In the Darcy-Boussinesq-Brinkman scheme, the onset of convection in a porous horizontal layer with depth-dependent permeability and viscosities is investigated. The linear instability is studied and the global nonlinear stability is investigated via the auxiliary system method. By looking for symmetries and skew-symmetries hidden in the Darcy-Boussinesq-Brinkman model, a condition, in closed form, guaranteeing the global nonlinear stability is furnished. Applications to the earth's mantle and to artificial porous materials are furnished.