skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

Abstract

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.

Authors:
 [1];  [2];  [3];  [4]
  1. Univ. of Edinburgh, Edinburgh (United Kingdom)
  2. Argonne National Lab. (ANL), Argonne, IL (United States)
  3. INRIA Sophia-Antipolis, Valbonne (France)
  4. Allstate Insurance Co., Northbrook, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1362124
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Geoscientific Model Development (Online)
Additional Journal Information:
Journal Name: Geoscientific Model Development (Online); Journal Volume: 9; Journal Issue: 5; Journal ID: ISSN 1991-9603
Publisher:
European Geosciences Union
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING

Citation Formats

Goldberg, Daniel N., Narayanan, Sri Hari Krishna, Hascoet, Laurent, and Utke, Jean. An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem. United States: N. p., 2016. Web. doi:10.5194/gmd-9-1891-2016.
Goldberg, Daniel N., Narayanan, Sri Hari Krishna, Hascoet, Laurent, & Utke, Jean. An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem. United States. doi:10.5194/gmd-9-1891-2016.
Goldberg, Daniel N., Narayanan, Sri Hari Krishna, Hascoet, Laurent, and Utke, Jean. Fri . "An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem". United States. doi:10.5194/gmd-9-1891-2016. https://www.osti.gov/servlets/purl/1362124.
@article{osti_1362124,
title = {An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem},
author = {Goldberg, Daniel N. and Narayanan, Sri Hari Krishna and Hascoet, Laurent and Utke, Jean},
abstractNote = {We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.},
doi = {10.5194/gmd-9-1891-2016},
journal = {Geoscientific Model Development (Online)},
number = 5,
volume = 9,
place = {United States},
year = {2016},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Flow speed within the Antarctic ice sheet and its controls inferred from satellite observations: FLOW SPEED IN THE ANTARCTIC ICE SHEET
journal, July 2015

  • Arthern, Robert J.; Hindmarsh, Richard C. A.; Williams, C. Rosie
  • Journal of Geophysical Research: Earth Surface, Vol. 120, Issue 7
  • DOI: 10.1002/2014JF003239

Automatic differentiation of algorithms
journal, December 2000

  • Bartholomew-Biggs, Michael; Brown, Steven; Christianson, Bruce
  • Journal of Computational and Applied Mathematics, Vol. 124, Issue 1-2
  • DOI: 10.1016/S0377-0427(00)00422-2

Reverse accumulation and attractive fixed points
journal, January 1994


Reverse aumulation and imploicit functions
journal, January 1998


Adaptive mesh, finite volume modeling of marine ice sheets
journal, January 2013

  • Cornford, Stephen L.; Martin, Daniel F.; Graves, Daniel T.
  • Journal of Computational Physics, Vol. 232, Issue 1
  • DOI: 10.1016/j.jcp.2012.08.037

Assessment of the importance of ice-shelf buttressing to ice-sheet flow: BUTTRESSING SENSITIVITY
journal, February 2005

  • Dupont, T. K.; Alley, R. B.
  • Geophysical Research Letters, Vol. 32, Issue 4
  • DOI: 10.1029/2004GL022024

What Is an Adjoint Model?
journal, November 1997


Retreat of Pine Island Glacier controlled by marine ice-sheet instability
journal, January 2014

  • Favier, L.; Durand, G.; Cornford, S. L.
  • Nature Climate Change, Vol. 4, Issue 2
  • DOI: 10.1038/nclimate2094

Bedmap2: improved ice bed, surface and thickness datasets for Antarctica
journal, January 2013

  • Fretwell, P.; Pritchard, H. D.; Vaughan, D. G.
  • The Cryosphere, Vol. 7, Issue 1
  • DOI: 10.5194/tc-7-375-2013

Generating efficient derivative code with TAF
journal, October 2005


Automatic differentiation and iterative processes
journal, January 1992


A variationally derived, depth-integrated approximation to a higher-order glaciological flow model
journal, January 2011


Parameter and state estimation with a time-dependent adjoint marine ice sheet model
journal, January 2013


Data assimilation using a hybrid ice flow model
journal, January 2011


Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation
journal, March 2000

  • Griewank, Andreas; Walther, Andrea
  • ACM Transactions on Mathematical Software, Vol. 26, Issue 1
  • DOI: 10.1145/347837.347846

Greenland ice-sheet volume sensitivity to basal, surface and initial conditions derived from an adjoint model
journal, January 2009


Basal conditions for Pine Island and Thwaites Glaciers, West Antarctica, determined using satellite and airborne data
journal, January 2009


Larsen B Ice Shelf rheology preceding its disintegration inferred by a control method
journal, January 2007

  • Khazendar, A.; Rignot, E.; Larour, E.
  • Geophysical Research Letters, Vol. 34, Issue 19
  • DOI: 10.1029/2007GL030980

A Community Ice Sheet Model for Sea Level Prediction: Building a Next-Generation Community Ice Sheet Model; Los Alamos, New Mexico, 18–20 August 2008
journal, January 2009

  • Lipscomb, William; Bindschadler, Robert; Bueler, Ed
  • Eos, Transactions American Geophysical Union, Vol. 90, Issue 3
  • DOI: 10.1029/2009EO030004

Toward a New Generation of Ice Sheet Models
journal, January 2007

  • Little, Christopher M.; Oppenheimer, Michael; Alley, Richard B.
  • Eos, Transactions American Geophysical Union, Vol. 88, Issue 52
  • DOI: 10.1029/2007EO520002

