Artificial Neural Network (ANN) Water-Level Prediction Model as a Tool for the Sustainable Management of the Vrana Lake (Croatia) Water Supply System

Abstract

With climate change and increasing summer tourism in Croatia, the protection and sustainable management of natural freshwater resources, such as lakes, are becoming crucial. This research aims to develop a predictive hydrological model that can forecast water levels in Vrana Lake to serve as a tool for the sustainable management of water supply systems. Therefore, in this paper, a data-driven predictive model based on an artificial neural network (ANN) is implemented. For this purpose, the multilayer perceptron (MLP) ANN architecture is chosen. For model development, the monthly data of rainfall amount, evaporation, losses, water supply pumping, and lake water levels at Vrana Lake from the years 1954–2022 were used, and the model for water level prediction is developed for time prediction steps: (i) Δt = 1 month, (ii) Δt = 2 months, (iii) Δt = 4 months, and (iv) Δt = 6 months. The model quality assessment indicated strong prediction capabilities for time steps of Δt = 1 month and Δt = 2 months. However, the models for time steps of Δt = 4 months and Δt = 6 months exhibited lower quality. Despite this, they can still serve as valid indicators for predicting trends in water level fluctuations.

1. Introduction

In times of climate change and the increase in summer tourism in the Republic of Croatia, quality and quantity protection as well as sustainable management of freshwater resources are becoming very important challenges. Moreover, Croatia, as a part of the European Union and the United Nations, is committed by the Water Framework Directive [1] and United Nations Sustainable Development Goals [2] to protect all types of waters, as well as to implement positive sustainable management practices in water use for people’s needs. The emphasis of this paper is placed on drinking water resources, such as natural lakes.

One such water resource is the cryptodepression of the Vrana Lake on the island Cres, which functions according to the principles of the Ghyben–Hertzberg law. It has an approximate volume of 220 million m³ of fresh water in the island’s karst, which is situated near the coastline. The lake water is of excellent quality and has been the only water supply source for the islands of Cres and Lošinj since 1952 [3].

Given the importance of Vrana Lake, numerous studies and analyses have been conducted to understand its hydrological features and the functioning of its hydrological system. This extensive research has yielded significant conclusions and results, and those which are relevant for this research will be outlined in this paper. The abovementioned was concluded through extensive analysis of the collected meteorological, hydrological, and hydrogeological data. The first meteorological and hydrological measurements were established in 1926.

According to the available research, the most extensive analysis of the functioning mechanisms of Vrana Lake was performed by the developed hydrological mathematical model “VRANA” [3]. The model analyzes the behavior of Vrana Lake according to the defined water balance equation in different hydrological conditions. The model is able to calculate inflow and outflow values from the lake system and the contribution of inflow from the watershed, determine values of runoff coefficients, and simulate the lake behavior. Based on the “VRANA” model, same study also developed an ARIMA model for predicting water levels based on hydrometeorological input data [3].

The water level fluctuation in the lake depends on meteorological and hydrological conditions and water supply pumping. The retention time (the water exchange) in the lake is calculated to be 31 years, which fits in with the results of natural isotope research; according to them it is between 30 and 40 years [4,5]. The results of the analysis of the dynamics of water level fluctuations in the lake show a pronounced trend of seasonal increases and decreases in the water levels.

In the context of using Vrana Lake as a water supply source, it is important to note that the recommendations for the maximum allowable pumping rate have changed over the years. Initially, Petrik [6] recommended that the average annual pumping rate should not exceed 250 L per second (L/s). However, subsequent research indicated that this amount was too optimistic. It was estimated that under strict control, the pumping could increase up to about 100 L/s. Based on the knowledge so far, for larger increases in the pumping rate, it will be necessary to carry out more detailed tests of the behavior of the lake system, in order to protect the lake from seawater intrusion [3].

The biggest concerns about lake water system’s stability were triggered by the previously unrecorded trend of a decrease in the mean lake level during the period between 1985 and 1990, causing fear among residents and experts for the future of the lake, especially concerning further pumping possibilities. Based on extensive research and analysis conducted at that time, the sharp and sudden drop in the lake’s water level occurred due to a coincidence of extremely dry and unfavorable hydrological conditions (among other things, the redistribution of monthly precipitation), along with significant pumping from the lake leading up to that point [3].

