## 3 Results
### Controlling Factors of \(R_{\rm S}\)
#### 3.2.2 Relationship between \(\rm R_{\rm S}\) to Flux and Biophysical Controls

Table 5: Annual means of global radiation (K), net radiation (Q*), air temperature (Tair), vapor deficit pressure (VPD), evapotranspiration (ET), gross primary production (GPP), soil volumetric water content (SWC) and soil temperature (TS) along a forest succession from tropical dry forest in northwestern Mexico. Data are presented as mean \(\pm\) standard error. Capital letters denote significant differences among sites (\(p<0.05\)). (\(p\) < 0.05) and ES (\(p\) < 0.001) sites but not in the OG site. Furthermore, a positive correlation between SWC\({}_{\text{site}}\) and R\({}_{\text{S}}\) was found in the OG and MS sites, while TS\({}_{\text{site}}\) did not show a relationship in any of the three sites. The structural equation models (SEM) revealed complex cause-effect significant interactions over R\({}_{\text{S}}\) (Figure 2). The squared multiple correlations highly explained the variance of the different biophysical controls over the variability of R\({}_{\text{S}}\) in the three sites: ES (R\({}^{2}\) = 0.76), OG (R\({}^{2}\) = 0.72) and MS (R\({}^{2}\) = 0.68). These analyses demonstrated that the relative importance of the biophysical controls varied according to the forest succession, highlighting the influence of considering these controls in TDF (Figure 2). As expected, relationships among the meteorological variables and ecosystem fluxes were found in all three sites. For instance, T\({}_{\text{air}}\) was strongly and directly correlated to VPD and SWC\({}_{\text{site}}\); while VPD resulted in a significant negative relationship (\(\sim\)0.72) to SWC\({}_{\text{site}}\) in the three sites. Moreover, in terms of ecosystem fluxes, the variability of ET depends on Q\({}^{*}\) by 0.27, 0.30 and 0.62 in ES, MS and OG sites, respectively. ET had a significant positive relationship over GPP by 0.84 in the ES site, 0.71 in the MS site and 0.36 in the OG site. VPD and T\({}_{\text{air}}\) played an important role in GPP and ET in sites, where VPD showed a significant negative effect, and T\({}_{\text{air}}\) had a significant positive relationship in the variability of these fluxes (Figure 2). In turn, soil respiration (R\({}_{\text{S}}\)) was consistently controlled by TS\({}_{\text{site}}\), having a positive and direct relationship at all sites; however, this effect had a stronger significant correlation in the ES (0.22) and MS (0.13) sites in contrast to OG (0.10). Then, a positive and direct relationship of SWC\({}_{\text{site}}\) and ET was identified at the OG and MS sites. However, we found that the tightest effect of SWC\({}_{\text{site}}\) over R\({}_{\text{S}}\) tended to be in the OG site (0.23), with the least being in the MS forest (0.13); meanwhile, the relationship with ET was highly significant in both sites (OG = 0.25, MS = 0.27). On the contrary, in the ES site, SWC\({}_{\text{site}}\) and ET did not have a significant effect over R\({}_{\text{S}}\) (Figure 2c). Additionally, K, seems to have a minor direct effect over R\({}_{\text{S}}\), only affecting it negatively in the OG site (Figure 2a). Notably, the SEM results showed that GPP exerted an overall direct effect over R\({}_{\text{S}}\) in the ES and OG sites, but not in the MS site. A strong control of GPP was identified in the ES site (0.70), in contrast to the OG site, where the least effect was detected (0.41), and a null effect was observed in the MS site (Figure 2b).