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SWAT+ incorporates a simple mass balance developed by Chapra (1997) to model the transformation and transport of pesticides in streams. The model assumes a well-mixed layer of water overlying a sediment layer. Only one pesticide can be routed through the stream network. The pesticide to be routed is defined by the variable IRTPEST in the .bsn file.
Pesticides in both the particulate and dissolved forms are subject to degradation. The amount of pesticide that is removed from the water via degradation is:
7:4.1.6
where is the amount of pesticide removed from the water via degradation (mg pst), is the rate constant for degradation or removal of pesticide in the water (1/day), is the amount of pesticide in the water at the beginning of the day (mg pst), and is the flow travel time (days). The rate constant is related to the aqueous half-life:
7:4.1.7
where is the rate constant for degradation or removal of pesticide in the water (1/day), and is the aqueous half-life for the pesticide (days).
Pesticide is removed from the reach segment in outflow. The amount of dissolved and particulate pesticide removed from the reach segment in outflow is:
7:4.1.13
7:4.1.14
where is the amount of dissolved pesticide removed via outflow (mg pst), is the amount of particulate pesticide removed via outflow (mg pst), is the rate of outflow from the reach segment (m HO/day), is the fraction of total pesticide in the dissolved phase, is the fraction of total pesticide in the particulate phase, is the amount of pesticide in the water (mg pst), and is the volume of water in the reach segment (m HO).
Table 7:4-1: SWAT+ input variables that pesticide partitioning.
Variable Name | Definition | Input File |
---|
Pesticides will partition into particulate and dissolved forms. The fraction of pesticide in each phase is a function of the pesticide’s partition coefficient and the reach segment’s suspended solid concentration:
7:4.1.1
7:4.1.2
where is the fraction of total pesticide in the dissolved phase, is the fraction of total pesticide in the particulate phase, is the pesticide partition coefficient (m/g), and is the concentration of suspended solids in the water (g/m).
The pesticide partition coefficient can be estimated from the octanol-water partition coefficient (Chapra, 1997):
7:4.1.3
where is the pesticide partition coefficient (m/g) and is the pesticide’s octanol-water partition coefficient (mg m(mg m)). Values for the octanol-water partition coefficient have been published for many chemicals. If a published value cannot be found, it can be estimated from solubility (Chapra, 1997):
7:4.1.4
where is the pesticide solubility (moles/L). The solubility in these units is calculated:
7:4.1.5
where is the pesticide solubility (moles/L), is the pesticide solubility (mg/L) and is the molecular weight (g/mole).
As in the water layer, pesticides in the sediment layer will partition into particulate and dissolved forms. Calculation of the solid-liquid partitioning in the sediment layer requires a suspended solid concentration. The “concentration” of solid particles in the sediment layer is defined as:
7:4.2.1
where is the “concentration” of solid particles in the sediment layer (g/m), is the mass of solid particles in the sediment layer (g) and is the total volume of the sediment layer (m).
Mass and volume are also used to define the porosity and density of the sediment layer. In the sediment layer, porosity is the fraction of the total volume in the liquid phase:
7:4.2.2
where is the porosity, is the volume of water in the sediment layer (m) and is the total volume of the sediment layer (m). The fraction of the volume in the solid phase can then be defined as:
7:4.2.3
where is the porosity, is the volume of solids in the sediment layer (m) and is the total volume of the sediment layer (m).
The density of sediment particles is defined as:
7:4.2.4
where is the particle density (g/m), is the mass of solid particles in the sediment layer (g), and is the volume of solids in the sediment layer (m).
Solving equation 7:4.2.3 for and equation 7:4.2.4 for and substituting into equation 7:4.2.1 yields:
7:4.2.5
where is the “concentration” of solid particles in the sediment layer (g/m), is the porosity, and is the particle density (g/m).
Assuming and g/m, the “concentration” of solid particles in the sediment layer is g/m.
The fraction of pesticide in each phase is then calculated:
7:4.2.6
7:4.2.7
where is the fraction of total sediment pesticide in the dissolved phase, is the fraction of total sediment pesticide in the particulate phase, is the porosity, is the particle density (g/m), and K is the pesticide partition coefficient (m/g). The pesticide partition coefficient used for the water layer is also used for the sediment layer.
Pesticide in the sediment layer underlying a reach segment is increased through addition of mass by settling and diffusion from the water. The amount of pesticide in the sediment layer is reduced through removal by degradation, resuspension, diffusion into the overlying water, and burial.
Pesticides in both the particulate and dissolved forms are subject to degradation. The amount of pesticide that is removed from the sediment via degradation is:
7:4.2.8
where is the amount of pesticide removed from the sediment via degradation (mg pst), is the rate constant for degradation or removal of pesticide in the sediment (1/day), and is the amount of pesticide in the sediment (mg pst). The rate constant is related to the sediment half-life:
7:4.2.9
where is the rate constant for degradation or removal of pesticide in the sediment (1/day), and is the sediment half-life for the pesticide (days).
Pesticide in the sediment layer is available for resuspension. The amount of pesticide that is removed from the sediment via resuspension is:
7:4.2.10
where is the amount of pesticide removed via resuspension (mg pst), is the resuspension velocity (m/day), is the flow depth (m), is the amount of pesticide in the sediment (mg pst), and is the flow travel time (days). Pesticide removed from the sediment layer by resuspension is added to the water layer.
