Threshold Values of Extreme Hydrometeorological Events on the Polish Baltic Coast
Abstract
:1. Introduction
2. Materials and Methods
- -
- Absolute extreme. The highest or lowest value that has been empirically evidenced for a given meteorological and hydrological event.
- -
- Extreme event. Values close to the absolute extremes for a given meteorological and hydrological event, whose probability of being exceeded is lower than 10%, i.e., the chances of their occurrence (or “return period”) is at most once every ten years. In quantile terms, extreme threshold values were designated using percentiles 5/100 and 95/100.
- -
- Exceptionally extreme event. Values close to the absolute extremes for a given meteorological and hydrological event, whose probability of being exceeded is lower than 1%, i.e., the chances of their occurrence (or “return period”) is at most once every hundred years. In quantile terms, exceptionally extreme threshold values were designated using percentiles 1/100 and 99/100.
3. Results
3.1. Absolute Extreme
3.2. Extreme Events—Probabilistic Analysis
3.3. Extreme Events—Quantile Analysis
4. Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Place | Maximum Air Temperaturę at 2 m AGL | Mean Air Temperaturę at 2 m AGL | Minimum Air Temperaturę at 2 m AGL | Precipitation | Maximum Sea Level | Mean Sea Level | ||
---|---|---|---|---|---|---|---|---|
Max | Max | Min | Min | Max | Max | Max | Min | |
Świnoujście | 37.4 | 27.7 | −16.5 | −22.2 | 76.6 | 661 | 624 | 401 |
Kołobrzeg | 38.0 | 28.1 | −16.5 | −21.9 | 85.2 | 644 | 618 | 401 |
Ustka | 37.8 | 29.8 | −16.1 | −22.2 | 94.2 | 636 | 611 | 428 |
Łeba | 37.2 | 28.4 | −16.5 | −25.0 | 141.0 | - | - | - |
Hel | 33.7 | 26.0 | −14.6 | −18.2 | 77.1 | 620 | 604 | 431 |
Gdynia | 35.0 | 27.2 | −16.0 | −18.7 | 82.1 | - | - | - |
Gdańsk | - | - | - | - | - | 644 | 620 | 436 |
Place | Hydrometeorological Conditions | |||||
---|---|---|---|---|---|---|
Maximum Air | Mean Air | Minimum Air | Precipitation | Maximum | Mean Sea | |
Temperature | Temperature | Temperature | Sea Level | Level | ||
Statistical Distribution | ||||||
Error (Exponential Power) Distribution | Log-Gamma Distribution | Generalized Logistic Distribution | ||||
Świnoujście | k = 3.91 | k = 3.39 | k = 2.42 | α = 70.59 | k = 0.10 | k = 0.05 |
σ= 8.19 | σ= 7.18 | σ = 6.72 | β = 0.048 | σ = 11.55 | σ = 10.78 | |
μ = 11.95 | μ = 8.62 | μ = 5.70 | μ = 506.46 | μ = 499.80 | ||
