CMS-Flow: Morphology Acceleration Factor

Notes on Morphological Acceleration Factor for Long-Term Simulation of Sediment Transport and Morphological Change

Yan Ding, ERDC-CHL-MS
Jan. 20, 2023

A morphological acceleration factor ($f_{morph}$) is often used to reduce the computational time associated with long-term morphodynamic simulations. The morphological acceleration factor is a scalar quantity applied to the Exner's sediment continuity equation, assuming that morphodynamic evolution occurs at longer time scales than the hydrodynamic processes (Sánchez et al. 2014). The use of $f_{morph}>1.0$ assumes a linear relationship between hydrodynamic and morphodynamic processes. In CMS, the fractional bed change ($\Delta z$) at each time step of simulation ($\Delta t$) is calculated as follows:

$\Delta z={\frac {f_{morph}\Delta t}{\rho _{s}(1-\rho )}}(\alpha _{t}\omega _{s}(C_{t}-C_{t}^{*})+S_{b})$

where $\rho _{s}$ = density of sediment, $\rho$ = porosity of sediment (sand), $\alpha _{t}$ = total-load adaptation coefficient, $C_{t}$ = actual depth-averaged total-load sediment concentration, $C_{t}^{*}$ = equilibrium depth-averaged total-load sediment concentration, $\omega _{s}$ = sediment fall velocity, $S_{b}$ = net sediment flux due to gravitational effect of sediments. Details on the morphological acceleration factor in the CMS model can be found on page 69 – 70 of the technical report (Sánchez et al. 2014).

Obviously, the purpose of the morphologic acceleration factor is to speed up the bed change so that the simulation time ($t_{sim}$) represents approximately the change that would occur in $t_{morph}=f_{morph}t_{sim}$. The CMS model recommends using $f_{morph}>1.0$ for simulating idealized cases or analyzing project alternatives, and not using morphological acceleration when validating sediment transport model.

Using the CMS model, Styles et al. (2016, 2018) simulated long-term (up to 100 years) morphological changes around idealized barrier island tidal inlets, based on average bathymetric conditions in Grays Harbor, WA. Through sensitivity tests of the morphological acceleration factor, $f_{morph}=10.0$ was applied to accelerate the long-term morphology modeling driven by tides and waves.

Other morphological simulation models also provide morphological acceleration capability for long-term modeling of morphological changes, such as in Delft3D (Lesser et al., 2004). Van der Wegen and Roelvink (2008) provides a general guide to choose the value of morphological factor for long-term modeling of estuarine morphology and suggested a large value of the morphological factor, up to 400, would be acceptable for 1-D and 2-D morphological modeling driven by tidal cycles. Dastgheib et al. (2008) used a 2DH Delft3D model with $f_{morph}=300.0$ to simulate long-term morphology evolution in a Tidal Basin in the Dutch Wadden Sea.

Morgan et al. (2020) use Delft3D to investigate the effect of morphological factor on river flood wave propagation, for which the values were set up to 50, which is much less than those typical values for coasts and estuaries. They found that the morphological acceleration creates increasingly attenuative flood waves, which is not favorable for prediction of flood peak arrival time. The recent advancements (Li, 2010; Ranasinghe et al., 2011) have provided a theoretical background to detect this value are significant, under the conditions of waves and tides.

Even though the morphological acceleration approach with $f_{morph}>1.0$ is now widely used by engineers for solving practical problems in coastal and estuarine environments, the value of the morphological acceleration factor is still often set by trial- and-error procedures.

References:

• Dastgheib, A., Roelvink, J.A., Wang, Z.B., 2008. Long-term process-based morphological modeling of the Marsdiep Tidal Basin. Mar. Geol. 256, 90–100.
• Lesser, G.R., Roelvink, J.A., Van Kester, J.A.T.M., Stelling, G.S., (2004). Development and validation of a three-dimensional morphological model. Coastal Engineering, 51, 883–915. https://doi.org/10.1016/j.coastaleng.2004.07.014
• Li, L., 2010. A Fundamental Study of the Morphological Acceleration Factor. Delft University of Technology Master’s thesis.
• Morgan, Jacob A. (2020), Nirnimesh Kumar, Alexander R. Horner-Devine, Shelby Ahrendt, Erkan Istanbullouglu, Christina Bandaragoda, The use of a morphological acceleration factor in the simulation of large-scale fluvial morphodynamics, Geomorphology, 356, 107088, 2020. https://doi.org/10.1016/j.geomorph.2020.107088
• Ranasinghe, R., Swinkels, C., Luijendijk, A., Roelvink, D., Bosboom, J., Stive, M., Walstra, D., 2011. Morphodynamic upscaling with the MORFAC ap- proach: dependencies and sensitivities. Coastal Eng. 58 (8), 806–811. https://doi.org/10.1016/j.coastaleng.2011.03.010.
• Sánchez, A., W. Wu, H. Li, M. Brown, C. Reed, J. D. Rosati, and Z. Demirbilek. 2014. Coastal Modeling System: Mathematical Formulations and Numerical Methods. ERDC/CHL TR-14-2. Vicksburg, MS: U.S. Army Engineer Research and Development Center.
• Styles, R., Brown, M.E., Brutsche, K. E., LI, H., Beck, T. M., Sánchez, A. (2016). Long-Term Morphological Modeling of Barrier Island Tidal Inlets, Journal of Marine Science and Engineering, 2016, 4, 65; doi:10.3390/jmse4040065.
• Styles, Richard, Mitchell E. Brown, Katherine E. Brutsché, Honghai Li, Tanya M. Beck, and Alejandro Sánchez (2018), Long-Term Morphology Modeling for Barrier Island Tidal Inlets, ERDC/CHL TR- 18-12. Vicksburg, MS: U.S. Army Engineer Research and Development Center. http://dx.doi.org/10.21079/11681/28013
• Van der Wegen, M., Roelvink, J.A., (2008). Long-term estuarine morphodynamics evolution of a tidal embayment using a 2-dimensional process based model. J. Geophys. Res.113, C03016. doi:10.1029/2006JC003983.