Prediction of Sea Level in the Arabian Gulf Using Artificial Neural Networks

Abstract

Creating an efficient model for predicting sea level fluctuations is essential for climate change research. This study examined the effectiveness of utilizing Artificial Neural Networks (ANNs), particularly the recurrent network approach. ANNs were chosen for their capacity to learn from extensive and intricate data and their ability to handle nonlinear correlations. The Long Short-Term Memory (LSTM) algorithm was employed to fill data gaps and predict future sea level records in the Arabian Gulf, especially in Mina Salman. The results were promising, with LSTM successfully filling a 6-year data gap while maintaining low Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) values. The first phase of the model yielded a RMSE value of 63.4 mm and a MAPE value of 3.14%. The same approach was used to retrain the model with a mix of real and predicted values, preserving historical patterns and yearly rates with an RMSE of 66.5 mm and a MAPE of 3.07%. These findings highlight LSTM’s advantages when considering only historical information for predicting the future sea level changes. The research provides valuable insights into predicting sea level changes in regions with limited field data, such as the Arabian Gulf, and emphasizes the potential for further research to enhance sea level prediction models through improved optimization techniques.

1. Introduction

Climate change is an increasingly significant and urgent topic that has far-reaching effects on both global and local climatic conditions. One of the consequences of climate change is the continuous rise in sea levels, which has been meticulously documented and quantified at an estimated rate of approximately 3 to 3.4 mm per year since the pivotal year of 1993, as corroborated by the report of Wuebbles et al. [1]. This phenomenon is inextricably linked with broader global warming trends, highlighting the intricate interplay between climate variables.

A closer examination within the context of the Arabian Gulf, also known as the Persian Gulf, conducted by Alothman et al. [2], has revealed intriguing insights. Their research, based on a comprehensive analysis of multiple tide gauge datasets, demonstrated that the Gulf region is undergoing a sea-level rise of 2.2 mm per year. However, data from the authoritative NOAA/NESDIS/STAR Laboratory for Satellite Altimetry (LSA) indicate a somewhat higher rate, pegging the annual sea-level increase in the Gulf at 4.6 mm. These varying rates of sea-level rise emphasize the complexity of this environmental challenge, which shows that having a comprehensive study to understand the underlying dynamics and implications is important.

The Arabian Gulf is important in this regard, particularly due to its remarkable economic growth and rapidly growing construction activities along its coastlines. This substantial development encompasses a wide array of critical infrastructure projects, ranging from ports and shipping facilities to desalination plants and coastal urban areas. As noted in the research conducted by Sheppard et al. [3], the Gulf region is witnessing a surge in the construction of vital facilities, both in proximity to and within its waters. These developments are pivotal to the region’s economic prosperity but also render it highly vulnerable to the consequences of sea-level fluctuations, emphasizing the urgency of conducting in-depth sea level studies tailored to this unique context.

Furthermore, demographic trends in the Arabian Gulf region have unveiled a significant correlation between human settlements and coastal areas. Countries such as Bahrain, Kuwait, Qatar, and the United Arab Emirates, as per the regional report of the Regional Organization For The Protection of The Marine Environment (ROPME), exhibit a coastal population percentage that exceeds 70% [4]. This demographic reality shows the intricate connection between coastal regions and human habitation, which is why a deep understanding of sea level change is necessary. The importance of studying and predicting these fluctuations cannot be overstated, as it directly informs the sustainable design and resilience of coastal structures, ensuring the safety and well-being of a substantial portion of the population.

In light of these intricate dynamics and compelling circumstances, the development and implementation of a robust sea level prediction model emerge as an indispensable step. Such a model not only aids in comprehending the nuances of sea level variability in the Arabian Gulf but also holds the potential to catalyze the region’s holistic development, promoting sustainable practices and safeguarding against the adverse impacts of climate change-induced sea-level rise.

Developing a sea level prediction model is a significant task in climate science and environmental research. It is imperative to keep improving the sea level prediction models because rising sea levels are causing problems for coastal regions around the world. A multitude of studies have been conducted utilizing both traditional and unconventional techniques to forecast sea level changes to improve our understanding of this complex phenomenon.

Among the traditional methods, harmonic analysis has established itself as a reliable method in predicting sea level changes. This approach, as exemplified by Hsieh et al. [5], has yielded remarkable results when coupled with modifications like the Modified Harmonic Analysis (MHA) method. MHA not only excels in capturing the intricate tidal harmonic motions but also adeptly delineates the long-term trends associated with sea-level rise. However, while harmonic analysis remains a reliable tool, its utility is contingent upon the availability of extensive sea level records over significant time spans. This requirement poses challenges in regions where comprehensive tidal measurements have not been effectively recorded [6].

