Coastal forecast through coupling of Artificial Intelligence and hydro-morphodynamical modelling

ABSTRACT As climate-driven risks for the world’s coastlines increase, understanding and predicting morphological changes as well as developing efficient systems for coastal forecast has become of the foremost importance for adaptation to climate change. Artificial Intelligence is a powerful technology that has been rapidly evolving recently and can offer new means of analysis for the coastal science field. Yet, the potential of these technologies for coastal geomorphology remains relatively unexplored with respect to other scientific fields. This article investigates the use of Artificial Neural Networks and Bayesian Networks in combination with fully coupled hydrodynamics and morphological models (Delft3D) for predicting morphological changes and sediment transport along coastal systems. Two sets of Artificial Intelligence models were tested, one set relying on localized modeling outputs or localized data sources and another set having reduced dependency from modeling outputs and, once trained, solely relying on boundary conditions and coastline geometry. The first set of models provides regression values greater than 0.95 and 0.86 for training and testing, respectively. The second set of reduced dependency models provides regression values greater than 0.84 and 0.76 for training and testing, respectively. Our results highlight the potential of AI and statistical models for coastal applications.


Introduction
More than 600 million people live along coastal areas less than 10 meters above sea level, and the ocean economy and associated ecosystem services are worth around 3 to 6 trillion annually (Deutz, Kellett, and Zoltani 2018;UNCC 2020). The unfolding impact of climate change on the coastal zone is expected to be increasingly disruptive at all spatial scales and derives from the complex overlaps of multiple agents including sea level rise, storms, and anthropogenic influences. For instance, in the UK alone, the need to realign coastal defenses in response to sea level rise is expected to increase the cost of coastal infrastructure maintenance by 150-400% (Dawson et al. 2016). Projections from IPCC indicate that Europe will face storms with higher frequency and the sea level rise will increase the risk of storms and tidal floods leading to greater erosion (Huang-Lachmann and Lovett 2016). In Europe, the Netherlands is expected to be most affected by sea level rise and more than 4 million people will be living below sea level by 2100 (Buchholz 2020). According to Nunez and Staff (2022), in 2050, the United States is predicted to receive damaging floods 10 times more than it does today. Population living in the East and Gulf Coasts are among the most vulnerable to flooding. Out of the huge number of people affected by the rising sea levels, 70% of the people are estimated to be living in just eight countries in Asia (Buchholz 2020). Most affected people will be from China followed by Bangladesh and India. People in Vietnam, Indonesia, Thailand, the Philippines, and Japan would also be largely affected.
Morphological change (i.e. bathymetric changes in elevation) results from the imbalance between the import and export of sediments, with sediment starvation being normally associated to coastal erosion. Coastline mobility takes place over a yearly time scale but high-intensity storm events can lead to significant coastline changes (Plant, Robert Thieler, and Passeri 2016). Understanding and predicting coastlines evolution is essential for climate adaptation and the correct management of coastal systems.
Numerical models have been one of the preferred tools for investigating coastal hydrodynamics and morphological change and underpinning a variety of coastal engineering applications (e.g. Ciavola et al. (2011) andUSGS (2015); Lyddon et al., 2019) with sophisticated modeling suits being able to predict both hydrodynamic and morphological conditions under different scenarios (Chen et al. 2022;Muñoz et al. 2022;Shchepetkin and McWilliams 2005). These numerical models can be computationally expensive and are not always easily available to a variety of stakeholders. Artificial Intelligence (AI) applications have also been used for various coastal applications. Kabiri-Samani et al. (2011) and Somayeh, Abbas, and Mohammad Hossein (2013) used Artificial Neural Network (ANN) and Regression trees, respectively, for prediction of net along shore sediment transport based on the input variables: wave period, wave height, breaking wave angle, beach slope, and grain size. Kabiri-Samani et al. (2011) used data from field and laboratory studies retrieved from Kamphuis et al. (1986) and Somayeh, Abbas, and Mohammad Hossein (2013) that used datasets from field campaigns at the U.S. Army Corps of Engineers Field Research Facility at Duck, NC. Tsekouras et al. (2015) investigated the potential of neural-fuzzy network in predicting the coastal erosion at the SW coastline of Lesvos island, Greece. Loureiro, Ferreira, and Cooper (2013) used Bayesian Network (BN) to probabilistically model the beach morphodynamic state classification at six embayed beaches along the rocky coastline in southwest Portugal based on inputs of peak period, tidal range, breaker height, and sediment fall velocity. Bulteau et al. (2015) utilized BN for modeling the shoreline change at La Réunion, a French volcanic island in the Western Indian Ocean. The shoreline change data for their study was extensive field data based on shoreline change indicators such as traces of fallen rocks, beach slope, and tree roots. Their probabilistic prediction of shoreline change was based on five input variables: presence of an estuary, geomorphic setting, exposure to energetic waves, presence of anthropic structures, and the rate of relative sea-level rise. Beuzen et al. (2018) developed BN to model the coastline recession caused by storm events at Narrabeen-Collaroy sandy beach on the southeast coast of Australia. Shoreline change was modeled based on storm wave data such as cumulative near shore wave power, mean water level, storm meteorological independence, pre-storm beach state, prestorm beach slope, and pre-storm beach width. Their main objective was to examine the network as predictive and descriptive tool. They concluded that the network developed for descriptive purposes can be used to gain insight on underlying processes that produce the data. Poelhekke et al. (2016) modeled morphodynamic impacts such as overwash depth, overwash velocity and erosion at buildings and infrastructure using BN at Praia de Faro (Faro Beach), Portugal based on variables such as water level, significant wave height, peak period, and storm duration. López et al. (2018) predicted the cross-shore beach profile using ANN for the sand beaches of coast of province of Valencia, Spain. These models are usually site specific (Cabaneros, Calautit, and Hughes 2017), i.e. they are usually only effective for the site for which the model has been trained on. Following the development of previous studies, this research explores the use of different AI models for predictions of suspended sediment transport and morphological change in Morecambe Bay, UK, and explores the capabilities of different types of architectures, model types, and input data in providing accurate results.
Within this context, two sets of AI models, aimed at predicting morphological change and suspended sediment transport, were tested in combination with hydro-morphodynamic modeling. One set relying on localized modeling outputs or localized data sources and another set having a reduced dependency from modeling outputs and, once trained, solely relying on boundary conditions information. Specifically, a hydro-morphodynamic model was developed for Morecambe Bay, UK, using Delft3D and was combined that with four different ANNs and two BNs models with the goal of forecasting sediment transport and morphological changes along the coastline.

