temporal and spatial evolution of dynamic support from river profiles a framework for madagascar 1 we present a strategy for calculating uplift rates as a function of space and time from large sets of longitudinal river profiles this strategy assumes that the shape of a river profile is controlled by the history of uplift rate and moderated by the erosional process we assume that upstream drainage area is invariant the algorithm was tested on a set of 100 river profiles which were extracted from a digital elevation model of madagascar this set of profiles was simultaneously inverted to obtain uplift rate as a smooth function of space and time the fit between observed and calculated profiles is excellent and suggests that madagascar was uplifted by 1 2 km at rates of 0 2 0 4 mm yr during the last 15 myrs the location of madagascar suggests that its topographic elevation is maintained by convective circulation of the sub lithospheric mantle residual depth anomalies of oceanic fragments encompassing the island show that the island straddles a dynamic topographic gradient which generates asymmetric neogene uplift volcanism warped peneplains and uplifted marine terraces corroborate the existence of youthful uplift we suggest that sets of longitudinal river profiles contain useful information about the history of regional uplift which can be extracted by inverse modeling and calibrated by independent geologic observations

keeping the edge a numerical method that avoids knickpoint smearing when solving the stream power law the stream power equation is commonly used to model river incision into bedrock although specific conditions allow an analytical approach finite difference methods fdms are most frequently used to solve this equation fdms inevitably suffer from numerical smearing which may affect their suitability for transient river incision modeling we propose the use of a finite volume method fvm which is total variation diminishing tvd to simulate river incision in a more accurate way the tvd fvm is designed to simulate sharp discontinuities making it very suitable to simulate river incision pulses we show that the tvd fvm is much better capable of preserving propagating knickpoints than fdms using niagara falls as an example comparison of numerical results obtained using the tvd fvm with analytical solutions shows a very good agreement furthermore the uncertainty associated with parameter calibration is dramatically reduced when the tvd fvm is applied the high accuracy of the tvd fdm allows correct simulation of transient incision waves as a consequence of older uplift pulses this implies that the tvd fvm is much more suitable than fdms to reconstruct regional uplift histories from current river profile morphology and to simulate river incision processes in general

inversion of fluvial channels for paleorock uplift rates in taiwan the transient response of erosion to changes in rock uplift rate leads to the preservation of rock uplift history in the long profiles of rivers however extracting this information is nontrivial as changes in channel steepness are the result of both spatial and temporal changes in rock uplift rate as well as other factors such as climate and rock type we exploit an analytical linear solution for river channel profile evolution in response to erosion and tectonic uplift to investigate the rock uplift history of taiwan the analytical approach allows us to solve the linear inverse problem efficiently extracting rock uplift as a function of space and time from digital elevation data we assess the potential of fluvial topography to resolve rock uplift rates using three approaches 1 a synthetic resolution test 2 analysis of the forward model to demonstrate where in space and time the fluvial topography constrains rock uplift rate and 3 interpretation of the model resolution matrix furthermore the potential to analyze large data sets reduces the influence of stochastic processes such as landslides small scale river network reorganization and also local lithological variability in taiwan our analysis suggests that current rock uplift rates exceed erosion rates across much of the island and that there has been an increase in rock uplift rates since 0 5 ma across the central range

river drainage patterns in the new zealand alps primarily controlled by plate tectonic strain the persistence of dendritic drainage patterns implies that rivers reorganize after a tectonic perturbation preserving no long term record of that tectonic event numerical simulations of the evolution of drainage patterns in the southern alps new zealand however reveal rivers that resist reorganization and thus preserve a record of plate tectonic strain over 10 million years

hybrid empirical ground motion prediction equations for eastern north america using nga models and updated seismological parameters in the field of earthquake engineering ground motion prediction models are frequently used to estimate the peak ground acceleration pga and the pseudos pectral acceleration psa in regions of the world where ground motion recordings are plentiful such as western north america wna the ground motion prediction equations are obtained using empirical methods in other regions such as eastern north america ena with insufficient ground motion data alternative methods must be used to develop ground motion prediction equations gmpes the hybrid empiri cal method is one such method used to develop ground motion prediction equations in areas with sparse ground motions this method employs the stochastic simulation method to adjust empirical gmpes developed for a region with abundant strong motion recordings in order to estimate strong motion parameters in a region with a sparse database the adjustments take into account differences in the earthquake source wave propagation and site response characteristics between the two regions in this study a hybrid empirical method is used to develop a new gmpe for ena using five new ground motion prediction models developed by the pacific earthquake engineering research center peer for wna a new ena gmpe is derived for a magnitude range of 5 to 8 and closest distances to the fault rupture up to 1000 km ground motion prediction equations are developed for the response spectra pseudoacceleration 5 damped and the pga for hard rock sites in ena the resulting ground motion prediction model developed in this study is compared with two ena ground motion models used in the 2008 national seismic hazard maps as well as with available observed data for ena

beyond threshold hillslopes channel adjustment to base level fall in tectonically active mountain ranges numerous empirical and model based studies argue that in general hillslopes and river channels increase their gradients to accommodate high rates of base level fall to date however few data sets show the dynamic range of both these relationships needed to test theoretical models of hillslope evolution and river incision here we utilize concentrations of 10 be in quartz extracted from river sand on the eastern margin of the tibetan plateau to explore relationships among short term 10 2 10 5 a erosion rate hillslope gradient and channel steepness our data illustrate nonlinear behavior and a threshold in the relationship between erosion rate and mean hillslope gradient confi rming the generalization that hillslopes around the world are limited by slope stability and cease to provide a metric for erosion at high rates 0 2 mm a the relationship between channel steepness index and erosion rate is also nonlinear but channels continue to steepen beyond the point where threshold hillslopes emerge up to at least 0 6 mm a demonstrating that channel steepness is a more reliable topographic metric than mean hillslope gradient for erosion rate and that channels ultimately drive landscape adjustment to increasing rates of base level fall in tectonically active settings

