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Predicting coastal variations in non-storm conditions with machine learning

  • Amir Jabari , Mehdi Adjami EMAIL logo and Saeid Gharechelou
Published/Copyright: April 7, 2025
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Open Geosciences
From the journal Open Geosciences Volume 17 Issue 1

Abstract

Coastal erosion, driven by natural factors and human activities, is a major threat to vulnerable regions like Narrabeen, Australia. This study investigates shoreline changes, berm crest elevation variations, and horizontal berm crest positions under non-storm conditions. Using a decision tree algorithm, key features influencing these phenomena were identified. For shoreline changes, berm width changes (∆BW), berm slope, sea level rise (SLR), and wave breaking index (ζ) were critical. Berm crest elevation was linked to BC height, ∆xShoreline, ∆xBC, and wave power (P), while horizontal berm crest positions were influenced by BW, berm slope, ∆yBC, BC height, wave energy (E), SLR, and ζ. The feedforward neural network (FNN) algorithm was then applied to predict these objectives. Shoreline changes were predicted with a root mean squared error (RMSE) of 3.3 m and R 2 of 92% (DS4 scenario). Berm crest elevation predictions achieved an RMSE of 0.35 m and R 2 of 75% (DY4 scenario), while horizontal berm crest positions reached an RMSE of 9.28 m and R 2 of 85.8% (DX7 scenario). These results demonstrate that parameter classification via decision trees enhances neural network predictions. The FNN proved to be a reliable tool for forecasting coastal dynamics, supporting effective monitoring and management strategies.

Graphical abstract

Keywords: coastal berm; coastal morphodynamic; non-storm condition; decision tree algorithm; artificial neural network

1 Introduction

Coastal areas are among the most densely populated and developed regions globally. This is due to high economic opportunities, maritime trade access, and a thriving tourism industry. However, these regions represent vulnerable environments facing threats such as storms and rising sea levels, predominantly resulting from human activities. These activities pose significant risks to the resident population, existing infrastructure, and the environment. Erosion is one of the most pressing threats to these regions. Erosion refers to the gradual loss of land due to natural forces such as waves, currents, and wind, as well as human activities like construction. This phenomenon significantly impacts the stability of coastlines, infrastructure safety, and surrounding ecosystems’ health. Thus, it is crucial to monitor these areas continuously, record beach profile changes, shoreline alterations, and control erosion.

Numerous studies have been conducted in this field. Alves et al. demonstrated in their study along the West African coasts that implementing a regional segmentation system and regular monitoring can establish a sustainable approach to coastal area management [1]. Puplampu et al. found in their investigations along the Eastern Ghana coasts that erosion rates in these areas were notably high, emphasizing the necessity of continuous surveillance coupled with ecosystem-based strategies for sustainable coastal management [2]. Ahmed et al. recommended monitoring erosion levels in parts of the Indian coast using satellite imagery to properly manage these areas [3]. Similarly, Baig et al. evaluated monitoring and managing Bangladesh’s Eastern coast as essential for erosion control [4]. In their study, Zollini et al. demonstrated that the J-Net dynamic algorithm is a powerful tool for accurately extracting shoreline positions, aiding in better coastal area management [5]. Other research efforts have introduced protective structures as an effective measure to control erosion [6,7]. Fernández-Montblanc et al. proposed coastal dune reconstruction through an increased sediment budget as an effective strategy to reduce erosion and associated hazards on the Blue Bay coast of Italy, suggesting its suitability as a viable solution for combating future sea-level rise [8]. Additionally, Flor-Blanco et al. evaluated the geomorphological changes along the Asturias coast in Spain from 1992 to 2014. The results indicate that intense storms are the primary catalyst for severe coastal dune erosion [9]. Lemke and Miller addressed the role of storm intensity and coastal vulnerability in controlling dune erosion, identifying peak erosion intensity (PEI) as the most significant factor influencing coastal dune changes [10]. Harley et al. showcased, in their research, spanning data retrieved from severe storms in regions such as Australia, Britain, and Mexico, that limited information on short-term sediment budgets during severe storms is a crucial parameter for enhancing confidence in shoreline predictions [11]. Zheng et al. introduced the importance of considering wave-induced processes such as currents, convergence, asymmetry, and bed slope effects for accurate sediment transport predictions [12]. Moreover, other studies have been conducted on sediment transport and erosion control in coastal areas [13,14].

Advancements in machine learning, the development of new algorithms, and extensive laboratory, field, and numerical research have greatly enhanced a deeper understanding of coastal areas. Numerous scientific research sites collect long-term environmental and field data in coastal regions of the Netherlands, England, the United States, Australia, and other countries, leading to valuable studies by coastal science researchers in recent years. Pearson et al. utilized the BEWARE model to estimate flood hazards on coral coasts. Bayesian networks were used to develop this model, which now incorporates the X-Beach non-hydrostatic (XBNH) model. The results demonstrated that BEWARE exhibits high skill in predicting flood conditions and has the potential to serve as a basis for early warning systems [15]. den Bieman et al. introduced a new machine learning model called XGBoost for predicting average wave run-up, showcasing better performance than other methods for datasets with regular waves [16]. Yin et al. conducted a study monitoring shoreline change in the Nha-Trang region using three models: moving average, neural network regression, and long short-term memory, compared to an empirical orthogonal function model. All three models ultimately outperformed the empirical model, proving to be highly effective, particularly in severe weather conditions when aided by surveillance cameras [17]. Additionally, Bellinghausen et al. predicted extreme sea conditions along the Baltic coasts 3 days in advance using the Random Forest algorithm, yielding satisfactory results. They concluded that this algorithm could serve as a maritime alert system [18]. Gomez-de la Peña et al. found that deep learning methods predict shoreline changes better than traditional approaches [19]. Rodriguez-Galiano et al. classified coastlines along the Andalusian coast of Spain from 1956 to 2011 based on erosion and sedimentation patterns. They used classification and regression trees to identify threshold values for these patterns and achieve the highest classification accuracy [20]. Moreover, review articles on machine learning applications in coastal processes have been presented by researchers [21,22]. Further related research has been conducted using machine learning algorithms [23,24,25,26,27,28,29].