From the 1990s until the present, the results of research into the most diverse ways of functioning of Vrana Lake were also published in the works from Ožanić and Rubinić [7], Tomec et al. [8], Szeroczyńska [9], Kuhta [10], Habdija et al. [11], Lončarić et al. [12], Kuhta and Brkić [13], Bonacci [14,15,16], Kuspilić et al. [17], Hrnjica and Bonacci [18], Biondić et al. [19], Brkić and Kuhta [20], Grofelnik and Maradin [21], and Brkić and Larva [22]. The primary goal of the overall research was to understand the properties of Vrana Lake and the mechanisms that govern its functioning, ultimately aiming to ensure the full protection and sustainable management of the invaluable karst phenomenon on the island.

Recent research from Cindrić et al. [23] also indicates that climate change contributes to an increasing trend in the evaporation rates, driven by rising air temperatures, as well as an increase in surface water temperature presented by Brkić and Kuhta [20]. This trend is causing water levels in the lake to decline further.

In conclusion, the available research highlights that the lake, being situated on an island, is part of an extremely limited hydrological and hydrogeological system. The small karst island possesses a unique local water inflow and outflow mechanism, necessitating a tailored approach to both research and water resource management [24]. Each karst island, particularly Cres, with its significant and valuable freshwater lake, is an ecologically and socially vulnerable environment that demands careful attention [25]. The sensitivity of the Vrana Lake hydrological system is highlighted by the impacts of climate change, potential pollution, and increasing water consumption driven by tourism development.

Although numerous studies have been conducted in this area, there is room for improvement in predicting the hydrological system behavior domain. Research has not yet led to the on-site implementation of water level prediction models for better water supply system management. Furthermore, there are only a few studies in which the modeling of Vrana Lake water level predictions was implemented [3,18]. In the mentioned studies, the ARIMA and artificial neural network (ANN) methods were used, and in a paper from Hrnjica and Bonacci [18], it was concluded that ANN methods are a better solution for the Vrana Lake water prediction than classical regression methods. In the research by Ožanić [17], the ARIMA model was used based on all available hydrological and meteorological data, while in the models presented by Hrnjica and Bonacci [18], only water level data were used as an input to the model.

Based on the available and aforementioned research information, a predictive hydrological model that will be able to predict future water levels in the lake by using an ANN model, and more precisely a Multiple Layer Perceptron (MLP) architecture, as a function of the meteorological and hydrological variables combined with the anthropological impact, can provide a further step in the development of the Vrana Lake water level prediction modeling. It is expected that the implementation of diverse data as the input to the model will result in better water level prediction possibilities. In this sense, the predictive model can be a valuable tool for optimizing water management systems, supporting decision-making processes, and enhancing overall protection, bridging the gap between extensive research and sustainable management.

One of the types of machine learning (ML) methods is the artificial neural network (ANN), which has become a common forecasting tool in hydrology. Still, the biggest challenge in hydrological modeling based on ANN can be recognized through the development of diverse prediction models, limiting their practical applications due to the variety of modeling approaches, their complexity, and the procedures for model validation and evaluation [26]. The need for a standardized approach to developing hydrological models based on ANN is therefore widely acknowledged. Nevertheless, a systematic review of the lake water level forecasting performed by Zhu et al. [27] has shown that the ANNs, and overall machine learning models, are able to effectively forecast the water level fluctuations in the lakes. The application of various ML models for water level prediction has been presented in several papers according to [27], and recent ones by Azad et al. [28], Ouma et al. [29], Zhu et al. [30], Shiri et al. [31], Shafaei and Kisi [32], and Young et al. [33].

Based on all available research and the indicated positive and negative sides to the implementation of the ANN models in general, the implementation of the ANN hydrological prediction model in this paper is based on the continuation of the author’s previous research on the development of a methodology for implementing ANN models [34]. The mentioned methodology is developed on the basis of the general methodology guidelines suggested by Maier et al. [35] and consists of precise procedural steps that help the standardization of the modeling approach, and allow the implementation of the model in the new case studies.

The abovementioned methodology for the ANN model implementation is already applied to different hydrological problems such as river water level [34] and is focused on the small-scale hydrological systems with significant collection of the meteorological and hydrological data, since the data are the most important part of the ANN modeling. Special challenges are the development of models for small-scale hydrological systems, which often face a lack of long-term collection of meteorological and hydrological data.

This research is also a continuation of and is coupled with the previous research conducted by the authors of this paper, since the research of Vrana Lake performed by Ožanić [3] served as a foundation for the description of the overall hydrological system and its functioning.