quantifying differential rock uplift rates via stream profile analysis despite intensive research into the coupling between tectonics and surface processes our ability to obtain quantitative information on the rates of tectonic processes from topography remains limited due primarily to a dearth of data with which to test and calibrate process rate laws here we develop a simple theory for the impact of spatially variable rock uplift rate on the concavity of bedrock river profiles application of the analysis to the siwalik hills of central nepal demonstrates that systematic differences in the concavity of channels in this region match the predictions of a stream power incision model and depend on the position and direction of the channel relative to gradients in the vertical component of deformation rate across an active fault bend fold furthermore calibration of model parameters from channel profiles argued to be in steady state with the current climatic and tectonic regime indicates that 1 the ratio of exponents on channel drainage area and slope m n is 0 46 consistent with theoretical predictions 2 the slope exponent is consistent with incision either linearly proportional to shear stress or unit stream power n 0 66 or n 1 respectively and 3 the coefficient of erosion is within the range of previously published estimates mean k 4 3 10 4 m 0 2 yr application of these model parameters to other channels in the siwalik hills yields estimates of spatially variable erosion rates that mimic expected variations in rock uplift rate across a fault bend fold thus the sensitivity of channel gradient to rock uplift rate in this landscape allows us to derive quantitative estimates of spatial variations in erosion rate directly from topographic data

landscape form and millennial erosion rates in the san gabriel mountains ca abstract it has been long hypothesized that topography as well as climate and rock strength exert first order controls on erosion rates here we use detrital cosmogenic 10 be from 50 basins ranging in size from 1 to 150 km 2 to measure millennial erosion rates across the san gabriel mountains in southern california where a strong e w gradient in relief compared to weak variation in precipitation and lithology allow us to isolate the relationship between topographic form and erosion rate our erosion rates range from 35 to 1100 m ma and generally agree with both decadal sediment fluxes and long term exhumation rates inferred from low temperature thermochronometry catchment mean hillslope angle increases with erosion rate until 300 m ma at which point slopes become invariant with erosion rate although this sort of relation has been offered as support for non linear models of soil transport we use 1 d analytical hillslope profiles derived from existing soil transport laws to show that a model with soil flux linear in slope but including a slope stability threshold is indistinguishable from a non linear law within the scatter of our data catchment mean normalized channel steepness index increases monotonically though non linearly with erosion rate throughout the san gabriel mountains even where catchment mean hillslope angles have reached a threshold this non linearity can be mostly accounted for by a stochastic threshold incision model though additional factors likely contribute to the observed relationship between channel steepness and erosion rate these findings substantiate the claim that the normalized channel steepness index is an important topographic metric in active ranges

a mechanistic model for river incision into bedrock by saltating bed load 1 abrasion by bed load is a ubiquitous and sometimes dominant erosional mechanism for fluvial incision into bedrock here we develop a model for bedrock abrasion by saltating bed load wherein the wear rate depends linearly on the flux of impact kinetic energy normal to the bed and on the fraction of the bed that is not armored by transient deposits of alluvium we assume that the extent of alluvial bed cover depends on the ratio of coarse sediment supply to bed load transport capacity particle impact velocity and impact frequency depend on saltation trajectories which can be predicted using empirical functions of excess shear stress the model predicts a nonlinear dependence of bedrock abrasion rate on both sediment supply and transport capacity maximum wear rates occur at moderate relative supply rates due to the tradeoff between the availability of abrasive tools and the partial alluviation of the bedrock bed maximum wear rates also occur at intermediate levels of excess shear stress due to the reduction in impact frequency as grain motion approaches the threshold of suspension measurements of bedrock wear in a laboratory abrasion mill agree well with model predictions and allow calibration of the one free model parameter which relates rock strength to rock resistance to abrasive wear the model results suggest that grain size and sediment supply are fundamental controls on bedrock incision rates not only by bed load abrasion but also by all other mechanisms that require bedrock to be exposed in the channel bed

geomorphology tectonically twisted rivers tracking diffuse shearing deformation of continents is difficult numerical modelling of drainage evolution in the southern alps new zealand suggests that rivers can act as dynamic markers of tectonic deformation over geological timescales

the control mechanisms of erosion and weathering at basin scale from cosmogenic nuclides in river sediment the study of a sample of river sediment enables the determination of spatially averaged denudation rates that provide an exceptional perspective on erosion and weathering processes that have taken place within a landscape these measurements are done with in situ produced cosmogenic nuclides e g 10be 26al mostly in quartz from alluvial sediment cosmogenic nuclides are produced when secondary cosmic rays interact with the very uppermost layer of the earth s surface they are produced within a characteristic depth scale of about 1 m which means that the measured concentrations record an integrated denudation history while material passed through this depth interval depending on the denudation rate the resulting integration time scales are 103 to 105 years and one obtains a robust long term estimate of natural denudation that is relatively insensitive to short term changes the last 10 years have seen significant research activity using these methods and an array of fascinating tectono geomorphologic and geochemical insights are emerging amongst these is the ability to identify the physical and chemical processes with which a landscape responds to tectonic activity or climate change a compilation of world wide denudation rates in non glaciated areas that however does not yet include some of the world s most active mountain belts has resulted in the following findings some of which have been unexpected 1 no obvious relationship between precipitation or mean annual temperature and total denudation is apparent 2 topographic relief alone does not result in high rates of denudation 3 denudation rates are high in areas of landscape rejuvenation that is triggered and controlled by tectonic activity faulting escarpment formation and retreat rifting surface uplift 4 rates of weathering using a combination of cosmogenic nuclides and zirconium normalised cation loss balances co vary primarily with physical erosion rates and much less with temperature or precipitation 5 in some areas of high land use short term rates from river load gauging exceed those from cosmogenic nuclides by several orders of magnitude which serves to highlight the severity of geomorphic change caused by human action in the future the control mechanisms over denudation will be determined on all spatial scales ranging from the single soil section to entire river basins the same analysis can be done back through time on well dated terraces lake records and marine sediment cores which is possible with 10be for the past 1 2 my the rates obtained will be used to develop a quantitative understanding of tectonic geomorphologic and geochemical landscape processes which in turn is a prerequisite to design and calibrate models of the response of landscapes to tectonic climate and anthropogenic forcing

