Open channel flow is defined as channel flow with a free surface, such as flow in a river or partially full pipe. SWAT+ uses Manning’s equation to define the rate and velocity of flow. Water is routed through the channel network using the variable storage routing method or the Muskingum river routing method. Both the variable storage and Muskingum routing methods are variations of the kinematic wave model. A detailed discussion of the kinematic wave flood routing model can be found in Chow et al. (1988).

Flow in a watershed is classified as overland or channelized. The primary difference between the two flow processes is that water storage and its influence on flow rates is considered in channelized flow. Main channel processes modeled by SWAT+ include the movement of water, sediment and other constituents (e.g. nutrients, pesticides) in the stream network, in-stream nutrient cycling, and in-stream pesticide transformations. Optional processes include the change in channel dimensions with time due to downcutting and widening.

The Muskingum routing method models the storage volume in a channel length as a combination of wedge and prism storages (Figure 7:1-3).

When a flood wave advances into a reach segment, inflow exceeds outflow and a wedge of storage is produced. As the flood wave recedes, outflow exceeds inflow in the reach segment and a negative wedge is produced. In addition to the wedge storage, the reach segment contains a prism of storage formed by a volume of constant cross-section along the reach length.

As defined by Manning’s equation (equation 7:1.2.1), the cross-sectional area of flow is assumed to be directly proportional to the discharge for a given reach segment. Using this assumption, the volume of prism storage can be expressed as a function of the discharge, $K*q_{out}$, where $K$ is the ratio of storage to discharge and has the dimension of time. In a similar manner, the volume of wedge storage can be expressed as $K*X*(q_{in}-q_{out})$, where $X$ is a weighting factor that controls the relative importance of inflow and outflow in determining the storage in a reach. Summing these terms gives a value for total storage

This format is similar to equation 7:1.3.7.

The definition for storage volume in equation 7:1.4.2 can be incorporated into the continuity equation (equation 7:1.3.2) and simplified to

To maintain numerical stability and avoid the computation of negative outflows, the following condition must be met:

Table 7:1-3: SWAT+ input variables that pertain to Muskingum routing.

The variable storage routing method was developed by Williams (1969) and used in the HYMO (Williams and Hann, 1973) and ROTO (Arnold et al., 1995) models.

For a given reach segment, storage routing is based on the continuity equation:

$V_{in}-V_{out}=\Delta V_{stored}$ 7:1.3.1

where $V_{in}$ is the volume of inflow during the time step (m$^3$ H$_2$O), $V_{out}$ is the volume of outflow during the time step (m$^3$ H$_2$O), and $\Delta V_{stored}$ is the change in volume of storage during the time step (m$^3$ H$_2$O). This equation can be written as

$\Delta t*(\frac{q_{in,1}+q_{in,2}}{2})-\Delta t*(\frac{q_{out,1}+q_{out,2}}{2})=V_{stored,2}-V_{stored,1}$ 7:1.3.2

where $\Delta t$ is the length of the time step (s), $q_{in,1}$ is the inflow rate at the beginning of the time step (m$^3$/s), $q_{in,2}$ is the inflow rate at the end of the time step (m$^3$/s), $q_{out,1}$ is the outflow rate at the beginning of the time step (m$^3$/s), $q_{out,2}$ is the outflow rate at the end of the time step (m$^3$/s), $V_{stored,1}$ is the storage volume at the beginning of the time step (m$^3$ H$_2$O), and $V_{stored,2}$ is the storage volume at the end of the time step (m$^3$ H$_2$O). Rearranging equation 7:1.3.2 so that all known variables are on the left side of the equation,

$q_{in,ave}+\frac{V_{stored,1}}{\Delta t}-\frac{q_{out,1}}{2}=\frac{V_{stored,2}}{\Delta t}+\frac{q_{out,2}}{2}$ 7:1.3.3

where $q_{in,ave}$ is the average inflow rate during the time step: $q_{in,ave}=\frac{q_{in,1}+q_{in,2}}{2}$.

Travel time is computed by dividing the volume of water in the channel by the flow rate.

$TT=\frac{V_{stored}}{q_{out}}=\frac{V_{stored,1}}{q_{out,1}}=\frac{V_{stored,2}}{q_{out,2}}$ 7:1.3.4

where $TT$ is the travel time (s), $V_{stored}$ is the storage volume (m$^3$ H$_2$O), and $q_{out}$ is the discharge rate (m$^3$/s).

