500-Year Flood Can It Be Reliably Estimated?

Transcription

1 500-Year Flood Can It Be Reliably Estimated? By Joseph D. Countryman PE; D. WRE President MBK Engineers, 2450 Alhambra Boulevard, Sacramento, California, 95817, PH (916) ; FAX (916) ; Abstract The 500-Year flood has been proposed for a national urban flood standard (Galloway 2005). This recommendation overlooks the problems associated with estimating the 500-Year flood. The approved pdf (IACWD 1982) for making these estimates in the United States is the LP III pdf. The approved methodology provides erratic and highly unreliable estimates of the 500-Year flood in several California watersheds. A case study of the American River flood estimates is presented to demonstrate the issues. A comparison of flood flow estimates for several probability distribution functions and the associated Confidence Intervals is presented. The paper finds that extrapolation of pdfs should be avoided and the use of Confidence Intervals for project formulation and levee certification should be abandoned. It is recommended to use physically based design floods rather than statistically-based design floods and/or Risk Analysis. Background The federal government, through the National Flood Insurance Program (NFIP), has established a defacto minimum flood control standard for urban areas of 100-year flood protection. A 100-year flood has a 1 percent chance of being exceeded in any given year. It is now understood that a very high residual risk of flooding resides with a 100-year level of flood protection. Concern that urban areas could be subject to an unreasonably high residual flood risk has resulted in recommendations for changing the current 100-year minimum standard. A recommendation that the Standard Project Flood (SPF), or 500-year flood, be considered as the new NFIP standard for urban areas was recently presented to congress (Galloway 2005). Reasonableness of a Flow Frequency Standard. The SPF is not defined by an exceedence frequency, but by a storm and runoff analysis. It is the most severe flood producing rainfall depth-area duration relationship and isohyetal pattern of any storm that is reasonably characteristic of the 1

2 region (USACE 1965). The SPF was the Corps designated design standard for urban areas. The Corps of Engineers (Corps) is no longer relying on the SPF as the preferred methodology for establishing an urban design standard. The Corps is currently requiring a Risk Analysis approach to project formulation (USACE 2005). This methodology relies on statistically derived frequency curves and their uncertainty bounds (Confidence Intervals) to design an optimized flood control project. This raises the following questions for the hydrologists and engineers that are tasked with developing the frequency curves that are the very essence of the Risk Analysis methodology: 1. Can the Log Pearson III, pdf, the current federally approved pdf (IACWD 1982, pg 3), or any other pdf be reliably used to estimate the 500-year flood? 2. Are the Confidence Intervals for the selected pdf reliable? Theoretically, a 100-year, 500-year, or 1250-year design flood definition is straight forward and easy to understand. Our ability to define these floods with any degree of certainty is in question. The remainder of this paper will analyze the 500- year flood estimates for the American River in California Watershed Description The American River watershed (see Figure 1) drains the west side of the Sierra Nevada mountain range and is located just east of Sacramento, California. The watershed includes 1888 square miles of drainage. The longest channel length is 170 miles and the maximum elevation of the basin is greater than 8,000 feet. The record flood for the basin occurred in 1997 and had a peak flow of approximately 290,000 cfs. Can the 500-year Flood be Reliably Estimated? An Interagency Advisory Committee on Water Data was established to recommend procedures for developing 100-year flood estimates. This advisory committee developed guidelines for estimating the 100-year flood and published their finding in Bulletin #17B (IACWD 1982). Bulletin #17B provided detailed information on estimating the 100-year flood. The adopted method was fitting the Log Pearson Type III probability distribution function (LP III WRC) to historic data. There are numerous problems with developing a design flood from a frequency analysis. Vit Klemes has identified a major issue for the statistical approach as described below: from a hydrological point of view, very extreme floods and their causes tend to be outliers by definition, i.e., very little, if any, information about their likelihood is contained in the frequencies of relative small floods of which the bulk of a typical flood sample is composed. Extrapolating distribution models fitted to these samples is tantamount to extrapolating the small flood dynamics beyond the range it can physically function. (Klemes 2000, pg 155) The following quote from Bulletin #17B illustrates the concern: 2

