# Multidecadal Analysis of an Engineered River System Reveals Challenges for Model-Based Design of Human Interventions

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## Abstract

**:**

## 1. Introduction

## 2. Data

#### 2.1. Case Study

#### 2.2. Geographical Database

#### 2.3. Hydraulic Data

## 3. Methods

#### 3.1. General Outline

#### 3.2. Hydraulic Modelling

#### 3.3. Rating Curve Construction

- For a, a moderately informative prior with a normal distribution was centred on the values obtained from deterministic optimisation.
- For b, a uniform distribution was chosen such that the values of b cannot overlap. This is necessary as the terms of (3) otherwise become interchangeable and therefore not identifiable by the algorithm.
- For p, an informative prior was centered on 1.7, following from rounding up from the expected value for p based on the Manning equation ($1.666\dots $).
- For $\varsigma $, a non-informative half-Cauchy following [29].

**Table 1.**Prior distributions. The notation $\mathcal{N}(\mu ,\sigma )$ stands for the normal distribution with mean $\mu $ and standard deviation $\sigma $. $\mathcal{U}({x}_{l},{x}_{u})$ stands for the uniform distribution with lower bound ${x}_{l}$ and upper bound ${x}_{u}$, and the HalfCauchy $\left(\gamma \right)$ is the truncated Cauchy distribution with scale parameter $\gamma $.

Parameter | Prior | Parameter | Prior | Parameter | Prior |
---|---|---|---|---|---|

${a}_{0}$ | $\mathcal{N}(100,20)$ | ${b}_{0}$ | $\mathcal{U}(2,6)$ | ${p}_{i}$ | $\mathcal{N}(1.6,0.25)$ |

${a}_{1}$ | $\mathcal{N}(150,20)$ | ${b}_{1}$ | $\mathcal{U}(6,12)$ | $\varsigma $ | $\mathrm{HalfCauchy}\left(2\right)$ |

${a}_{2}$ | $\mathcal{N}(200,20)$ | ${b}_{2}$ | $\mathcal{U}(12,14)$ |

## 4. Results

#### 4.1. Simulated Trend

#### 4.2. Rating Curves

#### 4.3. Long-Term Trends

## 5. Discussion

#### 5.1. Explanations for the Discrepancy between Simulated and Observed Trends

#### 5.2. Improvements to the Rating Curve Model

#### 5.3. Reducing the Uncertainty of the Hydraulic Model

#### 5.4. Interpreting the Implications of This Study

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Table of Stochasts

**Table A1.**Parameters of the floodplain roughness class distributions. Codes marked with an asterisk * are not used in the Waal model.

Class Code | Name | Parameters | |||
---|---|---|---|---|---|

Empirical distribution | |||||

612–637 | Alluvial bed | ||||

Uniform distribution | |||||

n/a | Classification map | ||||

Triangular distributions | min | mean | max | ||

102 | Deep bed | 0.025 | 0.03 | 0.033 | |

104 | Natural side channel | 0.03 | 0.035 | 0.04 | |

105 | Side channel | 0.025 | 0.03 | 0.033 | |

106 | Pond/Harbor | 0.025 | 0.03 | 0.033 | |

111 | Sand bank | 0.025 | 0.03 | 0.033 | |

121 | Field | 0.02 | 0.03 | 0.04 | |

Lognormal distributions | ${\mu}_{{h}_{v}}$ | ${\sigma}_{{h}_{v}}$ | ${\mu}_{{n}_{v}}$ | ${\sigma}_{{n}_{v}}$ | |

1201 | Production meadow | −3.18 | 0.47 | 2.40 | 0.77 |

1202 | Natural grass and hayland | −0.74 | 0.53 | −2.64 | 0.93 |

1203 | Herbaceous meadow | −1.64 | 0.32 | 2.59 | 0.33 |

1211 * | Thistle herb. Veg. | −1.29 | 0.33 | 1.05 | 0.43 |

1212 | Dry herbaceous vegetation | −0.59 | 0.39 | −3.06 | 0.65 |

1213 * | Brambles | −0.67 | 0.21 | −0.73 | 0.36 |

1214 * | Hairy willowherb | −1.89 | 0.56 | −0.25 | 0.49 |

1215 * | Reed herb. Veg. | 0.60 | 0.22 | −1.83 | 0.27 |

1221 | Wet herb. Veg. | −1.08 | 0.38 | −1.49 | 0.44 |

1222 * | Sedge | −1.32 | 0.67 | 0.04 | 0.63 |

1223 | Reed-grass | −0.92 | 0.86 | −2.19 | 0.16 |

1224 | Bulrush | −0.81 | 0.67 | 0.04 | 0.63 |

1225 * | Reed-mace | 0.37 | 0.23 | −1.12 | 0.57 |

1226 | Reed | 0.94 | 0.13 | −1.14 | 0.42 |

1231 | Softwood shrubs | 1.81 | 0.24 | −2.20 | 0.79 |

1232 | Willow plantation | 1.05 | 0.43 | −3.23 | 0.62 |

1233 | Thorny shrubs | 1.48 | 0.64 | −1.73 | 0.41 |

1241 * | Hardwood production forest | Deterministic | Deterministic | −4.68 | 0.67 |

