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Water Level Time Series Forecasting Using TCN Study Case in Surabaya

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Climate change is causing water levels to rise, leading to detrimental effects like tidal flooding in coastal areas. Surabaya, the capital of East Java Province in Indonesia, is particularly vulnerable due to its low-lying location. According to the Meteorological, Climatological, and Geophysical Agency (BMKG), tidal flooding occurs annually in Surabaya as a result of rising water levels, highlighting the urgent need for water level forecasting models to mitigate these impacts. In this study, we employ the Temporal Convolutional Network (TCN) machine learning model for water level forecasting using data from a sea level station monitoring facility in Surabaya. We divided the training data into three scenarios: 3, 6, and 8 months to train TCN models for 14-day forecasts. The 8-month training scenario yielded the best results. Subsequently, we used the 8-month training data to forecast 1, 3, 7, and 14 days using TCN, Transformers, and the Recurrent Neural Network (RNN) models. TCN consistently outperformed other models, particularly excelling in 1-day forecasting with coefficient of determination () and RMSE values of 0.9950 and 0.0487, respectively.
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JOIN (Jurnal Online Informatika)
p-ISSN: 2528-1682, e-ISSN: 2527-9165
Volume 9 Number 1 | June 2024: 61-69
DOI: 10.15575/join.v9i1.1312
61
Water Level Rise Forecasting Using TCN Study Case in
Surabaya Coastal Area
Deni Saepudin1, Egi Shidqi Rabbani2, Dio Navialdy3, Didit Adytia4
1,2,3,4School of Computing, Telkom University Bandung, Indonesia
Article Info
ABSTRACT
Article history:
Received February 28, 2024
Revised March 17, 2024
Accepted March 18, 2024
Available Online April 23, 2024
Climate change is causing water levels to rise, leading to detrimental
effects like tidal flooding in coastal areas. Surabaya, the capital of East
Java Province in Indonesia, is particularly vulnerable due to its low-lying
location. According to the Meteorological, Climatological, and
Geophysical Agency (BMKG), tidal flooding occurs annually in Surabaya
as a result of rising water levels, highlighting the urgent need for water
level forecasting models to mitigate these impacts. In this study, we
employ the Temporal Convolutional Network (TCN) machine learning
model for water level forecasting using data from a sea level station
monitoring facility in Surabaya. We chose the TCN due to its ability to
capture long-range dependency in sequential data and its ease of
implementation. We divided the training data into three scenarios: 3, 6,
and 8 months to train TCN models for 14-day forecasts. The 8-month
training scenario yielded the best results. Subsequently, we used the 8-
month training data to forecast 1, 3, 7, and 14 days using TCN,
Transformers, and the Recurrent Neural Network (RNN) models. TCN
consistently outperformed other models, particularly excelling in 1-day
forecasting with coefficient of determination () and RMSE values of
0.9950 and 0.0487, respectively. The contribution of the study is the
development of deep learning TCN to predict water levels in coastal
areas of Surabaya, which has the potential to be implemented in other
locations in Indonesia.
Keywords:
Water level rise
Coastal area
Water level forecasting
Machine learning
TCN
1. INTRODUCTION
The increase in water levels is one of the many changes caused by climate change [1]. Although
this rise happens slowly, it is happening faster now and has serious impacts [2], [3], and [4]. Due to their
typical flat terrain and low elevations close to the water's surface, coastal areas are particularly
vulnerable to the rise in water levels [5]. Surabaya, the capital city of East Java, predominantly lies in a
low-lying area with altitudes ranging from 3-6 meters above water level, while its southern part exhibits
higher elevations, reaching 20-50 meters above water level [6]. According to the Meteorological,
Climatological, and Geophysical Agency (BMKG), Surabaya's coastal areas experience tidal flooding
every year due to rising water levels [5]. In some years, the risk of flooding is four to five times higher
than usual. This poses a serious threat to the coastal community. To prevent further losses, it is essential
to take measures against tidal flooding caused by water level rise, and one effective approach is through
water level forecasting.
Water level forecasting is important to help us predict how water levels will increase in the
future, allowing us to minimize the impact of rising water levels, such as flooding in coastal areas [7].