3 The accuracy of flood probability estimates based upon statistical analysis of flood data deteriorates for probabilities more rare than those directly defined by the period of systematic record. This is partly because the basic underlying distribution of flood data is not known exactly. (IACWD 1982, pg 19) American River Flood Estimates An example of the condition articulated above is shown on Figure 2. The LP III pdf was fit to 102 years of American River flow data. Two different methods of fitting the LP III pdf to the data set were used. The method adopted by Bulletin #17B is the LP III WRC pdf on Figure 2. The LP III BOB (LP III MM, shown on Figure 2) fitting technique is described by Bernard Bobee and Fahim Ashkar (Bobee & Ashkar 1991, pgs 96-98). The differences between the estimates increase dramatically for floods greater than the 20-year flood, and are nearly 70 percent different for the 1,000-year flood. These differences are based only on the fitting technique for the LP III pdf. Since it is impossible to know the true underlying pdf of any given data set (if one actually exists!), flood frequency estimates were made using various pdfs accepted for use in hydrology (Bobee & Ashkar 1991). This analysis used the 102 years of American River flood data and the computing capability of the HYFRAN computer program (Univ. of Quebec 2002). A summary of these results is provided on Figure 3. All of the pdfs studied have similar estimates for the 10-year flood. The percentage differences dramatically increase for floods larger than the 100-year flood. The LP III WRC 500-year flood estimate of 331,000 cfs would be greater than the 10,000-year flood estimate based on the Exponential pdf. The Corps of Engineers, through the Hydrologic Engineering Center, contracted with MGS Engineering Consultants to develop a stochastic flood model for the purpose of estimating American River flood flow frequencies (USACE-HEC 2005). The NRC had recommended this procedure as a way of extrapolating the frequency curve beyond the historic data set (NRC 1999, pg 66). The MGS report found that the computed stochastic frequency curve values were lower than the LP III WRC frequency curve values. The stochastic model frequency values were adjusted such that the 100-year MGS flood estimate matched the LP III WRC 100-year flood estimate (USACE-HEC 2005, pg 30). For this paper the MGS stochastic frequency curve was adjusted to the 10-year flood rather than the 100-year flood, to minimize the extrapolation differences between the various pdf estimates. Table 1 compares the estimated 3-day flood flows utilizing various methods. Table 1 American River Flood Estimates Flow values in 3-Day-CFS LP III WRC Exponential MGS Stochastic MGS 10-year adj 10-year 73,000 74,500 67,000 73, year 151,000 96,000 89,000 97, year 196, , , , year 331, , , ,000 3

4 The data presented in Figure 3 and Table 1 demonstrates the inherent instability in extrapolating pdfs beyond the information available in the historic record. Figure 3 shows the LP III WRC quantile estimate increases much faster than for the other pdfs displayed and the LP III WRC extrapolation is unbounded on the upper end. This raises the question, Where will the precipitation come from to generate this unbounded estimate? The Probable Maximum Flood (PMF) is defined as follows: that flood discharge that would result from the combination of the most severe and critical meteorological and hydrologic conditions considered reasonably possible in a region (USACE 2001, pg. 1). During the 1960s and 1970s, it was considered standard practice at the Corps of Engineers (based on personal experience) to adjust frequency curve extrapolations such that the PMF would not have an annual exceedance probability greater than 1 in 10,000 (10,000-Year flood). The PMF for the American River has a volume of 430,000 3-day-cfs (USACE 2001, Chart 20). The American River PMF would have an annual exceedance probability of 1 in 1,500 based on the LP III WRC pdf. All of the other pdfs in Figure 3 show the PMF has an annual exceedance probability of less than 1 in 10,000. It is evident that selection of a pdf should include an evaluation of the physical hydrology of a drainage basin. If this is not done, very significant extrapolation errors may be introduced and project formulation and optimization procedures that rely on these extrapolations will not achieve the goal of project cost efficiency and safety. The LP III WRC pdf extrapolation for the American River does not include these evaluations and appears to be significantly overestimating floods greater than the 100-year flood. A much larger question must be addressed, Can the extrapolation of any pdf, beyond the data set used to curve fit the pdf, provide reliable information unless it is shown to be consistent with the physical watershed and meteorologic conditions in the region? The answer to this question is self evident; do not extrapolate the pdfs without physical verification/justification. Are the Confidence Intervals Reliable? Once flow frequency curves are adopted based on a given pdf, it is common practice in flood frequency analysis to calculate Confidence Intervals for the frequency curve. An example of this is shown on Figure 4. The fundamental scientific basis for the Confidence Intervals has not been clearly established. Mathematically, it can be shown that if the pdf for the population of data is known, then an approximation of the sampling error of the population can be estimated. This is the essence of Confidence Intervals. In flood hydrology, only one sample is available and the true underlying pdf of the population of flood flows is unknown. There is uncertainty that the annual maximum flows are a homogeneous population because the small annual floods do not have meteorologic commonality with the large floods. Further it is common to assume that there is no upper boundary of possible flows. All of these conditions make the calculation of Confidence Intervals 4

