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I j the United States." Each report provided techniques for estimating flood magnitude and frequency for a major drainage basin or subbasin, such as the Lower Mississippi River Basin. These reports were published as USGS Water-Supply Papers 1671-1689 during the period 1964-68, In three States, Alaska, Idaho, and Rhode Island, the index-flood procedure (documented in reports published since 1973) is still used to estimate flood frequency. Ordinary-least-Squares Regression Studies by Benson (I962a, 1962b, 1964) sug- gested that T-year flood-peak discharges could be esti- mated directly using watershed and climatic characteristics based on multiple regression tech- niques. As noted by Benson (1962a), the direct estima- tion of T-year flood peak discharges avoided the following deficiencies in the index-flood procedure: (I) the flood ratios for comparable streams may differ because of large differences in the index flood, (2) homogeneity of frequency curve slope can be estab- lished at the lO-year level, but individual frequency curves commonly show wide and sometimes system- atic differences at the higher recurrence levels, and (3) the slopes of the frequency curves generally vary inversely with drainage area, Benson (1962b and 1964) has also shown that the flood ratios vary not only with drainage area but with main-channel slope and climatic characteristics as well. On the basis of this early work of Benson and later work by Thomas and Benson (1970), direct regression on the T-year flood became the standard approach of the USGS for regionalizing flood characteristics in the 1970's. The T-year flood-peak discharges for each gag- ing station were estimated by fitting the Pearson 1)rpe III distribution to the logarithms of the annual peak dis- charges using guidelines in Bulletin 15 (U,S. Water Resources Council, 1967) or some version of Bulletin 17 (U.S. Water Resources Council, 1976, 1977, 1981; Interagency Advisory Committee on Water Data (IACWD), 1982). The regression equations that related the T-year flood-peak discharges to watershed and cli- matic characteristics were computed using ordinary- least-squares techniques. In ordinary-least-squares regression, equal weight is given to all stations in the analysis regardless of record length and the possible correlation of flood estimates among stations. In most statewide flood-frequency reports, the analysts divided their States into separate hydrologic regions. Regions of homogeneous flood characteristics were generally defined on the basis of major watershed boundaries and an analysis of the areal distribution of regression residuals to identify regions of residuals whose size and algebraic sign were similar within and dissimilar between regions. In several instances, the hydrologic regions were also defined on the basis of the mean elevation of the watershed. Although this proce- dure may improve the accuracy of the estimating tech- nique, it is somewhat subjective. More objective procedures are now being used for defining hydrologic regions. Generalized-Least-Squares Regression Recent developments in the regionalization of flood characteristics have centered on accounting for the deficiencies in the assumptions of ordinary-Ieast- squares regression and on more accurate and objective tests of regional homogeneity. Ordinary-least-squares regression procedures do not account for variable errors in flood characteristics that exist due to unequal record lengths at gaging stations. Tasker (1980) pro- posed the use of weighted-least-squares regression for flood characteristics where the variance of the observed flood characteristics was estimated as an inverse func- tion of record length. Tasker and Stedinger (1986) used weighted-least-squares regression to estimate regional skew of annual peak discharges, and showed greater accuracy in results as compared to using ordinary- least-squares regression. Both ordinary-least-squares and weighted-least-squares regression do not account for the possible correlation of concurrent annual peak flow records between sites. This problem may be par- ticularly significant where gages are located on the same stream, on similar and adjacent watersheds or where flood-frequency estimates have been determined from a rainfall-runoff model using the same long-term rainfall record. A new procedure, generalized-least-squares regression, was proposed by Stedinger and Tasker (1985, 1986). This procedure accounted for both the unequal reliability and the correlation of flood charac- teristics between sites. Stedinger and Tasker (1985) showed, in a Monte Carlo simulation, that generalized- least-squares regression procedures provided more accurate estimates of regression coefficients, better I j I i 1 ~ ~ 4 IIIllonwlde Summery of U.S. Geologlcel Survey Reglonel Regreaelon Equations for Estlmellng Megnltude end Frequency of Floods for Ungsged Sites, 1993 t