241 10 ANSWERS-2000: A Nonpoint Source Pollution Model for Water, Sediment, and Phosphorus Losses Faycal Bouraoui European Commission–DG Joint Research Centre, Institute for Environment and Sustainability, Ispra, Italy Theo A. Dillaha Virginia Polytechnic Institute and State University, Blacksburg, VA CONTENTS 10.1 Introduction 241 10.2 ANSWERS-2000 242 10.2.1 Underlying Concepts 242 10.2.2 Water Cycle 242 10.2.3 Sediment Detachment and Transport 247 10.2.4 Phosphorus Transformations and Losses 248 10.3 Validation and Applications 252 10.4 Recent ANSWERS Developments 257 10.5 Conclusions 257 References 258 10.1 INTRODUCTION Nutrients — nitrogen (N) and phosphorus (P) in particular — are indispensable for crop and animal production. However, used in excess they have detrimental effects on the environment and human health. Agriculture is the principal source of nutrient losses worldwide (Novotny 1999). Combating diffuse pollution from agriculture is complicated due to the temporal and spatial lag between the management actions © 2007 by Taylor & Francis Group, LLC 242 Modeling Phosphorus in the Environment taken at the farm level and the environmental response (Schröder et al. 2004). Beside the correct identification and quantification of sources, cost-effective P miti- gation requires the delineation of critical P source areas, which contribute dispropor- tionate amounts of P to receiving waters. According to Dickinson et al. (1990), targeting and prioritizing nonpoint source (NPS) pollution control potentially could triple pol- lutant reduction, is financially attractive, and minimizes the extent of area affected negatively by restrictive land practices. Modeling is essential to the implementation of cost-effective and environmentally friendly management strategies to optimize nutri- ent use and to reduce their losses in terrestrial ecosystems. Modeling, especially when using a distributed approach, can help prioritize critical source areas at various scales within a catchment and assess the impact of landscape factors on nutrient delivery. The Areal Nonpoint Source Watershed Environmental Response Simulation (ANSWERS) (Beasley et al. 1980, 1982; Dillaha and Beasley 1983) is a watershed- scale, distributed-parameter, physically based research model originally developed to simulate the impacts of watershed management practices on runoff and sediment loss. P and N transport components were added to the original event-based version of the model by Storm et al. (1988) and Bennett (1997), respectively. Bouraoui and Dillaha (1996) developed a continuous version of the model, ANSWERS-2000, which includes N and P transformations, transport, and losses. The following sections provide a detailed description of the continuous version of the ANSWERS model, with a focus on water, sediment, and P transport. 10.2 ANSWERS-2000 10.2.1 U NDERLYING C ONCEPTS ANSWERS-2000 is a process-oriented, distributed-parameter, continuous simulation model developed to simulate long-term runoff, sediment, N, and P losses in agricultural watersheds as affected by land management strategies such as the implementation of best management practices (BMPs). The ANSWERS model is based on the hypothesis that “at every point within a watershed, relationships exist between water flow rates and those hydrologic parameters which govern them, e.g., rainfall intensity, infiltration, topography, soil type, etc. Furthermore, these flow rates can be utilized in conjunction with appropriate component relationships as the basis for modeling other transport- related phenomenon such as soil erosion and chemical movement within that watershed” (Beasley and Huggins 1981, p. 4). ANSWERS-2000 represents a watershed as a matrix of square uniformly sized elements, where an element is defined as a homogeneous area within which all hydrologically significant parameters (e.g., soil properties, surface condition, vegetation, topography) are similar. Spatial variability is represented by allowing parameter values to vary in an unrestricted manner between elements. 