Assessing Uncertainty in Estimates of Nitrogen Loading to Estuaries for Research, Planning, and Risk Assessment

Parametric (propagation for normal error estimates) and nonparametric methods (bootstrap and enumeration of combinations) to assess the uncertainty in calculated rates of nitrogen loading were compared, based on the propagation of uncertainty observed in the variables used in the calculation. In addition, since such calculations are often based on literature surveys rather than random replicate measurements for the site in question, error propagation was also compared using the uncertainty of the sampled population (e.g., standard deviation) as well as the uncertainty of the mean (e.g., standard error of the mean). Calculations for the predicted nitrogen loading to a shallow estuary (Waquoit Bay, MA) were used as an example. The previously estimated mean loading from the watershed (5,400 ha) to Waquoit Bay (600 ha) was 23,000 kg N yr⁻¹. The mode of a nonparametric estimate of the probability distribution differed dramatically, equaling only 70% of this mean. Repeated observations were available for only 8 of the 16 variables used in our calculation. We estimated uncertainty in model predictions by treating these as sample replicates. Parametric and nonparametric estimates of the standard error of the mean loading rate were 12–14%. However, since the available data include site-to-site variability, as is often the case, standard error may be an inappropriate measure of confidence. The standard deviations were around 38% of the loading rate. Further, 95% confidence intervals differed between the nonparametric and parametric methods, with those of the nonparametric method arranged asymmetrically around the predicted loading rate. The disparity in magnitude and symmetry of calculated confidence limits argue for careful consideration of the nature of the uncertainty of variables used in chained calculations. This analysis also suggests that a nonparametric method of calculating loading rates using most frequently observed values for variables used in loading calculations may be more appropriate than using mean values. These findings reinforce the importance of including assessment of uncertainty when evaluating nutrient loading rates in research and planning. Risk assessment, which may need to consider relative probability of extreme events in worst-case scenarios, will be in serious error using normal estimates, or even the nonparametric bootstrap. A method such as our enumeration of combinations produces a more reliable distribution of risk.     

CLIMATE FACTOR FOR SMALL-BASIN FLOOD FREQUENCY1

ABSTRACT: A climate factor, C_T, (T = 2–, 25-, and 100-year recurrence intervals) that delineates regional trends in small-basin flood frequency was derived using data from 71 long-term rainfall record sites. Values of C_T at these sites were developed by a regression analysis that related rainfall-runoff model estimates of T-year floods to a sample set of 50 model calibrations. C_T was regionalized via kriging to develop maps depicting its geographic variation for a large part of the United States east of the 105th meridian. Kriged estimates of C_T and basin-runoff characteristics were used to compute regionalized T-year floods for 200 small drainage basins. Observed T-year flood estimates also were developed for these sites. Regionalized floods are shown to account for a large percentage of the variability in observed flood estimates with coefficients of determination ranging from 0.89 for 2-year floods to 0.82 for 100-year floods. The relative importance of the factors comprising regionalized flood estimates is evaluated in terms of scale (size of drainage area), basin-runoff characteristics (rainfall. runoff model parameters), and climate (C_T).     

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.     

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.     

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.     

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.     

Developing Peak Discharges for Future Flood Risk Studies Using IPCC's CMIP5 Climate Model Results and USGS WREG Program

Extreme climate events, floods, and drought, cause huge impact on daily lives. In order to produce society resilient to extreme events, it is necessary to assess the impact of frequent and high intensity storm events on design parameters. This article describes a methodology to develop future peak “design discharges” throughout the United States that can be used as a guidance to map future floodplains. In order to develop a lower and upper limit for anticipated peak flow discharges, two future growth scenarios — Representative Concentration Pathways (RCPs)‐RCP 2.6 and 8.5 were identified as the weak and strong climate scenario respectively based on the output from the global climate models. The Generalized Least Square technique in United States Geological Survey's Weighted Multiple Regression (WREG) program was used to develop regression equations that relate peak discharges to basin and climate parameters of the contributing watershed. The design discharges reflect the most recent climate model results. Number of frost days, heavy rainfall days, high temperature days, and snow depth were found to be the common extreme climate parameters influencing the regression equations. This methodology can be extended to other flood frequency events if rainfall data is available. The future discharges can be utilized in hydraulics models to estimate floodplains that can assist in resilient infrastructure planning and outline climate change adaptation strategies.     

