TiRiLab Report No. 1
Preliminary hydrodynamic investigation of water and sediment fluxes in the Maggia River
Christos Argyrakis Emmanouil Skourtis
March 2018
TiRiLab is part of the project HyMoCARES (HydroMorphological assessment and management at basin scale for the Conservation of Alpine Rivers and re- lated Ecosystem Services). Partial funding is provided under the EU Alpine Space Programme through the New Regional Policy of the Swiss Confederation and by the Republic and Canton of Ticino.
Disclaimer: This is a student report produced as part of the education pro- gramme in the Master of Environmental Engineering at ETH Zürich. The results reported here are not scientifically reviewed, do not necessarily represent the views of the supervisors, and should be used with caution.
For more information contact: Peter Molnar ([email protected])
Abstract
The riverine corridor in the Maggia Valley, extending from Bignasco to Ponte Brolla with a length of about 23 km, is the examined river reach in this project. The river bed is characterized by strong dynam- ics and high sediment transport rates. As a result, a braided river system with gravel bars and vegetated islands is noticed over a length of around 7.5 km near the village of Someo in the central part of the riverine corridor. The dynamic morphology of the area makes it attractive for hydrodynamic investigation of water and sediment fluxes.
The software system BASEMENT was used for a preliminary simulation of sediment transport in the Maggia riverine corridor in order to set the basis for the quantification of the erosion and deposition rates in the river bed as well as the required water discharge for a significant geomorphic work to take place. In the pre-processing phase the historical erosion and deposition patterns in the river reach were deter- mined based on cross-sectional data taken by BAFU and covering the period 1978-2015. In addition, a comparison of the elevations of the cross-sectional points with the values of the used Digital Terrain Model (DTM) was performed. This resulted in a mean absolute deviation of 0.50 m as well as in a histogram which indicates that the majority of the DTM values are higher than the observed cross-sec- tional elevations. This can be explained by the fact that points below water have not been surveyed for the production of the DTM.
The morphodynamic simulations with BASEMENT were performed on a smaller river reach, extending from the Riveo settlement until before the Maggia settlement and having approximately a length of 8.3 km. This river section contains a braided part of the river with gravel bars and vegetated islands. In the grid generation phase two computational meshes (one coarser and one finer) were produced using different maximum area constraints with the finer mesh having a mean cell size in the main channel of 95 m2, while in the coarser mesh this value is 126 m2. Two different friction zones were also defined at each mesh (one zone for gravel/cobbles and one zone for vegetation).
The calibration of the hydraulic model was implemented by comparing the simulated water depths with the observed ones at the Lodano station and the selected calibration parameter was the friction coeffi- cient of the gravel introduced with the Strickler value (kStr). Hydrodynamic simulations were run with
BASEMENT using three kStr values, which define the possible range of kStr of gravel, and then the mod- elled water depths were plotted against the measured ones. The resulted calibration was satisfactory.
For the identification of the threshold discharge for which we start having a large increase of the erosion rate and/or the eroded area for the two meshes, uniform sediment morphodynamic simulations were performed for two grain sizes and for different discharges. To evaluate the erosion, three different ap- proaches were used, and a threshold discharge of 220 m3/s was defined. To create the inflow hydro- graph for the main simulation in our project, only discharges above the defined threshold were used from the time series of hourly discharges from the Lodano gauge, this was done to reduce the duration of the simulation and only take into account the larger discharges.
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It was found that the simulated Δz values have a similar range of values as the observed ones in the study reach which indicates that the model reproduces successfully the order of magnitude of erosion and deposition in the study domain. It was also found that the observed volumes of eroded and depos- ited sediment are larger than the simulated ones. A main reason for this deviation is the usage of a digital terrain model (DTM) that does not give the true river bed elevation in the case of water cover, another important reason are the assumptions that were made during the calculation of the observed sediment budget due to the lack of a dense network of measured cross-sections.
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Acknowledgement
The authors wish to thank Prof. Dr. Peter Molnar for giving us the opportunity to work on this very inter- esting topic in the context of our master project as well as for his support by always having an open door for project related questions and scientific advice. Special thanks also go to Maria Magdali for the coordination of the data acquisition. But also for her help and support in many aspects during this project. We would also like to express our thanks to Francesco Caponi for his BASEMENT related tips on the mesh generation and the simulation.
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Table of contents
1 Introduction ______1 1.1 Objectives ______1
2 Study area ______2 2.1 Location and general information ______2 2.2 Data acquisition and origin ______3 2.3 Morphology and topography ______4 2.3.1 Historical erosion and deposition patterns ______4 2.3.2 Comparison of cross-sectional points with DTM ______5 2.4 Hydrology ______7
3 Methodology ______10 3.1 Model ______10 3.2 Pre-processing ______11 3.2.1 Model domain ______11 3.2.2 Grid generation ______12 3.3 Simulation process ______15 3.3.1 Simulation ______15 3.3.2 Simulation input files and parameters ______16 3.3.3 Calibration of hydraulic model ______17 3.3.4 Threshold identification for sediment transport ______19 3.3.5 Non-stationary flood wave morphodynamic simulation ______21 3.4 Calculation of observed sediment budget ______22
4 Results and discussion ______24 4.1 Thresholds for sediment transport ______24 4.2 Simulation results ______27 4.3 Observed vs Simulated data ______29 4.3.1 Reasons for deviation ______30
5 Conclusions ______31 5.1 Morphology and hydrology ______31 5.2 Modelling procedure ______31 5.3 Final remarks ______32
6 Bibliography ______33
Appendix ______a A. Morphology and topography ______a B. Hydrology ______e C. Command file of BASEMENT ______f
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List of Figures
Figure 1: Location of the Maggia valley (from Ruf, 2007). ------2 Figure 2: Overview map of the Maggia valley (Map by Swisstopo). ------2 Figure 3: Study site and common cross-sections for all the measurement years. ------4 Figure 4: Bed level change Δz along the study reach for the period 1978-2015. ------5 Figure 5: Distribution of the 92 cross-sections based on their aggradation and degradation rates for the period 1978-2015. ------5 Figure 6: Study site and bed cross-sectional points of the year 2015. ------6 Figure 7: Distribution of the bed cross-sectional points based on their elevation deviation Δz between the DTM and the measured values (2015).------6 Figure 8: Bed cross-sectional profile of the cross-section with code 25580. ------7 Figure 9: Flood statistics for the federal gauge at Bignasco. ------8 Figure 10: Flood statistics for the cantonal gauge at Lodano. ------8 Figure 11: Flood statistics for the federal gauge at Locarno. ------9 Figure 12: Cell of the computational mesh in BASEplane. ------10 Figure 13: Model domain. ------12 Figure 14: Mesh creation procedure. ------13 Figure 15: Model boundary and break lines for computational mesh creation. ------14 Figure 16: Coarser quality mesh. ------14 Figure 17: Finer quality mesh. ------15 Figure 18: Chart of the performed simulations. ------16 Figure 19: Fitted curve of h-Q data at Lodano station. ------18 Figure 20 Location of Lodano station and reference point for calibration for the two meshes. ------18 Figure 21: Observed vs. simulated water depth for the two meshes. ------19 Figure 22: Hydrograph of the generated flood wave. The points are the hourly streamflow data. ----- 21 Figure 23: Points of a measured cross-section (code 20731) in the simulated reach for the years 2007 and 2015. ------24 Figure 24: Change for different discharges of the erosion per element for the coarser mesh. ------25 Figure 25: Change for different discharges of the erosion per eroded element for the coarser mesh. 25 Figure 26: Change for different discharges of the percentage of eroded area for the coarser mesh. - 25 Figure 27: Change for different discharges of the erosion per element for the finer mesh. ------26 Figure 28: Change for different discharges of the erosion per eroded element for the finer mesh. ---- 26 Figure 29: Change for different discharges of the percentage of eroded area for the finer mesh. ----- 26 Figure 30: Simulated depth in the model domain at the last time step of the simulation (24 h). ------27 Figure 31: Simulated Δz values in the model domain at the last time step of the simulation (167 h). - 28 Figure 32: Simulated Δz values in the model domain at the last time step of the simulation (167 h) with the orthoimages as a background. ------28 Figure 33: Histograms of the a) observed and b) simulated Δz values. ------29 Figure 34: Empirical cumulative distribution function of the simulated and the observed Δz values. - 29
Appendix
Figure A 1: Change of the mean bed elevation ΔZ along the whole study reach (Bignasco-Ponte Brolla) for different measurement periods. ------d
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List of Tables
Table 1: Mean aggradation and degradation of the river bed along the study reach for 5 periods. ------4 Table 2: Mean and standard deviation values for the hourly streamflow data for the three gauges. ---- 7 Table 3: Discharges for different return periods for the three gauges. ------9 Table 4: Values for the beta factor for different discharge ranges for the two downstream gauges. ---- 9 Table 5: Zones of different characteristics in the two meshes. ------13 Table 6: Statistical properties of the two quality meshes. ------15 Table 7: Friction coefficients kStr of the gravel/cobbles for the different samples. ------17 Table 8: Threshold discharges for the two meshes and the two grain sizes for an acceleration of the erosion rate. ------21 Table 9: Observed and simulated sediment budget in the study reach. ------30
Appendix
Table A 1: Mean bed elevations of the whole study reach (Bignasco-Ponte Brolla) for the years 1978, 1988, 1996, 2007 and 2015. ------a Table B 1: R2 values for the different fitted distributions to the Q(R) plots for the three gauges. ------f
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1 Introduction
A numerical modelling tool can be used in various river engineering problems such as: design of hydro power facilities, hazard mapping, studies on river morphology, design of flood protection measures as well as studies on sediment budget. One-dimensional morpodynamic simulations can provide the water level, the mean flow velocity and the bed level change all averaged over flow depth and cross-section. Two dimensional morpodynamic sim- ulations can provide the same results as the one-dimensional simulation but for a specific area and only averaged over flow depth. Sediment transport in rivers is of major importance because it is related with several problems such as the future development of deltas and alluvial fans, the long-term evolution of the bottom of channels, or the aggradations of storage spaces and the consequences of their scavenging. Advanced numerical models have been developed to simulate sediment transport (both bed load and suspended load) in a channel.
