As HPC systems move towards exascale, the discrepancy between computational power and I/O transfer rate is only growing larger. Lossy in situ compression is a promising solution to address this gap, since it alleviates I/O constraints while still enabling traditional post hoc analysis. This dissertation explores the viability of such a solution with respect to a specific kind of compressor — wavelets. We especially examine three aspects of concern regarding the viability of wavelets: 1) information loss after compression, 2) its capability to fit within in situ constraints, and 3) the compressor's capability to adapt to HPC architectural changes. Findings from this dissertation inform in situ use of wavelet compressors on HPC systems, demonstrate its viabilities, and argue that its viability will only increase as exascale computing becomes a reality.