DrGarethRoberts

The following describes some of my work on geomorphic, lithospheric, mantle convection, geochemical and palaeobiological problems. It also contains a brief overview of some of the geophysical, computational, geochemical and seismological techniques that I have developed and applied with my students and colleagues to address these problems.

If you have trouble accessing my papers please email me. 

Link to my code: https://github.com/garethgroberts.

New methods to constrain origins of topography

The centrepiece of my work on geomorphological problems has been the development of new inverse, integral and spectral methodologies to extract information about the processes that develop continental drainage patterns. Probably the most 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: 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).

Erosional models and uplift histories 

It has also 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 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 (Roberts, 2021). 

Figure: (a) Australian cumulative uplift history calculated by inverting continental drainage patterns. (b) Model coverage (resolution; see Rudge et al., 2015, for full details). 

'Source to Sink' and landscape sensitivities

This work has been used to generate testable frameworks for understanding continental uplift and landscape evolution that match a broad suite of independent uplift constrains. It makes a suite of testable predictions about, for example, denudation histories and sedimentary flux estimates and provides a basis for tackling 'source to sink' problems in a quantitative, mass conservative, way. In this work we have tackled a number of issues related to how drainage patterns and landscapes are affected by precipitation, lithology/substrate, sea level, and planform changes (e.g. Czarnota et al., 2014; Paul et al., 2014; Wilson et al., 2014; Lodhia et al., 2019). 

Figure: (a) Relief of ancient landscape buried > 1 km beneath the seabed of the North Sea mapped using 3D seismic reflection and well data. (b) Drainage patterns extracted from the landscape (see Stucky de Quay et al., 2017, for full details).

Fieldwork and new observations

In general we lack observations that can calibrate or test model of erosion or landscape evolution. To this end, my students, colleagues and I continue to do field work and process samples to constrain rates of landscape evolution at continental scales (e.g. Stucky de Quay et al., 2019; Lipp et al., 2020). 

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). 

Chemical composition of eroding landscapes

Recently we have been exploring how the chemistry of drainage networks and source regions might be constrained by combining observations with forward and inverse modelling of bed sediments in drainage basins (e.g. Lipp et al., 2020, 2021).

Figure: (a) Circles = measurements of magnesium concentration in Scottish rivers. Coloured curves = predicted concentration calculated by forward modelling using independent observations of source region geochemistry and mixing calculated using Scotland's drainage patterns. (b & c) Comparison of observed (circles in panel a) and predicted (curves in panel a) chemistry. See Lipp et al. (2020) for more details. Figure courtesy Alex Lipp. 

At small scales the erosional process is often extremely complicated and there exists an apparent disagreement between our assertion that long wavelength uplift dictates most of the shapes of fluvial landscapes and many geomorphological studies that highlight the importance of erosional complexity at shorter wavelengths.

For example, our work measuring the evolution of 'Europe's most powerful waterfall', Dettifoss in Iceland, shows that erosion, at scales of kilometres and tens of thousands of years, can be controlled by the strength of the substrate and maximum annual discharge.

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). 

In an attempt to unify these different views on landscape evolution we have developed wavelet spectral techniques to map the distribution of signal power from drainage patterns across the scales of interest. This work shows that nearly all of the  power (>90%) of large rivers (e.g. Niger, Orange) resides at wavelengths > 100 km, where their longitudinal profiles have self-similar scaling best characterised as red noise. At shorter wavelengths there is a transition to spectra best described as pink and perhaps blue noise. These observations indicate that river shapes and the evolution of rivers can be thought of as systems that have simple large signals that emerge through local complexity.

Figure: Wavelet spectral analyses of the longitudinal profile of the Niger river (grey curve in panel a). Labelled arrows = man-made dams. Red solid/dashed curves = inverse wavelet transforms for low pass filters in which wavelengths < 100 or 1000 km have been removed. (b) Wavelet power spectrum of Niger river. Solid/dashed black lines show 100 and 1000 km wavelengths (see Roberts et al., 2019; Roberts 2019; Wapenhans et al., 2021; for more details). 

I have been exploring how simplicity could emerge despite local complexity using simple threshold-based models of erosion (see Roberts, 2021, for more details). 

In this way we can unify  process based models of landscape evolution that emphasis local complexity and phenomenological approaches (e.g. drainage inversion) at larger scales. 

