Many machine-learning applications and methods are emerging to solve problems associated with spatiotemporal climate forecasting; however, a prediction algorithm that considers only short-range sequential information may not be adequate to deal with periodic patterns such as seasonality. In this paper, we adopt a Periodic Convolutional Recurrent Network (Periodic-CRN) model to employ the periodicity component in our proposals of the periodic representation dictionary (PRD). Phase shifts and non-stationarity of periodicity are the key components in the model to support. Specifically, we propose a Soft Periodic-CRN (SP-CRN) with three proposals of utilizing periodicity components: nearby-time (PRD-1), periodic-depth (PRD-2), and periodic-depth differencing (PRD-3) representation to improve climate forecasting accuracy. We experimented on geopotential height at 300 hPa (ZH300) and sea surface temperature (SST) datasets of ERA-Interim. The results showed the superiority of PRD-1 plus or minus one month of a prior cycle to capture the phase shift. In addition, PRD-3 considered only the depth of one differencing periodic cycle (i.e., the previous year) can significantly improve the prediction accuracy of ZH300 and SST. The mixed method of PRD-1, and PRD-3 (SP-CRN-1+3) showed a competitive or slight improvement over their base models. By adding the metadata component to indicate the month with one-hot encoding to SP-CRN-1+3, the prediction result was a drastic improvement. The results showed that the proposed method could learn four years of periodicity from the data, which may relate to the El Niño–Southern Oscillation (ENSO) cycle.
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