This paper establishes a statistical framework of forest coverage models for spatio-temporal data. The forest coverage ratio of grid-cell data is modeled by taking human population density and relief energy as explanatory variables. The likelihood of the forest ratios is decomposed by the product of two likelihoods. The first likelihood discussed by Nishii and Tanaka (2010) is due to trinomial logistic distributions on three categories: the ratios take zero, one, or values between zero and one. We consider a precise modeling to the second likelihood for partly-deforested ratios by considering a) spline functions to the additive mean structure, b) wide spatial dependency of normal error terms, and c) an extended logistic type transform to the forest ratio. For spatio-temporal data, we implement auto-regressive terms based on the ratios observed in past. The proposed model was applied to real grid-cell data and resulted significant improvement compared to our previous model.