Fidéline Collin
email: <fideline.collin@isped.u-bordeaux2.fr

Xavier Duval

Vincent Lemoing

Lionel Piroth

Firas Al Kaied

Patrice Massip

Virginie Villes

Geneviève Chêne

François Raffi

Fid Line

1 4

Ten-year incidence and risk factors of bone fractures in a cohort of treated HIV1-infected adults

Fid line Collin é 1 * , Xavier Duval 2 3 4 , Vincent Lemoing 5 6 , Lionel Piroth 7 , Firas Al Kaied 4 , Patrice Massip 8 , Virginie Villes 9 10 Author Keywords fractures ; HIV ; alcohol ; protease inhibitor ; hepatitis Among emergent co-morbidities in the era of combination antiretroviral therapy (cART), bone complications such as osteonecrosis or osteoporosis are estimated to be more frequent in HIV infected treated patients than in the general population , , Many traditional [1 2 ] determinants such as smoking, alcohol consumption, low body mass index, sedentary lifestyle, digestive, renal and endocrine disorders can be identified in this population, while the role of HIV infection and antiretroviral treatment remains controversial , . As regards to [1 3 -6 ] the prevalence of usual risk factors in HIV-infected patients, incidence rate of bone fractures in those patients could increase over time .

[7 ]

However, there are little available data to quantify the risk in this population of patients. Our study estimated the incidence of bone fractures over a follow-up of 10 years in a national cohort of HIV1-infected patients on cART, described the type of fractures, and assessed potential determinants.

A total of 1,281 HIV1-infected adults were included into the ANRS CO8 APROCO-COPILOTE cohort when they were first prescribed a cART including a protease inhibitor, in 47 French centres between March 1997 and June 1999. Follow-up visits were performed one and four months after inclusion, then every four months. At each visit, a clinical examination and laboratory tests were performed; alcohol and tobacco consumption was assessed by a self-questionnaire administered to the patient. Severe and serious adverse events (SAE) were prospectively reported to the coordinating centre and reviewed by an Events Validation Committee . -

  . Specific monitoring of HCV/HIV-coinfected patients and active promotion of alcohol cessation should be recommended for the prevention of bone fractures.

[ 8 ]

 8 All grade 3 or 4 fractures, i.e. leading to severe or complete limitation of activity and/or to patient s hospitalization during follow-up, ' were included into the analysis. Incidence density was estimated by dividing the number of patients who underwent a first bone fracture by the period at risk for all included patients expressed in patient-years. Potential risk factors for fracture were assessed using a Poisson regression model. Between March 1997 and August 2007, a total of 27 fractures were recorded in 26 patients during a median follow-up of 7.1 years (interquartile range: 3.8 9.0). The incidence of a first bone fracture was 3.3 per 1,000 patient-years (95 confidence interval CI

Figure 1

 1 Figure 1 Cumulated probability of a first fracture estimated by the Kaplan-Meier method, ANRS CO8 APROCO-COPILOTE cohort (1997 2007).

11 , Genevi ve Ch ne è ê 1 12 , Fran ois Raffi ç 13 , ANRS Co8 Aproco-Copilote Study Group

	1	Centre pid miologie et biostatistique é é	INSERM : U897 , Universit Victor Segalen -Bordeaux II é	, FR
	2	Mod les et m thodes de l valuation th rapeutique des maladies chroniques è é 'é é	INSERM : U738 , Universit Paris-Diderot -Paris VII é	, Facult
	é	de m decine Paris 7 16, Rue Henri Huchard 75018 Paris,FR é
	3	CIC -CHU Bichat	INSERM : CIC7 , Gh Xavier Bichat -Claude Bernard PARIS VII 46, Rue Henri Huchard 75018 PARIS,FR
	4	Service de maladies infectieuses	AP-HP , H pital Bichat -Claude Bernard ô	, FR
	5	Service des Maladies Infectieuses et Tropicales	CHU montpellier , H pital Gui de Chauliac ô	, FR
	6	UMR 145, VIH/SIDA et maladies associ es é Universit Montpellier I é	, IRD 911 avenue Agropolis BP 64501 34394 Montpellier Cedex 5,FR
	7	Service des Maladies Infectieuses et Tropicales	CHU Dijon , FR
	8	Service des Maladies Infectieuses et Tropicales	H pital Purpan ô	, Toulouse,FR
	9	SE4S, Sciences conomiques et sociales, syst mes de sant , soci t s é è é é é INSERM : U912 , Universit de la M diterran e -Aix-Marseille II é é é	,
	FR
	10	Universit Aix-Marseille é	Universit Aix Marseille é	, UMR-S912 , IRD,FR
	11	Observatoire R gional de la Sant Provence Alpes C te d Azur é é ô '	ORS PACA , Marseille,FR
	12	Universit Victor Segalen Bordeaux 2 é	Universit Victor Segalen -Bordeaux II é	, FR
	13	Maladies Infectieuses	Universit de Nantes

: 2.0 to 4.6) (

). In most cases (81 ), an acute traumatism (eg, fall, mugging, skiing or other accident, blow) was reported as Figure 1 % having caused a fracture. In 19 of patients, fractures occurred during acute alcoholization. Fourteen fractures were located in lower % limbs: ankle in 4 patients (bi-malleolar in 3 patients; malleolar in 1 patient), femur in 7 patients (secondary to a femoral head osteonecrosis in one case), rotula, tibia, and foot in 1 patient, each; 5 fractures involved upper limbs: wrist, hand, elbow, clavicle and shoulder, in 1 patient each, fractured pelvis in 3 patients, vertebrae in 3 patients, and multiple fractured sites in 1 patient. Among the 26 patients who experienced bone fracture, osteoporosis was present in four of the five patients who had available osteodensitometry results. Two cases (located in foot and pelvis in 1 patient each) were considered by the physician in charge of the patient as possibly related to antiretroviral (d4T in one case and d4T/3TC/Nevirapine/Nelfinavir in the other case). Patients who experienced at least one fracture did not differ from others for age (median: 36.2 years overall), gender (77.2 male overall), AIDS (20.4 overall), baseline plasma HIV RNA (median: 4.5

%

protease inhibitor used (41 indinavir overall). Patients who experienced a bone fracture were more frequently excessive alcohol drinkers % than patients who did not (44 with 5 glasses per day versus 19.5 ), were more frequently co-infected with HCV (48 versus 24.5 )

and had a lower baseline level of CD4 cell count (194 cells/mm versus 277 cells/mm ). In the multivariate analysis, the incidence rate of 3 3 bone fracture was 2.9-fold (95 CI: 1.3 6.5) higher in patients with excessive alcohol consumption and 3.6-fold (95 CI: 1.6 8.1) higher

in HCV co-infected patients than in others.

Incidence rate of bone fractures estimated in our study population is in the same range as the one reported in the general population in Europe for the same age group, i.e 5 to 10 for 1,000 PY . However, we acknowledge that our estimation might be slightly [9 ] underestimated since only serious and severe adverse events were reported and monitored in our cohort and some fractures may have been treated on an outpatient basis.

Due to variable treatment exposure and frequent treatment modifications, we could not assess the role of a specific antiretroviral class or drug. In the context of a low number of fractures observed during this long follow-up, this study showed no association between specific markers of HIV disease (i.e HIV RNA, CD4 cell count, clinical stage or antiretroviral treatment) and the rate of bone fractures among our population. Alcohol consumption is a traditional determinant as it is known to increase both osteoporosis and risky behaviours and is, especially, higher in HCV/HIV-coinfected patients. Other studies have suggested that fractures and osteoporosis are more frequent in patients with chronic liver disease than in others, since patients with cirrhosis experience a decreased bone mass . This decreased bone [10 ] density might be due, in part, to vitamin D deficiency linked to cholestasis and/or hypogonadism.

Investigations in this field are to be carried on in a much larger number of patients and over extended follow-up periods. Although there is a lack of studies of specific drug treatment for prevention of bone fractures in HIV-infected patients, current HIV guidelines recommend the same preventive measures as in the general population, stressing the importance of non medicinal preventive measures.

Meanwhile, specific information, monitoring of HCV/HIV-coinfected patients and active promotion of alcohol cessation programs in HIV-infected patients are to be recommended for the prevention of bone fractures.

Ackowledgements:

We would like to thank Audrey Ta eb for advice regarding the statistical analyses, Catherine Barennes for her assistance and the patients for


Lorenz Wolf

Ritske S Huismans

Delphine Rouby

Robert Gawthorpe

Sebastian G Wolf

Link between faulting, topography, and sediment production during continental rifting: Insights from coupled surface process thermo-mechanical modelling

 Coupled, thermo-mechanical models show that during continental rifting, the sediment flux reflects the topographic evolution of rifts.

 High crustal strength, slow extension and efficient surface processes promote strain localization and sediment production.

