Diagnosing peak-discharge power laws observed in rainfall–runoff events in Goodwin Creek experimental watershed

Observations from the Goodwin Creek experimental watershed (GCEW), Mississippi show that peak-discharge Q(A) and drainage area A are related, on average, by a power law or scaling relationship, Q(A) = αA^θ, during single rainfall–runoff events. Observations also show that α and θ change between events, and, based on a recent analysis of 148 events, observations indicate that α and θ change because of corresponding changes in the depth, duration, and spatial variability of excess-rainfall. To improve our physical understanding of these observations, a 5-step framework for diagnosing observed power laws, or other space-time patterns in a basin, is articulated and applied to GCEW using a combination of analysis and numerical simulations. Diagnostic results indicate how the power laws are connected to physical conditions and processes. Derived expressions for α and θ show that if excess-rainfall depth is fixed then there is a decreasing concave relationship between α and excess-rainfall duration, and an increasing and slightly convex relationship between θ and excess rainfall duration. These trends are consistent with observations only when hillslope velocity v_h is given a physically realistic value near 0.1 m/s. If v_h ? 0.1 m/s, then the predicted trends deviate from observed trends. Results also suggest that trends in α and θ can be impacted by the dependence of v_h and link velocity v_l on excess-rainfall rate.     

Parametric study of a physically-based,plot-scale hillslope hydrological model through virtual experiments

Abstract

A physically-based hillslope hydrological model with shallow overland flow and rapid subsurface stormflow components was developed and calibrated using field experiments conducted on a preferential path nested hillslope in northeast India. Virtual experiments were carried out to perform sensitivity analysis of the model using the automated parameter estimation (PEST) algorithm. Different physical parameters of the model were varied to study the resulting effects on overland flow and subsurface stormflow responses from the theoretical hillslopes. It was observed that topographical shapes had significant effects on overland flow hydrographs. The slope profiles, surface storage, relief, rainfall intensity and infiltration rates primarily controlled the overland flow response of the hillslopes. Prompt subsurface stormflow responses were mainly dominated by lateral preferential flow, as soil matrix flow rates were very slow. Rainfall intensity and soil macropore structures were the most influential parameters on subsurface stormflow. The number of connected soil macropores was a more sensitive parameter than the size of macropores. In hillslopes with highly active vertical and lateral preferential pathways, saturation excess overland flow was not evident. However, saturation excess overland flow was generated if the lateral macropores were disconnected. Under such conditions, rainfall intensity, duration and preferential flow rate governed the process of saturation excess overland flow generation from hillslopes.

Editor D. Koutsoyiannis; Associate editor C. Perrin     

On the interpolation of volumetric water content in research catchments

Digital Soil Mapping (DSM) is widely used in the environmental sciences because of its accuracy and efficiency in producing soil maps compared to the traditional soil mapping. Numerous studies have investigated how the sampling density and the interpolation process of data points affect the prediction quality. While, the interpolation process is straight forward for primary attributes such as soil gravimetric water content (θ_g) and soil bulk density (ρ_b), the DSM of volumetric water content (θ_v), the product of θ_g by ρ_b, may either involve direct interpolations of θ_v (approach 1) or independent interpolation of ρ_b and θ_g data points and subsequent multiplication of ρ_b and θ_g maps (approach 2). The main objective of this study was to compare the accuracy of these two mapping approaches for θ_v. A 23 ha grassland catchment in KwaZulu-Natal, South Africa was selected for this study. A total of 317 data points were randomly selected and sampled during the dry season in the topsoil (0–0.05 m) for θ_g by ρ_b estimation. Data points were interpolated following approaches 1 and 2, and using inverse distance weighting with 3 or 12 neighboring points (IDW3; IDW12), regular spline with tension (RST) and ordinary kriging (OK). Based on an independent validation set of 70 data points, OK was the best interpolator for ρ_b (mean absolute error, MAE of 0.081 g cm⁻³), while θ_g was best estimated using IDW12 (MAE = 1.697%) and θ_v by IDW3 (MAE = 1.814%). It was found that approach 1 underestimated θ_v. Approach 2 tended to overestimate θ_v, but reduced the prediction bias by an average of 37% and only improved the prediction accuracy by 1.3% compared to approach 1. Such a great benefit of approach 2 (i.e., the subsequent multiplication of interpolated maps of primary variables) was unexpected considering that a higher sampling density (∼14 data point ha⁻¹ in the present study) tends to minimize the differences between interpolations techniques and approaches. In the context of much lower sampling densities, as generally encountered in environmental studies, one can thus expect approach 2 to yield significantly greater accuracy than approach 1. This approach 2 seems promising and can be further tested for DSM of other secondary variables.     