1242 | Softwood production forest | Deterministic | Deterministic | −4.72 | 0.66 |

1243 * | Pine forest | Deterministic | Deterministic | −4.18 | 0.54 |

1244 | Hardwood forest | Deterministic | Deterministic | −3.45 | 0.77 |

1245 | Softwood forest | Deterministic | Deterministic | −3.04 | 0.99 |

1246 | Orchard low | 1.10 | 0.10 | −3.72 | 0.25 |

1247 | Orchard high | 1.78 | 0.21 | −4.61 | 0.12 |

1250 | Pioneer vegetation | −2.87 | 0.18 | −1.93 | 0.50 |

## Appendix B. Table of Measurements

Discharge [m${}^{3}$s${}^{-1}$] | |||
---|---|---|---|

Year | n | Min. | Max. |

1988 | 50 | 914 | 6296 |

1989 | 53 | 708 | 2042 |

1990 | 41 | 741 | 4881 |

1991 | 29 | 628 | 4258 |

1992 | 8 | 889 | 1434 |

1993 | 20 | 1039 | 6958 |

1994 | 9 | 1231 | 4388 |

1995 | 26 | 1056 | 7844 |

1996 | 19 | 865 | 1835 |

1997 | 5 | 860 | 1461 |

1998 | 24 | 918 | 6077 |

1999 | 29 | 1184 | 5397 |

2000 | 38 | 1232 | 3736 |

2001 | 71 | 1150 | 6186 |

2002 | 55 | 1124 | 4652 |

2003 | 68 | 565 | 5863 |

2004 | 30 | 891 | 4623 |

2005 | 34 | 816 | 3740 |

2006 | 11 | 891 | 1596 |

2007 | 47 | 873 | 3690 |

2008 | 87 | 1042 | 2812 |

2009 | 62 | 688 | 2804 |

2010 | 66 | 1048 | 3894 |

2011 | 73 | 655 | 5451 |

2012 | 76 | 904 | 4440 |

2013 | 29 | 1245 | 3881 |

2014 | 40 | 932 | 2092 |

2015 | 31 | 755 | 3050 |

2016 | 38 | 768 | 3006 |

2017 | 44 | 735 | 2249 |

2018 | 44 | 584 | 4818 |

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**Figure 1.**A selection of interventions carried out in the River Waal between 1995 and 2017. The River Waal splits from the River Rhine at 51.872${}^{\circ}$ latitude, 6.038${}^{\circ}$ longitude.

**Figure 2.**Schematic outline of the methodology. The software used is indicated with red, italicised labels.

**Figure 3.**Simulated changes in the water level at a constant 10,165 m${}^{3}$s${}^{-1}$ since 1995. (

**a**) Annotation on how an intervention affects the water levels in time and space. (

**b**) Annotation of the major changes to the river system.

**Figure 4.**Simulated change in flood water level in 2015 compared to 1995. The location of the water level measurement stations are annotated.

**Figure 5.**Confidence intervals for the simulated change in flood levels since 1995 (projected on the primary (left) axis) and the size of the 90% interval, projected onto the secondary (right) axis.

**Figure 6.**The rating curves constrained on available data for 1988 (blue shaded area) and 2018 (orange shaded area), showing overall lower water levels in 2018 for the same discharge.

**Figure 7.**Years with fewer measurements have comparatively large uncertainty intervals, especially in extrapolation. Shown here is the rating curve for 1997 (five measurements).

**Figure 8.**Water levels trends for main channel flow (1000 m${}^{3}$s${}^{-1}$), bankful flow (2000 m${}^{3}$s${}^{-1}$), floodplain flow (5000 m${}^{3}$s${}^{-1}$) and extreme (10,165 m${}^{3}$s${}^{-1}$) discharge at Pannerdensche Kop. Note the break in the vertical axis to prevent overlap of the uncertainty intervals at 5000 m${}^{3}$s${}^{-1}$ and 10,165 m${}^{3}$s${}^{-1}$.

**Figure 9.**Comparing hydraulic model simulations with the rating curves for 1995 and 2018 shows that the model results fall within the uncertainty intervals of the rating curves. The decrease in water level due to human intervention may not be visible in the rating curves due to the uncertainty in extrapolation.

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**MDPI and ACS Style**

Berends, K.D.; Gensen, M.R.A.; Warmink, J.J.; Hulscher, S.J.M.H.
Multidecadal Analysis of an Engineered River System Reveals Challenges for Model-Based Design of Human Interventions. *CivilEng* **2021**, *2*, 580-598.
https://doi.org/10.3390/civileng2030032

**AMA Style**

Berends KD, Gensen MRA, Warmink JJ, Hulscher SJMH.
Multidecadal Analysis of an Engineered River System Reveals Challenges for Model-Based Design of Human Interventions. *CivilEng*. 2021; 2(3):580-598.
https://doi.org/10.3390/civileng2030032

**Chicago/Turabian Style**

Berends, Koen D., Matthijs R. A. Gensen, Jord J. Warmink, and Suzanne J. M. H. Hulscher.
2021. "Multidecadal Analysis of an Engineered River System Reveals Challenges for Model-Based Design of Human Interventions" *CivilEng* 2, no. 3: 580-598.
https://doi.org/10.3390/civileng2030032