 Models show that a time-lag of 2 -5 Myr between the main tectonic activity and the peak in sediment flux could exist for natural systems.

production evolve over time. We see that the degree of localization of deformation is decisive for the evolution of the rifts, and that localization correlates with sediment production. Furthermore, the temporal evolution of the sediment production reflects the tectonic and topographic evolution. Moving from models to natural examples, our findings indicate that the evolution of the sediment production is a good proxy for topography. However, a gap of 2 -5 Million years could exist between the main tectonic activity and the highest sediment production.

Introduction

The Earth's surface is shaped both by tectonic and surface processes. Identifying possible couplings and feedbacks between tectonic and surface processes has been a focus of research during the past decades (e.g., [START_REF] Champagnac | Tectonics, climate, and mountain topography[END_REF][START_REF] Molnar | Late Cenozoic uplift of mountain ranges and global climate change: chicken or egg?[END_REF][START_REF] Whipple | The influence of climate on the tectonic evolution of mountain belts[END_REF][START_REF] Whittaker | How do landscapes record tectonics and climate?[END_REF]. A plethora of studies focused on mountain belts and showed that orographic precipitation can focus deformation and exhumation [START_REF] Beaumont | Erosional control of active compressional orogens[END_REF][START_REF] Willett | Orogeny and orography: The effects of erosion on the structure of mountain belts[END_REF], that spatial and temporal variations in uplift and exhumation can be controlled by erosion (e.g., [START_REF] Enkelmann | Intense localized rock uplift and erosion in the St Elias orogen of Alaska[END_REF][START_REF] Grujic | Climatic forcing of erosion, landscape, and tectonics in the Bhutan Himalayas[END_REF], that variations in erosion reflect variations in tectonically-controlled rock uplift (e.g., [START_REF] Adams | Constraints on the tectonic and landscape evolution of the Bhutan Himalaya from thermochronometry: Late Cenozoic Evolution of Bhutan[END_REF][START_REF] Michel | Tectonic and glacial contributions to focused exhumation in the Olympic Mountains[END_REF][START_REF] Wang | Tectonic control of Yarlung Tsangpo Gorge revealed by a buried canyon in Southern Tibet[END_REF], and how sensitive the orogen-deformation is to erosion and deposition [START_REF] Erdős | First-order control of syntectonic sedimentation on crustal-scale structure of mountain belts[END_REF][START_REF] Wolf | Growth of Collisional Orogens From Small and Cold to Large and Hot-Inferences From Geodynamic Models[END_REF]. In extensional settings, a high lithospheric strength increases rift asymmetry and rift shoulder elevation (e.g., [START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF][START_REF] Corti | Control of Pre-rift Lithospheric Structure on the Architecture and Evolution of Continental Rifts: Insights From the Main Ethiopian Rift, East Africa[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF]. Studies documented that a feedback between footwall erosion and hanging wall deposition leads prolongs fault activity and offset [START_REF] Maniatis | Slip acceleration on normal faults due to erosion and sedimentation -Results from a new three-dimensional numerical model coupling tectonics and landscape evolution[END_REF][START_REF] Olive | Modes of extensional faulting controlled by surface processes: Normal faulting and surface processes[END_REF], which enhances the formation of large offset asymmetric normal faults [START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF], and that enhanced sediment supply to the rift basin owing to an antecedent river network can localize fault displacement [START_REF] Hemelsdaël | Interaction of an antecedent fluvial system with early normal fault growth: Implications for syn-rift stratigraphy, western Corinth rift (Greece)[END_REF]. All these studies demonstrate, how sensitive the evolution of orogens and rifts is to both tectonic and climatic boundary conditions. Tectonically-driven extension leads to uplift and subsidence of the landscape, resulting in rift shoulder uplift and basin subsidence. Depending on the crustal strength (left or right part of the cartoon), the resulting rift geometries can be different. Surface processes such as fluvial erosion or hillslope processes lower the elevated landscape and generate sediment. The efficiency of the surface processes affects the topography and the deposition of sediments in the basins (erosion increases from the front towards the back of the cartoon). The numbers indicate specific questions that are addressed in this work, and that are related to the effects of the tectonic (extension rate, crustal strength) and climatic boundary conditions (efficiency of surface processes).

Modified from [START_REF] Whittaker | Characterising the origin, nature and fate of sediment exported from catchments perturbed by active tectonics[END_REF].

At continental rifts, tectonically driven faulting leads to uplift and subsidence of the landscape, forming rifts with high-elevation shoulders and bounding basins (Fig. 1). Climatically influenced surface processes erode the landscape, create relief and produce sediments that infill the tectonically generated depressions creating the stratigraphic record of a basin (Fig. 1). Variations in the associated sediment flux can be related both to tectonic and climatic causes (e.g., [START_REF] Forzoni | Delayed delivery from the sediment factory: modeling the impact of catchment response time to tectonics on sediment flux and fluvio-deltaic stratigraphy[END_REF][START_REF] Mcneill | High-resolution record reveals climate-driven environmental and sedimentary changes in an active rift[END_REF][START_REF] Rohais | Source-to-Sink Analysis of the Plio-Pleistocene Deposits in the Suez Rift (Egypt)[END_REF][START_REF] Sømme | Manifestation of Tectonic and Climatic Perturbations in Deep-Time Stratigraphy -An Example From the Paleocene Succession Offshore Western Norway[END_REF] and in turn, the preserved stratigraphic record is often used to unravel the effects of tectonic or surface processes, for instance by inferring the history of rock uplift, the evolution of topography and the drainage network, and climatic variations (e.g., [START_REF] Armitage | Transformation of tectonic and climatic signals from source to sedimentary archive[END_REF][START_REF] Castelltort | How plausible are high-frequency sediment supplydriven cycles in the stratigraphic record?[END_REF][START_REF] Geurts | Transient landscape and stratigraphic responses to drainage integration in the actively extending central Italian Apennines[END_REF][START_REF] Guillocheau | Quantification and causes of the terrigeneous sediment budget at the scale of a continental margin: a new method applied to the Namibia-South Africa margin: Quantification and causes of the terrigeneous sediment budget at the scale of a continental margin[END_REF][START_REF] Rohais | Source-to-Sink Analysis of the Plio-Pleistocene Deposits in the Suez Rift (Egypt)[END_REF][START_REF] Sømme | Manifestation of Tectonic and Climatic Perturbations in Deep-Time Stratigraphy -An Example From the Paleocene Succession Offshore Western Norway[END_REF][START_REF] Stevens Goddard | Recognizing drainage reorganization in the stratigraphic record of the Neogene foreland basin of the Central Andes[END_REF][START_REF] Whittaker | Characterising the origin, nature and fate of sediment exported from catchments perturbed by active tectonics[END_REF]. Correlations between catchment area, runoff, relief, and sediment flux observed in present-day river systems [START_REF] Syvitski | Geology, Geography, and Humans Battle for Dominance over the Delivery of Fluvial Sediment to the Coastal Ocean[END_REF] are commonly used to invert the evolution of the sediment flux (as preserved in the stratigraphic record) for instance for the evolution of past relief and catchment area (e.g., [START_REF] Rohais | Source-to-Sink Analysis of the Plio-Pleistocene Deposits in the Suez Rift (Egypt)[END_REF][START_REF] Sømme | Manifestation of Tectonic and Climatic Perturbations in Deep-Time Stratigraphy -An Example From the Paleocene Succession Offshore Western Norway[END_REF]. One of the inherent assumptions for this approach is that temporal variations in the sediment flux are coeval and correlated with changes in relief or catchment area also on long timescales a (e.g., as induced by tectonically-controlled changes in rock uplift). However, obtaining independent constraints on past topographic evolution and linking this to sediment flux is challenging.

The simple correlation between tectonic activity, topography, and sediment flux on geologic timescales implicit in the BQART method is, furthermore, hampered by the transient response of landscapes to changes in tectonic and/or climatic conditions, and by possible feedbacks between tectonic and surface processes (e.g., [START_REF] Allen | Time scales of tectonic landscapes and their sediment routing systems[END_REF][START_REF] Allen | Dispersal and Preservation of Tectonically Generated Alluvial Gravels in Sedimentary Basins[END_REF][START_REF] Li | Some signals are not the same as they appear: How do erosional landscapes transform tectonic history into sediment flux records?[END_REF][START_REF] Whittaker | Characterising the origin, nature and fate of sediment exported from catchments perturbed by active tectonics[END_REF]. Here, we aim to circumvent these limitations and obtain coeval constraints on topography, tectonic activity, and sediment production using coupled forward modelling. We analyse the evolution of continental rifts from the syn-rift to the post-rift using a high-resolution 2D thermo-mechanical model coupled with a landscape evolution model, and subject the rifts to different tectonic and surface process boundary conditions. The landscape evolution model includes the temporally and spatially transient uplift field of faults and simulates the erosional response of the evolving landscape. In turn, the tectonic model includes the effects of erosion and deposition on the evolution of lithosphere deformation and fault formation. Hence, the model allows investigating the response of tectonics (i.e., evolution of the structure of a rift, number of faults, fault offset) to the redistribution of mass by erosion and sedimentation, and at the same time allows measuring the amount of sediment generated over time. We address the following questions (Fig. 1): (1) What is the influence of different boundary conditions, specifically crustal strength, erosional power, and extension rate on the structural and topographic evolution of rifts? (2) How do the boundary conditions affect sediment production? (3) How are the evolution of sediment flux, topography, and tectonic activity correlated on long timescales?