transient convective uplift of an ancient buried landscape sedimentary basins in the north atlantic ocean preserve a record of intermittent uplift during cenozoic times1 these variations in elevation are thought to result from temperature changes within the underlying icelandic mantle plume2 when parts of the european continental shelf were episodically lifted above sea level new landscapes were carved by erosion but these landscapes then subsided and were buried beneath marine sediments3 here we use three dimensional seismic data to reconstruct one of these ancient landscapes that formed off the northwest coast of europe during the palaeocene eocene thermal maximum we identify a drainage network within the landscape and by modelling the profiles of individual rivers within this network we reconstruct the history of surface uplift we show that the landscape was lifted above sea level in a series of three discrete steps of 200 400 m each after about 1 million years of subaerial exposure this landscape was reburied we use the magnitude and duration of uplift to constrain the temperature and velocity of a mantle plume anomaly that drove landscape formation we conclude that pulses of hot chemically depleted mantle material spread out radially beneath the lithospheric plate at velocities of 35 cm yr 1

channel changes in badlands stripping of the vegetation and soil from a 13 hectare site in virginia underlain by coastal plain sediments created a rapidly evolving badland topography two types of channels developed 1 sand bed alluvial channels were graded to transport the bed material load supplied from slope erosion with available runoff but they also generally eroded their beds slowly and 2 steeper bedrock floored channels incised rapidly in bedrock channels the erosion rate was proportional to the 4 9ths power of drainage area and the 2 3rds power of gradient these exponents are consistent with a model in which the erosion rate is proportional to the bed shear during high flows due to rapid mass wasting and reduced runoff the alluvial channels became as much as 50 steeper during the winter than the summer with an attendant yearly cycle of winter aggradation and summer entrenchment the gradients their seasonal variability and their downstream hydraulic geometry were consistent with the predictions of total load transport formulas for sand beds and high loads the hydraulic geometry of alluvial channels in the virginia badlands were similar to that on the morrison formation in the western united states

vegetation cover and topography rather than human disturbance control gully density and sediment production on the chinese loess plateau abstract the factors controlling topsoil erosion rates on the chinese loess plateau clp are currently relatively well understood and topsoil erosion rates can now be relatively accurately estimated this is however not the case for non topsoil erosion sediment production by gullying and landslides while it is well known that these processes produce significant amounts of sediment the factors controlling their intensity and spatial distribution on the clp are less well understood in this study we quantified the contribution of non topsoil erosion to total sediment production on the clp and investigated which factors control spatial and temporal variations in non topsoil erosion we estimated non topsoil erosion rates e nt by comparing the measured average sediment yields of 46 gauged catchments for the 1950 1970 period when soil conservation measures were nearly absent in the area with predicted topsoil erosion rates using a recently developed empirical model in addition gully density was estimated in each catchment using google earth data our results showed that the area weighted average catchment erosion rate e and e nt were 58 60 51 80 and 48 68 49 78 t ha 1 yr 1 respectively for the studied catchments the sediment contribution of non topsoil erosion to total sediment production ranged between ca 0 and 97 with a mean of 70 25 both e and e nt were significantly correlated to longitudinal river slope land use ndvi and gully density however gully density was the only variable explaining a major part of the variance in both e 60 and e nt 57 gully density itself was significantly related to topography and vegetation cover but not to rainfall erosivity importantly gully density was not only related to overall slope steepness but also to the longitudinal slope of the river network and the hypsometric integral suggesting that not only land cover disturbance but also tectonic uplift controls gully density and erosion rates the absence of a clear climate signal both with respect to the variation in gully density and in e can be explained by the overwhelming effect that climate has on vegetation cover our research showed that non topsoil erosion processes are the dominant sediment sources on the clp and are strongly controlled by natural factors the effect of human disturbance on non topsoil erosion processes is far less important than its effect on topsoil erosion given the dominance of non topsoil erosion processes on the clp this suggests that the high sediment production of the clp is mainly attributable to natural factors

knickpoint initiation and distribution within fluvial networks 236 waterfalls in the waipaoa river north island new zealand if knickpoints transmit signals of base level fall in river networks then improvements in our understanding of their retreat rate and basin wide distribution helps constrain the transient response following perturbation many studies of knickpoint retreat focus on the response of trunk streams to base level fall here we examine the response of an entire fluvial network as recorded by 236 active knickpoints distributed within the waipaoa river on the north island of new zealand base level fall within the waipaoa catchment initiated 18 000 years ago in response to a climatically triggered and tectonically exacerbated pulse of incision using observations from field work aerial photo analysis and a digital elevation model dem we study the knickpoint positions within the network we find that 70 of the knickpoints are located at drainage areas between 1 10 5 m 2 and 1 10 6 m 2 and more than half are b1 km upstream of a large change in drainage area for the knickpoints b1 km upstream of large tributary junctions we find that the retreat distances were well correlated with the tributaries drainage areas in order to determine how a pulse of incision distributes itself throughout a fluvial network we develop two simple end member models and compare their behavior to the observed knickpoint distribution in the waipaoa in the first model we propose that a knickpoint initiated at the basin outlet retreats upstream and distributes the signal throughout the network at a rate that is a power law function of drainage area in the second model we propose that knickpoints form near a threshold drainage area below which channels cannot incise with the same efficiency as possible in downstream reaches though neither model addresses the along stream variability in substrate or knickpoint form the misfit between the modeled and the observed knickpoints along stream positions are surprisingly low b1 km 1 25 of the total stream length for knickpoints with drainage areas b1 10 6 m 2 large misfits up to 3 5 km are observed for knickpoints with present day drainage areas greater than 1 10 6 m 2 the large single step in channel elevation that characterizes knickpoints presently observed in tributaries of the waipaoa river may not characterize the base level fall signal that propagated through the trunk streams evidence for progressive rather than instantaneous incision in the trunk streams the knickpoints vicinities to tributary junctions and the equivalent success of the two end member models lead us to conclude that the present positions of the 236 observed knickpoints are largely a consequence of thresholds in channel incision at low drainage areas