Water level data is also essential for port operations, particularly in scheduling ship transportation and
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p-ISSN: 2528-1682
e-ISSN: 2527-9165
Water Level Time Series Forecasting Using TCN Study Case in Surabaya
(Deni Saepudin1, Egi Shidqi Rabbani2, Dio Navialdy3, Didit Adytia4)
62
managing port services efficiently [8]. Additionally, past records of water level are fundamental for the
design and construction of coastal and offshore infrastructure, while precise forecasts of water level are
indispensable for planning and executing construction activities for these structures [9]. Tidal Harmonic
Analysis (THA) is a traditional method for water level forecasting. It involves decomposing water level
data into harmonic components using the Least Squares Estimation (LSE) based on observed data.
However, THA is limited to predicting only tidal components and relies on extensive historical data [10].
Various approaches have been suggested to enhance the accuracy of THA in water level
forecasting, such as employing multivariate least-squares harmonic estimation [11] and integrating the
LSE method with the Inaction Method (IM) [12]. For water level prediction, other methods based on time
series analysis have also been used. These include ARIMA (Autoregressive Integrated Moving Average)
[13], SARIMA (Seasonal Autoregressive Integrated Moving Averaged) [14], and Holtz-Winters
Exponential Smoothing [15]. ARIMA achieved a root mean square error (RMSE) of 0.270 for one-day-
ahead prediction, while SARIMA and the Holt-Winters approach yielded RMSE values of 0.155 and 0.134,
respectively, for seven-day-ahead forecasting. These results highlight the ongoing need to identify a
model capable of achieving greater forecasting accuracy. An effective strategy for enhancing predictive
models involves leveraging machine learning, a relatively novel approach. Ishida et al. (2020) [16]
conducted a study in which they looked at the use of machine learning for forecasting water levels.
Specifically, Long Short-Term Memory (LSTM) was employed to forecast water levels at the Osaka
Gauging Station in Japan, resulting in the highest accuracy with an Nash-Sutcliffe efficiency (NSE) value
of 0.720 for the forecasting period of 2016-2018. In a study conducted by Pan et al. (2020) [17], a model
combining Gated Recurrent Unit (GRU) and Convolutional Neural Network (CNN) was developed for
precise water level forecasting. The results showed that the GRU-CNN model did better than other
machine learning models, even the LSTM model. It had the highest accuracy, with an NSE value of 0.9966
for a 5-day forecasting period. While GRU and CNN models offer high forecasting accuracy, they suffer
from a notable drawback: high memory requirements during training. However, in 2018, Bai et al.
introduced a solution to this issue with their Temporal Convolutional Network (TCN), which features
shared filters across a layer, resulting in reduced memory requirements [18]. As a result, TCN holds
promise for accurate water level forecasting.
Temporal Convolutional Network (TCN), which was introduced by Bai et al. in 2018, is a deep
neural network architecture designed for processing time series data [19], [20]. TCN has been widely
employed in various time series challenges, consistently demonstrating strong performance and
yielding favorable outcomes. A study conducted by Hewage et al. in 2020 [21] explored the use of TCN
for weather forecasting using data collected from local weather stations. The findings revealed that TCN
outperformed LSTM and other traditional machine learning methods in terms of forecasting accuracy.
Benitez et al. (2020) employed the Temporal Convolutional Network (TCN) to forecast energy demand
in Spain, demonstrating its superior forecasting accuracy compared to LSTM models [22]. While TCN
has shown promising accuracy in numerous forecasting applications, its adoption for water level
prediction remains limited.
The objective of this paper is to design a precise water level forecasting model using machine
learning techniques. Specifically, we employ Temporal Convolutional Networks (TCN) for this purpose
and compare its performance with other contemporary machine learning models, including
transformers and RNN. The selected case study is Surabaya in Indonesia, characterized by its low-lying
terrain, where the coastal areas are prone to tidal flooding due to rising water levels [5]. The
contribution of this research is to find a better algorithm to predict the water level that could be
implemented in other locations in Indonesia due to the many cities with similar conditions.
