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.     

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.     

MULTIVARIATE EXTREME VALUE DISTRIBUTION WITH MIXED GUMBEL MARGINALS1

ABSTRACT: Bivariate and trivariate distributions have been derived from the logistic model for the multivariate extreme value distribution. Marginals in the models are extreme value type I distributions for two-component mixture variables (mixed Gumbel distribution). This paper is a continuation of the previous works on multivariate distribution in hydrology. Interest is focused on the analysis of floods which are generated by different types of storms. The construction of their corresponding probability distributions and density functions are described. In order to obtain the parameters of such a bivariate or trivariate distribution, a generalized maximum likelihood estimation procedure is proposed to allow for the cases of samples with different lengths of record. A region in Northern Mexico with 42 gauging stations, grouped into two homogeneous regions, has been selected to apply the models. Results produced by the multivariate distributions have been compared with those obtained by the Normal, log-Normal-2, log-Normal-3, Gamma-2, Gamma-3, log-Pearson-3, Gumbel, TCEV and General Extreme Value distributions. Goodness of fit is measured by the criterion of standard error of fit. Results suggest that the proposed models are a suitable option to be considered when performing flood frequency analysis.     

SOME TECHNIQUES FOR USING FREQUENCY ANALYSIS AND REALTIME DATA TO INTERPRET FLOOD POTENTIAL DATA1

ABSTRACT: Flood potential data can be effectively interpreted if simple frequency analysis concepts are used to explain the significance of flood potential. Instead of simply presenting data as a quantitative amount or as a percentage of the average condition, predictions can be discussed in terms of their probabilities of exceedance, or return periods. Criteria are presented for evaluating the significance of various return periods. Frequency interpretations are applied to snow course data, peak flow forecasts, and streamflow volume forecasts in northern Utah to illustrate these concepts. In addition, access to realtime data allows tracking of snowmelt progression and identification of any deviations from the forecast flood potential situation. Several data elements, including snowpack, streamfiow volume and peak, and realtime data are jointly evaluated to assess potential hazard and probable risk.     

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.     

REGIONALIZATION AND PREDICTION OF ANNUAL FLOODS IN THE FRASER RIVER CATCHMENT,BRITISH COLUMBIA1

A method of predicting probability distributions of annual floods is presented and is applied to the Fraser River catchment of British Columbia. The Gumbel distribution is found to adequately describe the observed flood frequency data. Using the estimated Gumbel parameters, discriminant analysis is performed to separate basins into flood regions. Within each region, regression analysis is used to relate physiographic and climatic variables to the means and standard deviations of the annual flood series. The regression equations are applied to four test basins and the results indicate that the method is suitable for an estimation of annual floods.     

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.     

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.     

Examining Flood Frequency Distributions in the Midwest U.S.1

Villarini, Gabriele, James A. Smith, Mary Lynn Baeck, and Witold F. Krajewski, 2011. Examining Flood Frequency Distributions in the Midwest U.S. Journal of the American Water Resources Association (JAWRA) 47(3):447‐463. DOI: 10.1111/j.1752‐1688.2011.00540.x Abstract: Annual maximum peak discharge time series from 196 stream gage stations with a record of at least 75 years from the Midwest United States is examined to study flood peak distributions from a regional point of view. The focus of this study is to evaluate: (1) “mixtures” of flood peak distributions, (2) upper tail and scaling properties of the flood peak distributions, and (3) presence of temporal nonstationarities in the flood peak records. Warm season convective systems are responsible for some of the largest floods in the area, in particular in Nebraska, Kansas, and Iowa. Spring events associated with snowmelt and rain‐on‐snow are common in the northern part of the study domain. Nonparametric tests are used to investigate the presence of abrupt and slowly varying changes. Change‐points rather than monotonic trends are responsible for most violations of the stationarity assumption. The abrupt changes in flood peaks can be associated with anthropogenic changes, such as changes in land use/land cover, agricultural practice, and construction of dams. The trend analyses do not suggest an increase in the flood peak distribution due to anthropogenic climate change. Examination of the upper tail and scaling properties of the flood peak distributions are examined by means of the location, scale, and shape parameters of the Generalized Extreme Value distribution.     

