Controls on the aerodynamic roughness length and the grain‐size dependence of aeolian sediment transport

Estimates of the wind shear stress exerted on Earth's surface using the fully rough form of the law‐of‐the‐wall are a function of the aerodynamic roughness length, z₀. Accurate prediction of aeolian sediment transport rates, therefore, often requires accurate estimates of z₀. The value of z₀ is determined by the surface roughness and the saltation intensity, both of which can be highly dynamic. Here we report field measurements of z₀ values derived from velocity profiles measured over an evolving topography (i.e. sand ripples). The topography was measured by terrestrial laser scanning and the saltation intensity was measured using a disdrometer. By measuring the topographic evolution and saltation intensity simultaneously and using available formulae to estimate the topographic contribution to z₀, we isolated the contribution of saltation intensity to z₀ and document that this component dominates over the topographic component for all but the lowest shear velocities. Our measurements indicate that the increase in z₀ during periods of saltation is approximately one to two orders of magnitude greater than the increase attributed to microtopography (i.e. evolving sand ripples). Our results also reveal differences in transport as a function of grain size. Each grain‐size fraction exhibited a different dependence on shear velocity, with the saltation intensity of fine particles (diameters ranging from 0.125 to 0.25 mm) saturating and eventually decreasing at high shear velocities, which we interpret to be the result of a limitation in the supply of fine particles from the bed at high shear velocities due to bed armoring. Our findings improve knowledge of the controls on the aerodynamic roughness length and the grain‐size dependence of aeolian sediment transport. The results should contribute to the development of improved sediment transport and dust emission models. © 2018 John Wiley & Sons, Ltd.     

Estimation of surface roughness (z0) over a stabilizing coastal dune field based on vegetation and topography

Accurate knowledge of the surface roughness and the resultant wind speed are important for many applications, such as climatic models, wind power meteorology, agriculture and erosion hazards, especially on sand dunes in arid and semi‐arid environments, where vegetation cover is scarce. In this study we aimed at quantifying the effects of vegetation cover and topography on surface roughness over a stabilizing dune field on the southern coast of Israel. Forty‐six wind measurements were made at various distances from the coastline, ranging from 10 to 2800 m, and z₀ values were calculated from the wind measurements based on the ratio between the wind gust and the average wind speed. We estimated vegetation cover using the soil adjusted vegetation index (SAVI) from Landsat satellite images for the upwind sector at various lengths, ranging from 15 to 400 m, and based on digital elevation models and differential GPS field measurements we calculated the topographic variable of the relative heights of the stations. z₀ values were positively correlated with the winter SAVI values (r = 0·87 at an upwind length of 200 m) and negatively correlated with the relative height (r = ?0·68 at an upwind length of 200–400 m for the inland dune stations). Using these variables we were able to create a map of estimated z₀ values having an accuracy of over 64%. Such maps provide a better understanding of the spatial variability in both wind speed and sand movement over coastal dune areas. Copyright © 2007 John Wiley & Sons, Ltd.     

Airflow and roughness characteristics over partially vegetated linear dunes in the southwest Kalahari Desert

There is little understanding of the flow-field surrounding semi-vegetated linear dunes, and predictions of dune mobility are hampered by a lack of empirical data concerning windflow. In an attempt to characterize the near-surface airflow upwind of and over partially vegetated linear dunes in the southwest Kalahari Desert, this study presents measurements of vertical and horizontal wind velocity profiles across cross-sectional transects of seven partially vegetated linear dunes. Vegetation surveys combined with velocity measurements from vertical arrays of cup-anemometers, placed up to 2·3 m above the ground surface, were used to gain information concerning the modification of airflow structure caused by the intrusion of the dunes into the atmospheric boundary layer and to predict the variability of aerodynamic roughness (z₀) from interdune to crest. The results suggest an acceleration of flow up the windward slopes of the dunes and, as such, the data correspond to classical theory concerning flow over low hills (essentially Jackson and Hunt (1975) principles). Where the theory is incapable of explaining the airflow structure and acceleration characteristics, this is explained, in part, by the presence of a spatially variable vegetation cover over the dunes. The vegetation is important both in terms of the varying aerodynamic roughness (z₀) and problems concerning the definition of a zero-plane displacement (d). It is considered that any attempts to characterize surface shear stress over the Kalahari linear dunes, in order to predict sand transport and dune mobility, will be hampered by two problems. These are the progressively non-log-linear nature of the velocity profiles over the dunes caused by flow acceleration, and the production of thin near-surface boundary layers caused by areally variable aerodynamic roughness as a result of the partially vegetated nature of the dunes.     

