Soil erosion is a complex geomorphological process with varying influences of different impacts at different spatio-temporal scales. To date, measurement of soil erosion is predominantly realisable at specific scales, thereby detecting separate processes, e.g. interrill erosion contrary to rill erosion. It is difficult to survey soil surface changes at larger areal coverage such as field scale with high spatial resolution. Either net changes at the system outlet or remaining traces after the erosional event are usually measured. Thus, either quasi-point measurements are extrapolated to the corresponding area without knowing the actual sediment source as well as sediment storage behaviour on the plot or erosion rates are estimated disrupting the area of investigation during the data acquisition impeding multi-temporal assessment. Furthermore, established methods of soil erosion detection and quantification are typically only reliable for large event magnitudes, very labour and time intense, or inflexible. To better observe soil erosion processes at field scale and under natural conditions, the development of a method is necessary, which identifies and quantifies sediment sources and sinks at the hillslope with high spatial resolution and captures single precipitation events as well as allows for longer observation periods. Therefore, an approach is introduced, which measures soil surface changes for multi-spatio-temporal scales without disturbing the area of interest. Recent advances regarding techniques to capture high resolution topography (HiRT) data led to several promising tools for soil erosion measurement with corresponding advantages but also disadvantages. The necessity exists to evaluate those methods because they have been rarely utilised in soil surface studies. On the one hand, there is terrestrial laser scanning (TLS), which comprises high error reliability and retrieves 3D information directly. And on the other hand, there is unmanned aerial vehicle (UAV) technology in combination with structure from motion (SfM) algorithms resulting in UAV photogrammetry, which is very flexible in the field and depicts a beneficial perspective. Evaluation of the TLS feasibility reveals that this method implies a systematic error that is distance-related and temporal constant for the investigated device and can be corrected transferring calibration values retrieved from an estimated lookup table. However, TLS still reaches its application limits quickly due to an unfavourable (almost horizontal) scanning view at the soil surface resulting in a fast decrease of point density and increase of noise with increasing distance from the device. UAV photogrammetry allows for a better perspective (birds-eye view) onto the area of interest, but possesses more complex error behaviour, especially in regard to the systematic error of a DEM dome, which depends on the method for 3D reconstruction from 2D images (i.e. options for additional implementation of observations) and on the image network configuration (i.e. parallel-axes and control point configuration). Therefore, a procedure is developed that enables flexible usage of different cameras and software tools without the need of additional information or specific camera orientations and yet avoiding this dome error. Furthermore, the accuracy potential of UAV photogrammetry describing rough soil surfaces is assessed because so far corresponding data is missing. Both HiRT methods are used for multi-temporal measurement of soil erosion processes resulting in surface changes of low magnitudes, i.e. rill and especially interrill erosion. Thus, a reference with high accuracy and stability is a requirement. A local reference system with sub-cm and at its best 1 mm accuracy is setup and confirmed by control surveys. TLS and UAV photogrammetry data registration with these targets ensures that errors due to referencing are of minimal impact. Analysis of the multi-temporal performance of both HiRT methods affirms TLS to be suitable for the detection of erosion forms of larger magnitudes because of a level of detection (LoD) of 1.5 cm. UAV photogrammetry enables the quantification of even lower magnitude changes (LoD of 1 cm) and a reliable observation of the change of surface roughness, which is important for runoff processes, at field plots due to high spatial resolution (1 cm²). Synergetic data fusion as a subsequent post-processing step is necessary to exploit the advantages of both HiRT methods and potentially further increase the LoD. The unprecedented high level of information entails the need for automatic geomorphic feature extraction due to the large amount of novel content. Therefore, a method is developed, which allows for accurate rill extraction and rill parameter calculation with high resolution enabling new perspectives onto rill erosion that has not been possible before due to labour and area access limits. Erosion volume and cross sections are calculated for each rill revealing a dominant rill deepening. Furthermore, rill shifting in dependence of the rill orientation towards the dominant wind direction is revealed. Two field plots are installed at erosion prone positions in the Mediterranean (1,000 m²) and in the European loess belt (600 m²) to ensure the detection of surface changes, permitting the evaluation of the feasibility, potential and limits of TLS and UAV photogrammetry in soil erosion studies. Observations are made regarding sediment connectivity at the hillslope scale. Both HiRT methods enable the identification of local sediment sources and sinks, but still exhibiting some degree of uncertainty due to the comparable high LoD in regard to laminar accumulation and interrill erosion processes. At both field sites wheel tracks and erosion rills increase hydrological and sedimentological connectivity. However, at the Mediterranean field plot especially dis-connectivity is obvious. At the European loess belt case study a triggering event could be captured, which led to high erosion rates due to high soil moisture contents and yet further erosion increase due to rill amplification after rill incision. Estimated soil erosion rates range between 2.6 tha-1 and 121.5 tha-1 for single precipitation events and illustrate a large variability due to very different site specifications, although both case studies are located in fragile landscapes. However, the susceptibility to soil erosion has different primary causes, i.e. torrential precipitation at the Mediterranean site and high soil erodibility at the European loess belt site. The future capability of the HiRT methods is their potential to be applicable at yet larger scales. Hence, investigations of the importance of gullys for sediment connectivity between hillslopes and channels are possible as well as the possible explanation of different erosion rates observed at hillslope and at catchment scales because local sediment sink and sources can be quantified. In addition, HiRT data can be a great tool for calibrating, validating and enhancing soil erosion models due to the unprecedented level of detail and the flexible multi-spatio-temporal application.

