Comment on “Particle dispersal due to interplay of motions in the surface layer of a small reservoir” (by P. Okely, J. Imberger, and K. Shimizu) and “Processes affecting horizontal mixing and dispersion in Winam Gulf, Lake Victoria” (by P. Okely, J. Imberger, and J. P. Antenucci)

Abstract

Okely et al. (2010a,b) are concerned with horizontal dispersion and mixing in lakes and employ numerical modeling to estimate horizontal dispersion coefficients. In both papers, the dispersal of four numerical Lagrangian particles is employed to estimate dispersion coefficients, and the authors explicitly claim that ‘‘...this method measures horizontal dispersion due to large-scale horizontal shear only, and the influence of other processes, such as turbulent diffusion, is not accounted for’’ (Okely et al. 2010b, p. 591). However, we demonstrate here that without a diffusive process, e.g., molecular or turbulent diffusion, the dispersal rate estimated from Lagrangian particles as in Okely et al. (2010a,b) should be zero in principal for largescale nondivergent horizontal flow fields, independent of the horizontal shear. The particle dispersal presented by Okely et al. (2010a,b) is not a measure of horizontal dispersion due to horizontal shear but depends on the initial position of the particles and the divergence of the simulated mean flow field and may be affected by undersampling of the flow field, since only four particles were considered. Whereas the study of Okely et al. (2010b) was entirely based on this Lagrangian particle technique, Okely et al. (2010a) compared horizontal dispersion coefficients estimated from this technique with coefficients determined from the spread of numerically simulated tracer distributions. According to Okely et al. (2010a), their horizontal dispersion coefficients agree reasonably well with an estimate based on the assumption that the effects of vertical shear and vertical turbulent mixing (Kz) determine horizontal dispersion (see Table 1 and Eq. 11 in Okely et al. 2010a). Okely et al. (2010a, p. 1875) state that ‘‘The vertical shear dispersion scaling was a good approximation for the magnitude and spatial variation of the average horizontal dispersion rates.’’ However, the horizontal dispersion coefficients obtained from Eq. 11 using the observed vertical diffusivities are an order of magnitude smaller than the values presented in Table 1 of Okely et al. (2010a) and thus are substantially smaller than the horizontal dispersion coefficients obtained from the tracer simulations. Hence, the combined effect of vertical shear and vertical diffusion cannot explain the large horizontal dispersion in the simulation of Okely et al. (2010a). Finally, the Lagrangian particle technique and also the dispersion of the simulated tracer clouds appear to depend mainly on the horizontal divergence of the simulated flow field. Comparison of simulated and observed particle tracks and horizontal currents at a single location indicates that the quality of the simulated flow field is not sufficient to provide the divergence of the true flow field in the lakes studied. Hence, Okely et al. (2010a,b) may provide estimates of the spread of particles and tracers in their simulated flow field but cannot contribute information on horizontal particle dispersal or horizontal dispersion and mixing under field conditions in lakes.