The response of sediment production to variations in tectonic and climatic boundary conditions has been the subject of previous work using surface process models (e.g., [START_REF] Armitage | Transformation of tectonic and climatic signals from source to sedimentary archive[END_REF][START_REF] Densmore | Development and response of a coupled catchment fan system under changing tectonic and climatic forcing[END_REF][START_REF] Forzoni | Delayed delivery from the sediment factory: modeling the impact of catchment response time to tectonics on sediment flux and fluvio-deltaic stratigraphy[END_REF][START_REF] Li | Some signals are not the same as they appear: How do erosional landscapes transform tectonic history into sediment flux records?[END_REF]Yuan et al., 2019). These models used either simple 1D geometries or were restricted to a limited-spatial extent (i.e., focusing on a single catchment), considered only short timescales (< 15 Myr), or simplified the tectonics using uniform uplift fields. Inherent to all of these studies is that they are not able to include the effect of erosion and deposition on fault offset owing to their lacking mechanical part. On the other hand, previous work using coupled models in rift settings often used simple tectonic boundary conditions and focused for instance solely on the role of the crustal rheology using fixed extension rates (e.g., [START_REF] Andrés-Martínez | Thermomechanical Implications of Sediment Transport for the Architecture and Evolution of Continental Rifts and Margins[END_REF][START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF][START_REF] Olive | Modes of extensional faulting controlled by surface processes: Normal faulting and surface processes[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF]. These studies demonstrated that rheology affects the coupling between crust and mantle [START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF][START_REF] Huismans | Asymmetric lithospheric extension: The role of frictional plastic strain softening inferred from numerical experiments[END_REF], 2003;[START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF] and showed a feedback between erosion, hanging wall deposition, and fault offset [START_REF] Andrés-Martínez | Thermomechanical Implications of Sediment Transport for the Architecture and Evolution of Continental Rifts and Margins[END_REF][START_REF] Olive | Modes of extensional faulting controlled by surface processes: Normal faulting and surface processes[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF]. Other work using purely thermomechanical models also highlighted the effect of extension rate on the width, asymmetry, and distribution of deformation of rifts and rifted margins [START_REF] Huismans | Asymmetric lithospheric extension: The role of frictional plastic strain softening inferred from numerical experiments[END_REF], 2003;[START_REF] Naliboff | Complex fault interaction controls continental rifting[END_REF][START_REF] Dias | Conjugate rifted margins width and asymmetry: The interplay between lithospheric strength and thermomechanical processes[END_REF][START_REF] Tetreault | The influence of extension rate and crustal rheology on the evolution of passive margins from rifting to break-up[END_REF]. We build upon these conclusions and as tectonic boundary conditions, we test the sensitivity of the models to both variable crustal rheologies and different extension rates. In order to test the sensitivity of the models to surface processes, we vary the erodibility between the models.

We present a series of 14 numerical experiments, where we systematically vary the tectonic and surface process efficiency parameters. We focus on elucidating changes in the sediment production both during the syn-rift and post-rift phase and on what the underlying mechanisms are.

We analyse (1) the structural and topographic evolution of the rifts and (2) how this impacts the evolution of the sediment flux. For selected models, we provide detailed analyses of fault activity, fault offset, and topography. Furthermore, we relate the temporal evolution of the sediment flux with the temporal evolution of elevation and rock uplift, identifying four phases that reflect the geomorphotectonic evolution of the rift. We also discuss, where they can be observed in natural examples. We finally assess, how our model results corroborate the approach to invert the sediment record for the topographic evolution of rifts.

Modelling Methods

The T-model: a coupled thermo-mechanical-surface-process model

We use a lithosphere-scale thermo-mechanical-surface-process model to investigate continental rifting [START_REF] Wolf | Growth of Collisional Orogens From Small and Cold to Large and Hot-Inferences From Geodynamic Models[END_REF]; see Fig. 2a). The model consists of the 2D thermo-mechanical code Fantom [START_REF] Thieulot | FANTOM: Two-and three-dimensional numerical modelling of creeping flows for the solution of geological problems[END_REF], coupled to the 2D landscape evolution code FastScape [START_REF] Braun | A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution[END_REF]Yuan et al., 2019). FastScape and Fantom are tightly coupled in a T-manner [START_REF] Beaumont | Erosional control of active compressional orogens[END_REF][START_REF] Wolf | Growth of Collisional Orogens From Small and Cold to Large and Hot-Inferences From Geodynamic Models[END_REF], so that uplift and subsidence arising from the thermo-mechanical model provide a cylindrical uplift signal to FastScape and average erosion and deposition feed back to the thermomechanical computation. The coupled model captures the temporally and spatially transient evolution of continental rifts subject to the interaction between surface processes and tectonics. In the following, we describe the setup and boundary conditions of the tectonic and surface process model and explain the strategy behind our modelling approach.

Setup and boundary conditions for Fantom

Fantom is a thermo-mechanically coupled, arbitrary Lagrangian-Eulerian, finite-element code that solves for plane-strain, incompressible, visco-plastic creeping flows and heat transfer in the model domain. Viscous deformation is approximated by nonlinear power law creep and material properties are based on flow laws of wet quartz [START_REF] Gleason | A flow law for dislocation creep of quartz aggregates determined with the molten salt cell[END_REF], dry Maryland diabase [START_REF] Mackwell | High-temperature deformation of dry diabase with application to tectonics on Venus[END_REF] and wet olivine [START_REF] Karato | Rheology of the Upper Mantle: A Synthesis[END_REF]. Frictional-plastic deformation is modelled using a pressure-dependent Drucker-Prager yield criterion, considering the effect of plastic strain-weakening on the materials [START_REF] Huismans | Symmetric and asymmetric lithospheric extension: Relative effects of frictional-plastic and viscous strain softening[END_REF]. A full explanation of the inherent equations and a table of all material constants is given in the electronic supplement (section S1 and Table S1). The model domain is 1200 km wide, 600 km deep, and vertically stratified (Fig. 2b). From top to bottom the model consists of continental crust (0-35 km), lithospheric mantle (35-120 km), and sub-lithospheric mantle (120-600 km). To test the sensitivity of the model to different crustal strengths, we discern two different crusts, R1, strong crust, and R2, intermediate strength crust (see strength envelopes in the inset of Fig. 2b). R1 uses dry Maryland diabase as material for the lower crust, R2 uses wet quartz for the lower crust. Otherwise, the two rheologies consist of the same materials, using wet quartz as material for the upper parts of the crust and wet olivine for the lithospheric and sublithospheric mantle. To account for stronger, melt-depleted conditions, the flow law of the lithospheric mantle is scaled by a factor 5. We do not consider models with an even weaker crust (see for instance, [START_REF] Huismans | Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF], because very weak crust does not result in significant rift initialization for the extension durations that we consider.

Material that is eroded and deposited as sediment during the model run (materials S1, S2 and S3 in Fig. 2b) has the same mechanical properties as upper crust.

We use a 400 km wide area in the centre of the model with initial strain inheritance (Fig. 2b), simulating inherited structures from previous tectonic events [START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF]. To localize rifting in the centre of this domain, we add a small thermal anomaly at the base of the lithosphere in the centre of the model (Fig. 2b). A more detailed explanation of the approach for strain inheritance can be found in the electronic supplement.

On each side of the model, the lithosphere is extended with half the extension rate as horizontal velocity boundary condition (v ext in Fig. 2b). Lateral outflow of material is balanced by a low velocity inflow of material in the sub-lithospheric mantle in order to preserve mass (v b in Fig. 2b).

The bottom and sides of the model are horizontal and vertical free slip boundaries, respectively, whereas the top of the model serves as free surface subject to erosion and deposition. As thermal boundary condition the base of the model is kept at a constant temperature of 1522 °C and the lateral boundaries are thermally insulated. The numerical resolution in our models is 500 m horizontally and the vertical resolution is depth dependent with a 200 m resolution in the upper 20 km. This high resolution allows investigating the basin-scale feedback of tectonics and surface processes.

Setup and boundary conditions for FastScape

We use a modified version of FastScape to model surface processes [START_REF] Braun | A very efficient O(n), implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution[END_REF]Yuan et al., 2019). Fastscape accounts for onshore erosion, sediment transport, and deposition in the marine part of the landscape. The rate of change of elevation (∂h/∂t) in the parts of the landscape above sea level is simulated by solving the stream power law (i.e., river incision; [START_REF] Whipple | Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs[END_REF], and hillslope processes [START_REF] Culling | Soil Creep and the Development of Hillside Slopes[END_REF]:

𝜕ℎ 𝜕𝑡 = 𝑈 -𝑘 𝑓 𝐴 𝑚 𝑆 𝑛 + 𝑘 𝐶 ∇ 2 ℎ, for h ≥ h sea level (1)
where h is elevation, U is uplift rate, k f is fluvial erodibility, A is upstream drainage area, S is slope, m and n are stream power law exponents, and k C is the transport coefficient of hillslope diffusion. We do not include continental deposition. Hence, no material is deposited above sea level and all eroded material is transported by the rivers to the marine domain or out of the model according to the drainage organisation.

