BIVARIATE FREQUENCY ANALYSIS OF FLOODS USING COPULAS1

Abstract: Bivariate flood frequency analysis offers improved understanding of the complex flood process and useful information in preparing flood mitigation measures. However, difficulties arise from limited bivariate distribution functions available to jointly model the correlated flood peak and volume that have different univariate marginal distributions. Copulas are functions that link univariate distribution functions to form bivariate distribution functions, which can overcome such difficulties. The objective of this study was to analyze bivariate frequency of flood peak and volume using copulas. Separate univariate distributions of flood peak and volume are first fitted from observed data. Copulas are then employed to model the dependence between flood peak and volume and join the predetermined univariate marginal distributions to construct the bivariate distribution. The bivariate probabilities and associated return periods are calculated in terms of univariate marginal distributions and copulas. The advantage of using copulas is that they can separate the effect of dependence from the effects of the marginal distributions. In addition, explicit relationships between joint and univariate return periods are made possible when copulas are employed to construct bivariate distribution of floods. The annual floods of Tongtou flow gauge station in the Jhuoshuei River, Taiwan, are used to illustrate bivariate flood frequency analysis.     

ANALYZING URBANIZATION IMPACTS ON PENNSYLVANIA FLOOD PEAKS1

ABSTRACT: The impact of man made change on the hydrology of developing watersheds is frequently measured in terms of the ratio: flood peak after development to flood peak before development over a range of return periods. However, the analysis of urbanization effects on flood frequency presents a vexing problem because of a general lack of flood data in urban areas and also because of nonstationarity in the development process. Clearly, the flood peak ratio depends on the impervious fraction and percent of basin sewered and these factors have been taken into account in recent urban flood peak models. In genral, these models are developed either by: (1) split sample analysis of available annual flood data, or (2) by computer simulation using mathematical watershed models capable of representing man made changes. The present paper discusses the results of work in progress to characterize the impact of urbanization on small developing watersheds in Pennsylvania.     

THE USE OF FLOOD POTENTIAL INDICES FOR FLOOD PEAK ESTIMATION ON UNGAGED WATERSHEDS1

: The construction of a flood peak index map was attempted for use by hydrologists in the simple format of rainfall maps. Since flood peaks are highly dependent on watershed area, the effect of area was removed. By regression analysis flood peaks of 2.33 and 100-year return periods were found to be proportional to watershed area to the 0.8 and 0.7 powers, respectively. Therefore, indices C_{2 33}= Q_{2 33}/_A0.7 were completed at each gage and plotted on a Pennsylvania map. It was attempted to further remove some of the scatter by regression of C with several other watershed parameters like slope, percent forest cover, and watershed shape, but no significant correlation could be found. The index maps, drawn without attenuation of the scatter, can be used by hydrologists to compute flood peaks as Q = CAⁿ (with n = 0.8 and 0.7 for the 2.33 and 100-year flood peaks, respectively). Flood peak safety factors can be based on visual observation of the index variation in the vicinity of the location for which the flood peak estimate is needed.     

Impacts of Climate Change on Extreme Precipitation Events Over Flamingo Tropicana Watershed1

Abstract: Climate change, particularly the projected changes to precipitation patterns, is likely to affect runoff both regionally and temporally. Extreme rainfall events are expected to become more intense in the future in arid urban areas and this will likely lead to higher streamflow. Through hydrological modeling, this article simulates an urban basin response to the most intense storm under anthropogenic climate change conditions. This study performs an event‐based simulation for shorter duration storms in the Flamingo Tropicana (FT) watershed in Las Vegas, Nevada. An extreme storm, defined as a 100‐year return period storm, is selected from historical records and perturbed to future climatic conditions with respect to multimodel multiscenario (A1B, A2, B1) bias corrected and spatially disaggregated data from the World Climate Research Programme's (WCRP's) database. The cumulative annual precipitation for each 30‐year period shows a continuous decrease from 2011 to 2099; however, the summer convective storms, which are considered as extreme storms for the study area, are expected to be more intense in future. Extreme storm events show larger changes in streamflow under different climate scenarios and time periods. The simulated peak streamflow and total runoff volume shows an increase from 40% to more than 150% (during 2041‐2099) for different climate scenarios. This type of analysis can help evaluate the vulnerability of existing flood control system and flood control policies.     