Wind tunnel tests of the dynamic processes that control wind erosion of a sand bed

Aeolian sand transport is a complicated process that is affected by many factors (e.g. wind velocity, sand particle size, surface microtopography). Under different experimental conditions, erosion processes will therefore produce different results. In this study, we conducted a series of wind tunnel experiments across a range of wind velocities capable of entraining sand particles (8.0, 10.0, 12.0, and 14.0 m s^-1) to study the dynamic changes of the shear velocity, aerodynamic roughness length, and sand transport. We found that the shear velocity and aerodynamic roughness length are not constant; rather, they change dynamically over time, and the rules that describe their changes depend on the free-stream air velocity. For wind tunnel experiments without feeding sand into the airflow, the sand bed elevation decreases with increasing erosion time, and this change significantly affected the values of shear velocity and aerodynamic roughness length. A Gaussian distribution function described the relationships between the sand transport rate (q_T) and the duration of wind erosion (T). It is therefore necessary for modelers to consider both deflation of the bed and the time scale used when calculating sand transport or erosion rates. © 2018 John Wiley & Sons, Ltd.     

Wind direction and complex sediment transport response across a beach–dune system

Evidence from a field study on wind flow and sediment transport across a beach–dune system under onshore and offshore conditions (including oblique approach angles) indicates that sediment transport response on the back‐beach and stoss slope of the foredune can be exceedingly complex. The upper‐air flow – measured by a sonic anemometer at the top of a 3·5 m tower located on the dune crest – is similar to regional wind records obtained from a nearby meteorological station, but quite different from the near‐surface flow field measured locally across the beach–dune profile by sonic anemometers positioned 20 cm above the sand surface. Flow–form interaction at macro and micro scales leads to strong modulation of the near‐surface wind vectors, including wind speed reductions (due to surface roughness drag and adverse pressure effects induced by the dune) and wind speed increases (due to flow compression toward the top of the dune) as well as pronounced topographic steering during oblique wind approach angles. A conceptual model is proposed, building on the ideas of Sweet and Kocurek (Sedimentology 37 : 1023–1038, 1990), Walker and Nickling (Earth Surface Processes and Landforms 28 : 111–1124, 2002), and Lynch et al. (Earth Surface Processes and Landforms 33 : 991–1005, 2008, Geomorphology 105 : 139–146, 2010), which shows how near‐surface wind vectors are altered for four regional wind conditions: (a) onshore, detached; (b) onshore‐oblique, attached and deflected; (c) offshore, detached; and (d) offshore‐oblique, attached and deflected. High‐frequency measurements of sediment transport intensity during these different events demonstrate that predictions of sediment flux using standard equations driven by regional wind statistics would by unreliable and misleading. It is recommended that field studies routinely implement experimental designs that treat the near‐surface wind field as comprising true vector quantities (with speed and direction) in order that a more robust linkage between the regional (upper air) wind field and the sediment transport response across the beach–dune profile be established. Copyright © 2012 John Wiley & Sons, Ltd.     