5 speculative, at best, and extremely misleading at worst. It would take 10,000 years of data (assuming stationarity of the meteorologic and hydrologic factors governing flood flows) to prove this bold statement. The proof should be on those that use Confidence Intervals in project optimization calculations or for levee certification guidelines to show that the Confidence Intervals have validity. American River Confidence Intervals Figure 5 displays the 500-year flood estimates and the 90 percent Confidence Intervals for eleven (11) different pdfs and/or fitting techniques. All pdf curve fitting is based on the identical 102 years of recorded flows. The HYFRAN (Univ. of Quebec 2002) computer program was used to perform all of the calculations summarized in Figures 5 & 6 with the exception of the LP III WRC pdf. The computer program HEC-SSP (USACE-HEC 2006) was used for the LP III WRC calculations. The 90 percent Confidence Intervals range from a low of 62,000 cfs for Pearson III pdf to 497,000 cfs for the GEV MM pdf and to 250,000 cfs for the approved LP III WRC pdf. This information raises serious questions about the efficacy of the Confidence Interval calculations. All calculations are based on the same relatively long record, yet enormous differences in the Confidence Intervals are evident. This data points to the conclusion that the Confidence Intervals are not primarily the result of record length. In fact, if it is assumed that the LP III WRC pdf statistics were based on 500 years of record instead of 102 years of record, the 90 percent Confidence Interval would change to 106,000 cfs. This would still be 170 percent larger than the 90 percent Confidence Interval of the Pearson III pdf based on 102 years of record. Another major defect in the Confidence Intervals displayed on Figure 5 is that the estimates show the upper bound exceeding the PMF. This Figure shows that the Gen Gamma ML, LP III WRC, GEV MWM and the Log-Nor ML pdfs all have upper bound estimates of the 90percent Confidence Interval greater than the PMF. This result is not supported by the physical hydrologic and meteorologic conditions in the region. What physical factors in the atmosphere, or in the watershed, exist that could conceivably result in the PMF becoming the 500-year flood? Is our 102 year sample this unrepresentative? If the climate changed, or the watershed changed in a very dramatic and currently inexplicable way, the stationarity of the data set would be called into question. No, we must imagine a situation that would not change the current physical watershed or climatic conditions and still result in the PMF becoming the 500-year flood. The proponents of the Confidence Interval calculations must explain this seeming flaw in the statistical result. The absolute magnitude of the Confidence Intervals appears to be unreasonably large. Figure 6 displays the 500-year flood Confidence Intervals for the various pdfs as a percentage of the Best Estimate of the 500-year flood. Common Sense dictates that the 90 percent Confidence Interval for the 500-year flood estimate should not be larger than the Best Estimate of the 500-year flood! Whenever the Confidence Interval is greater than 50 percent of the Best Estimate, it is likely that a serious problem exists. Yet with Risk Analysis in project formulation, this has not 5

