IDEAS home Printed from https://ideas.repec.org/p/gwc/wpaper/2025-002.html
   My bibliography  Save this paper

Modelling the dependence between recent changes in polar ice sheets: Implications for global sea-level projections

Author

Listed:
  • Luke P. Jackson
  • Katarina Juselius
  • Andrew B. Martinez
  • Felix Pretis

Abstract

Changes to the mass of the polar ice sheets are of scientific and socio-economic importance due to their effect on the wider Earth system and the potential to dominate future sea-level rise. Uncertainty remains around the joint behaviour of these ice sheets, leading sea-level modellers to make assumptions about their interdependence when making projections. We use a multi-cointegration vector autoregression model to assess the statistical relationships between time series of Greenland, West, and East Antarctic ice mass change (1992-2010). Since the ice sheet response to climate forcing integrates over time, we explore three alternative model specifications. We compare I(2) models of cumulative changes in ice mass (levels) with an I(1) model of changes in ice mass (rates), explore their model dynamics, and evaluate the out-of-sample forecasts (2011-2023) against observations. Our results support the use of an I(2) model, which identifies a significant relationship between Greenland and West Antarctica, and a persistent trend in both ice sheets that is correlated with global ocean heat content. Extensions of these forecasts to 2100 show Greenland and Antarctica contributions to global sea level that agree with projections from physical-process models and structured expert judgment compatible with high-emission scenarios.

Suggested Citation

  • Luke P. Jackson & Katarina Juselius & Andrew B. Martinez & Felix Pretis, 2025. "Modelling the dependence between recent changes in polar ice sheets: Implications for global sea-level projections," Working Papers 2025-002, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
  • Handle: RePEc:gwc:wpaper:2025-002
    as