A focus of my work has been developing observations and simple models to constrain histories of vertical lithospheric motions with a view to better understanding, for example, mantle convection. In many places plate tectonics (e.g. horizontal motion of plates and their subsequent extension and shortening) provides an excellent framework for understanding lithospheric vertical motions. However, it is now clear that significant, O(1 km), vertical motions can be generated by sub-plate processes (e.g. thermal expansion of the mantle).  Most of my work on developing methods that make use of drainage patterns to understand regional uplift has been focussed on filling in the gaps between reliable spot measurements (e.g. uplifted biostratigraphically dated marine terraces, see e.g. Fernandes & Roberts, 2020) to address these problems. 

Figure: Circles = Cretaceous to Recent uplift marine rock from the Paleobiology Database (see Fernandes & Roberts, 2021, for details).  

To better understand the role sub-plate processes play in modifying the evolution of passive margins we have been interrogating the stratigraphic archive using seismic reflection, well and seismic tomographic information with industry colleagues. This work has shown that continental margins can be uplifted or drawdown (subside) by hundreds of meters in a few million years on wavelengths of hundreds to thousands of kilometres (see e.g. Lodhia et al., 2018; Morris et al., 2020). This work indicates that drawdown by mantle convection is responsible for generating accommodation space for sedimentary deposition and for the subsequent generation of hydrocarbons.

Figure: Mantle convection beneath West Africa's passive margin from shear wave tomography, deep seismic reflection data and backstripped wells (see Lodhia et al., 2018, for full details).

Recently we have been working to understand the history of life on Earth. To map commonalities between palaeobiological time series (e.g. Phanerozoic marine genera) and environmental time series (e.g. stable isotopes as proxies for climate change)  we have been developing cross wavelet spectral techniques and applying them to  large inventories of palaeobiological data. This work is in its early stage but shows that we can reliably identify parts of these time series that have similar and large signals throughout time and as a function of frequency. They have helped us to address questions about the apparent existence of periodicities in palaeobiological time series and to map hysteresis (as phase differences) between biological and environmental time series. 

Figure: Comparison of the time-frequency content of SQS diversity, number of marine sedimentary packages and sea level time series. (a) Blue = sea level time series; black = SQS diversity. Gray labeled bands = mass extinction events. (b) Cross wavelet power spectrum of sea level and SQS diversity. (c) Blue = sea level; black = sedimentary packages. (d) Coloured contours = cross wavelet power spectrum for sea level and packages. Black contours = cross wavelet power spectrum from sea level and diversity (panel b): solid line = 0.1, dashed line = 1, dotted line = 10 (see Roberts & Mannion, 2019, for full details).

I am interested in most topics across the Earth sciences. A theme of my work has been to incorporate broad suites of observations to understand evolution of Earth's surface. These include geophysical/geodetic data (e.g. gravity, GPS), seismological information (e.g. reflection seismic, shear wave tomography), and geochemical (e.g. major element chemistry of basalts, organic geochemistry), stratigraphic and palaeobiological observations (e.g. for palaeowater depths, palaeobiological time series).

Mantle melting: To address questions about the modern and ancient state of the mantle I have worked with seismology colleagues to convert shear wave tomographic models to maps of the thermal structure of the upper mantle. This work has been augmented by work with geochemist colleagues and our work using forward and inverse modelling of major element chemistry of mafic extrusive rock to calculate pressures and temperatures at which mantle melting occurs.

Figure: Dynamic support and mantle melting of Borneo. (a) Long wavelength free air gravity data. (b) Uplift as a result of asthenospheric thermal expansion. (c) Topography. (d) Plate thickness from shear wave to temperature conversions and upper mantle shear wave velocities. Inset shows location of the dog-leg transect.  (e) Shear wave to temperature conversion. (f) Geotherms from shear wave model and pressure and temperature of melting and melt paths of young mafic rocks (see Roberts et al., 2018, for full details). 

Palaeoenvironments: We have worked with organic geochemist colleagues to determine to origin of organic material in buried terrestrial landscapes mapped using three dimensional seismic data.

Provenance and geochemical fluxes: I have worked to map and predict provenance and geochemical fluxes from evolving landscapes.

Basin analysis and industry: We work with industry on a range of problems from basin analysis (e.g. backstripping, subsidence, heat flow) to geomorphology (e.g. 'source to sink' predictions).

Faulting and geomorphology: We also work to understand the record of tectonic processes (e.g. extensional faulting) and associated hazards at long timescales (millions of years) preserved in the shape of landscapes and stratigraphy. 

