Some open-channel empirical parameters lack exact values due to (a) not having definitive measurement methods and/or (b) not rendering a "properly-posed" system of equations in the formulation of their inverse problems. The values of these parameters are therefore susceptible to dataerrors, imperfections in governing equations or insufficiency of the gauged data used in inverse problems. Best values of such parameters in a mathematical sense can be identified by the implementation of inverse problems using optimisation methods but there are potential pitfalls. A comprehensive review of inverse problems is presented in this paper outlining some of the pitfalls in their implementation and illustrating the parameter quality conditions of "identifiability, uniqueness and stability". The uniqueness condition was approached by statistical methods in this paper. Other considerations of equal importance were found to include the compliance with the assumptions underlying optimisation methods and a careful selection of the objective function.