# Evaluation of Catchments’ Similarity by Penalization in the Context of Engineering Tasks—A Case Study of Four Slovakian Catchments

^{*}

## Abstract

**:**

## 1. Introduction

^{2}) in practical engineering tasks, and its original contributions are as follows:

- (1)
- An evaluation model combining several aspects of catchments into a conjunct characteristic of their similarity utilizing a penalty approach
- (2)
- A newly proposed catchment characteristic designed to evaluate the overall suitability of a given catchment for tasks related to hydrological similarity, which we call “calibrability”

## 2. Study Area

^{2}), measured at the Horné Orešany water gauging station, the catchment of the Trnávka stream using the Buková gauging station (42.96 km

^{2}), the catchment of the Vištucký stream using the Modra-Piesok station (9.38 km

^{2}), and the Gidra stream catchment using the Píla gauging station (32.9 km

^{2}). We will henceforth refer to these catchments by the names of their measuring stations.

## 3. Methodology

_{mm/day}= 86.4 × a

^{−1}× Q

_{m3/s},

_{m3/s}is the flow in m

^{3}∗ s

^{−1}, Q

_{mm/day}is the flow in mm × day

^{−1}, and a is the catchment area in km

^{2}. We chose these units because the investigated catchments have/can have different areas (so that the flows can be compared). These units are also more advantageous in evaluating the hydrological balance, because evapotranspiration and precipitation are also in mm. The correlation of the specific flows was investigated because the catchments in the presented case study have different areas. In this verification process (Figure 2), the proposed manner of penalization and mentioned unified size of the penalty coefficient was verified. Therefore, the similarity between catchments was evaluated from two points of view, one based on the catchment descriptors (which is an evaluation of the physical similarity) and the other based on the similarity of runoff response. Runoff response of two or more catchments is similar, when flows (time series of flows) have good correlation (e.g., above 0.65). A comparison of these two methods of assessing the similarity of catchments served as verification. In this process, it was verified as to whether both the penalty procedure and the assessment of the hydrological response led to the identification of the same catchment as most similar to the ungauged catchment.

## 4. Results and Discussion

#### 4.1. Calibrability

#### 4.2. Overall Assessment of the Similarity of the Catchments

#### 4.3. Verification of Similarity Using Specific Flows

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Determination of Geometric Characteristics

#### Appendix A.1.1. Catchment Area (A), Catchment Perimeter (P) and Stream Length (Ls)

#### Appendix A.1.2. Catchment Length (LC)

_{f}= A/L

_{C}

- A
- Catchment area [km
^{2}] - L
_{C} - Catchment length [km]

_{c}= A/A

_{c}

- A
_{c} - the area of a circle having equal perimeter as the perimeter of drainage catchment in [km
^{2}]

_{C}× A

^{0.5}/π

^{0.5})

#### Appendix A.2. The Drainage Network Creation

#### Appendix A.3. Hydrologic Modelling in Context of the “Calibrability” Evaluation

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**Figure 12.**Box plots of the specific flows (in mm/day). (

**a**) y-axis has normal scale, (

**b**) y-axis has logarithmic scale.

Characteristics | Month | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

Monthly totals of precipitation (mm) | 37 | 37.1 | 37.7 | 38.1 | 62.2 | 66.6 | 65.3 | 62.2 | 57 | 42.9 | 47.3 | 43.3 |

Average monthly temperature (°C) | −0.9 | 0.7 | 4.9 | 9.9 | 14.8 | 17.9 | 20 | 19.4 | 14.8 | 9.6 | 4.4 | 0.3 |

