# Prediction of Ocean Weather Based on Denoising AutoEncoder and Convolutional LSTM
## 2 Theoretical Background
### Denoising AutoEncoder  
In general, when training time-series data, a delay prediction problem [13] occurs. When the data are insufficient, or the pattern of the data cannot be identified, it tends to bring values similar to the current value. When the prediction model is overfitted on the input data, if we put an input at a specific point in time, there is a problem of just shifting the data at that point in time. This is referred to as a delayed prediction problem. Figure 4 shows the delayed prediction results of SST. We trained a model to predict SST after 5 days using 60 days of data and applied it to three different ocean areas. For training of the prediction model, data collected from the European Center for Medium-Range Weather Forecasts (ECMWF) was used, and a total of eight years of data was used for training. Among them, the initial six years were used for learning, and two years were used as a test set. We performed the training using conventional LSTM based on the data for a point in the region included in Figure 4. As shown in Figure 4, it can be seen that the delayed prediction problem occurred clearly in all graphs. The same problem can also be found in other studies [4; 14]. The graphs show that the actual result and the predicted patterns are very similar, although there is a slight difference. Further, it seems that the predicted result has a phase shift with respect to the origin. The delay prediction problem is mostly caused by not being able to understand the data patterns properly. Using all of the predictors required for prediction as input can also be a way to solve the delayed prediction problem. However, as input is limited to eight parameters of ocean weather, we have to find another way to remove noise to solve this problem. There are two ways to solve this. The first is to gather sufficient training data to comprehend the data pattern. If the data for ocean weather can be obtained infinitely, it is possible to make a satisfactory model through a general DFN or LSTM. However, the data for ocean weather has limitations because it is based on the data that can be accessed from the weather centers. Second is to remove the noise from the data so that the pattern of the data is sufficiently revealed. The time-series data are generally composed of the trend component, seasonal component, and remainder component. The trend component represents the trend of data fluctuation, the seasonal component is the repeating pattern of data, and the remainder component usually refers to noise. These data can be decomposed into the three components described above using the seasonal and trend decomposition using loess (STL) decomposition method [15]. Figure 5 shows the decomposition of SST from 2014 to 2017 into the three components described previously. In the remainder component, the ocean weather has a large amount of noise. This noise hinders the learning of seasonal and trend components. Therefore, this study proposes a method to effectively remove the noise. When using the STL decomposition method, two main parameters are used. Two are the trend-cycle window and the seasonal window. In particular, as there is no default value for the seasonal window, the results of the STL decomposition method can be different depending on how much the seasonal window is set. In this study, one year was divided into four seasons, and a seasonal window was set considering this. In the case of ocean weather, one option is available-that is, to gather data provided by weather centers. In this situation, measurement and estimation errors exist depending on the method used by weather centers in acquiring data. Therefore, for training efficiency, noise should be removed. To remove noise from the ocean weather, weather centers have utilized various methods, such as a principal component analysis (PCA)-based noise filter [16] for a long time. However, noise still exists in the ocean weather. The residual component is one of the essential factors when predicting regionally correct values.