Predicting Flood Frequency with the LH-Moments Method: A Case Study of Prigor River, Romania
Abstract
:1. Introduction
2. Methods
2.1. Probability Distributions
2.2. Parameter Estimation
2.2.1. Pearson V (PV)
- if :
- if :
2.2.2. CHI
- if :
- if :
2.2.3. Inverse CHI (ICH)
- if :
- if :
2.2.4. Wilson–Hilferty (WH)
- if :
- if :
2.2.5. Pseudo-Weibull (PW)
2.2.6. Log-Normal (LN3)
2.2.7. Generalized Pareto Type I (PGI)
2.2.8. Fréchet (FR)
- if :
- if :
3. Case Study
4. Results
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
MOM | the method of ordinary moments |
L-moments | the method of linear moments |
LH-moments | the method of higher-order linear moments |
linear moments | |
higher-order linear moments | |
coefficient of variation based on the L-moments method | |
coefficient of skewness based on the L-moments method | |
coefficient of kurtosis based on the L-moments method | |
coefficient of variation based on the LH-moments method | |
coefficient of skewness based on the LH-moments method | |
coefficient of kurtosis based on the LH-moments method | |
PV | Pearson V distribution |
CHI | CHI distribution |
ICH | inverse CHI distribution |
WH | Wilson–Hilferty distribution |
PW | Pseudo-Weibull distribution |
LN3 | three-parameter Log-normal distribution |
GPI | generalized Pareto Type I distribution |
FR | three-parameter Fréchet distribution |
Appendix A. Parameter Estimation Using the Second-Order LH-Moments
- if :
- if :
Appendix B. The Frequency Factors for the Analyzed Distributions
Distr. | ||
---|---|---|
Quantile Function (Inverse Function) | ||
LH-Moments (First Order) | LH-Moments (Second Order) | |
PV | the expressions for and are explained in Section 2.2.1 | the expressions for and are explained in Appendix A |
CHI | the expressions for and are explained in Section 2.2.4 | the expressions for and are explained in Appendix A |
ICH | the expressions for and are explained in Section 2.2.3 | the expressions for and are explained in Appendix A |
WH | the expressions for and are explained in Section 2.2.4 | the expressions for and are explained in Appendix A |
PW | the expressions for and are explained in Section 2.2.5 | the expressions for and are explained in Appendix A |
LN3 | the expressions for and are explained in Section 2.2.6 | the expressions for and are explained in Appendix A |
PGI | ||
FR |
Appendix C. The First-Order LH-Moments Diagram
Appendix D. The Second-Order LH-Moments Diagram
Appendix E. Estimation of the Frequency Factor for the PV Distribution
P (%) | a | b | c | d | e | f | g | h |
---|---|---|---|---|---|---|---|---|
0.01 | 11.25716 | −131.20350 | 1949.68567 | −11,151.25939 | 37,380.04905 | −68,646.56566 | 70,412.75359 | −29,839.17905 |
0.1 | 5.95329 | 5.28685 | 105.58814 | −116.64929 | −37.55278 | 1085.44951 | −1235.53789 | 185.05204 |
0.5 | 5.20696 | −6.34402 | 171.13982 | −663.09642 | 1552.89993 | −1826.49212 | 975.79402 | −210.37970 |
