## 2 Materials and Methods
### Data Analysis  
Daily means for air temperature were calculated from 3 h and 30 min reanalysis and flux site data sets, respectively. Daily precipitation was calculated as the daily sum of 1 h and 30 min precipitation data from reanalysis and flux sites, respectively. Temperature anomalies were calculated by removing the daily mean, calculated for the period from 1991 to 2021. In order to account for the delayed response of few-day wet spells as well as the impact of prolonged drought on NEE and other components of the carbon budget, we additionally used the antecedent precipitation index (API) in our study. In our case, this index can be an indicator of soil moisture deficiency or surplus and therefore may be the best indicator to describe the influence of precipitation on CO\({}_{2}\) fluxes and evapotranspiration. To calculate the API for each day of the year at the flux station, we followed [PERSON] and Linsley [53] and [PERSON] et al. [54]:  
\[API=\sum_{t=1}^{M}P_{t}\ k^{t} \tag{1}\]  
where \(P_{t}\) is the precipitation in the \(t\)th antecedent day, \(M\) is the statistical number of antecedent days, and \(k\) is the decay constant. In our study, we assumed that \(M\) is equal to 14 days and \(k\) is equal to 0.8. Mean daily NEE and LE rates for each station were calculated by averaging 30 min flux data sets. The gaps in the flux time series, caused by equipment and power failures, weak turbulence, heavy rainfalls, etc., for all selected flux stations were filled out in our study using the REddyProc package [55] and the algorithms described by [PERSON] et al. [56]. The method was applied by taking into account the locations of most of the selected flux stations in mid-latitudes between 40\({}^{\circ}\) N and 55\({}^{\circ}\) N, where this method provides reasonable estimates [55] and does not produce the systematic bias in daily flux estimates that it does in high latitudes [57]. The choice of method was also influenced by the simplicity and robustness of its application for filling in gaps in experimental data series, although it may be less accurate compared to more complex approaches based on process-based mathematical modeling [58] and machine learning techniques [57]. Daily anomalies of NEE and LE were calculated as the difference between the daily and monthly means of NEE and LE over the available observation period at each station. Extreme temperature periods were defined as periods when the daily mean temperature anomaly exceeded the 95% quantile (for extremely high temperatures) or did not reach the 5% quantile (for extremely low temperatures) of the probability density function (PDF) [45]. The normal distribution for air temperature was used in our study as the most appropriate for long-term time series analysis [47]. The PDFs were calculated for each calendar month of the observation periods and averaged over the period from 1991 to 2021. Two approaches were used to analyze the effect of precipitation variability on NEE and LE fluxes. In the first approach, extremely heavy precipitation days were identified as days with daily precipitation exceeding the 95% quantile of the power density function, using the Weibull distribution for precipitation [47]. This method allows to highlight the immediate response of the ecosystem to heavy precipitation to be highlighted, which is mostly associated with increased soil respiration resulting in high CO\({}_{2}\) emissions. However, this approach is not suitable for identifying the effect of a precipitation deficit on NEE and LE fluxes, because the lack of precipitation during one or several days in mid-latitudes cannot be considered a stress condition for NEE and LE fluxes in temperate and boreal forests. The effect of sufficient or deficient soil moisture may be more important for NEE and LE fluxes than the effect of the presence or absence of precipitation. Soil moisture depends on the cumulative effect of precipitation, which can be estimated using the API index.