Reply to comment on “Validation of two innovative methods to measure contaminant mass flux in groundwater” by Goltz et al. (2009) Mark N. Goltz a, ⁎, Junqi Huang b a Air Force Institute of Technology, AFIT/ENV, 2950 Hobson Way, Bldg 640, Wright-Patterson AFB, OH 45433-7765, United States b EPA National Risk Management Research Laboratory, Ground Water and Ecosystems Restoration Division, P.O. Box 1198, Ada, OK 74821-1198, United States article info Article history: Received 16 October 2014 Accepted 19 October 2014 Available online xxxx Keywords: Groundwater flow Pump test Modeling We thank Sun (2014) for his comment on our paper, Goltz et al. (2009). The commenter basically makes two points: (1) equation (6) in Goltz et al. (2009) is incorrect, and (2) screen loss should be further considered as a source of error in the modified integral pump test (MIPT) experiment. We will address each of these points, below. Equation (6) is presented as: hx; y ð Þ¼ - q 0 b T x þ Q 0 2π T ln r r w 0 ½ ! ðA  6Þ where, r ¼ x 2 þ y 2   1=2 : This equation gives the hydraulic head (h) at an observation well as a function of spatial location (x, y), for the assumptions (e.g., steady flow in an isotropic confined aquifer) and conditions Journal of Contaminant Hydrology xxx (2014) xxx–xxx ⁎ Corresponding author. E-mail addresses: mark.goltz@afit.edu (M.N. Goltz), huang.junqi@epa.gov (J. Huang). CONHYD-03068; No of Pages 2 (e.g., pumping well of radius r w[0] located at x = y = 0) specified in both Goltz et al. (2009) and Sun (2014). This same equation was also presented by Bear (1979) and others. The equation can be derived from superposition and Darcy's law. Sun (2014) contends that equation (6) should be correctly presented as: hx; y ð Þ¼ - q 0 b T x þ Q 0 2π T ln r ðÞ: ðC  6Þ We argue that there is no substantial difference between these two formulations. Both (A-6) and (C-6) calculate the hydraulic potential (head) as a function of location. It should be realized that the head in both cases is calculated as the difference between the head at a reference location and the head at location (x, y). In Eq. (A-6) the reference location is established at r w[0] (so, for instance, at x = 0, y = r w[0], r = r w[0], and h(x, y)= 0) and in Eq. (C-6) the reference location is an implicit “1” that divides r, the argument of the natural logarithm function (so, for instance, at x = 0, y = 1, r = 1, and h(x, y)= 0). Notice that the implicit “1” in Eq. (C-6) must have the same dimension as r, so that the argument of the natural logarithm function is dimensionless. Thus, we would contend that our Eq. (A-6), which establishes the reference location at the radius of the pumping well, is more correct than Eq. (C-6), which establishes the reference location at an arbitrary distance (e.g., 1 mm, 1 cm, 1 m, depending on the units of r) from the origin. In practice, however, the discussion above is moot, since equation (9) of Goltz et al. (2009), which is subsequently used when applying the MIPT method, is correct, as Sun (2014) acknowledges. We do thank Sun (2014) for raising the issue though, as it allows us to clarify the apparent discrepancy in Eq. (C-6), which appears frequently in the literature, and where http://dx.doi.org/10.1016/j.jconhyd.2014.10.014 0169-7722/Published by Elsevier B.V. Contents lists available at ScienceDirect Journal of Contaminant Hydrology journal homepage: www.elsevier.com/locate/jconhyd Please cite this article as: Goltz, M.N., Huang, J., Reply to comment on “Validation of two innovative methods to measure contaminant mass flux in groundwater” by Goltz..., J. Contam. Hydrol. (2014), http://dx.doi.org/10.1016/j.jconhyd.2014.10.014