# New Insights on Flood Mapping Procedure: Two Case Studies in Poland

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, main river length (L) 34.0 and 33.1 km, average main river slope (I) 10.3 and 17.3‰, average catchment slope (Ψ) 18.6 and 31.0‰, soil imperviousness index (N) 34.0 and 33.0%, and runoff coefficient (Φ) 0.62 and 0.82. The Skawinka catchment area includes agricultural areas (75.6%), forests (20.8%), and artificial surfaces (3.6%). The Kamienica Nawojowska catchment is characterized by forests and seminatural areas (58.6%), agricultural areas (36.4%), and artificial surfaces (5.0%). The studied catchments have a different hydrographic system and the analyzed zones include estuary river sections with a length of about 9 km (Figure 1). The layout of the river network indicates differences between Kamienica Nawojowska and Skawinka. The tributaries of Kamienica are concentrated in the central part of the basin and the supply is mainly on the left bank. Skawinka has tributaries distributed more evenly along the entire length.

#### 2.2. Materials

#### 2.3. Methods

#### 2.3.1. The Proposed Approach

_{n}—excess rainfall cumulative value [mm], P—gross rainfall cumulative value [mm], S—maximum potential catchment retention [mm] that is determined based on the CN value of the investigated area.

_{0}

_{(t)}—infiltration rate, t

_{pon}—ponding time, I(t)—cumulative infiltration, K

_{s}—saturated hydraulic conductivity, Δθ—change in soil-water content between the initial value and the field saturated soil-water content, ΔH—the difference between the pressure head at the soil surface and the matrix pressure head at the moving wetting front.

_{c}, L

_{h}—length of the path for the channel and hill slope cell of the DEM, V

_{c}, V

_{h}—surface flow velocity for the channel and hillslope cell.

_{c}and V

_{h}, the hillslope surface flow velocity is linked according to empirical formulas to the local slope and land cover data. In contrast to the channel surface flow, velocity is calibrated so that the projection on the time axis of the WFIUH centre of mass is equal to the basin lag time(T

_{L}). The lag time is expressed as the 60% of T

_{c}, that is calculated using the Giandotti formula [29]. After having defined the WFIUH, the design hydrograph Q(t) can be calculated with the following equation:

^{2}], t—precipitation duration [h], P

_{n}($\tau $)—excess rainfall determined with the CN4GA method [mm].

_{o}—wave fall time [h], t

_{s}—wave rise time [h].

_{m},

_{max}—maximum flow with a specified return period, calculated using EBA4SUB [m

^{3}·s

^{−1}], Q

_{s},

_{max}—maximum flow with the same return period, calculated using the log-normal distribution [m

^{3}·s

^{−1}].

^{2}) and by the last 9 km for the Kamienica Nawojowska main channel (the total hydraulic modeling area is equal to 18 km

^{2}). The duration of computer simulations can take a few hours for each one. In the FLO-2D model, the flood-prone areas are expressed in a gridded way, and they are the result of the maximum flow depth occurring in the specific pixel in the whole simulation. In both investigated areas, the key parameters affecting the extension of the zones and their shape are the design hydrograph peak discharge and its total volume. The spatial resolution for the EBA4SUB data was 100 m, for FLO-2D input data 8m, for FLO-2D output data 50 m.

#### 2.3.2. The Standard Approach

_{p}versus the t/tp hydrograph, the peak discharge q

_{p}and the time to peak t

_{p}are computed, as:

_{r}—the duration of rainfall T

_{l}—the lag time from centroid of rainfall to peak discharge.

_{l}can be calculated from watershed characteristics using main stream length L, watershed slope s, and curve number (CN):

_{c}—Coriolis coefficient, t—time, g—gravitational acceleration.

^{−4}) and the area (10

^{−3}) and subsequent recalculation for the water surface elevation [34]. The duration of computer simulations last a few seconds (from 4 to 17). The Mike11 model was used for computation of water surface levels at cross-sections in main channel and flood zones. River models accounted for a river of the length of significance in terms of flood protection, i.e., for Kamienica Nawojowska 27.6 km and for Skawinka 35.0 km. Boundary conditions covered all required tributaries concentrated and distributed as provided for in the guidelines [35]. In Mike11 flood-prone areas are determined from the intersection of the numerical water surface model (WSM) with the DEM. WSM was generated using ordinates in cross-sections. Moreover, areas without a hydraulic connection in the riverbed were omitted, as were areas where the water depth is less than the accuracy of DEM. Regarding the input data, for Mike 11 flood zones generation procedure the resolution is less than 1 m.