Study site
The test case in analysis is Morecambe Bay, a macrotidal embayment located in the north-west of England. Morecambe Bay (Figure 1) opens south-west into the Irish sea and most of its shoreline is covered in fine sand (Mason, Scott, and Dance 2010). Intertidal zones are very susceptible to changes, mainly in sandbanks and subtidal channels, which can be noticed even within a single season. Morecambe Bay experiences spring tidal waves with amplitudes up to 10 m. The fetch length of waves for Morecambe Bay is constrained by landmasses such as Ireland and Isle of Man and sprints at bay mouth. However, the significant wave height at the mouth of the bay reaches up to 2 m for about 10% of the year, and for the remaining duration of the year significant, wave heights remain around 0.5 m. Morphological change and suspended sediment transport in Morecambe Bay were simulated under different external forcing conditions using Delft3D.
Delft3D solves the 3-D Navier-Stokes equations for incompressible free-surface flow under the shallow water approximation for unsteady, incompressible, and turbulent flow. The hydrodynamic and morphodynamic modules are fully coupled so that the flow field adjusts in real time as the bed topography changes. The module Delft3D-WAVE can be then used to simulate wave generation, propagation, and nonlinear wave-wave interactions. Within this module, bottom dissipation, whitecapping, and depth-induced breaking are fully accounted for in a dissipation term (Booij, Ris, and Holthuijsen 1999).
Modeling results were recorded at 286 observation points along the Morecambe Bay shoreline, as presented in Figure 1. ANN and BN were trained to predict morphological changes and depth averaged suspended sediment transport (SST) rate.

Artificial neural networks and Bayesian networks
ANN, sometime referred to as black-box (Akrami, El-Shafie, and Jaafar 2013;Pavitra;Kumar et al. 2021), mimics the human brain structure (El-Shafie et al. 2012;Kumar et al. 2020) to provide variable predictions through establishment of relationships between them and other pre-defined inputs (Akrami, El-Shafie, and Jaafar 2013). It has the capability of predicting nonlinear variables and has found widespread application across physics and engineering (Arqub and Abo-Hammour 2014). Figure 2. illustrates basic ANN structures. ANN models receive inputs at the input layer which contains as many nodes as the number of inputs. Nodes in the input layer are connected to those of the hidden layer. As an example, the ANN in Figure 2a consists of two hidden layers H 1 and H 2 containing five nodes each (N 1 , N 2 , N 3 , N 4 , and N 5 ). However, there can be any number of hidden layers with any number of nodes depending upon the level of complexity needed to deal with the inputs-outputs relationships. The hidden layer is followed by the output layer where the product of all the calculations  within the network is provided (Figure 2a). The information received at the input layer is processed forward through the hidden layers to reach the output layer (El-Shafie and Noureldin 2011). The structure of ANN shown in Figure 2a is an example of Feed-Forward Neural Network (FFNN), where the information provided at the input layer flows forward from the input layer to the output layer. In contrast to feed-forward, Figure 2b represents a Recurrent Neural Network (RNN), i.e. Elman Neural Network (ENN). In this case, a copy of the information flowing from input to output is diverted back in the hidden layers. ENN was designed for voice processing problems (Li et al. 2019) and is similar to the FFNN, except for the addition of the context layer (Tampelini et al. 2011) which stores a copy of the information to be provided to the hidden layers in the subsequent calculation steps (Mahdaviani et al. 2008). Each hidden layer has its own context layer with the number of nodes equal to the number of nodes in the corresponding hidden layer. The context layer acts as a memory to the ENN as it holds a copy of activations of previous time step (Sheela and Deepa 2013).
Bayesian Network is a statistical model which provides a framework for probabilistic prediction (Plant and Stockdon 2012). BN evaluates the probability of a certain outcome based on prior probabilities developed by the network among the output and input variables. BN can use relationships and inductive reasoning to calculate the joint probability between the input variables (Chen and Pollino 2012;Palmsten et al. 2014;Wilson et al. 2015). BN works on Bayes' theorem (Gutierrez, Plant, and Thieler 2011), which provides a relation (Eq. 1) to calculate the probability of occurrence of an event depending on the occurrence of other event(s) (Yates and Le Cozannet 2012).
is the probability of the occurrence of event R i , given a set of events O j . Occurrence of an event can be joint occurrence of different events. For example, occurrence of the event "morphological change" is a joint occurrence of higher wave height and greater depth averaged velocity. The event scenarios i and j refers to the number of event R and observation O. p R i jO j À � is said to be the likelihood of the set of observations (O) for the known event R, which represents the strength of the correlation between O and R. p R i ð Þ is the prior probability of the event R. p O j À � is the likelihood of the observations.

