River Model Calibration Based on Design of Experiments Theory. A Case Study: Meta River, Colombia
Abstract
:1. Introduction
2. Materials and Methods
2.1. Modeling Objective and Simplifications
2.2. Parameters Used as Hydrodynamic, Sedimentologic and Morphological Indicators
- WL = coefficient of determination (R2) related to water level;
- QL = coefficient of determination (R2) related to flow rate at control cross-sections;
- FD = coefficient of determination (R2) related to flow distribution through island branches;
- MP = coefficient of determination (R2) related to depth through the 2D domain;
- SST = coefficient of determination (R2) related to suspended-load sediment transport;
- SBT = coefficient of determination (R2) related to bed load sediment transport;
- ST = coefficient of determination (R2) related to total load sediment transport;
- BL = coefficient of determination (R2) related to bed level through the 2D sector;
- BE = coefficient of determination (R2) related to bank erosion rate.
2.3. Experiment Design and Calibration
2.4. Case Study: A Reach of the Meta River, Colombia
- Morphological Stability: this section presented a low riverbank variability between 1980 and 2012.
- Hydraulic and sedimentological stability: this section is downstream of the last significant tributary of the Meta River, thus, variations in the hydraulic and sedimentological regime up to its mouth are not significant.
- Morphological typology: presents a mix of braided, straight and sinuous reaches, indicating associated morphological response patterns along much of the river.
2.4.1. Indicators for the Meta River Model
- Adjustment of water level series (WL): Coefficient of determination (R2) between the hydrograph created from the water level series and the water level simulated by interpolation for the calibration period. The comparison point was set at the abscissa K310 corresponding to the upstream boundary condition.
- Adjustment of flow distribution (FD): Coefficient of determination (R2) between the percentages of flow distribution through river branches around islands, measured on-site and those calculated by the 2D model.
- Visual comparison of velocity vectors (Visual Indicator): A visual comparison was performed between the simulated velocity vectors and those recorded by the ADCP. It was considered that the average velocity value in the measured columns would occur close to 0.6 × H [45], where H is the height of the water column.
- Adjustment of suspended sediment transport rate (SST): The IDEAM station “Aceitico” (K127) holds information regarding suspended sediment transport, estimated through regression models from data between 1996 and 2010. Based on the information available, the following equation was used in this work for estimating suspended sediment transport rate:QS = 0.0096·QL1.774,
- Bed Level Adjustment (BL): The coefficient of determination (R2) was calculated between the mesh of riverbed levels created from the bathymetric surveys from field campaigns and those simulated by MIKE-21C.
- Adequate morphological evolution (Qualitative Indicator): This visual indicator refers to the morphological evolution of the riverbed and riverbanks. The modeler shall verify if the morphologic changes through time are coherent with the numerical capabilities of the model, for example, no sudden and intense sedimentation or erosion phenomena occurred during the time span considered in the simulation.
2.4.2. Parameters for Modeling the Meta River
- For the river reach under consideration, the Chézy coefficient is used for quantifying bed resistance. In MIKE-21C, this value is estimated as a function of water depth, following the approach explained by Talmon [46]:Chézy = C·h0.17
- According to the sedimentological information supplied by IDEAM, the median grain size in the riverbed (D50-bed) is 0.35 mm. Based on this grain size, García [48] suggests using Engelund-Hansen [49], Yang’s [50] and Van Rijn’s [51] equations for estimating sediment transport rates. From modeling studies carried out in 2003 Hidroconsultas LTDA [52] on the same river, it was observed that the sediment transport rates estimated by using Yang’s equation showed a good fit when compared to values from measurements. Based on this and aiming to reduce the number of variables in the study, the modelers decided to use only Yang’s and Van Rijn’s equations.
- From the available imagery, it was found that riverbank variations in time intervals shorter than three years were not significant for the representative section. Islands were defined as covered with vegetation, which favors stability. The erosion rate at the riverbank and the corresponding coefficients were not considered as calibration parameters.
- Due to absence of significant patterns and/or phenomena affecting the morphology, the helical flow coefficient HL was simplified to its default value of 1.00.
- Chézy Roughness coefficient as a function of depth; where C is the calibration parameter.
- Sediment Transport Equation;
- Riverbed Load Factor (Kb);
- Suspended Load Factor (Ks);
- Transverse Slope coefficient (TSC);
- Transverse Slope power (TSP).
3. Results
3.1. Hydrodynamic Calibration
• Sediment Transport Equation: | Van Rijn |
• Riverbed Load Factor (Kb): | 0.100 |
• Suspended Load Factor (Ks): | 0.300 |
• Transverse Slope coefficient (TSC): | 0.625 |
• Transverse Slope power (TSP): | 0.500 |
3.2. Screening Design—2k Experiment
3.3. Fit Design—3k Experiment
4. Discussion
4.1. Hydrodynamic Calibration
4.2. Screening Design—2k Experiment
4.3. Fit Design—3k Experiment
4.4. Additional Remarks
- The domain of quantitative variables must be continuous;
- It is possible to discard a significant calibration parameter value, because of an inadequate choice of levels or alternatives during the screening design;
- Some combinations of calibration parameter values might generate numeric instability during the simulation;
- The lack of replicates (with different results) for the same configuration limits the degrees of freedom of the experiment.
5. Conclusions
- Compare the efficiency of the method and calibration performance by using other DOE types (Fractional Factorials, Taguchi, Latin Square, etc.) and statistical measures of goodness of fit (Nash-Sutcliffe’s efficiency coefficient (NSE), P-Bias, etc.).
