Impoundments play an important role in water supply and flood control. SWAT+ models four types of water bodies: ponds, wetlands, depressions/potholes, and reservoirs. Ponds, wetlands, and depressions/potholes are located within a subbasin off the main channel. Water flowing into these water bodies must originate from the subbasin in which the water body is located. Reservoirs are located on the main channel network. They receive water from all subbasins upstream of the water body.

Impoundment structures modify the movement of water in the channel network by lowering the peak flow and volume of flood discharges. Because impoundments slow down the flow of water, sediment will fall from suspension, removing nutrient and chemicals adsorbed to the soil particles.

A reservoir is an impoundment located on the main channel network of a watershed. No distinction is made between naturally-occurring and man-made structures. The features of an impoundment are shown in Figure 8:1.1.

The water balance for a reservoir is:

$V=V_{stored}+V_{flowin}-V_{flowout}+V_{pcp}-V_{evap}-V_{seep}$ 8:1.1.1

The volume of water lost to evaporation on a given day is calculated:

$V_{evap}=10*\eta*E_o*SA$ 8:1.1.6

where $V_{evap}$ is the volume of water removed from the water body by evaporation during the day (m$^3$ H$_2$O), $\eta$ is an evaporation coefficient (0.6), $E_o$ is the potential evapotranspiration for a given day (mm H$_2$O), and $SA$ is the surface area of the water body (ha).

The surface area of the reservoir is needed to calculate the amount of precipitation falling on the water body as well as the amount of evaporation and seepage. Surface area varies with change in the volume of water stored in the reservoir. The surface area is updated daily using the equation:

$SA=\beta_{sa}*V^{expsa}$ 8:1.1.2

where $SA$ is the surface area of the water body (ha), $\beta_{sa}$ is a coefficient, $V$ is the volume of water in the impoundment (m$^3$ H$_2$O), and $expsa$ is an exponent.

The coefficient, $\beta_{sa}$, and exponent, $expsa$, are calculated by solving equation 8:1.1.2 using two known points. The two known points are surface area and volume information provided for the principal and emergency spillways.

$expsa=\frac{log_{10}(SA_{em})-log_{10}(SA_{pr})}{log_{10}(V_{em})-log_{10}(V_{pr})}$ 8:1.1.3

$\beta_{sa}=(\frac{SA_{em}}{V_{em}})^{expsa}$ 8:1.1.4

where $SA_{em}$ is the surface area of the reservoir when filled to the emergency spillway (ha), $SA_{pr}$ is the surface area of the reservoir when filled to the principal spillway (ha), $V_{em}$ is the volume of water held in the reservoir when filled to the emergency spillway (m$^3$ H$_2$O), and $V_{pr}$ is the volume of water held in the reservoir when filled to the principal spillway (m$^3$ H$_2$O).​

The volume of precipitation falling on the reservoir during a given day is calculated:

$V_{pcp}=10*R_{day}*SA$ 8:1.1.5

where $V_{pcp}$ is the volume of water added to the water body by precipitation during the day (m$^3$ H$_2$O), $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O), and $SA$ is the surface area of the water body (ha).

The volume of water lost by seepage through the bottom of the reservoir on a given day is calculated:

$V_{seep}=240*K_{sat}*SA$ 8:1.1.7

where $V_{seep}$ is the volume of water lost from the water body by seepage (m$^3$ H$_2$O), $K_{sat}$ is the effective saturated hydraulic conductivity of the reservoir bottom (mm/hr), and $SA$ is the surface area of the water body (ha).

The volume of outflow may be calculated using one of four different methods: measured daily outflow, measured monthly outflow, average annual release rate for uncontrolled reservoir, controlled outflow with target release.

When measured daily outflow (IRESCO = 3) is chosen as the method to calculate reservoir outflow, the user must provide a file with the outflow rate for every day the reservoir is simulated in the watershed. The volume of outflow from the reservoir is then calculated:

$V_{flowout}=86400*q_{out}$ 8:1.1.8

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), and $q_{out}$ is the outflow rate (m$^3$/s).

When measured monthly outflow (IRESCO = 1) is chosen as the method to calculate reservoir outflow, the user must provide a file with the average daily outflow rate for every month the reservoir is simulated in the watershed. The volume of outflow from the reservoir is then calculated using equation 8:1.1.8.