10.2.2 W ATER C YCLE Simulated hydrologic processes include interception, surface retention, infiltration, surface runoff, evapotranspiration (ET), and water movement through the root zone. The model maintains a daily water balance as follows: (10.1)SW SW P R DR TD AET dd+ =+−+++ 1 () © 2007 by Taylor & Francis Group, LLC Answers-2000: A Nonpoint Source Pollution Model 243 where SW represents the soil water content (cm) for the day (d), P is precipitation (cm), R represents surface runoff (cm), DR is the drainage below the root zone (cm), TD is tile drainage (cm), and AET is evapotranspiration (cm). Drainage and evapo- transpiration are represented as one-dimensional processes, whereas runoff and tile drainage are represented as two-dimensional processes. The model uses a dual time step: a daily time step on days without rainfall, and a 60-sec time step during periods of rainfall (Figure 10.1). The rainfall excess (i.e., rainfall minus interception) is subject to infiltration and runoff for each time step and element. Infiltration starts once the interception volume is filled. Interception volume is dependent on the plant type and stage of growth. Infiltration is simulated using the Green-Ampt (Green and Ampt 1911) equation. It assumes (1) a step water retention function describing the relation between soil water pressure, y (cm), and volumetric water content, q (cm 3 cm −3 ); and (2) a step hydraulic conductivity function K (cm/h). The infiltration process is represented as a saturated wetting front advancing down through the soil profile with q = q s and K = K s (where K s is the hydraulic conductivity for volumetric water content at natural saturation q s ) behind the wetting front and q = q 0 (initial soil moisture content) and K = 0 ahead of the wetting front. The basic Green-Ampt equation to compute cumulative infiltration is (10.2) where t is the time (h), F is the cumulative infiltration (cm), and y f is the wetting front matric potential (cm). The wetting front matric potential represents the suction gradient pulling the water downward from the saturated zone to the unsaturated zone. The wetting front matric potential is assumed to be invariant and is calculated in ANSWERS-2000 using the pedotransfer function given by Rawls and Brakensiek (1985): (10.3) where x is given by (10.4) where C L is the clay fraction (%), S A is the sand fraction (%), and h is the porosity (%). The hydraulic conductivity is also computed by default using the pedotransfer developed by Rawls and Brakensiek (1985): (10.5) Kt F F ssf sf =− − + − ()ln () θθψ θθψ 0 0 1 ψ f = e x xCCS=− + + + − 6 531 7 33 15 8 3 81 3 40 22 . . . LLA ηη 4498 161 160 140 22 22 2 AA L AL SS C SC ηη η ++ − −−−34 8 8 0 22 . LA CS ηη . KC s r r = − − 0 0002 1 2 2 3 2 . () () ηθ η ρ θ © 2007 by Taylor & Francis Group, LLC 244 Modeling Phosphorus in the Environment FIGURE 10.1 Flowchart for the ANSWERS-2000 model. Beginning simulation DAY = 1 Rainfall excess>0 Runoff> 0 Sediment submodel Runoff ended? Simulation period over? Output summary Water percolation Soil moisture> field capacity N & P uptake and transformation DAY = DAY +1 Sediment-bound P losses No No Yes Yes Yes No Infiltration and runoff submodels t = 0 Yes Yes No t = t + 60s Soluble P losses No Evapotranspiration © 2007 by Taylor & Francis Group, LLC Answers-2000: A Nonpoint Source Pollution Model 245 where r represents the soil bulk density (g cm −3 ), q r is the residual water (cm), and C is the soil texture coefficient, which is given by (10.6) where S I is the silt fraction (%). However, if measured values of the Green-Ampt parameters are available they should be used directly in the model. The infiltration rate f (cm h −1 ) is obtained by differentiating Equation 10.2 with respect to time: (10.7) ANSWERS-2000 takes into account ponding under unsteady rainfall as pre- sented by Chu (1978). Once the infiltration rate is determined, runoff is routed to the watershed outlet using Manning’s equation. Every square element of the discretized watershed acts as an overland flow plane with a computed slope and slope direction. For overland flow, the hydraulic radius is taken equal to the average detention depth. The slope direction is used to apportion runoff between the adjacent receiving cells. Channel elements collect flow from overland flow elements