# The Influence of Flow Projection Errors on Flood Hazard Estimates in Future Climate Conditions

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}emission scenario, through the downscaling of climatic forcing to a catchment scale, an estimation of flow using a hydrological model, and subsequent derivation of flood hazard maps with the help of a flow routing model. The procedure has been applied to the Biala Tarnowska catchment, Southern Poland. Future climate projections of rainfall and temperature are used as inputs to the precipitation-runoff model simulating flow in part of the catchment upstream of a modeled river reach. An application of a lumped-parameter emulator instead of a distributed flow routing model, MIKE11, substantially lowers the required computation times. A comparison of maximum inundation maps derived using both the flow routing model, MIKE11, and its lump-parameter emulator shows very small differences, which supports the feasibility of the approach. The relationship derived between maximum annual inundation areas and the upstream flow of the study can be used to assess the floodplain extent response to future climate changes. The analysis shows the large influence of the one-grid-storm error in climate projections on the return period of annual maximum inundation areas and their uncertainty bounds.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Approach

- calibration and validation of a distributed model (MIKE11) for the chosen river reach;
- development of an emulator for the selected cross sections of the model in the form of the input–output transformation;
- verification of the emulator using independent observation sets;
- comparison of the deterministic inundation extent maps obtained using both approaches;
- estimation of prediction error bands (uncertainty analysis of a flow routing model);
- derivation of dependence of annual maximum inundation area on the upstream flow;
- dependence of distribution of future annual maximum inundation areas on climate model instabilities.

#### 2.2. Case Study—The Biala Tarnowska Catchment

^{2}, has a forest-covered upper part and a lower part covered mainly by agricultural lands (Figure 1).

^{2}) with 97% classified as forest cover, was modeled by the HBV rainfall–runoff model.

#### 2.3. Routing Model for Biala Tarnowska River

^{®}was applied to optimize six MIKE11 roughness parameters. The Nash–Sutcliff index (NS) was used to describe the goodness of model fit for the observed flows and water levels at the Koszyce Wielkie gauging station. The values of the NS index in Koszyce Wielkie, using flows as a criterion for the calibration and validation periods, were 0.80 and 0.77, respectively, whilst the NS indices for water levels were 0.60 and 0.54, respectively.

#### 2.4. Input—The Hydrological Model for the Ciezkowice Gauging Station

#### 2.5. The Structure of the MIKE11 Emulator

## 3. Results

#### 3.1. Comparison of Deterministic Flood Inundation Maps

#### 3.2. The Uncertainty of Emulator Predictions

#### 3.3. Derivation of Flood Hazard Maps for the Future

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The location of the study catchment; left picture: county scale, whole catchment; right picture: local scale, routing model part.

**Figure 3.**Module of an emulator based on flow–water-level relationship; ${Q}_{1,k}$ denotes flow at the 1st cross section at time $k$, for $k=1,\dots ,T$; ${h}_{n,k}$ denotes water levels at the $n\mathrm{th}$ cross section at time $k$; $b{c}_{1,n}$ denotes the Box–Cox transformation between flow used as an input at the first cross section and the $n\mathrm{th}$ transfer function input ${x}_{n,k}$.

**Figure 4.**The STF-based MIKE11 emulator of water level predictions; on the Biala Tarnowska River—the meander near Tuchow city.

**Figure 5.**The STF-based MIKE11 emulator of water level predictions, validation stage, the Ciezkowice–Koszyce Wielkie model. The black dots denote MIKE11 simulations; the continuous black line denotes the emulator predictions; the red line denotes the observed water levels at the Koszyce Wielkie gauging station; the shaded area denotes 0.96 confidence limits.

**Figure 6.**Dependence on hydrological input (annual maxima) and routing model predictions for the Tuchow meander for the reference period 1971–2010. (

**a**) Water depth values at the 10th cross section of the meander versus the maximum annual flow; (

**b**) inundation areas at the Tuchow meander versus the maximum annual flow; (

**c**) inundation area versus the maximum annual water depth at the 10th cross section of the Tuchow meander. Blue dots denote the data, and green lines denote the fitted curve to the square polynomial.

**Figure 7.**Maximum inundation extent of MIKE11 (blue) and the emulator of MIKE11 (magenta) for the year 1997 for a part of the Tuchow meander, and the CSI-based difference (green).

**Figure 8.**Classification of high water levels at Koszyce Wielkie gauging station for the threshold value equal to the 75th percentile.