K − S = 0.021 | K − S = 0.033 | K − S = 0.042 | K − S = 0.108 | K − S = 0.015 | K − S = 0.015 | |
p < 0.001 | p < 0.001 | p < 0.001 | p = 0.590 | p < 0.001 | p < 0.001 | |
Kołobrzeg | k = 3.50 | k = 3.17 | k = 2.30 | α = 127.11 | k = 0.10 | k = 0.06 |
σ = 7.98 | σ = 7.12 | σ = 6.68 | β = 0.028 | σ = 12.01 | σ = 11.06 | |
μ = 11.67 | μ = 8.34 | μ = 5.34 | μ = 507.11 | μ = 500.73 | ||
K − S = 0.025 | K − S = 0.039 | K − S = 0.044 | K − S = 0.123 | K − S = 0.014 | K − S = 0.013 | |
p < 0.001 | p < 0.001 | p < 0.001 | p = 0.429 | p < 0.001 | p < 0.001 | |
Ustka | k = 3.35 | k = 3.14 | k = 2.30 | α = 89.93 | k = 0.09 | k = 0.05 |
σ = 7.97 | σ = 7.08 | σ = 6.75 | β = 0.040 | σ = 11.98 | σ = 11.13 | |
μ = 11.36 | μ = 8.20 | μ = 5.41 | μ = 508.11 | μ = 502.18 | ||
K − S = 0.031 | K − S = 0.036 | K − S = 0.041 | K − S = 0.090 | K − S = 0.017 | K − S = 0.018 | |
p < 0.001 | p < 0.001 | p < 0.001 | p = 0.797 | p < 0.001 | p < 0.001 | |
Łeba | k = 3.74 | k = 3.31 | k = 2.16 | α = 87.05 | - | - |
σ = 8.01 | σ = 7.12 | σ = 6.82 | β = 0.040 | |||
μ = 11.22 | μ = 7.92 | μ = 4.61 | ||||
K − S = 0.031 | K − S = 0.038 | K − S = 0.041 | K − S = 0.101 | |||
p < 0.001 | p < 0.001 | p < 0.001 | p = 0.672 | |||
Hel | k = 5.58 | k = 4.47 | k = 3.12 | α = 72.66 | k = 0.09 | k = 0.042 |
σ = 8.08 | σ = 7.07 | σ = 6.64 | β = 0.049 | σ = 12.15 | σ = 11.15 | |
μ = 11.30 | μ = 8.24 | μ = 5.52 | μ = 508.28 | μ = 503.29 | ||
K − S = 0.027 | K − S = 0.031 | K − S = 0.037 | K − S = 0.066 | K − S = 0.015 | K − S = 0.020 | |
p < 0.001 | p < 0.001 | p < 0.001 | p = 0.975 | p < 0.001 | p < 0.001 | |
Gdynia | k = 4.30 | k = 3.75 | k = 2.87 | α = 83.83 | - | - |
σ = 7.81 | σ = 7.23 | σ = 6.97 | β = 0.041 | |||
μ = 11.28 | μ = 8.51 | μ = 6.00 | ||||
K − S = 0.023 | K − S = 0.031 | K − S = 0.039 | K − S = 0.094 | |||
p < 0.001 | p < 0.001 | p < 0.001 | p = 0.758 | |||
Gdańsk | - | - | - | - | k = 0.07 | k = 0.02 |
σ = 12.17 | σ = 11.64 | |||||
μ = 513.45 | μ = 508.29 | |||||
K − S = 0.018 | K − S = 0.019 | |||||
p < 0.001 | p < 0.001 |
Place | Parameter | P(X) [%] | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
0.1 | 0.2 | 0.5 | 1 | 2 | 5 | 10 | 20 | 500 | 100 | ||
T [Years] | |||||||||||
1000 | 500 | 200 | 100 | 50 | 20 | 10 | 5 | 2 | 1 | ||
Świnoujście | Tmax | 36.7 | 36.2 | 35.6 | 35.0 | 34.5 | 33.7 | 33.1 | 32.4 | 31.3 | 30.5 |
T | 31.9 | 31.5 | 30.8 | 30.2 | 29.6 | 28.8 | 28.2 | 27.4 | 26.4 | 25.5 | |
