# Use of Monitoring Approaches to Verify the Predictive Accuracy of the Modeling of Particle-Bound Solid Inputs to Surface Waters

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Study Area: Kraichbach

^{2}.

^{3}per year, respectively, which corresponds to about 15% of the river discharge at the gauging station. The annual precipitation in the study area is about 700 mm a

^{−1}[33].

#### 2.2. Monitoring with the Large-Volume Sampler

#### 2.2.1. Monitoring Campaign

^{3}s

^{−1}. The LVS was used to sample a wide range of flow situations over the four-year period.

#### 2.2.2. Large-Volume Sampler

#### 2.2.3. River Mean Concentrations

^{3}. The SPMC is calculated for the parameter dry mass of the sediment and the remaining solid concentration in the supernatant water and represents therefore the complete amount of solids transported in the river [34]. The relationship between the SPMC and the maximum discharge during the sampling periods can be expressed by a rating curve.

#### 2.2.4. Annual River Loads

^{3}, representing the sampling periods. Since the rating curve represents the relationship between the maximum discharge during sampling and the resulting concentrations, each volume segment was assigned an average concentration from the rating curve based on the maximum discharge. The approach is described in detail by Allion et al. [34].

#### 2.2.5. Dry-Weather Load

^{3}s

^{−1}(approx. 2MQ) for the river Kraichbach. They stated that up to this discharge no systematic relation between discharge and solid concentration could be found. However, the authors point out that this dry-weather load also includes rainfall events. Therefore, the threshold for the dry-weather load was adapted and set to the limit of 1.65 m

^{3}s

^{−1}(1.5MQ) considering the measured values. Rainfall events cannot be completely excluded here neither. However, based on the given data it seems to be more likely that the concentrations are not systematically influenced by runoff processes. Because of the given uncertainties not only the median concentration but also the range of the 25th and 75th percentiles is considered.

^{3}s

^{−1}are extracted from the LVS data set.

#### 2.3. Modeling Approaches of the Sediment Input

^{−1}a

^{−1}] results as follows (Equation (1)):

^{−1}a

^{−1}, R as surface runoff and rainfall erosivity factor [N/(h∙a)], K as soil erodibility factor [(Mg∙h)/(ha∙N)], L as slope length factor (dimensionless), S as slope inclination factor, C as cover and tillage factor and P as factor to account for erosion control measures.

^{2}grid based on temporally high-resolution radar-based precipitation data, using the original equation of Wischmeier and Smith [23]:

_{e}= I

_{max30}× E

_{kin}

_{e}as the erosivity of a single rain event [N h

^{−1}], I

_{max30}as the maximum 30 min rain intensity [mm h

^{−1}] and E

_{kin}as the total kinetic energy per unit area [KJ m

^{−2}].

^{0.4}× (sinß/0.0896)

^{1.3})

^{2}], ß as the slope [°].

- Area connection to the watercourse system;
- Watercourse distance;
- Connectivity probability;
- Sediment delivery ratio;
- Grid-related sediment input.

_{flow}is derived from the flowpath lengths calculated as part of the hydrologic connectivity determination, measured from the respective grid cell to the point where it reaches the watercourse network under consideration of the DTM 10.

_{i}(s/l

_{flow})

^{(1−P)}

_{i}as the utilization coefficient, s as the slope [m m

^{−1}], l

_{flow}as the mean watercourse distance [m], and P as the connectivity probability. The coefficient of utilization x

_{i}is derived from the C-factor according to the following equation:

_{i}= 1.43 ln (C-factor) + 9.49

_{lflow}, the soil erosion P

_{A}, and the surface runoff P

_{RO}(see [58,60,61,62]:

_{lflow}

^{2}+ P

_{A}

^{2}+ P

_{RO}

^{2}) (0 ≤ P ≤ 1)

_{lflow}, P

_{A}and P

_{RO}:

_{Iflow}= −0.1358 ln (l

_{flow}) + 0.97107, R

^{2}= 0.94 (0 < l

_{flow}≤ 1000m)

_{A}= 0.0671 ln (A) + 0.1557, R

^{2}= 0.85 (A ≥ 0.1 t ha

^{−1}a

^{−1})

_{RO}= 0.0386 ln (RO) + 0.0994, R

^{2}= 0.96 (RO ≥ 0.1 mm a

^{−1})

^{−1}] as use-specific sediment input, and A [t ha

^{−1}a

^{−1}] as soil erosion by water.

## 3. Results

#### 3.1. River Concentrations

^{3}s

^{−1}(6MQ). The resulting rating curve is shown in Figure 3. It describes the dependence of the suspended solid concentration and the maximum discharge Q

_{max}of the sampling period. All composite samples taken represent a mean discharge volume of the Kraichbach river of 0.9 million m

^{3}. The threshold for the dry weather flow is marked with a line at 1.65 m

^{3}s

^{−1}.

#### 3.1.1. Concentrations during Dry Weather Flow

^{3}s

^{−1}are used (Figure 3). It is noticeable that there are four very high concentrations at discharge around MQ (up to 200 mg L

^{−1}, marked with a box). These are situations where the solid transport and discharge are obviously completely decoupled. These solid concentrations are excluded from further analysis because they do not represent a specific flow situation but are caused by random disturbances.

^{−1}.

#### 3.1.2. Concentrations during Erosion Events

^{−1}. At discharges in the range of 6MQ, up to 660 mg L

^{−1}are reached. These high concentrations in the Kraichbach river are influence by erosion processes.

