climate change; fuzzy linear regression; imprecision
Abstract :
[en] A fuzzy linear regression-based method to relate the depth and age of sediment layers is described. Because algae, moss or local plants respond to climatic change, the age and depth of sediment layers are interrelated variables but the link between them is often imprecise. In most cases, due to the limited number of layers in a core (i.e., small number of data points), estimation of the slope and uncertainties in classical regression analysis does not take into account the uncertainties in radiocarbon dating. Here, fuzzy linear regression, which may be applied even to a very small data set, is utilized. The method, illustrated through a practical example, with eight data points, appears to be a promising tool in stratigraphic studies to link sediment age to layer depth and takes into account uncertainties from radiocarbon dating.
Disciplines :
Mathematics
Author, co-author :
Boreux, Jean-Jacques ; Université de Liège - ULiège > Département des sciences et gestion de l'environnement > Surveillance de l'environnement
Pesti, G.
Duckstein, L.
Nicolas, Jacques ; Université de Liège - ULiège > Département des sciences et gestion de l'environnement > Surveillance de l'environnement
Language :
English
Title :
Age model estimation in paleoclimatic research : fuzzy regression and radiocarbon uncertainties
Bardossy, A., 1990. Notes on fuzzy regression. Fuzzy Sets Syst., 37(1): 65-79.
Bardossy, A., Bogardi, I. and Duckstein, L., 1990. Fuzzy regression in hydrology. Water Resour. Res., 26(7): 1497-1508.
Bardossy, A., Bogardi, I. and Duckstein, L., 1993. Fuzzy nonlinear regression analysis of dose-response relationships. Eur. J. Oper. Res., 66: 36-51.
Becker, B. and Kromer, B., 1993. The continental tree-ring record: absolute chronology, C14 calibration and climatic change at 11 ka. Palaeogeogr. Palaeoclimatol. Palaeoecol., 103: 67-71.
Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis. Springer, New York, p. 617.
Bogardi, I., Szidarovszky, F. and Duckstein, L., 1982. Bayesian analysis of underground floodings. Water Resour. Res., 18(4): 400-1116.
CLIMAP Project Members, 1981. Seasonal reconstruction of the Earth's surface at the Last Glacial Maximum. In: A. McIntyre and R. Cline (Editors), Map and Chart Series, MC-36. Geol. Soc. Am., Boulder, pp. 1-18.
Dubois, D. and Prade, H., 1980. Fuzzy Sets and Systems: Theory and Applications. Academic Press, San Diego, 393 pp.
Guiot, J., deBeaulieu, J.L., Cheddadi, R., David, F., Ponel, P. and Reille, M., 1993. The climate in Western Europe during the last glacial/interglacial cycle derived from pollen and insect remains. Palaeogeogr. Palaeoclimatol. Palaeoecol., 103: 73-93.
Huntley, B., 1988. Glacial and Holocene vegetation history: Europe. In: B. Huntley and T. Webb III (Editors), Vegetation History. Kluwer, Dordrecht, pp. 341-384.
Huntley, B., 1990. European vegetation history: paleovegetation maps from pollen data - 13,000 yr B.P. to present. J. Quat. Sci., 5: 103-122.
Kaufmann, A. and Gupta M.M., 1991. Introduction to Fuzzy Arithmetic: Theory and Applications. Van Nostrand Reinhold, New York, p. 361.
Neter, J., Wasserman, W. and Kutner, M.H., 1989. Applied Linear Regression Models. Irwin, Homewood, IL, 2nd ed., p. 667.
Ohno, M., Hamano, Y., Murayama, M., Matsumoto, E., Iwakura, H., Nakamura, T. and Taira, A., 1993. Paleomagnetic record over the past 35,000 years of a sediment core from off Siukoku, Southwest Japan. Geophys. Res. Lett., 20(13): 1395-1398.
Prentice, I.C., Bartlein, P.J. and Webb III, T., 1991. Vegetation and climate change in eastern North America since the last glacial maximum. Ecology, 72: 2038-2056.
Stuiver, M. and Braziunas, T.F., 1989. Atmospheric C14 and century-scale solar oscillations. Nature, 338: 405-408.
Tanaka, H., Uejima, S. and Asai, K., 1982. Linear regression analysis with fuzzy model. IEEE Trans. Syst. Man. Cybern., SMC-12: 903-907.
Viertl, R., 1996. Non-precise information in Bayesian inference. In: Proc. J. Bernier UNESCO Conf., Paris, September 1995. UNESCO Stud. Rep.
Zadeh, L.A., 1973. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man. Cybern., SMC3: 28-44.
Zimmermann, H.J., 1985. Fuzzy Set Theory and its Application. Martinus Nijhoff, Boston, p. 363.
