Imperial College London

DrGarethRoberts

Faculty of EngineeringDepartment of Earth Science & Engineering

Senior Lecturer
 
 
 
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Contact

 

+44 (0)20 7594 7363gareth.roberts

 
 
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Location

 

2.50Royal School of MinesSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

35 results found

Roberts G, 2021, Emergence of simplicity despite local complexity in eroding landscapes, Geology (Boulder), ISSN: 0091-7613

Much understanding of continental topographic evolution is rooted in measuring and predicting rates at which rivers erode. Flume tank and field observations indicate that stochasticity and local conditions play important roles in determining rates at small scales (e.g. < 10 km, thousands of years). Obversely, preserved river profiles and common shapes of rivers atop uplifting topography indicate that erosion rates are predictable at larger scales. These observations indicate that the response of rivers to forcing can be scale dependent. Here I demonstrate that erosional thresholds can provide an explanation for why profile evolution can be very complicated and unique at small scales yet simple and predictable at large scales.

Journal article

Wapenhans I, Fernandes VM, O'Malley C, White N, Roberts GGet al., 2021, Scale‐dependent contributors to river profile geometry, Journal of Geophysical Research: Earth Surface, Vol: 126, ISSN: 2169-9003

A range of complex hydraulic and geomorphic processes shape terrestrial landscapes. It remains unclear how these processes act to generate observed drainage networks across scales of interest. To address this issue, we transform observed and synthetic longitudinal river profiles into the spectral domain with a view to interrogating the different scales at which fluvial landscapes are generated. North American river profiles are characterized by red noise (i.e. spectral power, ϕ ∝ k−2, where k is wavenumber) at wavelengths > 100 km and pink noise (ϕ ∝ k−1) at shorter wavelengths. This observation suggests that river profile geometries are scale-dependent and using small-scale observations to develop a general understanding of large-scale landscape evolution is not straightforward. At wavelengths > 100 km, river profile geometries appear to be controlled by smoothly varying patterns of regional uplift and slope-dependent incision. Landscape simulations, based upon stream power, that are externally forced by regional uplift do not exhibit a spectral transition from red to pink noise because these simulations do not incorporate heterogeneous erodibility. Spectral analysis of erodibility extracted from patterns of lithologic variation along river profiles suggests that the missing spectral transition is accounted for by heterogeneous substrates which are characterized by white or blue noise (ϕ ∝ k0 or k1). Our results have implications for the way by which rivers record large-scale tectonic forcing whilst incising through complex lithologic patterns. [226/250 words]

Journal article

QuyeSawyer J, Whittaker AC, Roberts GG, Rood DHet al., 2021, Fault throw and regional uplift histories from drainage analysis: evolution of southern Italy, Tectonics, Vol: 40, Pages: 1-26, ISSN: 0278-7407

Landscapes can record elevation changes caused by multiple tectonic processes. Here, we show how coeval histories of spatially coincident normal faulting and regional uplift can be deconvolved from river networks. We focus on Calabria, a tectonically active region incised by rivers containing knickpoints and knickzones. Marine fauna indicate that Calabria has been uplifted by >1 km since ∼0.8–1.2 Ma, which we used to calibrate parameters in a stream power erosional model. To deconvolve the local and regional uplift contributions to topography, we performed a spatiotemporal inversion of 994 fluvial longitudinal profiles. Uplift rates from fluvial inversion replicate the spatial trend of rates derived from dated Mid-Late Pleistocene marine terraces, and the magnitude of predicted uplift rates matches the majority of marine terrace uplift rates. We used the predicted uplift history to analyze long-term fault throw, and combined throw estimates with ratios of footwall uplift to hanging wall subsidence to isolate the nonfault related contribution to uplift. Increases in fault throw rate—which may suggest fault linkage and growth—have been identified on two major faults from fluvial inverse modeling, and total fault throw is consistent with independent estimates. The temporal evolution of nonfault related regional uplift is similar at three locations. Our results may be consistent with toroidal mantle flow generating uplift, perhaps if faulting reduces the strength of the overriding plate. In conclusion, fluvial inverse modeling can be an effective technique to quantify fault array evolution and can deconvolve different sources of uplift that are superimposed in space and time.

Journal article

Lipp AG, Roberts GG, 2021, Scale‐dependent flow directions of rivers and the importance of subplate support, Geophysical Research Letters, Vol: 48, Pages: 1-12, ISSN: 0094-8276

Large rivers play crucial roles in determining locations of civilization, biodiversity, and efflux to the oceans. The paths they take across Earth's surface vary with scale. At long‐wavelengths rivers can have simple flow paths. At smaller scales, in meanders for example, their paths change rapidly as a consequence of lithology, biota, and other environmental variables. It is not straightforward to identify the scales at which river planforms are set. We overcome these issues by developing a spectral (wavelet) methodology to map flow‐directions as a function of distance and scale. This methodology allows short‐wavelength features (e.g., meanders) to be filtered from river flow‐paths. With short‐wavelength structure removed, the flow‐directions of rivers in Western USA correlate with long‐wavelength gravity anomalies suggesting control by subplate support. This relationship is replicated by an ensemble of landscape evolution models. These results combined suggest that drainage at large scales, O(103) km, is set by subplate support.