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.     

NONPARAMETRIC STATISTICAL ANALYSIS OF ANNUAL PEAK FLOW DATA FROM A RECENTLY URBANIZED WATERSHED1

ABSTRACT. In order to demonstrate the feasibility of a nonparametric statistical application in investigating the hydrologic impact of the rapid land use change accompanying intense urbanization, annual maximum peak flow data from an actual example (the Northeast Branch Basin, a recently urbanized Washington, D.C., suburban watershed) were analyzed. Annual peak flow data from the Patuxent Basin above Unity, Maryland, a rural watershed in close proximity to the study area, were compared to data from the Northeast Branch for the Same period utilizing the Wilcoxon matched-pairs signed-ranks test. A change in central tendency of each series was noted at the 0.01 significance level; however, the change was negative in the rural basin and positive in the urbanized Northeast Branch Basin. This central tendency change was considered indicative of an average decrease in the size of rainstorms producing annual maximum peak discharges. Rainstorm data from the Northeast Branch Basin were divided into two equal periods (before urbanization and after) and the Wilcoxon test was applied. It was found that rainstorms producing maximum annual peak discharges in the urbanized period were indeed smaller than those in the prior period (0.01 level of significance); however, larger annual peaks were produced. It was concluded that nonparametric statistical methods can be used readily with conventional methods to isolate and clearly analyze the various problems in an actual urban hydrologic study.     

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.     

ESTIMATING THE Q100 IN BRITISH COLUMBIA: A PRACTICAL PROBLEM IN FOREST HYDROLOGY1

ABSTRACT. Estimates of peak flows, with specified return periods, are needed in practice for the design of works that affect streams in forested areas. In the province of British Columbia (B.C.), Canada, the new Forest Practices Code specifies the 100-year instantaneous peak flow (Q100) for the design of bridges and culverts for stream crossings under forest roads; and many practitioners are engaged in making such estimates. The state of the art is still quite primitive, very similar to the state of urban hydrology 30 years ago, when popular estimating techniques were used with little consideration given to their applicability. Urban hydrology then evolved on a much more scientific basis, such that within about a 10-year period, standard approaches to design were developed. Forest hydrology should follow the same pattern, at least as far as estimating design flows is concerned. Popular present day design procedures include the rational method and other empirical approaches based on rainfall data, as use of the standard flood frequency approach is limited by the paucity of relevant flow data. Estimating procedures based on peak streamflow measurements and statistics are likely to evolve, and these will include distinctions for rain, snowmelt, and rain on snow floods. Guidelines will also be developed for selecting and applying appropriate procedures for particular areas.     

OPTICAL DATA PROCESSING AND PROJECTED APPLICATIONS OF THE ERTS-1 IMAGERY COVERING THE 1973 MISSISSIPPI RIVER VALLEY FLOODS1

ABSTRACT. Flooding along the Mississippi River and some of its tributaries was detected by the multispectral scanner (MSS) on the Earth Resources Technology Satellite (ERTS-1) on at least three orbits during the spring of 1973. The ERTS data provided the first opportunity for mapping the regional extent of flooding at the time of the imagery. Special optical data processing techniques were used to produce a variety of multispectral color composites enhancing flood-plain details. One of these, a 2-color composite of near infrared bands 6 and 7, was enlarged and registered to 1:250,000-scale topographic maps and used as the basis for preparation of flood image maps. Two specially filtered 3-color composites of MSS bands 5, 6, and 7 and 4, 5, and 7 were prepared to aid in the interpretation of the data. The extent of the flooding was vividly depicted on a single image by 2-color temporal composites produced on the additive-color viewer using band 7 flood data superimposed on pre-flood band 7 images. On May 24, when the floodwaters at St. Louis receded to bankfull stage, imagery was again obtained by ERTS. Analysis of temporal data composites of the pre-flood and post-flood band 7 images indicate that changes in surface reflectance characteristics caused by the flooding can be delineated, thus making it possible to map the overall area flooded without the necessity of a real-time system to track and image the peak flood waves. Regional planning and disaster relief agencies such as the Corps of Engineers, Office of Emergency Preparedness, Soil Conservation Service, interstate river basin commissions and state agencies, as well as private lending and insurance institutions, have indicated strong potential applications for ERTS image-maps of flood-prone areas.     

