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Statistics and Data Analysis in Geology

A century of gully erosion research: Urgency, complexity and study approaches

. Soil erosion is a major problem around the world because of its effects on
soil productivity, nutrient loss, siltation in water bodies, and degradation
of water quality. By understanding the driving forces behind soil erosion, we
can more easily identify erosion-prone areas within a landscape to address
the problem strategically. Soil erosion models have been used to assist in
this task. One of the most commonly used soil erosion models is the Universal
Soil Loss Equation (USLE) and its family of models: the Revised Universal
Soil Loss Equation (RUSLE), the Revised Universal Soil Loss Equation
version 2 (RUSLE2), and the Modified Universal Soil Loss Equation (MUSLE).
This paper reviews the different sub-factors of USLE and RUSLE, and analyses
how different studies around the world have adapted the equations to local
conditions. We compiled these studies and equations to serve as a reference
for other researchers working with (R)USLE and related approaches. Within each sub-factor section, the
strengths and limitations of the different equations are discussed, and
guidance is given as to which equations may be most appropriate for
particular climate types, spatial resolution, and temporal scale. We
investigate some of the limitations of existing (R)USLE formulations, such as
uncertainty issues given the simple empirical nature of the model and many of
its sub-components; uncertainty issues around data availability; and its
inability to account for soil loss from gully erosion, mass wasting events,
or predicting potential sediment yields to streams. Recommendations on how to
overcome some of the uncertainties associated with the model are given.
Several key future directions to refine it are outlined: e.g. incorporating
soil loss from other types of soil erosion, estimating soil loss at
sub-annual temporal scales, and compiling consistent units for the future
literature to reduce confusion and errors caused by mismatching units. The
potential of combining (R)USLE with the Compound Topographic Index (CTI) and
sediment delivery ratio (SDR) to account for gully erosion and sediment yield
to streams respectively is discussed. Overall, the aim of this paper is to
review the (R)USLE and its sub-factors, and to elucidate the caveats,
limitations, and recommendations for future applications of these soil
erosion models. We hope these recommendations will help researchers more
robustly apply (R)USLE in a range of geoclimatic regions with varying data
availability, and modelling different land cover scenarios at finer spatial
and temporal scales (e.g. at the field scale with different cropping
options).

/pdf/a-review-of-the-revised-universal-soil-loss-equation-r-usle-555n908jt3.pdf

A review of the (Revised) Universal Soil Loss Equation ((R)USLE): with a view to increasing its global applicability and improving soil loss estimates

Most fi eld erosion studies in agricultural areas provide little information on the probable errors involved. Here, for the fi rst time, we compare the accuracy, time and cost of conventional and new methodologies for gully surveying, and provide a model to estimate the effort required to achieve a specifi ed accuracy. Using a terrestrial LiDAR survey of a 7.1-m-long gully reach as a benchmark data set, the accuracies of different measurement methods (a new 3D photo-reconstruction technique, total station, laser profi lemeter, and pole) are assessed for estimating gully erosion at a reach scale. Based on further fi eld measurements performed over nine gullies (>100 m long), a simulation approach is derived to model the expected volume errors when 2D methods are used at the gully scale. All gullies considered were located near Cordoba, Spain. At the reach scale, the fi eld measurements using 3D photo-reconstruction and total station techniques produced cross-sectional area error values smaller than 4%, with other 2D methods exceeding 10%. For volume estimation, photo-reconstruction proved similar to LiDAR data, but 2D methods generated large negative volume error (EV) values (<–13% for laser profi lemeter and pole). We show that the proposed error expressions derived from the model are in line with the reach-scale fi eld results. A measurement distance factor (MDF) is defi ned that represents the ratio between cross-section distance and the gully length, and thus refl ects relative survey effort. We calculate the required MDF for specifi ed values of EV, illustrating how MDF decreases with increasing gully length and sinuosity.