Journal article

Quye-Sawyer J, Whittaker AC, Roberts GG, 2020, Calibrating fluvial erosion laws and quantifying river response to faulting in Sardinia, Italy, Geomorphology, Vol: 370, Pages: 1-14, ISSN: 0169-555X

It is now widely accepted that rivers modify their erosion rates in response to variable rock uplift rates, resulting in changes in channel slope that propagate upstream through time. Therefore, present-day river morphology may contain a record of tectonic history. The simple stream power incision model can, in principle, be used to quantify past uplift rates over a variety of spatial and temporal scales. Nonetheless, the erosional model's exponents of area and slope (m and n respectively) and ‘bedrock erodibility’ (k) remain poorly constrained. In this paper, we will use a geologically and geomorphically well constrained Plio-Pleistocene volcanic landscape in central Sardinia, Italy, to calibrate the stream power erosion equation and to investigate the slip rate of faults that have been seismically quiescent in the historic past. By analysing digital elevation models, geological maps and Landsat imagery, we have identified the geomorphic expression of several volcanic features (eruption centres and basaltic lava flows) and three normal faults with 6 to 8 km fault traces within the outcrop. Downstream, river longitudinal profiles show a similar transient response to relative base level fall, probably as a result of relief inversion at the edge of the volcanic outcrop. From measurements of incision, local slope and upstream catchment area across eight different rivers, we calculate n ≈ 1, m = 0.50 ± 0.02 and, using a landscape age from literature of 2.7 Ma, bedrock erodibility k = 0.10 ± 0.04 m(1−2m) Myr−1. There are also knickpoints on rivers upstream of two normal faults, and we used numerical inverse modelling of the longitudinal profiles to predict the slip rate of these faults since 2.7 Ma. The results from the inverse model show that the erosional parameter values derived in this study can produce theoretical longitudinal profiles that closely resemble observed river profiles upstream of the faults. The lowest misfit

Journal article

Lipp AG, Roberts GG, Whittaker AC, Gowing CJB, Fernandes VMet al., 2020, River sediment geochemistry as a conservative mixture of source regions: observations and predictions from the Cairngorms,, UK, Journal of Geophysical Research: Earth Surface, Vol: 125, ISSN: 2169-9011

The elemental composition of sediments in rivers is the product of physical and chemical erosion of rocks, which is then transported across drainage networks. A corollary is that fluvial sedimentary geochemistry can be used to understand geologic, climatic, and geomorphic processes. Here, we predict elemental compositions of river sediments using drainage networks extracted from digital elevation data and erosional models. The Geochemical Baseline Survey of the Environment was used to quantify substrate (i.e., source region) chemistry. Sedimentary compositions in rivers downstream are predicted by formally integrating eroding substrates with respect to distance downstream. Different erosional models, including the Stream Power model and uniform incision rates, are tested. Predictions are tested using a new suite of compositions obtained from fine grained (<150 μm) sediments at 67 sites along the Spey, Dee, Don, Deveron, and Tay rivers, Cairngorms, UK. Results show that sedimentary geochemistry can be predicted using simple models that include the topography of drainage networks and substrate compositions as input. The concentration of numerous elements including Magnesium, Rubidium, Uranium, Potassium, Calcium, Strontium, and Beryllium can be accurately predicted using this simple approach. Predictions are insensitive to the choice of erosional model, which we suggest is a consequence of broadly homogeneous rates of erosion throughout the study area. Principal component analysis of the river geochemical data suggests that the composition of most Cairngorms river sediments can be explained by mafic/felsic provenance and conservative mixing downstream. These results suggest that the elemental composition of river sediments can be accurately predicted using simple erosional models and digital elevation data.

Journal article

Fernandes VM, Roberts GG, 2020, Cretaceous to Recent net continental uplift from paleobiological data: Insights into sub-plate support, GSA Bulletin, Vol: 133, Pages: 1217-1236, ISSN: 0016-7606

There are many geoscience problems for which constraining histories of uplift or subsidence of Earth’s surface is of direct or indirect importance, for example reconstructing tectonics, mantle convection, geomorphology, sedimentary and chemical flux, biodiversity, glacio-eustasy, and climate change. The least equivocal constraints on timing and amplitude of vertical motions on geological timescales come from the distribution of rock formed in shallow marine environments. However, obtaining enough observations at sufficiently large spatial and temporal scales (∼100−10,000 km, ca. 1−100 Ma) to constrain histories of regional topographic evolution remains challenging. To address this issue, we adapted modern inventories of paleobiological and paleoenvironmental data to generate a new compilation of >24,000 spot measurements of uplift on all continents and numerous oceanic islands. Uncertainties associated with paleobathymetry, post-deposition compaction, and glacio-eustasy are assessed. The compilation provides self-consistent and, in places, high-resolution (<100-km-length scale, <1 Ma) measurements of Cretaceous to Recent (post-deposition) net uplift across significant tracts of most continents. To illustrate how the database can be used, records from western North America and eastern South America are combined with geophysical observations (e.g., free-air gravity, shear, and Pn-wave tomography) and simple isostatic calculations to determine the origins of topography. We explore how lithospheric thinning and mantle thermal anomalies may generate uplift of the observed wavelengths and amplitudes. The results emphasize the importance of large inventories of paleobiological data for understanding histories of tectonic and mantle convective processes and consequently landscapes, climate, and the environment.

