CORRELATION OF ANNUAL PEAK FLOWS FOR PENNSYLVANIA STREAMS1

A common assumption in flood frequency analysis is that annual peak flows are independent events. This study was undertaken to investigate the validity of this assumption with regard to Pennsylvania streams by statistically analyzing the dependence between annual peak flows and to determine if basin carryover effects relate to the degree of dependence. Five tests of dependence, the autocorrelation test, the median crossing test, the turning points test, the rank difference test, and the Spearman rank order serial correlation coefficient test were applied to the series of annual peak flows for 57 streams. Of the 57 streams analyzed, only two exhibited signs of dependence by at least two of the tests performed, and the baseflow component of annual peak flows was found to be unrelated to the degree of dependence exhibited between annual peak flows. It was concluded that the assumption of independence of annual peak flows is valid in flood frequency analysis for Pennsylvania streams.     

PREDICTION OF PEAK FLOWS ON SMALL WATERSHEDS IN OREGON FOR USE IN CULVERT DESIGN1

ABSTRACT: Using data from 80 Oregon watersheds that ranged in size from 0.54 km² to 27.45 km², equations were developed to predict peak flows for use in culvert design on forest roads. Oregon was divided into six physiographic regions based on previous studies of flood frequency. In each region, data on annual peak flow from gaging stations with more than 20 years of record were analyzed using four flood frequency distributions: type 1 extremal, two parameter-log normal, three parameter-log normal, and log-Pearson type III. The log-Pearson type III distribution was found to be suitable for use in all regions of the State, based on the chi-square goodness-of-fit-test. Flood magnitudes having recurrence intervals of 10, 25, 50, and 100 years were related to physical and climatic characteristics of drainage basins by multiple regression. Drainage basin size was the most important variable in explaining the variation of flood peaks in all regions. Mean basin elevation and mean annual precipitation were also significantly related to flood peaks in two regions of western Oregon. The standard error of the estimate for the regression relationships ranged from 26 to 84 percent.     

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.     

SAMPLE UNCERTAINTY IN FLOOD LEVEE DESIGN: BAYESIAN VERSUS NON-BAYESIAN METHODS1

ABSTRACT: Bayesian and non-Bayesian flood levee design methods that account for the uncertainty due to limited record length are compared using a case study. The first method, Bayesian decision theory (BDT), imbeds the uncertainty in the parameters of the yearly peak stage into a loss function. The optimum design of the flood levee, called Bayes design, corresponds to the minimum expected loss, called Bayes risk. The second method, induced safety algorithm (ISA), computes a margin of safety to be added to either an existing levee or a levee designed by classical benefit-cost analysis. The design decision is shown to fluctuate as different record lengths are considered. For short record lengths, BDT, which takes small sample bias into account, appears to yield a more conservative design than ISA. On the other hand, ISA, which is simple to implement, seems to be preferable to BDT for longer record lengths.     

Increased Frequency of Low‐Magnitude Floods in New England1

Armstrong, William H., Mathias J. Collins, and Noah P. Snyder, 2012. Increased Frequency of Low‐Magnitude Floods in New England. Journal of the American Water Resources Association (JAWRA) 48(2): 306‐320. DOI: 10.1111/j.1752‐1688.2011.00613.x Abstract: Recent studies document increasing precipitation and streamflow in the northeastern United States throughout the 20th and early 21st Centuries. Annual peak discharges have increased over this period on many New England rivers with dominantly natural streamflow – especially for smaller, more frequent floods. To better investigate high‐frequency floods (<5‐year recurrence interval), we analyze the partial duration flood series for 23 New England rivers selected for minimal human impact. The study rivers have continuous records through 2006 and an average period of record of 71 years. Twenty‐two of the 23 rivers show increasing trends in peaks over threshold per water year (POT/WY) – a direct measure of flood frequency – using the Mann‐Kendall trend test. Ten of these trends had p < 0.1. Seventeen rivers show positive trends in flood magnitude, six of which had p < 0.1. We also investigate a potential hydroclimatic shift in the region around 1970. Twenty‐two of the 23 rivers show increased POT/WY in the post‐1970 period when comparing pre‐ and post‐1970 records using the Wilcoxon rank‐sum test. More than half of these increases have p < 0.1, indicating a shift in flow regime toward more frequent flooding. Region wide, we found a median increase of one flood per year for the post‐1970 period. Because frequent floods are important channel‐forming flows, these results have implications for channel and floodplain morphology, aquatic habitat, and restoration.     

