modeling depth distributions of overland flows smith m w cox n j bracken l j 2011 modeling depth distributions of overland flows geomorphology 125 3 402 413

physically based modeling of bedrock incision by abrasion plucking and macroabrasion 1 many important insights into the dynamic coupling among climate erosion and tectonics in mountain areas have derived from several numerical models of the past few decades which include descriptions of bedrock incision however many questions regarding incision processes and morphology of bedrock streams still remain unanswered a more mechanistically based incision model is needed as a component to study landscape evolution major bedrock incision processes include among other mechanisms abrasion by bed load plucking and macroabrasion a process of fracturing of the bedrock into pluckable sizes mediated by particle impacts the purpose of this paper is to develop a physically based model of bedrock incision that includes all three processes mentioned above to build the model we start by developing a theory of abrasion plucking and macroabrasion mechanisms we then incorporate hydrology the evaluation of boundary shear stress capacity transport an entrainment relation for pluckable particles a routing model linking in stream sediment and hillslopes a formulation for alluvial channel coverage a channel width relation hack s law and exner equation into the model so that we can simulate the evolution of bedrock channels the model successfully simulates various features of bed elevation profiles of natural bedrock rivers under a variety of input or boundary conditions the results also illustrate that knickpoints found in bedrock rivers may be autogenic in addition to being driven by base level fall and lithologic changes this supports the concept that bedrock incision by knickpoint migration may be an integral part of normal incision processes the model is expected to improve the current understanding of the linkage among physically meaningful input parameters the physics of incision process and morphological changes in bedrock streams

scaling relationships of channel networks at large scales examples from two large magnitude watersheds in brittany france abstract we present a statistical analysis on two watersheds in french brittany whose drainage areas are about 10 000 and 2000 km 2 the channel system was analysed from the digitised blue lines of the 1 100 000 map and from a 250 m dem link lengths follow an exponential distribution consistent with the markovian model of channel branching proposed by smart 1968 the departure from the exponential distribution for small lengths that has been extensively discussed before results from a statistical effect due to the finite number of channels and junctions the strahler topology applied on channels defines a self similar organisation whose similarity dimension is about 1 7 that is clearly smaller than the value of 2 expected for a random organisation the similarity dimension is consistent with an independent measurement of the horton ratios of stream numbers and lengths the variables defined by an upstream integral drainage area mainstream length upstream length follow power law distributions limited at large scales by a finite size effect due to the finite area of the watersheds a special emphasis is given to the exponent of the drainage area a a that has been previously discussed in the context of different aggregation models relevant to channel network growth we show that a a is consistent with 4 3 a value that was obtained and analytically demonstrated from directed random walk aggregating models inspired by the model of scheidegger 1967 the drainage density and mainstream length present no simple scaling with area except at large areas where they tend to trivial values constant density and square root of drainage area respectively these asymptotic limits necessarily imply that the space dimension of channel networks is 2 equal to the embedding space the limits are reached for drainage areas larger than 100 km 2 for smaller areas the asymptotic limit represents either a lower bound drainage density or an upper bound mainstream length of the distributions because the fluctuations of the drainage density slowly converge to a finite limit the system could be adequately described as a fat fractal where the average drainage density is the sum of a constant plus a fluctuation decreasing as a power law with integrating area a fat fractal hypothesis could explain why the similarity dimension is not equal to the fractal capacity dimension as it is for thin fractals the physical consequences are not yet really understood but we draw an analogy with a directed aggregating system where the growth process involves both stochastic and deterministic growth these models are known to be fat fractals and the deterministic growth which constitutes a fundamental ingredient of these models could be attributed in river systems to the role of terrestrial gravity