Numerical simulations
Delft3D is used for simulating the hydrodynamics and morphdynamics of Morecambe Bay. The model grid has a varying resolution from around 120 × 200 m onshore to around 1000 × 300 m offshore. The simulation domain extends about 57 km along the coastline and around 20 km across the coastline with maximum distance from the sea boundary of about 50 km. The bathymetry of Morecambe Bay (Figure 1), based on tiles with a size of 30 × 30 m of the product Arcsecond Gridded Bathymetry, has been obtained from EDINA Marine Digimap download service (https://digimap.edina.ac.uk/roam/download/marine). DTM (digital terrain model) data from LiDAR surveys at 2 m resolution were then used for areas covering the shoreline and were downloaded from the UK Environment Agency's LiDAR data archive (https:// environment.data.gov.uk/DefraDataDownload/? Mode=survey). The model boundary is forced with 10 tidal harmonics (M2, S2, N2, K2, K1, O1, P1, Q1, S1, M4) interpolated across the two boundary extremes and derived from the global tidal model GOT-e 4.10c (Ray 1999;Stammer et al. 2014). The model was calibrated using OpenDA (n.d.) and through comparison of the simulated water level values, with values at the Heysham tidal station (https://ntslf.org/data/uk-net work-real-time). The model was calibrated using OpenDA (Carnacina et al. 2015;Karri et al. 2013;Kurniawan et al. 2011; "OpenDA: Integrating models and observations,"). OpenDA interfaces with Delft3D and uses a derivative-free algorithm (DUD or doesn't use derivative, Ralston and Jennrich, 1978), an algorithm for non-linear least squares minimization, to minimize a quadratic cost function based on differences between observed and model water levels through changing of roughness coefficient, water depth, and boundary conditions. Successive iterations of the numerical simulation were repeated until the convergence criteria was reached. The accuracy was evaluated using the Brier Skill Score (Murphy and Epstein 1989) defined as: which r is the correlation coefficient, σ is the standard deviation, ε is a normalization term, and X and Y are observed and modeled values. The model was calibrated from January 5 th to Invalid Date NaN NaN (Leonardi 2022). The Brier Skill score in this case was 0.99. The model was subsequently run for 89 days, with a time step of 1 min from 1 st of January to 30 th March. The hydrodynamic model is fully coupled with a morphological model and the bathymetry is updated with a morphological scale factor of 10, which is equivalent to running the model for 890 days and no morphological scaling factor. Non-Cohesive sediment type with specific density as 2650 kg/m 3 and dry bed density as 1600 kg/m 3 is used for simulating the sediment transportation. The initial sediment layer thickness at bed is set to 5 m. Depth averaged (2DH) advection diffusion equation is solved for suspended sediment load calculation (Brakenhoff et al. 2020;Galappatti and Vreugdenhil 1985). Van Rijn (1993) distinguished the bedload from suspended load based on a reference height (0.05 m for this case), above which is considered as suspended load transport and below which is considered as bedload. The depth-averaged equilibrium concentration, solved using expressions provided by Van Rijn (2007), is used for the calculation of sediment exchange between the bed and water column, which includes the computation of velocity profile and vertical concentration profile. Near-bed reference concentration (C a ), computed by Eq. 3, is required to compute the vertical sediment concentration profile.
where: τ b;cr is the critical bed shear stress, τ 0 b;cw is grain related bed shear stress due to current and waves, D 50 is median sediment diameter (120 μm, in this case), a is Van Rijn's reference height and D � is nondimensional grain size. The depth averaged suspended load transport is calculated by Eq. 4.
where: q s ! is depth averaged suspended sediment transport, Ũ is depth averaged velocity, c is depth averaged sediment concentration and h is water depth. Different boundary conditions were simulated by changing the significant wave height at the boundary (0.25 m, 0.5 m, 0.75 m, 1 m, 1.5 m, and 2 m). Modelling results were recorded every 10 minutes (simulated times) at 286 observation points plotted along the coastline at around 500 m from each other ( Figure 1). The following variables were considered: depth average velocity, water depth, significant wave height, peak wave period, wavelength, cumulative erosion/ sedimentation, and depth averaged suspended sediment transport rate (SST). The data of these variables from all 286 points and for all boundary forcing were then fed to FFNN, ENN, and BN models in different format as required by these models for training. Complete flow chart of the methodology is presented in Fig. S1.