1 | 4.67849 | −6.34289 | 145.23208 | −593.97206 | 1402.57612 | −1769.23389 | 1073.27459 | −257.35685 |
2 | 4.09166 | −5.72542 | 113.45047 | −479.90312 | 1119.04640 | −1438.61769 | 917.93954 | −231.36365 |
3 | 3.72488 | −5.34813 | 95.45312 | −411.10312 | 948.26394 | −1217.30511 | 786.82014 | −201.56570 |
5 | 3.23329 | −4.91688 | 74.39560 | −328.29622 | 747.90220 | −951.38916 | 618.18166 | −160.15142 |
10 | 2.49248 | −4.33153 | 48.49037 | −222.21910 | 502.38567 | −628.82146 | 406.76300 | −105.78320 |
20 | 1.61367 | −3.50095 | 24.39044 | −116.57543 | 265.83072 | −329.17366 | 211.21241 | −54.80899 |
40 | 0.46069 | −1.90237 | 0.28296 | −2.20461 | 6.47671 | −7.31658 | 4.39076 | −1.18922 |
50 | −0.02947 | −1.00147 | −8.04637 | 38.61740 | −88.73004 | 111.53103 | −71.90978 | 18.57044 |
80 | −1.63651 | 3.08779 | −30.87890 | 144.26162 | −339.62037 | 429.40736 | −277.82412 | 72.21398 |
90 | −2.46681 | 5.99191 | −42.14745 | 187.59670 | −439.64825 | 556.34369 | −360.55393 | 93.89877 |
P (%) | a | b | c | d | e | f | g | h |
---|---|---|---|---|---|---|---|---|
0.01 | 81.910475 | −1771.514355 | 16,819.397533 | −82,805.460187 | 235,276.652260 | −386,190.499025 | 346,280.769342 | −130,055.21879 |
0.1 | 2.228731 | 59.123754 | −391.394621 | 1911.377627 | −4602.449696 | 6513.540173 | −4024.546602 | 352.304188 |
0.5 | 3.512205 | 12.804180 | −28.860341 | 198.686814 | −458.874164 | 782.400511 | −811.234773 | 272.458238 |
1 | 3.314992 | 7.768633 | −2.463356 | 39.354768 | −38.467754 | 15.733888 | −88.865312 | 49.856120 |
2 | 2.925506 | 5.809312 | −5.173311 | 30.048369 | −37.998837 | −28.905010 | 31.467196 | −5.026159 |
3 | 2.655839 | 4.814207 | −8.278126 | 36.412452 | −73.682802 | 34.281005 | 1.400566 | −2.325368 |
5 | 2.277429 | 3.322797 | −9.645991 | 35.521977 | −91.128870 | 89.977174 | −41.449511 | 8.012619 |
10 | 1.656367 | 1.012819 | −7.248799 | 18.654250 | −56.540573 | 76.866583 | −48.609237 | 12.214375 |
20 | 0.806822 | −1.031876 | −3.526086 | 2.999739 | −6.727668 | 15.136075 | −13.329765 | 4.178605 |
40 | −0.520195 | −2.007167 | 0.079953 | 0.896835 | 5.241720 | −10.751092 | 7.944665 | −2.160109 |
50 | −1.161667 | −1.793933 | 1.853417 | −0.018740 | 3.201880 | −8.323464 | 7.222178 | −2.214021 |
80 | −3.651550 | 2.664287 | 5.060010 | −17.180213 | 27.188778 | −26.520914 | 14.982105 | −3.714598 |
90 | −5.224593 | 8.397516 | −2.422149 | −17.374685 | 41.178694 | −46.186319 | 27.185834 | −6.714774 |
Appendix F. Estimation of the Frequency Factor for the ICH Distribution
P (%) | a | b | c | d |
---|---|---|---|---|
0.01 | 6.52997 | 26.82067 | 14.85657 | 464.96943 |
0.1 | 5.44941 | 17.20176 | 11.39250 | 177.19999 |
0.5 | 4.55112 | 11.16190 | 4.43462 | 72.13282 |
1 | 4.11304 | 8.70764 | 1.40446 | 44.77481 |
2 | 3.63324 | 6.34343 | −1.21804 | 25.78376 |
3 | 3.32837 | 5.00664 | −2.44115 | 17.89105 |
5 | 2.91207 | 3.38007 | −3.53519 | 10.69300 |