#### 3.2. Determined Sediment Loads for Long-Term Discharges Based on Monitoring

_{year}) to the mean annual discharge volume over the period of 2003–2020 (V

_{mean}). This ratio indicates whether it is a wet (blue) or dry year (orange). The flood years of 2003 and 2013 highlight this in particular.

^{−1}[70] and an annual overflow volume of 757,000 m

^{3}per year [71].

#### 3.3. Results of the Modeling

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Schematic of the large-volume sampler: (

**a**) photo of the large-volume sampler; (

**b**) sketch of the large-volume sampler [38].

**Figure 3.**Rating curve of the Kraichbach with the threshold of 1.65 m

^{3}s

^{−1}for the dry weather flow. Outliers are marked with a box.

**Figure 4.**Annual suspended solid loads of the Kraichbach river for the years 2003–2020. Bars show the total suspended solid load, three variants of the dry-weather load calculations are shown as points (mean variant) and lines (minimum and maximum variants) in the bars. The ratio of the annual discharge volume (V

_{year}) to the mean annual discharge volume (V

_{mean}) is shown in blue for wet years and orange for dry years.

Property | Large-Volume Sampler |
---|---|

Sampling period | March 2017–June 2021 |

Number of sampling periods | 43 |

Sampling strategy | Volume-proportional, long-term |

Sampling interval | 13,300 m^{3} |

Subsample volume | 10–15 L |

Tank volume | Stainless steel, 1000 L |

Samples per container | 100 |

Pumping system | Peristaltic |

Pump capacity | 15,000 L∙h^{−1} |

Parameter | Suspended Solid Concentration in mg L^{−1} |
---|---|

25th percentile | 25.8 |

Median | 31.9 |

75th percentile | 51.1 |

Parameter | Dry-Weather Load Variant | ||
---|---|---|---|

Minimum | Mean | Maximum | |

Mean annual load in t a^{−1} | 2826 | 2826 | 2826 |

Mean dry-weather load in t a^{−1} | 467 | 577 | 925 |

Mean precipitation input in t a^{−1}, total | 2359 | 2249 | 1901 |

Thereof combined sewer overflow | 49 | 49 | 49 |

Thereof erosion | 2310 | 2200 | 1852 |

Factor | Arable Land | Grass-Land | Fruit Growing | Viticulture | Coniferous Forest | Deciduous Forest | Mixed Forest | Nature Land |
---|---|---|---|---|---|---|---|---|

R-factor | 88.3 | 87.5 | 90.1 | 86.6 | 86.7 | 87.9 | 86.8 | 88.1 |

K-factor | 0.47 | 0.43 | 0.29 | 0.28 | 0.53 | 0.49 | 0.47 | 0.50 |

LS-factor | 1.16 | 1.59 | 0.97 | 2.16 | 1.76 | 1.95 | 2.14 | 1.73 |

C-factor | 0.085 | 0.004 | 0.19 | 0.22 | 0.002 | 0.002 | 0.002 | 0.004 |

Sediment Input in t ha^{−1} | Arable Land | Grass-Land | Fruit Growing | Viticulture | Coniferous Forest | Deciduous Forest | Mixed Forest | Nature Land |
---|---|---|---|---|---|---|---|---|

Mean | 0.478 | 0.009 | 0.638 | 2.08 | 0.003 | 0.004 | 0.003 | 0.017 |

SD | 1.19 | 0.035 | 1.11 | 4.56 | 0.023 | 0.023 | 0.022 | 0.036 |

Min | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

Max | 82.9 | 3.69 | 6.96 | 134 | 0.57 | 0.98 | 1.29 | 0.80 |

Sum in t a^{−1} | Arable Land | Grass-Land | Fruit Growing | Viticulture | Coniferous Forest | Deciduous Forest | Mixed Forest | Nature Land | Total |
---|---|---|---|---|---|---|---|---|---|

Soil loss | 32,192 | 457.7 | 297.7 | 6286 | 16.3 | 228.1 | 217.3 | 157.4 | 39,853 |

Sediment input | 1460 | 7.2 | 5.3 | 158.5 | 0.2 | 2.1 | 1.2 | 3.3 | 1638 |

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**MDPI and ACS Style**

Allion, K.; Gebel, M.; Uhlig, M.; Halbfass, S.; Bürger, S.; Kiemle, L.; Fuchs, S.
Use of Monitoring Approaches to Verify the Predictive Accuracy of the Modeling of Particle-Bound Solid Inputs to Surface Waters. *Water* **2021**, *13*, 3649.
https://doi.org/10.3390/w13243649

**AMA Style**

Allion K, Gebel M, Uhlig M, Halbfass S, Bürger S, Kiemle L, Fuchs S.
Use of Monitoring Approaches to Verify the Predictive Accuracy of the Modeling of Particle-Bound Solid Inputs to Surface Waters. *Water*. 2021; 13(24):3649.
https://doi.org/10.3390/w13243649

**Chicago/Turabian Style**

Allion, Katharina, Michael Gebel, Mario Uhlig, Stefan Halbfass, Stephan Bürger, Lisa Kiemle, and Stephan Fuchs.
2021. "Use of Monitoring Approaches to Verify the Predictive Accuracy of the Modeling of Particle-Bound Solid Inputs to Surface Waters" *Water* 13, no. 24: 3649.
https://doi.org/10.3390/w13243649