Simulated interior floods and the flood experience in urban communities

The Hydrologic Engineering Center (HEC-1) model was used to construct synthetic hydrographs for isolated interior urban floods. Flood peak and lag time were very well preserved in simulated flows. Total volume was not adequately expressed. Lag time varied inversely with both urban development and storm intensity. Peak discharge varied with storm intensity, but this variability was well defined only at very high urbanization levels. An 175% increase in storm intensity produced a change of about 15% in peak discharge. Claims for flood damage correlated well with estimates of peak flow and lag time combined. Other measures of flood experience also correlated with the two features. Within the range of storms utilized, urban development factors consistently outranked storm intensity as a determining factor in flood damage.     

Nonparametric Monte Carlo Simulation for Flood Frequency Curve Derivation: An Application to a Korean Watershed1

Abstract: A mix of causative mechanisms may be responsible for flood at a site. Floods may be caused because of extreme rainfall or rain on other rainfall events. The statistical attributes of these events differ according to the watershed characteristics and the causes. Traditional methods of flood frequency analysis are only adequate for specific situations. Also, to address the uncertainty of flood frequency estimates for hydraulic structures, a series of probabilistic analyses of rainfall‐runoff and flow routing models, and their associated inputs, are used. This is a complex problem in that the probability distributions of multiple independent and derived random variables need to be estimated to evaluate the probability of floods. Therefore, the objectives of this study were to develop a flood frequency curve derivation method driven by multiple random variables and to develop a tool that can consider the uncertainties of design floods. This study focuses on developing a flood frequency curve based on nonparametric statistical methods for the estimation of probabilities of rare floods that are more appropriate in Korea. To derive the frequency curve, rainfall generation using the nonparametric kernel density estimation approach is proposed. Many flood events are simulated by nonparametric Monte Carlo simulations coupled with the center Latin hypercube sampling method to estimate the associated uncertainty. This study applies the methods described to a Korean watershed. The results provide higher physical appropriateness and reasonable estimates of design flood.     

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.     

COUPLING OF NONPARAMETRIC FREQUENCY AND L-MOMENT ANALYSES FOR MIXED DISTRIBUTION IDENTIFICATION 1

ABSTRACT: Both L-moment and nonparametric frequency analyses were performed on a series of annual maximum floods from New Brunswick, Canada. The L-moment analysis concluded that the data were generated from a unimodal Generalized Extreme Value (GEV) distribution. However, the nonparametric frequency analysis indicated that a majority of stations followed nonunimodal mixed distributions since peak flows occur during different seasons and are the result of different generating mechanisms. The coupling of L-moment and nonparametric analyses facilitates mixed distribution identification. Thus, the nonparametric method helps in identifying underlying probability distribution, especially when samples arise from mixed distributions.     

RAINFALL POINT INTENSITIES IN AN AIR MASS THUNDERSTORM ENVIRONMENT: WALNUT GULCH,ARIZONA1

ABSTRACT: Point rainfall intensities for a given return period are often used to formulate design storms for rainfall/runoff models to simulate design floods. These design floods are in turn used to design bridges, culverts, and a variety of drainage and flood control structures. The projected rapid growth in the southwestern United States will require very substantial monetary investments in drainage infrastructure. Accurate estimates of point rainfall intensities are critical to ensure both safe designs while not wasting dollars in overdesign. Rainfall point intensities (accumulated rainfall depth over a specified duration) for 5‐, 15‐, 30‐, and 60‐minute durations for the 2‐, 5‐, 10‐, 25‐, 50‐, and 100‐year return periods were determined for southeast Arizona. Thirty‐five years of rainfall record (1961 to 1995) were used in this study. The records came from 20 stations that were grouped into five sets of four independent stations to extend the rainfall records. The stations are in the USDA‐ARS Walnut Gulch Experimental Watershed (WGEW), which is representative of large portions of the Southwest whose runoff generation is dominated by air‐mass thunderstorms. The 5‐, 15‐, 30‐, and 60‐minute maximum intensities per year followed log‐normal distributions. The mean point rainfall intensities of the five sets of gages are very close (between 0 and 11 percent) to the NOAA values of the 5‐, 15‐, 30‐, and 60‐minute durations for all return periods. Much larger differences between the mean point rainfall intensities for all durations were found when these results were compared to those of a previous study done with a shorter rainfall record (between 14 and 33 percent for the 25‐, 50‐, and 100‐year return‐periods). The difference between the largest and the smallest values of point rainfall intensities recorded by each group, for all durations, usually increases as the return period increases.     

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.     