10 | 2.27033 | 1.30825 | −3.99266 | 4.64115 |
20 | 1.49234 | −0.51235 | −2.92430 | 1.11878 |
40 | 0.45076 | −1.78115 | 0.04530 | −2.15319 |
50 | 0.00178 | −1.91764 | 1.40809 | −3.60146 |
80 | −1.49132 | −0.60439 | 3.68532 | −7.00379 |
90 | −2.27256 | 1.15360 | 2.18165 | −5.73713 |
P (%) | a | b | c | d | e | f | g | h |
---|---|---|---|---|---|---|---|---|
0.01 | 79.883758 | −1679.417954 | 15,661.299605 | −76,196.141845 | 215,236.713 | −351,779.05466 | 315,145.61355 | −118,719.36587 |
0.1 | 2.439485 | 54.257459 | −349.512901 | 1696.329214 | −3847.028237 | 5154.772004 | −2931.225766 | 45.180979 |
0.5 | 3.640380 | 11.167621 | −27.074245 | 238.032175 | −608.858332 | 991.975375 | −943.188586 | 306.114622 |
1 | 3.513630 | 4.477591 | 14.966696 | 9.106453 | −49.568623 | 100.765426 | −176.345385 | 79.786789 |
2 | 3.146844 | 1.734343 | 22.157049 | −55.650510 | 94.739536 | −129.454331 | 62.029820 | −5.334231 |
3 | 2.864035 | 0.848887 | 20.078952 | −62.468499 | 105.677263 | −139.464427 | 86.184870 | −18.314985 |
5 | 2.447099 | 0.004927 | 15.332281 | −58.814530 | 98.385355 | −117.730239 | 76.491903 | −19.179270 |
10 | 1.753158 | −0.896712 | 7.695230 | −41.884058 | 75.958313 | −82.338902 | 50.779609 | −13.064095 |
20 | 0.834726 | −1.534456 | 0.288985 | −13.264633 | 32.253908 | −36.485557 | 21.964914 | −5.564021 |
40 | −0.531047 | −1.730709 | −2.509832 | 12.719488 | −22.304466 | 23.482121 | −13.881077 | 3.482139 |
50 | −1.176148 | −1.474153 | −0.968034 | 12.970906 | −28.143980 | 32.298762 | −19.777144 | 5.041014 |
80 | −3.667051 | 2.829186 | 4.750684 | −19.036152 | 35.510723 | −39.892243 | 24.957853 | −6.634231 |
90 | −5.248541 | 8.651554 | −2.624214 | −24.417599 | 70.138835 | −93.925739 | 63.986862 | −17.749432 |
Appendix G. Estimation of the Frequency Factor for the LN3 Distribution
P (%) | a | b | c | d | e | f | g | h | i |
---|---|---|---|---|---|---|---|---|---|
0.01 | 7.34577 | −11.93543 | 716.47126 | −4366.76433 | 13,233.45376 | −17,502.29426 | 9087.37090 | 0.13890 | −0.31483 |
0.1 | −182.8854 | 80,948.57367 | 69,705.91443 | 29,162.82665 | −47,509.61155 | −40,863.74927 | −86,394.5813 | 13,007.97382 | −22,817.9312 |
0.5 | 4.46079 | 768.03648 | 392.38804 | 2614.73022 | −5453.94909 | 4471.71101 | −2769.46863 | 161.69088 | −188.52368 |
1 | 5.05392 | 3381.94490 | 4190.83018 | 1683.11151 | −4342.06310 | −1032.28092 | −3834.14862 | 828.61007 | −638.47665 |
2 | 3.72540 | 559.11509 | 678.67334 | 283.47264 | −1231.65344 | 218.68686 | −530.59615 | 152.94462 | −60.42997 |
3 | 3.34676 | 268.95983 | 249.09931 | 62.99081 | −578.86038 | 94.48113 | −119.72659 | 79.34274 | −32.25046 |
5 | 2.90555 | 3.51178 | −4.44349 | 21.53572 | −56.29603 | 59.07715 | −27.31915 | −0.00055 | 0.00201 |
10 | 2.27392 | 10.31129 | 0.12209 | −25.46670 | 15.97668 | −30.11238 | 26.69439 | 4.08106 | −2.17704 |
20 | 1.47852 | 1457.8469 | −918.40881 | −2278.41631 | −529.77821 | 2130.23329 | −102.47085 | 977.02214 | −257.24175 |
