# CMS-Flow Sediment Transport

The sediment transport controls are located in the *Transport* section of the *CMS-Flow Model Control* window as shown in the figure below. The sediment transport is activated by going to the *Transport* section of the *CMS-Flow Model Control* and checking the box labeles *Calculate sediment transport*.
The CMS card used to turn on or off the sediment transport is described in the table below.

**Table 1. CMS-Flow card used for activating the sediment transport calculation.**

Card | Arguments | Default | Range | Description |
---|---|---|---|---|

CALC_SEDIMENT_TRANSPORT | CHARACTER | OFF | ON | OFF | Turns on or off the sediment transport calculation. |

# Transport model

There are currently three sediment transport models available in CMS: (1) Equilibrium total load, (2) Equilibrium bed load plus advection-diffusion for suspended load, and (3) Non-equilibrium total load. The first two models are selected by unchecking the checkbox which says "Use non-equilibrium transport" and selecting either "Total load" for the first model, or "Advection-diffusion" for the second next to input item named "Formulation". The third model is selected by checking the box "Use non-equilibrium transport".

**Table 2. CMS-Flow cards related to the transport model.**

Card | Arguments | Default | Range | Description | Versions |
---|---|---|---|---|---|

SED_TRAN_FORMULATION | CHARACTER | NET | WATANABE | LUND_CIRP | A-D | NET | Selects the sediment transport model. | >1.0 |

Note that the when selecting the equilibrium total load model, the SED_TRAN_FORMULATION card is set to either WATANABE or LUND_CIRP depending on the transport formula chosen. When selecting the equilibrium A-D model, the transport formula is specified through the concentration profile formula (described below).

## 1. Equilibrium Total load

In this model, both the bed load and suspended load are assumed to be in equilibrium. The bed change is solved using a simple mass balance equation known as the Exner equation.
More information on the this model can be found **here**.

## 2. Equilibrium Bed load plus Advection-Diffusion Suspended Load

Calculations of suspended load and bed load are conducted separately. The bed load is assumed to be in equilibrium and is included in the bed change equation while the suspended load is solved through the solution of an advection-diffusion equation. Actually the advection diffusion equation is a non-equilibrium formulation, but because the bed load is assumed to be in equilibrium, this model is referred to the "Equilibrium A-D" model.

More information on the this model can be found **here**.

## 3. Non-equilibrium Total Load

The non-equilibrium sediment transport algorithm (NET) simulates non-cohesive, single size sediment transport and bed change using a Finite Volume method and includes advection, diffusion, hiding and exposure, and avalanching. NET sediment transport is calculated with a non-equilibrium bed-material (total load) formulation. In this approach, the suspended- and bed-load transport equations are combined into a single equation and thus there is one less empirical parameter to estimate (adaptation length).

Additional information on NET can be found **here**.

All of the previously mentioned models account for hard bottom and effect of the bed slope on bed load.

# Time Steps

The sediment transport time step is the time step at which the sediment transport equation is solved. In the case of the equilibrium total load model, then the sediment balance equation (Exner equation) is solved every morphologic time step. The morphologic time step is the time step at which the bed elevation is updated. The CMS-Flow

**Table 3. CMS-Flow cards used for setting the sediment transport and morphologic time steps.**

Card | Arguments | Range | Description | Version | |
---|---|---|---|---|---|

SED_TRAN_CALC_INTERVAL | REAL | greater or equal to hydro time step for explicit scheme, or equal hydro time step for implicit scheme | Time step used for transport equation | <=v3.75 | |

MORPH_UPDATE_INTERVAL | REAL | greater or equal to hydro time step for explicit scheme, or equal hydro time step for implicit scheme | Time step used for updating bed elevation | <=v3.75 |

**Important Note:**

- When using the implicit solution (CMS versions 4.0 and greater), the sediment transport and morphologic time steps are set to the hydrodynamic time step. Therefore the above cards are ignored. The reason for this is because the implicit hydrodynamic time step is already big and using larger time steps for sediment transport and bed change is not necessary.

