Abstract: Methane (CH₄) is the second most critical greenhouse gas after carbon dioxide, contributing to 16-25% of the observed atmospheric warming. Wetlands are the primary natural source of methane emissions globally. However, wetland methane emission estimates from biogeochemistry models contain considerable uncertainty. One of the main sources of this uncertainty arises from the numerous uncertain model parameters within various physical, biological, and chemical processes that influence methane production, oxidation, and transport. Sensitivity Analysis (SA) can help identify critical parameters for methane emission and achieve reduced biases and uncertainties in future projections. This study performs SA for 19 selected parameters responsible for critical biogeochemical processes in the methane module of the Energy Exascale Earth System Model (E3SM) land model (ELM). The impact of these parameters on various CH₄ fluxes is examined at 14 FLUXNET- CH₄ sites with diverse vegetation types. Given the extensive number of model simulations needed for global variance-based SA, we employ a machine learning (ML) algorithm to emulate the complex behavior of ELM methane biogeochemistry. ML enables the computational time to be shortened significantly from 6 CPU hours to 0.72 milliseconds, achieving reduced computational costs. We found that parameters linked to CH₄ production and diffusion generally present the highest sensitivities despite apparent seasonal variation. Comparing simulated emissions from perturbed parameter sets against FLUXNET-CH₄ observations revealed that better performances can be achieved at each site compared to the default parameter values. This presents a scope for further improving simulated emissions using parameter calibration with advanced optimization techniques like Bayesian optimization.