USE OF HISTORIC FLOOD INFORMATION IN ESTIMATING FLOOD PEAKS ON UNGAGED WATERSHEDS1

Regional procedures to estimate flood magnitudes for ungaged watersheds typically ignore available site-specific historic flood information such as high water marks and the corresponding flow estimates, otherwise referred to as limited site-specific historic (LSSH) flood data. A procedure to construct flood frequency curves on the basis of LSSH flood observations is presented. Simple inverse variance weighting is employed to systematically combine flood estimates obtained from the LSSH data base with those from a regional procedure to obtain improved estimtes of flood peaks on the ungaged watershed. For the region studied, the variance weighted estimates of flow had a lower logarithmic standard error than either the regional or the LSSH flow estimates, when compared to the estimates determined by three standard distributions for gaged watersheds investigated in the development of the methodology. Use of the simple inverse variance weighting procedure is recommended when “reliable” estimates of LSSH floods for the ungaged site are available.     

COMPARISON OF MODELS FOR ESTIMATING FLOOD QUANTILES IN NEW HAMPSHIRE AND VERMONT1

We develop and compare three regression models for estimating flood quantiles at ungaged stream reaches in New Hampshire and Vermont. These models emerge from systematic analysis and validation of relations between flood magnitude and six candidate predictors reflecting basin size, topography, and climate and channel size at 36 gaging stations with record lengths exceeding 20 years. Of the candidate predictors, bank full width is most highly correlated with flood magnitude and the best prediction equation is based on width. Thus channel geometry is closely related to the current hydrologic regime in spite of geologically recent glaciation and apparently non-alluvial bank materials. We also develop models that use information obtainable from maps or GIS. The best of these uses drainage area and drainage-basin elevation as predictors, but it is substantially less precise than the width-based relation. A third relation using only drainage area as a predictor is even less precise but may be useful for some purposes. No other single predictors or combinations yielded useful predictions, although some had been included in previously-established models for the region. Model comparison included examination of residuals generated by regression using one-at-a-time suppression of data points and comparison with precision obtainable with gaging records of varying lengths.     

REGION OF INFLUENCE REGRESSION FOR ESTIMATING THE 50-YEAR FLOOD AT UNGAGED SITES1

ABSTRACT: Five methods of developing regional regression models to estimate flood characteristics at ungaged sites in Arkansas are examined. The methods differ in the manner in which the State is divided into subregions. Each successive method (A to E) is computationally more complex than the previous method. Method A makes no subdivision. Methods B and C define two and four geographic subregions, respectively. Method D uses cluster/discriminant analysis to define subregions on the basis of similarities in watershed characteristics. Method E, the new region of influence method, defines a unique subregion for each ungaged site. Split-sample results indicate that, in terms of root-mean-square error, method E (38 percent error) is best. Methods C and D (42 and 41 percent error) were in a virtual tie for second, and methods B (44 percent error) and A (49 percent error) were fourth and fifth best.     

ESTIMATING PROBABLE MAXIMUM FLOOD PROBABILITIES1

ABSTRACT: Methods of computing probabilities of extreme events that affect the design of major engineering structures have been developed for most failure causes, but not for design floods such as the probable maximum flood (PMF). Probabilities for PMF estimates would be useful for economic studies and risk assessments. Reasons for the reluctance of some hydrologists to assign a probability to a PMF are discussed, and alternative methods of assigning a probability are reviewed. Currently, the extrapolation of a frequency curve appears to be the most practical alternative. Using 46 stations in the Mid-Atlantic region, the log-gamma, log-normal, and log-Gumbel distributions were used to estimate PMF probabilities. A 600,000-year return period appears to be a reasonable probability to use for PMFs in the Mid-Atlantic region. The coefficient of skew accounts for much of the variation in computed probabilities.     

A COMPARISON OF METHODS FOR ESTIMATING LOW FLOW CHARACTERISTICS OF STREAMS1

ABSTRACT: Four methods for estimating the 7-day, 10-year and 7-day, 20-year low flows for streams are compared by the bootstrap method. The bootstrap method is a Monte Carlo technique in which random samples are drawn from an unspecified sampling distribution defined from observed data. The nonparametric nature of the bootstrap makes it suitable for comparing methods based on a flow series for which the true distribution is unknown. Results show that the two methods based on hypothetical distributions (Log-Pearson III and Weibull) had lower mean square errors than did the Box-Cox transformation method or the Log-Boughton method which is based on a fit of plotting positions.     

