When scaling up from microscale to macroscale, often one is not interested in a single global value such as a mean only, but rather in the variation of a continuum variable. The authors define a representative elementary volume (REV) at the microstate-macrostate boundary. Inside the REVs, a lattice Boltzmann (LB) method is used to compute the microdynamics. The result per REV is then used on global scale to solve global dynamics by a finite elements (FE) method.

I see a close link to Dynamic upscaling of decomposition kinetics for carbon cycling models. In the referenced paper, Eq. (16) describes the macroscale dynamics corresponding to FE. On macroscale the parameters $\sigma^2_{C_s}$, $\sigma^2_{C_b}$, $C’_s C’_b$, etc. are used and those can be obtained from microscale dynamics corresponding to LB.