Predicting the Influence of Ammonium Toxicity Levels in Water Using Fuzzy Logic and ANN Models

Abstract

The study aimed to address the complex and critical issue of surface water quality monitoring by proposing a diversified approach that incorporates a range of chemical indicators. (1) Background: the purpose of the study was to address the problem of surface water quality monitoring in relation to the toxic effects of ammonium on aquatic ecosystems by developing predictive models using fuzzy logic and artificial neural networks. (2) Water samples from the Styr River, influenced by the Rivne Nuclear Power Plant, were analyzed using certified standard methods and measured parameters, while fuzzy logic and artificial neural network models, including Mamdani’s algorithm and various configurations of activation functions and optimization algorithms, were employed to assess water quality and predict ammonium toxicity. (3) A fuzzy logic system was developed to classify water quality based on ammonia content and other parameters, and six Artificial Neural Network (ANN) models were tested, with the ANN#2 model (using ReLU activation and ADAM optimizer) showing the best performance. (4) This study emphasizes the critical need for precise monitoring and modeling of total ammonium in surface water, considering its variable toxicity and interactions with environmental factors, to effectively protect aquatic ecosystems, namely ichthyofauna.

1. Introduction

Surface water quality monitoring is a complex procedure that includes a number of chemical analyses performed on water. When analyzing water quality based on a comparison of nine indicators with their Maximum Permissible Concentration (MPC) values, important indicators such as pH, temperature, electrical conductivity, and acidity and alkalinity of water are usually not taken into account [1]. If the concentration of a chemical substance in water exceeds the established MPC, this may indicate contamination of the water body and the need to take measures to reduce the level of contamination and restore water quality [2]. Usually, the approach allows us to determine the extent to which water meets the established standards and whether it can be used for various needs, e.g., drinking, fishing, recreation, etc. [3]. Assessment of the quality of surface water is a difficult task, since measures to improve the condition of the water environment or, conversely, their absence, depend on its conclusion [4].

1.1. Sources and Regulation of Ammonia in Water Bodies

Ammonia contamination of aquatic ecosystems is a significant global problem, and robust water quality standards or criteria are needed to protect local water intakes. Ammonium (NH₄⁺) and ammonia (NH₃), which make up the TAN content of aquatic ecosystems, are of great interest to environmental scientists because they can be used to study the nitrogen cycle and are considered indicators of water quality [5]. The natural formation of TAN concentration in water bodies occurs as a result of the nitrogen biogeochemical cycle, as most organisms consume nitrogen in the form of NH₄⁺ (or organic nitrogen) or by reducing NO₃⁻ to NH₄⁺. Conversely, NH₄⁺ is returned to the environment when organisms die, and the variety of subsequent nitrogen forms depends on whether the local environment contains soluble oxygen [6]. The environmental risk caused by ammonia is of increasing worldwide interest due to high emissions of ammonia and its strong toxic effects on aquatic organisms [7].

Ammonia can be released into surface waters from point and non-point sources with treated and untreated wastewater. Point sources of TAN include sewage from animal husbandry, industrial sewage, municipal sewage, nitrogen emissions from aquaculture, and runoff and infiltration from waste disposal sites [8]. Additional point sources encompass runoff from operating mines, oil fields, and industrial facilities without sewage systems. Non-point sources include the cultivation of N₂-fixing crops, the use of animal manure, and the use of inorganic nitrogen fertilizers [9]. Additional non-point sources are runoff from N-saturated forests and meadows, urban runoff from unsewered and channelized areas, and septic leachate. Further sources include runoff from construction sites and abandoned mines, as well as activities such as biomass burning, land clearing, land conversion, and wetland drainage that mobilize nitrogen from long-term storage pools [10].

With regard to purpose, surface waters are traditionally divided into the following: drinking, fishing, recreational and touristic, ecological, and marine. Depending on the purpose of the water, appropriate standards for its quality are adopted. In Ukraine, water bodies used to meet drinking, household, and other needs of the population have a standard of total ammonium at 2 mg/dm³ [11,12]. According to the environmental safety standards of water bodies used for fish farming, the natural fresh water standard is at 0.5–1.0 mg/dm³, and the fishing water is at 1.0–2.0 mg/dm³ [13]. These concentration values do not correlate with water pH, electrical conductivity, temperature, and other water characteristics. The generally accepted rate of ammonium in water for ecological reservoirs is 0.05 mg/dm³. This norm ensures the normal functioning of aquatic ecosystems and is not toxic to fish and other aquatic organisms [14].

However, in some cases, such as in large rivers, the concentration of ammonium can be higher. For instance, in the Dnipro River, the ammonium level is 0.1 mg/dm³ [15]. This is attributed to the fact that the Dnipro is a large river with a fast current, facilitating the dissolution of ammonium in water. In contrast, in smaller lakes and ponds near pollution sources, the ammonium concentration may be lower. This is because such smaller bodies of water have a limited capacity and are more sensitive to pollution [16].

The United States Environmental Protection Agency (USEPA) developed this adjustment equation based on studies that examined the relationship between ionized and non-ionized ammonia as a function of pH and temperature in water. In Australia and New Zealand, jurisdictions have adopted the USEPA method for adjusting ammonia standard values based on temperature and pH [17].

