Chapter 4. Spatial and temporal interpolation of Sea Surface Salinity using deep learning
4.3. Methodology
CNN, one of the deep learning algorithms, is widely used for image analysis in computer vision, medical, and remote sensing applications (Lee et al., 2020). A typical CNN consists of convolutional layers, pooling layers, and fully connected (FC) layers (Yoo et al., 2020). After filtering is applied to the original image, an operation is performed on the image. Several filters of specific size perform a convolutional operation in the convolutional layer while sweeping through the image. The amount of movement of filters (stride) can be set, and the image becomes smaller according to the size of the filter and stride. By adding pixels of a specific value to the edge of the input image (padding), the size of the image is maintained. Pooling layers reduces the image size by extracting a representative value (i.e., mean or maximum) from a given window. As the image size decreases, model parameters and the computational cost are decreased, and overfitting is mitigated. FC layers produce the final result from previous layers based on multi-layer perceptron.
Various CNN architectures have been developed, such as Fully Convolutional Network (FCN), U- NET, and TreeUNET (Lee et al., 2020). We adopted FCN for the interpolation method in this study.
FCN uses a convolutional layer instead of the FC layer in the traditional CNN structure (Long et al., 2015). One of the main advantages of the FCN is that it can produce the result with the same size as the input image, which is a so-called image-to-image model. Moreover, it can have an arbitrary input and output size. The arbitrary data size is very helpful to the model generalization. Also, skip connection was applied to our model. The skip connection proposed by Srivastava et al. (2015) is used to avoid vanishing initial information during very deep neural network training (Ayzel et al., 2020). The pattern learned in the bottom layer is reused in the top layer to recover the lost information through deep layers (Ayzel et al., 2020; Long et al., 2015).
In this study, the daily GBRT-based SSS was interpolated using the past seven days of SSS based on the FCN approach. The target SSS needs to be fully filled to learn, so training samples were extracted in a 40X40 window size patch from the entire global grid (720X1440). Training samples were acquired differently in open oceans and coastal regions. In the open ocean, cases where the 40X40 window patch of the target day was fully covered were randomly selected. However, the patch cannot be fully in the coastal regions due to land. In the coastal regions, samples were selected when at least 100 pixels out of 1600 pixels (40X40 patch) had values using the land mask. Total 349,184 patches were extracted from the dataset. 80% of samples are used as the training dataset (279,342), and the rest 20% samples were used for model validation. The maximum training epoch is 100 iteration, and the training was stopped when the validation performance is not improved for three successive iterations. Figure 4.3 and Table 4.1 are the structure of the FCN model in this study. The model consists of 11 convolutional layers and two skip connections, and zero paddings were applied to each layer (Table 4.1). Pooling layers were
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not applied in our model because the patch size was too small. The same FCN model is applied twice (Figure 4.2). For the first time, the SSS of the target day is filled using the along-track SSS of the past seven days. Then, the SSS of the target day is predicted using the gap-filled SSS for the past seven days.
As the FCN approach is an image-based model, it is affected by the swath shape of the previous seven days. The swath boundary problem can be solved by applying the FCN model once more to the gap- filled data.
Figure 4.2. Flow chart of SSS interpolation model in this study.
Figure 4.3. The structure of the Fully Convolutional Network (FCN) model in this study.
61 Table 4.1. Information of layer of FCN model in this study.
Number of filters Filter size Stride Input layer Number of samples: 349,184, depth: 7
Convolutional layer1 32
3 Ⅹ 3 1
Convolutional layer2 64
Convolutional layer3 128
Convolutional layer4 256
Convolutional layer5 512
Convolutional layer6 512
Convolutional layer7 256
Convolutional layer8 128
Convolutional layer9 64
Skip connection 1 Concatenate with Convolutional layer1
Convolutional layer10 32 3 Ⅹ 3 1
Skip connection 2 Concatenate with the input layer
Convolutional layer11 39 3 Ⅹ 3 1
Output layer Number of samples: 349,184, depth: 1
The interpolation results are validated in two ways. First, the SSS of specific pixels with the original value was removed, and the result of interpolation was compared with the original value. Considering the distribution of SSS and the missing rate (Figure 4.1), six regions (i.e., North Pacific Ocean, North Atlantic Ocean, Equator, Amazon River Plume, Indian Ocean, and Antarctic ocean) were selected (Figure 4.4), and the values were removed with a 20X20 window size every 100 days. In total, 28,057 pixels have been withheld this way. Second, the pixel filled by the FCN model was validated by comparing it with the in-situ Argo data.
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Figure 4.4. Six regions (i.e., North Pacific Ocean, North Atlantic Ocean, Equator, Amazon River Plume, Indian Ocean, and Antarctic ocean) removed every 100 days for validation (blue boxes).