AN EVALUATION OF FLOOD FREQUENCY ESTIMATES BASED ON RAINFALL/RUNOFF MODELING1

ABSTRACT: An evaluation of flood frequency estimates simulated from a rainfall/runoff model is based on (1) computation of the equivalent years of record for regional estimating equations based on 50 small stream sites in Oklahoma and (2) computation of the bias for synthetic flood estimates as compared to observed estimates at 97 small stream sites with at least 20 years of record in eight eastern states. Because of the high intercorrelation of synthetic flood estimates between watersheds, little or no regional (spatial) information may be added to the network as a result of the modeling activity. The equivalent years of record for the regional estimating equations based totally on synthetic flood discharges is shown to be considerably less than the length of rainfall record used to simulate the runoff. Furthermore, the flood estimates from the rainfall/runoff model consistently underestimate the flood discharges based on observed record, particularly for the larger floods. Depending on the way bias is computed, the synthetic estimate of the 100-year flood discharge varies from 11 to 29 percent less than the value based on observed record. In addition, the correlation between observed and synthetic flood frequency estimates at the same site is also investigated. The degree of correlation between these estimates appears to vary with recurrence interval. Unless the correlation between these two estimates is known, it is not possible to compute a weighted estimate with minimum variance.     

Using Risk-Based Analysis and Geographic Information Systems to Assess Flooding Problems in an Urban Watershed in Rhode Island

This article provides an overview of the use of risk-based analysis (RBA) in flood damage assessment, and it illustrates the use of Geographic Information Systems (GIS) in identifying flood-prone areas, which can aid in flood-mitigation planning assistance. We use RBA to calculate expected annual flood damages in an urban watershed in the state of Rhode Island, USA. The method accounts for the uncertainty in the three primary relationships used in computing flood damage: (1) the probability that a given flood will produce a given amount of floodwater, (2) the probability that a given amount of floodwater will reach a certain stage or height, and (3) the probability that a certain stage of floodwater will produce a given amount of damage. A greater than 50% increase in expected annual flood damage is estimated for the future if previous development patterns continue and flood-mitigation measures are not taken. GIS is then used to create a map that shows where and how often floods might occur in the future, which can help (1) identify priority areas for flood-mitigation planning assistance and (2) disseminate information to public officials and other decision-makers.     

A New Flood Index for Use in Evaluation of Local Flood Severity: A Case Study of Small Ungauged Catchments in Korea1

Ahn, Jae Hyun and Hyun Il Choi, 2013. A New Flood Index for Use in Evaluation of Local Flood Severity: A Case Study of Small Ungauged Catchments in Korea. Journal of the American Water Resources Association (JAWRA) 49(1): 1‐14. DOI: 10.1111/jawr.12025 Abstract: The aim of this article is to develop a new index measuring the severity of floods in small ungauged catchments for initial local flood information by the regression analysis between the new flooding index and rainfall patterns. Although a rapid local flood caused by heavy storm in a short period of time is now one of common natural disasters worldwide, such a sudden and violent hydrologic event is difficult to forecast. As local flooding rises rapidly with little or no advance warning, the key to local flood forecasting is to quickly identify when and where local flooding above a threshold is likely to occur. The new flooding index to characterize local floods is measured by the three normalized relative severity factors for the flood magnitude ratio, the rising curve gradient, and the flooding duration time, quantifying characteristics of flood runoff hydrographs. The new flooding index implemented for the two selected small ungauged catchments in the Korean Peninsula shows a very high correlation with logarithm of the 2‐h maximum rainfall depth. This study proposes 30 mm of rainfall in a 2‐h period as a basin‐specific guidance of precaution for the incipient local flooding in the two study catchments. It is expected that the best‐fit regression equation between the new flooding index and a certain rainfall rate can provide preliminary observations, the flood threshold, and severity information, for use in a local flood alert system in small ungauged catchments. Editor's note: This paper is part of a featured series on Korean Hydrology. The series addresses the need for a new paradigm of river and watershed management for Korea due to climate and land use changes.     

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.     

