A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet. (English) Zbl 1446.62298

Summary: We consider the scientifically challenging and policy-relevant task of understanding the past and projecting the future dynamics of the Antarctic ice sheet. The Antarctic ice sheet has shown a highly nonlinear threshold response to past climate forcings. Triggering such a threshold response through anthropogenic greenhouse gas emissions would drive drastic and potentially fast sea level rise with important implications for coastal flood risks. Previous studies have combined information from ice sheet models and observations to calibrate model parameters. These studies have broken important new ground but have either adopted simple ice sheet models or have limited the number of parameters to allow for the use of more complex models. These limitations are largely due to the computational challenges posed by calibration as models become more computationally intensive or when the number of parameters increases.
Here, we propose a method to alleviate this problem: a fast sequential Monte Carlo method that takes advantage of the massive parallelization afforded by modern high-performance computing systems. We use simulated examples to demonstrate how our sample-based approach provides accurate approximations to the posterior distributions of the calibrated parameters. The drastic reduction in computational times enables us to provide new insights into important scientific questions, for example, the impact of Pliocene era data and prior parameter information on sea level projections. These studies would be computationally prohibitive with other computational approaches for calibration such as Markov chain Monte Carlo or emulation-based methods. We also find considerable differences in the distributions of sea level projections when we account for a larger number of uncertain parameters. For example, based on the same ice sheet model and data set, the 99th percentile of the Antarctic ice sheet contribution to sea level rise in 2300 increases from 6.5 m to 13.1 m when we increase the number of calibrated parameters from three to 11. With previous calibration methods, it would be challenging to go beyond five parameters. This work provides an important next step toward improving the uncertainty quantification of complex, computationally intensive and decision-relevant models.


62P12 Applications of statistics to environmental and related topics
62L12 Sequential estimation
65C05 Monte Carlo methods
86A08 Climate science and climate modeling
62-08 Computational methods for problems pertaining to statistics


Full Text: DOI arXiv Euclid


[1] Agapiou, S., Papaspiliopoulos, O., Sanz-Alonso, D. and Stuart, A. M. (2017). Importance sampling: Intrinsic dimension and computational cost. Statist. Sci. 32 405-431. · Zbl 1442.62026
[2] Alder, J. R., Hostetler, S. W., Pollard, D. and Schmittner, A. (2011). Evaluation of a present-day climate simulation with a new coupled atmosphere-ocean model GENMOM. Geosci. Model Dev. 4 69-83.
[3] 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.
[4] Bakker, A. M., Applegate, P. J. and Keller, K. (2016). A simple, physically motivated model of sea-level contributions from the Greenland ice sheet in response to temperature changes. Environmental Modelling & Software 83 27-35.
[5] Ballard, G., Siefert, C. and Hu, J. (2016). Reducing communication costs for sparse matrix multiplication within algebraic multigrid. SIAM J. Sci. Comput. 38 C203-C231. · Zbl 1339.65058
[6] Bastos, L. S. and O’Hagan, A. (2009). Diagnostics for Gaussian process emulators. Technometrics 51 425-438.
[7] Bayarri, M. J., Berger, J. O., Cafeo, J., Garcia-Donato, G., Liu, F., Palomo, J., Parthasarathy, R. J., Paulo, R., Sacks, J. et al. (2007). Computer model validation with functional output. Ann. Statist. 35 1874-1906. · Zbl 1144.62368
[8] Beskos, A., Jasra, A., Kantas, N. and Thiery, A. (2016). On the convergence of adaptive sequential Monte Carlo methods. Ann. Appl. Probab. 26 1111-1146. · Zbl 1342.82127
[9] Bhat, K. S., Haran, M., Goes, M. and Chen, M. (2010). Computer model calibration with multivariate spatial output: A case study. Frontiers of Statistical Decision Making and Bayesian Analysis 168-184.
[10] Bhattacharyya, A. (1946). On a measure of divergence between two multinomial populations. Sankhyā 7 401-406. · Zbl 0063.00366
[11] Bony, S. and Emanuel, K. A. (2001). A parameterization of the cloudiness associated with cumulus convection; evaluation using TOGA COARE data. J. Atmos. Sci. 58 3158-3183.
