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.

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.

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.

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.

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.

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 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

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.

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.

Evaporation losses from the reach are calculated:

7:1.6.1

where is the evaporation from the reach for the day (m HO), is an evaporation coefficient, is potential evaporation (mm HO), is the channel length (km), is the channel width at water level (m), and 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

7:1.5.1

where are the channel transmission losses (m HO), is the effective hydraulic conductivity of the channel alluvium (mm/hr), is the flow travel time (hr), is the wetted perimeter (m), and is the channel length (km). Transmission losses from the main channel are assumed to enter bank storage or the deep aquifer.

Typical values for 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.

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, , where 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 , where 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.

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

7:1.8.1

where is the volume of water in the reach at the end of the time step (m HO), is the volume of water in the reach at the beginning of the time step (m HO), is the volume of water flowing into the reach during the time step (m HO), is the volume of water flowing out of the reach during the time step (m HO), is the volume of water lost from the reach via transmission through the bed (m HO), is the evaporation from the reach for the day (m HO), is the volume of water added or removed from the reach for the day through diversions (m HO), and is the volume of water added to the reach via return flow from bank storage (m HO).

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.

7:2.1.1

7:2.1.2

7:2.1.3

7:2.1.4

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:

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.

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):

7:2.2.8

7:2.2.9

where – erosion rates of the bank and bed (m/s), – erodibility coefficient of bank and (cm/N-s) and – Critical shear stress acting on bank and bed (N/m). This equation indicates that effective stress on the channel bank and bed should be more than the respective critical stress for the erosion to occur.

The effective shear stress acting on the bank and bed are calculated using the following equations (Eaton and Millar, 2004):

7:2.2.10

7:2.2.11

7:2.2.12

where – proportion of shear stress acting on the bank, – effective shear stress on bed and bank (N/m), – specific weight of water (9800 N/m), – Depth of water in the channel (m), – Top width of channel (m), – Wetted perimeter of bed (bottom width of channel) (m), – Wetted perimeter of channel banks (m), – angle of the channel bank from horizontal, – Channel bed slope (m/m).

The effective shear stress calculated by the above equations should be more than the critical shear stress or the tractive force needed to dislodge the sediment. Critical shear stress for channel bank can be measured using submerged jet test (described later in this chapter). However, if field data is not available, critical shear stress is estimated using the third-order polynomial fitted to the results of Dunn (1959) and Vanoni (1977) by Julian and Torres (2006) :

7:2.2.19

where – percent silt and clay content and – channel vegetation coefficient (range from 1.0 for bare soil to 19.20 for heavy vegetation; see table 7:2-1):

Table 7:2-1. Channel vegetation coefficient for critical shear stress (Julian and Torres, 2006)

Using the above relationships, the bank/bed erosion rate (m/s) can be calculated using eqns. 7:2.2.14 and 7:2.2.15. This has to be multiplied by the sediment bulk density and area exposed to erosion to get the total mass of sediment that could be eroded. Due to the meandering nature of the channel, the outside bank in a meander is more prone to erosion than the inside bank. Hence, the potential bank erosion is calculated by assuming erosion of effectively one channel bank:

Similarly, the amount of bed erosion is calculated as:

SWAT+ currently has four stream power models to predict the transport capacity of channel. The stream power models predict the maximum concentration of bed load it can carry as a non-linear function of peak velocity:

1. Simplified Bagnold model: (same as eqn. 7:2.2.9)

2. Kodatie model

Kodatie (2000) modified the equations developed by Posada (1995) using nonlinear optimization and field data for different sizes of riverbed sediment. This method can be used for streams with bed material in size ranging from silt to gravel:

3. Molinas and Wu model:

Molinas and Wu (2001) developed a sediment transport equation for large sand-bed rivers based on universal stream power. The transport equation is of the form:

4. Yang sand and gravel model

and the gravel equation for D50 between 2mm and 10mm:

By using one of the four models discussed above, the maximum sediment transport capacity of the channel can be calculated. The excess transport capacity available in the channel is calculated as:

Table 7:2-3. Particle size distribution assumed by SWAT+ based on the median size of bank and bed sediments

Deposition of bedload sediments in channel is modeled using the following equations (Einstein 1965; Pemberton and Lara 1971):

It should be kept in mind that small aggregate and large aggregates in the bedload are contributed only from overland erosion and routed through the channel. Gravel is contributed only from channel erosion. Only sand, silt and clay in the bedload is contributed both from overland and channel erosion. If the water in the channel enters the floodplain during large storm events, then silt and clay particles are deposited in the floodplains and the main channel in proportion to their flow cross-sectional areas. Silt and clay deposited in the flooplain are assumed to be lost from the system and is not resuspended during subsequent time steps as in the main channel. The complete mass balance equations for sediment routing are as follows:

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

The channel cover factor, , 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.

