## 3 Results and Discussion
### Modeling Results  
The modeling with the T (Equation (1))-TP (Equation (2))-TPP (Equation (3a))-TPC (Equation (4))-TPPC (Equation (5)) models was conducted with using the non-linear regression for model fitting on the monthly-averaged measured SR, \(T_{soil}\) or \(T_{air}\), and precipitation datasets where the winter and summer values were double weighted to obtain the representativeness of the models regardless of the time of the year. In addition to this modeling, the results of the TPPrh (Equation (3b)) modeling with the quadratic temperature dependency were used for comparisons. The temperature-related coefficients \(R_{0}\) in \(Q\) were estimated from the T model with using the intercept \(\rightarrow\) 0+ constraint for the lm, comparing the measurements with the modeled data (T, TP, TPP, TPC, TPPC). These coefficient values were taken as the base for further modeling with more complex TP, TPP, TPC, TPPC, and also TPPrh (\(R_{0}\), \(Q\), and \(Q_{2}\)) models. This way, we separate the temperature-related effects (\(R_{0}\), \(Q\), and \(Q_{2}\)) and, sequentially, focus on the precipitation (\(K\)) and SOC (\(\psi\)) effects, and also on the effect of the precipitation redistribution between months (\(\alpha\)). Figures 5 and 6 show that the smallest SR values are observed during the dry years, while the maximal 30% larger values are reached in the normal years, and the SR becomes smaller again during the wet years. These observations agree well with the obtained \(R_{0}\) dependency from the soil moisture (colored lines, Figure 3) and also with the previous research results [55; 56; 57]. They can be explained by the reduced microbial activity when there is not enough water presented in soil in dry years [32; 58; 59] and also by the lack of available oxygen for the SOC oxidation when it is saturated with water in wet years [26; 36; 37]. After fixing the temperature coefficients (\(R_{0}\) in \(Q\)) determined by the T-TPTP-TPC-TPPC modeling by the method described above (Figures 5 and 6), the comparison among the modeling results shows the following similarities and differences among the models depending on (i) the soil type: Entic Podzol or Haptic Luvisol, and (ii) the sources of the temperature used for parameterization: \(T_{soil}\) or \(T_{air}\). _For Entic Podzol and \(T_{soil}\):_  
* The best slope-lm values (slope, Figure 7) were observed with the TPPC model in a dry environment (slope \(\approx\) 0.9), with the TPC model in a normal environment (slope \(\approx\) 0.9), and with the TPP model in a wet environment (slope \(\approx\) 0.9); the TPPC and TPPrh models show the slope \(>\) 0.85 for most of the conditions;
* The best R\({}^{2}\)-lm values (\(R^{2}\), Figure 7) were observed with the TPPC model in a dry environment (\(R^{2}\approx\) 0.7) and with the TPPrh model in normal and wet environments (\(R^{2}\approx\) 0.75); the TPPC and TPP models show the \(R^{2}>\) 0.7 for all moisture conditions;
* The best MBE values of the comparison between the models and measurements (\(|\)MBE\(|\), Figure 7) were observed with the TPC and TPPC models in a dry environment (\(|\)MBE\(|\)\(\approx\) 0.15), and with the TPPrh model in normal and wet environments (\(|\)MBE\(|\)\(\approx\) 0.08); the TPPC model shows \(|\)MBE\(|\)\(<\) 0.17 for all moisture conditions. * The best RMSE values of the comparison between the models and measurements (RMSE, Figure 7) were observed with the TPC \(\,\) ii TPPC in a dry environment (RMSE \(\approx\) 0.45), and with the TPPrh model in normal and wet environments (RMSE \(\approx\) 0.55); the TPPC model shows RMSE \(<\) 0.63 for all moisture conditions. Figure 5: The comparison between the modeled (SR_model) and measured (SR_meas) SR values (gCm\({}^{-2}\)day\({}^{-1}\)) for T (blue, Equation (1)) –TP (green, Equation (2))–TPP (orange, Equation (3a))–TPC (red, Equation (4))–TPPC (black, Equation (5))–TPPh (brown, Equation (3b)) models; lines—linear regression to determine the slope and intercept values; \(T_{sill}\) (local temperature) used for parameterizations.