REGIONALIZATION AND PREDICTION OF FLOODS IN THE FRASER RIVER CATCHMENT,B.C.1

Probability distributions that model the return periods of flood characteristics derived from partial duration series are proposed and tested in the Fraser River catchment of British Columbia. Theoretical distributions describing the magnitude, duration, frequency and timing of floods are found to provide a goof fit to the observed data. The five estimated parameters summarizing the flood characteristics of each basin are entered into a discriminant analysis procedure to establish flood regions. Three regions were identified, each displaying flood behavior closely related to the physical conditions of the catchment. Within each region, regression equations are obtained between parameter values and basin climatic and physiographic variables. These equations provide a satisfactory prediction of flood parameters and this allows the estimation of a comprehensive set of flood characteristics for areas with sparse hydrologic information.     

Classification and assessment of water bodies as adaptive structural measures for flood risk management planning

Severe rainfall events have become increasingly common in Europe. Flood defence engineering works are highly capital intensive and can be limited by land availability, leaving land and communities exposed to repeated flooding. Any adaptive drainage structure must have engineered inlets and outlets that control the water level and the rate of release. In Scotland, there are a relatively high number of drinking water reservoirs (operated by Scottish Water), which fall within this defined category and could contribute to flood management control. Reducing the rate of runoff from the upper reaches of a catchment will reduce the volume and peak flows of flood events downstream, thus allowing flood defences to be reduced in size, decreasing the corresponding capital costs. A database of retention basins with flood control potential has been developed for Scotland. The research shows that the majority of small and former drinking water reservoirs are kept full and their spillways are continuously in operation. Utilising some of the available capacity to contribute to flood control could reduce the costs of complying with the EU Flood Directive. Furthermore, the application of a previously developed classification model for Baden in Germany for the Scottish data set showed a lower diversity for basins in Scotland due to less developed infrastructure. The principle value of this approach is a clear and unambiguous categorisation, based on standard variables, which can help to promote communication and understanding between stakeholders.     

COMPREHENSIVE FLOOD PLAIN STUDIES USING SPATIAL DATA MANAGEMENT TECHNIQUES1

ABSTRACT: A pilot study undertaken to develop and test analytical methodologies for application in comprehensive flood plain information studies is described. The methodology permits and encourages comprehensive, systematic, practical assessments of present and alternative future basin-wide development patterns as reflected by alternative land use patterns and physical works in terms of flood hazard, economic damage potential and selected environmental consequences. The analysis methodologies are centered about integrated use of computerized spatial, gridded geographic and resource data files. A family of special purpose utility computer programs access the data file and extract appropriate variables and interpret and format the data into specific analytical parameters that are subsequently formatted for input to traditional modeling computer programs. An example application to Trail Creek in Clarke County, Georgia, is described.     

MANAGEMENT OF INSTREAM FLOWS THROUGH RUNOFF DETENTION AND RETENTION1

ABSTRACT: The use of reservoirs and land treatments to manage streamflow for the maintenance or enhancement of instream flow values is a valid concept. Historically, large reservoirs have been used for flood control and water-supply regulation. Smaller structures have enjoyed widespread use for soil and water conservation in headwater areas. Where reservoir releases can be controlled, it is technically feasible to regulate flows for the enhancement of instream values. However, institutional and political obstacles may preclude the operation of some reservoirs for this purpose. Retention and detention structures and land treatments, implemented for soil and water conservation purposes, have often had favorable effects on the streamflow hydrograph. Decreases in peak flows and increases in low flows have been documented. Design concepts for runoff-control structures are discussed in relation to instream flow management objectives. Hydro-logic simulation is offered as a potential tool for project design and feasibility analysis.     

