Model:Equilibrium Calculator

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Equilibrium Calculator

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Summary Contact Technical specs In/Output Process Testing Other Component info Also known as Model type Model part of larger framework Note on status model Date note status model Incorporated models or components: Spatial dimensions Spatial extent Model domain One-line model description Extended model description Keywords: Name Type of contact Institute / Organization Postal address 1 Postal address 2 Town / City Postal code State Country United States Email address Phone Fax Supported platforms Mac OS, Windows Other platform Programming language Other program language Visual Basic for Applications and Code optimized Single Processor Multiple processors implemented Nr of distributed processors Nr of shared processors Start year development 2020 Does model development still take place? No If above answer is no, provide end year model development 2021 Code development status As is, no updates are provided When did you indicate the 'code development status'? 2021 Model availability As code, As teaching tool Source code availability (Or provide future intension) Through web repository Source web address https://github.com/vipenrica/Channel-geometry Source csdms web address Program license type BSD or MIT X11 Program license type other Memory requirements Typical run time few minutes at the most Describe input parameters River hydrology is described with a flow duration curve, the mean annual sand load is specified, the mean annual mud load is computed with a user-specified rating curve, characteristic sand and mud grain size, friction coefficients for the channel and for the floodplain and other model parameters described in the excel caclulator Input format Other input format Numbers is an excel file Describe output parameters equilibrium channel slope, width and depth, bankfull discharge, point bar height, difference in elevation between eroding and depositing banks, channel migration rate, overbank deposition rates of sand and mud, volume fraction content of sand and mud in the floodplain. Output format Other output format Numbers in an excel file Pre-processing software needed? No Describe pre-processing software Post-processing software needed? No Describe post-processing software Visualization software needed? No If above answer is yes Other visualization software Describe processes represented by the model The model predicts bankfull geometry of single-thread, sand-bed rivers from first principles, i.e. conservation of channel bed and floodplain sediment, which does not require the a-priori knowledge of the bankfull discharge. Building on previous work on the equilibrium of engineered rivers, i.e. rivers with fixed banks and sinuosity (Blom et al., 2016, 2017, Arkesteijn et al., 2019), as well as formulations for floodplain morphodynamics (Lauer & Parker, 2008, Viparelli et al., 2013, Lauer et al., 2016) and bank migration (Parker et al., 2011, Eke et al., 2014, Davidson & Eaton, 2018, De Rego et al., 2020), we derive equilibrium solutions for channel geometry (width, depth, slope), floodplain sediment size distribution, bankfull discharge, channel migration and overbank deposition rates. References Arkesteijn, L., Blom, A., Czapiga, M. J., Chavarrias, V. & Labeur, R. J. (2019). The quasi-equilibrium longitudinal profile in backwater reaches if the engineered alluvial river: A space-marching method, Journal of Geophysical Research: Earth Surface 124, 2542-2560. Blom, A., Viparelli, E. & Chavarrias, V. (2016). The graded alluvial river: Profile concavity and downstream fining, Geophysical Research Letters 43 (12), 6285-6293. Blom, A., Arkesteijn, L., Chavarrias, V. & Viparelli, E. (2017). The equilibrium alluvial river under variable flow and its channel-forming discharge, Journal of Geophysical Research: Earth Surface 122, 1924-1948. Davidson, S.L. & Eaton, B. C. (2018). Beyond Regime: A stochastic model of floods, bank erosion, and channel migration. Water Resources Research, 54, 6282-6298. De Rego, K., Lauer, J. W., Eaton, B. & Hassan, M. (2020). A decadal-scale numerical model for wandering, cobble-bedded rivers subject to disturbance, Earth Surface Processes and Landforms 45, 912-927. Eke, E., Parker, G. & Shimizu, Y. (2014). Numerical modeling of erosional and depositional bank processes in migrating river bends with self-formed width: Morphodynamics of bar push and bank pull, Journal of Geophysical Research: Earth Surface 119, 1455-1483. Lauer, J. W. & Parker, G. (2008). Modeling framework for sediment deposition, storage, and evacuation in the floodplain of a meandering river: Theory, Water Resources Research 44, W04425, doi: 10.1029/2006WR005528. Lauer, J. W., Viparelli, E. & Piegay, H. (2016). Morphodynamics and sediment tracers in 1-D (MAST-1D): 1-D sediment transport that includes exchange with an off-channel sediment reservoir, Advances in Water Resources 93, 135-149. Parker, G., Shimizu, Y., Wilkerson, G. V., Eke, E. C., Abad, J. D., Lauer, J. W., Paola, C., Dietrich, W. E. & Voller, V. R. (2011). A new framework for modeling the migration of meandering