## 5 Discussion and Conclusions
The forecast slightly improves when the previous-day measurements are added as a predictor; however, the best forecast is obtained when the climatological value is added as well. The inclusion of the \(T_{\text{clim}}\) can improve the short-term forecast--this is interesting and somewhat surprising and shows how the NN models are capable of successfully utilizing the climatological information along the information on the current state atmosphere. Still, the most significant benefit of climatological information is seen for the long-term forecasts where the error is constrained to the climatological forecast error. The analysis by the XAI methods showed that in these cases, the NN prediction is almost solely based on the climatological value and that other predictors have a very small influence. One interesting observation is that, while the average error of the 50-member NN ensemble tends to be larger than the error of the climatological forecast after day three, the ensemble's minimum error is often a bit smaller. Although the NN ensemble performs worse on average, at least one ensemble member can nevertheless perform a bit better than the climatological forecast. This can happen even for very long-term forecasts (e.g., more than a year into the future). This again highlights the importance of performing multiple realizations of NN training. In the end, it is important to point out that although the NN-based prediction systems presented in the study are relatively simple, and cannot be expected to outperform the current state-of-the-art operational NWP models, the analysis nevertheless provides meaningful results, which might have implications for potential future data-driven prediction of the atmospheric evolution from raw observations. For example, the XAI analysis (Figure 6a-c) revealed that the NN is able to diagnose the vertical layers of \(T\), \(T_{d}\) and RH that impact the prediction of \(T_{max}\) the most. This resembles the vertical correlations built into the background-error covariance model for the assimilation of atmospheric observations into NWP models [29]. Analogously as in our case, these vertical correlations act to (objectively) spread the impact of observation across the model domain; however, in analogy to the NWP data assimilation, some localization of the observation impact would be beneficial to reduce the complexity of the network, as the mid- and upper-tropospheric measurements do not contribute anything to the short-range prediction. In the NN context, this can be achieved by dropping out some neurons so that the network only learns the most robust features. The findings derived from the long-range prediction experiments are also relevant for seasonal-to-subseasonal (S2S) climate prediction, where machine learning models have already demonstrated better prediction than the state-of-the-art operational prediction systems [30]. **Supplementary Materials:** The following are available online at [[https://www.mdpi.com/article/10.3390/app112210852/s1](https://www.mdpi.com/article/10.3390/app112210852/s1)]([https://www.mdpi.com/article/10.3390/app112210852/s1](https://www.mdpi.com/article/10.3390/app112210852/s1)), Figures S1-S6 show results of the XAI analysis for additional setups, forecast lead times and forecasts of \(T_{\text{min}}\), Figures S7-S8 show the spread of the results for the XAI analysis for forecasts of \(T_{\text{max}}\) by Setup X, Figure S9 shows the average seasonal \(T\) profiles. Conceptualization, G.S., Z.Z. ; methodology, G.S., D.H., Z.Z. ; software, G.S., D.H., Z.Z. ; formal analysis, G.S., D.H.; investigation, G.S., D.H.; data curation, G.S., D.H.; verification, G.S., D.H.; writing--original draft preparation, G.S., D.H., Z.Z. ; writing--review and editing, G.S., D.H., Z.Z. ; visualization, G.S., D.H.; supervision, G.S., Z.Z. ; project administration,G.S., Z.Z. ; funding acquisition, G.S., Z.Z. All authors have read and agreed to the published version of the manuscript.