A candidate explanation for Early Mars rivers is atmospheric warming due to surface release of H2 or CH4 gas. However, it remains unknown how much gas could be released in a single event. We model the CH4 release by one mechanism for rapid release of CH4 from clathrate. By modeling how CH4-clathrate release is affected by changes in Mars obliquity and atmospheric composition, we find that a large fraction of total outgassing from CH4 clathrate occurs following Mars first prolonged atmospheric collapse. This atmosphere-collapse-initiated CH4-release mechanism has three stages. (1) Rapid collapse of Early Mars carbon dioxide atmosphere initiates a slower shift of water ice from high ground to the poles. (2) Upon subsequent CO2-atmosphere re-inflation and CO2-greenhouse warming, low-latitude clathrate decomposes and releases methane gas. (3) Methane can then perturb atmospheric chemistry and surface temperature, until photochemical processes destroy the methane.
Within our model, we find that under some circumstances a Titan-like haze layer would be expected to form, consistent with transient deposition of abundant complex abiotic organic matter on the Early Mars surface. We also find that this CH4-release mechanism can warm Early Mars, but special circumstances are required in order to uncork 1017 ?kg of CH4, the minimum needed for strong warming. Specifically, strong warming only occurs when the fraction of the hydrate stability zone that is initially occupied by clathrate exceeds 10%, and when Mars first prolonged atmospheric collapse occurs for atmospheric pressure >1 ?bar.