Experiences with the use of mass-density maps in residual gravity forward modelling

In many modern local and regional gravity field modelling concepts, the short-wavelength gravitational signal modeled by the residual terrain modelling (RTM) technique is used to augment global geopotential models, or to smooth observed gravity prior to data gridding. In practice, the evaluation of RTM effects mostly relies on a constant density assumption, because of the difficulty and complexity of obtaining information on the actual distribution of density of topographic masses. Where the actual density of topographic masses deviates from the adopted value, errors are present in the RTM mass-model, and hence, in the forward-modelled residual gravity field. In this paper we attempt to overcome this problem by combining the RTM technique with a high-resolution mass-density model. We compute RTM gravity quantities over New Zealand, with different combinations of elevation models and mass-density assumptions using gravity and GPS/levelling measurements, precise terrain and bathymetry models, a high-resolution mass-density model and constant density assumptions as main input databases. Based on gravity observations and the RTM technique, optimum densities are detected for North Island of ~2500 kg m^?3, South Island of ~2600 kg m^?3, and the whole New Zealand of ~2590 kg m^?3. Comparison among the three sets of residual gravity disturbances computed from different mass-density assumptions show that, together with a global potential model, the high-resolution New Zealand density model explains ~89.5% of gravitational signals, a constant density assumption of 2670 kg m^?3 explains ~90.2%, while a regionally optimum mass-density explains ~90.3%. Detailed comparison shows that the New Zealand density model works best over areas with small residual heights. Over areas with larger residual heights, subsurface density variations appear to affect the residual gravity disturbance. This effect is found to reach about 30 mGal over Southern Alpine Fault. In order to improve the RTM modelling with mass-density maps, a higher-quality mass-density model that provides radially varying mass-density data would be desirable.     

A model of compensation of topographic masses

The compilation of new global Mohorovii (Moho) topographic data enables the density contrast between the crust and mantle to be estimated. Assuming that this contrast is constant, the minimization of the external gravitational potential induced by the Earth's topographic masses and the Moho discontinuity yields the value of 0.28 g/cm³ for the density jump at the Moho. Moreover, it is shown that the Airy Heiskanen model of compensation only partly compensates the surface topographic masses. To fit the external gravitational potential, induced by the surface topography, the Pratt-Hayford concept of compensation has to be considered. Employing the dynamical flattening of the Earth, the minimum depth of compensation has been estimated at 100–150 km. This means that the topographic masses are compensated throughout the Earth's lithosphere at least.     

The gravitational field of topographic-isostatic masses and the hypothesis of mass condensation II-the topographic-isostatic geoid

In Part I we focussed on a convergent representation of the gravitational potential generated bytopographic masses on top of the equipotential surface atMean Sea Level, thegeoid, and by those masses which compensate topography. Topographic masses have also been condensated, namely represented by a single layer. Part II extends the computation of the gravitational field of topographic-isostatic masses by a detailed analysis of itsforce field in terms ofvector-spherical harmonic functions. In addition, the discontinuous mass-condensated topographic gravitational force vector (head force) is given. Once we identify theMoho discontinuity asone interface of isostatically compensated topographical masses, we have computed the topographic potential and the gravitational potential which is generated by isostatically compensated masses atMean Sea Level, the geoid, and illustrated by various figures of geoidal undulations. In comparison to a data oriented global geoid computation ofJ. Engels (1991) the conclusion can be made that the assumption of aconstant crustal mass density, the basic condition for isostatic modeling, does not apply. Insteaddensity variations in the crust, e.g. betweenoceanic and continental crust densities, have to be introduced in order to match the global real geoid and its topographic-isostatic model. The performed analysis documents that thestandard isostatic models based upon aconstant crustal density areunreal.     

