Show Summary Details

Page of

PRINTED FROM the OXFORD RESEARCH ENCYCLOPEDIA,  ENVIRONMENTAL SCIENCE (environmentalscience.oxfordre.com). (c) Oxford University Press USA, 2016. All Rights Reserved. Personal use only; commercial use is strictly prohibited. Please see applicable Privacy Policy and Legal Notice (for details see Privacy Policy).

date: 28 April 2017

# Soil Sediment Loading and Related Environmental Impacts from Farms

## Summary and Keywords

Beyond damage to rainfed agricultural and forestry ecosystems, soil erosion due to water affects surrounding environments. Large amounts of eroded soil are deposited in streams, lakes, and other ecosystems. The most costly off-site damages occur when eroded particles, transported along the hillslopes of a basin, arrive at the river network or are deposited in lakes. The negative effects of soil erosion include water pollution and siltation, organic matter loss, nutrient loss, and reduction in water storage capacity. Sediment deposition raises the bottom of waterways, making them more prone to overflowing and flooding. Sediments contaminate water ecosystems with soil particles and the fertilizer and pesticide chemicals they contain. Siltation of reservoirs and dams reduces water storage, increases the maintenance cost of dams, and shortens the lifetime of reservoirs. Sediment yield is the quantity of transported sediments, in a given time interval, from eroding sources through the hillslopes and river network to a basin outlet. Chemicals can also be transported together with the eroded sediments. Sediment deposition inside a reservoir reduces the water storage of a dam.

The prediction of sediment yield can be carried out by coupling an erosion model with a mathematical operator which expresses the sediment transport efficiency of the hillslopes and the channel network. The sediment lag between sediment yield and erosion can be simply represented by the sediment delivery ratio, which can be calculated at the outlet of the considered basin, or by using a distributed approach. The former procedure couples the evaluation of basin soil loss with an estimate of the sediment delivery ratio SDRW for the whole watershed. The latter procedure requires that the watershed be discretized into morphological units, areas having a constant steepness and a clearly defined length, for which the corresponding sediment delivery ratio is calculated. When rainfall reaches the surface horizon of the soil, some pollutants are desorbed and go into solution while others remain adsorbed and move with soil particles. The spatial distribution of the loading of nitrogen, phosphorous, and total organic carbon can be deduced using the spatial distribution of sediment yield and the pollutant content measured on soil samples. The enrichment concept is applied to clay, organic matter, and all pollutants adsorbed by soil particles, such as nitrogen and phosphorous. Knowledge of both the rate and pattern of sediment deposition in a reservoir is required to establish the remedial strategies which may be practicable. Repeated reservoir capacity surveys are used to determine the total volume occupied by sediment, the sedimentation pattern, and the shift in the stage-area and stage-storage curves. By converting the sedimentation volume to sediment mass, on the basis of estimated or measured bulk density, and correcting for trap efficiency, the sediment yield from the basin can be computed.

# Introduction

Soil loss from land surfaces by erosion is widespread globally and affects the productivity of all land ecosystems such as agricultural, forest and rangeland ones (Pimentel, 2006). According to Pimentel et al. (1995) each year 75 billion metric tons of soil are removed from the land by wind and water erosion and most coming from agricultural land. Each year about 12 × 106 ha of arable land are destroyed and abandoned because of unsustainable farming practices; in other words, each year 0.8% of the arable land area ceases to be useful for agriculture.

Soil erosion is a complex process (see Box 1) that depends on soil properties, ground slope, vegetation, rainfall amount, and intensity. Surface erosion is a natural phenomenon that has occurred since the Earth was formed; however, the acceleration of this process through anthropogenic perturbations can have a severe impact on soil and environmental quality (Montgomery, 2007).

Box 1. A brief introduction to soil erosion and sediment yield.