Journal article

Brewer C, Hampson G, Whittaker A, Roberts G, Watkins Set al., 2020, Comparison of methods to estimate sediment flux in ancient sediment routing systems, Earth-Science Reviews, Vol: 207, ISSN: 0012-8252

The need to predict accurately the volume, timing and location of sediments that are transported from an erosional source region into a basin-depocentre sink is important for many aspects of pure and applied sedimentological research. In this study, the results of three widely used methods to estimate sediment flux in ancient sediment routing systems are compared, using rich input datasets from two systems (Eocene South Pyrenean Foreland Basin, Spain and late-Pleistocene-to-Holocene Gulf of Corinth Rift Basin, Greece) for which mapped, dated sediment volumes provide an independent reference value of sediment accumulation rates. The three methods are: (1) the empirical BQART model, which uses values of drainage basin area, relief, temperature, lithology and water discharge; (2) empirical scaling relationships between characteristic geomorphological parameters of sediment-routing-system segments; and (3) the “fulcrum” model, which uses the palaeohydrological parameters of trunk river channels to estimate downsystem sediment discharge. The BQART model and empirical geomorphological scaling relationships were originally developed using modern sediment routing systems, and have subsequently been applied to ancient systems. In contrast, the “fulcrum” model uses hydrological scaling relationships from modern systems, but was developed principally for application in ancient systems.Our comparative analysis quantifies the sensitivity of the three methods to their input parameters, and identifies the data required to make plausible estimates of sediment flux for ancient sediment routing systems. All three methods can generate estimates of sediment flux that are comparable with each other, and are accurate to at least one order of magnitude relative to independent reference values. The BQART model uses palaeoclimatic and palaeocatchment input data, which are accurate for sub-modern systems but may be highly uncertain in deep-time systems. Corresponding

Journal article

Lipp A, Shorttle O, Syvret F, Roberts Get al., 2020, Major-element composition of sediments in terms of weathering and provenance: Implications for crustal recycling, G3: Geochemistry, Geophysics, Geosystems: an electronic journal of the earth sciences, Vol: 21, ISSN: 1525-2027

The elemental composition of a sediment is set by the composition of its protolith and modified by weathering, sorting, and diagenesis. An important problem is deconvolving these contributions to a sediment's composition to arrive at information about processes that operate on the Earth's surface. We approach this problem by developing a predictive and invertible model of sedimentary major element composition. We compile a data set of sedimentary rock, river sediment, soil, and igneous rock compositions. Principal component analysis of the data set shows that most variation can be simplified to a small number of variables. We thus show that any sediment's composition can be described with just two vectors of igneous evolution and weathering. We hence define a model for sedimentary composition as a combination of these processes. A 1:1 correspondence is observed between predictions and independent data. The log ratios urn:x-wiley:ggge:media:ggge22195:ggge22195-math-0001 and urn:x-wiley:ggge:media:ggge22195:ggge22195-math-0002 are found to be simple proxies for, respectively, the model's protolith and weathering indices. Significant deviations from the model can be explained by sodium‐calcium exchange. Using this approach, we show that the major element composition of the upper continental crust has been modified by weathering, and we calculate the amount of each element that it must have lost to modify it to its present composition. By extrapolating modern weathering rates over the age of the crust, we conclude that it has not retained a significant amount of the necessarily produced weathering restite. This restite has likely been subducted into the mantle, indicating a crust‐to‐mantle recycling rate of 1.33 ± 0.89 ×1013 kg·year−1.

Journal article

Morris M, Fernandes VM, Roberts GG, 2020, Extricating dynamic topography from subsidence patterns: Examples from Eastern North America's passive margin, Earth and Planetary Science Letters, Vol: 530, Pages: 1-13, ISSN: 0012-821X

Global sea-level (eustatic) histories generated by backstripping stratigraphy are predicated upon the lithosphere having a well understood tectonic history. However, sub-plate processes play a role in governing lithospheric vertical motions with timescales and amplitudes akin to eustasy, which are difficult to predict. We examine how stratigraphic and geophysical observations combined with simple isostatic models can be used to disentangle histories of sub-plate support and eustasy. We focus on the passive margin of Eastern North America, where a generally accepted history of eustasy has been estimated. Negative long wavelength free-air gravity anomalies, residual ocean-age depth estimates, fast upper mantle shear wave velocities, and geodynamic models suggest that Cenozoic evolution of this passive margin has been influenced by upper mantle drawdown. We build on existing analyses to backstrip sixteen wells, which, combined with seismic data, constrain timing and extent of Cenozoic subsidence. Results indicate up to ∼1000 m of water-loaded subsidence between ∼20–0 Ma centered on the Baltimore Canyon Trough. Seismic data from the trough shows Neogene aggrading clinoforms. There is little evidence for faulting or stratigraphic growth, which indicates that Neogene lithospheric strain rates were low. Amplitude and spatial extent of Neogene subsidence are difficult to explain by glacio-eustasy or glacio-isostatic adjustment. Instead, sub-plate support calculated from conversion of shear wave velocities to temperature and isostatic calculations indicate that upper mantle drawdown was responsible for subsidence of the margin. Because mantle convection is vigorous such observations are expected throughout the stratigraphic archive.

Journal article

Lodhia B, Roberts G, Fraser A, Jarvis J, Cowan R, Newton Ret al., 2019, Observation and simulation of solid sedimentary flux: examples from northwest Africa, G3: Geochemistry, Geophysics, Geosystems: an electronic journal of the earth sciences, Vol: 20, Pages: 4613-4634, ISSN: 1525-2027