## 3. Results

#### 3.1. Initial Analysis

_{s}), and measures of shape of the studied variate distribution: coefficient of skewness (Ske) and kurtosis (K). The results are presented in Table 1.

#### 3.2. EBA4SUB Design Hydrographs

#### 3.3. Hydraulic Modeling and Flood-Prone Areas Determination

^{2}and the smallest (FLO-2D with B(2;2)) has the value A = 1.973 km

^{2}. FLO-2D with B (2;2) flood-prone area is 17.1% smaller than the corresponding obtained with Mike11/NWMA. The largest zone for Kamienica Nawojowska was also generated based on Mike11/NWMA, A = 1.156 km

^{2}, and the smallest based on the FLO-2D application (again with B(2;2)) presents A = 0.666 km

^{2}, with a difference of 42.4%. The smallest differences with Mike 11/NWMA were found in the case of Skawinka with the DVWK model and with the B(2;3) model in the case of Kamienica Nawojowska. As for the differences between the EBA4SUB models, the differences are up to 8.2% for Skawinka and 26.8% for Kamienica Nawojowska.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Pellicani, R.; Parisi, A.; Iemmolo, G.; Apollonio, C. Economic Risk Evaluation in Urban Flooding and Instability-Prone Areas: The Case Study of San Giovanni Rotondo (Southern Italy). Geosciences
**2018**, 8, 112. [Google Scholar] [CrossRef] [Green Version] - Apollonio, C.; Bruno, M.F.; Iemmolo, G.; Molfetta, M.G.; Pellicani, R. Flood Risk Evaluation in Ungauged Coastal Areas: The Case Study of Ippocampo (Southern Italy). Water
**2020**, 12, 1466. [Google Scholar] [CrossRef] - Directive 2007/60/EC on the Assessment and Management of Flood Hazards. Available online: https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:32007L0060&from=EN (accessed on 13 October 2020).
- Sojka, M.; Wróżyński, R. Impact of digital terrain model uncertainty on flood inundation mapping. Rocz. Ochr. Śr.
**2013**, 15, 564–574. [Google Scholar] - Młyński, D.; Wałęga, A.; Książek, L.; Florek, J.; Petroselli, A. Possibility of using selected rainfall-runoff models for determining the design hydrograph in mountainous catchments: A case study in Poland. Water
**2020**, 12, 1450. [Google Scholar] [CrossRef] - Mark, O.; Weesakul, S.; Apirumanekul, C.; Aroonnet, S.B.; Djordjevic, S. Potential and limitations of 1D modelling of urban flooding. J. Hydrol.
**2014**, 299, 284–299. [Google Scholar] [CrossRef] - Petroselli, A.; Vojtek, M.; Vojteková, J. Flood mapping in small ungauged basins: A comparison of different approaches for two case studies in Slovakia. Hydrol. Res.
**2018**, 50, 379–392. [Google Scholar] [CrossRef] [Green Version] - Vojtek, M.; Petroselli, A.; Vojteková, J.; Ashgarynia, S. Flood inundation mapping in small and ungauged basins: Sensitivity analysis using the EBA4SUB and HEC-RAS modeling approach. Hydrol. Res.
**2019**, 50, 1002–1019. [Google Scholar] [CrossRef] [Green Version] - Pijanowski, J.M. System Approach to Planning and Arranging Rural Areas in Poland; University of Agriculture in Krakow: Krakow, Poland, 2013. (In Polish) [Google Scholar]
- Czajkowska, A.; Osowska, J. The use of ArcGIS Desktop and Mike 11 for determining flood hazard zones. In Geochemia i Geologia Środowiska Terenów Uprzemysłowionych; Pozzi, M., Ed.; PA NOVA: Gliwice, Poland, 2014; pp. 220–235. (In Polish) [Google Scholar]
- Hejmanowska, B. Data Quality Effect on Risk of Decision Processes Supported by GIS Analyses; AGH: Krakow, Poland, 2005. (In Polish) [Google Scholar]
- Al-Khafaji, M.S.; Al-Sweiti, F.H. Integrated impact of digital elevation model and land cover resolutions on simulated runoff by SWAT Model. Hydrol. Earth Syst. Sci. Discuss.
