Frequency Analysis of Low Flows

Abstract

The transformations (i) SMEMAX (ii) Modified SMEMAX (iii) Power and Probability Distributions (iv) Weibull (a,P,y) or Extreme value type 111 (v) Weibull (a,P,O) (vi) Log Pearson Type 111 (vii) Log Boughton are considered for the low flow analysis. Also, different parameter estimating procedures are considered. Both the Weibull and log Pearson can have positive lower bounds and thus their use in fitting low flow probabilities may not be physically justifiable. A new derivation generalizing the SMEMAX transformation is proposed. A new estimator for the log Boughton distribution is presented. It is found that the Boughton distribution with Cunnane's plotting position provides a good fit to low flows for Virginia streams. Downloaded from https://iwaponline.com/hr/article-pdf/16/2/105/2359/105.pdf by guestPower Transformation -This transformation was first proposed by Box andCox (1964), andChander et al. (1978) used this transformation for flood frequency analysis. In a paper by Kumar and Devi (1982), the power transformation was applied to the frequency analysis of low flows for one station. The power transformation is formwhere: z is normally distributed with mean M, and standard deviation S,; y is the original sample value; h is a parameter of transformation. Also, y can be replaced by (y+ k) for y >k. Downloaded from https://iwaponline.com/hr/article-pdf/16/2/105/2359/105.pdf by guest + Z,) 12 Z1 largest (chosen arbitrarily). Considering Fig. 1 for f o r It is noted that Z1 = 22, for Z, = 0. For this special case the transformation given by Eqs. (4) and (5) becomes for X < X < X m S --Downloaded from https

The impacts of climate change on local hydrology and low flow frequency in the Geum River Basin, Korea

“…Based on the literature review, Gumbel has proposed that the third asymptotic distribution of the extreme (smallest) value is one of the most accepted theoretical probability distribution functions for a low flow study (Gumbel, 1958). Later, many scientists suggested that other distributions, such as the generalized extreme value type III (GEV3), the lognormal, and Pearson distributions (Matalas, 1963; Loganathan, 1985; Tasker, 1987), are also acceptable. The parameters of these distributions, however, should be estimated from several statistical methods.…”

The spatial distribution of low flows in Poland not exceeded at an assumed probability

“…Many studies have been devoted to the probability distributions most suitable for fi tting the sequences of annual minimum fl ows in different regions and for minima of different averaging intervals, as well as evaluating methods by which to estimate distribution parameters (Matalas 1963;Jozeph 1970;Prakash 1981;Beran and Rodier 1985;Loganathan et al 1985;McMahon and Mein 1986;Singh 1987;Waylen and Woo 1987;Khan and Mawdsley 1988;Sefe 1988;Leppajarvi 1989;Polarski 1989;FREND 1989;Nathan and McMahon 1990b;Russell 1992;Loaiciga et al 1992;Durrans 1996;Lawal and Watt 1996a;Lawal and Watt 1996b;Bulu andOnoz 1997, Jakubowski 2005). The author's task was not to investigate the real distribution of examined series but only to adjust one of the functions applied most frequently to ensure fulfi lment of the Kołmo-gorov λ test condition of conformability.…”

Comparison of the annual minimum flow and the deficit below threshold approaches: case study for the province of New Brunswick, Canada

“…In the present study, the minimum annual discharges were fitted using the threeparameter Weibull (WEI3) distribution (or extreme value type III). This distribution was chosen because it is theoretically the parent model of extreme low flows (Gumbel 1954), and hence it was one of the main models considered by Matalas (1963) and Loganathan et al (1985), among others, as suitable for low-streamflow analysis. The WEI3 cumulative distribution function (cdf) is of the form…”

“…The WEI2 distribution was chosen because its three-parameter counterpart, WEI3, has been widely applied for studying low flows (Matalas 1963). It was also noted that the WEI2 distribution has been used in peak over threshold (POT) flood frequency modeling in the past (Miquel 1984; Groupe de recherche en hydrologie statistique (GREHYS 1996) and in the frequency analysis of low flows (Loganathan et al 1985). Moreover, the generalized Pareto distribution was chosen because it has been widely suggested for exceedance distribution (Davison and Smith 1990;Wang 1991;Madsen et al 1997).…”