Various databases worldwide are actively recording morphodynamic and hydrodynamic data and monitoring coastlines. Locations such as Narrabeen, San Diego, and others are subsets of these databases. Beuzen et al. compared three primary discretization methods (manual, unsupervised, and supervised) within a Bayesian network for predicting coastal erosion along the Narrabeen coast. According to the findings, supervised methods had the highest predictive skill, followed by manual and unsupervised approaches [30]. Another study by Beuzen et al. focused on changes in the Narrabeen shoreline, leveraging Bayesian algorithms to predict and describe storm events. The outcomes showcased the Bayesian model’s capability to define and forecast complex coastal processes. The descriptive section’s output values consist of five parameters with an 85% skill level, whereas the predictive segment includes three parameters with a 65% skill level in data observation [31]. In their research along the Narrabeen coast, Zeinali et al. found that using artificial neural networks such as NARNET and NARXNET can provide reliable performance in predicting shoreline changes with fewer parameters [32]. Harley et al. also presented a substantial storm-induced erosion dataset. This dataset comprises 276 storm events along the Narrabeen–Collaroy coasts and accurately predicts erosion caused by storms using a multiple linear regression model [33].

The introduction underscores the susceptibility of coastal regions to erosion and other environmental hazards, highlighting the critical need for effective monitoring and management strategies. Advances in technology, particularly in machine learning, have significantly improved the analysis and prediction of coastal dynamics under varying conditions. While many studies have primarily focused on storm-induced changes, this research pivots to examining non-storm conditions, which are more frequent and play a crucial role in shaping long-term coastal trends.

This research focuses on changes that occur under non-storm conditions, which are more frequent throughout the year and significantly impact long-term coastal trends. Due to the stability of these conditions, accurate predictions can contribute to better coastal management and improved prediction models for storm scenarios. This study employs machine learning algorithms to predict changes in the berm crest and shoreline variations under non-storm conditions. Studies indicate that long-term predictions of coastal berm changes using machine learning algorithms have not been extensively explored, with most research concentrating on hydrodynamic sea studies and shoreline changes during storm conditions. One of the most relevant studies was conducted by Beuzen et al. [31], which described the parameters influencing the geometry of the Narrabeen coast and predicted general coastal changes (examining volumetric changes in internal coastal zones) using a Bayesian algorithm during and after storm events.

2 Materials and methods

2.1 The study area

Australia’s southeast coast comprises more than 700 embayed sandy beaches, with an average length of 1.3 km, that are separated by headlands. The Narrabeen–Collaroy embayment, spanning 3.6 km, is located on the northern shores of Sydney. Narrabeen lies in the northern section, while Collaroy occupies the southern part of the embayment. The grain size distribution along the coastline is relatively uniform, characterized by fine to medium quartz sand (D 50 ≅ 0.3 mm). In areas like Narrabeen–Collaroy, energy gradients vary along the coast due to curvature. The northern region has moderate dissipative energy conditions, but moving toward the south, the conditions change to moderate reflective energy because of decreased energy. In the northern section of Narrabeen–Collaroy, sandy dunes reach up to 9 m above sea level, accompanied by vegetation cover. In the southern section, urban development toward the coast has reduced the height of these dunes and their vegetation cover to approximately 3–4 m. Narrabeen–Collaroy is among the most crucial databases in coastal engineering. Field data from the nearshore and coastal strip have been collected in this database from 1976 to 2019 [34]. Narrabeen Beach’s ongoing efforts include extracting images through video monitoring and LiDAR imaging [35]. According to the data in this database, several other research works have been conducted [34,36,37,38]. Figure 1 shows Narrabeen–Collaroy Beach in Australia, highlighting the locations of the deep-water buoy and cross-shore profiles within this coastal area. The left image represents these profiles, labeled as “PF” for “Profile,” where data collection along the Narrabeen coastline is carried out at these specific locations.

Figure 1 Location of the Narrabeen–Collaroy Beach, the position of cross-shore profiles and deep-water buoy (Google Earth).
Figure 1

Location of the Narrabeen–Collaroy Beach, the position of cross-shore profiles and deep-water buoy (Google Earth).

2.2 Data preparation

Data relevant to coastal engineering studies have been continuously collected at the research site of Narrabeen–Collaroy Beach between 1976 and 2019.[1] In this regard, cross-shore profiles at five lines almost spaced 900 m apart were measured monthly with an accuracy of 10 m for each profile. Measurements were taken using a meter starting in 2006, and the frequency of collection increased to more than once per month. This study used data from 2006 to 2019 (14 years) with high measurement accuracy. Figure 1 illustrates the location of coast and cross-shore profiles 1, 2, 4, 6, and 8. To minimize errors and account for changes in the northern and southern sections due to headlands, only Profiles 2, 4, and 6 were employed in this study. Cross-shore beach profiles have been extracted from the raw data and depicted in Figure 2. It is important to note that the profiles shown in each line (2, 4, and 6) represent only a small subset of all profiles recorded during the period from 2006 to 2019.

