ERGODICITY AND THE SCALE EFFECT

Solute plume spreading in an aquifer exhibits a 'scale effect' if the second spatial concentration moment of a plume has a non-constant time -derivative. Stochastic approaches to modeling this scale effect often rely on the critical assumption that ensemble averages can be equated to spatial averages measured in a single field experiment. This ergod icity assumption should properly be evaluated in a strictly dynamical context, and this is done in the present paper. For the important case of trace plume convection by steady groundwater flow in an isotropic, heterogeneous aquifer, ergodicity does not obtain because of the exis tence of an invariant function on stream surfaces that is not uniform throughout the aquifer. The implications of this result for stochastic models of solute transport are discussed. (C) 1997 Elsevier Science L td.