[12] Brynjarsdóttir, J. and O’Hagan, A. (2014). Learning about physical parameters: The importance of model discrepancy. Inverse Probl. 30 114007, 24. · Zbl 1307.60042
[13] Chang, W., Haran, M., Olson, R. and Keller, K. (2014). Fast dimension-reduced climate model calibration and the effect of data aggregation. Ann. Appl. Stat. 8 649-673. · Zbl 1454.62438
[14] Chang, W., Haran, M., Applegate, P. and Pollard, D. (2016a). Calibrating an ice sheet model using high-dimensional binary spatial data. J. Amer. Statist. Assoc. 111 57-72.
[15] Chang, W., Haran, M., Applegate, P. and Pollard, D. (2016b). Improving ice sheet model calibration using paleoclimate and modern data. Ann. Appl. Stat. 10 2274-2302. · Zbl 1454.62437
[16] Chopin, N. (2002). A sequential particle filter method for static models. Biometrika 89 539-551. · Zbl 1036.62062
[17] Collins, M. (2007). Ensembles and probabilities: A new era in the prediction of climate change. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 365 1957-1970.
[18] Computational and Information Systems Laboratory (2017). Cheyenne: HPE/SGI ICE XA System (University Community Computing). Boulder, CO: National Center for Atmospheric Research. doi:10.5065/D6RX99HX.
[19] Cook, C. P., van de Flierdt, T., Williams, T., Hemming, S. R., Iwai, M., Kobayashi, M., Jimenez-Espejo, F. J., Escutia, C., González, J. J. et al. (2013). Dynamic behaviour of the East Antarctic ice sheet during Pliocene warmth. Nature Geoscience 6 765-769.
[20] Cook, C., Hill, D., van de Flierdt, T., Williams, T., Hemming, S., Dolan, A., Pierce, E., Escutia, C., Harwood, D. et al. (2014). Sea surface temperature control on the distribution of far-traveled Southern Ocean ice-rafted detritus during the Pliocene. Paleoceanography 29 533-548.
[21] Crisan, D. and Doucet, A. (2000). Convergence of sequential Monte Carlo methods. Technical Report CUED/F-INFENG/TR381, Signal Processing Group, Department of Engineering, University of Cambridge.
[22] Dal Gesso, S. and Neggers, R. (2018). Can we use single-column models for understanding the boundary layer cloud-climate feedback? J. Adv. Model. Earth Syst. 10 245-261.
[23] De Boer, B., Stocchi, P. and Van De Wal, R. (2014). A fully coupled 3-D ice-sheet-sea-level model: Algorithm and applications. Geosci. Model Dev. 7 2141-2156.
[24] DeConto, R. M. and Pollard, D. (2016). Contribution of Antarctica to past and future sea-level rise. Nature 531 591-597.
[25] Del Moral, P., Doucet, A. and Jasra, A. (2006). Sequential Monte Carlo samplers. J. R. Stat. Soc. Ser. B. Stat. Methodol. 68 411-436. · Zbl 1105.62034
[26] Deschamps, P., Durand, N., Bard, E., Hamelin, B., Camoin, G., Thomas, A. L., Henderson, G. M., Okuno, J. and Yokoyama, Y. (2012). Ice-sheet collapse and sea-level rise at the Bølling warming 14,600 years ago. Nature 483 559.
[27] Diaz, D. and Keller, K. (2016). A potential disintegration of the West Antarctic ice sheet: implications for economic analyses of climate policy. Am. Econ. Rev. 106 607-11.
[28] Dolan, A. M., Haywood, A. M., Hill, D. J., Dowsett, H. J., Hunter, S. J., Lunt, D. J. and Pickering, S. J. (2011). Sensitivity of Pliocene ice sheets to orbital forcing. Palaeogeography, Palaeoclimatology, Palaeoecology 309 98-110.
[29] Dolan, A. M., de Boer, B., Bernales, J., Hill, D. J. and Haywood, A. M. (2018). High climate model dependency of Pliocene Antarctic ice-sheet predictions. Nat. Commun. 9 2799.
[30] Doucet, A., de Freitas, N. and Gordon, N. (2001). An introduction to sequential Monte Carlo methods. In Sequential Monte Carlo Methods in Practice. Stat. Eng. Inf. Sci. 3-14. Springer, New York. · Zbl 1056.93576
[31] Doucet, A., Godsill, S. and Andrieu, C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering. Stat. Comput. 10 197-208.
[32] Dowsett, H. J. and Cronin, T. M. (1990). High eustatic sea level during the middle Pliocene: evidence from the southeastern US Atlantic Coastal Plain. Geology 18 435-438.