coupled numerical analytical approach to landscape evolution modeling the earth s topography is shaped by surface processes that operate on various scales in particular river processes control landscape dynamics over large length scales whereas hillslope processes control the dynamics over smaller length scales this scale separation challenges numerical treatments of landscape evolution that use space discretization large grid spacing cannot account for the dynamics of water divides that control drainage area competition and erosion rate and slope distribution small grid spacing that properly accounts for divide dynamics is computationally inefficient when studying large domains here we propose a new approach for landscape evolution modeling that couples irregular grid based numerical solutions for the large scale fluvial dynamics and continuum based analytical solutions for the small scale fluvial and hillslope dynamics the new approach is implemented in the landscape evolution model dac divide and capture the geometrical and topological characteristics of dac s landscapes show compatibility with those of natural landscapes a comparative study shows that even with large grid spacing dac predictions fit well an analytical solution for divide migration in the presence of horizontal advection of topography in addition dac is used to study some outstanding problems in landscape evolution i the time to steady state is investigated and simulations show that steady state requires much more time to achieve than predicted by fixed area calculations due to divides migration and persistent reorganization of low order streams ii large scale stream captures in a strike slip environment are studied and show a distinct pattern of erosion rates that can be used to identify recent capture events iii three tectono climatic mechanisms that can lead to asymmetric mountains are studied each of the mechanisms produces a distinct morphology and erosion rate distribution application to the southern alps of new zealand suggests that tectonic advection precipitation gradients and non uniform tectonic uplift act together to shape the first order topography of this mountain range copyright 2014 john wiley sons ltd

transient river response captured by channel steepness and its concavity mountain rivers draining tropical regions are known to be great conveyor belts carrying efficientlymore than half of the global sediment flux to the oceans many tropical mountain areas are located in tectonically active belts where the hillslope and stream channel morphology are rapidly evolving in response to changes in base level here we report basin wide denudation rates for an east west transect through the tropical andes hillslope and channel morphology vary systematically fromeast towest reflecting the transition from high relief strongly dissected topography in the escarpment zones into relatively low relief topography in the inter andean valley the spatial pattern of differential denudation rates reflects the transient adjustment of the landscape to rapid river incision following tectonic uplift and river diversion in the inter andean valley upstream of the wave of incision slopes and river channels display a relatively smooth concave up morphology and denudation rates time scale of 104 105 a are consistently low 3 to 200 mm ka in contrast slopes and river channels of rejuvenated basins draining the eastern cordillera are steep to very steep and the studied drainage basins show a wide range of denudation rate values 60 to 400 mm ka that increase systematically with increasing basin mean slope gradient channel steepness and channel convexity drainage basins that are characterised by strong convexities in their river longitudinal profiles systematically have higher denudation rates as such this is one of the first studies that provides field based evidence of a correlation between channel concavity and basin mean denudation rates consistent with process based fluvial incision models

drainage basin responses to climate change recent investigations have shown that the extent of the channel network in some drainage basins is controlled by a threshold for overland flow erosion the sensitivity of such basins to climate change is analyzed using a physically based model of drainage basin evolution the golem model simulates basin evolution under the action of weathering processes hillslope transport and fluvial bedrock erosion and sediment transport results from perturbation analyses reveal that the nature and timescale of basin response depends on the direction of change an increase in runoff intensity or a decrease in vegetation cover will lead to a rapid expansion of the channel network with the resulting increase in sediment supply initially generating aggradation along the main network followed by downcutting as the sediment supply tapers off by contrast a decrease in runoff intensity or an increase in the erosion threshold will lead to a retraction of the active channel network and a much more gradual geomorphic response cyclic changes in runoff intensity are shown to produce aggradational degradational cycles that resemble those observed in the field cyclic variations in runoff also lead to highly punctuated denudation rates with denudation concentrated during periods of increasing runoff intensity and or decreasing vegetation cover the sediment yield from threshold dominated basins may therefore exhibit significant variability in response to relatively subtle environmental changes a finding which underscores the need for caution in interpreting modern sediment yield data

a very efficient o n implicit and parallel method to solve the stream power equation governing fluvial incision and landscape evolution abstract we present a new algorithm to solve the basic stream power equation which governs channel incision and landscape evolution in many geomorphic settings the algorithm is highly efficient because computation time increases linearly with the number of points used to discretize the landscape and is ideally suited to parallelization it is also unconditionally stable because it uses an implicit scheme for the time integration of the landscape evolution equation which means that large time steps can be used without sacrificing accuracy in this paper we describe the algorithm and present results that demonstrate its efficiency and accuracy

geomorphic limits to climate induced increases in topographic relief recognition of the potential for strong dynamic coupling between atmospheric and tectonic processes has sparked intense cross disciplinary investigation and debate on the question of whether tectonics have driven long term climate change or vice versa it has been proposed that climate change might have driven the uplift of mountain summits through an isostatic response to valley incision because isostasy acts to compensate mean elevations the debate hinges on the question of whether climate change can significantly increase topographic relief or more precisely increase the volume of missing mass between summits and ridges here we show that in tectonically active mountain ranges geomorphic constraints allow only a relatively small increase in topographic relief in response to climate change thus although climate change may cause significant increases in denudation rates potentially establishing an important feedback between surficial and crustal processes neither fluvial nor glacial erosion is likely to induce significant isostatic peak uplift

