# Flash Flood Simulation for Ungauged Catchments Based on the Distributed Hydrological Model

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material and Data

#### 2.1. Study Area

^{2}, an annual runoff of 0.2 billion m

^{3}, a basin population of about 10,000 people, and a cultivated area of 5313.3 m

^{2}. Therefore, Tiezhuling is a mountainous stream in Tongcheng County. It has the characteristics of short process, large river slope, and rapid rise and fall of the river. Its peak flow is 1056 m

^{3}/s, and the annual average flow is 6.14 m

^{3}/s.

#### 2.2. Data

#### 2.3. Methodology

#### 2.3.1. Production Module

_{i}is the soil moisture, and WMM is the maximum point water storage capacity in the basin.

#### 2.3.2. Confluence Module

_{1}and q

_{2}are the inflows of the beginning and end of the period, respectively; S

_{1}and S

_{2}are the water storage capacities at the beginning and end of the river, respectively; K is the propagation time of the river under steady flow; and x is the proportion of flow.

_{0}is the reference flow, and V

_{w}is the wave velocity.

_{i1}and Q

_{i2}are the inflows at the beginning and end of the calculation period, respectively; Q

_{o1}and Q

_{o2}are the outflows at the beginning and end of the calculation period, respectively; V

_{1}and V

_{2}are the reservoirs at the beginning and end of the calculation period; and Δt is the length of the period.

#### 2.3.3. Model Accuracy Evaluation Index

_{E}), the relative error of the runoff depth (R

_{E}), and the peak time error (ΔT) were selected as the model accuracy index. The calculation method can be given as follows:

## 3. Results and Discussion

#### 3.1. Simulation Results of Qianyangxi

#### 3.2. Simulation Results of Tiezhuling

## 4. Conclusions

- (1)
- CNFF-HM is a distributed hydrological model with a physical mechanism. The model takes into account the spatial–temporal characteristics of various factors, covering all hydrological processes, including calculations of surface rainfall, runoff, evapotranspiration, sink, and river evolution.
- (2)
- Using the deterministic coefficient and the relative error of flood peak, runoff depth and peak time as the model accuracy index, we found that CNFF-HM has a good application effect in two UCs. In the Tiezhuling catchment, the model parameters are mainly obtained through parameter migration method, with the peak error of 0.5 h and the deterministic coefficient of 0.9; the corresponding figures for Qianyangxi are 0 h and 0.91, respectively, which contribute to the model’s higher precision parameters and better-predicted results in these two UCs.
- (3)
- Comparing the two watershed characteristic parameters, different soil layers have different WM. The sensitivity parameter SM mainly reflects surface runoff, which varies with soil composition and forest coverage. In addition to the KKS and KKG parameters representing the confluence, the other parameters are similar. Therefore, the two UCs have similarities in evapotranspiration, runoff, and water distribution, and the differences in confluence are significant. The reservoir has a significant impact on flood storage in the Tiezhuling catchment.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Hall, J.; Arheimer, B.; Borga, M.; Brázdil, R.; Claps, P.; Kiss, A.; Kjeldsen, T.R.; Kriauciuniene, J.; Kundzewicz, Z.W.; Lang, M.; et al. Understanding flood regime changes in Europe: A state-of-the-art assessment. Hydrol. Earth Syst. Sci.
**2014**, 18, 2735–2772. [Google Scholar] [CrossRef] - He, B.; Huang, X.; Ma, M.; Chang, Q.; Tu, Y.; Li, Q.; Zhang, K.; Hong, Y. Analysis of flash flood disaster characteristics in China from 2011 to 2015. Nat. Hazards
**2017**, 90, 1–14. [Google Scholar] [CrossRef] - Gourley, J.J.; Flamig, Z.L.; Vergara, H.; Kirstetter, P.E.; Clark, R.A., III; Argyle, E.; Arthur, A.; Martinaitis, S.; Terti, G.; Erlingis, J.M.; et al. The Flooded Locations And Simulated Hydrographs (FLASH) project: Improving the tools for flash flood monitoring and prediction across the United States. Bull. Am. Meteorol. Soc.
**2016**, 98, 361–372. [Google Scholar] [CrossRef] - Scolobig, A.; Marchi, B.D.; Borga, M. The missing link between flood risk awareness and preparedness: Findings from case studies in an Alpine Region. Nat. Hazards
**2012**, 63, 499–520. [Google Scholar] [CrossRef] - Groisman, P.Y.; Karl, T.R.; Easterling, D.R.; Knight, R.W.; Jamason, P.F.; Hennessy, K.J.; Suppiah, R.; Page, C.M.; Wibig, J.; Fortuniak, K.; et al. Changes in the Probability of Heavy Precipitation: Important Indicators of Climatic Change. Clim. Chang.
**1999**, 42, 243–283. [Google Scholar] [CrossRef] - Groisman, P.Y.; Karl, T.R.; Knight, R.W.; Stenchikov, G.L. Changes of Snow Cover, Temperature, and Radiative Heat Balance over the Northern Hemisphere. J. Clim.
**1994**, 7, 1633–1656. [Google Scholar] [CrossRef] [Green Version] - Refsgaard, J.C.; Knudsen, J. Operational Validation and Intel-comparison of Different Types of Hydrologic Models. Water Resour. Res.
**1996**, 32, 2189–2202. [Google Scholar] [CrossRef] - El-Nasr, A.A.; Arnold, J.G.; Feyen, J.; Berlamont, J. Modelling the hydrology of a catchment using a distributed and a semi-distributed model. Hydrol. Processes
**2005**, 19, 573–587. [Google Scholar] [CrossRef] - Reed, S.; Schaake, J.; Zhang, Z. A distributed hydrologic model and threshold frequency-based method for flash flood forecasting at ungauged locations. J. Hydrol.
**2007**, 337, 402–420. [Google Scholar] [CrossRef] - Wałęga, A.; Cupak AAmatya, D.M.; Drożdżal, E. Comparison of direct outflow calculated by modified SCS-CN methods for mountainous and highland catchments in upper Vistula Basin, Poland and lowland catchment in South Carolina, U.S.A. Acta Scientiarum Polonorum Seria Formatia Circumiectus
**2017**, 16, 187–207. [Google Scholar] - Zoccatelli, D.; Borga, M.; Viglione, A.; Chirico, G.B.; Schl, G.B. Spatial moments of catchment rainfall: Rainfall spatial organisation, Catchment morphology, and flood response. Hydrol. Earth Syst. Sci. Discuss.
