Assessment of dimension-reduction and grouping methods for catchment response time estimation in Hungary
Eszter Nagy, József Szilágyi, Péter Torma
Abstract
61 catchments located in Hungary, with drainage areas from 8.74 to 810 km2. Many engineering tasks require the estimation of the catchment response time (Tr). The most frequently used Tr parameters are the time of concentration and the lag time. At ungauged catchments, they are usually estimated by empirical equations that relate Tr to catchment characteristics. This paper provides a comparative study of three dimension-reduction techniques and seven clustering methods for fitting empirical equations to the observed values of Tr. 60 catchment descriptors were calculated for each catchment, then three subsets with 1–3 descriptors were extracted from the entire parameter set during the dimension-reduction analysis. Two and four catchment groups were created during a cluster analysis, by re-calibrating the three equations that resulted from the dimension-reduction analysis. It is demonstrated that the principal component analysis can be easily outperformed by the linear correlation and the all-possible-regressions methods, the latter yielding a root-mean-squared error (RMSE) of 6.77 h when applied with three catchment descriptors. The most interesting finding of the dimension reduction is that Tr is strongly connected to field capacity in the region of study. The performance of the clustering methods varies considerably (RMSE = 5.05–12.03 h). The best overall performance comes from the residual approach (RMSE = 8.14 h on average). It is shown that several of the methods outperform the grouping based on geographical regions, however, the estimation error is reduced only in a few cases when compared to the regional estimation (i.e., one cluster) method. Clusters created based on catchment width yields the best results, resulting in RMSE values of 5.80 and 5.77 h (with two and four clusters, respectively). The comparison of the new and the existing empirical equations clearly demonstrated that the estimation of Tr needs improvement in Hungary, while the application of more than two clusters is unwarranted for the study region.