Definition of Physical Height Systems for Telluric Planets and Moons

In planetary sciences, the geodetic (geometric) heights defined with respect to the reference surface (the sphere or the ellipsoid) or with respect to the center of the planet/moon are typically used for mapping topographic surface, compilation of global topographic models, detailed mapping of potential landing sites, and other space science and engineering purposes. Nevertheless, certain applications, such as studies of gravity-driven mass movements, require the physical heights to be defined with respect to the equipotential surface. Taking the analogy with terrestrial height systems, the realization of height systems for telluric planets and moons could be done by means of defining the orthometric and geoidal heights. In this case, however, the definition of the orthometric heights in principle differs. Whereas the terrestrial geoid is described as an equipotential surface that best approximates the mean sea level, such a definition for planets/moons is irrelevant in the absence of (liquid) global oceans. A more natural choice for planets and moons is to adopt the geoidal equipotential surface that closely approximates the geometric reference surface (the sphere or the ellipsoid). In this study, we address these aspects by proposing a more accurate approach for defining the orthometric heights for telluric planets and moons from available topographic and gravity models, while adopting the average crustal density in the absence of reliable crustal density models. In particular, we discuss a proper treatment of topographic masses in the context of gravimetric geoid determination. In numerical studies, we investigate differences between the geodetic and orthometric heights, represented by the geoidal heights, on Mercury, Venus, Mars, and Moon. Our results reveal that these differences are significant. The geoidal heights on Mercury vary from ? 132 to 166 m. On Venus, the geoidal heights are between ? 51 and 137 m with maxima on this planet at Atla Regio and Beta Regio. The largest geoid undulations between ? 747 and 1685 m were found on Mars, with the extreme positive geoidal heights under Olympus Mons in Tharsis region. Large variations in the geoidal geometry are also confirmed on the Moon, with the geoidal heights ranging from ? 298 to 461 m. For comparison, the terrestrial geoid undulations are mostly within ± 100 m. We also demonstrate that a commonly used method for computing the geoidal heights that disregards the differences between the gravity field outside and inside topographic masses yields relatively large errors. According to our estimates, these errors are ? 0.3/+ 3.4 m for Mercury, 0.0/+ 13.3 m for Venus, ? 1.4/+ 125.6 m for Mars, and ? 5.6/+ 45.2 m for the Moon.     

A priori models and inversion of gravity gradient data in hilly terrain

The increased popularity of airborne measurements of the gravity gradient tensor for resource studies and geological mapping has resulted in a new awareness of the importance of terrain effects. In these measurements, the terrain effect often overwhelms that of the underlying crust and it becomes important to formulate a strategy for taking it into account when presenting the data and when inverting the data into density models. Using newly acquired data from Northern Sweden, we first attempted to estimate a variable terrain density model by inverting the data using a terrain model with a laterally varying density. Using data weights related to the topography variations, we find the best estimate of the lateral variation of the terrain density. We translate this model into a full three-dimensional model such that all columns have the same vertical centre of mass as estimated from inspecting the radially averaged power spectrum of the area. This then defines a reference model for subsequent three-dimensional inversion of the gravity gradient tensor dataset. We tested this approach first on synthetic data calculated from the measured topography including two density anomalies before we applied it to the measured data. The result is a model in which the surface density variations are propagated downwards in a systematic manner now in better agreement with measured densities of rock samples in the area.     

Layer-Based Modelling of the Earth’s Gravitational Potential up to 10-km Scale in Spherical Harmonics in Spherical and Ellipsoidal Approximation

Global forward modelling of the Earth’s gravitational potential, a classical problem in geophysics and geodesy, is relevant for a range of applications such as gravity interpretation, isostatic hypothesis testing or combined gravity field modelling with high and ultra-high resolution. This study presents spectral forward modelling with volumetric mass layers to degree 2190 for the first time based on two different levels of approximation. In spherical approximation, the mass layers are referred to a sphere, yielding the spherical topographic potential. In ellipsoidal approximation where an ellipsoid of revolution provides the reference, the ellipsoidal topographic potential (ETP) is obtained. For both types of approximation, we derive a mass layer concept and study it with layered data from the Earth2014 topography model at 5-arc-min resolution. We show that the layer concept can be applied with either actual layer density or density contrasts w.r.t. a reference density, without discernible differences in the computed gravity functionals. To avoid aliasing and truncation errors, we carefully account for increased sampling requirements due to the exponentiation of the boundary functions and consider all numerically relevant terms of the involved binominal series expansions. The main outcome of our work is a set of new spectral models of the Earth’s topographic potential relying on mass layer modelling in spherical and in ellipsoidal approximation. We compare both levels of approximations geometrically, spectrally and numerically and quantify the benefits over the frequently used rock-equivalent topography (RET) method. We show that by using the ETP it is possible to avoid any displacement of masses and quantify also the benefit of mapping-free modelling. The layer-based forward modelling is corroborated by GOCE satellite gradiometry, by in-situ gravity observations from recently released Antarctic gravity anomaly grids and degree correlations with spectral models of the Earth’s observed geopotential. As the main conclusion of this work, the mass layer approach allows more accurate modelling of the topographic potential because it avoids 10–20-mGal approximation errors associated with RET techniques. The spherical approximation is suited for a range of geophysical applications, while the ellipsoidal approximation is preferable for applications requiring high accuracy or high resolution.     