rivers, Earth Surface Processes and Landforms 36, 70-86. Viparelli, E., Lauer, J. W., Belmont, P. & Parker, G. (2013). A numerical model to develop long-term sediment budgets using isotopic sediment fingerprints, Computers & Geosciences 53, 114-122. Describe key physical parameters and equations Model governing equations express the conservation of sand and mud in the floodplain and in the channel. Water depth and shear stress are computed with a Chezy formulation for a composite rectangular cross section. Total ((bedload plus suspended load) sand transport capacity is computed with an Engelund and Hansen-type of bulk load relation (see Parker, 2004). The mean annual sand load is determined by averaging the sand transport capacities over the flow duration curve. Channel migration rate is computed as in Eke et al. (2014). Overbank deposition rates are computed with the approach presented in Parker et al. (1996). References Eke, E., Parker, G. & Shimizu, Y. (2014). Numerical modeling of erosional and depositional bank processes in migrating river bends with self-formed width: Morphodynamics of bar push and bank pull, Journal of Geophysical Research: Earth Surface 119, 1455-1483. Parker, G. (2004). 1D sediment transport morphodynamics with applications to rivers and turbidity currents e-book available at http://hydrolab.illinois.edu/people/parkerg/morphodynamics_e-book.htm . Parker, G., Cui, Y., Imran, J. & Dietrich, W. E. (1996). Flooding in the lower Ok Tedi, Papua New Guinea due to the disposal of mine tailings and it’s amelioration, International Seminar on Recent trends of floods and their preventive measures, 20-21 June, Sapporo, Japan. Describe length scale and resolution constraints We use formulations describing rivers at large scale. Complex interactions between physical, chemical, biological and ecological processes that play a relevant role in floodplain construction are not accounted for, as their impacts on floodplain mass balance cannot be quantified. Model parameters should thus be interpreted as averages over a few meander bends, and over several years. Describe time scale and resolution constraints We present an equilibrium solution that may or may not be reached. The fundamental assumption is that in the absence of subsidence, uplift and change of downstream water surface base level, an alluvial river will evolve toward an equilibrium state in which overbank and bar deposition (floodplain construction) are perfectly balanced by the removal of floodplain sediment due to channel migration (floodplain shaving) (Lauer & Parker, 2006). This equilibrium state can be reached if hydrologic regime, sediment supply and caliber do not vary in time. Reference Lauer, J. W. & Parker, G. (2006). Net local removal of floodplain sediment by river meander migration, Geomorphology 96, 123-149. Describe any numerical limitations and issues Model limitations are related to the use of the goal seek function in excel to find the solution. Describe available calibration data sets The model was zeroed on the pre-1930 Minnesota River between Mankato and Jordan, Minnesota, using data available in the literature and on the USGS website. Upload calibration data sets if available: Describe available test data sets We performed a model sensitivity analysis and the results are reported in the Equilibrium_results_submit.xlsx file uploaded in the github repository Upload test data sets if available: Describe ideal data for testing N/A Do you have current or future plans for collaborating with other researchers? Yes, we plan to work with the full model. Is there a manual available? No Upload manual if available: Model website if any Model forum / discussion board Comments This part will be filled out by CSDMS staff OpenMI compliant Not yet"Not yet" is not in the list (Yes, No but planned, No but possible, No not possible) of allowed values for the "Code openmi compliant or not" property. BMI compliant Not yet"Not yet" is not in the list (Yes, No but planned, No but possible, No not possible) of allowed values for the "BMICompliant" property. WMT component Not yet"Not yet" is not in the list (Yes, In progress, No but possible, No not possible) of allowed values for the "Code CMT compliant or not" property. PyMT component Not yet"Not yet" is not in the list (Yes, In progress, No but possible, No not possible) of allowed values for the "Code PyMT compliant or not" property. Is this a data component No Can be coupled with:

Model info Authors Enrica Viparelli Eke Source code Go to external source code site Model citations Nr. of publications: 1 Total citations: 2 h-index: 1 m-quotient: 0.2 QR-code Link to this page Other models by author Equilibrium Calculator Tracer dispersion calculator

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Nr. of publications:	1
Total citations:	2
h-index:	1
m-quotient:	0.2

Featured publication(s)	Year	Model described	Type of Reference	Citations
Viparelli, E.; Eke, E. C.; 2021. Equilibrium of Self‐Formed, Single‐Thread, Sand‐Bed Rivers. Geophysical Research Letters, 48, . 10.1029/2021GL094591 (View/edit entry)	2021	Equilibrium Calculator	Model overview	2
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