Reply to comment by S. Neuman on “Is unique scaling of aquifer macrodispersivity supported by field data?”
2016-05-01

The paper Zech et al. [2015] was motivated by the apparent widespread use of what is assumed to be a unique (or universal) dependence of longitudinal macrodispersivity αL on the scale L by practitioners in order to predict pollution of contaminated sites; this dependence was inspired and justified by the collections of field data, primarily that of Gelhar et al. [1992]. We believe that this use is detrimental in several respects: first, because it is not supported by data and it could lead to erroneous predictions of the rate of spread of plumes, generally with underestimation of maximal concentration and overestimation of the plume size; second, it creates the wrong impression that thorough characterization of the particular aquifer under investigation is not necessary, and this effort can be circumvented by relying on the unique scaling relationships. We are glad to note that in his comment, Neuman advocates the need for an adequate hydrogeological characterization of aquifers [Neuman, 2016]. Considering the relevance of this issue for applications, as well as the large body of theoretical research related to it, our work was aimed at revisiting the available data starting from the work of Gelhar et al. [1992] of more than 20 years ago. The aim is to provide an updated collection of reliable values of longitudinal macrodispersivity from field experiments, which could be used for further analyses. In summary, our main findings are encapsulated in Figure 4, which presents the reliable values of macrodispersivity (with one value per aquifer), leading to the conclusions that there is no trend of increase of αL with distance L and that values are scattered and aquifer specific. Neuman [2016] has not addressed these results, which constitute the bulk of our paper, except for making a few general comments, which are discussed subsequently. As a matter of fact, most of his comments deal with models of transport and our overlooking them and not with the field data underlying the scaling graphs. However, we have explicitly stated that “The discussion of the theoretical works or modeling approaches which were developed in relation with the unique scaling are beyond the scope of the present paper. Its focus is on the analysis of the field data which were used in order to justify the universal scaling.” [Zech et al., 2015, p. 4]. Therefore, in our view, the criticism is largely not relevant to our paper. If we would have undertaken the task of reviewing the literature on modeling, we would undoubtedly have referred to the papers published by Neuman and his coworkers. Neuman criticizes our paper for not including the local, laboratory-determined pore-scale dispersivities. Pore-scale dispersivity and macrodispersivity are typically separated by at least 2 orders of magnitude, as stated in the paper [Zech et al., 2015, p. 2], and the focus of our work is on macrodispersivity, which is the relevant parameter quantifying the plumes spreading, while local dispersion affects primarily dilution. For this reason, we have excluded the values of local, laboratory-determined pore-scale dispersivities. In the same vein, and in line with Gelhar's comments [Gelhar et al., 1992, p. 13], we decided to exclude dispersivity values derived from single-hole tracer injection-withdrawal tests and from breakthroughs at individual depths as they are not representative of the spreading of the entire plume. We believe that incorporating local, pore-scale, dispersivities and field macrodispersivity data in a single plot creates a misleading perception of scale dependence. These data represent different processes which were treated in the literature by different methodologies. In his concluding remarks, Neuman [2016] reiterates that “this failure is an artifact of their outdated and narrow definition of macrodispersivities.” We wish to emphasize again that our paper does not deal with the definition of macrodispersivity on theoretical grounds, making most of the comment of little relevance. We reevaluated the large body of publications on field derivation of macrodispersivity by keeping the definition adopted by the authors and concentrated solely on their reliability. Again, Appendix A1, which recapitulates Taylor's theory of diffusion by continuous movements, was provided in order to offer the interested readers a general, conceptual, framework for modeling solute spreading. Taylor's general theory only requirement is that the covariance of Lagrangian velocities is stationary and it can accommodate increasing scales. Nevertheless, we were gratified to find out that the thorough field experiments summarized in Figure 5 support the existence of a finite correlation scale. Summarizing, we firmly stand behind the main conclusions of our paper, namely that a unique scaling of macrodispersivity displaying permanent increase with the scale is not supported by data. Referring to the theoretical works cited by Neuman [2016], as well as the large body of literature on the issue, we submit that to the extent they rely on the original data of Gelhar et al. [1992], their applicability to aquifer transport shall be reconsidered in view of the reevaluation by Zech et al. [2015].