1.1 Objectives
The current project aims to set the basis for the quantification of the erosion and deposition rates for a series of flood events in the Maggia valley by using a numerical modelling tool. This tool is the software system BASEMENT, developed by the Laboratory of Hydraulics, Hydrology and Glaciology (VAW: Ver- suchsanstalt für Wasserbau, Hydrologie und Glaziologie in German) at the ETH Zürich. BASEMENT is a simulation tool for hydro- and morphodynamic modelling and one of its fundamental capabilities is the simulation of sediment transport under steady and unsteady conditions in a river reach with arbitrary geometry.
This project was implemented in the frame of the TiRiLab (Ticino Rivers Lab) which is a river research and education laboratory in Environmental Engineering at ETH Zürich focused on rivers in the Canton of Ticino and is part of the project HyMoCARES (HydroMorphological assessment and management at basin scale for the Conservation of Alpine Rivers and related Ecosystem Services).
Besides the application of numerical modelling tool on a two-dimensional morphodynamic simulation of a natural, Alpine river with a braided gravel-bed, some further reasons for our interest in this master project topic were: • The opportunity to use the theoretical knowledge acquired from the courses at the ETH in a real application. • Τhe chance to understand and familiarize ourselves with all major steps in a simulation with BASE- MENT (data acquisition, creation of computational meshes, importance of the mesh for the com- putational time, choice of the parameters for the simulation).
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2 Study area
2.1 Location and general information
The study area is a part of the Maggia valley which is located in the south of Switzerland (see Figure 1 and 2). The study reach is in the main valley and extends from the village of Bignasco to Ponte Brolla. It has a total length of 23.2 km with a mean slope of 0.8%.
Figure 1: Location of the Maggia valley (from Ruf, 2007).
Figure 2: Overview map of the Maggia valley (Map by Swisstopo).
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The Maggia river is environmentally a very important river for Switzerland, it is characterized by a largely undisturbed braided gravel-bed part, with a very permeable river bed and aquifer (Ruf, et al., 2008). The flow regime is influenced by an upstream hydropower system which also controls the sediment budget in the area. The influence of this hydropower regulation on the hydrological regime of the region is mainly limited to low and moderate flow conditions because the hydropower system consists of rela- tively small reservoirs, and therefore large floods are not strongly affected by the regulation (Ruf, et al., 2008) (Molnar, et al., 2008). The streamflow regulation resulted in a 75 % drop in the average annual streamflow, it also led to a strong reduction of the variability in flow between seasons and to a drop in groundwater levels (Molnar, et al., 2008) (Ruf, et al., 2008). Despite the effect of the regulation on the streamflow and as a result also on the sediment budget, the Maggia valley retained its dynamic morphology and it evolves naturally during floods.
2.2 Data acquisition and origin
The data that was used in the current project are:
• Cross-sectional profiles as well as longitudinal profiles with the mean bed level from Bignasco to Ponte Brolla for five different measurement periods (1978-80, 1988-89, 1996, 2007, 2015). They come from the Federal Office for the Environment (FOEN or BAFU in German). • Digital Terrain Model (DTM) along the study river at a 2-meter resolution. It originates from swisstopo and corresponds to the 2016 edition. However, according to the report of the version of 2016, the surface elevation values for the study area are the ones that were measured in 2012. • Orthoimages (SWISSIMAGE 25) along the study river at a 0.25 m resolution by swisstopo. • Streamflow and water level data at three gauges (Bignasco, Locarno and Lodano). The first two are operated by BAFU and the last one is operated by the Canton of Ticino. • Six grain size distributions from sediment samples along the study river.
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2.3 Morphology and topography 2.3.1 Historical erosion and deposition patterns
The morphological evolution of the study reach was analysed for different periods from 1978 to 2015. In particular, the change of the mean river bed elevation for each of the available 92 cross-sections along the study reach was computed. The 92 measured cross-sections are common for the measure- ment years 1978, 1988, 1996, 2007 and 2015 and have a mean in-between distance of 255 m (see Table A1 in the Appendix). In the following map (Figure 3) the study site and the measured common cross-sections for all the measurement years are shown.
Figure 3: Study site and common cross-sections for all the measurement years. The mean bottom elevations of the cross-sections were used to calculate the bed level change Δz for each cross-section for five periods (1978-1988, 1988-1996, 1996-2007, 2007-2015 and 1978-2015). In the following Table 1 the average values of aggradation and degradation in the study reach are pre- sented. In addition, the longitudinal bed elevation change and the distribution of the 92 cross-sections based on their aggradation and degradation rates for the period 1978-2015 are shown in the Figures 4 and 5, respectively. The longitudinal profiles of Δz for the periods 1978-1988, 1988-1996, 1996-2007 and 2007-2015 are presented in the Figure A1 of the Appendix. Table 1: Mean aggradation and degradation of the river bed along the study reach for 5 periods. Time period Mean degrada- Mean aggrada- Mean degrada- Mean aggrada- tion [m] tion [m] tion [m/year] tion [m/year] 1978-1988 0.41 0.31 0.04 0.03
1988-1996 0.42 0.20 0.05 0.03 1996-2007 0.39 0.02 0.04 0.02
2007-2015 0.55 0.05 0.07 0.05
1978-2015 0.96 0.23 0.03 0.01
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Figure 4: Bed level change Δz along the study reach for the period 1978-2015.
Figure 5: Distribution of the 92 cross-sections based on their aggradation and degradation rates for the period 1978-2015.
From Table 1 it can be observed that the mean degradation of the study reach was almost constant at around 40 cm for each of the first three periods (1978-1988, 1988-1996, 1996-2007) and in the period 2007-2015 the mean degradation reached 55 cm. On the other hand, the mean aggradation was much lower with 31, 20, 2 and 5 cm in the periods 1978-1988, 1988-1996, 1996-2007 and 2007-2015, respec- tively. Finally, the degradation rate was 3 times the aggradation rate for the period 1978-2015 (3 cm/year degradation and only 1 cm/year aggradation).
2.3.2 Comparison of cross-sectional points with DTM
The simulations in BASEMENT were performed using the given Digital Terrain Model (DTM) at a 2- meter resolution. In order to validate it we compared it with the measured bed cross-sectional points of the year 2015 along the study reach taken by BAFU (see Figure 6). Totally 105 cross-sections were surveyed in the study reach in 2015 and they have an intermediate distance of 223 m.
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Figure 6: Study site and bed cross-sectional points of the year 2015.
The comparison of the elevations between the bed cross-sectional points and the DTM was performed in the following steps in ArcGIS:
• The DTM was converted to vector (points) from raster format. • With the tool ‘Spatial join’ the bed cross-sectional points were spatially joined with the closest DTM value. • The elevation differences Δz were calculated using the relation: Δz = zcross-section - zDTM • The absolute values of the elevation differences Δz were used to compute the mean absolute devi- ation which is Δz = 0.50 m and the median absolute deviation which is Δz = 0.36 m.
In Figure 7 it can be noticed that most of the elevation differences are negative which means that the DTM values are larger than the observed ones. This happens because points below water have not been surveyed for the production of the DTM.
Figure 7: Distribution of the bed cross-sectional points based on their elevation deviation Δz between the DTM and the measured values (2015).
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In Figure 8 an example of one bed cross-sectional profile is illustrated using the observed and the DTM values. It can be noticed that the DTM values are above the observed ones and they form a flat surface which is probably the water surface elevation. This is why we have this distribution with so many nega- tive differences in Figure 7. This fact should be kept in mind during the evaluation of the simulation results since this DTM was used as the input geometry file.
Figure 8: Bed cross-sectional profile of the cross-section with code 25580.
