Improving American River Flood Frequency Analyses (1999)

Sacramento, California, has grown literally at the edge of the Sacramento and American Rivers and for 150 years has struggled to protect itself from periodic floods by employing structural and land management measures. Much of the population lives behind levees, and most of the city's downtown business and government area is vulnerable to flooding.

A major flood in 1986 served as impetus for efforts by federal, state, and local entities to identify an acceptable and feasible set of measures to increase Sacramento's level of safety from American River floods. Numerous options were identified in 1991 by the U.S. Army Corps of Engineers (USACE) in a report known as the American River Watershed Investigation. Due to the controversial nature of many of the alternatives identified in that report, study participants were not able to reach consensus on any of the flood control options. In response, the Congress directed the USACE to reevaluate available flood control options and, at the same time, asked the USACE to engage the National Research Council (NRC) as an independent advisor on these difficult studies. In 1995 NRC's Committee on Flood Control Alternatives in the American River Basin issued Flood Risk Management and the American River Basin: An Evaluation. This report outlined an approach for improving the selection of a flood risk reduction strategy from the many available.

In March 1996, the USACE and its non-federal affiliates completed the Congressionally directed reevaluations of flood control options and submitted recommendations to Congress. In response, Congress authorized a component of the recommended plan but not an adequate plan for the reduction of flood risk for the Sacramento area. Thus, evaluations of alternatives continue. To add considerable complication to the technically and politically difficult decision process, in January 1997 the American River experienced a major flood, nearly as large as and hydrologically similar to the "flood of record" that occurred just 11 years before in 1986.

The occurrence of the 1997 flood suggests that it may be necessary to recompute flood flow frequency relationships for the American River at Sacramento. In February 1998, the USACE published a revised unregulated rain flood flow frequency analysis¹ for the American River at Fair Oaks. The analysis produced a flood frequency curve that indicates that large floods are appreciably more likely than

previously thought. Based on the newly estimated 100-year flood discharge, the levees protecting Sacramento no longer provide protection against the 100-year flood. The revised flow frequency relationships have immediate policy implications (e.g., "decertification" of levees by the Federal Emergency Management Agency, resulting in building restrictions and higher flood insurance rates) and also reduce the estimated level of protection provided by the flood control alternatives that are currently being considered for Sacramento.

Perhaps not surprisingly, recalculation of the flow frequency relationships has proven controversial. Occurrence of the 1997 flood has also brought into question many issues of technical methodology that bear on decisions about flood risk management in Sacramento.

Shortly after their release, the results of the USACE flood frequency analysis prompted a number of questions, comments, and criticisms from representatives of local, state, and federal government agencies, public interest groups, private citizens, as well as from the Corps itself. In response, the USACE requested the assistance of the NRC to extend the work of the former Committee on Flood Control Alternatives in the American River Basin. This report is a product of NRC's Committee on American River Flood Frequencies, which was organized to assist the USACE by providing an independent scientific assessment of flood frequency relationships for the American River at Sacramento.

A variety of data types can be used in estimating flood quantiles or exceedance probabilities for the American River. These include systematic streamflow and precipitation data, historical and paleoflood data, and regional hydrometeorological information on extreme events. Flood frequency analysis traditionally has been based on systematic streamflow or precipitation records, where use of the latter requires the application of precipitation runoff modeling.

Flood frequency analysis is commonly based on the assumption that flood flows are independent and identically distributed random variables. In reality, the probability distribution of floods can change in time (i.e., exhibit non-stationarity) as a result of local human activities, such as land use changes or reservoir operations, or regional or global climate change. As noted in NRC (1998a), there are many intrinsic modes of climatic variability at decadal to centennial time scales that may be independent of global warming effects or may confound them. Thus non-stationarity in the American River flood frequency due to climatic factors cannot be unambiguously attributed to changes in atmospheric composition over the last century. For example, there are relatively few gaged streams on watersheds that have not been affected by human activities. Unfortunately, there are also relatively few cases where human impacts on flood magnitude and frequency have been carefully documented. There is evidence of significant changes in land use and surface attributes of the American River basin over the last two centuries.