The surface area of the pond or wetland is needed to calculate the amount of precipitation falling on the water body as well as the amount of evaporation and seepage. Surface area varies with change in the volume of water stored in the impoundment. The surface area is updated daily using the equation:

$SA=\beta_{sa}*V^{expsa}$ 8:1.2.2

where $SA$ is the surface area of the water body (ha), $\beta_{sa}$ is a coefficient, $V$ is the volume of water in the impoundment (m$^3$ H$_2$O), and $expsa$ is an exponent.

The coefficient, $\beta_{sa}$, and exponent, $expsa$, are calculated by solving equation 8:1.1.2 using two known points. For ponds, the two known points are surface area and volume information provided for the principal and emergency spillways.

$expsa=\frac{log_{10}(SA_{em})-log_{10}(SA_{pr})}{log_{10}(V_{em})-log_{10}(V_{pr})}$ 8:1.2.3

$\beta_{sa}=(\frac{SA_{em}}{V_{em}})^{expsa}$ 8:1.2.4

where $SA_{em}$ is the surface area of the pond when filled to the emergency spillway (ha), $SA_{pr}$ is the surface area of the pond when filled to the principal spillway (ha), $V_{em}$ is the volume of water held in the pond when filled to the emergency spillway (m$^3$ H$_2$O), and $V_{pr}$ is the volume of water held in the pond when filled to the principal spillway(m$^3$ H$_2$O). For wetlands, the two known points are surface area and volume information provided for the maximum and normal water levels.

$expsa=\frac{log_{10}(SA_{mx})-log_{10}(SA_{nor})}{log_{10}(V_{mx})-log_{10}(V_{nor})}$ 8:1.2.5

$\beta_{sa}=(\frac{SA_{mx}}{V_{mx}})^{expsa}$ 8:1.2.6

where $SA_{mx}$ is the surface area of the wetland when filled to the maximum water level (ha), $SA_{nor}$ is the surface area of the wetland when filled to the normal water level (ha), $V_{mx}$ is the volume of water held in the wetland when filled to the maximum water level (m$^3$ H$_2$O), and $V_{nor}$ is the volume of water held in the wetland when filled to the normal water level (m$^3$ H$_2$O).​

When the average annual release rate (IRESCO = 0) is chosen as the method to calculate reservoir outflow, the reservoir releases water whenever the reservoir volume exceeds the principal spillway volume, $V_{pr}$. If the reservoir volume is greater than the principal spillway volume but less than the emergency spillway volume, the amount of reservoir outflow is calculated:

$V_{flowout}=V-V_{pr}$​ if $V-V_{pr}<q_{rel}*86400$ 8:1.1.9

$V_{flowout}=q_{rel}*86400$ if $V-V_{pr}>q_{rel}*86400$ 8:1.1.10

If the reservoir volume exceeds the emergency spillway volume, the amount of outflow is calculated:

$V_{flowout}=(V-V_{em})+(V_{em}-V_{pr})$

if $V_{em}-V_{pr}<q_{rel}*86400$ 8:1.1.11

$V_{flowout}=(V-V_{em})+q_{rel}*86400$​

if $V_{em}-V_{pr}>q_{rel}*86400$ 8:1.1.12

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $V$ is the volume of water stored in the reservoir (m$^3$ H$_2$O), $V_{pr}$ is the volume of water held in the reservoir when filled to the principal spillway (m$^3$ H$_2$O), $V_{em}$ is the volume of water held in the reservoir when filled to the emergency spillway (m$^3$ H$_2$O), and $q_{rel}$ is the average daily principal spillway release rate (m$^3$/s).

The volume of precipitation falling on the pond or wetland during a given day is calculated:

$V_{pcp}=10*R_{day}*SA$ 8:1.2.7

where $V_{pcp}$ is the volume of water added to the water body by precipitation during the day (m$^3$ H$_2$O), $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O), and $SA$ is the surface area of the water body (ha).

When target release (IRESCO = 2) is chosen as the method to calculate reservoir outflow, the reservoir releases water as a function of the desired target storage.

The target release approach tries to mimic general release rules that may be used by reservoir operators. Although the method is simplistic and cannot account for all decision criteria, it can realistically simulate major outflow and low flow periods.

