Das Modell sedFlow und Erfahrungen aus Simulationen des Geschiebetransportes in fünf Gebirgsflüssen der Schweiz. Synthesebericht
The sedFlow program was developed for the one-dimensional simulation of bedload transport in steep streams with gravel beds (Heimann et al. 2015a). The simulation program includes recent approaches both for calculating flow resistance and bedload transport. Another new element of the program is the option to specify lateral sediment inputs from torrents, which can provide significant amounts of sediment delivery to mountain rivers, particularly in the case of debris flows. The simulation program sedFlow was applied in five mountain rivers of Switzerland. In all study catchments observations of bedload transport were available, and thus the simulation model sedFlow could be calibrated. The selected study reaches cover a relatively large range of channel slopes typical of mountain rivers upstream of the piedmont lakes in Switzerland.
In sedFlow the stream channel is approximated by a rectangular profile. Using the Manning-Strickler equation for flow resistance, the kinematic wave propagation can be computed analytically for the discharge calculation along the channel (Liu and Todini 2002), resulting in fast calculation times. With the variable power equation (VPE) of Ferguson (2007) this method cannot be applied. Therefore this flow resistance equation must be combined, for example, with explicit flow routing, which requires relatively long computation times. An alternative is to use the VPE equation together with a simplified hydraulic calculation assuming a constant discharge per time step in the channel reaches without lateral inflow. This also results in fast calculation times, and in case of (important) lateral sediment input adverse channel slopes in the longitudinal profile are permissible. In most study cases reported here, the VPE equation was used to calculate flow resistance.
The simulations with sedFlow showed that in addition to choosing a suitable bed load transport formula also the minimum value for the critical dimensionless shear stress at the beginning of motion (θc50,min) in the bedload transport formula of Rickenmann (2001) and the reference shear stress (θref) in the formula of Wilcock and Crowe (2003) are important. For the five study mountain rivers, the values used in sedFlow for θc50,min are in a plausible range, as evidenced from a comparison with field data for the initiation of bedload transport (Bunte et al. 2013). For a five-year period in the Kleine Emme River and for a ten-year period in the Brenno River, the calibrated sedFlow program produced a reasonable agreement between simulated and observed bedload transport and bed level changes (Heimann et al. 2015b).
For the flood event of 2011 in the Lonza River, the transport formula of Rickenmann (2001) led to plausible results, both for different minimum values (θc50,min) of the dimensionless shear stress at incipient motion and for different hiding functions. For the bedload transport calculations, the reduced energy slope was computed with an exponent of 1.5. The choice of the value of θc50,min had only a small, insignificant influence on the level of the transported bedload. The transport formula of Wilcock and Crowe (2003) led to similarly plausible results, also computing the reduced energy slope with an exponent of 1.5. The long-term simulations of bedload transport in the Lonza River for periods with much smaller average discharges resulted in a clear overestimation when using the transport formula of Rickenmann (2001) and otherwise identical model parameters. When an exponent of 2 was used in the reduced energy slope computation, the overestimation of observed bedload transport was less strong but still amounted to a factor of 6 to 8 on average. The transport formula of Wilcock and Crowe (2003) resulted in plausible results for the long-term simulations if either a 5 % sand fraction was assumed or when a sand fraction of 20 % was used along with an exponent of 2 for the reduced energy slope computation.
The early simulations for the Hasliaare River showed partly supercritical flow conditions with elevated Froude numbers in the steepest channel reaches. These simulations resulted in too large sediment transport and an excessive erosion of convex knickpoints in the longitudinal profile. Therefore, an option was implemented in the model sedFlow to fix an upper limit of the Froude number so that supercritical flow can be prevented in the steeper reaches. By limiting the Froude number, higher energy losses are accounted for in the reduced energy slope computation. Thus, the energy available for bedload transport decreases for smaller Froude numbers, reducing also the amount of the transported bedload. For the Hasliaare River, limiting the Froude number can also be explained with the fact that in the channel bed of steeper reaches rough blocks are present, which had been insufficiently accounted for in the grain size distribution curves serving as model inputs. With the limitation of the Froude number to a maximum value of 0.9, excessive erosion of convex knickpoints in the longitudinal profile of the Hasliaare River could be avoided.
The influence of lateral sediment inputs on bedload transport in the receiving river was studied mainly for the Brenno and Hasliaare rivers. If the entries were fed continuously over the flood event duration, then the impact on the transported bedload volumes and the bed level changes tended to be the stronger, the greater were the lateral sediment inputs. The effects appear to be spatially limited to the local environment, extending only a few kilometers up- and downstream of the tributary location. If the entries were fed instantaneously during a flood event, the impact on the bedload transport in the receiving river was the stronger, the sooner the sediment input occurred during a flood. The effect on sediment deposition in the immediate vicinity of the confluence tends to be the greater, the later the lateral sediment input occurred during the flood, but somewhat further upstream in the main river an early entry can lead to more sediment deposition than a late entry.