The application of erosion slowness theory to hillslope formation

A method of analysis for predicting the time development of hillslope profiles is presented. The technique is based upon the assumption of weathering limited erosion and assumes that the local surface normal erosion rate is dependent upon the local flux of erosional agent and a function of the local slope gradient. This technique has been previously applied with success to analogous erosional processes in the sand blasting, chemical and energetic atom bombardment induced ablation of solids. The analysis shows how linearly segmented profiles can develop from initially curved surfaces and indicates the progress of profiles to stable end forms. Actual application to geomorphological situations is limited by lack of knowledge of micro-environmental erosion fluxes and the gradient dependence of erosion and it is suggested that field observations and laboratory simulations could be helpful in determining the utility of the analysis technique outlined here.     

Post‐Younger Dryas deglaciation of the Greenland western margin as revealed by spatial analysis of lakes

Lake shapes and their spatial distribution are important geomorphological indicators in previously glaciated areas. Their shapes are influenced by the underlying geological structure and processes of glacial sediment deposition or erosion. Since these processes act on large areas, distribution of lakes can reflect the intensity of glacial erosional/depositional processes and their spatial extent. Landsat imagery was used to extract lake outlines from a selected pilot‐study area on the widest ice‐free coastal margin of the south‐western Greenland north of Kangerlussuaq. Analysis included image classification and spatial analysis of lakes with elevation data using geographic information system (GIS) tools. A morphometric index was applied to extract kettle lakes as indicators of a specific glacial process – ice stagnation. Analysis of their spatial distribution helped in the reconstruction of glacial dynamics in formerly glaciated terrain. Our results show that spatial lake distribution combined with elevation analysis can be used to identify zones of glacial erosion and deposition. The highest concentrations of lakes within the study area occupy the elevation range between 164 and 361 m above sea level (a.s.l.). This zone can be identified as an area where intensive glacial erosion took place in the past. The widespread distribution of modeled kettle lake features within the same elevation range and across the study area suggests that the last deglaciation process was accompanied by abandonment of blocks of stagnant ice. This conclusion is supported by surface exposure ages obtained in the same study area and published elsewhere. Copyright © 2009 John Wiley & Sons, Ltd.     

Microtopography of bare peat: a conceptual model and objective classification from high‐resolution topographic survey data

Peatlands globally are at risk of degradation through increased susceptibility to erosion as a result of climate change. Quantification of peat erosion and an understanding of the processes responsible for their degradation is required if eroded peatlands are to be protected and restored. Owing to the unique material properties of peat, fine‐scale microtopographic expressions of surface processes are especially pronounced and present a potentially rich source of geomorphological information, providing valuable insights into the stability and dominant surface process regimes. We present a new process‐form conceptual framework to rigorously describe bare peat microtopography and use Structure‐from‐Motion (SfM) surveys to quantify roughness for different peat surfaces. Through the first geomorphological application of a survey‐grade structured‐light hand‐held 3D imager (HhI), which can represent sub‐millimetre topographic variability in field conditions, we demonstrate that SfM identifies roughness signatures reliably over bare peat plots (<1 m²), although some smoothing is observed. Across 55 plots, the roughness of microtopographic types is quantified using a suite of roughness metrics and an objective classification system derived from decision tree analysis with 98% success. This objective classification requires just five roughness metrics, each of which quantifies a different aspect of the surface morphology. We show that through a combination of roughness metrics, microtopographic types can be identified objectively from high resolution survey data, providing a much‐needed geomorphological process‐perspective to observations of eroded peat volumes and earth surface change. Copyright © 2018 John Wiley & Sons, Ltd.     

Surficial sediment erodibility from time-series measurements of suspended sediment concentrations: development and validation

Numerical models of fine sediment transport depend on different approaches to parameterize the erosion properties of surficial sediment strata. These properties, namely the critical shear stress for erosion and the erosion rate coefficient, are crucial for reproducing the short-term and long-term sediment dynamics of the system. Methods to parameterize these properties involve either specialized laboratory measurements on sediment samples or optimization by model calibration. Based on observations of regular patterns in the variation of suspended sediment concentrations (SSC) over the tidal cycle in a small, narrow estuary, an alternate approach, referred to as the entrainment flux method, for quantifying the erosion properties of surficial bed strata is formulated and applied. The results of this method are shown to be analogous to the erosion data used to formulate the standard linear erosion formulation developed by various authors. The erosion properties inferred from the entrainment flux method are also compared to direct measurements of erodibility on sediment samples from the same site using the Gust microcosm apparatus. The favorable comparison of the two approaches suggests that the entrainment flux method can be used to infer and quantify the erodibility of surficial sediment strata in similar small and narrow estuaries. This method has certain advantages, chiefly its ease of implementation and the fact that it uses SSC time series which would typically be expected to be available for the study of or for model application at a given site. Guidelines for selecting the appropriate dataset for the application of the method are also presented.     