To obtain a relationship between travel time and the storage coefficient, equation 7:1.3.4 is substituted into equation 7:1.3.3:

$q_{in,ave}+\frac{V_{stored,1}}{(\frac{\Delta t}{TT})*(\frac{V_{stored,1}}{q_{out,1}})}-\frac{q_{out,1}}{2}=\frac{V_{stored,2}}{(\frac{\Delta t}{TT})*(\frac{V_{stored,2}}{q_{out,2}})}+\frac{q_{out,2}}{2}$ 7:1.3.5

which simplifies to

$q_{out,2}=(\frac{2*\Delta t}{2*TT+\Delta t})*q_{in,ave}+(1-\frac{2*\Delta t}{2*TT+ \Delta t})*q_{out,1}$ 7:1.3.6

This equation is similar to the coefficient method equation

$q_{out,2}=SC*q_{in,ave}+(1-SC)*q_{out,1}$ 7:1.3.7

It can be shown that

Substituting this into equation 7:1.3.7 gives

To express all values in units of volume, both sides of the equation are multiplied by the time step

Manning’s equation for uniform flow in a channel is used to calculate the rate and velocity of flow in a reach segment for a given time step:

$q_{ch}=\frac{A_{ch}*R_{ch}^{2/3}*slp_{ch}^{1/2}}{n}$ 7:1.2.1

$v_c=\frac{R_{ch}^{2/3}*slp_{ch}^{1/2}}{n}$ 7:1.2.2

where $q_{ch}$ is the rate of flow in the channel (m$^3$/s), $A_{ch}$ is the cross-sectional area of flow in the channel (m$^2$), $R_{ch}$ is the hydraulic radius for a given depth of flow (m), $slp_{ch}$ is the slope along the channel length (m/m), $n$ is Manning’s “n” coefficient for the channel, and $v_c$ is the flow velocity (m/s).

SWAT+ routes water as a volume. The daily value for cross-sectional area of flow, $A_{ch}$, is calculated by rearranging equation 7:1.1.7 to solve for the area:

$A_{ch}=\frac{V_{ch}}{1000*L_{ch}}$ 7:1.2.3

where $A_{ch}$ is the cross-sectional area of flow in the channel for a given depth of water (m$^2$), $V_{ch}$ is the volume of water stored in the channel (m$^3$), and $L_{ch}$ is the channel length (km). Equation 7:1.1.4 is rearranged to calculate the depth of flow for a given time step:

$depth=\sqrt{\frac{A_{ch}}{z_{ch}}+(\frac{W_{btm}}{2*z_{ch}})^2}-\frac{W_{btm}}{2*z_{ch}}$ 7:1.2.4

where $depth$ is the depth of flow (m), $A_{ch}$ is the cross-sectional area of flow in the channel for a given depth of water (m$^2$), $W_{btm}$ is the bottom width of the channel (m), and $z_{ch}$ is the inverse of the channel side slope. Equation 7:1.2.4 is valid only when all water is contained in the channel. If the volume of water in the reach segment has filled the channel and is in the flood plain, the depth is calculated:

$depth=depth_{bnkfull}+\sqrt{\frac{(A_{ch}-A_{ch,bnkfull})}{z_{fld}}+(\frac{W_{btm,fld}}{2*z_{fld}})^2}-\frac{W_{btm,fld}}{2*z_{fld}}$ 7:1.2.5

where $depth$ is the depth of flow (m), $depth_{bnkfull}$ is the depth of water in the channel when filled to the top of the bank (m), $A_{ch}$ is the cross-sectional area of flow in the channel for a given depth of water (m$^2$), $A_{ch,bnkfull}$ is the cross-sectional area of flow in the channel when filled to the top of the bank (m$^2$), $W_{btm,fld}$ is the bottom width of the flood plain (m), and $z_{fld}$ is the inverse of the flood plain side slope.

Once the depth is known, the wetting perimeter and hydraulic radius are calculated using equations 7:1.1.5 (or 7:1.1.10) and 7:1.1.6. At this point, all values required to calculate the flow rate and velocity are known and equations 7:1.2.1 and 7:1.2.2 can be solved.

