Regionalization with hierarchical hydrologic similarity and ex situ data in the context of groundwater recharge estimation at ungauged watersheds

There are various methods available for annual groundwater recharge estimation with in situ observations (i.e., observations obtained at the site/location of interest), but a great number of watersheds around the world still remain ungauged, i.e., without in situ observations of hydrologic responses. One approach for making estimates at ungauged watersheds is regionalization, namely, transferring information obtained at gauged watersheds to ungauged ones. The reliability of regionalization depends on (1) the underlying system of hydrologic similarity, i.e., the similarity in how watersheds respond to precipitation input, as well as (2) the approach by which information is transferred. In this paper, we present a nested tree-based modeling approach for conditioning estimates of hydrologic responses at ungauged watersheds on ex situ data (i.e., data obtained at sites/locations other than the site/location of interest) while accounting for the uncertainties of the model parameters as well as the model structure. The approach is then integrated with a hypothesis of two-leveled hierarchical hydrologic similarity, where the higher level determines the relative importance of various watershed characteristics under different conditions and the lower level performs the regionalization and estimation of the hydrologic response of interest. We apply the nested tree-based modeling approach to investigate the complicated relationship between mean annual groundwater recharge and watershed characteristics in a case study, and apply the hypothesis of hierarchical hydrologic similarity to explain the behavior of a dynamic hydrologic similarity system. Our findings reveal the decisive roles of soil available water content and aridity in hydrologic similarity at the regional and annual scales, as well as certain conditions under which it is risky to resort to climate variables for determining hydrologic similarity. These findings contribute to the understanding of the physical principles governing robust information transfer.