How do streamflow generation mechanisms affect watershed hypsometry?

Several studies have shown that the dominant streamflow generation mechanism in a river basin can leave distinct geomorphological signatures in basin topography. In particular, it has been suggested previously that basins generated by groundwater discharge tend to have a larger hypsometric integral than surface runoff basins because fluvial erosion is more focused in the valleys where groundwater discharge tends to occur. In this analysis, we aim to clarify this relationship by developing an alternative method to quantify the effects of streamflow generation mechanisms on basin hypsometry and by using a numerical model that can generate streamflow by different processes to evaluate the sensitivity of the results to the hydrological and geomorphological properties of the basin. The model results suggest that the hypsometric characteristics that are usually associated with groundwater discharge basins, such as a larger hypsometric integral, occur primarily when drainage networks are still advancing in the watershed. During later stages of development, an additional factor such as lithological controls or a distinct geomorphological process would be needed to preserve these features. The model results also show that the hypsometric effects are stronger when the parameters of the fluvial erosion process promote the influence of small discharge rates. Copyright © 2007 John Wiley & Sons, Ltd.     

Calculating basal temperatures in ice sheets: an Excel spreadsheet method

The flow of ice sheets and their geomorphological impact is greatly influenced by their basal thermal regime. Calculations of basal temperatures in ice sheets are therefore fundamental in evaluating glacier dynamics and in determining the spatial distribution of zones of erosion and deposition beneath ice masses. Calculations of basal temperatures are not frequently attempted, however, primarily because of the techniques required to solve the heat conduction equation between the ice surface and the base. This paper describes a new Excel spreadsheet method of solving this equation that can readily be applied to both former and contemporary ice sheets. The application of the spreadsheet is illustrated with two examples. The first provides a calculation of basal thermal regime beneath the north eastern part of the Scottish ice sheet during the last glacial maximum; the second shows how basal ice temperatures can be calculated beneath the modern Antarctic ice sheet. Copyright © 2002 John Wiley & Sons, Ltd.     

Channel change and the significance of floodplain stratigraphy: 1990 flood event,lower river Tay,Scotland

During February 1990 a flood event on the River Tay with an estimated recurrence interval of 70 years in its lower reaches caused extensive flooding and geomorphological change. The most extensive area of flooding and dramatic geomorphological change, the erosion of two new channels across the floodplain, was in the vicinity of the village of Caputh, Perthshire. The location of the eroded channels relates to the position of former river courses, identifiable by depressions in the floodplain surface and floodplain stratigraphy. The lower floodplain surface elevation and occurrence of gravel and sand deposits along the line of the former river courses caused the area to be more vulnerable to erosion and controlled the morphology of the eroded channels.     

细胞自动机在地震波传播研究中的应用

本文基于细胞自动机在地震波传播研究中的最近成果，阐述了其基本的研究思路与理论框架，给出了一个计算实例．在此基础上就细胞自动机方法与传统波动方程的衔接关系及复杂介质中地震波正反问题作了讨论，并对研究前景进行展望．     

Creek enlargement in a low‐energy degrading saltmarsh in southern England

A low‐energy saltmarsh in the Beaulieu River Estuary, southern England was investigated. A geomorphological survey revealed that the creek bank geometry was characterized by the presence of cantilevers, a result of the protection provided by roots over the upper part of the bank. The saltmarsh deposits, consisting mainly of clay and organic matter, have a high resistance to flow‐induced erosion. Short‐term hydrographic deployments revealed that the tidal currents and waves recorded were insufficient to cause erosion of the bank surface. However, pin measurements over a 2‐year period revealed that the tidal creeks within the saltmarsh did experience bank erosion, particularly below the cantilevers, in spite of this low‐energy setting. Bank face erosion was therefore considered to be related to long‐term processes. The bases of the cantilevers were found to be located at a precise level, in relation to the tides. Water level data over a 2‐year period were examined against erosion measured below the cantilevers. The results suggest that the erosion on the bank faces, particularly below the cantilevers, is associated with the frequency of water level variations and long‐term submergence/emergence cycles, which can decrease the bonds between the particles and enable erosion by low tidal and wind‐wave currents within this low‐energy environment. This mechanism is probably responsible for tidal creek enlargement via erosion of the bank face and subsequent bank failure, a process which acts over a long temporal scale (1–10 years). Copyright © 2010 John Wiley & Sons, Ltd.     