**2017**, 653, 1–26. [Google Scholar] - Gądek, W.; Bodziony, M. The hydrological model and formula for determining the hypothetical flood wave volume in non-gauged basins. Meteorol. Hydrol. Water Manag.
**2015**, 3, 3–9. [Google Scholar] [CrossRef] [Green Version] - Egiazarova, D.; Kordzakhia, M.; Wałęga, A.; Drożdżal, E.; Milczarek, M.; Radecka, A. Application of Polish experience in the implementation of the flood directive in Georgia—Hydrological calculations. Acta Sci. Pol. Form. Circumiectus
**2017**, 16, 89–110. [Google Scholar] [CrossRef] - Gądek, W.J.; Baziak, B.; Tokarczyk, T. Nonparametric design hydrograph in the gauged cross sections of the Vistula and Odra basin. Meteorol. Hydrol. Water Manag.
**2017**, 5, 53–61. [Google Scholar] [CrossRef] [Green Version] - Rodriguez-Iturbe, I.; Valdez, J.B. The geomorphologic structure of hydrology response. Water Resour. Res.
**1979**, 15, 1409–1420. [Google Scholar] [CrossRef] [Green Version] - Wałęga, A.; Drożdżal, E.; Piórecki, M.; Radoń, R. Some problems of hydrology modelling of outflow from ungauged catchments with aspects of flood maps design. Acta Sci. Pol. Form. Circumiectus
**2012**, 11, 57–68. (In Polish) [Google Scholar] - Wałęga, A.; Książek, L. Influence of rainfall data on the uncertainty of flood simulation. Soil Water Res.
**2016**, 11, 277–284. [Google Scholar] [CrossRef] [Green Version] - Piscopia, R.; Petroselli, A.; Grimaldi, S. A software package for the prediction of design flood hydrograph in small and ungauged basins. J. Agric. Eng.
**2015**, 432, 74–84. [Google Scholar] - Petroselli, A.; Grimaldi, S. Design hydrograph estimation in small and fully ungauged basins: A preliminary assessment of the EBA4SUB framework. J. Flood Risk Manag.
**2018**, 8, 1–14. [Google Scholar] [CrossRef] - Młyński, D.; Petroselli, A.; Wałęga, A. Flood frequency analysis by an event-based rainfall-runoff model in selected catchments of Southern Poland. Soil Water Res.
**2018**, 13, 170–176. [Google Scholar] - Šraj, M.; Dirnbek, L.; Brilly, M. The influence of effective rainfall on modeled runoff hydrograph. J. Hydrol. Hydromech.
**2010**, 58, 3–14. [Google Scholar] [CrossRef] [Green Version] - Sikorska, A.E.; Viviroli, D.; Seibert, J. Effective precipitation duration for runoff peaks based on catchment modelling. J. Hydrol.
**2017**, 556, 510–522. [Google Scholar] [CrossRef] - Grimaldi, S.; Petroselli, A.; Romano, N. Curve-Number/Green-Ampt mixed procedure for streamflow predictions in ungauged basins: Parameter sensitivity analysis. Hydrol. Process.
**2013**, 27, 1265–1275. [Google Scholar] [CrossRef] - Green, W.H.; Ampt, G.A. Studies on soil physics. J. Agric. Sci.
**1911**, 4, 1–24. [Google Scholar] [CrossRef] [Green Version] - USDA. Estimation of direct runoff from storm rainfall. In National Engineering Handbook; Chapter 10, Part 630; United States Department of Agriculture (USDA) Soil Conservation Service: Washington, WA, USA, 2004; pp. 1–22. [Google Scholar]
- Nardi, F.; Grimaldi, S.; Santini, M.; Petroselli, A.; Ubertini, L. Hydrogeomorphic properties of simulated drainage patterns using DEMs: The flat area issue. Hydrol. Sci. J.
**2008**, 53, 1176–1193. [Google Scholar] [CrossRef] - Grimaldi, S.; Petroselli, A.; Nardi, F. A parsimonious geomorphological unit hydrograph for rainfall-runoff modelling in small ungauged basins. Hydrol. Sci. J.
**2012**, 57, 73–83. [Google Scholar] [CrossRef] - Giandotti, M. Previsione delle piene e delle magre dei corsi d’acqua (Estimation of floods and droughts of rivers). Ist. Poligr. Dello Stato
**1934**, 8, 107–117. [Google Scholar] - Kim, S.; Kim, H. A new metric of absolute percentage error for intermittent demand forecast. Int. J. Forecast
**2016**, 32, 669–679. [Google Scholar] [CrossRef] - O’Brien, J.S.; Julien, P.Y.; Fullerton, W.T. Two dimensional water flood and mud flow simulation. J. Hydraul. Eng.
**1993**, 119, 244–261. [Google Scholar] [CrossRef] - Książek, L.; Wałęga, A.; Bartnik, W.; Krzanowski, S. Calibration and verification of computational model of The Wislok River by means of flood wave. Infrastruct. Ecol. Rural Areas
**2010**, 8, 15–28. (In Polish) [Google Scholar] - Michalik, A.; Książek, L. Dynamics of Water Flow on Degraded Sectors of Polish Mountain Stream Channels. Pol. J. Environ. Stud.
**2009**, 18, 665–672. [Google Scholar] - Chow, V.T.; Maidment, D.K.; Mays, L.W. Applied of Hydrology; McGRAW Hill Book Company: New York, NY, USA, 1988. [Google Scholar]
- Stodolak, R.; Baran, J.; Knap, E. The influence of rain temopration on the results of rainfall-runoff model. Ecol. Eng.
