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Ice model calibration using semicontinuous spatial data. (English) Zbl 1498.62283

Summary: Rapid changes in Earth’s cryosphere caused by human activity can lead to significant environmental impacts. Computer models provide a useful tool for understanding the behavior and projecting the future of Arctic and Antarctic ice sheets. However, these models are typically subject to large parametric uncertainties, due to poorly constrained model input parameters that govern the behavior of simulated ice sheets. Computer model calibration provides a formal statistical framework to infer parameters, using observational data, and to quantify the uncertainty in projections due to the uncertainty in these parameters. Calibration of ice sheet models is often challenging because the relevant model output and observational data take the form of semicontinuous spatial data with a point mass at zero and a right-skewed continuous distribution for positive values. Current calibration approaches cannot handle such data. Here, we introduce a hierarchical latent variable model that handles binary spatial patterns and positive continuous spatial patterns as separate components. To overcome challenges due to high dimensionality, we use likelihood-based generalized principal component analysis to impose low-dimensional structures on the latent variables for spatial dependence. We apply our methodology to calibrate a physical model for the Antarctic ice sheet and demonstrate that we can overcome the aforementioned modeling and computational challenges. As a result of our calibration, we obtain improved future ice-volume change projections.

MSC:

62P12 Applications of statistics to environmental and related topics
62M30 Inference from spatial processes
62H25 Factor analysis and principal components; correspondence analysis
62-08 Computational methods for problems pertaining to statistics
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[1] 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
[2] BERDAHL, M., LEGUY, G., LIPSCOMB, W. H. and URBAN, N. M. (2020). Statistical emulation of a perturbed basal melt ensemble of an ice sheet model to better quantify Antarctic sea level rise uncertainties. Cryosphere 15 2683-2699.
[3] Berger, J. O., De Oliveira, V. and Sansó, B. (2001). Objective Bayesian analysis of spatially correlated data. J. Amer. Statist. Assoc. 96 1361-1374. · Zbl 1051.62095
[4] 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.
[5] CAO, F., BA, S., BRENNEMAN, W. A. and JOSEPH, V. R. (2018). Model calibration with censored data. Technometrics 60 255-262.
[6] 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
[7] CHANG, W., HARAN, M., OLSON, R. and KELLER, K. (2015). A composite likelihood approach to computer model calibration with high-dimensional spatial data. Statist. Sinica 25 243-259. · Zbl 1480.62093
[8] 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.
[9] 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
[10] CHANG, W., KONOMI, B. A., GEORGIOS, K., GUAN, Y. and HARAN, M. (2022). Supplement to “Ice model calibration using semicontinuous spatial data.” https://doi.org/10.1214/21-AOAS1577SUPP
[11] COOK, R. D. and NI, L. (2005). Sufficient dimension reduction via inverse regression: A minimum discrepancy approach. J. Amer. Statist. Assoc. 100 410-428. · Zbl 1117.62312
[12] DE OLIVEIRA, V. (2005). Bayesian inference and prediction of Gaussian random fields based on censored data. J. Comput. Graph. Statist. 14 95-115.
[13] 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. and WERNECKE, A. (2019). Revisiting Antarctic ice loss due to marine ice-cliff instability. Nature 566 58.
[14] FRETWELL, P., PRITCHARD, H. D., VAUGHAN, D. G., BAMBER, J. L., BARRAND, N. E., BELL, R., BIANCHI, C., BINGHAM, R. G., BLANKENSHIP, D. D. et al. (2013). Bedmap2: Improved ice bed, surface and thickness datasets for Antarctica. Cryosphere 7 375-393.
[15] Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398-409. · Zbl 0702.62020