CAUSES OF PEAK FLOWS IN NORTHWESTERN MONTANA AND NORTHEASTERN IDAHO1

ABSTRACT: Both catchment experiments and a review of hydrologic processes suggest a varying effect of forest harvest on the magnitude of peak flows according to the cause of those peak flows. In northwestern Montana and Northeastern Idaho, annual maximum flows can result from spring snowmelt, rain, mid-winter rain-on-snow, or rain-on-spring-snowmelt. Meteorologic and physical data were used to determine the cause of annual maximum flows in six basins which had the necessary data and were smaller than 150 mi². Rain-on-spring-snowmelt was the most frequent cause of annual maximum flows in all six basins, although there was a strong gradient in the magnitude and cause of peak flows from southwest to northeast. Less frequent mid-winter rain-on-snow events caused the largest flows on record in four basins. Mid-winter rain-on-snow should be distinguished from rain-on-spring-snowmelt because of differences in seasonal timing, the relative contributions of rain vs. snowmelt, and the projected effects of forest harvest. The effects of mixed flood populations on the flood-frequency curve varied from basin to basin. Annual maximum daily flows could not be reliably predicted from rainfall and snowmelt data.     

CLIMATE VARIABILITY AND FLOOD FREQUENCY ESTIMATION FOR THE UPPER MISSISSIPPI AND LOWER MISSOURI RIVERS1

ABSTRACT: This paper considers the distribution of flood flows in the Upper Mississippi, Lower Missouri, and Illinois Rivers and their relationship to climatic indices. Global climate patterns including El Niño/Southern Oscillation, the Pacific Decadal Oscillation, and the North Atlantic Oscillation explained very little of the variations in flow peaks. However, large and statistically significant upward trends were found in many gauge records along the Upper Mississippi and Missouri Rivers: at Hermann on the Missouri River above the confluence with the Mississippi (p = 2 percent), at Hannibal on the Mississippi River (p < 0.1 percent), at Meredosia on the Illinois River (p = 0.7 percent), and at St. Louis on the Mississippi below the confluence of all three rivers (p = 1 percent). This challenges the traditional assumption that flood series are independent and identically distributed random variables and suggests that flood risk changes over time.     

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.     

STREAMFLOW TRENDS IN WISCONSIN'S DRIFTLESS AREA1

ABSTRACT: Trends in streamflow characteristics were analyzed for streams in southwestern Wisconsin's Driftless Area by using data at selected gaging stations. The analyses indicate that annual low flows have increased significantly, whereas annual flood peaks have decreased. The same trends were not observed for forested areas of northern Wisconsin. Streamflow trends for other streams in southeastern Wisconsin draining predominantly agricultural land were similar to trends for Driftless Area streams for annual low flows. The causes for the trends are not well understood nor are the effects. Trends in annual precipitation do not explain the observed trends in streamflow. Other studies have found that erosion rates decreased significantly in the Driftless Area, and have attributed this reduction to a change of agricultural practices, which increase infiltration, decrease flood peaks, and increase low flows.     

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.     

Reconstructed Stream Flow for the Salt and Verde Rivers From Tree-Ring Data1

ABSTRACT: The Salt and Verde Rivers of central Arizona provide the water supply for metropolitan Phoenix and a considerable acreage of irrigated agriculture. Rapid urbanization has caused concern over future water supply and aggravated flooding in the already flood-prone Salt River Valley. Tree-ring data were used as a proxy source to extend the annual and seasonal runoff records back to A.D. 1580 and thus to determine whether the period of record for annual discharge adequately represents the long term flow characteristics of the two rivers. Results show that several periods of extended low flow have occurred during the past 400 years, many of which were more severe then any comparable period since 1890. The low flow periods appear to have a recurrence interval of about 22 years. Also the gaged records contain an above average number of high seasonal and annual flows when compared to the entire 400 years. The reconstructions contain important implications for future water supply and flood potentials in the Salt River Valley.     

EVALUATING RELIABILITY OF STORAGE SCHEMES WITH DENDROHYDROLOGY AND THE HURST PHENOMENON1

ABSTRACT: The mean annual flow at a damsite during a water project yield study of several decades may differ considerably from the mean flow of several hundred years. The frequency of the most severe droughts of record may be much different than apparent from the historical record as well. Dendrohydrology and the Hurst Phenomenon provide means to evaluate the validity of the study period for project reliability analysis. The most severe hydrologic drought (1928–1934) affecting the watersheds of the Sacramento River and tributaries in Northern California during the 75-year period 1906–1980 was also the worst drought in 421 years (1560–1980). In contrast, the most severe drought (1945–1951) in the Santa Ynez River watershed in Santa Barbara County, California, during the 62-year period 1918–1979 was the ninth worst drought in 443 years (1537–1979). Thus, in one case the drought risk indicated by the dendrohydrologic time series would actually be less; in the other, actual risk would be greater than perceived from the historical record. In the absence of a dendrohydrologic prehistoric time series, Hurst Phenomena would have provided clues to this outcome. Hurstian plotting of the accumulated deviation from the mean for long time series facilitates observation of the wet-dry regime of the examples and identification of characteristics that should be accounted for in water development planning.     

