## 3 Results
### Relationships Between Carbon Fluxes and Meteorological Variables  
The heatmap analysis reveals distinct site-specific responses to storm surge impacts (Figure 6), with PYR experiencing a temporary weakening of carbon flux-environment relationships that quickly recovered, whereas HK experienced stronger disruptions and more complex correlation shifts due to greater storm exposure. At the PYR site, NEE exhibited strong negative correlations with PPFD (r = \(-\)0.88), TA (r = \(-\)0.63), and VPD (r = \(-\)0.60) before the storm. However, these associations weakened markedly during the storm. Most correlations recovered close to pre-storm levels post-storm. Meanwhile, Reco became more closely correlated with TA, VPD, LE, and H during the storm. In contrast, GPP exhibited a significant decline in correlation with RH, VPD, PPFD, and TA, but partially recovered post-storm. At the HK site, pre-storm NEE showed strong correlations with RH (r = 0.63), VPD (r = \(-\)0.70), PPFD (r = \(-\)0.90), and TA (r = \(-\)0.51), but during the storm, correlations with RH (r = 0.31), VPD (r = \(-\)0.45), and WS (r = 0.02) significantly weakened, while the negative correlation between TA and NEE strengthened. Similarly, Reco became more strongly correlated with TA (r = 0.54), VPD (r = 0.36), LE (r = 0.37), and H (r = 0.41) during the storm. For GPP at the HK site, RH, VPD, and WS correlations weakened during the storm, while TA showed a slight increase in correlation with GPP (r = 0.66). CH\({}_{4}\) flux at HK also exhibited notable shifts, with stronger negative correlations with WS (r = \(-\)0.37) and WTD (r = \(-\)0.13), accompanied by a decrease in correlation with TA and TS. Figure 5: Violin plots showing the distributions of environmental factors—photosynthetic photon flux density ((**a**), PPFD), air temperature ((**b**), TA), soil temperature ((**c**), TS), vapor pressure deficit ((**d**), VPD), relative humidity ((**e**), RH), and wind speed ((**f**), WS)—at a natural mangrove site (HK) and a restored mangrove site (PYR) during three stages of a storm surge (before, during, and after). Distributions are split by site ((**left**), PYR; (**right**), HK), with embedded boxplots indicating medians and interquartile ranges. At the PYR site, during the storm surge, the direct effects of air temperature (TA) and water table depth (WTD) on CH\({}_{4}\) flux decreased, while relative humidity (RH) had an enhanced direct effect (standardized path coefficient: \(\alpha\) = 0.53, \(p\) < 0.001) on CH\({}_{4}\) flux (Figure 7a-c). Additionally, wind speed (WS), RH, and TA showed increased direct effects on ecosystem respiration (Reco), whereas the direct effect of soil temperature (TS) on Reco decreased. PPFD continued to play a significant direct role in regulating gross primary production (GPP) (\(\alpha\) = 0.84, \(p\) < 0.001), and TA indirectly influenced GPP by affecting VPD. NEE was primarily regulated by GPP and Reco, with all other factors exerting indirect effects on NEE through their influence on GPP and Reco. At the HK site, during the storm surge, the direct effects of TS, RH, and WTD on CH\({}_{4}\) flux all decreased (Figure 7d-f). However, the direct effect of TA and WS on CH\({}_{4}\) flux increased, with TA having a positive impact on CH\({}_{4}\) flux (\(\alpha\) = 0.24, \(p\) < 0.001) and WS showing a negative effect (\(\alpha\) = -0.35, \(p\) < 0.001). Compared to the PYR site, GPP at the HK site was directly controlled by PPFD, RH, and VPD, with PPFD playing a dominant positive role (\(\alpha\) = 0.9, \(p\) < 0.001), while VPD and RH were negatively correlated with GPP. During the storm surge, the regulation of GPP by PPFD became more pronounced, and the direct effects of VPD and RH on GPP decreased. Additionally, TA influenced GPP indirectly through its effect on VPD. Reco was primarily regulated by the direct effects of WTD, TA, TS, and RH.