and route the runoff to the watershed outlet using Manning’s equation. Channel elements are described in terms of their slope, width, and Manning’s roughness coefficient. All water draining below the root zone is added to a single reservoir representing a shallow aquifer. Groundwater contribution to surface water is represented as a fraction of the reservoir (shallow aquifer) being added to each channel element. Once a runoff event has ended, the internal soil moisture redistribution takes place. If soil moisture content exceeds field capacity, there is potential for percola- tion. The rate of percolation depends on the amount of water in excess of field capacity. Travel time of percolating water through the soil matrix is regulated by the hydraulic conductivity. This conductivity varies from near zero when the soil is at field capacity to a maximum value when the soil is at saturation and is expressed by Savabi et al. (1989) as (10.8) CCCS=− + − − 0170181 0 00000069 0 00000041 22 . . LLA SSS S C AI A L 22 22 22 0 000118 0 00069 0 000049 + ++ . ρ ρ SSC SC AL IL 2 2 0 000085− . fK F =+ − s sf ln () 1 0 θθψ KK ad s d = − θ η θ η 265. log © 2007 by Taylor & Francis Group, LLC 246 Modeling Phosphorus in the Environment where K ad is the adjusted hydraulic conductivity (cm h −1 ) and q d is the field-capacity water content (cm 3 cm −3 ). Travel time through a particular soil layer (TT, h) is computed using a linear storage equation: (10.9) where d i is the depth of the specific layer (cm). Percolation during a specific time step is determined using an exponential function: (10.10) where ∆t is the time step (h) and DR is the percolation (cm) during ∆t. Evapotranspiration is determined based on Ritchie’s (1972) equation. Potential ET is computed by (10.11) where E 0 is the potential evapotranspiration (cm day −1 ), H 0 is the net solar radiation (l), ∆ represents the slope of the saturation vapor pressure curve at the mean air tem- perature(mbar °C −1 ), and g is psychrometric constant (mbar °C −1 ). The net solar radiation is obtained from the daily solar radiation and the albedo. The leaf area index, LAI, is used to split the potential ET into potential soil evaporation and potential plant transpiration. Soil evaporation is assumed to take place in two dif- ferent stages. During the first stage, soil evaporation is energy limited and occurs at a rate equal to the potential evaporation rate. The potential soil evaporation is computed by (10.12) where E s is the potential soil evaporation (cm). The upper limit of the first stage evaporation, U (cm), is determined by (10.13) where a s is the soil evaporation parameter (cm day −0.5 ). The soil evaporation param- eter depends on soil water transmission characteristics. When the cumulative soil evaporation exceeds the upper limit of the first stage (U ), the second stage begins. The second stage begins when the surface starts to dry and water from within the soil starts to evaporate. During the second stage, also called the falling rate stage, the soil evaporation rate is given by (10.14) TT K d= − θθ d ad i DR d e t TT =− − − () () θθ di 1 ∆ 0 0 504 0 E H = + . ∆ ∆ γ EEe LAI s = − 0 04(. ) U =−09 3 042 .( ) . α s Ett ss0 05 05 1=−− () α () © 2007 by Taylor & Francis Group, LLC Answers-2000: A Nonpoint Source Pollution Model 247 where E s0 is the soil evaporation rate (cm day −1 ) for day t, and t is the time (days) since stage-two evaporation started. The potential plant transpiration, E p0 , is given by (10.15) If soil moisture is a limiting factor, plant transpiration is reduced accordingly. Plant growth is represented by a varying LAI and by simulating root growth. Ten values of the LAI are input to the model for each crop for 10 stages of plant growth. A linear interpolation is made daily between the different values. Root development is simulated using a sin function given by Borg and Williams (1986) as (10.16) where R d is the root depth (cm), R dx is the maximum root depth (cm), D m is the number of days to reach maturity, and D p is the number of days after planting. 