Characterizing the impact of model error in hydrologic time series recovery inverse problems
Hydrologic models are commonly oversmoothed relative to reality, owing to computational limitations and to the difficulty of obtaining accurate highresolution information. 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. In this paper, model error is considered for an 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 welldetermined and overdetermined inverse problems. It is seen that use of additional measurement locations does not improve expected performance in the face of model error. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. Finally, a possiblemore »
 Authors:

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 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Texas, Austin, TX (United States). Computational Hydraulics Group (CHG). Inst. for Computational Engineering and Sciences (ICES)
 Publication Date:
 Report Number(s):
 LAUR1628825
Journal ID: ISSN 03091708
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Advances in Water Resources
 Additional Journal Information:
 Journal Volume: 111; Journal ID: ISSN 03091708
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics
 OSTI Identifier:
 1412889
Hansen, Scott K., He, Jiachuan, and Vesselinov, Velimir V.. Characterizing the impact of model error in hydrologic time series recovery inverse problems. United States: N. p.,
Web. doi:10.1016/j.advwatres.2017.09.030.
Hansen, Scott K., He, Jiachuan, & Vesselinov, Velimir V.. Characterizing the impact of model error in hydrologic time series recovery inverse problems. United States. doi:10.1016/j.advwatres.2017.09.030.
Hansen, Scott K., He, Jiachuan, and Vesselinov, Velimir V.. 2017.
"Characterizing the impact of model error in hydrologic time series recovery inverse problems". United States.
doi:10.1016/j.advwatres.2017.09.030. https://www.osti.gov/servlets/purl/1412889.
@article{osti_1412889,
title = {Characterizing the impact of model error in hydrologic time series recovery inverse problems},
author = {Hansen, Scott K. and He, Jiachuan and Vesselinov, Velimir V.},
abstractNote = {Hydrologic models are commonly oversmoothed relative to reality, owing to computational limitations and to the difficulty of obtaining accurate highresolution information. 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. In this paper, model error is considered for an 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 welldetermined and overdetermined inverse problems. It is seen that use of additional measurement locations does not improve expected performance in the face of model error. A Monte Carlo study of a realistic hydraulic reconstruction problem is presented, and the lower error bound is seen informative about expected behavior. Finally, a possible diagnostic criterion for blind transfer function characterization is also uncovered.},
doi = {10.1016/j.advwatres.2017.09.030},
journal = {Advances in Water Resources},
number = ,
volume = 111,
place = {United States},
year = {2017},
month = {10}
}