The sedimentary archive preserved at passive margins provides important clues about the evolution of continental topography. For example, histories of African uplift, erosion, and deposition of clastic sedimentary rock provide information about mantle convection. Furthermore, relating histories of uplift and erosion from regions where sediment is generated to measurements of efflux is important for understanding basin evolution and the distribution of natural resources. We focus on constraining Mesozoic to Recent solid sedimentary flux to northwest Africa's passive margin, which today is fed by rivers draining dynamically supported topography. Histories of sedimentary flux are calculated by mapping stratigraphy using seismic reflection and well data courtesy of Tullow Oil Plc and TGS. Stratigraphic ages, conversion from two‐way time to depth and compaction, are parameterized using biostratigraphic and check‐shot records from exploration, International Ocean Discovery Program and Deep Sea Drilling Project wells. Results indicate that Late Cretaceous to Oligocene (∼100–23 Ma) sedimentary flux decreased gradually. A slight increase in Neogene sedimentary flux is observed, which is concomitant with a change from carbonate to clastic sedimentation. Pliocene to Recent (∼5–0 Ma) flux increased by an order of magnitude. This history of sedimentary flux and facies change is similar to histories observed at other African deltas. To constrain sources of sedimentary flux, 14,700 longitudinal river profiles were inverted to calculate a history of continental uplift. These results were used to parameterize a simple “source‐to‐sink” model of fluvial erosion and sedimentary efflux. Results suggest that increased clastic flux to Africa's deltas from ∼30 Ma was driven by denudation induced by dynamic support.

Journal article

Fernandes VM, Roberts GG, White N, Whittaker ACet al., 2019, Continental-scale landscape evolution: a history of North American topography, Journal of Geophysical Research: Earth Surface, Vol: 124, Pages: 2689-2722, ISSN: 2169-9011

The generation and evolution of continental topography are fundamental geologic and geomorphic concerns. In particular, the history of landscape development might contain useful information about the spatiotemporal evolution of deep Earth processes, such as mantle convection. A significant challenge is to generate observations and theoretical predictions of sufficient fidelity to enable landscape evolution to be constrained at scales of interest. Here, we combine substantial inventories of stratigraphic and geomorphic observations with inverse and forward modeling approaches to determine how the North American landscape evolved. First, stratigraphic markers are used to estimate postdepositional regional uplift. Present‐day elevations of these deposits demonstrate that >2 km of long‐wavelength surface uplift centered on the Colorado‐Rocky‐Mountain plateaus occurred in Cenozoic times. Second, to bridge the gaps between these measurements, an inverse modeling scheme is used to calculate the smoothest spatiotemporal pattern of rock uplift rate that yields the smallest misfit between 4,161 observed and calculated longitudinal river profiles. Our results suggest that Cenozoic regional uplift occurred in a series of stages, in agreement with independent stratigraphic observations. Finally, a landscape evolution model driven by this calculated rock uplift history is used to determine drainage patterns, denudation, and sedimentary flux from Late Cretaceous times until the present day. These patterns are broadly consistent with stratigraphic and thermochronologic observations. We conclude that a calibrated inverse modeling strategy can be used to reliably extract the temporal and spatial evolution of the North American landscape at geodynamically useful scales.

Journal article

Roberts G, Mannion P, 2019, Timing and periodicity of Phanerozoic marine biodiversity and environmental change, Scientific Reports, Vol: 9, ISSN: 2045-2322

We examine how the history of Phanerozoic marine biodiversity relates to environmental change. Our focus is on North America, which has a relatively densely sampled history. By transforming time series into the time-frequency domain using wavelets, histories of biodiversity are shown to be similar to sea level, temperature and oceanic chemistry at multiple timescales. Fluctuations in sea level play an important role in driving Phanerozoic biodiversity at timescales >50 Myr, and during finite intervals at shorter periods. Subsampled and transformed marine genera time series reinforce the idea that Permian-Triassic, Triassic-Jurassic, and Cretaceous-Paleogene mass extinctions were geologically rapid, whereas the Ordovician-Silurian and Late Devonian ‘events’ were longer lived. High cross wavelet power indicates that biodiversity is most similar to environmental variables (sea level, plate fragmentation, δ18O, δ13C, δ34S and 87Sr/86Sr) at periods >200 Myr, when they are broadly in phase (i.e. no time lag). They are also similar at shorter periods for finite durations of time (e.g. during some mass extinctions). These results suggest that long timescale processes (e.g. plate kinematics) are the primary drivers of biodiversity, whilst processes with significant variability at shorter periods (e.g. glacio-eustasy, continental uplift and erosion, volcanism, asteroid impact) play a moderating role. Wavelet transforms are a useful approach for isolating information about times and frequencies of biological activity and commonalities with environmental variables.

Journal article

Roberts G, 2019, Scales of similarity and disparity between drainage networks, Geophysical Research Letters, Vol: 46, Pages: 3781-3790, ISSN: 0094-8276

At large scales ( urn:x-wiley:grl:media:grl58789:grl58789-math-000110 km, urn:x-wiley:grl:media:grl58789:grl58789-math-00021 Ma) drainage networks appear to have a synchronized response to uplift and erosional processes. At smaller scales erosion generates complex landforms. Here, cross wavelet spectral transformation of longitudinal river profiles is performed to develop a framework that unifies these scale‐dependent views of landscape evolution. Distance‐elevation and time‐elevation profiles are transformed using a continuous wavelet approach to determine where signal power resides and appropriate scaling regimes. Cross wavelet spectral power is then calculated to determine scales of similarity and disparity between river channels. Spectral power of rivers draining Angola are compared to lithology, biota, precipitation, and gravity data to examine origins of river shapes and commonalities. Most power and commonalities reside at long wavelengths and timescales (>100 km, >1 Ma). The presence of commonalities between drainage networks is expected for systems in which large signals (e.g., uplift) are forced through random media (e.g., lithology, biota).

