“…The matrix approach was initially implemented in the Terrestrial ECOsystem model (TECO) for data assimilation studies (Luo et al, 2003;Xu et al, 2006). The matrix approach has recently been applied to global land models, such as the Community Atmosphere-Biosphere-Land Exchange model (CABLE) (Xia et al, 2012(Xia et al, , 2013, LPJ-GUESS (Ahlstrom et al, 2015), ORCHIDEE (Huang, Zhu, et al, 2018), CLM3.5 (Hararuk et al, 2015;Hararuk & Luo, 2014;Rafique et al, 2016), CLM4 (Rafique et al, 2017), CLM4.5 (Huang, Lu, et al, 2018), and CLM5 in this study. The CABLE matrix model was used to accelerate its spin-up (Xia et al, 2012) and for traceability analysis to trace sources of uncertainty in model simulations of terrestrial carbon storage (Xia et al, 2013).…”