[33] Dutton, A., Carlson, A. E., Long, A. J., Milne, G. A., Clark, P. U., DeConto, R., Horton, B. P., Rahmstorf, S. and Raymo, M. E. (2015). SEA-LEVEL RISE. Sea-level rise due to polar ice-sheet mass loss during past warm periods. Science 349 aaa4019.
[34] Edwards, T. L., Brandon, M. A., Durand, G., Edwards, N. R., Golledge, N. R., Holden, P. B., Nias, I. J., Payne, A. J., Ritz, C. et al. (2019). Revisiting Antarctic ice loss due to marine ice-cliff instability. Nature 566 58-64.
[35] Fan, W., Yu, W., Xu, J., Zhou, J., Luo, X., Yin, Q., Lu, P., Cao, Y. and Xu, R. (2018). Parallelizing sequential graph computations. ACM Trans. Database Syst. 43 Art. 18, 39.
[36] Fitzgerald, P., Bamber, J., Ridley, J. and Rougier, J. (2012). Exploration of parametric uncertainty in a surface mass balance model applied to the Greenland ice sheet. Journal of Geophysical Research: Earth Surface 117.
[37] Fretwell, P., Pritchard, H., Vaughan, D., Bamber, J., Barrand, N., Bell, R., Bianchi, C., Bingham, R., Blankenship, D. et al. (2012). Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. The Cryosphere Discussions 6 4305-4361.
[38] Fuller, R. W., Wong, T. E. and Keller, K. (2017). Probabilistic inversion of expert assessments to inform projections about Antarctic ice sheet responses. PLoS ONE 12 e0190115.
[39] Garner, G. G. and Keller, K. (2018). Using direct policy search to identify robust strategies in adapting to uncertain sea-level rise and storm surge. Environmental Modelling & Software 107 96-104.
[40] Gettelman, A., Truesdale, J. E., Bacmeister, J. T., Caldwell, P. M., Neale, R. B., Bogenschutz, P. A. and Simpson, I. R. (2019). The single column atmosphere model version 6 (SCAM6): Not a scam but a tool for model evaluation and development. J. Adv. Model. Earth Syst. 0.
[41] Gilks, W. R. and Berzuini, C. (2001). Following a moving target—Monte Carlo inference for dynamic Bayesian models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 127-146. · Zbl 0976.62021
[42] Giraud, F. and Del Moral, P. (2017). Nonasymptotic analysis of adaptive and annealed Feynman-Kac particle models. Bernoulli 23 670-709. · Zbl 1364.60131
[43] Golledge, N. R., Keller, E. D., Gomez, N., Naughten, K. A., Bernales, J., Trusel, L. D. and Edwards, T. L. (2019). Global environmental consequences of twenty-first-century ice-sheet melt. Nature 566 65-72.
[44] Goodman, J. and Weare, J. (2010). Ensemble samplers with affine invariance. Commun. Appl. Math. Comput. Sci. 5 65-80. · Zbl 1189.65014
[45] Gordon, N. J., Salmond, D. J. and Smith, A. F. (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In IEE Proceedings F-Radar and Signal Processing 140 107-113. IET.
[46] Gramacy, R. B. and Apley, D. W. (2015). Local Gaussian process approximation for large computer experiments. J. Comput. Graph. Statist. 24 561-578.
[47] Greve, R. (1997). Application of a polythermal three-dimensional ice sheet model to the Greenland ice sheet: Response to steady-state and transient climate scenarios. J. Climate 10 901-918.
[48] Hannart, A., Ghil, M., Dufresne, J.-L. and Naveau, P. (2013). Disconcerting learning on climate sensitivity and the uncertain future of uncertainty. Clim. Change 119 585-601.
[49] Higdon, D., Gattiker, J., Williams, B. and Rightley, M. (2008). Computer model calibration using high-dimensional output. J. Amer. Statist. Assoc. 103 570-583. · Zbl 1469.62414
[50] Isaac, T., Stadler, G. and Ghattas, O. (2015). Solution of nonlinear Stokes equations discretized by high-order finite elements on nonconforming and anisotropic meshes, with application to ice sheet dynamics. SIAM J. Sci. Comput. 37 B804-B833. · Zbl 1327.65242
[51] Isaac, T., Petra, N., Stadler, G. and Ghattas, O. (2015). Scalable and efficient algorithms for the propagation of uncertainty from data through inference to prediction for large-scale problems, with application to flow of the Antarctic ice sheet. J. Comput. Phys. 296 348-368. · Zbl 1352.86017
[52] Jackson, C. H., Jit, M., Sharples, L. D. and De Angelis, D. (2015). Calibration of complex models through Bayesian evidence synthesis: A demonstration and tutorial. Medical Decision Making 35 148-161.