Artificial neural network modeling
The first set of FFNN and ENN modeling was fed with modeling outputs: Depth average velocity, Water depth, Significant Wave Height, Peak Wave Period, and Wavelength at the observation points as input to the models and target of the models were morphological changes and SST at the same observation points. The time series of the variables obtained from Delft3D were averaged before feeding to the models. By averaging the dataset, we obtain nontime series values. FFNN models are generally used for non-time series data. ENN (a type of RNN) is generally used for time-series or sequential data. However, RNNs have also been successfully and efficiently tested on non-time series or non-sequential datasets (Alemohammad et al. 2020;Alvi et al. 2021;Chopra et al. 2017). Alemohammad et al. (2020) investigated application of several models, including RNNs, on non-time series dataset. They claimed that RNNbased kernels outperform range of baseline methods on 90 non-time series datasets. The list of methods they investigated are random forest, radial basis forward, polynomial, multi-layer perceptron, Laplace and exponential kernels, RNN, bi-directional RNN, RNN average pooling, bi-directional RNN average pooling, and RNN with permutation of input data. To feed the non-time series data to RNN, each data point was treated as a time step to which RNN performs recursive computations using data from previous time steps and previous layers. The output was collected for each time step from the final layer. However, they kept the output only from the last time step. Their results indicate that RNN with permutation of input data outperformed other models with average test accuracy of 82.34%. Alvi et al. (2021) used convolution and RNN (LSTM) to detect sepsis in neonates (a serious health condition in new-born child). They fed non-time series into convolution and LSTM models to classify based on 46 independent variables if the subject is affected by neonatal sepsis. For comparison, they used traditional algorithms such as K-nearest neighbor, support vector machine, logistic regression, and random forest. The results indicate that the LSTM model achieved highest accuracy of 99.40%. Based on their results, they concluded that LSTM still outperforms other models even when used on non-time series dataset. Chopra et al. (2017) used RNN to predict hospital readmission of diabetic patients with non-sequential data. They collected the clinical records of 10 years (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008) from 130 hospitals in US. They used about 33 features to classify if the patient will be readmitted to the hospital. They tried several models including Logistic regression, SVM, Decision tree, Random Forest, Simple Neural Network, and Recurrent Neural Network. Their results state that RNN outperformed other model with the highest accuracy of 81.12%. Considering the above-mentioned successful use of RNN on non-time series datasets, ENN is included as option to model the morphological change and SST.
For FFNN, data are divided into three datasets, training, testing, and validation dataset, with corresponding percentage of 80%, 10%, and 10% (Gazzaz et al. 2012), respectively. For ENN, data are divided into training and testing dataset with corresponding percentage of 80% and 20% (Chen et al. 2020;Liu et al. 2012). The training dataset is used for training the models, i.e. updating the weights and biases of the network (de Gennaro et al. 2013;Najah et al. 2011). The validation dataset is used for preventing the overfitting of the model. Weights and biases are not updated in the validation process. Testing dataset is used for testing the final predictive strength of the model (Kumar et al. 2020). Training of FFNN and ENN models requires a pre-defined configuration in terms of number of hidden layers and nodes because prediction accuracy of the model also depends on these factors. For instance, models having a smaller number of hidden layers and nodes fail to learn complete pattern of variations in the training dataset, thus lowering prediction accuracy. Similarly, models having greater number of hidden layers and nodes become more complex structure for the data with least variations leading to overfitting of the model, thus lowering prediction accuracy (Uzair and Jamil 2020). Hence, an optimum number of hidden layers and its nodes are to be chosen for greater accuracy. In this study, training of FFNN and ENN models have been done on different combinations of hidden layers and nodes as presented in Table 1. These models were trained using Levenberg-Marquardt (trainlm) backpropagation training function with mean square error as the loss function. The stopping criteria for the training was the loss function of the validation dataset. Training was stopped when the mean square error of the validation dataset was increasing. Optimum model, which provides better accuracy, is selected from these combinations based on the performance criteria. Training and analysis of FFNN and ENN models were done on MATLAB platform.

