Formulation of a mathematical approach to regional frequency analysis
Article first published online: 21 OCT 2013
©2013. American Geophysical Union. All Rights Reserved.
Water Resources Research
Volume 49, Issue 10, pages 6810–6833, October 2013
How to Cite
2013), Formulation of a mathematical approach to regional frequency analysis, Water Resour. Res., 49, 6810–6833, doi:10.1002/wrcr.20540., and (
- Issue published online: 27 NOV 2013
- Article first published online: 21 OCT 2013
- Accepted manuscript online: 23 SEP 2013 09:47AM EST
- Manuscript Accepted: 16 SEP 2013
- Manuscript Revised: 6 AUG 2013
- Manuscript Received: 27 JAN 2013
- region frequency analysis;
- index-flood approach
 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.