Heavy Rainfall Probabilistic Model for Zielona Góra in Poland
Abstract
:1. Introduction
Class | Description Due to Land Use | Frequency of Design Rainfall Occurrence [1 per C Years] | Probability p [%] | Frequency of Outflow Occurrence [1 per C Years] | Probability p [%] |
---|---|---|---|---|---|
I | Non-urban (rural) areas | 1 per 1 | 1 | 1 per 10 | 10 |
II | Residential areas | 1 per 2 | 50 | 1 per 20 | 5 |
III | City centers and service and industrial areas | 1 per 5 | 20 | 1 per 30 | 3.33 |
IV | Underground communication facilities, passages and crossings under streets, etc. | 1 per 10 | 10 | 1 per 50 | 2 |
2. Materials and Methods
2.1. Heavy Rainfall Records
2.2. Probabilistic Models
- Minutes: 5, 10, 20, 30, 40, and 50;
- Hours: 1, 1.5, 2, 3, 6, 12, and 18;
- Days: 1, 1.5, 2, 3, 4, 5, and 6.
3. Results
3.1. Climatological Background
3.2. Zielona Góra Maximum Precipitation Probabilistic Model
4. Comparison of the Regional Model with the PMAXTP Atlas
5. Discussion
6. Summary and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Distribution (Number of Parameters) | Likelihood Function |
---|---|
Fréchet (3) | |
Gamma (3) | |
GED (3) | |
Gumbel (2) | |
Log-normal (3) | |
Weibull (3) |
Month | Maximum Monthly Rainfall, mm | Minimum Monthly Rainfall, mm | Average Monthly Rainfall, mm |
---|---|---|---|
I | 107.2 | 2.0 | 40.3 |
II | 93.0 | 2.4 | 33.3 |
III | 129.9 | 8.1 | 38.2 |
IV | 81.4 | 1.7 | 37.7 |
V | 132.8 | 8.7 | 55.0 |
VI | 143.5 | 8.5 | 59.4 |
VII | 219.3 | 6.0 | 80.9 |
VIII | 196.4 | 6.9 | 68.4 |
IX | 144.4 | 1.1 | 46.3 |
X | 162.4 | 2.9 | 41.5 |
XI | 123.3 | 0.8 | 41.7 |
XII | 114.8 | 5.0 | 43.9 |
t, min | m = 1 p = 0.020 | m = 5 p = 0.098 | m = 10 p = 0.196 | m = 25 p = 0.490 | m = 50 p = 0.980 |
---|---|---|---|---|---|
mm | mm | mm | mm | mm | |
5 | 13.6 | 10.1 | 8.9 | 7.1 | 5.6 |
10 | 19.2 | 14.4 | 12.3 | 10.5 | 8.5 |
20 | 30.1 | 23.3 | 17.4 | 13.9 | 11.6 |
30 | 37.9 | 25.2 | 19.6 | 15.6 | 12.5 |
40 | 39.9 | 27.7 | 22.0 | 16.5 | 13.3 |
50 | 40.6 | 27.7 | 22.7 | 17.6 | 13.9 |
60 | 41.8 | 33.0 | 26.3 | 18.5 | 14.8 |
90 | 45.1 | 38.0 | 26.3 | 19.8 | 16.3 |
120 | 45.9 | 38.0 | 28.1 | 22.4 | 17.8 |
180 | 51.9 | 38.9 | 33.4 | 24.7 | 19.2 |
360 | 55.0 | 43.8 | 37.7 | 27.6 | 23.1 |
720 | 56.9 | 49.7 | 41.1 | 35.7 | 28.1 |
1080 | 73.6 | 55.7 | 49.3 | 39.7 | 30.9 |
1440 | 89.1 | 60.6 | 55.0 | 41.1 | 32.3 |