Copula-Based Bivariate Return Period Analysis and Its Implication to Hydrological Design Event

In univariate frequency analysis, the return period of an event has a one-to-one correspondence with its characteristic value, and the response of the hydraulic structure to hydrological load expressed by the hydrological event is monotonic. Thus, the design criteria of the hydraulic structure can be equivalently represented by the return period of the hydrological event, and consequently, design event-based design parameters evaluated have been widely used in practical engineering. However, the monotonic correspondence between the return period of the hydrological event and the response of the hydraulic structure does not exist in the multivariate context, and hydrological load with a larger joint return period does not always produce a more unsafe response. Misunderstandings of concepts of return periods of hydrological event, and estimation of hydrological design events usually take place in multivariate frequency analysis. This study theoretically derives the relations between different types of joint return periods, joint return period and its marginal return periods, the occurrence of bivariate extreme events and their return periods, and then the theoretical framework is tested. Results from the case contribute to the understanding of bivariate return periods of hydrological event, and the results demonstrate that design criteria cannot be equivalently represented by joint return periods of hydrological load, and design parameters of the hydraulic structure should not be determined by multivariate hydrological design events.     

A Framework to Develop Nationwide Flooding Extents Using Climate Models and Assess Forecast Potential for Flood Resilience

The methods used to simulate flood inundation extents can be significantly improved by high‐resolution spatial data captured over a large area. This paper presents a hydraulic analysis methodology and framework to estimate national‐level floodplain changes likely to be generated by climate change. The hydraulic analysis was performed using existing published Federal Emergency Management Agency 100‐year floodplains and estimated 100‐ and 10‐year return period peak flow discharges. The discharges were estimated using climate variables from global climate models for two future growth scenarios: Representative Concentration Pathways 2.6 and 8.5. River channel dimensions were developed based on existing regional United States Geological Survey publications relating bankfull discharges with channel characteristics. Mathematic relationships for channel bankfull topwidth, depth, and side slope to contributing drainage area measured at model cross sections were developed. The proposed framework can be utilized at a national level to identify critical areas for flood risk assessment. Existing hydraulic models at these “hot spots” could be repurposed for near–real‐time flood forecasting operations. Revitalizing these models for use in simulating flood scenarios in near–real time through the use of meteorological forecasts could provide useful information for first responders of flood emergencies.     

A METHOD FOR ESTIMATING PEAK WATER DEMAND OF MULTIFAMILY RESIDENCES1

ABSTRACT: The importance of estimating peak water demands for determining the dimensions of pipe size and meters which provide household water to multifamily residences is examined. Several methods utilized in North America and Europe are examined. The analysis makes clear the necessity of studying the peak water demand through statistics based on local data concerning multifamily residences. For different periods of return, the peak demand of a given apartment building is related to its size (the number of apartments) in order to compare the results obtained with existing formula. By use of Ridge-regression technique, the relationship between peak water demand, and building size (number of apartments) and available pressure is established. It can be concluded that peak demand can be estimated with the square root of number of apartment units in the building and the cube root of water pressure.     