Furthermore, the assumption that floods are independent and identically distributed in time is at odds with the recognition that climate naturally varies at all scales, and that climate additionally may be responding to human activities, such as

changes over the past century in atmospheric composition or in global land use patterns, which have changed the climate forcing and the hydroclimatic response on regional scales in recent decades. In this regard the committee notes that its understanding of climate variability suggests that (a) the uncertainty of flood frequency estimates is higher than that indicated by the usual statistical criteria, (b) climatic regime shifts may—slowly or abruptly—significantly affect the local flood frequency curve for protracted periods, and (c) at this time, given the limited understanding of the low frequency climate-flood connection, the traditional approach to flood frequency estimation entails a tradeoff between potential bias and variance. Bias arises from the use of long periods of record that are more likely to include time periods during which flood risk is different from that during the immediate planning period. On the other hand, longer periods of record allow the construction of risk estimators with less variance due to the larger sample with which the estimators are constructed.

Effective planning and design of flood risk management projects require accurate estimates of flood risk. Such estimates allow a quantitative balancing of flood control efforts and the resultant benefits, and also enhance the credibility of floodplain development restrictions. They allow determination of the flows associated with specified exceedance probabilities, as well as the expected benefits associated with alternative flood risk management proposals. These considerations are critical for the American River, where billions of dollars of property are at risk due to flooding.

Fitting a continuous mathematical distribution to data sets yields a compact and smoothed representation of the flood frequency distribution revealed by the available data, and a systematic procedure for extrapolation to flood discharges larger than those historically observed. Whereas the American River flood record at Fair Oaks is almost 100 years in length, there is a goal of providing flood protection for at least the flood that has a chance of 1 in 200 of being exceeded in any year. This requires extrapolation beyond the data, as well as smoothing the empirical frequency curve to obtain a more consistent and reliable estimate of the 100-year flood.

A variety of distribution functions and estimation methods are available for estimating a flood frequency distribution. The guidelines for frequency analysis presented in Bulletin 17-B were established to provide consistency in the federal flood risk management process. In estimating a flood frequency distribution for the American River, the committee believed it was desirable to follow the spirit of these guidelines, although not necessarily the exact letter. The committee based its estimation on the log-Pearson type III distribution, as specified in Bulletin 17-B. With only a traditional systematic gaged record, the report employs the conventional log-space method of moments, as recommended by Bulletin 17-B. When additional historical flood information is included or some peaks are censored, the Expected Moments Algorithm (EMA) is used as the generalization of the conventional log

space method of moments method. The EMA (Cohn, Lane, and Baier, 1997), developed well after the publication of Bulletin 17-B, makes more effective use of historical and paleoflood information than does the weighted-moments method recommended in Bulletin 17-B for use with historical information.

The committee explored alternative estimates of the flood frequency distributions for the American River using various combinations of systematic, historical, and paleoflood data and selected a recommended distribution, shown in Table ES.1 and Figure ES.1.

The recommended distribution is based on the systematic record of three-day rain flood flows estimated by the USACE from the U.S. Geological Survey flow record for Fair Oaks, and upon the historical record for 1848-1904 which included an estimated large three-day flow associated with the 1862 historic flood. Based on several independent analyses conducted by the committee and the USACE, the committee concludes that the three-day rain flood record is an accurate representation of the magnitude of the flood flows over the period of record, and that the observed increase in the frequency of large floods since 1950 is not an artifact of the method by which flood peaks were computed. The committee's estimate of the three-day flow associated with the 1862 flood is based on a regression model developed by the committee. In its frequency analysis the committee assumes that this flow was the largest three-day flow in the historical period from 1848 to 1904.

The recommended frequency distribution assumes a log-skew of -0.1. This skew is based on a weighted average of a regional skew (-0.1) and the sample skew (-0.06). The committee estimated the regional skew by averaging the sample log-skew of three-day flow series from seven rivers on the west slope of the central Sierra Nevada. Sensitivity analysis using the committee's recommended approach indicates that censoring below various flows with exceedance probabilities ranging from about 0.94 to 0.31 does not significantly affect the estimated distribution.

