Depth-based regional index-flood model

Abstract

[1] Regional flood frequency analysis aims to estimate flood risk at sites where little or no hydrological data are available. The index-flood model is one of the commonly employed models for this purpose. In this model, the predicted value depends on the growth curve and its regional parameters. The latter are estimated as weighted averages of the at-site parameters. Traditional approaches are mainly based on site record lengths or region size to define these weights. Hence, they are not representative of the hydrological similarity between sites within a region. In addition, they are not defined to reach optimality in terms of model performance. To overcome these limitations, the present paper aims to propose a new optimal iterative weighting scheme to the index-flood model. The proposed approach is based on a number of elements : a statistical depth function to introduce similarity between sites, a weight function to amplify and control the depth values, an iterative procedure to improve estimation accuracy, and an optimization algorithm to objectively automate the choice of the weight function. A data set from the Island of Sicily (Italy) is used to compare the proposed approach with traditional ones. On the basis of the L-moments and using cluster analysis techniques, the studied region is subdivided into three homogeneous subregions. The results indicate that the proposed approach performs significantly better than traditional ones both in terms of relative bias and relative root mean squares error. The proposed approach allows identification of cross correlation in the region and provides a significant performance improvement.

Spatial clustering of maximum 24‐h rainfall over Urmia Lake Basin by new weighting approaches

“…Ward's method is used to minimize inter‐cluster variance and at each step; two clusters with minimum distance are pooled to each other. To implement this method, for each cluster of r with s station and p attributes in the form of ( X = X 1 , X 2, …, X p ), the following equation can be defined (Wazneh et al ., ). where ESS r is the error sum of squares, X j = ( X j 1 , X j 2 , …, X jp ) is a vector of the attributes at station j , and is a vector of the mean of attributes into cluster r .…”

“…Ward's method is used to minimize inter-cluster variance and at each step; two clusters with minimum distance are pooled to each other. To implement this method, for each cluster of r with s station and p attributes in the form of (X = X 1 , X 2, … , X p ), the following equation can be defined (Wazneh et al, 2013).…”

“…where ESS r is the error sum of squares, X j = (X j1 , X j2 , … , X jp ) is a vector of the attributes at station j, and X r is a vector of the mean of attributes into cluster r. ESS r is calculated for any pooled pair of the clusters at each step, and the final pooled clusters which minimize the increase in total ESS r across all clusters, are then selected (Murtagh and Legendre, 2014;Wazneh et al, 2013).…”

“…In various studies, a variety of attributes has been used for regionalization. Among these attributes, the basin physical attributes such as drainage area, average basin slope, basin's main river slope, and river length (Merz and Bloeschl, 2004;Heuvelmans et al, 2006;Samaniego et al, 2010;Razavi and Coulibaly, 2013); geographical attributes such as longitude and latitude (Burn and Goel, 2000;Goswami et al, 2007;Samuel et al, 2011); measurements of the basin's time of concentration, delay time, and peak time (Potter and Faulkner, 1987;Castiglioni et al, 2010); meteorological characteristics such as wind direction, average annual rainfall, rainfall intensity, temperature, solar radiation, and evapotranspiration (Chebana and Ouarda, 2008;Zhang et al, 2008;Post, 2009;Bulygina et al, 2011); and statistical measures of available time series in the study region (Lima and Lall, 2010;Wazneh et al, 2013) can be used. These attributes are selected based on their availability, degree of importance, and research goals (Bates et al, 1998).…”

Nonparametric catchment clustering using the data depth function

“…Application of the data depth function is relatively new in the field of water resources. It has been used in the field of regional flood frequency analysis (Chebana and Ouarda 2008, Wazneh et al 2013a, Wazneh et al 2013b (Chebana and Ouarda 2011b), regionalization of hydrological model parameters (Bardossy and Singh 2011) and robust estimation of hydrological model parameters (Bárdossy and Singh 2008), defining predictive uncertainty of a model , and in selection of critical events for model calibration (Singh and Bárdossy 2012). For more detailed information about the data depth function and its uses in field of water resources, please refer to Chebana and Ouarda (2011a), Chebana and Ouarda (2011c), Guerrero et al (2013), Krauße and Cullmann (2009) and Singh and Bárdossy (2012).…”