Figure 2 Bach profiles 2, 4, and 6 of the Narrabeen coast, years 2006–2019.
Figure 2

Bach profiles 2, 4, and 6 of the Narrabeen coast, years 2006–2019.

Wave data at the deep-water buoy location (Figure 1) are extracted from the European Centre for Medium-Range Weather Forecasts (ECMWF) and the ERA5 dataset[2] with a 1-h time interval [39]. Figure 3(a) and (b) display the time series of significant wave height and peak wave period. Furthermore, to better understand the 122,712-wave data, the data dispersion based on the frequency and magnitude is presented in Tables 1 and 2. The minimum and maximum wave heights are 0.48 and 5.72 m, respectively, while the maximum period ranges from 3.24 to 18.62 s.

Figure 3 The data of significant wave height and peak wave period at deep water buoy location, years 2006 to 2019. (a) Time series of significant wave height at deep water buoy location. (b) Time series of peak wave period at deep water buoy location.
Figure 3

The data of significant wave height and peak wave period at deep water buoy location, years 2006 to 2019. (a) Time series of significant wave height at deep water buoy location. (b) Time series of peak wave period at deep water buoy location.

Table 1

Significant wave height data in each profile consist of the number of observations, the range of variations, and the averages for every range in 10 m depth

Distribution
Profile 2 Range (m) <0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0<
No. of data 9,675 71,995 33,083 6,271 1,688
Average height (m) 0.34 0.78 1.17 1.69 2.34
Total recorded data 122,712
Profile 4 Range (m) <0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0<
No. of data 8,417 61,791 40,645 8,785 3,074
Average height (m) 0.33 0.79 1.19 1.70 2.39
Total recorded data 122,712
Profile 6 Range (m) <0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0<
No. of data 13,603 69,049 32,206 6,116 1,738
Average height (m) 0.35 0.76 1.18 1.69 2.37
Total recorded data 122,712
Table 2

Peak wave period data in each profile consist of the number of observations, the range of variations, and the averages for every range in 10 m depth

Distribution
Profile 2 Range (s) <4 4–6 6–8 8–10 10–12 12–14 14<
No. of data 1,481 27,841 49,275 31,841 9,106 2,372 796
Average period (s) 3.65 5.21 6.99 8.84 10.75 12.84 14.63
Total recorded data 122,712
Profile 4 Range (s) <4 4–6 6–8 8–10 10–12 12–14 14<
No. of data 1,569 23,706 44,614 37,447 11,971 2,506 899
Average period (s) 3.64 5.20 7.03 8.88 10.74 12.83 14.60
Total recorded data 122,712
Profile 6 Range (s) <4 4–6 6–8 8–10 10–12 12–14 14<
No. of data 1,385 24,415 44,195 36,081 12,602 2,911 1,123
Average period (s) 3.67 5.2 7.01 8.88 10.76 12.81 14.77
Total recorded data 122,712

Refraction occurs as waves move toward the shore, making orthogonal wave lines perpendicular to the coastline. This phenomenon leads to variations in wave characteristics from deep to shallow water. Therefore, it is desirable to consider wave data close to shore profiles and align them with each other. The SWAN code model has been employed to transfer wave data from deep to shallow water, shifting the data from a depth of 80 to 10 m and aligning it with each shore profile. This model has been evaluated, validated, and assessed for accuracy in the investigated coastal area [34]. The classified data of significant wave height and maximum wave period at positions of Profiles 2, 4, and 6 are presented in Tables 1 and 2. These tables contain the number of observations, the range of variations, and the averages for every range.

Global mean sea level rise (SLR) data from 2006 to 2019 have been extracted from the AVISO[3] database [40]. Figure 4 depicts the time series of these data.

Figure 4 Global SLR time series, years 2006–2019.
Figure 4

Global SLR time series, years 2006–2019.

As previously explained, for the modeling process, profiles under storm conditions (identified based on wave height changes and wind speed) were excluded from the dataset. Based on this criterion, 73 out of the 960 recorded profiles were classified as storm conditions. Eventually, 887 profiles were selected from 2006 to 2019 for analysis. The study first examines shoreline variations, focusing on the continuous area that consistently interacts with waves, which plays a crucial role in evaluating model and algorithm performance. Following this, the geometric changes of the coastal berm within the shoreface zone are analyzed. In this section, after preparing the data, the features of morphodynamics and hydrodynamics are extracted. Figure 5 depicts a beach profile schematic, including the coastal morphodynamic components, and Table 3 presents the symbols and abbreviations for morphodynamic features derived from measured beach profiles, as well as hydrodynamic features, including wave parameters and SLR.

Figure 5 Beach profile schematic, including the coastal morphodynamic components.
Figure 5

Beach profile schematic, including the coastal morphodynamic components.

Table 3

Symbols and abbreviations for morphodynamic and hydrodynamic features

Features Definition Features Definition Features Definition
Hydrodynamic features
Hs Significant wave height TP Peak wave period SLR Sea level rise
Hmean Mean wave height E Wave energy H/L Wave steepness
Hmax Maximum wave height P Wave power L Wave length
Tmean Mean wave period ζ Iribarren
Morphodynamic features
BW Berm width DT Height Dune toe height ∆xDT Horizontal changes of dune toe
∆BW Berm width changes ∆yDT Dune toe height changes ∆xShoreline Shoreline changes
Berm Slope Slope between shoreline and berm crest ∆yBC Berm crest height changes XlocDT Horizontal position of dune toe
Beach Slope Slope between shoreline and dune toe XlocBC Horizontal position of berm crest
BC Height Berm crest height ∆xBC Horizontal changes of berm crest

2.3 Machine learning algorithms

This research employed a decision tree classifier algorithm for classifying influential features. Additionally, for the prediction part, objective functions were predicted using a feedforward neural network (FNN) algorithm.

