Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment
Over the past 3 decades, inversions for ice sheet basal drag have become commonplace in glaciological modeling. Such inversions require regularization to prevent over-fitting and ensure that the structure they recover is a robust inference from the observations, confidence which is required if they...
Published in: | The Cryosphere |
---|---|
Main Authors: | , , , |
Format: | Text |
Language: | English |
Published: |
2023
|
Subjects: | |
Online Access: | https://doi.org/10.5194/tc-17-5027-2023 https://tc.copernicus.org/articles/17/5027/2023/ |
id |
ftcopernicus:oai:publications.copernicus.org:tc110877 |
---|---|
record_format |
openpolar |
spelling |
ftcopernicus:oai:publications.copernicus.org:tc110877 2023-12-31T10:01:26+01:00 Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment Wolovick, Michael Humbert, Angelika Kleiner, Thomas Rückamp, Martin 2023-11-29 application/pdf https://doi.org/10.5194/tc-17-5027-2023 https://tc.copernicus.org/articles/17/5027/2023/ eng eng doi:10.5194/tc-17-5027-2023 https://tc.copernicus.org/articles/17/5027/2023/ eISSN: 1994-0424 Text 2023 ftcopernicus https://doi.org/10.5194/tc-17-5027-2023 2023-12-04T17:24:16Z Over the past 3 decades, inversions for ice sheet basal drag have become commonplace in glaciological modeling. Such inversions require regularization to prevent over-fitting and ensure that the structure they recover is a robust inference from the observations, confidence which is required if they are to be used to draw conclusions about processes and properties of the ice base. While L-curve analysis can be used to select the optimal regularization level, the treatment of L-curve analysis in glaciological inverse modeling has been highly variable. Building on the history of glaciological inverse modeling, we demonstrate general best practices for regularizing glaciological inverse problems, using a domain in the Filchner–Ronne catchment of Antarctica as our test bed. We show a step-by-step approach to cost function normalization and L-curve analysis. We explore the spatial and spectral characteristics of the solution as a function of regularization, and we test the sensitivity of L-curve analysis and regularization to model resolution, effective pressure, sliding nonlinearity, and the flow equation. We find that the optimal regularization level converges towards a finite non-zero limit in the continuous problem, associated with a best knowable basal drag field. Nonlinear sliding laws outperform linear sliding in our analysis, with both a lower total variance and a more sharply cornered L-curve. By contrast, geometry-based approximations for effective pressure degrade inversion performance when added to a sliding law, but an actual hydrology model may marginally improve performance in some cases. Our results with 3D inversions suggest that the additional model complexity may not be justified by the 2D nature of the surface velocity data. We conclude with recommendations for best practices in future glaciological inversions. Text Antarc* Antarctica Ice Sheet Copernicus Publications: E-Journals The Cryosphere 17 12 5027 5060 |
institution |
Open Polar |
collection |
Copernicus Publications: E-Journals |
op_collection_id |
ftcopernicus |
language |
English |
description |
Over the past 3 decades, inversions for ice sheet basal drag have become commonplace in glaciological modeling. Such inversions require regularization to prevent over-fitting and ensure that the structure they recover is a robust inference from the observations, confidence which is required if they are to be used to draw conclusions about processes and properties of the ice base. While L-curve analysis can be used to select the optimal regularization level, the treatment of L-curve analysis in glaciological inverse modeling has been highly variable. Building on the history of glaciological inverse modeling, we demonstrate general best practices for regularizing glaciological inverse problems, using a domain in the Filchner–Ronne catchment of Antarctica as our test bed. We show a step-by-step approach to cost function normalization and L-curve analysis. We explore the spatial and spectral characteristics of the solution as a function of regularization, and we test the sensitivity of L-curve analysis and regularization to model resolution, effective pressure, sliding nonlinearity, and the flow equation. We find that the optimal regularization level converges towards a finite non-zero limit in the continuous problem, associated with a best knowable basal drag field. Nonlinear sliding laws outperform linear sliding in our analysis, with both a lower total variance and a more sharply cornered L-curve. By contrast, geometry-based approximations for effective pressure degrade inversion performance when added to a sliding law, but an actual hydrology model may marginally improve performance in some cases. Our results with 3D inversions suggest that the additional model complexity may not be justified by the 2D nature of the surface velocity data. We conclude with recommendations for best practices in future glaciological inversions. |
format |
Text |
author |
Wolovick, Michael Humbert, Angelika Kleiner, Thomas Rückamp, Martin |
spellingShingle |
Wolovick, Michael Humbert, Angelika Kleiner, Thomas Rückamp, Martin Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment |
author_facet |
Wolovick, Michael Humbert, Angelika Kleiner, Thomas Rückamp, Martin |
author_sort |
Wolovick, Michael |
title |
Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment |
title_short |
Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment |
title_full |
Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment |
title_fullStr |
Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment |
title_full_unstemmed |
Regularization and L-curves in ice sheet inverse models: a case study in the Filchner–Ronne catchment |
title_sort |
regularization and l-curves in ice sheet inverse models: a case study in the filchner–ronne catchment |
publishDate |
2023 |
url |
https://doi.org/10.5194/tc-17-5027-2023 https://tc.copernicus.org/articles/17/5027/2023/ |
genre |
Antarc* Antarctica Ice Sheet |
genre_facet |
Antarc* Antarctica Ice Sheet |
op_source |
eISSN: 1994-0424 |
op_relation |
doi:10.5194/tc-17-5027-2023 https://tc.copernicus.org/articles/17/5027/2023/ |
op_doi |
https://doi.org/10.5194/tc-17-5027-2023 |
container_title |
The Cryosphere |
container_volume |
17 |
container_issue |
12 |
container_start_page |
5027 |
op_container_end_page |
5060 |
_version_ |
1786800732533424128 |