Below sea level, sediment transport and deposition are simulated using a diffusion equation as described in Yuan et al. (2019). Using the amount of sediment flux coming from the continental domain of the model (Q s ), the rate of elevation change can be approximated by:

𝜕ℎ 𝜕𝑡 = 𝑘 𝑀 ∇ 2 ℎ + 𝑄 𝑠 , for h < h sea level (3)
where k M is the marine diffusion coefficient. Equation ( 3) is valid if the material transported below consists of one grainsize. In our case we consider two different grainsizes and use a coupled-diffusion with distinct transport coefficients for the two grainsizes (having values of 200 m 2 /yr and 100 m 2 /yr, respectively). We refer to the paper of Yuan et al. (2019) for further technical details about this approach.

FastScape truly sits on top of Fantom and has the same spatial dimension of 500 m. We choose a model depth of 400 km for the FastScape model, resembling a typical width of a continental rift system. The left and right-side boundaries of the landscape are open so that water flows out and the top and bottom boundaries are periodic.

Modelling strategy

To investigate the variability of tectonic and surface processes in continental rifts, we test the sensitivity of our models to crustal rheology, extension rate, and fluvial erodibility. The resulting parameter combinations yield 14 different models (Table 1). We consider two different crustal rheologies (R1 and R2; Fig. 2b) with a total 75 km of extension. This is sufficient to develop a rift without reaching crustal breakup. The duration of extension depends on the extension rate and we consider four combinations of extension rate and duration: 7.5 Myr at a rate of 10 km/Myr, 15 Myr at a rate of 5 km/Myr, and 30 Myr at a rate of 2.5 km/Myr. All models have a total duration of 40 Myr with variable durations of the syn-and post-rift phases (Fig. 2c).

Model name Rheology Extension rate [km/Myr

Fluvial incision controls the erosional efficiency, erosion rate, and sediment yield. In the Stream Power Law, coefficients m and n are relatively well known [START_REF] Stock | Geologic constraints on bedrock river incision using the stream power law[END_REF], but fluvial erodibility (k f, ) spans a wide range as it incorporates effects related to climate, rock type, vegetation, and abrasive agents [START_REF] Stock | Geologic constraints on bedrock river incision using the stream power law[END_REF]. We keep m=0.4 and n=1 and test the effect of erosional efficiency by changing fluvial erodibility, considering k f values of 0.1, 0.25, 0.5 and 1 x 10 -5 m 0.2 /yr (Table 1). These values cover a wide range, leading to very little erosion and a long-lasting landscape or very efficient erosion and rapid degradation of the landscape. This can be envisioned as rifts experiencing arid to humid climatic boundary conditions. We use a reference k f value of 0.5 x 10 -5 m 0.2 /yr for all of our extension rates and rheologies (Table 1). To account for pre-existing relief,

we set the sea level to -1000 m below the initial model surface (which is at 0 m).

We analyse the output from both the tectonic and surface processes models (see electronic supplement, section S4 for details of analyses procedure). We focus on five models (models M1 -M5

in Table 1), for which we provide detailed analyses of the structural and topographic evolution . Supplementary models (SM1 -SM9) are included in the analyses of the evolution of topography and sediment flux . For all models we provide animations of topography and structures in the electronic supplement.

Results

We provide a detailed description of the evolution of the rift geometry for selected models (M1 -M5, Table 1). We focus on the reference model M1 and highlight changes in the evolution of rifting. We then describe the sensitivity of the evolution of elevation and sediment production to extension rate and erodibility.

Evolution of rift geometry and faults

Reference model M1

The reference model has a high crustal-strength (rheology R1; Fig. 2b), intermediate erodibility (k f = 0.5 x 10 -5 m 0.2 /yr), and an extension rate of 10 km/Myr for 7.5 Myr. At 3 Ma two boundary faults (F1 and F2) form a 75 km wide asymmetric rift system (Fig. 3a).

Major fault F1 forms a crustal scale shear-zone cutting into the upper mantle lithosphere (Fig. 3a) and is associated with significant rift shoulder elevation, ~ 3000 m (Fig. 3b). Fault F2 exhibits only ~6 km displacement and is associated with more subdued topography (Fig. 3a). On both sides of the rift minor fluvial valleys orthogonal to the main drainage divides form.

At 6 Ma, displacement along F1 and F2 reaches 10.8 and 6.4 km respectively (Figs. 3a and3b), new fault F4 dissects the footwall of F2, and deformation shifts to the centre of the rift forming faults F3 and F5 (Fig. 3a). Footwall uplift of F4 on the left side reduces the area draining towards the rift basin. Erosion of the right rift flank is associated with headward migration of the drainage divide.

Material eroded from both rift flanks is deposited in the hanging wall grabens of F1 and F2. Activity of F1 ceases at 6.5 Ma with a total offset of 10.8 km, while F2 remains active until 7.5 Ma with a total offset of 7.3 km (Fig. 3b).

At 7.5 Ma deformation is partitioned between left flank faults F2 and F4 and the centre of the rift F3 and F6 (Fig. 3a). The final rift geometry is asymmetric with the highest offset and topography associated with F1 on the right side (Fig. 3a). On the left side, rift topography is associated with F4, while the fault block between F2 and F4 forms a low-lying fluvial floodplain next to the basin (Fig. 3a).

At 15 Ma both rift flanks are significantly eroded down to ~1 km elevation (Fig. 3a).

Landward drainage divide retreat forms wide low-lying floodplains allowing transit of sediments to the basin that first fill up the rift bounding half grabens and then the central part of the basin (Fig. 3a).

At 30 Ma, onshore rift flank morphology has been further warped down, and the lateral floodplains and the central basin are submerged (Fig. 3a).

Sediment flux varies strongly throughout the model evolution (Fig. 3c). On the right side of the rift sediment flux reaches a maximum value of 2000 km 3 /Myr around the end of activity of F1 at ∼6.5 Ma (Fig. 3c) and then decreases exponentially to a steady value at 25 Ma (Fig. 3c). On the left rift side, the sediment flux peaks earlier and at a lower value ~1500 km 3 /Myr and then similarly decreases exponentially during the post rift. The contrasting evolution of sediment flux through time is also reflected in the cumulative sediment volumes, 17 x 10 3 km 3 and 28 x 10 3 km 3 at 40 Ma for the left and right side, respectively (Fig. 3c).

Effect of decreasing extension rate

Model M2 (Fig. 4) uses half the extension rate of the reference model ( 5 coincide with the timing of cessation of activity on F1 and F2 (Fig. 4c). Cumulative sediment volume at 40 Ma is higher than in model M1 reaching the same magnitude on both rift sides (Fig. 4c).

Effect of decreasing crustal strength

Model M3 (Fig. 5) investigates the influence of intermediate crustal strength (rheology R2), lower than in the reference model, with the same extension rate (10 km/Myr), and erodibility (k f = 0.5

x 10 -5 m 0.2 /yr).

Intermediate crustal strength results in a significantly different rift style compared to models M1 and M2, with more distributed deformation. At 4 Ma and 40 km extension, a broad 150 km wide, symmetric graben has formed with equal offset on main rift boundary faults F1 and F2, and secondary hanging wall faults F3 and F4 (Fig. 5a). Offset along F1 and F2 leads to a maximum rift flank Sediment flux (Fig. 5c) varies strongly throughout the model evolution. Peaks from both the left (900 km 3 ) and right (1250 km 3 ) side occur at ~6 Ma, coeval with the end of main activity on F2 and F1, respectively (Fig. 5b). On the right rift side, a significant peak in sediment flux (~2000 km 3 ) during the post-rift is observed at 25 Ma, related to river capture on the right rift side. The horst uplifted between F3 and F6 (Fig. 5a) forms a transient, topographic barrier. This prevents the sediment coming from the left rift side from reaching the central basin, resulting in decreased sediment flux from the left rift side during 25 -30 Ma, also reflected in the difference of the cumulative volume of 12 x 10 3 km 3 and 22 x 10 3 km 3 for the left and right side, respectively.

Effect of erodibility

Models M4, M2, and M5 (Table 1) explore the sensitivity to changing erodibility with k f values 0.25, 0.5, and 1 x 10 -5 m 0.2 /yr, respectively. They have a high crustal-strength rheology R1 and a low extension rate 5 km/Myr. We compare the models at the end of extension at 15 Ma (e.g., Fig. 6; see supplementary animations for full model evolution).

Varying erodibility affects both the number and the offset of faults. Model M4 with very low erodibility exhibits five faults and minor rift flank erosion. In contrast model M2 with intermediate erodibility is dominated by two main rift boundary faults and moderate rift flank erosion. Model M5 with even higher erodibility shows strongly enhanced offset along F1 and F2 (>14 km), significant rift flank erosion, and thick, tilted sediment wedges.