Pesticide in the dissolved phase is available for diffusion. Diffusion transfers pesticide between the water and sediment layers. The direction of movement is controlled by the pesticide concentration. Pesticide will move from areas of high concentration to areas of low concentration. The amount of pesticide that is transferred between the water and sediment by diffusion is:
7:4.2.11
where is the amount of pesticide transferred between the water and sediment by diffusion (mg pst), is the rate of diffusion or mixing velocity (m/day), is the flow depth (m), is the fraction of total sediment pesticide in the dissolved phase, is the amount of pesticide in the sediment (mg pst), is the fraction of total water layer pesticide in the dissolved phase, is the amount of pesticide in the water (mg pst), and is the flow duration (days). If , is transferred from the sediment to the water layer. If , is transferred from the water to the sediment layer.
The diffusive mixing velocity, , can be estimated from the empirically derived formula (Chapra, 1997):
7:4.2.12
where is the rate of diffusion or mixing velocity (m/day), is the sediment porosity, and is the molecular weight of the pesticide compound.
Pesticide in the particulate phase may be removed from the water layer by settling. Settling transfers pesticide from the water to the sediment layer. The amount of pesticide that is removed from the water via settling is:
7:4.1.12
where is the amount of pesticide removed from the water due to settling (mg pst), is the settling velocity (m/day), is the flow depth (m), is the fraction of total pesticide in the particulate phase, is the amount of pesticide in the water (mg pst), and is the flow travel time (days).
Pesticide in the dissolved phase is available for volatilization. The amount of pesticide removed from the water via volatilization is:
7:4.1.8
where is the amount of pesticide removed via volatilization (mg pst), is the volatilization mass-transfer coefficient (m/day), is the flow depth (m), is the fraction of total pesticide in the dissolved phase, is the amount of pesticide in the water (mg pst), and is the flow travel time (days).
The volatilization mass-transfer coefficient can be calculated based on Whitman’s two-film or two-resistance theory (Whitman, 1923; Lewis and Whitman, 1924 as described in Chapra, 1997). While the main body of the gas and liquid phases are assumed to be well-mixed and homogenous, the two-film theory assumes that a substance moving between the two phases encounters maximum resistance in two laminar boundary layers where transfer is a function of molecular diffusion. In this type of system the transfer coefficient or velocity is:
7:4.1.9
where is the volatilization mass-transfer coefficient (m/day), is the mass-transfer velocity in the liquid laminar layer (m/day), is the mass-transfer velocity in the gaseous laminar layer (m/day), is Henry’s constant (atm m mole), is the universal gas constant ( atm m (K mole)), and is the temperature (K).
For rivers where liquid flow is turbulent, the transfer coefficients are estimated using the surface renewal theory (Higbie, 1935; Danckwerts, 1951; as described by Chapra, 1997). The surface renewal model visualizes the system as consisting of parcels of water that are brought to the surface for a period of time. The fluid elements are assumed to reach and leave the air/water interface randomly, i.e. the exposure of the fluid elements to air is described by a statistical distribution. The transfer velocities for the liquid and gaseous phases are calculated:
7:4.1.10
where is the mass-transfer velocity in the liquid laminar layer (m/day), is the mass-transfer velocity in the gaseous laminar layer (m/day), is the liquid molecular diffusion coefficient (m/day), is the gas molecular diffusion coefficient (m/day), is the liquid surface renewal rate (1/day), and is the gaseous surface renewal rate (1/day).
O’Connor and Dobbins (1958) defined the surface renewal rate as the ratio of the average stream velocity to depth.
7:4.1.11
where is the liquid surface renewal rate (1/day), is the average stream velocity (m/s) and is the depth of flow (m).
Pesticide in a reach segment is increased through addition of mass in inflow as well as resuspension and diffusion of pesticide from the sediment layer. The amount of pesticide in a reach segment is reduced through removal in outflow as well as degradation, volatilization, settling and diffusion into the underlying sediment.
The processes described above can be combined into mass balance equations for the well-mixed reach segment and the well-mixed sediment layer: \
7:4.3.1
7:4.3.2
where is the change in pesticide mass in the water layer (mg pst), is the change in pesticide mass in the sediment layer (mg pst), is the pesticide added to the reach segment via inflow (mg pst), is the amount of dissolved pesticide removed via outflow (mg pst), is the amount of particulate pesticide removed via outflow (mg pst), is the amount of pesticide removed from the water via degradation (mg pst), is the amount of pesticide removed via volatilization (mg pst), is the amount of pesticide removed from the water due to settling (mg pst), is the amount of pesticide removed via resuspension (mg pst), is the amount of pesticide transferred between the water and sediment by diffusion (mg pst), is the amount of pesticide removed from the sediment via degradation (mg pst), is the amount of pesticide removed via burial (mg pst).
CHPST_KOC | : Pesticide partition coefficient (m/g) | .swq |
CHPST_REA | : Rate constant for degradation or removal of pesticide in the water (1/day) | .swq |
CHPST_VOL | : Volatilization mass-transfer coefficient (m/day) | .swq |
CHPST_STL | : Pesticide settling velocity (m/day) | .swq |
Pesticide in the sediment layer may be lost by burial. The amount of pesticide that is removed from the sediment via burial is:
7:4.2.13
where is the amount of pesticide removed via burial (mg pst), is the burial velocity (m/day), is the depth of the active sediment layer (m), and is the amount of pesticide in the sediment (mg pst).
Table 7:4-2: SWAT+ input variables related to pesticide in the sediment.
Variable Name | Definition | Input File |
---|---|---|
CHPST_KOC
: Pesticide partition coefficient (m/g)
.swq
SEDPST_REA
: Rate constant for degradation or removal of pesticide in the sediment (1/day)
.swq
CHPST_RSP
: Resuspension velocity (m/day)
.swq
SEDPST_ACT
: Depth of the active sediment layer (m)
.swq
CHPST_MIX
: Rate of diffusion or mixing velocity (m/day)
.swq
SEDPST_BRY
: Pesticide burial velocity (m/day)
.swq