The Rock–Water–Ice Topographic Gravity Field Model RWI_TOPO_2015 and Its Comparison to a Conventional Rock-Equivalent Version

RWI_TOPO_2015 is a new high-resolution spherical harmonic representation of the Earth’s topographic gravitational potential that is based on a refined Rock–Water–Ice (RWI) approach. This method is characterized by a three-layer decomposition of the Earth’s topography with respect to its rock, water, and ice masses. To allow a rigorous separate modeling of these masses with variable density values, gravity forward modeling is performed in the space domain using tesseroid mass bodies arranged on an ellipsoidal reference surface. While the predecessor model RWI_TOPO_2012 was based on the \(5'\times 5'\) global topographic database DTM2006.0 (Digital Topographic Model 2006.0), the new RWI model uses updated height information of the \(1'\times 1'\) Earth2014 topography suite. Moreover, in the case of RWI_TOPO_2015, the representation in spherical harmonics is extended to degree and order 2190 (formerly 1800). Beside a presentation of the used formalism, the processing for RWI_TOPO_2015 is described in detail, and the characteristics of the resulting spherical harmonic coefficients are analyzed in the space and frequency domain. Furthermore, this paper focuses on a comparison of the RWI approach to the conventionally used rock-equivalent method. For this purpose, a consistent rock-equivalent version REQ_TOPO_2015 is generated, in which the heights of water and ice masses are condensed to the constant rock density. When evaluated on the surface of the GRS80 ellipsoid (Geodetic Reference System 1980), the differences of RWI_TOPO_2015 and REQ_TOPO_2015 reach maximum amplitudes of about 1 m, 50 mGal, and 20 mE in terms of height anomaly, gravity disturbance, and the radial–radial gravity gradient, respectively. Although these differences are attenuated with increasing height above the ellipsoid, significant magnitudes can even be detected in the case of the satellite altitudes of current gravity field missions. In order to assess their performance, RWI_TOPO_2015, REQ_TOPO_2015, and RWI_TOPO_2012 are validated against independent gravity information of current global geopotential models, clearly demonstrating the attained improvements in the case of the new RWI model.     

The Time-Varying Gravitational Potential Field of a Massive,Deformable Body

The internal as well as the external gravitational field of the Earth is computed under the assumption that (i) the mass distribution of the deformable body as well as (ii) the heights of the topographic surface and the depths of the interfaces (dynamic isostasy) vary in time. In order to represent those shape variations properly, the topographic masses as well as the interface masses are regarded as condensed following a proposal by F.R. Helmert (1884, p. 149-163). Accordingly time-varying simple layer mass densities are generated. Basic results are collected in 4 boxes.     

Velocity and Attenuation Structure of the Tibetan Lithosphere Under the Hi-CLIMB Array From the Modeling of Pn Attributes

