|This is an interesting paper trying to prove that stochastic groundwater modeling is possible. The authors discuss a modular approach to incorporate heterogeneity into groundwater flow modeling. Then they apply to one of the experiments in the well-known MADE site. I recommend publication after some "minor" corrections, in the sense that they will take little time to implement, but "major," in the sense that they lower the author's claims. I like the paper because it shows that stochastic modeling is possible. I do not like some of the claims and discussions. I do not like that the model is two-dimensional, either.|
1. There is nothing new in this modular approach to incorporating heterogeneity into aquifer modeling. Any claim of originality in this respect should be toned down, and references to similar approaches in groundwater modeling or reservoir engineering included. (A few references implementing this concept could be Damsleth et al., 1992, Huysmans and Dassargues, 2009, Neto et al., 1994, Proce et al., 2004, to cite a few dating back to the past century). Please, rewrite lines 64-65 with proper referencing.
2. Already in the abstract, the authors claim that their model is constructed with as minimal data as possible. This is clearly not so in the description of the application. The amount of data used is substantial and hardly available in most sites. Even if some of the data are not used as conditioning data, they are needed to infer the different parameters of the nested heterogeneous models.
3. In the introduction, some statements should be toned down, and a few historical references are missing.
3.1. In line 40, it says that huge amounts of data are needed for kriging. Certainly, you need data to infer the variograms, but not as many as the one you need in the latter application, where you claim that hardly any data are used.
3.2. In line 42, it says that stochastic methods, on the other hand, need a limited amount of data. Kriging is a stochastic method, which apparently needs a huge amount of data. In any case, the statement is not true, stochastic methods need data, large amounts, as it is shown later.
3.3. When listing the common methods, some historical references are missing, such as Gómez-Hernández and Gorelick, 1989, for Gaussian random fields; Journel and Gómez-Hernández, 1990, for indicator simulation; and Strebelle for multiple-point statistics. (By the way, Freeze, 1975 is not the best example of the use of Gaussian random fields, since he used uncorrelated values.)
3.4 Line 76, it seems that the number of data used is not minimal. Previous works have shown that properly accounting for hydraulic conductivity heterogeneity at the MADE site is sufficient to reproduce the mass transport behavior at the MADE site (i.e., Salamon et al. (2006), or Li et al. (2011))
4. For the paper to really serve its purpose of enticing practitioners to use stochastic modeling, the model would have had to be three-dimensional. But it is not! How much does the dimensionality reduction influence the results? This must be discussed.
Damsleth, E., Tjolsen, C. B., Omre, H., & Haldorsen, H. H. (1992). A two-stage stochastic model applied to a North Sea reservoir. Journal of Petroleum Technology, 44(04), 402-486.
Gómez‐Hernández, J. J., & Gorelick, S. M. (1989). Effective groundwater model parameter values: Influence of spatial variability of hydraulic conductivity, leakance, and recharge. Water Resources Research, 25(3), 405-419.
Li, L., Zhou, H., & Gómez-Hernández, J. J. (2011). A comparative study of three-dimensional hydraulic conductivity upscaling at the macro-dispersion experiment (MADE) site, Columbus Air Force Base, Mississippi (USA). Journal of Hydrology, 404(3-4), 278-293.
Huysmans, M., & Dassargues, A. (2009). Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium). Hydrogeology Journal, 17(8), 1901.
Journel, A. G., & Gomez-Hernandez, J. J. (1993). Stochastic imaging of the Wilmington clastic sequence. SPE formation Evaluation, 8(01), 33-40.
Neton, M. J., Dorsch, J., Olson, C. D., & Young, S. C. (1994). Architecture and directional scales of heterogeneity in alluvial-fan aquifers. Journal of Sedimentary Research, 64(2b), 245-257.
Proce, C. J., Ritzi, R. W., Dominic, D. F., & Dai, Z. (2004). Modeling multiscale heterogeneity and aquifer interconnectivity. Groundwater, 42(5), 658-670.
Salamon, P., Fernandez‐Garcia, D., & Gómez‐Hernández, J. J. (2007). Modeling tracer transport at the MADE site: the importance of heterogeneity. Water resources research, 43(8).
Strebelle, S. (2002). Conditional simulation of complex geological structures using multiple-point statistics. Mathematical geology, 34(1), 1-21.