Table 7:1-2: SWAT+ input variables that pertain to channel flow calculations.

The amount of water entering bank storage on a given day is calculated:

7:1.7.1

where is the amount of water entering bank storage (m HO), are the channel transmission losses (m HO), and is the fraction of transmission losses partitioned to the deep aquifer.

Bank storage contributes flow to the main channel or reach within the subbasin. Bank flow is simulated with a recession curve similar to that used for groundwater. The volume of water entering the reach from bank storage is calculated:

7:1.7.2

where is the volume of water added to the reach via return flow from bank storage(m HO), is the total amount of water in bank storage (m HO), and is the bank flow recession constant or constant of proportionality.

Water may move from bank storage into an adjacent unsaturated zone. SWAT+ models the movement of water into adjacent unsaturated areas as a function of water demand for evapotranspiration. To avoid confusion with soil evaporation and transpiration, this process has been termed ‘revap’. This process is significant in watersheds where the saturated zone is not very far below the surface or where deep-rooted plants are growing. ‘Revap’ from bank storage is governed by the groundwater revap coefficient defined for the last HRU in the subbasin.

The maximum amount of water than will be removed from bank storage via ‘revap’ on a given day is:

7:1.7.3

where is the maximum amount of water moving into the unsaturated zone in response to water deficiencies (m HO), is the revap coefficient, is the potential evapotranspiration for the day (mm HO), is the channel length (km), and is the width of the channel at water level (m). The actual amount of revap that will occur on a given day is calculated:

if 7:1.7.4

if 7:1.7.5

where is the actual amount of water moving into the unsaturated zone in response to water deficiencies (m HO), is the maximum amount of water moving into the unsaturated zone in response to water deficiencies (m HO), and is the amount of water in bank storage at the beginning of day (m HO).

Table 7:1-7: SWAT+ input variables that pertain to bank storage.

SWAT+ assumes the main channels, or reaches, have a trapezoidal shape (Figure 7:1-1).

Users are required to define the width and depth of the channel when filled to the top of the bank as well as the channel length, slope along the channel length and Manning’s “n” value. SWAT+ assumes the channel sides have a 2:1 run to rise ratio ( = 2). The slope of the channel sides is then ½ or 0.5. The bottom width is calculated from the width and depth with the equation:

7:1.1.1

For a given depth of water in the channel, the width of the channel at water level is:

When the volume of water in the reach exceeds the maximum amount that can be held by the channel, the excess water spreads across the flood plain. The flood plain dimensions used by SWAT+ are shown in Figure 7:1-2.

When flow is present in the flood plain, the calculation of the flow depth, cross-sectional flow area and wetting perimeter is a sum of the channel and floodplain components:

7:1.1.9

7:1.1.10

Table 7:1-1: SWAT+ input variables that pertain to channel dimension calculations.

Williams (1980) used Bagnold’s (1977) definition of stream power to develop a method for determining degradation as a function of channel slope and velocity. In this version, the equations have been simplified and the maximum amount of sediment that can be transported from a reach segment is a function of the peak channel velocity. The peak channel velocity, $v_{ch,pk}$, is calculated:

$v_{ch,pk}=\frac{q_{ch,pk}}{A_{ch}}$ 7:2.2.1

where $q_{ch,pk}$ is the peak flow rate (m$^3$/s) and $A_{ch}$ is the cross-sectional area of flow in the channel (m$^2$). The peak flow rate is defined as:

$q_{ch,pk}=prf*q_{ch}$ 7:2.2.2

where $prf$ is the peak rate adjustment factor, and $q_{ch}$ is the average rate of flow (m$^3$/s). Calculation of the average rate of flow, $q_{ch}$, and the cross-sectional area of flow, $A_{ch}$, is reviewed in Section 7, Chapter 1.

The maximum amount of sediment that can be transported from a reach segment is calculated:

$conc_{sed,ch,mx}=c_{sp}*v_{ch,pk}^{spexp}$ 7:2.2.3

where $conc_{sed,ch,mx}$ is the maximum concentration of sediment that can be transported by the water (ton/m$^3$ or kg/L), $c_{sp}$ is a coefficient defined by the user, $v_{ck,pk}$ is the peak channel velocity (m/s), and spexp is an exponent defined by the user. The exponent, $spexp$, normally varies between 1.0 and 2.0 and was set at 1.5 in the original Bagnold stream power equation (Arnold et al., 1995).

