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CHAPTER 4
SURFACE WATER AND SEDIMENT ALGORITHMS
Resuspension of sediment to surface water (solid phase):
e 7
O . L, „
y. r ~~jfaitv ~r ^ olid
V n 7
v sed Pfcj ^w/a/
where:
Tsed-sw ~ advective transfer factor for resuspension of sediment to surface water
(I/day)
Asedsw = area of surface water/sediment interface (m2)
Vsed = volume of sediment compartment (m3)
Sr = resuspension rate of benthic sediment to water column (kg [benthic
sediment]/m2 (area)-day)
pbs - density of benthic sediment (kg [benthic sediment]/m3 [benthic sediment])
Zsolld = fugacity of the solid phase (Pa)
Zlolai = total fagacity (Pa).
4.2.3 ADVECTIVE PROCESSES BETWEEN SEDIMENT/SURFACE WATER AND
ADVECTIVE SINKS
The surface water advection sink represents outflow of the chemical from the study area.
For sediment, the advection sink represents the burial of the chemical beneath the sediment layer.
Burial is calculated so that the net flow of sediment into the sediment layer is zero. That
is, there is no loss of sediment mass due to burial, only loss of pollutant. This is done by setting
the amount of sediment buried equal to the sediment deposition rate minus the sediment
resuspension rate, both of which are specified input parameters. If the resuspension rate is larger
than the deposition rate, then the burial flow is set to 0. A more sophisticated approach may be
implemented in which the sediment layer depth could change, depending on the deposition and
resuspension rates. Further, the deposition rates can be calculated to correspond to the suspended
sediment concentration, which could change depending on the erosion of soil to the water body
and the outflow.
Following is a summary of advective processes between sediment/surface water and
advective sinks, and algorithms used to calculate flow velocities:
Outflow from surface water to surface water advection sink (total phase):
(4-6)
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CHAPTER 4
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where:
Outflow
outflow of water from surface water compartment to advection
sink (m3/day)
volume of surface water compartment (m3)
Resuspension of sediment to surface water (solid phase):
\ S A f ^ 7
'T total
;;;;; = max o,-
Pa
sed
Pbs )
(4-7)
where:
p total
' seds\v
A
.secMr
Pbs
Pss
7
^lotal
net advective transfer factor for deposition and resuspension of
sediment to surface water (I/day)
area of surface water/sediment interface (m2)
volume of sediment compartment (m3)
resuspension rate of benthic sediment to water column (kg [benthic
sediment]/m2 (area)-day)
density of benthic sediment (kg [benthic sediment]/m3 (benthic
sediment])
volume of surface water compartment (m3)
deposition rate of suspended sediment to sediment bed (kg
[suspended sediment]/m2 (area)-day) (Mackay et al. 1983b; use
0.096 mVhr for a lake of volume 7 x 10"6 m)
density of suspended sediment (kg [suspended sediment]/m3
[suspended sediment])
fugacity of the solid phase (Pa)
total fugacity (Pa).
4.3 DERIVATION OF RIVER COMPARTMENT TRANSFER FACTORS
The transfer factor from one river compartment to another, or to a lake compartment, was
derived based on advective flow rates of a total pollutant mass between two compartments as
developed in Section 2.3.1. By substituting river flow velocity for the total volumetric flow
velocity, the following transfer factor is derived.
Advection from one river compartment to another river or lake compartment:
(4-9)
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where:
utj = annual averaged river flow between river compartments / and/ (m/day)
A = area of interface between compartments / and/ (m2)
volume of compartment / (m ).
Because advection is being simulated for the total phase, no phase partitioning is applied in this
equation.
4.4 DISPERSIVE PROCESSES
4.4.1 DISPERSIVE TRANSPORT BETWEEN SURFACE WATER COMPARTMENTS
Dispersive transport between water compartments can be approximated as a first order
process using the method describe in the WASP water quality simulation program (Ambrose et
al. 1995). Dispersive water column exchanges significantly influence the transport of dissolved and
particulate pollutants in such water bodies as lakes, reservoirs, and estuaries. Even in rivers,
longitudinal dispersion can be the most important process diluting peak concentrations that may
result from unsteady loads or spills.
Based on the WASP model, the dispersive exchange flux between two surface water
compartments / and/ at time is modeled by:
H • A
*, jL/ yi
(4-10)
where:
F,^ = dispersive flux from water compartment / to water compartment j (mass
[chemical]/day)
C,, Cj = concentration of chemical in water compartments / and j (g/m3)
M,, Mj = mass of chemical in water compartments i and/ (g/m3)
Ey = dispersion coefficient for exchange between water compartments / and/
(m2/day)
A,! = interfacial area between water compartments / and/ (m2)
Ly = characteristic mixing length between water compartments / and/ (m)
Vt = volume of compartment / (nr)
Vt ~ volume of compartment/(nr').
The distance between the midpoints of the two water compartments is used for the
characteristic mixing length. Values for dispersion coefficients can range from 10"'° nr/sec (8.64x
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10"6 m2/day) for molecular diffusion to 5xl02 m2/sec (4.32x107 m2/day)for longitudinal mixing in
estuaries (Ambrose et al. 1995, p. 35). A value of 2.25X10"4 nr/day is chosen as the default value;
this is median of the range cited in Ambrose et al. (1995) (p. 112) from a study of Lake Erie
conducted by Di Toro and Connolly (1980).
4.4.2 DISPERSIVE TRANSPORT BETWEEN SURFACE WATER AND SEDIMENT
COMPARTMENTS
As for dispersive transport between surface water compartments, dispersive transport
between surface water and sediment compartments is approximated as a first order process using
the method described in the WASP water quality simulation program (Ambrose et al. 1995).
Based on the WASP model, the net dispersive exchange flux between a surface water
compartment / and sediment compartment j is modeled by:
fnC,'
(4-11)
where:
Fj. , = Net dispersive flux between surface water compartment / and sediment
compartment j, mass[chemical]/day
C,,Cj = Bulk concentration of chemical in surface water compartment /and
sediment compartment j mg/L (g[chemical]/m3[compartment])
M,, Mj = Mass of chemical in surface water compartment i and sediment
compartment j (mass[chemical])
Ev = Dispersion coefficient for exchange between compartments / andy, m2/day
Ay = Interfacial area between compartments i and j, m2
Ly = Characteristic mixing length between compartments / andy, m
V,, Vj = volume of compartments / andy, m3
foi-fpi = dissolved fraction of chemical in compartments / and/ (calculated)
n,, rij - porosity of compartments z andy
riy = average porosity at interface ( (n, + n)/2 )
The resulting transfer factors (units of /day) between the surface water / and sediment
compartmenty are given by:
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T - 'L
LJn,J
fD,
(4-12)
(4-13)
Following the method used in WASP (Amborse et al., p. 25), the sediment compartment height is
used as the characteristic mixing length L . The porosity of the sediment compartment («,) is
calculated from the specified benthic solids concentration and solids density. The porosity of the
surface water compartment is set to the volume of water compartment that is water. Values for
dispersion coefficients can range from 10"'° m2/sec (8.64xlO~6 mVday) for molecular diffusion to
5xl02 mVsec (4.32xl07 m2/day)for longitudinal mixing in estuaries (Ambrose et al. 1995, p. 35).
