Interactive comment on “ Analysis of Groundwater Response to Oscillatory Pumping Test in Unconfined Aquifers : Consider the Effects of Initial Condition and Wellbore Storage

Abstract. Oscillatory pumping test (OPT) is an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters without water extraction. There is a large number of analytical models presented for the analyses of OPT. The combined effects of wellbore storage and initial condition regarding the hydraulic head prior to OPT are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by OPT in an unconfined aquifer. The model contains a typical flow equation with an initial condition of static water table, inner boundary condition specified at the rim of a finite-radius well for incorporating wellbore storage effect, and linearized free surface equation describing water table movement. The analytical solution of the model is derived by the Laplace transform and finite integral transform. Sensitivity analysis is carried out for exploring head response to the change in each of hydraulic parameters. Results suggest that head fluctuation due to OPT starts from the initial condition and gradually tends to simple harmonic motion (SHM) after a certain pumping time. A criterion for estimating the time to have SHM since OPT is graphically presented. The validity of assuming an infinitesimal well radius without wellbore storage effect is investigated. The present solution agrees well to head fluctuation data observed at the Boise hydrogeophysical research site in southwestern Idaho.

some reading errors but their influence on the parameter estimation is negligible from the least-squares sense.We think there might be a misunderstanding in their comments as follows "the authors have misrepresented and misused in the original manuscript" and "they are not at the same relative amplitude and phase positions".
Furthermore, as also noted by Dr. Cardiff, the authors missed the essential details that the experiment was conducted in wells subdivided by straddle packers, i.e., not conducted in open fully penetrating wells.And the actual oscillatory pumping configuration does not involve any wellbore storage.*** That is, their premise for using the data is unfounded.*** Response: As we stated in the Reply to Reviewer 2, the inner boundary condition in the previous manuscript describing flux across the screen of a fully penetrating well is changed to a new one that is applicable to a partially penetrating well as below where h is hydraulic head, r is radial distance from the centerline of the pumping well, z is elevation,  data with an inappropriate model (which the authors explicitly acknowledge is their intention in their reply) in order to compare the results with modeling using data appropriate for the model.*** If the analysis is conducted correctly, it will be a foregone conclusion that the results will differ and the real data from the BHRS will look bad by comparison.This is not an appropriate use of the OHT data we collected, and there is no sound reason to put the data in the literature in a confusing context.
Anyone who is competent in collecting and modeling/analyzing OHT field data would know not to use a wellbore storage model with data such as the BHRS data.
I strongly recommend that the ms by the authors not be published with BHRS OHT data.I recommend that the authors find other data that are appropriate for their analysis, or better yet, collect their own data.
Response: Rabinovich et al. (2015) applied the analytical solution of Dagan and Rabinovich (2014) to analyze data obtained from the oscillatory piston pumping test conducted at the Boise Hydrogeophysical Research Site (BHRS).In spite of no wellbore storage effect (i.e., rc = 0), our new solution in the revised manuscript has two superiorities over their solution.One is to consider the finite radius of an oscillatory pumping well expressed as Eq.(R1), and the other is to include the delayed yield effect denoted as where Kz is vertical aquifer hydraulic conductivity, b is aquifer thickness,  is an empirical constant, and the term on the right-hand side accounts for the effect of delayed gravity drainage (Moench, 1995).
Since their solution is applicable to the BHRS data, our new solution should be applicable as well.The comment "It doesn't make sense to analyze data with an inappropriate model" is his prejudice.
Furthermore, on another issue, the authors have missed the point about small specific yield values for short duration tests that have been reported repeatedly in the literature (see citations at the end of these comments to Neuman 1975;Moench 1994;Chen and Ayers 1998;Barrash et al. 2006 -all from or cited in Barrash et al. 2006 on the BHRS aquifer -which is cited in Rabinovich et al. 2015).The authors cite general text books that give specific yield values from drainage over considerably longer periods of time than those of a short-duration pumping test -i.e., inappropriate for the subject of the paper and missing the relevant and well-documented parameter range.
Response: We didn't miss the point about the reasonable values of Sy.Reviewer 2 gave the following comments: "The authors seem to have chosen parameters that are unrealistic for most aquifers.For example, they use a specific yield value of Sy = 0.1."We think the value of Sy = 0.1 is reasonable for most aquifers as clearly explained in our response to his comment.Huang and Yeh (2007) proposed an approach for on-line aquifer parameter estimation based on the sensitivity analysis.In their paper, three sets of pumping drawdown data were analyzed.Two sets of them, data sets 1 and 2, are synthetic Fig. 8 of our paper.Therefore, we sincerely hope that the reviewers can kindly provide us the full time series and f1(FFT) data shown in their figure (i.e., in Fig. 4(a) of Rabinovich et al. (2015)).The email I received in October 2016 was very perfunctory and did not indicate an understanding of the need to consider context and metadata in order to use field data properly.I do not feel obligated to respond to such inquiries that essentially say: "send me the data," and I do not have the time to engage in discussion to find out what the person wants or needs, and then (as may be necessary if people are unfamiliar with field experiments or field data) to guide and review to be sure the data are treated and/or used properly.I am speaking from experience on this.Response: Our email explicitly stated the need of time-varying hydraulic head data in Figure4ofRabinovich et al. (2015) for parameter estimation.The original letter by the second author to the reviewer Dr. W. Barrash is given below: "I'm a graduate student working on a study related to the topic of parameter estimation for oscillatory pumping test data.… In the paper, the hydraulic head data measured at the Boise Site was analyzed and illustrated in Figure4.Would you please provide the original measured hydraulic head versus time data and the after applying the Fourier analysis data? …" So now, given the above experience with the authors, the Reply to Reviewer 2 states they want to do a reanalysis and modify their analytical model to include partially penetrating wells and thereby match the OHT field pumping configuration.But they go on to say "Curve fitting to the data will be conducted using the present solution with and without considering the wellbore storage effect."*** But this is still an inappropriate use of the data they are requesting.It doesn't make sense to analyze

Figure R4 .
Figure R1.Field test results for hydraulic head as a function of time and our digitized data from is time,   is radial hydraulic conductivity,   and   are respectively inner and outer radiuses of the well,   and   are respectively lower and upper elevations of screen interval, and  =   −