Long-term memory in climate variability: A new look based on fractional integral techniques

Long-term memory (LTM) in climate variability is studied by means of fractional integral techniques. We establish a new model, Fractional Integral Statistical Model (FISM), with which one can reproduce LTM of any given time series of climatic variability successfully. By using FISM, we further propose a new variable, Memory Kernel, based on which a clear picture of how the historical states maintain their impacts on the states in far future is drawn quantitatively. We find any climatic variability time series with LTM can be decomposed into two components: the weather-scale (or more accurately, smaller-scale) excitation and the cumulative memory component. By analyzing these two components, we reach an interpretation of climate memory in the end of the paper, that is, smaller time scale excitation pushes the present climate regime to begin to change, while slower response subsystems, such as the ocean, usually "remember" the forcing first, and then exhibit the influence slowly on a larger time scale. Since LTM is ubiquitous in climate, our findings in this paper may suggest a new perspective on the research of climate predictability.