Journal article

Conway-Jones BW, Roberts GG, Fichtner A, Hoggard Met al., 2019, Neogene epeirogeny of Iberia, Geochemistry, Geophysics, Geosystems, Vol: 20, Pages: 1138-1163, ISSN: 1525-2027

The origin of Iberia's topography is examined by combining gravity, magmatic, topographic and seismological observations with geomorphic considerations. We have four principal results. First, highest coherence between free‐air gravity and topography is at wavelengths ≲250 km where admittance indicates that elastic thickness of Iberia's plate is 20 ± 3 km. These results imply that flexural and sub‐plate support of Iberian topography could be expressed at wavelengths of O(100) km. Secondly, P‐to‐S receiver functions and simple isostatic calculations indicate that whilst crustal thickness variations and flexural loading (e.g. as a result of plate shortening) partially explain the elevation of Pyrenean, Betics, Cantabrian, Spanish Central System and Iberian Chain topography, they fail to explain the elevation of large parts of Iberia. Thirdly, a new full waveform shear wave tomographic model and velocity to temperature conversions suggest that the asthenosphere beneath Iberia is anomalously slow and has excess temperatures of up to 162 ± 14°C. Simple isostatic calculations indicate asthenospheric support of topography of up to 1 km. Neogene‐Recent (∼23–0 Ma) extrusive magmatism (e.g. Calatrava, Catalan) sit atop many of the slow shear wave velocity anomalies. Finally, biostratigraphic data, combined with inversion of 3217 river profiles, show that most of Iberia's topography grew during the last ∼30 Ma at rates of up to 0.3 mm yr−1. Best‐fitting theoretical rivers have a low residual rms misfit (=0.96) and calculated uplift is consistent with an independent inventory of stratigraphic and biostratigraphic observations. We suggest that Neogene‐Recent growth of most of central Iberia's topography was a result of asthenospheric support.

Journal article

Stucky de Quay G, Roberts GG, Rood DH, Fernandes VMet al., 2019, Holocene uplift and rapid fluvial erosion of Iceland: a record of post-glacial landscape evolution, Earth and Planetary Science Letters, Vol: 505, Pages: 118-130, ISSN: 0012-821X

In actively deforming regions fluvial systems are strongly regulated by uplift. River geometries record histories of vertical motions that can be used to examine the driving forces generating topographic relief. Iceland's rapidly evolving landscapes provide an opportunity to disentangle histories of uplift generated by postglacial rebound, volcanism, dynamic support, and plate spreading. Broad knickzones observed along Iceland's large rivers, and its powerful waterfalls and deep canyons, hint that regional processes have generated significant relief. We combine high-resolution drone photogrammetry and cosmogenic 3He dating of fluvial terraces to measure the erosional history of one of Iceland's largest knickzones, Jökulsárglúfur, in the northeast part of the island. Progressive younging of terraces indicates knickpoint propagation rates of up to ∼70 cm a−1 during the last 8 ka. Knickpoint velocities appear to be controlled partly by toppling of basalt columns. These rates were used to calibrate a model that inverts Iceland's drainage networks for uplift rate histories. Calculated uplift and isostatic calculations indicate that rifting, sub-plate support, and isostatic adjustment resulted in tens to hundreds of meters of regional Holocene uplift. Our results suggest regional uplift and fluvial erosion can rapidly generate hundreds of meters of relief in post-glacial landscapes.

Journal article

Roberts GG, White N, Lodhia BH, 2019, The generation and scaling of longitudinal river profiles, Journal of Geophysical Research: Earth Surface, Vol: 124, Pages: 137-153, ISSN: 2169-9003

The apparent success of inverse modeling of continent‐wide drainage inventories is perplexing. An ability to obtain reasonable fits between observed and calculated longitudinal river profiles implies that drainage networks behave simply and predictably at length scales of O(102–103) km and timescales of O(100–102) Ma. This behavior suggests that rivers respond in a predictable way to large‐scale tectonic forcing. On the other hand, it is acknowledged that stream power laws are empirical approximations since fluvial processes are complex, non‐linear, and probably susceptible to disparate temporal and spatial shocks. To bridge the gap between these different perceptions of landscape evolution, we present and interpret a suite of power spectra for African river profiles that traverse different climatic zones, lithologic boundaries, and biotic distributions. At wavelengths ≳ 102 km, power spectra have slopes of −2, consistent with red noise, demonstrating that profiles are self‐similar at these length scales. At wavelengths ≲ 102 km, there is a cross‐over transition to slopes of −1, consistent with pink noise, for which power scales according to the inverse of wavenumber. Onset of this transition suggests that spatially correlated noise, perhaps generated by instabilities in water flow and by lithologic heterogeneities, becomes more prevalent at wavelengths shorter than ∼100 km. At longer wavelengths, this noise gradually diminishes and self‐similar scaling emerges. Our analysis is consistent with the concept that complexities of river profile development are characterized by an adaptation of the Langevin equation, by which simple advective models of erosion are driven by a combination of external forcing and noise.