40 | 0.44943 | −1.71341 | −0.58245 | −0.17569 | 2.15788 | −1.99608 | 0.85851 | − | − |
50 | −0.00005 | −1.81172 | −0.02237 | 0.94326 | −0.20718 | 0.17417 | −0.07598 | − | − |
80 | −1.49191 | −0.52177 | 1.78568 | −0.41759 | −0.93231 | 0.93656 | −0.35804 | − | − |
90 | −2.27165 | 1.17186 | 1.28540 | −1.61220 | 0.18629 | 0.49903 | −0.25817 | − | − |
P (%) | a | b | c | d |
---|---|---|---|---|
0.01 | 20.4560566 | 0.0157214 | 7.6751191 | 0.1690430 |
0.1 | 19.9223136 | 0.0157565 | 7.7306869 | 0.1694185 |
0.5 | 19.4863608 | 0.0157853 | 7.7760593 | 0.1697253 |
1 | 19.2751529 | 0.0157992 | 7.7980364 | 0.1698740 |
2 | 19.0445424 | 0.0158144 | 7.8220289 | 0.1700363 |
3 | 18.8983187 | 0.0158240 | 7.8372399 | 0.1701393 |
5 | 18.6989591 | 0.0158372 | 7.8579761 | 0.1702796 |
10 | 18.3922410 | 0.0158574 | 7.8898737 | 0.1704956 |
20 | 18.0212465 | 0.0158819 | 7.9284472 | 0.1707569 |
40 | 17.5258663 | 0.0159145 | 7.9799386 | 0.1711059 |
50 | 17.3127762 | 0.0159286 | 8.0020827 | 0.1712560 |
80 | 16.6059721 | 0.0159752 | 8.0755103 | 0.1717541 |
90 | 16.2371749 | 0.0159996 | 8.1138096 | 0.1720141 |
Appendix H. Estimation of the Frequency Factor for the FR Distribution
P (%) | a | b | c | d | e | f | g | h |
---|---|---|---|---|---|---|---|---|
0.01 | 4.79878 | −4.79613 | −6.32125 | 17.28586 | −25.92369 | 22.32216 | −10.40520 | 2.04267 |
0.1 | 4.60163 | −4.60769 | −4.90472 | 10.51612 | −12.27707 | 7.99307 | −2.64179 | 0.31910 |
0.5 | 4.22930 | −4.25399 | −3.71518 | 5.66451 | −3.27906 | −1.32316 | 2.62737 | −0.95280 |
1 | 3.91982 | −3.96379 | −3.31247 | 4.71382 | −2.66524 | −0.95161 | 1.98933 | −0.73158 |
2 | 3.54772 | −3.62982 | −2.86477 | 3.75946 | −2.06788 | −0.65905 | 1.46457 | −0.55126 |
3 | 3.29251 | −3.41148 | −2.58280 | 3.23198 | −1.80321 | −0.41053 | 1.11661 | −0.43379 |
5 | 2.92396 | −3.11434 | −2.19334 | 2.52840 | −1.27243 | −0.51770 | 1.05146 | −0.40659 |
10 | 2.31559 | −2.67844 | −1.61581 | 1.72570 | −0.89911 | −0.20951 | 0.61552 | −0.25426 |
20 | 1.53537 | −2.24054 | −0.93998 | 1.02318 | −0.49957 | −0.06099 | 0.30917 | −0.12674 |
40 | 0.45853 | −1.89670 | −0.07881 | 0.41672 | 0.13819 | −0.05952 | −0.06296 | 0.08501 |
50 | −0.00696 | −1.84955 | 0.26139 | 0.40009 | 0.16243 | 0.00554 | −0.01990 | 0.04712 |
80 | −1.52193 | 0.01607 | −0.14440 | 0.92152 | −0.44753 | 0.00190 | 0.33891 | −0.16508 |
90 | −2.28341 | 1.29295 | 0.04646 | 0.24771 | −0.28723 | −0.06346 | 0.06346 | −0.05894 |
P (%) | a | b | c | d |
---|---|---|---|---|
0.01 | 20.4560566 | 0.0157214 | 7.6751191 | 0.1690430 |
0.1 | 19.9223136 | 0.0157565 | 7.7306869 | 0.1694185 |
0.5 | 19.4863608 | 0.0157853 | 7.7760593 | 0.1697253 |
1 | 19.2751529 | 0.0157992 | 7.7980364 | 0.1698740 |
2 | 19.0445424 | 0.0158144 | 7.8220289 | 0.1700363 |
3 | 18.8983187 | 0.0158240 | 7.8372399 | 0.1701393 |
5 | 18.6989591 | 0.0158372 | 7.8579761 | 0.1702796 |
10 | 18.3922410 | 0.0158574 | 7.8898737 | 0.1704956 |