**2018**, 19, 87–93. [Google Scholar] [CrossRef] - GUGiK. Polish Central Office of Geodesy and Cartography, State Surveying and Cartographic Resources. 2020. Available online: www.gugik.gov.pl/pzgik (accessed on 19 March 2020).
- European Commission. CORINE (Coordination of Information on Environment) Database, a Key Database for European Integrated Environmental Assessment; Programme of the European Commission; European Environmental Agency (EEA): Copenhagen, Denmark, 2000. [Google Scholar]
- FLO-2D (2012) FLO-2D Reference Manual. Available online: https://www.flo-2d.com/download/ (accessed on 5 February 2019).
- Młyński, D.; Wałega, A.; Ozga-Zieliński, B.; Ciupak, M.; Petroselli, A. New approach for determining the quantiles of maximum annual flows in ungauged catchments using the EBA4SUB model. J. Hydrol.
**2020**, 589, 125198. [Google Scholar] [CrossRef] - Jowett, J.G.; Duncan, M.J. Effectiveness of 1D and 2D hydraulic models for instream habitat analysis in a braided river. Ecol. Eng.
**2012**, 48, 92–100. [Google Scholar] [CrossRef] - Gibson, S.A.; Pasternack, G.B. Selecting between one-dimensional and two-dimensional hydrodynamic models for ecohydraulic analysis. River Res. Appl.
**2016**, 32, 1365–1381. [Google Scholar] [CrossRef] [Green Version] - Dimitriadis, P.; Tegos, A.; Oikonomou, A.; Pagana, V.; Koukouvinos, A.; Mamassis, N.; Koutsoyiannis, D.; Efstratiadis, A. Comparative evaluation of 1D and quasi-2D hydraulic models based on benchmark and real-world applications for uncertainty assessment in flood mapping. J. Hydrol.
**2016**, 534, 478–492. [Google Scholar] [CrossRef] - Development and Calibration of a One-Dimensional Hydraulic Model and Designation of Flood Hazard Zones in the Wisłoka Catchment Area; Regional Water Management Authorityin Krakow: Krakow, Poland, 2010.
- Development of a One-Dimensional Hydraulic Model of the CzarnaStaszowska Catchment Area; Calibration and Verification, Determination of the Water Surface Level for Discharges with a Probability of Exceedance p=50%, p=20%, p=10%, p=5%, p=2%, p=1%, p=0.5% and p=0.2%; Regional Water Management Authority in Krakow: Krakow, Poland, 2013.
- Development and Verification of Hydraulic Models of Dry Dams and Water Reservoirs Based on Water Management Manuals of Holding Reservoirs; 2013–2014, Project “Analysis of the investment programme in the catchment area of the Raba River”; Regional Water Management Authority in Krakow: Krakow, Poland, 2014.
- Analysis of Condition for the Transformation of Flood Wave in the Catchment Areas of the Soła, the Skawa and the Dunajec; 2014–2015, Flood Protection Programme in the Upper Vistula; Regional Water Management Authority in Krakow: Krakow, Poland, 2015.
- Gabryś, Z.; Grela, J.; Laskosz, E.; Piszczek, M.; Wybraniec, K.; Bartnik, W.; Książek, L. Approach to the development of investment programme of flood protection on the Dunajec River including environmental protection aspects. Acta Hydrol. Slovaca
**2015**, 16, 142–151. [Google Scholar] - Risk management in Nature 2000 sites under condition of flooding on the example of “Małopolski Przełom Wisły” (km 254+000-307+000) Tarnobrzeg; Słupia, project under Norwegian and EEA Funds; National Fund for Environmental Protection and Water Management; University of Agriculture in Krakow: Krakow, Poland, 2017.