In contrast, European environmental quality standards and Canadian water quality regulatory values are set for the concentration of non-ionized ammonia, regardless of pH and temperature [18]; the share of non-ionized ammonia is calculated using speciation equations [19]. Non-ionized ammonia NH₃ is more toxic than ammonium NH₄⁺, especially for aquatic flora and fauna, because it is neutral and diffuses through the membranes of biological cells more easily than NH₄⁺ [20]. Therefore, biotic toxicity is usually determined for NH₃ rather than NH₄⁺. However, NH₄⁺ also contributes to the total ammonia toxicity under certain conditions; therefore, its contribution to the total toxicity cannot be ignored [21]. The pH value and water temperature strongly influence the NH₃ and NH₄⁺ ratio, and therefore the toxicity; the higher the temperature and pH, the higher the proportion of NH₄⁺ and the higher the contribution of NH₄⁺ to the total toxicity of ammonia [22]. Such a dependence can be seen in Figure 1. The toxicity of non-ionized ammonia NH₃ in water is greater, because it is soluble in fats and can penetrate into the cells of living organisms.

In addition to pH and temperature, the balance of ionized and non-ionized ammonia is also influenced to a lesser extent by other physicochemical parameters, such as water hardness, alkalinity, and ionic strength. Reduction of ammonia toxicity by calcium ions, as well as sodium Na⁺ and potassium K⁺ ions, was demonstrated in the amphipod Hyalella azteca [23]. Extremely soft water (hardness < 5 mg/dm³) in its living environment may lead to increased toxicity of many pollutants, including ammonia. Regulations appropriate to the region are necessary to adequately protect these unique ecosystems [24].

In waters defined by the European Commission, the EQSs for the protection of freshwater fish are 0.021 and 0.78 mg/dm³ for non-ionized ammonia and total ammonia, respectively [25]. An EQS of 0.015 mg/dm³ for non-ionized ammonia expressed as an annual average has been proposed for non-EU waters [26].

Anthropogenic sources of ammonia pollution are diverse and include process waters from mining and petrochemical industries, waste from pharmaceutical production, and nitrogen fertilizers used in agriculture. Nuclear power plants are one of the important enterprises in Ukraine that may affect the chemical composition of surface waters of the country [27]. Nuclear power plants (NPPs) produce wastewater containing TAN and having elevated temperatures and pH levels [28,29]. Heating, evaporation, and concentration of cooling water components occur in NPP cooling systems; in particular, the concentration of bicarbonate and carbonate ions causes an increase in the pH of hydrogen in NPP discharge waters to 9.0 [30,31]. NPP water discharge in terms of temperature impact and chemical composition in Ukraine is regulated by [32,33]. Nitrogen-containing substances are discharged with NPP return waters due to the use of corrective additives for cleaning the second circuit (ammonia, hydrazine, morpholine, monoethanolamine, etc.) due to the discharge of mixed-action regeneration water filters [34]. Therefore, such waters also have an increased content of nitrogenous substances, phosphates, and carbonates [35] and are discharged into natural bodies of water (seas, oceans, rivers, lakes) [36]. Therefore, the study of the effect of total ammonium on the water body which comes with NPP waters is a very relevant issue.

Generally, the relevance of the influence of total ammonium at elevated temperatures is given a lot of attention, particularly for tropical freshwater species. This is mainly due to the fact that such surface waters are characterized by the presence of ammonia in water with low ionic strength and elevated temperature (over 27 °C), which can lead to its higher toxicity [18,37]. The pH value also affects the ratio of TAN forms and thus the toxicity. There are a number of countries and regions around the world that have consistently established aquatic life criteria for ammonia based on the appropriate relationship between ammonia toxicity, temperature, and pH [38].

Although studies on the environmental risks of ammonia were conducted in Ukraine and environmental standards for TAN were established, none of them took into account the influence of water environment factors (temperature, pH, etc.) on the toxicity of TAN forms [11,12,13,14]. Our study addresses this knowledge gap.

There are several [39] analytical methods that allow for the separate determination of NH₃ and NH₄⁺ forms (electrochemical, chromatographic, etc.), but these methods are time-consuming and require the use of expensive equipment. Total ammonium is usually measured in monitoring programs along with physicochemical parameters (pH, temperature, and conductivity or salinity), and then non-ionized ammonia is calculated. Current analytical methodologies provide detection limits of about 20 μg/dm³, which does not provide sufficient sensitivity for ammonia analysis with the proposed PNECs [18].

There are various indices used to evaluate and monitor water quality in water systems [40]. One of the first systems developed by Horton [41] was the creation of general indices that allow systematizing various parameters of water quality. This methodology was later improved by the US National Sanitation Foundation (NSF), resulting in the well-known water quality index (WQI) [42]. WQI is an index that shows the level of cumulative influence of selected parameters on the overall water quality in the form of a single numerical value, and this indicator is widely used worldwide to assess water quality [43,44].

1.2. Advanced Techniques in Water Quality Assessment: Fuzzy Modelling and Artificial Neural Networks

In recent years, fuzzy modelling has been one of the most active and promising areas of research applied in the field of management and decision making. Fuzzy modelling is particularly useful when there is uncertainty in the description of systems and business processes that complicates or even precludes the application of precise quantitative methods and approaches. In the field of systems management, fuzzy modelling allows us to obtain more adequate results compared to results based on the use of traditional analytical models and control algorithms. One of the characteristic features of the complexity of building a model is uncertainty in the presentation of the structure or behavior of the original system.

