Long-term persistence in climate and the detection problem

We have analyzed six recently reconstructed records (Jones et al., 1998; Mann et al.,1999; Briffa, 2000; Esper et al., 2002; McIntyre and McKitrick, 2003; and Moberg et al., 2005) of the Northern Hemisphere temperatures and found that all are governed by long-term persistence. Due to the long-term persistence, the mean temperature variations σ(m, L) between L years, obtained from moving averages over m years, are considerably larger than for uncorrelated or short-term correlated records. We compare the values for σ(m, L) with the most recent temperature changes ΔT_i(m, L) in the corresponding instrumental record and determine the year i_c where ΔT_i(m, L)/σ(m, L) exceeds a certain threshold and the first year i_d when this could be detected. We find, for example, that for the climatologically relevant parameters m = 30, L = 100, and the threshold 2.5, the values (i_c, i_d) range, for all records, between (1976, 1990) for Mann et al. (1999) and (1988, 2002) for Jones et al. (1998). Accordingly, the hypothesis that at least part of the recent warming cannot be solely related to natural factors, may be accepted with a very low risk, independently of the database use.