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.     

COMPARISON OF DESIGN STORM CONCEPTS USING CONTINUOUS SIMULATION WITH SHORT DURATION STORMS1

ABSTRACT: The objectives of this paper were to test the ability of various design storm distributions to simulate the actual rainfall pattern and to compare the runoff rates used in the design of stormwater management devices in the State of Florida using continuous simulation approach. The analyses were performed for four gaged stations to evaluate the applicability of design storm distributions in different parts of the State of Florida. The approach used in this study compared the peak runoff rates from design storms based on the various distributions to those that would result from actual rainfall events. A series of continuous runoff rates were developed through the use of actual fifteen-minute recorded rainfall data, Horton type infiltration decay and recovery rate, and a continuous simulation model. The runoff rates were analyzed using frequency distributions to obtain peak runoff rates associated with different return periods based on the assumption that the continuous simulation approach closely predicts the actual runoff rates from the gaged stations. The results show that the behavior of the design storm distributions varies for different watershed characteristics in different parts of the state. The study also suggests that in general the Florida Department of Transportation and the Suwanne River Water Management (FDOT/ SRWMD) distributions appeared to agree with the continuous simulation results.     

HISTORICAL EVOLUTION OF FLOODING DAMAGE ON A USA/QUEBEC RIVER BASIN1

ABSTRACT: There is a general belief in the public eye that extreme events such as floods are becoming more and more common. This paper explores this hypothesis by examining the historical evolution of annual expected flooding damage on the Chateauguay River Basin, located at the border between the United States and the province of Quebec, Canada. A database of basin land use was constructed for the years 1930 and 1995 to assess anthropogenic changes and their impact on the basin's hydrology. The progressive modification of the likelihood of a flooding event over the same period was then investigated using homogeneity and statistical tests on available hydrometric data. The evolution of the annual expected flooding damage was then evaluated using a coupled hydrologic/hydraulic simulator linked to a damage analysis model. The simulator and model were used to estimate flooding damage over a wide range of flooding return periods, for conditions prevailing in 1963 and 1995. Results of the analysis reveal the absence of any increasing or decreasing trend in the historical occurrence of flooding events. However, a general increase in the annual expected flooding damage was observed for all studied river sections. This increase is linked to an historical increase in damages for a given flooding event, and is the result of unbridled construction and development within the flood zone. To assess for future trends, this study also examined the potential impacts linked to the anticipated global warming. Results indicate that a significant increase in seasonal flooding events and annual expected flooding damage is possible over the next century. In fact, what is now considered a 100‐year flooding event for the summer/fall season could become a ten‐year event by the end of this century. This shows that potential future impacts linked to climate change should be considered now by engineers, land planners, and decision makers. This is especially critical if a design return period is part of the decision making process.     

Assessment of grate sag inlets in a residential area based on return period and clogging factor

Storm in-sag inlets, which typically have inflow capture efficiency of 100%, can violate the allowable water spread criterion of roadways, thus slowing the traffic movement and contributing to accidents. This is especially evident during severe storms of high return periods and when a storm sewer inlet of grate type is adopted, because it is subject to debris and trash clogging factors. In this study, the water spread on pavement for in-sag grates located in a residential area in Kuwait is analyzed in terms of return period and clogging factor. It is found that for a single grate inlet with a return period of 10 years, a clogging factor of 50% can lead to a water spread value exceeding the local design constraint assigned for residential areas, which is one traffic lane of 4m width. It is also shown that for in-sag locations, a double-grate inlet is more preferable than the single one, because the former tends to reduce the adverse hydraulic effect of total inflow on water spread width. The effect of clogging factor on a multiple-grate inlet located in sag is determined from a simple expression suggested in this study.     

REGIONAL RAINFALL INTENSITY-DURATION-FREQUENCY CURVES FOR PENNSYLVANIA1

ABSTRACT: A statistical analysis of all available continuous hourly and 15-minute duration rainfall records for Pennsylvania was performed to develop an updated procedure to estimate design storms. As a resuit of this study, Pennsylvania was divided into five homogeneous rainfall regions and a set of rainfall intensity-duration curves developed for each region, for return periods of 1 to 100 years and durations ranging from 5 minutes to 24 hours. The PDT-IDF curves were judged to be a better representation of Pennsylvania rainfall than the nationwide TP-40 maps, particularly for storm events of 10-years and lower return periods. The average time distribution of 24-hour storms in Pennsylvania was found to be well represented by the SCS Type II distribution. The Corps of Engineers SPS 24-hour distribution was found to differ appreciably from both the SCS Type H and the Pennsylvania 24-hour storm distribution. For storm durations between 15 and 90 minutes the standard Yarnell intensity-duration curves closely resemble Pennsylvania storm distributions.     

