Switching the pooling similarity distances: Mahalanobis for Euclidean

Abstract

[1] In recent years, catchment similarity measures based on flood seasonality have become popular alternatives for identifying hydrologically homogeneous pooling groups used in regional flood frequency analysis. Generally, flood seasonality pooling measures are less prone to errors and are more robust than measures based on flood magnitude data. However, they are also subject to estimation uncertainty resulting from sampling variability. Because of sampling variability, catchment similarity in flood seasonality can significantly deviate from the true similarity. Therefore sampling variability should be directly incorporated in the pooling algorithm to decrease the level of pooling uncertainty. This paper develops a new pooling approach that takes into consideration the sampling variability of flood seasonality measures used as pooling variables. A nonparametric resampling technique is used to estimate the sampling variability for the target site, as well as for every site that is a potential member of the pooling group for the target site. The variability is quantified by Mahalanobis distance ellipses. The similarity between the target site and the potential site is then assessed by finding the minimum confidence interval at which their Mahalanobis ellipses intersect. The confidence intervals can be related to regional homogeneity, which allows the target degree of regional homogeneity to be set in advance. The approach is applied to a large set of catchments from Great Britain, and its performance is compared with the performance of a previously used pooling technique based on the Euclidean distance. The results demonstrate that the proposed approach outperforms the previously used approach in terms of the overall homogeneity of delineated pooling groups in the study area.

Regional flood frequency analysis using kernel‐based fuzzy clustering approach

“…The ROI [Burn, 1990] is a widely used approach for quantile estimation at ungauged sites. To arrive at quantile estimate corresponding to T-years return period for the target (ungauged) site, ROI involves forming the site-specific region by pooling gauged sites (in order of their Euclidean distance to the target site) till their collective record length exceeds 5T station-years [Cunderlik and Burn, 2006]. In this study, pooling groups are designed to have 1000 station-years of record, so that they are adequate to determine quantiles corresponding to T up to 200 years.…”

“…The regional estimates were compared to the ''true'' T-year quantiles computed for the ungauged sites (based on data available at those sites), in terms of three performance measures: Absolute bias (A-bias), Absolute Relative-bias (AR-bias), and Relative Root Mean Square Error (R-RMSE). value'' of flood quantile for site k [e.g., Cunderlik and Burn, 2006]. Values of A-bias, AR-bias, and R-RMSE closer to zero indicate better performance.…”

Correcting and complementing freeway traffic accident data using Mahalanobis distance based outlier detection

“…One possible reason might be that few researchers are considering more than one metric together, so M-distance is not necessary. Even if multivariate data is considered, another problem is Mdistance is only for multivariate data that is clustering like filled ellipses, i.e., data is normally distributed [24,28,29]. However, traffic data in traditional speed-flow fundamental diagram [30] cannot hold this assumption as shown in Fig.…”

Delineation of homogenous regions using hydrological variables predicted by projection pursuit regression

“…For simplicity, the Euclidian metric d is considered throughout the present study, but other metrics or dissimilarity measures can be employed as well. In particular, the Mahalanobis distance, the weighted distance or the depth functions could be considered (Chebana and Ouarda, 2008;Cunderlik and Burn, 2006;Ouarda et al, 2000).…”