HYDROLOGIC DESIGN CONSIDERATIONS OF CONSTRUCTED WETLANDS FOR URBAN STORMWATER RUNOFF1

ABSTRACT: The successful design of constructed wetlands requires a continuous supply of water or vegetation that can withstand drought conditions. Having a constant water source is the best alternative to insure species diversity throughout the season. Consequently, detention structure designs should be based on times between events as well as on hydrologic return periods, since between events is when most evaporation and infiltration losses are likely to occur. In arid or semi-arid environments, this is a difficult process because of long interevent times and seasonal changes in precipitation patterns. This discussion is predicated on the assumption that phytoplankton, epiphytic algae, and emergent vegetation require moist conditions to be effective at removing nutrients, metals and other pollutants. There are drought tolerant species of vegetation that can be used in constructed wetlands but it may take several days to re-establish the attached bacteria communities necessary for optimum pollutant removal. This paper examines a stochastic framework to examine the probability of extended dry periods based on historic rainfall data. The number of consecutive dry days is selected for a specified level of assurance. By multiplying this value by the sum of daily system losses, an overall pond volume can be determined that ensures a minimum depth of water. To illustrate the utility of the approach, the method is applied to a site in Spokane, Washington.     

AN APPLICATION OF DISCRIMINANT ANALYSIS TO PREDICT INDUSTRIAL/COMMERCIAL FLOOD PLAIN LOCATION1

ABSTRACT: This paper describes the techniques of factor and discriminant analyses to isolate and quantify the statistical differences between firms located on flood plains and those located off flood plains. The research effort described consists of three segments: data collection, isolation of potential classification variables, and the determination of the appropriate discriminant functions to classify a given fm as either on or off the flood plain. Significant classification functions are developed for both manufacturing and commercial establishments, whose arguments include dollar sales volume, total shipping cost, total employee cost, dollar valuations on the building and inventories, all on an annual basis, and the square footage of the site.     

Improvements on Flood Alleviation in Germany: Lessons Learned from the Elbe Flood in August 2002

The increase in damage due to natural disasters is directly related to the number of people who live and work in hazardous areas and continuously accumulate assets. Therefore, land use planning authorities have to manage effectively the establishment and development of settlements in flood-prone areas in order to avoid the further increase of vulnerable assets. Germany faced major destruction during the flood in August 2002 in the Elbe and Danube catchments, and many changes have been suggested in the existing German water and planning regulations. This article presents some findings of a “Lessons Learned” study that was carried out in the aftermath of the flood and discusses the following topics: 1) the establishment of comprehensive hazard maps and flood protection concepts, 2) the harmonization of regulations of flood protection at the federal level, 3) the communication of the flood hazard and awareness strategies, and 4) how damage potential can be minimized through measures of area precaution such as resettlement and risk-adapted land use. Although attempts towards a coordinated and harmonized creation of flood hazard maps and concepts have been made, there is still no uniform strategy at all planning levels and for all states (Lae nder) of the Federal Republic of Germany. The development and communication of possible mitigation strategies for “unthinkable extreme events” beyond the common safety level of a 100-year flood are needed. In order to establish a sustainable and integrated flood risk management, interdisciplinary and catchment-based approaches are needed.     

ESTIMATION OF SOIL MOISTURE FROM SEASAT SAR DATA1

ABSTRACT A study was made to determine if Seasat Synthetic Aperture Radar (SAR) data could be used to make practical estimates of soil moisture. Extensive ground measurements were collected at two primary sites near Guymon, Oklahoma, and Sublette, Kansas. The relative sensitivity of the SAR to differences in soil moisture, tillage roughness, and vegetation was determined. To validate the effects detected in the SAR data, an airborne scatterometer with a similar wavelength was flown repeatedly over the Guymon site. Soil moisture variations in the surface 2 cm and surface 15 cm of fields with bare soil, milo and alfalfa produce similar responses in the scattering coefficient from both systems. Roughness due to tillage in row crops produced as much as 12–15 dB increase in the scatterometer return. Most agricultural vegetation was effectively penetrated by the L-band frequencies; however, corn produced an exceptionally high radar return either standing or after combine harvesting. When corn had ripened, there was some evidence that tillage roughness could be detected through the canopy. Moderate tillage roughness produced by grain drill furrows caused over 12 dB increase in return when row directions changed from parallel to perpendicular with respect to the SAR look direction. Dramatic increases in return occurred when vegetation surfaces were wet. Increased radar returns from tillage roughness, some vegetation and wet vegetation surfaces, all dyanmic in nature, were significant and may limit the practical estimation of soil moisture from the radar data.