W. L. Hogarth

Anaemia of acute malaria infections in non-immune patients primarily results from destruction of uninfected erythrocytes.

While anaemia has long been recognized as a consequence of acute infections with malaria, the relative contributions of direct erythrocyte destruction by parasites, destruction of uninfected erythrocytes and changes in erythropoiesis have been unclear. Fitting of parasitaemia and anaemia data from neurosyphilis patients undergoing malaria therapy to a mathematical model shows that in these patients, an average of 8.5 erythrocytes were destroyed in addition to each erythrocyte observed to become parasitized. The model also showed that dyserythropoiesis plays an insignificant role in the resulting anaemia. The anaemia occurs before a substantial antibody response to parasites or erythrocytes could be generated. We postulate that uninfected erythrocyte destruction occurs through phagocytosis of erythrocytes bound to merozoites killed as a result of the accompanying malaria paroxysms.

Exact nonlinear solution for constant flux infiltration

Recently∗ an analytical nonlinear solution to the problem of two phase oil and water infiltration under a constant flux boundary condition was derived. We show that this solution also applies to the problem of constant infiltration of water by introducing a very simple change in the independent variables of space and time.

Unsteady soil erosion model, analytical solutions and comparison with experimental results

Hairsine and Rose developed a soil erosion model which described the erosion transport of the multiparticle sizes in sediment for rain-impacted flows in the absence of entrainment in overland flow. In this paper we extend their steady-state solutions to account for the time variation of suspended sediment concentration during an erosion event. A very simple approximate analytical solution is found which agrees extremely well with experimental data obtained from nine experiments. We are able to reproduce the rapid initial increase to a peak in the total sediment concentration, which occurs about 3–5 min after the commencement of rainfall, as well as the subsequent declining exponential tail towards steady-state conditions. We are also able to show that the fraction of shielding of the original soil bed resulting from depositing sediment reaches its equilibrium value on about the same time-scale as the total peak suspended sediment concentration. Interestingly, we find that the masses of the individual particles which form this deposited layer are far from equilibrium, and that there is a great deal of continuous reworking and sorting of this material during the erosion event. Finally, our solution shows that the initial peak in the total sediment concentration is due to the enrichment of this sediment by the finer size classes and that as the event continues their percentage contribution diminishes.

Stochastic sediment transport in soil erosion

A stochastic model governing the downslope transport of a sediment particle during an erosion event is described. Particles alternate between resting on the soil bed and being transported by the overland flow. Probability densities and moments are constructed for the distribution of a particles position at a given time, and also for time of passage to a given location. We show that a suitable averaging of the stochastic particle motions in our model gives rise to the deterministic erosion differential of Hairsine and Rose (Hairsine, P., Rose, C., 1991. Soil Sci. Soc. Am. J. 55 (2), 320–324). The model generalized H. Einsteins stochastic model (Der Geschiebebetrieb als Wahrscheinlichkeitsproblem, Verlag Rascher, Zurich, 1937) for bedload transport in streams.

Testing a mechanistic soil erosion model with a simple experiment

A simple experiment was used to test the development of a “shield” over the original soil and associated changes in sediment concentrations as described in the mechanistic Rose erosion model. The Rose model, developed for rain-induced erosion and sediment transport on hillslopes (J. Hydrol., 217 (1999) 149; Trends Hydrol., 1 (1994) 443), was applied to a simple experimental set-up, consisting of a small horizontal soil surface (7 £ 7c m 2 ) under constant shallow (5 mm) overland flow with raindrop impact. The soil consisted of two particle size classes, clay and sand, greatly simplifying the analytical solution of the Rose model by reducing the unknown system parameters to one, the soil detachability. Photographic documentation of shield formation corroborated the conceptual validity of the Rose model. Using a single, best-fit value for the soil detachability, quantitative agreement between modeled and experimental results is excellentOR 2 a 0:9U: This research provides lucidity to the primary processes enveloped in the Rose model and these mechanisms can be extrapolated to more complicated or realistic systems in which the individual processes may be more difficult to recognize. q 2001 Elsevier Science B.V. All rights reserved.

