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.,
Trang 1Nonpoint 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
Trang 2taken 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 UNDERLYING CONCEPTS
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 WATER CYCLE
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)
SWd+1=SWd+ −P (R+DR+TD+AET)
Trang 3where 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 (cm3 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 = qs and
K = Ks (where Ks is the hydraulic conductivity for volumetric water content at natural
saturation qs) behind the wetting front and q = q0 (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 yf 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 CL is the clay fraction (%), SA 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)
−
θ θ ψ
θ θ ψ
0
0 1
ψf=e x
−
6 531 7 33 η 15 8 L2 3 81 η2 3 40 L A 4
4 98 SAη+16 1 SA2η2+16 0 CL2η2−14 0 SA2CL
−−34 8 CL2η−8 0 SA2η
r
−
0 0002
1
2 2
η θ η ρ θ
Trang 4FIGURE 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
Trang 5where r represents the soil bulk density (g cm−3), qr is the residual water (cm), and
C is the soil texture coefficient, which is given by
(10.6)
where SI 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)
−
0 00000041
2 2
C
L
2 2
0 000118
+
ρ
S C
I L
2
2
0 000085
−
−
s
ln
1
0
θ θ ψ
Kad Ks
d
=
−
θ η
θ η
2 65 log
Trang 6where Kad is the adjusted hydraulic conductivity (cm h−1) and qd is the field-capacity water content (cm3 cm−3) Travel time through a particular soil layer (TT, h) is
computed using a linear storage equation:
(10.9)
where di 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 E0 is the potential evapotranspiration (cm day−1), H0 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 Es is the potential soil evaporation (cm) The upper limit of the first stage
evaporation, U (cm), is determined by
(10.13)
where as 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
= −
θ θd
ad i
t TT
= − −
−
( )
θ θd i 1
∆
0
0 504 0
+
∆ γ
E E e LAI
0 (0 4. )
U=0 9 (αs−3)0 42
Es0=αs(t0 5 − −(t 1)0 5 )
Trang 7where Es0 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, Ep0, 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 Rd is the root depth (cm), R dx is the maximum root depth (cm), Dm is the
number of days to reach maturity, and Dp is the number of days after planting
10.2.3 S EDIMENT D ETACHMENT AND T RANSPORT
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), Ai (m2) 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 (%), Qw is the flow per unit width (m2 s−1), and CE4 is a calibration coefficient.
Values of 6.54 106 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
p
0 0
3
= − >
D
d dx
p
m
−
0 5 0 5 sin 3 03 1 47
DETR=CE CDR SKDR A R3 2
i
DETF=CE CDR SKDR A SL Q4 i w
Trang 8Detachment 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,
FVi is the fall velocity for particle i (m s−1), A is the surface area (m2) of an overland
flow or channel element, and Q is the surface runoff (m3 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 rw 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
=
14600
0 5
25
for for
>>0 046
Q
TFi=Pe Sgi iρwg d Vi
i
i
i
1
σ
δ δ
∑
Trang 9and 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−1day−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 Kphos
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
Fertilizers Labile P
Mineralization
MINP CMN SORGP POTMIN
POTMIN SOILN SWFA TEMPFA
=
+ ( )0 0 5
K
= +
0 1
1 0 1
phos
Kphos = 100 + 2 5 CL
Trang 10Crop 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 P0 is the concentration of P in the cell
TDMPi=PGRT YP DMY CP
100
P P
t t
t t
j j
j j
j
j +
∆
∆
∆
∆
Pj+1− =Pj Pij+Pij+1 t− Poj+Poj+1 t
P
P
t Po
j
j j
+
+
=( + )+ −
PCELL=P SEDNEW0