The sensitivity of soil carbon dynamics to climate change is a major uncertainty in carbon cycle models. Of particular interest is the response of soil biogeochemical cycles to variability in hydroclimatic states and the related quantification of soil memory. Toward this goal, the power spectra of soil hydrologic and biogeochemical states were analyzed using measurements of soil temperature, moisture, oxygen, and carbon dioxide at two sites. Power spectra indicated multiscale power law scaling across sub-hourly to annual timescales. Precipitation fluctuations were most strongly expressed in the soil biogeochemical signals at monthly to annual timescales. Soil moisture and temperature fluctuations were comparable in strength at one site, while temperature was dominant at the other. The effect of soil hydrologic, thermal, and biogeochemical processes on gas concentration variability was evidenced by low spectral entropy relative to the white noise character of precipitation. A full mass balance model was unable to capture high-frequency soil temperature influence, indicating a gap in commonly used model assumptions. A linearized model was shown to capture the main features of the observed and modeled gas concentration spectra and demonstrated how the means and variances of soil moisture and temperature interact to produce the gas concentration spectra. Breakpoints in the spectra corresponded to the mean rate of gas efflux, providing a first-order estimate of the soil biogeochemical integral timescale ($\sim 1$ minute). These methods can be used to identify biogeochemical system dynamics to develop robust, process-based soil biogeochemistry models that capture variability in addition to long-term mean values.