Comparing methods for estimating flow duration curves at ungauged sites

Flow duration curves (FDCs) are a useful tool for characterising hydrological regimes and flow variability. FDCs observed at 379 gauging stations located across New Zealand were analysed with the aim of investigate how parameterisation and generalisation combine to influence the accuracy of empirically predicted FDCs at ungauged sites. The appropriateness of four strategies for estimating FDCs was compared: (a) parameterise then generalise; (b) parameterise then regionalise then generalise; (c) parameterise and generalise together; and (d) FDC substitution. These strategies were deployed using various combinations of methods for calculating parameters that describe the shape of FDCs (polynomial expressions and probability distribution functions) and then methods for estimating these parameters at ungauged sites using available catchment characteristics (stepwise linear regression and random forests). A parameterise and generalise together strategy was devised by applying a mixed-effects approach. A jack-knife cross-validation procedure was used to provide an independent test of each method for estimating the FDC at ungauged sites. For parameterise then regionalise strategies, it was found that the combination of parameterisation method and generalisation method together, rather than either in isolation, was important in determining overall performance. Results indicated that predictive capability varied between methods and across exceedence percentiles. The mixed-effects approach provided the most parsimonious method for estimating FDC at ungauged sites. A method using the generalised extreme value probability distribution that was generalised using random forests was the most accurate method of estimating flow duration curves at ungauged sites across New Zealand.