A HYDROCLIMATIC APPLICATION STRATEGY FOR THE POISSON PARTIAL DURATION MODEL1

ABSTRACT: A strategy for formulating and testing the Poisson partial duration extreme value model is presented. The procedure is demonstrated using recorded Streamflow series from a humid subtropical region of the southern United States. The observed data series are partitioned by climatic causes and tested for both the Poisson assumption and the validity of the exponential as marginal distributions. Several statistical tests are utilized in making these determinations. Some important aspects of the model as applied to humid climates are demonstrated. It was found that a majority of Streamflow series could be represented by the model and that significant differences do exist between the arrival structures of floods resulting from different climatic mechanisms. However, these differences generally do not exist in the distribution of the flood magnitudes. In addition, it is possible that model validity is restricted by drainage basin size.     

Braided River Flow and Invasive Vegetation Dynamics in the Southern Alps, New Zealand

In mountain braided rivers, extreme flow variability, floods and high flow pulses are fundamental elements of natural flow regimes and drivers of floodplain processes, understanding of which is essential for management and restoration. This study evaluated flow dynamics and invasive vegetation characteristics and changes in the Ahuriri River, a free-flowing braided, gravel-bed river in the Southern Alps of New Zealand’s South Island. Sixty-seven flow metrics based on indicators of hydrologic alteration and environmental flow components (extreme low flows, low flows, high flow pulses, small floods and large floods) were analyzed using a 48-year flow record. Changes in the areal cover of floodplain and invasive vegetation classes and patch characteristics over 20 years (1991–2011) were quantified using five sets of aerial photographs, and the correlation between flow metrics and cover changes were evaluated. The river exhibits considerable hydrologic variability characteristic of mountain braided rivers, with large variation in floods and other flow regime metrics. The flow regime, including flood and high flow pulses, has variable effects on floodplain invasive vegetation, and creates dynamic patch mosaics that demonstrate the concepts of a shifting mosaic steady state and biogeomorphic succession. As much as 25 % of the vegetation cover was removed by the largest flood on record (570 m³/s, ~50-year return period), with preferential removal of lupin and less removal of willow. However, most of the vegetation regenerated and spread relatively quickly after floods. Some flow metrics analyzed were highly correlated with vegetation cover, and key metrics included the peak magnitude of the largest flood, flood frequency, and time since the last flood in the interval between photos. These metrics provided a simple multiple regression model of invasive vegetation cover in the aerial photos evaluated. Our analysis of relationships among flow regimes and invasive vegetation cover has implications for braided rivers impacted by hydroelectric power production, where increases in invasive vegetation cover are typically greater than in unimpacted rivers.     

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.     

APPLICATION OF ADVANCES IN FLOOD FREQUENCY ANALYSIS1

ABSTRACT: Flood frequency analyses are frequently being made using widely available computer programs. Serious errors can result from blind acceptance of such results. Visual interpretation of observed flood series can be used for evaluation on frequency paper with compatible scales. Such frequency papers are presented in the paper. In ephemeral streams, more infrequent floods may constitute a separate set from the more frequent floods because (a) runoff producing storms cover only a portion of the contributing area, (b) transmission losses in the normally dry streambed may reduce the peak flow, and (c) some runoff may be stored in stock water ponds which therefore leads to partial area runoff. The Cunnane plotting position used in this paper is superior to the more widely used Weibull equation, having a mathematically sound basis for locating observed floods on an assumed probability.     

Climate Change Impacts and Uncertainties on Spring Flooding of Lake Champlain and the Richelieu River

The source of the Richelieu River is Lake Champlain, located between the states of New York, Vermont, and Québec. In 2011, the lake and the Richelieu River reached historical flood levels, raising questions about the influence of climate change on the watershed. The objectives of this work are to model the hydrology of the watershed, construct a reservoir model for the lake and to analyze flooding trends using climate simulations. The basin was modeled using the HSAMI lumped conceptual model from Hydro‐Québec with a semi‐distributed approach in order to estimate the inflows into Lake Champlain. The discharge at the Richelieu River was computed by using a mass balance equation between the inputs and outputs of Lake Champlain. Future trends were estimated over the 2041‐2070 and 2071‐2100 periods using a large number of outputs from general circulation models and regional climate models downscaled with constant scaling and daily translation methods. While there is a certain amount of uncertainty as to future trends, there is a decreasing tendency in the magnitude of the mean spring flood. A flood frequency analysis showed most climate projections indicate the severity of most extreme spring floods may be reduced over the two future periods although results are subject to a much larger uncertainty than for the mean spring flood. On the other hand, results indicate summer‐fall extreme events such as caused by hurricane Irene in August 2011 may become more frequent in the future.