**Figure 1.**River network layout for Kamienica Nawojowska and Skawinka. The modelled sections included in both methods (Mike11/National Water Management Authority (NWMA) and FLO-2D) modeling are marked blue.

**Figure 2.**Design hydrographs determined with the Event-Based Approach for Small and Ungauged Basins (EBA4SUB) model, return period 100 years: (

**a**) The Kamienica Nawojowska River, (

**b**) The Skawinka River.

**Figure 3.**(

**A**) Flood-prone areas; the Kamienica Nawojowska River—FLO-2D: (a) B(2;2), (b) B(2;3), (c) DVWK (we report only the cases with the major differences). (

**B**) Flood-prone areas; the Skawinka River—model FLO-2D: (a) B(2;2), (b) B(2;3), (c) DVWK (we report only the cases with the major differences). (

**C**) Flood-prone areas; Mike11/NWMA: (a) Kamienica Nawojowska, (b) Skawinka.

**Figure 4.**Comparison of flood hazard zones of Skawinka between the Mike11/NWMA procedure (white line) and FLO-2D B22, (

**a**) underestimation, (

**b**) overestimation.

**Table 1.**Values of descriptive statistics for the annual maximum flows time series for analyzed catchments.

Catchment | Min | Average | Max | S | Cs | Ske | K |
---|---|---|---|---|---|---|---|

Kamienica | 26.2 | 147.3 | 405.0 | 110.8 | 0.8 | 1.0 | −0.2 |

Skawinka | 13.0 | 92.4 | 346.0 | 82.8 | 0.9 | 1.6 | 2.2 |

Standard * | Advanced Approach | |||||
---|---|---|---|---|---|---|

Parameters | B(2;2) | B(2;3) | B(5;2) | DVWK | Chicago | |

Kamienica Nawojowska | ||||||

Q_{max} [m^{3}·s^{−1}] | 576.39 | 438.8 | 450.6 | 472.7 | 456.4 | 499.8 |

V [mln·m^{3}] | 15.08 | 8.751 | ||||

t [h] | 34.0 | 19.25 | ||||

α [–] | 1.026 | 1.265 | 0.878 | 0.925 | 1.333 | |

MAPE [%] | 23.0 | 21.0 | 17.0 | 20.0 | 12.0 | |

Skawinka | ||||||

Q_{max} [m^{3}·s^{−1}] | 470.38 | 220.8 | 244.9 | 277.9 | 303.2 | 263.5 |

V [mln·m^{3}] | 26.41 | 6.815 | ||||

t [h] | 89.4 | 30.5 | ||||

α [–] | 0.605 | 0.794 | 0.525 | 0.768 | 0.794 | |

MAPE [%] | 45.0 | 39.0 | 31.0 | 25.0 | 35.0 |

Model | Case | Kamienica Nawojowska [m^{2}] | Skawinka [m^{2}] |
---|---|---|---|

EBA4SUB/FLO-2D | B(2;2) | 666,025 | 1,972,525 |

B(2;3) | 910,125 | 2,027,650 | |

B(5;2) | 733,525 | 2,094,875 | |

Chicago | 732,475 | 2,065,725 | |

DVWK | 872,525 | 2,148,300 | |

Mike11/NWMA | SCS-CN | 1,156,400 | 2,380,275 |

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**MDPI and ACS Style**

Petroselli, A.; Florek, J.; Młyński, D.; Książek, L.; Wałęga, A.
New Insights on Flood Mapping Procedure: Two Case Studies in Poland. *Sustainability* **2020**, *12*, 8454.
https://doi.org/10.3390/su12208454

**AMA Style**

Petroselli A, Florek J, Młyński D, Książek L, Wałęga A.
New Insights on Flood Mapping Procedure: Two Case Studies in Poland. *Sustainability*. 2020; 12(20):8454.
https://doi.org/10.3390/su12208454

**Chicago/Turabian Style**

Petroselli, Andrea, Jacek Florek, Dariusz Młyński, Leszek Książek, and Andrzej Wałęga.
2020. "New Insights on Flood Mapping Procedure: Two Case Studies in Poland" *Sustainability* 12, no. 20: 8454.
https://doi.org/10.3390/su12208454