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.     

MULTIYEAR DROUGHT SIMULATION1

ABSTRACT: Previous studies on multiyear droughts have often been limited to the analysis of historic annual flow series. A major disadvantage in this approach can be described as the unavailability of long historic flow records needed to obtain a significant number of drought events for the analysis. To overcome this difficulty, the present study proposes to use synthetically generated annual flow series. A methodology is presented to model annual flows based on an analysis of the harmonic and stochastic properties of the observed flows. Once the model is determined, it can be utilized to generate a flow series of desired length so as to include many hydrologic cycles within the process. The key parameter for a successful drought study is the truncation level used to distinguish low flows from high flows. In this paper, a concept of selecting the truncation level is also presented. The drought simulation procedure is illustrated by a case study of the Pequest watershed in New Jersey. For the above watershed, multiyear droughts were derived from both historic and generated flow series. Three important drought parameters, namely, the duration, severity, and magnitude, were determined for each drought event, and their probability distributions were studied. It was found that gamma and log normal probaility functions produce the best fit for the duration and severity, respectively. The derived probability curves from generated flows can be reliably used to predict the longest drought duration and the largest drought severity within a given return period.     

EFFECT OF SURFACE MINING ON STORM FLOW AND PEAK FLOW FROM SIX SMALL BASINS IN EASTERN KENTUCKY1

ABSTRACT: Hydrologic records from six small Eastern Kentucky watersheds were analyzed to determine the effect of surface mining on storm flows and peak flows. Average storm flow volumes were not changed by surface mining, whereas average peak flows were increased 36 percent. Peak flow increases were only in the summer. Smaller peak flows are doubled; moderate ones are increased by about a third; peak flows around 100 csm seem to be largely unaffected; and the larger peak flows may have been reduced by surface mining. The maximum annual storm flows, usually in winter or spring, appeared slightly reduced. No time trend in either storm flows or peak flows could be detected in five years of postmining record. Surface mining is not a serious floodwater discharge problem.     

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.     

ESTIMATING ANNUAL FLOOD PROBABILITIES USING FOURIER SERIES METHOD1

ABSTRACT: The Fourier series method is proposed as a feasible non-parametric approach for the estimation of the density and distribution functions of annual floods. Clearly, the goodness of fit to empirical data improves as higher Fourier terms are incorporated, and the choice of a higher term depends on whether the inclusion of this term will reduce the fitting error to within a specified tolerance level. This method was applied to the flood data from eight rivers, and to data simulated from known distributions. The results are clearly better than other parametric methods, just like other non-parametric techniques currently used to estimate annual flood probabilities.     

Application of Index Procedures to Flood Frequency Analysis in Turkey1

Abstract: This study investigates the regional analysis of annual maximum flood series of 48 stream gauging stations in the basins of the West Mediterranean Region in Turkey. The region is divided into three homogeneous subregions according to both Student‐t test and Dalrymple homogeneity test. The regional relationships of mean annual flood per unit area‐drainage area and coefficient of skew‐coefficient of variation are obtained. Two statistically meaningful relationships of the mean flood per unit area‐drainage area and a unique relationship between skewness and variation coefficients exist. Results show that the index‐flood method may be applicable to each homogenous subregion to estimate flood quantiles in the study area.     

LONG‐TERM CHANGES IN REGIONAL HYDROLOGIC REGIME FOLLOWING IMPOUNDMENT IN A HUMID‐CLIMATE WATERSHED1

ABSTRACT: We analyzed the type of hydrologic adjustments resulting from flow regulation across a range of dam types, distributed throughout the Connecticut River watershed, using two approaches: (1) the Index of Hydrologic Alteration (IHA) and (2) log‐Pearson Type III flood frequency analysis. We applied these analyses to seven rivers that have extensive pre‐and post‐disturbance flow records and to six rivers that have only long post‐regulation flow records. Lastly, we analyzed six unregulated streams to establish the regional natural flow regime and to test whether it has changed significantly over time in the context of an increase in forest cover from less than 20 percent historically to greater than 80 percent at present. We found significant hydrologic adjustments associated with both impoundments and land use change. On average, maximum peak flows decrease by 32 percent in impounded rivers, but the effect decreases with increasing flow duration. One‐day minimum low flows increase following regulation, except for the hydro‐electric facility on the mainstem. Hydrograph reversals occur more commonly now on the mainstem, but the tributary flood control structures experience diminished reversals. Major shifts in flood frequency occur with the largest effect occurring downstream of tributary flood control impoundments and less so downstream of the mainstem's hydroelectric facility. These overall results indicate that the hydrologic impacts of dams in humid environments can be as significant as those for large, multiple‐purpose reservoirs in more arid environments.     

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.