Comparing and combining physically-based and empirically-based approaches for estimating the hydrology of ungauged catchments

• Methods for estimating various hydrological indices at ungauged sites were compared.
• Methods included a TopNet rainfall-runoff model and a Random Forest empirical model.
• TopNet estimates were improved through correction using Random Forest estimates.
• Random Forests provided the best estimates of all indices except mean flow.
• Mean flow was best estimated using an already published empirical method.

SummaryPredictions of hydrological regimes at ungauged sites are required for various purposes such as setting environmental flows, assessing availability of water resources or predicting the probability of floods or droughts. Four contrasting methods for estimating mean flow, proportion of flow in February, 7-day mean annual low flow, mean annual high flow, the all-time flow duration curve and the February flow duration curve at ungauged sites across New Zealand were compared. The four methods comprised: (1) an uncalibrated national-coverage physically-based rainfall-runoff model (TopNet); (2) data-driven empirical approaches informed by hydrological theory (Hydrology of Ungauged Catchments); (3) a purely empirically-based machine learning regression model (Random Forests); and (4) correction of the TopNet estimates using flow duration curves estimated using Random Forests. Model performance was assessed through comparison with observed data from 485 gauging stations located across New Zealand. Three model performance metrics were calculated: Nash–Sutcliffe Efficiency, a normalised error index statistic (the ratio of the root mean square error to the standard deviation of observed data) and the percentage bias. Results showed that considerable gains in TopNet model performance could be made when TopNet time-series were corrected using flow duration curves estimated from Random Forests. This improvement in TopNet performance occurred regardless of two different parameterisations of the TopNet model. The Random Forests method provided the best estimates of the flow duration curves and all hydrological indices except mean flow. Mean flow was best estimated using the already published Hydrology of Ungauged Catchments method.