Bayesian modeling
The data received from Delft3D for Bayesian modeling is divided into two datasets: training and testing dataset, with percentage division of 80 and 20%, respectively. Like the ANN modeling, Depth average velocity, Water depth, Significant Wave Height, Peak Wave Period, and Wavelength are used as input to train the model for prediction of morphological changes and SST. Each variable is represented by a node in BN (Gutierrez et al. 2015;Zeigler et al. 2017). The joint correlation within the variables in BN P E i ð Þ; P S i ð Þ ð Þ can be expressed as: where E i and S i represents the probability of morphological change and SST, given the joint probability distribution with other variables (V: depth average velocity, D: water depth, WH: significant wave height, WP: peak wave period, WL: wavelength). The data for Bayesian modeling is divided into different bins for training. The number of bins selected for training determines the ability of the network to fit the data (Wang, Oldham, and Hipsey 2016). For this study, input data was divided into five bins, and the target data were divided into two bin scenarios (Table 2). Training and analysis of these BN models were done using the Netica software package developed by Norsys Software Corporation.

Reduced dependency neural networks modeling
Models developed in the above sections are capable of predicting morphological changes and SST at the observation points along the coastline. But these models require input data, such as Depth average velocity, Water depth, Significant Wave Height, Peak Wave Period, and Wavelength, at the same observation points for prediction and thus rely on localized data sources, which might not necessarily be easily available without an existing modeling run or data stations. Hence, this section proposes a model  2  10  10  -2  15  15  -2  20  20  -2  25  25  -3  10  10  10  3  15  15  15  3  20  20  20  3  25  25  25  ENN  2  10  10  -2  15  15  -2  20  20  -2  25  25  -3  10  10  10  3  15  15  15  3  20  20  20  3  25  25  25 which was trained solely through boundary conditions of significant wave height, distance of the coastline from the boundary, and angle of the coastline with respect to simulation sea boundary (which is 164.6 degree from north) for prediction of morphological changes and SST at the observation points. The boundary being discussed here is the simulation domain's sea boundary (West boundary), which is where the waves are forced into the domain. Each observation point has varying distance from the boundary. Hence, training the model using distance as an input will help the model to learn the distance dependency and thus will be capable of predicting at unknown locations. As shown in Figure 1, there are possibilities of getting more than one observation points with same distance; hence, the angle of coastline in combination with distance makes a unique combination to identify certain location, thus reducing the ambiguity of the input and target data to the model. The distance of each observation point from the boundary and the direction of the coastline in proximity of the observation point are two of the simplest indicators that can be inferred from coastline geometry (e.g. from remote sensing images) and are thus chosen as relevant variables. The distance from the boundary provides a rough approximation and indirect indicator of the level of transformation and shallow water effects that external forcing has gone through before reaching the concerned observation point, which together with the fact that it can be easily inferred is another reason to be included here. This set of reduced dependency models bypasses the need for numerical simulations and localized data sources. For this scenario, FFNN and ENN models were trained using the same data division percentage mentioned in the above sections and using the same sets of hidden layers and nodes as presented in Table 1.

Reduced dependency Bayesian modeling
Bayesian models were also developed using boundary conditions, distance, and angle of the coastline as input variables. The joint correlation within the variables in BN is thus: where E i and S i represents the probability of morphological changes rate and SST, given the joint probability distribution with other variables (WH: significant wave height, Dt: distance, A: angle of the coastline).
For training and analysis of these BN models, same data division process was followed as done in previous BN models. Number of bins for the target data was same as presented in Table 2. However, the classification of inputs into the number of bins were as presented in Table 3.

Performance criteria
Prediction accuracy of ANN models is measured using regression, mean square error, and Nash-Sutcliffe efficiency parameters (Eq. 9, 10, and 11). The regression value is a statistical measure indicating how the data are fitting to its best fit line but does not reflect the   Figure 3 provides an example of numerical modeling outputs at one of the 286 observation points (Figure 1).

Simulation
Modeling outputs were recorded every 10 minutes for the whole simulation period (89 days) and include Depth average velocity, Water depth, Significant Wave Height, Peak Wave Period, Wavelength, and Cumulative Erosion/Sedimentation, which were converted to morphological change rate (m/y) by dividing the last time step value (which is the cumulative of erosion/sedimentation for the entire simulation duration) by the duration of simulation (in days) and multiplying by 365, as this is a unit of measurement (m/y) frequently utilized when evaluating morphological changes. For the other variables, the whole time series was averaged to get the average value throughout the simulation duration (3 months) (Fig. S1).