Traditional algorithms easily work with simple linear processes [45], but algorithms with fuzzy logic can work in complex or nonlinear processes, such as pH control, where nonlinearities arise together with time-varying parameters or dead times [46,47]. Control strategies based on fuzzy logic are not based on mathematical modelling depicting chemical or physical relationships between the system components; instead, they deal with a set of rules related to the changes observed in the process when the variable also changes and are therefore more easy to implement.

Modelling ecological systems is a complex scientific task, as researchers often fail to make accurate statements about inputs and outputs. To solve this problem, fuzzy logic can be applied in the development of environmental monitoring indicators [48]. It is known that tools and possibilities of fuzzy logic are actively used to assess water quality by calculating WQI [42].

A large volume of data is used to assess the quality of natural waters. The study indicates the effective use of artificial neural network (ANN) models, which are built on the structure of biological neural networks [49]. The primary advantage of ANNs is their ability to detect implicit relationships between input and output data and predict the water quality index (WQI) [50]. Creating an ANN requires an appropriate network structure and a significant amount of data, with the optimal structure determined through experience and trial and error [51]. ANN models show high potential for forecasting the quality of underground and surface water. Many scientific reports demonstrate successful applications of ANNs in predicting WQI and changes in concentrations of NO₃⁻, DO, and BOD [52].

Thus, the novelty of this study consists of the proposal to modify the WQI natural water quality assessment methodology used in Ukraine and to use an additional water quality index based on the effect of ammonium WQIAM on flora and fauna. The urgency of implementing such an index is related to the importance of assessing the impact of NPP wastewater discharges into the river.

The aim of the work was the following. We aimed to conduct an analysis of the main factors influencing the NH₃-NH⁴⁺ balance, that is, the level of ammonium toxicity in surface waters, and to use them in modelling. Based on this, it was necessary to create a water quality assessment model based on ammonium content using fuzzy logic and ANN to predict the toxic effect of ammonium on aquatic living organisms. The practical value of the obtained results was to establish for which consumers and which water organisms the ammonium-containing surface waters would have a valuable practical value.

2. Material and Methods

2.1. Study Area and Water Quality Analysis

The research was conducted on the Styr River, within the Rivne Nuclear Power Plant (RNPP) water discharge influence zone. Sampling and monitoring of parameters were carried out by the certified measuring laboratory of the RNPP (Certificate of Recognition of Measuring Capabilities No. R-8/11-57-5 dated 22.12.17), using measuring instruments verified by the State Metrological Supervision of Ukraine. Standard measurement methods were used to control the concentration. This study used the monitoring RNPP results for 2018–2022 (

Table 1. Characteristics of the measurement methods (CI is the measurement range, δ is the relative measurement error, ∆ is the absolute measurement error).

Indicator	CI	δ (∆)	Measurement Method (Standard in Ukraine)
pH25	1–12	(± 0.2)	[53]
TAN, mg/dm3	0.1–50	±5%	[54]
CO32−, mg/dm3	-	-	[55]
PO43−, mg/dm3	0.05–0.5	±15%	[56]
Temperate, °C	1.5–70	(0.1 °C)	[57]
Cl−, mg/dm3	7–1500	±20%	[58]
SO42−, mg/dm3	5–500	±9%	[59]
DO, mg/dm3	0.5–50	0.5 to 5: δ = ±25; 5 to 20: δ = ±20; 20 to 50: δ = ±10	[60]
NO2−, mg/dm3	0.03–10	0.05 to 1.0: ±δ = 50%, more than 1.0: 25%	[61]

).

The flow rate in the Styr River, Q [m³/s], was measured at the hydrological station below the water intake of the RAPP using an acoustic flow rate meter; the flow rate was calculated as the product of the cross-sectional area (m²) by the average flow rate (m/s).

The Styr River basin is located in northwestern Ukraine, within the Lviv, Volyn, and Rivne regions. The river is 494 km long and its catchment covers an area of 13,100 km² with an average annual water flow of 49.5 m³/s at the mouth, decreasing to 10–20 m in the upper reaches and increasing to 30–50 m in the middle and lower reaches. The riverbed is composed of sandstones and shales of Cretaceous and Paleogene age, as well as Miocene clays in the lower reaches. According to surface water typology, the Styr River is a lowland-type, sandy loamy river [36].

Two water sampling sites were selected (Figure 2). Their selection was carried out for the purpose of monitoring whether there is a negative impact from the discharge of cooling water into the Styr River by the RNPP in terms of ammonium content.

2.2. Fuzzy Logic

The theory of fuzzy sets, the main ideas of which were proposed by the mathematician Lotfi Zadeh [57], allows us to describe qualitative, fuzzy concepts and knowledge about the surrounding world, as well as to operate on the knowledge in this theory to form an independent direction of scientific and applied research—fuzzy modelling [58]. Development and application of fuzzy inference systems include a number of stages (Figure 3).

Next, Mamdani’s algorithm was used, which is one of the first that was used in fuzzy inference systems [62]. Mamdani’s algorithm consists of the following steps:

• Formation of the rule base of fuzzy inference systems.
• Fuzzification of input variables.
• Aggregation of terms according to fuzzy rules. Paired fuzzy logical operations are used to find the degree of truth of the conditions in each of the fuzzy rules.
• Activation of sub-conclusions in fuzzy rules; at the same time, only active fuzzy rules are taken into account to reduce the output time.
• Accumulation of the conclusions of vague rules.
• Defuzzification of source variables.