In developing its recommended flood frequency distribution, the committee chose not to use the paleoflood information to compute a frequency curve for the American River. When the paleoflood data are used in conjunction with the systematic and historical data in an estimation framework consistent with the spirit of Bulletin 17-B, the resulting log-Pearson type III distribution provides a poor fit to the systematic data (Figure 3.3). While it might be possible to improve the fit by using a method outside the framework of Bulletin 17-B (e.g., censoring the systematic data at a very high threshold), the committee chose not to take this approach for several reasons. First, the committee was committed to following the spirit of Bulletin 17-B. Second, the committee was uneasy about using the paleoflood data because of questions about climatic variability during the 3,500-year period represented by this information. In particular, given present understanding of global climate variations during the past 10,000 years, the committee questions whether it is prudent to assume that flood magnitudes during this period are independent and identically distributed.

While the committee's preferred estimate of the frequency distribution of three-day rain flood flows on the American River is consistent with the systematic and historic data, the committee cautions against extrapolating much beyond these data. Frequency analysis of basin average precipitation data (as well as the paleoflood information) indicates that the upper tail of the "true" distribution flattens for very large flows.

The committee did not have time to develop a recommendation regarding extrapolation of the frequency distribution beyond the flow with an annual exceedance probability of 1 in 200. This is clearly an area in need of analysis. One complicating factor is the observed post-1950 increase in large floods. This increase may reflect structural changes in the flood generation process wrought by human activity (e.g., atmospheric composition changes or global land use changes) or by natural factors that have always been present.

Based on the USACE 1998 100-year flood estimate, the Federal Emergency Management Agency (FEMA) issued new floodplain maps for Sacramento. As result of these new maps, most of the floodprone areas of Sacramento were classified as being in the so-called AR zone (area of special flood risk). Generally, this designation would have resulted in building restrictions and higher flood insurance rates. In this case, FEMA waived the increases in flood insurance rates, but enforced

the building restrictions.

If adopted, the 100-year flood estimate recommended by this committee may result in removal of some floodprone areas of Sacramento from the AR zone.² This would result in suspension of the building restrictions. It would also likely reduce the political pressure to achieve a solution to the acute flooding threat facing Sacramento.

If our 100-year flood estimate does indeed imply that floodprone areas of Sacramento along the American River levees are not in the 100-year floodplain, it will be by the thinnest of margins. But because the uncertainties in this estimate are so large, the evidence that these areas are not in the 100-year floodplain would be far from compelling. In fact, there is about equal evidence that these areas belong or do not belong in the 100-year regulatory floodplain. The worst consequence of falsely designating such floodprone areas to be in the regulatory floodplain would be the requirement of building restrictions that in the future may prove to be unnecessary. The worst consequence of falsely designating such floodprone areas to be out of the regulatory floodplain would be a prolonged delay in solving acute flood problems, a delay that could have catastrophic results. Given the gross inequality of these two consequences, the committee strongly recommends that authorities carefully consider the situation and the large uncertainties in the estimated 100-year floods, and attempt to develop a flood risk management strategy that addresses the significant risk of flooding in Sacramento.

Flood frequency analysis has been practiced for nearly a century and has seen significant developments in both technological and sociopolitical contexts. Despite the progress that has been made, much remains to be learned. But this improved understanding may present policy issues to be resolved if and when new knowledge and methods are proposed to be incorporated into nationwide guidelines, such as Bulletin 17-B. In particular, it will raise questions as to whether previously completed flood frequency analyses need to be revised, and whether such revisions should significantly change the boundaries of regulatory floodways and floodplains.

To address issues such as these will require both scientific study and informed public debate. But, as was pointed out by the NRC Committee on Flood Risk Management in the American River Basin (NRC, 1995), needs for future research and issue resolution should not be used as an excuse for not taking action now. While that committee's comment was directed specifically to the American River situation, the present committee believes that the ongoing needs and opportunities being experienced by Sacramento suggest that the time is ripe to begin

The committee recommends the establishment of a new interagency effort for flood risk assessment and management. The impetus for such action is clear: rising property damages and loss of life; 30 years of experience with the National Flood Insurance Program; aging federal policy and technical guidance; improvements in scientific methods of computing and modeling; emergence of understanding of paleohydrologic and climate variability issues; and a growing data base and availability of information. Virtually all these issues have arisen in the Sacramento case, and can be expected to arise in others as well.

The committee proposes that this interagency effort should emphasize research focused on coordinated and cooperative flood risk reduction, including meteorologic, hydrologic, hydraulic, and policy and socio-economic aspects of flood management. In Chapter 5, a number of specific issues that should be addressed in the recommended interagency effort are discussed.