2160 | 96.0 | 68.8 | 61.0 | 46.6 | 36.9 |
2880 | 103.5 | 72.1 | 63.3 | 51.6 | 39.2 |
4320 | 109.6 | 77.1 | 68.0 | 57.0 | 44.1 |
t, min | GED | Weibull | LogN | Fréchet | Gumbel | Gamma | |
---|---|---|---|---|---|---|---|
5 | α | 1.2073 | 1.2218 | 0.8047 | 1.1158 | 2.8022 | 1.1974 |
β | 0.5373 | 6.9021 | 0.5524 | 2.1726 | 2.8019 | 1.7482 | |
γ | 5.588 | 5.336 | 5.593 | 3.887 | 5.589 | ||
10 | α | 0.934 | 1.4506 | 0.7255 | 1.1155 | 3.6127 | 1.1751 |
β | 0.3835 | 10.0798 | 0.8429 | 2.6083 | 4.5195 | 2.1422 | |
γ | 8.499 | 8.014 | 8.485 | 5.357 | 8.479 | ||
20 | α | 0.8478 | 2.4935 | 1.0529 | 0.898 | 1.5692 | 0.8506 |
β | 0.2291 | 13.7787 | 0.8868 | 3.71 | 2.4516 | 4.5979 | |
γ | 11.599 | 11.432 | 11.599 | 10.667 | 11.599 | ||
30 | α | 0.828 | 3.0051 | 1.0079 | 0.8971 | 1.9607 | 0.8329 |
β | 0.1833 | 15.2481 | 1.1671 | 4.5722 | 4.179 | 5.7783 | |
γ | 12.499 | 12.172 | 12.499 | 10.378 | 12.499 | ||
40 | α | 0.6898 | 3.4532 | 1.0405 | 0.8176 | 1.8469 | 0.6995 |
β | 0.1445 | 16.3324 | 1.2689 | 4.8956 | 4.4391 | 7.7066 | |
γ | 13.299 | 12.897 | 13.299 | 11.065 | 13.299 | ||
50 | α | 0.6259 | 3.8474 | 1.0765 | 0.7734 | 1.6968 | 0.6359 |
β | 0.1232 | 17.209 | 1.3334 | 5.2324 | 4.4171 | 9.302 | |
γ | 13.899 | 13.497 | 13.899 | 11.805 | 13.899 | ||
60 | α | 0.7971 | 4.0984 | 1.1353 | 0.8748 | 1.379 | 0.8045 |
β | 0.1373 | 18.2752 | 1.3024 | 5.8697 | 3.4332 | 7.7877 | |
γ | 14.799 | 14.594 | 14.799 | 13.63 | 14.799 | ||
90 | α | 0.508 | 4.302 | 1.3958 | 0.6597 | 1.2201 | 0.516 |
β | 0.1005 | 19.5611 | 1.1018 | 4.9403 | 2.9965 | 12.0712 | |
γ | 16.299 | 16.131 | 16.299 | 15.181 | 16.299 | ||
120 | α | 0.678 | 4.441 | 1.1378 | 0.8105 | 1.5574 | 0.6887 |
β | 0.1142 | 21.5927 | 1.4142 | 6.117 | 4.5909 | 9.8078 | |
γ | 17.799 | 17.454 | 17.799 | 15.775 | 17.799 | ||
180 | α | 0.7391 | 4.871 | 1.1002 | 0.8511 | 1.7216 | 0.7496 |
β | 0.1092 | 23.4419 | 1.5583 | 6.947 | 5.8069 | 9.991 | |
γ | 19.199 | 18.754 | 19.199 | 16.39 | 19.199 | ||
360 | α | 0.7853 | 4.8504 | 0.981 | 0.884 | 1.9674 | 0.7949 |
β | 0.1106 | 27.5004 | 1.6845 | 7.2844 | 6.8062 | 9.6907 | |
γ | 23.099 | 22.438 | 23.099 | 19.605 | 23.099 | ||
720 | α | 0.9482 | 5.1145 | 0.7429 | 1.0834 | 3.5905 | 0.9625 |
β | 0.1116 | 33.5368 | 2.0793 | 8.9322 | 15.8564 | 9.0007 | |
γ | 28.099 | 26.407 | 28.079 | 16.966 | 28.099 | ||
1080 | α | 1.2541 | 6.1379 | 0.6378 | 1.1797 | 4.9274 | 1.2749 |
