Effective hydration temperature of obsidian: a diffusion theory analysis of time-dependent hydration rates

An estimate of effective hydration temperature (EHT) is needed for chronological use of obsidian hydration data. This paper describes a method for calculating EHT by the practicing archaeologist, replacing three techniques that are in general use today: estimates based on mean temperature, numerical integration of models of diurnal and annual temperature variations, and use of temperature cells. The hydration (or diffusion) coefficient of obsidian is a function of temperature and thus is time varying, while the classic quadratic law of hydration is not valid for time-varying diffusion coefficients. This paper presents a mathematical solution to the case of a time-varying hydration coefficient, based on diffusion theory, with a concise definition of EHT. It is shown that the results are not affected by concentration dependence in the diffusion coefficient. A computer program to compute the rigorous solution is described, and data are presented to explore the resulting range of variation. That use of the Lee equation to compute EHT is not appropriate for obsidian hydration studies is evident from the data presented. The effects of paleoclimatic variation are estimated, and an algebraic best fit equation and worksheet are provided as practical aids to the archaeologist.