Formulation of a mathematical approach to regional frequency analysis

Abstract

[1] Estimation of design quantiles of hydrometeorological variables at critical locations in river basins is necessary for hydrological applications. To arrive at reliable estimates for locations (sites) where no or limited records are available, various regional frequency analysis (RFA) procedures have been developed over the past five decades. The most widely used procedure is based on index-flood approach and L-moments. It assumes that values of scale and shape parameters of frequency distribution are identical across all the sites in a homogeneous region. In real-world scenario, this assumption may not be valid even if a region is statistically homogeneous. To address this issue, a novel mathematical approach is proposed. It involves (i) identification of an appropriate frequency distribution to fit the random variable being analyzed for homogeneous region, (ii) use of a proposed transformation mechanism to map observations of the variable from original space to a dimensionless space where the form of distribution does not change, and variation in values of its parameters is minimal across sites, (iii) construction of a growth curve in the dimensionless space, and (iv) mapping the curve to the original space for the target site by applying inverse transformation to arrive at required quantile(s) for the site. Effectiveness of the proposed approach (PA) in predicting quantiles for ungauged sites is demonstrated through Monte Carlo simulation experiments considering five frequency distributions that are widely used in RFA, and by case study on watersheds in conterminous United States. Results indicate that the PA outperforms methods based on index-flood approach.Citation: Basu, B., and V. V. Srinivas (2013), Formulation of a mathematical approach to regional frequency analysis, Water Resour.

Evaluation of Various Probability Distributions for Deriving Design Flood Featuring Right-Tail Events in Pakistan

“…Later, we employed three performance indexes, namely, relative bias (RB), absolute relative bias (ARB), and relative root mean square error (RRMSE), for the flood quantiles secured by PDs at the extreme events. These are defined by the following equations [40,41]:…”

Distributional Regression Forests Approach to Regional Frequency Analysis With Partial Duration Series

“…The index‐flood approach (Dalrymple, 1960) and its variants (e.g., Basu & Srinivas, 2013, 2016; Stedinger, 1983; Sveinsson et al., 2001, 2003) are widely used for RFA. Several assumptions underlying the conventional index‐flood approach may not be valid in a real‐world scenario (Basu & Srinivas, 2013; Sveinsson et al., 2001).…”

“…It involves (a) identification of a group of gauged watersheds resembling watershed of the target site (in flood generating mechanism), and (b) use of pooled information (on peak flows) from the group to perform regional frequency analysis (RFA) for arriving at the desired risk estimates. The index‐flood approach (Dalrymple, 1960) and its variants (e.g., Basu & Srinivas, 2013, 2016; Stedinger, 1983; Sveinsson et al., 2001, 2003) are widely used for RFA. Several assumptions underlying the conventional index‐flood approach may not be valid in a real‐world scenario (Basu & Srinivas, 2013; Sveinsson et al., 2001).…”

Flood Frequency Analyses over Different Basin Scales in the Blue Nile River Basin, Ethiopia

“…The samples for flood frequency analysis can be chosen based on the annual maximum flow or the annual peak flows over some defined truncation levels. The annual maximum flow method has been widely used for flood frequency analysis in different regions [2,[7][8][9][10][11][12][13][14][15][25][26][27][28], in which the sample is defined by the maximum flow of each year of the study period. It is essential to note that the main drawbacks of relying on peaks over threshold method are the threshold selection and assuring independence criteria [27].…”

“…Several studies have been reported to be related to the investigation of the most suitable probability distribution for flood frequency analysis in different regions worldwide [2,[7][8][9][10][11][12][13][14][15][26][27][28][29][30][31][32][33]. Ahilan et al [29] compared the family of extreme value distributions using the data from 172 gauging stations in Ireland; they reported that the Gumbel distribution outperformed the other two types of extreme value distributions (i.e., Frechet, and Weibull).…”