TY - JOUR

T1 - Regularization techniques for ill-posed inverse problems in data assimilation

AU - Budd, Christopher

AU - Freitag, Melina A

AU - Nichols, N K

N1 - Proceedings paper from 10th Institute for Computational Fluid Dynamics (ICFD) Conference, Reading, England, 2010.

PY - 2011/7

Y1 - 2011/7

N2 - Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L 2, regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the presence of model error, this approach does not capture the initial state of the system accurately, as the initial state estimate is derived by minimizing the average error between the model predictions and the observations over a time window. Here we examine an alternative L 1 regularization technique that has proved valuable in image processing. We show that for examples of flow with sharp fronts and shocks, the L 1 regularization technique performs more accurately than standard L 2 regularization.

AB - Optimal state estimation from given observations of a dynamical system by data assimilation is generally an ill-posed inverse problem. In order to solve the problem, a standard Tikhonov, or L 2, regularization is used, based on certain statistical assumptions on the errors in the data. The regularization term constrains the estimate of the state to remain close to a prior estimate. In the presence of model error, this approach does not capture the initial state of the system accurately, as the initial state estimate is derived by minimizing the average error between the model predictions and the observations over a time window. Here we examine an alternative L 1 regularization technique that has proved valuable in image processing. We show that for examples of flow with sharp fronts and shocks, the L 1 regularization technique performs more accurately than standard L 2 regularization.

KW - model error

KW - variational data assimilation

KW - Tikhonov and L-1 regularization

KW - Burgers' equation

KW - nonlinear least-squares optimization

KW - ill-posed inverse problems

UR - http://www.scopus.com/inward/record.url?scp=79954922089&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.compfluid.2010.10.002

U2 - 10.1016/j.compfluid.2010.10.002

DO - 10.1016/j.compfluid.2010.10.002

M3 - Article

SN - 0045-7930

VL - 46

SP - 168

EP - 173

JO - Computers and Fluids

JF - Computers and Fluids

IS - 1

ER -