Time-Series Prediction of Sea Level Change in the East Coast of Peninsular Malaysia from the Supervised Learning Approach

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Figure 1. Location of tide gauge at the three areas on the ECPM

The selected study areas in this study are Kerteh which in the district of Kemaman in Terengganu; Tanjung Sedili is a coastal region in Kota Tinggi district, Johor, and finally Tioman Island which is in a district of Tompin, Pahang. The geographical of these study locations are located at the ECPM, Malaysia as shown in Figure 1. The data used in the analyses were historical monthly mean sea level (MMSL) for the period from 2007 to 2017 and was collected from the Department of Survey and Mapping Malaysia (DSMM). A total of 396 (11 years x 12 months x 3 regions) historical data points were generated from the tide data. However, data for certain periods are not available when maintenance work was carried out on the tide gauge meters. The method used to normalize these missing data is discussed in the data normalization section.

The data for the period from January 2007 to December 2015 were used to train while the data from January 2016 to December 2017 were used for analysis by the proposed algorithm. A total of 132 data points for each meteorological parameter were used, where 92 (70%) data points were used for training and 40 (30%) data points were used for validating and testing [19].

A Comprehensive description of the theory for the Regression Support Vector Machine (RSVM) was given by Lai et al. [10]. The use of a kernel function to map the non-linear input space into a linear feature space is very dependent on the nature of the data. In RSVM, there are three types kernel function, viz., Normalized polynomial kernel (NP), Radial basis kernel (RBF), and Pearson VII Universal Kernel. It has been reported that the performace RSVM with Pearson VII Universal Kernel outperformed RSVM with other kernel functions [20]. Therefore, in this study, the Pearson VII Universal Kernel was applied as a kernel function for RSVM and is referred to as the Pearson Universal Kernel (PUK) (Eq. 1):

$f(x)=H /\left[1+\left(\frac{2\left(x-x_{o}\right) \sqrt{2^{\left(\frac{1}{\omega}\right)}-1}}{\sigma}\right)^{2}\right]^{\omega}$    (1)

This model is also known as the regression support vector machine.

The predicted monthly mean sea level (MMSL) (Najah et al.) can be expressed as:

MSL_predicted = (MSL + SST +Rainfall + MCC)_obs     (2)

The input dataset for the proposed model is sea surface temperature (SST), rainfall and mean cloud cover (MCC) for the period from January 2007 to December 2017.

The independent dataset with missing values was normalized using the common artificial intelligence model function.

$Z_{i}=\frac{y_{i}-y_{\min }}{y_{\max }-y_{\min }}$     (3)

where, Z_i is the missing value after normalization, y_i is the value before the missing value, y_max is the maximum value, and y_min is the minimum value.

The model structure has to be optimized in order to minimize the uncertainties from model misspecifications and to ensure the efficiency of the proposed model. In this study, the model performance of the proposed algorithm was assessed using root-mean-square error (RMSE), correlation coefficient (R) and  scatter index (SI) [21].

1. Root Mean Square Error, RMSE is a comparison of the observed and the predicted value.
2.  

$\mathrm{RMSE}=\sqrt{\frac{\sum_{i=1}^{n}\left(M S L_{p}-M S L_{0}\right)^{2}}{N}}$     (4)

3. Correlation Coefficient, R, is used to measure the strength of the relationship between variables.
4.  

$\mathrm{R}=\frac{\sum_{i=1}^{n}\left(M S L_{o}-\overline{M S L}_{o}\right)\left(M S L_{p}-\overline{M S L}_{p}\right)}{\sqrt{\sum_{i=1}^{n}\left(M S L_{o}-\overline{M S L}_{o}\right)^{2}} \sum_{i=1}^{n}\left(M S L_{p}-\overline{M S L}_{p}\right)^{2}}$     (5)

where, $M S L_{p}$ and $M S L_{o}$ are the predicted and the observed monthly mean sea levels, respectively; $\mathrm{N}$ is the number of the data, $\overline{M S L}_{p}$ and $\overline{M S L}_{o}$ are the mean values of the predicted and observed monthly mean sea levels, respectively and $\bar{x}$ is the mean of the number of data.

The cross-validation method is one of the adopted methods for evaluating model architecture parameter values after traning process is completed. Different v-fold numbers will be investigated in this study and as the stopping criteria to meet the desire model performance.

As an example, Figure 2 shows the flowchart of the developed support vector machine model.

This research aimed to develop Artificial Intelligence technique viz. Regression Support Vector Machine (RSVM) in order to simulate accurately Mean Sea Level Rise at three different crucial stations in Malaysian coastal. The results revealed that the proposed RSVM can be considered as a powerful algorithm in predicting the changes in the sea level. The hyper-parameters tuning technique such as V-fold introduced as stopping criteria and the optimal number found to be equal to 10. The selected meteorological parameters as input to the model have a profound influence on the accuracy of the proposed model.

It can be seen from the findings that the proposed model outperformed the conventional one and proved its capabilities in capturing the changes in the sea level of all three stations that been investigated in this study. High level of accuracy obtained at Kerteh and Tioman Island followed by Tanjung Sedili for both training and testing datasets. The finding of this study can be very significant in assessing the vulnerability of Tioman Island due to the changes in the rise of mean sea level. Future work can be conducted to validate the accuracy of the proposed model by using it in other countries and region.

The author declares that there is no conflict of interest regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancy have been completely observed by the authors.