Other possible reasons for the elevation difference between the DTM and the observed values are the resolution of the DTM (there may be meaningful elevation changes over a 2m x 2m cell) and also the years of measurements for the two cases are not the same (DTM-2012 and observed-2015).
2.4 Hydrology
The hydrological analysis of the region was performed by using hourly streamflow data from the three gauges (Bignasco, Locarno and Lodano). The hourly streamflow data for the federal gauge at Bignasco were available for 35 years and data for the federal gauge at Locarno were available for 42 years. For the gauge at Lodano only 15 years of 5-minute, 10-minute and 15-minute streamflow data were availa- ble. To be able to compare the data between the three gauges, these data were aggregated to hourly streamflow data. Because of the different availability in data for the three gauges, only the data corre- sponding to the 35 years for which data are also available for the gauge at Bignasco were used for the gauge at Locarno. Whereas for the gauges at Bignasco and Lodano all available data were used. Listed in the following Table 2 are the mean hourly streamflow value and the corresponding standard deviation for the three gauges. The mean hourly streamflow values for the Lodano and the Locarno gauge are larger than the one for the Bignasco gauge. This indicates a large inflow from the tributaries to the Maggia river in the reach between the Bignasco and the Lodano gauge. This is also the case for the reach between the Lodano and the Locarno gauge.
Table 2: Mean and standard deviation values for the hourly streamflow data for the three gauges. Station Mean [m3/s] SD [m3/s] Bignasco 4.0 16.4 Lodano 9.8 25.6 Locarno 22.7 73.8
Flood statistics were computed for the gauges at Bignasco and at Locarno for the period 1982-2016, while for the gauge at Lodano they were computed for the period 2002-2016.
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On these data, five distributions that are known to be good for extreme data statistics were fitted. These distributions are: the Generalized extreme value (GEV) distribution, the Gumbel distribution, the Gamma distribution, the Lognormal distribution, and the Weibull distribution. The flood statistics with the corre- sponding fitted distributions for the three gauges are illustrated in the Figures 9, 10 and 11. To determine which of the five distributions is the best in every case, the R2-values were calculated for every one of the five distributions and all three gauges (see Table B1 in the chapter B of the Appendix). The distributions with the highest R2-value for the three gauges are: the Generalized extreme value distribution for the Bignasco gauge, the Gumbel distribution for the Lodano gauge and the Lognormal distribution for the Locarno gauge. These distributions were then used to calculate the discharge for different return periods for the three gauges (see Table 3).
Figure 9: Flood statistics for the federal gauge at Bignasco.
Figure 10: Flood statistics for the cantonal gauge at Lodano. ~ 8 ~
Figure 11: Flood statistics for the federal gauge at Locarno.
Table 3: Discharges for different return periods for the three gauges. 3 3 3 3 3 Station HQ2 [m /s] HQ5 [m /s] HQ10 [m /s] HQ30 [m /s] HQ70 [m /s] Bignasco 298 424 495 585 642 Lodano 558 725 796 873 - Locarno 1179 1879 2398 3256 3964
To evaluate the contribution in discharge of the tributaries to the Maggia river in our study reach, a beta factor was used. The beta factor quantifies the percentage of discharge at the gauges of Lodano and Locarno that originates upstream of the Bignasco gauge. In this way it quantifies the contribution in discharge of the main river and of the tributaries at the two downstream stations. The beta factor was calculated with the following equation:
Q̅̅̅a̅ βa−b [%] = × 100 (1) Q̅̅̅b̅
The calculated values for the beta factor for two different discharge ranges for the two downstream gauges are illustrated in Table 4. From these values it can be understood that for the mean discharge the contribution of the tributaries to the discharge corresponds to 59% at the Lodano station and to 82% at the Locarno station. For a higher discharge (larger than the discharge that corresponds to a flood with a return period of two years) the contribution of the tributaries to the discharge decreases and corre- sponds to 47% at the Lodano station and to 75% at the Locarno station. These values emphasize the large contribution of the tributaries to the discharge in the Maggia valley. They also reveal the fact that for large floods this contribution decreases.
Table 4: Values for the beta factor for different discharge ranges for the two downstream gauges.
for Qmean for Q>HQ2
βBignasco-Lodano [%] 41 53
βBignasco-Locarno [%] 18 25
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3 Methodology
3.1 Model
The software system BASEMENT (basic-simulation-environment) was used to examine the erosion and deposition in the study reach. One of the fundamental capabilities of BASEMENT is the simulation of sediment transport in a river reach with arbitrary geometry under steady as well as unsteady conditions. The two-dimensional numerical tool BASEplane of BASEMENT allows the simulation of river reaches and floodplains (based on a digital terrain model) with respect to sediment transport. The governing equations for 2D modelling with uniform sediment are the Shallow Water Equations (mass and momen- tum conservation) and the Exner equation (sediment mass conservation) which are written as follows:
∂h ∂q ∂qy + x + = 0 (2) ∂t ∂x ∂y
2 ∂q ∂ q ∂h ∂ qxqy ∂z x + ( x) + gh + ( ) = −gh ( B + S ) (3) ∂t ∂x h ∂x ∂y h ∂x fx
2 ∂qy ∂ qy ∂h ∂ qxqy ∂z + ( ) + gh + ( ) = −gh ( B + S ) (4) ∂t ∂y h ∂y ∂x h ∂y fy
∂z ∂q ∂qBy (1 − p) B + Bx + = 0 (5) ∂t ∂x ∂y
Where: h (m) water depth 2 qx,qy (m /s) water discharges per unit width along x and y axes, respectively Sfx, Sfy (-) friction terms along x and y axes, respectively 2 qBx,qBy (m /s) bedload transport rates per unit width along x and y axes, respectively p (-) porosity of sediment in bed deposit g (m/s2) acceleration of gravity zB (m) bed elevation y
x
Figure 12: Cell of the computational mesh in BASEplane.
The first equation (2) expresses the mass conservation over the control volume of one cell of the com- putational mesh (see Figure 12), the next two equations (3 and 4) represent the momentum conservation along the x and y axes and the fourth equation (5) expresses the bed sediment conservation over the control volume. It should be noticed that here in the shallow water equations the turbulent and viscous shear stresses were neglected.
The computation of sediment transport is performed by using a variety of empirical bed load transport formulas. In this project the bed load transport formula of Meyer-Peter and Müller (MPM,1948) was used and it is written as follows:
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3 m qBg = α√(s − 1)gdg (θg − θcr,g) (6) where α is the bed load factor (α=1 was chosen), m the bed load exponent (m=1.5 was chosen), qBg is the specific bed load transport rate of grain class g, θg is the effective dimensionless shear stress for grain class g, θcr,g is the critical dimensionless shear stress for grain class g, dg is the diameter of the grain class g, s = ρs/ρ and g is the gravitational acceleration.
3.2 Pre-processing 3.2.1 Model domain
For the morphodynamic simulations we focused on a smaller river reach which extends from the Riveo settlement until before the Maggia settlement. This river section contains the braided area of the Maggia river with gravel bars and vegetated islands (see Figure 13). In addition, 31 cross sections have been surveyed in this river reach (measurement year 2015) with a mean intermediate distance of 278 m. Furthermore, it has a length of 8.35 km, a mean slope of 0.8% and a mean bed width of 137 m. The maximum bed width reaches 294 m in the braided part while the minimum bed width is 35 m in the upper boundary.
The upper boundary of the model domain lies just after the quarry, it corresponds to the cross section with the code 25178 given by BAFU and in 2015 it had a mean bed elevation of 382.7 m. The lower boundary is located just before the settlement of Maggia, it corresponds to the cross section with the code 15938 given by BAFU and in 2015 it had a mean bed elevation of 314 m.
The north boundary of the model domain is the main road along the river reach, while the south boundary follows the contour line of 400 m near the inflow boundary and reaches the contour line of 340 m near the outflow boundary with a stepwise approach of 10 m. It should be mentioned that those contour lines from 400 to 340 m were smoothed to straight lines in order to produce appropriate computational meshes for the simulations. The real contour lines have many curves and edges, and this would result in the generation of hundreds of small triangles at those parts during the triangulation which would have impacts on the speed, the accuracy and the stability of the simulation.
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Figure 13: Model domain. 3.2.2 Grid generation
For the creation of computational meshes the plugin BASEmesh of the free and open source geographic information system software QGIS was used. BASEmesh supports the automated creation of meshes consisting of triangular elements and these meshes can directly be used for computations with BASE- MENT. The procedure of creating a computational mesh within BASEmesh is described as follows (see Figure 14):
Quality mesh generation The quality mesh contains all the geometric information but has no topographical information. Two basic steps compose the quality mesh generation: • Specification of all geometric information about the computational domain: ➢ Model boundary: extent of the computational domain (see Figure 13). ➢ Break lines: distinct interruptions of the surface slopes which shall be preserved in the compu- tational mesh. First, we drew in our model domain the break lines that define the main channel and separate it from the floodplain (the red lines in Figure 15) according to the slope map, the orthoimages and the given cross sections in the study reach. Then we set two different friction zones (one zone for gravel, cobbles and water and a second zone for vegetation) and we drew break lines that separate those zones based on the orthoimages (the blue lines in Figure 15). We also drew a break line along the bridge where the Lodano station is located in order to calibrate the hydraulic model. ➢ Holes: parts within the mesh which are excluded from modelling (e.g. buildings). We drew break lines that define those holes and they are shown with orange colour in Figure 15.