2. METHOD
2.1. Design System
In this study, we utilized water level data obtained from the sea level monitoring facility
provided by UNESCO for the location of Surabaya, Indonesia. During pre-processing, we addressed
spikes and outliers within the data and handled missing values through interpolation. Subsequently, the
dataset was divided into training and testing subsets, and the TCN model was trained using the training
data. The model was then evaluated for forecasting performance, with several scenarios tested, varying
the forecast horizon from 1 to 14 days. If the forecasting accuracy doesn’t meet the expected result,
hyperparameter tuning is conducted to improve model performance. Finally, we compared the
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forecasting accuracy of the TCN model with other machine learning models using the coefficient of
determination and Root Mean Squared Error metrics. These steps are illustrated in Figure 1.
Figure 1. Flowchart of the TCN-based water level forecast
2.2. Water Level Data
The water level data utilized in this study was sourced from the sea level station monitoring
facility provided by UNESCO. The station is situated in the northern region of Surabaya, Indonesia, with
coordinates between -7.19996944 latitude and 112.74058611 longitude, as depicted in Figure 2. This
dataset is publicly accessible online through the following link: https://www.ioc-
sealevelmonitoring.org/station.php?code=sura.
Figure 2. Location of the water level station monitoring facility in Surabaya
2.3. Pre-Processing
To ensure the reliability and usability of the water level data, we conducted a series of
preprocessing steps. These steps were designed to handle missing values, outliers, and spikes, as well as
to resample and interpolate the data. This process aimed to generate high-quality input data suitable for
the machine learning model.
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p-ISSN: 2528-1682
e-ISSN: 2527-9165
Water Level Time Series Forecasting Using TCN Study Case in Surabaya
(Deni Saepudin1, Egi Shidqi Rabbani2, Dio Navialdy3, Didit Adytia4)
64
The raw water level data can be seen in Figure 3. It is recorded at three-second intervals,
spanning from March 1, 2023, to December 25, 2023. In water level forecasting, utilizing such detailed
period intervals in the data may introduce unnecessary harmonic components, potentially impacting
forecasting accuracy. To address this, we transformed the raw water level data into hourly intervals.
Figure 3. Plot of raw water level data in Surabaya
Next, we established threshold values to detect spikes within the data. The first threshold value
was determined by adding three times the standard deviation to the mean water level, while the second
threshold value was determined by subtracting three times the standard deviation from the mean water
level. Any water level exceeding the first threshold value or falling below the second threshold value was
identified as a spike, and these spikes were subsequently removed. Subsequently, rolling window
statistics are computed to evaluate the median and standard deviation of the water level using a 6-hour
window. Through this process, outliers are identified and subsequently removed, enhancing the
dataset's reliability. However, addressing spikes and outliers in the data leads to the creation of
additional missing values. To that end, we identified empty values within the dataset to pinpoint periods
of missing data. The plot displaying the water level data alongside the flagged missing values is depicted
in Figure 4.
Figure 4. Plot of resampled water level data with flagged missing values (red bars)
The final step of data pre-processing involves addressing missing values through cubic
interpolation, resulting in the processed data depicted in Figure 5. Additionally, the preprocessed data
is partitioned into training and testing datasets, as illustrated in Figure 6. We partitioned the training
dataset into three distinct periods: 3 months (from September 11, 2023, to December 11, 2023), 6
months (from June 11, 2023, to December 11, 2023), and 8 months (from April 11, 2023, to December
11, 2023). This division aims to evaluate the sensitivity of the training data to the model's performance
and optimize the training dataset for improved model accuracy.
Figure 5. Plot of the processed hourly water level data with no missing values
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Figure 6. Plot of data splitting with training periods of 8 months (top), 6 months (middle) and 3 months (bottom)
2.4. Temporal Convolutional Neworks (TCN)
In recent years, Temporal Convolutional Networks (TCN) have gained attention as a robust
solution for analyzing sequential data by effectively capturing temporal patterns and long-term
dependencies. The unique architecture of TCN incorporates several essential components, including
causal and dilated convolution and residual connections, which enhance its effectiveness [23].
2.4.1. Causal Convolutions
One notable feature of TCN is its utilization of causal convolution, ensuring that the network's
output at each time step relies solely on past inputs. This property is particularly beneficial for tasks
involving sequential data, as it prevents information leakage from future time steps.
2.4.2. Dilated Convolutions
Wang et al. (2023) [23] explained that adding more than one causal convolutional layer can
make the network more receptive, but it can also cause gradient problems in longer sequences. To tackle
this, TCN introduces dilated convolutions, which progressively expand the network's receptive field.