Impacts of Climate Change on Extreme Precipitation Events Over Flamingo Tropicana Watershed1

Abstract: Climate change, particularly the projected changes to precipitation patterns, is likely to affect runoff both regionally and temporally. Extreme rainfall events are expected to become more intense in the future in arid urban areas and this will likely lead to higher streamflow. Through hydrological modeling, this article simulates an urban basin response to the most intense storm under anthropogenic climate change conditions. This study performs an event‐based simulation for shorter duration storms in the Flamingo Tropicana (FT) watershed in Las Vegas, Nevada. An extreme storm, defined as a 100‐year return period storm, is selected from historical records and perturbed to future climatic conditions with respect to multimodel multiscenario (A1B, A2, B1) bias corrected and spatially disaggregated data from the World Climate Research Programme's (WCRP's) database. The cumulative annual precipitation for each 30‐year period shows a continuous decrease from 2011 to 2099; however, the summer convective storms, which are considered as extreme storms for the study area, are expected to be more intense in future. Extreme storm events show larger changes in streamflow under different climate scenarios and time periods. The simulated peak streamflow and total runoff volume shows an increase from 40% to more than 150% (during 2041‐2099) for different climate scenarios. This type of analysis can help evaluate the vulnerability of existing flood control system and flood control policies.     

A TRIANGULAR MODEL OF DIMENSIONLESS RUNOFF PRODUCING RAINFALL HYETOGRAPHS IN TEXAS1

ABSTRACT: A synthetic triangular hyetograph for a large data base of Texas rainfall and runoff is needed. A hyetograph represents the temporal distribution of rainfall intensity at a point or over a watershed during a storm. Synthetic hyetographs are estimates of the expected time distribution for a design storm and principally are used in small watershed hydraulic structure design. A data base of more than 1,600 observed cumulative hyetographs that produced runoff from 91 small watersheds (generally less than about 50 km²) was used to provide statistical parameters for a simple triangular shaped hyetograph model. The model provides an estimate of the average hyetograph in dimensionless form for storm durations of 0 to 24 hours and 24 to 72 hours. As a result of this study, the authors concluded that the expected dimensionless cumulative hyetographs of 0 to 12 hour and 12 to 24 hour durations were sufficiently similar to be combined with minimal information loss. The analysis also suggests that dimensionless cumulative hyetographs are independent of the frequency level or return period of total storm depth and thus are readily used for many design applications. The two triangular hyetographs presented are intended to enhance small watershed design practice in applicable parts of Texas.     

SIZING OF SURFACE WATER RUNOFF DETENTION PONDS FOR WATER QUALITY IMPROVEMENT1

ABSTRACT: Historically, storm water management programs and criteria have focused on quantity issues related to flooding and drainage system design. Traditional designs were based on large rainfall‐runoff events such as those having two‐year to 100‐year return periods. While these are key criteria for management and control of peak flows, detention basin designs based on these criteria may not provide optimal quality treatment of storm runoff. As evidenced by studies performed by numerous public and private organizations, the water quality impacts of storm water runoff are primarily a function of more frequent rainfall‐runoff events rather than the less frequent events that cause peak flooding. Prior to this study there had been no detailed investigations to characterize the variability of the more frequent rainfall events on Guam. Also, there was a need to develop some criteria that could be applied by designers, developers, and agency officials in order to reduce the impact of storm water runoff on the receiving bodies. The objectives of this paper were three‐fold: (1) characterize the hourly rainfall events with respect to volume, frequency, duration, and the time between storm events; (2) evaluate the rainfall‐runoff characteristics with respect to capture volume for water quality treatment; and (3) prepare criteria for sizing and designing of storm water quality management facilities. The rainfall characterization studies have provided insight into the characteristics of rainstorms that are likely to produce non‐point source pollution in storm water runoff. By far the most significant fmdings are the development of a series of design curves that can be used in the actual sizing of storm water detention and treatment facilities. If applied correctly, these design curves could lead to a reduction of non‐point source pollution to Guam's streams, estuaries, and coastal environments.     