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• Generation of triangles respecting specific quality criteria using the free program TRIANGLE. Pa- rameters of major importance are: ➢ Maximum area constraints: definition of the mesh density using maximum area constraints for the triangular mesh elements. We produced two different quality meshes (one coarser and one finer) by choosing different maximum cell sizes for the main channel and the floodplain. For the coarser mesh we set a maximum cell size of 200 m2 in the main channel and 500 m2 in the floodplain. On the other hand, for the finer mesh we set a maximum cell size of 150 m2 in the main channel and 400 m2 in the floodplain. ➢ Minimum triangle angle: no elements with angles smaller than the minimum angle specified are generated. In this project a minimum triangle angle of 28 degrees was chosen.
Overall, we determined four different zones (thus four material indices) in the model domain for each mesh which are presented in Table 5 and we produced two quality meshes which are shown in Figures 16 and 17. In Table 6 some statistical parameters of the two generated meshes are presented. The finer mesh contains 30% more cells than the coarser one and its mean cell size in the main channel is 25% smaller than the one in the coarser mesh.
Quality mesh Elevation Model Computational grid without topography Only topography • Breakline definition • As TIN from xyz data • Including buildings • As DEM from raster data • Controlling element size and shape • From cross-sections
Interpolation
Computational mesh
Figure 14: Mesh creation procedure.
Table 5: Zones of different characteristics in the two meshes. Maximum cell area [m2]
Material index Type Coarser mesh Finer mesh
Main channel 1 Gravel/water 200 150 Main channel 2 Vegetation 200 150
Floodplain 3 Gravel/water 500 400
Floodplain 4 Vegetation 500 400
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Figure 15: Model boundary and break lines for computational mesh creation.
Figure 16: Coarser quality mesh.
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Figure 17: Finer quality mesh.
Table 6: Statistical properties of the two quality meshes. Coarser mesh Finer mesh Number of cells 24438 31756
Mean cell size in main channel [m2] 126 95
Mean cell size in floodplain [m2] 283 228
Interpolation of elevation data The topographical information contained in the elevation model is interpolated on the quality mesh, i.e. an elevation value is assigned to each node of the computational grid. In our case the elevation model is the DTM with a 2-meter resolution obtained by swisstopo. The interpolation of the two quality meshes with the DTM generated two computational meshes in .2dm-format, which can be directly used for nu- merical simulations with BASEMENT.
3.3 Simulation process 3.3.1 Simulation
Over the course of the project, many different simulations were performed. First, the calibration of the model was carried out, by performing hydrodynamic simulations. Then a threshold for an acceleration of the erosion rate was identified for two grain sizes, by performing morphodynamic simulations. At the end a morphodynamic simulation was carried out for an unsteady flood wave. In Figure 18 an overview of all the performed simulations is illustrated.
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Figure 18: Chart of the performed simulations.
3.3.2 Simulation input files and parameters
For a hydrodynamic 2D simulation with BASEMENT where usually <
A command file of BASEMENT for a morphodynamic 2D simulation is presented in the chapter C of the Appendix (BASEMENT tutorials).
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3.3.3 Calibration of hydraulic model
It is important to have a calibrated hydraulic model either for further hydraulic modelling or for morpho- logical modelling in a further step (BASEMENT tutorials). The hydraulic model in this project was cali- brated based on flood level marks by comparing the simulated water depths with the observed ones at the Lodano station. The calibration parameter that was chosen is the friction coefficient of the gravel introduced with the Strickler value (kStr). Gravel and cobbles is the dominant land cover type in the main channel and thus the change of its friction coefficient influences the simulation results.
For the estimation of kStr of the gravel/cobbles two equations (Strickler, 1923 and MPM, 1948) were used which are a function of the d50 and d90 (surface grain size such that 50%, 90% of the material is finer), respectively: 21.1 kStr = 6 (7) √d50
26 kStr = 6 (8) √d90 In the study reach there are available six grain size distributions from sediment samples and thus six d90 and d50 values and using the above equations we computed the corresponding kStr values and some statistical parameters (see Table 7).
Table 7: Friction coefficients kStr of the gravel/cobbles for the different samples. 1/3 kStr [m /s]
Sample location d90 [cm] d50 [cm] Eq. (7) Eq. (8) Giumaglio1 17 9 31 35 Giumaglio2 17 10 31 35 Someo1 24 11 30 33 Someo2 21 12 30 34 Riveo1 31 15 29 32 Riveo2 33 15 29 31 Mean 30 33 Min 29 31 Max 31 35
Hydrodynamic simulations with BASEMENT
Three kStr values were used to perform hydrodynamic simulations with BASEMENT. Based on Table 7 1/3 1/3 the values of 25, 35 and 30 m /s were selected. For the vegetation zone a kStr value of 20 m /s was chosen.
The boundary conditions were defined as follows: • Inflow boundary: Stationary hydrographs from 20 to 600 m3/s • Outflow boundary: Zero gradient (the flux entering the boundary element leaves the computational area with the flux over the boundary).
Two input geometry files were used (the coarser and the finer mesh) and the total run time was set to 40000 s (about 11 hours).
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Fitting of water depth and discharge data At the Lodano station there are available water depth and discharge data for the period 2001-2017. But we received the data for the period 2014-2017 in the final stages of our project, after we had already completed this step and therefore the data used here were for the period 2001-2014. Those h-Q data 0.4295 were fitted with a two-term power series model: h = 0.213*Q + 0.6692 with R2=0.98 (see Figure 19).
h = 0.213*Q0.4295 + 0.6692 R2 = 0.98 R2 = 0.98
Figure 19: Fitted curve of h-Q data at Lodano station.
The exact location of the pressure gauge (which measures the water depth) is not known but we know that it is located on the left side of the river (looking at downstream) and under the bridge (see Figure 20). Therefore, we considered the node in the red rectangular as the reference point to compare the measured water depth with the modelled one. This node is common for both meshes and it is on the left side of the river and under the bridge.
Figure 20: Location of Lodano station and reference point for calibration for the two meshes.
Comparison of observed with simulated water depths From the h-Q curve in Figure 19 it can be seen that for zero discharge there is a non-zero water depth and according to the fitted curve that depth is h(Q=0) = 0.6692 = 0.67 m.
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This depth can be explained by the fact that the pressure gauge is in a pool of a depth of 0.67 m and thus there is no flow below this depth. Therefore, the constant term of the equation of the fitted curve (h=0.6692) was removed in order to compare the observed with the simulated water depths.
Finally, the plots with the measured and the modelled water depths for the two meshes were created (see Figure 21). Linear trendlines fitted the plotted points for each of the three used kStr values and the diagonal line y=x was also plotted which represents equal values of measured and modelled water depth. From Figure 21 it can be noticed that from the three trendlines the one with the kStr value of 25 1/3 m /s is the closest to the diagonal y=x for both meshes. Therefore, the friction coefficient kStr for the gravel/cobbles was set to 25 m1/3/s.
We also performed hydrodynamic simulations by varying the kStr value of vegetation but there was no change in the results because the water flow takes place mostly on the gravel/cobbles which are the dominant land cover type in the main channel.
4 4 y=x y=x kstr_gr=25 kstr_gr=25 3.5 kstr_gr=30 3.5 kstr_gr=30 kstr_gr=35 kstr_gr=35 3 Linear (kstr_gr=25) 3 Linear (kstr_gr=25) Linear (kstr_gr=30) Linear (kstr_gr=30) Linear (kstr_gr=35) Linear (kstr_gr=35)
2.5 2.5 [m]
2 [m] 2
sim
sim
h h 1.5 1.5
1 1
0.5 0.5
0 0 0 0.5 1 1.5 2 2.5 3 3.5 4 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
hobs [m] hobs [m]
a) Coarser mesh b) Finer mesh
Figure 21: Observed vs. simulated water depth for the two meshes.
3.3.4 Threshold identification for sediment transport
Generally speaking if the sediment inflow in a river reach is not changing with increasing discharge, then the erosion rate and/or the eroded area should increase with increasing discharge. Our goal was to identify the threshold discharge for which we start having a large increase of the erosion rate and/or the eroded area.
Morphodynamic simulations with BASEMENT Two different grain sizes were used to perform uniform sediment morphodynamic simulations with BASEMENT. The smaller grain size had a size of 28 mm and corresponds to the average d16 value from the six grain size distributions that are available in our study reach. The larger grain size had a size of 120 mm and this corresponds to the average d50 value from the six grain size distributions available in our study reach. The following hydraulic boundary conditions were used: • Inflow boundary: Stationary hydrographs from 20 to 400 m3/s for the smaller grain size (d=28mm) and from 100 to 400 m3/s for the larger grain size (d=120mm).