- Compare the performance of the method with other calibration approaches for different conditions: numerical models, river characteristics, quantity and type of calibration parameters, etc.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Component | Parameter | Description |
---|---|---|
Hydrodynamics |
| This is related to the riverbed’s resistance to flow. For MIKE-21C, the value at each cell is determined as a function of water depth and Manning’s or Chézy’s coefficient. The model uses as input a constant value or maps corresponding to their spatial distribution. |
| Parameter related to the calibration of the velocity vector and depends on the turbulence state. For MIKE-21C, usually between 0.2 m2/s and 5.0 m2/s. | |
Sedimentology/ Morphology |
| The selection of sediment transport equation defines the parameters to be used in the model, and it mainly depends on granulometry (i.e., particle size and shape). A complete description of the transport formulae can be found in the MIKE-21C user’s guide [28]. |
| The total sediment load is estimated through a sediment transport equation (MIKE-21C includes a set of options for this purpose). | |
| These parameters modify sediment transport rates in the stream current, considering morphological changes affecting transverse and longitudinal slopes. | |
| In MIKE-21C this parameter defines the intensity of the helical flow on the riverbed due to the secondary currents. It is usually assumed to be equal to 1; however and ranges from 0.4 to 1.2, according to [34]. | |
| According to MIKE-21C, the erosion rate on the riverbanks can be calibrated using three different parameters, : Transversal slope of the riverbank. : Fraction of sediment transport rate near the bank. : Erosion constant which does not depend on the hydraulic condition. |
Abscissa (km) | Arm | Observed | C = 50 | C = 55 | C = 60 |
---|---|---|---|---|---|
204 | Right | 0.7076 | 0.6875 | 0.6915 | 0.6962 |
Left | 0.2924 | 0.3125 | 0.3085 | 0.3038 | |
289 | Right | 0.1598 | 0.1757 | 0.1694 | 0.1514 |
Left | 0.8402 | 0.8243 | 0.8306 | 0.8486 | |
267 | Right | 0.2580 | 0.2718 | 0.2453 | 0.2516 |
Left | 0.7420 | 0.7282 | 0.7547 | 0.7484 | |
248 | Right | 0.0560 | 0.0527 | 0.0436 | 0.0327 |
Left | 0.9440 | 0.9473 | 0.9564 | 0.9673 |
C | R2 | OWIHD | |
---|---|---|---|
Water Level (WL) | Flow Distribution (FD) | ||
50 | 0.7893 | 0.9979 | 0.8727 |
55 | 0.8450 | 0.9981 | 0.9062 |
60 | 0.8272 | 0.9984 | 0.8957 |
Level | Sediment Transport Equation (A) * | Suspended Load Factor—Ks (B) * | Riverbed Load Factor Kb (C) * | Transverse Slope Coeff.—TSC (D) * | Transverse Slope Power—TSP (E) * |
---|---|---|---|---|---|
High | Yang | 0.1 | 0.1 | 0.625 | 0.5 |
Low | Van Rijn | 0.9 | 0.5 | 1.250 | 1.0 |
Source | Sum of Squares | Df | Mean Square | F-Ratio | P-Value |
---|---|---|---|---|---|
A: Transport Eq | 0.084400 | 1 | 0.084400 | 245.66 | 0.0000 |
B: Ks | 0.106300 | 1 | 0.106300 | 309.35 | 0.0000 |
C: Kb | 0.007400 | 1 | 0.007400 | 21.76 | 0.0001 |
AB | 0.040200 | 1 | 0.040200 | 117.23 | 0.0000 |
BC | 0.010200 | 1 | 0.010200 | 29.90 | 0.0000 |
ABC | 0.010200 | 1 | 0.010200 | 29.67 | 0.0000 |
Total error | 0.008200 | 24 | 0.000340 | ||
Total (corrected) | 0.267200 | 31 |
Level | Sediment Transport Equation (A)* | Suspended Load Factor—Ks (B)* | Riverbed Load Factor Kb (C)* |
---|---|---|---|
High | Yang | 0.1 | 0.1 |
Mid | - | 0.5 | 0.3 |
Low | Van Rijn | 0.9 | 0.5 |
Source | Sum of Squares | Df | Mean Square | F-Ratio | P-Value |
---|---|---|---|---|---|
A: Transport Eq | 0.1033940 | 1 | 0.1033940 | 91.53 | 0.0000 |
B: Ks | 0.0666866 | 2 | 0.0333433 | 29.52 | 0.0000 |
C: Kb | 0.0196977 | 2 | 0.0098489 | 8.72 | 0.0016 |
AB | 0.0281542 | 2 | 0.0140771 | 12.46 | 0.0002 |
BC | 0.0134977 | 2 | 0.0067489 | 5.97 | 0.0085 |
ABC | 0.0231324 | 4 | 0.0057831 | 5.12 | 0.0045 |
Total error | 0.0248521 | 22 | 0.0011296 | ||
Total (corrected) | 0.2794150 | 35 |
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Acuña, G.J.; Ávila, H.; Canales, F.A. River Model Calibration Based on Design of Experiments Theory. A Case Study: Meta River, Colombia. Water 2019, 11, 1382. https://doi.org/10.3390/w11071382
Acuña GJ, Ávila H, Canales FA. River Model Calibration Based on Design of Experiments Theory. A Case Study: Meta River, Colombia. Water. 2019; 11(7):1382. https://doi.org/10.3390/w11071382
Chicago/Turabian StyleAcuña, Guillermo J., Humberto Ávila, and Fausto A. Canales. 2019. "River Model Calibration Based on Design of Experiments Theory. A Case Study: Meta River, Colombia" Water 11, no. 7: 1382. https://doi.org/10.3390/w11071382