To summarize, the overall aim of this research is to propose a Vrana Lake water level prediction ANN model, based on the hydrological, meteorological, and anthropological impact data that are developed on the basis of a precise developed methodology [34] in order to provide key information for the sustainable planning of the water supply.

2. Materials and Methods

According to all the aforementioned, the focus of this paper is placed on hydrological modeling as a foundation and step towards more comprehensive and effective sustainable water management. It is expected that an appropriate hydrological model can help in the protection of the lake’s dynamic water balance system, and in the optimization of the water supply system, especially in the summertime when it is under the pressure of large water consumption needs.

2.1. Development of ANN Prediction Models

A data-driven model based on ANN will be developed to predict lake water levels, serving as a foundation for development of a sustainable water supply management.

Within this paper, the steps of the methodology for the development of the ANN model are going to be briefly described, while in the research performed by Sušanj [34], a detailed description of the methodology is provided. The developed methodology consists of four main process groups: (i) monitoring, (ii) modeling, (iii) validation, and (iv) evaluation.

2.1.1. Monitoring

The initial process group in the mentioned methodology is monitoring. It involves the collection of relevant data, both historical and monitoring data, and procedures for how it should be conducted. The relevant and accurate data, including meteorological, hydrological, and anthropological factors, must be collected to determine their impact on the observed hydrological system. The time step for collecting monitored data should align with the response of the observed hydrological system to meteorological and hydrological variables. Also, based on availability, other data, such as, for example, anthropological impact data, can be implemented. The collected data string can vary from a 2 min time step up to monthly data. Monitoring and data collection are considered the most important and delicate parts in the domain of ANN hydrological modeling, or hydrological modeling in general.

2.1.2. Modeling

The second group refers to the modeling process comprising the implementation of the ANN. In this process, the model input and output data have to be identified. Additionally, data preprocessing, elimination of data errors, and division of data into training, validation, and evaluation sets have to be performed. When data are prepared, the implementation of the ANN can be conducted. In the proposed methodology [34], the implementation of the Multiple Layer Perceptron (MLP) architecture with three layers (input, hidden, and output) is recommended as shown in Figure 1.

The input layer should be formed as a matrix of meteorological and hydrological time series, or other available data that are multiplied by the weight coefficient matrix w_k that is obtained by the learning algorithm in the training process. The data should, in a hydrological and meteorological sense, have an influence on the output data. The input matrix should be formed from previously measured data time steps according to the type of the hydrological system response to changes in meteorological and hydrological variables as pointed out earlier. Also, the number of previous time steps in the input layer should be in accordance with the memory of the specific hydrological system. In other words, in systems with a fast response of a few hours, the time step of data measurement should be short and input layer data should include one to two hours of previous data. In other cases, with a hydrological system’s slow response, monthly data can be used with an input layer that encompasses one or two previous seasons of the year data depending on the climatic characteristics of the area.

The hidden layer of the model should consist of ten neurons. A number of neurons can be adjusted, but prior research indicates it may not improve model quality overall [34,35,36]. Also, the increase in the number of neurons can lead to unnecessary deceleration of the model training process [34,36,37].

The output layer consists of the time series data that are supposed to be predicted. The model developer chooses the time prediction step, after which the process of the ANN training, validation, and evaluation can be conducted. The prediction step depends on the observed hydrological system. The model is usually trained with different prediction time steps in the output layer to examine the maximum possible time span prediction.

The quality and learning capability of the ANN model is influenced by the activation functions and training algorithms used [38]. Activation functions direct data between the layers, and the training algorithm has the task of optimizing the weight coefficient w_k in every iteration of the training process to provide a more accurate model response. It is recommended to choose a nonlinear activation function and learning algorithm because of their adaptability to nonlinear problems, which are often encountered in hydrology. Therefore, bipolar sigmoid activation functions and the Levenberg Marquardt (LM) learning algorithm are recommended. The schematic presentation for the ANN model training process function is shown in Figure 2.