Assessing watershed transport of atrazine and nitrate to evaluate conservation practice effects and advise future monitoring strategies

Continued public support for U.S. taxpayer funded programs aimed at reducing agricultural pollutants depends on clear demonstrations of water quality improvements. The objective of this research was to determine if implementation of agricultural best management practices (BMPs) in the Goodwater Creek Experimental Watershed (GCEW) resulted in changes to atrazine and nitrate (NO₃–N) loads during storm events. An additional objective was to estimate future monitoring periods necessary to detect a 5, 10, 20, and 25% reduction in atrazine and NO₃–N event load. The GCEW is a 73 km² watershed located in northcentral Missouri, USA. Linear regressions and Akaike Information Criteria were used to determine if reductions in atrazine and NO₃–N event loads occurred as BMPs were implemented. No effects due to any BMP type were indicated for the period of record. Further investigation of event sampling from the long-term GCEW monitoring program indicated errors in atrazine load calculations may be possible due to pre-existing minimum threshold levels used to trigger autosampling and sample compositing. Variation of event loads was better explained by linear regressions for NO₃–N than for atrazine. Decommissioning of upstream monitoring stations during the study period represented a missed opportunity to further explain variation of event loads at the watershed outlet. Atrazine requires approximately twice the monitoring period relative to NO₃–N to detect future reductions in event load. Appropriate matching of pollutant transport mechanisms with autosampling protocols remains a critical information need when setting up or adapting watershed monitoring networks aimed at detecting watershed-scale BMP effects.     

POTENTIAL EFFECTS OF CHANGED CLIMATES ON HEAVY RAINFALL FREQUENCIES IN TIlE MIDWEST1

ABSTRACT: An important question posed by potential future shifts in climate relates to possible shifts in heavy rainfall events (intensity and/or frequency) used to design hydraulic structures. Heavy rain events were defined as those producing amounts having average recurrence intervals of two years or longer for a specific storm period at a given location. Estimates of such heavy rainfall shifts in the humid continental climate of the midwest were derived by using spatial and temporal analogs. Comparisons in areas of relatively warm, wet conditions were made with those having measurably cooler, drier average conditions. The spatial-temporal analogs provided comparative differences in precipitation and temperature similar to the magnitude of changes obtained from GCM estimates. Spatial analogs/analyses indicated 10 to 15 percent increases in the frequency distribution of rain events having recurrence intervals of 5 to 50 years. Two periods of notably drier and warmer conditions during the past 90 years revealed 5 to 15 percent decreases in the number of 2- to 10-year heavy rain events. The suppression percentages showed a strong tendency to increase with increasing recurrence interval from 2 to 10 years.     

AN APPLICATION OF COMPUTER GRAPHICS TO ANALYSIS OF EXTREMES1

ABSTRACT: A convenient method for the statistical analysis of hydrologic extremes is to use probability papers to fit selected theoretical distributions to extremal observations. Three commonly accepted statistical distributions of extreme hydrologic events are: the double exponential distribution, the bounded exponential distribution, and the Log Pearson Type III distribution. In most cases, probability papers are distribution specific. But, for the Log Pearson Type III distribution, the probability paper is characterized by a population-specific parameter, namely, the coefficient of skewness. It is not practicable to procure probability papers for all possible values of this parameter. Therefore, a computer program is developed to generate population-specific probability papers and to perform statistical analysis of the data using computer graphics. Probability papers covering return periods up to 1000 years or more are generated for the three distributions mentioned above. Using a plot routine, available extremal observations are plotted on selected probability papers and a linear regression analysis is used to fit a straight line to the data. Predictions of hydrologic extremes for higher recurrence intervals can be made by extrapolating the fitted straight lines.     

Illinois State Water Survey Bulletin 75: New Precipitation Frequency Study for Illinois

Storm frequency estimates and their temporal distributions are important in determining estimates of runoff or peak flow rates in many engineering and hydrological problems. Illinois State Water Survey Bulletin 70 has been serving as the design rainfall standard in Illinois since its publication in 1989. Although Bulletin 70 represented the best available data at the time of its publication, the standards needed to be reevaluated and updated after more than three decades and with the growing evidence of the nonstationary nature of heavy precipitation. The trends in heavy precipitation in Illinois prompted the creation of a new frequency study named Bulletin 75, providing precipitation frequencies for event durations ranging from 5 min to 10 days and for recurrence intervals ranging from 2 months to 500 years. The results are presented for the same 10 geographic sections in Illinois as in Bulletin 70 to maintain the continuity of hydrologic studies and compatibility with regulations. The primary goal of this paper is to outline some of the key methodological issues and challenges, to compare the results with the previous sources, and to highlight the effects of the changing precipitation standards on the development of amendments to existing ordinances. Lake County in Illinois, as one of the most affected urban areas with the highest change in heavy precipitation, was selected to illustrate issues related to the application of modified precipitation standards.     