impacts of surface elevation on the growth and scaling properties of simulated river networks we investigate the connection between surface elevation and the growth and scaling of river networks three planar models scheidegger eden and invasion percolation are first considered these models develop aggregating networks according to stochastic rules but do not simulate erosion because the network growth is independent of the surface elevation we show that none of these planar growth models produces scaling results consistent with observations for natural river basins we then modify the models to include elevation simulating the effects of fluvial erosion by enforcing the slope area relationship the resulting configurations have scaling properties that still depend on the model scheidegger eden or invasion percolation but are closer to natural river networks when compared with those from the planar growth rules we conclude that inclusion of the vertical dimension in these three models is critical for explaining the formation and regularities of fluvial networks c 2001 elsevier science bn all rights reserved

generation of complex karstic conduit networks with a hydrochemical model in this paper we present a hydro chemical model that can be used to generate plausible karstic conduit networks that honor what is known about geology hydrology and topography of a karst system to make the model applicable to a range of natural karst systems we introduce a flexible and physically realistic flow boundary condition along the land surface moreover whereas comparable existing speleogenesis models use an explicit reactive transport scheme we propose an implicit reactive transport scheme to permit a coarser spatial discretization of the conduit cells an application to a real karst system illustrates that the model can generate a realistic karstic network that reproduces observed hydrologic behavior in terms of current spring flow rates regional hydraulic head field as well as average groundwater residence times our model provides a useful tool to generate ensembles of possible karstic conduit networks that may be used within a stochastic framework to analyze flow and transport prediction uncertainty associated with a lack of knowledge about network geometry

gully processes and gully dynamics this synthetic review of gully morphology and genesis focuses on incised semi permanent gully systems rather than on shallow ephemeral gullies it examines the conditions for gully formation a sharp step to initiate a headcut a sufficiently low effective bedload fraction to evacuate eroded material and the potential to maintain steep sidewalls usually dominated by mass movement processes gully formation is also favoured by an indurated surface layer which maintains steep sideslopes often with armouring material from the capping layer and a sharp headcut which does not diffuse away two different approaches towards the areal modelling of gully system development agree in treating the ratio of advective channel to diffusive sideslope processes as a key determinant of the morphology of a gully system as it evolves implications for gully prevention and remediation are briefly discussed copyright 2009 john wiley sons ltd

early oligocene vegetation and climate of southwestern china inferred from palynology abstract the early oligocene represents the beginning of the modern icehouse world to better understand how vegetation and climate changed during this period we reconstruct quantitively the early oligocene vegetation and climate by analyzing fossil spore and pollen assemblages from luhe basin yunnan province in southwestern china the reconstructed paleoclimate using bioclimatic analysis shows that the mean annual temperature mat ranged from 14 4 to 15 4 c the mean annual precipitation map was 1070 1 1297 8 mm and the range of mean temperature of coldest quarter mtcq was 6 7 to 7 c lower than that of the present day 9 3 c the reconstructed regional vegetation indicates a deciduous broadleaved forest mixed with evergreen broadleaved elements considering other paleogene floras in yunnan deciduous broadleaved elements dominated in this area from the late eocene to the early oligocene the paleoclimate reconstruction suggests that this vegetation composition may have been controlled mainly by cold winter temperatures

self organization and scaling relationships of evolving river networks the power spectra s of linear transects of earth s topography is often observed to be a power law function of wave number k with exponent close to 2 s k k 2 in addition river networks are fractal trees that satisfy several power law relationships between their morphologic components a model equation for the evolution of earth s topography by transport limited erosional processes which produces fractal topography and fractal river networks is presented and its solutions are compared in detail to real topography the model is the diffusion equation for sediment transport on hillslopes and channels with the diffusivity constant on hillslopes and proportional to the three halves power of discharge in channels the dependence of diffusivity on discharge is consistent with sediment rating curves we study the model in two ways in the first analysis the diffusivity is parameterized as a function of elevation and a taylor expansion procedure is carried out to obtain a differential equation for the landform elevation which includes the spatially variable diffusivity to first order in the elevation the solution to this equation is a self affine or fractal surface with linear transects that have power spectra s k k 1 8 independent of the age of the topography consistent with observations of real topography the hypsometry produced by the model equation is skewed such that lowlands make up a larger fraction of the total area than highlands as observed in real topography in the second analysis we include river networks explicitly in a numerical simulation by calculating the discharge at every point we characterize the morphology of real river basins with five independent scaling relations between six morphometric variables scaling exponents are calculated for seven river networks from a variety of tectonic environments using high quality digital elevation models river networks formed in the model match the observed scaling laws and satisfy tokunaga side branching statistics

