorption precipitation dissolution Solution P Soil P Transformations HPO 4 2- H 2 PO 4 - Organic P immobilization mineralization Organic P © 2007 by Taylor & Francis Group, LLC Basic Approaches to Modeling Phosphorus Leaching 85 Wegehenkel 2000). The general equation for determining percolation by the field capacity method is Perc = (SWC – FC) * β if SWC > FC, (4.2) Perc = 0 if SWC ≤ FC, (4.3) where Perc is the percolation (cm), SWC is the soil water content of the layer (cm), FC is the field capacity of the layer (cm), and β is a coefficient that determines the fraction of soil water excess (SWC – FC) that can drain during a time step, usually a function of saturated hydraulic conductivity. The simplifications of the FCWB method greatly reduce the computational complexity and the required inputs com- pared to the Richards equation. Although the FCWB method requires fewer soil parameters than the Richards equation, field capacity is a somewhat arbitrarily defined soil property. Field capacity is generally defined as the content of water, on a mass or volume basis, remaining in a soil two or three days after having been wetted with water and after free drainage is negligible (Soil Science Society of America 1997). Field capacity is often determined as the water content at –33 kPa soil water potential, but soil water potential at field capacity can be as high as – 4 kPa (Wierenga 1995). Furthermore, field capacity is affected by soil structure, texture, layering, and ante- cedent moisture (Hillel 1982). Field capacity can also change throughout the year (Romano and Santini 2002) and should not be viewed as an intrinsic soil property (de Jong and Bootsma 1996). The FCWB method only considers water flow at water contents in excess of field capacity, neglecting any water redistribution at lower water contents. This results in a few relatively large percolation events rather than continuous drainage predicted with models employing the Richards equation (Diekkruger et al. 1995). Using a FCWB method will generally preclude the use of the advection-dispersion equation because large spatial and temporal increments are usually used with FCWB methods. Large spatial and temporal increments can result in numerical instability in solutions to the advection-dispersion equation, especially for longer simulations and when solutes undergo sorption and precipitation reactions (Leij and van Genuchten 2002). Although models employing the FCWB method may not be able to account for the effects of diffusion and dispersion on P transport, multiple soil layers (e.g., soil horizons) tend to reduce the overall effect of hydrodynamic dispersion on solute transport (Porro et al. 1993), and the coefficient of hydrodynamic dispersion is not a sensitive parameter in P leaching models (Notodarmojo et al. 1991). In situations with shallow water tables, such as those requiring artificial drainage, the field-capacity concept does not apply. The free vertical drainage assumption for determining the field capacity is violated since the vertical drainage rate is confined by the presence of a water table. As the unsaturated soil reaches hydraulic equilib- rium, the water contents tend to be determined by the water table and not field capacity. Modeling approaches such as those in DRAINMOD (Skaggs 1978) employ a drained-to-equilibrium profile and allow the water table fluctuations to govern vertical water fluxes in the unsaturated zone. © 2007 by Taylor & Francis Group, LLC 86 Modeling Phosphorus in the Environment Several studies have compared results from hydrology models employing the one- dimensional Richards equation to those using various FCWB methods (de Jong and Bootsma 1996; Diekkruger et al. 1995; Eitzinger et al. 2004; Wegehenkel 2000). The use of small spatial increments in FCWB models increases the accuracy of predictions. Simplified FCWB methods, using small spatial increments (<10 cm), are capable of predicting average soil water contents and long-term percolation amounts with accuracy similar to models using the one-dimensional Richards equation. However, models employing the FCWB method tend to use large spatial increments (>10 cm); therefore, they tend to overpredict percolation volumes and predict percolation in only a few relatively large events. Despite its drawbacks, the FCWB method is a very common method of predicting percolation in field- and watershed-scale models (Table 4.1). 