(a–e) Natural trends in long-term correlated Gaussian data (LTP; 1,000 time series with a length of 1,692 months) versus natural trends in long-term correlated Gaussian data with additive AR1 noise (LTPAR1). The different colour shades correspond to the weight with which the AR1 noise was added to the long-term correlated data (1–10 times larger than the s.d. of the purely long-term correlated Gaussian data; in the North Sea the s.d. of the ATM exceeds that of the RES by 1–3 times). The natural trends correspond to a time series with a unit s.d. of 10 cm in the combined time series (which is roughly the median in the analysed North Sea records). Simulation results are shown for long-term correlated Gaussian data with (a) α=0.6, (b) α=0.7, (c) α=0.8, (d) α=0.9 and (e) α=1.0. For the lag-1 autocorrelation a value of c=0.1, which is the maximum value obtained from the ATM, has been applied.