Dynamic controls on wind erosion and dust generation on west‐central Free State agricultural land,South Africa

The west‐central part of South Africa's Free State Province falls within the transition zone between South Africa's sub‐humid, temperate grasslands to the east, and the semi‐arid Karoo and arid Kalahari to the south and west, respectively. The area is characterized by low rainfall (typically 500 mm or less) with high variability, but environmental conditions allow widespread dryland commercial agriculture (maize, sunflowers and stock farming). However, human activity promotes wind erosion and the area is susceptible to dust emissions. This study is the first to quantify the degree of wind erosion on the agricultural soils in the region under prevailing winter to spring climatic conditions and land management practices. Using arrays of cup anemometers, dust deposition traps and saltation impact sensors (Safires), measurements were made of the key erosivity and erodibility drivers that control the degree of wind erosion. Results demonstrate that significant quantities of dust are mobilized, particularly during the months of September and October. Thresholds of wind erosion are shown to respond particularly closely to changes in surface and aerodynamic roughness (z₀) with the amount of collected dust correlating well with measures of wind erosivity that weight the impact of higher wind speeds. Given the importance of surface roughness in controlling erosion thresholds, results show that the opportunity exists for well designed farming practices to control wind erosion. However, it is likely that climatically driven environmental change will impact on some of the identified controls on erosion (wind power, moisture availability) with the result that the wind erosion hazard is likely to increase within this marginal environment. Copyright © 2010 John Wiley & Sons, Ltd.     

Determination of Ventilation Channels In Urban Area: A Case Study of Wrocław (Poland)

Urban areas are among the roughest landscapes in the Earth and its aerodynamical properties are responsible for a lot of processes and phenomena of urban climate, such as surface drag and pollutant dispersion. These properties can be quantitatively expressed by various parameters, with zero plane displacement height (z _d) and roughness length (z ₀) as the most frequently applied. Based on remotely gathered (LIDAR scan) height data and morphometric methods of roughness calculations, the comprehensive procedure to determine ventilation channels in urban area is proposed and implemented on the example from Wroc?aw, Poland. Morphometric analysis of urban structure allowed establishing a proper database of aerodynamic parameters of the city. Then a series of maps of the city showing the distribution of two roughness parameters were prepared. GIS tools were used to carry out the analysis of roughness data, assuming various directions of wind flow. It enabled to determine the locations of potential ventilation paths in the city which, if combined, form large ventilation channels. They may have a significant role in improving air quality and be a valuable source of information for local government responsible for the appropriate development of the city.     

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.     

Aeolian sediment flux decay: Non-linear behaviour on developing deflation lag surfaces

Wind tunnel simulations of the effect of non-erodible roughness elements on sediment transport show that the flux ratio q/q_s, shear velocity U*, and roughness density λ are co-dependent variables. Initially, the sediment flux is enhanced by kinetic energy retention in relatively elastic collisions that occur at the roughness element surfaces, but at the same time, the rising surface coverage of the immobile elements reduces the probability of grain ejection. A zone of strong shearing stress develops within 0·03 to 0·04 m of the rough bed because of a relative straightening of velocity profiles which are normally convex with saltation drag. This positive influence on fluid entrainment is opposed by declining shear stress partitioned to the sand bed. Similarly, because the free stream velocity U_f is fixed while U_* increases, velocity at height z and particle momentum gain from the airstream decline, leading eventually to lower numbers of particles ejected on average at each impact. When the ratio of the element basal area to frontal area σ is approximately equal to 3·5, secondary flow effects appear to become significant, so that the dimensionless aerodynamic roughness parameter Z₀/h and shear stress on the exposed sand bed T_s decrease. It is at this point that grain supply to the airstream and saltation drag appear to be significantly reduced, thereby intensifying the reduction in U_*. The zone of strong fluid shear near the bed dissipates.     