faunal turnovers of palaeogene mammals from the mongolian plateau most orders and many families of modern mammals were established during the palaeogene mammalian evolution during this period of time has been correlated with global climatic events1 2 3 4 although the timing mode and scale of such a climate evolution link remain debatable1 5 6 the palaeogene global climate was step punctuated by a warming across the palaeocene eocene boundary about 55 myr ago and a cool off throughout the late eocene and early oligocene epochs1 2 7 8 9 10 the most severe cooling was at 33 5 myr slightly after the eocene oligocene boundary and was characterized by a drop in the mean annual temperature and by changes in vegetation from eocene dense forests to oligocene more open country5 here we analyse 33 palaeogene mammal faunas from the mongolian plateau of china and mongolia there is a distinct pattern of faunal turnovers perissodactyl dominant faunas of the eocene were abruptly replaced by rodent lagomorph dominant faunas of the oligocene we interpret the turnovers as having been effected by global climatic shifts and name the prominent biotic reorganization across the eocene oligocene boundary the mongolian remodelling which correlates to the european grande coupure

an invasion percolation model of drainage network evolution stream networks evolve by headward growth and branching away from escarpments such as rift margins the structure of these networks and their topographic relief are known to be fractal1 3 but no model so far has been able to generate the observed scaling properties here i present a statistical model of network growth in which stream heads branch and propagate at a rate that depends only on the local strength of the substrate this model corresponds to the process of invasion percolation4 with the added requirement of self avoidance it is a self organized critical system5 with properties similar to those of standard percolation models6 a description based on self avoiding invasion percolation reproduces the known scaling behaviour of stream networks and may provide a valuable tool for delineation of drainage patterns from digital topographic data sets7 8

a variscan pressure temperature time path for the n e mont blanc massif the northeastern portion of the mont blanc massif in western switzerland is predominantly comprised of the granitic rocks of the mont blanc intrusive suite and the mont blanc basement gneisses within these metamorphic rocks are a variety of sub economic fe skarns the mineral assemblages and fluid inclusions from these rocks have been used to derive age pressure temperature and fluid composition constraints for two variscan events metamorphic hornblendes within the assemblages from the basement amphibolites and iron skarns have been dated using 40ar 39ar and indicate that these metamorphic events have a minimum age of approximately 334 ma garnet hornblende plagioclase thermobarometry and stable isotope data obtained from the basement amphibolites are consistent with metamorphic temperatures in the range 515 to 580 c and pressures ranging from 5 to 8 kbar garnet hornblende magnetite thermobarometry and fluid inclusion studies indicate that the iron skarns formed at slightly lower temperatures ranging from 400 to 500 c in the presence of saline fluids at formational pressures similar to those experienced by the basement amphibolites late paleozoic minimum uplift rates and geothermal gradients calculated using these data and the presence of ladinien ichnofossils are on the order of 0 32 mm year and 20 c km respectively these uplift rates and geothermal gradients differ from those obtained from the neighbouring aiguilles rouges massif and indicate that these two massifs experienced different metamorphic conditions during the carboniferous and permian periods during the early to late carboniferous period the relative depths of the two massifs were reversed with the aiguilles rouges being initially unroofed at a much greater rate than the mont blanc but experiencing relatively slower uplift rates near the termination of the variscan orogeny