Journal article

Roberts GG, White N, Hoggard M, Ball P, Meenan Cet al., 2018, A neogene history of mantle convective support beneath Borneo, Earth and Planetary Science Letters, Vol: 496, Pages: 142-158, ISSN: 0012-821X

Most, but not all, geodynamic models predict 1–2 km of mantle convective draw-down of the Earth's surface in a region centered on Borneo within southeast Asia. Nevertheless, there is geomorphic, geologic and geophysical evidence which suggests that convective uplift might have played some role in sculpting Bornean physiography. For example, a long wavelength free-air gravity anomaly of +60 mGal centered on Borneo coincides with the distribution of Neogene basaltic magmatism and with the locus of sub-plate slow shear wave velocity anomalies. Global positioning system measurements, an estimate of elastic thickness, and crustal isostatic considerations suggest that regional shortening does not entirely account for kilometer-scale regional elevation. Here, we explore the possible evolution of the Bornean landscape by extracting and modeling an inventory of 90 longitudinal river profiles. Misfit between observed and calculated river profiles is minimized by smoothly varying uplift rate as a function of space and time. Erosional parameters are chosen by assuming that regional uplift post-dates Eocene deposition of marine carbonate rocks. The robustness of this calibration is tested against independent geologic observations such as thermochronometric measurements, offshore sedimentary flux calculations, and the history of volcanism. A calculated cumulative uplift history suggests that kilometer-scale Bornean topography grew rapidly during Neogene times. This suggestion is corroborated by an offshore Miocene transition from carbonate to clastic deposition. Co-location of regional uplift and slow shear wave velocity anomalies immediately beneath the lithospheric plate implies that regional uplift could have been at least partly generated and maintained by temperature anomalies within an asthenospheric channel.

Journal article

Roberts GG, Lodhia B, Fraser A, Fishwick S, Goes S, Jarvis Jet al., 2018, Continental margin subsidence from shallow mantle convection: example from West Africa, Earth and Planetary Science Letters, Vol: 481, Pages: 350-361, ISSN: 0012-821X

Spatial and temporal evolution of the uppermost convecting mantle plays an important role in determining histories of magmatism, uplift, subsidence, erosion and deposition of sedimentary rock. Tomographic studies and mantle flow models suggest that changes in lithospheric thickness can focus convection and destabilize plates. Geologic observations that constrain the processes responsible for onset and evolution of shallow mantle convection are sparse. We integrate seismic, well, gravity, magmatic and tomographic information to determine the history of Neogene-Recent (<23 Ma) upper mantle convection from the Cape Verde swell to West Africa. Residual ocean-age depths of +2 km and oceanic heat flow anomalies of +16 ± 4 mW m−2 are centered on Cape Verde. Residual depths decrease eastward to zero at the fringe of the Mauritania basin. Backstripped wells and mapped seismic data show that 0.4–0.8 km of water-loaded subsidence occurred in a ∼500 × 500 km region centered on the Mauritania basin during the last 23 Ma. Conversion of shear wave velocities into temperature and simple isostatic calculations indicate that asthenospheric temperatures determine bathymetry from Cape Verde to West Africa. Calculated average excess temperatures beneath Cape Verde are View the MathML source °C providing ∼103 m of support. Beneath the Mauritania basin average excess temperatures are View the MathML source °C drawing down the lithosphere by ∼102 to 103 m. Up- and downwelling mantle has generated a bathymetric gradient of ∼1/300 at a wavelength of ∼103 km during the last ∼23 Ma. Our results suggest that asthenospheric flow away from upwelling mantle can generate downwelling beneath continental margins.

Journal article

Tribaldos VR, White NJ, Roberts GG, Hoggard MJet al., 2017, Spatial and temporal uplift history of South America from calibrated drainage analysis, Geochemistry, Geophysics, Geosystems, Vol: 18, Pages: 2321-2353, ISSN: 1525-2027

A multidisciplinary approach is used to analyze the Cenozoic uplift history of South America.Residual depth anomalies of oceanic crust abutting this continent help to determine the pattern of present-day dynamic topography. Admittance analysis and crustal thickness measurements indicate that the elasticthickness of the Borborema and Altiplano regions is  10 km with evidence for sub-plate support at longerwavelengths. A drainage inventory of 1827 river profiles is assembled and used to investigate landscapedevelopment. Linear inverse modeling enables river profiles to be fitted as a function of the spatial and tem-poral history of regional uplift. Erosional parameters are calibrated using observations from the BorboremaPlateau and tested against continent-wide stratigraphic and thermochronologic constraints. Our results pre-dict that two phases of regional uplift of the Altiplano plateau occurred in Neogene times. Regional uplift ofthe southern Patagonian Andes also appears to have occurred in Early Miocene times. The consistencybetween observed and predicted histories for the Borborema, Altiplano, and Patagonian plateaux impliesthat drainage networks record coherent signals that are amenable to simple modeling strategies. Finally,the predicted pattern of incision across the Amazon catchment constrains solid sedimentary flux at the Fozdo Amazonas. Observed and calculated flux estimates match, suggesting that erosion and deposition weretriggered by regional Andean uplift during Miocene times.

Journal article

Stucky de Quay G, Roberts GG, Watson J, Jackson CA-Let al., 2017, Incipient mantle plume evolution: constraints from ancient landscapes buried beneath the North Sea, Geochemistry, Geophysics, Geosystems, Vol: 18, Pages: 973-993, ISSN: 1525-2027

Geological observations that constrain the history of mantle convection are sparse despite its importance in determining vertical and horizontal plate motions, plate rheology, and magmatism. We use a suite of geological and geophysical observations from the northern North Sea to constrain evolution of the incipient Paleocene-Eocene Icelandic plume. Well data and a three-dimensional seismic survey are used to reconstruct a 58–55 Ma landscape now buried ∼1.5 km beneath the seabed in the Bressay region. Geochemical analyses of cuttings from wells that intersect the landscape indicate the presence of angiosperm debris. These observations, combined with presence of coarse clastic material, interpreted beach ridges, and a large dendritic drainage network, indicate that this landscape formed subaerially. Longitudinal profiles of palaeo-rivers were extracted and inverted for an uplift rate history, indicating three distinct phases of uplift and total cumulative uplift of ∼350 m. Dinoflagellate cysts in the surrounding marine stratigraphy indicate that this terrestrial landscape formed in <3 Ma and was rapidly drowned. This uplift history is similar to that of a slightly older buried landscape in the Faeroe-Shetland basin ∼400 km to the west. These records of vertical motion are consistent with pulses of anomalously hot asthenosphere spreading out from the incipient Icelandic plume. Using simple isostatic calculations we estimate that the maximum thermal anomaly beneath Bressay was 50–100◦C. Our observations suggest that a thermal anomaly departed the Icelandic plume around 57.4±2.2 Ma at the latest, and travelled with a velocity >∼150 km/Ma.

