Model:Equilibrium Calculator

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Equilibrium Calculator


Metadata

Also known as
Model type Tool
Model part of larger framework
Incorporated models or components:
Spatial dimensions 2D
Spatial extent Reach-Scale
Model domain Terrestrial, Hydrology
One-line model description Equilibrium solver of Self-formed, Single-thread, Sand-bed Rivers
Extended model description 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.
Keywords:

sand-bed rivers, bankfull geometry,


First name Enrica
Last name Viparelli
Type of contact Model developer
Institute / Organization University of South Carolina
Postal address 1
Postal address 2
Town / City Columbia
Postal code 29208
State South Carolina
Country United States
Email address viparell@cec.sc.edu
Phone
Fax


First name Esther
Last name Eke
Type of contact Model developer
Institute / Organization Idaho Department of Labor
Postal address 1
Postal address 2
Town / City
Postal code
State Idaho
Country United States
Email address
Phone
Fax


Supported platforms Mac OS, Windows
Other platform
Programming language
Other program language Visual Basic for Applications
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 No not possible
BMI compliant No not possible
WMT component No not possible
PyMT component No not possible
Is this a data component No
Can be coupled with:
Model info
Nr. of publications: 1
Total citations: 0
h-index: --"--" is not a number.
m-quotient: 0
Qrcode Equilibrium Calculator.png
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Introduction

History

References




Nr. of publications: 1
Total citations: 0
h-index: --"--" is not a number.
m-quotient: 0



Featured publication(s)YearModel describedType of ReferenceCitations
Viparelli, E.; Eke, E. C.; 2021. Equilibrium of Self‐Formed, Single‐Thread, Sand‐Bed Rivers. Geophysical Research Letters, 48, . 10.1029/2021GL094591
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2021 Equilibrium Calculator

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