The characteristics of the fuzzy set are the membership function. In this study, a triangular membership function was used, which can be expressed as:

$$\mu \left(x\right)=\left\{\begin{array}{c}0,x\le a\vee x\ge c\\ \frac{x-a}{b-a},a\le x\le b\\ \frac{c-x}{c-b},b\le x\le c\end{array}\right.$$

(1)

where a is the minimum possible value, b is the most expected value, and c is the maximum possible value.

2.3. Artificial Neural Networks

The basis of the next stage of research was the creation, training, and testing of ANN models (Figure 4).

To create and effectively use an ANN model, it is very important to correctly choose the model parameters. The learning parameters can be classified as follows:

• Parameters related to the network architecture:

  -

  Number of hidden layers and their characteristics;

  -

  Initialization of network weights;

  -

  Selection of the activation function.

• Parameters related to the learning process:

  -

  Batch size—the number of data subsets used for the unit weight calibration process. Depending on the processing power, the batch size can be from a few data points to an entire dataset. A batch size that is too small may result in a longer learning process. On the other hand, an excessively large batch size may lead to the impossibility of achieving convergence.

  -

  Number of epochs—the number of times the entire training dataset is exposed to the network during training. The number of epochs can vary from a few to several thousand and depends on the size of the training set, the type of network, and the specifics of the problem.

  -

  Loss function—a function that compares target values and predicted output values. The main goal of training is to minimize the loss function between those values.

  -

  Optimization algorithm—a function or algorithm that adjusts the learning parameters of a neural network. To implement the learning process of the neural network, backpropagation algorithms are used for multiple iterative comparisons of the network’s output value with the expected value. The number of performed comparisons depends on the size of the training set, the expected number of iterations, and the training progress of the network. Without the use of backpropagation algorithms, a simple comparison of the output values would only update the weights on the last layer of the hidden network, since its inner layers act as a black box. To update them, the backpropagation algorithm calculates the derivative values of the activation function of each neuron in the network based on the input vector for each level [63].

The key indicator when calculating various loss indicators is the observation error $e_i$, which is defined as the difference between the target value and the value predicted by the model for a given observation i [64].

$$e_i=y_i^{\prime }-y_i$$

(2)

where $y_i^{\prime }$—predicted value; $y_i$—target value.

Measures based on absolute errors include the mean squared error (MSE):

$$MSE=\frac{1}{n}{\sum }_{i=1}^n{e}_i^2,$$

(3)

A group of indicators based on the part of the main measure is expressed as a percentage of $p_i$, including the mean absolute percentage error (MAPE):

$$pi=\left|ei\right|yi,$$

(4)

MAPE is calculated from the formula:

$$MAPE=\frac{1}{n}{\sum }_{i=1}^{n}100·\left|p_i\right|,$$

(5)

The MSE indicator was calculated to evaluate the model effectiveness. MAPE and ${\mathrm{R}}^2$ were used for comparative analysis of the model performance.

R² is a statistical measure used to predict future outcomes or test hypotheses based on other related information. R² is determined using Formula (6) [65]:

$$R^2=1-\frac{\sum {\left(y_i-y_i^{\prime }\right)}^2}{\sum {\left(y_i-\overline{y_i}\right)}^2}.$$

(6)

In the next stage of the study, six ANN models were created which had the same architecture but differing activation functions (ReLU, softmax, tanh) and optimization algorithms (ADAM, RMSprop) [66].

The network structure, with an input layer consisting of 4 neurons, one hidden layer (128 neurons), and an output layer with 1 neuron, was optimal (Figure 5).

3. Results and Discussion

The water quality of the river after the discharge of cooling water in the Styr River is indicated in

Table 2. Indicators of the water quality of the Styr River before (C1) and after (Ce) discharge of cooling water (M ± SD during 2018–2022, M—is the mean value, SD is the standard deviation).