Comparing the accuracy of several field methods for measuring gully erosion

Soil erosion, in its myriad forms, devastates arable land and infrastructure. As an integral landscape feature, gully erosion is a complex system as its evolution is controlled by upstream migration of a gully head (headcut face), incision of the gully bed (plunge pool) and gravitational mass-movement (widening) on gully channel sidewalls. Bed incision is often limited by the presence of a less erodible soil layer. When erosion reaches such a layer, the gully typically widens, creating a wide shallow cross section. Once a gully is initiated, transport and deposition of the eroded soil and widening of the channel further govern its evolution. Our knowledge of these processes within agricultural regions, however, is still quite limited with theory largely borrowed from river hydraulics. Experiments were conducted to examine gully expansion (widening) as a function of channel slope and overland flow discharge. Packed soil beds were subjected to simulated rainstorms followed by clear-water overland flow. As bed slope and discharge increased, channel widening increased. An empirical equation, based upon measured channel width from constant discharge experiments, was developed in terms of slope and discharge. By further quantifying key aspects of gully erosion processes, results from this experimental campaign will significantly improve soil erosion prediction technology for use in agricultural regions.

https://pubag.nal.usda.gov/pubag/downloadPDF.xhtml?id=58898&content=PDF

An empirical investigation of gully widening rates in upland concentrated flows

The formation of ephemeral gullies in agricultural fields has been recognized as an important source of sediment contributing to environmental degradation and compromising crop productivity Methodologies are being developed for assessing gully formation and gully sediment yield The Annualized Agricultural Non-Point Source (AnnAGNPS) pollution model is an important tool for multi-temporal watershed-scale simulations because it contains the necessary components for ephemeral gully investigation, making AnnAGNPS a commonly used tool for evaluations of agricultural conservation and operation practices AnnAGNPS requires the user to define the location of ephemeral gullies throughout the watershed, what often constitutes a time consuming task where users may not accurately locate and describe all ephemeral gully locations Alternatively, herein a GIS-based graphical user interface is described for the automated identification of areas with high probability of forming ephemeral gullies, referred to as potential ephemeral gullies (PEGs), based on the modified Compound Topographic Index (CTI) Through the aid of a study case, PEG mouth locations along with their attributes are generated through an iterative procedure by varying different CTI threshold values (999%, 995%, 990%, 985%, and 98%) Three sets of yielded PEG mouth locations and corresponding attributes were then integrated with AnnAGNPS for assessment of the impact of potential ephemeral gullies in the watershed sediment erosion Analysis of the spatial distribution of estimates of annual average of gully erosion identifies the sub-watersheds prone to ephemeral gully erosion, thus enhancing the applicability of AnnAGNPS to evaluate conservation practices and/or targeted interventions designed to address ephemeral gully erosion at the watershed-scale

AGNPS GIS-Based Tool for Watershed-Scale Identification and Mapping of Cropland Potential Ephemeral Gullies

When flowing water concentrates on hillslopes, the erosivity of the water may only be limited by the erodibility of the soil. Over time, concentrated flow paths may become permanent drainage channels, and such rills and ephemeral gullies often have negative impacts on crop yield and downstream sedimentation. Spatiotemporal topographic assessments of rill and gully dimensions compliment hydraulic erosion estimates, and they can elucidate soil erosion processes and provide data for model validation. Accurate and detailed topographic assessments, however, can be cost prohibitive. The objectives of this study are to describe and evaluate a topographic assessment method with relatively high spatial and temporal resolution, to discuss its costs and limitations, and to provide an assessment procedure for erosion characterization and data optimization. Three locations are evaluated that are pertinent to soil erosion research on the field, plot, and laboratory scale. In each setting, the sites are monumented and monitored using photogrammetric techniques. Photogrammetry is a simple, robust means to track landscape evolution and morphodynamic changes in rills and ephemeral gullies. The assessment procedure describes study site attributes at a variety of spatial and temporal scales, it is cost-effective, workforce empowering, and reliable, and the analysis and presentation can be automated. Capturing this type of information is critical to an improved understanding of the fundamental principles necessary to enhance modeling technology to estimate erosion potential at various scales and to assess the efficacy of conservation practices.