**2011**, 8, 5811–5847. [Google Scholar] [CrossRef] - Anquetin, G.; Horgan, G.; Rawe, S.; Murray, D.; Madden, A.; Macmathuna, P.; Doran, P.; Murphy, P.V. Synthesis of novel macrolactam and macroketone analogues of migrastatin from d-glucal and comparison with macrolactone and acyclic analogues: A dorrigocin a congener is a potent inhibitor of gastric cancer cell migration. Eur. J. Organ. Chem.
**2008**, 2008, 1953–1958. [Google Scholar] [CrossRef] - Barthold, F.E.; Workoff, T.E.; Cosgrove, B.A.; Gourley, J.J.; Novak, D.R.; Mahoney, K.M. Improving Flash Flood Forecasts: The HMT-WPC Flash Flood and Intense Rainfall Experiment. Bull. Am. Meteorol. Soc.
**2015**, 96, 1859–1866. [Google Scholar] [CrossRef] - Douinot, A.; Roux, H.; Garambois, P.A.; Larnier, K.; Labat, D.; Dartus, D. Accounting for rainfall systematic spatial variability in flash flood forecasting. J. Hydrol.
**2016**, 541, 359–370. [Google Scholar] [CrossRef] [Green Version] - Sivapalan, M.; Takeuchi, K.; Franks, S.W.; Gupta, V.K.; Karambiri, H.; Lakshmi, V.; Liang, X.; McDonnell, J.J.; Mendiondo, E.M.; O’connell, P.E.; et al. Iahs decade on predictions in ungauged Catchments (pub), 2003-2012: Shaping an exciting future for the hydrological sciences. Int. Assoc. Sci. Hydrol. Bull.
**2003**, 48, 857–880. [Google Scholar] [CrossRef] - Wagner, W.; Scipal, K.; Pathe, C.; Gerten, D.; Lucht, W.; Rudolf, B. Evaluation of the agreement between the first global remotely sensed soil moisture data with model and precipitation data. J. Geophys. Res.
**2003**, 108. [Google Scholar] [CrossRef] [Green Version] - Beven, K.J. Rainfall-Runoff Modeling: The Primer; John Wiley & Sons: Chichester, UK, 2012; pp. 84–96. [Google Scholar]
- Beven, K. Runoff Production and Flood Frequency in Catchments of Order n: An Alternative Approach. In Scale Problems in Hydrology; Springer: Dordrecht, the Netherlands, 1986; pp. 107–131. [Google Scholar]
- Kuriqi, A.; Ardiclioglu, M.; Muceku, Y. Investigation of seepage effect on river dike’s stability under steady state and transient conditions. Pollack Periodica
**2016**, 11, 87–104. [Google Scholar] [CrossRef] - Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Binger, R.L.; Harmel, R.D.; Veith, T. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE
**2007**, 50, 885–900. [Google Scholar] [CrossRef] - Gironas, J. Morphologic Characterization of Urban Watersheds and Its Use in Quantifying Hydrologic Response; Dissertations & Theses-Gradworks; Colorado State University: Fort Collins, CO, USA, 2009. [Google Scholar]
- Khaleghi, M.R.; Gholami, V.; Ghodusi, J.; Hosseini, H. Efficiency of the geomorphologic instantaneous unit hydrograph method in flood hydrograph simulation. Catena
**2011**, 87, 163–171. [Google Scholar] [CrossRef] - Kavetski, D.; Kuczera, G.; Franks, S.W. Bayesian Analysis of Input Uncertainty in Hydrological Modeling: 2. Application. Water Resour. Res.
**2006**, 42, W03407. [Google Scholar] [CrossRef] - Selenica, A.; Kuriqi, A.; Ardicioglu, M. Risk assessment from flooding in the rivers of Albania. In Proceedings of the International Balkans Conference on Challenges of Civil Engineering, Tirana, Albania, 23–25 May 2013. [Google Scholar]
- Chen, M.; Pang, J.; Wu, P. Flood Routing Model with Particle Filter-Based Data Assimilation for Flash Flood Forecasting in the Micro-Model of Lower Yellow River, China. Water
**2018**, 10, 1612. [Google Scholar] [CrossRef] - Liu, R.; Guo, L.; Wang, Y.; Zhang, X.; Liu, Q.; Shang, Y.; Zhai, X.; Tian, J.; Huang, X. A Parallel Flood Forecasting and Warning Platform Based on HPC Clusters. EPiC Ser. Eng.
**2018**, 3, 1232–1239. [Google Scholar] - Standardization Administration of the People’s Republic of China. GB/T 22484-2008, Standard for Hydrological Information and Hydrological Forecasting; Standards Press of China: Beijing, China, 2009. (In Chinese) [Google Scholar]
- Wang, Y.; Liu, R.; Guo, L.; Tian, J.; Zhang, X.; Ding, L.; Wang, C.; Shang, Y. Forecasting and Providing Warnings of Flash Floods for Ungauged Mountainous Areas Based on a Distributed Hydrological Model. Water
**2017**, 9, 776. [Google Scholar] [CrossRef]