Localized model results
The dataset was randomly divided into three datasets (training, testing, and validation) for FFNN and two datasets (training and testing) for ENN. The division was such that all the datasets were statistically similar, i.e. datasets have similar mean values. While dividing, it was ensured that the maximum and minimum values of the target data lie in the training dataset so that the models experience the extreme levels of the data pattern. FFNN and ENN models were trained with different number of hidden layers having different number of nodes in them. Separate models were trained for the prediction of morphological change and SST. The results of the models trained for prediction of morphological changes and SST are presented in Tables 4  and 5.
Models trained with different configuration have different level of accuracy (    0.9059 and 0.8790 for FFNN and ENN, respectively. ENN has its maximum training regression as 0.9656, but it has less testing regression and more testing mean square error in comparison to the selected optimum ENN model; hence, it was not considered fit to be chosen as optimum model. This is the case when model overfits. Overfitting of model is recognized when it performs well while training but cannot provide good results while testing (Ying 2019). The regression plots containing training and testing regression plots of selected optimum FFNN and ENN models are presented in Figure 4. SST values obtained from Delft3D were normalized within the range of − 1 to 1, using mapminmax function in MATLAB, and all the training process and result analysis process were performed with the normalized data (note that the original values of all other variables were used for training, only SST values were normalized because of their very low values (Figure 3)). The training and testing regression obtained for the model for predicting SST was about 0.99 and 0.98 (Table 5), respectively, which represents high prediction skill of the model. The optimum FFNN model, selected based on the testing results, has two hidden layers with 25 nodes each and provides training regression as 0.9928 and testing regression as 0.9852. It has the NSE value very close to 1 (0.9846) and testing MSE as 0.0024. As mentioned earlier, this mean square error is of the normalized data. The optimum ENN model, having two hidden layers with 25 nodes each, has similar training and testing accuracy with training regression as 0.9939 and testing regression as 0.9866 with testing MSE as 0.0024 and NSE value of 0.9849. The maximum NSE value obtained by ENN models is 0.9855 but the corresponding testing MSE is greater than the selected optimum model; hence, it is not selected as an optimum model. The regression plots consisting of training and testing regression plots for optimum FFNN and ENN models for predicting SST are presented in Figure 5. Figure 6 represents the Bayesian models developed for the probabilistic prediction of morphological changes and SST with seven bins (Figure 6(a)) and 5five bins (Figure 6(b)). As shown in Figure 6, there are some connections within the input nodes. Mean depth-averaged velocity is depended on the mean  depth at the observation points. Also, mean wave height, mean wavelength, and mean wave height are inter-related. Hence, these nodes have connections within input nodes. Nodes contain the list of bins and corresponding prior probabilities (plotted next to it) (Plant, Robert Thieler, and Passeri 2016), learned by the network from the training data. Like the ANN models, the data are divided into two sets: training and testing sets. Two BNs were trained by varying the number of bins in the target nodes from 5 to 7, while keeping the number of bins in the input nodes equal to 5. In Erosion/Accretion rate node with 7 bins, classification of bins is as follows: <-2 representing extreme erosion, −2 to − 1 and − 1 to 0 as moderate erosion, 0 as stable, 0 to 1 and 1 to 2 as moderate accretion and ≥-2 as extreme accretion.
The erosion rate/Accretion rate node with 5 bins has its classification as follows: <-2 represents the extreme erosion, −2 to − 1 represents moderate erosion, −1 to 1 represents stable condition, 1 to 2 represents moderate accretion and ≥ 2 represents extreme accretion. In similar fashion, bins of SST nodes are divided in 7 and 5 bins.
The results of BN trained and tested on the data from Delft3D are presented in Table 6. The strength of the BN models is measured as the percentage success in predicting correct bins of morphological change and SST. There is significant increase in the percentage success when the bins are reduced by increasing the bin size. BN model has high percentage success rate in case of SST with 84.31% with 7 bins and 86.57% with 5 bins. Model was also performing good in its testing phase. BN model has  high percentage success rate for morphological change prediction with 5 bins (81.97%) but has less percentage success rate when number of bins were increased to 7 bins (65.33%). Model performance improves when prediction of next to correct bin is counted as success prediction, i.e. percentage success rate in ±1 bin is higher than the normal percentage success rate.

Reduced dependency models
For the reduced dependency models, the training of FFNN and ENN was done using the same configurations as before but with limited input variables. These models were trained to predict morphological rates of change solely based on boundary condition values and basic geometrical features of the coastline. The optimum FFNN model for prediction of morphological change (Table 7) has two hidden layers with 25 nodes each and provides the training regression of 0.8424 and testing regression of 0.7627 with testing MSE of 0.3426 m/ year and NSE value as 0.6777. The optimum ENN model for prediction of morphological change (Table 7) has threehidden layers with 15 nodes each and provides the training regression of 0.9022 and has the testing regression of 0.8358 with the testing MSE of 0.2629 m/ year and NSE value as 0.7874. The regression plots of these two optimum models are presented in Figure 7. Models for prediction of SST based on the boundary condition values and basic geometrical features of the coastline were trained on the same configuration and same normalized data as in previous paragraphs. The optimum FFNN model for prediction of SST (Table 8) has two hidden layers with 15 nodes each and provides the training regression of 0.9704 and testing regression of 0.9538 with the testing mean square error of 0.0085 and NSE value as 0.9347. The optimum ENN model for prediction of SST (Table 8) has three hidden layers with 25 nodes each and provides the training regression of 0.9367 and testing regression of 0.8801 with testing mean square error of 0.0205 and  NSE value as 0.8562. Figure 8 represents the regression plot of these two optimum models. Figure 9 represents the BN models trained for prediction of morphological changes and SST using 7 bins and 5 bin, respectively. Process of classification of bins for the target nodes were same as that followed in earlier BN models. The bins of input nodes (wave height, distance, and angle) were classified based on the limits of the data available for training. The probabilities of bins displayed in Figure 9 is the prior probabilities learned by the network based on the training data. Table 9 presents the result of the BN models trained using boundary data. The maximum percentage success rate obtained was 77.88% for morphological change prediction with testing percentage success rate of 78.61% with 5 bins. Percentage success rate increased to 95.40% for training and to 96.82% for testing when ±1 bin is included. However, for SST percentage success rate increased slightly for 5 bins (74.60%) when compared to 7 bins (73.58%).

