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

Abstract

In continuation to Part I,1 which dealt with the steady state, tracer theory is extended to timevarying systems. Most geophysical systems are recognized as time-varying when observed for a prolonged time and in sufficient detail. We distinguish between explicit and implicit system variability. The unique composition system response of the steady-state system, hc(τ), is replaced by three time-dependent system functions which relate to input and output conditions. Time relations of the steady state are also generalized and illustrated heuristically by analogies to biological populations. Input and output average transit times are defined, as well as their ensemble or time averages. The distributions over transit time and age in the flux and volume are generalized to the non-steady state. Examples of the different categories of non-steady state in natural systems are indicated.