Microtopographic evolution of mineral surfaces as a tool to identify and date young fault scarps in bedrock

Faulting that results in surface ruptures through bedrock can be particularly difficult to date. For example, stratigraphic control on the age of faulting, based on the age of the bedrock, often leaves unacceptably large uncertainty on the age of the faulting. From a paleoseismological perspective, there is a clear need to determine if a bedrock fault scarp is actually a young feature. For young fault ruptures that create fresh mineral surfaces, analysis of microtopography developed by weathering of the mineral surface may provide a quantifiable method for determining the fault age. The direct quantitative measurement of mineral surface microtopography using Atomic Force Microscopy affords a novel method to study the rupture ages of active faults. The method for using microtopographic evolution of mineral surfaces depends on three conditions. The first condition is that freshly exposed mineral cleavage surfaces, which can be described geometrically as planes, are formed during a rupture event. The formation of these fresh surfaces is analogous to the initiation of a weathering ‘clock’ that defines time t=0. Following cleavage formation dissolution of the planar mineral surface occurs. The rate of dissolution for a mineral species under given climatic conditions, governs the rate of mineral surface alteration. Thus as dissolution proceeds, the roughness of the mineral surface increases. We suggest that the progression of microtopographic roughness over time, which can be estimated by computing quantitative statistics derived from digital mineral surface topography, will systematically vary until a steady state surface topography is reached. The fractal dimension, D_f, is one such measure of surface roughness where, D_f at time t=0 is 2. The dissolution of the mineral surface increases the fractal dimension as the removal of material proceeds. We posit that somewhere between D_f=2 and D_f=3, the microtopography reaches a steady state. Therefore, in the pre-steady state stage of surface roughness, the quantitative measure of roughness of the mineral may serve as a measure of time elapsed since faulting. The period of time this initial stage of surface roughening represents is dependent on the mineral and as a consequence, its dissolution rate, in a specific set of environmental conditions. The time elapsed since fault rupture and grain cleavage can also be estimated from the measurement of the volume of material removed through dissolution. If part of the original cleavage surface remains and can be identified then AFM measurements of the surface microtopography can be used to calculate the dissolved volume per unit area.     

Estimation of key surface parameters in semi-arid region and their impacts on improvement of surface fluxes simulation

Uncertainties in some key parameters in land surface models severely restrict the improvement of model capacity for successful simulation of surface-atmosphere interaction. These key parameters are related to soil moisture and heat transfer and physical processes in the vegetation canopy as well as other important aerodynamic processes. In the present study, measurements of surface-atmosphere interaction at two observation stations that are located in the typical semi-arid region of China, Tongyu Station in Jilin Province and Yuzhong Station in Gansu Province, are combined with the planetary boundary layer theory to estimate the value of two key aerodynamic parameters, i.e., surface roughness length z_0m and excess resistance κB^-1. Multiple parameterization schemes have been used in the study to obtain values for surface roughness length and excess resistance κB^-1 at the two stations. Results indicate that z_0m has distinct seasonal and inter-annual variability. For the type of surface with low-height vegetation, there is a large difference between the default value of z_0m in the land surface model and that obtained from this study. κB^-1 demonstrates a significant diurnal variation and seasonal variability. Using the modified scheme for the estimation of z_0m and κB^-1 in the land surface model, it is found that simulations of sensible heat flux over the semi-arid region have been greatly improved. These results suggest that it is necessary to further evaluate the default values of various parameters used in land surface models based on field measurements. The approach to combine field measurements with atmospheric boundary layer theory to retrieve realistic values for key parameters in land surface models presents a great potential in the improvement of modeling studies of surface-atmosphere interaction.     

Estimation of flow resistance in gravel-bedded rivers: A physical explanation of the multiplier of roughness length

The need to estimate velocity and discharge indirectly in gravel-bedded rivers is a commonly-encountered problem. Semilogarithmic friction equations are used to estimate mean velocity using a friction factor obtained from depth and grain size information. Although such equations have a semi-theoretical basis, in natural gravel-bed channels, an empirical constant (6.8 or 3.5) has to be introduced to scale-up the characteristic grain size (D₅₀ or D₈₄) to represent the effective roughness length. In this paper, two contrasting approaches are used to suggest that the multiplier of characteristic grain size is attributable to the effect of small-scale form resistance, reflecting the occurrence of microtopographic bedforms in gravel-bedded environments. First, spatial elevation dependence in short, detailed bed profiles from a single gravel-bedded river is investigated using semivariogram and zero-crossing analyses. This leads to objective identification of two discrete scales of bed roughness, associated with grain and microtopographic roughness elements. Second, the autocorrelation structure of the three-dimensional near-bed velocity field is examined to identify regularities associated with eddy shedding and energy losses from larger grains and microtopographic bedforms. Apart from improving the capacity to determine friction factors for velocity and discharge estimation, the findings have implications in general for the initial motion of gravelly bed material.     