Submarine platform development by erosion of a Surtseyan cone at Capelinhos,Faial Island,Azores

Erosion of volcanic islands ultimately creates shallow banks and guyots, but the ways in which erosion proceeds to create them over time and how the coastline retreat rate relates to wave conditions, rock mass strength and other factors are unclear. The Capelinhos volcano was formed in 1957/58 during a Surtseyan and partly effusive eruption that added an ~2.5 km² tephra and lava promontory to the western end of Faial Island (Azores, central North Atlantic). Subsequent coastal and submarine erosion has reduced the subaerial area of the promontory and created a submarine platform. This study uses historical information, photos and marine geophysical data collected around the promontory to characterize how the submarine platform developed following the eruption. Historical coastline positions are supplemented with coastlines interpreted from 2004 and 2014 Google Earth images in order to work out the progression of coastline retreat rate and retreat distance for lava- and tephra-dominated cliffs. Data from swath mapping sonars are used to characterize the submarine geometry of the resulting platform (position of the platform edge, gradient and morphology of the platform surface). Photographs collected during SCUBA and ROV dives on the submarine platform reveal a rugged surface now covered with boulders. The results show that coastal retreat rates decreased rapidly with time after the eruption and approximately follow an inverse power-law relationship with coastal retreat distance. We develop a finite-difference model for wave attenuation over dipping surfaces to predict how increasing wave attenuation contributed to this trend. The model is verified by reproducing the wave height variation over dipping rock platforms in the UK (platform gradient 1.2° to 1.8°) and Ireland (1.8°). Applying the model to the dipping platform around Capelinhos, using a diversity of cliff resistance predicted from known lithologies, we are able to predict erosion rate trends for some sectors of the edifice. We also explore wider implications of these results, such as how erosion creates shallow banks and guyots in reef-less mid-oceanic archipelagos like the Azores. © 2019 John Wiley & Sons, Ltd. © 2019 John Wiley & Sons, Ltd.     

Hillslope and point based soil erosion – an evaluation of a Landscape Evolution Model

Excessive soil erosion and deposition is recognised as a significant land degradation issue. Quantifying soil erosion and deposition is a non-trivial task. One of these methods has been the mathematical modelling of soil erosion and deposition patterns and the processes that drive them. Here we examine the capability of a landscape evolution model to predict both soil erosion rate and pattern of erosion and deposition. This numerical model (SIBERIA) uses a Digital Elevation Model (DEM) to represent the landscape and calculates erosion and deposition at each grid point in the DEM. To assess field soil redistribution rates (SRR) and patterns the distribution of the environmental tracer ¹³⁷Cs has been analysed. Net hill slope SRR predicted by SIBERIA (a soil loss rate of 1.7 to 4.3 t ha^-1 yr^-1) were found to be in good agreement with ¹³⁷Cs based estimates (2.1 – 3.4 t ha^-1 yr^-1) providing confidence in the predictive ability of the model at the hillslope scale. However some differences in predicted erosion/deposition patterns were noted due to historical changes in landscape form (i.e. the addition of a contour bank) and possible causes discussed, as is the finding that soil erosion rates are an order of magnitude higher than likely soil production rates. The finding that SIBERIA can approximate independently quantified erosion and deposition patterns and rates is encouraging, providing confidence in the employment of DEM based models to quantify hillslope erosion rates and demonstrating the potential to upscale for the prediction of whole catchment erosion and deposition. The findings of this study suggest that LEMs can be a reliable alternative to complex and time consuming methods such as that using environmental tracers for the determination of erosion rates. The model and approach demonstrates a new approach to assessing soil erosion that can be employed elsewhere. © 2018 John Wiley & Sons, Ltd.     

COMMON UNITGRAPHS FOR SETS OF RUNOFF EVENTS. PART 1: UNITGRAPH IDENTIFICATION FROM STREAMFLOW DATA

It is demonstrated that a unitgraph can be obtained without using rainfall data, provided data from at least two runoff events are available. A numerical method has been devised which calculates this common unitgraph for a set of surface runoff events and at the same time determines the input (rainfall excess) for each event. The method has been successfully tested on catchments ranging in size from 0.4 to 600 km²; it requires streamflow observations taken at intervals which retain all significant frequencies in the runoff hydrographs. The method also requires application of a baseflow separation procedure which is consistent for all events. The new approach has the potential to lead to more objective studies of the effects of catchment changes on the unitgraph and provides scope for comparisons of the common unitgraphs with geomorphological instantaneous unitgraphs.     

