“…In these three approaches, the HB framework has been proven to be the most efficient method to incorporate the spatial coherence to reduce the estimation uncertainty because it has the advantage of shrinking the local parameter toward the common regional mean and including an estimation of its variance or covariance across the catchments (Bracken et al, 2018;Sun and Lall, 2015;Sun et al, 2015). In the field of hydrological modeling, most preceding studies were focused on no-pooling models that neglect the spatial coherence between catchments (Heuvelmans et al, 2006;Lebecherel et al, 2016;Merz and Bloschl, 2004;Oudin et al, 2008;Singh et al, 2012;Tegegne and Kim, 2018;Xu et al, 2018); little attention has been paid to the HB framework. Thus, we want to fill this gap and explore the applicability of the spatial coherence through the HB framework in hydrological modeling with the time-varying parameters.…”