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• Outflow boundary: h-Q relation with a slope of 8‰ which corresponds to the average slope in our study reach (the defined average slope at the outflow, is used to calculate the outflow discharge assuming normal flow).
The following bed load boundary conditions were used: • Inflow boundary: IOUp (the same amount of sediment leaving the first computational cell in flow direction enters the cell from the upstream boundary). • Outflow boundary: IODown (all the sediments entering the last computational cell leave the cell over the downstream boundary). The bed load formula that was used is the Meyer-Peter and Mueller’s formula with the bedload factor equal to 1. Two input geometry files were used (the coarser and the finer mesh) and the total run time was set as a compromise to 86400 s (24 hours). Initially the first simulations (with stationary hydrographs from 100 to 400 m3/s as an inflow boundary condition) were carried out with a total run time of 86400 s (24 hours). In the output files of these simulations it was observed that the morpodynamic equilibrium was not reached for any of the simulations. Therefore, further simulations with the same inflow boundary but with a run time of 432000 s (5 days) were performed. However, even for this longer run time the mor- podynamic equilibrium was not reached. For this reason, a compromise was made and all simulations in this section were performed with a run time of 24 hours, to ensure a reasonable computational time.
Evaluation of the output files of BASEMENT From the output files created with BASEMENT, the one used in this case was the element centered Δz dat-file, which contains the Δz values for all the elements of the computational mesh for every time step of the simulation. To evaluate the erosion in the study reach only the Δz values for the last time step were used. Three different approaches were used to evaluate the erosion for different discharges for the two different grain sizes and the two meshes:
• In the first one the total erosion from all eroded* elements was computed and then divided by the total number of elements of the computational mesh. The result is the mean erosion per element. Figures 24 and 27 in chapter 4.1 show the results for the first approach. • In the second one the total erosion from all eroded* elements was computed and then divided by the number of eroded elements in the computational mesh. The result is the mean erosion per eroded element. Figures 25 and 28 in chapter 4.1 show the results for the second approach. • In the third one the total area of the eroded* elements was computed and then divided by the total area of the computational mesh. The result is the percent of the total area of the computational mesh that is being eroded. Figures 26 and 29 in chapter 4.1 show the results for the third approach.
* Eroded elements were the elements that had a negative Δz value.
The generated figures for all three approaches were analysed to define a threshold discharge for an acceleration of the erosion rate. For the definition the results of all previously introduced approaches were used. The main goal was to identify a discharge rate at which the erosion rate and/or the eroded area start accelerating rapidly, this state corresponds to a steep slope in the generated figures (see Figure 24 to 29 in chapter 4.1). By evaluating the generated figures, a threshold discharge was defined for every mesh and grain size. These values are illustrated in the following table (see Table 8).
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Table 8: Threshold discharges for the two meshes and the two grain sizes for an acceleration of the erosion rate. Threshold discharge [m3/s] Coarser mesh Finer mesh d=28 mm 80 80 Grain size d=120 mm 240 220
Due to the relatively short duration of the master project and therefore the lack of time to perform a large number of simulations, only one grain size was used in the following steps (d=120mm) and for this grain size the threshold discharge for the finer mesh was used (220 m3/s).
3.3.5 Non-stationary flood wave morphodynamic simulation
Having the threshold discharge for an acceleration of the erosion rate, the next step was to use this value to identify which floods are relevant for the change in the river bed elevation. Then perform a morphodynamic simulation with BASEMENT by using these floods as an inflow hydrograph and finally, compare the results of the simulation with the measured changes of the bottom elevations (BAFU). The only available gauge in our model domain was the gauge at Lodano. For this gauge only 15 years of hourly streamflow data were available, for the period 2002-2017. During this period only two measurements of the bottom elevations of the cross-sections were available by the Federal Office for the Environment (BAFU). The first measurements were from March of 2007 and the second from March of 2015. The time series of hourly streamflow data for the period between 23 March 2007 and 27 March 2015 (These dates correspond to the last day of measurements for the measurement of 2007 and the first day of measurements for the measurement of 2015) for the Lodano gauge was analysed to detect all the flood events with a larger discharge than the identified threshold discharge of 220 m3/s. Twenty-three flood events that meet these criteria were detected for this period, having a duration from one to forty-five hours. From these flood events, all events with a duration of at least two hours were combined into one large flood event (a flood wave). The hydrograph of this flood wave which has a total duration of 167 hours is shown in Figure 22.
900
800
700
600 /s)
3 500
Q (m Q 400
300
200
100
0 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 t (h)
Figure 22: Hydrograph of the generated flood wave. The points are the hourly streamflow data.
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Morphodynamic non-stationary simulation with BASEMENT Due to the lack of time only one grain size was used to perform this uniform sediment morphodynamic simulation. The grain size that was used had a size of 120 mm.
The following hydraulic boundary conditions were used: • Inflow boundary: Non-stationary hydrograph which corresponds to the generated flood wave. • Outflow boundary: h-Q relation with a slope of 8‰.
The following bed load boundary conditions were used: • Inflow boundary: IOUp (the same amount of sediment leaving the first computational cell in flow direction enters the cell from the upstream boundary). • Outflow boundary: IODown (all the sediments entering the last computational cell leave the cell over the downstream boundary). The bed load formula that was used is the Meyer-Peter and Mueller’s formula with the bedload factor equal to 1. Two input geometry files were used (the coarser and the finer mesh), but the simulation with the finer mesh for the flood wave generated errors during the simulation and therefore was not evaluated. The total run time was set to 601200 s (167 hours) which corresponds to the duration of the generated flood wave input file.
Evaluation of the output files of BASEMENT From the output files created from BASEMENT, the ones used in this case were the element centered Δz dat-file and the node centered sol-files.
To evaluate the change in the topography due to bedload transport in the study reach only the Δz values (dat-file) for the last time step were used. The Δz values for the last time step, represent the change in topography (compared to the initial topography) generated by the entire flood wave. The Δz values for all the elements were used to quantify the total volume of erosion* and deposition* in the study reach. For every element the Δz values were multiplied with the area of the element to calcu- late the eroded or deposited volume for every element. Afterwards the total volume of erosion and dep- osition was calculated by aggregating all the eroded and all the deposited volume. Very small * erosion or ** deposition values (smaller than 5 cm) are most of the time just creations of the program due to the large area of every element or due to numerical artifacts produced during the simulation. For a better visualization of the erosion and deposition in the study reach and to get rid of numerical artifacts, all erosion and deposition values smaller or equal to 5 cm were not considered for the production of the histogram illustrating the results of the simulation (Figure 33 b). * Elements where we had erosion were the elements that had a negative Δz value. ** Elements where we had deposition were the elements that had a positive Δz value. The node centred sol-file for the Δz values was used to visualise and evaluate the change in the topog- raphy with the Crayfish plugin of QGIS.
3.4 Calculation of observed sediment budget
For the evaluation of the simulation results we calculated the observed sediment budget in the study reach for the simulation period 2007-2015. In the model domain there are 31 cross-sections that were surveyed in the years 2007 and 2015. In particular, cross-sectional points with their coordinates (x,y,z) for the two above mentioned measurement years are given. Based on these cross-sectional points the sediment budget for the simulation period 2007-2015 was computed and the calculation procedure is the following: • The measured bed cross-sectional points for the years 2007 and 2015 were spatially joined using the tool 'Spatial Join’ of ArcGIS and the match option ‘CLOSEST’ (see Figure 23).
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• The bed level change Δz between the years 2007 and 2015 was calculated for each cross-sectional point of the 31 available cross-sections. • A width w was calculated for each cross-sectional point taking the sum of the half distances to the two neighbouring points. • The erosion and deposition volumes per unit length were computed for each cross-section using the following relations: 푛
푒 = ∑((Δz < 0) ∙ 푤푒) 푖=1 푚
푑 = ∑((Δz > 0) ∙ 푤푑) 푖=1 where: e (m3/m) erosion volume per unit length d (m3/m) deposition volume per unit length Δz (m) bed level change of a cross-sectional point we (m) width of each eroded cross-sectional point wd (m) width of each aggraded cross-sectional point n (-) number of eroded cross-sectional points in a cross-section m (-) number of aggraded cross-sectional points in a cross-section
The resulted values of erosion and deposition volumes per unit length for each cross-section are given in Table A2 in the Appendix. • The total volumes of eroded and deposited sediment on the whole domain were calculated using the following relation: 푛 푙 + 푙 푉 = ∑ 푒 ∙ 푖−1,푖 푖,푖+1 푒 푖 2 푖=1 푛 푙 + 푙 푉 = ∑ 푑 ∙ 푖−1,푖 푖,푖+1 푑 푖 2 푖=1 where: 3 Ve (m ) volume of eroded sediment 3 Vd (m ) volume of deposited sediment 3/ ei (m m) erosion volume per unit length of a cross section i 3 di (m /m) deposition volume per unit length of a cross section i n (-) number of cross-sections (n=31) li-1,i,li,i+1 (m) distances of a cross section i from the previous one i-1 and the next one i+1
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Figure 23: Points of a measured cross-section (code 20731) in the simulated reach for the years 2007 and 2015.