Estimating overland flow erosion capacity using unit stream power

Soil erosion caused by water flow is a complex problem. Both empirical and physically based approaches were used for the estimation of surface erosion rates. Their applications are mainly limited to experimental areas or laboratory studies. The maximum sediment concentration overland flow can carry is not considered in most of the existing surface erosion models. The lack of erosion capacity limitation may cause over estimations of sediment concentration. A correlation analysis is used in this study to determine significant factors that impact surface erosion capacity. The result shows that the unit stream power is the most dominant factor for overland flow erosion which is consistent with experimental data. A bounded regression formula is used to reflect the limits that sediment concentration cannot be less than zero nor greater than a maximum value. The coefficients used in the model are calibrated using published laboratory data. The computed results agree with laboratory data very well. A one dimensional overland flow diffusive wave model is used in conjunction with the developed soil erosion equation to simulate field experimental results. This study concludes that the non-linear regression method using unit stream power as the dominant factor performs well for estimating overland flow erosion capacity.     

Dating alluvial fan surfaces in Owens Valley,California, using weathering fractures in boulders

A wide range of sedimentological and geomorphological field research depends on the availability of accurate and detailed depositional age models. Although exposure dating techniques such as cosmogenic nuclide and luminescence dating are now widely available, they remain expensive and time‐consuming, and this frequently limits the density of age constraints and the resolutions of age models for many study areas. We present a simple and effective, field‐based approach for extending and correlating existing age models to un‐dated surfaces. In Owens Valley, California, we make use of detailed beryllium‐10 (¹⁰Be) chronologies reported for four different alluvial fan systems, to precisely calibrate the rate at which weathering fractures are enlarged in granitic surface boulders. We show that these fractures have widened at a time‐integrated rate of 1.05 ± 0.03 mm ka^?1 for at least 140 ka at this location, and this relationship can be represented by a linear regression that makes them ideal chronometers for surface dating. Our analysis offers a new approach to refining the uncertainties of both surface erosion rate and cosmogenic age estimates at this location. Ultimately, we integrate our observations to devise a robust age calibration for clast fracture widths in Owens Valley, and we demonstrate its application by estimating the ages of 27 additional local fan surfaces. We present an updated and extended stratigraphy for eight Sierra Nevada fan systems in total, with exceptional age control. This novel approach to dating sedimentary surfaces is inexpensive and easily applied in the field, and has the potential to significantly increase the temporal and spatial density of age constraints available for a particular study area. Copyright © 2014 John Wiley & Sons, Ltd.     

Slope–channel coupling between pipes,gullies and tributary channels in the Mocatán catchment badlands,Southeast Spain

The dispersive nature of the highly sodic silts of the Triassic‐rich unit of the Góchar formation plays a fundamental role in the erosion of the Mocatán catchment badlands in Almería, where a rejuvenating pipe and incised channel network is rapidly evacuating slope materials. Referring to concepts of medium‐ and long‐term landscape evolution, and incorporating contemporary thoughts on the role of connectivity in system evolution from the geomorphological literature, this paper attempts to develop a conceptual model of the way geologic, topographic, material property and ecological factors combine to explain the complex geomorphological evolution of the site. An electronic distance measurement (EDM) survey was undertaken using a Leica TC3100, to produce a detailed topographic map. This database was supplemented by geomorphological, geological and ecological data derived from ground survey and remote sensing, and further morphometric analysis undertaken. Preferred orientations of channel segments, and the topographic distribution of pipe‐roof‐collapse features and outfalls in relation to known stratigraphic controls, suggests that, once coupled to the slope‐base channel, pipe networks develop in a systematic, sequential way. A wave of incision moving up the main channel reconnects channels with slopes, and the resulting increased hydraulic gradients on sideslopes encourage extensive deep pipe development for the first time in these materials. Once major pipe development is possible, three‐dimensional pipe networks enlarge and then collapse to form an extensive, partially coupled steep‐sided gully network. From this perspective, the coupling of the pipe to a rejuvenating channel is a significant intrinsic threshold event and the main reason that badlands have developed locally in these dispersive materials. It is concluded that erosion in this landscape will only be suppressed after a considerable period of slope‐base stability, which could allow a gradual loss of sodium from the surface by leaching or organic exchanges. Both theoretical and management implications are explored. Copyright © 2007 John Wiley & Sons, Ltd.     

