## 3 Results and Discussion  
Our research implemented a rigorous methodology for assessing interpolation techniques using the Mures River's monthly average flow dataset. The evaluation framework was designed to comprehensively test different imputation methods performance across various data missingness scenarios. Data preparation involved utilizing a complete monthly average flow dataset from the Mures River into which we systematically introduced data  
Figure 5: Imputation and performance assessment steps including forward and backward imputation phase, without relying on complete dataset. gaps with 5%, 10%, 15%, and 20% missingness levels, generating 1000 distinct samples for each gap percentage. The gap preparation methodology ensures a controlled and reproducible comparison environment by applying a uniform missing data pattern across the dataset, effectively eliminating potential biases in gap placement. The selected gap rates were chosen to reflect real-world data characteristics, where environmental and scientific datasets frequently exhibit similar levels of missingness. This approach enhances the practical relevance of our research findings, bridging the gap between theoretical methodologies and actual observational challenges. By implementing a large sample size of 1000 distinct datasets for each missingness level, we significantly enhanced the analytical robustness of our research. This expansive approach minimizes the influence of random variations and enables statistically rigorous conclusions. The comprehensive testing framework allows for an objective assessment of various imputation methods' suitability by measuring their performance against a known ground truth. Visualization of an imputation result is exemplified in Figure 6, which provides a representative illustration showcasing the original data series, identified gap sections with their original values, and the imputed data for those gap sections. To ensure transparency and reproducibility, the complete research datasets are publicly available on GitHub at [[https://github.com/zsmagyari/SelfImpute](https://github.com/zsmagyari/SelfImpute)]([https://github.com/zsmagyari/SelfImpute](https://github.com/zsmagyari/SelfImpute)). There are various basic metrics for evaluating imputation errors, of which we chose the Mean Absolute Error (MAE), as it is less sensitive to outliers [56]. Alongside this, our performance evaluation utilized another two statistical metrics: the number of outliers in error values (OUTL) and the standard deviation of errors (SD). These metrics were calculated as average values across the 1000 sample datasets, providing a comprehensive and nuanced understanding of each imputation method's effectiveness. To ensure precise outlier identification, we employed [PERSON]'s method [57], which relies on the interquartile range of the data. The R function collecting the basic statistical metrics of evaluation are publicly available on GitHub at [[https://github.com/zsmagyari/SelfImpute](https://github.com/zsmagyari/SelfImpute)]([https://github.com/zsmagyari/SelfImpute](https://github.com/zsmagyari/SelfImpute)). Figure 6: _Cont._  
Figure 7 presents a comprehensive comparative analysis of three key performance metrics across different imputation methodologies, focusing on the **P** scenario for machine learning methods. The results reveal significant insights into the effectiveness of various interpolation techniques. The Ratio method consistently demonstrated inferior performance compared to the ARIMA-based Kalman filter. Both methods exhibited an increasing (MAE) as the percentage of data gaps expanded, indicating reduced accuracy with greater data missingness. Machine learning algorithms demonstrated superior performance due to their advanced pattern recognition capabilities. Unlike traditional methods that rely on single-column data, these algorithms leverage complex internal learning mechanisms to identify and reconstruct missing information across multiple dimensions.