Agriculture is one of the several major sources of nitrate pollution, and therefore the EU Nitrate Directive, designed to decrease pollution, has been implemented. Point sources like septic systems and broken sewage systems also contribute to water pollution. Pollution of groundwater by nitrate from 19 shallow wells was studied in a typical agricultural region, middle Podravina, in northwest Croatia. The concentration of nitrate ranged from <0.1 to 367 mg/l in water from wells, and 29.8 % of 253 total samples were above maximum acceptable value of 50 mg/l (MAV). Among regions R1–R6, there was no statistically significant difference in nitrate concentrations (F = 1.98; p = 0.15) during the years 2002–2007. Average concentrations of nitrate in all 19 wells for all the analyzed years were between recommended limit value of 25 mg/l (RLV) and MAV except in 2002 (concentration was under RLV). The results of the repeated measures ANOVA showed statistically significant differences between the wells at the point source distance (proximity) of 20 m (F = 10.6; p < 0.001). Average annual concentrations of nitrate during the years studied are not statistically different, but interaction between proximity and years is statistically significant (F = 2.07; p = 0.04). Results of k-means clustering confirmed division into four clusters according to the pollution. Principal component analysis showed that there is only one significant factor, proximity, which explains 91.6 % of the total variability of nitrate. Differences in water quality were found as a result of different environmental factors. These results will contribute to the implementation of the Nitrate Directive in Croatia and the EU.

This study investigates the risk to contamination of groundwater in public water supply wells in the Koprivnica-Križevci county (northwest Croatia). Five physicochemical parameters were monitored in all groundwater samples from 2008 to 2017 to identify major differences between the wells, assess temporal variations and understand the capacity for rainfall to alter groundwater pollution loadings. Multivariate discriminant analysis showed statistically significant differences between the six sampled wells based on the analyzed parameters (Wilks' lambda: 0.001; F = 26.2; p < 0.0000). Principal component analysis revealed two significant factors, including factor 1 which explained 32.8% of the variance (suggesting that the quality of the groundwater was mainly controlled by nitrate) and factor 2, accounting for 16.2% of the total variance (which corresponded to KMnO₄/oxidizability and to a lesser extent, pH). The time series data showed disparate trends, with nitrate concentrations increasing, whereas pH and KMnO₄ decreased, while electrical conductivity and chloride levels remained stable. Although rainfall can impact groundwater pollution loadings through dilution processes in aquifers, the resulting fluctuations in physicochemical parameters are complicated by variations in rainfall events and local topography, as well as from climate change. Therefore, it is important to predict the contamination of groundwater quality in the future using machine learning algorithms using artificial neural network or similar methods. Multivariate statistical techniques are useful in verifying temporal and spatial variations caused by anthropogenic factors and natural processes linked to rainfall. The resulting identified risks to groundwater quality would provide the basis for further groundwater protection, particularly for decisions regarding permitted land use in recharge zones.

In groundwater quality analysis, nonlinear models are typically used, with domains spanning the entire real number line. In this study, alongside these models (Logistic, Gompertz and Richards), nonlinear models defined based on functions whose domain is only the positive part of the real number line are presented (Michaelis–Menten, Hill 1 and 2 and Rosin–Rammler 1 and 2). Two case studies were observed in the paper: (i) the dependence of nitrate concentration on the pumping rate in the Bartolovec wellfield, and (ii) the dependence of nitrate concentration on the distance from the source of pollution in the Varaždin wellfield. Both wellfields are located in the alluvial aquifer in northwestern Croatia. In this way, the curves obtained on the basis of the mentioned mathematical functions were fitted to the experimental data. The results show a good fit, so that the values of the coefficients of determination R² are greater than 0.82 for the case study (i) and greater than 0.96 for the case study (ii). Since the models differ in the number of parameters (e.g., three parameters for Michaelis–Menten and five parameters for Rosin–Rammler), the corrected Akaike information criterion (AIC_c) was used for their comparison. In this way, the best fit for the case study (i) was obtained for the Rosin–Rammler 1 model, while for the case study (ii), it was for the Hill 1 model. A t-test was performed for all models, and they can be considered reliable at a significance level of 0.05. However, t-values and p-values were also calculated for each parameter of each model. Based on these results, it is concluded that all model parameters can be considered reliable at a significance level of 0.05 only for the Hill 1 and Rosin–Rammler 1 models in both case studies. For this reason, these models can generally be considered the best fit to the experimental data. The study demonstrates the superiority of nonlinear models with domains restricted to positive real numbers (e.g., Hill 1, Rosin–Rammler 1) over traditional models (e.g., Logistic, Richards) in groundwater quality analysis. These findings offer practical tools for predicting contaminant extremes (e.g., maximum/minimum concentrations) and optimizing groundwater management strategies.