Identifying the sources of seasonal potential predictability using Fractional Integral Statistical Model with a Variance Decomposition Method

It is well recognized that climate predictability has three origins: (i)climate memory (inertia of the climate system) that accumulated from the historical conditions, (ii) responses to external forcings, and (iii) dynamical interactions of multiple processes in the climate system. However, how to systematically identify these predictable sources is still an open question. Here, we combine a recently developed Fractional Integral Statistical Model (FISM) with a Variance Decomposition Method (VDM), to systematically estimate the potential sources of predictability. With FISM, one can extract the memory component from the considered variable. For the residual parts, VDM can then be applied to extract the slow varying covariance matrix, which contains signals related to external forcings and dynamical interactions of multiple processes in climate. To show the improvement of our methodology, we have tested it on realistic data, using monthly temperature observations over China during 1960-2017.  It is found that the climate memory component contributes a large portion of the seasonal predictability in the temperature records. Our results offer the potential for more skillful seasonal predictions compared with the results obtained using FISM or VDM alone.