6 been considered. A distressing aspect of this is that the Corps of Engineers, as part of their adoption of Risk Analysis methodology, has embraced Confidence Intervals for levee certification (Davis 2006). The Corps will no longer certify a levee unless it includes an analysis of the Confidence Intervals. As can be seen from the data presented herein, certification of a levee to a 500-year flood standard may well require the ability of the levee to pass the PMF or larger flood. The data presented shows that the calculated Confidence Intervals can be extreme and not consistent with the hydrology or meteorology of a watershed. The use of Confidence Intervals for project formulation or for levee certification is not advised. Conclusion The use of historic data to estimate floods larger than those that have been experienced is the essence of stochastic hydrology. The fitting of mathematical functions (pdfs) to the ordered historic annual maximum flood flow data set for a given watershed is the accepted procedure. The pdfs (the LP III WRC pdf is the adopted pdf for the United States) and the parameters of the pdfs that are used to adjust the mathematical functions to fit the available data are not related to physical features of the landscape or to hydrologic or meteorologic conditions in a region. The accepted procedures provide reasonably consistent estimates of annual flood flow exceedance probabilities for floods that are smaller than the maximum flood in the historic data set. As shown in this paper and as supported by numerous authorities cited herein, the extrapolation of the pdfs beyond the data set is problematic and potentially unreliable. Therefore, any estimate of the 500-year flood should include hydrologic and meteorologic support for the extrapolation. Common sense items such as the PMF representing a maximum value for the pdf and Confidence Interval extrapolations should be utilized. A wiser and more scientifically justifiable path would be to develop design floods that are based on hydrologic and meteorologic conditions in the area of a proposed project. Risk Analysis software requires the frequency curves to be extrapolated in order to purportedly allow optimization of a project formulation process. As with all software, if the hydrologic input represented by the frequency curve extrapolation is unreliable, then the optimization that is the object of the analysis is also unreliable. It is the responsibility of the hydrologist to point out this inconvenient reality! The utilization of Confidence Intervals is currently being promoted by the Corps of Engineers as part of their adoption of Risk Analysis in project formulation and in levee certification. The fact that the Confidence Intervals are dependent upon the assumption that the adopted pdf represents the true population of flood events for a given watershed is often overlooked. There is no evidence that the pdf that is calibrated to a limited number of data points accurately represents the full population of flood events. The use of Confidence Intervals should be restricted to situations to which their efficacy can be demonstrated. 6

7 World Environmental and Water Resources Congress 2007: Restoring Our Natural Habitat Figure 1 Location Map Figure 2 American River Curve Fitting Techniques for LP III pdf 7

8 Figure 3 American River pdf Comparison Figure 4 American River Confidence Interval for LP III WRC pdf 8

9 Figure 5 American River 500-year Flood 90% Confidence Interval Figure year Flood Confidence Interval as % Best Estimate Flood 9

10 References Bobée B. and Ashkar, F., (1991). The Gamma Family and Derived Distributions Applied in Hydrology, Water Resources Publications, Colorado. Davis, Darryl, P.E., D.WRE, (December 2006), Policy letter USACE Levee Certification Policy and Risk Analysis. Gallaway, G.E., (2005). Statement to Committee on Transportation and Infrastructure, U.S. House of Representatives. Interagency Advisory Committee on Water Data, Hydrology Subcommittee (IACWD) (1982). Guidelines for Determining Flood Flow Frequency, Bulletin #17B. Klemes, Vit, (2000). Common Sense and Other Heresies: Selected Papers in Hydrology and Water Resources Engineering, Canadian Water Resources Association, Cambridge, Ontario. National Research Council (NRC), (1999). Improving American River Flood Frequency Analysis, National Academy Press, Washington, D.C. Univ. of Quebec, (2002). Chair in Statistical Hydrology, INRS-ETE. Software HYFRAN for hydrologic frequency analysis, version 1.1 USACE, (1965). Engineer Manual USACE (2001). American River Basin, California, Folsom Dam and Lake, Revised PMF Study. USACE, (2005). Engineer Regulation Risk Analysis for Flood Damage Reduction Studies. USACE-HEC, (2005). Stochastic Modeling of Extreme Floods on the American River at Folsom Dam. USACE-HEC, (2006). Software: HEC-SSP ver. 1.0 Beta. 10