“…In addition, because computing bending angles requires a ray tracing model, assimilating of bending angles is computationally very expensive (Liu & Zou, 2003;Shao & Zou, 2002). Therefore, many studies (Boyaj et al, 2022;Chen et al, 2015Chen et al, , 2020Chen et al, , 2021Cheng et al, 2018;Healy et al, 2005;Miller et al, 2023;Singh et al, 2021;Zhou & Chen, 2014), assimilate refractivity using a less computationally expensive observation operator in regional models. We also assimilated refractivities using the computationally affordable 3D-Var assimilation technique due to our limited computational resources.…”