The local specific growth rate of algae is a function of the availability of required nutrients, light and temperature. SWAT+ first calculates the growth rate at 20°C and then adjusts the growth rate for water temperature. The user has three options for calculating the impact of nutrients and light on growth: multiplicative, limiting nutrient, and harmonic mean.

The multiplicative option multiplies the growth factors for light, nitrogen and phosphorus together to determine their net effect on the local algal growth rate. This option has its biological basis in the mutiplicative effects of enzymatic processes involved in photosynthesis:

7:3.1.3

where is the local specific algal growth rate at 20°C (day or hr), is the maximum specific algal growth rate (day or hr), is the algal growth attenuation factor for light, is the algal growth limitation factor for nitrogen, and is the algal growth limitation factor for phosphorus. The maximum specific algal growth rate is specified by the user.

The limiting nutrient option calculates the local algal growth rate as limited by light and either nitrogen or phosphorus. The nutrient/light effects are multiplicative, but the nutrient/nutrient effects are alternate.

The algal growth rate is controlled by the nutrient with the smaller growth limitation factor. This approach mimics Liebig’s law of the minimum:

7:3.1.4

where is the local specific algal growth rate at 20°C (day or hr), is the maximum specific algal growth rate (day or hr), is the algal growth attenuation factor for light, is the algal growth limitation factor for nitrogen, and is the algal growth limitation factor for phosphorus. The maximum specific algal growth rate is specified by the user.

The harmonic mean is mathematically analogous to the total resistance of two resistors in parallel and can be considered a compromise between equations 7:3.1.3 and 7:3.1.4. The algal growth rate is controlled by a multiplicative relation between light and nutrients, while the nutrient/nutrient interactions are represented by a harmonic mean.

7:3.1.5

where is the local specific algal growth rate at 20°C (day or hr), is the maximum specific algal growth rate (day or hr), is the algal growth attenuation factor for light, is the algal growth limitation factor for nitrogen, and is the algal growth limitation factor for phosphorus. The maximum specific algal growth rate is specified by the user.

Calculation of the growth limiting factors for light, nitrogen and phosphorus are reviewed in the following sections.

Algal Growth Limiting Factor for Light.

A number of mathematical relationships between photosynthesis and light have been developed. All relationships show an increase in photosynthetic rate with increasing light intensity up to a maximum or saturation value. The algal growth limiting factor for light is calculated using a Monod half-saturation method. In this option, the algal growth limitation factor for light is defined by a Monod expression:

7:3.1.6

where is the algal growth attenuation factor for light at depth , is the photosynthetically-active light intensity at a depth below the water surface (MJ/m-hr), and is the half-saturation coefficient for light (MJ/m-hr). Photosynthetically-active light is radiation with a wavelength between 400 and 700 nm. The half-saturation coefficient for light is defined as the light intensity at which the algal growth rate is 50% of the maximum growth rate. The half-saturation coefficient for light is defined by the user.

Photosynthesis is assumed to occur throughout the depth of the water column. The variation in light intensity with depth is defined by Beer’s law:

For daily simulations, an average value of the algal growth attenuation factor for light calculated over the diurnal cycle must be used. This is calculated using a modified form of equation 7:3.1.8:

Algal Growth Limiting Factor for Nutrients

The algal growth limiting factor for nitrogen is defined by a Monod expression. Algae are assumed to use both ammonia and nitrate as a source of inorganic nitrogen.

The algal growth limiting factor for phosphorus is also defined by a Monod expression.

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, , is calculated:

7:2.2.1

where is the peak flow rate (m/s) and is the cross-sectional area of flow in the channel (m). The peak flow rate is defined as:

7:2.2.2

where is the peak rate adjustment factor, and is the average rate of flow (m/s). Calculation of the average rate of flow, , and the cross-sectional area of flow, , is reviewed in Section 7, Chapter 1.

