Discussion of “Theoretical Analysis of Wing Dike Impact on River Flood Stages” by Fredrik Huthoff, Nicholas Pinter, and Jonathan W. F. Remo

The theoretical analysis proposed in the original paper is an oversimplified method to quantify an extremely complex and dynamic hydraulic problem. The basis of this analysis is the effective n value formula developed by Yossef (2004, 2005). Although these relationships can give insight into the relationship between the effective roughness in the dike zone and submergence, it is only suitable to deduce trends rather than quantify accurate magnitudes of change. Background into the development of Eq. (3) is necessary to understand its limitations. Eq. (3) was developed using a fixed bed physical model scaled to the dimensions and geometry of a dike field in the Dutch River Waal where the wing dike crest elevation, spacing, and length remained fixed throughout the study. There are major differences in geometry and spacing of dikes used by the Dutch and those on the Middle Mississippi River. The dikes used by the Dutch have a much higher crest elevation, closer spacing, and higher contraction ratios. Eq. (3) is dependent on the drag coefficient CD found in Eq. (4). The drag coefficient, CD, was developed using empirical data from the previously mentioned flume study and assumed to be in accordance with a power function. The coefficients a and b in Eq. (4) are only appropriate for the dimensions and channel geometry tested, and are not applicable to the much different geometry and dimensions of the Middle Mississippi River. The limitations of the relationships, which are the foundation of the original paper [Eqs. (3) and (4)], combined with concerns of the applicability of the relationship to the geometrically different Middle Mississippi River, make it difficult for the authors of the original paper to base sweeping conclusions off small changes (decimeter range) in an overly simplistic analysis. Another limitation the conclusions presented by the authors of the original paper is the model used in the original paper is extremely sensitive to the input data; small changes to in bank and/or channel roughness, wing dike crest height, and/or bed level change can have major impacts on the resulting water level difference, including resulting in negative values. An example of the sensitivity of the model to the input values is the resulting water level differences using the input values in the original paper. As detailed in the publisher’s note, the model developed by the authors of the original paper originally had an inadvertent error in the calculation of Manning’s n from Eq. (3). This resulted in effective roughness values in the bank zone with dikes (neff ) of approximately 0.6 s m−1=3, which is an order of magnitude too high. In combination with the correction of the math error, critical input values were changed in the corrected analysis. The bank roughness values (nb) used in the original version were 0.031, 0.032, 0.027, and 0.027 for St. Louis, Chester, Grand Tower, and Thebes, respectively. In the corrected analysis the original n values were decreased by over 40% to physically unrealistic values (Table 1). Had the authors of the original paper only corrected the math error and used the original values of base roughness in the bank zone with resulting calibrated bed changes of−0.80,−0.26,þ0.72, and −0.27 m at St. Louis, Chester, Grand Tower, and Thebes, respectively, the resulting water level difference would have been −0.12 m at St. Louis, þ0.21 m at Chester, þ0.84 m at Grand Tower, and −0.00 m at Thebes for 4Qave. These values of water level change lead to a conclusion on the impact of wing dikes on flood stages that is in conflict with what is presented in the original paper, but shared by many scientists (Watson et al. 2013; USGAO 2011; Huizinga 2009). A major issue with the roughness values used in the corrected paper is the resulting velocity distribution in the channel. Main channel velocities for the no dike, T0, condition at St. Louis were taken from a reconstruction of the model used in the original paper. At Qave, both main channel and bank zone velocities were equal. At 4Qave, the bank zone velocity was 135% of the channel velocity [Fig. 1(a)]. Conversely, had the authors of the original paper used similar roughness values for the channel and bank zone (as done in the