4 Results and discussion
4.1 Thresholds for sediment transport
The figures used to identify the threshold discharge for an acceleration of the erosion rate, with the three different approaches described in chapter 3.3.3 are shown in this section (see Figure 24 to 29). Figures 24 and 27 illustrate the mean erosion per element for different discharges for the coarser and the finer mesh respectively. Figures 25 and 28 show the mean erosion per eroded element for different discharges for the coarser and the finer mesh respectively. Figures 26 and 29 present the percentage of the total area of the computational mesh that is being eroded for different discharges for the coarser and the finer mesh respectively. Similar trends can be observed in the corresponding figures for the two different meshes. Clearly, there is an increase of the erosion rate and of the eroded area with increasing discharge. There is only one major exception, this is the mean erosion per eroded element for the larger grain size for both meshes (see Figures 25a and 28a). It can be observed in Figure 25a that the erosion rate increases for a dis- charge from 100 to 140 m3/s and then decreases for a discharge from 140 to 180 m3/s and finally in- creases again. This drop in the mean erosion per eroded element from the discharge of 140 m3/s to the discharge of 160 m3/s is the effect of the behaviour of the flow in the main channel. As can be seen in Figure 30, for a discharge of 140 m3/s we have some pools and ponds that have appeared in the north- west region of the model domain, these are not connected to the main channel and therefore have no contribution to the erosion. Because of the water in these ponds, there is less water in the main channel and the flow is concentrated in one channel, as a consequence the erosion per eroded cell is high because we have a small area that is being eroded. For a discharge of 160 m3/s these pools and ponds disappear, there are two big channels in the upstream area of our model domain and the flow shifts to another channel in this area which has a larger width. The result is that there is a larger area being eroded, but the erosion per eroded cell is for this case smaller than for a discharge of 140 m3/s. As one might expect, the erosion rate and the erosion area are larger for the smaller grain size.
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Figures 25 and 28 show that, the mean erosion per eroded element is much larger for the smaller grain size than for the larger grain size. For a discharge of 80 m3/s it reaches a value that is not even reached for the larger grain size at a discharge of 400 m3/s. The same also holds true for the mean erosion per element (see Figures 24 and 27), but for a discharge of 100 m3/s for the smaller grain size. It can be observed in figures 26 and 29, that the eroded area for the smaller grain size is much larger than the one for the larger grain size. For a discharge of 120 m3/s it reaches 9% of the total area, this is a percentage that is not even reached for the larger grain size at a discharge of 400 m3/s.
a) Larger grain size (d=120mm) b) Smaller grain size (d=28mm) Figure 24: Change for different discharges of the erosion per element for the coarser mesh.
a) Larger grain size (d=120mm) b) Smaller grain size (d=28mm) Figure 25: Change for different discharges of the erosion per eroded element for the coarser mesh.
a) Larger grain size (d=120mm) b) Smaller grain size (d=28mm) Figure 26: Change for different discharges of the percentage of eroded area for the coarser mesh.
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a) Larger grain size (d=120mm) b) Smaller grain size (d=28mm)
Figure 27: Change for different discharges of the erosion per element for the finer mesh.
a) Larger grain size (d=120mm) b) Smaller grain size (d=28mm) Figure 28: Change for different discharges of the erosion per eroded element for the finer mesh.
a) Larger grain size (d=120mm) b) Smaller grain size (d=28mm) Figure 29: Change for different discharges of the percentage of eroded area for the finer mesh.
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a) Discharge of 140 m3/s b) Discharge of 160 m3/s Figure 30: Simulated depth in the model domain at the last time step of the simulation (24 h).
4.2 Simulation results
In Figures 31 and 32 the bed level change Δz in the model domain at the last time step of the simulation (167 h) is illustrated. In Figure 32 the background with the corresponding orthoimages is shown. It can be noticed that there is high deposition and erosion (about 3 meters) close to the inflow boundary, while close to the outflow boundary erosion is dominant with a maximum bed level degradation of 5 meters. These extreme Δz values close to the boundaries are probably due to the specified boundary conditions which have always an impact on the simulation results near the boundaries. Furthermore, it can be observed that there are areas along the river reach that have been eroded followed by areas where deposition occurs. There are also some parallel zones of erosion and deposition in the river reach. It should be mentioned that in the braided part the aggradation and degradation of the river bed take place in the major channel. Another remark for the simulation results is that there is a break in the sediment transport along the river reach which is illustrated in the red rectangle in Figures 31,32. Specifically, there are some areas with deposition and erosion in this rectangle, but they are disconnected from each other and this indicates that there is no sediment transport continuity along the study reach.
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Figure 31: Simulated Δz values in the model domain at the last time step of the simulation (167 h).
Figure 32: Simulated Δz values in the model domain at the last time step of the simulation (167 h) with the or- thoimages as a background. ~ 28 ~
4.3 Observed vs Simulated data
The Figure 33a with the distribution of the cross-sectional points with respect to their Δz values shows that the majority of the cross-sectional points (around 80%) has a Δz value from -1 m to 1 m and in half of them (about 40%) there was deposition and in the other half there was erosion. There are also some extreme values of erosion at the interval (-3.5, -3) and deposition at the interval (2, 2.5) of the histogram in Figure 33a. From the histogram in Figure 33b it can be noticed that the distribution of the mesh elements with respect to their Δz values (with a threshold of 5 cm) is approximately symmetrical. In addition, most of the elements (above 70%) have Δz values in the interval (-0.5, 0.5) and almost 85% of the elements has a Δz value from -1 m to 1 m (similar to the observed cross-sectional points in Figure 33a).
a) Observed b) Simulated
Figure 33: Histograms of the a) observed and b) simulated Δz values.
The empirical cumulative distributions of the simulated and observed Δz values illustrated in Figure 34 show that the range of values is similar for the observed and the simulated case. A difference that can be observed in the empirical cumulative distributions is that most of the Δz values from the simulation are close to 0, whereas the observed Δz values have a smaller percentage close to 0. It has to be considered that the observed values are far less than the simulated ones.
Figure 34: Empirical cumulative distribution function of the simulated and the observed Δz values.
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The observed and the simulated calculated volumes of erosion and the corresponding portion being deposited and transported away are listed in Table 9. It can be seen that the observed volumes of eroded and deposited sediment are about 3 and 4 times the simulated ones, respectively. In addition, the observed volumes show that 32% of the eroded volume leaves the study reach as a sediment out- flow from the downstream boundary, while according to the simulation results this percentage is only 5%. Table 9: Observed and simulated sediment budget in the study reach. Observed Simulated Volume of sediment eroded [m3] 860384 194137 Volume of sediment deposited [m3] 582696 184430 Deposited [%] 68 95 Transported away [%] 32 5
4.3.1 Reasons for deviation
As previously mentioned we have a deviation in the eroded volume and the percentage of the eroded volume being deposited in the study reach between the simulated and the observed results. This devi- ation could have many possible reasons.
The most important reason is the usage of a DTM that gives the water surface elevation in the areas covered with water during the acquisition of the DTM. The DTM was used as the elevation mesh that was interpolated with the quality mesh to generate the computational mesh for the simulations. The usage of this DTM in the mesh generation, results in a quite different initial topography between the real river (where the observed data was measured) and the simulation. Since, no other source for a DTM of the area with such a good resolution is available, a possible solution would be to use the cross-sectional measurements and interpolate the measurements between the cross sections, to create an elevation mesh that could be used in the grid generation.
A further reason is the assumptions and simplification that were made during the calculation of the corresponding volumes of erosion and deposition in the study reach. Specifically, for the computation of the observed sediment budget the erosion and deposition volumes per unit length of each cross- section were assumed constant on the half distances of the cross-section from the next and the previous ones. A possible solution for the future would in this case be to perform many more cross-sectional measure- ments in the area, in this way the effect of the assumptions and simplification made for the computation of the observed Δz values and for the calculation of the volumes of erosion and deposition would be much smaller. This solution can only be applied in the future measurements and has no use for the measurements taken in the past, and it also has the disadvantages of being too slow and too costly.
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5 Conclusions
5.1 Morphology and hydrology
There is a general tendency of the Maggia river bed towards a decrease in exposed sediment according to cross-sectional data of the years 1978, 1988, 1996, 2007 and 2015. There is a large contribution of the tributaries to the discharge in the Maggia valley. At the Lodano gauge 59% of the mean discharge comes from the tributaries in the reach between the Bignasco and the Lodano gauge. The tributary contribution to the discharge decreases for larger floods (for Q>HQ2) and for the Lodano gauge it cor- responds to 47%.
