Development and evaluation of an extended inverse distance weighting method for streamflow estimation at an ungauged site

In spatial interpolation, one of the most widely used deterministic methods is the inverse distance weighting (IDW) technique. The general idea of IDW is primarily based on the hypothesis that the attribute value of an ungauged site is the weighted average of the known attribute values within the neighborhood, and the 'weights' are merely associated with the horizontal distances between the gauged and ungauged sites. However, here we propose an extended version of IDW (hereafter, called the EIDW method) to provide 'alternative weights' based on the blended geographical and physiographical spaces for estimation of streamflow percentiles at ungauged sites. Based on the leave-one-out cross-validation procedure, the coefficient of determination had a value of 0.77 and 0.82 for the proposed EIDW models, M1 and M2, respectively, with low root mean square errors. Moreover, after investigating the relationship between the prediction efficiency and the distance decay parameter (C), the better performance of the M1 and M2 resulted at C=2. Furthermore, the results of this study show that the EIDW could be considered as a constructive way forward to provide more accurate and consistent results in comparison to the traditional IDW or the dimension reduction technique-based IDW.