estimating uplift rate histories from river profiles using african examples 1 we describe and apply a method for estimating uplift rate histories from longitudinal river profiles our strategy is divided into three parts first we develop a forward model which calculates river profiles from uplift rate histories height variation along a river profile is controlled by uplift rate and moderated by the erosional process we assume that the erosional process can be represented by a combination of advection and diffusion which are parameterized using four erosional constants second we have posed and solved the geologically more interesting inverse problem which uplift rate history minimizes the misfit between calculated and observed river profiles the inverse algorithm has been tested on synthetic river profiles which demonstrates that uplift rate histories can be reliably retrieved our tests show that the erosional process is dominated by advection i e knickpoint retreat and that changes in lithology and discharge play a secondary role in determining the transient form of a river profile finally we have inverted river profiles from a series of african topographic swells namely the bie south african namibian hoggar and tibesti domes fits between calculated and observed river profiles are excellent calculated uplift rate histories suggest that these domes grew rapidly during the last 30 40 million years uplift rate histories vary significantly from dome to dome but cumulative uplift histories agree closely with independent geologic estimates

knickpoint recession rate and catchment area the case of uplifted rivers in eastern scotland knickpoint behaviour is a key to understanding both the landscape responses to a base level fall and the corresponding sediment fluxes from rejuvenated catchments and must be accommodated in numerical models of large scale landscape evolution knickpoint recession in streams draining to glacio isostatically uplifted shorelines in eastern scotland is used to assess whether knickpoint recession is a function of discharge here represented by its surrogate catchment area knickpoints are identified using ds plots log slope versus log downstream distance a statistically significant power relationship is found between distance of headward recession and catchment area such knickpoint recession data may be used to determine the values of m and n in the stream power law e kamsn the data have too many uncertainties however to judge definitively whether they are consistent with m n 1 bedrock erosion is proportional to stream power and kps should be maintained and propagate headwards or m 0 3 n 0 7 bedrock incision is proportional to shear stress and kps do not propagate but degrade in place by rotation or replacement nonetheless the e scotland m and n values point to the dominance of catchment area discharge in determining knickpoint retreat rates and are therefore more consistent with the stream power law formulation in which bedrock erosion is proportional to stream power copyright 2005 john wiley sons ltd

hillslope and channel evolution in a marine terraced landscape santa cruz california a flight of marine terraces along the central california coastline provides a unique setting for the study of topographic evolution wavecut platforms mantled by 2 6 m of marine terrace cover deposits are separated by 10 50 m tall decaying sea cliffs paleocliff edges become more rounded with age yet the details of the profiles and frequent bedrock exposure on the upper slopes imply weathering limited transport five bedrock stream channels etched through the marine terrace sequence display one to three distinct convexities in their longitudinal profiles detailed hand level surveys of the hillslopes and of the stream channel longitudinal profiles constrain hillslope evolution and channel incision components of a numerical model of landscape evolution we account for regolith production as a function of regolith depth in accord with the field observation that hillslope processes are presently dominated by the activities of burrowing rodents the transport process is taken to be diffusive stream incision is assumed to be controlled by stream power for which we use the surrogate of local drainage area slope product best fits of the numerical model to field data imply hillslope diffusivity is 10 m2 kyr 1 regolith production rate on bare bedrock is 0 3 m kyr 1 and falls off rapidly with regolith cover and the constant controlling the efficiency of stream incision is 5 to 7 10 7m 1 kyr1

tectonic and climatic controls on knickpoint retreat rates and landscape response times 1 the rate at which transient knickpoints propagate through a landscape fundamentally controls the rate of geomorphic response to tectonic and climatic perturbation here we present knickpoint retreat rates upstream of active faults for 19 bedrock catchments in turkey and 11 bedrock catchments in italy where we have very good constraints on both the magnitude and timing of the tectonic perturbation and where climate histories are well documented we show that the knickpoints have average retreat rates of between 0 2 and 2 mm yr for catchments with drainage areas between 6 and 65 km2 and we test whether differences in rock mass strength and catchment size are sufficient to explain this range in retreat rates our analysis suggests that even accounting for these two variables knickpoint propagation velocities differ markedly and we show that channels crossing faults with higher throw rates have knickpoints that are retreating faster the dependence of knickpoint retreat velocity on throw rate is at least as important as catchment drainage area these results indicate counterintuitively that landscapes forced by large amplitude tectonic perturbations will have shorter response times than those perturbed by smaller amplitude changes the link between the knickpoint propagation velocity and throw rate is largely but not completely explained by channel narrowing in areas of high uplift rate channel steepening upstream of the active faults may explain all of the residual dependency of knickpoint retreat rate on fault throw rate but only if the slope exponent n in the standard stream power model is greater than 1 3 however we cannot rule out a role for sediment supply in driving enhanced knickpoint retreat rate in addition to the well documented channel narrowing effect finally we find that mean knickpoints retreat rates in turkey are only half of those in italy for catchments of equivalent size crossing faults with similar throw rates this difference in fluvial response time is accounted for by long term differences in the ratio of precipitation to infiltration in the two areas over the last 1 my

decoupling of erosion and precipitation in the himalayas the hypothesis that abrupt spatial gradients in erosion can cause high strain rates in active orogens has been supported by numerical models that couple erosional processes with lithospheric deformation via gravitational feedbacks1 2 3 most such models invoke a stream power rule in which either increased discharge or steeper channel slopes cause higher erosion rates spatial variations in precipitation and slopes are therefore predicted to correlate with gradients in both erosion rates and crustal strain here we combine observations from a meteorological network across the greater himalaya nepal along with estimates of erosion rates at geologic timescales greater than 100 000 yr from low temperature thermochronometry across a zone of about 20 km length spanning the himalayan crest and encompassing a more than fivefold difference in monsoon precipitation significant spatial variations in geologic erosion rates are not detectable decreased rainfall is not balanced by steeper channels instead additional factors that influence river incision rates such as channel width and sediment concentrations must compensate for decreasing precipitation overall spatially constant erosion is a response to uniform upward tectonic transport of greater himalayan rock above a crustal ramp