Using seismic data from regional earthquakes in Tibet recorded by the Hi-CLIMB experiment, Pn attributes are used to constrain the velocity gradient and attenuation structure of the Tibetan lithosphere under the Hi-CLIMB array. Numerical modeling is performed using the spectral-element method (SEM) for laterally varying upper-mantle velocity and attenuation, and the seismic attributes considered include the Pn travel-time, envelope amplitude, and pulse frequency. The results from the SEM modeling provide two alternative models for the upper-mantle beneath the Hi-CLIMB array in Tibet. The first model is derived from the 3D velocity model of Griffin et al. (Bull Seism Soc Am 101:1938–1947, 2011) with a constant upper-mantle velocity gradient, and laterally varying upper mantle attenuation. The second model has a laterally varying upper-mantle velocity gradient, and constant upper-mantle attenuation. In both cases, the Qiangtang terrane is distinguished from the Lhasa terrane by a change in Moho depth and upper-mantle velocities. The lower upper-mantle velocities, as well as higher Pn attenuation, suggest hotter temperatures beneath the Qiangtang terrane as compared to the Lhasa terrane. Although the fits to the Pn amplitude and pulse frequency data are comparable between the two models, the first model with the constant upper-mantle velocity gradient fits the travel times somewhat better in relation to the data errors.     

Complex polynomials for the computation of 2D gravity anomalies

We present an efficient algorithm using a complex variables formulation for the computation of the gravity effect of 2D polygonal bodies having densities varying both laterally and with depth. The first derivatives of the gravity effect are also provided in order to enable the computation of the Jacobian matrix, which is necessary for linear inverse gravity problems. A geophysical example based on numerical assumptions about the density contrast on a well-studied basin area shows the applicability of the algorithm.     

Spectral expressions for modelling the gravitational field of the Earth’s crust density structure

We derive expressions for computing the gravitational field (potential and its radial derivative) generated by an arbitrary homogeneous or laterally varying density contrast layer with a variable depth and thickness based on methods for a spherical harmonic analysis and synthesis of gravity field. The newly derived expressions are utilised in the gravimetric forward modelling of major known density structures within the Earth’s crust (excluding the ocean density contrast) beneath the geoid surface. The gravitational field quantities due to the sediments and crust components density contrasts, shown in numerical examples, are computed using the 2 × 2 arc-deg discrete data from the global crustal model CRUST2.0. These density contrasts are defined relative to the adopted value of the reference crustal density of 2670 kgm⁻³. All computations are realised globally on a 1 × 1 arc-deg geographical grid at the Earth’s surface. The maxima of the gravitational signal due to the sediments density contrast are mainly along continental shelf regions with the largest sedimentary deposits. The corresponding maxima due to the consolidated crust components density contrast are over areas of the largest continental crustal thickness with variable geological structure.     

The information content theory for the estimation of the topographic index distribution used in TOPMODEL

This paper analyses the significance of the entropy concept in the topography parameterization within the model TOPMODEL proposed by Beven and Kirkby (1979), by means of the hydrological behaviour of an experimental basin in southern Italy. For a significant number of flood events recorded at the basin outlet, the performance of TOPMODEL for different spatial distributions of the topographic index, ln(a/tan β), has been observed. Performance is related to the information content estimated as an entropy measure, corresponding to each of the spatial distributions of the topographic index, with the aim of identifying the procedures most suitable to represent the hydrological process of rainfall–runoff. The results obtained have shown that for flood events corresponding to brief, heavy precipitation, some procedures provide better performances than others. Moreover, these improvements are justified by greater information content in the corresponding spatial distributions of the topographic index. Finally, TOPMODEL performances for some procedures have been analysed, varying the resolution scale of the topographic index. For analogous hydrological performances, scale change produced variations in some of the subsurface hydraulic parameters. These variations were proportional to a spatial variability measure of the topographic index distribution, derived from the corresponding information content. © 1997 John Wiley & Sons, Ltd.     

Combining Seismic Noise Techniques for Landslide Characterization

A strong topographic relief and the presence of weakly consolidated sediments create favorable conditions for the development of landslides around the eastern rim of the Fergana Basin (Central Asia). In summer 2012, a field experiment employing small aperture seismic arrays was carried out on an unstable slope, using ambient vibration recordings. The aim of the study was to constrain the seismic response of a potential future landslide and to map lateral and vertical changes in the shear-wave velocity of the surficial soil layers. Strong variations of horizontal-to-vertical spectral ratios in terms of amplitude and directionality indicated clear differences in local site effects, probably reflecting the stability of different sections of the slope. Results further showed resonant frequencies of both the entire unstable block, as well as for smaller, individual parts. The use of an ad hoc, passive seismic tomography approach based on noise correlograms allowed for the mapping of the shear-wave velocities of the sliding material, even in cases of significant topography relief. Based on the recording of seismic noise only, we clearly identified a low-velocity body of weakly consolidated claystone and limestone material, which can be interpreted as the landslide body, with laterally varying thickness.     