Dilated convolution samples the input of the upper layer at intervals, with the dilation rate growing
exponentially based on 2. This method allows for a broader receptive field with fewer network layers.
The computation formula for dilated convolution is represented as follows:
󰇛󰇜󰇛 󰇛󰇜󰇛󰇜


󰆚
(1)
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p-ISSN: 2528-1682
e-ISSN: 2527-9165
Water Level Time Series Forecasting Using TCN Study Case in Surabaya
(Deni Saepudin1, Egi Shidqi Rabbani2, Dio Navialdy3, Didit Adytia4)
66
In this context, the rate of dilation is referred to as , the size of the filter is denoted as , and 
represents the convolution of the previous state. This approach effectively decreases network
complexity while improving computational efficiency. Moreover, the architecture of dilated
convolutions can be illustrated, as depicted in Figure 7 [24].
Figure 7. Architecture of dilated convolutions with = 1, 2, 4 and = 3
In this study, we employ the TCN machine learning model to design a water level forecasting
system. Details of the TCN configuration are provided in Table 1.
Table 1. The configuration of TCN
Model
Model Setting
TCN
Layer = 1 (5 hidden layer)
Batch size = 32
Epoch = 10000
Patient = 10
Activation = linear
Optimizer = adam(1e-3)
Loss = huber
2.5. Peformance Metrics
To determine the model with the best forecasting accuracy, we utilize the coefficient of
determination () and Root Mean Squared Error (RMSE) as performance metrics. The coefficient of
determination (), a commonly used quantitative metric for evaluating a model's predictive capability,
ranges from 0 to 1 [10]. The formula for is as follows (2-4):


(2)
󰇛
 󰇜
(3)
󰇛󰇛
󰇜󰇜


(4)
In Equation (2)-(4), RSS is Residual Sum of Squares, while TSS represents Total Sum of Squares. Here,
denotes the individual observed value, represents the total number of data points, and
represents
the predicted value [10].
The RMSE serves as a measure to assess the average error's magnitude. The formula for RMSE
is as follows [25]:
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
󰇛󰇜

(5)
3. RESULT AND DISCUSSION
In this section, we conduct water level forecasting using data from the water level station
monitoring facility in Surabaya, Indonesia. To optimize the model's performance, we divide the training
data into several scenarios to assess their sensitivity. These scenarios consist of periods spanning 3
months (from September 11, 2023, to December 11, 2023), 6 months (from June 11, 2023, to December
11, 2023), and 8 months (from April 11, 2023, to December 11, 2023). Each scenario is then utilized as
training data for the TCN model to generate 14-day forecasts (from December 11, 2023, to December
25, 2023). The best results can be seen in Table 2, which shows that using a training dataset that spans
8 months gives the highest coefficient of determination () and lowest RMSE values of 0.9903 and
0.0613, respectively.
Table 2. Table result of TCN 14 days forecasting with various scenarios
Length of Training Data
Coefficient of Determination ()
RMSE
3 Months
0.7569
0.3065
6 Months
0.9453
0.1454
8 Months
0.9903
0.0613
Subsequently, employing an 8-month training dataset, we conducted forecasting for 1, 3, 7, and 14 days
using TCN forecasts (from December 11, 2023, to December 25, 2023). Additionally, we employed other
machine learning models, specifically Transformers and RNN, for comparison to determine their relative
performance compared to TCN. The findings indicate that TCN outperforms Transformers and RNN in
water level forecasting. These comparative results are presented in Table 3.
Table 3. Table result of 1 to 14 days of forecasting using various models
Forecast
(Day)
Transformers
RNN
TCN
RMSE
RMSE
RMSE
1
0.9727
0.1135
0.9688
0.1213
0.9950
0.0487
3
0.9763
0.1112
0.9639
0.1372
0.9925
0.0626
7
0.9755
0.1109
0.9665
0.1296
0.9914
0.0656
14
0.9587
0.1263
0.9650
0.1162
0.9903
0.0613
Table 3 shows that TCN outperforms other models in forecasting accuracy, especially as the
forecast duration shortens. Notably, TCN achieves its highest accuracy when predicting 1 day ahead,
with impressive and RMSE values of 0.9950 and 0.0487, respectively. The forecasting accuracy of
TCN becomes more evident when considering qualitative results. Figure 8 illustrates the 14-day
forecasting outcomes from the Transformers, RNN, and TCN models. Notably, TCN consistently
demonstrates accurate forecasting across all time points, unlike Transformers and RNN, which
encounter challenges on specific days.
