Ever since the middle of last century when the well-known Hurst phenomenon was discovered, it has been widely recognized that the variability of many climatic variables on different time scales is not arbitrary, but follows a scaling law x(at)=a^H x(t). This means time series x(t) remains statistically similar if one zooms in or out, and its variability exhibits scale invariance. However, how to properly apply this idea to climate research, is still an open question.
In this talk, the concepts of scaling and climate memory will be introduced, and three potential applications are proposed. Of the three applications, climate predictability/prediction is the most noteworthy research area, which will be discussed in great detail. Recent progresses includes: i) quantifying climate predictability from the perspective of climate memory, ii) evaluating the performance of CMIP5 models in simulating the scaling behaviors, and iii) developing a new climate prediction methods based on both climate memory and the variance decomposition method.