Stratigraphy and internal structure of wind-dominated barrier islands (dune and machair) of the Outer Hebrides,Scotland

The barrier islands that fringe the western shore of the Outer Hebrides are globally unusual in that they are developed on a planated bedrock (strandflat) surface. They also contain the most extensive area of machair (a distinctive vegetated sandy plain) in the British Isles. This paper presents the first investigation of the internal structure and morphology of these barrier islands and investigates the controls on their structure. The barriers form extensive (300-1000 metres wide) but thin (1.5-2 m) surficial deposits typically resting on bedrock. In areas where depressions exist in the bedrock, and where sediment supply permits, transgressive dunes underlie the machair. A distinctive machair facies of sub-horizontal, undulating reflections, which are laterally continuous over tens of metres is the dominant component of the barriers at each site. This reflects episodic deposition of windblown sand up to the level of the water table. Thereafter any additional sand is transported through the system to accumulate in topographic lows as lake fills, or on topographic highs as ‘high machair’. Eight radar facies were identified, the extent and presence of which vary between the study sites. Bedrock topography and sediment supply are interpreted as the dominant controls on variability in barrier structure. © 2019 John Wiley & Sons, Ltd.     

Gravimetric survey terrain correction using linear analytical approximation

Various methods for computing the terrain correction in a high‐precision gravity survey are currently available. The present paper suggests a new method that uses linear analytical terrain approximations. In this method, digital terrain models for the near‐station topographic masses are obtained by vectorizing scan images of large‐scaled topographic maps, and the terrain correction computation is carried out using a Fourier series approximation of discrete height values. Distant topography data are represented with the help of digital GTOPO30 and Shuttle Radar Topography Mission cartographic information. We formulate linear analytical approximations of terrain corrections for the whole region using harmonic functions as the basis of our computational algorithm. Stochastic modelling allows effective assessment of the accuracy of terrain correction computation. The Perm Krai case study has shown that our method makes full use of all the terrain data available from topographic maps and digital terrain models and delivers a digital terrain correction computed to a priori precision. Our computer methodology can be successfully applied for the terrain correction computation in different survey areas.     

Impact of tidal mixing with different scales of bottom roughness on the general circulation

The current study deals with a parameterization of diapycnal diffusivity in an ocean model. The parameterization estimates the diapycnal diffusivity depending on the location of tidal-related energy dissipation over rough topography. The scheme requires a bottom roughness map that can be chosen depending on the scales of topographic features. Here, we implement the parameterization on an ocean general circulation model, and we examine the sensitivity of the modeled circulations to different spatial scales of the modeled bottom roughness. We compare three simulations that include the tidal mixing scheme using bottom roughness calculated at three different ranges of spatial scales, with the largest scale varying up to 200 km. Three main results are discussed. First, the dependence of the topographic spectra with depth, characterized by an increase in spectral energy over short length scales in the deep ocean, influences the vertical profile of the diffusivity. Second, the changes in diffusivities lead to different equilibrium solutions in the Atlantic meridional overturning circulation and bottom circulation. In particular, the lower cell of the Atlantic overturning and the bottom water transport in the Pacific Ocean are stronger for stronger diffusivities at the corresponding basins and depths, and the strongest when using the small-scale roughness map. Third, a comparison of the density fields of the three simulations with the density field of World Ocean Atlas dataset, from which the models are initialized, shows that among the simulations with three different roughness maps, the one using small-scale bottom roughness map has the smallest density bias.

     

Wave-induced topographic formstress in baroclinic channel flow

Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ ^–2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ ² acts as a vertical eddy viscosity, and the transport is λ ²/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.     

