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.