Google Scholar

Basin Analysis and Mantle Convection

• Morris, M., V. Fernandes, G. G. Roberts, 2019. Extricating dynamic topography from subsidence patterns: Examples from Eastern North America's passive margin, Earth and Planetary Science Letters, doi:10.1016/j.epsl.2019.115840.
• Roberts G. G., N. White, M. Hoggard & C. Meenan, 2018. A Neogene History of Convective Support Beneath Borneo. Earth and Planetary Science Letters, 496, 142–158.
• Lodhia, B. H., G. G. Roberts, A. Fraser, S. Fishwick, S. Goes, J. Jarvis, 2018. Continental margin subsidence from shallow mantle convection: Example from West Africa. Earth and Planetary Science Letters, doi:10.1016/j.epsl.2017.10.024.
• Stucky de Quay, G., G. G. Roberts, J. Watson & C. Jackson, 2017. Incipient mantle plume evolution: Constraints from ancient landscapes buried beneath the North Sea. G-Cubed, doi:10.1002/2016GC006769.
• Hartley, R., G. G. Roberts, & N. J. White, 2011. Transient convective uplift of an ancient buried landscape. Nature Geoscience, 4, doi:10.1038/ngeo1191. Related commentary by Philip Allen in same issue.

Fundamentals of Landscape Evolution

• Roberts, G. G., 2021. Emergence of Simplicity Despite Local Complexity in Eroding Landscapes, Geology, doi:10/1130/G48942.1. 
• Wapenhans, I., Fernandes, V., O’Malley, C., White, N., Roberts, G. G., 2021. Scale-Dependent Contributors to River Profile Geometry, JGR: Earth Surface, doi:10/1029/2020JF005879.
• Lipp, A. G. & G. G. Roberts, 2021. Scale-dependent flow directions of rivers and the importance of sub-plate support, Geophysical Research Letters, doi:10.1029/2020GL091107.
• Roberts, G. G., 2019. Scales of Similarity and Disparity Between Drainage Networks, Geophysical Research Letters, doi:10.1029/2019GL082446.
• Roberts, G. G., N. J. White & Lodhia, B. H., 2019. Generation and Scaling of Longitudinal River Profiles. Journal of Geophysical Research, doi:10.1029/2018JF004796.
• Stucky de Quay, G., G. G. Roberts, D. Rood, V. Fernandes, 2019. Holocene uplift and rapid fluvial erosion of Iceland: A record of post-glacial landscape evolution, Earth and Planetary Science Letters, 505, 118–130. On EPSL’s most downloaded list.
• Rudge, J., G. G. Roberts, N. J. White & C. N. Richardson, 2015. Uplift Histories of Africa and Australia From Linearised Inversion of River Profiles. Journal of Geophysical Research, doi:10.1002/2014JF003297.
• Roberts, G. G. & N. J. White, 2010. Estimating uplift rate histories from river profiles using African examples. Journal of Geophysical Research, 115(B02406), doi:10.1029/2009JB006692.
• Pritchard, D., G. G. Roberts, N. J. White & C. N. Richardson, 2009. Uplift histories from river profiles. Geophysical Research Letters, 36(L24301), doi:10.1029/2009GL040928.

Tectonics From Topography and Inverse Modelling

• Quye-Sawyer, J., A. C. Whittaker, G. G. Roberts, D. Rood, 2021. Fault Throw and Regional Uplift Histories from Drainage Analysis: Evolution of Southern Italy, Tectonics, doi:10.1029/2020TC006076.
• Fernandes, V., G. G. Roberts, N. J. White, A. C. Whittaker, 2019. Continental Scale Landscape Evolution: A History of North American Topography, Journal of Geophysical Research, doi:10.1029/2018JF004979.
• Conway-Jones, B., G. G. Roberts, A. Fichtner, M. Hoggard, 2019. Neogene Epeirogeny of Iberia, G-Cubed, doi:10.1029/2018GC007899.
• Rodriguez-Tribaldos, V., N. White, G. G. Roberts & M. Hoggard, 2017. Spatial and Temporal Uplift History of South America from Drainage Analysis. G-Cubed, doi:10.1002/2017GC006909.
• Stephenson, S., G. G. Roberts , M. Hoggard & A. Whittaker, 2014. A Cenozoic Uplift History of Mexico and its Surroundings From Longitudinal River Profiles. G-Cubed , doi:10.1002/2014GC005425.
• Wilson, J., G. G. Roberts, M. Hoggard & N. J. White, 2014. Cenozoic Epeirogeny of Arabian Peninsula from Drainage Modeling. G-cubed, doi:10.1002/2014GC005283.
• Paul, J., G. G. Roberts & N. J. White, 2014. The African Landscape Through Space and Time. Tectonics, doi:10.1002/2013TC003479.
• Czarnota, K., G. G. Roberts, N. J. White & S. Fishwick, 2014. Cretaceous-Recent Dynamic Support of Australia. Journal of Geophysical Research, doi: 10.1002/2013JB010436.
• Roberts, G. G., N. J. White & B. Shaw, 2013. An uplift history of Crete, Greece, from inverse modeling of longitudinal river profiles. Geomorphology, doi:10.1016/j.geomorph.2013.05.026.
• Roberts, G. G., N. J. White, G. L. Martin-Brandis & A. G. Crosby, 2012b. An Uplift History of the Colorado Plateau and its Surroundings from Inverse Modeling of Longitudinal River Profiles. Tectonics, doi:10.1029/2012TC003107.
• Roberts, G. G., J. D. Paul, N. J. White & J. Winterbourne, 2012a. Temporal and Spatial Evolution of Dynamic Support From River Profiles: A Study of Madagascar. G-cubed, doi:10.1029/2012GC004040.