β | 0.1061 | 37.7856 | 2.426 | 11.3887 | 27.3413 | 8.5104 | |
γ | 30.752 | 27.841 | 30.783 | 9.801 | 30.732 | ||
1440 | α | 1.1821 | 7.0333 | 0.7759 | 1.1033 | 3.0399 | 1.1734 |
β | 0.0916 | 39.8475 | 2.3453 | 12.5417 | 17.7746 | 10.3342 | |
γ | 32.239 | 30.489 | 32.266 | 20.934 | 32.242 | ||
2160 | α | 0.7879 | 8.751 | 1.0153 | 0.8997 | 1.9386 | 0.8 |
β | 0.0625 | 44.9462 | 2.2479 | 13.0911 | 12.4994 | 17.1124 | |
γ | 36.899 | 35.843 | 36.899 | 30.372 | 36.899 | ||
2880 | α | 0.8456 | 9.5142 | 0.8784 | 0.9531 | 3.0244 | 0.859 |
β | 0.0585 | 48.5409 | 2.5137 | 15.0585 | 24.0482 | 17.8585 | |
γ | 39.199 | 37.16 | 39.199 | 22.938 | 39.199 | ||
4320 | α | 0.9199 | 9.0368 | 0.694 | 1.0791 | 3.8322 | 0.9335 |
β | 0.0606 | 53.9953 | 2.7247 | 16.1135 | 30.142 | 16.7588 | |
γ | 44.099 | 40.491 | 44.06 | 22.648 | 44.099 |
t, min | Fréchet | Gamma | GED | Gumbel | Log-Normal | Weibull |
---|---|---|---|---|---|---|
5 | 0.287 | 0.114 | 0.115 | 0.695 | 0.201 | 0.120 |
10 | 0.398 | 0.383 | 0.951 | 0.592 | 0.350 | 0.368 |
20 | 0.254 | 0.503 | 0.514 | 2.169 | 0.207 | 0.458 |
30 | 0.308 | 0.423 | 0.427 | 1.524 | 0.313 | 0.401 |
40 | 0.207 | 0.541 | 0.538 | 1.448 | 0.206 | 0.525 |
50 | 0.293 | 0.835 | 0.828 | 1.601 | 0.243 | 0.845 |
60 | 0.431 | 0.352 | 0.359 | 2.032 | 0.272 | 0.319 |
90 | 0.541 | 0.759 | 0.743 | 2.113 | 0.537 | 0.964 |
120 | 0.426 | 0.392 | 0.392 | 1.573 | 0.320 | 0.388 |
180 | 0.422 | 0.285 | 0.285 | 1.556 | 0.383 | 0.291 |
360 | 0.392 | 0.688 | 0.693 | 2.182 | 0.444 | 0.660 |
720 | 0.344 | 0.587 | 0.611 | 0.631 | 0.318 | 0.315 |
1080 | 0.239 | 0.314 | 0.699 | 0.445 | 0.213 | 0.275 |
1440 | 0.284 | 0.266 | 0.268 | 0.861 | 0.258 | 0.273 |
2160 | 0.514 | 0.292 | 0.295 | 1.101 | 0.406 | 0.272 |
2880 | 0.545 | 0.508 | 0.515 | 0.628 | 0.575 | 0.449 |
4320 | 0.287 | 0.959 | 0.985 | 0.579 | 0.279 | 0.521 |
A2crit | 0.757 | 0.762 | 0.723 | 0.757 | 0.752 | 0.757 |
t, min | Fréchet | Gamma | GED | Log-Normal | Weibull |
---|---|---|---|---|---|
5 | 203.02 | 199.40 | 199.36 | 201.54 | 199.38 |
10 | 240.50 | 228.44 | 228.28 | 237.28 | 229.66 |
20 | 276.14 | 251.04 | 250.58 | 271.24 | 255.42 |
30 | 287.38 | 272.58 | 272.34 | 282.98 | 274.20 |
40 | 299.92 | 289.36 | 289.24 | 296.18 | 289.86 |
50 | 303.58 | 295.20 | 295.14 | 300.38 | 295.38 |
60 | 309.08 | 303.02 | 303.00 | 307.08 | 302.60 |
90 | 312.30 | 303.32 | 303.16 | 309.62 | 304.38 |