During one training epoch, the output data from the network will contain errors that depend on the difference between the target output and the model’s response in the output layer. Therefore, an algorithm is required to calculate the change Δw_k in the weight coefficient w_k. The optimization of the weight coefficient can be defined as shown in Equation (1).

$${\mathrm{w}}_{\mathrm{k}+1}={\mathrm{w}}_{\mathrm{k}}+\Delta {\mathrm{w}}_{\mathrm{k}}$$

(1)

The LM algorithm is the quickest and most appropriate for training simpler structures within the MLP architecture and has been specifically developed for training ANNs. [38]. In second-order local algorithms, the change measure Δw_k is derived from the squared approximation of the error function, represented by the Hessian matrix. However, the Hessian matrix is usually impractical for training artificial neural networks (ANNs) because it often does not meet the necessary conditions and can be unsolvable. Therefore, algorithms that do not require solving the Hessian matrix, such as the LM algorithm, are preferred. The LM algorithm [38] is a specific combination of the Gauss–Newton and error backpropagation algorithms, utilizing a conjugate gradient method by incorporating the Jacobian matrix rather than the Hessian matrix. The change measure Δw_k can be defined as shown in Equation (2).

$$\Delta {\mathrm{w}}_{\mathrm{k}}=-{({\mathbf{J}}^{\mathrm{T}}\ast \mathbf{J}+\mathsf{\mu }\ast \mathbf{I})}^{-1}\times {\mathbf{J}}^{\mathrm{T}}\ast \mathbf{e}$$

(2)

In Equation (2), J is the Jacobian matrix of the error vector e with respect to the weight coefficients in the kth epoch of the calculation, J^T is the transpose of the Jacobian matrix, and µ is a scalar representing the learning rate.

At the end of every calculating epoch, the sum squared error E(e) is calculated as shown in Equation (3).

$$\mathrm{E}(\mathrm{e})=\sum _{\mathrm{k}=1}^{\mathrm{n}}{\left({\mathrm{e}}_{\mathrm{k}}\right)}^2=\sum _{\mathrm{k}=1}^{\mathrm{n}}{({\mathrm{d}}_{\mathrm{k}}-{\mathrm{o}}_{\mathrm{k}})}^2$$

(3)

In Equation (3), e_k represents the error in kth epoch of the calculation, d_k is the target value, and o_k is the response model value in kth epoch of the calculation. Depending on whether the sum squared error E(e) increases or decreases, the learning rate scalar µ adjusts during each epoch of the calculation. This adjustment is made by either dividing or multiplying µ by a constant factor (e.g., β within the range [0, 1]). This approach helps to make the LM algorithm more akin to the Gauss–Newton error backpropagation algorithm, while also enhancing the training speed. If the E(e) increases, the learning rate scalar µ will be multiplied by a constant amount β, and the LM algorithm will be more similar to the Gauss–Newton algorithm; otherwise, it will be more similar to the backpropagation algorithm [38].

Once the architecture of the ANN model is defined and the training algorithm and prediction steps are chosen, the programming language and environment for implementing the model should be selected. There are many prepared program packages with prefabricated ANN models, but completing the whole programming process is advisable for this purpose. Therefore, usage of MATLAB R2010b (MathWorks, Natick, MA, USA) or any other programming software is recommended. After the model is prepared, the training process through the calculation iterations should be conducted. To prevent overtraining of the artificial neural network (ANN) model, it is recommended to limit the training process using a numerical method. In this approach, the Mean Squared Error (MSE) is calculated for the model’s results after each epoch of training. When the MSE reaches its minimum value, the training process is halted. This method ensures the best possible regression correlation (R) between the model outputs and the target values during training.

2.1.3. Validation

The third group of the model development process refers to the model validation process. This is defined as the model’s quality response as the training process is completed. The model should be validated with an earlier prepared set of the input and output data for that purpose (10–15% of data) in order to compare the model response with the measured data [37,38]. The model response based on the validation dataset has to be evaluated graphically and by applying numerical quality measures which are going to be appraised according to each used numerical model quality criteria. Therefore, it is advisable to use at least two numerical quality measures: (i) Mean Squared Error (MSE) and (ii) Coefficient of Determination (r²).

2.1.4. Evaluation

The final group of methodology steps emphasizes the model evaluation process, which assesses the quality of the model’s responses using a dataset that was not included in the training or validation phases. For this evaluation, a pre-prepared input and output dataset (comprising 15% of the total data) should be used to compare the model’s responses with the actual measured data.

The model evaluation process is similar to the validation process, with the primary difference being the number of numerical quality measures used. It is generally recommended to employ the following measures: (i) Mean Squared Error (MSE), (ii) Root Mean Squared Error (RMSE), (iii) Mean Absolute Error (MAE), (iv) Mean Squared Relative Error (MSRE), (v) Coefficient of Determination (r²), (vi) Index of Agreement (d), (vii) Percentage BIAS (PBIAS), (viii) Root Mean Squared Error to Standard Deviation (RSR), and (ix) Mean Higher Order Error (MS4E). However, not all numerical quality measures may be appropriate for specific hydrological problems, so it is the responsibility of the model developer to select the measures that best reflect the model’s overall quality.