Geomorphology, geochemistry and sedimentary flux

• Lipp, A. G., G. G. Roberts, A. C. Whittaker, C. Gowing, V. Fernandes, 2020. Source region geochemistry from unmixing downstream sedimentary elemental compositions, G-Cubed, doi: 10.1029/2021GC009838.
• Lipp, A. G., G. G. Roberts, A. C. Whittaker, C. Gowing, V. Fernandes, 2020. River sediment geochemistry as a conservative mixture of source regions: Observations and predictions from the Cairngorms, UK, JGR: Earth Surface, doi: 10.1029/2020JF005700.
• Lipp, A. G., O. Shorttle, F. Syvret, G. G. Roberts, 2020. Major-element composition of fine grained sediments in terms of weathering and provenance: Implications for crustal recycling, G-Cubed, doi:10.1029/2019GC008758.
• Brewer, C., G. Hampson, A. C. Whittaker, G. G. Roberts, S. Watkins, 2020. Comparison of methods to estimate sediment flux in ancient sediment routing systems, Earth Sci. Reviews, doi:10.1016/j.earscirev.2020.103217.
• Lodhia, B. H., G. G. Roberts, A. Fraser, J. Jarvis, R. Newton, R. J. Cowan, 2019. Observation and Simulation of Solid Sedimentary Flux: Examples From Northwest Africa, G-Cubed, doi:10.1029/2019GC008262.

Palaeobiology

• Roberts G. G., P. Mannion, 2019. Timing and periodicity of Phanerozoic marine biodiversity and environmental change, Scientific Reports.

Postdocs

Fred Richards 

Conor O'Malley

Victoria Fernandes

PhD Students

2014-2018, Gaia Stucky de Quay, Uplift and erosion histories of ancient and modern landscapes: examples from the North Sea, Iceland, and Mars. Gaia won the Iain Hillier Academic Award from the London Petrophysical Society. PDRA at Chicago, UT Austin. 

2014-2019, Bhavik Lodhia, Dynamic Subsidence, Continental Uplift and Sedimentary Deposition to West Africa’s Passive Margin. Bhavik won a Best Student Paper Award at PESGB. PDRA at Imperial & UNSW.

2015-2019, Jen Quye-Sawyer, Evolution of sub-plate support and active tectonics, W. Mediterranean. Jen won the Bernie Smith award from British Society for Geomorphology.

2017-2021, Victoria Fernandes, Landscape evolution in four dimensions. Victoria  won an AGU Outstanding Student Presentation Award. PDRA at Imperial. 

2017-2021, Ikenna Okwara, Sedimentary mass balance in ancient sedimentary routing systems

2018-2022, Alex Lipp, Deep-time chemical fluxes from evolving landscapes. CASP CASE funding. Invited talk Goldschmidt 2021.

2020-2024, James Hazzard, Mantle convection and glaciation.

• Mantle Circulation Constrained, NERC Large Grant, NE/T012501/1, 2020-2024.
• Scaling Regimes of Landscapes and Biodiversity,  Leverhulme Trust Research Project Grant, RPG-2019-073, 2019-2023 
• How did the West Arabian Swell acquire its landscape?, NERC Argon Isotope Support, IP-1635-0516, 2017-2022. 
• Landscape evolution from incision histories of large rivers, Royal Society, RG160020, 2016-2018.
• Imperial College Research Fellowship, 2013-2016.