Pseudospectral methods provide fast and accurate solutions for the horizontal infiltration equation

An extremely fast and accurate pseudospectral numerical method is presented, which can be used in inverse methods for estimating soil hydraulic parameters from horizontal infiltration or desorption experiments. Chebyshev polynomial dierentiation in conjunction with the flux concentration formulation of Philip (1973) results in a numerical solution of high order accuracy that is directly dependent on the number of Chebyshev nodes used. The level of accuracy (< 0:01% for 100 nodes) is confirmed through a comparison with two dierent, but numerically demanding, exact closed-form solutions where an infinite derivative occurs at either the wetting front or the soil surface. Application of our computationally ecient method to estimate soil hydraulic parameters is found to take less than one second using modest laptop computer resources. The pseudospectral method can also be applied to evaluate analytical approximations, and in particular, those of Parlange and Braddock (1980) and Parlange et al (1994) are chosen. It is shown that both these approximations produce excellent estimates of both the sorptivity and moisture profile across a wide range of initial and boundary conditions and numerous physically realistic diusivity functions

Revisiting Salvucci’s Semi-analytical Solution for Bare Soil Evaporation with New Consideration of Vapour Diffusion and Film Flow

Bare soil evaporation is controlled by a combination of capillary flow, vapour diffusion and film flow. Relevant analytical solutions mostly assume horizontal flow conditions and ignore gravitational effects. Salvucci (1997) provided a rare example of a semi-analytical solution for vertical bare soil evaporation. However, they did not explicitly represent vapour diffusion and film flow, which are likely to account for a significant proportion of total flow during vertical evaporation from soils. Vapour diffusion and film flow can be incorporated via Salvucci’s desorptivity parameter, which represents the proportionality constant relating Stage 2 cumulative evaporation to the square root of time under horizontal flow conditions. The objective of this article is to implement vapour diffusion and film flow within Salvucci’s semi-analytical solution and test its performance by comparison with isothermal numerical simulation and relevant experimental data. The following important conclusions are drawn. Analytical solutions that assume horizontal flow conditions are inadequate for understanding vertical evaporation problems because they overestimate evaporation rates and mostly predict vapour diffusion and film flow to be of negligible influence. Salvucci’s semi-analytical solution is effective at predicting the order-of-magnitude reduction in evaporation caused by gravitational effects. However, it is unable to identify the correct importance of vapour diffusion and film flow because these processes can only be represented through its desorptivity parameter

Hysteretic sediment fluxes in rainfall-driven soil erosion: Particle size effects

A detailed laboratory study was conducted to examine the effects of particle size on hysteretic sediment transport under time-varying rainfall. A rainfall pattern composed of seven sequential stepwise varying rainfall intensities (30, 37.5, 45, 60, 45, 37.5 and 30 mm h‑1), each of 20-mins duration, was applied to a 5-m × 2-m soil erosion flume. The soil in the flume was initially dried, ploughed to a depth of 20 cm and had a mechanically smoothed surface. Flow rates and sediment concentration data for seven particle size classes ( 1000 µm) were measured in the flume effluent. Clockwise hysteresis loops in the sediment concentration versus discharge curves were measured for the total eroded soil and the finer particle sizes ( 1000 µm). Overall, it is found that hysteresis varies amongst particle sizes and that the predictions of the HR model are consistent with hysteretic behavior of different sediment size classes

Modelling hysteresis in the transport of eroded sediment

Sediment transport hysteresis refers to the different sediment fluxes that can occur for the same discharge. For a single rainfall event, the overland flow hydrograph has rising and falling limbs, for which different hysteresis loops have been observed: (i) clockwise, (ii) anti-clockwise and (iii) figure 8 with both flow orientations. It has been suggested that the shape of these loops can be used to identify the different processes of runoff and sediment transport and the sediment source area. We present simulations carried out using the Hairsine-Rose (HR) soil erosion model that reproduce all of the above hysteresis loops for flow conditions that are straightforward to establish in a laboratory soil-erosion flume Based on the HR model, it is possible to explain the causes of the various types of hysteresis loops, in particular the role of the particle size distribution and the deposited layer of previously eroded sediment. Both of these aspects of the HR model, which are not typically included in commonly used erosion models, are crucial to produce these loops. Furthermore, we found that more involved hysteresis patterns do not depend on complicated rainfall distributions. Instead, spatial distributions of deposited sediment from a previous erosion event play a dominant role in determining the overall form and shape of the loop

Estimation of rainfall-driven soil erosion from different rainfall intensities, exposed areas and initial soil conditions

The factors influencing the rain-splash soil erosion include rainfall characteristics, area exposed to raindrops and soil properties. Understanding of these factors and of their interactions is crucial for better predictions of soil erosion yields. To this end, laboratory flume experiments were conducted varying the precipitation rate, the fraction of exposed soil area and initial soil conditions. The discharge rate and concentrations of individual size classes were measured at the flume outlet. These data were used to investigate the dependence of soil sediment yield on the precipitation rate, area exposed and soil initial conditions. In particular, we examined the role of these factors on predicting experimental results based on a prototype experiment. Results revealed that estimates of the concentrations of individual size classes, taking the area-based approach into account, reproduce satisfactorily the measured data at steady state. It was also found that, under carefully controlled conditions, this proportionality (to area of exposed soil) holds for the entire erosive event. These findings, in terms of sediment concentrations of individual size classes, generalized previous results for the total sediment concentration. At short times, most sediment size classes have an early concentration peak, which was found not to be proportional to the area exposed and effective rainfall rate. Rather, short time behaviour is mainly controlled by the soil antecedent conditions, such as surface roughness, bulk density and soil moisture. For predictions based on precipitation rate, results showed that erosion rates based on a prototype were within a factor two of measured rates. Overall, the results indicate that, for a given soil, experimental data based on a given rainfall rate can be used as a crude estimator of the steady rate of erosion for a different rainfall rate

