## 6 Discussion and Conclusions  
In this section, we will briefly summarize the main features of the three regression procedures previously presented. We developed two mathematical regression formulas and an ML regression model based on GP to predict the effective length of a subset of the type-A grounding system with varying degrees of accuracy. All developed procedures are practically interpolant predictive models, which are valid for the following ranges of input parameters: \(10\,\Omega\text{m}\leq\rho\leq 3000\,\Omega\text{m}\), \(1\,\upmu\leq T_{1}\leq 10\,\upmu\)s, and \(0.25\,\text{m}\leq d\leq 2\,\text{m}\). We believe these intervals encompass most practical cases of potential use. The analyzed subset of the type-A grounding system consists of two opposing grounding electrodes. This configuration is used mainly in grounding systems of very small dislocated objects such as, for example, hydrological or meteorological stations. These kinds of objects, due to their size, most often have only one down conductor, whereas the standard [16] prescribes a minimum of two ground electrodes per grounding system--thus the centrally fed observed system. The standard [16] also prescribes curves of minimal length \(\ell_{1}\) of type-A grounding electrodes depending only on the soil resistivity and the Lightning Protection Level (LPL) chosen. In our paper, we analyzed the effective lengths of the electrodes for different values of soil resistivity, rise time, and even burial depth for this subset of the type-A grounding system. Although a comparison between these two lengths would be interesting, it is somewhat difficult to perform since the standard provides, for example, a curve of minimal length for the LPLI independent of the lightning current rise time and the burial depth. If we, for example, consider our subset of type-A grounding system buried at a depth of 0.5 m in a soil of resistivity 3000 \(\Omega\text{m}\), our analysis yields effective lengths of each of the electrodes ranging from 78.25 m for a 1 \(\upmu\)s rise time to 134 m for a 10 \(\upmu\)s rise time. The standard [16] yields a minimal length \(\ell_{1}\) of the grounding electrode of 80 m for our chosen scenario for all cases. On the other hand, our proposed regression formula and the ML regression model based on GP provide the readers with optimal lengths of the grounding electrodes for the considered subset of the type-A grounding system. All the presented regression approaches yield satisfactory results, especially when the accuracy of the prediction is put into context with the complexity of usage of that particular approach. Naturally, the simplest regression formula, which is the easiest to use, produces results with the highest deviations between the predicted effective length values and the actual values, although these deviations are not substantial. The slightly more complex regression formula produces significantly lower deviations, as demonstrated in the previous sections. Both formulas are intended for quick engineering estimates. In contrast, the last approach, a GP-based ML regression model, is designed for more complex estimations of the effective length of the considered grounding system where accuracy is more important. This model provides significantly more accurate prediction results compared to the other two models, as seen in the previous section. We presented only one ML regression model in the paper--the one that consistently yielded the best prediction results in our numerical experiments. Many other models were tested but were intentionally excluded from the paper to maintain clarity and avoid clutter. It is worth pointing out at the end of the paper that in our future work we plan to extend our effective length analysis to complex grounding systems. These include, for example, end-fed simple grounding rods as well as various interpretations of the type-A and type-B grounding systems according to [16]. In addition to this, we will explore