catchment drainage network scaling laws found experimentally in overland flow morphologies the scaling relation between the drainage area and stream length hack s law along with exceedance probabilities of drainage area discharge and upstream flow network length is well known for channelized fluvial regions we report here on a laboratory experiment on an eroding unconsolidated sediment for which no channeling occurred laser scanning was used to capture the morphological evolution of the sediment high intensity spatially nonuniform rainfall ensured that the morphology changed substantially over the 16 hr experiment based on the surface scans and precipitation distribution overland flow was estimated with the d8 algorithm which outputs a flow network that was analyzed statistically the above mentioned scaling and exceedance probability relationships for this overland flow network are the same as those found for large scale catchments and for laboratory experiments with observable channels in addition the scaling laws were temporally invariant even though the network dynamically changed over the course of experiment

normal fault control on bedrock channel incision and sediment supply insights from numerical modeling 1 the evolution of footwall drainage basins sediment supply and hanging wall stratigraphy in rift basins is investigated using a coupled numerical model of detachment limited stream network evolution and coarse grained fan delta deposition the response of bedrock channel networks to repeated footwall uplift events leads to increasing sediment supply over tens of thousands of years as the networks initiate and then expand followed by relatively constant sediment supply as the stream networks reach their maximum spatial extent the distinct time lag between the onset of tectonic activity and attainment of maximum sediment supply leads to stratigraphies that are initially aggradational and then progradational much of the variation in sediment supply is the product of the complex response and reorganization of the stream networks to faulting related perturbations and is not directly related to specific faulting events increasing fault displacement drives the system toward a new steady state with a higher sediment supply but is initially expressed as a retrogradation as sediment supply lags behind increased displacement the converse is true for a decrease in fault displacement which is initially expressed as progradation continual stochastic variation in recurrence interval leads to a system that does not achieve a steady state and as a result exhibits continual variation in sediment supply the model results emphasize the local tectonic controls on stratigraphic architectures developed within extensional basins and the complex manner in which stream network growth and response to tectonic activity can be expressed in the stratigraphic record

the geological evolution of the tibetan plateau the geological evolution of the tibetan plateau is best viewed in a context broader than the india eurasia collision zone after collision about 50 million years ago crust was shortened in western and central tibet while large fragments of lithosphere moved from the collision zone toward areas of trench rollback in the western pacific and indonesia cessation of rapid pacific trench migration 15 to 20 million years ago coincided with a slowing of fragment extrusion beyond the plateau and probably contributed to the onset of rapid surface uplift and crustal thickening in eastern tibet the latter appear to result from rapid eastward flow of the deep crust probably within crustal channels imaged seismically beneath eastern tibet these events mark a transition to the modern structural system that currently accommodates deformation within tibet

cluster growth modeling of plateau erosion the pattern of erosion of a plateau along an escarpment may be modeled using cluster growth techniques recently popularized in models of drainage network evolution if erosion on the scarp takes place in discrete events at rates subject to local substrate strength the whole range of behavior is described by a combination of three cluster growth mechanisms invasion percolation eden growth and diffusion limited aggregation dla these model the relative importance of preexisting substrate strength background weathering and seepage weathering and erosion respectively the rate of seepage processes is determined by the efflux of groundwater at the plateau margin which in turn is determined by the pressure field in the plateau aquifer if this process acted alone it would produce erosion patterns in the form of laplacian fractals with groundwater recharge from a distant source or poissonian fractals with groundwater recharge uniform over the plateau dla is used to mimic the laplacian or poissonian potential field and the corresponding seepage growth process the scaling structure of clusters grown by pure dla invasion percolation or eden growth is well known this study presents a model which combines all three growth mechanisms for the first time mixed growth processes create clusters with different scaling properties and morphologies over distinct length scale ranges and this is demonstrable in natural examples of plateau erosion