[16] GILKS, W. R., RICHARDSON, S. and SPIEGELHALTER, D. J., eds. (1995). Markov Chain Monte Carlo in Practice. Interdisciplinary Statistics. CRC Press, London.
[17] GLADSTONE, R. M., LEE, V., ROUGIER, J., PAYNE, A. J., HELLMER, H., LE BROCQ, A., SHEPHERD, A., EDWARDS, T. L., GREGORY, J. et al. (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.
[18] Goodfellow, I., Bengio, Y. and Courville, A. (2016). Deep Learning. Adaptive Computation and Machine Learning. MIT Press, Cambridge, MA. · Zbl 1373.68009
[19] Gu, M. and Berger, J. O. (2016). Parallel partial Gaussian process emulation for computer models with massive output. Ann. Appl. Stat. 10 1317-1347. · Zbl 1391.62184
[20] GU, M., PALOMO, J. and BERGER, J. O. (2019). RobustGaSP: Robust Gaussian stochastic process emulation in R. R J. 11 112-136.
[21] Gu, M., Wang, X. and Berger, J. O. (2018). Robust Gaussian stochastic process emulation. Ann. Statist. 46 3038-3066. · Zbl 1408.62155
[22] HARVILLE, D. A. (2008). Matrix Algebra from a Statistician’s Perspective. Springer, Berlin. · Zbl 1142.15001
[23] HASTIE, T. J. (1992). Generalized additive models. In Statistical Models in S 249-307. Routledge, London. · Zbl 0645.62068
[24] HEATON, M. J., DATTA, A., FINLEY, A. O., FURRER, R., GUINNESS, J., GUHANIYOGI, R., GERBER, F., GRAMACY, R. B., HAMMERLING, D. et al. (2019). A case study competition among methods for analyzing large spatial data. J. Agric. Biol. Environ. Stat. 24 398-425. · Zbl 1426.62345
[25] 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
[26] 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
[27] 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 Syst. Sci. Data 2 247-260.
[28] LEE, S., HUANG, J. Z. and HU, J. (2010). Sparse logistic principal components analysis for binary data. Ann. Appl. Stat. 4 1579-1601. · Zbl 1202.62084
[29] 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.
[30] Loeppky, J. L., Sacks, J. and Welch, W. J. (2009). Choosing the sample size of a computer experiment: A practical guide. Technometrics 51 366-376.
[31] 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.
[32] POLLARD, D. and DECONTO, R. M. (2012). Description of a hybrid ice sheet-shelf model, and application to Antarctica. Geosci. Model Dev. 5 1273-1295.
[33] POLLARD, D., DECONTO, R. M. and ALLEY, R. B. (2015). Potential Antarctic Ice Sheet retreat driven by hydrofracturing and ice cliff failure. Earth Planet. Sci. Lett. 412 112-121.
[34] POLLARD, D., CHANG, W., HARAN, M., APPLEGATE, P. and DECONTO, R. (2016). Large-ensemble modeling of last deglacial and future ice-sheet retreat in the Amundsen Sea Embayment, West Antarctica. Geosci. Model Dev. 9 1697-1723.
[35] Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P. (1989). Design and analysis of computer experiments. Statist. Sci. 4 409-435. · Zbl 0955.62619
[36] Salter, J. M., Williamson, D. B., Scinocca, J. and Kharin, V. (2019). Uncertainty quantification for computer models with spatial output using calibration-optimal bases. J. Amer. Statist. Assoc. 114 1800-1814. · Zbl 1428.62117
[37] Sansó, B. and Forest, C. (2009). Statistical calibration of climate system properties. J. R. Stat. Soc. Ser. C. Appl. Stat. 58 485-503.
[38] STACKLIES, W., REDESTIG, H., SCHOLZ, M., WALTHER, D. and SELBIG, J. (2007). pcaMethods—A bioconductor package providing PCA methods for incomplete data. Bioinformatics 23 1164-1167.
[39] STEIN, M. L. (1992). Prediction and inference for truncated spatial data. J. Comput. Graph. Statist. 1 91-110.
[40] 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.
[41] SUNG, C.-L., HUNG, Y., RITTASE, W., ZHU, C. and WU, C. F. J. (2020). A generalized Gaussian process model for computer experiments with binary time series. J. Amer. Statist. Assoc. 115 945-956. · Zbl 1445.62242
[42] TIPPING, M. E. and BISHOP, C. M. (1999). Probabilistic principal component analysis. J. R. Stat. Soc. Ser. B. Stat. Methodol. 61 611-622. · Zbl 0924.62068
[43] WOODBURY, M. A. (1950). Inverting Modified Matrices. Princeton Univ., Princeton, NJ. Statistical Research Group, Memo. Rep. no. 42
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