A value of 2.25e-4 m2/day is chosen as the default value; this is median of the range cited in
Ambrose et al. 1995 [p. 112] from a study of Lake Erie conducted by DiToro and Connolly
(1980).
4.5 DIFFUSIVE PROCESSES
4.5.1 DIFFUSIVE EXCHANGE BETWEEN SURFACE WATER AND AIR
The algorithms describing the diffusive exchange of chemical mass between surface
water and air are presented in Section 3.3.2.
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CHAPTER 5
SOIL ALGORITHMS
5. SOIL ALGORITHMS
In this chapter the algorithms for the transport and transformation of chemical species
within and among soil compartments and between the soil compartments and the lower
atmosphere and between the soil compartment and surface water are presented. The text box on
the next page and continued on the following pages provides a quick summary of tfie algorithms
developed in this chapter and provides a definition of all parameters used.
5.1 INTRODUCTION
Two of the primary processes in subsurface soil are exchange by diffusion and advection.
These are key components of the overall rate constant. The transport occurs both in the gas and
liquid phase for organic chemicals. The predominant transport mechanism in the aqueous phase
is advection, and that in the gas phase is diffusion. The advective transport of contaminants in
the liquid or gas phase is dependent on the velocity of that phase. In this application, the total
contaminant mass is estimated for each soil compartment. Important physicochemical properties
include solubility, molecular weight, vapor pressure, and diffusion coefficients in air and water.
The important landscape properties include temperatures of air, rainfall rates, soil properties
(bulk density, porosity), and depth of each soil compartment.
There are three advective processes considered in the prototype that can potentially
transport a chemical from a soil domain to surface water: erosion of surface soil, runoff from
surface soil, and recharge from ground water. Erosion applies to the solid phase, while runoff
and recharge applies to the dissolved phase.
5.2 SOIL COMPARTMENTS AND TRANSPORT PROCESSES
In the TRIM.FaTE model, soil is modeled as three distinct compartment types — surface
soil, rooting-zone soil, and vadose-zone soil above the saturated zone. In TRIM.FaTE these
three regions can be sub-divided into one or more compartments for the purpose of assessing
mass transfer. Among these compartment types there are two kinds of transport considered —
diffusion and advection. In addition, the uppermost surface soil compartment exchanges mass
with the lowest compartment of the atmosphere by a combination of diffusion and advection
processes.
5.3 TRANSFORMATIONS IN SOIL COMPARTMENTS
The transformation of contaminants in soil layers can have a profound effect on their
potential for persistence. Chemical transformations, which may occur as a result of biotic or
abiotic processes, can significantly reduce the concentration of a substance. For all chemical
reactions, knowledge of a compound's half-life for any given transformation process provides a
very useful index of persistence in environmental media. Because these processes determine the
persistence and form of a chemical in the environment, they also determine the amount and type
of substance to which a human or ecological receptor could be exposed. In the TRIM.FaTE soil
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Summary of Transport Algorithms Developed in this Chapter
Lowest air compartment to upper surface soil compartment:
r_. =
U^xArea, xZair
V xZ
a a
First soil compartment to lowest air compartment.
TV =
Downward flow from soil compartment /to soil compartment/
r _ ,
'->' dZ
Upward flow from soil compartment./ to soil compartment /:
Y.
T =
~
Horizontal runoff from compartment /to compartment/
T,^, (runoff) = Runoff x frun (ij) x Z, (rain) I (Z,d, *)
where
Area =
mass transfer coefficient on the air side of the air/soil boundary, m/d (It is typical to
represent the mass transfer coefficient in air as ratio of the diffusion coefficient in
air, Dair, divided by the turbulent boundary compartment thickness, 6air. For many
compounds, Da,r is on the order of 0.4 m/d and 6air is on the order of 0.0005 m, so
that Uair is on the order of 800 m/d.)
horizontal area of the soil compartment, m2 (This is the area assumed to be shared
between the top soil compartment and the atmosphere: and between any two
adjacent soil compartments)
volume of the air compartment, m3.
fugacity capacity of pure air, = 1/RT, mol/(m3-Pa)
total fugacity capacity of the air compartment (includes gas and particle phase of
the atmosphere), mol/(m3-Pa).
fugacity capacity of air particles, mol/(m3-Pa).
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Summary of Transport Algorithms Developed in this Chapter (cont.)
Vd = air-to-soil deposition ratio, mol/m2/d per mol/m3 (includes only deposition that is not
intercepted by plants, and is calculated as the total deposition velocity times one
minus the plant interception fraction), ~ 400 m/d.
PC = particulate matter concentration in air, ~ 6.0 x 10"8 kg/m3.
pp = density of particulate matter in air, ~ 2600 kg/m3 (Wilson and SpenglerT996).
rain = rate of rainfall, m/d.
Zwater = fugacity capacity of the moving phase, water, mol/(m3-Pa).
Area, = area of contact between the surface soil compartment and the lowest air
compartment, m2.
Z, = total fugacity capacity of soil compartment /, mol/(m3-Pa).
Zs, = fugacity capacity of soil compartment /', mol/(m3-Pa),
d, = thickness of soil compartment;', m.
YtJ = fugacity-capacity adjusted mass transfer coefficient between compartments / and j,
mol/(m2-Pa-day), and is given by:
y =•
De, = effective diffusion coefficient in soil compartment /, m2/d.
ve, = effective advection velocity of a chemical in the soil compartment /, m/d, and equal
to the rate of soil-solution movement, v,, multiplied by the fugacity capacity of soil
compartment /; ve, = vZ^JZ,.
v, = average velocity of the moving phase (assumed to be water) in the soil
compartment/, m"1.
Y, - gradient of soil concentration change in soil compartment /, m"1. Obtained from the
inverse of the normalized or characteristic depth X*, that is y, = 1/X*
X* is obtained as follows:
If X, > 0 then X* = Minimum (DX,, DX2)
Otherwise, if A, = 0, then X* = DX2.
DX, is the Damkoehler distance (the distance at which the soil concentration
falls by 1/e based on the competition among diffusion, advection, and
reaction) and is given by:
ve + Jve, + 4De
DX,=— ^
i
2A,.