Tmin | −21.0 | −20.2 | −19.2 | −18.4 | −17.5 | −16.3 | −15.4 | −14.4 | −12.9 | −11.8 | |
P | 117.2 | 105.4 | 90.8 | 80.5 | 70.8 | 58.6 | 49.8 | 41.1 | 29.0 | 1.0 | |
Hmax | 817.0 | 787.6 | 752.0 | 727.0 | 703.9 | 675.8 | 656.3 | 638.1 | 616.0 | 600.6 | |
H | 686.4 | 673.3 | 656.7 | 644.5 | 632.7 | 617.7 | 606.7 | 596.1 | 582.5 | 572.6 | |
Kołobrzeg | Tmax | 37.1 | 36.6 | 35.9 | 35.3 | 34.7 | 33.8 | 33.1 | 32.3 | 31.2 | 30.2 |
T | 32.3 | 31.8 | 31.1 | 30.5 | 29.8 | 29.0 | 28.2 | 27.5 | 26.3 | 25.4 | |
Tmin | −22.1 | −21.3 | −20.2 | −19.4 | −18.5 | −17.2 | −16.2 | −15.1 | −13.6 | −12.3 | |
P | 101.1 | 93.4 | 83.6 | 76.4 | 69.3 | 60.0 | 53.0 | 45.7 | 34.8 | 1.0 | |
Hmax | 820.5 | 791.3 | 755.9 | 731.0 | 707.9 | 679.7 | 660.1 | 641.7 | 619.4 | 603.7 | |
H | 711.3 | 695.4 | 675.5 | 661.0 | 647.2 | 629.7 | 617.0 | 604.9 | 589.6 | 578.6 | |
Ustka | Tmax | 37.4 | 36.9 | 36.1 | 35.5 | 34.8 | 33.9 | 33.2 | 32.3 | 31.2 | 30.2 |
T | 32.2 | 31.6 | 30.9 | 30.3 | 29.7 | 28.8 | 28.0 | 27.3 | 26.1 | 25.2 | |
Tmin | −22.4 | −21.6 | −20.5 | −19.6 | −18.7 | −17.4 | −16.3 | −15.3 | −13.7 | −12.5 | |
P | 129.3 | 117.3 | 102.3 | 91.6 | 81.3 | 68.3 | 58.7 | 49.1 | 35.4 | 1.0 | |
Hmax | 786.0 | 762.0 | 732.5 | 711.5 | 691.8 | 667.4 | 650.2 | 634.0 | 614.0 | 599.8 | |
H | 707.6 | 692.5 | 673.4 | 659.5 | 646.1 | 629.2 | 617.0 | 605.2 | 590.3 | 579.5 | |
Łeba | Tmax | 35.9 | 35.5 | 34.8 | 34.3 | 33.7 | 32.9 | 32.2 | 31.5 | 30.4 | 29.5 |
T | 31.3 | 30.8 | 30.1 | 29.6 | 29.0 | 28.1 | 27.5 | 26.7 | 25.6 | 24.7 | |
Tmin | −24.7 | −23.8 | −22.6 | −21.6 | −20.6 | −19.2 | −18.1 | −16.9 | −15.2 | −13.8 | |
P | 120.3 | 109.2 | 95.2 | 85.3 | 75.7 | 63.6 | 54.7 | 45.8 | 33.1 | 1.0 | |
Hel | Tmax | 32.3 | 32.0 | 31.6 | 31.3 | 30.9 | 30.4 | 30.0 | 29.5 | 28.8 | 28.2 |
T | 28.3 | 28.0 | 27.5 | 27.2 | 26.7 | 26.2 | 25.7 | 25.2 | 24.4 | 23.7 | |
Tmin | −17.1 | −16.5 | −15.8 | −15.3 | −14.7 | −13.8 | −13.1 | −12.4 | −11.3 | −10.5 | |
P | 142.2 | 127.5 | 109.4 | 96.7 | 84.7 | 69.7 | 58.9 | 48.4 | 33.8 | 1.0 | |
Hmax | 801.6 | 775.7 | 743.8 | 721.3 | 700.2 | 674.2 | 656.0 | 638.8 | 617.7 | 602.9 | |
H | 692.3 | 679.3 | 662.7 | 650.5 | 638.6 | 623.5 | 612.5 | 601.7 | 588.0 | 577.9 | |
Gdynia | Tmax | 33.9 | 33.5 | 32.9 | 32.5 | 32.0 | 31.4 | 30.8 | 30.2 | 29.3 | 28.6 |
T | 30.8 | 30.4 | 29.8 | 29.3 | 28.8 | 28.0 | 27.4 | 26.8 | 25.8 | 25.0 | |
Tmin | −18.8 | −18.2 | −17.4 | −16.8 | −16.1 | −15.1 | −14.3 | −13.4 | −12.2 | −11.2 | |