Orientadora: Teresa Cristina Tarlé Pissarra / Banca: Renato Farias do Valle Junior / Banca: Sérgio Campos / Banca: José Frederico Centurion / Banca: João Antonio Galbiatti / Resumo: A retirada da cobertura vegetal original e a implantação de áreas de pastagem e canade- açúcar, com práticas de manejo inadequadas, acarretam modificações nas propriedades químicas, físicas e biológicas dos solos, com limitações na utilização agrícola e susceptibilidade à erosão. Assim, estudos dos processos físicos e químicos são importantes para avaliar as mudanças de origem natural ou antrópica sobre os meios. O estudo teve como objetivos avaliar os atributos químicos e físicos de um Argissolo Vermelho-Amarelo em três microbacias hidrográficas, em áreas de vegetação nativa, pastagem e cana-de-açúcar bem como analisar a ocorrência das áreas de maior escoamento superficial e, consequentemente, maior predisposição ao processo erosivo nas microbacias. A área de estudo compreendeu a microbacia hidrográfica do Córrego da Fazenda Glória, Município de Taquaritinga, Estado de São Paulo. Para a amostragem do solo foi realizada a caracterização do volume superficial, e essas amostras foram coletadas na superfície das vertentes das microbacias e em cada uso/ocupação selecionado. Os resultados obtidos foram avaliados por meio da comparação de médias para o teste de Tukey a 5%. A partir das curvas de nível da carta topográfica e dos pontos levantados com receptor geodésico de navegação com metodologia diferencial foi gerado uma malha de pontos georreferenciados em cada microbacia, para gerar o modelo numérico do terreno a partir da incorporação dos divisores de água e da rede de drenagem. As avaliações dos atributos físicos e químicos dos solos nas microbacias hidrográficas e em diferentes tipos de uso e ocupação demonstraram uma diferença significativa entre as áreas. O manejo do solo alterou os atributos químicos e físicos com impacto nas camadas superficiais do solo. A matéria orgânica foi um dos atributos mais sensíveis... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The removal of original vegetation cover and the deployment of pastures and sugarcane, with inadequate management practices, cause changes in the chemical, physical and biological properties of soils, with limitations on agricultural use and susceptibility to erosion. Thus, studies of physical and chemical processes are important to assess changes of natural development or anthropic on the means. The study was conducted to evaluate the physical and chemical attributes of a Ultisol in three watersheds, in areas of native vegetation, pasture and sugarcane, as well as, analyze the occurrence of the areas of greatest runoff and, consequently, greater predisposition to erosive processes in watersheds. The study area was the Córrego da Fazenda Glória watershed, Municipality of Taquaritinga, State of São Paulo. Soil sampling was performed to characterize the superficial volume, and these samples were collected on the surface of the watersheds and in three different land use selected. The results obtained were evaluated by the comparison of averages for the Tukey test at 5%. From the curves in a topographical map and from points collected with geodetic navigation receiver in a differential methodology was generated a digital elevation method in each watersheds. The assessments of physical and chemical attributes of soils in hydrographic watersheds and different land uses demonstrated a significant difference between the areas. Soil management altered the chemical and physical attributes impact in the soil superficial layers. The organic matter was one of the attributes more sensitive to changes due to agricultural practices. The digital terrain model showed a great potential, considering the scale of study of watersheds; and can help in spatial planning, urban and regional planning and zoning / Doutor

The theme of the work is the creation of the characteristics of the erozních and drainage conditions in the cadastral territory of the commune and the subsequent proposal Kujavy erosion control measures. Analysis of erozion ratios was processed using GIS method of the grid. Characteristics of runoff ratios was carried out for major service area of the critical points (SPKB) using model DesQ and numbers of the CN. In the design of erosion control measures was drawn up in the economic evaluation.