DX2 is the depth that establishes the concentration gradient in soil in the
absence of any reaction or transformation processes. It is obtained as
follows:
If ve, > 0, then DX2 = Minimum (4De/ve,, DXsat)
If ve, = 0, then DX2 = Minimum (2d,, V(n), DXsat)
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Summary of Transport Algorithms Developed in this Chapter (cont.)
A, = removal rate constant for a chemical in soil compartment, based on chemical
transformation, day"1.
Respnd - rate at which dust is resuspended from the soil surface, kg/m2/d.
Ps, - density of dust particles, kg/m3. _ _
a - volume fraction of the soil compartment that is gas, unitless.
/? = volume fraction of the soil compartment that is water, unitless.
= a + (3
Rh - hydraulic radius of water flowing over surface soil during a rain event, assumed to be
0.005 m.
d, - depth of surface soil compartment during periods of no rain, m.
d* - effective depth of saturated surface soil during a rain event, m,
d,* = Rh + d,
Runoff - flux of water transported away from surface soil compartment/,
m3/m2-day.
frun(ij) ~ fraction of water that runs off of surface soil compartment / that s transported to
compartment;, unitless.
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layers, all transformation processes are modeled as first-order processes; that is, linear with
inventory (i.e., the quantity of chemical substances contained in a compartment). The rate of
mass removal in a first-order transformation is calculated as the product of the total inventory
and the transformation rate constant. The transformation rate constant is the inverse of the
residence time with respect to that reaction.
5.4 VERTICAL TRANSPORT ALGORITHMS
The transfer factors in the subsurface are a function of the advective flux (gas phase plus
liquid phase) and the diffusive flux (gas phase plus liquid phase). In the sections below, upward
and downward transfer factors are developed for the soil compartments. No provisions are made
for preferential flow regions in the vadose zone that could lead to higher concentrations in the
ground water because in most cases, the proportion of exposure from ground water is minimal
for air pollutants.
5.4. 1 THEORETICAL BASIS FOR THE TRANSPORT ALGORITHMS
The algorithms below are developed by assuming that chemical concentration in each
compartment decreases exponentially with depth in that compartment. This type of
concentration gradient has been demonstrated as the correct analytical solution of the one-
dimensional, convective-dispersive, solute-transport equation in a vertical layer with a steady-
state concentration maintained at its upper surface (ARS 1982). With the assumption of
exponentially decreasing vertical concentration for each soil compartment, /, the variation in
concentration with depth in that compartment is given by:
= C1(0)exp(-y,A:) (5-1)
where:
x = distance into the soil compartment measured from the top of the soil
column (m);
C,(0) - peak chemical concentration in soil compartment i (mol/m3), which is
related to the total inventory A', (moles) in this soil compartment (this
relationship is provided below):
Y, - the gradient of soil concentration change in soil compartment / (m"1), and
is obtained from the inverse of the normalized or characteristic depth X*,
that is Y, = 1/X*.
X* is obtained as follows:
If A, > 0 then X* = Minimum (DX,, DX2)
Otherwise, if A, = 0, then X* = DX2. (5-2)
DX, is the Damkoehler distance (the distance at which the soil
concentration falls by 1/e based on the competition among diffusion,
advection, and reaction) in units of meters and is given by:
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ve, + Jve,
^- (5-3)
DX2 is the depth that establishes the concentration gradient in soil in the
absence of any reaction or transformation processes, in units -of meters. It
is obtained as follows:
If ve, > 0, then DX2 = Minimum (4De,/ve,, DXsat)
If ve, = 0, then DX2 = Minimum (2d,, V"(n), DXsat) (5-4)
ve, = the effective advection velocity of a chemical in the soil compartment, /
(m/day), and equal to the rate of soil-solution movement, v,, multiplied by
the fugacity capacity of the moving phase and divided by the fugacity
capacity of soil compartment /;
ve>, = v,ZMUK/Z, [5-5]
v, = the average velocity of the moving liquid phase (assumed to be water) in
the soil column / (m/day);
DXsal = depth to saturation in the soil column (m);
d, = the thickness of soil compartment / (m);
Zwaler = the fugacity capacity of the moving phase, water (mol/[m3-Pa]);
Z, = the total fugacity capacity of soil compartment / (mol/[m3-Pa]);
2, = removal rate constant for a chemical in soil compartment /, based on
chemical transformation (day"1); and
De, = effective diffusion coefficient in soil compartment / (nr/d), and is derived
below.
Compartments such as soils and sediments are neither homogeneous nor single phase.
When air and water occupy the tortuous pathways between stationary particles in a porous
medium such as a soil or sediment, Millington and Quirk (1961) have shown that the effective
diffusivity, Defr, of a chemical in each fluid of the mixture is given by:
Dtff =(a>lon/4r)D_ (5-6)
where co (a for gas fraction and ft for water fraction) is the volume fraction occupied by this
fluid, (p is me total void fraction in the medium (the volume occupied by all fluids) , and Dplire is
the diffusion coefficient of the chemical in the pure fluid. Jury et al. (1983) have shown that the
effective tortuous diffusivity in the water and air of a soil compartment, such as the root-zone
soil(s), is given by:
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)D8ir
)DW
(5-7)
where De, is the effective tortuous, mixed phase diffusion coefficient in the root-zone seil
compartment, the Z's are the fugacity capacities derived previously.
5.4.2 RELATIONSHIP BETWEEN INVENTORY, Nw AND PEAK CONCENTRATION,
The assumptions of a peak chemical concentration and an exponential gradient of
chemical concentration within a soil compartment makes it possible to define C,(0) in terms of
N-
,
N, = Area, Jc,(0)exp(-7(jt)djc
(5-8)
(5-9)
where:
N, -
C, =
d, =
Area =
compartment inventory (mol)
compartment-eoncentration (mol/m3)
thickness of soil compartment / (m); and
horizontal area of the soil compartment (m2).
Rearranging the right term of Equation 5-9 gives:
C (0) =
Nj
(5-10)
5.4.3 VERTICAL MASS EXCHANGE BETWEEN AIR AND THE UPPER SURFACE
SOIL COMPARTMENT
The algorithm for representing diffusion exchange at the air/soil interface is based on
defining the flux from air to soil in terms of the concentration gradient at the point of contact
between air and soil.
Flux = U
Cair-C.(QY
(5-11)
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where:
Uair = mass transfer coefficient on the air side of the air/soil boundary (m/d) (It
is typical to represent the mass transfer coefficient in air as the ratio of the
diffusion coefficient in air, Da^ divided by the turbulent boundary
compartment thickness, 6air. For many compounds, Dair is on-the-order of
0.4 m/d and 6air is on the order of 0.0005 m, so that Uair is on the order of
800 m/d.)
Cair = bulk concentration of chemical agent in the lowest compartment of the
atmosphere, mol/m3 and given by Cair = Na Za,/[Va ZJ, where Na is the
inventory (in mol) of the air compartment above the soil, Za:r is the
fugacity capacity of pure air, Va is the volume (in m3) of this compartment,
and Za is the total fugacity capacity of the air compartment (includes gas
and particle phase of the atmosphere).