A SEMI-DISTRIBUTED ADAPTIVE MODEL FOR REAL-TIME FLOOD FORECASTING1

ABSTRACT: A semi-distributed deterministic model for real-time flood forecasting in large basins is proposed. Variability of rainfall and losses in space is preserved and the effective rainfall-direct runoff model segment based on the Clark procedure is incorporated. The distribution of losses in space is assumed proportional to rainfall intensity and their evolution in time is represented by the φ-index; furthermore, an initial period without production of effective rainfall is considered. The first estimation of losses and the associated forecasts of flow are performed at the time corresponding to the first rise observed in the hydrograph. Then the forecasts of flow are corrected at each subsequent time step through the updating of the φ-index. The model was tested by using rainfall-runoff events observed on two Italian basins and the predictions of flow for lead times up to six hours agree reasonably well with the observations in each event. For example, for the coefficient of persistence, which compares the model forecasts with those generated by the no-model assumption, appreciable positive values were computed. In particular, for the larger basin with an area of 4,147 km², the mean values were 0.4, 0.4 and 0.5 for forecast lead times of two hours, four hours and six hours, respectively. Good performance of the model is also shown by a comparison of its flow predictions with those derived from a unit hydrograph based model     

FLOOD FREQUENCY ANALYSIS FOR EVALUATING WATERSHED CONDITIONS WITh RAINFALL-RUNOFF MODELS1

ABSTRACT: Many rainfall-runoff modeling studies compare flood quantiles for different land-use and/or flood mitigation scenarios. However, when flood quantiles are estimated using conventional statistical methods, comparisons may be misleading because the estimates often misrepresent the quantile relationship between scenarios. An alternate statistical procedure is proposed, in which rainfall-runoff modeling is used to evaluate an approximate relationship between flood quantiles for different scenarios. Monte Carlo experiments show that the proposed method produces flood quantile estimates that better reflect the differences between scenarios. The ratio between quantiles for different scenarios is more accurate, so comparisons of the scenarios using flood quantiles are more reliable.     

ESTIMATION OF VOLUME-DURATION-FREQUENCY RELATIONS OF UNGAGED SMALL URBAN STREAMS IN OHIO1

ABSTRACT: This paper describes methods for estimating volume-duration-frequency relations of urban streams in Ohio with drainage areas less than 6.5 square miles. The methods were developed to assist engineers in the design of hydraulic structures on urban streams for which temporary storage of water is an important element of the design criteria. Multiple-regression equations were developed for estimating maximum flood volumes of d-hour duration and T-year recurrence interval (dV_T). Maximum annual flood-volume data for all combinations of six durations (1, 2, 4, 8, 16, and 32 hours) and six recurrence intervals (2, 5, 10, 25, 50, and 100 years) were analyzed. The significant explanatory variables in the resulting 36 volume-duration-frequency equations are drainage area, average annual precipitation, and basin-development factor. Standard errors of prediction for the 36 dV_T equations range from ±28 percent to ±44 percent.     

FLOOD FREQUENCY ANALYSIS FOR SMALL WATERSHEDS IN SOUTHERN ILLINOIS1

ABSTRACT: Twenty-two gaging stations were selected for developing a regional flood frequency curve for small (area less than 2 square miles) watersheds in southern Illinois. Five probability functions were compared, and the extreme value type I function was selected to develop the regional flood curve. The curve was generated with the index flood method and also another empirical method that related the function parameters to the watershed area. Estimated peak discharges with various return periods were compared with the results obtained from multiple regression analysis.     

