Assessment of Ice Volume Changes in the Cryosphere via Simplified Heat Transport Model
Affiliation(s)
1 Department of Mathematical Sciences, United States Military Academy, West Point, New York, USA. 2 Hromadka & Associates, Rancho Santa Margarita, CA, USA.
1 Department of Mathematical Sciences, United States Military Academy, West Point, New York, USA. 2 Hromadka & Associates, Rancho Santa Margarita, CA, USA.
ABSTRACT
In order to describe changes in ice volume in the cryosphere, a differential equation mathematical model is used in this paper. The dominating effects of freezing and thawing in the cryosphere enable simplification of the heat transport equations. This results in a mathematical model that can be solved exactly and is useful in investigating other climatic components, which in turn may be similarly analyzed for possible Global Circulation Model (GCM) validation. Data forms representing temperature and ice volume during the Pleistocene are available and can be directly compared with the exact solution of the simplified differential equation used in this paper. The model parameters may then be adjusted to approximate the effects of climate change; the adjusted model then run in reverse time, to develop an alternative history of ice volume of the cryosphere to be compared with the actual data interpretations previously published in the literature. In this fashion, an assessment may be made as to possible climate impacts in the cryosphere.
In order to describe changes in ice volume in the cryosphere, a differential equation mathematical model is used in this paper. The dominating effects of freezing and thawing in the cryosphere enable simplification of the heat transport equations. This results in a mathematical model that can be solved exactly and is useful in investigating other climatic components, which in turn may be similarly analyzed for possible Global Circulation Model (GCM) validation. Data forms representing temperature and ice volume during the Pleistocene are available and can be directly compared with the exact solution of the simplified differential equation used in this paper. The model parameters may then be adjusted to approximate the effects of climate change; the adjusted model then run in reverse time, to develop an alternative history of ice volume of the cryosphere to be compared with the actual data interpretations previously published in the literature. In this fashion, an assessment may be made as to possible climate impacts in the cryosphere.
Cite this paper
Hromadka II, T. , McInvale, H. , Phillips, M. and Espinosa, B. (2014) Assessment of Ice Volume Changes in the Cryosphere via Simplified Heat Transport Model. American Journal of Climate Change, 3, 421-428. doi: 10.4236/ajcc.2014.35037.
Hromadka II, T. , McInvale, H. , Phillips, M. and Espinosa, B. (2014) Assessment of Ice Volume Changes in the Cryosphere via Simplified Heat Transport Model. American Journal of Climate Change, 3, 421-428. doi: 10.4236/ajcc.2014.35037.
References
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http://dx.doi.org/10.1038/20859 [8] Petit, J.R., et al. (2001) Vostok Ice Core Data for 420,000 Years, IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series #2001-076. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA. [9] Jouzel, J., Lorius, C., Petit, J.R., Genthon, C., Barkov, N.I., Kotlyakov, V.M. and Petrov, V.M. (1987) Vostok Ice Core: A Continuous Isotope Temperature Record over the Last Climatic Cycle (160,000 Years). Nature, 329, 403-408.
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http://dx.doi.org/10.1126/science.1141038 [13] Jouzel, J. and Masson-Delmotte, V. (2007) EPICA Dome C Ice Core 800KYr Deuterium Data and Temperature Estimates. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2007-091. NOAA/NCDC Paleoclimatology Program, Boulder CO, USA. [14] Lisiecki, L. and Raymo, M. (2005) A Pliocene-Pleistocene Stack of 57 Globally Distributed Benthic δ18O Records. Paleoceanography, 20, PA1003. [15] Alexiades, V. and Solomon, A.D. (1993) Mathematical Modeling of Melting and Freezing Processes. Chapter 2. Problems with Explicit Solutions. Hemisphere Publishing Corporation, Washington, 33-124. [16] Bitz, C.M. and Marshall, S.J. (2012) Encyclopedia of Sustainability Science and Technology. Springer Reference, Section on Climate Change Modeling and Methodology, 2761. [17] Kawamura, K., et al. (2007) Dome Fuji Ice Core Preliminary Temperature Reconstruction, 0-340 kyr. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2007-074. NOAA/NCDC Paleoclimatology Program, Boulder. [18] Zachos, J., Pagani, M., Sloan, L., Thomas, E. and Billups, K. (2001) Trends, Rhythms, and Aberrations in Global Climate Change 65 Ma to Present. Science, 292, 686-693.
