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 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.

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

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).

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:

8:1.1.2

where is the surface area of the water body (ha), is a coefficient, is the volume of water in the impoundment (m HO), and is an exponent.

The coefficient, , and exponent, , 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.

8:1.1.3

8:1.1.4

where is the surface area of the reservoir when filled to the emergency spillway (ha), is the surface area of the reservoir when filled to the principal spillway (ha), is the volume of water held in the reservoir when filled to the emergency spillway (m HO), and is the volume of water held in the reservoir when filled to the principal spillway (m HO).​

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

8:1.1.5

where is the volume of water added to the water body by precipitation during the day (m HO), is the amount of precipitation falling on a given day (mm HO), and is the surface area of the water body (ha).

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 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).

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.

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.