Journal article

Rudge JF, Roberts GG, White NJ, Richardson CNet al., 2015, Uplift histories of Africa and Australia from linear inverse modeling of drainage inventories, Journal of Geophysical Research: Earth Surface, Vol: 120, Pages: 894-914, ISSN: 2169-9011

We describe and apply a linear inverse model which calculates spatial and temporal patterns of uplift rate by minimizing the misfit between inventories of observed and predicted longitudinal river profiles. Our approach builds upon a more general, nonlinear, optimization model, which suggests that shapes of river profiles are dominantly controlled by upstream advection of kinematic waves of incision produced by spatial and temporal changes in regional uplift rate. Here we use the method of characteristics to solve a version of this problem. A damped, nonnegative, least squares approach is developed that permits river profiles to be inverted as a function of uplift rate. An important benefit of a linearized treatment is low computational cost. We have tested our algorithm by inverting 957 river profiles from both Africa and Australia. For each continent, the drainage network was constructed from a digital elevation model. The fidelity of river profiles extracted from this network was carefully checked using satellite imagery. River profiles were inverted many times to systematically investigate the trade-off between model misfit and smoothness. Spatial and temporal patterns of both uplift rate and cumulative uplift were calibrated using independent geologic and geophysical observations. Uplift patterns suggest that the topography of Africa and Australia grew in Cenozoic times. Inverse modeling of large inventories of river profiles demonstrates that drainage networks contain coherent signals that record the regional growth of elevation.

Journal article

Stephenson SN, Roberts GG, Hoggard MJ, Whittaker ACet al., 2014, A Cenozoic Uplift History of Mexico and its Surroundings From Longitudinal River Profiles, Geochemistry, Geophysics, Geosystems, Vol: 15, Pages: 4734-4758, ISSN: 1525-2027

Geodynamic models of mantle convection predict that Mexico and western North America share a history of dynamic support. We calculate admittance between gravity and topography, which indicates that the elastic thickness of the plate in Mexico is 11 km and in western North America it is 12 km. Admittance at wavelengths > 500 km in these regions suggests that topography is partly supported by subcrustal processes. These results corroborate estimates of residual topography from isostatic calculations and suggest that the amount of North American topography supported by the mantle may exceed 1 km. The Cenozoic history of magmatism, sedimentary flux, thermochronometric denudation estimates, and uplifted marine terraces imply that North American lithosphere was uplifted and eroded during the last 30 Ma. We jointly invert 533 Mexican and North American longitudinal river profiles to reconstruct a continent-scale rock uplift rate history. Uplift rate is permitted to vary in space and time. Erosional parameters are calibrated using incision rate data in southwest Mexico and the Colorado Plateau. Calculated rock uplift rates were 0.15–0.2 mm/yr between 25 and10 Ma. Central Mexico experienced the highest uplift rates. Central and southern Mexico continued to uplift at 0.1 mm/yr until recent times. This uplift history is corroborated by independent constraints. We predict clastic flux to the Gulf of Mexico and compare it to independent estimates. We tentatively suggest that the loop between uplift, erosion, and deposition can be closed here. Mexico's staged uplift history suggests that its dynamic support has changed during the last 30 Ma.

Journal article

Wilson JWP, Roberts GG, Hoggard MJ, White NJet al., 2014, Cenozoic epeirogeny of the Arabian Peninsula from drainage modeling, GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS, Vol: 15, Pages: 3723-3761

Journal article

Paul JD, Roberts GG, White N, 2014, The African landscape through space and time, Tectonics, Vol: 33, Pages: 898-935, ISSN: 0278-7407

It is generally accepted that Cenozoic epeirogeny of the African continent is moderated by convective circulation of the mantle. Nevertheless, the spatial and temporal evolution of Africa's “basin-and-swell” physiography is not well known. Here we show how continental drainage networks can be used to place broad constraints on the pattern of uplift through space and time. First, we assemble an inventory of 710 longitudinal river profiles that includes major tributaries of the 10 largest catchments. River profiles have been jointly inverted to determine the pattern of uplift rate as a function of space and time. Our inverse model assumes that shapes of river profiles are controlled by uplift rate history and modulated by erosional processes, which can be calibrated using independent geologic evidence (e.g., marine terraces, volcanism and thermochronologic data). Our results suggest that modern African topography started to develop ∼30 Myr ago when volcanic swells appeared in North and East Africa. During the last 15–20 Myr, subequatorial Africa was rapidly elevated, culminating in the appearance of three large swells that straddle southern and western coasts. Our results enable patterns of sedimentary flux at major deltas to be predicted and tested. We suggest that the evolution of drainage networks is dominated by rapid upstream advection of signals produced by a changing pattern of regional uplift. An important corollary is that, with careful independent calibration, these networks might act as useful tape recorders of otherwise inaccessible mantle processes. Finally, we note that there are substantial discrepancies between our results and published dynamic topographic predictions.