A Decision Tree (DT) is a versatile supervised learning algorithm used in both classification and regression problems. It functions by iteratively splitting the dataset based on specific feature values to maximize the distinction between different target classes. The tree is built by selecting the most informative features, measured by criteria like Information Gain, Gini Index, or Entropy, enabling accurate predictions on unseen data as it navigates from the root to a leaf node. Information Gain measures how much information a particular feature provides for classifying the data [41]. It is defined asfollows:

(1) Information Gain ( D , A ) = Entropy ( D ) − ∑ υ ∈ Values ( A ) | D υ | | D | × Entropy ( D υ ) ,

where D is the original dataset, A is the feature being evaluated, D υ is the subset of data where feature A has value υ , and Values(A) is the set of all possible values for feature A.

This equation helps determine the best feature for splitting the data at each node of the decision tree.

Artificial neural network, FNN, is a type of artificial neural network where data flows in a single direction starting from the input layer, passing through one or more hidden layers, and finally reaching the output layer without forming any cycles or loops. In an FNN, each neuron processes its inputs by calculating a weighted sum, applying an activation function, and then passing the result to the next layer. This architecture is well-suited for approximating complex nonlinear functions and is widely used in tasks such as classification and regression [42]. The y output of a neuron in a FNN is calculated as follows:

(2) y = ϕ ∑ i = 1 n ω i x i + b ,

where x i is the input, w i is the corresponding weights, b is the bias term, and ϕ is the activation function.

In the following, evaluation criteria will be employed to evaluate the performance of machine learning models. In the classification phase, metrics like F1-score and accuracy are commonly used. Accuracy measures the overall correctness of the predictions, while F1-score, a harmonic mean of precision and recall, is particularly useful for assessing models that deal with imbalanced data. Root mean squared error (RMSE), R 2 (coefficient of determination, which indicates what proportion of the variance in the dependent variable is explained by the model or independent variables), and CC% (the correlation coefficient measures the strength and direction of the linear relationship between two variables) are utilized to evaluate the model’s predictive performance. RMSE quantifies prediction errors in absolute and squared terms, respectively, while R 2 assesses the proportion of variance in the dependent variable explained by the model. They are defined as follows:

(3) Accuracy = TP + TN TP + TN + FP + FN ,

(4) F 1 -score = Precision × Rcall Precision + Rcall × 2 ,

(5) RMSE = 1 n ∑ i = 1 n ( x i − y i ) 2 ,

(6) R 2 = 1 − ∑ i = 1 n ( x i − y i ) 2 ∑ i = 1 n ( x i − x ̄ ) 2 ,

(7) CC = n ∑ x i y i − ∑ x i ∑ y i n ∑ x i 2 − ∑ x i 2 n ∑ y i 2 − ∑ y i 2 .

In equation (3), TP (True Positive) refers to the count of correctly identified positive cases, TN (True Negative) is the count of correctly identified negative cases, FP (False Positive) represents the number of cases incorrectly classified as positive, and FN (False Negative) refers to the count of cases incorrectly classified as negative. In equations (5)–(7), n represents the number of data points, x i denotes observed values, y i signifies predicted values, and x ̄ stands for the mean of observed data. Figure 6 illustrates the flowchart of this research methodology.

Figure 6 Flowchart of the research methodology.
Figure 6

Flowchart of the research methodology.

3 Data analysis and results

3.1 Physical description

Initially, from the total of 24 features encompassing morphodynamic and hydrodynamic data, those with less relevance or no correlation to the target functions were eliminated based on coastal engineering knowledge. This step ensures that the training process is conducted using pertinent and significant data. The DT algorithm was then employed to classify the selected features for each target function, allowing for the identification of the most influential parameters based on their impact. The performance of each feature in terms of its influence was evaluated using the F1-score and accuracy metrics. It is worth noting that this algorithm was used to establish relationships between the features and target functions to construct predictive scenarios.

The results of the DT algorithm for all three targets consisting of shoreline changes, Berm Crest elevation variation, and the horizontal position of the Berm Crest, are presented subsequently. Also, in Figure 7, the comparison charts for accuracy and F1-score across all three targets are presented. The F1-score results were used to validate the values obtained from accuracy.

Figure 7 Graph of DT algorithm evaluation results in the ΔxShoreline, ΔyBC, and XlocBC.
Figure 7

Graph of DT algorithm evaluation results in the ΔxShoreline, ΔyBC, and XlocBC.

Based on the results obtained from Figure 7:

Shoreline changes (ΔxShoreline): The curves in blue represent “accuracy,” while the curve in red represents “F1-score.” An analysis of the output results from the two-evaluation metrics indicates that in scenario 3, an increase in sea level had a significant impact of approximately 30% on increasing accuracy, highlighting the strong influence of this feature. Additionally, according to the graph, the accuracy and F1-score values increase up to scenario 6. The features of the first six scenarios include berm width changes (ΔBW), berm slope, SLR, wave breaking index (ζ), wave power (P), and maximum wave height (H max). The trend and magnitude of F1-score changes closely mirror the accuracy metric, confirming the obtained results. Therefore, the first six scenarios will be used for predicting, and scenarios 7–9 will be excluded from further analysis.

