Greenhouse gas monitoring satellites are crucial for understanding climate change and assessing the effectiveness of climate policies. This project explores a novel concept for a metasurfaced-based spectrometer in the short-wave infrared domain. Metasurfaces are artificial planar materials with subwavelength structures that can manipulate light. This project's metasurface is designed with phase change materials to function as a reconfigurable spectral filter. Filter-based spectroscopy is realized by exploiting a compressive sensing algorithm. Using the rigorous coupled wave analysis solver of Ansys Lumerical, different metasurface designs are simulated and evaluated on their transmission response and compressive sensing performance. The final metasurfaces are obtained using particle swarm optimization with a performance metric that balances computation time and accuracy. The results show great promise for accurate and precise reconstruction of the atmospheric absorption spectrum, required for greenhouse gas monitoring.