The maximum concentration of sediment calculated with equation 24.1.3 is compared to the concentration of sediment in the reach at the beginning of the time step, $conc_{sed,ch,i}$. If $conc_{sed,ch,i}>conc_{sed,ch,mx}$, deposition is the dominant process in the reach segment and the net amount of sediment deposited is calculated:

$sed_{dep}=(conc_{sed,ch,i}-conc_{sed,ch,mx})*V_{ch}$ 7:2.2.4

where $sed_{dep}$ is the amount of sediment deposited in the reach segment (metric tons), $conc_{sed,ch,i}$ is the initial sediment concentration in the reach (kg/L or ton/m$^3$), $conc_{sed,ch,mx}$ is the maximum concentration of sediment that can be transported by the water (kg/L or ton/m$^3$), and $V_{ch}$ is the volume of water in the reach segment (m$^3$ H$_2$O).

If $conc_{sed,ch,i}<conc_{sed,ch,mx}$, degradation is the dominant process in the reach segment and the net amount of sediment reentrained is calculated:

$sed_{deg}=(conc_{sed,ch,mx}-conc_{sed,ch,i})*V_{ch}*K_{CH}*C_{CH}$ 7:2.2.5

where $sed_{deg}$ is the amount of sediment reentrained in the reach segment (metric tons), $conc_{sed,ch,mx}$ is the maximum concentration of sediment that can be transported by the water (kg/L or ton/m$^3$), $conc_{sed,ch,i}$ is the initial sediment concentration in the reach (kg/L or ton/m$^3$), $V_{ch}$ is the volume of water in the reach segment (m$^3$ H$_2$O), $K_{CH}$ is the channel erodibility factor, and $C_{CH}$ is the channel cover factor.

Once the amount of deposition and degradation has been calculated, the final amount of sediment in the reach is determined:

$sed_{ch}=sed_{ch,i}-sed_{dep}+sed_{deg}$ 7:2.2.6

where $sed_{ch}$ is the amount of suspended sediment in the reach (metric tons), $sed_{ch,i}$ is the amount of suspended sediment in the reach at the beginning of the time period (metric tons), $sed_{dep}$ is the amount of sediment deposited in the reach segment (metric tons), and $sed_{deg}$ is the amount of sediment reentrained in the reach segment (metric tons).

The amount of sediment transported out of the reach is calculated:

$sed_{out}=sed_{ch}*\frac{V_{out}}{V_{ch}}$ 7:2.2.7

where $sed_{out}$ is the amount of sediment transported out of the reach (metric tons), $sed_{ch}$ is the amount of suspended sediment in the reach (metric tons), $V_{out}$ is the volume of outflow during the time step (m$^3$ H$_2$O), and $V_{ch}$ is the volume of water in the reach segment (m$^3$ H$_2$O).

In this method, the erosion is assumed to be limited only by the transport capacity, i.e., the sediment supply from channel erosion is unlimited. If the bedload entering the channel is less than the transport capacity, then channel erosion is assumed to meet this deficit. On the other hand if the bedload entering the channel is more than the transport capacity, the difference in the load will get deposited within the channel. Hence, in the default method, the bed load carried by the channel is almost always near the maximum transport capacity given by the simplified Bagnold equation and only limited by the channel cover and erodibility factors (eq. 7:2.2.11). During subsequent floods, the deposited sediments will be resuspended and transported before channel degradation.

If this method is chosen for sediment transport modeling, it does not keep track of particle size distribution through the channel reaches and all are assumed to be of silt size particles. Further, the channel erosion is not partitioned between stream bank and stream bed and deposition is assumed to occur only in the main channel; flood plain deposition of sediments is also not modeled separately.