C,(0) = chemical concentration at the top of the uppermost soil compartment in a
vertical set of soil compartments, ml/m3, as given by Equation 5-6. There
can be several vertical soil compartment sets in a model run.
Zair = fugacity capacity of pure air, = 1/RT, mol/(m3--Pa).
Making the appropriate substitutions, the net flow of mass between air and soil by diffusion is
calculated as:
Net Diffusion Flow (a<->f) (mol/day)
= Flux x Area, = U
Areat x Zt
V. xZ.
•N
7,
Z
•N
(5-12)
It is important to note that the area used to calculate the flux is Area,, the surface area of
the soil compartment / that is shared with the lowest atmosphere corrpartment. This is not
necessarily the surface area of the lowest atmosphere compartment.
For dry and wet deposition of particles from air to soil, the rate of mass flow is given by:
Particle Advection Flow (a-*i) (mol/d)
= Vd(PCIpp}(AreaiIVa}(ZapIZa]Na (5-13)
where:
V
PC
air-to-soil deposition ratio (includes only deposition that is not intercepted
by plants, and is calculated as the total deposition velocity times one
minus the plant interception fraction (mol/m2/d per mol/m3) ~ 400 m/d;
particulate matter concentration in air ~ 6.0 x 10"8 kg/m3;
density of the particulate matter in air ~ 2600 kg/m3;
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Area, = area of contact between the surface soil compartment and the lowest air
compartment (m2); and
Va = volume of the air compartment (m3).
For rainfall, the advection flow of chemical from air to the upper surface soil
compartment is given by: — -
Rain Advection Flow (a ->/') (mol/d)
= rain[ZwalerIZa][Areai/Va]Na
where:
Zwaier = fugacity capacity of pure water (i.e., no suspended sediments)
Za = fugacity capacity of the air compartment (mol/nr'-Pa)
rain = the rate of rainfall (m/d).
For re-suspension of dust from the first surface soil compartment to the lower
compartment of the atmosphere, the chemical flow from soil to air is given by:
Advection Flow (/' ->d) (mol/d)
where:
Respnd
A,
= [Respnd/p,l}[ZJZl][ArealIVtt}Nt
rate at which dust is resuspended from the soil surface
(kg/m2/d); and
density of the dust particles (kg/m3).
(5-14)
(5-15)
Combining Equations 5-12 through 5-15 provides the following transfer-rate factors for
the exchange of chemical species between the lowest atmosphere compartment and the surface
soil compartment:
(5-16)
UairxAreaixZair~
V xZ
a a
,{,
PC
_pp _
1X1
LZJ
+ rain
7
water
. zfl
Ix
J
Area:
va
r... =
u . r
air / i
_[l-exp(-yl.rf,)]_
x,~
Z5
+
Respnd
P»
"Z/
Z, _
X
Ar^a,
Vfl
(5-17)
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5.4.4 VERTICAL MASS EXCHANGE BETWEEN TWO VERTICALLY ADJACENT
SOIL COMPARTMENTS
The vertical exchange of a chemical substance between two vertically adjacent soil
compartments occurs through advection and diffusion. Only the net advection in the downward
direction is considered due to long-term infiltration of rainwater. According to Equation 5-1, the
concentration in each soil compartment i is given by:
Ct(x) = C,(0)exp(-7(j:) (same as 5-1 above)
where x is measured from the top of the soil compartment /'. Thus, the diffusion flow at the lower
boundary of soil compartment / to compartment/ is given by:
diffusion flow = -Area xDet-
dC
(5-18a)
d.
dx
where:
De, - effective diffusion coefficient in soil compartment /', m2/d
d, = the thickness of soil compartment i, m;
Conservation of mass requires that flow specified by equation 5-18 out of compartment / must
equal the flow into compartment/ at the upper boundary of compartment/, that is:
dC
diffusion flow = -Area X De —
1 dx
Combining equations 5-18a and 5-18b gives:
= AreaxDe XC (Q)xy (5-18b)
[pe,xC.(0)xY.«-*-+Pe,xC,(0)XY,] "
diffusion flow = Area x- l ;
C,(0) is found from the condition:
c (fn ,
(5-20)
o
Rearranging gives:
C(0) = 7Jj 77T (5-21)
Areax(\-e-''d')
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In order to conserve concentration equilibrium at the boundary between two soil compartments,
the following condition must hold:
xe
7 |V~'- 7
Li ^i
Substituting equations 5-21 and 5-22 into equation 5-19 gives
(5-22)
diffusion flow -
Then in order to express mass transfer between two compartments, the diffusion flow is
represented in the following form:
(5-23)
diffusion flow = Area xY
N
(5-24)
where:
Y(J = fugacity-capacity adjusted mass transfer coefficient between compartments
z and j, mol/(m2-Pa-day).
N the total inventory in compartment y is given by:
N =
= Areax
C,(0)
(5-25)
Substituting equation 5-23 in equation 5-25 gives:
N .= —
(5-26)
An expression for 7y is obtained by substituting equation 5-26 for NJ in equation 5-24 and then
setting equation 5-24 equal to equation 5-23:
N
y
,x('-
,4
+J'd>
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CHAPTER 5
SOIL ALGORITHMS
Rearranging gives:
2
~ ( +Y
(e
'•-0
(l-^V0~
YA Y/,
(5-28)
The definition of YtJ in equation 5-28 completes the definition of all terms in equation 5-24.
The advection flux from soil compartment i toy at the lower end, d,, of compartment / is given
by:
advection flow(i to j) = Area x vet x C(
where:
ve.
(5-29)
the effective advection velocity of a chemical in the soil compartment, /;
m/d, and equal to the rate of soil-solution movement, v,, multiplied by the
fugacity capacity of the moving phase and divided by the fugacity capacity
of soil compartment /;
_ ve: - V| *
the average velocity of the moving phase (assumed to be water) in the soil
compartment, /; m .
Substituting Equation 5-21 for C,(0) in Equation 5-29 gives:
advection flow(i to jj =
(5-30)
Combining Equations 5-24 and 5-30 and multiplying by Area,, gives the flow from / toy as:
net total flow (mol/d) (/ toy) = [net diffusion flow + advection flow] (i toy)
\
N
1 V \ = T. . N
N
"
(5-31)
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CHAPTER 5
SOIL ALGORITHMS
From this equation, we can derive terms for T, ^ and T}.
T =+_ (5.32)
- dZ
Y
T = —— (5-33)
dJZJ
5.5 STORM WATER RUNOFF PROCESSES
Horizontal transport processes included in TRIM.FaTE include solution runoff and
erosion.