MATHEMATICAL SIMULATIONS OF THE TOCCOA FALLS,GEORGIA, DAM-BREAK FLOOD1

ABSTRACT: Four dam-break models were selected for testing with an observed data set from the November 6, 1977, disaster at Toccoa Falls, Georgia. The Kelly Barnes Dam failure occurred with a 35-ft head of water and produced a peak discharge of 23,000 ft³/s. The selected models included: (1) Modified Puls (MP), (2) U. S. Army Corps of Engineers Gradually Varied Unsteady Flow Profiles (USTFLO), (3) National Weather Service's Dam-Break Flood Forecast (DBFF), and (4) U. S. Geological Survey's method of characteristics (MOC) coupled with a general purpose streamflow simulation (J879DB). Achieving a successful simulation was easiest with the MP model. The DBFF model required a moderate effort while the MOC-J879DB models required some data alterations and considerable effort. The USTFLO model failed to simulate this test case. In the stream segment near the dam, the computed peak stages were generally within 5 feet of the observed high water marks. Elsewhere, the peak stage results were much better, generally within 2 feet. The peak discharges computed by the models were generally within 20 percent of discharges estimated by slope area and contracted opening measurements, except near the dam where the MOC-J879DB model's results was 80 percent too high.     

THE MEASUREMENT OF IMPACTS IN SMALL WATERSHEDS FOR FLOOD CONTROL1

ABSTRACT: An analogue method of ex post evaluation is proposed as a method of measuring the effectiveness of small watershed projects in obtaining flood control and economic benefits. Two watersheds were compared on a “with vs. without” project basis by both direct and indirect measurement of economic benefits. Direct measurements indicated that small watershed flood control projects did not generate the expected economic benefits. However, the indirect measurements of the same watersheds using land value enhancement as a surrogate suggested that the expected economic benefits were reflected in differential land values. The economic efficiency of small watershed projects should be measured ex ante and ex post on a “with vs. without” project basis rather than on a “before vs. after” basis whether using direct or surrogate variables.     

INSTANTANEOUS PEAK FLOW ESTIMATION PROCEDURES FOR NEWFOUNDLAND STREAMS1

ABSTRACT: A procedure of estimating instantaneous flood flows for various return periods on the Island of Newfoundland is presented. The procedure is based on annual maximum instantaneous flows rather than annual maximum daily-mean flows, as the latter requires the conversion of estimated daily-mean flows into instantaneous flows. Regression equations were developed for each of three homogeneous regions for the desired return periods. The flood flow estimation capability of the presented procedure is demonstrated to be better than any other currently available procedure on the Island.     

GENERALIZED SKEW COEFFICIENTS OF ANNUAL FLOODS FOR LOUISIANA STREAMS1

ABSTRACT: A generalized skew map for Louisiana streams was developed using data from Louisiana, Mississippi, Arkansas, and Texas with 20 or more years of annual flood records. A comparison between the newly developed Louisiana Generalized Skew Map (LGSM) and the generalized skew map recommended by the U.S. Water Resources Council (WRCGSM) was performed. The mean square error for the LGSM was 16 percent less than that of WRCGSM in direct application of the two maps. Performance of the new map was compared with the WRCGSM and with a regional analysis procedure through its application to the Log Pearson Type 3 (LP3) distribution. Two-thirds of the stations tested had lower standardized root mean square deviations (SRMSD) by a narrow margin using the skew coefficients obtained from LGSM instead of WRCGSM. The regional analysis also performed as well as the LGSM in terms of SRMSD. Thus, it was concluded that both LGSM and the regional analysis provide a more reliable tool for flood frequency analysis for Louisiana streams with short annual flood records.     

PLOTTING FORMULA FOR FLOOD FREQUENCY1

ABSTRACT: In flood frequency analysis it is required to estimate the values of probabilities based on plotting formula. All of the many existing formula provide different results, particularly at the tails of the distribution. The existing practice in selection of a particular formula is rather arbitrary; and often Weibull's formula is recommended, which provided biased and conservative results. Based on the mean square criterion, a new plotting formula is developed, and it is given by F_m= (m - 0.24)/(N + 0.5).     

REGIONAL FLOOD EQUATIONS FOR THE PROVINCES OF ONTARIO AND QUEBEC1

ABSTRACT: When nonparametric frequency analysis was performed on 183 stations from Ontario and Quebec, unimodal and multimodal maximum annual flood density functions were discovered. In order to determine generating mechanisms, a monthly partitioning of the annual maximum floods was undertaken. The timing of the floods revealed that the unimodal distributions reflected a single flood generating mechanism while the multi-modal densities reflected two or more mechanisms. Based on the division of the flood series by mechanisms, nine homogeneous regions were delineated. L-moment distributional homogeneity tests along with smaller standard errors for the regional equations supported the delineation.     

