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.     

A DISTRIBUTED DYNAMIC WATERSHED MODEL1

ABSTRACT: A distributed watershed model was developed to mathematically simulate overland and channel flow for a single-event storm. The modeled watersheds in the study were subdivided into rectangular grid elements. All hydrologically significant parameters, such as land slope, rainfall and precipitation excess, were assumed to be uniform within each element. The Green-Ampt method was adopted to generate precipitation excess for each element during the simulation period. A two-dimensional diffusion wave model was used for overland flow routing and an iterative Alternative Direction Implicit scheme was used to solve the simultaneous overland flow equations. Once the overland flow became inflow to the channel, a one-dimensional dynamic wave flood routing technique, based on a four-point, implicit, non-linear finite difference solution of the St. Venant equation of unsteady flow, was applied. A limited number of comparisons were made between simulated and observed hydrographs for areas of about one square mile. Given the appropriate parameters, the model was able to accurately simulate runoff for single-event storms. This paper describes a distributed watershed model developed to simulate overland and channel flow. Comparisons were made between simulated and observed hydrographs for three watersheds. The model was able to accurately simulate the runoff for single-event storms using 61-m by 61-m (200 ft by 200 ft) watershed grid elements.     

COMPUTATION OF STAGE-DISCHARGE RELATIONSHIPS AFFECTED BY UNSTEADY FLOW1

ABSTRACT: The dynamic relationship between stage and discharge which is unique to a particular flood for a selected station along the river can be determined via a mathematical model based on the complete one-dimensional equations of unsteady flow, i.e., the equations for the conservation of mass and momentum of the flood wave, and the Manning equation which accounts for energy losses. By assuming the bulk of the flood wave moves as a kinematic wave, the need for spatial resolution of the flood can be eliminated, and only the time variation of either the discharge or stage at the selected station is necessary for the computation of the other. The mathematical model can be used in river forecasting to convert the forecast discharge hydrograph into a stage hydrograph which properly reflects the unique dynamic stage-discharge relationship produced by the variable energy slope of the flood discharge. The model can be used also in stream gaging to convert a recorded stage hydrograph into a discharge hydrograph which properly accounts for the effects of unsteady flow. The model is applied to several observed floods at selected stations along the Lower Mississippi, Red, and Atchafalaya Rivers. The root mean square errors between observed and computed discharges are in the range of 3 to 7 percent, values well within the accuracy of the observations. A simple, easily-applied graphical procedure is also provided for estimating the magnitude of the effect of the unsteady flow on stage-discharge ratings. As a general rule, the dynamic effect may be significant if the channel bottom slope is less than 0.001 ft/ft (about 5 ft/mi) when the rate of change of stage is greater than about 0.10 ft/hr.     

A NUMERICAL ESTUARINE FLOW MODEL1

A novel estuarine flow model is proposed. It provides some two-dimensional features while using an essentially one-dimensional approach. The model is applied to the Upper Delaware Estuary, and is shown to match available field data with acceptable accuracy. The model is shown to be numerically stable and reasonably mass conservative.     

FLOOD ROUTING THROUGH A FLAT,COMPLEX FLOODPLAIN USING A ONE-DIMENSIONAL UNSTEADY FLOW COMPUTER PROGRAM1

ABSTRACT: The routing of flood waves through the Central Basin of the Passaic River in New Jersey is complex because of flat gradients and flow reversals. The one-dimensional unsteady flow program DWOPER, developed by the National Weather Service, was used to simulate flood wave movement through the Basin. A historical event was used for calibration and two synthetic events were simulated. Boundary conditions consisted of discharge hydrographs at inflow points to the study area, local flow hydrographs at interior points, and a stage discharge relation for flow over the crest of a diversion dam at the basin outlet. Manning's n values were adjusted based on stage and discharge data for the historical event; however, verification data were not available for events comparable in magnitude to the synthetic events. Aspects of the investigation reported include techniques for characterizing the flow system, model calibration, techniques for representing a tunnel diversion, and simulation results.     

OPTIMIZATION OF TRANSPORTATION NETWORKS DURING URBAN FLOODING1

ABSTRACT: In this paper a numerical model for flood propagation in urban areas is proposed. It has been applied to evaluate flooding hydraulic characteristics in terms of potential flood elevations, depths, and inundated areas. Furthermore, the algorithm efficiency and the consequent reduced computation time allow the use of the hydraulic model as a part of a more complex system for civil protection actions, planning, and management. During flood events, the transportation network plays a main role both in rescuing people when they are more vulnerable and in moving people and materials from and toward affected areas. The reduced efficiency of this transportation network is evaluated based on a least‐flood‐risk path‐finding algorithm. The results of a case study concerning the northern part of the city of Rome, show that the numerical model for unsteady flow in open channel networks achieves the proposed aims. It has proven to be able to describe the flood hydraulic characteristics and to be suitable for real‐time flood emergency management in urban areas.     

