The Annals of Applied Statistics

Improving ice sheet model calibration using paleoclimate and modern data

Won Chang, Murali Haran, Patrick Applegate, and David Pollard

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Human-induced climate change may cause significant ice volume loss from the West Antarctic Ice Sheet (WAIS). Projections of ice volume change from ice sheet models and corresponding future sea-level rise have large uncertainties due to poorly constrained input parameters. In most future applications to date, model calibration has utilized only modern or recent (decadal) observations, leaving input parameters that control the long-term behavior of WAIS largely unconstrained. Many paleo-observations are in the form of localized time series, while modern observations are non-Gaussian spatial data; combining information across these types poses nontrivial statistical challenges. Here we introduce a computationally efficient calibration approach that utilizes both modern and paleo-observations to generate better constrained ice volume projections. Using fast emulators built upon principal component analysis and a reduced dimension calibration model, we can efficiently handle high-dimensional and non-Gaussian data. We apply our calibration approach to the PSU3D-ICE model which can realistically simulate long-term behavior of WAIS. Our results show that using paleo-observations in calibration significantly reduces parametric uncertainty, resulting in sharper projections about the future state of WAIS. One benefit of using paleo-observations is found to be that unrealistic simulations with overshoots in past ice retreat and projected future regrowth are eliminated.

Article information

Ann. Appl. Stat., Volume 10, Number 4 (2016), 2274-2302.

Received: May 2016
Revised: August 2016
First available in Project Euclid: 5 January 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Paleoclimate West Antarctic Ice Sheet computer model calibration Gaussian process dimension reduction


Chang, Won; Haran, Murali; Applegate, Patrick; Pollard, David. Improving ice sheet model calibration using paleoclimate and modern data. Ann. Appl. Stat. 10 (2016), no. 4, 2274--2302. doi:10.1214/16-AOAS979.

