We newly propose a methodology to extract and model the effect of small-scale on large-scale fluctuations, for applications to disparate-scale turbulence problem having energy injections not only at large but also at small scales. For this purpose, we applied the Mori–Zwanzig projection operator method to analyze direct numerical simulation (DNS) data. It allows us to split the cross-scale contributions from cutoff scale into correlated (Markov and memory) and uncorrelated terms with regard to large-scale fluctuations. The present model can represent damping, phase shift, and excitation of large-scale fluctuations by small-scale contributions, which are distinctive features not included in a conventional sub-grid scale model such as an eddy viscosity. An application to the... Kuramoto–Sivashinsky equation demonstrates that the constructed sub-grid scale model reproduces an energy spectrum comparable to DNS.