Discussion
This article is proposing FFNN, ENN and BN models for prediction of morphological change and SST at the coastline based on only the boundary condition values and basic geometrical features of the coastline. Comparison of the accuracy of all the models is presented in Table 10.
Optimum FFNN and ENN models seem to have similar regression values. Hence, any model can be used for the prediction of morphological change and SST. However, it is recommended to use both FFNN and ENN models and average the outputs, which will create an ensemble effect, and thus, will help in reducing the final output error (Yang and Browne 2004). BN models with seven bins in target nodes have lower percentage success rates than that with five bins. Creating a greater number of bins reduces the size of each bin. Classifying bins with reduced size (lower range) is a tough task for models, thus, reducing the percentage success rate. However, creating too few bins reduces the usability of the model. For instance, a model having only two bins (erosion vs accretion) will have greater percentage success rate but will provide less information in comparison to models having a number of bins sufficient to identify conditions of moderate, severe, or stable morphological changes. Thus, a model with five bins is considered adequate  as it can provide the prediction of severe erosion rate (<-2 m/year), moderate erosion rate (−2 to −1 m/year), stable (−1 to 1 m/year), moderate accretion (1 to 2 m/ year), and severe accretion (>2 m/year). BN models with five bins trained on the localized data at observation points have percentage success rate greater than 80% in training and greater than 75% in testing. However, when measured with ±1 bins, the percentage success is found to be greater than 94%. BN models trained on boundary data have percentage success rate greater than 73%, which is acceptable being this, to our knowledge, the first attempt in  literature of developing predictive data-driven modeling using solely boundary data and coastline features. FFNN, ENN, and BN models, trained in this study, have comparable or higher accuracy with respect to ANN and BN models previously developed for prediction of shoreline change. Kabiri-Samani et al. (2011) used laboratory and other field data to train different models for the prediction of long-shore sediment transport. The best accuracy they achieved was 0.981 (regression value) using fuzzy gradient descent method. Somayeh, Abbas, and Mohammad Hossein (2013) trained regression tree for the prediction of longshore sediment transport with an accuracy of 0.95 (regression value). Poelhekke et al. (2016) used BN for the prediction of coastal hazards including erosion at buildings and infrastructure with an accuracy ranging from 81-88%. Plant, Robert Thieler, and Passeri (2016) proposed BN model for the prediction of shoreline change in the Gulf of Mexico. The prediction skill of BN obtained for the prediction of shoreline change was 0.6. Yates and Le Cozannet (2012) proposed BN model for evaluating the European coastline evolution which was accurately reproducing more than 65% of shoreline evolution trend. The ANN model proposed in this study has the best accuracy of 0.9586 and 0.9939 (regression values) for morphological change and SST, respectively, whereas the BN models proposed in this study has the best percentage success rate of 81.97% and 86.57% in predicting morphological changes and SST, respectively, at Morecambe Bay.
ANN models, in this study, are trained on the data obtained from the simulation, whereas few abovementioned studies are trained on laboratory and field measurement data. Such real-world data sources are susceptible to various sources of noise resulting to uncertainties in the dataset. Sources of uncertainties in field measured data include environmental factor ("Direct Measurements," 2005), human factor, instrument limitations ("General Information About Measurements," 2005), random observation error, and systematic observation error (Kennedy 2014). In contrast, simulated datasets offer the advantage of being recorded in controlled environments, which generally reduces the presence of such uncertainties. Consequently, this is one of the reasons why the models in this study exhibit higher accuracy compared to the findings in existing literature.
The prediction strength of a model is determined through its testing accuracy, i.e. how accurately the model is predicting the testing dataset, the dataset for which model has not seen earlier. For this case, the testing dataset (10% for FFNN, 20% for ENN and BN) was separated randomly from the complete dataset. Selected optimum models have great accuracy (best regression of 0.90 for morphological change and 0.98 for SST) for these testing datasets, which indicate that the models are robust enough for the prediction of morphological change and SST.
The prediction models proposed in this study have the advantage, over other morphological change and SST predicting models, of eliminating the dependency on localized data. Once trained, these models can predict morphological evolution based on the boundary conditions of significant wave height, distance of the coastline from the boundary, and angle of the coastline with respect to sea boundary. However, models trained on localized data provide a double advantage for the purposes of this manuscript. First, because they are trained on a large number of inputs, the localized data models serve as a baseline for the best accuracy ANN can provide for morphological changes and SST predictions. Second, they demonstrate the capability of our methodology to be adapted to the use of field data (rather than modeling data) as inputs for ANN models, as the localized data used here may be available for other coastal embayments as part of high resolution field programmes that typically provide high temporal but low spatial resolution.
Generally speaking, ANN models have the advantage of reducing the computation time utilized by the simulation software packages. Hence, ANN models have the potential to serve as emulator for prediction of morphological change and SST and save huge computational resource and several hours of time required for simulation. The limitation of these models is that they are site-specific (Cabaneros, Calautit, and Hughes 2017), i.e. these models provide accurate predictions only for the location where models have been trained on. For this study, the data used for FFNN, ENN, and BN training was simulated for Morecambe Bay; hence, these models will provide accurate predictions for Morecambe Bay only. For predictions at other coasts, these models need to be re-configured and re-trained on the data patterns of that coasts. Another limitation is that even though realistic waves magnitudes were used, these were constant rather than varying throughout the simulation period. The application of simplified forcing conditions is not uncommon as part of exploratory studies for coastal systems (e.g. Donatelli et al. (2018), Pannozzo et al. (2021), Nardin and Fagherazzi (2012), and X. Li et al. (2019)), but future advances in this research should address this limitation and we expect this to require adjustment to the ANN. Specifically, wave height varies in a complex non-stationary pattern which require additional pre-processing to handle (such as Normalization, wavelet transform, detrending etc.), as ANN models have limitations and problems in handling non-stationary data Li et al. 2020). Ogasawara et al. (2010) proposed a novel method of normalization, i.e. adaptive normalization (AN), for normalizing non-stationary time series of U.S. Dollar to Brazilian Real Exchange Rate, Brazilian Agricultural Gross Product, and São Paulo Unemployed Rate. The complete process of adaptive normalization is divided into three steps: first to transform the nonstationary time series into stationary sequence, followed by outlier removal and data normalization (for detailed steps see (Ogasawara et al. 2010)). AN is the modified version of sliding window method and has the advantage of converting time series into data sequence from which global statistical properties can be calculated. The novel method was compared with three traditional normalization methods: min-max, decimal scaling, and z-score. Results stated that adaptive normalization method used with ANN for time series forecasting outperformed other normalization methods.  predicted landslide displacement using extreme learning machine model and used wavelet transform to capture its non-stationary characteristics. Wavelet analysis is an analytical technique that enables the decomposition of time series into components from both the spatial and temporal domains using dilation and translation procedures. Wavelet analysis was used to transform the non-stationary landslide displacement into several stationary landslide displacements, which helped the model to effectively predict the non-linear and non-stationary displacement. Altunkaynak and Nigussie (2018) used wavelet transform, first order differencing, and linear detrending with multilayer perceptron model for monthly water demand prediction. First order differencing is a detrending method which detrends the time series by subtracting the value at t-1 time step with value at t time step. Linear detrending is the method of removing the trend by removing the difference from its regression line. These three methods helped in detrending and modeling the non-stationary water demand time series. Their results showed that the first order differencing method outperformed other two methods. The current study recommends the involvement of varying wave height and implementing above-mentioned detrending methods as scope for future research.
ANN and BN models have an advantage in terms of computational time with respect to a full hydro-morphodynamical models. The latter can require several hours of computational time. ANN and BN models, once trained, can predict the morphological changes close to simulated values within the order of a few minutes, saving time and computational resources.

