“…As discussed by MW10, the 1D implicit diffusion operator is closely linked to the recursive filter (Lorenc, 1992;Hayden and Purser, 1995), which has been developed extensively in meteorology for constructing correlation models in multiple dimensions (Wu et al, 2002;Purser et al, 2003aPurser et al, , 2003bLiu et al, 2007). The recursive filter has also been employed in ocean data assimilation systems (Martin et al, 2007;Dobricic and Pinardi, 2008;Liu et al, 2009).…”