ADAPTATION OF FLOOD PEAKS AND DESIGN HYDROGRAPHS FROM GAGED TO NEARBY UNGAGED WATERSHEDS1

ABSTRACT: Equations were developed to transform peak flows and to adapt design hydrographs and unit hydrographs from gaged watersheds to ungaged watersheds with similar hydrologic characteristics. Dimensional analysis was used to develop adjustment equations for peak flow and time base, and these equations were reinforced with results from regional flood frequency research. The authors believe that the use of these transformation equations should yield more reliable flood peak values and hydrogrphs than the common use of empirical flood estimating curves or equations.     

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

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

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.     

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.     

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.     

Assessment of cropland inundation due to the operation of the Reelfoot Lake spillway in West Tennessee

Running Reelfoot Bayou (RRB) is the outlet canal of Reelfoot Lake, the largest natural lake in Tennessee. RRB is not able to contain discharge from Reelfoot Lake greater than the bankfull discharge of 28 m³/s (1000 ft³/s), which typically occurs at the beginning of the growing season (April–June). Historically, the planting of crops has been delayed until flooding subsides and cropland has drained. The objective of this study is a preliminary quantification of cropland inundation to determine its spatial distribution in the RRB floodplain. Inundated croplands in the RRB floodplain were delineated over a range of spillway discharges from 2 to 57 m³/s (70–2000 ft³/s), using one-dimensional–two-dimensional hydrodynamic modeling and multispectral satellite images (Landsat 8 and Sentinel-2). The composite maps made by combining the simulated and image-derived flood maps were overlaid on the United States Department of Agriculture CropScape layer to determine the inundation of individual summer crops during the growing season. About 25% of the inundated croplands are flooded at discharges of RRB less than 28 m³/s, implying wetland hydrology. The results of this analysis can be used to inform operational management of the Reelfoot Lake spillway.     

HUMAN STABILITY IN A HIGH FLOOD HAZARD ZONE1

ABSTRACT: The delineation of high flood hazard zones within a flood plain is usually independent of the hydraulic parameters that constitute a life threatening situation. In order to define human instability in high hazard areas, a study was conducted to identify when an adult human could not stand or maneuver in a simulated flood flow. An analysis was performed on a rigid body monolith resulting in a toppling hazard envelope curve (velocity vs. depth). A 120 lb monolith was then constructed and tested to relate the actual flow velocity and depth at toppling to theory. A series of human subjects (90–201 Ibs) were placed in a recirculating flume and tested to determine the velocity and depth of flow that caused their instability. The test results determined that the product number, which is the product of the velocity and depth at toppling of the monolith, closely compared to the theoretical envelope curve. The monolith results represent the lower limit of human stability. Also, the product number appeared to be a predictor of human instability in flood flow. A relationship was developed to estimate the product number at which a human subject becomes unstable as a function of the height and weight of the subject.     

A NEW LOOK AT FLOOD RISK DETERMINATION1

ABSTRACT: The probability distributions of annual peak flows used in flood risk analysis quantify the risk that a design flood will be exceeded. But the parameters of these distributions are themselves to a degree uncertain and this uncertainty increases the risk that the flood protection provided will in fact prove to be inadequate. The increase in flood risk due to parameter uncertainty is small when a fairly long record of data is available and the annual flood peaks are serially independent, which is the standard assumption in flood frequency analysis. But standard tests for serial independence are insensitive to the type of grouping of high and low values in a time series, which is measured by the Hurst coefficient. This grouping increases the parameter uncertainty considerably. A study of 49 annual peak flow series for Canadian rivers shows that many have a high Hurst coefficient. The corresponding increase in flood risk due to parameter uncertainty is shown to be substantial even for rivers with a long record, and therefore should not be neglected. The paper presents a method of rationally combining parameter uncertainty due to serial correlation, and the stochastic variability of peak flows in a single risk assessment. In addition, a relatively simple time series model that is capable of reproducing the observed serial correlation of flood peaks is presented.     

