forecast model; fuzzy algorithm; Linear regression
Abstract :
[en] A so-called fuzzy linear regression is used in dendroecology to model empirically tree growth as a function of a bioclimatic index representing the water stress, i.e., the ratio of actual evapotranspiration to potential evapotranspiration. The response function predicts tree growth as (fuzzy) intervals, narrow in the domain where the bioclimatic index is most limiting and becoming progressively larger elsewhere. The method is tested with a population of Pinus pineaL. from the Provence region in France. It is shown that fuzzy linear regression gives results comparable with those obtained using a linear response function. The interval of credibility given by the fuzzy regression suggests that more precise expected growth is obtained for high water stress, which is typical of Mediterranean climate. Fuzzy linear regression can be also a method to test different hypotheses on several potential predictors when any further experimental approach is quite impossible as it is for trees in their natural environment. To sum up, fuzzy regression could be a first step before the construction of a kind of growth simulator adapted to different environments of a given species. In environmental sciences, the fuzzy response function thus appears to be an approach between the mechanistic and the statistical descriptive approaches.
Disciplines :
Mathematics
Author, co-author :
Boreux, Jean-Jacques ; Université de Liège - ULiège > Département des sciences et gestion de l'environnement > Surveillance de l'environnement
Gadbin-Henry, C.
Guiot, Joël
Tessier, L.
Language :
English
Title :
Radial tree-growth modelling with fuzzy regression.
Badeau, V., Dupouey, J.L., Becker, M., and Picard, J.F. 1995. Long-term growth trends of Fagus sylvatica L. in northeastern France. A comparison between high and low density stands. Acta Oecol. 16: 571-583.
Bardossy, A., Bogardi, I., and Duckstein, L. 1990. Fuzzy regression in hydrology. Water Resour. Res. 26: 1497-1508.
Bardossy, A., Duckstein, L., and Bogardi, I. 1993. Fuzzy non-linear regression analysis of dose response relationship. Eur. J. Oper. Res. 66: 36-51.
Berger, J.O. 1985. Statistical decision theory and Bayesian analysis. Springer-Verlag, New York.
Bernier, J. 1987. Elements of Bayesian analysis of uncertainty in hydrological reliability and risk models. In Engineering reliability and risk in water resources. Edited by L. Duckstein and E. Plate. Martinus Nijhoff, Boston, Mass. pp. 405-421.
Bert, G.D. 1992. Influence du climat, des facteurs stationnels et de la pollution sur la croissance et l'état sanitaire du sapin pectiné (Abies alba) dans le jura. Ph.D. thesis, Université de Nancy, Nancy, France.
Boreux, J.J., Pesti, G., Nicolas, J., and Duckstein, L. 1997. Age model estimation in paleoclimatic research: fuzzy regression and radiocarbon uncertainties. Palaeogeogr. Palaeoclim. Palaeoecol, 128: 29-37.
Burman, R., and Pochop, L. 1994. Evaporation, evapotranspiration and climatic data. Dev. Atmos. Sci. No. 22.
Caselton, W.F., and Luo, W. 1994. Inference and decision under near ignorance conditions. Engineering risk in natural resources management with special references to hydrosystems under changes of physical or climatic environment. Edited by L. Duckstein and E. Parent. Kluwer Academic Publishers, Dordrecht, the Netherlands. pp. 291-303.
Chu, C., and Marron, J. 1991. Choosing a kernel regression estimator (with discussion). Stat. Sci. 6: 404-436.
Cropper, J.P. 1982. Comment on response functions. In Climate from tree-rings. Edited by M.K. Hughes, P.M. Kelly, J.R. Pilcher, V.C. LaMarche Jr. Cambridge University Press, Cambridge, U.K. pp. 38-45.
Douglass, A.E. 1936. Climatic cycles and tree-growth. Vol. 3. A study of cycle. Carnagie Inst. Wash. Publ. No. 289.
Dubois, D., and Prade, H. 1980. Fuzzy sets and system theory and applications. Academic Press, San Diego, Calif.
Efron, B. 1979. Bootstrap methods: another look at the jackknife. Ann. Stat. 7: 1-26.
Efron, B. 1983. Estimating the error rate of a prediction rule: improvement on cross-validation. J. Am. Stat. Assoc. 78: 316-331.
Emberger, L. 1930. La végétation de la région méditerranéenne. Essai d'une classification des groupements végétaux. Rev. Gen. Bot. 42: 641-662 and 705-721.
Fan, J., and Gijbels, I. 1982. Local polynomial modelling and its applications. Chapman & Hall, London, U.K.
Federer, C.A. 1982. Transpirational supply and demand: plant, soil, and atmospheric effects evaluated by simulation. Water Resour. Res. 18: 355-362.
