### Abstract

We propose an infinite-dimensional adjoint-based inexact Gauss-Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the number of Stokes solutions required to solve the inverse problem is insensitive to the number of inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.

Original language | English (US) |
---|---|

Pages (from-to) | 889-903 |

Number of pages | 15 |

Journal | Journal of Glaciology |

Volume | 58 |

Issue number | 211 |

DOIs | |

State | Published - Sep 2012 |

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### ASJC Scopus subject areas

- Earth-Surface Processes

### Cite this

*Journal of Glaciology*,

*58*(211), 889-903. https://doi.org/10.3189/2012JoG11J182

**An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model.** / Petra, Noemi; Zhu, Hongyu; Stadler, Georg; Hughes, Thomas J R; Ghattas, Omar.

Research output: Contribution to journal › Article

*Journal of Glaciology*, vol. 58, no. 211, pp. 889-903. https://doi.org/10.3189/2012JoG11J182

}

TY - JOUR

T1 - An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model

AU - Petra, Noemi

AU - Zhu, Hongyu

AU - Stadler, Georg

AU - Hughes, Thomas J R

AU - Ghattas, Omar

PY - 2012/9

Y1 - 2012/9

N2 - We propose an infinite-dimensional adjoint-based inexact Gauss-Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the number of Stokes solutions required to solve the inverse problem is insensitive to the number of inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.

AB - We propose an infinite-dimensional adjoint-based inexact Gauss-Newton method for the solution of inverse problems governed by Stokes models of ice sheet flow with nonlinear rheology and sliding law. The method is applied to infer the basal sliding coefficient and the rheological exponent parameter fields from surface velocities. The inverse problem is formulated as a nonlinear least-squares optimization problem whose cost functional is the misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. Our findings show that the inexact Newton method is significantly more efficient than the nonlinear conjugate gradient method and that the number of Stokes solutions required to solve the inverse problem is insensitive to the number of inversion parameters. The results also show that the reconstructions of the basal sliding coefficient converge to the exact sliding coefficient as the observation error (here, the noise added to synthetic observations) decreases, and that a nonlinear rheology makes the reconstruction of the basal sliding coefficient more difficult. For the inversion of the rheology exponent field, we find that horizontally constant or smoothly varying parameter fields can be reconstructed satisfactorily from noisy observations.

UR - http://www.scopus.com/inward/record.url?scp=84867214339&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867214339&partnerID=8YFLogxK

U2 - 10.3189/2012JoG11J182

DO - 10.3189/2012JoG11J182

M3 - Article

AN - SCOPUS:84867214339

VL - 58

SP - 889

EP - 903

JO - Journal of Glaciology

JF - Journal of Glaciology

SN - 0022-1430

IS - 211

ER -