Quantifying flow resistance in mountain streams using computational fluid dynamics modeling over structure-from-motion photogrammetry-derived microtopography

Flow resistance in mountain streams is important for assessing flooding hazard and quantifying sediment transport and bedrock incision in upland landscapes. In such settings, flow resistance is sensitive to grain-scale roughness, which has traditionally been characterized by particle size distributions derived from laborious point counts of streambed sediment. Developing a general framework for rapid quantification of resistance in mountain streams is still a challenge. Here we present a semi-automated workflow that combines millimeter- to centimeter-scale structure-from-motion (SfM) photogrammetry surveys of bed topography and computational fluid dynamics (CFD) simulations to better evaluate surface roughness and rapidly quantify flow resistance in mountain streams. The workflow was applied to three field sites of gravel, cobble, and boulder-bedded channels with a wide range of grain size, sorting, and shape. Large-eddy simulations with body-fitted meshes generated from SfM photogrammetry-derived surfaces were performed to quantify flow resistance. The analysis of bed microtopography using a second-order structure function identified three scaling regimes that corresponded to important roughness length scales and surface complexity contributing to flow resistance. The standard deviation σ_z of detrended streambed elevation normalized by water depth, as a proxy for the vertical roughness length scale, emerges as the primary control on flow resistance and is furthermore tied to the characteristic length scale of rough surface-generated vortices. Horizontal length scales and surface complexity are secondary controls on flow resistance. A new resistance predictor linking water depth and vertical roughness scale, i.e.  H/σ_z, is proposed based on the comparison between σ_z and the characteristic length scale of vortex shedding. In addition, representing streambeds using digital elevation models (DEM) is appropriate for well-sorted streambeds, but not for poorly sorted ones under shallow and medium flow depth conditions due to the missing local overhanging features captured by fully 3D meshes which modulate local pressure gradient and thus bulk flow separation and pressure distribution. An appraisal of the mesh resolution effect on flow resistance shows that the SfM photogrammetry data resolution and the optimal CFD mesh size should be about 1/7 to 1/14 of the standard deviation of bed elevation. © 2019 John Wiley & Sons, Ltd.     

The impact of stress history on bed structure

Recent research has started to focus on how prolonged periods of sub‐threshold flows may be capable of imparting structural changes that contribute to increased bed stability. To date, this effect (termed ‘stress history’) has been found to be significant in acting to increase a bed's critical shear stress at entrainment threshold. However, it is supported by only limited, qualitative and often speculative information on the mechanisms of this stabilization process in grade‐specific studies. As such, this paper uses high resolution laser scanning to quantitatively ascertain the granular mechanics underpinning the relationship between stress history and entrainment threshold for beds of a range of grain size distributions. Employing a bed slope of 1/200, three grain size distributions with median grain sizes (D₅₀) of 4·8 mm [uniform (σ_g = (D₈₄/D₁₆)^0.5 = 1·13; bimodal (σ_g = 2·08); and, unimodal (σ_g = 1·63)] were exposed to antecedent stress histories of 60 and 960 minutes duration. Antecedent shear stress magnitude was set at 50% of the critical shear stress for the D₅₀ when no stress history period was employed. Two laser displacement scans of the bed surface (approximate area 100 mm × 117 mm) were taken, one prior to the antecedent period and one after this period, so that changes to surface topography could be quantified (resolution of x = 0·10 mm, y = 0·13 mm and z = 0·24 mm). Rearrangement of bed surface structure is described using statistical analysis and two‐dimensional (2D) semi‐variograms to analyse scaling behaviour. Results reveal vertical settlement, changes to bed roughness and particle repositioning. However, the bed grain size distribution influences the relative importance of each mechanism in determining stress history induced bed stability; this is the focus of discussion in this paper. Copyright © 2012 John Wiley & Sons, Ltd.     