[53] Jasra, A., Stephens, D. A., Doucet, A. and Tsagaris, T. (2011). Inference for Lévy-driven stochastic volatility models via adaptive sequential Monte Carlo. Scand. J. Stat. 38 1-22. · Zbl 1246.91149
[54] Jeremiah, E., Sisson, S., Marshall, L., Mehrotra, R. and Sharma, A. (2011). Bayesian calibration and uncertainty analysis of hydrological models: A comparison of adaptive Metropolis and sequential Monte Carlo samplers. Water Resour. Res. 47.
[55] Johnson, D. R., Fischbach, J. R. and Ortiz, D. S. (2013). Estimating surge-based flood risk with the coastal Louisiana risk assessment model. Journal of Coastal Research 67 109-126.
[56] 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. · Zbl 1171.62316
[57] Kalyanaraman, J., Kawajiri, Y., Lively, R. P. and Realff, M. J. (2016). Uncertainty quantification via Bayesian inference using sequential Monte Carlo methods for CO2 adsorption process. AIChE Journal 62 3352-3368.
[58] Kantas, N., Beskos, A. and Jasra, A. (2014). Sequential Monte Carlo methods for high-dimensional inverse problems: A case study for the Navier-Stokes equations. SIAM/ASA J. Uncertain. Quantificat. 2 464-489. · Zbl 1308.65010
[59] Kantas, N., Doucet, A., Singh, S. S., Maciejowski, J. and Chopin, N. (2015). On particle methods for parameter estimation in state-space models. Statist. Sci. 30 328-351. · Zbl 1332.62096
[60] Keller, K. and McInerney, D. (2008). The dynamics of learning about a climate threshold. Clim. Dyn. 30 321-332.
[61] Kennedy, M. C. and O’Hagan, A. (2001). Bayesian calibration of computer models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 63 425-464. · Zbl 1007.62021
[62] Kim, S. H., Edmonds, J., Lurz, J., Smith, S. J. and Wise, M. (2006). The objECTS framework for integrated assessment: Hybrid modeling of transportation. Energy J. 63-91.
[63] Kong, A. (1992). A note on importance sampling using standardized weights. University of Chicago, Dept. of Statistics, Tech. Rep, 348.
[64] Kopp, R. E., Simons, F. J., Mitrovica, J. X., Maloof, A. C. and Oppenheimer, M. (2009). Probabilistic assessment of sea level during the last interglacial stage. Nature 462 863-867.
[65] Larour, E., Seroussi, H., Morlighem, M. and Rignot, E. (2012). Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM). Journal of Geophysical Research: Earth Surface 117.
[66] Le Bars, D., Drijfhout, S. and de Vries, H. (2017). A high-end sea level rise probabilistic projection including rapid Antarctic ice sheet mass loss. Environ. Res. Lett. 12 044013.
[67] Le Brocq, A. M., Payne, A. J. and Vieli, A. (2010). An improved Antarctic dataset for high resolution numerical ice sheet models (ALBMAP v1). Earth System Science Data 2 247-260.
[68] Le Cozannet, G., Manceau, J.-C. and Rohmer, J. (2017). Bounding probabilistic sea-level projections within the framework of the possibility theory. Environ. Res. Lett. 12 014012.
[69] Lee, B. S., Haran, M., Fuller, R. W., Pollard, D. and Keller, K. (2020). Supplement to “A fast particle-based approach for calibrating a 3-D model of the Antarctic ice sheet.” https://doi.org/10.1214/19-AOAS1305SUPP.
[70] Lele, S. R., Dennis, B. and Lutscher, F. (2007). Data cloning: easy maximum likelihood estimation for complex ecological models using Bayesian Markov chain Monte Carlo methods. Ecol. Lett. 10 551-563.
[71] Levitus, S., Antonov, J. I., Boyer, T. P., Baranova, O. K., Garcia, H. E., Locarnini, R. A., Mishonov, A. V., Reagan, J., Seidov, D. et al. (2012). World ocean heat content and thermosteric sea level change (0-2000 m). Geophys. Res. Lett. 39 1955-2010.