Erodibility also strongly impacts the topography through the drainage system. Low erodibility model M4 develops numerous small catchments with a drainage divide at ∼30 km from the shoreline, whereas the high erodibility model M5 develops fewer larger catchments and a drainage divide that migrates to ~55 km from the shoreline (Fig. 6). Rift shoulders are lowered down faster for higher erodibility (< 1500 m at 15 Ma) than for lower erodibility (2000 -2500 m at 15 Ma).

Sensitivity of elevation and sediment production to extension rate and erodibility

We next explore how varying extension rate and erodibility affect elevation and sediment production.

Models SM1, M1 and M2 (Table 1) explore the sensitivity to varying extension rates, equal to 2.5 km/Myr, 5 km/Myr, and 10 km/Myr, respectively, for identical erodibility k f = 0.5 x 10 -5 m 0.2 /yr and crustal strength R1 (Fig. 7). In contrast, models M4, SM3, M2 and M5 (Table 1) explore the effect of varying erodibility with k f = 0.1, 0.25, 0.5, 1 x 10 -5 m 0.2 /yr, respectively for an identical extension rate 5 km/Myr and crustal strength R1 (Fig. 8).

Maximum elevation follows a similar evolution for the models with variable extension rate with four characteristic phases (Fig. 7a). During Phase 1, initial rifting with distributed deformation generates almost no topography. Maximum topography increases rapidly during Phase 2 when deformation localizes, and the main rift shoulders are uplifted (Fig. 7a). Maximum elevation is reached systematically reached before the respective end of extension. The faster the extension rate, the earlier the peak, which is also slightly higher (Fig. 7a). During Phase 3, rift activity migrates to the centre of the basin, with maximum topography slowly decreasing towards the end of the syn-rift phase. After the end of extension, during Phase 4, elevation decays gradually and the rift shoulders are completely eroded away with a timescale depending primarily on fluvial erodibility (Fig. 7a,8a).

Sediment flux similarly exhibits four characteristic phases in the models (Fig. 7b). Initial

Phase 1 shows a slow increase of sediment flux with time. During Phase 2 sediment flux increases rapidly after the basin reaches sea level (time t b ), and reaches a peak shortly after maximum topography is reached. Subsequently sediment flux decreases slowly during Phase 3 until the end of extension (Fig. 7b). The timing of peak sediment flux depends on the extension rate (Fig. 7b). During

Phase 4 the sediment flux decreases exponentially to a steady state value 10 -15 Myr after the end of extension (Fig. 7b). Cumulative sediment volume slowly increases with time and mirrors the evolution of sediment flux. At 40 Myr cumulative sediment volumes are notably higher for lower extension rates (Fig. 7c).

Models with varying erodibility (e.g., Fig. 8) show features similar to those with varying extension rate. All reach a maximum elevation of ∼3000 m except for the high erodibility model that has maximum topography ~2800 m (Fig. 8a). The timing of maximum topography occurs earlier with increasing erodibility and occurs, in all cases, well before the end of extension. Subsequently, during the post-rift maximum elevation decreases progressively to a few hundreds of metres (Fig. 8a).

Maximum sediment flux is proportional to erosional efficiency (Figs. 8b,c). Models with varying erosional efficiency exhibit maximum sediment flux values of about 800, 1800, 4000, and 8000 km 3 /Myr, respectively, for k f ranging [0.1, 0.25, 0.5, 1.0] x 10 -5 m 0.2 /yr. Maximum sediment flux is systematically later than peak elevation. The case with high erodability (k f = 1.0 x 10 -5 m 0.2 /yr)

shows a sudden increase in sediment flux (> 6000 km 3 /Myr) at ∼33 Ma, marking a river capture event (Fig. 8b). Cumulative sediment volume at 40 Ma increases with erodibility (from 20 to 120 x 10 3 km 3 ; Fig. 8c).

Discussion

In the following, we first discuss the first-order controls of rheology, extension rate, and surface process efficiency on the evolution of modelled rifts. Next, we address how the different factors are reflected in the sediment production and compare with natural rift examples. We then discuss limitations of our modelling approach and compare our results to other modelling studies.

Influence of extension rate, rheology, and erodibility on rift evolution

Our results show that the evolution of a rift is mostly controlled by the degree of strain localization.

High degree of strain localization results in a simpler rift geometry, with less active faults and more offset. Models M1 to M5 demonstrate how crustal rheology, surface process efficiency, and extension rate affect the degree of strain localization.

Comparison between model M1 with strong crust (Fig. 3) and M3 with intermediate crustal strength (Fig. 5) illustrates the effect of rheology on strain localization. Intermediate crustal strength limits the coupling between crust and mantle [START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF], and results in faults terminating at the top of the viscous middle crust (Fig. 5). The weaker coupling reduces strain localization and leads to a wide symmetric rift with multiple active faults with moderate offset. In contrast, strong crust promotes strain localization in a narrow rift with few large offset crustal-scale faults that connect to the strong upper mantle lithosphere (Figs. 3 and4). Rift flank topography associated with footwall uplift is directly controlled by the amount of fault offset and by the strength of the crust. The strong crust cases promote large offset normal faults that generate high topography (>3000 m), while in contrast intermediate crustal strength cases promote reduced offset and lower rift flank topography (~1500 m).

The relative importance of tectonic uplift and erosion in the models can be understood considering the non-dimensional uplift-erosion number 𝑁 𝑒 [START_REF] Whipple | Dynamics of the stream-power river incision model: Implications for height limits of mountain ranges, landscape response timescales, and research needs[END_REF] that can be formulated for n=1 as 𝑁 𝑒 ∝ 𝑈 (𝑘 𝑓 x ℎ) ⁄ , where U is tectonic uplift rate, and h is elevation. 𝑁 𝑒 only weakly scales with drainage area or river length, which are therefore omitted. This simple relationship

shows that for large 𝑁 𝑒 uplift dominates over erosion, and vice versa for low 𝑁 𝑒 . We observe in our models that halving the extension rate (which reduces the uplift rates) has the same effect as doubling 𝑘 𝑓 , both in terms of structure and sediment flux. This is easy to explain with 𝑁 𝑒 , because the resulting erosion number 𝑁 𝑒 will be the same when either halving the extension rate or doubling 𝑘 𝑓 . Similarly, models with strong rheology result in higher topography (3000 m) than those with intermediate rheology (1500 m). Accordingly, if we choose an intermediate rheology, we need to either half the extension rate, or double 𝑘 𝑓 in order to obtain a similar 𝑁 𝑒 , that is, the same surface process efficiency.

The behavior of models M1, M2, M4, M5 is consistent with this simple scaling of the trade off and relative importance of extension rate that controls rock uplift rates along the main rift bounding faults and of fluvial erodibility that controls the rate of erosion of topography generated along these faults, counteracting rock uplift. Models M1 (fast extension, Fig. 3) and M2 (slow extension, Fig. 4), with an identical erodibility, show that slower extension promotes localization of deformation with only four active faults in model M2 with higher offset as compared to six faults in model M1. In contrast Models M2, M4, and M5 (Fig. 6) illustrate the effect of varying erodibility for an identical extension rate. Higher erodibility promotes strain localization resulting in fewer faults with more offset and more symmetric rifting. Erosional efficiency is increased for either a higher erodibility or for slower extension. A positive feedback between footwall erosion, hanging wall sedimentation, and fault offset has been demonstrated by earlier studies (e.g., [START_REF] Maniatis | Slip acceleration on normal faults due to erosion and sedimentation -Results from a new three-dimensional numerical model coupling tectonics and landscape evolution[END_REF][START_REF] Olive | Modes of extensional faulting controlled by surface processes: Normal faulting and surface processes[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF]. Our models show that a higher erosional efficiency increases this feedback owing to more erosion in the footwall and deposition in the hanging wall. Efficient erosion and deposition promote the evolution of large displacement boundary faults (Figs. 4 and6). The increased offset on the boundary faults delays the basin-ward migration of deformation and limits the development of other faults. Intermediate crustal strength cases result in lower rift shoulders resulting in lower surface process efficiency given the same 𝑘 𝑓 value, which limits the feedback between tectonic uplift and erosion.

In summary, rheology, extension rate, and erodibility impact the structural evolution of rifts.

For a given erodibility, a stronger crust and slower extension increase strain localization: less faults are active, more fault offset is generated, the rift is more symmetric, and the feedback between erosion and deposition is stronger. This, in turn, also has important implications for the evolution of the sediment production of rift systems, further discussed below.

Sediment production of the rift

Total volume of sediment

The amount of sediment produced during rifting scales with (1) topography, and (2) surface process efficiency. Syn-rift tectonic rock uplift generates elevated rift shoulders and fluvial erosion provides the main source of sediments. During the post-rift, rivers can capture the hinterland drainage network, yielding additional sediment. These two sources of sediment depend on the evolution of the rift and the total sediment volume is controlled by rift structural style and rheology, by extension rate, and by erodibility. Fig. 9 summarizes the volumes of sediment produced after 40 Myr of simulation for all models (M1 to M5 and SM1 to SM9, Table 1).