P | 117.1 | 106.1 | 92.4 | 82.6 | 73.3 | 61.5 | 52.8 | 44.1 | 31.8 | 1.0 | |
Gdańsk | Hmax | 767.7 | 747.2 | 721.8 | 703.5 | 686.1 | 664.4 | 648.9 | 634.2 | 615.8 | 602.6 |
H | 678.8 | 668.3 | 654.8 | 644.7 | 634.8 | 621.9 | 612.3 | 602.8 | 590.4 | 581.3 |
Place | Percentile | Maximum Air Temperature at 2 m AGL [°C] | Mean Air Temperature at 2 m AGL [°C] | Minimum Air Temperature at 2 m AGL [°C] | Precipitation [mm] | Maximum Sea Level [cm] | Mean Sea Level [cm] |
---|---|---|---|---|---|---|---|
Świnoujście | 1/100 | −4.6 | −7.7 | −11.2 | 0.1 | 464 | 455 |
5/100 | −0.5 | −2.9 | −5.4 | 0.1 | 478 | 471 | |
95/100 | 24.7 | 19.4 | 15.8 | 12.0 | 548 | 535 | |
99/100 | 29.0 | 22.2 | 18.1 | 22.3 | 576 | 557 | |
Kołobrzeg | 1/100 | −4.6 | −8.2 | −12.0 | 0.1 | 464 | 458 |
5/100 | −0.4 | −3.2 | −6.0 | 0.1 | 478 | 472 | |
95/100 | 24.2 | 18.9 | 15.3 | 13.0 | 550 | 538 | |
99/100 | 28.8 | 21.7 | 17.4 | 26.1 | 577 | 558 | |
Ustka | 1/100 | −4.7 | −8.2 | −11.8 | 0.1 | 465 | 459 |
5/100 | −0.6 | −3.1 | −6.0 | 0.1 | 478 | 473 | |
95/100 | 24.3 | 18.8 | 15.5 | 13.8 | 550 | 539 | |
99/100 | 29.0 | 21.7 | 17.8 | 25.7 | 573 | 558 | |
Łeba | 1/100 | −5.0 | −8.4 | −12.9 | 0.1 | − | − |
5/100 | −0.8 | −3.5 | −6.8 | 0.1 | − | − | |
95/100 | 24.1 | 18.6 | 14.9 | 13.5 | − | − | |
99/100 | 28.5 | 21.5 | 17.3 | 26.2 | − | − | |
Hel | 1/100 | −4.8 | −7.0 | −9.9 | 0.1 | 464 | 460 |
5/100 | −1.0 | −2.8 | −5.0 | 0.1 | 478 | 474 | |
95/100 | 23.8 | 18.9 | 15.6 | 12.2 | 548 | 539 | |
99/100 | 26.9 | 21.3 | 17.9 | 23.6 | 570 | 556 | |
Gdynia | 1/100 | −4.8 | −7.5 | −10.5 | 0.1 | − | − |
5/100 | −0.9 | −3.0 | −5.4 | 0.1 | − | − | |
95/100 | 23.2 | 19.4 | 16.4 | 12.4 | − | − | |
99/100 | 26.7 | 21.9 | 18.9 | 23.4 | − | − | |
Gdańsk | 1/100 | − | − | − | − | 468 | 463 |
5/100 | − | − | − | − | 483 | 478 | |
95/100 | − | − | − | − | 555 | 545 | |
99/100 | − | − | − | − | 578 | 563 |
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Tylkowski, J.; Hojan, M. Threshold Values of Extreme Hydrometeorological Events on the Polish Baltic Coast. Water 2018, 10, 1337. https://doi.org/10.3390/w10101337
Tylkowski J, Hojan M. Threshold Values of Extreme Hydrometeorological Events on the Polish Baltic Coast. Water. 2018; 10(10):1337. https://doi.org/10.3390/w10101337
Chicago/Turabian StyleTylkowski, Jacek, and Marcin Hojan. 2018. "Threshold Values of Extreme Hydrometeorological Events on the Polish Baltic Coast" Water 10, no. 10: 1337. https://doi.org/10.3390/w10101337