4.3.1.2 Nonequilibrium and Preferential Flow The terms nonequilibrium flow and preferential flow are used to describe the rapid transport of water and solutes through certain soil channels (e.g., cracks, root channels, macropores) while bypassing a fraction of the soil matrix (Hendricks and Flury 2001). Because preferential flow transports solutes through large pores, bypassing the soil matrix, breakthrough of conservative tracers in structured soils occurs sooner than would be expected based on the advection-dispersion equation (Gerke and Kohne 2004). Furthermore, solute transport through preferential flow reduces soil–solute interaction, a particularly important factor when considering adsorbed solutes such as P. Various approaches for modeling preferential flow in soils were reviewed by Simunek et al. (2003) and included single-porosity, dual-porosity, and dual-perme- ability models. Single-porosity models are the simplest of the three approaches, where the Richards equation is used with one additional parameter to represent nonequilibrium water contents in the soil. The advantage of the single-porosity model is that it only requires one additional parameter; however, the model results are independent of the antecedent moisture content. Dual-porosity models divide the soil into two regions: fractures, which have mobile water; and the soil matrix, which has immobile water. Although the soil matrix will not conduct water in a dual- porosity model, it can exchange and retain water. Dual-permeability models divide the soil into two flow regimes: one representing the fractures and the other repre- senting the matrix, both of which conduct water. Simunek et al. (2003) and Hendricks and Flury (2001) provide a comprehensive explanation of the aforementioned models. The major drawback of dual-porosity and dual-permeability models is the large number of parameters needed for their implementation. For example, dual-permeability models may require as many as 16 parameters to describe water flux (Gerke and van Genuchten 1993), compared to six parameters generally required to solve the Richards equation and only three parameters to solve the FCWB model. Dual- permeability models not only require a large number of parameters, but there is also little guidance on how to obtain these parameters (Simunek et al. 2003). Despite the large number of soil parameters required, dual-porosity models have been implemented for water and solute transport at the field scale. Gerke and Kohne (2004) developed a dual-permeability model that described bromide transport in a tile- drained field. Their model showed substantial improvement over model simulations © 2007 by Taylor & Francis Group, LLC Basic Approaches to Modeling Phosphorus Leaching 87 TABLE 4.1 Hydrological Classification of Selected Field- and Watershed-Scale Models Model Vertical Flow Preferential Flow Tile Drainage Interflow Base Flow AnnAGNPS FCWB with two soil layers a,b NI Hooghoudt equation a Darcy’s equation a NI ANSWERS-2000 FCWB single layer profile b,c NI Constant drainage rate d Empirical equation d NI GWLF FCWB e NI NI Empirical equation e,f Empirical equation f HSPF Empirical equation g NI NI Empirical equation g Empirical equation g SWAT FCWB with 10 soil layers h,i Bypass- or crack-flow, intended for use with high shrink/swell soils (Vertisols), not intended for use in other soils 8 Empirical equation based on field capacity concept h Kinematic storage model based on field capacity concept h Based on a steady state groundwater recharge equation assuming a linear relationship to changes in water table height h EPIC FCWB with 14 soil layers j NI NI Empirical equation based on field capacity concept j NI (continued) © 2007 by Taylor & Francis Group, LLC 88 Modeling Phosphorus in the Environment TABLE 4.1 (CONTINUED) Hydrological Classification of Selected Field- and Watershed-Scale Models Model Vertical Flow Preferential Flow Tile Drainage Interflow Base Flow GLEAMS FCWB with 12 soil layers k NI Hooghoudt equation with GLEAMS- WT l NI NI RZWQM Green-Ampt infiltration and Richards equation for redistribution m Dual-porosity model with Richards equation for matrix and gravitational flow in fractures n Richards equation with source/sink component linked to the Hooghoudt equation m NI NI Note: AnnAGNPS = Annualized Agricultural Non-Point Source; ANSWERS = Areal Non-Point Source Watershed Environment Response Simulation; BRC = Blackland Research Center; EPIC = Erosion Productivity Impact Calculator; FCWB = field capacity-water balance; GLEAMS = Groundwater Loading Effects of Agricultural Management Systems; WT = Water Table; GSWRL = Grassland, Soil and Water Research Laboratory; GWLF = Generalized Watershed Loading Functions; HSPF = Hydrologic Simulation Program- Fortran; NI = Not Included; RZWQM = Root Zone Water Quality Model; SWAT = Soil and Water Assessment Tool; TWRI = Texas Water Resources Institute. a b D.K. Borah and M. Bera, 2003, Trans. ASAE 46, 1553–1566. c F. Bouraoui, 1994, Ph.D. dissertation, Virginia Polytechnic Institute and State Uni versity, Blacksburg. d ANSWERS user’s manual. e D.A. Haith and L.L. Shoemaker, 1987, Water Resour. Bull. 23, 471–478. f K.Y. Lee, T.R. Fisher, and E. Rochell-Newall, 2001, Biogeochem. 56, 311–348. g B.R. Bicknell, J.C. Imhoff, J.L. Kittle, Jr., T.H. Jobes, and A.S. Donigian, Jr., 2001, Hydrological Simulation Program-FORTRAN (HSPF): user’s manual for release 12, U.S. Environmental Protection Agency National Exposure Research Laboratory , Athens, GA, in cooperation with U.S. Geological Survey, Water Resources Division, Reston, VA. h S.L. Neitsch, J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King, 2002a, Soil and water assessment tool theoretical documen tation: version 2000, GSWRL Report 02- 01, BRC Report 02-05, TWRI Report TR-191, College Station, TX. i S.L. Neitsch, J.G. Arnold, J.R. Kiniry, J.R. Williams, and K.W. King, 2002b, Soil and water assessment tool user’s manual version 2000, GSWRL Report 02-02, BRC Report 02-06, TWRI Report TR-192, College Station, TX. j J.R. Williams, 1995, Pp. 909–1000 in Computer Models of Watershed Hydrology, V.J. Singh (Ed.), Highlands Ranch, CO: Water Resources Publications. k W.G. Knisel and J.R. Williams, 1995, Pp. 1069–1114 in Computer Models of Watershed Hydrology, V. J. Singh (Ed.), Highlands Ranch, CO: Water Resources Publications. l M.R. Reyes, R.L. Bengtson, and J.L. Fouss, 1994, Trans. ASAE 37, 1115–1120. m K.E. Johnsen, H.H. Liu, J.H. Dane, L.R. Ahuja, and S.R. Workman, 1995, Trans. ASAE 38, 75–83. n J. Simunek, N.J. Jarvis, M.Th. van Genuchten, and A. Gardenas, 2003, J. Hydrol. 272, 14–35. © 2007 by Taylor & Francis Group, LLC R.L. Bingner and F.D. Theurer, 2005, AnnAGNPS technical processes: documentation version 3.2, http://www.ars.usda.gov/Research/docs.htm?docid=5199. Basic Approaches to Modeling Phosphorus Leaching 89 employing the equilibrium-based Richards equation. RZWQM, a field-scale model employing a dual-porosity hydrologic model (Table 4.1), was used to model the transport of metribuzin, a pesticide that adsorbs to soil, through structured soils (Malone et al. 2004). Predicted metribuzin losses from RZWQM were in close agree- ment with observed values, whereas Groundwater Loading Effects of Agricultural Management Systems (GLEAMS) simulations produced a ten-fold underprediction of metribuzin losses. The MACRO model, employing a dual-porosity hydrologic model, has been used to model preferential P transport through macropores following slurry spreading (McGechan 2002a) and from grazing cattle (McGechan 2003). 4.3.1.3 Lateral Flow Lateral flow within field- and watershed-scale models can generally be categorized as tile drainage, interflow, or base flow (Figure 4.1); however, many models may interchange terminology for these processes. A complete P model would have allow- ances for P transport by each pathway. Tile drainage refers to interception of shallow groundwater with an artificial drainage system, which then transports the water directly to a surface ditch or canal. Tile drainage systems expedite the flow of shallow ground water to surface water and greatly decrease solution–soil interaction. Hooghoudt’s equation is often used to quantify the amount of drainage flux: (4.4) where q is the drainage rate (cm h −1 ), K is the lateral saturated conductivity (cm h −1 ), d e is the effective depth to the impermeable layer (cm), m is the water table height above the drain at the midpoint between drains (cm), and L is the drain spacing (cm) (van der Ploeg et al. 1999). The depth from the drains to the impermeable layer is often adjusted to account for the convergence of the flow lines near the drains. The adjusted depth, d e , corrects the flow for this and depends on the size and spacing of the drains (van der Ploeg et al. 1999). Models described in the following chapters simulate tile drain flow in a variety of ways, including the Richards equation linked with the Hooghoudt equation using