## 1. Introduction

[2] Global mean surface air temperature shows a positive trend in the 20th century [*Brohan et al.*, 2006; *Hansen et al.*, 2006; *Smith and Reynolds*, 2005]. After an initial “flat” development at a pre-industrial level, a clear warming took place from the 1910s to the 1940s, leveling off in the 1970s. Since 1980 temperatures show a positive trend of about 0.18°C per decade [*Trenberth et al.*, 2007]. This temperature increase and its geographical patterns have been subject to detection studies [*Hegerl et al.*, 1996; *Barnett et al.*, 2005], which are partially based on sophisticated statistical analyses of observations and climate simulations. Here, we pursue a simpler and intuitive idea, more accessible to the non-expert, to estimate the likelihood that the recent observed warming is consistent with the natural variability.

[3] The increasing anthropogenic greenhouse forcing would, according to simple physical reasoning [*Arrhenius*, 1896], cause a clustering of record warm years at the end of the observed record, and in fact, the 13 warmest years in 1880–2006 have all occurred in or after 1990. A clustering of record years at the beginning of the record would be in contradiction to anthropogenic greenhouse forcing. The probability of this clustering occurring by chance at the end of the record can be estimated under different null hypotheses of the statistical characteristics of natural variability. The most simple of those is that the annual values of mean global temperatures are independent of one another. In this case, the probability *p* of the event *E* of finding at least 13 of the largest values of a sequence of 127 independent random numbers on the last 17 places (year 1990 to 2006) is *p*(*E*) = (114!17!)/(127!4!) = 1.25 × 10^{−14}. Such clustering appears as an extremely improbable random event in a stationary climate. However, the annual surface air-temperatures displays a serial correlation, even in a stationary natural climate, due to processes occurring on the land surface, ocean, and cryosphere. We conceptualize this natural memory with two statistical models, namely “short term” and “long term” memory. Within the former, annual mean temperature is assumed to be the result of an autoregressive process, which displays an exponentially decaying auto-covariance function. In the latter, it is described by a *long-term persistence* process with a power-law decay of the auto-covariance function. Some processes that may be relevant in the climate context have been shown to display such type of behavior [*Bunde et al.*, 2005; *Rybski et al.*, 2006]. Although it is quite difficult to ascertain whether a short time series such as the observed global mean annual temperature obeys this type of behavior, the present approach can be readily applied to other more complex null models. It also offers the advantage that it can be extended to regional spatial scales using some of the longest individual station records.