Water storage in the reach at the end of the time step is calculated:

$V_{stored,2}=V_{stored,1}+V_{in}-V_{out}-tloss-E_{ch}+div+V_{bnk}$ 7:1.8.1

where $V_{stored,2}$ is the volume of water in the reach at the end of the time step (m$^3$ H$_2$O), $V_{stored,1}$ is the volume of water in the reach at the beginning of the time step (m$^3$ H$_2$O), $V_{in}$ is the volume of water flowing into the reach during the time step (m$^3$ H$_2$O), $V_{out}$ is the volume of water flowing out of the reach during the time step (m$^3$ H$_2$O), $tloss$ is the volume of water lost from the reach via transmission through the bed (m$^3$ H$_2$O),$E_{ch}$ is the evaporation from the reach for the day (m$^3$ H$_2$O), $div$ is the volume of water added or removed from the reach for the day through diversions (m$^3$ H$_2$O), and $V_{bnk}$ is the volume of water added to the reach via return flow from bank storage (m$^3$ H$_2$O).

SWAT+ treats the volume of outflow calculated with equation 7:1.3.11 or 7:1.4.7 as the net amount of water removed from the reach. As transmission losses, evaporation and other water losses for the reach segment are calculated, the amount of outflow to the next reach segment is reduced by the amount of the loss. When outflow and all losses are summed, the total amount will equal the value obtained from 7:1.3.11 or 7:1.4.7.

The sediment size distribution of the detached sediment is estimated from the primary particle size distribution (Foster et al., 1980). The values are typical of many Midwestern soils.

$PSA=(SAN)(1.-CLA)^{2.4}$ 7:2.1.1

$PSI=0.13SIL$ 7:2.1.2

$PCL=0.20CLA$ 7:2.1.3

$SAG=\begin{cases}2.0CLA & for &CLA < 0.25 \\ 0.28(CLA -0.25)+0.5 & for &CLA 0.25 CLA 0.5 \\ 0.57 & for &CLA>0.5 \end{cases}$ 7:2.1.4

$LAG=1.0-PSA-PSI-PCL-SAG$ 7:2.1.5

where SAN, SIL and CLA are the fractions of primary sand, silt, and clay in the original soil mass, and PSA, PSI, PCL, SAG and LAG are the fractions of sand, silt, clay, small aggregates, and large aggregates for the detached sediment before deposition. Total sediment yield from landscape calculated by MUSLE is multiplied by these fractions to get the corresponding yield distributions of sand, silt, clay, small aggregate and large aggregate. The particle diameters assumed are:

$Sand=0.20mm \\ Silt=0.01mm \\Clay=0.002mm\\SmallAggregate=0.03mm\\LargeAggregate=0.50mm$

Sediment yield from landscape is lagged (see the chapter on Erosion) and routed through grassed waterway, vegetative filter strips, and ponds, if available, before reaching the stream channel. Thus, the sediment yield reaching the stream channel is the sum of total sediment yield calculated by MUSLE minus the lag, and the sediment trapped in grassed waterway, vegetative filter strips and/or ponds. Please refer to the individual chapters for sediment routing through these elements. Based on the total sediment trapping calculated in these elements, coarser sediments such as sand and large aggregate are assumed to settle/trap first followed by fine sediments such as clay. This gives the final particle size distribution of sediment reaching the stream from landscape portion.

Sediment transport in the channel network is a function of two processes, deposition and degradation, operating simultaneously in the reach. SWAT+ will compute deposition and degradation using the same channel dimensions for the entire simulation. Alternatively, SWAT+ can also simulate downcutting and widening of the stream channel and update channel dimensions throughout the simulation. Sediment transport consists of two components 1) Landscape component and 2) Channel component. From the landscape component, SWAT+ keep tracks of the particle size distribution of eroded sediments and routes them through ponds, channels, and surface water bodies. In the channel, degradation or deposition of sediment can occur depending on the stream power, the exposure of channel sides and bottom to the erosive force of the stream and the composition of channel bank and bed sediment.

Each subbasin has a main routing reach where sediment from upland subbasins is routed and then added to downstream reaches. In SWAT+, a simplified version of Bagnold (1977) stream power equation was used to calculate the maximum amount of sediment that can be transported in a stream segment. It does not keep track of sediment pools in various particle sizes.

In the current version, four additional stream power equations with more physically based approach have been incorporated for modeling sediment transport, bank and bed erosions in channel containing various bed materials and sediment deposition. If one among these four physically based approach is selected, then the sediment pool in six particle sizes are tracked by the model.

