  Despite surface liquid water's importance to habitability, observationally
diagnosing its presence or absence on exoplanets is still an open problem.
Inspired within the Solar System by the differing sulfur cycles on Venus and
Earth, we investigate thick sulfate (H2SO4-H2O) aerosol haze and high trace
mixing ratios of SO2 gas as observable atmospheric features whose sustained
existence is linked to the near absence of surface liquid water. We examine the
fundamentals of the sulfur cycle on a rocky planet with an ocean and an
atmosphere in which the dominant forms of sulfur are SO2 gas and H2SO4-H2O
aerosols (as on Earth and Venus). We build a simple but robust model of the
wet, oxidized sulfur cycle to determine the critical amounts of sulfur in the
atmosphere-ocean system required for detectable levels of SO2 and a detectable
haze layer. We demonstrate that for physically realistic ocean pH values (pH >
6) and conservative assumptions on volcanic outgassing, chemistry, and aerosol
microphysics, surface liquid water reservoirs with greater than 1e-3 Earth
oceans are incompatible with a sustained observable H2SO4-H2O haze layer and
sustained observable levels of SO2. Thus, we propose the observational
detection of a H2SO4-H2O haze layer and of SO2 gas as two new remote indicators
that a planet does not host significant surface liquid water.