Large-scale ice flow over a viscous basal sediment: Theory and application to ice stream B, Antarctica
journal, April 1989

  • MacAyeal, Douglas R.
  • Journal of Geophysical Research: Solid Earth, Vol. 94, Issue B4
  • DOI: 10.1029/JB094iB04p04071

The basal stress distribution of Ice Stream E, Antarctica, inferred by control methods
journal, January 1992

  • MacAyeal, Douglas R.
  • Journal of Geophysical Research, Vol. 97, Issue B1
  • DOI: 10.1029/91JB02454

Basal friction of Ice Stream E, West Antarctica
journal, January 1995

  • MacAyeal, Douglas R.; Bindschadler, Robert A.; Scambos, Theodore A.
  • Journal of Glaciology, Vol. 41, Issue 138
  • DOI: 10.3189/S0022143000016154

ADISM v.1.0: an adjoint of a thermomechanical ice-sheet model obtained using an algorithmic differentiation tool
journal, January 2013

  • McGovern, J.; Rutt, I.; Utke, J.
  • Geoscientific Model Development Discussions, Vol. 6, Issue 4
  • DOI: 10.5194/gmdd-6-5251-2013

Increased ice losses from Antarctica detected by CryoSat-2
journal, June 2014

  • McMillan, Malcolm; Shepherd, Andrew; Sundal, Aud
  • Geophysical Research Letters, Vol. 41, Issue 11
  • DOI: 10.1002/2014GL060111

Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM)
journal, January 2008

  • Pattyn, F.; Perichon, L.; Aschwanden, A.
  • The Cryosphere, Vol. 2, Issue 2
  • DOI: 10.5194/tc-2-95-2008

Optimal initial conditions for coupling ice sheet models to Earth system models: PEREGO ET AL.
journal, September 2014

  • Perego, Mauro; Price, Stephen; Stadler, Georg
  • Journal of Geophysical Research: Earth Surface, Vol. 119, Issue 9
  • DOI: 10.1002/2014JF003181

An inexact Gauss-Newton method for inversion of basal sliding and rheology parameters in a nonlinear Stokes ice sheet model
journal, January 2012

  • Petrat, Noemi; Zhu, Hongyu; Stadler, Georg
  • Journal of Glaciology, Vol. 58, Issue 211
  • DOI: 10.3189/2012JoG11J182

Ice Flow of the Antarctic Ice Sheet
journal, August 2011


Large-scale rheology of the Ross Ice Shelf, Antarctica, computed by a control method
journal, January 1997


Thin-Film Flows with Wall Slip: An Asymptotic Analysis of Higher Order Glacier Flow Models
journal, January 2010

  • Schoof, C.; Hindmarsh, R. C. A.
  • The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 63, Issue 1
  • DOI: 10.1093/qjmam/hbp025

Ice stream basal conditions from block-wise surface data inversion and simple regression models of ice stream flow: Application to Bindschadler Ice Stream
journal, January 2008

  • Sergienko, O. V.; Bindschadler, R. A.; Vornberger, P. L.
  • Journal of Geophysical Research, Vol. 113, Issue F4
  • DOI: 10.1029/2008JF001004

Inland thinning of the Amundsen Sea sector, West Antarctica: INLAND THINNING OF THE AMUNDSEN SEA
journal, May 2002

  • Shepherd, Andrew; Wingham, Duncan J.; Mansley, Justin A. D.
  • Geophysical Research Letters, Vol. 29, Issue 10
  • DOI: 10.1029/2001GL014183

Warm ocean is eroding West Antarctic Ice Sheet: WARM OCEAN IS ERODING WAIS
journal, December 2004

  • Shepherd, Andrew; Wingham, Duncan; Rignot, Eric
  • Geophysical Research Letters, Vol. 31, Issue 23
  • DOI: 10.1029/2004GL021106

OpenAD/F: A Modular Open-Source Tool for Automatic Differentiation of Fortran Codes
journal, July 2008

  • Utke, Jean; Naumann, Uwe; Fagan, Mike
  • ACM Transactions on Mathematical Software, Vol. 34, Issue 4
  • DOI: 10.1145/1377596.1377598

CLIMATE CHANGE: Why Is It Hard to Predict the Future of Ice Sheets?
journal, March 2007


Application of control methods for modelling the flow of Pine Island Glacier, West Antarctica
journal, January 2003


    Works referencing / citing this record:

    How Accurately Should We Model Ice Shelf Melt Rates?
    journal, January 2019

    • Goldberg, D. N.; Gourmelen, N.; Kimura, S.
    • Geophysical Research Letters, Vol. 46, Issue 1
    • DOI: 10.1029/2018gl080383

    How Accurately Should We Model Ice Shelf Melt Rates?
    journal, January 2019

    • Goldberg, D. N.; Gourmelen, N.; Kimura, S.
    • Geophysical Research Letters, Vol. 46, Issue 1
    • DOI: 10.1029/2018gl080383

    SICOPOLIS-AD v1: an open-source adjoint modeling framework for ice sheet simulation enabled by the algorithmic differentiation tool OpenAD
    journal, January 2020

    • Logan, Liz C.; Narayanan, Sri Hari Krishna; Greve, Ralf
    • Geoscientific Model Development, Vol. 13, Issue 4
    • DOI: 10.5194/gmd-13-1845-2020