an uplift history of crete greece from inverse modeling of longitudinal river profiles we jointly invert cretan drainage networks to determine a temporal and spatial history of regional uplift our model assumes that longitudinal river profiles are controlled by uplift rate history and moderated by the erosional process we have parameterized fluvial erosion using an advective diffusive formulation the inverse model recovers the smoothest uplift rate history that best fits a data set of 250 longitudinal river profiles residual misfit between theoretical and observed river profiles decreases from 18 to 4 during optimization results suggest that crete has been uplifted by 1 2 km during the last 4 ma the central iraklion ridge first became emergent at 4 ma with eastern and western ends of crete emerging 1 ma later maximum uplift rates of 1 1 2 mm yr occurred in central and western crete between 0 and 1 ma this calculated history of uplift is consistent with independent sedimentological stratigraphic and paleontological constraints

minimal climatic control on erosion rates in the sierra nevada california climate is widely thought to regulate erosion rates but the relationships among precipitation temperature and erosion rate have remained speculative because long term erosion rates have been difficult to measure we used cosmogenic nuclides to measure long term erosion rates at climatically diverse sites in the sierra nevada california spanning 20 180 cm yr in annual precipitation and 4 15 8c in mean annual temperature average erosion rates vary by only 2 5 fold across these sites and are not correlated with climate indicating that climate only weakly regulates nonglacial erosion rates in mountainous granitic terrain

dynamic reorganization of river basins river networks evolve as migrating drainage divides reshape river basins and change network topology by capture of river channels we demonstrate that a characteristic metric of river network geometry gauges the horizontal motion of drainage divides assessing this metric throughout a landscape maps the dynamic states of entire river networks revealing diverse conditions drainage divides in the loess plateau of china appear stationary the young topography of taiwan has migrating divides driving adjustment of major basins and rivers draining the ancient landscape of the southeastern united states are reorganizing in response to escarpment retreat and coastal advance the ability to measure the dynamic reorganization of river basins presents opportunities to examine landscape scale interactions among tectonics erosion and ecology

postglacial recession of niagara falls in relation to the great lakes abstract the recessional history of niagara falls in the present niagara gorge during the postglacial period has been a focus of study throughout this century radiocarbon ages of clam shells suggest that niagara falls migrated very slowly around the narrowed gorge section at niagara glen from 10 500 to 5500 yr b p when upper great lakes water bypassed lake erie and flowed to the ottawa river via the outlet at north bay ontario prior to that interval river discharge and recession rates were similar to those at present and similar rates resumed after 5200 yr b p by about 4500 yr b p the present gorge had intersected a buried gorge of the pre late wisconsinan niagara river st davids gorge the sediment derived from the excavated buried valley fill may be present as a distinct marker horizon in the sediments in southwestern lake ontario

cenozoic epeirogeny of the arabian peninsula from drainage modeling it is generally accepted that the arabian peninsula has been uplifted by subcrustal processes positive residual depth anomalies from oceanic crust in the red sea and in the gulf of aden suggest that a region surrounding this peninsula is dynamically supported admittance calculations surface wave tomography studies and receiver function analyses all imply that regional topography is generated and maintained by some combination of mantle convective circulation and lithospheric thickness changes despite these significant advances the spatial and temporal uplift rate history of the arabian peninsula is not well known here we show that a regional uplift rate history can be obtained by jointly inverting 225 longitudinal river profiles that drain this peninsula our strategy assumes that shapes of individual river profiles are controlled by uplift rate history and moderated by erosional processes we used local measurements of incision rate to calibrate the relevant erosional parameters in our inverse algorithm uplift rate is permitted to vary smoothly as a function of space and time but upstream drainage area remains invariant we also assume that knickzone migration is not lithologically controlled implications of these important assumptions have been investigated our results suggest that the arabian peninsula underwent two phases of asymmetric uplift during the last 20 30 ma at rates of 0 05 0 1 mm a 1 the southwestern flank of the peninsula has been uplifted by 1 5 2 5 km regional stratigraphic constraints the age and composition of volcanism paleosol formation incised peneplains emergent marine terraces and thermochronometric measurements corroborate our calculated patterns of uplift progressive development of three domal swells along the western margin of the peninsula is consistent with localized upwelling of hot asthenospheric mantle

expression of active tectonics in erosional landscapes understanding the manner and degree to which topography in active mountain ranges reflects deformation of the earth s surface remains a first order goal of tectonic geomorphology a substantial body of research in the past decade demonstrates that incising channel systems play a central role in setting relationships among topographic relief differential rock uplift rate and climatically modulated erosional efficiency this review provides an introduction to the analysis and interpretation of channel profiles in erosional mountain ranges we show that existing data support theoretical expectations of positive monotonic relationships between channel steepness index a measure of channel gradient normalized for downstream increases in drainage area and erosion rate at equilibrium and that the transient response to perturbations away from equilibrium engenders specific spatial patterns in channel profiles that can be used to infer aspects of the forcing these aspects of channel behavior lay the foundation for a series of case studies that we use to illustrate how focused quantitative analysis of channel morphology can provide insight into the spatial and temporal dynamics of active deformation although the complexities of river response to climate lithology and uplift patterns mean that multiple interpretations of topographic data alone will always possible we show that application of stream profile analysis can be a powerful reconnaissance tool with which to interrogate the rates and patterns of deformation in active mountain belts

factors influencing the recession rate of niagara falls since the 19th century abstract the rate of recession of niagara falls horseshoe and american falls in northeastern north america has been documented since the 19th century it shows a decreasing trend from ca 1 m y 1 a century ago to ca 0 1 m y 1 at present reduction of the flow volume in the niagara river due to diversion into bypassing hydroelectric schemes has often been taken to be the factor responsible but other factors such as changes in the waterfall shape could play a role and call for a quantitative study here we examine the effect of physical factors on the historically varying recession rates of niagara falls using an empirical equation which has previously been proposed based on a non dimensional multiparametric model which incorporates flow volume waterfall shape and bedrock strength the changes in recession rates of niagara falls in the last century are successfully modeled by this empirical equation these changes are caused by variations in flow volume and lip length this result supports the validity of the empirical equation for waterfalls in rivers carrying little transported sediment our analysis also suggests that the decrease in the recession rate of horseshoe falls is related to both artificial reduction in river discharge and natural increase in waterfall lip length whereas that of american falls is solely due to the reduction in flow volume

