Discussions and Closures

Discussion of “Adaptive Time Stepping–Operator Splitting Strategy to Couple ImplicitNumerical Hydrodynamic and Water QualityCodes” by Gaurav Savant and R. C. BergerSeptember 2012, Vol. 138, No. 9, pp. 979–984.DOI: 10.1061/(ASCE)EE.1943-7870.0000547

Kyeong Park1; Jian Shen2; and Albert Y. Kuo, M.ASCE3

1Professor, Dept. of Marine Sciences, Univ. of South Alabama, DauphinIsland Sea Lab, 101 Bienville Blvd., Dauphin Island, AL 36528(corresponding author). E-mail: kpark@disl.org

2Research Professor, Virginia Institute of Marine Science, College ofWilliam and Mary, Gloucester Point, VA 23062.

3Professor Emeritus, Virginia Institute of Marine Science, College ofWilliam and Mary, Gloucester Point, VA 23062.

The authors proposed an operator splitting–derived method of link-ing hydrodynamic and water-quality models. The topic is no doubtimportant, but the concept and its application are not new at all.The operator-splitting method that decouples the mass-balanceequation into the physical transport (advection–diffusion) andkinetic equations has long been used in the water-quality modelingof surface water (e.g., Kuo and Neilson 1988) and groundwater(Valocchi and Malmstead 1992). Operator-splitting methods iden-tical to the one presented in the original paper (with one excep-tion that is discussed in the next paragraph) were developedand applied to intertidal (Park and Kuo 1996) and intratidal (Parket al. 1998) water-quality models, but the authors failed to citethem. For example, Eqs. (9) and (10) in the original paper are iden-tical to Eqs. (3) and (4) in Park et al. (1998), respectively. Theoperator-splitting method in Park and Kuo (1996) was imple-mented to a tidal prism water-quality model (Kuo and Park1994; Kuo et al. 2005) and the one in Park et al. (1998) was imple-mented to the Environmental Fluid Dynamics Code, also referred toas the three-dimensional hydrodynamic-eutrophication model(HEN-3D) (Park et al. 1995, 2005). These models have been avail-able in public domain and listed as tools for total maximum dailyload (TMDL) development by U.S. EPA [EPA841-B-97-006 (U.S.EPA 1997) and EPA/600/R-05/149 (U.S. EPA 2005)]. They havebeen successfully used for many modeling studies.

The only new aspect of the proposed method presented in theoriginal paper, compared with Park and Kuo (1996) and Park et al.(1998), is the use of an adaptive time stepping when solving thekinetic equation [Eq. (10)]. The authors, however, do not showany evidence of the computational benefits that may have been at-tained from this adaptive time stepping. The information in Figs. 4and 5 (x marks), by contrast, indicates that this adaptive time step-ping results in relatively short computation time steps during theperiod of rapid changes in concentration, suggesting that this adap-tive time stepping may not be computationally efficient after all.

References

Kuo, A. Y., and Neilson, B. J. (1988). “A modified tidal prism modelfor water quality in small coastal embayments.” Water Sci. Technol.,20(6/7), 133–142.

Kuo, A. Y., and Park, K. (1994). “A PC-based tidal prism water qualitymodel for small coastal basins and tidal creeks.” Special Rep. in AppliedMarine Science and Ocean Engineering (SRAMSOE) No. 324, Schoolof Marine Science/Virginia Institute of Marine Science, College ofWilliam and Mary, Gloucester Point, VA.

Kuo, A. Y., Park, K., Kim, S.-C., and Lin, J. (2005). “A tidal prismwater quality model for small coastal basins.” Coastal Manage.,33(1), 101–117.

Park, K., Jung, H.-S., Kim, H.-S., and Ahn, S.-M. (2005). “Three-dimensional hydrodynamic-eutrophication model (HEM-3D): Applica-tion to Kwang-Yang Bay, Korea.” Mar. Environ. Res., 60(2), 171–193.

Park, K., and Kuo, A. Y. (1996). “A multi-step computation schemedecoupling kinetic processes from physical transport in water qualitymodels.” Water Res., 30(10), 2255–2264.

Park, K., Kuo, A. Y., Shen, J., and Hamrick, J. M. (1995). “A three-dimensional hydrodynamic-eutrophication model (HEM-3D): Descrip-tion of water quality and sediment process submodels.” SRAMSOE No.327, School of Marine Science/Virginia Institute of Marine Science,College of William and Mary, Gloucester Point, VA.

Park, K., Shen, J., and Kuo, A. Y. (1998). “Application of a multi-step com-putation scheme to an intratidal estuarine water quality model.” Ecol.Modell., 110(3), 281–292.

Valocchi, A. J., and Malmstead, M. (1992). “Accuracy of operator splittingfor advection-diffusion-reaction problems.” Water Resour. Res., 28(5),1471–1476.

U.S. EPA. (1997). “Compendium of tools for watershed assessment andTMDL development.” EPA841-B-97-006, Washington, DC.

U.S. EPA. (2005). “TMDL model evaluation and research needs.” EPA/600/R-05/149, Washington, DC.

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