    Download full text from publisher

    File URL: https://www2.gwu.edu/~forcpgm/2025-002.pdf
    File Function: First version, 2025
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Castle, Jennifer L. & Clements, Michael P. & Hendry, David F., 2015. "Robust approaches to forecasting," International Journal of Forecasting, Elsevier, vol. 31(1), pages 99-112.
    2. Jurgen A. Doornik, 2017. "Maximum Likelihood Estimation of the I(2) Model under Linear Restrictions," Econometrics, MDPI, vol. 5(2), pages 1-20, May.
    3. Diebold, Francis X. & Rudebusch, Glenn D., 2022. "Probability assessments of an ice-free Arctic: Comparing statistical and climate model projections," Journal of Econometrics, Elsevier, vol. 231(2), pages 520-534.
    4. Nicholas R. Golledge & Elizabeth D. Keller & Natalya Gomez & Kaitlin A. Naughten & Jorge Bernales & Luke D. Trusel & Tamsin L. Edwards, 2019. "Global environmental consequences of twenty-first-century ice-sheet melt," Nature, Nature, vol. 566(7742), pages 65-72, February.
    5. Francesca Di Iorio & Stefano Fachin & Riccardo Lucchetti, 2016. "Can you do the wrong thing and still be right? Hypothesis testing in I(2) and near-I(2) cointegrated VARs," Applied Economics, Taylor & Francis Journals, vol. 48(38), pages 3665-3678, August.
    6. Stephane Hallegatte & Colin Green & Robert J. Nicholls & Jan Corfee-Morlot, 2013. "Future flood losses in major coastal cities," Nature Climate Change, Nature, vol. 3(9), pages 802-806, September.
    7. Philippe Goulet Coulombe & Maximilian Gobel, 2020. "Arctic Amplification of Anthropogenic Forcing: A Vector Autoregressive Analysis," Papers 2005.02535, arXiv.org, revised Mar 2021.
    8. Nielsen, Bent, 2001. "The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes," Econometrica, Econometric Society, vol. 69(1), pages 211-219, January.
    9. Nielsen, Heino Bohn & Rahbek, Anders, 2007. "The Likelihood Ratio Test For Cointegration Ranks In The I(2) Model," Econometric Theory, Cambridge University Press, vol. 23(4), pages 615-637, August.
    10. Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 145-159, Supplemen.
    11. Johansen, Soren, 2006. "Statistical analysis of hypotheses on the cointegrating relations in the I(2) model," Journal of Econometrics, Elsevier, vol. 132(1), pages 81-115, May.
    12. Kyle R. Clem & Ryan L. Fogt & John Turner & Benjamin R. Lintner & Gareth J. Marshall & James R. Miller & James A. Renwick, 2020. "Record warming at the South Pole during the past three decades," Nature Climate Change, Nature, vol. 10(8), pages 762-770, August.
    13. Robert M. DeConto & David Pollard & Richard B. Alley & Isabella Velicogna & Edward Gasson & Natalya Gomez & Shaina Sadai & Alan Condron & Daniel M. Gilford & Erica L. Ashe & Robert E. Kopp & Dawei Li , 2021. "The Paris Climate Agreement and future sea-level rise from Antarctica," Nature, Nature, vol. 593(7857), pages 83-89, May.
    14. Perry C. Oddo & Ben S. Lee & Gregory G. Garner & Vivek Srikrishnan & Patrick M. Reed & Chris E. Forest & Klaus Keller, 2020. "Deep Uncertainties in Sea‐Level Rise and Storm Surge Projections: Implications for Coastal Flood Risk Management," Risk Analysis, John Wiley & Sons, vol. 40(1), pages 153-168, January.
    15. Søren Johansen, 2012. "The Analysis of Nonstationary Time Series Using Regression, Correlation and Cointegration," Contemporary Economics, University of Economics and Human Sciences in Warsaw., vol. 6(2), June.
    16. Diebold, Francis X. & Rudebusch, Glenn D. & Göbel, Maximilian & Goulet Coulombe, Philippe & Zhang, Boyuan, 2023. "When will Arctic sea ice disappear? Projections of area, extent, thickness, and volume," Journal of Econometrics, Elsevier, vol. 236(2).
    17. Kevin D. Hoover & Soren Johansen & Katarina Juselius, 2008. "Allowing the Data to Speak Freely: The Macroeconometrics of the Cointegrated Vector Autoregression," American Economic Review, American Economic Association, vol. 98(2), pages 251-255, May.
    18. Katarina Juselius & Katrin Assenmacher, 2017. "Real exchange rate persistence and the excess return puzzle: The case of Switzerland versus the US," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(6), pages 1145-1155, September.
    19. Robert M. DeConto & David Pollard, 2016. "Contribution of Antarctica to past and future sea-level rise," Nature, Nature, vol. 531(7596), pages 591-597, March.
    20. Le Bars, Dewi, 2018. "Uncertainty in sea level rise projections due to the dependence between contributors," Earth Arxiv uvw3s, Center for Open Science.
