NONPARAMETRIC STATISTICAL METHODS IN URBAN HYDROLOGIC RESEARCH1

ABSTRACT. In urban hydrologic studies, it is often necessary to determine the effect of changes in urban land use patterns on such runoff characteristics as flood peaks and flow volumes. Nonparametric statistical methods have certain properties that make them a valuable tool for detecting hydrologic change caused by a treatment, such as urbanization, that changes watershed over a period of time. As many hydrologists do not have a working familiarity with nonparametric methods, a number of them are used for illustrative purposes to analyze the effect of urbanization on 24 years of annual flood peaks for a Louisville, Kentucky, watershed. In the example, urbanization was found to increase the central tendency, but not the dispersion of the peaks. Peak flows modeled by holding watershed parameters constant were also found to be increasing because of an upward trend in precipitation. By following the numerical examples in the paper and looking up test statistics in referenced sources, the reader can easily apply these methods to other situations.     

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.     

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.     

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.     

DETECTING UNKNOWN INTERVENTIONS WITH APPLICATION TO FORECASTING HYDROLOGICAL DATA1

To accommodate possible parameter changes in time series at times which are not specified in advance, we propose an adaptive procedure for estimating parameters and for forecasting. The mechanism for activating the adaptive procedure is a successively updated change-detection statistic. The statistic has small expected value when no change is present and has large value when change takes place - the larger the change, the larger the statistic. The statistic defines discounting factors which determine how much of the past will be used both for estimating parameters and for forecasting. The change-detection statistic is designed to effect major changes to parameter estimates and to forecasts in a discrete fashion only, as opposed to certain other adaptive procedures that react continuously to perceived fluctuations in data, and so indicate change even when parameters remain fixed. The procedure is illustrated using exponential smoothing and Holt's linear exponential smoothing and is applied to a hydrological series.     

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.     

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.     

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.     

PERIODIC AUTOREGRESSIVE-MOVING AVERAGE (PARMA) MODELING WITH APPLICATIONS TO WATER RESOURCES1

Results involving correlation properties and parameter estimation for autoregressive-moving average models with periodic parameters are presented. A multivariate representation of the PARMA model is used to derive parameter space restrictions and difference equations for the periodic autocorrelations. Close approximation to the likelihood function for Gaussian PARMA processes results in efficient maximum-likelihood estimation procedures. Terms in the Fourier expansion of the parameters are sequentially included, and a selection criterion is given for determining the optimal number of harmonics to be included. Application of the techniques is demonstrated through analysis of a monthly streamflow time series.     

PARAMETER ESTIMATION FOR TPLN DISTRIBUTION FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The principle of maximum entropy (POME) was used to derive an alternative method for parameter estimation for the three parameter lognormal (TPLN) distribution. Six sets of annual peak discharge data were used to evaluate this method and compare it with the methods of moments and maximum likelihood estimation.     

INDEXED SEQUENTIAL HYDROLOGIC MODELING FOR HYDROPOWER CAPACITY ESTIMATION1

ABSTRACT: The indexed sequential hydrologic modeling (ISM) methodology is utilized by the Western Area Power Administration as the basis for risk-based estimation of project-dependable hydropower capacity for several federally owned/operated projects. ISM is a technique based on synthetic generation of a series of overlapping short-term inflow sequences obtained directly from the historical record. The validity of ISM is assessed through application to the complex multireservoir hydropower system of the Colorado River basin for providing risk estimates associated with determination of reliable hydrogeneration capacity. Performance of ISM is compared with results from stochastically generated streamflow input data to the Colorado River Simulation System (CRSS). Statistical analysis and comparison of results are based on monthly power capacity, energy generation, and downstream water deliveries. Results indicate that outputs generated from ISM synthetically generated sequences display an acceptable correspondence with those obtained from stochastically generated hydrologic data for the Colorado River Basin.     

DETERMINISTIC-SYSTEMIC RELATIONSHIPS IN OVERLAND FLOW ANALYSIS1

ABSTRACT: An analysis of storm runoff is presented, giving primary attention to deterministic-systemic relationships. So that system aspects can be emphasized, other aspects are kept simple; analysis is made for uniform rainfall on a strip of uniform width, limiting direct applicability to small areas. Two relationships between excess rain and time of concentration, one based on hydraulic parameters, the other on hydrologic characteristics, are combined in a solution for peak discharge. The hydraulic expression gives the interrelationship of time of concentration, excess rain, friction, length, and slope. The hydrologic relationship is achieved by converting ordinary intensity-duration curves to corresponding excess rain intensity-duration curves, thereby interrelating excess rain, time of concentration, and loss characteristics. The resulting solution for peak discharge allows for systemic feedback among both hydraulic and hydrologic parameters.     

ANALYSIS AND MODELING OF LONG-TERM STREAM TEMPERATURES ON THE STEAMBOAT CREEK BASIN,OREGON: IMPLICATIONS FOR LAND USE AND FISH HABITAT1

ABSTRACT: Steamboat Creek basin is an important source of timber and provides crucial spawning and rearing habitat for anadromous steelhead trout (Oncorhynchus mykiss). Because stream temperatures are near the upper limit of tolerance for the survival of juvenile steelhead, the possible long-term effect of clear-cut logging on stream temperatures was assessed. Twenty-year (1969–1989) records of summer stream temperature and flow from four tributaries and two reaches of Steamboat Creek and Boulder Creek (a nearby unlogged watershed) were analyzed. Logging records for the Steamboat Creek basin and air temperature records also were used in the analysis. A time-series model of the components of stream temperature (seasonal cycle of solar radiation, air temperature, streamflow, an autoregressive term of order 1, and a linear trend variable) was fitted to the water-temperature data. The linear trend variable was significant in all the fitted models except Bend Creek (a tributary fed by cool ground-water discharge) and Boulder Creek. Because no trends in either climate (i.e., air temperature) or streamflow were found in the data, the trend variable was associated with the pre-1969 loss and subsequent regrowth of riparian vegetation and shading canopies.     

Trends in Rainfall Exceedances in the Observed Record in Selected Areas of the United States1

Bonnin, Geoffrey M., Kazungu Maitaria, and Michael Yekta, 2011. Trends in Rainfall Exceedances in the Observed Record in Selected Areas of the United States. Journal of the American Water Resources Association (JAWRA) 47(6): 1173–1182. DOI: 10.1111/j.1752‐1688.2011.00603.x Abstract: Semantic differences have led to a gap in the understanding of the impacts of climate change on precipitation frequency estimates. There is popular perception that heavy rainfalls have become more frequent, and that this trend will increase with global warming. Most of the literature examines this question from the point of view of climatology using definitions of “heavy,”“very heavy,” or “extreme” rainfall, which are different from those commonly used by civil engineers. This article identifies the differences in meaning used by the climate and civil engineering communities and examines trends in the observed record in the frequency of exceedances (not trends in magnitudes). Using concepts recognized as the basis for design of the Nation’s civil infrastructure, we look at trends in the number of exceedances of thresholds for a variety of precipitation frequencies and event durations used by civil engineers. We found that the estimated trends in exceedances at one‐day and multiday durations were statistically significant and increasing for the Ohio River Basin and surrounding states but the reverse was true for the Semiarid Southwest (i.e., not significant and decreasing trends). In addition, we found the magnitude of the trends was small for all but the more frequent events and also small with respect to the uncertainty associated with the precipitation frequency estimates themselves.