Estimating present climate in a warming world: a model-based approach

Abstract

Weather services base their operational definitions of “present” climate on past observations, using a 30-year normal period such as 1961–1990 or 1971–2000. In a world with ongoing global warming, however, past data give a biased estimate of the actual present-day climate. Here we propose to correct this bias with a “delta change” method, in which model-simulated climate changes and observed global mean temperature changes are used to extrapolate past observations forward in time, to make them representative of present or future climate conditions. In a hindcast test for the years 1991–2002, the method works well for temperature, with a clear improvement in verification statistics compared to the case in which the hindcast is formed directly from the observations for 1961–1990. However, no improvement is found for precipitation, for which the signal-to-noise ratio between expected anthropogenic changes and interannual variability is much lower than for temperature. An application of the method to the present (around the year 2007) climate suggests that, as a geographical average over land areas excluding Antarctica, 8–9 months per year and 8–9 years per decade can be expected to be warmer than the median for 1971–2000. Along with the overall warming, a substantial increase in the frequency of warm extremes at the expense of cold extremes of monthly-to-annual temperature is expected.

Appendix: Brier score and the continuous ranked probability score

Consider a binary event E. For example, E might be defined to occur when the mean temperature of a given month in a given place exceeds a given threshold ξ. The Brier score B (Brier 1950; Wilks 1995) for this threshold value is defined as

$$ B(\xi ) = \frac{1} {N}{\sum\limits_{i = 1}^N {{\left( {p_{i} (\xi ) - o_{i} (\xi )} \right)}^{2} } } $$

(A1)

where o _i (ξ) = 1 (0) if E occurs (does not occur) in case i and p _i (ξ) is the corresponding forecast probability. N is the total number of cases verified. The better the forecast, the lower the Brier score. For a perfect deterministic forecast system, which forecasts a probability of 1 (0) always when E occurs (does not occur), B = 0.

The Brier score can be evaluated for any threshold value ξ. Integrating B over ξ gives the continuous ranked probability score CRPS (Stanski et al. 1989; Hersbach 2000; Candille and Talagrand 2005). When all values of ξ are given the same weight, as is done in this study

$$ {\text{CRPS}} = {\int\limits_{ - \infty }^\infty {B(\xi )} }d\xi . $$

(A2)

By this definition, CRPS gets the units of the forecast variable: °C for temperature and mm/day for precipitation.