# Soft Periodic Convolutional Recurrent Network for Spatiotemporal Climate Forecast
## 1 Introduction  
Increasing climate remote sensing (e.g., weather satellite, AMeDAS), including reanalysis data that combine numerical simulations with observations, generates a massive amount of data. Furthermore, it consumes a lot of computational resources to make a forecast by using numerical weather prediction (NWP) models [1], and requires climatology knowledge to build a model, unlike machine learning (ML). Currently, many applications are using ML in the climate domain, such as tropical cyclone forecasting [2, 3], long-term rainfall prediction [4], and more [5, 6, 7]. Time-series forecasting models [8] have emerged to forecast climate variables by learning from the historical data. Long short-term memory (LSTM) [9] is a kind of recurrent neural network (RNN) capable of learning long-term dependencies [10, 11]. Recent works in ML [12, 13, 14] have proven that LSTM is beneficial for solving time-series climate forecasting problems. The spatiotemporal forecasting problem in the climate domain given by the spatial and temporal data is crucial for predicting the next time frame. The convolutionallong short-term memory network (ConvLSTM) [15] is the first ML method to tackle spatiotemporal climate forecasting by extending a fully connected LSTM (FC-LSTM) with convolutional structures. ConvLSTM was tested on precipitation nowcasting (up to 6 hours) in Hongkong from radar echo dataset. Our previous work [16] also showed that ConvLSTM outperformed Convolutional Neural Networks (CNNs) and linear regression for predicting geopotential height at a pressure of 300 hPa. Meanwhile, periodic patterns, e.g., seasonality, exist in a global spatiotemporal climate pattern. For example, the positive and negative phases of the North Atlantic Oscillation (NAO) predominantly appear in boreal winter over the Northern Hemisphere [17]. In the study of Lanchang-Mekong [18], the sub-region periodicity pattern of temperature and precipitation significantly increased. Looking deeper into the periodic patterns, there are two periodic patterns that we consider in this research; (1) the phase shift, such as the late summer and early autumn [19], and (2) non-stationarity of periodicity [20; 21; 22]. Climate seasonal shifts in terms of spatial and intensity may not be the same every year [23]. The study of El Nino-Southern Oscillation (ENSO) [21] on South African rainfall showed that the periodic cycle may vary in many ranges of years. The study of upstream sub-basins of the Yangtze River [22] also shows statistically significant 2- to 4-year periodicities for mean areal precipitation. To tackle the problem of phase shift and non-stationarity of periodicity patterns, the model should consider the nearby time (months) and multiple cycles. Although ConvLSTM and other novel spatiotemporal forecasting methods [24; 25; 26] are suitable for spatiotemporal forecasting, they do not consider periodicity, which is an essential component in climate forecasting. Periodic Convolutional Recurrent Network (Periodic-CRN) [27] has been proposed in a different domain (Taxi transportation) as a spatiotemporal forecasting model that makes use of the data's periodicity. The idea is to store the CRN component's output in the periodic representation dictionary (PRD) for re-use. Representations from the dictionary were used through an attention mechanism [28] to improve the forecasting accuracy of the crowd density across two taxi datasets from Beijing and Singapore. In this paper, we adapt Periodic-CRN to climate forecasting and validate the effectiveness of using periodic representation in forecasting climate variables.