Use of historical information in a maximum-likelihood framework
This paper discusses flood-quantile estimators which can employ historical and paleoflood information, both when the magnitudes of historical flood peaks are known, and when only threshold-exceedance information is available. Maximum likelihood, quasi-maximum likelihood and curve fitting methods for...
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| Published in | Journal of hydrology (Amsterdam) Vol. 96; no. 1; pp. 215 - 223 |
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| Main Authors | , |
| Format | Journal Article Conference Proceeding |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
15.12.1987
Elsevier Science |
| Subjects | |
| Online Access | Get full text |
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| Abstract | This paper discusses flood-quantile estimators which can employ historical and paleoflood information, both when the magnitudes of historical flood peaks are known, and when only threshold-exceedance information is available. Maximum likelihood, quasi-maximum likelihood and curve fitting methods for simultaneous estimation of 1, 2 and 3 unknown parameters are examined. The information contained in a 100 yr record of historical observations, during which the flood perception threshold was near the 10 yr flood level (i.e., on average, one flood in ten is above the threshold and hence is recorded), is equivalent to roughly 43, 64 and 78 years of systematic record in terms of the improvement of the precision of 100 yr flood estimators when estimating 1, 2 and 3 parameters, respectively. With the perception threshold at the 100 yr flood level, the historical data was worth 13, 20 and 46 years of systematic data when estimating 1, 2 and 3 parameters, respectively. |
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| AbstractList | Flood-quantile estimators using historical and paleoflood information are discussed. Simultaneous estimation of 1, 2, and 3 unknown parameters was assessed using maximal likelihood, quasi-maximal likelihood and curve-fitting methods. The information contained in a 100 year record of historical observations where on average 1 flood in 10 was above the flood perception threshold and was recorded as equivalent to approximately 43, 64 and 78 years of systematic record in terms of the improvement of the precision of 100 year estimators when estimating 1, 2 and 3 parameters respectively. Setting the perception threshold at the 100 year flood level gave values of 13, 20 and 46 years of systematic data when estimating 1, 2 and 3 parameters. This paper discusses flood-quantile estimators which can employ historical and paleoflood information, both when the magnitudes of historical flood peaks are known, and when only threshold-exceedance information is available. Maximum likelihood, quasi-maximum likelihood and curve fitting methods for simultaneous estimation of 1, 2 and 3 unknown parameters are examined. The information contained in a 100 yr record of historical observations, during which the flood perception threshold was near the 10 yr flood level (i.e., on average, one flood in ten is above the threshold and hence is recorded), is equivalent to roughly 43, 64 and 78 years of systematic record in terms of the improvement of the precision of 100 yr flood estimators when estimating 1, 2 and 3 parameters, respectively. With the perception threshold at the 100 yr flood level, the historical data was worth 13, 20 and 46 years of systematic data when estimating 1, 2 and 3 parameters, respectively. |
| Author | Cohn, Timothy A. Stedinger, Jery R. |
| Author_xml | – sequence: 1 givenname: Timothy A. surname: Cohn fullname: Cohn, Timothy A. organization: U.S. Geological Survey, 410 National Center, Reston, VA 22092 U.S.A – sequence: 2 givenname: Jery R. surname: Stedinger fullname: Stedinger, Jery R. organization: Department of Environmental Engineering, Cornell University, Ithaca, NY 14853 U.S.A |
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| Cites_doi | 10.1029/WR022i004p00543 10.1214/aoms/1177729751 10.1029/TR031i003p00419 10.1029/WR009i006p01534 10.1029/WR022i005p00785 10.1029/WR023i004p00715 10.1029/WR014i004p00626 10.2307/1267922 10.1029/WR018i004p00859 10.1016/0022-1694(82)90068-3 10.1029/WR016i003p00481 10.1130/0091-7613(1974)2<301:SMAPEO>2.0.CO;2 10.1061/JYCEAJ.0005273 |