Correlations between electrical and elastic properties of solid–liquid composites with interfacial energy-controlled equilibrium microstructures

Electrical conductivity and seismic velocity are studied for plausible pore geometries in the Earth's interior for reliable quantitative analysis of experimental data such as seismic tomography and magnetotelluric explorations. Electrical conductivity of a two-phase system with equilibrium, interfacial energy-controlled phase geometry is calculated for the dihedral angles θ = 40°–100° that are typical for rock–aqueous fluid and θ = 20°–60° for rock–melt systems of lower crust and upper mantle for the case of tetrakaidecahedral grains. Electrical conductivity vs. seismic velocity correlations are acquired by combining of the simulated electrical conductivities with the seismic velocity calculated with the help of equilibrium geometry model Takei [Takei, Y., Effect of pore geometry on V_P/V_S: From equilibrium geometry to crack. J. Geophys. Res. 107 (2002): 10.1029/2001JB000522.] for the same pore geometries. The results show that electrical conductivity gradually decreases reaching zero when seismic velocities reach seismic velocities of intact rock for rock–melt systems, while for rock–aqueous fluid systems with θ ≥ 60° conductivity drops to zero at velocities up to 10% smaller. This can explain the seeming discrepancy of the low seismic velocity region, attributed to the high fluid fraction, and the low electrical conductivity of the same region, which is sometimes faced at collocated electromagnetic and seismic experiments.     

A similarity approach to determine response times to steady-state saturation in landscapes

Relationships describing response times for landscape saturation and subsurface flow for idealised hillslopes after a change in water balance are derived in terms of similarity parameters given by their topographic, soil and climatic attributes. The study was carried out under a set of specific assumptions.The work quantitatively describes effects of each of these attributes on travel time. For example, divergent hillslopes can exhibit travel times that are double those of convergent hillslopes, and concave slopes tend to have lower travel times than planar or convex slopes. It is shown that the hillslope travel time T is dependent on hillslope length L, hydraulic conductivity K and slope S such that T = f(L/KS, B, CR, Δq/smd) and if saturation does not occur in the lower reaches of a hillslope, this can be simplified to T = f(L/KS, B). Here, Δq is change in net external flux and smd is soil moisture deficit; CR and B are the convergence ratio and profile factor respectively. The relative importance of these attributes on response time is discussed.It is shown that subsurface flow hydrographs of simple hillslopes of different scale, derived numerically, can be collapsed into a single curve by normalising them by means of a form of response time, the time constant.Results from the analytical derivation were compared with numerical analysis with good agreement. The theory was applied to a natural catchment using observed data from a bushfire event. Comparison of analytically calculated response time with observed response time for the event showed a large discrepancy. The reason is discussed.     

The role of run-on for overland flow and the characteristics of runoff generation in the Loess Plateau,China

Abstract

The Loess Plateau in China is overlain by deep and loose soil. As in other semi-arid regions, convective precipitation produces storms, typically of short duration, relatively high intensity and limited areal extent. Infiltration excess (Hortonian mechanism) of precipitation is conventionally assumed to be more prominent than saturation excess (Dunne mechanism) for storm runoff generation. This assumption is true at a point during the storm. However, the runoff generation mechanism is altered when the runoff is conditioned by a lateral redistribution movement of water, i.e. run-on, as the spatial scale increases. In the Loess Plateau, the effects of run-on may be significant, because of the deep and loose surface soil layer. In this study, the role of run-on for overland flow in the Upper Wei River basin, located in the Loess Plateau, is evaluated by means of a simple numerical model at the hillslope scale. The results show that almost all the Hortonian overland flow infiltrates into the soil along the flat hillslope and dry gully before it reaches the river channel. Most of the runoff is generated from the saturated soil near the river channel and from the subsurface. The run-on process takes much longer than the infiltration, facilitating rainfall–runoff modelling at a daily time step. A hydrological model is employed to investigate the characteristics of runoff generation in the Upper Wei River basin. The analysis shows that the subsurface flow contribution to total streamflow is more than 53% from October to March, while the overland flow contribution exceeds 72% from April to September.

