Travel times and nonlinearity of flood runoff from tracer measurements on a small watershed

Abstract

Flood runoff has been traced from seven inje.ction points to the outlet of a 96-acre watershed. Each radioactivity time record at the outlet provides a hydrograph of outflow of the labeled drop of water. The results yield direct information on the flood process of a type and accuracy not possible from conventional analysis of rainfall and runoff records. The relationships of travel time and average velocity with discharge are examined together with the variations of these relationships over the watershed. Average travel times are shown to be similar to the watershed lag. The nature of the nonlinearity of the flood runoff process is demonstrated. Although the process is grossly nonlinear at low flows, linearity is approximated at high flows. Spatial variations of travel time and hydrograph shape are shown to make contributions to nonlinearity that are additional to the lumped dependence on flood magnitude that is normally considered. Although time of travel is a basic characteristic and descrip-tor of the flood hydrograph, very little direct and quantitative information is available on values and variations of travel times of actual flood runoff for use in research on hydrograph behavior. Values are generally inferred from, or implicit in, measures of time differences between effective or excess rainfall and the resulting flood hydrograph or from assumed analytical functions used in representing or synthesizing the hydrograph. Unfortunately, such measures a re generally subject to considerable systematic and random errors or are of questionable validity. The true temporal and spatial distributions of rainfall and losses to storm runoff and hence of effective rainfall cannot be directly observed, the initial state of the watershed is only partially known, and doubtful separations of flow components are often involved. These uncertainties have resulted in doubt regarding trends in measures of travel time and consequently nonlinear behavior of flood runoff in many studies. Linsley [1967] has attributed much apparent nonlinearity to these uncertainties, while Amorocho [1967] and Eagleson et al. [1966] have suggested that they have been a major factor in the justification of the continued development of linear approximations for hydrograph analysis and synthesis.Tracing of flood runoff provides an alternative means of measuring travel times that is subject to much lower uncertainty. A direct measure is given, and travel times from different points on the watershed can be determined to investigate spatial variations, a result that is not generally available from other methods. Results can only be obtained over a long period of time, and the physical presence of the investigator is generally required on the watershed during floods. The technique is thus only useful for research and not for operational purposes, but it can provide valuable information to aid in the understanding of the flood runoff process and the assessment of the degree of nonlinearity involved. This information is of a type and accuracy that cannot be ...

Generalized hydraulic geometry: Derivation based on a multiscaling formalism

“…These observations are (1) there is significant uncertainty in HG relationships in terms of considerable scatter in the log-log plots, (2) a single power law cannot reproduce the change in slope and sometimes discontinuities in HG near bank-full conditions [e.g., see Pilgrim, 1976;Wong and Laurenson, 1984;Bates, 1990], and (3) a mixed distribution might be needed to represent discharges, especially for both below and above bank-full conditions [e.g., see Singh and Sinclair, 1972;Leytham, 1984;LeBoutillier and Waylen, 1993]. Here we propose an extension of the lognormal multiscaling model to a mixed bivariate lognormal multiscaling model which can accommodate the above considerations.…”

“…[3] For at-station HG, the single power law relationships are widely used although some deviations from a single power law have been reported in the literature, either as a change in the exponent in the log-log plot of velocity and discharge with increasing discharge, or in general as loss of log-log linearity when discharge increases [e.g., Richards, 1976;Wong and Laurenson, 1984;Bates, 1990;Pilgrim, 1976]. In contrast, the log-log linearity in downstream HG has been supported by many empirical [Carlston, 1969;Park, 1977] and theoretical [Parker, 1979;Huang et al, 2002] studies.…”

A Research on a Revised Application of Unit Hydrograph Variant According to Rainfall Intensity in a Rainstorm

“…이는 선형적 특성을 갖는 단위유량도 이론의 유용성과 적용의 간편성 으로 인하여 국내 도입 초창기 연구 (김상용, 1972; 건설 부, 1974; 윤용남과 선우중호, 1975; 윤용남과 심순보, 1976; 김재한과 이원한, 1980 등) 이후부터 최근 연구 (안 태진 등, 2000; 정성원과 문장원, 2001; 허창환과 이순탁, 2002; 김주철 등, 2003; 전민우, 2003; 성기원, 2008; 김홍 태와 신현석, 2009 등)까지 이어 온 것이다. 그러나 실제 유 역 유출이 단위유량도 가정 사항에 부합되는지에 대한 논 란이 계속되어 왔다 (Minshall, 1960;Amorocho and Orlob, 1961;Amorocho, 1963;Amorocho and Hart, 1964;Singh, 1964;Diskin, 1964;Kulandaiswamy, 1964;Dooge, 1967;Pilgrim, 1976;Singh, 1979;1988;선우중호, 2006;유주환, 2010b 등 …”

An Offer of Relation between Rainfall and Unit Hydrograph in a Small Basin

“…즉 강우가 유역 시스템에 입력되어 홍수량으로 유출되는 경우 유역을 시불변한 (Time-Invariant) 선형 시스템(Linear System)으로 보 는 것이다. 그러나 실제적으로 유역 유출에서 이와 같은 선형성(Linearity)의 가정에 대한 논란은 오래되어 왔다 (Minshall, 1960;Amorocho and Orlob, 1961;Amorocho, 1963;Amorocho and Hart, 1964;Singh, 1964;Diskin, 1964;Kulandaiswamy, 1964;Dooge, 1967;Pilgrim, 1976;Singh, 1979;1988). 그럼에도 불구하고 비선형 유출해석 의 어려움에 비하여 단위유량도 이론의 간편성 때문에 국 내에서도 단위유량도에 관하여 많이 연구되고 이용되어 왔다 (김상용, 1972; 건설부, 1974; 윤용남과 선우중호, 1975; 윤용남과 심순보, 1976; 김재한과 이원한, 1980; 선 우중호와 고영찬, 1986; 이순탁과 박종권, 1987; 이정식 등, 1987; 한국건설기술연구원, 1989; 권오헌 등, 1993; 김 재한과 윤석영, 1993; 전시영, 1994; 김상단 등, 2000; 박진 욱 등, 2000; 안태진 등, 2000; 정성원과 문장원, 2001; 허 창환과 이순탁, 2002; 김주철 등, 2003; 전민우, 2003; 신현 석 등, 2004; 성기원, 2008; 김홍태와 신현석, 2009 Class A Sample Classified Derived Unit Hydrographs by the Rainstorms Ⅰ G1-3 G1-3, G1-4, G1-8, G1-10, G2-4 Ⅱ G2-3 G1-1, G1-2, G1-7, G1-9, G2-2, G2-3, G2-5, G2-6, G2-10, G2-12, G2-14, G2-16 Ⅲ G2-13 G2-1, G2-9, G2-11, G2-13, G2-15 Ⅳ G1-6 G1-5, G1-6, G2-7, G2-8 …”