# Transport Formula

The nearbed sediment concentation or concentration capacity are calculated with one of the following transport formula:

- Lund-CIRP (2006)
- Van Rijn (1984,2007)
- Watanabe (1987)
- Soulsby-van Rijn (1997) (>=V4.0)

**Table 4. CMS-Flow cards used for setting the sediment transport formula.**

Card | Arguments | Default | Range | Description | |
---|---|---|---|---|---|

NET_TRANSPORT_CAPACITY | CHARACTER | LUND-CIRP | LUND-CIRP | VAN_RIJN | WATANABE | SOULSBY | Selects the transport formula. Note that SOULSBY is only available in v>=4.0 | |

TRANSPORT_FORMULA | CHARACTER | LUND-CIRP | LUND-CIRP | VAN_RIJN | WATANABE | SOULSBY | Selects the transport formula. Note that SOULSBY is only available in v>=4.0. | |

SED_TRANS_FORMULATION | CHARACTER | LUND-CIRP | LUND-CIRP | A-D | WATANABE | NET | Selects the transport formula for the equilibrium total load model. Does not specify the transport formula for the equilibrium A-D and non-equilibrium total load models. | |

CONCENTRATION_PROFILE | CHARACTER | LUND-CIRP | LUND-CIRP|EXPONENTIAL| ROUSE| VAN_RIJN | Selects the concentration profile to be used either in the equilibrium A-D or total load nonequilibrium models. | |

A_COEFFICIENT_WATANABE | REAL | 0.1 | 0.05-0.5 | Empirical coefficient which goes into the Watanabe transport formula. |

**Important Notes:**

- Different transport formula may produce very different results in morphology change.
- The Lund-CIRP does well in predicting the surf zone sediment transport but tends to overestimate the transport rates near the wetting and drying limit and in deep water (>10 m).
- The van Rijn transport formula tends to underestimate the transport for conditions near the critical shear stress of motion. The formula also tends to underestimate the transport close to the shoreline.
- The Soulsby-van Rijn transport formula also

# Scaling Factors

## Transport Scaling Factors

The bed and suspended transport scaling factors multiply directly by the transport capacity or near-bed sediment concentration calculated from the transport formula. These factors should be used to calibrate sediment transport rates and due to the large uncertainty in the transport formula, it is generally acceptable to use scaling factors in the range of 0.5-2.0.

**Table 5. CMS-Flow cards used for setting the bed and suspended load scaling factors.**

Card | Arguments | Default | Range | Description |
---|---|---|---|---|

BED_LOAD_SCALE_FACTOR | REAL | 1.0 | 0.5-2.0 | Calibration factor for bed load transport capacity formula |

SUSP_LOAD_SCALE_FACTOR | REAL | 1.0 | 0.5-2.0 | Calibration factor for suspended load transport capacity formula |

## Morphologic Acceleration Factor

The morphologic acceleration or scaling factor is directly multiplied by the calculated bed change at every time step and is intended as a means of speeding up the computational time. It is only recommended for periodic boundary conditions or conditions that do not change rapidly over time. The morphologic acceleration factor is set in the **Sediment** tab of the *CMS-Flow Model Control* window in SMS.

**Table 6. CMS-Flow card used for setting the morphologic acceleration factor.**

Card | Arguments | Default | Range | Description |
---|---|---|---|---|

MORPH_ACCEL_FACTOR | REAL | 1.0 | 1-100 | Morphologic acceleracion factor. Directly multiplies by calculated bed change. |

**Note**: The morphologic acceleration factor is NOT a calibration parameter. It should only be used in cases with periodic forcing and boundary conditions and even then it should be used with caution. It is NOT recommended to use larger values than 20-30.

## Schmidt Number

The sediment mixing coefficient is calculated as the eddy viscosity divided by the Schmidt number. For simplicity the Schmidt number is assumed to be constant and the default value is 1.0. The Schmidt number can only be changed using the advanced card described below.

**Table 7. CMS-Flow card used for setting the Schmidt number.**

Card | Arguments | Default | Range | Description | Versions |
---|---|---|---|---|---|

SCHMIDT_NUMBER | REAL | 1.0 | none | Controls the sediment mixing strength | v>=4.0 |

**Note**: The Schmidt number should NOT be used as a calibration number and showed only be changed in sensitivity analysis or model testing.

