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David Litwin’s Research Showcase: Landscape co-evolution, dimensional analysis and transcendin

I am a PhD candidate studying geography and environmental engineering at Johns Hopkins University in the Landscape Hydrology Lab. I am broadly interested in understanding how landscape history and the co-evolution of landscape form and hydrological processes affect watershed function. Water movement through catchments drives processes like mineral weathering and erosion that ultimately shape the landscape. At the same time, the form and structure of the landscape determine water flow pathways and response to precipitation. Understanding these complex feedbacks may allow us to generalize our knowledge of how landscapes work and provide insight into places we have not studied in detail. In my dissertation research, I focus particularly on the relationship between erosional landscape evolution and runoff generation.

Upland landscapes are shaped by incision by overland flow, gravitationally-driven fluxes of sediment due to processes including biogenic disturbance and frost heaving, and baselevel change (Howard, 1994). These processes produce emergent topography over long timescales, so numerical approaches are particularly useful (e.g. reviews by Chen et al., 2014; Valters, 2016). However, models of landscape evolution often have simplistic, linear treatments of hydrology that are too limiting for my purposes. I want to know how the hydrology is changing the landscape and vice versa. This requires coupling landscape evolution processes with runoff generation processes that are affected by topographic form, such as shallow groundwater flow and the development of saturated areas. At University of Colorado Boulder in 2019, I developed a new model component for shallow groundwater flow (Litwin et al., 2020) in Landlab, a widely used open-source Earth surface modeling platform (Barnhart et al., 2020). With my new model and the existing erosion components in Landlab, I was ready to examine the coevolution of topography and runoff generation.

Even the simplest coupling of shallow groundwater and landscape evolution has a lot of parameters, though. How do we understand how this model really works? What are the limits of the morphologies and emergent hydrologic properties it can produce? One approach to answering these questions is dimensional analysis: reworking the governing equations into a dimensionless form where the model parameters appear in dimensionless groups. These groups act like “knobs” that one can “turn” to observe possible results of different parameter combinations without having to vary each parameter individually. I used this approach to reveal that the degree of stream dissection (or drainage density) of the landscapes is a power law function of the subsurface drainage capacity, our name for a dimensionless group of parameters that acts like a characteristic Darcy flux (groundwater flux) relative to available precipitation. The larger the drainage capacity, the more water passes through the subsurface, decreasing the extent of surface runoff and erosion. As the topography evolves, this results in less dissection and lower drainage density. This is the first demonstration of the hydro-geomorphic link between subsurface hydraulic properties and emergent topography in a long-term landscape evolution model. If you want to dig into this, we have a preprint out here.


Three model simulations showing difference when drainage capacity is increased. Blue lines outline a few channels and show how hillslope length Lh is related to dissection.

Do we see a relationship between subsurface drainage capacity and drainage density outside of this model? Researchers have been looking for relationships between hydrologic and hydraulic properties of landscapes and their drainage density for decades, often with weak or contradictory results (e.g. Jefferson et al., 2010; Luo et al., 2016; Yoshida & Troch, 2016). Why is such an obvious hydro-geomorphic metric so hard to tie to the processes that seem to be responsible for its existence? I don’t think I have a definitive answer to this, but it is clear from our model that drainage density has many dependencies besides hydrologic and hydraulic properties, including geomorphic coefficients that determine the effectiveness of erosion in channels and on hillslopes, which can be challenging to measure.

This suggests that we should be looking for relationships between emergent, measurable landscape properties that transcend the particularity of model parameters and local geologic history. While I’m continuing to explore this with numerical simulations, I’m also taking a field-based approach. Specifically, I will be examining the differences in hydrologic response and water transit times of two watersheds in the same climatic and tectonic setting but with distinctly different lithology. I’m looking forward to where this work takes me next.

References:

Barnhart, K. R., Hutton, E. W. H., Tucker, G. E., Gasparini, N. M., Istanbulluoglu, E., Hobley, D. E. J., et al. (2020). Short communication: Landlab v2.0: a software package for Earth surface dynamics. Earth Surface Dynamics, 8(2), 379–397. https://doi.org/10.5194/esurf-8-379-2020 Chen, A., Darbon, J., & Morel, J.-M. (2014). Landscape evolution models: A review of their fundamental equations. Geomorphology, 219, 68–86. https://doi.org/10.1016/j.geomorph.2014.04.037

Howard, A. D. (1994). A detachment-limited model of drainage basin evolution. Water Resources Research, 30(7), 2261–2285. https://doi.org/10.1029/94WR00757

Jefferson, A., Grant, G. E., Lewis, S. L., & Lancaster, S. T. (2010). Coevolution of hydrology and topography on a basalt landscape in the Oregon Cascade Range, USA. Earth Surface Processes and Landforms, 35(7), 803–816. https://doi.org/10.1002/esp.1976

Litwin, D., Tucker, G., Barnhart, K., & Harman, C. (2020). GroundwaterDupuitPercolator: A Landlab component for groundwater flow. Journal of Open Source Software, 5(46), 1935. https://doi.org/10.21105/joss.01935

Luo, W., Jasiewicz, J., Stepinski, T., Wang, J., Xu, C., & Cang, X. (2016). Spatial association between dissection density and environmental factors over the entire conterminous United States. Geophysical Research Letters, 43(2), 692–700. https://doi.org/10.1002/2015GL066941

Valters, D. (2016). Modelling Geomorphic Systems: Landscape Evolution (p. 6.5.12). https://doi.org/10.13140/RG.2.1.1970.9047

Yoshida, T., & Troch, P. A. (2016). Coevolution of volcanic catchments in Japan. Hydrology and Earth System Sciences, 20(3), 1133–1150. https://doi.org/10.5194/hess-20-1133-2016

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