    21. J. L. Bamber & W. P. Aspinall, 2013. "An expert judgement assessment of future sea level rise from the ice sheets," Nature Climate Change, Nature, vol. 3(4), pages 424-427, April.
    22. Bruns, Stephan B. & Csereklyei, Zsuzsanna & Stern, David I., 2020. "A multicointegration model of global climate change," Journal of Econometrics, Elsevier, vol. 214(1), pages 175-197.
    23. Juselius, Katarina, 2014. "Testing for near I(2) trends when the signal-to-noise ratio is small," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 8, pages 1-30.
    24. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    25. Xianyao Chen & Xuebin Zhang & John A. Church & Christopher S. Watson & Matt A. King & Didier Monselesan & Benoit Legresy & Christopher Harig, 2017. "The increasing rate of global mean sea-level rise during 1993–2014," Nature Climate Change, Nature, vol. 7(7), pages 492-495, July.
    26. Hendry, David F., 2006. "Robustifying forecasts from equilibrium-correction systems," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 399-426.
    27. Tamsin L. Edwards & Sophie Nowicki & Ben Marzeion & Regine Hock & Heiko Goelzer & Hélène Seroussi & Nicolas C. Jourdain & Donald A. Slater & Fiona E. Turner & Christopher J. Smith & Christine M. McK, 2021. "Projected land ice contributions to twenty-first-century sea level rise," Nature, Nature, vol. 593(7857), pages 74-82, May.
    28. Chris R. Stokes & Nerilie J. Abram & Michael J. Bentley & Tamsin L. Edwards & Matthew H. England & Annie Foppert & Stewart S. R. Jamieson & Richard S. Jones & Matt A. King & Jan T. M. Lenaerts & Brook, 2022. "Response of the East Antarctic Ice Sheet to past and future climate change," Nature, Nature, vol. 608(7922), pages 275-286, August.
    29. David F. Hendry & Katarina Juselius, 2001. "Explaining Cointegration Analysis: Part II," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 75-120.
    30. Jun-Young Park & Fabian Schloesser & Axel Timmermann & Dipayan Choudhury & June-Yi Lee & Arjun Babu Nellikkattil, 2023. "Future sea-level projections with a coupled atmosphere-ocean-ice-sheet model," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    31. Johansen, Søren & Juselius, Katarina & Frydman, Roman & Goldberg, Michael, 2010. "Testing hypotheses in an I(2) model with piecewise linear trends. An analysis of the persistent long swings in the Dmk/$ rate," Journal of Econometrics, Elsevier, vol. 158(1), pages 117-129, September.
    32. Shfaqat A. Khan & Kurt H. Kjær & Michael Bevis & Jonathan L. Bamber & John Wahr & Kristian K. Kjeldsen & Anders A. Bjørk & Niels J. Korsgaard & Leigh A. Stearns & Michiel R. van den Broeke & Lin Liu &, 2014. "Sustained mass loss of the northeast Greenland ice sheet triggered by regional warming," Nature Climate Change, Nature, vol. 4(4), pages 292-299, April.
    33. Castle, Jennifer L. & Kurita, Takamitsu, 2021. "A dynamic econometric analysis of the dollar-pound exchange rate in an era of structural breaks and policy regime shifts," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    34. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    35. Tamsin L. Edwards & Mark A. Brandon & Gael Durand & Neil R. Edwards & Nicholas R. Golledge & Philip B. Holden & Isabel J. Nias & Antony J. Payne & Catherine Ritz & Andreas Wernecke, 2019. "Revisiting Antarctic ice loss due to marine ice-cliff instability," Nature, Nature, vol. 566(7742), pages 58-64, February.
    36. Frank Pattyn & Catherine Ritz & Edward Hanna & Xylar Asay-Davis & Rob DeConto & Gaël Durand & Lionel Favier & Xavier Fettweis & Heiko Goelzer & Nicholas R. Golledge & Peter Kuipers Munneke & Jan T. M., 2018. "The Greenland and Antarctic ice sheets under 1.5 °C global warming," Nature Climate Change, Nature, vol. 8(12), pages 1053-1061, December.
    37. Juselius, Katarina, 2006. "The Cointegrated VAR Model: Methodology and Applications," OUP Catalogue, Oxford University Press, number 9780199285679, Decembrie.
    38. Pretis, Felix, 2020. "Econometric modelling of climate systems: The equivalence of energy balance models and cointegrated vector autoregressions," Journal of Econometrics, Elsevier, vol. 214(1), pages 256-273.
    39. Michael Oppenheimer & Christopher M. Little & Roger M. Cooke, 2016. "Expert judgement and uncertainty quantification for climate change," Nature Climate Change, Nature, vol. 6(5), pages 445-451, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Katarina Juselius, 2017. "Using a Theory-Consistent CVAR Scenario to Test an Exchange Rate Model Based on Imperfect Knowledge," Econometrics, MDPI, vol. 5(3), pages 1-20, July.