Laboratory flume studies of microflow environments of aquatic plants

The microflow environments of aquatic plants with reference to Myriophyllum and Hydrilla are simulated in a laboratory flume. A Nix Streamflow microflow meter was used to measure the mean velocity profiles of flow at different densities of plants, flow ranges and measurement positions. Each mean velocity profile consists of three hydrodynamic regimes (i.e. within‐canopy zone, above‐canopy zone and a transitional zone between them), which indicate the presence of two benthic boundary layers (internal and external ones). Out of 38 measured mean velocity profiles, most do not fit a logarithmic relationship. The following hydrodynamic parameters are used in characterizing the flow regimes: local shear velocity (u_*), roughness length (z_o), canopy roughness Reynolds number (Re_*), bed shear stress (τ_o) and laminar sublayer (σ). Copyright © 2002 John Wiley & Sons, Ltd.     

Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

Wind effects on sediment transport by raindrop‐impacted shallow flow: a wind‐tunnel study

In wind‐driven rains, wind velocity and direction are expected to affect not only energy input of rains but also shallow ?ow hydraulics by changing roughness induced by raindrop impacts with an angle on ?ow and the unidirectional splashes in the wind direction. A wind‐tunnel study under wind‐driven rains was conducted to determine the effects of horizontal wind velocity and direction on sediment transport by the raindrop‐impacted shallow ?ow. Windless rains and the rains driven by horizontal wind velocities of 6 m s^?1, 10 m s^?1, and 14 m s^?1 were applied to three agricultural soils packed into a 20 by 55 cm soil pan placed on both windward and leeward slopes of 7 per cent, 15 per cent, and 20 per cent. During each rainfall application, sediment and runoff samples were collected at 5‐min intervals at the bottom edge of the soil pan with wide‐mouth bottles and were determined gravimetrically. Based on the interrill erosion mechanics, kinetic energy ?ux (E_rn) as a rainfall parameter and product of unit discharge and slope in the form of q^bS^c_o as a ?ow parameter were used to explain the interactions between impact and ?ow parameters and sediment transport (q_s). The differential sediment transport rates occurred depending on the variation in raindrop trajectory and rain intensity with the wind velocity and direction. Flux of rain energy computed by combining the effects of wind on the velocity, frequency, and angle of raindrop impact reasonably explained the characteristics of wind‐driven rains and acceptably accounted for the differences in sediment delivery rates to the shallow ?ow transport (R₂ ≥ 0·78). Further analysis of the Pearson correlation coef?cients between E_rn and qS_o and q_s also showed that wind velocity and direction signi?cantly affected the hydraulics of the shallow ?ow. E_rn had a smaller correlation coef?cient with the q_s in windward slopes where not only reverse splashes but also reverse lateral raindrop stress with respect to the shallow ?ow direction occurred. However, E_rn was as much effective as qS_o in the sediment transport in the leeward slopes where advance splashes and advance lateral raindrop stress on the ?ow occurred. Copyright © 2004 John Wiley & Sons, Ltd.     

Characterisation of Fulvic Acids and Glycyrrhizic Acid by Time‐of‐Flight Secondary Ion Mass Spectrometry