5.5.1 AQUEOUS PHASE TRANSPORT PROCESSES
During a rainfall event, some of the water travels laterally across the soil as runoff. As
the water travels over the soil, the concentration of the water approaches that of the soil pore
water beneath it. Although the water flowing over the soil does not necessarily reach equilibrium
instantaneously, some researchers use an approximation that runoff is in equilibrium with the soil
pore water (Wallach et al. 1989). Currently in TRIM.FaTE, a steady-state relationship between
the runoff water and the pore water is used. Runoff water is considered a phase of surface soil
compartment at each spatial location. A mass-balance approach is used to determine the
concentration in run-off water that moves from one soil compartment to a horizontally adjacent
compartment.
Runoff transport is assumed to carry chemical from the surface soil compartment of one
land unit to the next. During a rain event the surface soil compartment is assumed to be saturated
with rain water and this water is assumed to be in equilibrium with the soil solids on Jhe surface.
It should be recognized that at times (e.g., short rain events, during very dry periods of the year)
the soil will not necessarily be fully saturated with rain water. However, the assumption of
saturation by rain is not expected to have a large impact on results for events when the soil is not
saturated. Moreover, a lack of information on the extent to which soil is saturated during rain
makes this a convenient starting point. The assumption of that chemical equilibrium has more
uncertainty and needs further research. During periods of no rain, the fugacity capacity of the
surface soil compartment is given by:
Z, =aZuir+/3Zlia/fr+(l-0)Zs, (5-34)
During periods of rain, the fugacity capacity of the surface soil compartment is given by:
Z,(rain) = [(Rh+dl)Zlialer + (I - d, )Z J / d, * (5-35)
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SOIL ALGORITHMS
where:
Zwaur ~ fugacity capacity of pure water (i.e., no suspended sediments)
Zs, = fugacity capacity of the solids (or solid phase) in the ith soil layer (mol/m3-
Pa)
a = volume fraction of the surface soil that is gas; — -
P = volume fraction of soil that is water;
(f) = total void fraction in surface soil, (f) = a + /?;
Rh = hydraulic radius of the water flowing over the surface soil during a rain
event, assumed to be 0.005 m;
d, = depth of the surface soil compartment during periods of no rain (m); and
d* = effective depth of the saturated surface soil during a rain event (m),
d,*=Rh + dr
The hydraulic radius, Rh, for flow of water on top of the soil surface is site specific and
depends on the hydraulic gradient (slope of the flow), the rainfall rate, and the recharge rate. It is
considered an uncertain variable, but is assigned a default value of 0.005 m. A hydraulic balance
is needed to determine the flow of the water and the depth of the runoff stream. From the
Geographic Information System (GIS) data, the runoff is estimated.
During a rain event, the horizontal flow of chemical from surface soil compartment / to
adjacent compartment 7 is given by:
Runoff flow (i -> j) = Runoff x frun(i -> j^Z^rain} /Zjd t * (5-36)
where:
Runoff = flux of water that is transported away from surface soil
compartment / (m3/m2-day); and
frunft ~*J) = fraction of water that runs off of surface soil compartment / that is
transported to compartment 7 (unitless).
From Equation 5-36, the expression for T, ^(runoff) can be obtained:
T,^ (runoff ) = Runoff X frun (i -> ;) x Z, (rain)/(Zldl *) (5-37)
5.5.2 SOLID PHASE TRANSPORT PROCESSES
The algorithm for erosion runoff is based on knowledge of the erosion factor for the
region being modeled. Similar to solution runoff, erosion is also applied only to the surface soil
layer. Although erosion is most likely to occur during rain events, erosion can be modeled as a
continuous event. The flow of chemical (mol/d) from one surface soil compartment to another
by erosion is represented by the following expression:
Erosion flow (i->j) = erosion xfcro (i->j) * ZW/Z, x N,/ (p^d) (5-38)
NOVEMBER 1999 M4 TRIM. FATE TSD VOLUME II (DRAFT)
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where:
erosion = erosion factor (kg of soil solids eroded per day per m2);
ferofi ~J') = fraction of soil eroded from surface soil compartment / that is
transported to compartment y (unitless);
ZSI - fugacity capacity of the soil particles in soil compartment/ (mol/
[m3-Pa]);
psl = density of the soil particles,-2600 kg/m3.
From Equation 5-36, the expression for T^(erosion) can be obtained:
T_.,/erosion) = erosion *fji~>j) x ZSI/(Z, psl d) [5-39]
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CHAPTER 6
GROUND WATER ALGORITHMS
6. GROUND WATER ALGORITHMS
The horizontal flow of pollutants in the saturated zone (ground water) is not expected to
be a significant pathway when considering air pollutants. Transport has been simulated because
it is a more significant process than diffusion/dispersion. In the prototype, ground water is
modeled as a receiving cell from the vadose zone and a sending cell to surface water. The
transfer factors for soil to ground water and for ground water to surface water are based on the
aqueous phase advection only by substituting recharge for flow velocity:
soihgrounawater V 7
soil total
grounder „
^ '
and
A Z
reroundwater surfacewaler water n ; _
, , —2 J- Recharge (6-2\
groundwater-surjacewater i/- ^ ° V" *•/
groundnaler total
where:
A = cross section area between cells (m2)
V = volume of cell (m3)
Recharge = annual recharge into ground water (m/h).
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CHAPTER 7
BIOTIC ALGORITHMS
7. BIOTIC ALGORITHMS
In this section algorithms for transfers between a biotic compartment type and another
biotic or abiotic compartment type are presented. Algorithms are based on diffusive or advective
transfer, and most common instances of the latter are transfers via the wildlife diet. _Mqst
algorithms apply to all air pollutants, though some that involve octanol-water partition
coefficients are only applicable to organic chemicals and mercury species. Some of the equations
represent dynamic processes, and others are simple models for which a time-to-equilibrium is
calculated. The text box on the next page and continued on the following pages provides a quick
summary of the algorithms developed in this chapter and provides a definition of all parameters
used. The derivation of chemical-specific algorithms and input parameters is presented in
Appendix A.
7.1 SELECTING THE BIOTIC COMPONENTS OF TRIM.FATE
The methodology for determining biotic compartment types is described in Section 3.3 of
Volume I of the Technical Support Document for TRIM.FaTE. All major trophic levels in
terrestrial and aquatic systems are represented. Default, representative species are chosen based
on their prevalence at the test location and/or the availability of parameters for them. Additional
species may be chosen based on policy considerations, such as the Endangered Species Act.
General algorithms for plants (Section 7.2.1). soil detritivores (Section 7.2.2), terrestrial
mammals and birds (Section 7.2.3) and aquatic biota (Section 7.3) are listed below.
