Calvin Wyatt Rose

Modeling water erosion due to overland flow using physical principles: 1. Sheet flow

A new model for erosion of plane soil surfaces by water is developed using physical principles. Raindrop impact and overland flow remove soil from the original cohesive soil. Once eroded soil enters overland flow, either as aggregates or primary particles, a significant proportion of it returns to the soil bed, forming a cohesionless deposited layer from which it can be removed again by the same erosion processes. The action of the eroding agents will be divided between eroding the unshielded original cohesive soil and reintroducing sediment from the deposited layer. The theory recognizes that the nature of the surface is modified by the erosion and deposition processes affecting it. Solutions of the governing differential equations describing sediment concentration are developed for two distinct equilibrium cases. The first case, when the deposited layer completely shields the original soil, appears to correspond with what has been previously called a “transport-limited” situation. The second case occurs when such shielding is incomplete, and sediment concentration is affected by the cohesive strength of the soil. The resulting equations for sediment concentration at equilibrium are compared with existing equations. Firstly, the equation for the case where the soil is lacking cohesion is shown to be similar to the semiempirical equation of Yang (1973). Secondly, when the soil is cohesive the slope length relationships are shown to be in good agreement with the universal soil loss equation over a wide range of slope steepness.

Developments in Soil Erosion and Deposition Models

Research on water-induced soil erosion illustrates two useful approaches to mathematical modeling. The first, and often the prior type of model, is designed to produce order from a possibly large body of data about the system of interest and to derive conclusions from and summaries of that data base. This type of model may be informed by physical or other appropriate insight into system structure or behavior but depends strongly on the data and on mathematical or statistical modeling concepts.

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.

PLOT-SCALE RAINFALL-RUNOFF CHARACTERISTICS AND MODELING AT SIX SITES IN AUSTRALIA AND SOUTHEAST ASIA

During major runoff events when most soil loss occurs, runoff is likely to dominate the rainfall-driven erosion processes. Thus accurate estimation of the runoff rate is critical to soil loss predictions. At plot scale, the Green-Ampt infiltration model is commonly assumed to be able to describe the temporal variation of the infiltration rate over a storm event. Field measurements of both rainfall intensity and runoff rate at 1-min intervals at six sites in the tropical and subtropical regions of Australia and Southeast Asia, however, strongly suggest that the apparent infiltration rate is closely related to the rainfall intensity and it is essentially independent of the cumulative infiltration amount, features not accord with the Green-Ampt infiltration equation. Furthermore, the storage effect and runoff rate attenuation are not negligible at the plot scale. With an initial infiltration amount to determine when runoff begins, an exponential distribution to describe the spatial variation in the maximum infiltration rate and a linear storage formulation to model the lag between runoff and rainfall, we were able to develop a satisfactory three-parameter model for the runoff rate at 1-min intervals within a storm event.

Soil erosion processes and nutrient loss. I, The interpretation of enrichment ratio and nitrogen loss in Runoff sediment

The ratio of nutrient concentration in eroded sediment to that in the original soil (the enrichment ratio, ER) commonly varies with the accumulated soil loss. The objective of this study was to investigate possible factors contributing to this change in ER when erosion was accompanied by a significant depth of water. The enrichment ratio was directly measured on sediment from a sandy clay loam soil. ER was followed as a function of time for eight erosion experiments in which the mix of erosion processes and the fractional surface cover was varied. By using a simulated rainfall tilting flume facility, experiments covered low slope (0.1%), when rainfall detachment was the only erosion process, and 3% soil surface slope, where the processes of rainfall detachment and entrainment occurred. The type and extent of fractional surface cover was varied for the experiments with the 3% slope. In all cases, the rainfall rate was 100 mm h-1and the drop size was 2.2 mm. A new analytical framework is described, showing that ER can be interpreted from the product of two component distributions. The first component distribution is the concentration of sediment as a function of sediment size (a distribution found to vary with time and mix of erosion processes). The second distribution is nitrogen concentration (largely organic) as a function of size (found to be much less time-variable than sediment size). The conclusions reached, after analysis of these experimental data by using this framework, were: (i) time variation in ER was largely due to time variation in the first component distribution; (ii) values of ER different from unity require some variation with sediment size (or settling velocity) in the concentration of the nutrient sorbed to the soil or closely associated with the soil organic matter; (iii) the more that rainfall detachment dominates runoff erosion as the major erosion process, the more likely it is that ER is greater than unity.

Methodology for a multi-country study of soil erosion management

Abstract This paper describes the theoretical framework used in interpreting data on runoff and soil loss from field experiments to yield information on soil erodibility. This theory has been employed in the form of computer programs in the field experiments in various tropical countries and Australia which have collaborated in the Australian Centre for International Agricultural Research Project 8551 entitled “The Management of Soil Erosion for Sustained Crop Production”. The paper also describes common features of the experimental methodology employed in this project, including a description of the set of data management programs employed. These programs are used to retrieve electronically logged data, to field-check, summarise and compile these data in a form suitable for the analysis programs employed. Subsequent papers in this series illustrate application of the theoretical and experimental methodology outlined in this paper.

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.