STATISTICAL TERMINOLOGY: DEFINITIONS AND INTERPRETATION FOR FLOOD PEAK ESTIMATION1

ABSTRACT: Considerable effort is expended each year in making flood peak estimates at both gaged and ungaged sites. Many methods, both simplistic and complex, have been proposed for making such estimates. The hydrologist that must make an estimate at a particular site is interested in the accuracy of the estimate. Most methods are developed using either statistical analyses or analytical optimization schemes. While publications describing these methods often include some statistical measure of goodness-of-flt, the terminology often does not provide the potential user with an answer to the question,‘How accurate is the estimate?’ That is, statistical terminology often are not used properly, which may lead to a false sense of security. The use of the correct terminology will help potential users evaluate the usefulness of a proposed method and provide a means of comparing different methods. This study provides definitions for terms often used in literature on flood peak estimation and provides an interpretation for these terms. Specific problems discussed include the use of arbitrary levels of significance in statistical tests of hypotheses, the identification of both random and systematic variation in estimates from hydrologic methods, and the difference between accuracy of model calibration and accuracy of prediction.     

A PROBABILISTIC BENEFIT-COST ANALYSIS OF A ZONING PROGRAM FOR FLOOD PLAINS1

ABSTRACT: Various techniques, one of which is zoning, are used to control the extent of flood damage. The benefit-cost analysis of zoning programs must take into account the random nature of flooding. This paper outlines a method for determining not only the expected value of the benefit-cost ratio, but also the probability of such a zoning program being profitable. It also presents an application of the method to the assessment of the Outaouais Regional Community zoning program.     

COMPREHENSIVE FLOOD PLAIN MANAGEMENT1

Flooding and the susceptibility to flood damage inherent in all land uses constitute the flood hazard. Resolution of the hazard while properly recognizing flood plain environmental attributes within the context of overall community or area needs is the essence of comprehensive flood plain management. The traditional approach–flood control–has effected modification of only the flooding component of the hazard whether it be coastal or inland. Until recently Federal programs have overlooked the possibilities of modifying the susceptibility component, for which the major responsibility lies with non-Federal interests. Beginning with actions in the TVA area, the latter is now being strongly encouraged through Federal programs and actions notably the Flood Plain Management Services and Survey Programs of the Corps of Engineers, those stemming from Executive Order 11296, and those required for eligibility under the National Flood Insurance Act of 1968. Flood plain management objectives must be stated in planning, e.g., economic efficiency, reduction in threat to life and health, environmental improvement, and regional development, to permit proper evaluation of the optional means and approaches for achieving them.     

A NONTRADITIONAL METHODOLOGY FOR FLOOD STAGE-DAMAGE CALCULATIONS1

ABSTRACT: This paper presents a new methodology to calculate economic losses from hypothetical, extreme flood events, such as the Probable Maximum Flood. The methodology uses economic data compiled from already-available secondary sources, such as U.S. Census data on magnetic tapes, utilizing microcomputer and other electronic media. Estimates of land elevations are obtained from topographic maps, and flood elevations axe estimated using, for example, a dam breach and flood routing (DAMBRK) model (Fread, 1984). The calculations are performed at a disaggregate spatial scale, by various land use and industrial classification categories. The basic areal units are city blocks (for urbanized areas), enumeration districts, and Census tracts. Depth-damage functions, which provide an estimate of damages as a proportion of the existing value of the structure, are estimated statistically. Computer software (called DAMAGE) is used to combine the economic, flood elevation, and depth-damage information to compute economic losses for different possible flood stages and for different inflow events. Two case studies are presented as illustrations of the method.     