	T, °C	Q, m3/s	pH	DO, mg/dm3	TAN, mg/dm3	NO2−, mg/dm3	SO42−, mg/dm3	Cl−, mg/dm3	CO32−, mg/dm3	PO43−, mg/dm3
S1
January	1.2 ± 2.7	34.8 ±14.1	792 ± 0.08	12.29 ± 0.42	0.62 ± 0.11	0.07 ± 0.03	51.7 ± 8.9	13.7 ± 2.2	241 ± 10	0.22 ± 0.06
February	2.6 ± 4.5	36.4 ± 18.2	8.03 ± 0.06	12.22 ± 1.15	0.57 ± 0.12	0.06 ± 0.02	52.9 ± 13.3	15.7 ± 1.5	237 ± 15	0.15 ± 0.05
March	5.5 ± 5.1	44.2 ± 22.3	8.16 ± 0.07	12.24 ± 1.49	0.43 ± 0.09	0.07 ± 0.04	45.2 ± 9.5	14.9 ± 2.8	229 ± 16	0.16 ± 0.13
April	12.0 ± 4.6	43.2 ± 9.8	8.15 ± 0.10	11.63 ± 1.07	0.47 ± 0.08	0.09 ± 0.07	39.8 ± 11.1	13.7 ± 3.1	253 ± 18	0.19 ± 0.09
May	17.3 ± 1.9	39.2 ± 9.3	8.29 ± 0.06	8.99 ± 1.41	0.36 ± 0.10	0.17 ± 0.06	42.4 ± 8.8	13.6 ± 1.5	228 ± 10	0.28 ± 0.14
June	21.8 ± 0.3	29.6 ± 7.4	8.42 ± 0.07	9.24 ± 0.7	0.29 ± 0.08	0.14 ± 0.09	37.4 ± 11.0	14.0 ± 1.6	243 ± 12	0.39 ± 0.15
July	21.7 ± 2.4	25.0 ± 4.9	8.41 ± 0.08	8.79 ± 1.52	0.22 ± 0.07	0.08 ± 0.03	39.6 ± 12.2	13.0 ± 2.5	227 ± 22	0.42 ± 0.05
August	22.7 ± 5.2	14.6 ± 9.3	8.32 ± 0.10	9.43 ± 0.62	0.23 ± 0.09	0.08 ± 0.02	36.7 ± 7.2	14.1 ± 2.4	218 ± 26	0.41 ± 0.08
September	16.9 ± 5.5	17.4 ± 7.6	8.18 ± 0.10	10.33 ± 0.91	0.21 ± 0.09	0.06 ± 0.02	35.2 ± 6.2	15.6 ± 2.3	226 ± 28	0.34 ± 0.08
October	9.6 ± 3.6	24.0 ± 6.6	8.18 ± 0.09	10.67 ± 1.44	0.26 ± 0.09	0.05 ± 0.01	36.3 ± 13.7	14.8 ± 2.3	218 ± 30	0.32 ± 0.03
November	4.9 ± 1.9	24.4 ± 17.3	7.97 ± 0.09	11.38 ± 0.87	0.30 ± 0.08	0.08 ± 0.02	44.8 ± 12.9	15.5 ± 1.8	235 ± 15	0.22 ± 0.07
December	1.8 ± 1.7	26.6 ± 16.9	7.94 ± 0.03	12.49 ± 0.93	0.48 ± 0.11	0.05 ± 0.02	35.5 ± 9.4	15.8 ± 5.4	223 ± 20	0.20 ± 0.07
S2
January	2.1 ± 2.4	34.8 ± 14.1	8.06 ± 0.16	11.72 ± 0.55	0.57 ± 0.12	0.06 ± 0.03	52.6 ± 9.1	14.5 ± 1.7	245 ± 11	0.25 ± 0.07
February	3.6 ± 4.9	36.4 ± 18.2	8.12 ± 0.18	11.42 ± 0.90	0.59 ± 0.14	0.04 ± 0.03	54.4 ± 13.2	14.4 ± 0.6	246 ± 18	0.18 ± 0.04
March	6.1 ± 5.5	44.2 ± 22.3	8.28 ± 0.11	11.79 ± 1.31	0.51 ± 0.11	0.07 ± 0.04	45.2 ± 9.1	14.8 ± 2.9	246 ± 17	0.17 ± 0.14
April	13.0 ± 4.5	43.2 ± 9.8	8.23 ± 0.08	11.00 ± 1.06	0.53 ± 008	0.09 ± 0.06	41.9 ± 11.4	13.1 ± 2.9	250 ± 15	0.19 ± 0.12
May	18.4 ± 1.9	39.2 ± 9.3	8.37 ± 0.09	8.88 ± 1.56	0.41 ± 0.09	0.14 ± 0.08	42.3 ± 8.9	14.8 ± 1.2	232 ± 16	0.29 ± 0.12
June	22.5 ± 0.9	29.6 ± 7.4	8.44 ± 0.09	8.86 ± 0.87	0.31 ± 0.11	0.13 ± 0.03	39.6 ± 12.33	16.9 ± 1.6	248 ± 15	0.38 ± 0.12
July	22.4 ± 2.6	25.0 ± 4.9	8.47 ± 0.07	8.65 ± 0.82	0.24 ± 0.12	0.09 ± 0.03	40.7 ± 7.9	15.1 ± 1.6	237 ± 12	0.44 ± 0.14
August	23.0 ± 5.8	14.6 ± 9.3	8.35 ± 0.13	8.80 ± 0.95	0.25 ± 0.14	0.07 ± 0.03	37.3 ± 6.18	14.0 ± 2.2	239 ± 10	0.42 ± 0.06
September	17.4 ± 5.2	17.4 ± 7.6	8.26 ± 0.11	9.68 ± 1.20	0.23 ± 0.08	0.05 ± 0.02	36.3 ± 14.2	16.2 ± 2.3	232 ± 11	0.37 ± 0.08
October	10.3 ± 3.6	24.0 ± 6.6	8.26 ± 0.09	10.26 ± 1.26	0.28 ± 0.07	0.05 ± 0.01	37.8 ± 14.1	14.6 ± 2.5	221 ± 28	0.33 ± 0.07
November	5.8 ± 2.3	24.4 ± 17.3	8.04 ± 0.07	11.03 ± 1.25	0.36 ± 0.06	0.08 ± 0.03	46.2 ± 11.0	16.9 ± 3.4	240 ± 18	0.23 ± 0.06
December	2.3 ± 1.6	26.6 ± 16.9	8.10 ± 0.07	12.02 ± 1.12	0.51 ± 0.11	0.05 ± 0.02	35.0 ± 8.6	16.6 ± 2.9	233 ± 18	0.21 ± 0.05

