Landscape Evolution
Banner image shows African drainage patterns atop long wavelength gravity.
Origins of topography: New insights from theory and continental-scale observations
The centrepiece of my work with Nicky White, our students and colleagues on geomorphological problems has been the development of new inverse, integral and spectral methodologies to extract information about processes that develop continental drainage patterns. An important result from this work is a realisation that long wavelength processes (e.g. uplift generated by mantle convection) determine nearly all of the shapes of drainage networks (both planform and elevation; see e.g. Roberts & White, 2010; Rudge et al., 2015; Roberts et al., 2019; Fernandes et al., 2019; Roberts, 2019; Lipp & Roberts, 2021; Wapenhans et al., 2021).
Figure. Red curve in panel c (bottom) shows a synthetic river profile generated from the uplift history shown in the top (rate) and middle (cumulative) panels and a stream power erosional model. Black curves show theoretical river profiles and associated uplift histories generated by inverting the 'observed' theoretical river profile. Numbers = number of iterations of inverse model. See Roberts & White (2010) for details. Note increasing similarity of uplift used to generate the 'observed' river profile and results from the inversion after ~1500 iterations.
Work on the fundamentals of erosion and landscape form are given on this page.
Erosional models and uplift histories
Our work has shown that remarkably simple (advective) erosional models with broadly constant erosional parameter values (i.e. constant precipitation, no requirement for lithological contrasts) can generate drainage networks of sufficient complexity to match most observed drainage patterns at large scales, where most signal power (i.e. elevation of longitudinal river profiles) resides. It appears that erosional thresholds explain why fluvial erosion tends to simplicity at large scales. We have used these approaches to calculate histories of uplift for most continents and a few buried ancient landscapes extracted from reflection seismic data.
Figure: (a) Cumulative uplift history of Australia since 110 million years ago calculated by inverting continental drainage patterns. (b) Model coverage (resolution; red = high). See Rudge et al. (2015) for details.
Inverse and forward modeling for palaeoenvironment
Inverting entire landscapes for uplift histories remains a very expensive computational problem. We have been examining sensitivities of landscape evolution models forced with uplift histories estimated from inverse modelling of river profiles. An example for North America is shown here (see Fernandes et al., 2019 for details). A closed-loop modelling strategy for Africa is presented in O'Malley et al. (2021).
Figure: Landscape evolution model of North America. (a–d) Four panels show calculated Mesozoic to Cenozoic topographic evolution compared with coeval independent paleogeographic constraints. Red circles = magmatic record from NAVDAT database; blue circles = stratigraphic shoreline markers/marine fossils from PBDB; light blue shading = maximum flooded surface from Smith et al. (1994) revised with stratigraphic and biostratigraphic constraints presented here.
Erosional model sensitivities
We have developed a variety of means to test the sensitivity of calculated uplift histories and landscape evolution to environmental variables (e.g. precipitiation rate, planform changes, lithology), and to assess the likelihood of emergent signals (e.g. coherent river profile shapes and planforms) in the presence of a complex substrate and climate.
Figure: Testing the role precipitation rate changes play in generating longitudinal river profiles. (a) Blue line = constant precipitation rate. Solid and dashed black lines = 50 Ma wet-dry-wet and dry-wet-dry cycles, respectively. (b) Zoom of gray box in panel a showing 0.1 Ma precipitation rate variation. (c–d) Calculated rock uplift rate and cumulative rock uplift histories for Rio Grande de Santiago, Mexico; gray band = results for constant precipitation rate. Colored lines correspond to precipitation rates in panels a and b. (e) Gray line = observed river profile; colored lines = best- fitting theoretical river profiles for different precipitation rates. Note good fit for all tests. (f–h) Tributary of Rio Grande de Santiago. (i–k) Rio Panuco. (l–n) Rio Fuerte (see Stephenson et al., 2014, for more details).
Origins of drainage planform and elevation
Determining the origins of river planforms and their variability through space and time continues to be hotly debated. We have developed forward modeling and spectral strategies to estimate the likelihood of drainage networks in response to external forcing (e.g. Lipp & Roberts, 2021). We have shown, with our colleagues and students, that sub-plate support likely plays a fundamental role in determining drainage planforms at continental scales (e.g. Paul et al., 2014).
Figure: African drainage patterns extracted from SRTM DEM atop map of calculated dynamic support of topography. Note radial drainage patterns atop many of Africa's domal swells (red blobs). Thick black lines labelled N = Niger, C = Congo, O = Orange, Z = Zambezi rivers (see Roberts et al., 2019, for full details).
Erosion rates
In general we lack observations that can calibrate or test models of erosion or landscape evolution. To this end, my students, colleagues and I do fieldwork and process samples to constrain erosion rates. An example of estimating retreat rates for Europe's 'most powerfall' waterfall, Dettifoss (Iceland), and its neighbours, from cosmogenic exposure dating of terraces downstream, are shown here.
Figure: Waterfalls from the Jökulsárgljúfur canyon, northeastern Iceland (see Stucky de Quay et al., 2019, for more details).
Figure: Retreat rates of Icelandic waterfalls from cosmogenic (exposure) dating of fluvial terraces (see Stucky de Quay et al., 2019, for more details).
'Source to Sink' and landscape sensitivities
We have used our forward and inverse models to predict continental uplift histories and landscape evolution, which match a broad suite of independent geological observations. These models make a suite of testable predictions about, for example, denudation and sedimentary flux histories. Sensitivities of predictions to, for example, changes in precipitation, lithology/substrate, sea level and planform can be quantified (e.g. Czarnota et al., 2014; Paul et al., 2014; Wilson et al., 2014). This work provides a basis for tackling 'source to sink' problems in a quantitative, mass conservative, way (e.g. Lodhia et al., 2019; Fernandes et al., 2019; O'Malley et al., 2021).
Figure: (a) Relief of ancient (~55 million year old) landscape (in two way time) now buried > 0.4 km beneath the seabed of the North Sea. The ancient landscape was mapped using 3D seismic reflection data. Red/blue arrows = fluvial channels/deltaic deposits; dashed curve = coastline (see Stucky de Quay et al., 2022, for full details).
Chemical composition of landscapes and material fluxes
Recently we have been exploring how the chemistry of drainage networks and source regions can be constrained by combining new and existing observations with forward and inverse modelling of bed sediments and water in drainage basins (e.g. Lipp et al., 2020, 2021). It is essentially a means for prediciting provenance and river composition, which we are exploring as a tool for environmental monitoring and pollutant tracking. We have recently completed the NERC funded project 'tracking pollutants as continua in the Thames basin' NE/X010805/1.
Figure: Predicting provenance: Composition of sediments in rivers and upstream sources from forward and inverse modeling. (a) Schematic showing composition of source regions (X, Y, Z), drainage network (white lines), and composition of sampled river sediments (white circles). In this simple scheme, composition of sediment in rivers (e.g., colored pie charts) is determined by the composition of upstream source regions. (b) Schematic shows the forward, “mixing,” problem when the source region geochemistry is known and the downstream composition at sample sites is predicted (see Lipp et al., 2020). (c) The inverse, “unmixing,” problem attempts to reconstruct the composition of source regions from the point observations of downstream sediment composition.