modeling fluvial incision and transient landscape evolution influence of dynamic channel adjustment 1 channel geometry exerts a fundamental control on fluvial processes recent work has shown that bedrock channel width depends on a number of parameters including channel slope and is not solely a function of drainage area as is commonly assumed the present work represents the first attempt to investigate the consequences of dynamic gradient sensitive channel adjustment for drainage basin evolution we use the channel hillslope integrated landscape development child model to analyze the response of a catchment to a given tectonic perturbation using as a template the topography of a well documented catchment in the footwall of an active normal fault in the apennines italy that is known to be undergoing a transient response to tectonic forcing we show that the observed transient response can be reproduced to first order with a simple detachment limited fluvial incision law transient landscape is characterized by gentler gradients and a shorter response time when dynamic channel adjustment is allowed the differences in predicted channel geometry between the static case width dependent solely on upstream area and dynamic case width dependent on both drainage area and channel slope lead to contrasting landscape morphologies when integrated at the scale of a whole catchment particularly in presence of strong tilting and or pronounced slip rate acceleration our results emphasize the importance of channel width in controlling fluvial processes and landscape evolution they stress the need for using a dynamic hydraulic scaling law when modeling landscape evolution particularly when the relative uplift field is nonuniform

the african landscape through space and time 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

the influence of large landslides on river incision in a transient landscape eastern margin of the tibetan plateau sichuan china deep landscape dissection by the dadu and yalong rivers on the eastern margin of the tibetan plateau has produced high relief narrow river gorges and threshold hillslopes that frequently experience large landslides large landslides inundate river valleys and overwhelm channels with large volumes 10 5 m 3 of coarse material commonly forming stable landslide dams that trigger extensive and prolonged aggradation upstream these observations suggest that strong feedbacks among hillslope processes channel morphology and incision rate are prevalent throughout this landscape and are likely characteristic of transient landscapes experiencing large increases in local relief in general landslide effects are a by product of rapid incision initiated by regional uplift however over timescales relevant to landscape evolution 10 4 yr large landslides can also act as a primary control on channel morphology and longitudinal river profiles inhibiting incision and further preventing the complete adjustment of rivers to regional tectonic climatic and lithologic forcing we explore a probabilistic numerical model to provide a quantitative framework for evaluating how landslides influence bedrock river incision and landscape evolution the time average number of landslide dams along a river course and thus the magnitude of the landslide influence is set by two fundamental timescales the time it takes to erode landslide deposits and erase individual dams and the recurrence interval of large landslides that lead to stable dams stable gradually eroding landslide dams create mixed bedrock alluvial channels with spatial and temporal variations in incision ultimately slowing long term rates of river incision thereby reducing the total amount of incision occurring over a given length of river a stronger landslide effect implies that a higher percentage of channel length is buried by landslide related sediment leading to reduced river incision efficiency the longer it takes a river channel to incise into a landslide dam and remove all landslide related sediment the more control these events have on the evolution of the river profile and landscape evolution this can be the result of slow erosion of stable dams or a higher frequency of large events

solutions of the stream power equation and application to the evolution of river longitudinal profiles 1 erosion by bedrock river channels is commonly modeled with the stream power equation we present a two part approach to solving this nonlinear equation analytically and explore the implications for evolving river profiles first a method for non dimensionalizing the stream power equation transforms river profiles in steady state with respect to uniform uplift into a straight line in dimensionless distance elevation space second a method that tracks the upstream migration of slope patches which are mathematical entities that carry information about downstream river states provides a basis for constructing analytical solutions slope patch analysis explains why the transient morphology of dimensionless river profiles differs fundamentally if the exponent on channel slope n is less than or greater than one and why only concave up migrating knickpoints persist when n 1 at migrating knickpoints slope patches and the information they carry are lost a phenomenon that fundamentally limits the potential for reconstructing tectonic histories from bedrock river profiles stationary knickpoints which can arise from spatially varying uplift rates differ from migrating knickpoints in that slope patches and the information they carry are not lost counterparts to migrating knickpoints called stretch zones are created when closely spaced slope patches spread to form smooth curves in distance elevation space these theoretical results are illustrated with examples from the california king range and the central apennines

climatic control of denudation in the deglaciated landscape of the washington cascades erosion in the washington cascades mountains was dominated by glacier activity until the end of the last glacial maximum when fluvial incision and mass wasting became the dominant drivers an analysis of millennial scale rates of denudation in the range suggest erosion is sensitive both to spatial variations in precipitation and inherited topography

geologic constraints on bedrock river incision using the stream power law denudation rate in unextended terranes is limited by the rate of bedrock channel incision often modeled as work rate on the channel bed by water and sediment or stream power the latter can be generalized as ka m s n where k represents the channel bed s resistance to lowenng whose variation with lithology is unknown a is drainage area a surrogate for discharge s is local slope and m and n are exponents whose values are debated we address these uncertainties by simulating the lowering of ancient river profiles using the finite difference method we vary m n and k to match the evolved profile as closely as possible to the corresponding modern river profile over a time period constrained by the age of the mapped paleoprofiles we find at least two end member incision laws ka 0 3 0 5 s for australian rivers with stable base levels and k f a 0 1 0 2 s n for rivers in kauai subject to abrupt base level change the long term lowering rate on the latter expression is a function of the frequency and magnitude of knickpoint erosion characterized by k f incision patterns from japan and california could follow either expression if they follow the first expression with m 0 4 k varies from 10 7 10 6 m 0 2 yr for granite and metamorphic rocks to 10 5 10 4 m 0 2 yr for volcaniclastic rocks and 10 4 10 2 m 0 2 yr for mudstones this potentially large variation in k with lithology could drive strong variability in the rate of long term landscape change including denudation rate and sediment yield

