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Reworking of a simple centerline migration model that simulates meander bend cutoff distributions with statistical tests for spatiotemporal clustering

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Cutoffs Cluster on Meandering Rivers from Self-Induced Migration

Josie Arcuri and Doug Edmonds
Indiana University, Department of Earth and Atmospheric Sciences

A model for simulating channel centerline migration that accounts for nonlocal effects from cutoffs, based on meanderpy[1]. We also include code to test hypothesis concerning what makes cutoffs cluster along channel centerlines through time.

Abstract

Cutoffs are iconic features of meandering floodplains that limit the lateral extent of channels. When and where cutoffs occur along a river decides the distribution of oxbow lakes and influences the character of channel deposits. Lakes and deposits left behind after cutoffs contribute to the ecology and underlying stratigraphy of their floodplain. Despite this relevance, it is unclear what controls cutoff spacing and timing along a meandering river. Here we show how nonlocal effects following a cutoff can temporally elevate channel migration rate and cause cutoffs along a given reach to cluster in space and time. Using remote sensing data, we measure nonlocal effects on 9 rivers in the Amazon River Basin. We find that the migration rate after a cutoff increases up to 3.5 times greater in adjacent bends than elsewhere on the river for up to 12 years. On 5 out of the 9 rivers, these nonlocal effects appear to reduce the time to cutoff in nearby bends and cause some cutoffs to cluster. To understand why certain rivers show cutoff clustering and others do not, we add nonlocal effects to a well-known meandering bank migration model. We conduct 28 experiments that vary the migration rate constant, as well as the magnitude and decay of nonlocal effects. Cutoff clustering in those experiments is evaluated with a spatiotemporal version of Ripley’s K. When nonlocal effects are ignored, cutoffs occur with regular spacing and timing along channel centerlines. As the magnitude of nonlocal effects increases, cutoffs aggregate, and clustering emerges. Cutoffs on real and simulated rivers cluster because their nonlocal effects hasten additional cutoffs on neighboring bends. Our remote sensing and numerical modeling suggest that nonlocal effects can cause clustering of cutoffs and contribute to the evolution of floodplains through channel deposits and oxbow lakes.

HKplus

This module builds upon a previous implementation of Howard and Knutson's centerline migration model[1], meanderpy, based on local and weigthed upstream curvatures[2]. With its main structure nearly identical to meanderpy, this version considers how cutoffs affect bank migration beyond their impact on curvature. We include a general representation of how cutoffs enhance sediment transport along a cutoff bend for years after occurrence. In calculating a nominal migration rate, each point along a centerline is moved according to a migration rate constant muliplied by local curvature and the sum of any present nonlocal effects from cutoffs at that point. The spatial and temporal extent of each cutoff's nonlocal effects are set according to ours remote sensing analyses and previously measured cutoff nonlocal effects[3]. Following, nominal migration rate modified based on upstream curvature, which has been shown to reasonably predict bank migration rates[4].

SpaceTime

A set of functions used to test cutoff distributions for spatiotemporal clustering based on their location and time of occurrence. This includes a monte carlo sampling method to test cutoff distibutions against randomly-generated point patterns[5].

Implementation

For an example of one experiment, Run

jupyter notebook cutoffs.ipynb 

To reproduce Figure 3:

python Figure3.py

Getting the code

You can download a copy of all the files in this repository by cloning this repository:

git clone https://github.com/josiearcuri/Cutoffs.git/

Dependencies

conda nev create -f cutoffenv.yml

References

[1]Alan Howard;Thomas Knutson; Sufficient Conditions for River Meandering: A Simulation Approach. Water Resources Research (1984) 20: 1659–1667. DOI:10.1029/WR020i011p01659 [2]https://github.com/zsylvester/meanderpy
[3]Zoltán Sylvester; Paul Durkin; Jacob A. Covault; High curvatures drive river meandering. Geology (2019) 47 (3): 263–266. DOI: 10.1130/G45608.1
[4]Jon Schwenk, Efi Foufoula‐Georgiou; Meander cutoffs nonlocally accelerate upstream and downstream migration and channel widening. Geophysical Research Letters (2016) 43 (24): 12,437-12,445. DOI: 10.1002/2016GL071670
[5]Peter Diggle; Statistical Analysis of Spatial and Spatio-Temporal Point Patterns. CRC Press (2014), Third Edition. ISBN:978-1-4665-6023-9

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Reworking of a simple centerline migration model that simulates meander bend cutoff distributions with statistical tests for spatiotemporal clustering

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