You-Kuan Zhang

NONERGODIC SOLUTE TRANSPORT IN THREE-DIMENSIONAL HETEROGENEOUS ISOTROPIC AQUIFERS

The general expressions for the time-dependent ensemble averages of the second spatial moments ^A&and the effective dispersivities g, defined as (1/2m)(d^A&/dt) where mis the magnitude of the meanflow velocity m, are evaluated in order to study the effect of initial plume size on ^A&and gin three-dimensional heterogeneous isotropic aquifers under thefirst-order approximation to the particle displacement. The results confirm previousfindings that ^A&and ggenerally approach their respective ergodic limits Xand aas the size of a source increases, whereXand aare the single particle displacement covariance and the associated dispersivity, and that the transverse lengths of a source are more important than the longitudinal length for the ergodic condition to be met. The longitudinal dispersion of a nonergodic plume becomes Fickian or the effective asymptotic longitudinal dispersivity is constant at late time as long as one of the initial lateral lengths of the plume is nonzero, while the transverse dispersion is always non- Fickian and the effective asymptotic transverse dispersivities are always zero regardless of the initial plume size. The most important and interestingfindings are, when the longitudinal lengthl1 of an initial plume is larger than the lateral lengthsl2 andl3, both effective longitudinal and transverse dispersivities gii(i 51, 2, 3) increase to their respective peaks at early time, then g11decreases toward an asymptotic constant, whose value depends on the values of l2 and l3 (g113 0i f l 2 5 l 3 50), whereas g22 and g33 decrease to below zero (i.e., become negative), increase again, andfinally approach zero independent of the lateral lengths of the source. Comparison of the current study with a numerical simulation shows good agreement between the calculated and simulated longitudinal second spatial moments.

Temporal scaling of groundwater level fluctuations near a stream

Temporal scaling in stream discharge and hydraulic heads in riparian wells was evaluated to determine the feasibility of using spectral analysis to identify potential surface and groundwater interaction. In floodplains where groundwater levels respond rapidly to precipitation recharge, potential interaction is established if the hydraulic head (h) spectrum of riparian groundwater has a power spectral density similar to stream discharge (Q), exhibiting a characteristic breakpoint between high and low frequencies. At a field site in Walnut Creek watershed in central Iowa, spectral analysis of h in wells located 1 m from the channel edge showed a breakpoint in scaling very similar to the spectrum of Q (∼20 h), whereas h in wells located 20 and 40 m from the channel showed temporal scaling from 1 to 10,000 h without a well-defined breakpoint. The spectral exponent (β) in the riparian zone decreased systematically from the channel into the floodplain as groundwater levels were increasingly dominated by white noise groundwater recharge. The scaling pattern of hydraulic head was not affected by land cover type, although the number of analyses was limited and site conditions were variable among sites. Spectral analysis would not replace quantitative tracer or modeling studies, but the method may provide a simple means of confirming potential interaction at some sites.

Effect of heterogeneity on spatiotemporal variations of groundwater level in a bounded unconfined aquifer

Spatiotemporal variations of groundwater level due to a white noise recharge time series and a random transmissivity field in a bounded unconfined aquifer was studied. The analytical solutions for the variance and covariance of groundwater level were derived with non-stationary spectral analyses and superposition principle. It was found that the fluctuations of groundwater level are spatially non-stationary due to a fixed head boundary condition and temporal non-stationary at early time but gradually became stationary as time progresses due to effect of the initial condition. The variation in groundwater level is mainly caused by the random source/sink in the case of temporally random recharge and spatially random transmissivity. The effect of heterogeneity is to increase the variation of groundwater level and the maximum effect occurs close to the constant head boundary because of the linear mean hydraulic gradient. The heterogeneity also enhances the correlation of groundwater level, especially at large time intervals and small spatial distances.

An evaluation of nonlinearity in spatial second moments of ensemble mean concentration in heterogeneous porous media

The integrodifferential equation for the spatial second moments X of the ensemble mean concentration in a heterogeneous aquifer is nonlinear due to statistical dependence of the particle displacement on X. This nonlinear equation is either linearized or quasi-linearized in previous studies to derive the linear and quasi-linear theories of time-dependent macrodispersion in aquifers. In this study a fully nonlinear analysis is carried out by solving the integrodifferential equation for X numerically and iteratively. The effects of the variance of log hydraulic conductivities σY2, the local Peclet number Pe, and the anisotropic ratio e are then investigated. Results show that in both statistically isotropic and anisotropic media, as compared with the linear theories, the effect of nonlinearity in X is to reduce the spatial longitudinal variance, X11, and enhance the transverse spreading of a solute plume except in isotropic media with σY2 ≤ 1, where the linear theories may underestimate the longitudinal spreading of a solute. It is also shown that the effect of local dispersion on X11 can be neglected when Pe ≥ 10 but on the transverse macrodispersion, this effect is significant for Pe as large as 100. Nevertheless, the effect of Pe on macrodispersion is secondary as compared with the effect of nonlinearity in X. Application of the nonlinear results shows good fits to the observed spatial variances of tracer concentration in the Borden experiment and excellent agreement with the simulated variances from recent Monte Carlo simulations.

ON THE VARIANCES OF SECOND SPATIAL MOMENTS OF A NONERGODIC PLUME IN HETEROGENEOUS AQUIFERS

The expressions for the variances of the second spatial moments of a solute plume, Var[Sij], were formulated and evaluated for a line source of finite length either normal or parallel to the uniform mean flow velocity, μ, in a two-dimensional heterogeneous and statistically isotropic aquifer. The evaluations were performed by using the analytical solutions for the velocity covariance derived previously under the first-order approximation to the particle displacement. The main finding is that for the special case of a line source either normal or parallel to the mean flow, not all the variances of the second spatial moments decrease but all the coefficients of variation of the second spatial moments, CV[Sii], decrease as the initial length of a line source increases. The first-order longitudinal CV[S11] is independent of the variance of transmissivity, σY2, and the transverse CV[S22] is inversely proportional to σY in the case of a line source normal to μ. Comparison between the first-order theoretical results obtained in this study with previous Monte Carlo simulations shows that the match between the theoretical and simulated CV[S11] improves as τ2 increases and in a less heterogeneous aquifer.

Effects of temporally correlated infiltration on water flow in an unsaturated–saturated system

Effects of temporally correlated infiltration on water flow in an unsaturated–saturated system were investigated. Both white noise and exponentially correlated infiltration processes were considered. The moment equations of the pressure head (ψ) were solved numerically to obtain the variance and autocorrelation functions of ψ at 14 observation points. Monte Carlo simulations were conducted to verify the numerical results and to estimate the power spectrum of ψ (Sψψ). It was found that as the water flows through the system, the variance of the ψ (

Increasing streamflow and baseflow in Mississippi River since the 1940 s: Effect of land use change

\sigma_{\psi }^{2}

Baseflow contribution to nitrate-nitrogen export from a large, agricultural watershed, USA

σψ2) were damped by the system: the deeper in the system, the smaller the