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| Keywords | Graphics Monte Carlo method Flood Monte Carlo analysis Floods History Case history Graphic methods |
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Stat. doi: 10.1214/aoms/1177729751 contributor: fullname: Cohen – volume: 31 start-page: 419 issue: 3 year: 1950 ident: 10.1016/0022-1694(87)90154-5_BIB2 article-title: Use of historical data in flood frequency analysis publication-title: Trans. Am. Geophys. Union doi: 10.1029/TR031i003p00419 contributor: fullname: Benson – volume: 64 start-page: 712 issue: 65 year: 1983 ident: 10.1016/0022-1694(87)90154-5_BIB33 article-title: Use of limited at-site flood data in estimating flood peaks publication-title: EOS, Trans. Am. Geophys. Union contributor: fullname: Wall – volume: 9 start-page: 1534 issue: 6 year: 1973 ident: 10.1016/0022-1694(87)90154-5_BIB23 article-title: Use of censored data in the estimation of gumbel distribution parameters for annual maximum flood series publication-title: Water Resour. Res. doi: 10.1029/WR009i006p01534 contributor: fullname: Leese – start-page: 189 year: 1977 ident: 10.1016/0022-1694(87)90154-5_BIB24 article-title: Geomorphic response of Central Texas stream channels to catastrophic rainfall contributor: fullname: Patton – volume: 104 start-page: 249 issue: 2 year: 1978 ident: 10.1016/0022-1694(87)90154-5_BIB30 article-title: Flood frequency analysis with pre-record information publication-title: Am. Soc. Civ. Eng., J. Hydraul. Div. ASCE (HY2) contributor: fullname: Tasker – start-page: 144 year: 1986 ident: 10.1016/0022-1694(87)90154-5_BIB8 article-title: Flood frequency analysis with historical flood information contributor: fullname: Cohn – volume: 1779-M start-page: 105 year: 1964 ident: 10.1016/0022-1694(87)90154-5_BIB31 article-title: Historical floods in New England publication-title: U.S. Geol. Surv. Water Supply Pap. contributor: fullname: Thomson – volume: 22 start-page: 785 issue: 5 year: 1986 ident: 10.1016/0022-1694(87)90154-5_BIB29 article-title: Flood frequency analysis with historical and paleoflood information publication-title: Water Resour. Res. doi: 10.1029/WR022i005p00785 contributor: fullname: Stedinger – year: 1962 ident: 10.1016/0022-1694(87)90154-5_BIB1 article-title: Statistical methods in hydrology publication-title: U.S. Army Corps Eng., Civ. Works Invest. Proj., Rep. CW-151 contributor: fullname: Beard – start-page: 11 year: 1983 ident: 10.1016/0022-1694(87)90154-5_BIB10 article-title: Fitting the log-pearson type III distribution to censored samples: An application to flood frequency analysis with historic information contributor: fullname: Condie – volume: 32 start-page: 119 issue: 1/2 year: 1949 ident: 10.1016/0022-1694(87)90154-5_BIB17 article-title: Maximum likelihood estimation of the parameters of a normal distribution which is truncated at a known point publication-title: Skand. Aktuarietidskr. contributor: fullname: Hald – volume: 65 start-page: 890 issue: 45 year: 1984 ident: 10.1016/0022-1694(87)90154-5_BIB14 article-title: Fluvial paleoflood hydrology publication-title: EOS, Trans. Am. Geophys. Union contributor: fullname: Costa – volume: 485-A start-page: 35 year: 1964 ident: 10.1016/0022-1694(87)90154-5_BIB26 article-title: Botanic evidence of floods and flood plain development publication-title: U.S. Geol. Surv., Prof. Pap. contributor: fullname: Sigafoos – volume: 25 start-page: 119 issue: 2 year: 1987 ident: 10.1016/0022-1694(87)90154-5_BIB28 article-title: Surface water hydrology: historical and paleoflood information publication-title: U.S. Natl. Rep. Int. Union Geodesy Geophys., 1983–1986. Rev. Geophys. contributor: fullname: Stedinger – year: 1967 ident: 10.1016/0022-1694(87)90154-5_BIB32 article-title: Guidelines for determining flood flow frequency contributor: fullname: U.S. Water Resources Council, Hydrology Committee – volume: 23 start-page: 715 issue: 4 year: 1987 ident: 10.1016/0022-1694(87)90154-5_BIB20 article-title: Plotting positions for historical floods and their precision publication-title: Water Resour. Res. doi: 10.1029/WR023i004p00715 contributor: fullname: Hirsch – volume: 14 start-page: 626 issue: 4 year: 1978 ident: 10.1016/0022-1694(87)90154-5_BIB13 article-title: Holocene stratigraphy