**Figure 1.**(

**A**) Location of study area. (

**B**,

**C**) Hydrological station including rainfall stations and watershed of Tiezhuling and Qianyangxi, respectively.

**Figure 3.**Simulating the flow process in the Qianyangxi watershed (from 12:00 on 27 September 2017 to 12:00 on 29 September 2017).

**Figure 4.**Diagram of simulated and measured flood in the Tiezhuling watershed (from 12:00 on 11 August 2017 to 06:00 on 14 August 2017).

**Figure 5.**The flow process in the Tiezhuling watershed (from 12:00 on 11 August 2017 to 00:00 on 15 August 2017).

**Figure 7.**Schematic diagram of the flow distribution of Qianyangxi (

**a**) and Tiezhuling (

**b**) at simulation time.

Catchment | Province | County | Area (km^{2}) | Length (km) | Discharge Process (km) | Discharge Time (h) | Slope (‰) | Average Annual Rainfall (mm) | Average Annual Flow (mm) |
---|---|---|---|---|---|---|---|---|---|

Tiezhuling | Hubei | Tongcheng | 250.5 | 28.1 | 26 | 19 | 1.5 | 1497.7 | 791.2 |

Qianyangxi | Fujian | Zherong | 198 | 22 | 52 | 35 | 7.5 | 1680 | 1230 |

Order Number | Start and Stop Time | Rainfall (mm) | Net Rainfall (mm) | ${\mathit{Q}}_{\mathit{E}}$ (%) | T (h) | DC |
---|---|---|---|---|---|---|

170815 | From 12:00 on 27 September 2017 to 12:00 on 29 September 2017 | 467 | 448.8 | 0.41 | 0 | 0.91 |

Order Number | Start and Stop Time | Rainfall (mm) | Net Rainfall (mm) | Measured Water Level Depth (mm) | ${\mathit{R}}_{\mathit{E}}$ (%) | ${\mathit{Q}}_{\mathit{E}}$ (%) | ∇T (h) | DC |
---|---|---|---|---|---|---|---|---|

170815 | From 12:00 on 11 August 2017 to 06:00 on 14 August 2017 | 292.7 | 123.8 | 106.2 | 13.7 | 11.3 | 0.5 | 0.93 |

Parameter | Parameter Meaning | Parameter Value | |
---|---|---|---|

Qianyangxi | Tiezhuling | ||

B | Exponent parameter | 0.275 | 0.2 |

IMP | Percentage of impervious areas in the catchment (%) | 0.0075 | 0.01 |

WUM | Average soil moisture storage capacity of the upper layer (mm) | 20 | 15 |

WLM | Average soil moisture storage capacity of the middle layer (mm) | 60 | 70 |

WDM | Average soil moisture storage capacity of the deep layer (mm) | 40 | 40 |

EX | The exponent of the free water capacity curve | 1.275 | 1.2 |

SM | Storage of surface free water (mm) | 32.5 | 50 |

KS | Outflow coefficients of surface free water to interflow relationship | 0.45 | 0.7 |

KG | Outflow coefficients of surface free water to groundwater relationship | 0.375 | 0.2 |

KKS | Recession constants of the interflow storage | 0.2 | 0.5 |

KKG | Recession constants of the groundwater storage | 0.1 | 0.55 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jia, P.; Liu, R.; Ma, M.; Liu, Q.; Wang, Y.; Zhai, X.; Xu, S.; Wang, D.
Flash Flood Simulation for Ungauged Catchments Based on the Distributed Hydrological Model. *Water* **2019**, *11*, 76.
https://doi.org/10.3390/w11010076

**AMA Style**

Jia P, Liu R, Ma M, Liu Q, Wang Y, Zhai X, Xu S, Wang D.
Flash Flood Simulation for Ungauged Catchments Based on the Distributed Hydrological Model. *Water*. 2019; 11(1):76.
https://doi.org/10.3390/w11010076

**Chicago/Turabian Style**

Jia, Pengfei, Ronghua Liu, Meihong Ma, Qi Liu, Yali Wang, Xiaoyan Zhai, Shuaishuai Xu, and Dacheng Wang.
2019. "Flash Flood Simulation for Ungauged Catchments Based on the Distributed Hydrological Model" *Water* 11, no. 1: 76.
https://doi.org/10.3390/w11010076