Appendix C.2:   Numerical errors in groundwater and overland flow models

This paper contains certain grammatical and other errors that need to be corrected (see below).

    Page 6, Abstract,last line:   Replace "in in" with "in"

    Page 6, Abstract,last line:   Replace "finite difference model" with "finite-difference model"

    Page 7, Introduction, paragraph 1:   Ackward phrasing "increased recently due to the increased need". Reword.

    Page 7, Introduction, paragraph 1:   Replace "The current study" with "This study" or "The present study"

    Page 7, Introduction; paragraph 2:   Replace "rainfall, and evapotranspiration" with "rainfall and evapotranspiration"

    Page 8, Introduction, paragraph 1:   The statement "Various unconditionally stable numerical methods using implicit or other methods have made it possible for modelers to use almost any discretization with computer models" is too strong and possibly misleading. While fully implicit methods generally feature unconditional stability, this is usually at the expense of reduced convergence, i.e, loss of accuracy. To mention the unconditional stability without saying anything about accuracy implies that the strategy is one of stability "at all cost," which is self-defeating.

    Page 8, Introduction, paragraph 1:   The statement "compiled many of the basis developments" is weak. Prefer "have described many of the basic principles"

    Page 9, paragraph 1:   Replace "are arbitrarily chosen" with "are usually arbitrarily chosen." In some diffusion-flow formulations, the space and time follow the Courant convergence law (See Ponce, 1989, Chapter 9, "Engineering Hydrology, Principles and Practices.")

    Page 9, paragraph 3:   Replace "two dimensional" with "Two-dimensional"

    Page 10, paragraph 1:   Replace "St Venant equations." with "St. Venant equations" (no period at the end, before a reference)

    Page 10, paragraph 1:   Replace "Manning's" with "Manning"

    Page 10, paragraph 1:   Replace "weighted implicit finite volume formulation" with "weighted-implicit finite-volume formulation"

    Page 10, paragraph 1:   Replace "semi-implicit" with "implicit" (There are implicit and fully implicit schemes; the term semi-implicit is redundant).

    Page 11, paragraph 1:   Replace "explicit and the implicit methods are obtained by using α = 0 and 1.0" with "explicit and implicit schemes are obtained by using α = 0 and α = 1, respectively"

    Page 11, paragraph 2:   Replace "explaining" with "describing"

    Page 11, paragraph 2:   Replace "current paper" with "present paper"

    Page 12, paragraph 1:   Replace "numerical approximations for derivatives, etc" with "numerical approximations for derivatives and other terms"

    Page 12, paragraph 2:   Replace "maximum percentage" with "maximum-percentage"

    Page 13, paragraph 1:   Replace "Quantity φ" with "the quantity φ"

    Page 13, paragraph 1:   Three discretizations per half sine wave appears very coarse. The error < 4.5% in what? Stage?

    Page 13, paragraph 2:   Replace "sinusoidal water level variation" with "sinuosidal water-level variation"

    Page 13, paragraph 2:   Replace "problems respectively" with "problems, respectively"

    Page 14, paragraph 1:   Eq. 9 is not clear.

    Page 15 and 16:   Replace "explicit, implicit, and semi-explicit" with "explicit, implicit, and fully implicit"

    Page 16:   All methods that solve many grid points at-a-time are implicit. So, there is no semi-implicit. There is implicit and fully implicit, the latter to show that the functions and/or derivatives are being taken at the advanced time step.

    Page 19, paragraph 1:   Replace "measured as the (numerical value - analytical value) is small" with "measured as the numerical minus the analytical value is small"

    Page 19:   Replace "water level subsidence" with "water-level subsidence"

    Page 19, paragraph 1, last line:   Delete "in the paper"

    Page 24, paragraph 1:   Replace "time lag error" with "time-lag error"

    Page 25, paragraph 1:   Replace "in head for for a given frequency" with "in head for a given frequency"

    Page 26, paragraph 1:   Replace "steady state" with "steady-state"

    Page 26, paragraph 1:   Replace "Thiem" with "The Thiem"

    Page 28, paragraph 2:   Replace "(rainfall - evapotranspiration)" with "rainfall minus evapotranspiration" Avoid algebra in text.

    Page 29, last paragraph:   Replace "two one dimensional rainfall patterns" with "two one-dimensional rainfall patterns"

    Page 30, paragraph 1:   Replace "source induced flow condition" with "source-induced flow condition".

    Page 31:   Do not use italics for units.

    Page 31, paragraph 2:   Replace "14 day intervals" with "14-day intervals"

    Page 32, paragraph 2:   Replace "rain driven water level fluctuations" with "rain-driven water-level fluctuations"

    Page 32, paragraph 2:   Replace "driving forces of hydrology" with "driving forces"

    Page 34, paragraph 2:   Replace "spatial discretizations" with "spatial discretization" The word "discretization" applies to the entire grid, in either 1-D or 2-D.