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

7:2.2.3

where is the maximum concentration of sediment that can be transported by the water (ton/m or kg/L), is a coefficient defined by the user, is the peak channel velocity (m/s), and spexp is an exponent defined by the user. The exponent, , 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, . If , deposition is the dominant process in the reach segment and the net amount of sediment deposited is calculated:

7:2.2.4

where is the amount of sediment deposited in the reach segment (metric tons), is the initial sediment concentration in the reach (kg/L or ton/m), is the maximum concentration of sediment that can be transported by the water (kg/L or ton/m), and is the volume of water in the reach segment (m HO).

If , degradation is the dominant process in the reach segment and the net amount of sediment reentrained is calculated:

7:2.2.5

where is the amount of sediment reentrained in the reach segment (metric tons), is the maximum concentration of sediment that can be transported by the water (kg/L or ton/m), is the initial sediment concentration in the reach (kg/L or ton/m), is the volume of water in the reach segment (m HO), is the channel erodibility factor, and 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:

7:2.2.6

where is the amount of suspended sediment in the reach (metric tons), is the amount of suspended sediment in the reach at the beginning of the time period (metric tons), is the amount of sediment deposited in the reach segment (metric tons), and is the amount of sediment reentrained in the reach segment (metric tons).

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

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.

Growth and decay of algae/chlorophyll is calculated as a function of the growth rate, the respiration rate, the settling rate and the amount of algae present in the stream. The change in algal biomass for a given day is:

7:3.1.2

where is the change in algal biomass concentration (mg alg/L), is the local specific growth rate of algae (day or hr), is the local respiration or death rate of algae (day or hr), is the local settling rate for algae (m/day or m/hr), is the depth of water in the channel (m), is the algal biomass concentration at the beginning of the day (mg alg/L), and is the flow travel time in the reach segment (day or hr). The calculation of depth and travel time are reviewed in Chapter 7:1.

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, 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:

The amount of organic nitrogen in the stream may be increased by the conversion of algal biomass nitrogen to organic nitrogen. Organic nitrogen concentration in the stream may be decreased by the conversion of organic nitrogen to NH or the settling of organic nitrogen with sediment. The change in organic nitrogen for a given day is:

7:3.2.1

where is the change in organic nitrogen concentration (mg N/L), is the fraction of algal biomass that is nitrogen (mg N/mg alg biomass), is the local respiration or death rate of algae (day or hr), is the algal biomass concentration at the beginning of the day (mg alg/L), is the rate constant for hydrolysis of organic nitrogen to ammonia nitrogen (day or hr), is the organic nitrogen concentration at the beginning of the day (mg N/L), is the rate coefficient for organic nitrogen settling (day or hr), and is the flow travel time in the reach segment (day or hr). The fraction of algal biomass that is nitrogen is user-defined. Equation 7:3.1.17 describes the calculation of the local respiration rate of algae. The calculation of travel time is reviewed in Chapter 7:1.

The user defines the local rate constant for hydrolysis of organic nitrogen to NH at 20C. The organic nitrogen hydrolysis rate is adjusted to the local water temperature using the relationship:

7:3.2.2

where is the local rate constant for hydrolysis of organic nitrogen to NH (day or hr), is the local rate constant for hydrolysis of organic nitrogen to NH at 20C (day or hr), and is the average water temperature for the day or hour (C).

The user defines the rate coefficient for organic nitrogen settling at 20C. The organic nitrogen settling rate is adjusted to the local water temperature using the relationship:

7:3.2.3

where is the local settling rate for organic nitrogen (day or hr), is the local settling rate for organic nitrogen at 20C (day or hr), and is the average water temperature for the day or hour (C).

The local respiration or death rate of algae represents the net effect of three processes: the endogenous respiration of algae, the conversion of algal phosphorus to organic phosphorus, and the conversion of algal nitrogen to organic nitrogen. The user defines the local respiration rate of algae at 20C. The respiration rate is adjusted to the local water temperature using the relationship:

7:3.1.17

where is the local respiration rate of algae (day or hr), is the local algal respiration rate at 20C (day or hr), and is the average water temperature for the day or hour (C).