As expected, for a strong crust and a given extension rate (for instance for models with 15

Myr of extension), a higher erodibility increases the total sediment volume (Fig. 9). However, for a given erodibility, slower extension models with lower topography and rock uplift rates (i.e., 30 and 15

Myr of extension) yield substantially more sediment (70 -80 x 10 3 km 3 ), than faster extension models with higher topography and rock uplift rates (i.e., 45 x 10 3 km 3 for 7.5 of extension; Fig. 9). This is intuitive, as the volume of generated sediment scales with the magnitude of topography and cumulative rock uplift; the latter is higher for lower extension rates (Figs 3 and4). Slower extension localizes deformation on fewer structures sustaining more fault offset over a longer duration and can be explained by the more efficient feedback between continued fault localization and surface processes at lower extension rates (Figs. 7 and9).

For intermediate crustal strength, higher erodibility similarly increases the total sediment volume (Fig. 9). However, comparison between models with intermediate and high crustal strength

shows that cases with stronger crust generate 10 -100 % more sediment (e.g., models M1 vs. M3 or M5 vs. SM7, Fig. 9). Lower fault offset and associated footwall uplift for the intermediate crustal strength cases limits the feedback between erosion and deformation and the lower maximum elevation of the rift shoulders results in lower sediment volumes.

The amount of syn-rift sediment relative to the total sediment volume increases systematically with increasing erodibility, irrespective of the rheology and extension rate (Fig. 9). This effect is stronger for lower rates of extension, as the feedback between erosion/deformation is stronger. For example, models with intermediate extension duration (15 Myr) and erodibility (i.e., models M2, M5

and SM7 with k f ≥ 0.5 x 10 -5 m 0.2 /yr), produce over 50 % of the total sediment volume during the synrift. This results in a rift, where the majority of sediment is deposited during active deformation and subjected to faulting.

For the models with very high erodibility (i.e., k f = 1 x 10 -5 m 0.2 /yr), river capture events during the post-rift phase may result in a transient increase of the volume of sediment delivered to the basin. However, the volume of sediment generated by river capture is small compared to that generated during the syn-rift phase (i.e., Fig. 8c).

In summary, total sediment volume produced during rift evolution primarily reflects the combined effects of strain localization and erodibility. Slow extension, strong crust, and efficient surface processes yield higher total volumes of sediment. For a given erodibility, a reduction of 50% in the extension rate results in a 15 to 40 % higher sediment volume (Fig. 9). Sediment volume is directly proportional to erodibility (Fig. 9). Efficient erosion increases the proportion of syn-rift to post-rift sediments (Fig. 9). These observations point toward a complex interaction of tectonic and surface processes controlling sediment production. A rift system may generate a large amount of sediment based on its tectonic boundary conditions (i.e., the degree of strain localization could be high, because the crust is strong, and extension is slow). Low erosional efficiency may in turn affect the degree of strain localization limiting the feedback between deformation and erosion and reducing sediment production. We suggest that the phases of rifting shown by our models reproduce many characteristics of natural rift systems. Phases 1 to 3 can be recognized in the northern North Sea [START_REF] Fazlikhani | Strain migration during multiphase extension, Stord Basin, northern North Sea rift[END_REF][START_REF] Fossen | From widespread faulting to localised rifting: Evidence from K-Ar fault gouge dates from the Norwegian North Sea rift shoulder[END_REF], where deformation was initially distributed over several 100s of kilometers of width (e.g., Phase 1), before localizing on the boundary faults that accommodate most of the strain forming a 150 km wide rift (Phase 2), and subsequent basin-ward migration of deformation at the end of the syn-rift (e.g., Phase 3) [START_REF] Fazlikhani | Strain migration during multiphase extension, Stord Basin, northern North Sea rift[END_REF]. Similarly, the Gulf of Suez [START_REF] Gawthorpe | Normal fault growth, displacement localisation and the evolution of normal fault populations: the Hammam Faraun fault block, Suez rift, Egypt[END_REF] exhibits both initial distributed deformation (Phase 1), followed by localization of deformation on the boundary faults (Phase 2), and a subsequent basin-ward shift in deformation (Phase 3). The Gulf of Corinth exhibits an initial phase of wide distributed extension (Phase 1) before shifting deformation into the present day Gulf (Phase 2/3) [START_REF] Ford | Rift migration and lateral propagation: evolution of normal faults and sediment-routing systems of the western Corinth rift (Greece)[END_REF][START_REF] Gawthorpe | Tectono-sedimentary evolution of the Plio-Pleistocene Corinth rift, Greece[END_REF].

Full coverage of the evolution of sediment flux for the active stages of rifting is scarce for natural examples. However, the Gulf of Suez and Lake Albert rift provide sufficient data coverage and corroborate our proposed pattern. In the Gulf of Suez, the syn-rift peak in sediment flux coincides with the rift climax (Phase 2-3), with a strong decrease to low steady sediment flux in the post-rift (Phase 4), followed by a second, climate-induced peak in sediment flux [START_REF] Rohais | Pre-salt to salt stratigraphic architecture in a rift basin: insights from a basin-scale study of the Gulf of Suez (Egypt)[END_REF][START_REF] Rohais | Source-to-Sink Analysis of the Plio-Pleistocene Deposits in the Suez Rift (Egypt)[END_REF]. The Lake Albert rift (East African Rift system) exhibits low sedimentation rates during the first 11 Myr of slow extension (Phase 1) [START_REF] Simon | Rift du Lac Albert, Ouganda, Rift Est Africain : déformation, érosion, sédimentation et bilan de matière depuis 17 Ma[END_REF], followed by a strong increase and maximum sedimentation rates during the next 4 Myr, reflecting localization and increased fault offset on the main rift boundary fault (Phase 2). Lastly, a major river capture event, characteristic for Phase 4, explains the increase in sediment flux in the Zambezi Delta of the East Africa rifted margin [START_REF] Walford | Solid sediment load history of the Zambezi Delta[END_REF].

The BQART method [START_REF] Syvitski | Geology, Geography, and Humans Battle for Dominance over the Delivery of Fluvial Sediment to the Coastal Ocean[END_REF]) that empirically relates present-day values of sediment flux of modern river systems to relief, catchment area, and climatic factors, is used to invert the evolution of sediment flux to infer the past topographic evolution of rifts (e.g., [START_REF] Rohais | Source-to-Sink Analysis of the Plio-Pleistocene Deposits in the Suez Rift (Egypt)[END_REF][START_REF] Sømme | Manifestation of Tectonic and Climatic Perturbations in Deep-Time Stratigraphy -An Example From the Paleocene Succession Offshore Western Norway[END_REF]. Our model results allow independent validation of the BQART method on geologic timescales. We use maximum topography as a measure of relief and compare this to the sediment flux of our models. Peak elevation systematically predates peak sediment flux by 1 -3

Myr in models with sufficiently high erosion for a river network to develop (Figs. 7 and8). The magnitude in peak sediment flux correlates strongly with erodibility consistent with the climatic factors in the BQART method. These observations show that long time scale temporal changes in sediment flux reflect coeval changes in topography, consistent with one of the basic assumptions of the BQART method. However, the magnitude of the peak in sediment flux does not necessarily scale with the magnitude of topography, indicating a complex relationship between the sediment flux and relief/topography. This is in accordance with observations from [START_REF] Brewer | Comparison of methods to estimate sediment flux in ancient sediment routing systems[END_REF] suggesting that relief and paleo-topography are a significant source of uncertainty for estimation of sediment flux with the BQART method. In our models, the magnitude of topography is mostly sensitive to crustal strength and to a lesser degree to extension rate. Both peak sediment flux and cumulative sediment volume are critically dependent on the feedback between erosion, deposition, and fault offset. A system with a strong feedback, i.e. slow extension combined with high erodibility, yields more sediment, compared to a system with fast extension, higher rock uplift rates and topography, and a weaker feedback. In natural systems independent constraints on tectonic and climatic boundary conditions and their effect on topography and sediment flux may help to refine the BQART method for reconstructing the topographic evolution of rifts from the sedimentary record. Our results also demonstrate a time lag between peak rock uplift rate, topography, and sediment flux, which is mostly a function of the extension rate (Fig. 7,S3a). If the extension rate is low, peak uplift rate precedes the major pulse in sediment that is delivered to a basin by several million years (e.g., 5 Myr for model M2). This may help to refine the understanding and interpretation of sedimentary records, when it comes to attributing changes in sediment flux to tectonic events.

In summary, the temporal evolution of the sediment flux follows a distinctive pattern. It reflects the successive phases of the tectonic and geomorphic evolution of the rift system, which can also be observed in natural systems. The magnitude of the peak in sediment flux depends on the erosional efficiency, but also on the magnitude of topography as controlled by crustal rheology. The duration of the phases and the timing of the sediment flux peak(s) depend on the extension rate and the erosional efficiency.