Characteristic | Catchment | |||
---|---|---|---|---|

Buková | Modra-Piesok | Horné Orešany | Píla | |

area [km^{2}] | 42.96 * | 9.38 | 37.33 | 32.90 |

perimeter [km] | 39.65 | 15 | 29 | 24.55 |

catchment length [m] | 10950 | 5740 | 8764 | 7326 |

catchment boundary segmentation | 1.71 | 1.38 | 1.34 | 1.21 |

form factor | 0.36 | 0.28 | 0.49 | 0.61 |

circular ratio | 0.34 | 0.52 | 0.56 | 0.69 |

elongation ratio | 0.38 | 0.34 | 0.44 | 0.5 |

shape factor | 2.79 | 3.51 | 2.06 | 1.63 |

Sum of geometric penalties | 3 | 2 | 0 | 1 |

Characteristic | Catchment | ||||
---|---|---|---|---|---|

Horné Orešany | Píla | Buková | Modra-Piesok | ||

Altitude | max | 693.65 | 684.92 | 738.35 | 704.64 |

min | 238.26 | 269.05 | 195.31 | 286.94 | |

mean | 406.97 | 434.25 | 332.47 | 488.21 | |

sd | 82.41 | 79.50 | 72.40 | 85.94 | |

skewness | 0.44 | 0.34 | 0.91 | −0.13 | |

Slope | max | 29.02 | 27.66 | 27.17 | 25.55 |

mean | 11.12 | 9.91 | 9.47 | 8.92 | |

sd | 5.25 | 4.76 | 5.71 | 4.46 | |

skewness | 0.22 | 0.31 | 0.46 | 0.72 | |

Aspect | mean | 134.23 | 145.61 | 149.56 | 102.18 |

sd | 96.16 | 91.79 | 94.55 | 87.72 | |

skewness | 0.27 | 0.14 | 0.05 | 0.69 |

Characteristics | Catchment | ||||
---|---|---|---|---|---|

Horné Orešany | Píla | Buková | Modra-Piesok | ||

Land use | Deciduous forest | 88.91 | 91.17 | 51.17 | 89.13 |

Arable land | - | - | 20.24 | - | |

Bushy or herbaceous vegetation with scattered trees | 9.25 | 7.13 | 5.33 | 10.87 | |

Urbanized areas | - | 1.70 | 10.17 | - | |

Tallgrass | 1.84 | - | 2.16 | - | |

Evergreen coniferous forest | - | - | 1.14 | - | |

Mixed forest | - | - | 9.80 | - |

Catchment | Calibrability (NSE) |
---|---|

Horné Orešany | 0.617 |

Píla | 0.681 |

Buková | 0.426 |

Modra-Piesok | 0.683 |

Characteristic | Catchment | |||
---|---|---|---|---|

Horné Orešany | Píla | Buková | Modra-Piesok | |

Geometry | 1 | |||

Topography—altitudes | 1 | 1 | ||

Topography—slopes | 1 | |||

Topography—aspect | 1 | |||

Hypsometry | 1 | |||

Drainage network | 1 | |||

Soil | 1 | |||

Land use | 1 | |||

Calibrability | 1 | |||

Total: | 0 | 0 | 7 | 3 |

Donor Catchment | ||||
---|---|---|---|---|

Target Catchment | Horné Orešany | Píla | Buková | Modra-Piesok |

Horné Orešany | - | 1 * | - | 2 ** |

Píla | 1 | - | - | 2 |

Modra-Piesok | 1 | 1 | - | - |

Buková | - | - | too different *** | - |

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**MDPI and ACS Style**

Cisty, M.; Povazanova, B.; Aleksic, M.
Evaluation of Catchments’ Similarity by Penalization in the Context of Engineering Tasks—A Case Study of Four Slovakian Catchments. *Water* **2021**, *13*, 2894.
https://doi.org/10.3390/w13202894

**AMA Style**

Cisty M, Povazanova B, Aleksic M.
Evaluation of Catchments’ Similarity by Penalization in the Context of Engineering Tasks—A Case Study of Four Slovakian Catchments. *Water*. 2021; 13(20):2894.
https://doi.org/10.3390/w13202894

**Chicago/Turabian Style**

Cisty, Milan, Barbora Povazanova, and Milica Aleksic.
2021. "Evaluation of Catchments’ Similarity by Penalization in the Context of Engineering Tasks—A Case Study of Four Slovakian Catchments" *Water* 13, no. 20: 2894.
https://doi.org/10.3390/w13202894