For the target release approach, the principal spillway volume corresponds to maximum flood control reservation while the emergency spillway volume corresponds to no flood control reservation. The model requires the beginning and ending month of the flood season. In the non-flood season, no flood control reservation is required, and the target storage is set at the emergency spillway volume. During the flood season, the flood control reservation is a function of soil water content. The flood control reservation for wet ground conditions is set at the maximum. For dry ground conditions, the flood control reservation is set at 50% of the maximum.

The target storage may be specified by the user on a monthly basis or it can be calculated as a function of flood season and soil water content. If the target storage is specified:

$V_{targ}=starg$ 8:1.1.13

where $V_{targ}$ is the target reservoir volume for a given day (m$^3$ H$_2$O), and $starg$ is the target reservoir volume specified for a given month (m$^3$ H$_2$O). If the target storage is not specified, the target reservoir volume is calculated:

$V_{targ}=V_{em}$ if $mon_{fld,beg}<mon<mon_{fld,end}$ 8:1.1.14

$V_{targ}=V_{pr}+\frac{(1-min[\frac{SW}{FC},1])}{2}*(V_{em}-V_{pr})$

if $mon \le mon_{fld,beg}$ or $mon \ge$$mon_{fld,end}$ 8:1.1.15

where $V_{targ}$ is the target reservoir volume for a given day (m$^3$ H$_2$O), $V_{em}$ is the volume of water held in the reservoir when filled to the emergency spillway (m$^3$ H$_2$O), $V_{pr}$ is the volume of water held in the reservoir when filled to the principal spillway (m$^3$ H$_2$O), $SW$ is the average soil water content in the subbasin (mm H$_2$O), $FC$ is the water content of the subbasin soil at field capacity (mm H$_2$O), $mon$ is the month of the year, $mon_{fld,beg}$ is the beginning month of the flood season, and $mon_{fld,end}$ is the ending month of the flood season.

Once the target storage is defined, the outflow is calculated:

$V_{flowout}=\frac{V-V_{targ}}{ND_{targ}}$ 8:1.1.16

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $V$ is the volume of water stored in the reservoir (m$^3$ H$_2$O), $V_{targ}$ is the target reservoir volume for a given day (m$^3$ H$_2$O), and $ND_{targ}$ is the number of days required for the reservoir to reach target storage.

Once outflow is determined using one of the preceding four methods, the user may specify maximum and minimum amounts of discharge that the initial outflow estimate is checked against. If the outflow doesn’t meet the minimum discharge or exceeds the maximum specified discharge, the amount of outflow is altered to meet the defined criteria.

$V_{flowout}=V'_{flowout}$ if $q_{rel,mn}*86400 \le V'_{flowout} \le q_{rel,mx}*86400$ 8:1.1.17

$V_{flowout}=q_{rel,mn}*86400$ if $V'_{flowout} <q_{rel,mn}*86400$ 8:1.1.18

$V_{flowout}=q_{rel,mx}*86400$ if ​ $V'_{flowout} >q_{rel,mx}*86400$ 8:1.1.19

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $V'_{flowout}$ is the initial estimate of the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $q_{rel,mn}$ is the minimum average daily outflow for the month (m$^3$/s), and $q_{rel,mx}$ is the maximum average daily outflow for the month (m$^3$/s).

Table 8:1-1: SWAT+ input variables that pertain to reservoirs.

The primary difference between ponds and wetlands is the method in which the outflow is calculated.

Pond outflow is calculated as a function of target storage. The target storage varies based on flood season and soil water content. The target pond volume is calculated:

$V_{targ}=V_{em}$ if $mon_{fld,beg}<mon<mon_{fld,end}$ 8:1.2.11

$V_{targ}=V_{pr}+\frac{(1-min[\frac{SW}{FC},1])}{2}*(V_{em}-V_{pr})$

if ​ $mon \le mon_{fld,beg}$ or $mon \ge mon_{fld,end}$ 8:1.2.12

where $V_{targ}$ is the target pond volume for a given day (m$^3$ H$_2$O), $V_{em}$ is the volume of water held in the pond when filled to the emergency spillway (m$^3$ H$_2$O), $V_{pr}$ is the volume of water held in the pond when filled to the principal spillway (m$^3$ H$_2$O), $SW$ is the average soil water content in the subbasin (mm H$_2$O), $FC$ is the water content of the subbasin soil at field capacity (mm H$_2$O), $mon$ is the month of the year, $mon_{fld,beg}$ is the beginning month of the flood season, and $mon_{fld,end}$ is the ending month of the flood season.