Comparison with previous model work and limitations of our modelling approach

Earlier studies investigated continental extension using numerical models, emphasizing the evolution of the late stages of rifting or passive margin formation. Several of these studies focused on the role of crustal rheology and surface processes (e.g., [START_REF] Andrés-Martínez | Thermomechanical Implications of Sediment Transport for the Architecture and Evolution of Continental Rifts and Margins[END_REF][START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF][START_REF] Buiter | Dissipation analysis as a guide to mode selection during crustal extension and implications for the styles of sedimentary basins[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF], whereas others focused on the interplay of crustal rheology and extension rate (e.g., [START_REF] Naliboff | Complex fault interaction controls continental rifting[END_REF][START_REF] Dias | Conjugate rifted margins width and asymmetry: The interplay between lithospheric strength and thermomechanical processes[END_REF][START_REF] Tetreault | The influence of extension rate and crustal rheology on the evolution of passive margins from rifting to break-up[END_REF]. Our study is the first to test the sensitivity of continental rifting and the associated surface process response to the combined effects of crustal rheology, extension rate, and erodibility.

Our results corroborate the role of crustal rheology controlling the coupling between crust and mantle, with stronger coupling resulting in more localized and focused deformation (e.g., Theunissen & Huismans, 2019) leading to higher elevation of the rift shoulders (e.g., [START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF][START_REF] Tetreault | The influence of extension rate and crustal rheology on the evolution of passive margins from rifting to break-up[END_REF]. Extension rate and erodibility have a subordinate control on crust-mantle coupling. For a strong coupling, we observe asymmetric rifts (in terms of fault offset and elevation)

during the initial stages of rifting, irrespective of the extension rate. However, in case of slower extension enhanced offset along the second rift bounding fault leads to symmetric rift structure towards the end of extension.

The feedback effect between erosion, sedimentation, and deformation during rifting has been described in earlier studies [START_REF] Andrés-Martínez | Thermomechanical Implications of Sediment Transport for the Architecture and Evolution of Continental Rifts and Margins[END_REF][START_REF] Buiter | Dissipation analysis as a guide to mode selection during crustal extension and implications for the styles of sedimentary basins[END_REF][START_REF] Maniatis | Slip acceleration on normal faults due to erosion and sedimentation -Results from a new three-dimensional numerical model coupling tectonics and landscape evolution[END_REF][START_REF] Olive | Modes of extensional faulting controlled by surface processes: Normal faulting and surface processes[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF]. Also in our case, stronger surface processes lead to more strain localization [START_REF] Andrés-Martínez | Thermomechanical Implications of Sediment Transport for the Architecture and Evolution of Continental Rifts and Margins[END_REF], more fault offset and prolonged fault activity [START_REF] Beucher | Morphotectonic Evolution of Passive Margins Undergoing Active Surface Processes: Large-Scale Experiments Using Numerical Models[END_REF][START_REF] Olive | Modes of extensional faulting controlled by surface processes: Normal faulting and surface processes[END_REF][START_REF] Theunissen | Long-Term Coupling and Feedback Between Tectonics and Surface Processes During Non-Volcanic Rifted Margin Formation[END_REF] and more symmetric basins with fewer active faults [START_REF] Buiter | Dissipation analysis as a guide to mode selection during crustal extension and implications for the styles of sedimentary basins[END_REF]. In addition, we show that the feedback of surface processes on tectonics is stronger for slower (but longer duration) extension, resulting in larger fault offset, generating more sediment.

Our models have the following inherent limitations: We do not include temporal or spatial variations of erodibility in our models and 3D effects of deformation are excluded owing to the 2D nature of the thermo-mechanical model. We only consider sedimentation offshore below sea level, and no material is deposited in the continental domain. Thus, any onshore sediment that could be remobilized later on, is not considered in our analysis of the sediment flux or the total sediment volume. No material is deposited during the early stages of rifting before the basin has reached sea level and sediment produced during this time leaves the model domain. However, not including the sediment generated during early rifting does not significantly change total sediment volume estimates.

Conclusions

We use a thermo-mechanical model coupled with a landscape evolution model to investigate the evolution of continental rifts. Our models aim at resolving the evolution of tectonic activity, the associated topography and sediment production during rifting, and how they are affected by the tectonic and surface processes boundary conditions. We show that the degree of strain localization is critical for the evolution of a rift, and that it is controlled by crustal rheology, extension rate, and erodibility. Our results corroborate that an increase in erodibility promotes a strong coupling between tectonic and surface processes, through the feedback between footwall erosion, hanging wall deposition, and increased fault offset. We demonstrate that for an intermediate crustal strength, weak coupling between crust and mantle limits fault offset, which reduces the efficiency of the feedback.

Feedback between tectonics and surface processes is strongest for slower and extended extension owing to lower uplift rates and prolonged fault activity. Slowly extending rift systems with strong crust and efficient erosion exhibit a strong coupling between tectonics and surface processes, resulting in a structurally simple rift, with large fault offset and high sediment production. We reach the following specific conclusions:

1. Structure, topography, and sediment volume of the rifts are primarily controlled by the degree of strain localization.

2. Rift systems with strong crust and a high degree of strain localization generate the highest sediment volumes. For a given erodibility, slower extending rifts produce more sediment than faster extending rifts, such that a reduction in extension rate by 50% increases the amount of sediment by 15 -40 %.

3. Feedback between erosion and deformation increases fault offset, enhancing rock uplift, and yielding more sediment. The effect is strongest for systems with efficient erosion (slow extension and high erodibility) and limited if the coupling between crust and mantle is low. In summary, the evolution of a rift in terms of structures, topography and sediment flux reflects the complex interactions that can occur between tectonic and surface processes. We suggest that future work could include a more detailed analysis of geomorphic metrics (e.g., catchment area) or of the stratigraphic architecture. A comparison of these metrics from the model output with natural cases could also lead to a better understanding of the complicated processes behind continental rifting.

Figure 1 :

 1 Figure 1: Cartoon illustrating the effects of tectonic and surface processes on the development of rifts.

Figure 2 :

 2 Figure 2: Model setup (a) Overview, model dimensions, and resolutions of the T-model, where a 2D landscape evolution model (FastScape) is coupled with a 2D thermo-mechanical model (Fantom). (b) Model setup and geometry for Fantom, illustrating the layered structure (all thermal and mechanical properties are summarized in Table S1 in the supplement), the boundary conditions (V ext = extension rate, V b = velocity of basal counter flow) and the initial thermal state (red lines). Location and extent of features that promote strain localization at the beginning of extension are indicated: initial temperature anomaly (notch in the 1330°C isotherm) and strain inheritance. The inset displays a close-up view of the upper 130 km of the model, and the strength envelopes of the two different rheologies considered in our models, which differ in the strength of the lower crust (R1 = high crustal strength, R2 = intermediate crustal strength). (c) Temporal evolution of the models: The models have a total duration of 40 Myr and syn-rift duration depends on the extension rate (7.5 Myr, 15 Myr, 30 Myr).

Figure 3 :

 3 Figure 3: Results of the reference model M1. Model results for model M1 with high crustal strength, 7.5 Myr of extension (extension rate of 10 km/Myr) and intermediate erodibility (k f = 0.5 x 10 -5 m 0.2 /yr): (a) Structures (left column) and topography (right column) at selected time steps. Major faults are labelled in accordance with their onset of activity (faults active during the respective timestep are labelled in bold). Numbers in the grey boxes indicate vertical fault offset on the two boundary faults (F1 and F2). The black arrows indicate lithosphere-scale faults that reach a depth over 15 km. The topography transitions from onshore to offshore at the sea level (-1000 m). (b) Evolution of the vertical fault offset on the two boundary faults F1 (blue, right side) and F2 (red, left side). (c) Evolution of incremental (dashed curves) and cumulative (solid curves) sediment volumes from the two rift sides over time (blue = right side, red = left side).

  km/Myr until 15 Ma) and identical other parameters (high crustal-strength rheology R1, intermediate erodibility k f = 0.5 x 10 -5 m 0.2 /yr). Slower extension in M2 delays localization of deformation and rift formation with respect to reference model M1. At 5.5 Ma, an asymmetric rift has developed with 2.5 km of offset on right boundary rift fault F1 and rift flank elevation of ∼1500 m and insipient fault F2 on the left side (Figs. 3a and 3b). With ongoing extension both F1 and F2 take up most of the deformation leading to a largely symmetric rift at 11 Ma. Activity on F1 ceases around ∼13.5 Ma, whereas F2 remains active until the end of extension at 15 Ma. Subsequently, deformation shifts basin-ward breaking up the central block between F1 and F2, forming conjugate faults F3 and F4 in the centre. In contrast to model M1 most of the deformation is accommodated by the rift boundary faults F1 and F2 with a similar total offset (∼11.5 km) at the end of extension (Figs. 4b). Sediment flux peaks are similar in magnitude on both sides of the rift and

Figure 4 :

 4 Figure 4: Effect of decreasing the extension rate. Results for model M2 with high crustal strength, 15 Myr of extension (extension rate of 5 km/Myr) and intermediate erodibility (k f = 0.5 x 10 -5 m 0.2 /yr): (a) Structures (left column) and topography (right column) at selected time steps. Major faults are indicated and labelled in accordance with their onset of activity (faults active during the respective timestep are labelled in bold). Numbers in the grey boxes indicate vertical fault offset on the two boundary faults (F1 and F2). The black arrows indicate lithosphere-scale faults that reach a great depth (>15 km). The topography transitions from onshore to offshore at the sea level (-1000 m). (b) Evolution of the vertical fault offset on the two boundary faults F1 (blue, right side) and F2 (red, left side). (c) Evolution of incremental (dashed curves) and cumulative (solid curves) sediment volumes from the two rift sides over time (blue = right side, red = left side).