**Figure 10.**Empirical cumulative distribution function (cdf) of water levels with 1-in-10 year return period (upper panel) and 1-in-5 year return period (lower panel) obtained for the Monte Carlo (MC) simulations of peak water levels at Koszyce Wielkie (blue lines); red dotted lines show the cdf 0.95 confidence bounds; black stars show the 0.025, 0.5, and 0.975 quantiles water levels with 1-in-10 and 1-in-5 year return periods; the observed water levels corresponding to 1-in-10 and 1-in-5 year return periods are shown by the red lines.

**Figure 11.**Maximum annual inundation from Models 1–7. Median: red lines in the boxes. The bottom and top edges of the blue box indicate the 25th and 75th percentiles, respectively. Maximum and minimum values: dashed black line in each box; red ‘+’: outliers.

**Figure 12.**Return period for 130 annual maxima of inundation area for seven models without a one-grid-storm (‘o’) and with a one-grid-storm (solid line).

**Figure 13.**Annual maximum inundation area over a 100-year return period (marked with a black double arrow) and a 200-year return period (marked with a black double arrow), with instabilities (

**left plot**) and without instabilities (

**right plot**), the 95% and 5% confidence bounds (respectively with the Models, solid colorful lines), and MLE (dashed lines).

HBV Routines | Name of the Parameter | Ciezkowice | Koszyce Wielkie | Unit |
---|---|---|---|---|

soil routine | P.FC | 61.19 | 119.55 | mm |

P.BETA | 1.68 | 2.89 | non | |

P.LP | 1 | 1 | non | |

P.CFLUX | 0.6 | 0.23 | mm/day | |

surface water balance routine | P.ALFA | 0.24 | 0.27 | non |

P.KF | 0.3 | 0.11 | day | |

P.KS | 0.11 | 1.64 | day | |

soil moisture routine | P.PERC | 1.33 | 1.12 | mm/day |

snow routine | O.TT | 1.23 | 1.05 | °C |

O.TTI | 4.93 | 7 | °C | |

O.FOCFMAX/DTTM | 0.01 | 1.36 | °C/mm day | |

O.CFMAX | 1.27 | 1.00 | °C/mm day | |

O.CFR | 0.71 | 0.00 | non | |

O.WHC | 0 | 0 | mm/mm |

Time of Processing | Map Based on MIKE11 Results (s) | Map Based on the Emulator of MIKE11 Results (s) |
---|---|---|

Routing | 19,035 | 147 |

calculating a flooded area and saving the inundation map based on 1 m × 1 m resolution DTM | 990 | 990 |

TOTAL | 20,015 (≈5 h 34 min) | 1137 (≈19 min) |

**Table 3.**Parameter values of the emulator of the MIKE11 Ciezkowice–Koszyce Wielkie model and their uncertainty. Parameters are defined by Equations (1) and (2), where P/R denotes the cross-correlation between P and R.

Parameter [Unit] | Mean | Variance |
---|---|---|

P [-] | 0.8710 | 0.1943 × 10^{−6} |

R [-] | 0.0199 | 0.0045 × 10^{−6} |

P/R [-] | - | 0.029 × 10^{−6} |

δ [h] | 13 | 0 |

c [-] | −0.2740 | 0.03 |

b [-] | 0.5246 | 0.03 |

ε [-] | 0 | 0.008 |

Model Number | GCM | RCM | Full Name | Source Institution |
---|---|---|---|---|

1 | EC-EARTH | RCA | Rossby Center regional | Swedish Meteorological and Hydrological Institute |

2 | EC-EARTH | HIRHAM | Not applicable | Danish Meteorological Institute |

3 | EC-EARTH | CCLM | Community Land Model | Not applicable |

4 | EC-EARTH | RACMO | Regional Atmospheric Climate Model | Not applicable |

5 | MPI | CCLM | Community Land Model | Not applicable |

6 | MPI | REMO | Regional-scale Model | Max Planck Institute for Meteorology |

7 | CNRM | CCLM | Community Land Model | CERFACS, France |

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**MDPI and ACS Style**

Doroszkiewicz, J.; Romanowicz, R.J.; Kiczko, A.
The Influence of Flow Projection Errors on Flood Hazard Estimates in Future Climate Conditions. *Water* **2019**, *11*, 49.
https://doi.org/10.3390/w11010049

**AMA Style**

Doroszkiewicz J, Romanowicz RJ, Kiczko A.
The Influence of Flow Projection Errors on Flood Hazard Estimates in Future Climate Conditions. *Water*. 2019; 11(1):49.
https://doi.org/10.3390/w11010049

**Chicago/Turabian Style**

Doroszkiewicz, Joanna, Renata J. Romanowicz, and Adam Kiczko.
2019. "The Influence of Flow Projection Errors on Flood Hazard Estimates in Future Climate Conditions" *Water* 11, no. 1: 49.
https://doi.org/10.3390/w11010049