Methane (CH4) is the second most potent greenhouse gas (GHG), and China emerges as the largest anthropogenic CH4 emitter by country. Current limited CH4 monitoring systems in China are unfortunately inadequate to support carbon management. Here we use the Weather Research and Forecasting model (WRF) coupled with a GHG module and satellite constrained emissions to simulate the spatiotemporal distribution of CH4 over East Asia in 2017. Model evaluations using both satellite retrievals and ground-based observations indicate reliable performance. We further inter-compare four proper orthogonal decomposition (POD)-based sensor placement algorithms and find they are able to capture main spatial features of surface CH4 under an oversampled condition. The QR pivot algorithm exhibits superiority in capturing high CH4, and it offers the best reconstruction with both high efficiency and accuracy. Areas with high CH4 concentrations and intense anthropogenic activities remain underrepresented by current CH4 sampling studies, leading to notable reconstruction error over central and eastern China. Optimal planning of 160 sensors guided by the QR pivot algorithm can yield reasonable reconstruction performance and costs of site construction. Our results can provide valuable references for future planning of CH4 monitoring sites.