, showing the result of the discharge of RNPP return water in the area of the Styr River. Temperatures vary considerably between the two sections (S1 and S2), ranging from 1.2 °C to 23.0 °C. Section S1 has higher average temperatures compared to Section S2. The highest temperatures occur in July and August, while the lowest values are observed in January and December. Peak water flow in the Styr River occurs in March and April, while the lowest values are observed in August and September. pH values remain within a range from 7.92 to 8.47 throughout the year in both sections. Temperatures vary considerably between the two sections (S1 and S2), ranging from 1.2 °C to 23.0 °C. Section S1 has higher average temperatures compared to Section S2 (Table 2). The highest temperatures occur in July and August, while the lowest values are observed in January and December. Peak runoff occurs in March and April, while the lowest values are observed in August and September. pH values remain within a range from 7.92 to 8.47 throughout the year in both sections. On average, the DO concentration is higher in Section S1 than in Section S2. The concentration of TAN ranges from 0.23 mg/dm³ to 0.62 mg/dm³ in both sections during the year. The highest concentration of TAN is observed in January and February and the lowest in July and August. There are no significant seasonal variations in the concentration of NO₂⁻, CO₃²⁻, Cl⁻, and SO₄²⁻. The highest concentration of PO₄³⁻ is observed in May and June and the lowest in December and January.

• Justification of the effect of electrical conductivity and anions of weak acids on the level of ammonium toxicity

When monitoring the quality of surface water, according to the current methodology in Ukraine [1], indicators such as water pH, temperature, and the main anions of weak inorganic acids (for example, CO₃²⁻ and SiO₄⁴⁻), except for PO₄³⁻, are not taken into account. This approach does not take into consideration the influence of weak acid anions, which can be present in relatively high concentrations in surface waters. When assessing the TAN impact on flora and fauna, it is advisable to also pay attention to the content of soluble silicates (SiO₄⁴⁻). This anion is not in the list of controlled chemical indicators of water quality, but it can play a similar function as carbonates (CO₃²⁻) in relation to macrophytes. Ionized silicates can be perceived by plants as inorganic fertilizers, which are extremely necessary, e.g., for diatoms and various other submerged macrophytes. Its main purpose is to strengthen the stem and roots of the plant [67]. Water electrical conductivity is also an important parameter, but it affects only the balance of ionized and non-ionized ammonia in water [18,24]. As evidenced by modern scientific results of experimental research, it is believed that water with an electrical conductivity of more than 500 mS/cm or more than 200–300 mg/dm³ has a relatively stable percentage of non-ionized ammonium, i.e., the chemical balance does not shift in the direction of increasing NH₃. Therefore, it is very important to monitor the water quality with electrical conductivity below 500 mS/cm [68].

At a neutral or alkaline water pH, the concentration of inorganic weak acid anions (PO₄³⁻, CO₃²⁻, SiO₄⁴⁻) can affect the balance between ammonia and ammonium. Thus, their content can determine the toxicity of ammonia in aquatic environments. Their influence on the content of non-ionized ammonia can be more pronounced, especially in alkaline conditions. In this case, the reason is that ammonia and anions of weak acids can react with each other and form inorganic salts, which are weak electrolytes. For example, at a temperature of 25 °C in aqueous solutions with the same molar concentration of 0.1 M, the dissociation constant Ka is 1.86·10⁻⁵ for NH₄HCO₃, 2.9·10⁻⁵ for NH₄H₂PO₄, and 2.9·10⁻⁵ for NH₄HSiO₄. Thus, ammonia is retained by these anions, and the balance between ionized and non-ionized forms is shifted toward the ionized (less toxic) form. In water at a high pH (in alkaline environments), carbonates may be more dominant compared to sulphates, and therefore the effect of carbonates on ammonia distribution may be more pronounced [69]. In the case of anions of strong acids (Cl⁻, SO₄²⁻), although they can interact with ammonia, forming ammonium sulphates and chlorides, their effect is less noticeable in an alkaline environment compared to anions of weak acids.

• WQIAM approach

The process of creating the WQIAM is to summarize a number of different indicators (pH, temperature, concentration of weak inorganic acid anions, water electrical conductivity) into a single compressed value that determines the water quality and its impact on flora and fauna after the discharge of cooled water to River Styr and to make it understandable to a wide number of people, including local residents, who influence the decision making of local authorities [40,70]. Building and modelling with WQIAM will provide the decision makers with a reliable and simple tool to control and monitor water resources downstream of industrial areas.

In order to translate quantitative data into something more sustainable, fuzzy membership functions must first be defined so as to represent an acceptable level. For developing a WQIAM index for the assessment of water quality with regard to ammonium content, the following procedure should be applied [71]. In the first stage, water quality classes are determined for all selected and substantiated variables (chemical parameters of water). Each set of variable values is then assigned to a corresponding quality class value. The next steps are to apply the membership function, create a rule base, and use a fuzzy algorithm. Defuzzification of the conclusions is carried out using the centroid method, the calculation of which is based on the concept of the gravity center of the original function.

Complex relationships occur between the concentration of ammonia nitrogen and various external factors [72]. These factors may affect the TAN concentration differently at different times and in different places, forming complex schemes that greatly complicate the forecast. Taking into account all of the above, the method of water quality assessment based on the content of total ammonium TAN should differentiate chemical indicators according to the level of the negative impact. The conducted literature analysis on the degree of TAN impact on flora and fauna allowed us to make the following assumptions and reasonable conclusions for the preparation of fuzzy logic rules. A fragment of the table with such rules is presented in

Table 3. Fragment of fuzzy logic rules.