INFLUENCE OF DIFFERENT TEMPORAL SAMPLING STRATEGIES ON ESTIMATING TOTAL PHOSPHORUS AND SUSPENDED SEDIMENT CONCENTRATION AND TRANSPORT IN SMALL STREAMS1

ABSTRACT: Various temporal sampling strategies are used to monitor water quality in small streams. To determine how various strategies influence the estimated water quality, frequently collected water quality data from eight small streams (14 to 110 km²) in Wisconsin were systematically subsampled to simulate typically used strategies. These subsets of data were then used to estimate mean, median, and maximum concentrations, and with continuous daily flows used to estimate annual loads (using the regression method) and volumetrically weighted mean concentrations. For each strategy, accuracy and precision in each summary statistic were evaluated by comparison with concentrations and loads of total phosphorus and suspended sediment estimated from all available data. The most effective sampling strategy depends on the statistic of interest and study duration. For mean and median concentrations, the most frequent fixed period sampling economically feasible is best. For maximum concentrations, any strategy with samples at or prior to peak flow is best. The best sampling strategy to estimate loads depends on the study duration. For one‐year studies, fixed period monthly sampling supplemented with storm chasing was best, even though loads were overestimated by 25 to 50 percent. For two to three‐year load studies and estimating volumetrically weighted mean concentrations, fixed period semimonthly sampling was best.     

AN ANALYSIS OF REGION‐OF‐INFLUENCE METHODS FOR FLOOD REGIONALIZATION IN THE GULF‐ATLANTIC ROLLING PLAINS1

ABSTRACT: Region‐of‐influence (RoI) approaches for estimating stream flow characteristics at ungaged sites were applied and evaluated in a case study of the 50‐year peak discharge in the Gulf‐Atlantic Rolling Plains of the southeastern United States. Linear regression against basin characteristics was performed for each ungaged site considered based on data from a region of influence containing the n closest gages in predictor variable (PRoI) or geographic (GRoI) space. Augmentation of this count based cutoff by a distance based cutoff also was considered. Prediction errors were evaluated for an independent (split‐sampled) dataset. For the dataset and metrics considered here: (1) for either PRoI or GRoI, optimal results were found when the simpler count based cutoff, rather than the distance augmented cutoff, was used; (2) GRoI produced lower error than PRoI when applied indiscriminately over the entire study region; (3) PRoI performance improved considerably when Rol was restricted to predefined geographic subregions.     

STATE-OF-THE-ART OF ESTIMATING FLOOD DAMAGE IN URBAN AREAS1

ABSTRACT: With implementation of the Flood Insurance Act of 1968 many additional local flood protection projects are being considered. Consulting engineers and local agencies need consistent methods to estimate flood damage in order to perform feasibility studies. Federal agencies have a great deal of data and long experience in making damage estimates but no comprehensive guides are available at the local level. Curves of flood damages to different residential structure types are presented. The relationships in use by the U. S. Federal Insurance Administration are shown to be reasonable and are recommended for use as approximate guides. Additional research is recommended and discussion of the paper is invited in order to make additional data available in the literature.     

A COMPARISON OF TRANSFORMATION METHODS FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The SMEMAX transformation, its modified versions and power transformation were applied to 55 long-term records of annual maximum flood flows tested previously for independence, homogeneity and completeness. Even though SMEMAX transformation reduced the coefficient of skewness to near zero for flood data, their distribution was not a true normal distribution. In almost all cases, the coefficient of kurtosis was quite different from 3.0 of the normal distribution. Empirical criteria showed that SMEMAX transformation performed well only for 40 (70 percent) of the 55 stations tested. Its performance level dropped, especially for stations which had both the coefficient of skewness and kurtosis greater than 3.0 and 10.0, respectively. Power transformation was generally better in transforming the flood data to a normal distribution. It performed well for 50 (90 percent) of the 55 stations tested. The coefficient of skewness in case of the data transformed by power transformation was much closer to the zero value than in the case of SMEMAX transformed series. The SMEMAX transformation and its two modified versions yielded identical results when flood frequency analysis was performed. Computationally, all three methods were equally simple and easy to apply for flood frequency analysis. In some cases, the coefficient of kurtosis for the transformed distributions obtained both by SMEMAX and power transformations deviated farther from that for the normal distribution than for the parent distribution.