1. YODEN Shigeo Dept. of Geophysics, Kyoto Univ., JAPAN Highlights for SPARC Temperature Trend Meeting at Tabard Inn in Washington DC April 12-13, 2007 Seasonally Dependent Detectability of a Linear Trend Submitted to JGR

2.  detectability of a linear trend in a finite-length dataset natural internal variability causes a spurious trend it may have a non-Gaussian nature  we argue the minimum length of dataset necessary for the detection of a given magnitude of trend with a given statistical significance level the minimum magnitude of trend for a given length of dataset with a given statistical significance level  Edgeworth expansion of the distribution function of the spurious trend estimation of higher moments by long time integrations of numerical models under a purely periodic annual forcing  two examples stratospheric polar temperature (15,200-year dataset) precipitation (1,000-year dataset)

3.  Labitzke diagram seasonal variation of histograms of monthly mean T (30hPa) North Pole (Berlin) North Pole (NCEP) Nishizawa and Yoden(2005) An MCM result observational data are too short model output could be used to estimate the moments

4.  the minimum magnitude of trend for a 20-year dataset with the confidence coefficient of 90% < 0.5 K/decade > 5 K/decade

5.  statistical significance of the three trends estimated with the moments of our numerical model output JAN JUL ERA40 NCEP Berlin 99% 95% 90% 95% 99%

6. Concluding remarks  The detectability depends on distribution function of the spurious trend due to the limited length of dataset with natural internal variability. Gaussian: Student’s t distribution of the spurious trend Non-Gaussian: use of the Edgeworth expansion  We can estimate the distribution function with the moments of the internal variability obtained by long time integrations of atmospheric numerical models.  the minimum length of dataset necessary for the detection of a given magnitude of trend  the minimum magnitude of trend for a given length of dataset

7.  Two typical examples that have large seasonal and regional dependence of natural internal variability: stratospheric polar temperature in the Northern Hemisphere precipitation in the equatorial region  The detectability has large dependence on season and region. it is not always appropriate to use annual or global average careful consideration is necessary to choose season and region as well as quantity for detection of a statistically significant linear trend with a given length of dataset