T 5–15	T 15–25	T 5–15	T 15–25	T 15–25
pH 6–7.5	pH 6–7.5	pH 8–9.5	pH 8–9.5	pH 8–9.5
EC 500  mS/cm or TDS 200–300 mg/dm3	EC 500  mS/cm or TDS 200–300 mg/dm3	EC 500  mS/cm or TDS 200–300 mg/dm3	EC 500  mS/cm or TDS 200–300 mg/dm3	EC 500  mS/cm or TDS 200–300 mg/dm3
Anions of weak inorganic acids ≥50%	Anions of weak inorganic acids ≥50%	Anions of weak inorganic acids ≥50%	Anions of weak inorganic acids ≥50%	Anions of weak inorganic acids ≥50%
Water quality is good	Water quality is satisfactory	Water quality is satisfactory	Water quality is satisfactory	Water quality is poor

.

Four factors were used as independent variables: T, pH, EC, and AWIA. The triangular membership function was used for the fuzzification of the independent variables (Figure 6).

The linguistic meaning of the independent variables and the distribution of ranges are given in

Table 4. Ranges of linguistic values for particular factors.

Factors	T	pH	EC	AWIA
low	[1, 5, 9]	[5.4, 6, 6.6]	[−100, 500, 1100]	[−4, 0, 4]
middle	[6, 10, 14]	[6.15, 6.75, 7.35]	[650, 1250, 1850]	[1, 5, 9]
high	[11, 15, 19]	[6.9, 7.5, 8.1]	[1400, 2000, 2600]	[6, 10, 14]

. Each of the variables was described by three terms: low, middle, and high.

The inference system checks the value of each linguistic variable using fuzzy logic rules and transforms the input set into an output linguistic variable. The next step of fuzzy inference is to aggregate the input data based on the generated rules. Multiple rules are processed simultaneously, followed by their aggregation into the final solution using a fuzzy logical conclusion. The set of rules in this study included 125 rules (Figure 7). This study used the Mamdani-type inference based on an IF-THEN logic function using an AND function as a conjunction.

The centroid defuzzification method was used to calculate the output value, in which the original value was determined based on the gravity center of the original fuzzy set. The output variable was described by five terms: very good, good, satisfactory, poor, and very poor (Figure 8).

The linguistic value of the source variable and the distribution of ranges are given in

Table 5. Linguistic meaning of the source variable and distribution of ranges.

very good	[−1.5, 0, 1.5]
good	[1, 2.5, 4]
satisfactory	[3.5, 5, 6.5]
poor	[6, 7.5, 9]
very poor	[8.5, 10, 11.5]

.

The final step involves defuzzification, where the fuzzy linguistic output variables are converted into numbers. Figure 9 shows an example of the defuzzification step.

The output variable WQIAM was calculated for 448 monitoring records. After using the fuzzy logic model, a table was formed which contained 448 rows and 5 columns: the first 4 are the input variables (T, pH, EC and AWIA), and the last column is the output variable (WQIAM).

During the next stage of the study, six ANN models were created.

Table 6. Comparison of the ANN model performance.

ANN Models	ANN#1	ANN#2	ANN#3	ANN#4	ANN#5	ANN#6
activation function	ReLU	ReLU	softmax	softmax	tanh	tanh
optimization algorithm	ADAM	RMSprop	ADAM	RMSprop	ADAM	RMSprop
R2	0.9686	0.9754	0.7436	0.7229	0.5228	0.5641
MAPE, %	5.8	5.2	14.9	13.3	16.6	15.9

shows the characteristics of ANN models and a comparison of their performance. Performance testing of the models was carried out for 100 epochs; increasing the number of epochs did not lead to an increase in the model efficiency. The dataset was divided into three parts—training/testing/validation at the ratio of 70%/15%/15%. The batch size was set to one batch.

It should be noted that the use of the activation function ReLU compared to the functions softmax and tanh showed a significant increase in performance. Analysis of MAPE and R² indicated that the ANN#2 model achieved the best performance results (lowest MAPE and highest R²). This network used the ReLU activator for the hidden layers of neurons and the ADAM loss function optimizer. The best performance was achieved for MAPE = 5.8%; R² = 0.9686.

Figure 9 and Figure 10 show a comparison of the MSE and MAE results for the training and validation datasets for the best (ANN#2) and worst (ANN#5) ANN models.

Figure 10a shows the MSE comparison results for the training and validation datasets of the ANN#2 model. The maximum value of MSE was reached in the first epoch and was 11.933 for the training sample; the validation set was 4.504. The minimum MSE values were as follows: 0.1826 for the training set in the 96th epoch and 0.0336 for the validation set in the 88th epoch.

Figure 10b shows the results of MSE comparison for the training and validation datasets of the ANN#5 model. The maximum value of MSE was reached in the first epoch and was 28.469 for the training sample or 27.357 for the validation set. The minimum MSE values were reached in the 95th epoch and were 0.986 for the training set and 0.825 for the validation set.

Figure 11 shows the distribution of predicted and target values of the ANN#2 (a) and ANN#5 (b) networks. In the case of the ANN#2 network, the vast majority of predicted values are as close as possible and do not deviate from the regression line.

