Accounting for the surface temperature persistence by using signal energy

The autocorrelation function (ACF) and its finite Fourier transform, referred to as signal energy, have been investigated using the ECMWF daily surface temperature data. ACF itself provides a measure of the influence of leading fluctuation between two different time points. Considering the decay of ACF, it is found that the scaling power-rule of ACF is only valid in a very short period, as the decay of ACF exists before it reaches a random noise state. Therefore, the method of the critical exponent of ACF is limited in the short length of the temporal interval. On the other hand, the distributions of the signal energy always show nice patterns, indicating the degree of persistence change. It is found, for a short period, that the distributions of the signal energy and the critical exponent are very similar, with a correlation coefficient over 0.97. For a longer period, though the critical exponent of ACF becomes invalid, the signal energy can always provide an effective method to investigate climate persistence in different lengths of time. In a 5-day period of boreal winter, the southern part of North America has a larger value of signal energy compared to the northern part; thus, the surface temperature is more stable in the north part. The result becomes opposite in the boreal summer. The method of signal energy can also be applied to a particular interval of time. In different temporal intervals, the signal energy presents very different results, especially over the El Nino regions