In the quest for accurate sea level predictions, researchers have explored diverse statistical models, each tailored to specific contexts and constraints. An example can be found in the work of Srinivas et al. [7], who endeavored to forecast monthly mean sea levels along the Indian coastline. Their study encompassed 15 different monitoring stations and assessed various statistical models, including autoregressive, sinusoidal, and exponentially weighted moving average techniques. The findings showed the nuanced nature of sea level predictions, with models proving suitable for certain months and stations but falling short of generalized applicability. Such nuances echo the inherent variability in sea level behavior across diverse geographical and temporal scales.

Similarly, the application of the Auto Regressive Integrated Moving Average (ARIMA) model, as explored by Balogun and Adebisi [8], unveiled the dynamic nature of predictive performance. ARIMA, a statistical method, exhibited varying degrees of accuracy in sea level prediction across different locations. These insights accentuate the multifaceted nature of sea level forecasting, where one approach is seldom sufficient, thus requiring modern techniques such as deep learning to create predictive sea level models.

In today’s world of better technology and faster computers, using advanced methods like deep learning is really important for making sea level predictions. Deep learning is a powerful tool because it is capable of handling a massive amount of data and also working with missing information. This combination of fast computers and smart modeling methods results in more accurate sea level predictions.

Nowadays, methods such as neural network (NN), a type of machine learning algorithm, have been used in different applications and fields. NN is an artificial adaptive system that mimics the human brain and the way it functions [9]. It works by modifying an internal structure based on a certain function objective. The reason behind it being an effective method is its ability when dealing with nonlinear problems since it can create and rebuild the non-clear rules that control the solution of the problem. NN is a combination of many layers, and each layer has different neurons called units. The layers are an input layer, hidden layer, output layer, and some complex NN architectures have more than one hidden layer. Over the past years, it has been used by researchers to predict sea level changes. Makarynskyy et al. [10] developed an artificial intelligence meshless method of neural networks to predict hourly sea level changes. In another study, researchers used meteorologic factors such as air temperature, humidity, and air pressure combined with sea level heights to create prediction models [11]. Also, other researchers tried combining the least squares method with neural network, and the results show how reliable the approach is with short-term predictions compared to a traditional model such as Autoregressive Moving Average [12].

In response to this gap, the challenge addressed in this research involves harnessing the potential of a supervised deep learning algorithm known as Long Short-Term Memory (LSTM). LSTM has demonstrated its prowess in hydrologic modeling by excelling in identifying long-term relationships between input variables and target outputs, as substantiated by prior studies [13]. A notable attribute that sets LSTM apart is its capacity to derive precise sea level predictions exclusively from historical sea level data. This distinctive capability renders LSTM a valuable tool, particularly in geographical areas such as the Arabian Gulf, where tidal measurements either lack consistency or exhibit data gaps. Within the context of these circumstances, the central objective of this study is to transcend the constraints imposed by incomplete or insufficient data records. A dedicated effort is being made to conduct a comprehensive evaluation of the efficacy and precision of LSTM neural networks for sea level forecasting within the specific domain of the Arabian Gulf. This study aims to provide valuable insights into the domain of sea level prediction, with a special emphasis on regions that encounter data challenges such as the Arabian Gulf.

2. Methodology

2.1. Study Area and Data

The Arabian Gulf, a strategically situated body of water, occupies a prominent position between the northeastern reaches of the Arabian Peninsula and the expanse of Iran. The Arabian Gulf spans the latitudinal coordinates of 24 °N to 30 °N and the longitudinal span of 48 °E to 57 °E as shown in Figure 1. Its dimensions are indeed noteworthy, stretching across an impressive length of approximately 1000 km, while its width varies between 200 to 300 km, providing a sense of the vastness of this aquatic expanse. In terms of its hydrographic profile, the Arabian Gulf maintains an average depth of approximately 35 m, a characteristic that significantly shapes its dynamics and responses to environmental forces [14]. Understanding the fluctuations in sea level within the Arabian Gulf necessitates a nuanced perspective, as it is profoundly influenced by a confluence of factors. The changes in sea level in the Arabian Gulf are influenced by both water exchange of Strait of Hormuz and the meteorological conditions in the region such as wind patterns, atmospheric pressure, and temperature fluctuations [15].