a source/sink term, the FCWB linked with the Hooghoudt equation, and empirical methods (Table 4.1). Interflow refers to lateral flow below and near the soil surface (Figure 4.1), usually during periods of saturation resulting from a perched water table. Interflow returns to streams within minutes to hours of rainfall events (Haygarth and Sharpley 2000). Interflow modeling techniques include the kinematic storage model, Darcy’s equation based on the lateral gradient from the source area to the exit to the stream, and empirical methods (Table 4.1). Base flow is background, low-magnitude flow arising from groundwater dis- charge to the stream. Travel time for base flow is on the order of days to months (Preedy et al. 1999). Soil and Water Assessment Tool (SWAT) determines base flow with a steady-state lateral groundwater recharge equation using a form of Hooghoudt’s equation (Neitsch et al. 2002b), whereas Hydrologic Simulation Program-Fortran q Kd m Km L = +84 2 2 e © 2007 by Taylor & Francis Group, LLC 90 Modeling Phosphorus in the Environment (HSPF) and Generalized Watershed Loading Functions (GWLF) determine base flow with empirical equations (Bicknell et al. 2001; Lee et al. 2001). 4.3.2 PHOSPHORUS CHEMISTRY Subsurface P transport is the product of water flux and P concentration; therefore, modeling the leaching process requires a description of P transformations within the soil combined with one of the aforementioned hydrologic models (Figure 4.1). Total P concentration in soil water includes inorganic and organic forms of dissolved and particulate P (Heathwaite and Dils 2000; Toor et al. 2003; Turner and Haygarth 2000). Because of the complexities of the organic P cycle and vertical particulate P transport, many models only consider dissolved inorganic P in the leaching process. 4.3.2.1 Inorganic P Leaching Inorganic P reacts with a variety of solutes and mineral surfaces in the soil system. Phosphorus is generally thought to precipitate as calcium (Ca) phosphates in alkaline to neutral soils or aluminum (Al) and iron (Fe) phosphates in more acidic soils but can also precipitate as magnesium (Mg) or manganese (Mn) phosphates depending on soil solution characteristics. Phosphorus is also strongly adsorbed to mineral surfaces. Phosphate adsorption can be simplified into two processes: (1) a fast, reversible reaction of P adsorption to surface sites; and (2) a slow, more irreversible reaction of P diffusion followed by precipitation (van der Zee and van Riemsdijk 1988). The combination of adsorption or desorption and precipitation or dissolution reactions control inorganic P concentrations in soil solution. Sorption and precipi- tation reactions are affected by organic and inorganic solutes and solution pH; therefore, complete descriptions of the transformations require modeling the dynam- ics of solution pH and chemical speciation of the solution. Grant and Heaney (1997) modeled the P leaching process for one-dimensional flow in small soil columns with the advection-dispersion equation using a ligand exchange model to represent adsorption or desorption reactions and a comprehensive solution speciation model for determining precipitation or dissolution reactions. Advantages of this approach are that all model inputs are determined independently of the model and model parameters are not soil dependent. However, the model required extensive information on soil chemical composition and supercomputer facilities to iteratively solve numerically intensive algorithms at fine spatial and temporal scales (ranging from 2.5 to 10 mm depth with time steps of 2 to 60 min). Because of these drawbacks, the authors concluded that this approach was not feasible for routine use. The processes of adsorption or desorption and precipitation or dissolution are difficult to separate in macroscale observations and are often collectively described by relating solid-phase (sorbed) P to dissolved P with a variety of nonlinear equations (McGechan 2002b; McGechan and Lewis 2002). Two of the more common equations are the Freundlich and Langmuir equations. The general form of the Freundlich equation is Q = k F C b (4.5) © 2007 by Taylor & Francis Group, LLC [...]... transport in tile drainage and interflow Colleen Green, personal communication, December 21, 2005 b Basic Approaches to Modeling Phosphorus Leaching GLEAMSf/ EPICg 93 © 2007 by Taylor & Francis Group, LLC 94 Modeling Phosphorus in the Environment Freundlich and Langmuir equations in field- and watershed-scale models First, determination of parameters for Equation 4. 