During the day, algae increase the stream’s dissolved oxygen concentration via photosynthesis. At night, algae reduce the concentration via respiration. As algae grow and die, they form part of the in-stream nutrient cycle. This section summarizes the equations used to simulate algal growth in the stream.

Parameters which affect water quality and can be considered pollution indicators include nutrients, total solids, biological oxygen demand, nitrates, and microorganisms (Loehr, 1970; Paine, 1973). Parameters of secondary importance include odor, taste, and turbidity (Azevedo and Stout, 1974).

The SWAT+ in-stream water quality algorithms incorporate constituent interactions and relationships used in the QUAL2E model (Brown and Barnwell, 1987). The documentation provided in this chapter has been taken from Brown and Barnwell (1987). The modeling of in-stream nutrient transformations has been made an optional feature of SWAT+. To route nutrient loadings downstream without simulating transformations, the variable IWQ in the basin input (.bsn) file should be set to 0. To activate the simulation of in-stream nutrient transformations, this variable should be set to 1.

The phosphorus cycle is similar to the nitrogen cycle. The death of algae transforms algal phosphorus into organic phosphorus. Organic phosphorus is mineralized to soluble phosphorus which is available for uptake by algae. Organic phosphorus may also be removed from the stream by settling. This section summarizes the equations used to simulate the phosphorus cycle in the stream.

Reaeration occurs by diffusion of oxygen from the atmosphere into the stream and by the mixing of water and air that occurs during turbulent flow.

In aerobic water, there is a stepwise transformation from organic nitrogen to ammonia, to nitrite, and finally to nitrate. Organic nitrogen may also be removed from the stream by settling. This section summarizes the equations used to simulate the nitrogen cycle in the stream.

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.

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.

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 channel erodibility factor is conceptually similar to the soil erodibility factor used in the USLE equation. Channel erodibility is a function of properties of the bed or bank materials.

Channel erodibility can be measured with a submerged vertical jet device. The basic premise of the test is that erosion of a vegetated or bare channel and local scour beneath an impinging jet are the result of hydraulic stresses, boundary geometry, and the properties of the material being eroded. Hanson (1990) developed a method for determining the erodibility coefficient of channels in situ with the submerged vertical jet. Allen et al. (1999) utilized this method to determine channel erodibility factors for thirty sites in Texas.

A submerged, vertical jet of water directed perpendicularly at the channel bed causes erosion of the bed material in the vicinity of the jet impact area (Figure 7:2-1). Important variables in the erosion process are: the volume of material removed during a jetting event, elevation of the jet above the ground surface, diameter of the jet nozzle, jet velocity, time, mass density of the fluid and coefficient of erodibility.

Hanson (1991) defined a jet index, J$_i$, to relate erodibility to scour created by the submerged jet. The jet index is a function of the depth of scour beneath the jet per unit time and the jet velocity. The jet index is determined by a least squares fit following the procedures outlined in ASTM standard D 5852-95.

Once the jet index is determined, the channel erodibility coefficient is calculated:

$K_{d,bank|bed}=0.003*exp[385*J_i]$ 7:2.3.1

where $K_{d,bank|bed}$ is the channel bankd/bed erodibility coefficient (cm$^3$/N-s) and $J_i$ is the jet index. In general, values for channel erodibility are an order of magnitude smaller than values for soil erodibility.

Evaporation losses from the reach are calculated:

$E_{ch}=coef_{ev}*E_o*L_{ch}*W*fr_{\Delta t}$ 7:1.6.1

where $E_{ch}$ is the evaporation from the reach for the day (m$^3$ H$_2$O), $coef_{ev}$ is an evaporation coefficient, $E_o$ is potential evaporation (mm H$_2$O), $L_{ch}$ is the channel length (km), $W$ is the channel width at water level (m), and $fr_{\Delta t}$ is the fraction of the time step in which water is flowing in the channel.

The evaporation coefficient is a calibration parameter for the user and is allowed to vary between 0.0 and 1.0.

The fraction of the time step in which water is flowing in the channel is calculated by dividing the travel time by the length of the time step.

Table 7:1-6: SWAT+ input variables that pertain to evaporation losses.

