Closure to “Modeling Groundwater Flow under Transient Nonlinear Free Surface,” by Sergio E. Serrano

I respond to the discussion by Barry et al. 2005, this issue about my article Serrano 2003 . The results presented in the paper constitute a new, simple analytical procedure to solve the complex problem of groundwater flow subject to a steady or transient nonlinear free surface. The results were obtained with Adomian’s method of decomposition Adomian 1994; see Serrano 1997, 2001 for simple introductions in hydrology . The results are very accurate for most cases of regional groundwater flow and sometimes even for the pathological cases conceived in Barry et al. 2005 , as I show below. I prove that every item in Barry et al. 2005 reflects either a misunderstanding of the application of the method presented in the paper, an incorrect application of the method of decomposition, or a failure to produce a properly posed groundwater boundary-value problem. I have also documented and shown beyond any doubt that the claims by Barry et al. to original authorship of any new solution to the Boussinesq equation are false. The closed-form solution presented in Parlange et al. 2000 , and claimed in Barry et al. 2000 to be the first one, is actually a limited case of a more general solution developed nearly 50 years earlier by Sokolov 1956 , as documented in Kacimov and Serrano 2003 . The derivations in Barry et al. 2000 , claimed in Barry et al. 2005 as the first decomposition solution to the Boussinesq Eq. 17 in my paper, lead to an incorrect expression that does not satisfy the Boussinesq equation. Only the first correct solution should be quoted in the literature. It is also shown that the first correct decomposition solution of Eq. 17 was developed in Serrano and Workman 2000 . The first decomposition solution of a Boussinesq equation in groundwater was developed by Serrano and Unny 1987 . Here are specific answers to the item numbers listed by the discussers: 1. Barry et al. 2005 are incorrect. Contrary to their opinion, all of the models considered in the paper are specific illustrations of groundwater flow cases with significant vertical gradients where the Dupuit assumptions of no vertical gradient collapse. For example, Fig.. 1 of the original paper conclusively proves this point: At certain locations e.g., x=250 m there is vertical flow only, and no horizontal flow. For the example illustrated in Fig. 3 of the paper, it is clear that the average slope of the free surface is about 10%, which significantly surpasses the recommended 3% maximum in Dupuit-based models with no vertical flow assumptions. Furthermore, the field application illustrated in Fig. 5 conclusively proves that strong vertical gradients completely dominate the flow. The discussers also misinterpret the application of Eqs. 9 and 13 of the paper when stating that these equations are included in the classical solutions of Poluvarinova-Kochina 1962 . The latter are applicable to steady flow in tall dams with no recharge, whereas the new solutions of the writer are applicable to steady or unsteady regional aquifers with significant recharge from rainfall. 2. Barry et al. 2005 are incorrect in their assessment. One of