Model settings
Besides the input date, further setting needs to be provided to start the calculation.
Maximum time step
The time step Δt is adjusted during the calculation according Courant–Friedrichs–Lewy condition to maintain numerical stability. The length of the time step depends on the surface runoff velocity and the spatial step size (DMT cell size). Therefore a maximum time step needs to be set.
The maximum time step depends on the desired detail of the output data, especially during a precipitation episode when flow velocities are already lower and when the stability criterion would allow too large a time step. The implementation of the numerical stability are described in reference manual.
The maxim time step is also user as the initial time step in the calculation.
Total runnig time
The total simulation time refers to the duration over which the model performs its computations. To calculate the overall runoff volume accurately, the simulation duration must extend beyond the period of the simulated rainfall event. Conversely, to determine the peak flow rate, the simulation time may be shorter than the precipitation duration.
Output directory
This specifies the location where the results will be stored. Note that this folder may be overwritten.
Extra output
If the extra outputs are check, temp and control data will be saved in output folder. Description of extra output these parameters described in the reference manual.
Computation settings
Flow direction
Flow direction algorithm controls to which computational cell or cells the water flows i.e. it controls the flow routing. Two options are implemented in SMODERP2D:
- D8 a single direction flow algorithm and
- multiple flow direction algorithm (MFD) (Seibert, 2013).
If D8 is set, all of the sheet flow volume from a cell flows to single adjacent cell with highest elevation difference. If MFD is set, the sheet flow volume from a cell is divided proportionally to multiple downslope cells based on elevation difference between cells.
note: If MDF is set, the rill flow still uses the D8 flow direction algorithm since the rill is essentially small channel that can only flow in on direction.
In watercourse network, the water from the surface flow is further conducted through a network based on the topology of the network.
Shallow water flow equation approximation
The model is capable of using kinematic and diffusive wave approximation of Saint-Venant equations.
Kinematic wave approximation assumes that the slope of the water level is parallel to the slope of the soil surface. This approximation is valid for step slopes where substantial backwater effect does not occur.
The diffusive wave is driven be the waster surface slope. Therefore, the backwater effect is considered. The diffusive wave approximation should be used if flat areas as presented in the model. However, the diffusive wave is computationally more intensive compared to kinematic wave approximation.
For more details about the flow equation approximation see the reference manual.
Time derivative approximation
The SMODERP2D calculated the transient water flow. Therefore, the time derivation takes place in the equation. To solve the time approach of the solution this derivative has to be solved.
Ordinary explicit and implicit Euler methods are implemented in SMODERP2D to solve the time derivative. Essentially, the explicit method is usually more sensitive to time step length. In some cases this can cause slow down in the computation due to extremely small time step. The implicit generally allows the model to run with larger time step (depends on the model setting). However, a system of linear equations need to be constructed and solved.
Usually, the advantages of implicit method are pronounced for computation of larger areas (>1,000,000 cells in raster). For smaller areas (<1,000 cells in raster) the computation time to construct and solve the system of linear equations slows down the computation and explicit method may lead to shorter computational time, especially for larger raster cell size (>5 m).
No general recommendation to which method to use can be given. It is recommended to test both methods for each specific model, if necessary.
For further information about the explicit and implicit Euler method see the reference manual.
reference manual.
SEIBERT J., MCGLYNN B.L.: A new triangular multiple flow direction algorithm for computing upslope areas from gridded digital elevation models [online], http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.79.977&rep=rep1&type=pdf