Unsteady soil erosion due to rainfall impact: a model of sediment sorting on the hillslope

A new method is presented for predicting sediment sorting associated with soil erosion by raindrop impact for non-equilibrium conditions. The form of soil erosion considered is that which results from raindrop impact in the presence of shallow overland flow itself where the flow is not capable of eroding sediment. The method specifically considers early time runoff and erosion when sediment leaving an eroding area is generally finer and thus may have a higher potential for transport of sorbed pollutants. The new mechanism described is the formation of a deposited layer on the soil surface, which is shown to lead to sediment sorting during an erosion event. The deposited layer is taken to have two roles in this process: to temporarily store sediment on the surface between successive trajectories, and to shield the underlying soil from erosive stresses. Equations describing the dynamics of the suspended sediment mixture and the deposited layer are developed. By integrating these equations over the length of eroding land element and over the duration of the erosion event, an event-based solution is proposed which predicts total sediment sorting over the event. This solution is shown to be consistent with experimentally observed trends in enrichment of fine sediment. Predictions using this approach are found to only partly explain measured enrichment for sets of experimental data for two quite different soils, but to be in poor agreement for an aridsol of dispersive character. It is concluded that the formation of the deposited layer is a significant mechanism in the enrichment of fine sediment and associated sorbed pollutants, but that processes in the dispersive soil are not as well described by the theory presented.

An analysis of an ordinary differential equation model for a two-species predator-prey system with harvesting and stocking

An analysis is presented for a model of a two-species predator-prey system where each species can be harvested or stocked. Using methods from bifurcation theory the qualitative nature of the steady-state solutions is examined. The effect of harvesting and stocking rates and the prey carrying capacity is examined in detail.

The influence of grass and porous barrier strips on runoff hydrology and sediment transport.

A series of experiments was conducted in a large tilting flume to investigate the effects of buffer strips on flow hydrology and sediment transport/deposition in and around the strips. Changes in flow depth caused by buffer strips of either nails or grass were recorded, photographed, and measured with a high degree of accuracy. Flow retardation took place at some distance ahead of the strips, causing the water level to rise. This distance is dependent upon flume slope and strip density for any given flow rate. With any increase in flume slope, the point at which water depth increased moved closer to the strip, entering it at around 6% slope. An exponential relationship exists between flume slope and backwater length. Backwater length is also dependent on strip density, and the relationship between these two factors is linear. Under our experimental conditions, sediment deposition did not take place within the strips, but before and after it. The lack of deposition inside the strips appears to be contrary to the common expectation from this technique. The bulk of sediment load in the sediment–laden flow approaching the strips was deposited ahead of the strips, commencing at the point where flow depth started to rise. The finer fraction of sediment load that entered the strip with the flow emerged from the other end unchanged. Some deposition took place as fans downstream of the strips, an indication of resistive flow velocity being slower before and after the strips than within them. When the soil or sand were not consolidated, significant erosion took place inside the strips, creating a head fall at the exit end of the strips, which moved upslope within the strips as experiments continued. For the range of slopes and strip widths studied, the efficiency of the grass or nail strips in slowing down the flow and unloading its sediment in the backwater region was independent of the width of strips in the flow direction. Grass strips thus appear to behave more like “grass barriers” or “grass buffers” than “filter strips,” as they are referred to in some literature. The process interpretation of these results is discussed in this article.

Application of a simple soil-water hysteresis model.

Abstract A simple hysteresis model is reformulated on the basis of the Brooks and Corey equation for the relationship between soil-water content and matric potential. In principle, the method requires the knowledge of a drying curve (boundary or primary) to predict the wetting boundary and all scanning curves. Experimental observations used recently to assess a variety of soil-water hysteresis models show that the present model is simple, accurate and general.

Sudden drawdown and drainage of a horizontal aquifer

Drainage of a saturated horizontal aquifer following a sudden drawdown is reanalyzed using the Boussinesq equation. The effect of the finite length of the aquifer is considered in detail. An analytical approximation based on a superposition principle yields a very good estimate of the outflow when compared to accurate numerical solutions. An illustration of the new analytical approach to analyze basin-scale field data is used to demonstrate possible field applications of the new solution.