[72] Li, T., Sun, S., Sattar, T. P. and Corchado, J. M. (2014). Fight sample degeneracy and impoverishment in particle filters: A review of intelligent approaches. Expert Systems with Applications 41 3944-3954.
[73] Liang, F. and Wong, W. H. (2001). Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models. J. Amer. Statist. Assoc. 96 653-666. · Zbl 1017.62022
[74] Liang, X., Lettenmaier, D. P., Wood, E. F. and Burges, S. J. (1994). A simple hydrologically based model of land surface water and energy fluxes for general circulation models. J. Geophys. Res., Atmos. 99 14415-14428.
[75] Liu, F., Bayarri, M. J. and Berger, J. O. (2009). Modularization in Bayesian analysis, with emphasis on analysis of computer models. Bayesian Anal. 4 119-150. · Zbl 1330.65033
[76] Liu, J. S. and Chen, R. (1998). Sequential Monte Carlo methods for dynamic systems. J. Amer. Statist. Assoc. 93 1032-1044. · Zbl 1064.65500
[77] Liu, X. and Guillas, S. (2017). Dimension reduction for Gaussian process emulation: An application to the influence of bathymetry on tsunami heights. SIAM/ASA J. Uncertain. Quantificat. 5 787-812. · Zbl 1403.62217
[78] Liu, J. S., Liang, F. and Wong, W. H. (2000). The multiple-try method and local optimization in Metropolis sampling. J. Amer. Statist. Assoc. 95 121-134. · Zbl 1072.65505
[79] Liu, J. and West, M. (2001). Combined parameter and state estimation in simulation-based filtering. In Sequential Monte Carlo Methods in Practice. Stat. Eng. Inf. Sci. 197-223. Springer, New York. · Zbl 1056.93583
[80] Liu, Z., Otto-Bliesner, B., He, F., Brady, E., Tomas, R., Clark, P., Carlson, A., Lynch-Stieglitz, J., Curry, W. et al. (2009). Transient simulation of last deglaciation with a new mechanism for Bølling-Allerød warming. Science 325 310-314.
[81] Llopis, F. P., Kantas, N., Beskos, A. and Jasra, A. (2018). Particle filtering for stochastic Navier-Stokes signal observed with linear additive noise. SIAM J. Sci. Comput. 40 A1544-A1565. · Zbl 1391.60083
[82] Lorenz, E. N. (1972). Predictability: Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas? Presented at the 139th Meeting of the AAAS. Available at http://eaps4.mit.edu/research/Lorenz/Butterfly_1972.pdf. Accessed: 2019-08-04.
[83] Maniyar, D., Cornford, D. and Boukouvalas, A. (2007). Dimensionality reduction in the emulator setting. Technical report, Neural Computing Research Group, University of Aston.
[84] Martino, L. (2018). A review of multiple try MCMC algorithms for signal processing. Digit. Signal Process. 75 134-152.
[85] Martino, L., Elvira, V. and Louzada, F. (2017). Effective sample size for importance sampling based on discrepancy measures. Signal Process. 131 386-401.
[86] McGranahan, G., Balk, D. and Anderson, B. (2007). The rising tide: Assessing the risks of climate change and human settlements in low elevation coastal zones. Environment and Urbanization 19 17-37.
[87] McKay, M. D., Beckman, R. J. and Conover, W. J. (2000). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 421 55-61. · Zbl 0415.62011
[88] Meinshausen, M., Smith, S. J., Calvin, K., Daniel, J. S., Kainuma, M., Lamarque, J.-F., Matsumoto, K., Montzka, S., Raper, S. et al. (2011). The RCP greenhouse gas concentrations and their extensions from 1765 to 2300. Clim. Change 109 213.
[89] Monier, E., Scott, J., Sokolov, A., Forest, C. and Schlosser, C. (2013). An integrated assessment modelling framework for uncertainty studies in global and regional climate change: The MIT IGSM-CAM (version 1.0). Geoscientific Model Development Discussions 6.