COMPARISON OF METHODS FOR ESTIMATING FLOOD MAGNITUDES ON SMALL STREAMS IN GEORGIA1

ABSTRACT: The U.S. Geological Survey has collected flood data for small, natural streams at many sites throughout Georgia during the past 20 years. Flood-frequency relations were developed for these data using four methods: (1) observed (log-Pearson Type HI analysis) data, (2) rainfall-runoff model, (3) regional regression equations, and (4) map-model combination. The results of the latter three methods were compared to the analyses of the observed data in order to quantify the differences in the methods and determine if the differences are statistically significant. Comparison of regression-estimates with observed discharges for sites having 20 years (1966 to 1985) and 10 years (1976 to 1985) of record at different sites of annual peak record indicate that the regression-estimates are not significantly different from the observed data. Comparison of rainfall-runoff-model simulated estimates with observed discharges for sites having 10 years and 20 years of annual peak record indicated that the model-simulated estimates are significantly and not significantly different, respectively. The biasedness probably is due to a “loss of variance” in the averaging procedures used within the model and the short length of record as indicated in the 10 and 20 years of record. The comparison of map-model simulated estimates with observed discharges for sites having 20 years of annual-peak runoff indicate that the simulated estimates are not significantly different. Comparison of “improved” map-model simulated estimates with observed discharges for sites having 20 years of annual-peak runoff data indicate that the simulated estimates are different. The average adjustment factor suggested by Lichty and Liscum to calculate the “improved” map-model overestimates in Georgia by an average of 20 percent for three recurrence intervals analyzed.     

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.     

Measuring the Effects of a Flood Control Project: Hedonic Land Price Approach

This article aims to measure the effects of a flood control project planned for the Chitose River Basin in Hokkaido Prefecture, Japan, using hedonic land price functions. In these functions, "annual expected depth of flood water" is introduced as an explanatory variable to represent the effect of the flood control project. Comparing the approach with the method of "the economic analysis of flood control projects", which has been a conventional evaluation method widely used in Japan, the efficiency and limitations of our approach are discussed.     

PROBLEMS OF REESTABLISHING COMMERCIAL RECREATION BUSINESSES IN NEW YORK FOLLOWING HURRICANE AGNES1

ABSTRACT: Forty-two commercial campgrounds and 34 commercial marinas were studied to determine the amount and types of flood-related damages incurred from Hurricane Agnes, and to evaluate the institutional measures available to help management overcome these losses. Economic losses incurred by firms due to inability to operate, and declines in the number of recreationists, were over twice the magnitude of losses suffered via direct physical damages from flooding. The Federal Flood Insurance Program, as presently constituted, is of very little use to firms having structural investments in and over water. Most firms were complimentary of the Small Business Administration's loan programs. It appears that active programs of communication and promotion are needed following restoration of regions involved in natural diasters to reestablish the tourist industry of those regions.     

Study on the damage statistical strength criterion of backfill with crack under thermo-mechanical coupling

ABSTRACT

Aiming at backfill with crack under the thermo-mechanical (TM) coupling, the concepts of crack macro-damage, loading meso-damage, thermal meso-damage, and total damage of backfill were proposed. Based on the statistical damage theory, considering the coupling effects of temperature, load and initial crack, a damage evolution model of backfill with crack under TM coupling effects was established. Based on this, the strength criterion of backfill with crack considering the effects of thermal and mechanical coupling was constructed by multivariate function full differential method. The research shows that: (1) The theoretical curves of damage evolution model and strength criterion of backfill with crack under TM coupling are in good agreement with the test curves, which verifies the rationality of the model. (2) The initial thermal damage decreases first and then increases with increasing temperature, reaches a minimum value at 40°C, and generally shows a “V” -shaped distribution law. The coupling effect of temperature and crack aggravates the total damage of the backfill. (3) The strength criterion can reflect the relationship between the stress and strain of each limit state and the parameters of backfill with crack under different temperature conditions and can provide a certain reference for the evaluation of the stability of backfill with geological defects such as joints and crack in deep high temperature mines.     

