Comment on “A note on the recent natural gradient tracer test at the Borden site” by R. L. Naff, T.‐C. Jim Yeh, and M.W. Kemblowski

[1] Highly resolved data from the Borden research site provide a unique opportunity to study the horizontal spatial bivariate correlation of hydraulic and reactive attributes affecting subsurface transport. The data also allow quantitatively relating this correlation to the hierarchical sedimentary architecture of the aquifer. The data include collocated samples of log permeability, Y, the log of the perchloroethene sorption distribution coefficient, Ä, and lithologic unit type. The horizontal Y and Ä autosemivariograms and the Ä-Y cross-semivariogram have the same underlying correlation structure (shape and range in the rise to a sill). The common structure is not due to Ä-Y point correlation or in-unit spatial correlation. The common structure is defined by how the proportion of lag transitions crossing different unit types (i.e., the cross-transition probability structure) increases with increasing lag distance. The common underlying cross-transition structure contains two substructures with different correlation ranges corresponding to two scales of unit types within the sedimentary architecture. For each substructure, a large standard deviation in the length of units relative to the mean length gives rise to an exponential-like shape and the proportions and mean length of units define the ranges. The horizontal Ä-Y spatial cross correlation is primarily defined by the larger-scale substructure and the differences in mean Ä and Y between larger-scale unit types.

Section: Discussionmentioning

confidence: 99%

Horizontal spatial correlation of hydraulic and reactive transport parameters as related to hierarchical sedimentary architecture at the Borden research site

Ritzi

Huang

Ramanathan

et al. 2013

“…The nonlinear variogram fitting procedure also revealed that considerable uncertainty can exist in the values of the geostatistical parameters, which, in turn, will lead to uncertainty in the values of effective, large‐scale transport parameters predicted by stochastic theory. Other discussions pertaining to the Borden tracer experiment and subsequent interpretations are given by Sudicky [1988a, 1988b, 1988c], Kemblowski [1988], White [1988], Molz and Güven [1988], Naff et al [1988, 1989], Dagan [1989], Zhang and Neuman [1990], Rajaram and Gelhar [1991], Ritzi and Allen‐King [2007], Woodbury and Sudicky [1992], and others.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneity in hydraulic conductivity and its role on the macroscale transport of a solute plume: From measurements to a practical application of stochastic flow and transport theory

Sudicky

Illman

Goltz

et al. 2010

[1] The spatial variability of hydraulic conductivity in a shallow unconfined aquifer located at North Bay, Ontario, composed of glacial-lacustrine and glacial-fluvial sands, is examined in exceptional detail and characterized geostatistically. A total of 1878 permeameter measurements were performed at 0.05 m vertical intervals along cores taken from 20 boreholes along two intersecting transect lines. Simultaneous three-dimensional (3-D) fitting of Ln(K) variogram data to an exponential model yielded geostatistical parameters for the estimation of bulk hydraulic conductivity and solute dispersion parameters. The analysis revealed a Ln(K) variance equal to about 2.0 and 3-D anisotropy of the correlation structure of the heterogeneity (l 1 , l 2 , and l 3 equal to 17.19, 7.39, and 1.0 m, respectively). Effective values of the hydraulic conductivity tensor and the value of the longitudinal macrodispersivity were calculated using the theoretical expressions of Gelhar and Axness (1983). The magnitude of the longitudinal macrodispersivity is reasonably consistent with the observed degree of longitudinal dispersion of the landfill plume along the principal path of migration. Variably saturated 3-D flow modeling using the statistically derived effective hydraulic conductivity tensor allowed a reasonably close prediction of the measured water table and the observed heads at various depths in an array of piezometers. Concomitant transport modeling using the calculated longitudinal macrodispersivity reasonably predicted the extent and migration rates of the observed contaminant plume that was monitored using a network of multilevel samplers over a period of about 5 years. It was further demonstrated that the length of the plume is relatively insensitive to the value of the longitudinal macrodispersivity under the conditions of a steady flow in 3-D and constant source strength. This study demonstrates that the use of statistically derived parameters based on stochastic theories results in reliable large-scale 3-D flow and transport models for complex hydrogeological systems. This is in agreement with the conclusions reached by Sudicky (1986) at the site of an elaborate tracer test conducted in the aquifer at the Canadian Forces Base Borden.Citation: Sudicky, E. A., W. A. Illman, I. K. Goltz, J. J. Adams, and R. G. McLaren (2010), Heterogeneity in hydraulic conductivity and its role on the macroscale transport of a solute plume: From measurements to a practical application of stochastic flow and transport theory, Water Resour. Res., 46, W01508,

“…Further discussion centering on the applicability of stochastic theories to explain the observed tracer behavior can be found in a number of works. Relevant examples include Dagan [1989a, 1989b], Naff et al [1988, 1989], Kemblowski [1988], Sudicky [1988], Barry and Sposito [1990], Rajaram and Gelhar [1991], and Fitts [1996].…”

Section: Introductionmentioning

confidence: 99%

“…As a part of the discussion under points 1 and 2, there have been a number of conjectures about the stratal architecture of the Borden aquifer. Examples include discussions by Dagan [1989a, 1989b], Naff et al [1988, 1989], Woodbury and Sudicky [1991], and Rajaram and Gelhar [1991].…”

Section: Introductionmentioning

confidence: 99%

Linking hierarchical stratal architecture to plume spreading in a Lagrangian‐based transport model: 2. Evaluation using new data from the Borden site

Ramanathan

Ritzi

Allen‐King

2010

[1] A new data set collected at the well-documented Borden research site was used in order to evaluate a newly published but as yet untested idea for stochastic modeling (Ramanathan et al., 2008). The new data set reveals the stratal architecture of the Borden aquifer and allowed us to determine how the stratal architecture, at different scales, controlled the macrodispersion observed in the original natural gradient tracer test. The newly published idea for modeling uses a Lagrangian-based model for the particle displacement variance developed from independent, physically based, quantifiable univariate statistics, including the proportions and mean length of the strata. The method for defining model parameters avoids the often equivocal step of fitting sample bivariate permeability statistics. The model parameters were developed from the new data from the Borden site. The new data included geologic data in much greater abundance than permeability data. There are two scales of unit types delineated in a hierarchy of stratal architecture. Their shapes are complex, not simple layers or lenses. The method facilitated the direct use of both geologic and permeability data, which need not be collocated. The dispersion model developed from these data represents the field-measured particle displacement variance that occurred in the natural gradient tracer test well. The contributions to time-dependent macrodispersion by strata at each scale were computed and analyzed independently. This analysis revealed that macrodispersion at the Borden site is primarily controlled by the proportions, and the mean and variance in length of larger-scale strata of medium sand (M) and strata of fine sand and silt (FZ), with secondary contributions by smaller-scale strata types occurring within the larger-scale units. When sampling the pattern in the longitudinal direction, M and FZ couplets repeat at 10 m intervals on average, with a high length variance. To reach a time-constant macrodispersivity, the stratal length variability must be fully sampled by the plume. The macrodispersivity becomes asymptotic beyond an advective distance of about 60 m, corresponding to about 12 longitudinal transitions between M and FZ unit types.Citation: Ramanathan, R., R. W. Ritzi Jr., and R. M. Allen-King (2010), Linking hierarchical stratal architecture to plume spreading in a Lagrangian-based transport model: 2. Evaluation using new data from the Borden site, Water Resour.