in flood frequency analysis publication-title: Water Resour. Res. doi: 10.1029/WR014i004p00626 contributor: fullname: Costa – volume: 21 start-page: 23 year: 1967 ident: 10.1016/0022-1694(87)90154-5_BIB18 article-title: A flood-frequency graph based on tree-scar data contributor: fullname: Harrison – volume: 18 start-page: 99 issue: 1 year: 1976 ident: 10.1016/0022-1694(87)90154-5_BIB6 article-title: Progressively censored sampling in the three parameter log-normal distribution publication-title: Technometrics doi: 10.2307/1267922 contributor: fullname: Cohen – year: 1984 ident: 10.1016/0022-1694(87)90154-5_BIB34 article-title: Parameter estimation in flood frequency analysis contributor: fullname: Wang – volume: 18 start-page: 859 issue: 4 year: 1982 ident: 10.1016/0022-1694(87)90154-5_BIB36 article-title: Plotting positions of annual flood extremes considering extraordinary values publication-title: Water Resour. Res. doi: 10.1029/WR018i004p00859 contributor: fullname: Zhang – year: 1979 ident: 10.1016/0022-1694(87)90154-5_BIB11 contributor: fullname: Cong – start-page: 79 year: 1984 ident: 10.1016/0022-1694(87)90154-5_BIB7 article-title: The incorporation of historical information in flood frequency analysis contributor: fullname: Cohn – start-page: 360 year: 1970 ident: 10.1016/0022-1694(87)90154-5_BIB15 article-title: Order Statistics contributor: fullname: David – start-page: 557 year: 1975 ident: 10.1016/0022-1694(87)90154-5_BIB3 article-title: Discrete Multivariate Analysis: Theory and Practice contributor: fullname: Bishop – volume: 58 start-page: 47 issue: 1/2 year: 1982 ident: 10.1016/0022-1694(87)90154-5_BIB9 article-title: Flood frequency analysis with historic information publication-title: J. Hydrol. doi: 10.1016/0022-1694(82)90068-3 contributor: fullname: Condie – volume: 1296 start-page: 42 year: 1983 ident: 10.1016/0022-1694(87)90154-5_BIB35 article-title: Evidence of floods on the Potomac river from anatomical abnormalities in the wood of flood-plain trees publication-title: U.S. Geol. Surv., Prof. Pap. contributor: fullname: Yanosky – volume: 16 start-page: 481 issue: 3 year: 1980 ident: 10.1016/0022-1694(87)90154-5_BIB27 article-title: Fitting log-normal distributions to hydrologic data publication-title: Water Resour. Res. doi: 10.1029/WR016i003p00481 contributor: fullname: Stedinger – volume: 96 start-page: 185 year: 1987 ident: 10.1016/0022-1694(87)90154-5_BIB19 article-title: Probability plotting position formulas for flood records with historical information contributor: fullname: Hirsch – volume: 2 start-page: 301 issue: 6 year: 1974 ident: 10.1016/0022-1694(87)90154-5_BIB12 article-title: Stratigraphic, morphologic, and pedologic evidence of large floods in humid environments publication-title: Geology doi: 10.1130/0091-7613(1974)2<301:SMAPEO>2.0.CO;2 contributor: fullname: Costa – start-page: 15 year: 1974 ident: 10.1016/0022-1694(87)90154-5_BIB4 article-title: The important role of historical flood data in the estimation of spillway design floods contributor: fullname: Chen – year: 1981 ident: 10.1016/0022-1694(87)90154-5_BIB22 article-title: Instructions for peak flow file publication-title: U.S. Geol. Surv., Open File Rep. 79-1336-I contributor: fullname: Kirby – volume: 105 start-page: 1153 issue: HY9 year: 1979 ident: 10.1016/0022-1694(87)90154-5_BIB16 article-title: Probability analysis of historical flood data publication-title: J. Hydraul. Div. ASCE doi: 10.1061/JYCEAJ.0005273 contributor: fullname: Gerard – start-page: 1 year: 1980 ident: 10.1016/0022-1694(87)90154-5_BIB25 article-title: Peak flood estimation program contributor: fullname: Russell |
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| Snippet | This paper discusses flood-quantile estimators which can employ historical and paleoflood information, both when the magnitudes of historical flood peaks are... Flood-quantile estimators using historical and paleoflood information are discussed. Simultaneous estimation of 1, 2, and 3 unknown parameters was assessed... |
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| SubjectTerms | Earth sciences Earth, ocean, space Exact sciences and technology Hydrology. Hydrogeology |
| Title | Use of historical information in a maximum-likelihood framework |
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