Fritts, H.C. 1976. Tree-rings and climate. Academic Press, London, U.K.
Fritts, H.C. 1982. The climate growth response. In Climate from tree-rings. Edited by M.K. Hughes, P.M. Kelly, J.R. Pilcher, V.C. LaMarche Jr. Cambridge University Press, Cambridge, U.K. pp. 38-45.
Fritts, H.C., Blasing, T.J., Hayden, B.P. and Kutzbach, J.E. 1971. Multivariate techniques for specifying tree-growth and climate relationships and for reconstructing anomalies in paleoclimate. J. Appl. Meteorol. 10: 845-864.
Gadbin-Henry, C. 1994. Études dendroécologiques de Pinus pinea L. Aspects méthodologiques. Ph.D. thesis, Université d'Aix-Marseille III, Aix-en-Provence, France.
Guiot, J. 1989. Method of calibration and comparison of methods. In Methods of dendrochronology. Edited by E.R Cook. and L.A Kairiukstis. Kluwer Academic Publishers and International Institute for Applied Systems Analysis, Dordrecht, the Netherlands. pp. 165-178 and 185-193.
Guiot, J., and Tessier, L. 1997. Detection of pollution signals in tree-ring series using AR processes and neural networks. In Applications of time-series analysis in astronomy and meteorology. Edited by T.S. Rao, M.B. Priestley, and O. Lessi. Chapman & Hall, London, U.K. pp. 413-426.
Guiot, J., Berger, A.L., and Munaut, A.V. 1982a. Response functions. In Climate from tree-rings. Edited by M.K. Hughes, P.M. Kelly, J.R. Pilcher, V.C. LaMarche Jr. Cambridge University Press, Cambridge, U.K. pp. 38-45.
Guiot, J., Berger, A.L. Munaut, A.V., and Till, C. 1982b. Some new mathematical procedures in dendroclimatology with examples for Switzerland and Morocco. Tree-Ring Bull. 42: 33-48.
Harrison, S.P., Prentice, I.C., and Guiot, J. 1993. Climatic controls of Holocene lake-level changes in Europe. Clim. Dyn. 8: 189-200.
Hastie, T., and Loader, C. 1993. Local regression: automatical kernel carpentry (with discussion). Stat. Sci. 8: 120-143.
Heshmaty, B., and Kandel, A. 1985. Fuzzy linear regression and its applications to forecasting in uncertain environment. Fuzzy Sets Syst, 15: 159-191.
Jarvis, P.G., and MacNaughton, K.G. 1986: Stomatal control of transpiration: scaling up from leaf to region. Adv. Ecol. Res. No. 15. pp. 1-49.
Kaufmann, A., and Gupta, M.M. 1991. Introduction to fuzzy arithmetic: theory and applications. Van Nostrand Reinhold, New York.
Lebourgeois, F. 1995. Étude dendroécologique et écophysiologique du Pin laricio de Corse (Pinus nigra A. ssp. laricio) en région pays de Loire. Ph.D. thesis, Université de Paris-Sud, Orsay, Paris, France.
Neter, J., Wasserman, W., and Kutner, M.H. 1989. Applied linear regression models. 2nd ed. Irwin, Homewood, III.
Prentice, I.C., Cramer, W., Harrison, S.P., Leemans, R., and Monserud, R.A. 1992. A global biome model based on plant physiology and dominance, soil properties and climate. J. Biogeogr. 19: 117-134.
Prentice, I.C., Sykes, M.T., and Cramer, W. 1993. A simulation model for the transient effects of climate change on forest landscapes. Ecol. Modell. 65: 51-71.
Redden, D.T., and Woodall, H. 1996. Further examination of fuzzy linear regression. Fuzzy Sets Syst. 79: 203-211.
Schweingruber, F.H., Kairiukstis, L., and Shiyatov, S. 1990. Sample selection. In Methods of dendrochronology. Edited by E.R Cook and L.A Kairiukstis. Kluwer Academic Publishers and IIASA, Dordrecht, the Netherlands. pp. 23-96.
Shashkin, A.V., and Fritts, H.C. 1995. A model that simulates cambial activity and ring structure in conifers. In Tree rings, from the past to the future. Edited by S. Ohta and M.K. Hughes. Forestry and Forest Products Research Institute, Tsukuba, Japan. pp. 24-30.
Tanaka, H., Uejima, S., and Asai, K. 1982. Linear regression analysis with fuzzy model. IEEE Trans. Syst. Man Cybern. 12: 903-907.
Viertl, R. 1997. Non-precise information in Bayesian inference. In Statistical and Bayesian methods in hydrological sciences. Edited by E. Parent and B. Bobie. UNESCO Press, Paris. pp. 465-478.