Berm crest elevation variation (ΔyBC): The curves in yellow represent “accuracy,” while the curve in green represents “F1-score.” The results indicate that the overall trend continues with a relatively moderate slope up to scenario 6. The features of the first six scenarios include BC height, ΔxShoreline, horizontal position changes of the BC (ΔxBC), P, mean wave height (H mean), and SLR. The trend and magnitude of F1-score changes closely match the Accuracy metric, confirming the results. Therefore, the first six scenarios will be used for predicting the results, and scenarios 7–10 will be excluded from further analysis.

The horizontal position of the berm Crest (XlocBC): The curves in gray represent “Accuracy,” while the curve in black represents “F1-score.” The results indicate that the overall trend continues to rise to scenario 7. The features of the first seven scenarios include BW, berm slope, ΔyBC, E, BC height, E, SLR, and ζ. The trend and magnitude of the F1-score change closely match the accuracy metric, confirming the results. Therefore, the first seven scenarios will be used to predict the results, and scenarios 8–10 will be excluded from further analysis. Finally, based on the summary of the results obtained from the descriptive section, the scenarios for the prediction sections are presented in Table 4.

Table 4

Final scenarios for prediction models

Targets Prediction scenarios Accuracy % F1-score %
∆x Shoreline 1 ∆BW 0.455 0.457
2 ∆BW−Berm Slope 0.449 0.466
3 ∆BW−Berm Slope−SLR 0.798 0.799
4 ∆BW−Berm Slope−SLR−ζ 0.753 0.755
5 ∆BW−Berm Slope−SLR−ζ−P 0.792 0.805
6 ∆BW−Berm Slope−SLR−ζ−P−Hmax 0.820 0.825
∆y BC 1 BC Height 0.605 0.610
2 BC Height−∆xShoreline 0.595 0.597
3 BC Height−∆xShoreline−∆xBC 0.600 0.595
4 BC Height−∆xShoreline−∆xBC−P 0.640 0.620
5 BC Height−∆xShoreline−∆xBC−P−Hmean 0.630 0.620
6 BC Height−∆xShoreline−∆xBC−P−Hmean−SLR 0.670 0.660
Xloc BC 1 BW 0.477 0.480
2 BW−Berm Slope 0.505 0.502
3 BW−Berm Slope−∆yBC 0.585 0.582
4 BW−Berm Slope−∆yBC−BC Height 0.610 0.610
5 BW−Berm Slope−∆yBC−BC Height−E 0.640 0.630
6 BW−Berm Slope−∆yBC−BC Height−E−SLR 0.650 0.660
7 BW−Berm Slope−∆yBC−BC Height−E−SLR−ζ 0.660 0.670

3.2 Prediction

Headlands at the northern and southern ends of the coast, along with the Narrabeen curve’s indentation, create a varying energy gradient along the shoreline. The northern part of Narrabeen Beach is characterized by high-energy dissipative conditions while moving toward the southern areas, the beach transitions to moderately reflective conditions with lower energy. The coast width in this area is significantly narrower than that of Profiles 2 and 4. In the vicinity of Profile 6, the coastal dune height is approximately 4 m, while in the northern and central sections of the beach, it ranges between 6 and 9 m. Additionally, these profiles are spaced 900 m apart. The morphological conditions in the southern part of Narrabeen Beach, particularly around Profiles 6 and 8, are different from those in the northern and central sections. For the testing part, the data of Profile 6, which covers the years 2014–2019, has been used. As a result, given the limitations of the available field data and the focus on this section of the coast, it can be concluded that Profile 6 largely satisfies the conditions needed for testing the model in different scenarios across other datasets. Following this, the prediction of the targets will be conducted using the FNN algorithm based on the scenarios developed in the physical description section. Table 5 presents the data combination of the training, validation, and test.

Table 5

The data combination of the training, validation, and test

Data parts Profile no. Period (year) Number of data Explanation
Training (65%) PF2 2006–2019 260 Stormy profiles have been removed
PF4 2006–2019 265
PF6 2006–2013 79
Validation (15%) PF2, PF4, and PF6 2006–2013 105
Test (20%) PF6 2014–2019 178 Stormy profiles have not been removed

Shoreline changes: In this section, the prediction scenarios are defined as DS1–DS6. After developing the initial model and conducting multiple tests to achieve stabilized and reliable outputs, as detailed in Table 5, the Levenberg–Marquardt algorithm was employed to solve the models. Each scenario underwent 30 test iterations, and the average results, with a confidence level exceeding 90%, were recorded. The outputs of Scenarios DS1–DS6 are presented in Figures 8 and 9. Figure 8 shows the R 2 total (overall results of R 2 in both training and testing) values for each scenario, while Figure 9 displays the RMSE and R 2% for testing and training for each scenario. Table 6 provides a summary of the results from both figures.

Figure 8 Graphs of R 2 total for scenarios DS1–DS6 on shoreline changes.
Figure 8

Graphs of R 2 total for scenarios DS1–DS6 on shoreline changes.

Figure 9 Summary of the results of training and predicting in each scenario in shoreline change, Chart A shows training data and Chart B testing data.
Figure 9

Summary of the results of training and predicting in each scenario in shoreline change, Chart A shows training data and Chart B testing data.

