A priori identifiability of unsaturated soil parameters

A priori identifiability (i.e., identifiability under perfect data) is a ne cessary condition for posteriori identifiability (i.e., identifiability und er real data), and by implication a priori nonidentifiability is a sufficie nt condition for posteriori nonidentifiability. Therefore, it is important to prove a priori identifiability before attempting to estimate model param eters through nonlinear regression with real noisy data. This paper investi gates the a priori (also called classical, structural, or deterministic) id entifiability of soil parameters using Richards's equation with perfect dis tributed pressure data and prescribed initial and boundary conditions. The study of a priori identifiability is made possible through the concept of l inear independence of vectors. As expected, it is shown that the unsaturate d soil parameters are not a priori identifiable, and thus not posteriori id entifiable, with either zero flow pressure data or steady-state flow pressu re data. In addition, it is shown that models with more than two parameters are not a priori identifiable with transient pressure data. Therefore, mod els with more than two parameters are not posteriori identifiable with real pressure data regardless of the quantity and quality of this data. However , it is found that two parameter models are a priori identifiable with tran sient pressure data. Hence, the necessary condition for the posteriori iden tifiability of two parameter models is proven.