Journal article

Czarnota K, Roberts GG, White NJ, Fishwick Set al., 2014, Spatial and temporal patterns of Australian dynamic topography from River Profile Modeling, Journal of Geophysical Research. Solid Earth, Vol: 119, Pages: 1384-1424, ISSN: 2169-9313

Despite its importance, the temporal and spatial evolution of continental dynamic topography is poorly known. Australia's isolation from active plate boundaries and its rapid northward motion within a hot spot reference frame make it a useful place to investigate the interplay between mantle convection, topography, and drainage. Offshore, dynamic topography is relatively well constrained and can be accounted for by Australia's translation over the mantle's convective circulation. To build a database of onshore constraints, we have analyzed an inventory of longitudinal river profiles, which is sensitive to uplift rate history. Using independently constrained erosional parameters, we determine uplift rates by minimizing the misfit between observed and calculated river profiles. Resultant fits are excellent and calculated uplift histories match independent geologic constraints. We infer that western and central Australia underwent regional uplift during the last 50 Myr and that the Eastern Highlands have been uplifted in two stages. The first stage from 120 to 80 Ma, coincided with rifting along the eastern margin and its existence is supported by thermochronological measurements. A second stage occurred at 80–10 Ma, formed the Great Escarpment, and coincided with Cenozoic volcanism. The relationship between topography, gravity anomalies, and shear wave tomographic models suggest that regional elevation is supported by temperature anomalies within the lithosphere's thermal boundary layer. Morphology and stratigraphy of the Eastern Highlands imply that these anomalies have been coupled to the base of the plate during Australia's northward motion over the last 70 Myr.

Journal article

Roberts GG, White NJ, Shaw B, 2013, An uplift history of Crete, Greece, from inverse modeling of longitudinal river profiles, GEOMORPHOLOGY, Vol: 198, Pages: 177-188, ISSN: 0169-555X

Journal article

Hilton RG, Galy A, West AJ, Hovius N, Roberts GGet al., 2013, Geomorphic control on the &delta;<sup>15</sup>N of mountain forest, Biogeosciences Discussions, Vol: 10, Pages: 1693-1705, ISSN: 1810-6277

Mountain forests are subject to high rates ofphysical erosion which can export particulate nitrogen fromecosystems. However, the impact of geomorphic processeson nitrogen budgets remains poorly constrained. We haveused the elemental and isotopic composition of soil and plantorganic matter to investigate nitrogen cycling in the mountainforest of Taiwan, from 24 sites with distinct geomorphic(topographic slope) and climatic (precipitation, temperature)characteristics. The organic carbon to nitrogen ratio of soilorganic matter decreased with soil 14C age, providing constrainton average rates of nitrogen loss using a mass balancemodel. Model predictions suggest that present day estimatesof nitrogen deposition exceed contemporary and historic nitrogenlosses. We found ∼ 6 ‰ variability in the stable isotopiccomposition (δ15N) of soil and plants which was not relatedto soil 14C age or climatic conditions. Instead, δ15N wassignificantly, negatively correlated with topographic slope.Using the mass balance model, we demonstrate that the correlationcan be explained by an increase in nitrogen loss bynon-fractioning pathways on steeper slopes, where physicalerosion most effectively removes particulate nitrogen. Publisheddata from forests on steep slopes are consistent withthe correlation. Based on our dataset and these observations,we hypothesise that variable physical erosion rates can significantlyinfluence soil δ15N, and suggest particulate nitrogenexport is a major, yet underappreciated, loss term in thenitrogen budget of mountain forests.

Journal article

Hilton RG, Galy A, West AJ, Hovius N, Roberts GGet al., 2013, Geomorphic control on the delta N-15 of mountain forests, BIOGEOSCIENCES, Vol: 10, Pages: 1693-1705, ISSN: 1726-4170

Journal article

Roberts GG, White NJ, Martin-Brandis GL, Crosby AGet al., 2012, An uplift history of the Colorado Plateau and its surroundings from inverse modeling of longitudinal river profiles, Tectonics, Vol: 31, ISSN: 0278-7407

It is generally agreed that a region encompassing the Colorado Plateau has been uplifted by sub-crustal processes. Admittance calculations, tomographic studies and receiver function analyses suggest that dynamic support is generated by some combination of convective upwelling and lithospheric thickness changes. Notwithstanding advances in our understanding of present-day setting, uplift rate histories are poorly constrained and debated: an improved history will aid discrimination between proposed models. Here, we show that a regional uplift rate history can be obtained by inverting longitudinal river profiles. We assume that the shape of a river profile is controlled by uplift rate and moderated by erosion. In our model, uplift rate is allowed to vary smoothly as a function of space and time, upstream drainage area is invariant with time. Simultaneous inversion of river profiles from the Colorado, Rio Grande, Columbia and Mississippi catchments shows that three phases of regional uplift occurred. The first phase occurred between 80 and 50 Myrs, when ∼1 km of uplift was generated at a rate of ∼0.03 mm/yr. A second phase occurred between 35 and 15 Myrs, when ∼1.5 km of uplift was generated at a faster rate of ∼0.06 mm/yr. A final phase of uplift commenced ∼5 Myrs ago. These distinct phases of Late Cretaceous and Oligocene uplift are corroborated by stratigraphic considerations, by thermochronometric data, and by stratigraphic evidence of periodic clastic efflux delivered into the Gulf of Mexico. An episodic uplift history is consistent with staged removal of thick lithospheric mantle beneath a large region, which is currently centered on Yellowstone.

Journal article

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