# Sediment Characteristics

The sediment characteristics are set in the *Sediment* tab of the *CMS-Flow Model Control* window. The sediment characteristics are the porosity, density, shape, and fall velocity.

**Table 7. CMS-Flow card used for setting the Schmidt number.**

Card | Arguments | Range | Default | Description | Versions |
---|---|---|---|---|---|

SEDIMENT_POROSITY | REAL | 0-1 | 0.4 | Sets the sediment porosity | |

SEDIMENT_DENSITY | REAL | none | 2650 | Sets the sediment density in kg/m^3 | |

SEDIMENT_FALL_VELOCITY | REAL | 4.0e-4 - 0.4 | none | Sets the sediment fall velocity to a constant in m/s | v>=3.5 |

SEDIMENT_FALL_VELOCITIES | INTEGER REAL REAL ... | none | none | Sets the sediment fall velocity to a constant in m/s for multiple grain size classes. The first number is the number of size classes and is followed by the fall velocities for each size class in ascending order. | v>=4.0 |

SEDIMENT_FALL_VEL_FORM | CHARACTER | SOULSBY| WU-WANG | SOULSBY | Sets the sediment fall velocity formula. | v>=4.0 |

SEDIMENT_FALL_VELOCITY_FORMULA | CHARACTER | SOULSBY| WU-WANG | SOULSBY | Sets the sediment fall velocity formula. Same as SEDIMENT_FALL_VEL_FORM. | v>=4.0 |

SEDIMENT_COREY_SHAPE_FACTOR | REAL | none | 0.7 | Sets the Corey shape factor which is used in the Wu-Wang sediment fall velocity formula. | v>=4.0 |

**Important Notes:**

- It is NOT recommended to use the sediment fall velocity, porosity, density or shape factor as calibration parameters. These parameters should be estimated using field or literature data.
- The sediment porosity and density are assumed constant for the whole domain and all grain size classes. For most coastal applications these assumptions are reasonable but need to be taken into consideration.

# Avalanching

Avalanching is the process of sediment sliding when the critical angle of repose is reached. In CMS, avalanching is simulated using a mass conservative relaxation method which limits the bed slope to the critical angle of repose. For most coastal applications, the critical angle of repose is never reached, so it is not needed. The CMS-Flow cards used for specifying avalanching, and its options, are described in the below.

**Table 8. CMS-Flow cards related to avalanching.**

Card | Arguments | Range | Default | Description |
---|---|---|---|---|

USE_AVALANCHING | CHARACTER | ON | OFF | ON | Turns On or Off the avalanching. |

RESPOSE_ANGLE | REAL | none | 32º | Specifies the angle of repose in degrees. |

AVALANCHE_MAX_ITERATIONS | INTEGER | none | 200 | Specifies the maximum number of iterations used in the implicit solution scheme. For the explicit solution scheme, the avalanching is calculated every transport time step for one iteration. |

# Bedslope term

The bedslope term accounts for the effect of gravity on sloped beds. The larger the bed slope coefficient, the more sediment tends to move downslope, thus smoothing the solution. The CMS-Flow used to specify the slope coefficient is described in the table below. The bedslope coefficient is set in the *Sediment* tab of the *CMS-Flow Model Control* window in SMS 11.0.

**Table 9. CMS-Flow card used for setting the bedslope coefficient.**

Card | Arguments | Default | Range | Description | Versions |
---|---|---|---|---|---|

SLOPE_COEFFICIENT | REAL | 1.0 | 0-5 | Bed slope coefficient which controls enters a diffusion term which moves sediment down slope |

**Note:**It is recommended that the bed slope be set to 0.1 for the nonequilibrium total load model to avoid excessive smoothing.

# Ramp Period

The option is available to not calculate the morphology change during the ramp period. The best practice is the start the model simulation so that the time when the ramp period ends corresponds to the time of the measured bathymetry. This avoid the initial bed erosion (although slight) of the bed. This also facilities calculating simulation statistics such as transport rates and residual currents.