20 | 18.0212465 | 0.0158819 | 7.9284472 | 0.1707569 |
40 | 17.5258663 | 0.0159145 | 7.9799386 | 0.1711059 |
50 | 17.3127762 | 0.0159286 | 8.0020827 | 0.1712560 |
80 | 16.6059721 | 0.0159752 | 8.0755103 | 0.1717541 |
90 | 16.2371749 | 0.0159996 | 8.1138096 | 0.1720141 |
Appendix I. The Probability Density Functions and Complementary Cumulative Distribution Function
Distribution | ||
---|---|---|
PV | ||
CHI | ||
ICH | ||
WH | ||
PW | ||
LN3 | ||
GPI | ||
FR |
Appendix J. The Confidence Intervals of the Analysed Distributions
Appendix K. Built-In Function in Mathcad
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New Elements | Method of Parameter Estimation |
---|---|
LH−Moments | |
Exact parameter estimation | PV, CHI, ICH, WH, PW, PGI, FR |
Approximate estimation of parameters | PV, CHI, ICH, WH, PW, PGI, FR, LN3 |
Expression of the inverse function with the frequency factor | PV, CHI, ICH, WH, PW, PGI, FR |
Exact relationships of the frequency factors | PV, CHI, ICH, WH, PW, PGI, FR |
Approximate estimation of the frequency factors | PV, CHI, ICH, WH, PW, PGI, FR |
The confidence interval with Chow’s relationship | PV, CHI, ICH, WH, PW, PGI, FR |
The skewness−kurtosis variation graph and relationships | PV, CHI, ICH, WH, PW, PGI, FR |
Distribution | Distribution | ||
---|---|---|---|
PV | WH | ||
CHI | PW | ||
LN3 | ICH | ||
PGI | FR |
Length (km) | Average Stream Slope (‰) | Sinuosity Coefficient (−) | Average Altitude (m) | Watershed Area (km2) |
---|---|---|---|---|
33 | 22 | 1.83 | 713 | 153 |
AMS | ||||||||||||
1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | ||
Flow | (m3/s) | 9.96 | 15 | 10.1 | 14.8 | 7.30 | 21.2 | 18.2 | 21.4 | 13.1 | 14.5 | 35 |
2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | ||
Flow | (m3/s) | 19.9 | 22.1 | 11.8 | 80.3 | 88 | 51.6 | 72.2 | 16.2 | 42.6 | 28.5 | 12.8 |
2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | ||||
Flow | (m3/s) | 31.2 | 24.1 | 52.2 | 21.1 | 18.9 | 6.40 | 24.9 | 15.1 | 36.6 |
Prigor River | Statistical Indicators | ||||||
L-moments | |||||||
(m3/s) | (m3/s) | (m3/s) | (m3/s) | (−) | (−) | (−) | |
27.2 | 10.7 | 4.26 | 2.43 | 0.386 | 0.399 | 0.228 | |
LH-moments (first order) | |||||||
(m3/s) | (m3/s) | (m3/s) | (m3/s) | (−) | (−) | (−) | |
38.3 | 11.2 | 4.46 | 1.99 | 0.292 | 0.398 | 0.177 |
Distr. | Annual Maximum Series (AMS) | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Exceedance Probabilities (%) | ||||||||||||||||||
L-Moments | LH-Moments (First Order) | |||||||||||||||||
0.01 | 0.1 | 0.5 | 1 | 2 | 3 | 5 | 80 | 90 | 0.01 | 0.1 | 0.5 | 1 | 2 | 3 | 5 | 80 | 90 | |
PV | 562 | 270 | 159 | 125 | 97.2 | 83.6 | 68.5 | 12.4 | 9.63 | 467 | 244 | 151 | 121 | 96.5 | 83.7 | 69.4 | 11.4 | 8.16 |
CHI | 165 | 137 | 114 | 103 | 90.9 | 83.4 | 73.4 | 11.1 | 10.4 | 178 | 147 | 121 | 108 | 94.9 | 86.4 | 75.1 | 13.4 | 13.2 |