Once the target storage is defined, the outflow is calculated:

$V_{flowout}=\frac{V-V_{targ}}{ND_{targ}}$ 8:1.2.13

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $V$ is the volume of water stored in the pond (m$^3$ H$_2$O), $V_{targ}$ is the target pond volume for a given day (m$^3$ H$_2$O), and $ND_{targ}$ is the number of days required for the pond to reach target storage.

The volume of water entering the pond or wetland on a given day is calculated:

$V_{flowin}=fr_{imp}*10*(Q_{surf}+Q_{gw}+Q_{lat})*(Area-SA)$ 8:1.2.8

where $V_{flowin}$ is the volume of water flowing into the water body on a given day (m$^3$ H$_2$O), $fr_{imp}$ is the fraction of the subbasin area draining into the impoundment, $Q_{surf}$ is the surface runoff from the subbasin on a given day (mm H$_2$O), $Q_{gw}$ is the groundwater flow generated in a subbasin on a given day (mm H$_2$O), $Q_{lat}$ is the lateral flow generated in a subbasin on a given day (mm H$_2$O), $Area$ is the subbasin area (ha), and $SA$ is the surface area of the water body (ha). The volume of water entering the pond or wetland is subtracted from the surface runoff, lateral flow and groundwater loadings to the main channel.

The volume of water lost by seepage through the bottom of the pond or wetland on a given day is calculated:

$V_{seep}=240*K_{sat}*SA$ 8:1.2.10

where $V_{seep}$ is the volume of water lost from the water body by seepage (m$^3$ H$_2$O), $K_{sat}$ is the effective saturated hydraulic conductivity of the pond or wetland bottom (mm/hr), and $SA$ is the surface area of the water body (ha).

The volume of water lost to evaporation on a given day is calculated:

$V_{evap}=10*\eta*E_o*SA$ 8:1.2.9

where $V_{evap}$ is the volume of water removed from the water body by evaporation during the day (m$^3$ H$_2$O), $\eta$ is an evaporation coefficient (0.6), $E_o$ is the potential evapotranspiration for a given day (mm H$_2$O), and $SA$ is the surface area of the water body (ha).

Ponds and wetlands are water bodies located within subbasins that received inflow from a fraction of the subbasin area. The algorithms used to model these two types of water bodies differ only in the options allowed for outflow calculation.

The water balance for a pond or wetland is:

8:1.2.1

where is the volume of water in the impoundment at the end of the day (m HO), is the volume of water stored in the water body at the beginning of the day (m HO), is the volume of water entering the water body during the day (m HO), is the volume of water flowing out of the water body during the day (m HO), is the volume of precipitation falling on the water body during the day (m HO), is the volume of water removed from the water body by evaporation during the day (m HO), and is the volume of water lost from the water body by seepage (m HO). is added to shallow aquifer storage.

In areas of low relief and/or young geologic development, the drainage network may be poorly developed. Watersheds in these areas may have many closed depressional areas, referred to as potholes. Runoff generated within these areas flows to the lowest portion of the pothole rather than contributing to flow in the main channel. Other systems that are hydrologically similar to potholes include playa lakes and fields that are artifically impounded for rice production. The algorithms reviewed in this section are used to model these types of systems.

To define an HRU as a pothole, the user must set IPOT (.hru) to the HRU number. To initiate water impoundment, a release/impound operation must be placed in the .mgt file. The water balance for a pothole is:

$V=V_{stored}+V_{flowin}-V_{flowout}+V_{pcp}-V_{evap}-V_{seep}$ 8:1.3.1

where $V$ is the volume of water in the impoundment at the end of the day (m$^3$ H$_2$O), $V_{stored}$ is the volume of water stored in the water body at the beginning of the day (m$^3$ H$_2$O), $V_{flowin}$ is the volume of water entering the water body during the day (m$^3$ H$_2$O), $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $V_{pcp}$ is the volume of precipitation falling on the water body during the day (m$^3$ H$_2$O), $V_{evap}$ is the volume of water removed from the water body by evaporation during the day (m$^3$ H$_2$O), and $V_{seep}$ is the volume of water lost from the water body by seepage (m$^3$ H$_2$O).

