Title: Characterizing the impact of model error in hydrogeologic time series recovery inverse problems,
Abstract: Hydrogeologic models are commonly over-smoothed relative to reality, owing to
the difficulty of obtaining accurate high-resolution information about the
subsurface. When used in an inversion context, such models may introduce
systematic biases which cannot be encapsulated by an unbiased "observation
noise" term of the type assumed by standard regularization theory and typical
Bayesian formulations. Despite its importance, model error is difficult to
encapsulate systematically and is often neglected. Here, model error is
considered for a hydrogeologically important class of inverse problems that
includes interpretation of hydraulic transients and contaminant source history
inference: reconstruction of a time series that has been convolved against a
transfer function (i.e., impulse response) that is only approximately known.
Using established harmonic theory along with two results established here
regarding triangular Toeplitz matrices, upper and lower error bounds are
derived for the effect of systematic model error on time series recovery for
both well-determined and over-determined inverse problems. A Monte Carlo study
of a realistic hydraulic reconstruction problem is presented, and the lower
error bound is seen informative about expected behavior. A possible diagnostic
criterion for blind transfer function characterization is also uncovered.