Table 6

Summary of the results for predicting shoreline changes

Scenario nos. Train RMSE (m) Train R 2 Test RMSE (m) Test R 2
DS1 3.03 93.30 3.96 86.70
DS2 2.96 93.20 3.27 91.80
DS3 2.83 94.00 3.56 91.30
DS4 2.78 94.30 3.03 92.00
DS5 2.69 93.90 3.25 92.50
DS6 2.73 94.10 3.47 92.10

Figure 8 illustrates the overall R 2 values for each prediction scenario (DS1–DS6), encompassing both training and testing datasets. These values represent the extent to which the model’s predictions align with the actual shoreline changes, providing a comprehensive measure of the model’s accuracy. The R 2 values exhibit an upward trend from DS1 to DS4, indicating a progressive enhancement in the model’s performance across these scenarios. In scenarios DS5 and DS6, the R 2 values remain relatively stable, showing no significant improvement compared to DS4. This suggests that further increases in complexity do not substantially enhance the model’s predictive capability.

In Figure 9, chart A displays a relatively downward trend in RMSE changes. Additionally, the trend of R 2 changes ascends with minimal differences in values up to scenario DS4. Additionally, comparing the scenarios reveals no significant difference between the R 2 and RMSE results. Overall, the training data and scenarios yield acceptable outputs. In Chart B (testing data), the RMSE error displays a descending trend up to scenario DS4, while the R 2 values show a relatively ascending trend. Scenario DS4 provides better prediction. The reduction in error compared to scenario DS3 is 16%. Moreover, there is no significant difference in R 2 values between scenarios DS3 and DS4, but the reduction in error, despite the similarity in R 2 values, highlights the significance of scenario DS4.

To conclude this section, scenario DS4 has been identified as the most suitable scenario for predicting shoreline change. It presents acceptable results with an RMSE value of 3.03 m and an R 2 value of 92%.

Berm crest elevation variation: In this section, predictions regarding changes in coastal berm height have been made, maintaining a predictive model structure similar to the previous section. Scenarios DY1–DY6 have been examined according to decision tree results. Based on the findings, Figure 10 shows the R 2 total values for each scenario, while Figure 11 displays the RMSE and R 2% for testing and training for each scenario. Table 7 provides a summary of the results from both figures.

Figure 10 Graphs of R 2 total for scenarios DY1–DY6 on berm crest elevation variation.
Figure 10

Graphs of R 2 total for scenarios DY1–DY6 on berm crest elevation variation.

Figure 11 Summary of the results of training and predicting in each scenario in the berm crest elevation variation: Chart A shows training data and Chart B test data.
Figure 11

Summary of the results of training and predicting in each scenario in the berm crest elevation variation: Chart A shows training data and Chart B test data.

Table 7

Summary of the results for predicting berm crest elevation variation

Scenario nos. Train RMSE (m) Train R 2 Test RMSE (m) Test R 2
DY1 0.48 55.50 0.46 46.00
DY2 0.46 53.60 0.52 55.50
DY3 0.33 77.40 0.38 71.20
DY4 0.33 80.20 0.34 73.00
DY5 0.32 81.70 0.40 71.00
DY6 0.33 80.00 0.37 75.50

Figure 11 presents the overall R 2 values for predicting berm crest changes under different scenarios (DY1–DY6). The R 2 values show a noticeable increase from DY1 (R 2 = 0.52) to DY4 (R 2 = 0.79), indicating a steady improvement in model performance. This trend suggests that the model becomes more accurate as input data or scenario complexity increases in this range. For scenarios DY5 and DY6, R 2 values stabilize around 0.79, with no significant improvement compared to DY4. This implies that additional scenario complexity or input modifications beyond DY4 do not enhance predictive accuracy substantially. Scenario DY4 achieves the highest R 2 value (0.79), marking it as the most effective configuration for predicting berm crest changes.

In Figure 11, chart A displays the training data, the trend of RMSE changes continues to decline steeply up to scenario DY3 and remains relatively consistent with minor variations from scenarios DY3 to DY6. Additionally, the R 2 changes show a sharp increase up to scenario DY3 and minimal alterations from DY3 to DY6. The training data results show that scenarios DY3 and DY4 perform the best (the next scenarios do not cause any significant changes in results). In Chart B (testing data), the RMSE changes exhibit a declining trend up to scenario DY4, indicating a 23% reduction in error compared to DY1 and a 10% decrease compared to DY3. Moreover, the difference in error between scenarios DY4 and DY5 is 14%. The R 2 changes also exhibit an ascending trend up to scenario DY4. The results show a strong alignment between scenarios DY3 and DY4 in both the training and testing data, with scenario DY4 outperforming DY3 overall. As a result, scenario DY4 has been selected for predicting variations in berm crest elevation.

Horizontal position of the berm crest: In this section, a prediction was made regarding the horizontal position of the coastal berm crest, utilizing a prediction model structure similar to the preceding sections. Scenarios DX1–DX7 have been examined according to DT results. The outputs of scenarios DX1 to DX7 are presented in Figures 12 and 13. Figure 12 shows the R 2 total values for each scenario, while Figure 13 displays the RMSE and R 2% for testing and training for each scenario. Table 8 provides a summary of the results from both figures.

Figure 12 Graphs of R 2 total for scenarios DX1–DX7 on the horizontal position of the berm crest.
Figure 12

Graphs of R 2 total for scenarios DX1–DX7 on the horizontal position of the berm crest.

Figure 13 Summary of the results of training and predicting in each scenario in the horizontal position of the berm crest: Chart A shows training data and Chart B test data.
Figure 13

Summary of the results of training and predicting in each scenario in the horizontal position of the berm crest: Chart A shows training data and Chart B test data.