NEAR REAL-TIME MAPPING OF THE 1975 MISSISSIPPI RIVER FLOOD IN LOUISIANA USING LANDSAT IMAGERY1

ABSTRACT: The project described in this report was undertaken by the Louisiana State Planning Office to establish the extent of backwater flooding in Louisiana in April 1975. Band 7 Landsat imagery, enlarged to a scale of 1:250,000 was used to visually identify flooded areas. Inundated areas were delineated on overlays keyed to 1:250,000 U.S. Geological Survey topographic quadrangles. Tabular data identifying acres flooded, according to land use type, were derived by merging the flood map overlays with computerized 1972 land use data. Approximately 1.12 million acres of the state were inundated by flood waters. The total acreage and land use types affected by flooding were determined within 72 hours from the time the flood areas were imaged. Flooded maps were prepared for 26 parishes. Field observations were made by Louisiana Cooperative Extension Service county agents in order to determine the accuracy of parish flood maps and flood acreage figures by land use type. Results indicated that this was a fast, accurate, and relatively inexpensive method of compiling flood data for disaster planning and postflood analysis.     

FLOOD INUNDATION IN THE SOUTHEASTERN UNITED STATES FROM AIRCRAFT AND SATELLITE IMAGERY1

ABSTRACT: Panchromatic black and white, color, and color infrared photographs and thermal infrared imagery are compared for a capability to show flood boundaries. In open agricultural and urban areas, these boundaries are easily delineated on all types of am. Boundaries are more difficult to see in wooded areas. In March, hardwood trees are dormant, but black and white photographs and color photographs show only the tops of these trees. Color infrared photographs in January and March have a distinctive color or tone in inundated woods; the limit of this tone is the flood boundary. Daytime thermal infrared imagery in March shows that inundated woods are cooler than dry land but warmer than open water. After about April 1, both color infrared photography and thermal infrared imagery show only the top of the tree canopy and do not reflect underlying flood water. Inundated areas can be delineated easily on ERTS satellite imagery from December through March. On imagery from May 4–5, 1973, however, most inundation boundaries had to be drawn as dashed lines; the tree canopy obscures flood waters in wooded areas. Despite this problem, the results of mapping flood boundaries on May imagery are believed to be reasonable for the scale of the imagery.     

FLOOD WARNINGS AND FLOOD RESPONSES FOR THE RED RIVER OF THE NORTH1

ABSTRACT The flooding conditions in the basin of the Red River of the North are reviewed in terms of the accuracy of the flood forecasts and the response of both the floodplain occupants and government agencies to these forecasts. The flood prediction methods in Canada and the United States are compared. The accuracy of these prediction measures for the major floods in recent history is reviewed. The differences between the way in which the American and Canadian authorities approach the flood emergencies are outlined. The accuracy of the forecasts are plotted against a number of parameters which reflect the efficiency of the flood fighting measures initiated by those flood forecasts. The significant features of these plots are discussed.     

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.     

EVALUATION OF NINE MODELS FOR UNGAUGED URBAN BASINS IN LOUISIANA1

ABSTRACT: Nine flood-estimation models used for ungauged urban watersheds in Louisiana were evaluated. Flood-quantile predictions from simple regression models calibrated by local data were found to be more reliable than those more complicated models or models with many parameters that may not be accurately estimated. Flood prediction from models developed by using regionalization techniques were found to be reasonably good. Finally, application of a model outside of its limitations or domain may lead to substantial prediction error.     

EVALUATION OF PRACTICES IN WATER SUPPLY FORECASTING1

ABSTRACT: Snowmelt runoff is a primary source of water supply in much of the Western United States. Multipurpose planning requires long-range forecasts and the accuracy of the forecasts has a significant effect on economic benefits. In an effort to increase the accuracy of snowrnelt runoff forecasts, selected practices in water supply forecasting were evaluated. These practices include 1) using multiple regression in developing forecasting models;2) using a model that was calibrated to make forecasts an April 1 for making forecasts at other times;3) using maximum snow water equivalent measurements in forecast equations; and 4) using weighted snow water equivalent measurements for making forecasts. The results of a case study indicate that forecasting accuracy is significantly affected by these practices. Goodness-of-fit statistics may not be indicative of the accuracy of forecasts when the prediction equations are used to make forecasts for dates other than that used in calibration. The use of maximum snow water equivalentmeasurements and weighted averages did not improve forecast accuracy.