Editor D. Koutsoyiannis; Associate editor Dawen Yang

Citation Liu, D.F., Tian, F.Q., Hu, H.C., and Hu, H.P., 2012. The role of run-on for overland flow and the characteristics of runoff generation in the Loess Plateau, China. Hydrological Sciences Journal, 57 (6), 1107–1117.     

Climate‐invariant area–slope relations in channel heads initiated by surface runoff

We use a dataset of 38 field‐mapped channel heads from a semi‐arid environment in western Colorado to examine relationships between contributing drainage area (A) and local hillslope gradient (θ) in relation to dominant process of initiation (surface runoff versus subsurface flow). Channel heads resulting primarily from subsurface flow have significantly greater values of A, longer basin lengths, and shallower local gradients than channel heads resulting primarily from surface runoff. We also compare the data from western Colorado to six analogous datasets from more humid regions in other portions of the United States and in southeast Australia. Comparison of the confidence intervals for the exponent values of A–θ regression lines reveals that the confidence intervals for the exponent of western Colorado channel heads with both surface and subsurface flow overlap with the confidence intervals for the exponent of all other datasets. This suggests that A–θ relationships do not differ significantly between diverse geographic locations. Copyright © 2017 John Wiley & Sons, Ltd.     

Temperature dependence of the elastic moduli of ringwoodite

The elastic moduli of polycrystalline ringwoodite, (Mg_0.91Fe_0.09)₂SiO₄, were measured up to 470 K by means of the resonant sphere technique. The adiabatic bulk (K_S) and shear (μ) moduli were found to be 185.1(2) and 118.22(6) GPa at room temperature, and the average slopes of dK_S/dT and dμ/dT in the temperature range of the study were determined to be −0.0193(9) and −0.0148(3) GPa/K, respectively. Using these results, we estimate seismic wave velocity jumps for a pure olivine mantle model at 520 km depth. We find that the jump for the S-wave velocity is about 1.5 times larger than that for the P-wave velocity at this depth. This suggests that velocity jumps at the 520 km discontinuity are easier to detect using S-waves than P-waves.     

MODELING OF INTERRILL EROSION IN THE LOESS PLATEAU OF CHINA

IINTRODUCTIONTheinterrillerosiononafieldplotisaffectedbythekineticenergyoftherainfall,wind,topographyfactors,propertiesofsoilandthecanopy.Theinterrillerosionoccursasthefirstdropimpactsthehillslopes.Theinterrillerosionoccursinallkindsofrainfallandtheamountofthesplasherosion,whichisthemainpartofinterrillerosion,canaccountforagreatpanofthetotalerosionamountinaheavystorm(Baner1990,Glymph1957,QianandWan1986,Zhou1981).Therefore,itisveryimportanttorevealthemechanismtoestimatetheamountofinterri…     

Exact solutions to radially symmetric two-phase flow for an arbitrary diffusivity

Over the past decade there have been a variety of exact solutions developed for one-dimensional two-phase flow, however when higher dimensions are considered there is a distinct scarcity of solutions. In this paper we consider the problem of radially symmetric two-phase flow, into an infinite medium of uniform initial saturation, subject to a constant flux V from a line source at the origin. We show that in the absence of gravity and when the two-phase diffusivity D is related to the fraction flow function f by βD = V df/dθ, where θ is the water content and β is a constant of proportionality, a new class of exact solutions can be found. In particular, when β = 2, we show that the solution is given by a simple quadrature for arbitrary D, and is fully integrable for specific functional forms of D. It has been shown by Weeks et al. [Weeks SW, Sander GC, Parlange J-Y. n-Dimensional first integral and similarity solutions for two-phase flow. ANZIAM J 2003;44:365–80] that when D obeys the above relation, a saturated zone does not grow around the line of injection, consequently we find for β = 1, the flow equation maps to one-dimensional single-phase flow under a saturated boundary condition. Consequently solutions developed for one-dimensional single-phase flow (exact or approximate) apply to radially symmetric two-phase flow. Solutions for β = 1 or 2 can be derived for either a wetting fluid displacing a non-wetting fluid, or a non-wetting fluid displacing a wetting fluid, however for arbitrary β numerical methods are required.     