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The nutrient status of the soils in Shenchong Basin and the effects of soil erosion were examined during the summer of 1987. Eight raingauges and two thermographs provided meteorological data. Soil samples were collected from different land use categories in the uplands and lowlands, including agricultural areas. Water and sediment samples were collected from 1) surface discharge from the upland slope, rills and a gully during storms and 2) surface and ground waters during dry weather. Analysis was carried out on water samples to determine ammonia-nitrogen, nitrate-nitrogen, orthophosphate, soluble iron, calcium and potassium concentrations. The soil and sediment samples were analyzed for nitrate-nitrogen, available phosphorus, exchangeable potassium, calcium, magnesium and iron. Concentrations of nitrate and orthophosphate in the water samples were very low. Potassium showed the highest concentrations. Ammonia was the dominant inorganic nitrogen species in water and possibly the soils. The soils were highly acidic (pH < 5) and the soluble iron concentrations were high in the upland soils. Total aluminum concentrations were also high. Potassium concentrations were high in soils from vegetated areas. The higher levels of calcium and magnesium in the agricultural soils were were related to lime additions. Available phosphorus concentrations were very low. Nitrate showed no spatial trend except for the high concentration in the cassava field which was attributed to the peanut plants that were previously planted there. In general, nutrient concentrations were low compared to other tropical areas in the world. / Thesis / Master of Science (MSc)

Forestry Best Management Practices (BMPs) include guidelines, recommendations, and protocols utilized to protect forest water quality from nonpoint source pollutants (NPSP). Sediment is the most common NPSP associated with forest operations, and BMPs are implemented primarily to reduce erosion and potential sediment delivery to streams. Skid trails, stream crossings, forest roads, decks, and harvest areas are major forest operational features that have the potential to erode and deliver sediment to streams. These five features are also common BMP categories evaluated by states across the southeastern U.S. Although BMPs are designed to minimize erosion and sediment delivery, the exact relationship between BMP implementation rates, erosion rates, and potential sediment delivery is largely unexamined. Specifically, the inherently intuitive but unverified concept that increasing levels of BMP implementation decreases erosion and sediment delivery associated with forest harvesting. This hypothesis was tested in this project at five operational features located within three physiographic regions, including the Mountains, Piedmont, and Coastal Plain, across clearcut harvest sites in the southeastern U.S. First, BMP implementation rates, audit questionnaires, and state guidelines were compared across 13 states in the southeastern region at 116 clearcut harvest sites. Overall, BMPs were implemented at an average rate of 90.1% in the southeastern United States, thus demonstrating that BMPs are currently being implemented consistently at high levels throughout the region. Across all regions, average BMP implementation rates were highest at harvest areas (95.6%), followed by decks (92.7%), haul roads (91.9%), stream crossings (88.2%), and skid trails (82.9%). Average BMP implementation rates for Mountain stream crossings (83.9%) and skid trails (76.1%) were significantly lower than rates calculated in the Piedmont and Coastal Plain, and had the lowest implementation rate for any feature in any region. These findings indicate that skid trails and stream crossings, especially in the Mountains, may benefit the most from enhanced BMP implementation and resources. In the second manuscript, the relationship between BMP implementation, estimated erosion, and potential sediment delivery were examined in three regions of Virginia and North Carolina. This study is one of the only forestry studies that have presented sediment delivery ratios by operational feature and physiographic region. BMP implementation rates and sediment delivery ratios were poorly correlated, however, a significant inverse relationship existed between BMP implementation and the total sediment mass delivered to streams (Spearman ρ = -0.2206, p-value = 0.0027). Generally, as BMP implementation increased, erosion rates and the amount of sediment delivered to streams also decreased. Additionally, this study demonstrated that most of the erosion generated by clearcutting operations in the southeast is trapped in either the harvest area or in Streamside Management Zones (SMZs) prior to reaching the stream. In the third manuscript, BMP implementation rates and erosion estimates were categorized into three BMP levels (BMP−, BMP-standard, BMP+) which represent low, moderate, and high levels of BMP implementation, respectively. Skid trails and haul roads generally had the highest erosion estimates, regardless of BMP level and physiographic region. Non-parametric correlation analyses indicated that significant inverse relationships existed between BMP implementation rates and erosion estimates at skid trails (Spearman ρ = -0.589, p-value < 0.0001), haul roads (Spearman ρ = -0.388, p-value < 0.0001), and harvest areas (Spearman ρ = -0.2305, p-value = 0.0169), while decks and stream crossings were more poorly correlated with erosion estimates. This reinforces the need for BMP audit questions that specifically address ground cover and bare soil, water control structures, gradients, and stabilization to better address potential erosion and sedimentation. Clearcut areas, erosion and sediment estimates, and sediment removal efficiencies were presented for the Mountains, Middle/Lower Coastal Plain, and Piedmont/Upper Coastal Plain for the fourth, fifth, and sixth manuscripts, respectively. Regardless of BMP level and physiographic region, a combination of harvest areas, skid trails, and haul roads were responsible for over 95% of potential sediment delivery. Increasing site-wide BMP implementation from BMP− to BMP+ could reduce sediment delivery by 70% in all physiographic regions. High levels of BMP implementation were most effective at reducing potential erosion and sediment delivery from skid trails and haul roads throughout the southeast. Findings from these studies demonstrate that current BMPs are highly effective at mitigating sediment. In the southeastern U.S., increasing levels of BMP implementation effectively reduce both potential erosion and sedimentation associated with forest harvesting. Generally, both estimated erosion and sedimentation associated with clearcutting in the region is much lower than rates associated with other land uses such as development or agriculture, especially when BMPs are implemented at standard or high levels. However, several opportunities exist to improve the effectiveness of BMPs in the southeastern U.S. Skid trails, haul roads, and stream crossings consistently had the lowest BMP implementation rates and highest estimated erosion rates and sediment delivery ratios. While these features only represent a small proportion of total clearcut area in the southeast, they are responsible for a disproportionate amount of sediment delivery and should receive more attention and resources during the pre-harvest planning and closure processes. Conclusively, this project addresses several knowledge gaps pertaining to water quality impacts resulting from harvesting operations in the southeastern U.S. For instance, this is only the third project that has presented sediment delivery ratios associated with forest operations in the southeastern U.S., and the first to do so for the Mountains and Coastal Plain regions. On average, SMZs and harvest areas trap 66-96% of sediment on-site before it can be deposited into streams. Additionally, this project provides one of the first and most comprehensive regional comparisons of state BMP manuals, audits, and programs in-field using a third-party approach. Several significant differences existed among state BMP programs and protocol, and states may need to design specific BMP guidelines and audit protocol for major physiographic regions to address the challenges and variation of on-site conditions inherent of each region. Additionally, this project presents one of the only regional-scale estimates of sediment and efficiencies of increased levels of BMP implementation at mitigating sediment associated with forest operations in the southeastern U.S. Conclusively, this project provides forest managers, state and federal agencies, and policymakers with a robust assessment on the effectiveness of forestry BMPs in the southeast. / Doctor of Philosophy / Forestry Best Management Practices (BMPs) are used throughout the southeastern U.S. to minimize the impacts that harvesting has on soil and water resources. Eroded soil that is eventually deposited into streams as sediment is the most important pollutant that BMPs address in forestry. Common BMP guidelines utilized to minimize sediment include leaving riparian buffers along streams, providing ground cover, minimizing slopes on roads, and using water control structures to divert runoff from road systems. The exact relationship between forestry BMPs, erosion, and sediment delivery is largely unexamined. Objectively, this study was designed to provide a better understanding of this relationship, and to present estimates of erosion and sediment delivery resulting from clearcut harvesting on over 100 harvest sites across 13 states with diverse conditions and topography in the southeastern U.S. Forestry BMPs are being implemented at an average rate of 90.1% across the southeast. BMPs are implemented at higher rates in the Coastal Plain, followed by the Piedmont and Mountains. Generally, harvest areas had the highest BMP implementation rates, followed by decks, haul roads, stream crossings, and skid trails, respectively. This relationship was consistent across most regions and states. Logging decks, which are areas where wood was transported for processing and loading onto logging trucks, were generally located distantly from streams and followed most state-approved BMPs. Whereas skid trails, which are low-standard temporary roads trafficked during primary transport and require water diversion structures such as waterbars, occupied a much larger area and were generally located on much steeper slopes. Mountain skid trails leading to stream crossings are concerning because of their low BMP implementation rates and high erosion potential. These features would greatly benefit from increased ground cover and water control structures. Forestry BMPs reduce both erosion and sedimentation associated with clearcutting. The highest