3.4. Synergistic characteristics of impact factors and prediction models
In order to accurately explore the effects of temperature, moisture, SOC on soil CO2 flux, multivariate correlation analysis was carried out among the three factors and soil CO2 flux at deep and shallow layers. The results showed that there were significant correlations between soil temperature, moisture, concentration of soil organic carbon and soil CO2 flux in the shallow layers (5-20 cm) (P<0.01). Moreover, there was a significant correlation between soil moisture and temperature.(P<0.01) (Fig7. Heat map: A). In deep layers( 80-200 cm), soil temperature, moisture, concentration of soil organic carbon and soil CO2 flux were significantly correlated (P<0.01), and there was a significant correlation between temperature, moisture and concentration of soil organic carbon (P<0.01) (Fig7. Heat map: B). For generality, whether in deep or shallow layers, soil temperature, moisture, and SOC had a synergistic effect on responses to soil CO2 flux.
Because soil temperature, moisture, and concentration of soil organic carbon cooperatively contributed to on soil CO2 flux, and there was a certain interaction between these influencing factors (Fig.7). The CO2 flux under different temperature, moisture and SOC distributed relatively concentrated in deep layers, and the distribution of CO2 flux in shallow layers was discrete (Fig.8). If only a single-factor model or hydrothermal two-factor model was used to predict soil CO2 flux, it is inevitable that the influence of other factors will be ignored, and the change law of soil CO2 flux would not be well described. Therefore, on the basis of  previous research in the hydrothermal two-factor models (Exponential-Power model, Q10-hyperbolic model )(Table 4), we adopted piecewise fitting method to build up a mathematic model for soil temperature, moisture, concentration of soil organic carbon and soil CO2 flux at different layer (Table 5).
In general, value of R2 in T&M&C model was further improved compared to the T&M model, and the fitting results of these models were significant (Table 4, Table 5). In order to further analyze the prediction accuracy of the model and the possibility of model generalization, we integrated some literatures which study on the vertical CO2 flux, especially the deep CO2 flux and its influencing factors, to obtain the required data including CO2 flux, temperature, moisture and SOC of each profile for analysis (Appendix A ). Based on T&M&C model and T&M model, we used the obtained temperature, moisture, and organic carbon data to simulate the predicted CO2 flux and compare it with the measured CO2 flux, the simulated CO2 flux and measured CO2 flux fit well with the linear relationship in various types of plots (Fig.9, Fig.10). The prediction accuracy was evaluated by three variables of different dimensions (R2, RMSE, MAE). Compared with the T&M model, the R2 value of T&M&C model increased, but RMSE and MAE differently decreased(Appendix B ). The prediction accuracy of T&M&C model had an increase of about 20%-25%, and prediction accuracy of CO2 flux steadily improved in deep layers rather than shallow layers (Fig. 11).