MATHEMATICAL MODEL OF OVERLAND FLOW AND MECHANISM OF SOIL CONSERVATION FOR FORESTED STEEP HILLSLOPE

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Overland runoff erosion dynamics on steep slopes with forages under field simulated rainfall and inflow

Although numerous studies have acknowledged that vegetation can reduce erosion, few process-based studies have examined how vegetation cover affect runoff hydraulics and erosion processes. We present field observations of overland flow hydraulics using rainfall simulations in a typical semiarid area in China. Field plots (5 × 2 m²) were constructed on a loess hillslope (25°), including bare soil plot as control and three plots with planted forage species as treatments—Astragalus adsurgens, Medicago sativa and Cosmos bipinnatus. Both simulated rainfall and simulated rainfall + inflow were applied. Forages reduced soil loss by 55–85% and decreased overland flow rate by 12–37%. Forages significantly increased flow hydraulic resistance expressed by Darcy–Weisbach friction factor by 188–202% and expressed by Manning's friction factor by 66–75%; and decreased overland flow velocity by 28–30%. The upslope inflow significantly increased overland flow velocity by 67% and stream power by 449%, resulting in increased sediment yield rate by 108%. Erosion rate exhibited a significant linear relationship with stream power. M. sativa exhibited the best in reducing soil loss which probably resulted from its role in reducing stream power. Forages on the downslope performed better at reducing sediment yield than upslope due to decreased rill formation and stream power. The findings contribute to an improved understanding of using vegetation to control water and soil loss and land degradation in semiarid environments.     

Paleomagnetism of the Late Cretaceous ignimbrite from the Okhotsk-Chukotka Volcanic Belt,Kolyma-Omolon Composite Terrane: Tectonic implications

New Late Cretaceous paleomagnetic results from the Okhotsk-Chukotka Volcanic Belt in the Kolyma-Omolon Composite Terrane yield stable and consistent remanent directions. The Late Cretaceous (86–81 Ma) ignimbrites from the Kholchan and Ola suites were sampled at 19 sites in the Magadan area (60.4° N, 151.0° E). We isolated the characteristic paleomagnetic directions from 16 sampled sites using an alternating field demagnetization procedure. The primary nature of these directions is ascertained by dual polarities and positive fold tests. A tilt-corrected mean direction (D = 42.8°, I = 84.7°, k = 46.0, α₉₅ = 10.0°) yields a paleomagnetic pole of 66.7° N, 168.5° E (A₉₅ = 18.8°) which appears almost identical to the 90–67 Ma pole reported from the Lake El’gygytgyn area of the Okhotsk-Chukotka Volcanic Belt (Chukotka Terrane). This consistency suggests that the Kolyma-Omolon Composite Terrane and Chukotka Terrane has acted as a single tectonic unit since 80 Ma without any significant internal deformation. Accordingly, we calculate a combined 80 Ma characteristic paleomagnetic pole (Long. = 164.7° E, Lat. = 68.0°, A₉₅ = 10.9°, N = 12) for the Kolyma-Omolon-Chukotka Block which falls 16.5–17.5° south of the same age poles from Europe and East Asia. We ascribe this discrepancy in pole positions to tectonic activity in the area and infer a southward displacement of 1640 ± 1380 km for the Kolyma-Omolon-Chukotka Block with respect to the North American and Eurasian blocks since 80 Ma; more than 260 km of it is attributed to tectonic displacement in the Arctic Ocean due to the opening of the Canadian Basin.     

Evapotranspiration in the Pampean Region using field measurements and satellite data

Evapotranspiration (LE) is an important factor for monitoring crops, water requirements, and water consumption at local and regional scale. In this paper, we applied the semi-empirical model to estimate the daily latent heat flux (LE_d = Rn_d + A − B(Ts − Ta)). LE_d has been estimated using satellite images (Thematic Mapper sensor) and a local dataset (incoming and outgoing short- and long-wave radiation) measured during three years. We first estimated the daily net Radiation (Rn_d) from a linear equation derived from the instantaneous net Radiation (Rn_d = CRn_i + D). Subsequently, coefficients A and B have been estimated for two different cover vegetations (pasture and soybean). For each vegetation cover, an error analysis combining Rn_d, A, B, and surface and air temperatures has been calculated. Results showed that Rn_d had good performance (nonbias and low RMSE). LE_d errors for pasture and soybean were ±28 W m⁻² and ±40 W m⁻² respectively.     