Water entering the pothole on a given day may be contributed from any HRU in the subbasin. To route a portion of the flow from an HRU into a pothole, the variable IPOT (.hru) is set to the number of the HRU containing the pothole and POT_FR (.hru) is set to the fraction of the HRU area that drains into the pothole. This must be done for each HRU contributing flow to the pothole. Water routing from other HRUs is performed only during the period that water impoundment has been activated (release/impound operation in .mgt). Water may also be added to the pothole with an irrigation operation in the management file (.mgt). Chapter 6:2 reviews the irrigation operation.

The inflow to the pothole is calculated:

$V_{flowin}=irr+\sum_{hru=1}^n[fr_{pot,hru}*10*(Q_{surf,hru}+Q_{gw,hru}+Q_{lat,hru})*area_{hru}]$

8:1.3.4

where $V_{flowin}$ is the volume of water flowing into the pothole on a given day (m$^3$ H$_2$O), $irr$ is the amount of water added through an irrigation operation on a given day (m$^3$ H$_2$O), $n$ is the number of HRUs contributing water to the pothole, $fr_{pot,hru}$ is the fraction of the HRU area draining into the pothole, $Q_{surf,hru}$ is the surface runoff from the HRU on a given day (mm H$_2$O), $Q_{gw,hru}$ is the groundwater flow generated in the HRU on a given day (mm H$_2$O), $Q_{lat,hru}$ is the lateral flow generated in the HRU on a given day (mm H$_2$O), and $area_{hru}$ is the HRU area (ha).

The volume of water lost to evaporation on a given day is calculated:

$V_{evap}=5*(1-\frac{LAI}{LAI_{evap}})*E_o*SA$ if $LAI<LAI_{evap}$ 8:1.3.5

$V_{evap}=0$ if $LAI \ge LAI_{evap}$ 8:1.3.6

where $V_{evap}$ is the volume of water removed from the water body by evaporation during the day (m$^3$ H$_2$O), $LAI$ is the leaf area index of the plants growing in the pothole, $LAI_{evap}$ is the leaf area index at which no evaporation occurs from the water surface, $E_o$ is the potential evapotranspiration for a given day (mm H$_2$O), and $SA$ is the surface area of the water body (ha).

The surface area of the pothole is needed to calculate the amount of precipitation falling on the water body as well as the amount of evaporation and seepage. Surface area varies with change in the volume of water stored in the impoundment. For surface area calculations, the pothole is assumed to be cone-shaped. The surface area is updated daily using the equation:

$SA=\frac{\pi}{10^4}*(\frac{3*V}{\pi *slp})^{2/3}$ 8:1.3.2

where $SA$ is the surface area of the water body (ha), $V$ is the volume of water in the impoundment (m$^3$ H$_2$O), and $slp$ is the slope of the HRU (m/m).

The volume of precipitation falling on the pothole during a given day is calculated:

$V_{pcp}=10*R_{day}*SA$ 8:1.3.3

where $V_{pcp}$ is the volume of water added to the water body by precipitation during the day (m$^3$ H$_2$O), $R_{day}$ is the amount of precipitation falling on a given day (mm H$_2$O), and $SA$ is the surface area of the water body (ha).

The wetland releases water whenever the water volume exceeds the normal storage volume, $V_{nor}$. Wetland outflow is calculated:

$V_{flowout}=0$ if $V<V_{nor}$ 8:1.2.14

$V_{flowout}=\frac{V-V_{nor}}{10}$ if $V_{nor} \le V \le V_{mx}$ 8:1.2.15

$V_{flowout}=V-V_{mx}$ if $V>V_{mx}$ 8:1.2.16

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $V$ is the volume of water stored in the wetland (m$^3$ H$_2$O), $V_{mx}$ is the volume of water held in the wetland when filled to the maximum water level (m$^3$ H$_2$O), and $V_{nor}$ is the volume of water held in the wetland when filled to the normal water level (m$^3$ H$_2$O).

Table 8:1-2: SWAT+ input variables that pertain to ponds and wetlands.

Water may be removed from the pothole in three different types of outflow. When the volume of water in the pothole exceeds the maximum storage, the excess water is assumed to overflow and enter the main channel in the subbasin. When the retaining wall or berm is removed (this is done with a release/impound operation in the management file), all water stored in the pothole enters the main channel. The third type of flow from the pothole is via drainage tiles installed in the pothole.