2.2. Research Area

Vrana Lake, located in the central part of the island of Cres, is a unique natural–geographical karstic phenomenon, as shown in Figure 3. Cres is an elongated island situated in the northern part of the Adriatic Sea and it stretches in an NW-SE direction. The island of Cres is built mainly of carbonate weathered rocks, limestone, and dolomite of the Cretaceous and Eocene age. In terms of lithology, dolomites prevail over limestones, and minor occurrences of flysch rocks of Paleogene age are also identified. The impermeable flysch structures are responsible for Vrana’s Lake formation 1.8 million years ago during the transition from the Pliocene to the Pleistocene [39].

According to an overview of available research, it was established that the area of the immediate watershed of Vrana Lake is not unambiguously determinable and changes depending on different hydrological conditions (Figure 4).

On the basis of the conducted analyses, it was also determined that the mean value of the watershed is approximately 24 km², with the regionally acceptable value of the average year runoff coefficient of 0.5 [3].

Vrana Lake is the largest cryptodepression in Croatia and operates according to the principles of the Ghyben–Hertzberg law, as illustrated in Figure 4. The lake is elongated, extending approximately 5.5 km in the same direction as the island, with a maximum width of about 1.45 km. At the average water level, the lake covers an area of approximately 5.69 km² and has a volume of around 220 million m³ of fresh water. The water quality in the lake is excellent, and it has served as the sole source of water for the islands of Cres and Lošinj since 1952 [3].

The need for the comprehensive and sustainable management of the Vrana Lake system is clearly evident based on the information provided in the Introduction. Therefore, this paper presents the development of a water level prediction model, which is an initial and essential step toward implementing a sustainable management system.

Data Collection

According to the previously described methodology, the first step in the implementation of the ANN model for predicting water levels is data collection and preparation. As mentioned, the first established measurements of meteorological and hydrological data were established in 1926. The collected data encompass the monthly rainfall amount, average monthly relative air humidity, average monthly air temperature, monthly evaporation from the water body, average monthly water temperature, monthly lake water levels, and monthly water supply pumping. The data are collected according to standardized methods for meteorological and hydrological data measurement procedures [40]. Since some measurements were carried out periodically, and some have large time gaps without measurements, for the purpose of data preparation the results of the hydrological model “VRANA” were also used, since the model provides mathematical functions between different meteorological and hydrological data on the basis of the water balancing equation in this closed water system of the Vrana Lake [3]. After the collection of all available measured and historical data, the selection of the relevant data for the implementation of the ANN model is carried out.

3. Results

According to all the described steps, the ANN model to predict water levels in Vrana Lake on the island of Cres is implemented. In continuation, a detailed description of the data preparation as well as the steps in the implementation of the ANN model is provided.

Development of ANN Vrana Lake Water Level Prediction Model and Model Quality Assessment

Preparation of the collected data is performed firstly by evaluation of data string length and the availability of significant data. Significant data consider data that have an impact on the model’s defined outputs and, in this case, impacts on the hydrological functioning of the lake system. The determination of the significant data for this model was not studied in detail in this research, since the impact of the diverse meteorological and hydrological variables on the lake water balance was already studied in detail in previous research by Ožanić [3]. In that sense, the data of the monthly rainfall amount, monthly water supply pumping, and monthly lake water levels were established as significant and good quality data. For model development, data from January 1954 to December 2022 were used because the objective of this research is to analyze the function of the lake system with anthropogenic impacts, which began significantly with water pumping in 1954. Also, for the model development, a significant impact on the water balance in the lake has infiltration losses and the amount of evaporation. Lake infiltration losses G [m³/s] are defined within this research according to results from the hydrological water balance model “VRANA” and defined by a mathematical function depending on the lake water level H [m] as shown in Equation (4). Also, measurement of the evaporation was conducted from January 1977 to December 1997 without continuity, and therefore for the purpose of model development, evaporation data are prepared according to the results of the model “VRANA” [3]. In the mentioned model, evaporation is calculated as the average monthly evaporation according to the available data.

$$G=0.028098\ast H$$

(4)

Further preparation of the input and output data is performed by converting data into the water lake elevations, expressed in meters [m], according to the mathematical function of depth dependence on the volume and surface of the lake.