10.2.3 SEDIMENT DETACHMENT AND TRANSPORT Soil particles can be detached by rainfall impact and from shear stress and lift forces generated by overland flow. Detachment of soil particles by raindrop impact depends on the kinetic energy of the raindrops and is calculated as described by Meyer and Wischmeier (1969): (10.17) where DETR (kg s −1 ) is the rainfall detachment rate, CDR and SKDR are the cropping and management and the soil erosivity factors from the Universal Soil Loss Equation (USLE) (Wischmeier and Smith 1978), A i (m 2 ) is the area increment, R (m s −1 ) is the rainfall intensity, and CE3 is a calibration constant. The detachment of soil particles by overland flow was described by Meyer and Wischmeier (1969) and modified by Foster (1976) as follows: (10.18) where DETF (kg s −1 ) is overland flow detachment rate, SL is the slope steepness (%), Q w is the flow per unit width (m 2 s −1 ), and CE4 is a calibration coefficient. Values of 6.54 10 6 and 52.5 were proposed for CE3 and CE4, respectively, by Bouraoui and Dillaha (1996). The model allows seasonal variations of the cropping and management factor. It is varied from a maximum value at planting day to a minimum value when plants reach maturity. The CDR factor is assumed to vary linearly between these two values based on the LAI. The soil erosivity factor is assumed constant and does not vary with time. E ELAI LAI EEELAI p ps 0 0 00 3 03 3 =≤≤ =− > RR D D ddx p m =+ − 05 05 303 147 sin. . DETR CE CDR SKDR A R= 3 2 i DETF CE CDR SKDR A SL Q= 4 iw © 2007 by Taylor & Francis Group, LLC 248 Modeling Phosphorus in the Environment Detachment and transport are calculated for various particle classes according to the particle size distribution of the sediments. Yalin’s (1963) equations as extended by Mantz (1977) for small particles are used to calculate actual transport capacity for each particle. The transport capacity (TC, kg s −1 -m −1 ) is expressed as (10.19) Sediments are transported both as suspended and bedload. It is assumed that particles of diameter less than 10 µm do not deposit due to the extremely low fall velocity (Dillaha and Beasley 1983). The fraction of larger particles depositing in case of transport capacity deficit is a function of the fall velocity of discrete particles in water: (10.20) where RE is the fraction of particles larger than 10 µm in class i that are deposited, FV i is the fall velocity for particle i (m s −1 ), A is the surface area (m 2 ) of an overland flow or channel element, and Q is the surface runoff (m 3 s −1 ). The actual transport rate, TF (g s −1 ), for each particle class in a mixture is calculated using Yalin’s equation: (10.21) where r w is the density of water (g cm −3 ), g is the acceleration due to gravity (m s −2 ), d is the equivalent sand diameter of particle i (cm), V is the shear velocity, Sg is the particle specific gravity (g cm −3 ), and Pe is computed as follows: (10.22) where s (a function of Sg and d) represents the dimensionless excess of tractive force, which is a function of critical shear stress. A more detailed description of the ANSWERS-2000 erosion module is given by Dillaha and Beasley (1983) and Dillaha (1981). Some basic assumptions of the model are that flow detachment occurs only if there is excess transport capacity and that flow detachment and deposition can not occur simultaneously for the same particle class. 10.2.4 PHOSPHORUS TRANSFORMATIONS AND LOSSES ANSWERS-2000 simulates the transformations of N and P following the approach described by Knisel et al. (1993). The following section focuses on P transformation TC SL Q Q TC SL Q Q =≤ = 146 0 046 14600 05 25 ww ww for for . . >> 0 046. RE FV A Q ii = min ; 1 TF Pe Sg gd V iiiwi = ρ Pe n ii i i i i =− + 0 635 1 1 1 . ln( ) δ σ σ δ δ ∑∑ © 2007 by Taylor & Francis Group, LLC Answers-2000: A Nonpoint Source Pollution Model 249 and fate. Details on the nitrogen transport portion of the model are available in Bennett (1997). A flowchart of the P cycle considered in ANSWERS-2000 is given in Figure 10.2. The model considers the following soil P compartments: active organic P, labile P, active mineral P, a stable (inactive) mineral P, and a stable (fresh) organic P pool. The ratio of potentially mineralizable P to total organic P is assumed to be identical to the ratio of