Figure 8 demonstrates the poor performance of the Transformers and RNN models in predicting
data around peak points and valley points. Transformer and RNN models underestimate most data
around peak points and valley points generally. Otherwise, the TCN model provides closer estimation
results around peak and trough points.
One of the problems that usually occurs in coastal areas such as Surabaya is tidal flooding due
to peak sea tides. Therefore, better predictions for data around peak points will provide very useful
information for anticipating the impact of extreme tides. This is the contribution of this study, where the
TCN model succeeds in estimating the peak point more closely than the Transformer and RNN models,
which tend to underestimate points around the peak. Given that numerous other coastal locations in
Indonesia are facing comparable water level issues, these results hold promise for predicting potential
sea level rise over an extended period.
JOIN (Jurnal Online Informatika)
p-ISSN: 2528-1682
e-ISSN: 2527-9165
Water Level Time Series Forecasting Using TCN Study Case in Surabaya
(Deni Saepudin1, Egi Shidqi Rabbani2, Dio Navialdy3, Didit Adytia4)
68
Figure 8. 14 days forecasting results from Transformers (top), RNN (middle) and TCN (bottom) using 8 months training period
4. CONCLUSION
In this study, we design a water level forecasting model using machine learning techniques,
specifically TCN, and compare its performance with other models such as Transformers and RNN.
Initially, we partitioned the training data into three scenarios spanning 3 months, 6 months, and 8
months to assess the sensitivity of the training data and optimize input for the TCN model. Each scenario
serves as input for the TCN model to conduct 14-day forecasting. The results indicate that the 8-month
training data scenario yields the most favorable outcomes. Subsequently, utilizing an 8-month training
dataset, we conduct 1, 3, 7, and 14-day forecasting using TCN, Transformers, and RNN models. The
results show that TCN consistently does better than the other models at all forecasting intervals. It is
most accurate at 1-day forecasting, with an value of 0.9950 and an RMSE value of 0.0487. For future
research, leveraging a larger dataset could enhance the validation of TCN's accuracy. Additionally,
conducting comparisons with other machine learning models, such as XGBoost, could provide further
insights into evaluating the TCN model's performance.
ACKNOWLEDGEMENTS
This research was funded by Telkom University NO. 659/PNLT3/PPM/2023.
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Neural Network Approach,” Marine Geodesy, vol. 42, no. 4, pp. 344366, 2019, doi: 10.1080/01490419.2019.1626306.
Conference Paper
The implications of sea level fluctuations, mostly attributed to global warming, pose significant challenges for naval operations, navigation, coastal economies, and infrastructure resilience. Accurate sea-level prediction is vital to mitigate these challenges, particularly in areas prone to tidal flooding and infrastructure damage. This study introduces a cutting-edge deep-learning model, iTransformer, for sea level prediction, utilizing six months of data with four months allocated for training and two months for validation and testing. The dataset used originates from Singaraja, Bali, Indonesia, and projects sea levels over a 14-day timeframe. Our findings reveal that iTransformer outperforms both Temporal Convolutional Networks (TCN) and Transformer models in terms of prediction accuracy and has a significant amount of short-term computational efficiency. iTransformer achieves the prediction score with an RMSE of 0.0041 for the 24-hour, 0.0415 for the 48-hour, and 0.0455 for the 96-hour. MAE of 0.0489 for the 24-hour, 0.0323 for the 48-hour, and 0.0368 for the 96-hour, and R2 scores of 0.9713 for the 24-hour, 0.9882 for 48-hour, and 0.9863 for the 96-hour prediction windows, respectively. Furthermore, iTransformer demonstrates lower computational times, requiring only 0.1 minutes for a 24-hour window and 0.3 minutes for a 48-hour window. These results underscore iTransformer's potential as a robust model for sea level prediction and indicate that its application could be extended to multivariate datasets to enhance performance.
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