Export citation


  • Applegate, P. J., Kirchner, N., Stone, E. J., Keller, K. and Greve, R. (2012). An assessment of key model parametric uncertainties in projections of Greenland ice sheet behavior. Cryosphere 6 589–606.
  • Bayarri, M. J., Berger, J. O., Cafeo, J., Garcia-Donato, G., Liu, F., Palomo, J., Parthasarathy, R. J., Paulo, R., Sacks, J. and Walsh, D. (2007). Computer model validation with functional output. Ann. Statist. 35 1874–1906.
  • Bhat, K. S., Haran, M. and Goes, M. (2010). Computer model calibration with multivariate spatial output: A case study. In Frontiers of Statistical Decision Making and Bayesian Analysis (M. H. Chen, P. Müller, D. Sun, K. Ye and D. K. Dey, eds.) 168–184. Springer, New York.
  • Bhat, K. S., Haran, M., Olson, R. and Keller, K. (2012). Inferring likelihoods and climate system characteristics from climate models and multiple tracers. Environmetrics 23 345–362.
  • Bindschadler, R. A., Nowicki, S., Abe-Ouchi, A., Aschwanden, A., Choi, H., Fastook, J., Granzow, G., Greve, R., Gutowski, G., Herzfeld, U., Jackson, C., Johnson, J., Khroulev, C., Levermann, A., Lipscomb, W. H., Martin, M. A., Morlighem, M., Parizek, B. R., Pollard, D., Price, S. F., Ren, D., Saito, F., Sato, T., Seddik, H., Seroussi, H., Takahashi, K., Walker, R. and Wang, W. L. (2013). Ice-sheet model sensitivities to environmental forcing and their use in projecting future sea level (the SeaRISE project). J. Glaciol. 59 195–224.
  • Briggs, R., Pollard, D. and Tarasov, L. (2013). A glacial systems model configured for large ensemble analysis of Antarctic deglaciation. Cryosphere 7 1533–1589.
  • Briggs, R. D., Pollard, D. and Tarasov, L. (2014). A data-constrained large ensemble analysis of Antarctic evolution since the Eemian. Quat. Sci. Rev. 103 91–115.
  • Briggs, R. D. and Tarasov, L. (2013). How to evaluate model-derived deglaciation chronologies: A case study using Antarctica. Quat. Sci. Rev. 63 109–127.
  • Brynjarsdóttir, J. and O’Hagan, A. (2014). Learning about physical parameters: The importance of model discrepancy. Inverse Probl. 30 114007, 24.
  • Chang, W., Haran, M., Olson, R. and Keller, K. (2014a). Fast dimension-reduced climate model calibration and the effect of data aggregation. Ann. Appl. Stat. 8 649–673.
  • Chang, W., Applegate, P., Haran, H. and Keller, K. (2014b). Probabilistic calibration of a Greenland ice sheet model using spatially-resolved synthetic observations: Toward projections of ice mass loss with uncertainties. Geosci. Model Dev. 7 1933–1943.
  • Chang, W., Haran, M., Applegate, P. and Pollard, D. (2016). Supplement to “Improving ice sheet model calibration using paleoclimate and modern data.” DOI:10.1214/16-AOAS979SUPP.
  • Chang, W., Haran, M., Applegate, P. and Pollard, D. (2016). Calibrating an ice sheet model using high-dimensional binary spatial data. J. Amer. Statist. Assoc. 111 57–72.
  • Cornford, S. L., Martin, D. F., Payne, A. J., Ng, E. G., Le Brocq, A. M., Gladstone, R. M., Edwards, T. L., Shannon, S. R., Agosta, C., Van Den Broeke, M. R., Hellmer, H. H., Krinner, G., Ligtenberg, S. R. M., Timmermann, R. and Vaughan, D. G. (2015). Century-scale simulations of the response of the West Antarctic Ice Sheet to a warming climate. Cryosphere 9 1579–1600.
  • Favier, L., Durand, G., Cornford, S. L., Gudmundsson, G. H., Gagliardini, O., Gillet-Chaulet, F., Zwinger, T., Payne, A. J. and Le Brocq, A. M. (2014). Retreat of Pine Island Glacier controlled by marine ice-sheet instability. Nature Climate Change 4 171–121.
  • Feldmann, J. and Levermann, A. (2015). Collapse of the West Antarctic Ice Sheet after local destabilization of the Amundsen Basin. Proc. Natl. Acad. Sci. USA 112 14191–14196.
  • Flegal, J. M., Haran, M. and Jones, G. L. (2008). Markov chain Monte Carlo: Can we trust the third significant figure? Statist. Sci. 23 250–260.
  • Fretwell, P., Pritchard, H. D., Vaughan, D. G., Bamber, J. L., Barrand, N. E., Bell, R., Bianchi, C., Bingham, R. G., Blankenship, D. D., Casassa, G., Catania, G., Callens, D., Conway, H., Cook, A. J., Corr, H. F. J., Damaske, D., Damm, V., Ferraccioli, F., Forsberg, R., Fujita, S., Gim, Y., Gogineni, P., Griggs, J. A., Hindmarsh, R. C. A., Holmlund, P., Holt, J. W., Jacobel, R. W., Jenkins, A., Jokat, W., Jordan, T., King, E. C., Kohler, J., Krabill, W., Riger-Kusk, M., Langley, K. A., Leitchenkov, G., Leuschen, C., Luyendyk, B. P., Matsuoka, K., Mouginot, J., Nitsche, F. O., Nogi, Y., Nost, O. A., Popov, S. V., Rignot, E., Rippin, D. M., Rivera, A., Roberts, J., Ross, N., Siegert, M. J., Smith, A. M., Steinhage, D., Studinger, M., Sun, B., Tinto, B. K., Welch, B. C., Wilson, D., Young, D. A., Xiangbin, C. and Zirizzotti, A. (2013). Bedmap2: Improved ice bed, surface and thickness datasets for Antarctica. Cryosphere 7 375–393.
  • Gladstone, R. M., Lee, V., Rougier, J., Payne, A. J., Hellmer, H., Le Brocq, A., Shepherd, A., Edwards, T. L., Gregory, J. and Cornford, S. L. (2012). Calibrated prediction of Pine Island Glacier retreat during the 21st and 22nd centuries with a coupled flowline model. Earth Planet. Sci. Lett. 333 191–199.
  • Golledge, N. R., Menviel, L., Carter, L., Fogwill, C. J., England, M. H., Cortese, G. and Levy, R. H. (2014). Antarctic contribution to meltwater pulse 1A from reduced Southern Ocean overturning. Nature Comm. 5.
