On the applicability of analytical methods for estimating solute travel time statistics in nonuniform groundwater flow

Groundwater recharge from the unsaturated zone results in a nonuniform mean groundwater flow. We report closed-form expressions for the mean and varia nce of advective solute travel time under such nonuniform flow conditions. These expressions are derived directly from velocity statistics, based on a n analytical direct evaluation method (DEM). Am alternative, indirect evalu ation method- (IEM) has previously been used for deriving and evaluating th e cumulative distribution function of solute travel time in nonuniform mean flow, through its relation to an assumed Gaussian probability density func tion of solute displacement. For negative groundwater recharge we argue tha t neither of the two analytical methods DEM and IEM can be considered relia ble. For positive groundwater recharge we show that (1) the DEM results rep orted here remain as reliable for nonuniform as for uniform mean groundwate r flow; (2) an assumed lognormal cumulative distribution function based on the DEM-derived travel time moments is consistent with the IEM-derived solu te travel time cumulative distribution function (cdf), which is in turn con sistent with numerical simulation results reported in the literature; and ( 3) the detailed differences between the DEM-based lognormal cdf and the IEM -derived cdf for nonuniform flow are such that the former (DEM) may exhibit even better agreement with reported numerical simulation results than the latter (IEM).