http://dx.doi.org/10.1126/science.1059412 [19] Mix, A.C. and Ruddiman, W.F. (1984) Oxygen-Isotope Analyses and Pleistocene Ice Volumes. Quaternary Research, 21, 1-20. [20] Ruddiman, W.F. (2001) Earth’s Climate: Past and Future. W.H. Freeman & Sons, New York. [21] Kawamura, K., et al. (2007) Dome Fuji Ice Core 340KYr (2500m) δ18O Data. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2007-074. NOAA/NCDC Paleoclimatology Program, Boulder. [22] Imbrie, J. and Imbrie, J.Z. (1980) Modeling the Climatic Response to Orbital Variations. Science, 207, 943-953.
http://dx.doi.org/10.1126/science.207.4434.943 [23] Imbrie, J., Hays, J.D., Martinson, D.G., McIntyre, A., Mix, A.C., Morley, J.J., Pisias, N.G., Prell, W.L. and Shackleton, N.J. (1984) The Orbital Theory of Pleistocene Climate: Support from a Revised Chronology of the Marine δ18O Record. In: Berger, A., Ed., Milankovitch and Climate, Part 1, Springer, New York, 269-305. [24] Imbrie, J.Z., Imbrie-Moore, A. and Lisiecki, L. (2011) A Phase-Space Model for Pleistocene Ice Volume. Earth and Planetary Science Letters, 307, 94-102.
[1] Randall, D.A., Wood, R.A., Bony, S., Colman, R., Fichefet, T., Fyfe, J., Kattsov, V., Pitman, A., Shukla, J., Srinivasan, J., Stouffer, R.J., Sumi, A. and Taylor, K.E. (2007) Climate Models and Their Evaluation. In: Climate Change 2007: The Physical Science Basis, Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on climate Change, Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA. [2] Anagnostopoulos, G.G., Koutsoyiannia, D., Christofides, A., Efstratiadis, A. and Mamassis, N. (2010) A Comparison of Local and Aggregated Climate Model Outputs with Observed Data. Hydrological Sciences Journal, 55, 1094-1110.
http://dx.doi.org/10.1080/02626667.2010.513518 [3] Bounoua, L., Hall, F.G., Sellars, P.J., Kumar, A., Collatz, G.J., Tucker, C.J. and Imhoff, M.L. (2010) Quantifying the Negative Feedback of Vegetation to Greenhouse Warming: A Modeling Approach. Geophysical Research Letters, 37, L23701.
http://dx.doi.org/10.1029/2010GL045338 [4] Hromadka II, T.V., McInvale, H.D., Gatzke, B., Phillips, M. and Espinosa, B., (2014) Cumulative Departure Model of the Cryosphere during the Pleistocene. ASCE Journal of Cold Regions Engineering, 28.
http://dx.doi.org/10.1061/(ASCE)CR.1943-5495.0000071 [5] Dyurgerov, M.B. and Meier, M.F. (1999) Twentieth Century Climate Change: Evidence from Small Glaciers. INSTAAR, University of Colorado at Boulder, Colorado (2005), Paper No.58, Institute of Arctic and Alpine Research. [6] Bamber, J.L. and Payne, A.J. (2004) Mass Balance of the Cryosphere. Cambridge University Press, Cambridge, 145.
http://dx.doi.org/10.1017/CBO9780511535659 [7] Petit, J.R., Jouzel, J., Raynaud, D., Barkov, N.I., Barnola, J.M., Basile, I., Bender, M., Chappellaz, J., Davis, J., Delaygue, G., Delmotte, M., Kotlyakov, V.M., Legrand, M., Lipenkov, V., Lorius, C., Pépin, L., Ritz, C., Saltzman, E. and Stievenard, M. (1999) Climate and Atmospheric History of the Past 420,000 Years from the Vostok Ice Core, Antarctica. Nature, 399, 429-436.
http://dx.doi.org/10.1038/20859 [8] Petit, J.R., et al. (2001) Vostok Ice Core Data for 420,000 Years, IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series #2001-076. NOAA/NGDC Paleoclimatology Program, Boulder CO, USA. [9] Jouzel, J., Lorius, C., Petit, J.R., Genthon, C., Barkov, N.I., Kotlyakov, V.M. and Petrov, V.M. (1987) Vostok Ice Core: A Continuous Isotope Temperature Record over the Last Climatic Cycle (160,000 Years). Nature, 329, 403-408.
