William H. Asquith

L-moments and TL-moments of the generalized lambda distribution

The 4-parameter generalized lambda distribution (GLD) is a flexible distribution capable of mimicking the shapes of many distributions and data samples including those with heavy tails. The method of L-moments and the recently developed method of trimmed L-moments (TL-moments) are attractive techniques for parameter estimation for heavy-tailed distributions for which the L- and TL-moments have been defined. Analytical solutions for the first five L- and TL-moments in terms of GLD parameters are derived. Unfortunately, numerical methods are needed to compute the parameters from the L- or TL-moments. Algorithms are suggested for parameter estimation. Application of the GLD using both L- and TL-moment parameter estimates from example data is demonstrated, and comparison of the L-moment fit of the 4-parameter kappa distribution is made. A small simulation study of the 98th percentile (far-right tail) is conducted for a heavy-tail GLD with high-outlier contamination. The simulations show, with respect to estimation of the 98th-percent quantile, that TL-moments are less biased (more robost) in the presence of high-outlier contamination. However, the robustness comes at the expense of considerably more sampling variability.

Estimation of Volumetric Runoff Coefficients for Texas Watersheds Using Land-Use and Rainfall-Runoff Data

The rational method for peak discharge (Qp) estimation was introduced in the 1880s. Although the rational method is considered simplistic, it remains an effective method for estimating peak discharge for small watersheds. The runoff coefficient (C) is a key parameter for the rational method and can be estimated in various ways. Literature-based C values (Clit) are listed for different land-use/land cover (two words, no hyphen) (LULC) conditions invarious design manuals and textbooks; however, these Clit values were developed with little basis on observed rainfall and runoff data. In this paper, Clit values were derived for 90 watersheds in Texas by using LULC data for 1992 and 2001; the Clit values derived from the two data sets were essentially the same. Also for this study, volumetric runoff coefficients (Cv) were estimated by using observed rainfall and runoff depths from more than 1,600 events observed in the watersheds. Watershed-median and watershed- average Cv values were computed, and both are consistent with data from the National Urban Runoff Program. In addition, Cv values were estimated by using rank-ordered pairs of rainfall and runoff depths (i.e., frequency matching). As anticipated, C values derived by all three methods (literature based, event totals, and frequency matching) consistently had larger values for developed watersheds than for undeveloped watersheds. Two regression equations of Cv versus percent impervious area were developed and combined into a single equation that can be used to rapidly estimate Cv values for similar Texas watersheds. DOI: 10.1061/(ASCE)IR.1943-4774.0000368.

Generalized Additive Regression Models of Discharge and Mean Velocity Associated with Direct-Runoff Conditions in Texas: Utility of the U.S. Geological Survey Discharge Measurement Database

AbstractA database containing more than 17,700 discharge values and ancillary hydraulic properties was assembled from summaries of discharge measurement records for 424 U.S. Geological Survey streamflow-gauging stations (stream gauges) in Texas. Each discharge exceeds the 90th-percentile daily mean streamflow as determined by period-of-record, stream-gauge-specific, flow-duration curves. Each discharge therefore is assumed to represent discharge measurement made during direct-runoff conditions. The hydraulic properties of each discharge measurement included concomitant cross-sectional flow area, water-surface top width, and reported mean velocity. Systematic and statewide investigation of these data in pursuit of regional models for the estimation of discharge and mean velocity has not been previously attempted. Generalized additive regression modeling is used to develop readily implemented procedures by end-users for estimation of discharge and mean velocity from select predictor variables at ungauged st...

Return period adjustment for runoff coefficients based on analysis in undeveloped Texas watersheds

The rational method for peak discharge (Qp) estimation was introduced in the 1880s. The runoff coefficient (C) is a key parameter for the rational method that has an implicit meaning of rate proportionality, and the C has been declared a function of the annual return period by various researchers. Rate-based runoff coefficients as a function of the return period, CðTÞ, were determined for 36 undeveloped water- sheds in Texas using peak discharge frequency from previously published regional regression equations and rainfall intensity frequency for return periods T of 2, 5, 10, 25, 50, and 100 years. The CðTÞ values and return period adjustments CðTÞ=CðT ¼ 10 yearÞ determined in this study are most applicable to undeveloped watersheds. The return period adjustments determined for the Texas watersheds in this study and those extracted from prior studies of non-Texas data exceed values from well-known literature such as design manuals and textbooks. Most importantly, the return period adjustments exceed values currently recognized in Texas Department of Transportation design guidance when T > 10 years. DOI: 10.1061/(ASCE)IR.1943-4774.0000571.

Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R

The implementation characteristics of two method of L-moments (MLM) algorithms for parameter estimation of the 4-parameter Asymmetric Exponential Power (AEP4) distribution are studied using the R environment for statistical computing. The objective is to validate the algorithms for general application of the AEP4 using R. An algorithm was introduced in the original study of the L-moments for the AEP4. A second or alternative algorithm is shown to have a larger L-moment-parameter domain than the original. The alternative algorithm is shown to provide reliable parameter production and recovery of L-moments from fitted parameters. A proposal is made for AEP4 implementation in conjunction with the 4-parameter Kappa distribution to create a mixed-distribution framework encompassing the joint L-skew and L-kurtosis domains. The example application provides a demonstration of pertinent algorithms with L-moment statistics and two 4-parameter distributions (AEP4 and the Generalized Lambda) for MLM fitting to a modestly asymmetric and heavy-tailed dataset using R.

Unit Hydrograph Estimation for Applicable Texas Watersheds

The unit hydrograph is defined as a direct runoff hydrograph resulting from a unit pulse of excess rainfall generated uniformly over the watershed at a constant rate for an effective duration. The unit hydrograph method is a well-known hydrologic-engineering technique for estimation of the runoff hydrograph given an excess rainfall hyetograph. Four separate approaches are used to extract unit hydrographs from the database on a per watershed basis. A large database of more than 1,600 storms with both rainfall and runoff data for 93 watersheds in Texas is used for four unit hydrograph investigation approaches. One approach is based on 1-minute Rayleigh distribution hydrographs; the other three approaches are based on 5-minute gamma-distribution hydrographs. The unit hydrographs by watershed from the approaches are represented by shape and time to peak parameters. Weighted least-squares regression equations to estimate the two unit hydrograph parameters for ungaged watersheds are provided on the basis of the watershed characteristics of main channel length, dimensionless main channel slope, and a binary watershed development classification. The range of watershed area is approximately 0.32 to 167 square miles. The range of main channel length is approximately 1.2 to 49 miles. The range of dimensionless main channel slope is approximately 0.002 to 0.020. The equations provide a framework by which hydrologic engineers can estimate shape and time to peak of the unit hydrograph, and hence the associated peak discharge. Assessment of equation applicability and uncertainty for a given watershed also is provided. The authors explicitly do not identify a preferable approach and hence equations for unit hydrograph estimation. Each equation is associated with a specific analytical approach. Each approach represents the optimal unit hydrograph solution on the basis of the details of approach implementation including unit hydrograph model, unit hydrograph duration, objective functions, loss model assumptions, and other factors.

Rate-Based Estimation of the Runoff Coefficients for Selected Watersheds in Texas

AbstractThe runoff coefficient, C, of the rational method is an expression of rate proportionality between rainfall intensity and peak discharge. Values of C were derived for 80 developed and undeveloped watersheds in Texas using two distinct methods. First, the rate-based runoff coefficient, Crate, was estimated for each of about 1,500 rainfall-runoff events. Second, the frequency-matching approach was used to derive a runoff coefficient, Cr, for each watershed. Published C values, Clit, or literature-based runoff coefficients were compared to those obtained from the methods investigated here. Using the 80 Texas watersheds, comparison of the two methods shows that about 75% of literature-based runoff coefficients are greater than Cr and the watershed-median Crate, but for developed watersheds with more impervious cover, literature-based runoff coefficients are less than Cr and Crate. An equation applicable to many Texas watersheds is proposed to estimate C as a function of impervious area.

Watershed Slope Lower Bounds for Hydrologic Methods

Engineers design a substantial fraction portion of infrastructure that accommodates storm water drainage and conveyance. Estimation models of the response for a watershed typically contain some form of watershed slope as a principal parameter, and the response is usually inversely proportional to that slope. Therefore, as topographic slope decreases, the watershed timing parameter increases. The consequences at low enough slope, is that the timing parameters approach infinite time and the precipitation intensity that is associated with a long averaging time is so small as to be meaningless -- yet low slope environments exist, are populated, and precipitation does generate runoff. BACKGROUND The parameters important for understanding overland flow are topography, surface roughness, soil infiltration characteristics (abstractions), and the distribution, duration, and intensity of precipitation. Of these components, the focus of this research was the impact of topographic slope on hydrologic estimates of runoff.

Bed-material entrainment and associated transportation infrastructure problems in streams of the Edwards Plateau, central Texas

Printed on recycled paper The Texas Department of Transportation (TxDOT) commonly builds and maintains low-water crossings (LWCs) over streams (fig. 1) in the Edwards Plateau in Central Texas. LWCs are low-height structures, typically constructed of concrete and asphalt, that provide acceptable passage over seasonal rivers or streams with relatively low normal-depth flow. They are designed to accommodate flow by roadway overtopping during highflow events. The streams of the Edwards Plateau are characterized by cobbleand gravel-sized bed material and highly variable flow regimes. Low base flows that occur most of the time occasionally are interrupted by severe floods. The floods entrain and transport substantial loads of bed material in the stream channels. As a result, LWCs over streams in the Edwards Plateau are bombarded and abraded by bed material during floods and periodically must be maintained or even replaced.