In a model, quantity A is modelled. A is influenced by unknown B. Parameterization is to express B using A and/or other known quantities, such that A can be estimated. Parameterization schemes usually consist of parameters to be determined empirically.
Example, we model population density ρ using model (conservation equation) dρ/dt = s, where s is birth-death rate, but unknown. Because of this, the model is not “closed”. Since s is too difficult to estimate, we express s using ρ, e.g., s = r ρ, where r is a parameter. The model is now
dρ/dt = r ρ
which is the Mathus (1798) population growth theory. We use parameterization to describe our understanding of the processes. It is a vital technique for representing cross-scale and cross-compartment interactions in complex systems. (YS, 12.06.2024).