7.2 ALGORITHMS FOR TERRESTRIAL AND SEMI-AQUATIC BIOTA
7.2.1 PLANTS
The plant consists of four compartment types: leaf, stem, root, and the leaf surface
(particulate on leaf Lp). Although the leaf surface is not in the plant, it is useful to track because:
(1) it is a reservoir of chemical moving to leaves and (2) wildlife diets include particylate matter
on leaves.
Several problems arise in modeling uptake and emissions of chemicals by plants.
Little information is available on the transformations of chemicals within plants.
The volatilization of chemicals from soils and uptake by plant foliage occurs at a scale
that is not easy to model in TRIM.FaTE.
Little is known about the rate at which chemicals enter plant leaves from particulate
matter or rain water on the leaf surface.
The transport of many chemical species within the plant is not well understood.
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Summary of Transport Algorithms Developed in this Chapter
PLANTS
Participate phase of air to surface of plant leaf (when no rain):
V ,/ , Ar
/-i a a j
y
V A
Surface of plant leaf to particulate phase of air (when no rain)1
Lp-^fAp ~ TT
A
Vapor phase of air to the leaf surface (during rain):
1
Particles in air to the leaf surface (during rain)
Surface of leaf to surface soil (during rain)
7^=57.6
Leaf surface to leaf:
T - k
1 LP-+L ~ * LP-L
Leaf to leaf surface:
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Summary of Transport Algorithms Developed in this Chapter (cont.)
PLANTS (cont.)
Leaf to air (diffusion):
1 Z,
^A = (2LAI x As x gc + As x gs) x — x
V 7
V L Ll
Air to leaf (diffusion):
T
-ln(l-0.95)
'0 95
Root-zone soil to root.
Root to root-zone soil:
X
parea R K R_Sr
X
pvolR dsr
T.
r->Sr
-ln(l-0.95)
t,
0.95
Root-zone soil to stem:
Tc
-xTSCF
Leaf to stem:
Stem to leaf:
V
Si St-Xy
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Summary of Transport Algorithms Developed in this Chapter (cont.)
PLANTS (cont.)
Leaf to surface soil (litterfall):
T -I
1 t-»Si ~ ^
Leaf surface (paniculate matter) to surface soil (litterfall):
T = L
1 Lp-*Ss ^
where:
VA = volume of air volume element (m3)
va = dry deposition velocity of particles (m/d)
ld = fraction of dry-depositing chemical that is intercepted by plant canopy
As = soil area (m2)
Jrain = rain rate (m/d)
wr = washout ratio (mass chemical/volume rain - mass chemical/volume air)
lw = interception fraction for wet deposition (unitless)
kip-L = first-order rate constant for transfer of chemical from particles on leaf surface to leaf
LAI = 1-sided leaf-area index (m2 total leaf area / m2 underlying scil area)
VL = volume of leaves (m3)
Zp ~ fugacity capacity (Z-factor) of chemicals in plant (mol-Pa"1nr3)
ZL - fugacity capacity (Z-factor) of chemicals in leaf (mol-Pa~1nT3)
gs = conductance of stomatajjiathway, including mesophyll (m/d)
gc = total conductance of the"cuticular path, including the air boundary layer (m/d)
ZA = fugacity capacity of chemicals in the vapor phase of air (mo!Pa"1m3)
KR-sr = root-soil partition coefficient (wet kg/kg per wet kg/kg)
pareaR = areal density of root in root-zone soil (kg root fresh wt/m2)
pvolR - wet density of root (kg/m3)
dsr = depth of root-zone soil (m)
Qxy = flow of transpired water in cell area (m3/d, below)
TSCF - transpiration stream concentration factor (mg/m3 of xylem per mg/m3 of soil pore water)
VSrW - volume of water in root-zone soil (m3)
Zwater - fugacity capacity (Z-value) for water
2Sr = fugacity capacity (Z-value) for root-zone soil
VSr - volume of root-zone soil volume element (m3)
QP = phloem flux into fruit (m3/d), due to advection (assume 5 pe'cent of Q^, Paterson et al.
1991)
KLfhh - partition coefficient between leaves and phloem water (mass/vol to mass/vol)
Qxy = flow of transpired water (m3/d)
Vst = volume of stem (m3)
Kst.Xy - partition coefficient between stem and xylem water (mass/vol to mass/vol)
L = litterfall rate (d'1)
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Biouc ALGORITHMS
Summary of Transport Algorithms Developed in this Chapter (cont.)
SOIL DETRITIVORES
Root-zone soil to earthworm:
T
Sr—tworm
-ln(l-0.95)
[0.95
A
worm—Sr
Sr
Earthworm to root-zone soil:
' K orrn —>5r
-ln(l-0.95)
'095
Root-zone soil to soil arthropod:
T.
Sr—>arth
-ln(l-0.95)
'0 95
xpareaar:h x As x
• arlh-Sr
M
Sr
Soil arthropod to root-zone soil:
-ln(l-0.95)
1 arth-tSr
where:
[095
IS
^
areal density of earthworm community in root-zone soil (kg worm fresh wt/m2)
wet density of earthworm (kg/m3)
earthworm-soil partition coefficient (wet kg/kg per wet kg/kg)
depth of root-zone soil (vsr/As)
soil area (m2)
arthropod-soil partition coefficient (wet kg/kg per wet kg/kg)
total mass of root zone soil which contains arthropods (kg)
areal density of arthropod community in root-zone soil (kg arthropod fresh
wt/m2)
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Summary of Transport Algorithms Developed in this Chapter (cont.)
TERRESTRIAL WILDLIFE
Water to terrestrial vertebrate:
/, x A,
=par«flH./xAJ x
H1 H1
H
Surface soil to terrestrial vertebrate:
55 55
Plant leaf to terrestrial vertebrate:
p p X I D X Ap
Surface of plant leaf to terrestrial vertebrate'
Earthworm to terrestrial vertebrate:
'
D
Soil arthropod to terrestrial vertebrate:
/^X/DX
Terrestrial vertebrate to terrestrial vertebrate
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CHAPTER 7
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Summary of Transport Algorithms Developed in this Chapter (cont.)
TERRESTRIAL WILDLIFE (cont.)
Fish to terrestrial vertebrate:
pf xID x
K, = pareaw! x As x
ASH. x pareaf
Benthic invertebrate or flying insect to terrestrial vertebrate:
MV, = parea wlxAs x
P BI x ID
x
Asw x parea
BI
Air to terrestrial vertebrate:
1
TA_+wl = pareawl X As x-
Terrestnal vertebrate to surface soil:
T — f F
i ,..i vcc — j uss £< u
A x AA
V,
Terrestrial vertebrate to water:
T - f E
«'/—>«' J UW U
where.
