A method for estimating the potential long-range predictability of precipitation over Western Australia

A methodology for estimating the potential predictability of seasonal mean climate variables where the daily data consist of dichotomous (on/off) events, such as precipitation, is described and applied to Western Australian rainfall for the period 1951--2000. The method relies on determining an estimate for the intermonth correlations for precipitation and utilizes a stochastic, two state, first order, Markov chain model fitted to the daily data. References W. Feller. An Introduction to Probability Theory and Its Applications. Vol. 2. John Wiley and Sons, 626pp, 1966. C. S. Frederiksen and X. Zheng. Coherent Structures of Interannual Variability of the Atmospheric Circulation: The Role of Intraseasonal Variability. Frontiers in Turbulence and Coherent Structures, World Scientific Lecture Notes in Complex Systems, Vol. 6, Eds Jim Denier and Jorgen Frederiksen, World Scientific Publications, 87--120, 2007. D. A. Jones and G. Weymouth. An Australian monthly rainfall data set. Technical Report No. 70, Bur. Met. Australia, 1997. R. W. Katz and X. Zheng. Mixture Model For Overdispersion of Precipitation. J. Climate, 12:2528--2537, doi:10.1175/1520-0442(1999)012<2528:MMFOOP>2.0.CO;2, 1999. E. N. Lorenz. On the existence of extended range predictability. J. Appl. Meteor., 12:543--546, doi:10.1175/1520-0450(1973)012<0543:OTEOER>2.0.CO;2, 1973. R. A. Madden, D. J. Shea, R. W. Katz and J. W. Kidson. The potential long-range predictability of precipitation over New Zealand. Int. J. Clim., 19:405--421, http://ejournals.ebsco.com/direct.asp?ArticleID=UWLQUYU54E2X7BYBW3DT, 1999. D. S. Wilks. Statistical Methods in the Atmospheric Sciences. (second edition). Academic Press, 627pp, 2006. X. Zheng and C. S. Frederiksen. A study of predictable patterns for seasonal forecasting of New Zealand rainfall. J. Climate, 19:3320--3333, doi:10.1175/JCLI3798.1, 2006. X. Zheng, H. Nakamura and J. A. Renwick. Potential predictability of seasonal means based on monthly time series of meteorological variables. J. Climate, 13:2591--2604, doi:10.1175/1520-0442(2000)013<2591:PPOSMB>2.0.CO;2, 2000