[90] Morzfeld, M., Tu, X., Wilkening, J. and Chorin, A. J. (2015). Parameter estimation by implicit sampling. Commun. Appl. Math. Comput. Sci. 10 205-225. · Zbl 1328.86002
[91] Morzfeld, M., Day, M. S., Grout, R. W., Pau, G. S. H., Finsterle, S. A. and Bell, J. B. (2018). Iterative importance sampling algorithms for parameter estimation. SIAM J. Sci. Comput. 40 B329-B352. · Zbl 1385.65007
[92] Murray, L. M., Lee, A. and Jacob, P. E. (2016). Parallel resampling in the particle filter. J. Comput. Graph. Statist. 25 789-805.
[93] Murray, T., Selmes, N., James, T. D., Edwards, S., Martin, I., O’Farrell, T., Aspey, R., Rutt, I., Nettles, M. et al. (2015). Dynamics of glacier calving at the ungrounded margin of Helheim Glacier, southeast Greenland. J Geophys Res Earth Surf 120 964-982.
[94] Naish, T., Powell, R., Levy, R., Wilson, G., Scherer, R., Talarico, F., Krissek, L., Niessen, F., Pompilio, M. et al. (2009). Obliquity-paced Pliocene West Antarctic ice sheet oscillations. Nature 458 322-328.
[95] Neal, R. M. (2001). Annealed importance sampling. Stat. Comput. 11 125-139.
[96] Nguyen, T. L. T. (2014). Sequential Monte-Carlo sampler for Bayesian inference in complex systems. PhD thesis, Lille 1.
[97] Nicholls, R. J., Tol, R. S. and Vafeidis, A. T. (2008). Global estimates of the impact of a collapse of the West Antarctic ice sheet: an application of FUND. Clim. Change 91 171.
[98] O’Neill, B. C., Crutzen, P., Grübler, A., Duong, M. H., Keller, K., Kolstad, C., Koomey, J., Lange, A., Obersteiner, M. et al. (2006). Learning and climate change. Climate Policy 6 585-589.
[99] Oppenheimer, M. and Alley, R. B. (2016). How high will the seas rise? Science 354 1375-1377.
[100] Pal, J. S., Giorgi, F., Bi, X., Elguindi, N., Solmon, F., Gao, X., Rauscher, S. A., Francisco, R., Zakey, A. et al. (2007). Regional climate modeling for the developing world: the ICTP RegCM3 and RegCNET. Bull. Am. Meteorol. Soc. 88 1395-1410.
[101] Papaioannou, I., Papadimitriou, C. and Straub, D. (2016). Sequential importance sampling for structural reliability analysis. Structural Safety 62 66-75.
[102] Petra, N., Martin, J., Stadler, G. and Ghattas, O. (2014). A computational framework for infinite-dimensional Bayesian inverse problems, Part II: Stochastic Newton MCMC with application to ice sheet flow inverse problems. SIAM J. Sci. Comput. 36 A1525-A1555. · Zbl 1303.35110
[103] 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.
[104] Pollard, D. and DeConto, R. (2012). Description of a hybrid ice sheet-shelf model, and application to Antarctica. Geosci. Model Dev. 5 1273.
[105] Pollard, D., DeConto, R. M. and Alley, R. B. (2015). Potential Antarctic ice sheet retreat driven by hydrofracturing and ice cliff failure. Earth and Planetary Science Letters 412 112-121.
[106] Pollard, D., Gomez, N. and Deconto, R. M. (2017). Variations of the Antarctic ice sheet in a coupled ice sheet-Earth-sea level model: Sensitivity to viscoelastic Earth properties. Journal of Geophysical Research: Earth Surface 122 2124-2138.
[107] Pollard, D., Chang, W., Haran, M., Applegate, P. and DeConto, R. (2016). Large ensemble modeling of the last deglacial retreat of the West Antarctic ice sheet: comparison of simple and advanced statistical techniques. Geosci. Model Dev. 9 1697-1723.
[108] Queipo, N. V., Haftka, R. T., Shyy, W., Goel, T., Vaidyanathan, R. and Tucker, P. K. (2005). Surrogate-based analysis and optimization. Progress in Aerospace Sciences 41 1-28.
[109] Reese, C. S., Wilson, A. G., Hamada, M., Martz, H. F. and Ryan, K. J. (2004). Integrated analysis of computer and physical experiments. Technometrics 46 153-164.
[110] Rovere, A., Raymo, M. E., Mitrovica, J., Hearty, P. J., O’Leary, M. and Inglis, J. (2014). The Mid-Pliocene sea-level conundrum: glacial isostasy, eustasy and dynamic topography. Earth and Planetary Science Letters 387 27-33.