In light of the exploration and investigation for relevant sea level data in the Arabian Gulf region, it was found that the information is either outdated or has a lot of missing elements. However, the University of Hawaii Sea Level Center (UHSLC) provided access to their data from their only station in the region. The station is Mina Salman in Bahrain, which is located approximately in the middle of the Arabian Gulf, as shown in Figure 1. Being in the center might help in forming a data source that can provide a comprehensive view of the Gulf. The obtained information has a time span of 22 years of data taken daily from the end of 1985 to 2007 with a gap of 6 years from the end of 1997 to the end of 2003 as shown in Figure 2. Although the UHSLC does not explicitly explain the reasons behind the gap in their data, this interruption might have occurred due to alterations in the tide gauge’s location or insufficient maintenance. While the dataset spanning 22 years may appear relatively short in duration, it is imperative to highlight that the primary research challenge arises from the limited availability of data within the region of interest. The study is inherently focused on devising a robust methodology and a technique capable of effectively extrapolating and interpolating missing information within a dataset of constrained temporal scope. There are multiple small quantities of missing information that were dropped to make the process of model training more manageable.

Tidal ranges in the region were reported to vary from 1500 mm in the central part to 3000 mm in the northwest, near Shatt Al Arab [16]. The calculated average sea level of 1498 mm, derived from all available observations preceding the data gap, aligns with the reported tidal variations. Additionally, the observed seasonality aligns with Al-Subhi [17], and this phenomenon is anticipated due to natural processes. Warmer temperatures in summer lead to ocean warming and expansion, resulting in higher sea levels. Conversely, in winter, cooler temperatures cause ocean cooling and contraction, leading to lower sea levels. This pattern is commonly observed, with higher sea levels during summer and early autumn, and lower levels in winter and early spring. The information was either normalized or standardized, depending on the model’s requirements. These two procedures are essential to ensure that the data have a common scale, and they help in improving the quality and performance of the models. The data were split into three sets—train, validation, and test—and the ratio of splitting was selected differently subjected to the model’s constraints.

2.2. Long Short-Term Memory (LSTM)

LSTM is a type of Recurrent Neural Network (RNN), and RNNs are advanced neural networks that are well suited for time series [18]. They can be trained for time series by processing the historical data sequences at a time and predicting the next value [19]. Despite the excellent ability of RNNS in predicting time series information, they have a vanishing gradient problem [20]. Thus, to solve this problem, LSTM was presented, which has several gates. LSTM gates are forget gates that decide which data should be eliminated, input gates that decide which current data should be passed to the cell state, and output gates that decide which current data should be allowed to impact the output. The flowing way that the data take in the LSTM block from the input layer to the output layer is formed by the following equations [21].

$$\begin{array}{c}{f}_t=\sigma (W_f[h_{t-1},x_t]+b_f)\end{array}$$

(1)

$$\begin{array}{c}{i}_t=\sigma (W_i[h_{t-1},x_t]+b_i)\end{array}$$

(2)

$$\begin{array}{c}{\tilde{c}}_t=tanh(W_c[h_{t-1},x_t]+b_c)\end{array}$$

(3)

$$\begin{array}{c}{c}_t=f_t\ast c_{t-1}+i_t\ast c{}_t\end{array}$$

(4)

$$\begin{array}{c}{o}_t=\sigma (W_o[h_{t-1},x_t]+b_o)\end{array}$$

(5)

$$\begin{array}{c}{h}_t=o_t\ast tanh\left(c_t\right)\end{array}$$

(6)

$$\begin{array}{c}{y}_t=W_o{h}_t+b_o,\end{array}$$

(7)

where $f_t$ is the forget gate at time step t, $i_t$ is the input gate at time step t, ${\tilde{c}}_t$ is the candidate memory cell at time step t, $c_t$ is the memory cell at time step t, $o_t$ is the output gate at time step t, $h_t$ is the hidden state at time step t, and $y_t$ is the output at time step t. Also, $W_x$ and $b_x$ are the weights and biases of the respective gate(x) neuron. Lastly, tanh is the hyperbolic tangent activation function. Figure 3 shows the architecture of LSTM cell.

2.3. Model Development

The initial step in constructing the predictive models involves defining and addressing a significant challenge; a data gap spanning approximately six years, where crucial information is missing from the sea level records. Filling this gap is imperative to ensure the availability of continuous and uninterrupted data for subsequent modeling and analysis. In tackling this issue, the Long Short-Term Memory (LSTM) neural network was selected as the primary tool of choice. LSTM exhibits distinct advantages in addressing temporal data gaps compared to other neural network architectures, as discussed in prior studies [20].