**Table 10. CMS-Flow card used to turn On or Off bed updating during the ramp period.**

Card | Arguments | Range | Default | Description | Versions |
---|---|---|---|---|---|

CALC_MORPH_DURING_RAMP | CHARACTER | ON | OFF | ON | Turns On or Off the morphology change calculation during the ramp period | v>=4.0 |

# Total Load Correction Factor

The total load correction factor accounts for the nonuniform vertical profile of sediment concentration and current velocity and produces temporal lag in between the flow and sediment transport. The factor is used in the nonequilibrium total load sediment transport formula. The factor is obtained by integrated the

**Table 11. CMS-Flow cards related to the total load correction factor.**

Card | Arguments | Default | Range | Description |
---|---|---|---|---|

TOTAL_LOAD_CORR_FACTOR_CONSTANT | REAL | 0.3-1.0 | none | Sets the total load correction factor to a constant. |

CONCENTRATION_PROFILE | CHARACTER | LUND-CIRP | VAN_RIJN | EXPONENTIAL | ROUSE | none | Sets the concentration profile to be used either in the pickup and deposition functions or the total load correction factor calculation. |

# Boundary and Initial Conditions

In the case of the Equilibrium Total Load sediment transport model, all boundaries are set to the equilibrium transport rate. For the Equilibrium Bed Load plus Advection Diffusion model, the suspended load is specified as the equilibrium concentration at inflow cells and a zero gradient at outflow cells. For the Total load nonequilibrium sediment transport model, the sediment concentration is set to the equilibrium concentration at inflow cells and a zero gradient boundary condition is applied at outflow cells.

In the case an initial conditions file is NOT specified both the hydrodynamics and sediment concentrations are initialized as zero. If an initial conditions file is specified, than the initial sediment concentrations are read in. If an initial conditions file is specified but without the sediment concentration, than the initial sediment concentration is set to the equilibrium concentration.

**Table 12. CMS-Flow cards related to the boundary conditions**

Card | Arguments | Default | Range | Description | Versions |
---|---|---|---|---|---|

NET_LOADING_FACTOR | REAL | 1.0 | 0.5-2.0 | Used to specify under- or overloading at sediment inflow boundaries. Only for NET. | 3.5=>v<=4.0 |

SEDIMENT_INFLOW_LOADING_FACTOR | REAL | 1.0 | 0.5-2.0 | Used to specify under- or overloading at sediment inflow boundaries. | >=4.0 |

CALC_MORPH_DURING_RAMP | CHARACTER | ON | ON | OFF | Determines whether to calculate the morphology change during the ramp period | v>=3.5 |

# Hard Bottom

Hard Bottom is a morphologic constraint that provides the capability to simulate mixed bottom types within a single simulation. This cell-specific feature limits the erodibility of the constrained cells down to a specified depth below the water surface. During sediment transport calculations, exposed hard bottom cells may become covered through deposition. By default, CMS-Flow cells are fully-erodible cells with no specified hard bottom depth (inactive cells; denoted by the CMS-Flow null value of -999.0). Hard bottom only needs to be specified only for computational (ocean) cells.

Within the *CMS-Flow Model Control* window, the hard bottom dataset can be created from the *Sediment* tab. If the dataset does not exist, it can be created using the *Create Dataset* button. If a dataset exists (created using the Data Calculator) which represents the intended hard bottom specifications, the *Select Dataset..* button can be used to select such dataset and copy the values to the hard bottom dataset.

When specified, cell hard bottom depths will appear in the Project Explorer as a scalar dataset beneath the CMS-Flow grid. This dataset can not be deleted, though it can be edited like any other dataset. A CMS-Flow simulation must contain the hard bottom dataset (even if it is not specified) so SMS will create a defaulted (inactive cells) dataset if it does not already exist when saving the simulation. The hard bottom dataset can created, edited, viewed and verified using the following SMS interface features.

## Hard Bottom Specification

Although the hard bottom dataset can be edited (when its the active dataset) by selecting a cell (or group of cells) and changing the scalar (S) value in the Edit Window, an user-friendly window exists which provides specification options. With the *Select Grid Cell* tool active, make a selection, right click to bring up the tool menu and choose the *Specify Hard Bottom...* option.
This will open the CMS-Flow Hard Bottom Specification window.