Figure 5 :

 5 Figure 5: Effect of decreasing crustal strength. Results for model M3 with intermediate crustal strength, 7.5 Myr of extension (extension rate of 10 km/Myr) and intermediate erodibility (k f = 0.5 x 10 -5 m 0.2 /yr): (a) Structures (left column) and topography (right column) at selected time steps. Major faults are indicated and labelled in accordance with their onset of activity (faults active during the respective timestep are labelled in bold). Numbers in the grey boxes indicate vertical fault offset on the two boundary faults (F1 and F2). The black arrows indicate faults that terminate at the transition from upper (UC) to middle crust (MC). The topography transitions from onshore to offshore at the sea level (which is at -1000 m). (b) Evolution of the vertical fault offset on the two boundary faults F1 (blue, right side) and F2 (red, left side). (c) Evolution of incremental (dashed curves) and cumulative (solid curves) sediment volumes from the two rift sides over time (blue = right side, red = left side).

Figure 6 :

 6 Figure 6: Sensitivity to erodibility. Structures (left column) and topography (right column) at the end of extension at 15 Ma for models M2, M4, and M5 with high crustal strength, 15 Myr of extension and variable erosional efficiency: (a) M4 with k f = 0.25 x 10 -5 m 0.2 /yr, (b) M2 with k f = 0.5 x 10 -5 m 0.2 /yr, and (c) M5 with k f = 1 x 10 -5 m 0.2 /yr. Faults are labelled according to their onset of activity, and active faults at 15 Ma are labelled in bold. Numbers in the grey boxes indicate vertical fault offset on the two boundary faults (F1 and F2). The topography transitions from onshore to offshore at the sea level (-1000 m).

Figure 7 :

 7 Figure 7: Influence of extension rate on the evolution of elevation (a), sediment flux (b) and sediment volume (c). Results are for models M1, M2, SM1 with high crustal strength, intermediate erosional efficiency (k f = 0.5 x 10 -5 m 0.2 /yr), and variable extension rates/extension durations of 30 Myr (black), 15 Myr (red) and 7.5 Myr (blue). In all panels, the colored triangles indicate the end of extension of the respective model. Note that sediment flux in the slowest model (2.5 km/Myr) does not reach a steady value within the 40 Myr simulation. Sediment flux and volume are only recorded after the basin has reached sea level at time t b (which depends on the respective extension rate). Prior to t b sediment is transported out of the model domain. The total volumes of sediment lost this way are 4952 km 3 , 2016 km 3 , 904 km 3 and 322 km 3 for models with extension rates of 2.5 km/Myr, 5 km/Myr, 10 km/Myr and 15 km/Myr, respectively.

Figure 8 :

 8 Figure 8: Influence of erosional efficiency on the evolution of elevation (a), sediment flux (b) and sediment volume (c). Results for models with high crustal strength, 15 Myr of extension and variable erosional efficiencies of k f = 0.1 x 10 -5 m 0.2 /yr (yellow), k f = 0.25 x 10 -5 m 0.2 /yr (orange), k f = 0.5 x 10 -5 m 0.2 /yr (red) and k f = 1 x 10 -5 m 0.2 /yr (purple). In all panels, the yellow triangles indicate the end of extension of the models. In panel (a), t max refers to the timing of maximum elevation, which occurs earlier for more efficient erosion.Sediment flux and cumulative sediment volume are only recorded after the basin of the respective model has reached sea level at time t b (which varies between 4.5 -5 Ma). Prior to t b sediment is transported out of the model domain. The total volumes of sediment lost this way are 3358 km 3 , 2016 km 3 , 726 km 3 and 393 km 3 (for models with k f values of 1, 0.5, 0.25 and 0.1 x 10 -5 m 0.2 /yr, respectively). Note that sediment flux in model with low erosional efficiency k f = 0.25 x 10 -5 m 0.2 /yr exhibits several maxima and minima, due to fault activity in the footwalls of F1 and F2, which lead to drainage reorganization (see Fig.6)

Figure 9 :

 9 Figure 9: Sediment volumes generated during rifting. Comparison of the sediment volumes (deposited since the basin has reached sea level) for the 14 models (Table 1). Models are grouped according to their rheology (red = strong, R1; grey = intermediate, R2) and subsequently ordered with respect to extension duration/rate. Models with dark-colored bars share the same k f value (i.e., k f = 0.5), in order to easily compare the sediment volumes for models with the same intermediate erosional efficiency. Models with other k f values (i.e., 0.1, 0.25 and 1) are pale colored. For each model, the height of the bar indicates the total sediment volume, whereas the height of the hatched bar indicates the synrift volume.

4. 2 . 2

 22 Temporal evolution of rift structure, sediment flux, and comparison to natural cases The evolution of rift structure and associated sediment flux (Fig. 10a) follows four distinct temporal geomorpho-tectonic phases (Fig. 10b). Phase 1 early-stage rift initiation is marked by distributed deformation, limited offset on several faults that produces little elevation, and low erosion rates, generating little sediment. Growth Phase 2 exhibits localization of deformation on the main rift bounding faults with rapid rift flank uplift, basin subsidence, river incision into the uplifting rift flanks, and steep relief resulting in high erosion rates and a strong increase in sediment flux. Phase 3 basinward migration of fault activity, associated with a decrease in uplift and erosion rates, is characterized by sediment flux slowly decreasing from its peak. After the end of extension, decay Phase 4 shows exponential decrease in sediment flux reflecting post rift fluvial erosion of rift flank topography and landward migration of river divides. Drainage capture of the hinterland during Phase 4 may lead to a transient increase in sediment flux. These four phases can be recognized in both strong and intermediate crustal strength models. In the case of intermediate crustal strength, the general trend of the flux is similar, but the magnitude of the different peaks is lower compared to the high crustal strength case (Fig. S4 and S5).

Figure 10 :

 10 Figure 10: Evolution of the sediment flux related to rifting phases. (a) General evolution of the sediment flux subdivided into four phases, and (b) cartoons of the four geomorpho-tectonic phases of the rift. After an initial phase of distributed deformation (Phase 1), the rifts have a different tectonic and topographic evolution (Phase 2 to 4), depending on the crustal strength: The left column displays the evolution in case of a high crustal strength, the right column in case of intermediate crustal strength. Red arrows indicate the magnitude of rock uplift, and grey arrows the magnitude of erosion, such that if uplift exceeds erosion the surface is uplifting, and when erosion exceeds uplift the surface is lowered.

4.

  We identify four characteristic phases for the evolution of sediment flux. Phase 1 early-stage rift initiation is associated with low topography, erosion rates, generating little sediment. Phase 2 rift growth is associated with uplift along the main rift bounding faults resulting in high erosion rates and a strong increase in sediment flux. Phase 3 basin-ward migration of fault activity is associated with slowly decreasing sediment flux. Post rift Phase 4 displays exponential decrease in sediment flux. Drainage capture of the hinterland during Phase 4 may lead to a transient increase in sediment flux. The phases of rifting reproduce many characteristics of natural rift systems and can be, for example, recognized in the northern North Sea, the Gulf of Suez, and the Gulf of Corinth. 5. Our modelling results indicate that for natural examples, the approach of inverting the sedimentary record for the topographic evolution of rifts is promising. However, the peaks in rock uplift/maximum elevation predate the peak in sediment flux by 2 -5 Myr (depending on the extension rate).

Table 1 :

 1 Summary

of parameters of the 14 models with varying tectonic parameters (rheology, extension rate) and erodibility (k f value). R1 refers to strong crust, R2 to intermediate strength crust, see also Fig.

2b

. Detailed analyses of the evolution of structures and topography for the main models (M1 -M5) are provided in

Acknowledgements:

The work presented in this study was funded by Total Energies through the COLORS project. We acknowledge computational resources by Uninett Sigma2 for project NN4704K. We thank Thomas Theunissen for fruitful discussions and his help for setting up the strain inheritance of the models. We also acknowledge discussions with Brendan Simon about the geology and sedimentary history of Lake Albert.

Open research

As earth surface process model, we use the freely-available, open source code FastScape (https://fastscape.org/), as outlined in the methods section. As thermo-mechanical model, we use the code Fantom (Thielot, 2011), using the equations and procedure as outlined in the methods section. In the supplementary material, we provide animations of all 14 models containing the essential data for our analyses.