Once the data have been prepared and processed, the implementation of the artificial neural network (ANN) model is performed using MATLAB software (MathWorks, Natick, MA, USA). For this task, the multilayer perceptron (MLP) artificial neural network (ANN) architecture, which comprises three sets, training data (75% of the data), validation data (10% of the data), and evaluation data (15% of the data). The input layer consists of the data with six delay steps that can be defined as input data from previous time steps. For this purpose, six delay steps represent six previous monthly data points, providing insight into model seasonal changes in meteorological, hydrological, and anthropological variables. The input layer encompasses the monthly data of rainfall, groundwater outflow (losses), evaporation, water levels, and water consumption from 1954 to 2022. The hidden layer consists of ten neurons, while the output layer represents water levels in chosen prediction time steps. Unipolar sigmoid activation functions link these layers. During the training process, the second-order local LM algorithm is utilized. The basic statistical analysis of the prepared data is shown in

Table 1. Statistics of data used for training, validation, and evaluation of the ANN water level prediction model.

Model Training Data (75% of Data)
	Input Layer					Output Layer
Statistics *	Rainfall	Losses	Pumping	Evaporation	Water Level	Water Level
	[m]	[m]	[m]	[m]	[m]	[m]
n	621	621	621	621	621	621
Max.	0.377	0.201	0.069	0.255	15.973	15.973
Min.	0	0.122	0.001	0.012	9.194	9.194
µ	0.090	0.162	0.017	0.095	12.541	12.541
σ	0.063	0.014	0.015	0.062	1.343	1.343
Model validation data (10% of data)
	Input layer					Output layer
Statistics *	Rainfall	Losses	Pumping	Evaporation	Water level	Water level
	[m]	[m]	[m]	[m]	[m]	[m]
n	83	83	83	83	83	83
Max.	0.315	0.166	0.070	0.278	12.687	12.687
Min.	0	0.126	0.019	0.008	9.228	9.228
µ	0.083	0.147	0.034	0.086	11.082	11.082
σ	0.066	0.011	0.015	0.080	1.007	1.007
Model evaluation data (15% of data)
	Input layer					Output layer
Statistics *	Rainfall	Losses	Pumping	Evaporation	Water level	Water level
	[m]	[m]	[m]	[m]	[m]	[m]
n	125	125	125	125	125	125
Max.	0.373	0.167	0.079	0.282	12.826	12.826
Min.	0	0.126	0.014	0.005	9.219	9.219
µ	0.099	0.150	0.036	0.091	11.392	11.392
σ	0.078	0.009	0.017	0.079	0.822	0.822

* n = Number of observation; Max. = maximum; Min. = minimum; µ = sample mean; σ = standard deviation.

.

The schematic representation of the model is illustrated in Figure 5. Model training is conducted for various time prediction steps: (i) Δt = 1 month, (ii) Δt = 2 months, (iii) Δt = 4 months, and (iv) Δt = 6 months. Prediction steps are chosen in accordance with the sessional changes, in the meteorological sense, of the analyzed hydrological system and to examine maximum possible prediction time.

The training process is continued until the MSE value reaches its minimum. Therefore, Figure 6 presents the R value at the end of the training process for every time step of the model training. Once the model is trained, it undergoes visual and numerical validation and evaluation. Visual evaluation measures are considered to be graphical representations of the ANN model response and target data in the form of a graph, which provides insights into errors in the model output. Visual validation and evaluation are shown in Figure 7, Figure 8, Figure 9 and Figure 10, which display a comparison of the measured and predicted water levels at Vrana Lake during the training, validation, and evaluation phases, categorized by the time prediction steps: (i) Δt = 1 month, (ii) Δt = 2 months, (iii) Δt = 4 months, and (iv) Δt = 6 months.

Numerical validation and evaluation of the model are conducted according to the previously described methodology. Considering the specificity of the analyzed hydrological system, MSE and r² were selected for validation purposes, while MSE, RMSE, MSRE, r², PBIAS, and RSR were chosen for the evaluation process. The results of the validation and evaluation processes and assessment of the model quality are shown in

Table 2. Performance statistics of the ANN model during validation and evaluation processes.