/ss
''ss
/cvo/sgwef
/\
PP
/n
pareaL
Pworm
A
wet wildlife biomass density per unit area (kg/m3, may be calculated as
number of animals times average body weight)
area of surface soil (m2)
water ingestion rate (m3/kg body weight/d)
volume of water (m3)
assimilation efficiency of chemical from water (unitless)
surface soil ingestion rate (kg/kg body weight/d)
volume of surface soil (kg)
wet bulk density of soil (kg/m3)
assimilation efficiency of chemical from surface soil (unitless)
proportion of plant matter in diet (unitless)
dietary ingestion rate (kg/kg body weight/d)
assimilation efficiency of chemical from plant in diet (unitless)
areal biomass density of foliage (kg/m2, wet weight)
proportion of earthworm in diet (unitless)
assimilation efficiency of chemical from earthworm in diet (unitless)
areal biomass density of earthworms (kg/m2, wet weight)
NOVEMBER 1999
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Summary of Transport Algorithms Developed in this Chapter (cont.)
TERRESTRIAL WILDLIFE (cont.)
partrt = proportion of soil arthropods in diet (unitless)
Aanh = assimilation efficiency of chemical from soil arthropods in diet (uriitless)
pwl = proportion of terrestrial wildlife in diet (unitless)
Aw, = assimilation efficiency of chemical from other wildlife in diet (unitless)
p, = proportion of fish in diet (unitless)
Af = assimilation efficiency of chemical from fish in diet (unitless)
parea, = areal biomass density of fish (kg/m2, wet weight, use correct size range for
diet)
pbl = proportion of benthic invertebrates or emergent Hying insects in diet (unitless)
Abl = assimilation efficiency of chemical from benthic invertebrates or flying insects
in diet (unitless)
Asw = area of surface of surface water body (m2)
pareabl = areal biomass density of benthic invertebrates (kg/m2, wet weight)
IA = inhalation rate (m3/kg body weight/d)
VA = volume of air (m3)
AA - assimilation efficiency of chemical from air (unitless)
Eu = chemical elimination through excretory processes (urine and feces) (d"1)
f,,„, = fraction of urine and feces excreted to water
uw
fuss = fraction of urine and feces excreted to surface soil
AQUATIC BIOTA
Water to macrophytes'
_, mp mp,acc—sw
w — >mp if
w
Macrophytes to water:
T -I
—
mp,dep-sw
Water (interstitial or overlying) to benthic invertebrates.
Hbi mbi Hi.acc-w
I/
w
Benthic invertebrates to water (interstitial or overlying)
T -k
bi—*w bi,dep-w
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Summary of Transport Algorithms Developed in this Chapter (cont.)
AQUATIC BIOTA (cont.)
Sediment to benthic invertebrates:
y
v sed Psed
Benthic invertebrates to sediment:
T =k
biased bi,dep-sed
Water to a specific fish domain (i.e., herbivore, omnivore, or carnivore), using the bioenergetic-based
kinetic model for nonionic organic chemicals:
_
water — >fish TJ
IV
A specific fish domain (i.e., herbivore, omnivore, or carnivore) to water, using the bioenergetic-based
kinetic model for nonionic organic chemicals:
T — k
fish — twater eg
A specific fish domain (i.e., benthic omnivore, benthic carnivore, water column herbivore, water
column omnivore, or water column carnivore) to the water domain, using the bioenergetic-based
kinetic model for mercury:
T"1 _ T^"
receptor ( fish) — > water E
Dietary items to a specific fish domain (;.e., benthic omnivore, benthic carnivore, water column
herbivore, water column omnivore, or water column carnivore), using the bioenergetic-based kinetic
model:
„ n receptor m receptor
1 diet->receptor(fish) ~ A Trf A £,
ndiet mdiet
Dietary items to a specific fish domain (;.e., benthic omnivore, benthic carnivore, water column
herbivore, water column omnivore, or water column carnivore), using the time to steady-state-based
kinetic model :
receptor receptor
diet-^receptor (fish)
'-ln(l-a)
'«
receptor—diet
NOVEMBER 1999 7-9 TRIM.FATETSDVOLUMF.il (DRAFT)
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CHAPTER 7
BIOTIC ALGORITHMS
Summary of Transport Algorithms Developed in this Chapter (cont.)
AQUATIC BIOTA (cont.)
A specific fish domain (i.e., benthic omnivore, benthic carnivore, water column herbivore, water
column omnivore, or water column carnivore) to the associated dietary items, using the-iime_to
steady-state-based kinetic model:
receptor (fish)^>diet
where'
//
^
receptor-diet
mp,acc-sw
I/
mp.dep-sw
bi acc-sed
if
bi acc-w
"fci.dep-sed
receptor
mbl
md,et
m,
receptor
vsed
V,.,
-ln(l-a)
receptor-diet partition coefficient
accumulation from surface water, for macrophy:es (1/day)
depuration to surface water, for macrophytes (1/day)
accumulation from sediment, for benthic infauna (1/day)
accumulation from water, for benthic infauna (1/day)
depuration to sediment, for benthic infauna (1/day)
depuration to water, for benthic infauna (1/day)
elimination via the gills, for fish (1/day)
uptake rate constant for fish from water via the gills (1/kg-day)
number of organisms comprising the benthic invertebrate domain
number of contaminated items comprising the potential diet
number of organisms comprising a specific fish domain
number of receptors
mass of individual organisms comprising the benthic invertebrate domain
mass of individual items comprising the potential diet (ug)
mass of individual organisms comprising a specific fish domain (ug)
mass of individual receptors (ug)
time required to reach a percent of the steady-state value when the
concentration in the source is approximately constant with time (day)
volume of the macrophyte in the cell (L)
volume of sediment in the cell (L)
volume of water in the cell (L)
bulk density of sediment (g/L)
feeding rate constant (kg[prey]/kg[predator]-day)
efficiency of transfer of chemical
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• The accumulation of chemicals by wood is not well understood; therefore, trees in
TRIM.FaTE consist of leaves only and not stems or roots, except to the extent that stems
are conduits of chemicals from leaves.
7.2.1.1 Transfer of Particles and Rain to Surface of Leaf
The surface of the leaf includes: dry particulate matter deposited to the plant surface,
particles deposited to the plant surface in rain water, and rain water containing gaseous chemical.
Deposition is defined here as the mass transfer of suspended particulates from air to the plant
surface. Elsewhere (e.g., Lindberg et al. 1992), the deposition of chemicals to plants is defined
to include the gaseous fraction of the pollutants that come into contact with plants. The uptake of
gaseous pollutants in TRIM.FaTE is treated below.
Dry or wet deposition to the surface of the leaf is the deposition velocity times the leaf
interception fraction. The leaf interception fraction (I) is the fraction of particles that land on the
leaf; thus 1-1 is the fraction that lands on soil. It is common for a concentration of a deposited
particulate chemical to be estimated with respect to the leaf or above-ground plant mass.