  • Golledge, N. R., Kowalewski, D. E., Naish, T. R., Levy, R. H., Fogwill, C. J. and Gasson, E. G. W. (2015). The multi-millennial Antarctic commitment to future sea-level rise. Nature 526 421–425.
  • Gomez, N., Pollard, D. and Holland, D. (2015). Sea-level feedback lowers projections of future Antarctic ice-sheet mass loss. Nature Comm. 6.
  • Hastie, T., Tibshirani, R. and Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd ed. Springer, New York.
  • Hellmer, H. H., Kauker, F., Timmermann, R., Determann, J. and Rae, J. (2012). Twenty-first-century warming of a large Antarctic ice-shelf cavity by a redirected coastal current. Nature 485 225–228.
  • Higdon, D., Gattiker, J., Williams, B. and Rightley, M. (2008). Computer model calibration using high-dimensional output. J. Amer. Statist. Assoc. 103 570–583.
  • Jones, G. L., Haran, M., Caffo, B. S. and Neath, R. (2006). Fixed-width output analysis for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 101 1537–1547.
  • Joughin, I., Smith, B. E. and Medley, B. (2014). Marine ice sheet collapse potentially under way for the Thwaites Glacier Basin, West Antarctica. Science 344 735–738.
  • Kennedy, M. C. and O’Hagan, A. (2001). Bayesian calibration of computer models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 425–464.
  • Kirshner, A. E., Anderson, J. B., Jakobsson, M., O’Regan, M., Majewski, W. and Nitsche, F. O. (2012). Post-LGM deglaciation in Pine Island Bay, West Antarctica. Quat. Sci. Rev. 38 11–26.
  • Larter, R. D., Anderson, J. B., Graham, A. G., Gohl, K., Hillenbrand, C.-D., Jakobsson, M., Johnson, J. S., Kuhn, G., Nitsche, F. O. and Smith, J. A. (2014). Reconstruction of changes in the Amundsen Sea and Bellingshausen sea sector of the West Antarctic Ice Sheet since the last glacial maximum. Quat. Sci. Rev. 100 55–86.
  • Lempert, R., Sriver, R. L. and Keller, K. (2012). Characterizing uncertain sea level rise projections to support investment decisions. California Energy Commission. Publication Number: CEC-500-2012-056.
  • Liu, Z., Otto-Bliesner, B. L., He, F., Brady, E. C., Tomas, R., Clark, P. U., Carlson, A. E., Lynch-Stieglitz, J., Curry, W., Brook, E., Erickson, D., Jacob, R., Kutzbach, J. and Cheng, J. (2009). Transient simulation of last deglaciation with a new mechanism for Bølling–Allerød warming. Science 325 310–314.
  • Maris, M. N. A., Van Wessem, J. M., Van De Berg, W. J., De Boer, B. and Oerlemans, J. (2015). A model study of the effect of climate and sea-level change on the evolution of the Antarctic Ice Sheet from the Last Glacial Maximum to 2100. Clim. Dynam. 45 837–851.
  • McNeall, D. J., Challenor, P. G., Gattiker, J. R. and Stone, E. J. (2013). The potential of an observational data set for calibration of a computationally expensive computer model. Geosci. Model Dev. 6 1715–1728.
  • Pollard, D. and DeConto, R. M. (2009). Modelling West Antarctic Ice Sheet growth and collapse through the past five million years. Nature 458 329–332.
  • Pollard, D. and DeConto, R. M. (2012a). A simple inverse method for the distribution of basal sliding coefficients under ice sheets, applied to Antarctica. Cryosphere 6 1405–1444.
  • Pollard, D. and DeConto, R. M. (2012b). Description of a hybrid ice sheet-shelf model, and application to Antarctica. Geosci. Model Dev. 5 1273–1295.
  • Pritchard, H. D., Ligtenberg, S. R. M., Fricker, H. A., Vaughan, D. G., Van den Broeke, M. R. and Padman, L. (2012). Antarctic ice-sheet loss driven by basal melting of ice shelves. Nature 484 502–505.
  • RAISED Consortium (2014). A community-based geological reconstruction of Antarctic Ice Sheet deglaciation since the Last Glacial Maximum. Quat. Sci. Rev. 100 1–9.
  • Ritz, C., Edwards, T. L., Durand, G., Payne, A. J., Peyaud, V. and Hindmarsh, R. C. (2015). Potential sea-level rise from Antarctic ice-sheet instability constrained by observations. Nature 528 115–118.
  • Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P. (1989). Design and analysis of computer experiments. Statist. Sci. 4 409–435.
  • Stone, E. J., Lunt, D. J., Rutt, I. C. and Hanna, E. (2010). Investigating the sensitivity of numerical model simulations of the modern state of the Greenland ice-sheet and its future response to climate change. Cryosphere 4 397–417.
  • Whitehouse, P. L., Bentley, M. J. and Le Brocq, A. M. (2012). A deglacial model for Antarctica: Geological constraints and glaciological modeling as a basis for a new model of Antarctic glacial isostatic adjustment. Quat. Sci. Rev. 32 1–24.
  • Whitehouse, P. L., Bentley, M. J., Milne, G. A., King, M. A. and Thomas, I. D. (2012). A new glacial isostatic model for Antarctica: Calibrated and tested using observations of relative sea-level change and present-day uplifts. Geophysical Journal International 190 1464–1482.
  • Winkelmann, R., Levermann, A., Ridgwell, A. and Caldeira, K. (2015). Combustion of available fossil fuel resources sufficient to eliminate the Antarctic Ice Sheet. Sci. Adv. 1 e1500589.

Supplemental materials

  • Supplement to “Improving ice sheet model calibration using paleo and 2 modern observations: A reduced dimensional approach”. We provide additional supporting plots that show more example model outputs for modern binary patterns and the leading principal components used in our calibration method.