	Validation		Evaluation
Δt	MSE	r2	MSE	RMSE	MSRE	r2	PBIAS	RSR
[Month]	[m2]	[-]	[m2]	[m]	[-]	[-]	[%]	[-]
1	0.015	0.994	0.021	0.145	0.021	0.984	−0.245	0.187
2	0.063	0.976	0.081	0.285	0.080	0.967	−0.609	0.390
4	0.552	0.801	0.591	0.769	0.602	0.707	−2.501	1.078
6	0.831	0.458	0.793	0.890	0.753	0.105	0.152	1.164

Quality criterion for r² and PBIAS [18,41]: Very good; Good; Not good and Poor.

. Since some of the numerical model quality measures criteria are not precisely determined (measures: MSE, RMSE, MAE, MSRE, and RSR), it is recommended that the results should be close to zero. For others, the used measures criteria are precise, and models are assessed according to them [36,41].

4. Discussion

On the developed model, the results for the water level prediction in the Vrana Lake research area, visual and numerical validation, and the evaluation of the model are conducted. In continuation, the discussion on results is provided.

Firstly, the model training process results and the value of the R for time step prediction of Δt = 1 month, Δt = 2 months, and Δt = 4 months show a very strong correlation between model outputs and target water levels, with a high value near R = 1. The value of R for the time step prediction of Δt = 6 months is also, according to all criteria for the correlation [18,41], very high, but the visual representations of results in Figure 6 shows considerable dissipation around the correlation line, indicating that the model training did not succeed in providing a precise mathematical function between model outputs and targets.

From the visual analysis of the model validation and evaluation, it is evident that the model’s accuracy decreases as the prediction time step increases, which is an expected outcome. The numerical validation measure r² has confirmed that the models with time steps Δt = 1 month, Δt = 2 months, and Δt = 4 months have noticeably better prediction possibilities (since they are assessed as “very good”) than models with time steps Δt = 6 months which are assessed as “poor”. Also, the MSE values, in the validation of the models, for time steps Δt = 1 month, and Δt = 2 months are near zero, while Δt = 4 months, and Δt = 6 months are significantly bigger. Validation measures are therefore indicating that models with time steps Δt = 1 month, and Δt = 2 months have overall very good prediction possibilities, and the model for the prediction of the time step Δt = 4 months has considerably good prediction possibilities.

The process of the model evaluation has confirmed the aforementioned indications. The models for the time step Δt = 1 month, and Δt = 2 months are according to the r² quality criterion assessed as “very good”, Δt = 4 months as “good”, and Δt = 6 months as “poor”. On the other hand, according to the PBIAS quality criterion, all the models are assessed as “very good”. Also, the MSE, RMSE, MSRE, and RSR evaluation measures have shown values near zero for the models with the time step Δt = 1 month, and Δt = 2 months, while for the models Δt = 4 months, and Δt = 6 months, the values are considerable bigger.

Considering all the applied model quality measures, both visual and numerical, through training, validation, and evaluation processes, models with the time step Δt = 1 month, and Δt = 2 months are considered to be “very good” in the precise prediction of water level in Vrana Lake up to two months in advance. Also, a model with the time step Δt = 4 months can be considered “good” and as having the capability to predict considerably underestimated values of water levels four months in advance. The model with a time step of Δt = 6 months shows poor quality results, but according to visual analysis, it still shows a prediction indication of a trend (increase or decrease) in water level, and therefore this prediction can be used, but carefully.

A comparison of the model quality assessment results obtained with other ANN models is quite challenging. Firstly, as is already mentioned in the Introduction, there is a significant amount of ANN models for the prediction of lake water levels, but they use different ANN architectures, training algorithms, data types, data lengths, the ratio of the training to evaluation data, and at the end different model quality assessment measurements. Also, models are usually prepared for the specific research area which makes it difficult to carry out a direct comparison.

For example, in the paper [28] SARIMA, ANN, and hybrid SARIMA-ANN models for the water level prediction were implemented. The modeling is based on monthly water level data over a 16-year period. The model quality assessment is performed by MAE, MAPE, RMSE, and R² measures. Comparing the described model is challenging due to its many differences; for example, input data, ANN architecture, prediction time step, etc. However, the evaluation results indicate that having larger and more diverse meteorological and hydrological input datasets enhances the model’s accuracy. Furthermore, in the research [29], diverse models such as multilinear regression (MLR) and stochastic Vector Auto Regression (VAR) models, along with Random Forest Regression (RFR) and Multilayer Perceptron Neural Network (MLP-ANN) techniques were compared. The input data consist of a relatively short time set, but it includes diverse meteorological and hydrological information to predict the water levels. The model quality assessment measures used are the same as those in the paper [28]. Here, it is again challenging to compare models due to their differences; however, the paper [29] establishes the superiority of the ANN technique for predicting lake water levels. In other studies [30,31,32,33], various ANN architectures were implemented, utilizing different model quality assessment measures, data lengths, and time prediction steps. From all the studies described here, it can be concluded that diverse and extensive meteorological and hydrological input data enhance the prediction efficiency of ANN techniques as expected. Some papers lack detailed descriptions of prediction time steps, hindering direct comparisons with the model presented here.

