“…Subsurface flow modeling usually involves large uncertainty due to the heterogeneous nature of geologic properties and limited knowledge we have about the subsurface situation. Therefore, it is necessary to quantify the propagation of such uncertainty for subsurface flow problems, and many studies have been conducted on this topic (Dodwell et al., 2015; Durlofsky & Chen, 2012; Li & Zhang, 2007; Linde et al., 2017; Mo, Zhu, et al., 2019; Thibaut et al., 2021; Tripathy & Bilionis, 2018; Vilhelmsen et al., 2018; Zhang, 2001). The uncertainty of subsurface flow modeling can be reduced by calibrating the geologic models with observations of model responses, for example, hydraulic heads, pressure, and so on, which is also known as data assimilation or inverse modeling (Chang et al., 2010; Gharamti et al., 2015; Oliver et al., 2008; Reichle et al., 2002; Wang et al., 2021a).…”