The following options are provided in the Hard Bottom Specification window:

**Use bathymetric cell depth**- Sets the cell hard bottom depth to be the cell geometry value thereby creating an exposed non-erodible condition. If multiple cells were selected, then each cell will use its respective bathymetric depth.**Specified distance below bathymetric cell depth**- Sets the cell hard bottom depth to be the cell geometry value plus the specified distance thereby creating a sediment-covered non-erodible condition. The distance is limited to positive values to ensure the hard bottom depth is greater than the geometry value. The cell can provide sediment for transportation, however, the amount of erosion is limited. If multiple cells were selected, then each cell will use its respective bathymetric depth.**Specified depth**- Sets the cell hard bottom depth to the specified depth thereby creating a sediment-covered non-erodible condition similar to specified distance. The depth is limited to greater than the geometry value. If multiple cells were selected, then the depth is limited to greater than the largest geometry value and all cells will have the same value.**Unspecified**- Resets to an inactive hard bottom condition. The cell hard bottom depth is set to the CMS-Flow null value. If multiple cells were selected, then all cells will be reset.

If no cells are selected when opening the Hard Bottom Specification window, then all computational (ocean) cells will be used. If a selection of only non-computational cells, then specification cannot occur. If a selection contains computational and non-computational cells, then the specification will only apply to the computational cells.

If multiple computational cells with differing specifications are selected, the window will not display a selected specification type and the *OK* button will be disabled. This is to protect the previous specifications from being overwritten by mistake. The *OK* button will be enabled when an option is selected. The minimum hard bottom depth of the multiple computational cells selected will be displayed in the *Depth* edit field and the minimum hard bottom depth minus the maximum geometry depth of the multiple computational cells selected will be displayed in the *Distance* edit field.

## Display Options

The hard bottom dataset (when its the active dataset) will only display the cells with hard bottom specified if the *Ocean cell* display option is turned on. Inactive hard bottom cells are not displayed.

CMS-Flow includes hard bottom symbols to differentiate specifications. On the *Cartesian Grid* page of the Display Options window (when CMS-Flow is the active model), the *Hard bottom symbols* check box controls the display of symbols that will appear in hard bottom cells (even if the hard bottom dataset is not active). If this is turned on, then the user must be aware of the individual symbol settings accessed by clicking on the *Options...* button. The *Options...* button displays the CMS-Flow Hard Bottom Symbols window.

Hard bottom symbols can be selected for three hard bottom specification types:

**Non-erodible**- Displayed in exposed hard bottom cells (cell hard bottom depth is equal to cell bathymetric depth).**Erodible to specified depth**- Displayed in sediment-covered hard bottom cells (cell hard bottom depth is greater than cell bathymetric depth).**Invalid specification**- Displayed in hard bottom cells where the hard bottom depth is less than cell bathymetric depth (the geometry is below the erosion limit).

If the *Hard bottom symbols* check box is turned off, no symbols will be displayed and the individual settings cannot be accessed, however, the individual settings will not be changed.

## Model Check

The CMS-Flow Model Checker, accessed from the CMS-Flow | Model Check... menu item, includes a check to ensure that no invalid hard bottom specifications exist in the grid. An invalid specification may be created, for example, by setting an infeasible hard bottom scalar value in the Edit Window or adjusted the grid's geometry without updating the hard bottom. It is suggested that the model checker be used prior to running CMS-Flow.

# Variable D50

This cell-specific parameter allows for the single-sized sediment transport model to make a hiding and exposure correction factor. More information on the use of variable grain size (D50) can be found **here**.

**Table 13. CMS-Flow cards related to the variable D50 feature.**

Card | Arguments | Default | Range | Description |
---|---|---|---|---|

TRANSPORT_GRAIN_SIZE | REAL | none | none | Transport grain size in mm. The transport grain size is the sediment size which is eroded, transported, and deposited. When this card is specified the D50 dataset is used to make a hiding and exposure correction to the critical shear stress. |

HIDING_EXPOSURE_COEFFICIENT | REAL | 1.0 | none | Hiding and exposure coefficient. |

**Important Notes**

- If the no transport grain size is specified, then the transport grain size is calculated based on the mean grain size of the whole domain.
- If the card CONSTANT_GRAIN_SIZE is used, then the D50 dataset will be ignored.