The classification of a stream as ephemeral, intermittent or perennial is a function of the amount of groundwater contribution received by the stream. Ephemeral streams contain water during and immediately after a storm event and are dry the rest of the year. Intermittent streams are dry part of the year, but contain flow when the groundwater is high enough as well as during and after a storm event. Perennial streams receive continuous groundwater contributions and flow throughout the year.

During periods when a stream receives no groundwater contributions, it is possible for water to be lost from the channel via transmission through the side and bottom of the channel. Transmission losses are estimated with the equation

$tloss=K_{ch}*TT*P_{ch}*L_{ch}$ 7:1.5.1

where $tloss$ are the channel transmission losses (m$^3$ H$_2$O), $K_{ch}$ is the effective hydraulic conductivity of the channel alluvium (mm/hr), $TT$ is the flow travel time (hr), $P_{ch}$ is the wetted perimeter (m), and $L_{ch}$ is the channel length (km). Transmission losses from the main channel are assumed to enter bank storage or the deep aquifer.

Typical values for $K_{ch}$ for various alluvium materials are given in Table 7:1-4. For perennial streams with continuous groundwater contribution, the effective conductivity will be zero.

Table 7:1-5: SWAT+ input variables that pertain to transmission losses.

While sediment transport calculations have traditionally been made with the same channel dimensions throughout a simulation, SWAT+ will model channel downcutting and widening. When channel downcutting and widening is simulated, channel dimensions are allowed to change during the simulation period.

Three channel dimensions are allowed to vary in channel downcutting and widening simulations: bankfull depth, $depth_{bnkfull}$, channel width, $W_{bnkfull}$, and channel slope, $slp_{ch}$. Channel dimensions are updated using the following equations when the volume of water in the reach exceeds 1.4 × 106 m$^3$.

The amount of downcutting is calculated (Allen et al., 1999):

$depth_{dcut}=358.6*depth*slp_{ch}*K_{CH}$ 7:2.5.1

where $depth_{dcut}$ is the amount of downcutting (m), $depth$ is the depth of water in channel (m), $slp_{ch}$ is the channel slope (m/m), and $K_{CH}$ is the channel erodibility coefficient (cm/h/Pa).

The new bankfull depth is calculated:

$depth_{bnkfull}=depth_{bnkfull,i}+depth_{dcut}$ 7:2.5.2

where $depth_{bnkfull}$ is the new bankfull depth (m), $depth_{bnkfull,i}$ is the previous bankfull depth, and $depth_{dcut}$ is the amount of downcutting (m).

The new bank width is calculated:

$W_{bnkfull}=ratio_{WD}*depth_{bnkfull}$ 7:2.5.3

where $W_{bnkfull}$ is the new width of the channel at the top of the bank (m), $ratio_{WD}$ is the channel width to depth ratio, and $depth_{bnkfull}$ is the new bankfull depth (m).

The new channel slope is calculated:

$slp_{ch}=slp_{ch,i}-\frac{depth_{dcut}}{1000*L_{ch}}$ 7:2.5.4

where $slp_{ch}$ is the new channel slope (m/m), $slp_{ch,i}$ is the previous channel slope (m/m), $depth_{bnkfull}$ is the new bankfull depth (m), and $L_{ch}$ is the channel length (km).

Table 7:2-2: SWAT+ input variables that pertain to channel downcutting and widening.

The channel cover factor, $C_{CH}$, is defined as the ratio of degradation from a channel with a specified vegetative cover to the corresponding degradation from a channel with no vegetative cover. The vegetation affects degradation by reducing the stream velocity, and consequently its erosive power, near the bed surface.

Table 7:2-1: SWAT+ input variables that pertain to sediment routing.

For the channel erosion to occur, both transport and supply should not be limiting, i.e., 1) the stream power (transport capacity) of the water should be high and the sediment load from the upstream regions should be less than this capacity and 2) The shear stress exerted by the water on the bed and bank should be more than the critical shear stress to dislodge the sediment particle. The potential erosion rates of bank and bed is predicted based on the excess shear stress equation (Hanson and Simon, 2001):

$\xi_{bank}=k_{d,bank}*(\tau_{e,bank}-\tau_{c,bank})*10^{-6}$ 7:2.2.8

$\xi_{bed}=k_{d,bed}*(\tau_{e,bed}-\tau_{c,bed})*10^{-6}$ 7:2.2.9