    2. Kurita, Takamitsu, 2020. "Likelihood-based tests for parameter constancy in I(2) CVAR models with an application to fixed-term deposit data," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    3. Brock, William A. & Miller, J. Isaac, 2024. "Polar amplification in a moist energy balance model: A structural econometric approach to estimation and testing," Journal of Econometrics, Elsevier, vol. 245(1).
    4. Juselius, Katarina & Stillwagon, Josh R., 2018. "Are outcomes driving expectations or the other way around? An I(2) CVAR analysis of interest rate expectations in the dollar/pound market," Journal of International Money and Finance, Elsevier, vol. 83(C), pages 93-105.
    5. Jung, Alexander & Carcel Villanova, Hector, 2020. "The empirical properties of euro area M3, 1980-2017," The Quarterly Review of Economics and Finance, Elsevier, vol. 77(C), pages 37-49.
    6. Jasper Verschuur & Dewi Bars & Caroline A. Katsman & Sierd de Vries & Roshanka Ranasinghe & Sybren S. Drijfhout & Stefan G. J. Aarninkhof, 2020. "Implications of ambiguity in Antarctic ice sheet dynamics for future coastal erosion estimates: a probabilistic assessment," Climatic Change, Springer, vol. 162(2), pages 859-876, September.
    7. David F. Hendry, 2020. "A Short History of Macro-econometric Modelling," Economics Papers 2020-W01, Economics Group, Nuffield College, University of Oxford.
    8. Neil R. Ericsson, 2021. "Dynamic Econometrics in Action: A Biography of David F. Hendry," International Finance Discussion Papers 1311, Board of Governors of the Federal Reserve System (U.S.).
    9. Katarina Juselius, 2021. "Searching for a Theory That Fits the Data: A Personal Research Odyssey," Econometrics, MDPI, vol. 9(1), pages 1-27, February.
    10. Jung, Alexander, 2020. "An empirical analysis of loan supply and demand in the euro area," International Review of Economics & Finance, Elsevier, vol. 70(C), pages 187-201.
    11. Stillwagon, Josh R., 2015. "Testing the expectations hypothesis with survey forecasts: The impacts of consumer sentiment and the zero lower bound in an I(2) CVAR," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 35(C), pages 85-101.
    12. H. Peter Boswijk & Paolo Paruolo, 2017. "Likelihood Ratio Tests of Restrictions on Common Trends Loading Matrices in I(2) VAR Systems," Econometrics, MDPI, vol. 5(3), pages 1-17, June.
    13. Beckmann, Joscha & Czudaj, Robert, 2013. "Is there a homogeneous causality pattern between oil prices and currencies of oil importers and exporters?," Energy Economics, Elsevier, vol. 40(C), pages 665-678.
    14. Bjørnar Karlsen Kivedal, 2023. "Long run non-linearity in CO2 emissions: the I(2) cointegration model and the environmental Kuznets curve," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 50(4), pages 899-931, November.
    15. Jennifer L. Castle & Michael P. Clements & David F. Hendry, 2016. "An Overview of Forecasting Facing Breaks," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 12(1), pages 3-23, September.
    16. Katarina Juselius, 2017. "A CVAR scenario for a standard monetary model using theory-consistent expectations," Discussion Papers 17-08, University of Copenhagen. Department of Economics.
    17. Johansen, Søren & Nielsen, Morten Ørregaard, 2018. "The cointegrated vector autoregressive model with general deterministic terms," Journal of Econometrics, Elsevier, vol. 202(2), pages 214-229.
    18. Piotr Wdowiński, 2011. "Model monetarny kursu równowagi złoty/euro: analiza kointegracyjna," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 3, pages 67-86.
    19. James R. Jordan & B. W. J. Miles & G. H. Gudmundsson & S. S. R. Jamieson & A. Jenkins & C. R. Stokes, 2023. "Increased warm water intrusions could cause mass loss in East Antarctica during the next 200 years," Nature Communications, Nature, vol. 14(1), pages 1-11, December.
    20. Ladislav Kristoufek, 2022. "On the role of stablecoins in cryptoasset pricing dynamics," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-26, December.

    More about this item

    Keywords

    Cointegration; dynamic analysis; ice sheets; sea level;
    All these keywords.

    JEL classification:

    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gwc:wpaper:2025-002. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: GW Economics Department (email available below). General contact details of provider: https://edirc.repec.org/data/pfgwuus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.