ICH | 624 | 284 | 162 | 126 | 97.5 | 83.5 | 68.2 | 12.4 | 9.46 | 498 | 251 | 152 | 122 | 96.2 | 83.3 | 70 | 11.4 | 7.94 |
WH | 139 | 121 | 106 | 97.4 | 88.2 | 82.1 | 73.5 | 11.2 | 10.7 | 152 | 131 | 113 | 104 | 93.2 | 86.1 | 76.1 | 13.9 | 13.8 |
PW | 292 | 198 | 141 | 118 | 97.4 | 85.8 | 72 | 11.8 | 9.64 | 297 | 200 | 142 | 119 | 97.7 | 86 | 72 | 11.9 | 9.82 |
LN3 | 480 | 266 | 165 | 132 | 103 | 87.9 | 71.4 | 12.4 | 10.3 | 367 | 222 | 147 | 121 | 97.4 | 85 | 70.7 | 11.6 | 8.88 |
GPI | 329 | 207 | 142 | 118 | 96.8 | 85.1 | 71.4 | 11.7 | 9.60 | 340 | 211 | 144 | 119 | 97.1 | 85.2 | 71.3 | 11.8 | 9.76 |
FR | 623 | 285 | 162 | 126 | 97.7 | 83.6 | 68.2 | 12.4 | 9.47 | 489 | 250 | 152 | 122 | 96.3 | 83.5 | 69 | 11.4 | 7.90 |
Annual Maximum Series (AMS) | ||||||||
---|---|---|---|---|---|---|---|---|
Parameters | Distribution | |||||||
PV | CHI | ICH | WH | PW | LN3 | GPI | FR | |
L-moments | ||||||||
4.3055 | 0.3887 | 1.5005 | 0.1099 | 0.5467 | 2.601 | 7.1344 | 3.0516 | |
69.4 | 44.4 | 32.3 | 73.2 | 2.41 | 0.9569 | 122 | 31.2 | |
−2.46 | 10.3 | −8.83 | 10.7 | 7.23 | 6.34 | −114 | −14.2 | |
LH-moments (first order) | ||||||||
4.8615 | 0.2929 | 1.7617 | 0.081 | 0.5375 | 2.894 | 6.6853 | 3.6925 | |
98.2 | 48.7 | 43.2 | 80.1 | 2.24 | 0.8072 | 112 | 42.5 | |
−6.95 | 13.2 | −15.04 | 13.8 | 7.52 | 2.47 | −104 | −26.03 |
Distr. | Statistical Measures | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Methods of Parameter Estimation | Observed Data | |||||||||||
L-Moments | LH-Moments | L-Moments | LH-Moments | |||||||||
RME | RAE | RME | RAE | |||||||||
PV | 0.0152 | 0.0649 | 0.3987 | 0.2728 | 0.0188 | 0.0842 | 0.3981 | 0.2456 | 0.3987 | 0.2277 | 0.3981 | 0.1773 |
CHI | 0.0301 | 0.1238 | 0.1438 | 0.0468 | 0.1367 | 0.1584 | ||||||
ICH | 0.0151 | 0.0637 | 0.2797 | 0.0209 | 0.0912 | 0.2495 | ||||||
WH | 0.0334 | 0.1382 | 0.1214 | 0.0521 | 0.1508 | 0.1408 | ||||||
PW | 0.0173 | 0.0735 | 0.2219 | 0.018 | 0.0739 | 0.2175 | ||||||
LN3 | 0.0199 | 0.0759 | 0.2800 | 0.0148 | 0.0673 | 0.2330 | ||||||
GPI | 0.0181 | 0.0765 | 0.2211 | 0.0187 | 0.0766 | 0.2205 | ||||||
FR | 0.0152 | 0.0636 | 0.2816 | 0.0213 | 0.0925 | 0.2499 |
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Anghel, C.G.; Ilinca, C. Predicting Flood Frequency with the LH-Moments Method: A Case Study of Prigor River, Romania. Water 2023, 15, 2077. https://doi.org/10.3390/w15112077
Anghel CG, Ilinca C. Predicting Flood Frequency with the LH-Moments Method: A Case Study of Prigor River, Romania. Water. 2023; 15(11):2077. https://doi.org/10.3390/w15112077
Chicago/Turabian StyleAnghel, Cristian Gabriel, and Cornel Ilinca. 2023. "Predicting Flood Frequency with the LH-Moments Method: A Case Study of Prigor River, Romania" Water 15, no. 11: 2077. https://doi.org/10.3390/w15112077
APA StyleAnghel, C. G., & Ilinca, C. (2023). Predicting Flood Frequency with the LH-Moments Method: A Case Study of Prigor River, Romania. Water, 15(11), 2077. https://doi.org/10.3390/w15112077