http://dx.doi.org/10.1038/329403a0 [10] Jouzel, J., Barkov, N.I., Barnola, J.M., Bender, M., Chappellaz, J., Genthon, C., Kotlyakov, V.M., Lipenkov, V., Lorius, C., Petit, J.R., Raynaud, D., Raisbeck, G., Ritz, C., Sowers, T., Stievenard, M., Yiou, F. and Yiou, P. (1993) Extending the Vostok Ice-Core Record of Palaeoclimate to the Penultimate Glacial Period. Nature, 364, 407-412.
http://dx.doi.org/10.1038/364407a0 [11] Jouzel, J., Waelbroeck, C., Malaize, B., Bender, M., Petit, J.R., Stievenard, M., Barkov, N.I., Barnola, J.M., King, T., Kotlyakov, V.M., Lipenkov, V., Lorius, C., Raynaud, D., Ritz, C. and Sowers, T. (1996) Climatic Interpretation of the Recently Extended Vostok Ice Records. Climate Dynamics, 12, 513-521.
http://dx.doi.org/10.1007/BF00207935 [12] Jouzel, J., Masson-Delmotte, V., Cattani, O., Dreyfus, G., Falourd, S., Hoffmann, G., Minster, B., Nouet, J., Barnola, J.M., Chappellaz, J., Fischer, H., Gallet, J.C., Johnsen, S., Leuenberger, M., Loulergue, L., Luethi, D., Oerter, H., Parrenin, F., Raisbeck, G., Raynaud, D., Schilt, A., Schwander, J., Selmo, E., Souchez, R., Spahni, R., Stauffer, B., Steffensen, J.P., Stenni, B., Stocker, T.F., Tison, J.L., Werner, M. and Wolff, E.W. (2007) Orbital and Millennial Antarctic Climate Variability over the Past 800,000 Years. Science, 317, 793-797.
http://dx.doi.org/10.1126/science.1141038 [13] Jouzel, J. and Masson-Delmotte, V. (2007) EPICA Dome C Ice Core 800KYr Deuterium Data and Temperature Estimates. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2007-091. NOAA/NCDC Paleoclimatology Program, Boulder CO, USA. [14] Lisiecki, L. and Raymo, M. (2005) A Pliocene-Pleistocene Stack of 57 Globally Distributed Benthic δ18O Records. Paleoceanography, 20, PA1003. [15] Alexiades, V. and Solomon, A.D. (1993) Mathematical Modeling of Melting and Freezing Processes. Chapter 2. Problems with Explicit Solutions. Hemisphere Publishing Corporation, Washington, 33-124. [16] Bitz, C.M. and Marshall, S.J. (2012) Encyclopedia of Sustainability Science and Technology. Springer Reference, Section on Climate Change Modeling and Methodology, 2761. [17] Kawamura, K., et al. (2007) Dome Fuji Ice Core Preliminary Temperature Reconstruction, 0-340 kyr. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2007-074. NOAA/NCDC Paleoclimatology Program, Boulder. [18] Zachos, J., Pagani, M., Sloan, L., Thomas, E. and Billups, K. (2001) Trends, Rhythms, and Aberrations in Global Climate Change 65 Ma to Present. Science, 292, 686-693.
http://dx.doi.org/10.1126/science.1059412 [19] Mix, A.C. and Ruddiman, W.F. (1984) Oxygen-Isotope Analyses and Pleistocene Ice Volumes. Quaternary Research, 21, 1-20. [20] Ruddiman, W.F. (2001) Earth’s Climate: Past and Future. W.H. Freeman & Sons, New York. [21] Kawamura, K., et al. (2007) Dome Fuji Ice Core 340KYr (2500m) δ18O Data. IGBP PAGES/World Data Center for Paleoclimatology Data Contribution Series # 2007-074. NOAA/NCDC Paleoclimatology Program, Boulder. [22] Imbrie, J. and Imbrie, J.Z. (1980) Modeling the Climatic Response to Orbital Variations. Science, 207, 943-953.
http://dx.doi.org/10.1126/science.207.4434.943 [23] Imbrie, J., Hays, J.D., Martinson, D.G., McIntyre, A., Mix, A.C., Morley, J.J., Pisias, N.G., Prell, W.L. and Shackleton, N.J. (1984) The Orbital Theory of Pleistocene Climate: Support from a Revised Chronology of the Marine δ18O Record. In: Berger, A., Ed., Milankovitch and Climate, Part 1, Springer, New York, 269-305. [24] Imbrie, J.Z., Imbrie-Moore, A. and Lisiecki, L. (2011) A Phase-Space Model for Pleistocene Ice Volume. Earth and Planetary Science Letters, 307, 94-102.