On tracer theory in geophysical systems in the steady and non-steady state. Part I

Abstract

Elements of tracer theory in the steady and non-steady state are presented in unified form, in terms common to system analysis in electronic and chemical engineering. Use of tracers requires re-examination of concepts used so far. Previous treatment is shown to be based on tacit assumptions of steady flux of matter through the system, resulting in steady state treatment. Description of tracer response in steady state system requires distinction between mass response and composition response. A system mass is described in terms of bivariate distribution in transit time, ι, and age, T. The non-steady state is shown to be of more common occurrence in description of tracer systems than for mass response systems.The non-steady state requires separation of the concepts of weighting function from system response, and of composition response, hC(ι), from tracer response, hT (ι). Differences in normalization and in linearity properties of these functions are indicated. Several formal and heuristic examples demonstrate the properties and applications of these functions. While the theory of non-steady state system is still in the development stage, several analytical and numerical methods are available to provide deeper insight into the significance and utilization of tracer data in geoscience.