120 | 312.44 | 306.56 | 306.50 | 309.80 | 306.80 |
180 | 327.50 | 316.30 | 316.20 | 323.58 | 316.88 |
360 | 339.42 | 329.12 | 329.00 | 351.54 | 329.68 |
720 | 348.72 | 340.70 | 340.62 | 361.34 | 341.20 |
1080 | 355.64 | 346.66 | 346.58 | 367.32 | 346.98 |
1440 | 375.40 | 368.20 | 368.08 | 373.66 | 368.52 |
2160 | 390.50 | 378.82 | 378.70 | 386.38 | 379.60 |
2880 | 404.30 | 393.42 | 393.30 | 400.72 | 394.20 |
4320 | 433.02 | 404.46 | 404.46 | 410.28 | 8.4031 |
t, min | Gamma | GED | Weibull |
---|---|---|---|
5 | 1.87 | 1.83 | 2.00 |
10 | 2.41 | 2.88 | 2.50 |
20 | 3.94 | 4.01 | 3.67 |
30 | 4.23 | 4.30 | 4.00 |
40 | 3.02 | 3.11 | 2.63 |
50 | 3.44 | 3.45 | 3.36 |
60 | 3.69 | 3.72 | 3.60 |
90 | 3.61 | 3.56 | 4.47 |
120 | 2.96 | 2.93 | 3.10 |
180 | 3.02 | 3.02 | 3.03 |
360 | 3.86 | 3.87 | 3.83 |
720 | 2.89 | 2.93 | 2.50 |
1080 | 2.26 | 2.34 | 2.23 |
1440 | 3.25 | 3.24 | 3.30 |
2160 | 2.39 | 2.38 | 2.34 |
2880 | 3.33 | 3.35 | 3.02 |
4320 | 3.50 | 3.55 | 3.11 |
t, min | α | λ | γ |
---|---|---|---|
5 | 0.947 | 0.2766 | 4.59 |
10 | 0.2766 | 8.29 | |
20 | 0.1980 | 11.29 | |
30 | 0.1753 | 12.49 | |
40 | 0.1531 | 12.99 | |
50 | 0.1454 | 13.69 | |
60 | 0.1454 | 13.69 | |
90 | 0.1323 | 16.49 | |
120 | 0.1294 | 18.19 | |
180 | 0.1165 | 19.99 | |
360 | 0.1036 | 23.89 | |
720 | 0.0924 | 28.59 | |
1080 | 0.0872 | 32.39 | |
1440 | 0.0746 | 35.69 | |
2160 | 0.0628 | 38.69 | |
2880 | 0.0491 | 41.29 | |
4320 | 0.0447 | 41.29 |
t, Duration | Probability of Occurrence, p | |||||||
---|---|---|---|---|---|---|---|---|
1% | 2% | 5% | 10% | 20% | 33% | 50% | 99.9% | |
5 | 19.14 | 17.29 | 14.94 | 13.25 | 11.60 | 10.45 | 9.44 | 7.35 |
10 | 22.99 | 20.80 | 18.01 | 15.97 | 13.98 | 12.57 | 11.34 | 8.78 |
15 | 25.59 | 23.17 | 20.08 | 17.82 | 15.59 | 14.01 | 12.62 | 9.75 |
30 | 30.73 | 27.87 | 24.20 | 21.48 | 18.79 | 16.87 | 15.17 | 11.65 |
45 | 34.20 | 31.06 | 26.99 | 23.97 | 20.96 | 18.80 | 16.88 | 12.93 |
60 | 36.90 | 33.53 | 29.17 | 25.90 | 22.64 | 20.30 | 18.22 | 13.93 |
90 | 41.07 | 37.36 | 32.53 | 28.90 | 25.26 | 22.62 | 20.28 | 15.46 |
120 | 44.32 | 40.34 | 35.15 | 31.23 | 27.29 | 24.43 | 21.89 | 16.65 |
180 | 49.32 | 44.95 | 39.20 | 34.84 | 30.44 | 27.23 | 24.37 | 18.48 |
360 | 59.23 | 54.07 | 47.24 | 42.01 | 36.68 | 32.78 | 29.27 | 22.09 |
720 | 71.13 | 65.05 | 56.92 | 50.65 | 44.21 | 39.45 | 35.16 | 26.40 |