5.2 Modelling procedure
The software system BASEMENT enables the simulation of sediment transport in naturally shaped wa- tercourses. The Maggia riverine corridor is an example of natural river with braided morphology which was studied using BASEMENT. The pre-processing activities which include the acquisition of all needed data (topography, boundary conditions) and the setup of this data were a very important and time-con- suming part of the modelling procedure. It should be noticed that the construction of the computational grid influences strongly the accuracy of the results and the computational time needed for the simulation. In the mesh creation process it is sometimes required that the input data are manually adapted, and compromises are made between mesh quality and accuracy in certain regions. During the grid genera- tion in the current project the model boundary and the break lines were drawn in such way that there are smooth transitions between elements with varied sizes and to avoid the creation of distorted ele- ments with small angles or very small sizes. Specifically, the break lines that separate the two defined zones (gravel/water and vegetation) do not follow their real borderline because of the many edges and vertices and this fact may have an impact in the simulation results since the bed roughness coefficient is different in the two zones. Two quality meshes were produced using different maximum area con- straints with the finer mesh having 30% more cells and a smaller mean cell size in the main channel by 25% than the coarser mesh. In addition, the morphodynamic simulation runtime in the finer mesh for a constant inflow discharge of 400 m3/s was 3 times the respective one in the coarser mesh. Further improvements of the computational meshes concerning the stability, the computation time and the ac- curacy of the results could be achieved by manually editing the vertices and the edges of the generated mesh elements. To create the inflow hydrograph for the main simulation in our project, only discharges above 220 m3/s were used from the time series of hourly discharges from the Lodano gauge, this was done to reduce the duration of the simulation and only take into account the larger discharges. However as can be seen in Figures 24 to 29, we also have erosion for lower discharges. To have a better result the inflow hydro- graph should be created with discharges above the threshold discharge for which we start having ero- sion. This would lead to a much longer simulation and it would require a considerably higher computa- tional power to be able to stay under one day of simulation time.
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5.3 Final remarks
The comparison of the simulated with the observed Δz values illustrates that the distribution of the sim- ulated Δz values is similar to the one of the observed Δz values in the surveyed cross-sections. In addition, the simulated values have a similar range of values as the observed ones which highlights the fact that the model reproduces successfully the order of magnitude of erosion and deposition in the study domain. The comparison of the simulated with the observed sediment budget results in significant differences, however, one has to be careful with the interpretation of this result in view of the fact that, there were important assumptions and simplifications made during the simulation setup and the computation of the observed sediment budget. The digital terrain model (DTM) that was used to generate the computational meshes does not give the true river bed elevation in the case of water cover and this fact has also a significant impact on the simulation results. A possible solution would be to use the cross-sectional measurements and interpolate the measurements between the cross sections, to create an initial to- pography that would be closer to the real one.
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6 Bibliography
Bezzola, G. R. (2017). Vorlesungsmanuskript Flussbau. 2017.
Böhringer, D., Wanner P. (2010). Master Project Thesis: Application of a 2D-hydrodynamic flow model to a braided Alpine river reach. 2010.
Meyer-Peter, E., Muller, R. (1948). Formulas for bed-load transport. 1948.
Molnar, P., Ruf, W., Favre, V., Perona, P., Burlando, P., & Randin, C. (2008). Floodplain forest dy- namics in a hydrologically altered mountain river. 2008.
Ruf, W. (2007). Numerical Modelling of Distributed River - Aquifer Coupling in an Alpine Floodplain. 2007.
Ruf, W., Foglia, L., Perona, P., Molnar, P., Faeh, R., & Burlando, P. (2008). Modelling the interac- tion between groundwater and river flow in an active alpine floodplain ecosystem. 2008.
Siviglia A. (2017). Lectures slides, River Morphodynamic Modelling (Spring semester 2017).
Strickler, A. (1923). (Roesgan, T., and Brownie, W. R., translation T-10 (1981)). Contributions to the Question of a Velocity Formula and Roughness Data for Streams, Channels and Closed Pipelines. 1923.
VAW (Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie): Basement: Basic Simulation Environment, Homepage:
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Appendix
A. Morphology and topography
Table A 1: Mean bed elevations of the whole study reach (Bignasco-Ponte Brolla) for the years 1978, 1988, 1996, 2007 and 2015. Mean bottom elevation [m a.s.l.]
Cross-section Distance from lake Mag- 1978 1988 1996 2007 2015 code giore [m]
6444 6065 241.7 241.1 240.6 240.0 240.1
6662 6281 247.1 247.2 247.3 247.2 246.5 6919 6523 250.2 250.6 250.2 249.8 249.9
7203 6757 252.4 252.3 252.2 252.0 251.7
7387 6930 253.9 253.9 253.8 253.8 253.8 7676 7170 256.6 255.6 255.3 255.2 255.4
7826 7309 256.2 257.1 256.4 256.2 256.4
8021 7505 258.4 258.6 258.6 258.3 257.8 8213 7690 260.7 260.8 261.8 261.1 259.7
8436 7911 264.1 264.1 264.2 263.6 263.0
8696 8138 267.5 268.3 267.8 267.8 267.9 8949 8420 274.0 273.6 274.1 273.5 271.2
9228 8770 274.8 274.3 273.2 273.1 273.0
9493 8890 276.5 275.6 272.2 272.3 274.1 9673 9087 276.4 276.1 275.3 274.3 274.3
9901 9258 277.6 276.7 275.5 274.5 276.9
9988 9347 277.4 277.2 276.1 276.0 277.2 10181 9482 280.3 278.3 276.7 278.2 279.2
10291 9614 281.6 281.6 281.3 280.8 279.0
10375 9714 282.7 282.5 281.7 281.4 279.7
10534 9838 282.7 281.9 281.4 281.3 280.5
10822 10098 285.1 284.7 284.3 284.0 283.9
11047 10306 286.1 285.6 285.5 284.8 284.6 11228 10483 286.5 286.2 285.8 285.4 285.1
11337 10595 287.0 286.6 286.5 286.3 286.1
11549 10810 287.5 287.8 287.9 287.1 287.2 11777 11021 290.7 290.8 290.7 290.3 289.1
a 11995 11231 292.5 291.5 291.6 291.2 291.0 12211 11433 292.5 292.2 292.1 291.9 291.9
12409 11639 292.6 293.4 293.5 293.4 293.1
12581 11810 294.7 294.6 294.5 294.4 294.3 12784 12015 295.7 295.2 295.2 295.2 294.9
12968 12200 296.3 295.9 295.9 295.9 295.8
13170 12400 296.6 296.1 296.4 296.6 296.1 13366 12597 298.2 297.7 298.0 298.4 298.1
13573 12800 300.4 301.2 300.7 300.9 300.9
13876 13090 302.5 302.7 302.8 302.5 302.3 14147 13358 303.7 303.9 303.9 303.5 302.9
14296 13506 304.1 303.6 303.7 303.6 303.4
14497 13702 306.2 306.1 306.1 306.1 306.0 14801 14000 308.2 308.2 308.4 308.0 308.1
15003 14200 309.1 309.3 309.4 309.1 309.1
15288 14488 310.9 311.1 311.1 310.7 311.0 15489 14687 312.1 312.3 312.2 311.8 311.7
15744 14937 312.7 313.1 312.9 312.5 312.3
15938 15129 314.0 314.6 314.3 313.9 314.0
16230 15425 318.4 318.9 319.0 318.8 318.5
16565 15721 321.9 321.8 321.5 321.3 321.3
17060 16100 325.2 324.9 325.0 324.7 323.5 17631 16619 327.5 327.3 326.6 325.9 325.2
17983 16969 330.1 330.0 329.6 329.6 328.6
18140 17127 329.8 329.8 329.3 329.0 329.0 18371 17345 330.9 330.7 330.9 330.8 330.8
18601 17562 332.1 332.2 332.7 331.9 331.8
18770 17720 333.3 333.6 333.6 333.3 333.3
19097 18000 336.2 336.6 336.5 336.5 336.3
19379 18283 336.9 337.7 337.4 337.0 336.6
19733 18588 340.3 340.5 340.5 340.8 340.4 20314 19072 344.3 344.3 344.4 343.8 344.2
20731 19477 347.5 347.5 347.3 347.4 347.4
21201 19840 350.3 350.6 351.0 350.6 349.7 21739 20379 355.0 354.9 354.8 353.9 354.1
b 21891 20529 356.1 355.9 355.9 355.3 355.9 22340 20907 359.5 359.6 359.5 359.6 358.7
22830 21343 364.0 364.3 363.9 363.0 362.5
23378 21777 368.4 368.3 368.7 368.2 367.1 23917 22303 373.6 373.3 373.1 373.0 372.6
24554 22894 378.7 379.2 378.9 378.2 377.0
25178 23476 383.0 383.9 383.2 382.7 382.7 25580 23870 385.3 385.9 385.1 384.3 383.3
26215 24429 392.9 393.1 392.0 391.4 392.5
26450 24683 396.3 396.1 395.5 394.8 395.0 26970 25146 401.1 401.3 400.6 400.1 399.3
27428 25564 402.0 402.3 403.1 402.5 402.5
27654 25780 405.8 406.1 405.8 405.7 403.3 27879 25997 407.3 407.5 407.4 406.7 406.5
28097 26210 408.1 408.4 408.3 407.6 407.7
28334 26433 409.9 409.7 409.7 408.8 409.2 28554 26635 412.8 412.6 412.7 412.6 412.8
28818 26899 414.3 414.5 414.6 414.1 414.1
29015 27097 414.9 414.7 414.8 414.7 414.7
29217 27285 415.5 415.9 415.3 415.5 415.2
29491 27545 418.2 418.1 418.1 417.9 418.0
29707 27760 421.8 421.2 420.9 420.9 420.6 29852 27909 422.6 422.0 421.9 421.7 421.5
30086 28140 424.1 423.5 423.4 423.1 422.6
30284 28338 427.4 427.0 426.9 427.0 425.8 30503 28547 428.0 427.8 427.6 427.6 427.5
30680 28731 430.0 429.9 429.8 429.7 429.7
30835 28886 430.9 430.9 431.0 430.9 430.9
31089 29140 433.2 432.9 432.7 432.2 432.4
31186 29236 434.8 434.6 434.8 434.4 433.0
c a)1978-1988 b)1988-1996
c)1996-2007 d)2007-2015
Figure A 1: Change of the mean bed elevation Δz along the whole study reach (Bignasco-Ponte Brolla) for differ- ent measurement periods.
