Reply to Comment on “Analysis of pumping test data for determining unconfined-aquifer parameters: Composite analysis or not?”: paper published in Hydrogeology Journal (2009) 17:1133–1147, by Hund-Der Yeh and Yen-Chen Huang

1. The Comment states that “... the Cape Cod aquifer is relatively homogeneous to flow ...” and “... the Cape Cod aquifer was shown by Moench et al. (2001) to be remarkably homogeneous”. However, the abstract of Moench (2004a) states “... in Cape Cod, Massachusetts, in a slightly heterogeneous, coarse-grained glacial outwash deposit ...”. Moreover, “The Cape Cod aquifer ...in slightly heterogeneous and anisotropic, coarse-grained alluvial aquifers” (Moench 2004a). The aquifer test (Moench et al. 2001) was performed at the Cape Cod Toxic Substances Hydrology Research Site in Falmouth, Massachusetts. The tracer test site near Otis Air Force Base at Cape Cod, referred to in LeBlanc et al. (1991), is about 15 km to the north of Falmouth. LeBlanc et al. (1991, p. 898) gave a figure, which shows a geological profile with stratified sand and gravel formation, for an unsaturated zone about 5 m above the water table at the tracer test site. LeBlanc et al. (1991, p. 897) mentioned that the estimated hydraulic conductivity of the outwash varies about one order of magnitude and this variation results from the interbedded lenses and layers of sands and gravels. So it is not appropriate to state that the aquifer formation at Cape Cod is relatively homogeneous or remarkably homogeneous. 2. Physically, the time-drawdown distribution due to pumping in an unconfined aquifer can be divided into three segments. In the early stage, water is instantaneously released from storage by the compaction of the aquifer and the expansion of the water. In the second stage, the vertical gradient near the water table causes flow of the porous matrix. The gravity drainage starts to replenish the depression and the rate of decline in the hydraulic head slows or stops after a period of time. The second stage is also called ‘the delayed yield stage’ in Batu (1998, p. 459). Finally, the flow exhibits Theis behavior and most of the pumping is supplied by the specific yield in the third stage. Boulton’s model (Boulton 1954) can reproduce all three segments of the delayed process by introducing an empirical constant α with specific yield in the confined aquifer flow equation. However, the physical meaning of the constant remains unclear, as mentioned in the groundwater literature. One example is the comment given by Neuman (1979, p. 899) as “Although Boulton’s model appears to fit data quite well, it nevertheless fails to provide insight into the physical nature of the delayed yield phenomenon.” On the other hand, Neuman’s model (Neuman 1972, 1974), which replaces the term ‘delayed yield’ with a more general concept called ‘delayed water-table response’ (Neuman 1972, p. 1033), leads to a solution that is also capable of reproducing all three segments of the time-drawdown curve. Batu (1998, p. 492) wrote a comment on Boulton’s and Neuman’s models: “The main difference between the two models is that the Neuman model is based on welldefined physical parameters of the aquifer system.” Truly speaking, Neuman’s model can successfully predict delayed water-table response and gives very good fit to the Cape Cod aquifer test data using single-well data analysis as demonstrated in the subject article (Yeh and Huang 2009). Received: 18 February 2010 /Accepted: 24 September 2010 Published online: 20 October 2010