Defining the Diurnal Pattern of Snowmelt Using a Beta Distribution Function

Snow is an important component of the hydrologic cycle for many regions worldwide. In addition to vital water resources, snowmelt can be important for forest ecosystem dynamics and flood risk. However, standard design events in the United States lack a design snowmelt event, including only precipitation events, though snowmelt has been shown to be larger than rainfall. In this article, we present a method using hourly snow water equivalent data to develop and test a function for representing the diurnal pattern of snowmelt. A two‐parameter beta distribution function is modified for the purposes of this study and found to fit the pattern of snowmelt well with a root mean squared error of 0.008. Soil moisture sensors were additionally utilized to assess the timing of the snowmelt water outflow from the base of the snowpack that supports the shape of the function, but suggests that the timing of losses recorded on snow pillows lag as much as 3 h. Further testing of the function showed the shape of the function to be accurate. The methods developed and tested in this paper can be applied for design purposes comparing snowmelt and rainfall events or to improve hydrological models investigating processes such as streamflow or groundwater recharge.     

RELIABILITY OF THE DESIGN STORM CONCEPT IN EVALUATING RUNOFF PEAK FLOW1

A comparative study was undertaken to evaluate peak runoff flow rates using (1) a continuous series of actual rainfall events and (2) design storms. The ILLUDAS computer model was used to simulate runoff over a catchment within the city of Montreal, Canada. A ten-year period, five-minute increment rainfall data base was used to derive peak flow frequency curves. Two types of design storms were analyzed: one derived from intensity duration frequency curves (Chicago type), the other from averaging actual rainfall patterns (Huff type). Antecedent soil moisture conditions were considered in the analyses. It was found that the probability distribution of runoff peak flow was sensitive to the choice of design storm pattern and to the antecedent soil moisture condition. A symmetrical, Chicago-type design storm with antecedent dry soil moisture produced a flow frequency curve similar to the one obtained from a series of historical rainfall events.     

SPACE-TIME VALIDATION OF A THUNDERSTORM RAINFALL MODEL1

A probability model for predicting the occurrence and magnitude of thunderstorm rainfall developed in the southwestern United States was tested in the metropolitan Chicago area with reasonable success, especially for the moderate to the extreme runoff-producing events. The model requires the estimation of two parameters, the mean number of events per year and the conditional probability of rain given that an event has occurred. To tie in the data from more than one gage in an area, an event can be defined in several ways, such as the areal mean rainfall exceeding 0.50 inch and at least one gage receiving more than 1.0 inch. This type of definition allows both of the model parameters to be obtained from daily warm-season rainfall records. Regardless of the definition used a Poisson distribution adequately described the number of events per season. A negative binomial distribution was derived as representing the frequency density function for rainfall where several gages are employed in defining a storm. Chicago data fit both distributions very well at events with relatively high return periods. The results indicate the possibility of using the model on a regional basis where limited amount of data may be used to estimate parameters for extensive areas.     

Integrating contributing areas and indexing phosphorus loss from agricultural watersheds

Most states in the USA have adopted P Indexing to guide P-based management of agricultural fields by identifying the relative risk of P loss at farm and watershed scales. To a large extent, this risk is based on hydrologic principles that frequently occurring storms can initiate surface runoff from fields. Once initiated, this hydrological pathway has a high potential to transport P to the stream. In regions where hydrologically active areas of watersheds vary in time and space, surface runoff generation by "saturation excess" has been linked to distance from stream, with larger events resulting in larger contributing distances. Thus, storm-return period and P loss from a 39.5-ha mixed-land-use watershed in Pennsylvania was evaluated to relate return-period thresholds and distances contributing P to streams. Of 248 storm flows between 1997 and 2006, 93% had a return period of 1 yr, contributing 47% of total P (TP) export, while the largest two storms (10-yr return period) accounted for 23% of TP export. Contributing distance thresholds for the watershed were determined (50-150 m) for a range of storm-return periods (1-10 yr) from hydrograph analysis. By modifying storm-return period thresholds in the P Index and thereby contributing distance, it is possible to account for greater risk of P loss during large storms. For instance, increasing return period threshold from 1 (current P indices) to 5 yr, which accounted for 67% of TP export, increased the P-management restricted area from 20 to 58% of the watershed. An increase in impacted area relative to a decreased risk of P loss creates a management-policy dilemma that cannot be ignored.     