Table A 2: Volume of deposited and eroded sediment per unit length in the study reach for the simulation period 2007-2015. Volume per unit length at each cross-section (m3/m)
Cross-section code Deposition Erosion
15938 7 1
16230 59 37
16565 59 42
17060 45 98
17340 107 30
17631 4 31
17817 15 45
17983 36 47
18140 20 24
d 18371 27 37
18601 17 18
18770 43 29
19097 49 149
19379 33 47
19733 79 194
20314 124 170
20731 107 155
21201 119 116
21460 97 87
21739 155 138
21891 206 154
22340 37 11
22570 34 58
22830 49 289
23378 62 134
23664 115 180
23917 148 229
24249 18 120
24554 22 102
24880 63 29
25178 74 85
B. Hydrology
Table B 1: R2 values for the different fitted distributions to the Q(R) plots for the three gauges. R2 value Bignasco Lodano Locarno Generalized extreme value distribution 0.954 0.945 0.771 Gumbel distribution 0.934 0.946 0.708 Gamma distribution 0.911 0.836 0.743 Lognormal distribution 0.838 0.794 0.843 Weibull distribution 0.952 0.884 0.717
e C. Command file of BASEMENT
Command file of BASEMENT The command file is structured in the following way: PROJECT {…} DOMAIN { multiregion = unnamed_multiregion PHYSICAL_PROPERTIES {…} BASEPLANE_2D { region_name = morphodynamic_150_400_200 GEOMETRY {…} HYDRAULICS {…} TIMESTEP {…} MORPHOLOGY {…} OUTPUT {…} } }
Project: The PROJECT block gives the ability to define the project name, the author and the date. PROJECT { title = Master_Project author = Argyrakis_Skourtis }
Domain: The DOMAIN block includes all blocks necessary for a simulation. DOMAIN { multiregion = unnamed_multiregion PHYSICAL_PROPERTIES { gravity = 9.81 // [m/s2] viscosity = 1e-006 // [m2/s] rho_fluid = 1000 // [kg/m3] } PARALLEL { number_threads = 0 // if it set to zero it is automatically set to the number // of available cores on the system. } BASEPLANE_2D {…} }
Baseplane_2D: The BASEPLAIN_2D block is included in the DOMAIN-block and it contains all infor- mation that are relevant for the two-dimensional simulation and it has the following structure: BASEPLANE_2D {
f region_name = morphodynamic_150_400_200 GEOMETRY {…} HYDRAULICS {…} TIMESTEP {…} MORPHOLOGY {…} OUTPUT {…} }
Geometry: The GEOMETRY block defines the computational mesh file and all the necessary strings of nodes. Strings are additionally used for the inflow and outflow boundaries and can also be used for discharge control. GEOMETRY { file = 150_400.2dm type = 2dm STRINGDEF { name = Inflow node_ids = (367 2334 1428 1429 267 1427 222 223) upstream_direction = left } STRINGDEF { name = Outflow node_ids = (431 12732 498) upstream_direction = left } STRINGDEF { name = bridge node_ids = (509 793 792 824 791 795 796 508) upstream_direction = left } }
Hydraulics: The HYDRAULIC block defines all the necessary information for the hydraulic part of the simulation: the hydraulic boundary conditions (BOUNDARY block), the Initial conditions (INITIAL block), the friction term (FRICTION block) and the computational parameters (PARAMETER block). HYDRAULICS { BOUNDARY { name = water_inflow type = hydrograph // Inflow boundary condition string_name = Inflow file = stationary_hydrograph.txt // Inflow hydrograph slope = 8 // [per mill] } BOUNDARY { name = water_outflow type = hqrelation // Outflow boundary condition string_name = Outfllow slope = 8 // [per mill]
g } INITIAL { // Defines flow variables at the beginning of the simulation. type = continue file = hydrodynamic_150_400_200_restart.cgns // Restart file restart_solution_time = -1.0 // Restart time } FRICTION { // Defines everything related to the friction term in the shallow // water equations. type = strickler default_friction = 30 input_type = index_table index = (1 2 3 4) friction = (25 20 25 20) // Strickler values for the // corresponding indices wall_friction = off } PARAMETER { // Defines the control parameters for the numerical simulation // of the hydraulic part simulation_scheme = exp riemann_solver = exact minimum_water_depth = 0.05 } }
Timestep: The TIMESTEP block defines the timestep of the simulation. TIMESTEP { start_time = 0 total_run_time = 86400 CFL = 1.0 minimum_time_step = 0.001 }
Morphology: The MORPHOLOGY block defines all the necessary information for the morphological part of the simulation: the morphological parameters (PARAMETER block), the Initial conditions (INI- TIAL block), the bed material (BEDMATERIAL block) and the bedload (BEDLOAD block). MORPHOLOGY { PARAMETER { // Defines important parameters for morphological simulation porosity = 37 // [%] density = 2650 // [kg/m3] control_volume_typ = constant control_volume_thickness = 0.1 // [m] } INITIAL { // Defines the initial bed elevation type = initial_mesh } BEDMATERIAL { GRAIN_CLASS { // The single-grain simulation is performed with only // one grain class of a given diameter diameters = (120) } MIXTURE { name = single_grain
h volume_fraction = (100) } SOIL_DEF { // Soil layers and the according sediment mixture are defined name = soil_gravel LAYER { mixture = single_grain bottom_elevation = -10 // fixed bed 10 m below the // surface } } SOIL_DEF { // Soil layers and the according sediment mixture are defined name = soil_vegetation LAYER { Mixture = single_grain bottom_elevation = -10 // fixed bed 10 m below the // surface
} } SOIL_ASSIGNMENT { // Assignment of the defined soil types Type = index_table Index = (1 2 3 4) Soil = (soil_gravel soil_vegetation soil_gravel soil_vegetation ) } } BEDLOAD { // Needed data for bedload transport and boundary conditions // are defined FORMULA { bedload_formula = mpm // The bed load transport is // computed with the // Meyer-Peter and Mueller’s // formula bedload_factor = 1 } BOUNDARY { // Bed load inflow boundary condition type = IOUp string_name = Inflow mixture = single_grain name = Sed_up } BOUNDARY { // Bed load outflow boundary condition type = IODown string_name = Outfllow name = Sed_down } DIRECTION { // The lateral transport caused by a lateral_bed_slope with // respect to the main flow direction is taken into account lateral_transport_type = lateral_bed_slope lateral_transport_factor = 2.05 lateral_index = (1 2 3 4) } PARAMETER { // The control parameters for the bed load simulation
i // are defined limit_bedload_wetted = on use_cell_averaged_bedload_flux = off } } }
Output: In the OUTPUT block the output files of the simulation can be defined. OUTPUT { console_time_step = 1800 SPECIAL_OUTPUT { // Node centered sol-files for the selected variables format = sms // Output format to visualize the 2D // results with QGIS Crayfish type = node_centered output_time_step = 1800 values = (depth velocity wse tau deltaz z_node) } SPECIAL_OUTPUT { type = boundary_history boundary_values = (Q Qsed integrate[Q] integrate[Qsed]) output_time_step = 1800 history_one_file = yes } SPECIAL_OUTPUT { type = stringdef_history output_time_step = 1800 stringdefs = (bridge) stringdef_values = (Q Qsed wse zbed) } SPECIAL_OUTPUT { type = balance balance_values = (timestep water_volume sediment) output_time_step = 1800 } SPECIAL_OUTPUT { // Element centered dat-files for the selected variables type = element_centered Format = ascii output_time_step = 1800 values = (depth velocity wse tau deltaz z_node) } }
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