History and Development of the NRCS Lag Time Equation1

Abstract: Many of the hydrologic methods that are used in engineering practice today resulted from the Spring Flood of 1936, which blanketed the Northeastern portion of the United States. Because of the flood damage that was caused by this rainfall‐snowmelt event, many federal agencies including the U.S. Army Corp of Engineers and the Soil Conservation Service (SCS) implemented the hydrologic theories that were available in the literature at this time and developed hydrologic procedures for design flow estimation. Sherman had recently published his unit hydrograph theory in 1932, and later in 1938 Snyder, who had been charged by the Water Resource Council to develop a synthetic unit hydrograph, published his famous paper. The SCS unit hydrograph theory was developed by Victor Mockus in the late 1950s. Most if not all of the theories at that time reported the rainfall‐runoff process for floods as a surface phenomenon, and as such those theories all required some type of a timing parameter to estimate watershed response time. This article documents the development of the SCS lag equation.     

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.     

PARAMETER UNCERTAINTY IN RAINFALL-RUNOFF MODELING FOR POLDER SYSTEM DESIGN1

ABSTRACT: An approach is developed for incorporating the uncertainty of parameters for estimating runoff in the design of polder systems in ungaged watersheds. Monte Carlo Simulation is used to derive a set of realizations of streamflow hydrographs for a given design rainstorm using the U. S. Soil Conservation Service (SCS) unit hydrograph model. The inverse of the SCS curve number, which is a function of the antecedent runoff condition in the SCS model, is the random input in the Monte Carlo Simulation. Monte Carlo realizations of streamfiow hydrographs are used to simulate the performance of a polder flood protection system. From this simulation the probability of occurrence of flood levels for a particular hydraulic design may be used to evaluate its effectiveness. This approach is demonstrated for the Pluit Polder flood protection system for the City of Jakarta, Indonesia. While the results of the application indicate that uncertainty in the antecedent runoff condition is important, the effects of uncertainty in rainfall data, in additional runoff parameters, such as time to peak, in the hydraulic design, and in the rainfall-runoff model selected should also be considered. Although, the SCS model is limited to agricultural conditions, the approach presented herein may be applied to other flood control systems if appropriate storm runoff models are selected.     

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.     

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.     

Public Perception of Flood Hazard in the Niger Delta,Nigeria

Summary Our study had the aim of understanding how floodplain dwellers regard the risk of flooding. About 500 questionnaires were administered to landowners in the selected settlements in the study area using systematic random sampling. The results of analysis show, among other things, that the population regards most important the causes of floods as heavy, prolonged rainfall and river overflow. Nevertheless, they have little knowledge of the frequency of severe floods, and flood alleviation schemes. Most flood victims do not get compensation or relief during flood disaster, and the reason why they remain in the study area is influenced by their occupations, especially fishing, subsistence agriculture, and the presence of crude oil in the region which has attracted many migrants who cannot afford the high cost of accommodation and are therefore forced to live in vulnerable areas of the floodplain. Finally, the study concludes that flood control in the region needs the cooperation of government, community efforts and an enlightenment programmes through environmental education and mass media.     

Impact of Changing Climate and Land Cover on Flood Magnitudes in the Delaware River Basin,USA

Changing climate and land cover are expected to impact flood hydrology in the Delaware River Basin over the 21st Century. HEC‐HMS models (U.S. Army Corps of Engineers Hydrologic Engineering Center‐Hydrologic Modeling System) were developed for five case study watersheds selected to represent a range of scale, soil types, climate, and land cover. Model results indicate that climate change alone could affect peak flood discharges by ?6% to +58% a wide range that reflects regional variation in projected rainfall and snowmelt and local watershed conditions. Land cover changes could increase peak flood discharges up to 10% in four of the five watersheds. In those watersheds, the combination of climate and land cover change increase modeled peak flood discharges by up to 66% and runoff volumes by up to 44%. Precipitation projections are a key source of uncertainty, but there is a high likelihood of greater precipitation falling on a more urbanized landscape that produces larger floods. The influence of climate and land cover changes on flood hydrology for the modeled watersheds varies according to future time period, climate scenario, watershed land cover and soil conditions, and flood frequency. The impacts of climate change alone are typically greater than land cover change but there is substantial geographic variation, with urbanization the greater influence on some small, developing watersheds.     

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.