5 and 4. 6 requires time- and labor-intensive... Resour Res 29:305–319 Grant, R.F and D.J Heaney 1997 Inorganic phosphorus transformation and transport in soils: mathematical modeling in ecosystems Soil Sci Soc Am J 61:752–7 64 Groenendijk, P and J.G Kroes 1999 Modelling the nitrogen and phosphorus leaching to groundwater and surface water with ANIMO 3.5 Report 144 , Winand Staring Centre, Wageningen, the Netherlands Available at http://www.alterra.wur.nl/NL/Producten/... model 4. 4 MODEL EVALUATION As previously stated, the characteristics of an adequate model for P leaching are dependent on the characteristics of the agroecosystem being modeled and the modeling objectives A detailed description of vertical P leaching, including the nonlinear P adsorption isotherm, is important for long-term simulations when P applications exceed crop removal — as with many animal-waste... with modeling routines depicting P leaching in the soil profile Recent interest in determining P leaching losses may lead to alternative methods for modeling P leaching Simplified forms of the adsorption relationships have been made with relationships between quantity and intensity (Q/I), which relate a quantity of adsorbed P (e.g, soil test P concentration) to its intensity (e.g, concentration in solution)... pool according to the following equation: Plabile = Pactive (PAI/(1 – PAI)) (4. 7) where PAI is the phosphorus availability index The PAI is conceptually defined as the fraction of applied fertilizer that remains labile after a six-month incubation with multiple wetting and drying cycles (Jones et al 19 84) The PAI is a function of soil properties and can be estimated with a series of soil-dependent empirical... Poulton, and K.W.T Goulding 1995 Phosphorus leaching from soils containing different phosphorus concentrations in the Broadbalk experiment J Environ Qual 24: 9 04 910 Hendricks, J.M.H and M Flury 2001 Uniform and preferential flow, mechanisms in the vadose Zone Pp 149 –187 in Conceptual Models of Flow and Transport in the Fractured Vadose Zone, National Research Council (Ed.) Washington, D.C.: National... fieldcapacity water-balance approach for simulating vertical water flux and various other approaches for tile-drainage, interflow, and base-flow simulation Only four of the evaluated models simulated P leaching processes, none of which contained complete continuity and conservation of mass in describing P transformations and transport from the soil surface to surface water via tile drainage, interflow, and... problems of unremediable long-term P leaching A review of the literature on vadose zone modeling reveals a disconnect between the sophisticated laboratory-scale models reported in the literature and the simplified model techniques present in the widely available watershed-scale models This disconnect arises from a few factors First, there is great difficulty in scaling up the column or detailed soil profile... Approaches to Modeling Phosphorus Leaching 99 many watershed-scale models are a conglomeration of previously developed field- and profile-scale models Although great progress has been made in improving computer interfaces, data input, and watershed characterization used in these models, very little effort as of yet has been focused on updating the nutrient models to correspond with advances in scientific... Approaches to Modeling Phosphorus Leaching 91 Sorbed P (mg kg-1) 250 200 150 100 Data Langmuir Freundlich 50 0 0.0 5.0 10.0 15.0 -1 Solution P (mg L ) FIGURE 4. 2 Freundlich and Langmuir equations fit to P adsorption data for a Norfolk sandy loam A horizon (Fine-loamy, kaolinitic, thermic typic kandiudults) Coefficients for Equations 4. 5 and 4. 6 are as follows: kF = 1 04, b = 0.309, Qmax = 1 94, and kL = 1 .45 (N.O . on the size and spacing of the drains (van der Ploeg et al. 1999). Models described in the following chapters simulate tile drain flow in a variety of ways, including the Richards equation linked with. of mass linking them in an actual setting. 4. 3 MODEL COMPONENTS AFFECTING P LEACHING Incorporating complete or partial descriptions of P leaching into a simulation model requires coupling models. pathways. NI = not included; PARTLE = particulate. 94 Modeling Phosphorus in the Environment Freundlich and Langmuir equations in field- and watershed-scale models. First, deter- mination of parameters