The architecture, weights, and configuration of the ANN#2 model after training and testing were saved in H5 and JSON files. This allows the model to be used without retraining. Additionally, the model can make predictions about datasets that it has not yet “seen”. The next step was to check the effectiveness of the model and compare its forecast with real data. The dataset contained 8 records, one record for each grade level, which were obtained during the Fuzzy Logic model application phase. Data were loaded into the ANN model and the predicted values (y′) were calculated.

Table 7. Evaluation of the prediction efficiency of the ANN#2 model.

Target Value (y)	Predicted Value (y′)	Deviation ∆y, %
2	2.004	0.18
3	2.994	0.19
4	3.974	0.65
5	5.004	0.07
6	5.993	0.12
7	7.32	4.57
8	8.086	1.07
9	8.548	5.02

shows target values (y), predicted values (y′), and the percentage deviation ∆y between these values.

Table 7 shows that the deviation levels between the target and forecast values can be estimated as low, which confirms the modelling efficiency and the high quality of the obtained forecasts.

Since the purpose of this work was to assess the impact of an NPP which discharges ammonium-containing wastewater into the Styr River, it is appropriate to choose ichthyofauna for predicting the impact of ammonium, due to the fact that when comparing the norm of total ammonium for drinking water and fisheries, the requirements for fisheries are stricter.

The development of a water quality assessment model and a water quality prediction model based on ammonium content is of not only scientific but also practical importance. The practical significance of the obtained results lies in the search for users of ammonium-containing natural waters, for which even a slight increase in its concentration or other indicators of water quality (T, pH, electrical conductivity, concentration of anions of weak inorganic acids, etc.) can lead to negative consequences. Thus, for consumers of surface water who use it as a source of drinking water, the change in the concentration of ammonium and other listed indicators is important, but not as important as for flora and fauna. Surface water, which is the source of the water supply, is required to be cleaned, and most often the water treatment station will ensure compliance with the necessary requirements for this indicator [73,74].

Surface waters with ammonium are the immediate environment for the creation of flora and fauna. Therefore, when evaluating and comparing the impact of TAN on flora and fauna, it is necessary to understand mainly which living organisms are extremely sensitive to its toxicity. As reported in a number of scientific studies, a significant number of macrophytes perceive ammonium as a nutrient element [75,76]. Plants fix it especially well together with soluble carbon dioxide, which in turn is consumed for their growth (photosynthesis) [18]. In paper [77], it was demonstrated that Lemna aequinoctialis was moderately sensitive to ammonia, but an increase in ammonia concentration inhibited the growth of the macrophyte Ceratophyllum demersum due to the decrease in the content of non-structural carbohydrates in the leaves.

In paper [76], it was stated that ammonia toxicity is most pronounced in the macrophyte Elodea canadensis at higher temperatures (25 °C) and low pH values of 6. They suggested that this was due to a limited amount of inorganic carbon required for the construction of carbohydrates, necessary for ammonia detoxification. The two forms of inorganic carbon available to macrophytes are CO₂ and carbonates. At high temperatures, CO₂ is limited due to the lower concentration of dissolved gases; at low pH, carbonate availability is limited due to the interaction with hydrogen ions [78,79]. Thus, it can be assumed that when managing a water body with an increased TAN content and a low carbon content, it may be appropriate to introduce natural limestone into the water [69,79]. This should allow improved growth of submerged macrophytes that consume TAN together with carbon as inorganic fertilizers.

It is known that fish are the most sensitive species to both chronic and acute exposure to ammonia. However, there is overlap between the sensitivities of representatives of different taxonomic groups, and furthermore, the range of acute toxicity values for all taxa is within approximately two orders of magnitude. The toxicity of ammonia to fish is well documented, and some mechanisms of this process are well explained. These include proliferation of gill tissue cells [18], violation of osmoregulatory and circulatory activity, and subsequent violation of the metabolic function of the liver and kidneys [80]. Most fish produce ammonia as the end product of protein metabolism, which is excreted through the gills into the surrounding water. The increased content of ammonia in the environment worsens its removal from water, and the increased content of ammonia leads to an imbalance of ion regulation in the body of fish [26].

4. Conclusions

The research presented in the article emphasizes the need to improve the methodology of comprehensive ecological assessment of surface waters, especially for reservoirs receiving ammonium-containing wastewater from nuclear power plants. The proposed WQIAM Total Ammonium Exposure Water Quality Index resulted from a modification of the WQI calculation methodology. It was established that the percentage of the highly toxic non-ionized form of ammonium (NH₃) increases significantly not only with an increase in temperature and pH, but also with other parameters (electrical conductivity, concentration of anions of weak inorganic acids). This approach makes it possible to predict the concentration balance of ionized and non-ionized forms of ammonium under the influence of local variations of established factors in reservoirs. The creation of an ANN model for predicting the toxic effect of ammonium on aquatic living organisms showed its effectiveness through the analysis of the obtained values (MAPE = 5.8%; R² = 0.9686). The practical importance of this research can be useful in several areas of environmental management and sustainable water management. First, forecasting the levels of toxicity in reservoirs is a necessary condition for effective management of wastewater discharge of industrial facilities, ensuring their compliance with environmental norms and standards. Secondly, modeling the relationships between the chemical indicators of water increases the probability of avoiding a crisis state of receiving reservoirs of nuclear power plants and the level of their environmental safety. Third, the proposed WQIAM index for estimating and predicting the content of non-ionized ammonia allows for the development of more effective strategies for the protection of ichthyofauna, which is important for the preservation of biodiversity.