level of BMP implementation reduces potential sediment by over 70% in all regions, and the highest BMP level is most effective at reducing sediment from skid trails and forest roads. Average sedimentation rates, especially at the highest BMP level, calculated for Mountains, Piedmont, and Coastal Plain clearcuts are considerably lower than sedimentation rates associated with agricultural and developmental land uses. Clearcut forestland, which is generally the most erodible time period during a forest's cycle, only makes up 1-2% of total forestland in the southeast annually. Both erosion and sedimentation rates should decrease further in the years following harvesting as the site revegetates and trees begin to reestablish. This study verifies that BMPs are highly effective at reducing erosion and sediment while subsequently providing estimates of erosion and sediment delivery based on ranges of BMP implementation that state forestry agencies can use to better quantify the effectiveness of their BMPs.

Identifying areas of the hillslope that are most sensitive to soil erosion and contribute significantly to sediment yield is a primary concern in environmental protection and conservation. Therefore the ability to predict the magnitude and variability of soil erosion and sediment yield is important to catchment managers in order to select the appropriate conservation practices that keep soil erosion and sediment yield within the tolerable limits. A number of models have been developed for simulating soil erosion and sediment yield from a catchment. However, none of them are universally applicable and most of them require extensive data which are extremely costly, time consuming and sometimes not available except in research catchments. Hence it was concluded that the combined use of an empirically based soil loss model, RUSLE, Geographic Information Systems (GIS) techniques, and a Sediment Delivery Ratio (SDR) concept would be a candidate modelling tool, which would be a compromise between the advantages of simplicity, data availability, the complex spatial variability of hydrological and geomorphological characteristics of a catchment and the economic limitation of field data measurements in sediment yield studies. Such a modelling tool was developed in this research and was able to identify sediment source areas and predict annual sediment yield from catchments. Data from the Henley catchment, South Africa have been used for demonstrating the potential use of the model in soil erosion and sediment yield studies. Arcview GIS grid functions were used to define the flow direction, accumulation, pathways, and velocity in a catchment as a function of topography and land use and to describe spatially variable input and output information. In addition the Arcview GIS grid function was used to discretise the catchment into hydrologically homogeneous grid cells to capture the catchment heterogeneity. The gross soil erosion in each cell was calculated using the soil loss model RUSLE while a distributed topography based SDR parameter was used to determine the mass of eroded sediment that would be transported to the nearest stream and ultimately to the catchment outlet. The average annual soil loss and sediment yield values were 26 t. ha-1.yr -1 and 1.6 t. ha-1.yr -1 respectively. High soil erosion and sediment yield rates are evident in the residential and agricultural areas, which are characterised by degradation due to overgrazing and traditional and peri-urban settlements with mixed crops. The average annual SDR value was 0.19 for the Henley catchment and large SDR values are associated with areas adjacent to the channel system. This can be explained by recognizing that the SDR is significantly influenced by characteristics of the drainage system. Comparison of event based simulations of sediment yields to those estimated from measurements demonstrated that the proposed model predictions ranged between 13 % and 60 % of the measured estimates, consistently over predicting. This is because the SDR component of the model is developed as a mean annual parameter, assuming that over a long period a stream system must intimately transport all the sediments delivered to it. Hence the channel network sediment delivery parameters would have to be considered at short temporal scales. Comparing the results of the model prediction against other sediment modelling techniques in South Africa demonstrated the usefulness of the model as an effective catchment management tool. The model has advantages over these other techniques since it includes a distributed grid based component, which enables the identification of sediment source areas in the catchment. The sensitivity analysis shows that the model was highly sensitive to parameters derived from topography and land use of the catchment. Future research with the model should include further testing and analysis of its components on different catchments. The topography based SDR concept which is a key component in sediment routing for prediction of either long term average sediment yield or isolated storm event simulation from a catchment warrants specific attention. Effort in future should focus on identifying parameters which affect the sediment delivery within a catchment. This may be achieved by incorporating processes describing the movement of sediments in the channel network of the catchment. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2004.