Conclusion
This article proposes two set of FFNN, ENN, and BN models: one set trained on localized modeling outputs or localized data sources and one having reduced dependency from modeling outputs and, once trained, solely relying on boundary conditions and coastline geometry. The morphological change and SST data for training the models are obtained from simulation for Morecambe Bay on Delft3D software package. These data are simulated for 89 days and are recorded at an interval of 10 min along with other input data. Simulated input variables are Depth average velocity, Water depth, Significant Wave Height, Peak Wave Period, and Wavelength. These input and target data are transformed into the required format for training FFNN, ENN, and BN models. FFNN and ENN models trained on localized data at observation points provide training regression greater than 0.95 and testing regression greater than 0.86. BN models, when trained with five bins, provide higher percentage success rate which is greater than 80% for training and greater than 76% for testing. FFNN and ENN models trained on boundary conditions, provide regression values greater than 0.84 for training and greater than 0.76 for testing. BN model with five bins trained on boundary conditions provide percentage success rate greater than 74% for training and greater than 73% for testing. These models provide sufficient accuracy for prediction of morphological change and SST. FFNN and ENN models, for this study, are providing similar regression values. Hence, it is recommended to use both the models for prediction and average the outputs, which will provide more accurate morphological change and SST values. For future studies, it is recommended to further improve the accuracy of the models trained on boundary conditions by adding more relevant input variables upon which the morphological change and SST depends.