Comparison of Local and Global Optimization Methods for Calibration of a 3D Morphodynamic Model of a Curved Channel
Abstract
:1. Introduction
2. Methodology
2.1. Experimental Data
2.2. Numerical Model
2.3. Calibration Procedure
2.3.1. Local Optimization Method
2.3.2. Global Optimization Methods
2.3.3. Investigated Parameters
- Roughness height at the bed (ks): For fixed beds, this parameter is typically assumed to be proportional to the representative grain size dn (the diameter where n% of sediment grains are finer) (i.e., Nikoradse’s equivalent grain roughness). For movable beds, however, the roughness caused by bedforms has to be added to the grain roughness, which may increase it with a higher factor than the grain roughness itself. A collection of different equations regarding the roughness height can be found in the literature (e.g., [87]). In this study, despite the dynamic nature of the roughness coefficient due to the formation of bedforms, the roughness height is considered to be uniform along the whole domain, because of the focus on the automatic calibration procedure. The range of this parameter is selected to be between d50 and 10d90.
- Active layer thickness (ALT): This parameter is described as a function of the representative grain diameter and the bedform height as a dynamic value that depends on the sediment properties and the flow conditions. ALT determines the maximum depth of erosion during one time-step in the numerical model. For this study, a constant value of ALT is also chosen, with a range between d50 and 5dmax [88,89].
- The volume fraction of compacted sediments (VFS): This parameter describes the proportion of deposited sediments in the bed compared to the water content, which depends on the bulk density as a function of grain size distribution and packing of sediment depositions. This parameter’s range is adjusted between 40% and 60% in the calibration process.
2.4. Work Structure
3. Results and Discussion
3.1. Testing the Performance of Different Optimization Methods
- PEST#2 (ks = d90, ALT = 2dmax, and VFS = 55%)
- PEST#3 (ks = 2d90, ALT = 4dmax, and VFS = 45%)
- PEST#4 (ks = 5d90, ALT = 2dmax, and VFS = 50%)
3.2. Application of the Selected Calibration Method for Additional Numerical Setups
4. Summary and Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Sediment Size Classes | ||||||||
---|---|---|---|---|---|---|---|---|
Size (mm) | 0.25 | 0.42 | 0.84 | 1.19 | 2.00 | 3.36 | 4.76 | 8.52 |
Proportion (%) | 6.55 | 10.56 | 25.36 | 15.06 | 20.11 | 13.02 | 4.88 | 4.46 |
Cumulative proportion (%) | 6.55 | 17.11 | 42.47 | 57.53 | 77.64 | 90.66 | 95.54 | 100 |
Fall velocity (m/s) | 0.03 | 0.06 | 0.11 | 0.14 | 0.20 | 0.26 | 0.32 | 0.43 |
Run# | Peak Flow Discharge (m3/s) | Peak Flow Depth (cm) | Duration (min) |
---|---|---|---|
1 | 0.0750 | 12.9 | 180 |
3 | 0.0613 | 11.3 | 240 |
5 | 0.0436 | 9.10 | 420 |
Calibration Results | Calibration Method | ||||||
---|---|---|---|---|---|---|---|
PEST#1 | PEST#2 | PEST#3 | PEST#4 | SCE-UA | CMA-ES | PSO | |
ks (cm) | 0.904 | 0.894 | 0.899 | 0.903 | 0.898 | 0.892 | 0.904 |
ALT (cm) | 1.639 | 1.644 | 1.629 | 1.638 | 1.635 | 1.631 | 1.647 |
VFS (%) | 48.1 | 47.9 | 48.4 | 48 | 48.1 | 48.1 | 47.9 |
Minimum of SSR (cm) | 0.28249 | 0.28251 | 0.28240 | 0.28249 | 0.28247 | 0.28247 | 0.28241 |
Number of model runs | 26 | 30 | 28 | 27 | 176 | 440 | 448 |
Calibration Parameters | Sediment Transport Formula | ||||||||
---|---|---|---|---|---|---|---|---|---|
Wu | Van Rijn | Engelund-Hansen | |||||||
Run#1 | Run#3 | Run#5 | Run#1 | Run#3 | Run#5 | Run#1 | Run#3 | Run#5 | |
ks (cm) | 1.52 | 1.34 | 0.90 | 0.63 | 0.61 | 0.37 | 0.48 | 0.31 | 0.25 |
ALT (cm) | 2.04 | 1.85 | 1.64 | 2.20 | 1.94 | 1.24 | 1.31 | 1.12 | 0.74 |
VFS (%) | 49 | 51 | 48 | 60 | 60 | 60 | 52 | 51 | 53 |
Goodness of Fit | Sediment Transport Formula | ||||||||
---|---|---|---|---|---|---|---|---|---|
Wu | Van Rijn | Engelund-Hansen | |||||||
Run#1 | Run#3 | Run#5 | Run#1 | Run#3 | Run#5 | Run#1 | Run#3 | Run#5 | |
R2 (-) | 0.90 | 0.89 | 0.95 | 0.90 | 0.89 | 0.94 | 0.88 | 0.83 | 0.90 |
RMSE (cm) | 1.49 | 1.04 | 0.67 | 1.57 | 1.08 | 0.69 | 1.63 | 1.33 | 0.81 |
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Shoarinezhad, V.; Wieprecht, S.; Haun, S. Comparison of Local and Global Optimization Methods for Calibration of a 3D Morphodynamic Model of a Curved Channel. Water 2020, 12, 1333. https://doi.org/10.3390/w12051333
Shoarinezhad V, Wieprecht S, Haun S. Comparison of Local and Global Optimization Methods for Calibration of a 3D Morphodynamic Model of a Curved Channel. Water. 2020; 12(5):1333. https://doi.org/10.3390/w12051333
Chicago/Turabian StyleShoarinezhad, Vahid, Silke Wieprecht, and Stefan Haun. 2020. "Comparison of Local and Global Optimization Methods for Calibration of a 3D Morphodynamic Model of a Curved Channel" Water 12, no. 5: 1333. https://doi.org/10.3390/w12051333