However, when that concentration is estimated, it is often forgotten that most of the chemical
mass is still on the plant rather than in it.
Dry Deposition of Particles to Surface of Plant Leaves
Dry deposition is estimated by multiplying the predicted air concentration at ground level
by the deposition velocity (U.S. EPA 1997a). Thus, a flux equation that expresses dry deposition
to the leaf, from van de Water (1995) follows. Note that the area of soil and that associated with
an air volume element may be different.
dN
LP
dt
N
Ap
(7-1)
where:
*AP
mass of chemical depositing on leaf surfaces from particulate matter in air
(kg)
mass of particle-bound chemical in air (kg)
volume of air volume element (m3)
dry deposition velocity of particles (m/d)
fraction of dry-depositing chemical that is intercepted by plant canopy
(unitless, below)
soil area (m2)
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The interception fraction for dry deposition (Ij) may be calculated using the following
equation (Baes et al. 1984):
T _ i _ ( \-WL)(-axparea) (7-2}
where: __ _
a = vegetation attenuation factor (m2/kg)
parea = wet above-ground non-woody vegetation biomass inventory per unit area
(kg/m2)
WL = water content of leaf (mass/mass, unitless)
The water content adjusts parea to represent dry biomass. The equation was originally
derived for pasture grasses and hay and expanded to other crops. Foi this reason, the biomass
should not include wood. The vegetation attenuation factor (sometimes called the foliar
interception constant) is sometimes equivalent to the surface area of leaves divided by plant
biomass (van de Water 1995) or the leaf biomass if the plant is woody.
Thus,
V ./ , A
T d *
1
where: _
TAp.Lp = transfer factor from particulate phase of air to surface of plant leaf (process
occurs when it is not raining)
If it is assumed that particles are blown off the plant with wind at a rate that equals the deposition
rate to leaves, and all particles are dispersed in air,
( }
where:
TI.P >AP = transfer factor from surface of plant leaf to particulate phase of air (process
occurs when it is not raining)
Wet Deposition to Plants
Rain scavenges some of the chemical mass from the vapor phase and particulate phase of
air. Wet deposition resulting from these processes may be modeled distinctly with the same
equation. The rate of mass transfer of vapor-phase or particulate phase mercury from air to rain
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water and to the surface of the plant leaf is described by the following equation (modified from
van de Water 1995):
dt VA
where:
NLp = mass of chemical on surface of leaf (kg)
NA = mass of chemical in gas phase of air (kg)
VA = volume of air (m3)
Jram = rain rate (m/d)
wr = washout ratio (mass chemical/volume rain + mass chemical/volume air)
As = area of soil (m2)
Iw = interception fraction for wet deposition (unitless)
The interception fraction may be calculated using the following equation from Muller and
Prohl (1993). The fraction is dependent on how much water the leaf can hold, the total amount
of rainfall, and the ability of the element or compound to stick to the leaf.
/.., =
LA/"" '~'n2
ram
(7-6)
where:
LAI = 1-sided leaf-area index (m2 total leaf area / m2 underlying soil area)
S = vegetation-dependent leaf-wetting factor (retention coefficient) (m)
rain = amount of rainfall of a rainfall event (m)
If Iw is calculated to be greater than 1, then the value must be set to 1. Thus,
V
TA-LP =—XwrxJra,«*AsXlw (7-7)
A
where:
TA_!n = the transfer factor from the vapor phase of air to the leaf surface
The rate of mass transfer of particulate-phase mercury from air to rain water and to the
surface of the plant leaf may be described by an analogous equation:
(7-8)
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CHAPTER 7
BIOTIC ALGORITHMS
where:
^
N
Ap
w
Thus,
mass of chemical on surface of leaf (kg)
mass of chemical in particulate phase of air
volume of air (m3)
washout ratio (mass chemical/volume rain -^ mass chemical/volume air)
rate of rainfall (m/d)
area of soil (m2)
interception fraction (unitless, see equation above)
T
(7-9)
where:
1 Ap -Lp
the transfer factor from particles in air to the leaf surface
Washoff of Chemical from Plant Surface
It has been observed that particles on the surface of conifer leaves are washed off (during
rain events) according to first-order kinetics with a rate constant of 0.04 per min (McCune and
Lauver 1986). The rate of 0.04 per min is equivalent to 2.4 per hour or 57.6 per day. It may be
assumed that the particles deposited in rain water and the chemical dissolved in rain water is
washed off at the same rate. Thus,
dN
Lp
dt —57.6XA,,
(7-10)
and
where:
T -
1 Lp ASs
7^=57.6
transfer factor from surface of leaf to surface soil during rain (d"1)
(7-11)
An alternative type of transfer would be an instantaneous transfer at the end of a rain event,
where the transfer would also be derived from McCune and Lauver (1986):
-0 0003rain
(7-12)
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7-14
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CHAPTER 7
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where:
TLp _,& = transfer factor from surface of leaf to surface soil during rain
(instantaneous)
rain = cumulative amount of rain during rain event (m)
The implementation of this transfer may be required if the high first-order rate constant above
(which is equivalent to 2.4 per hour) causes instability in LSODE, the differential equation
solver.
Note that it may not be assumed that the transfer factor for loss to soil is the same as the
transfer from the vapor phase of air or particles in air via rain (as is assumed with dry
deposition). In order to have this option, the vapor phase and particulate phase of the chemical in
rain water on the surface of the leaf would have to be tracked separately, and two transfer factors
to surface soil would be required.
Transfer of Chemical to Leaf from Particles on Plant
The fraction of deposited chemical that enters the plant cuticle per day is very uncertain.
It depends on the relative concentrations in the plant and particles at equilibrium (which is
unknown), as well as the time to equilibrium. It is sometimes assumed that chemicals attached to
particles reach instantaneous solution equilibrium with plant tissues when they land on the plant.
If that assumption is made for some chemicals (e.g., mercury), TRIM.FaTE is likely to
overestimate the contribution of the particles to uptake of the chemical by the plant (Lindberg
1999a). For a chemical that is tightly and chemically bound to particles in air (e.g., Hg), an
initial assumption of 0.2 per day may be appropriate. Because particles cover only a small
fraction of the surface of the plant, it is assumed that the rate of transfer from leaves to particles
is 1 percent of the rate of transfer in the other direction (0.002 per day). The rate may be higher
for the transfer of mercury from the plant to a dissolved state in rain water, but no information is
available on this. Note that these default values will change if units of time change.
where:
Tlf v = transfer factor from leaf surface to leaf
TL.Lp = transfer factor from leaf to leaf surface
Transformations on the Leaf
Transformations of chemicals in particulate matter on the surface of plant leaves are
assumed to occur at the same rate as transformations in air.
NOVEMBER 1999 7-15 TRIM.FATE TSDVoLUMt II (DRAFT)