A Measurement Method for Rill and Ephemeral Gully Erosion Assessments

Concentrated surface runoff, such as associated with ephemeral gully channels, increases erosion and transfers fine sediment and associated agrichemicals from upland areas to stream channels. Ephemeral gully erosion on cropland may contribute up to 40 % or more of the sediment delivered to the edge of agricultural fields, significantly threatening the health of downstream ecological services. Typically, conservation practices developed for sheet and rill erosion are also expected to treat ephemeral gully erosion, but technology and tools are needed to account for the separate benefits and effects of practices on various sediment sources. Without improved research studies, subjective observations will continue to be used to satisfy quality criteria in lieu of scientifically defensible, quantitative methods to estimate the impact of gully erosion. Ephemeral gully channels evolve by one, or combination of, complex physical process in the form of incision, headcut migration upslope, and channel sidewalls expansion (widening). This study focused on the latter, ephemeral gully channel widening relationships. The impact of various width functions on erosion can be very significant and is dependent on discharge, slope, soil properties, and management conditions. A description is provided on six ephemeral gully widening relationships, followed by recommended improvements, comparative application, and identification of future research needs. Improvements in the development of ephemeral gully width algorithms are critical to understanding the impact of conservation practices on controlling ephemeral gully erosion. Tools are needed to predict and quantify ephemeral gully erosion, including the capability to evaluate the effect of conservation practices to control erosion. An improved critical shear stress equation was developed and described that provides an approach to incorporating impacts of management practices on the resulting gully erodibility. Conservation management planning by organizations needs a systematic approach to determining the extent of ephemeral gully erosion problems on a field, watershed, or national basis, or to predict the recurring or new locations of ephemeral gullies prior to their development.

Ephemeral gully channel width and erosion simulation technology

. Sediment loads from gully erosion contribute to water quality problems, reduction in crop productivity by removal of nutrient-rich topsoil, and damage to downstream ecosystems. The identification of areas with high potential for gully channel development is often performed using spatially derived stream power estimates from second-order topographic indices, such as the compound topographic index (CTI). The utilization of CTI to identify where gullies develop is affected by field and local topographic characteristics and DEM resolution. In this study, the effect of overall terrain slope, local relief variance, and raster grid cell size on CTI cumulative distribution values was investigated using theoretical and observed catchment methodology. In the theoretical analysis, stochastic methods were used to generate simulated catchments to quantify the influence of overall terrain slope, local relief variance, and raster grid cell size (each considered individually). The observed methodology used three sites with distinct topographic characteristics, measured gully channels, and high-resolution topographic information. Raster grids for the three observed study sites were generated at varying raster grid cell sizes. Critical CTI values were determined through comparison of measured gully thalwegs with threshold CTI raster grids of the observed watersheds at different resolutions. Results from the theoretical investigation indicate that CTI values were linearly influenced by changes in relief variance and overall slope, while variations in raster grid cell size caused an inverse power variation in CTI values. In addition, variations in raster grid cell size, produced changes in cumulative distributions of the top 0.1% CTI values. The use of normalized CTI values (CTI n ) produced merged cumulative distribution curves when varying overall slope, terrain relief variance, and to a lesser degree DEM resolution. Similar findings were obtained from the analysis of observed catchments. When DEM resolution varied, the differences in critical CTI n values in the same field were significantly reduced when compared to original critical CTI values, although differences were not fully eliminated. Normalization of the CTI cumulative distributions improved comparisons between different sites with distinct drainage area sizes and topographic characteristics, providing a possible alternative for investigations of large watersheds with more than one topographic characteristic. Results suggest that a normalized critical CTI between 1 and 2 could be used for the identification of areas with high potential for gully development. Knowing where gullies develop is important in understanding the effect of conservation practices on soil erosion through the use of field-scale and watershed-scale simulation models. Effective watershed management plans depend on this information to target the placement of conservation practices for the efficient use of available resources.

Henrique G. Momm

Papers

An empirical investigation of gully widening rates in upland concentrated flows

AGNPS GIS-Based Tool for Watershed-Scale Identification and Mapping of Cropland Potential Ephemeral Gullies

A Measurement Method for Rill and Ephemeral Gully Erosion Assessments

Ephemeral gully channel width and erosion simulation technology

Effect of topographic characteristics on compound topographic index for identification of gully channel initiation locations