Estimating the intermonth covariance between rainfall and the atmospheric circulation

Abstract

The seasonal mean of a climate variable consists of a slow and intraseasonal component. Existing methods for deriving coupled patterns between intraseasonal components assume stationarity and first order autoregressive processes. This does not hold for a variable such as rainfall where the daily data consists of dichotomous (on/off) events. It is possible to formulate a more general method for such two-state climate variables but it requires an estimate of the intermonth covariance. We use a stochastic two-state first-order Markov chain model fitted to daily Australian rainfall data to provide an estimate of the intermonth covariance with daily 500hPa atmospheric geopotential height anomalies. We show that the estimate of the intermonth covariance is much smaller than the within-month covariance between rainfall and the 500hPa height intraseasonal component. References

• 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.
• X. Zheng and C. S. Frederiksen. Variability of seasonal-mean fields arising from intraseasonal variability. Part 1, methodology. Climate Dynamics, 23:177--191, 2004. doi:10.1007/s00382-004-0428-7
• C. S. Frederiksen and X. Zheng. A Method for constructing skilful seasonal forecasts using slow modes of climate variability. ANZIAM J., 48:C89--C103, 2007. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/114
• X. Zheng and C. S. Frederiksen. A study of predictable patterns for seasonal forecasting of New Zealand rainfall. J. Climate, 19:3320--3333, 2006. doi:10.1175/JCLI3798.1
• X. Zheng and C. S. Frederiksen. Statistical Prediction of Seasonal Mean Southern Hemisphere 500hPa Geopotential Heights. J. Climate, 20:2791--2809, 2006. doi:10.1175/JCLI4180.1
• C. S. Frederiksen and X. Zheng. A Method for extracting coupled patterns of predictable and chaotic components in pairs of climate variables. ANZIAM J., 46:C276--C289, 2005. http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/959
• C. S. Frederiksen, S. Grainger and X. Zheng. A Method for estimating the potential long-range predictability of precipitation over Western Australia. ANZIAM J., 2008. 50:C569--C583, http://anziamj.austms.org.au/ojs/index.php/ANZIAMJ/article/view/1411
• R. W. Katz and X. Zheng. Mixture Model For Overdispersion of Precipitation. J. Climate, 12:2528--2537, 1999. doi:10.1175/1520-0442(1999)012<2528:MMFOOP>2.0.CO;2
• D. S. Wilks. Statistical Methods in the Atmospheric Sciences. (second edition). Academic Press, 627pp, 2006.
• W. Feller. An Introduction to Probability Theory and Its Applications. Vol. 2. John Wiley and Sons, 626pp, 1966.
• D. A. Jones and G. Weymouth. An Australian monthly rainfall data set. Technical Report No. 70, Bur. Met. Australia, 1997.
• E. Kalnay, M. Kanamitsu, R. Kistler, W. Collins, D. Deaven, L. Gandin, M. Iredell, S. Saha, G. White, J. Woollen, Y. Zhu, M. Chelliah, W. Ebisuzaki, W. Higgins, J. Janowiak, K. C. Mo, C. Ropelewski, J. Wang, A. Leetmaa, R. Reynolds, Roy Jenne, and D. Joseph. The NCEP/NCAR 40-year reanalysis project. Bull. Amer. Meteor. Soc., 77:437--471, 1996. doi:10.1175/1520-0477(1996)077<0437:TNYRP>2.0.CO;2