finite volume two dimensional unsteady flow model for river basins the paper presents a two dimensional unsteady flow model rbfvm 2d based on the finite volume method with a combination of unstructured triangular and quadrilateral grids in a river basin system the attractive feature of this model is that it calculate of the mass and momentum flux across each side of elements as a riemann problem which is solved using the osher scheme this feature enables this model to deal with the wetting and drying processes for flood plain and wetland studies dam breaking phenomena involving discontinuous flows subcritical and supercritical flows and other cases the computations of tributary inflows and regulated flows through gates weirs and culverts or bridges are also included sample applications of this model to two dam break problems showed fairly satisfactory results also this model was applied to a portion of the kissimmee river basin in florida for flow simulations and the results agreed well with the field and laboratory data in a physical model study of this ri

a statistical framework to quantify spatial variation in channel gradients using the integral method of channel profile analysis 1 we present a statistical technique for analyzing longitudinal channel profiles our technique is based on the integral approach to channel analysis drainage area is integrated over flow distance to produce a transformed coordinate which has dimensions of length assuming that profile geometry is conditioned by the stream power law defined as e kamsn where e is erosion rate k is erodibility a is drainage area s is channel gradient and m and n are constants the slope of a transformed profile in elevation space should reflect the ratio of erosion rate to channel erodibility raised to a power 1 n this quantity is often referred to as the channel steepness and represents channel slope normalized for drainage area our technique tests all possible contiguous segments in the channel network to identify the most likely locations where channel steepness changes and also identifies the most likely m n ratio the technique identifies locations where either erodibility or erosion rates are most likely to be changing tests on a simulated landscape demonstrate that the technique can accurately retrieve both the m n ratio and the correct number and location of segments eroding at different rates where model assumptions apply tests on natural landscapes illustrate how the method can distinguish between spurious channel convexities due to incorrect selection of the m n ratio from those which are candidates for changing erodibility or erosion rates we also show how given erosion or uplift rate constraints the method can be used to constrain the slope exponent n

tectonics from fluvial topography using formal linear inversion theory and applications to the inyo mountains california tectonic activity generates topography and the variability of tectonic forcing is responsible for topographic patterns and variability of relief in fluvial landscapes despite this basic relation the inverse problem by which features of the topography are used for inferring tectonic uplift rates has proven challenging here we develop formal linear inversion schemes to infer a record of the rate of relative uplift as a function of space and time from the long profiles of rivers the relative uplift rate is the difference between the rates of rock uplift and of the base level change the inversion schemes are based on a closed form analytic solution to the transient linear stream power model and to increase model resolution they make use of the multiplicity of information made available by multiple rivers and their tributaries the distribution of the fluvial response time to tectonic perturbations is a key component of the inversion scheme as this determines which tectonic events are preserved in the topography we develop two inversion parameterizations that differ in their assumptions about the tectonic forcing space invariant and time space variability with an assumed spatial distribution the inversion schemes are applied to the inyo mountains an uplifted block along the western boundary of the basin and range province in california inversion results indicate that the range has been experiencing an acceleration of the relative uplift in the past 2 3 ma we use the inversion results to constrain the paleotopography and paleo erosion rate along the range and to recover the throw rate history along the fault that bounds the inyo range

implications of sediment flux dependent river incision models for landscape evolution 1 developing a quantitative understanding of the factors that control the rate of river incision into bedrock is critical to studies of landscape evolution and the linkages between climate erosion and tectonics current models of long term river network incision differ significantly in their treatment of the role of sediment flux we analyze the implications of various sediment flux dependent incision models for large scale topography in an attempt 1 to identify quantifiable and diagnostic differences between models that could be detected from topographic data or from the transient responses of perturbed systems and 2 to explain the apparent ubiquity of mixed bedrock alluvial channels in active orogens although certain forms of the various models can be discarded as inconsistent with morphological data we find that the relative intrinsic concavity indices of detachment and transport limited systems defined herein largely dictate whether the various models can be tied to distinctive steady state morphologies preliminary data suggest that no such diagnostic differences may exist and other methods must be developed to test models accordingly we develop and explore differences in the scaling behavior of topographic relief and the extent of detachment versus transport limited channels as a function of rock uplift rate that may allow discrimination among various models further we explore potentially diagnostic differences in the rates and patterns of transient channel response to changes in rock uplift rate in addition to general differences between detachment and transport limited systems our analysis identifies an interesting hysteresis in landscape evolution hybrid channels at the threshold between detachment and transport limited conditions are expected to act as detachment limited systems in response to an increase in rock uplift rate or base level fall and as transport limited systems in response to a decrease in rock uplift rate especially during postorogenic topographic decline the analyses presented set the stage for field studies designed to test quantitatively the various river incision models that have been proposed

climatic control of bedrock river incision bedrock river incision drives the development of much of earth s surface topography and thereby shapes the structure of mountain belts and modulates earth s habitability through its effects on soil erosion nutrient fluxes and global climate although it has long been expected that river incision rates should depend strongly on precipitation rates quantifying the effects of precipitation rates on bedrock river incision rates has proved difficult partly because river incision rates are difficult to measure and partly because non climatic factors can obscure climatic effects at sites where river incision rates have been measured here we present measurements of river incision rates across one of earth s steepest rainfall gradients which show that precipitation rates do indeed influence long term bedrock river incision rates we apply a widely used empirical law for bedrock river incision to a series of rivers on the hawaiian island of kaua i where mean annual precipitation ranges from 0 5 metres to 9 5 metres ref 12 over 70 per cent of the global range and river incision rates averaged over millions of years can be inferred from the depth of river canyons and the age of the volcanic bedrock both a time averaged analysis and numerical modelling of transient river incision reveal that the long term efficiency of bedrock river incision across kaua i is positively correlated with upstream averaged mean annual precipitation rates we provide theoretical context for this result by demonstrating that our measurements are consistent with a linear dependence of river incision rates on stream power the rate of energy expenditure by the flow on the riverbed these observations provide rare empirical evidence for the long proposed coupling between climate and river incision suggesting that previously proposed feedbacks among topography climate and tectonics may occur