# Soft Periodic Convolutional Recurrent Network for Spatiotemporal Climate Forecast
## 2 Related Work  
Firstly, we introduce the works on ML-based spatiotemporal climate forecasting. Generally, a CNN is the method used to capture the spatial relationship of spatial input. However, it cannot by itself capture spatiotemporal relationships because there is no temporal memory for temporal changed patterns. A ConvLSTM [15] improves an FC-LSTM by capturing both spatial and temporal patterns, and was applied to precipitation nowcasting (short period, up to 6 hours). Since then, spatiotemporal climate forecasting has widely mentioned ConvLSTM as a baseline method [24; 25; 26] or adopted in other model architectures [29; 30; 31]. Predictive RNN (PredRNN) [24] adds extra connections between adjacent time steps in a core stack of spatiotemporal LSTM (ST-LSTM), which outperforms ConvLSTM in precipitation nowcasting. Memory-in-memory (MIM) networks [25] improve the learning of non-stationarity properties in spatiotemporal input, such as spatial correlations or temporal dependencies of local pixel values for low-level non-stationarity, and the accumulation, deformation or dissipation of radar echoes in precipitation forecasting for high-level non-stationarity. MIM captures those non-stationarity properties by adding stationary and non-stationary modules separately inside the ST-LSTM block [24]. Lastly, the most recent work on spatiotemporal climate forecasting is the spatiotemporal convolutional sequence-to-sequence network (STConvS2S) [26]. STConvS2S comprises three components, the sets of convolutional layers responsible for different tasks: the temporal block, which learns the temporal representation of sequential input by two approaches (temporal casual block [32] and temporal reversed block); spatial block, which extracts the spatial features from the temporal block; and temporal generator block, designed to output a sequence of arbitrary length. The STConvS2S outperformed or was competitive with ConvLSTM, PredRNN, MIM models for temperature (CFSR [[https://climatedataguide.ucar.edu/climate-data/climate-forecast-system-reanalysis-cfsr](https://climatedataguide.ucar.edu/climate-data/climate-forecast-system-reanalysis-cfsr)]([https://climatedataguide.ucar.edu/climate-data/climate-forecast-system-reanalysis-cfsr](https://climatedataguide.ucar.edu/climate-data/climate-forecast-system-reanalysis-cfsr)), accessed on 22 February 2021) and rainfall (CHIRPS [[https://chc.ucsb.edu/data/chirps](https://chc.ucsb.edu/data/chirps)]([https://chc.ucsb.edu/data/chirps](https://chc.ucsb.edu/data/chirps)), accessed on 22 February 2021) prediction. Secondly, we introduce ML-based climate forecasting methods that use the periodicity component to improve prediction accuracy. A seasonally integrated autoencoder (SSAE) [33] is proposed to improve short-term daily precipitation forecasting. SSAE architecture has two LSTM autoencoders: the short-term autoencoder, which learns the short-term sequential input (less than seven days), and the seasonal autoencoder which captures the seasonal change in a long-term sequential input long enough to cover the period of the wet or dry season (60-120 days). The other way is to introduce the metadata idea to the network. The prediction of a streamflow in a river [34] improves the prediction results by adding a digit for the month as one of inputs in the final position of the sequential input of LSTM, Extreme Learning Machines (ELM), and Random Forest (RF) algorithms. Committee ELM (Comm-ELM) [35] also forecasts the monthly standardized precipitation index (SPI) by adding a digit for the month to indicate yearly periodicity at the end of a sequential input to improve the prediction. However, all of these methods assume stationary periodicity, which means they can not capture the phase shift or non-stationarity of periodicity patterns.