Site-level uncertainty quantification is essential for Earth system modeling before scaling up to regional simulations. This study introduces a novel computational framework designed to enhance model predictability by reducing parametric uncertainty and assessing site and observable heterogeneity using various observational constraints. The framework integrates five components: Model Simulation, Statistical Emulation, Global Sensitivity Analysis (GSA), Model Calibration, and Model Prediction. Using the Energy Exascale Earth System Model (E3SM) land model (ELM), we simulated site-level land-atmosphere carbon and energy fluxes from 2003 to 2007 across five evergreen needleleaf FLUXNET sites, perturbing 26 vegetation-related model parameters. Gaussian Process emulators were employed to expedite GSA and model calibrations. Four critical parameters were identified by GSA that strongly influence selected land-atmosphere fluxes. Bayesian approaches were used to infer parameter probability distributions leveraging synthetic data and FLUXNET observations. The results reveal that posterior parameter distributions vary significantly across different sites and observables within the same Plant Functional Type. Probabilistic predictions indicate that parameters calibrated at one site can enhance predictive accuracy at other sites, although site heterogeneity may sometimes outweigh parametric uncertainty. Additionally, the probabilistic predictions demonstrate that calibration for one variable can also improve predictability for other variables, maximizing predictive capabilities with limited observation. This framework provides a powerful approach for reducing parametric uncertainty in Earth system models while deepening our understanding of carbon dynamics and energy cycles. Its adaptability makes it a valuable tool for broader applications in Earth system modeling.