The Hairsine-Rose Soil Erosion Model: Analysis for Total Sediment Concentration

The Hairsine-Rose (HR) model considers rainfall- and shear-driven erosion of the soil bed, overland transport and sediment deposition. Here, we consider the model for rainfall-driven erosion. The model takes account of the different erodabilities of the original soil and deposited material, as well as onsidering the spatial and temporal behaviour of the different sediment sizes in the eroded bed. This latter feature is crucial, as different grain sizes are transported differently due to the wide range of possible settling velocities. Nevertheless, many experiments, both in the laboratory and the field, measure only total sediment concentrations of eroded material (e.g., at the outlet of a laboratory erosion flume). The HR model equations were summed to obtain a model for total sediment concentration (HRTS model). It was found that the HRTS model includes as a parameter an integral term that gives rise to a closure problem. Consequently, in general solutions must be found by (numerical) iteration in which, essentially, discretization leads to calculation of the sediment size classes in the standard HR model. Nevertheless, we show that accurate approximations can be produced by exploiting the behaviour of the model’s predictions of the deposition of previously eroded material, also known as the shield layer. That is, for circumstances where the spatial dependence of this layer can be neglected (e.g., erosion of a uniform bed by constant rainfall), the shielding of the original soil by the deposited layer can be estimated a priori. Based on this estimate, closed-form solutions for the total sediment eroded can be deduced, from which the transport of any given sediment size class can be calculated. We present closed-form approximations, which compare very well with numerical solutions of the HR model, and which are directly applicable to experiments in which the total sediment concentrations in runoff are measured

Effect of antecedent conditions and fixed rock fragment coverage on soil erosion dynamics through multiple rainfall events

The effect of antecedent conditions and specific rock fragment coverage on precipitation-driven soil erosion dynamics through multiple rainfall events was investigated using a pair of 6-m × 1-m flumes with 2.2% slope. Four sequential experiments – denoted E1, E2, E3 and E4, involved 2-h precipitation (rates of 28, 74, 74 and 28 mm h-1, respectively) and 22 h without rainfall – were conducted. In each experiment, one flume was bare while the other had 40% rock fragment coverage. The soil was hand-cultivated and smoothed before the first event (E1) only, and left untouched subsequently. Sediment yields at the flume exit reached steady-state conditions over time scales that increased with sediment size. Experiments were designed such that both steady and non-steady effluent sediment yields were reached at the conclusion of E1. Results from subsequent experiments showed that short-time soil erosion was dependent on whether steady-state erosion was achieved during the preceding event, although consistent steady-state effluent sediment yields were reached for each sediment size class. Steady-state erosion rates were, however, dependent on the rainfall intensity and its duration. If steady-state sediment yields were reached for a particular size class, that class’s effluent sediment yield peaked rapidly in the next rainfall event. The early peak was followed by a gradual decline to the steady-state condition. On the other hand, for size classes in which steady state was not reached at the end of the rainfall event (i.e., E1), in the following event (E2), the sediment yields for those classes increased gradually to steady state, i.e., the sharp peak was not observed. The effect of rock fragment cover (40%) on the soil surface was also found to be significant in terms of the time to reach steady state, i.e., their presence reduced the time for steady conditions to be attained. Effluent sediment yields for the bare and rock fragment-covered flumes (E1) showed steady conditions were reached for the latter, in contrast to the former. We used the Hairsine-Rose (H-R) model to simulate the experimental data as it explicitly models soil particle size classes. Experiments E1 and E2 involved soil compaction by raindrops, and in this case the model predictions were found to be unsatisfactory. However, compaction was effectively completed by the end of experiment E2, and the model provided reasonable predictions for experiments E3 and E4

Histological interpretation of differentiated vulvar intraepithelial neoplasia (dVIN) remains challenging-observations from a bi-national ring-study

Differentiated vulvar intraepithelial neoplasia (dVIN) is a premalignant lesion that is known to progress rapidly to invasive carcinoma. Accurate histological diagnosis is therefore crucial to allow appropriate treatment. To identify reliable diagnostic features, we evaluated the inter-observer agreement in the histological assessment of dVIN, among a bi-national, multi-institutional group of pathologists. Two investigators from Erasmus MC selected 36 hematoxylin-eosin-stained glass slides of dVIN and no-dysplasia, and prepared a list of 15 histological features of dVIN. Nine participating pathologists (i) diagnosed each slide as dVIN or no-dysplasia, (ii) indicated which features they used for the diagnosis, and (iii) rated these features in terms of their diagnostic usefulness. Diagnoses rendered by > 50% participants were taken as the consensus (gold standard). p53-immunohistochemistry (IHC) was performed for all cases, and the expression patterns were correlated with the consensus diagnoses. Kappa statistics were computed to measure inter-observer agreements, and concordance of the p53-IHC patterns with the consensus diagnoses. For the diagnosis of dVIN, overall agreement was moderate (= 0.42), and pair-wise agreements ranged from slight (= 0.10) to substantial (= 0.73). Based on the levels of agreement and ratings of usefulness, the most helpful diagnostic features were parakeratosis, cobblestone appearance, chromatin abnormality, angulated nuclei, atypia discernable under x 100, and altered cellular alignment. p53-IHC patterns showed substantial concordance (= 0.67) with the consensus diagnoses. Histological interpretation of dVIN remains challenging with suboptimal inter-observer agreement. We identified the histological features that may facilitate the diagnosis of dVIN. For cases with a histological suspicion of dVIN, consensus-based pathological evaluation may improve the reliability of the diagnosis