Crustal velocity structure in the southern edge of the Central Alborz (Iran)

Inversion of local earthquake travel times and joint inversion of receiver functions and Rayleigh wave group velocity measurements were used to derive a simple model for the velocity crustal structure beneath the southern edge of the Central Alborz (Iran), including the seismically active area around the megacity of Tehran. The P and S travel times from 115 well-located earthquakes recorded by a dense local seismic network, operated from June to November 2006, were inverted to determine a 1D velocity model of the upper crust. The limited range of earthquake depths (between 2 km and 26 km) prevents us determining any velocity interfaces deeper than 25 km. The velocity of the lower crust and the depth of the Moho were found by joint inversion of receiver functions and Rayleigh wave group velocity data. The resulting P-wave velocity model comprises an upper crust with 3 km and 4 km thick sedimentary layers with P wave velocities (V_p) of ～5.4 and ～5.8 km s^?1, respectively, above 9 km and 8 km thick layers of upper crystalline crust (V_p ～6.1 and ～6.25 km s^?1 respectively). The lower crystalline crust is ～34 km thick (V_p ～ 6.40 km s^?1). The total crustal thickness beneath this part of the Central Alborz is 58 ± 2 km.     

Aerosol microphysics over a tropical coastal station inferred from the spectral dependence of Angstrom wavelength exponent and inversion of spectral aerosol optical depths

Six years of spectral aerosol optical depth (AOD) measurements have been analyzed from a tropical coastal site, Trivandrum (8.55°N, 76.9°E, 3 m msl) to infer on the seasonal changes in the microphysical properties of columnar aerosols, by examining the derivatives of the Angstrom wavelength exponent (α) in the wavelength domain (α′_λ) as well as in AOD domain (α′_τ) and by retrieving the columnar size distribution by numerical inversion of the AODs. The inference of the changes in the aerosol microphysics drawn from the features of the derivatives α′_λ and α′_τ is consistent with the pattern revealed by the aerosol properties obtained from the columnar size distributions retrieved from the AOD spectra as well as from the surface measurements of mass-size distributions, which are supported by the back-trajectory cluster analysis and the results of chemical species analysis.     

Testing Taylor’s hypothesis in Amazonian rainfall fields during the WETAMC/LBA experiment

Taylor’s hypothesis (TH) for rainfall fields states that the spatial correlation of rainfall intensity at two points at the same instant of time can be equated with the temporal correlation at two instants of time at some fixed location. The validity of TH is tested in a set of 12 storms developed in Rondonia, southwestern Amazonia, Brazil, during the January–February 1999 Wet Season Atmospheric Meso-scale Campaign. The time Eulerian and Lagrangian Autocorrelation Functions (ACF) are estimated, as well as the time-averaged space ACF, using radar rainfall rates of storms spanning between 3.2 and 23 h, measured at 7–10-min time resolution, over a circle of 100 km radius, at 2 km spatial resolution. TH does not hold in 9 out of the 12 studied storms, due to their erratic trajectories and very low values of zonal wind velocity at 700 hPa, independently from underlying atmospheric stability conditions. TH was shown to hold for 3 storms, up to a cutoff time scale of 10–15 min, which is closely related to observed features of the life cycle of convective cells in the region. Such cutoff time scale in Amazonian storms is much shorter than the 40 min identified in mid-latitude convective storms, due to much higher values of CAPE and smaller values of storm speed in Amazonian storms as compared to mid-latitude ones, which in turn contribute to a faster destruction of the rainfall field isotropy. Storms satisfying TH undergo smooth linear trajectories over space, and exhibit the highest negative values of maximum, mean and minimum zonal wind velocity at 700 hPa, within narrow ranges of atmospheric stability conditions. Non-dimensional parameters involving CAPE (maximum, mean and minimum) and CINE (mean) are identified during the storms life cycle, for which TH holds: CAPE mean/CINE mean = [30–35], CAPE max/CINE mean = [32–40], and CAPE min/CINE mean = [22–28]. These findings are independent upon the timing of storms within the diurnal cycle. Also, the estimated Eulerian time ACF’s decay faster than the time-averaged space and the Lagrangian time ACF’s, irrespectively of TH validity. The Eulerian ACF’s exhibit shorter e-folding times, reflecting smaller correlations over short time scales, but also shorter scale of fluctuation, reflecting less persistence in time than over space. No significant associations (linear, exponential or power law) were found between estimated e-folding times and scale of fluctuation, with all estimates of CAPE and CINE. Secondary correlation maxima appear between 50 and 70 min in the Lagrangian time ACF’s for storms satisfying TH. No differences were found in the behavior of each of the three ACF’s for storms developed during either the Easterly or Westerly zonal wind regimes which characterize the development of meso-scale convective systems over the region. These results have important implications for modelling and downscaling rainfall fields over tropical land areas.     