The only possible approximative valid comparison is therefore with the models based on ANN, which have already been used on the Vrana Lake; but firstly, all the similarities and differences have to be addressed. In the study conducted by Hrnjica and Bonacci [18], in comparison with the presented model, different ANN architectures were implemented (feed forward (FF) and long short-term memory (LSTM)). Both studies use the same water level data in the modeling process, but in the ANN model presented here, the input data also include the monthly data of rainfall amount, evaporation, losses, and water supply pumping at Vrana Lake. The models [18] were developed for the following prediction steps: (i) Δt = 6 months, (ii) Δt = 12 months. In this study, the model is prepared for the following prediction steps: (i) Δt = 1 month, (ii) Δt = 2 months, (iii) Δt = 4 months, and (iv) Δt = 6 months. The only same model quality measures obtained in the training process of the compared studies were R. Therefore, between those two studies, only a rough comparison can be performed for Δt = 6 months prediction step. Here, the introduced ANN model has shown a slightly better R value (R = 0.929), than the FF (R = 0.898) and LSTM (R = 0.897) models in the training process. The models presented in study of Hrnjica and Bonacci [18] use a different ratio of training and evaluation data in the models, and therefore, it is difficult to compare those models in the process of the evaluation. Nevertheless, both model quality assessments have shown good prediction capabilities. The overall conclusions provided in the paper by Hrnjica and Bonacci [18] refer to the good prediction possibilities of the ANN models in regards to predicting the lake water levels at Vrana Lake. The extensive review conducted by Zhu et al. [27] on the ANN model’s implementation of the lake water level prediction also indicated good results.

Therefore, it can be concluded that the relevant quality comparison of the ANN models can be only performed by standardizing the model quality assessment measures.

The conducted model quality assessment and comparison to other examples of ANN implementation showed that the proposed ANN model can serve as a water supply management tool. On the basis of the proposed model, decision-makers in water supply management can make timely optimization decisions with accurate predictions extending up to 4 months in advance. This allows them to implement early water protection measures, such as reducing water pumping. If water levels in the lake, for example, according to model prediction, are expected to decline due to unfavorable hydrometeorological conditions and increased consumption of the water, preemptive reductions in water pumping can be implemented to preserve water and prevent system destabilization. In other words, one of the model’s uses can be as some kind of early warning system for the preservation of the lake’s water balance system.

Regarding future research and improvements, we will focus on implementing the proposed methodology in other hydrologically similar areas to enhance the assessment of model quality. Additionally, different machine learning models will be applied to the same dataset to compare their prediction quality and capabilities.

5. Conclusions

This paper presents the application of artificial neural networks in the predicting process of water levels in the research area of Vrana Lake in Croatia, in order to provide a tool for sustainable water supply system management and decision support. The Vrana Lake is a natural cryptodepression freshwater phenomenon located on the island of Cres, near the coastline. This lake is known for its excellent water quality and has served as the primary source of water supply for the islands of Cres and Lošinj.

The main objectives of this research were to develop the model to achieve a successful prediction of lake water levels based on meteorological, hydrological, and anthropological impact data, and to serve as a decision support tool in the proposed hydrological system.

The proposed methodology for implementation of the ANN model on the small hydrological systems developed by the authors of this paper has been proven to be usable for the prediction of lake water levels with strong prediction capabilities for time steps of 1 and 2 months, and lower for the 4 and 6 month time steps. Also, it needs to be pointed out that the presented model has been developed on, in the sense of ANN modeling, a small dataset according to the available monthly data. Therefore, the results of the model quality evaluation can be considered as very good. With the inclusion of additional data during the model training process, we can expect improved prediction capabilities, particularly for larger time intervals.

The performed research indicates that it is possible and desirable to apply artificial neural networks to the prediction process of small hydrological systems, because that type of model is a valuable and accurate tool that can serve as a support for the sustainable management of water supply systems, their optimization, and protection.