1080 | 79.17 | 72.48 | 63.48 | 56.51 | 49.30 | 43.97 | 39.15 | 29.30 |
1440 | 85.42 | 78.26 | 68.59 | 61.07 | 53.27 | 47.48 | 42.24 | 31.55 |
2160 | 95.07 | 87.20 | 76.50 | 68.13 | 59.42 | 52.92 | 47.03 | 35.02 |
2880 | 102.58 | 94.15 | 82.66 | 73.63 | 64.20 | 57.15 | 50.75 | 37.71 |
4320 | 114.17 | 104.90 | 92.19 | 82.14 | 71.61 | 63.70 | 56.49 | 41.86 |
t, Duration | Probability of Occurrence, p | |||||||
---|---|---|---|---|---|---|---|---|
1% | 2% | 5% | 10% | 20% | 33% | 50% | 99.9% | |
5 | −0.84 | −0.69 | −0.83 | −0.54 | −0.55 | −0.60 | −0.74 | −0.25 |
10 | −0.79 | −0.60 | −0.85 | −0.61 | −0.57 | −0.68 | −0.74 | −0.18 |
15 | −0.69 | −0.57 | −0.89 | −0.58 | −0.62 | −0.69 | −0.82 | −0.05 |
30 | −0.53 | −0.47 | −0.94 | −0.60 | −0.68 | −0.79 | −0.87 | 0.05 |
45 | −0.40 | −0.46 | −0.95 | −0.49 | −0.67 | −0.86 | −0.88 | 0.07 |
60 | −0.30 | −0.33 | −0.89 | −0.47 | −0.70 | −0.84 | −0.92 | 0.17 |
90 | −0.07 | −0.26 | −0.82 | −0.43 | −0.70 | −0.86 | −0.88 | 0.34 |
120 | 0.08 | −0.14 | −0.84 | −0.45 | −0.63 | −0.89 | −0.89 | 0.45 |
180 | 0.38 | 0.05 | −0.70 | −0.30 | −0.64 | −0.84 | −0.87 | 0.62 |
360 | 1.07 | 0.53 | −0.55 | −0.14 | −0.61 | −0.88 | −0.87 | 1.01 |
720 | 1.97 | 1.15 | −0.27 | 0.18 | −0.45 | −0.81 | −0.76 | 1.50 |
1080 | 2.63 | 1.62 | −0.03 | 0.42 | −0.31 | −0.80 | −0.75 | 1.90 |
1440 | 3.28 | 2.04 | 0.18 | 0.61 | −0.17 | −0.77 | −0.64 | 2.15 |
2160 | 4.23 | 2.70 | 0.59 | 1.00 | −0.03 | −0.72 | −0.53 | 2.68 |
2880 | 4.92 | 3.25 | 0.88 | 1.24 | 0.07 | −0.60 | −0.45 | 3.09 |
4320 | 6.23 | 4.10 | 1.35 | 1.71 | 0.36 | −0.41 | −0.19 | 3.74 |
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Wdowikowski, M.; Nowakowska, M.; Bełcik, M.; Galiniak, G. Heavy Rainfall Probabilistic Model for Zielona Góra in Poland. Water 2025, 17, 1673. https://doi.org/10.3390/w17111673
Wdowikowski M, Nowakowska M, Bełcik M, Galiniak G. Heavy Rainfall Probabilistic Model for Zielona Góra in Poland. Water. 2025; 17(11):1673. https://doi.org/10.3390/w17111673
Chicago/Turabian StyleWdowikowski, Marcin, Monika Nowakowska, Maciej Bełcik, and Grzegorz Galiniak. 2025. "Heavy Rainfall Probabilistic Model for Zielona Góra in Poland" Water 17, no. 11: 1673. https://doi.org/10.3390/w17111673
APA StyleWdowikowski, M., Nowakowska, M., Bełcik, M., & Galiniak, G. (2025). Heavy Rainfall Probabilistic Model for Zielona Góra in Poland. Water, 17(11), 1673. https://doi.org/10.3390/w17111673