The calculation and mapping of linear trends over time in climate data represents one of the most direct means of describing the climate change currently affecting Australia and the world. The National Climate Centre has published maps of linear trends in a range of climate variables (precipitation, land surface maximum, minimum and mean temperature, diurnal temperature range, and sea surface temperature for the surrounding oceans) on the Bureau's website (www.bom.gov.au/silo/products/cli_chg/).

The trends in these variables are rarely completely linear, and accordingly the trend maps are given for a range of periods with start years available at decadal intervals (the ends of the periods being the present). The annual time series of the associated areal averages reinforce the necessity to interpret the trend maps in the light of interannual and interdecadal variability.

There are many advantages and much economy which flow from using linear trends to describe data. Trend values are easily computed, have a well-established and well-understood statistical basis, and delivery a very concise view of climate change. However, there is good evidence that the linear model is a rather poor representation of large scale temperature trends (e.g., Soon et al. 2004), with the “global warming” since the 1970s occurring at a rate about three times faster than over the past century as a whole (Vinikov et al. 2006; Shein et al. 2006).

In this presentation, we investigate a range of ways of characterizing the non-linearity present in the Australian temperature signal. Higher-order polynomial (i.e., quadratic, cubic) regressions can be attempted, although these are problematic with regard to the extrapolation of trends. Piecewise linear regressions show some promise. Figure 1 shows a piece-wise linear curve of best fit (under the assumption of one break point) for the Australian annual mean temperature time series. The different trend regimes are quite distinct. The results show that traditional linear trend estimate (0.092°C/decade) for the full period underestimates the recent rate of warming of Australian temperatures (0.16°C/decade). For maximum temperature, the recent rate of warming is even higher, at 0.23°C/decade.

References

[1] K.A. Shein, A.M. Waple, H.J. Diamond and J.M. Levy (2006). State of the Climate in 2005. Bull. Amer. Met. Soc., 87, S1-S102. [2] K.Y. Vinnikov, M.C. Grody, A. Robock, R.J. Stouffer, P.D. Jones, and M.D. Goldberg (2006). Temperature trends at the surface and in the troposphere, J. Geophy. Res.. 111, D03106, 14pp. [3] W.W.-H. Soon, D.R. Legates, and S.L. Baliunas (2004). Estimation and representation of long-term (>40 year) trends of Northern-Hemisphere-gridded surface temperature: A note of caution. Geophy. Res. Let., 31, L03209, 4pp.

Figure 1: Time series of Australian annual mean temperature (1910 – 2005), with a piece-wise linear curve of best fit.