Furthermore, the rationale for opting for LSTM extends beyond its robustness in gap filling. LSTM possesses a remarkable capability to forecast future values with a reliance solely on historical data sequences, making it well-suited for this task. To train and evaluate the LSTM model effectively, approximately the initial 12 years of sea level records were utilized. These records were thoughtfully split into training and testing sets, with an 80% and 20% split ratio, respectively. This division resulted in a dataset comprising 3308 observations for training and 827 observations for testing, enabling a robust assessment of the model’s performance.

To facilitate the LSTM model’s learning process, the data were further organized into subsets. Each subset encompassed a specific width of information, including 365 timestamps, effectively representing one year’s worth of data as input. Subsequently, the LSTM model was tasked with predicting the sea level values that followed this width of information. A visual representation of this subset processing approach can be observed in Figure 4, which provides insight into the structure of the first two subsets used in the training and evaluation of the model. This comprehensive data preprocessing and model setup lay the foundation for addressing the critical data gap challenge and developing a robust sea level prediction framework.

In order to find the optimal hyperparameters or the ideal neural network structure, Random Search Tuner was employed, enabling the exploration of random combinations of hyperparameters until an optimal neural network configuration was attained. The optimal number of epochs was determined through the application of early stopping, which is a technique used to prevent overfitting during training. Early stopping monitors the validation loss during training, and when it starts to increase, it stops training to prevent the model from becoming too specialized to the training data. It is noteworthy that the research commenced with the imperative task of addressing a significant data gap, a factor that profoundly shapes the research direction. Following the gap-filling process, a unified dataset comprising approximately 15 years of actual observational data and 7 years of predicted data was created. This 22-year dataset formed the basis for a subsequent neural network model, which also employed the same gap-filling technique, ensuring data continuity. As a pivotal component of the methodology, it’s important to highlight that during the second modeling phase, a significant adjustment occurred in the input configuration. This adjustment held remarkable importance as it allowed the model to effectively capture and adapt to the evolving patterns and changing rates within the sea level data.

The decision to modify the input configuration resulted from a meticulous trial-and-error process. This iterative approach was instrumental in ensuring that the model could seamlessly process smaller subsets of data, thereby extending its capacity to predict sea level measures beyond the initial dataset. This adjustment was a strategic response to maintain the model’s ability to accurately capture patterns and fluctuations in the sea level data.

The analysis focused on the period spanning from 1993 to 2021, widely recognized as the starting point in tidal record studies, aligning with the initiation of tidal data collection through the TOPEX/Poseidon satellite mission, which commenced data recording in late September 1992 [22]. The linear yearly trend of both models was calculated and compared to the linear trends of NOAA/NESDIS/STAR Laboratory for Satellite Altimetry (LSA) data and other research in the region. The performance of the results of the sea level prediction models was measured by the Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) using the following formulas:

$$\begin{array}{c}RMSE=\sqrt{\frac{{\sum }_{i=1}^n{(y_i-\widehat{y_i})}^2}{n}}\end{array}$$

(8)

$$\begin{array}{c}MAPE=\frac{1}{n}\sum _{i=1}^n\frac{|y_i-{\widehat{y}}_i|}{y_i},\end{array}$$

(9)

where y is the original sea level record, ŷ is the predicted sea level value, and n is the number of data points.

3. Results

LSTM learns from taking a block of historical patterns while predicting a future pattern [23]. This concept was shown in the first phase of this research; LSTM learned from the sea level information from 1985 to 1997 and then applied a data imputation procedure which filled the gap from 1997 to the end of 2003. Due to the limited and noisy nature of the data, the model struggled to capture the sharp spikes in the records’ pattern. However, it successfully followed a similar historical pattern, maintaining seasonality consistent with the original data, as illustrated in Figure 5. However, for long-term analysis, the yearly linear trend of both real and predicted values was determined and compared to the yearly linear trend measured by the National Oceanic and Atmospheric Administration (NOAA). When averaging the entire set of actual and predicted values into yearly records, it is demonstrated that the model’s generated pattern closely resembles the information from NOAA, Figure 6. When contrasting the two sets, it becomes evident that there is a slight sea-level rise between 2000 and 2002. This rise, as shown in Figure 6, was entirely generated by the model based on historical patterns, and notably resembles a similar slight increase observed in NOAA data during the same period. This finding may lend support to the model’s robustness in capturing historical sea-level trends. The linear trend of the model’s results is 2.71 ± 1.11 mm per year, which is close to the linear trend of 2.79 ± 2.78 mm per year extracted from NOAA satellite measures. This convergence of the two trend values brings the model’s results to a point where further modeling can proceed. This is due to two justifications; the first one is that it can complete the set, making it compatible with further modeling and simulations, and the second one is keeping the rate of change as close as real records. This first modeling phase revealed an RMSE value of 63.4 mm and MAPE value of 3.14%. The error values were not comparable to other studies. However, given that it is a small value compared to the range of the recorded sea level values, it is a low error which indicates that the performance of the modeling can be considered robust.