potentially mineralizable N to soil organic N (Knisel et al. 1993). Mineralization rate is determined as (10.23) where MINP is the mineralization rate (kg ha −1 day −1 ), SORGP is the soil organic P content (kg ha −1 ), CMN is a mineralization constant (0.0003 day −1 ) (Sharpley and Williams 1990), and SWFA and TEMPFA are unitless soil water and temperature correction factors, respectively. The mineralized P is added to the pool of labile P. The active and stable inorganic P pools are dynamic, and at equilibrium the stable mineral P pool is assumed to be four times the active mineral P pool (Sharpley and Williams 1990). Dissolved inorganic P losses are a function of the labile P content in the topsoil and runoff. Due to the large adsorptivity of P and since ANSWERS- 2000 does not consider preferential flow, the P losses through percolation are neglected. The amount of dissolved inorganic P potentially lost is given by (10.24) where PSOL represents dissolved inorganic P (kg), PLAB is labile P (kg), and K phos is the partition coefficient for P, which is a function of the clay content of the soil (Knisel et al. 1993): (10.25) FIGURE 10.2 Flowchart of the P cycle simulated in the ANSWERS-2000 model. Stable Mineral P Active Mineral P Uptake Plants Residue Active Organic P FertilizersLabile P Mineralization MINP CMN SORGP POTMIN POTMIN SOILN SWFA TEMPFA= + () 005. PSOL PLAB K = + 01 101 . . phos KC phos L =+100 2 5. © 2007 by Taylor & Francis Group, LLC 250 Modeling Phosphorus in the Environment Crop uptake of P is based on a supply-and-demand approach. Only dissolved labile P is available for crop uptake. The potential supply of dissolved labile P is expressed as the product of the concentration of dissolved labile P and plant tran- spiration. The cumulative P demand on day i, TDMP, (kg ha −1 ) is based on the plant growth (PGRT): (10.26) where PGRT corresponds to the ratio between the actual LAI and the maximum LAI, YP is the yield potential (kg ha −1 ), DMY is the ratio of total dry matter to harvestable yield, and CP is the crop P concentration (% crop biomass). The daily demand is then taken as the difference in cumulative demand between two consecutive days. If the demand is greater than the supply, then the actual uptake is limited to the supply; otherwise the uptake is not limited and is met fully. The P losses via particulate or dissolved form occur only during a runoff producing rainfall event. Sediment-bound P transport is derived from the sediment transport submodel and is based on the conservation of mass written as (10.27a) or in the discrete form as (10.27b) where Pi is the sediment-bound P inflow (kg s −1 ), Po is the sediment-bound P outflow (kg s −1 ), P is the sediment-bound P in transit (kg), and the subscript j refers to the jth time interval. Equation 10.27b can be rearranged as (10.28) To compute the sediment outflow at any time step, a storage outflow relationship is required. At any time step, if the discharge is equal to zero, all the sediment is deposited; no P outflow occurs. The input of sediment-bound P comes from adjacent cells or from within the cell with newly detached sediment. The amount of sediment- bound P added from within the cell is expressed as (10.29) where PCELL is the newly generated sediment-bound P (kg s −1 ), SEDNEW is newly generated sediment (kg s −1 ), and P 0 is the concentration of P in the cell TDMP PGRT YP DMY CP i = 100 dP Pi dt Po dt P P t t t t j j j j j j + ∫∫ ∫ =− ++ 1 11 ∆ ∆ ∆ ∆() () PP Pi Pi t Po Po t jj jj j j + ++ −= + − + 1 11 22 ∆∆ 22 1 11 P t Po Pi Pi P t Po j jjj j j + ++ + =+ () +− ∆∆ PCELL P SEDNEW= 0 © 2007 by Taylor & Francis Group, LLC [...]... cm) NH4-N 107 kg Harvest corn 0 4-2 9-1 974 0 6-1 1-1 974 0 9-1 6-1 974 1 0-1 9-1 974 0 4-1 5-1 975 0 4-2 9-1 974 0 5-1 4-1 975 0 5-2 1-1 974 0 6-2 5-1 975 1 0-0 3-1 975 1 0-3 0-1 975 P4 NH4-N 38 kg PO4-P 33 kg NH4-N 100 kg Plant rye Harvest rye Fertilizer application and incorporation (15 cm) NH4-N 11kg, NO3-N 11 kg PO4-P 21 kg Plow and plant corn Fertilizer application and incorporation (15 cm) NH4-N 112 kg Harvest corn NH4-N 11kg,... Value -8 35 - -7 50 -7 50 - -6 00 -6 00 - -4 50 -4 50 - -3 00 -3 00 - -1 50 -1 50 - 0 0 -1 50 150 - 300 300 - 450 FIGURE 10. 