On the effective hydraulic conductivity in mean vertical unsaturated steady flows

Water flow in partially saturated heterogeneous porous formations is modelled by regarding the hydraulic parameters as stationary random space functions (RSFs). As a consequence, the flow variables are also RSFs, and we aim to develop a procedure to derive the effective hydraulic conductivity (EHC). The methodology relies on a perturbation approach which regards the variances of the hydraulic parameters as small quantities. By using the Gardner’s [Gardner WR. Some steady state solutions of unsaturated moisture flow equations with application to evaporation from a water table. Soil Sci 1958;85:228–32] two-parameters (K_s, α) model for the local unsaturated conductivity, we obtain the EHC for any dimensionality d of the flow domain, and arbitrary correlation functions of the input RSFs. Unlike previous studies [e.g. Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 1. Statistically isotropic media. Water Resour Res 1985;21;447–56, Yeh T-CJ, Gelhar J, Gutjahr A. Stochastic analysis of unsaturated flow in heterogenous soils. 2. Statistically anisotropic media with variable α. Water Resour Res 1985:21:457–64], the EHC is represented here as product between the local scale conductivity valid for a domain of mean parameters, and a correction function κ¹ which depends on the medium heterogeneity structure and the mean pressure head.Generally, the correction function κ¹ is expressed by d-fold quadrature. These quadratures are further reduced after adopting specific (i.e. exponential and Gaussian) structure for the (cross) correlation functions involved in the computation of κ¹. We have also focused on some particular formation structures which are relevant for the applications, and permit simplification of the computational aspect, as well.We investigate effects of the heterogeneity formation properties as well as the mean head on the structure of κ¹. Overall, results suggest that, given the formation statistics, the impact of the heterogeneity upon κ¹ is enhanced as the medium becomes drier. This is particularly so when the variability of the fluctuation of Y = ln K_s is small compared with that of ζ = ln α. Conversely, when the heterogeneity of Y is prevalent upon that of ζ, κ¹ is influenced solely by the anisotropic structure of the formation unless the horizontal correlation scales are much greater than the vertical ones.     

Age estimation of the deposition of the cretaceous Upper Sandstones and a later remagnetization event,from Hirna area,SE Ethiopia

Outcrops of the Cretaceous Upper sandstone formation some 375 km to the East of Addis Ababa on the motor Highway to Harar was paleomagnetically investigated. About seventy core samples were collected at various stratigraphic levels from 250–300 meters thick sedimentary formation. After standard sample preparations in the laboratory the resulting specimens were subjected to routine paleomagnetic demagnetization protocol. In the first steps of demagnetizations process the recent and viscous magnetizations were removed by heating until a temperature of level of 300 °C. Further demagnetization of the samples resulted in the isolation of the final magnetization with stable line segments that is directed towards the origin, which is interpreted as Characteristic Remanent Magnetization (ChRM). Rock – magnetic experiments have identified goethite (αFeOOH), hematite (αFe₂O₃), detritial hematite, and magnetite as the magnetic mineral phases carrying the remanence. The ChRM identified resulted in an average value of (D_s = 0.5°, I_s = ?0.7°, α₉₅ = 4.3°, N = 34) for the red sandstones while an average value of (D_s = 335.8°, I_s = ?31.8°, α₉₅ = 4.7°, N = 14) for the limestone intercalations. The former ChRM in the red sandstone is determined to be secondary while the latter ChRM is known to be primary. Comparison of these directional results and their pole equivalents with the African plate Apparent Polar Wander Path curve established by Besse and Courtillot (2003) give ages of between 115–130 Million years for the limestone intercalation and ages of 30 million years for red sandstone unit. These are interpreted respectively as estimates of the age of deposition and a later remagnetization respectively.     

Landscape form and millennial erosion rates in the San Gabriel Mountains,CA

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 ¹⁰Be from 50 basins, ranging in size from 1 to 150 km², 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.