Pothole outflow caused by overflow is calculated:

$V_{flowout}=V-V_{pot,mx}$ if $V >V_{pot,mx}$ 8:1.3.10

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $V$ is the volume of water stored in the pothole (m$^3$ H$_2$O), and $V_{pot,mx}$ is the maximum amount of water that can be stored in the pothole (m$^3$ H$_2$O).

When a release operation is scheduled, all water in the pothole becomes outflow:

$V_{flowout}=V$ 8:1.3.11

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), and $V$ is the volume of water stored in the pothole (m$^3$ H$_2$O).

SWAT+ incorporates a simple mass balance model to simulate the transport of sediment into and out of water bodies. SWAT+ defines four different types of water bodies: ponds, wetlands, reservoirs and potholes. Sediment processes modeled in ponds, wetlands, reservoirs, and potholes are identical.

When calculating sediment movement through a water body, SWAT+ assumes the system is completely mixed. In a completely mixed system, as sediment enters the water body it is instantaneously distributed throughout the volume.

The volume of water lost by seepage through the bottom of the pothole on a given day is calculated as a function of the water content of the soil profile beneath the pothole.

$V_{seep}=240*K_{sat}*SA$ if $SW<0.5*FC$ 8:1.3.7

$V_{seep}=240*(1-\frac{SW}{FC})*K_{sat}*SA$ if $0.5*FC \le SW <FC$ 8:1.3.8

$V_{seep}=0$ if $SW \ge FC$ 8:1.3.9

where $V_{seep}$ is the volume of water lost from the water body by seepage (m$^3$ H$_2$O), $K_{sat}$ is the effective saturated hydraulic conductivity of the 1st soil layer in the profile (mm/hr), $SA$ is the surface area of the water body (ha), $SW$ is the soil water content of the profile on a given day (mm H$_2$O), and $FC$ is the field capacity soil water content (mm H$_2$O). Water lost from the pothole by seepage is added to the soil profile.

When drainage tiles are installed in a pothole, the pothole will contribute water to the main channel through tile flow. The pothole outflow originating from tile drainage is:

$V_{flowout}=q_{tile}*86400$ if $V>q_{tile}*86400$ 8:1.3.12

$V_{flowout}=V$ if $V \le q_{tile}*86400$ 8:1.3.13

where $V_{flowout}$ is the volume of water flowing out of the water body during the day (m$^3$ H$_2$O), $q_{tile}$ is the average daily tile flow rate (m$^3$/s), and $V$ is the volume of water stored in the pothole (m$^3$ H$_2$O).

Table 8:1-3: SWAT+ input variables that pertain to potholes.

Assuming that the volume of the water body remains constant over time, the processes described above (inflow, settling, outflow) can be combined into the following mass balance equation for a well-mixed water body:

$V*\frac{dc}{dt}=W(t)-Q*c-v*c*A_s$ 8:3.2.1

where $V$ is the volume of the system (m$^3$ H$_2$O), $c$ is the concentration of nutrient in the system (kg/m$^3$ H$_2$O), $dt$ is the length of the time step (1 day), $W(t)$ is the amount of nutrient entering the water body during the day (kg/day), $Q$ is the rate of water flow exiting the water body (m$^3$ H$_2$O/day), $v$ is the apparent settling velocity (m/day), and $A_s$ is the area of the sediment-water interface (m$^2$).

The mass balance equation for sediment in a water body is:

$sed_{wb}=sed_{wb,i}+sed_{flowin}-sed_{stl}-sed_{flowout}$ 8:2.1.1

where $sed_{wb}$ is the amount of sediment in the water body at the end of the day (metric tons), $sed_{wb,i}$ is the amount of sediment in the water body at the beginning of the day (metric tons), $sed_{flowin}$ is the amount of sediment added to the water body with inflow (metric tons), $sed_{stl}$ is the amount of sediment removed from the water by settling (metric tons), $sed_{flowout}$ is the amount of sediment transported out of the water body with outflow (metric tons).

The amount of sediment transported out of the water body on a given day is calculated as a function of the final concentration. The initial suspended solid concentration is:

$sed_{flowout}=conc_{sed,f}*V_{flowout}$ 8:2.3.1