The erosion and transport of fertile topsoil is a serious problem in the U.S., Australia, China and throughout Europe. It results in extensive environmental damage, reduces soil fertility and productivity, and causes significant environmental loss. It is as big a threat to the future sustainability of global populations as climate change, but receives far less attention. With both chemicals (fertilizers, pesticides, herbicides) and biological pathogens (bacteria, viruses) preferentially sorbing to silt and clay sized soil particles, estimating contaminant fluxes in eroded soil also requires predicting the transported soils particle size distribution. The Hairsine-Rose (HR) erosion model is considered in this thesis as it is one of the very few that is specifically designed to incorporate the effect of particle size distribution, and differentiates between non-cohesive previously eroded soil compared with cohesive un-eroded soil. This thesis develops a new extended erosion model that couples the HR approach with the one-dimensional St Venant equations, and an Exner bed evolution equation to allow for feedback effects from changes in the local bed slope on surface hydraulics and erosion rates to be included. The resulting system of 2I +3 (where I = number of particle size classes) nonlinear hyperbolic partial differential equations is then solved numerically using a Liska-Wendroff predictor corrector finite difference scheme. Approximate analytical solutions and series expansions are derived to overcome singularities in the numerical solutions arising from either boundary or initial conditions corresponding to a zero flow depth. Three separate practical applications of the extended HR model are then considered in this thesis, (i) flow through vegetative buffer strips, (ii) modelling discharge hysteresis loops and (iii) the growth of antidunes, transportational cyclic steps and travelling wave solutions. It is shown by comparison against published experimental flume data that predictions from the extended model are able to closely match measurements of deposited sediment distribution both upstream and within the vegetative buffer strip. The experiments were conducted with supercritical inflow to the flume which due to the increased drag from the vegetative strip, resulted in a hydraulic jump just upstream of the vegetation. As suspended sediment deposited at the jump, this resulted in the jump slowly migrating upstream. The numerical solutions were also able to predict the position and hydraulic jump and the flow depth throughout the flume, including within the vegetative strip, very well. In the second application, it is found that the extended HR model is the first one that can produce all known types of measured hysteresis loops in sediment discharge outlet data. Five main loop types occur (a) clockwise, (b) counter-clockwise, (c,d) figure 8 of both flow orientations and (e) single curve. It is clearly shown that complicated temporal rainfall patterns or bed geometry are not required to developed complicated hysteresis loops, but it is the spatial distribution of previously eroded sediment that remains for the start of a new erosion event, which primarily governs the form of the hysteresis loop. The role of the evolution of the sediment distribution in the deposited layer therefore controls loop shape and behavior. Erosion models that are based solely on suspended sediment are therefore unable to reproduce these hysteretic loops without a priori imposing a hysteretic relationship on the parameterisations of the erosion source terms. The rather surprising result that the loop shape is also dominated by the suspended concentration of the smallest particle size is shown and discussed. In the third application, a linear stability analysis shows that instabilities, antidunes, will grow and propagate upstream under supercritical flow conditions. Numerical simulations are carried out that confirm the stability analysis and show the development and movement of antidunes. For various initial parameter configurations a series of travelling antidunes, or transportational cyclic steps, separated by hydraulic jumps are shown to develop and evolve to a steady form and wave speed. Two different forms arise whereby (a) the deposited layer completely shields the underlying original cohesive soil so that the cohesive layer plays no role in the speed or shape of the wave profile or (b) the cohesive soil is exposed along the back of the wave such that both the non-cohesive and cohesive layers affect the wave profile. Under (a) the solutions are obtained up to an additive constant as the actual location of the boundary of the cohesive soil is not required, whereas for (b) this constant must be determined in order to find the location on the antidune from where the cohesive soil becomes accessible. For single size class soils the leading order travelling wave equations are fairly straightforward to obtain for both cases (a) and (b). However for multi-size class soils, this becomes much more demanding as up to 2I + 3 parameters must be found iteratively to define the solution as each size class has its own wave profile in suspension and in the antidune.