[111] Ruckert, K. L., Shaffer, G., Pollard, D., Guan, Y., Wong, T. E., Forest, C. E. and Keller, K. (2017). Assessing the impact of retreat mechanisms in a simple Antarctic ice sheet model using Bayesian calibration. PLoS ONE 12 e0170052.
[112] Rutt, I. C., Hagdorn, M., Hulton, N. and Payne, A. (2009). The Glimmer community ice sheet model. Journal of Geophysical Research: Earth Surface 114.
[113] Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P. (1989). Design and analysis of computer experiments. Statist. Sci. 4 409-435. With comments and a rejoinder by the authors. · Zbl 0955.62619
[114] Salzmann, U., Dolan, A. M., Haywood, A. M., Chan, W.-L., Voss, J., Hill, D. J., Abe-Ouchi, A., Otto-Bliesner, B., Bragg, F. J. et al. (2013). Challenges in quantifying Pliocene terrestrial warming revealed by data-model discord. Nature Climate Change 3 969-974.
[115] Sansó, B., Forest, C. E. and Zantedeschi, D. (2008). Inferring climate system properties using a computer model. Bayesian Anal. 3 1-37. · Zbl 1330.86029
[116] Schäfer, C. and Chopin, N. (2013). Sequential Monte Carlo on large binary sampling spaces. Stat. Comput. 23 163-184. · Zbl 1322.62035
[117] Schlegel, N.-J., Seroussi, H., Schodlok, M. P., Larour, E. Y., Boening, C., Limonadi, D., Watkins, M. M., Morlighem, M. and van den Broeke, M. R. (2018). Exploration of Antarctic ice sheet 100-year contribution to sea level rise and associated model uncertainties using the ISSM framework. Cryosphere 12 3511-3534.
[118] Shaffer, G. (2014). Formulation, calibration and validation of the DAIS model, a simple Antarctic ice sheet model sensitive to variations of sea level and ocean subsurface temperature. Geosci. Model Dev. 7 1803-1818.
[119] Shields, C. A. and Kiehl, J. T. (2016). Atmospheric river landfall-latitude changes in future climate simulations. Geophys. Res. Lett. 43 8775-8782.
[120] Sorooshian, S., Duan, Q. and Gupta, V. K. (1993). Calibration of rainfall-runoff models: Application of global optimization to the Sacramento soil moisture accounting model. Water Resour. Res. 29 1185-1194.
[121] Sriver, R. L., Lempert, R. J., Wikman-Svahn, P. and Keller, K. (2018). Characterizing uncertain sea-level rise projections to support investment decisions. PLoS ONE 13 e0190641.
[122] Stein, M. (1987). Large sample properties of simulations using Latin hypercube sampling. Technometrics 29 143-151. · Zbl 0627.62010
[123] Steinberg, D. M. and Lin, D. K. J. (2006). A construction method for orthogonal Latin hypercube designs. Biometrika 93 279-288. · Zbl 1153.62349
[124] Stone, E., Lunt, D., Rutt, I., Hanna, E. et al. (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.
[125] Urban, N. M. and Fricker, T. E. (2010). A comparison of Latin hypercube and grid ensemble designs for the multivariate emulation of an Earth system model. Comput. Geosci. 36 746-755.
[126] Whiteley, N., Lee, A. and Heine, K. (2016). On the role of interaction in sequential Monte Carlo algorithms. Bernoulli 22 494-529. · Zbl 1388.65009
[127] Willems, J. C. (1972). Dissipative dynamical systems. I. General theory. Arch. Ration. Mech. Anal. 45 321-351. · Zbl 0252.93002
[128] Williamson, D., Goldstein, M., Allison, L., Blaker, A., Challenor, P., Jackson, L. and Yamazaki, K. (2013). History matching for exploring and reducing climate model parameter space using observations and a large perturbed physics ensemble. Clim. Dyn. 2 1703-1729.
[129] Wong, T. E., Bakker, A. M. and Keller, K. (2017). Impacts of Antarctic fast dynamics on sea-level projections and coastal flood defense. Clim. Change 144 347-364.
[130] Zhou, Y., Johansen, A. M. and Aston, J. A. D. (2016). Toward automatic model comparison: An adaptive sequential Monte Carlo approach. J. Comput. Graph. Statist. 25 701-726.
[131] Zhu, G.
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