A Priori Identifiability of Unsaturated Soil Parameters

Abstract

A priori identifiability (i.e., identifiability under perfect data) is a necessary condition for posteriori identifiability (i.e., identifiability under real data), and by implication a priori nonidentifiability is a sufficient condition for posteriori nonidentifiability. Therefore, it is important to prove a priori identifiability before attempting to estimate model parameters through nonlinear regression with real noisy data. This paper investigates the a priori (also called classical, structural, or deterministic) identifiability of soil parameters using Richards's equation with perfect distributed pressure data and prescribed initial and boundary conditions. The study of a priori identifiability is made possible through the concept of linear independence of vectors. As expected, it is shown that the unsaturated soil parameters are not a priori identifiable, and thus not posteriori identifiable, with either zero flow pressure data or steady-state flow pressure data. In addition, it is shown that models with more than two parameters are not a priori identifiable with transient pressure data. Therefore, models 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 transient pressure data. Hence, the necessary condition for the posteriori identifiability of two parameter models is proven.