Predicting the impact of linear landscape elements on surface runoff,soil erosion,and sedimentation in the Wahnbach catchment,Germany

Model predictions concerning the endangerment of on‐site and off‐site damages due to runoff, soil erosion and sedimentation under alternative design and operation policies are of particular importance in recent catchment planning and management. By using the raster‐based model approach, linear landscape elements, such as streets and roads, and their impacts on flow paths are often neglected. Therefore, the aim of this study was to analyse the effects of linear landscape elements on patterns of soil erosion, sediment transport and sedimentation. To accomplish this, roads are considered while determining flow paths. Simulations in the well‐investigated catchment of the Wahnbach River (54 km²) in a low mountain range in Germany were carried out using a combination of different models for hydrology and soil erosion. Although the study focuses on the catchment scale of the Wahnbach River, detailed investigations concerning the sub‐catchment scale (21 ha) were also conducted. The simulation results show that these spatial structures mainly affect the pattern of soil erosion and sedimentation. On the sub‐catchment scale, improved identification of active zones for sediment dynamic becomes possible. On the catchment scale, the predicted runoff is about 20% higher, and sediment outputs were four times larger than predicted when roads were considered. Soil erosion increases by 37% whereas sedimentation is reduced by 29%. The model improvement could not be evaluated on the catchment scale because of the high variability and heterogeneity of land use and soils, but road impacts could be explained by simulations on the sub‐catchment scale. It can be concluded that runoff concentration due to rerouted flow paths leads to lower non‐concentrated and higher concentric‐linear surface runoff. Thus, infiltration losses decline and surface runoff and soil erosion increase because sedimentation is reduced. Further, runoff concentration can cause soil erosion hot spots. In the model concept used in this study, buffering of runoff and sediments on the upslope side of roads and in local depressions adjacent to roads cannot be simulated. Flow paths will only be rerouted because of road impacts, but the temporal ponding of water is not simulated. Therefore, the drastic increase of predicted sediment output due to road impact does not seem to be reliable. However, results indicate that the consideration of roads when determining flow paths enabled more detailed simulations of surface runoff, soil erosion and sedimentation. Thus, progress in model‐based decision‐making support for river catchment planning and management can be achieved. Copyright © 2011 John Wiley & Sons, Ltd.     

Peak surface motion due to scattering of plane harmonic P,SV, or Rayleigh waves by a rough cavity embedded in an elastic half-space

Scattering of plane harmonic P, SV, or Rayleigh waves by a two-dimensional rough cavity completely embedded in an isotropic elastic half-space is investigated by using a direct boundary integral equation method. The cavity’s roughness is assumed to be in the form of periodic or random perturbations of arbitrary amplitude superimposed to a smooth elliptical shape. For the randomly corrugated cavities the normal or the uniform probability distribution functions are assumed. Based on multiple random cavity results, the corresponding average surface response is computed. These are compared with the corresponding periodically corrugated and smooth cavity responses. The surface response is evaluated for different cavity shapes and incident waves and for a range of frequencies. The surface motion results are used to determine the peak surface motion frequencies. They depend strongly upon the basic inclusion shape (the principal axes) and the nature of the incident wave. Strong similarity in the peak surface motion frequencies can be observed for the rough and smooth cavity models for both circular and elliptical shapes. In order to quantify the importance of the cavity corrugation upon the surface motion, a roughness influence factor is defined in terms of the rough and smooth cavity surface responses. This factor strongly depends upon the type of the incident wave, the nature of the cavity corrugation, the basic cavity shape, and the frequency. The factor clearly shows the effect of the cavity roughness upon the surface motion.     

Optimization approach to automatic first arrival picking for three‐component three‐dimensional vertical seismic profiling data

A new, adaptive multi‐criteria method for accurate estimation of three‐component three‐dimensional vertical seismic profiling of first breaks is proposed. Initially, we manually pick first breaks for the first gather of the three‐dimensional borehole set and adjust several coefficients to approximate the first breaks wave‐shape parameters. We then predict the first breaks for the next source point using the previous one, assuming the same average velocity. We follow this by calculating an objective function for a moving trace window to minimize it with respect to time shift and slope. This function combines four main properties that characterize first breaks on three‐component borehole data: linear polarization, signal/noise ratio, similarity in wave shapes for close shots and their stability in the time interval after the first break. We then adjust the coefficients by combining current and previous values. This approach uses adaptive parameters to follow smooth wave‐shape changes. Finally, we average the first breaks after they are determined in the overlapping windows. The method utilizes three components to calculate the objective function for the direct compressional wave projection. An adaptive multi‐criteria optimization approach with multi three‐component traces makes this method very robust, even for data contaminated with high noise. An example using actual data demonstrates the stability of this method.