×

Modelling changes in Arctic sea ice cover: an application of generalized and inflated beta and gamma densities. (English) Zbl 1329.86022

Summary: A modelling framework for changing Arctic sea ice extent is developed reflecting different trends and seasonal extremes in nine Arctic sub-regions. Core sub-regions retain partial ice cover throughout the year, and in winter show complete ice cover, while in peripheral sub-regions, winter coverage is not complete, and there is no ice cover at all in the summer. A generalized beta representation is developed for monthly ice extents in core sub-regions, with inflation to model maximum winter extents. For peripheral sub-regions, a gamma time series with excess zeroes (representing summer sea ice absence) is developed. Different trend representations (deterministic vs. stochastic) are compared for non-extreme observations. Other potential applications of the generalized beta density allowing zero or maximum inflation are discussed.

MSC:

86A32 Geostatistics
86A05 Hydrology, hydrography, oceanography
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-07 Data analysis (statistics) (MSC2010)
65C60 Computational problems in statistics (MSC2010)

Software:

BUGS
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aitchison J, Egozcue J: Compositional data analysis: Where are we and where should we be heading?Math. Geol 2005, 37:829-850. 10.1007/s11004-005-7383-7 · Zbl 1177.86017 · doi:10.1007/s11004-005-7383-7
[2] Blundell R, Griffith R, Windmeijer F: Individual effects and dynamics in count data models.Journal of Econometrics 2002, 108:113-131. 10.1016/S0304-4076(01)00108-7 · Zbl 1043.62100 · doi:10.1016/S0304-4076(01)00108-7
[3] Brooks S, Gelman A: General methods for monitoring convergence of iterative simulations.J. Comput. Graph.l Stat 1998, 7:434-455.
[4] Butler A, Glasbey C: A latent Gaussian model for compositional data with zeros.J. R. Stat. Soc. Series C 2008, 57:505-520. 10.1111/j.1467-9876.2008.00627.x · doi:10.1111/j.1467-9876.2008.00627.x
[5] Comiso J, Parkinson C, Gersten R, Stock L: Accelerated decline in the Arctic sea ice cover.Geophys. Res. Lett 2008, 35:L01703. doi:10.1029/2007GL031972 · doi:10.1029/2007GL031972
[6] Fissel, D.; de Saavedra Álvarez, M.; Kulan, N.; Mudge, T.; Marko, J., Long-term trends for Sea Ice in the Western Arctic Ocean: implications for shipping and offshore oil and gas activities (2011), Hawaii, USA
[7] Gelfand A: Model determination using sampling based methods. Edited by: W. Gilks, S. Richardson, D. Spiegelhalter. Boca Raton, pp. 145-157: Markov Chain Monte Carlo in Practice, Chapman and Hall/CRC; 1996.
[8] Höhle M, Paul M: Count data regression charts for the monitoring of surveillance time series.Comput. Stat. & Data Anal 2008, 52:4357-4368. 10.1016/j.csda.2008.02.015 · Zbl 1452.62810 · doi:10.1016/j.csda.2008.02.015
[9] Huang X, Oosterlee C: Generalized beta regression models for random loss-given-default. Department of Applied Mathematical Analysis, Delft University of Technology, Report 08-10; 2008.
[10] Jung R, Kukuk M, Liesenfeld R: Time series of count data: modeling, estimation and diagnostics.Comput. Stat. Data Anal 2006, 51:2350-2364. 10.1016/j.csda.2006.08.001 · Zbl 1157.62492 · doi:10.1016/j.csda.2006.08.001
[11] Laud P, Ibrahim J: Predictive model selection.J R Stat Soc 1995, 57B:247-262. · Zbl 0809.62024
[12] Ledolter J, Abraham B: Parsimony and its importance in time series forecasting.Technometrics 1981, 23:411-414. 10.1080/00401706.1981.10487687 · Zbl 0472.62092 · doi:10.1080/00401706.1981.10487687
[13] Leininger T, Gelfand A, Allen J, Silander J: Spatial regression modeling for compositional data with many zeros.J. Agricultural Biol. Environ. Stat 2013,18(3):314-334. 10.1007/s13253-013-0145-y · Zbl 1303.62085 · doi:10.1007/s13253-013-0145-y
[14] Liu J, Curry J, Wang H, Song M, Horton R: Impact of declining Arctic sea ice on winter snowfall.Proc. Nat. Acad. Sci 2012, 109:4074-4079. 10.1073/pnas.1114910109 · doi:10.1073/pnas.1114910109
[15] Lunn D, Spiegelhalter D, Thomas A, Best N: The BUGS project: Evolution, critique and future directions.Stat. Med 2009, 28:3049-3067. 10.1002/sim.3680 · doi:10.1002/sim.3680
[16] National Snow and Ice Data Center 2012.http://nsidc.org/arcticseaicenews/2012/04/arctic-sea-ice-enters-the-spring-melt-season/ · Zbl 1303.62085
[17] Ospina R, Ferrari S: Inflated beta distributions.Stat. Papers 2010, 51:111-126. 10.1007/s00362-008-0125-4 · Zbl 1247.62043 · doi:10.1007/s00362-008-0125-4
[18] Pham-Gia T, Duong Q: The generalized beta- and F-distributions in statistical modelling.Math. Comput. Modell 1989, 12:1613-1625. 10.1016/0895-7177(89)90337-3 · Zbl 0697.62010 · doi:10.1016/0895-7177(89)90337-3
[19] Screen, J.; Deser, C.; Simmonds, I.; Tomas, R., Atmospheric impacts of Arctic sea-ice loss 1979-2009: separating forced change from atmospheric internal variability (2013)
[20] Serreze M, Maslanik J, Key J, Kokaly R, Robinson D: Diagnosis of the record minimum in arctic sea ice area during 1990 and associated snow cover extremes.Geophys. Res. Lett 1995, 22:2183-2186. 10.1029/95GL02068 · doi:10.1029/95GL02068
[21] Stroeve J, Holland M, Meier W, Scambos T, Serreze M: Arctic sea ice decline: faster than forecast.Geophys. Res. Lett 2007, 34:L09501. · doi:10.1029/2007GL029703
[22] Stroeve J, Serreze M, Holland M, Kay J, Malanik J, Barrett A: The Arctic’s rapidly shrinking sea ice cover: a research synthesis.Climatic Change 2012, 110:1005-1027. 10.1007/s10584-011-0101-1 · doi:10.1007/s10584-011-0101-1
[23] Zhao X, Luo Y, Wang S, Huang W, Lian J: Is desertification reversion sustainable in northern China: a case study in Naiman county, part of a typical agro-pastoral transitional zone in Inner-Mongolia, China.Global Environ. Res 2010, 14:63-70.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.