6 Sediment loss (kg) distribution over the Nomini Creek watershed for the May 26, 1989, storm Negative values indicate a net loss, whereas positive values refer to a net gain of sediments sediment yields The unit reduction (i.e., percentage reduction in runoff, sediment, and total P at the. .. predicted PO4-P loss 450 400 350 300 0.6 250 200 0.4 PO4-P (g) Runoff (mm) 0.8 150 100 0.2 50 0 200 0 400 600 800 100 0 1200 Time (mn) 1400 1600 1800 FIGURE 10. 5 Predicted and measured runoff for the May 26, 1989, rainfall event for the Nomini Creek watershed The dashed line represents the PO4-P losses occurring during the storm © 2007 by Taylor & Francis Group, LLC 256 Modeling Phosphorus in the Environment. .. j+1 = Pj+1 S (10. 31) Q where S represents the storage volume at the end of the time increment The value of Poj+1 is then replaced into Equation 10. 28 to determine the value of the sedimentbound P in storage and then to calculate the outflow of sediment-bound P for each time step The initial concentration of sediment-bound P is distributed among the different particle sizes in proportion to the specific... approach The dissolved inorganic P present in runoff water is composed of dissolved P in ow from adjacent cells and dissolved P from within the cell During a runoff event, it is assumed that there is an instantaneous equilibrium between the dissolved inorganic P present in the top 10 mm of the soil profile —called effective depth of interaction (EDI) — and the total water present, transiting or in storage in. ..Answers-2000: A Nonpoint Source Pollution Model 251 soil (kg kg−1-soil) The sediment-bound nutrient in ow at the end of the time increment, Pij+1, is determined by Pi j+1 = PI + PCELL (10. 30) where PI represents the in ow from adjacent cells The outflow of sediment-bound P is determined as the concentration of sediment-bound P in transit multiplied by the runoff volume, Q, which... NO3-N 11 kg PO4-P 31 kg Plow and plant corn NH4-N 112 kg Harvest corn The discretization scheme for P2 (1.4 ha) is shown in Figure 10. 3 The time series for the runoff and the dissolved inorganic P predictions are shown in Figure 10. 4 for the P2 watershed, and the overall performance of the model is summarized in Table 10. 2 The uncalibrated model predicted mean monthly runoff, sediment, and dissolved inorganic... September 1991, during which five major runoff-producing storms occurred Information on the parameterization of the model is given by Bouraoui and Dillaha (1996) Over the five-month simulation period, © 2007 by Taylor & Francis Group, LLC 254 Modeling Phosphorus in the Environment 180 2 160 4 140 6 120 8 100 10 80 12 60 14 40 16 20 18 PO4-P (g) 0 0 runoff (cm) 200 Measured PO4-P Predicted PO4-P Measured Runoff... and P in view of an integrated management of P at the field and watershed level The model is based on a dual time step: minutes during a storm event and daily in- between storms © 2007 by Taylor & Francis Group, LLC 258 Modeling Phosphorus in the Environment The model can thus produce on a time-continuous basis daily and subdaily hydrograph and pollutograph (i.e., sediment bound and dissolved P) The model... Agency, EPA-600/ 3-7 8-0 56, Environmental Research Laboratory, Athens, GA Storm, D.E et al 1988 Modeling phosphorus transport in surface runoff Trans ASAE 31:117–127 Veith, T.L et al 2002 Questions: a user-friendly interface to ANSWERS-2000 Biological Systems Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg Wischmeier, W.H and D.D Smith 1978 Predicting rainfall erosion . a net gain of sediments. sed_loss Value -8 35 - -7 50 -7 50 - -6 00 -6 00 - -4 50 -4 50 - -3 00 -3 00 - -1 50 -1 50 - 0 0 -1 50 150 - 300 300 - 450 © 2007 by Taylor & Francis Group, LLC Answers-2000:. and incorporation (15 cm) 0 6-2 5-1 975 NH 4 -N 112 kg NH 4 -N 112 kg 1 0-0 3-1 975 Harvest corn 1 0-3 0-1 975 Harvest corn © 2007 by Taylor & Francis Group, LLC 254 Modeling Phosphorus in the Environment cumulative. PO 4 -P 33 kg NH 4 -N 38 kg PO 4 -P 33 kg Fertilizer application and incorporation (15 cm) 0 6-1 1-1 974 NH 4 -N 107 kg NH 4 -N 100 kg 0 9-1 6-1 974 Harvest corn 1 0-1 9-1 974 Plant rye 0 4-1 5-1 975 Harvest