TWO-DIMENSIONAL DAM-BREAK FLOOD-FLOW ANALYSIS FOR ORANGE COUNTY RESERVOIR1

ABSTRACT: A two-dimensional dam-break model was used to predict the inundated area on an alluvial fan downslope from the Orange County Reservoir. The model is based upon a diffusion form of the continuity and momentum equations for long waves in shallow water, and the governing equation is solved by an explicit numerical scheme. In a comparison with a one-dimensional model, the two-dimensional model predicts a wider inundated area.     

Evidence for Changing Flood Risk in New England Since the Late 20th Century1

Abstract: Long‐term flow records for watersheds with minimal human influence have shown trends in recent decades toward increasing streamflow at regional and national scales, especially for low flow quantiles like the annual minimum and annual median flows. Trends for high flow quantiles are less clear, despite recent research showing increased precipitation in the conterminous United States over the last century that has been brought about primarily by an increased frequency and intensity of events in the upper 10th percentile of the daily precipitation distribution – particularly in the Northeast. This study investigates trends in 28 long‐term annual flood series for New England watersheds with dominantly natural streamflow. The flood series are an average of 75 years in length and are continuous through 2006. Twenty‐five series show upward trends via the nonparametric Mann‐Kendall test, 40% (10) of which are statistically significant (p < 0.1). Moreover, an average standardized departures series for 23 of the study gages indicates that increasing flood magnitudes in New England occurred as a step change around 1970. The timing of this is broadly synchronous with a phase change in the low frequency variability of the North Atlantic Oscillation, a prominent upper atmospheric circulation pattern that is known to effect climate variability along the United States east coast. Identifiable hydroclimatic shifts should be considered when the affected flow records are used for flood frequency analyses. Special treatment of the flood series can improve the analyses and provide better estimates of flood magnitudes and frequencies under the prevailing hydroclimatic condition.     

Statistical and Hybrid Methods Implemented in a Web Application for Predicting Reservoir Inflows during Flood Events

Reservoir management is a critical component of flood management, and information on reservoir inflows is particularly essential for reservoir managers to make real‐time decisions given that flood conditions change rapidly. This study's objective is to build real‐time data‐driven services that enable managers to rapidly estimate reservoir inflows from available data and models. We have tested the services using a case study of the Texas flooding events in the Lower Colorado River Basin in November 2014 and May 2015, which involved a sudden switch from drought to flooding. We have constructed two prediction models: a statistical model for flow prediction and a hybrid statistical and physics‐based model that estimates errors in the flow predictions from a physics‐based model. The study demonstrates that the statistical flow prediction model can be automated and provides acceptably accurate short‐term forecasts. However, for longer term prediction (2 h or more), the hybrid model fits the observations more closely than the purely statistical or physics‐based prediction models alone. Both the flow and hybrid prediction models have been published as Web services through Microsoft's Azure Machine Learning (AzureML) service and are accessible through a browser‐based Web application, enabling ease of use by both technical and nontechnical personnel.     

TWO-DIMENSIONAL DIFFUSION-PROBABILISTIC MODEL OF A SLOW DAM BREAK1

ABSTRACT: A two-dimensional model of a dam-break flood wave is developed by simplifying the St. Venant equations to eliminate local acceleration and inertial terms and combining the simplified equations with continuity to form a diffusion type partial differential equation. This model is cascaded with a two point probability estimate scheme to account for uncertainty in the dam break flood hydrograph and channel roughness. The development and application of the probabilistic model is the main contribution of this paper. The approach is applied to a hypothetical dam break of Long Valley Dam on the Owens River above Bishop, California.     

RECHARGE TO ALLUVIAL VALLEY AQUIFERS FROM OVERBANK FLOW AND EXCESS INFILTRATION1

ABSTRACT: Recharge is an important parameter for models that simulate water and contaminant transport in unconfined aquifers. Unfortunately, measurements of actual recharge are not usually available causing recharge to be estimated or possibly added to the calibration procedure. In this study, differences between observed water-table elevations and water-table elevations simulated with a model based on the one-dimensional Boussinesq equation were used to identify both the timing and quantity of recharge to an alluvial valley aquifer. Observed water table elevations and river stage data were recorded during a five-year period from 1991 to 1995 at the Ohio Management Systems Evaluation Area located in south-central Ohio. Direct recharge attributed to overbank flow during and shortly after flood conditions accounted for 65 percent of the total recharge computed during the five-year study period. Recharge of excess infiltration to the aquifer was intermittent and occurred soon after large rainfall events and high river stage. Specification of constant recharge with time values in ground-water simulation models seems inappropriate for stream-aquifer systems given the strong influence of the river on water table elevations in these systems.