Fulvic acids of different origin, spray deposited on polished silicon after dissolution in high‐purity water without any additives, were analysed by time‐of‐flight secondary ion mass spectrometry (TOF‐SIMS) in combination with oblique 24...36 keV SF₅⁺ ion bombardment. The observed, highly reproducible mass spectra cover more than five orders of magnitude in dynamic range, without background subtraction. Apart from lines due to atomic ions and low‐mass ion fragments, the mass spectra exhibit broad maxima between m/z 200...350, mainly due to a beat‐like superposition of lines at every single mass number, up to at least m/z 400. In the negative ion spectra the beats have a spacing of m/z 14, corresponding to a CH₂‐unit. The high‐mass tails of the spectra extend well beyond m/z 5000, with similar slopes in the positive and the negative ion mass spectra. The negative spectra appear to be less affected by fragmentation products than the positive spectra. Fulvic acids (FAs) of different origin show distinctly different spectra, with mean masses ranging between m/z ≈ 450 and 580 (for a low‐mass cut‐off m/z 150). To further verify the ability of TOF‐SIMS to detect molecules and clusters with masses significantly above the maxima of the FA spectra, samples of glycyrrhizic acid (GA, as GA ammonium salt with molecular weight 840) were also analysed. Parent ions as well as multimers (GA)_n were observed as positive and negative ions, up to n = 4 (m/z 3320). The results are compared with spectra recently obtained by other mass spectrometric techniques.     

The surface roughness and planetary boundary layer

Applications of the entrainment process to layers at the boundary, which meet the self similarity requirements of the logarithmic profile, have been studied. By accepting that turbulence has dominating scales related in scale length to the height above the surface, a layer structure is postulated wherein exchange is rapid enough to keep the layers internally uniform. The diffusion rate is then controlled by entrainment between layers. It has been shown that theoretical relationships derived on the basis of using a single layer of this type give quantitatively correct factors relating the turbulence, wind and shear stress for very rough surface conditions. For less rough surfaces, the surface boundary layer can be divided into several layers interacting by entrainment across each interface. This analysis leads to the following quantitatively correct formula compared to published measurements. 1 $$\begin{gathered} \frac{{\sigma _w }}{{u^* }} = \left( {\frac{2}{{9Aa}}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \left( {1 - 3^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \frac{a}{k}\frac{{d_n }}{z}\frac{{\sigma _w }}{{u^* }}\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ = 1.28(1 - 0.945({{\sigma _w } \mathord{\left/ {\vphantom {{\sigma _w } {u^* }}} \right. \kern-\nulldelimiterspace} {u^* }})({z \mathord{\left/ {\vphantom {z L}} \right. \kern-\nulldelimiterspace} L})^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \hfill \\ \end{gathered} $$ where \(u^* = \left( {{\tau \mathord{\left/ {\vphantom {\tau \rho }} \right. \kern-0em} \rho }} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) , σ _w is the standard deviation of the vertical velocity,z is the height andL is the Obukhov scale lenght. The constantsa, A, k andd _n are the entrainment constant, the turbulence decay constant, Von Karman's constant, and the layer depth derived from the theory. Of these,a andA, are universal constants and not empirically determined for the boundary layer. Thus the turbulence needed for the plume model of convection, which resides above these layers and reaches to the inversion, is determined by the shear stress and the heat flux in the surface layers. This model applies to convection in cool air over a warm sea. The whole field is now determined except for the temperature of the air relative to the water, and the wind, which need a further parameter describing sea surface roughness. As a first stop to describing a surface where roughness elements of widely varying sizes are combined this paper shows how the surface roughness parameter,z ₀, can be calculated for an ideal case of a random distribution of vertical cylinders of the same height. To treat a water surface, with various sized waves, such an approach modified to treat the surface by the superposition of various sized roughness elements, is likely to be helpful. Such a theory is particularly desirable when such a surface is changing, as the ocean does when the wind varies. The formula, 2 $$\frac{{0.118}}{{a_s C_D }}< z_0< \frac{{0.463}}{{a_s C_D (u^* )}}$$ is the result derived here. It applies to cylinders of radius,r, and number,m, per unit boundary area, wherea _s =2rm, is the area of the roughness elements, per unit area perpendicular to the wind, per unit distance downwind. The drag coefficient of the cylinders isC _D . The smaller value ofz _o is for large Reynolds numbers where the larger scale turbulence at the surface dominates, and the drag coefficient is about constant. Here the flow between the cylinders is intermittent. When the Reynolds number is small enough then the intermittent nature of the turbulence is reduced and this results in the average velocity at each level determining the drag. In this second case the larger limit forz ₀ is more appropriate.