RESPONSE OF GREEN‐AMPT MEIN‐LARSEN SIMULATED RUNOFF VOLUMES TO TEMPORALLY AGGREGATED PRECIPITATION1

ABSTRACT: Data collection frequency in automated systems is user determined and can range from seconds to hours or days. Currently, there is no standard or recommended frequency interval for collecting precipitation data from automated systems for input to event‐based models such as Green‐Ampt Mein‐Larsen (GAML). Data from 47 storm events at seven locations were used to simulate the response of GAML excess rainfall to temporally aggregated precipitation data. No difference in model efficiency was recognized when comparing one‐minute interval data (R²= 1.00) to five‐minute data (R²= 1.00). Very little model efficiency was lost at a 10‐minute (R²= 0.96) interval. After 10‐minutes, decline in efficiency became more rapid with R²= 0.16 at one hour. The combined effect of time interval with respect to drainage area, hydraulic conductivity, maximum 30‐minute intensity, and total precipitation also revealed similar results.     

Characterization of Drought in the South Atlantic,United States

Drought has been less extensively characterized in the humid South Atlantic compared to the arid western United States. Our objective was to characterize drought in the South Atlantic and to understand whether drought has become more severe in this region over time. Here we used monthly streamflow to characterize hydrological drought. Hydrological drought occurred when streamflow fell below the 20th percentile over three consecutive months and terminated once streamflow remained above the 20th percentile for three consecutive months. We characterized the frequency, duration, magnitude, and severity of events using the above definition. Significant changes in drought characteristics were tested with Mann‐Kendall over three periods: 1930‐2010, 1930‐1969, and 1970‐2010. We show that 71% of drought events were shorter than six months, while 7% were multiyear events. There was little evidence of trends in drought characteristics to support the claim of drought becoming more severe in the South Atlantic over the 20th Century. The one exception was a significant increase in the joint probability of nearby basins being simultaneously in drought conditions in the southern portion of the study area from 1970 to 2010. While drought characteristics have changed little through time, decreasing average streamflow in non drought periods coupled with increasing water demand provide the context within which recent multiyear drought events have produced significant stress on existing water infrastructure.     

Quantifying Reductions of Mass‐Failure Frequency and Sediment Loadings From Streambanks Using Toe Protection and Other Means: Lake Tahoe,United States1

Abstract: Streambank erosion by mass‐failure processes represents an important form of channel adjustment and a significant source of sediment in disturbed streams. Mass failures regularly occur by a combination of hydraulic processes that undercut bank toes and geotechnical processes that cause bank collapse by gravity. Little if any quantitative information is available on the effectiveness of bank treatments on reducing erosion. To evaluate potential reduction in sediment loadings emanating from streambanks, the hydraulic and geotechnical processes responsible for mass failure were simulated under existing and mitigated conditions using a Bank‐Stability and Toe‐Erosion Model (BSTEM). Two critical erosion sites were selected from each of the three watersheds known to contribute the greatest amounts of fine sediment by streambank processes in the Lake Tahoe Basin. A typical high‐flow annual hydrograph was selected for analysis. Bank‐material strength data were collected for each layer as were species‐specific root‐reinforcement values. The effects of the first flow event on bank‐toe erosion were simulated using an excess shear‐stress approach. The resulting geometry was then exported into the bank‐stability submodel to test for the relative stability of the bank under peak flow and drawdown conditions. In this way, BSTEM was used iteratively for all flow events for both existing and mitigated conditions. On average, 13.6% of the material was eroded by hydraulic shear, the remainder by mass failures, which occurred about five times over the simulation period. Simulations with 1.0 m‐high rock‐toe protection showed a dramatic reduction in streambank erosion (69‐100%). Failure frequency for the simulation period was reduced in most cases to a single episode. Thus, an almost 90% reduction in streambank loadings was achieved by virtually eliminating the erosion of only 14% of the material that was entrained by hydraulic forces. Consequently, simulations show average load reductions of about an order of magnitude. Results stress the critical importance of protecting the bank toe‐region from steepening by hydraulic forces that would otherwise entrain previously failed and in situ bank materials, thereby allowing the upper bank to flatten (by failure) to a stable slope.