Similarly, the same approach as the first modeling phase was again applied. However, it is essential to be aware that, for this second phase, the model is retrained with a mix of real and predictive values. This fact could influence the performance of the prediction, yet the seasonality and the linear trend were examined to ensure the robustness of the model. It is also essential to know that, for the second modeling phase, the input size changed from one year of information to half a year of information. This minor adjustment was necessary so the model could still carry out the pattern and the changing rate. A trial-and-error process accomplished this step, making the training duration longer since it is processing smaller subsets. As a result, the model could predict sea level measures beyond 2007, showing a similar sea change pattern as shown in Figure 7. In this scenario, the model’s RMSE was 66.5 mm and the MAPE was 3.07%, which is not that different from the first phase error values. However, similar to the previous model, this approach failed to capture spikes. This might be resolved by several aspects, such as increasing the training data and adjusting the regularization techniques. The yearly linear trend of this approach was 2.82 ± 0.47 mm per year. However, a difference between the trends could be found when comparing the period from 1993 to late 2020. NOAA’s linear trend within the same period is 4.59 mm per year. Many factors could cause this difference in the trends, and one important one is not specifying an exact location. In addition, the trend of the model is measured by only sea level records of Mina Salman station, while NOAA’s trend is an averaged value derived from multiple altimeters covering the entire Arabian Gulf basin. However, when comparing the results of Al-Subhi and Abdulla [24], which showed a rate of change of 2.92 mm per year from 1993 to 2019, it can be seen that this research approach showed a 2.82 mm per year rate of change, shown in Figure 8. This helps to support the robustness of the technique. A comprehensive summary of all findings has been compiled within

Table 1. Results summary.

Phase #	Gap Size	Model’s Trend	Trend from Alternative Sources	RMSE	MAPE
1	6 Years	2.71 ± 1.11 mm/yr	2.79 ± 2.78 mm/yr (NOAA)	63.4 mm	3.14%
2	13 Years	2.82 ± 0.47 mm/yr	4.59 ± 0.4 mm/yr (NOAA) 2.92 mm/yr [24]	66.5 mm	3.07%

.

4. Conclusions

This present study aimed to explore and investigate utilizing neural networks to obtain a sea level predictive model that can fill gaps in recorded observations and predict future sea levels. The LSTM approach was able to complete missing data of a gap of 6 years while keeping a similar historical sea level pattern, and it maintained a rising sea level rate of change. It also populated sea level records of approximately 13 years beyond 2007 using a mix of real and previously predicted information. Therefore, this model can potentially be useful in areas like coastal planning and infrastructure development and contribute to climate change studies. Some limitations that should be acknowledged for further studies are present in this research. This study dropped short periods of missing information to simplify the approach. However, the study’s final findings might slightly enhance the model’s performance if the small missing periods were completed by regression or interpolation. Another limitation is using a Random Search tuner; despite its efficiency, it is completely random and might never reach an optimal network structure. The Grid Search tuner provides a superior solution if time constraints are not a primary concern. Additionally, it is essential to clarify that noise reduction was intentionally omitted in this study to assess the LSTM model’s performance under noisy data conditions, and applying a noise reduction technique might improve the performance of the LSTM model [25]. In this study, it is important to acknowledge that the error indicators used may not provide a complete assessment of model performance. Additionally, depending solely on the examination of linear trends may be insufficient for a comprehensive evaluation of the models. To ensure the reliability and robustness of the forecasting models, it is essential that comparisons are made with other forecasting tools. Furthermore, the use of data from various locations can significantly enhance the accuracy and reliability of the results, contributing to a more comprehensive and rigorous analysis. This study is notable for introducing a model that only focuses on sea level data within the Arabian Gulf, without factoring in external variables like meteorological parameters. This research takes a unique approach by applying neural networks to examine sea level trends within the Arabian Gulf, an area where such a method has been less commonly explored. This application of neural networks offers a meaningful contribution to the understanding of sea level dynamics within this specific geographic region.