Table 8

Summary of the results for predicting the horizontal position of the berm crest

Scenario nos. Train RMSE (m) Train R 2 Test RMSE (m) Test R 2
DX1 11.17 79.50 11.90 72.00
DX2 11.05 78.30 11.45 77.00
DX3 10.60 81.00 11.10 79.00
DX4 10.00 83.30 10.84 79.90
DX5 9.75 83.20 10.40 82.50
DX6 9.16 86.10 10.40 81.80
DX7 8.10 89.20 9.28 85.80

Figure 12 illustrates the overall R 2 values for predicting changes in the horizontal position of the berm crest in scenarios DX1–DX7. A consistent increase in R 2 values is observed from scenarios DX1 (R 2 = 0.77) to DX7 (R 2 = 0.88). This progression highlights the model’s improving ability to predict the horizontal position of the berm crest as the scenarios evolve. Scenario DX7 achieves the highest R 2 value (R 2 = 0.88), indicating the strongest correlation between predicted and actual values. Unlike the observed in other targets (e.g., shoreline change or berm crest), the R 2 values for cross-shore position predictions demonstrate a steady upward trajectory, suggesting that additional complexity in scenarios yields continuous improvement.

In Figure 13, chart A displays the training data; the RMSE exhibits a steep change and decreases until scenario number DX7 the reduction in error from scenarios DX1 to DX7 amounts to 28%. Moreover, comparing scenario DX7 to the one preceding it (DX6), there is a relatively 8.5% decrease in error. There is an upward trend in the R 2 values, with variations approaching 10% from scenarios DX1 to DX7. Consequently, scenario DX7 demonstrated the best performance in the training data section. In Section B testing data, the RMSE error trend shows a significant improvement, with a 22% reduction in error from scenarios DX1 to DX7. Notably, when comparing DX7–DX6, there is a further 10.7% decrease in errors. Additionally, the R 2 values exhibit a clear upward trend, improving by 14% from DX1–DX7. At least, DX7 is the final scenario for suitable coastal berm horizontal position prediction. It should be noted that the wave-breaking index parameter had a significant impact on improving predictive performance.

4 Discussion

Shoreline changes: Based on the results, the prediction of shoreline changes across the initial six scenarios demonstrated that scenario DS4 provided the best prediction values. To finalize the results, a comparison of the predicted values for the period from 2014 to 2019 in this scenario with observational data is presented in Figure 14. Additionally, the error histogram for this scenario illustrates how many of the data points were predicted with an error less than the RMSE = 3.03 m of this scenario (used as the error metric for comparison).

Figure 14 (a) The error histogram and (b) a comparison between observational data and test data in shoreline changes.
Figure 14

(a) The error histogram and (b) a comparison between observational data and test data in shoreline changes.

The results shown in chart A are explained in Table 9, and chart B demonstrates that the model successfully predicted shoreline changes in close alignment with the observational data. Additionally, a comparison with the study by Zeinali et al. [32] indicates that the FNN algorithm offers a stronger prediction of shoreline changes. The better predictions in this study, compared to the referenced research, can be attributed to several factors: (1) the exclusion of profiles 1 and 8, which are located near headlands, due to the complex flow conditions in those areas; (2) the use of descriptive algorithms such as DT to select features that significantly impact shoreline changes; and (3) the exclusion of profiles from before 2006 due to the lower accuracy of those measurements.

Table 9

Summary of prediction results and comparison with other studies

Prediction name Test conditions Evaluation criteria Error histogram (no. of data under 3.03 m)
RMSE CC%
FNN-DS4 Narrabeen Beach, Profiles 2, 4, and 6 from 2006 to 2014, FNN algorithm + DT algorithm 3.03 89 138
Zeinali et al. (2021) Narrabeen Beach, all Profiles from 1989 to 2013, Narxnet and Narnet algorithm 13.33–16.59 39–26 —

It is worth mentioning that the CC coefficient was calculated and presented for comparison with Zeinali’s study, and it was not included in the results analysis section. Therefore, scenario DS4 is the most effective in predicting shoreline changes.

Berm crest elevation variation: Based on the obtained results, the berm crest elevation variation prediction across the initial six scenarios demonstrated that scenario DY4 provided the best prediction values. To finalize the results, a comparison of the predicted values with observational data is presented in Figure 15. Additionally, the error histogram for this scenario illustrates how many of the data points were predicted with an error less than the RMSE = 0.34 m of this scenario.

Figure 15 (a) The error histogram and (b) a comparison between observational data and test data in berm crest elevation variation.
Figure 15

(a) The error histogram and (b) a comparison between observational data and test data in berm crest elevation variation.

Horizontal position of the berm crest: The results indicate that among the initial seven scenarios, scenario DX7 provided the most accurate predictions for the horizontal position of the berm crest. To validate these findings, Figure 16 presents a comparison between the predicted values and the observational data. Additionally, the error histogram for this scenario shows the number of data points predicted with an error smaller than the RMSE of 9.28 m.

Figure 16 (a) The error histogram and (b) a comparison between observational data and test data in the horizontal position of the berm crest.
Figure 16

(a) The error histogram and (b) a comparison between observational data and test data in the horizontal position of the berm crest.

The closest study to predicting berm changes is the research by Beuzen et al. [31]. However, their study focused on using a Bayesian algorithm to predict overall volume changes in the inner coastal areas in storm conditions, whereas this research emphasizes predicting the elevation changes of the berm crest and its horizontal position under non-storm conditions. Although comparing the results of these two studies may not be entirely appropriate, a summary of the findings from both studies is presented in Table 10.