a diffusion limited aggregation model for the evolution of drainage networks abstract we propose a modified diffusion limited aggregation dla model for the evolution of fluvial drainage networks random walkers are introduced randomly on a grid and each two dimensional random walk proceeds until the walker finds a drainage network on which to accrete this model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages the model also predicts statistical features which agree with actual networks including the frequency order bifurcation ratio r b 3 98 and the stream length order r r 2 09 using the definition of network fractal dimension d logr b logr r we find that our dla model gives d 1 87 near the observed range of d 1 80 1 85

chaos fractals nonlinear phenomena in earth sciences many problems in geophysics can be solved using linear equations examples include seismic waves the earth s gravity and magnetic field and problems involving heat flow and elasticity however other problems are essentially non linear the classic example is fluid turbulence in the past twenty years major advances have been made in the understanding of nonlinear problems in the past four years many of these advances have been applied to geophysical problems

fracking in tight shales what is it what does it accomplish and what are its consequences fracking is a popular term referring to hydraulic fracturing when it is used to extract hydrocarbons we distinguish between low volume traditional fracking and the high volume modern fracking used to recover large volumes of hydrocarbons from shales shales are fine grained rocks with low granular permeabilities during the formation of oil and gas large fluid pressures are generated these pressures result in natural fracking and the resulting fracture permeability allows oil and gas to escape reducing the fluid pressures these fractures may subsequently be sealed by mineral deposition resulting in tight shale formations the objective of modern fracking is to reopen these fractures and or create new fractures on a wide range of scales modern fracking has had a major impact on the availability of oil and gas globally however there are serious environmental objections to modern fracking which should be weighed carefully against its benefits

tectonic interpretation of transient stage erosion rates at different spatial scales in an uplifting block 1 we explore the extent to which it is possible to convert erosion rate data into uplift rate or erosion laws using a landscape evolution model transient stages of topography and erosion rates of a block uplifting at a constant rate are investigated at different spatial scales for a constant climate and for various erosion laws and initial topographies we identify three main model types for the evolution of the mountain scale mean erosion rate linear type sigmoid type and exponential type linear type models are obtained for topographies without drainage system reorganization in which river incision rates never exceed the uplift rate and stepped river terraces converge upstream in sigmoid type and exponential type models typically detachment limited or transport limited models with a significant transport threshold drainage growth lasts a long time and correspond to more than linear transport laws in water discharge and slope in exponential type models the mean erosion rate passes through a maximum that is higher than the rock uplift rate this happens when the time taken to connect the drainage network exceeds half the total response time to reach dynamic equilibrium river incision rates can be much greater than the uplift rate in both cases in the exponential type model river terraces converge downstream observations of a mountain in the gobi altay range in mongolia support the exponential type model this suggests that the erosion of this mountain is either detachment limited or transport limited with a significant transport threshold this study shows that drainage growth could explain differences in erosion rate measurements on different spatial scales in a catchment

vegetation and climatic changes of sw china in response to the uplift of tibetan plateau abstract to understand the vegetation succession and climatic changes at the southeastern margin of the tibetan plateau in the neogene we reconstructed the middle miocene vegetation and climate based on palynological data from four localities which are at different latitudes along the ailao mountains in yunnan southwest china the palynological assemblages suggest that the vegetation there was composed of mixed evergreen and deciduous broad leaved forests growing under subtropical conditions based on the palynological data the palaeoclimatic parameters from the four localities are established the new parameters were compared with those of the late miocene of the late pliocene and of today the comparison revealed that the temperatures were obviously lower in the middle miocene than they are today this suggested that the ailao mountains were not high enough to block the asian winter monsoon in the middle miocene the middle miocene vegetation at the southeastern edge of the tibetan plateau was also compared to that of central tibet it would appear that the palaeoclimate at the southeastern edge of the tibetan plateau was warmer and wetter than in central tibet in contrast to the neogene cooling in central europe the climate at the southeastern edge of the tibetan plateau has gradually warmed since the middle miocene this phenomenon was most likely caused by the uplift of the tibetan plateau which has succeeded in blocking the asian winter monsoon since the middle miocene