Probabilistic Quantification in the Analysis of Flood Risks in Cross-Border Areas of Poland and Germany
Abstract
:1. Introduction
- The course of the river is typical for this part of Europe, it is a flat area, highly urbanized in some parts, with high urbanizing pressure, the area is considered highly vulnerable and exposed to flood risk;
- There is a clear climatic trend observable in the area: occurrence of periodical drought with an increase in the intensity and frequency of heavy rainfall.
2. Materials and Methods
2.1. Theoretical Background
2.2. Method
- corresponds to mean value of distribution,
- corresponds to distribution median,
- is variance.
- (1)
- An observation sample of random variable X with set size N is selected from the studied population. With study conducted by authors, the random variables were daily water levels on the Oder River in three measurement points located at the border between Poland and Germany.
- (2)
- In next step, the selected sample is divided into m blocks (series), with n observations each, i.e., nm = N. The division must be done in such way, so that j block contains consecutive observations for j = 1, …, m. For each of the three locations, the authors of the study selected three five-year periods. The values of maximum daily water levels were selected from 30-day periods. Therefore, each five-year period was composed of m = 60 blocks with n = 30 observations in each block (with 31-day months, one non-maximum observation was rejected).
- (3)
- Maximum observation was determined from each block, as expression of random variable Mn;j, which, according to Formula (2)has the following form:
- distribution of GEV variable,
- length of n block,
- critical water level hcr.
3. Results
- Słubice and Gozdowice: frequency of flood-related socio-economic damage is decreasing over the studied period of 15 years. There are however periods of increased risk. The probability of extreme phenomena is getting lower.
- Widuchowa: measurements and calculations obtained from the measurement point in the location indicate a clear increase in extreme value index in period two and decrease in period three to the level recorded in period one. This means that, based on the value of extreme value index, it is concluded that the frequency of adverse flooding phenomena in this location decreased over a period of fifteen years compared to the beginning of the study period.
4. Discussion
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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1 | Acquiring hydrometrical data from hydrometeorological agencies. |
2 | Determining maximum values for the selected n-element data sub-sets. |
3 | Selecting distribution and estimating its parameters. |
4 | Model quality assessment (compatibility test between theoretical and empirical distribution of hydrometrical data). |
5 | Determining the critical level. |
6 | Estimating the risk level, using probabilistic risk measure. |
7 | Descriptive assessment of risk based on the developed measurement scale. |
City | Period | Expected Value | Median | Standard Deviation | Anderson-Darling test | Kolmogorov-Smirnov Test | |||
---|---|---|---|---|---|---|---|---|---|
GEV Parameters | Statistics of Set | p-Value | |||||||
Slubice/Frankfurt (Oder) | I | −0.049 | 210.86 | 68.02 | 250.12 | 235.79 | 49.21 | 0.965 | 0.969 |
II | −0.145 | 269.39 | 83.78 | 317.75 | 300.10 | 60.61 | 0.739 | 0.492 | |
III | −0.297 | 194.6 | 65.63 | 232.74 | 218.91 | 47.48 | 0.993 | 0.85 | |
Gozdowice | I | −0.075 | 301.25 | 67.36 | 340.13 | 325.94 | 48.73 | 0.766 | 0.723 |
II | −0.138 | 361.94 | 80.48 | 408.39 | 391.44 | 58.22 | 0.732 | 0.547 | |
III | −0.336 | 305.98 | 68.49 | 345.51 | 331.08 | 49.55 | 0.992 | 0.984 | |
Widuchowa | I | −0.004 | 559.84 | 24.13 | 573.77 | 568.68 | 17.46 | 0.990 | 0.997 |
II | 0.195 | 573.58 | 29.62 | 590.68 | 584.44 | 21.43 | 0.907 | 0.75 | |
III | −0.03 | 556.58 | 20.49 | 568.41 | 564.09 | 14.82 | 0.984 | 0.997 |
City | Period | ||
---|---|---|---|
Slubice/Frankfurt (Oder) | I | 0.0415 | 0.0936 |
SAhcr= 410 cm | II | 0.1360 | 0.2654 |
SOhcr= 360 cm | III | 0.000005 | 0.0096 |
Gozdowice | I | 0.0350 | 0.1012 |
SAhcr= 500 cm | II | 0.1317 | 0.2974 |
SOhcr= 440 cm | III | 0.0001 | 0.0404 |
Widuchowa | I | 0.0229 | 0.0523 |
SAhcr= 650 cm | II | 0.1164 | 0.1796 |
SOhcr= 630 cm | III | 0.0074 | 0.0223 |
color scale key: | Very high risk | ||
High risk | |||
Moderate | |||
Low/Insignificant |
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Kuźmiński, Ł.; Nadolny, M.; Wojtaszek, H. Probabilistic Quantification in the Analysis of Flood Risks in Cross-Border Areas of Poland and Germany. Energies 2020, 13, 6020. https://doi.org/10.3390/en13226020
Kuźmiński Ł, Nadolny M, Wojtaszek H. Probabilistic Quantification in the Analysis of Flood Risks in Cross-Border Areas of Poland and Germany. Energies. 2020; 13(22):6020. https://doi.org/10.3390/en13226020
Chicago/Turabian StyleKuźmiński, Łukasz, Michał Nadolny, and Henryk Wojtaszek. 2020. "Probabilistic Quantification in the Analysis of Flood Risks in Cross-Border Areas of Poland and Germany" Energies 13, no. 22: 6020. https://doi.org/10.3390/en13226020