Table 10

Summary of prediction results and comparison with other studies

Prediction name Test conditions Evaluation criteria Error histogram (no. of data under 0.34 m for ∆yBC and 9.28 m for XlocBC)
R 2%
FNN-DY4 Narrabeen Beach, Profiles 2, 4, and 6 from 2006 to 2014, FNN Algorithm + DT Algorithm 73 143
FNN-DX7 Narrabeen Beach, Profiles 2, 4, and 6 from 2006 to 2014, FNN Algorithm + DT Algorithm 85.8 129
Beuzen et al. (2018) Narrabeen Beach, Santa Rosa, and Fire Island, Lidar Photos, Bayesian Algorithm 61–76 —

As shown in Table 10, the model has successfully predicted all targets. Furthermore, it achieved a high percentage of predictions with errors below the RMSE in both cases. Also, it is worth noting that the obtained error values for all targets, relative to their range of variations (calculated based on the initial data), indicate that the results are highly appropriate. Table 11 presents a comparison between the average and median of the data and the prediction errors.

Table 11

Comparison of average and median values of the objective functions with the prediction error

Target Observation data average (m) Observation data median (m) Prediction error (m)
∆xShoreline 7.70 5.30 3.03
∆yBC 0.42 0.29 0.34
XlocBC 21.00 30.30 9.28

5 Conclusion

This study applied machine learning algorithms to predict berm crest and shoreline changes under non-storm conditions, focusing on the coastal area of Narrabeen, Australia. Coastal berms are essential as the first defense against erosion, and non-storm conditions, which occur more frequently, impact long-term coastal patterns. The stability of these conditions allows for more accurate predictions, enhancing coastal management and supporting storm scenario modeling.

Using regression decision tree algorithms, this study identified hydrodynamic and morphodynamic parameters affecting shoreline and berm crest changes. An engineering filter was initially applied to exclude irrelevant features. Shoreline changes are affected by parameters such as ∆BW, Berm Slope, SLR, and ζ in scenario DS4. Also, Berm Crest Height, ∆xShoreline, ∆xBC, and P in scenario DY4 describe coastal berm crest elevation variation. Additionally, the parameters BW, Berm Slope, ∆yBC, Berm Crest Height, E, SLR, and ζ identified in scenario DX7 are among the most influential parameters in describing the horizontal position of the berm crest.

In the final prediction phase, an FNN was used, demonstrating that scenario DS4, incorporating the wave-breaking index, achieved a high determination coefficient of 92% and low RMSE of 3.03 m for shoreline predictions. Similarly, scenario DY4 improved berm crest elevation predictions by adding the wave power parameter, achieving an R 2 of 73% and an RMSE of 0.35 m. Scenario DX7, which included the wave-breaking index, further refined berm crest horizontal position predictions, reaching an R 2 of 85.8% and an RMSE of 9.28 m. These results confirm that the accurate identification of influential parameters is vital for reliable coastal morphodynamic predictions. The findings demonstrate that the FNN model effectively predicts shoreline and berm crest changes.

Acknowledgments

The present paper is originated from the content and achievements doctoral dissertation of Mr. Amir Jabari K., who is our Ph.D. student at Shahrood University of Technology. All relevant data used in this article are taken from the content of his dissertation (that will be defensed and published in Persian by the end of autumn 2024) and many other free available papers/reports, national and international data banks listed in the references section or referenced in the article text or acknowledgment section. So, we declare that all of the data of this paper is derived from public/free domain resources.

  1. Funding information: The authors did not receive support/fund from any organization for the submitted work.

  2. Author contributions: The authors contributed equally to the conception, design, and execution of the research paper. Each author played a significant role in the interpretation of results and the drafting of the manuscript. All authors discussed the results and contributed to the final manuscript. *Amir Jabari Khameneh: deep and detailed literature review; designed the modification framework programming; software/code development; implementation of the computer code and supporting algorithms; testing of code components. *Mehdi Adjami: conceptual ideation of the research (finalization of necessary modifications and changes); development of methodology; selection of final comparison scenarios for cases; verification of the overall replication/reproducibility of results; oversight and leadership responsibility for the research activity planning and execution; finalizing the structure of the article. *Saeid Gharechelou: provision and assortment of study materials; developing the setups and runs of codes/Software; tests scenario extracting; specifically writing the initial draft (including substantive translation).

  3. Conflict of interest: The authors hereby declare that there are no conflicts of interest regarding the publication of this article. This statement confirms that no financial, professional, or personal relationships have influenced the research, analysis, or conclusions presented in this study.

  4. Data availability statement: Beach Profile Data’s: Main Article: A multi-decade dataset of monthly beach profile surveys and inshore wave forcing at Narrabeen, Australia – 2016: https://www.nature.com/articles/sdata201624. Data from: https://datadryad.org/stash/dataset/doi:10.5061/dryad.28g01. Narrabeen–Collaroy Beach Survey Program: http://narrabeen.wrl.unsw.edu.au/download/narrabeen/. Meteorological Data’s: ECMWF data series: ERA5 hourly data on single levels from 1940 to present: https://cds.climate.copernicus.eu/cdsapp#!/dataset/10.24381/cds.adbb2d47?tab=overview. Aviso data series: Mean Sea level: https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level.html.

  5. Supplemental data: All data, information, codes, and calculations are provided in the zip file “BermPrediction_Supplementary.rar,” which can be downloaded from this shared Google link: https://drive.google.com/file/d/1LSNpDcyPA66BoEhe1ATaWNgJm_dJib4f/view?usp=drive_link.

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Received: 2024-11-28
Revised: 2025-01-29
Accepted: 2025-01-29
Published Online: 2025-04-07

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2025-0770
Keywords for this article
coastal berm; coastal morphodynamic; non-storm condition; decision tree algorithm; artificial neural network
Creative Commons
BY 4.0

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