二维不均匀介质中点源P-SV波响应的有限差分近似算法

本文从一阶方程组形式的波动方程出发,发展了一种计算二维不均匀介质中点源P-SV波响应的近似方法。该方法通过引入线分布的应力作为震源,利用二维有限差分方法计算出线源响应,然后再经过波形校正和几何扩散校正得出相应的近似点源响应。通过把波形和振幅与精确解比较表明,该方法具有较好的精度。由于有限差分方法对于介质中速度和密度的分布没有特殊要求,另一方面,本文所给出的震源可以适用于位错点源、爆炸源或集中力源,因此上述方法十分适合于研究横向不均匀介质中的近场强地运动、爆炸振动或地震勘探等问题。     

Eruptive conditions and depositional processes of Narbona Pass Maar volcano,Navajo volcanic field,Navajo Nation,New Mexico (USA)

Phreatomagmatic deposits at Narbona Pass, a mid-Tertiary maar in the Navajo volcanic field (NVF), New Mexico (USA), were characterized in order to reconstruct the evolution and dynamic conditions of the eruption. Our findings shed light on the temporal evolution of the eruption, dominant depositional mechanisms, influence of liquid water on deposit characteristics, geometry and evolution of the vent, efficiency of fragmentation, and the relative importance of magmatic and external volatiles. The basal deposits form a thick (5–20 m), massive lapilli tuff to tuff-breccia deposit. This is overlain by alternating bedded sequences of symmetrical to antidune cross-stratified tuff and lapilli tuff; and diffusely-stratified, clast-supported, reversely-graded lapilli tuffs that pinch and swell laterally. This sequence is interpreted to reflect an initial vent-clearing phase that produced concentrated pyroclastic density currents, followed by a pulsating eruption that produced multiple density currents with varying particle concentrations and flow conditions to yield the well-stratified deposits. Only minor localized soft-sediment deformation was observed, no accretionary lapilli were found, and grain accretion occurs on the lee side of dunes. This suggests that little to no liquid water existed in the density currents during deposition. Juvenile material is dominantly present as blocky fine ash and finely vesiculated fine to coarse lapilli pumice. This indicates that phreatomagmatic fragmentation was predominant, but also that the magma was volatile-rich and vesiculating at the time of eruption. This is the first study to document a significant magmatic volatile component in an NVF maar-diatreme eruption. The top of the phreatomagmatic sequence abruptly contacts the overlying minette lava flows, indicating no gradual drying-out period between the explosive and effusive phases. The lithology of the accidental clasts is consistent throughout the vertical pyroclastic stratigraphy, suggesting that the diatreme eruption did not penetrate below the base of the uppermost country rock unit, a sandstone aquifer ∼360 m thick. By comparison, other NVF diatremes several tens of kilometers away were excavated to depths of ∼1,000 m beneath the paleosurface (e.g., Delaney PT. Ship Rock, New Mexico: the vent of a violent volcanic eruption. In: Beus SS (ed) Geological society of America Centennial Field Guide, Rocky Mountain Section 2:411–415 (1987)). This can be accounted for by structurally controlled variations in aquifer thickness beneath different regions of the volcanic field. Variations in accidental clast composition and bedding style around the edifice are indicative of a laterally migrating or widening vent that encountered lateral variations in subsurface geology. We offer reasonable evidence that this subsurface lithology controlled the availability of external water to the magma, which in turn controlled characteristics of deposits and their distribution around the vent. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Numerical modelling of aeolian erosion over rough surfaces

The presence of non‐erodible roughness elements on erodible surfaces has the effect of absorbing part of the wind shear stress and thus protecting the erodible surface from wind erosion. This paper examines the shear stress distribution over roughness arrays of varying density, representing the progress of erosion on a bed of erodible and non‐erodible particles. Three‐dimensional numerical simulations, simulating wind flow over a bed of particles covered by roughness elements, were conducted in order to investigate the effect of roughness elements on the shear stress near the surface. The results of these simulations confirm that the erosion of soil by wind is strongly attenuated by the presence of roughness elements on the surface and depends on the geometric properties of the roughness elements. Based on the new numerical results obtained, a refinement of existing theoretical approaches is developed to describe the dependence of the friction velocity upon roughness frontal area and real exposed cover rate. The new formulation proposed will allow a more accurate evaluation of shear stress partitioning as a function of topographic changes. Copyright © 2010 John Wiley & Sons, Ltd.