 Soil erosion and sedimentation processes include detachment, entrainment, transport, and deposition of soil particles. Soil loss is the amount of soil particles detached by rainfall and rill flow and transported by overland and rill flow. “Sediment yield” and “sediment delivery” express the amount of sediment transported from the point in which the soil particles are detached to the base of a hillslope, to a boundary of a field, in a stream channel or at the basin outlet. Erosion prediction technology is a powerful tool used in quantitative assessment of soil loss rates, conservation planning, and engineering design. Erosion prediction technologies use mathematical equations and input data (rainfall, soil type, topography, land use, and land management) for computing soil erosion variables (soil loss, sediment yield). Many mathematical models are available and are characterized by different spatial or temporal scales and various levels of complexity. Models range from empirical to physically based or process-oriented, and their complexity and the required input data vary considerably. The simplest model is an empirical correlation between one or more input variables or controlling factors (rainfall, soil type, crop cover) and the output variable such as soil loss. This type of model is usually termed “black-box” and no understanding or modelling of the processes linking the input and the output erosion variables is used for deducing the model which is usually expressed by a statistical relationship. The model is termed “gray-box” when its deduction is based on some understanding of the relationship between input and output variables. Typically the Universal Soil Loss Equation (USLE) is a good example of this type of model, in which the relationship between soil loss, rainfall erosivity, and soil type is corrected using information on slope steepness, slope length, crop cover, and anti-erosive measures management. Finally, in “white-box” models, an attempt is made to mathematically describe the processes of detachment, entrainment, transport, and deposition of soil particles. In these models, with the exception of the equations based on the laws of conservation of mass and energy, many of the other equations used are actually empirical or similar to those used in the gray-box models. Sediment problems can occur at scales ranging from the field to small or large basins. When the aim of the study is to estimate the sediment yield at the basin outlet a lumped approach coupling a soil erosion model, such as USLE, with the basin sediment delivery ratio (the ratio between sediment yield and gross erosion). Since most practical applications require to know where erosion and deposition take place within a basin, for example to locate protection measures in sediment source areas or along pathway of sediment movement, distributed models are used. Distributed models, such as Sediment Delivery Distributed (SEDD) model, divide the basin into discrete land units and use mathematical procedures to route water and sediment from one unit to another.

Soil erosion can be a manifestation of soil degradation because it produces physical removal of soil in a vertical and horizontal direction leading to a degradation of soil quality (Lal, 2001).

Changes in land use are capable of accelerating soil erosion, and when soil erosion exceeds soil production, reduction of agricultural potential can occur.

Ellison (1947a, 1947b) defined soil erosion as “a process of detachment and transportation of soil material by erosive agents.” According to a classic scheme of the erosive process, the following four phases are distinguished: rainsplash, overland flow, rill, and gully erosion.

The impelling force, caused by raindrops hitting the soil surface, determines soil particle detachment and transport (splash erosion). Soil detachment by rainfall impact is the main process controlling interrill soil erosion because the detachment capability of overland flow is negligible. Overland flow is characterized by both small water depths and shear stresses and is only able to transport soil particles detached by rainfall.

The hillslope flow rarely is distributed evenly on the soil surface. More commonly, some ephemeral features, named rills, form on the hillslope. Rills (Figure 1) are small and intermittent water channels that do not interfere with conventional tillage operations. Once obliterated, rills will not reform at the same site. Gullies are relative permanent, steep-sided channels in which ephemeral flows occur during the rainfall event and cannot be obliterated by usual tillage operations. Ephemeral and permanent gullies are usually deep channels (Figure 2) with a narrow cross-section.

Click to view larger

Figure 1. View of an experimental plot and the incised rills after a rainfall event.

Click to view larger

Figure 2. View of an ephemeral gully and of the profilometer used for measuring the cross-sections.

Soil erosion has both on-farm and off-farm effects. Typically reduction of soil depth can affect the land’s productivity while the transport of sediments on hillslopes can degrade streams and lakes. When eroded soil particles wash off a field, they will be transported by overland flow and channelized flows on the hillslopes until discharged into a water body or stream. Not all agricultural or pollutant constituents are transported from the field to the water system, but a significant portion of pollutants, which are chemically active, is carried by finer soil particles which are the most transportable by runoff.

Eroded soil particles carry away nutrients such as nitrogen phosphorus, potassium, and calcium. Typically, eroded soil particles contain about three times more nutrients than are left in the remaining soil (Young, Olness, Mutchler, & Moldenhauer, 1986). Often, large quantities of fertilizers are applied at farm scale to mitigate the debilitating effect that soil erosion has on the productive capacity of agricultural lands. The fertilizer input creates an environmental pollution problem, since it increases the chemicals transported at hillslope scale and it contributes to high energy consumption and unsustainable agricultural systems. Pollutants from agricultural activities entering streams in diffuse patterns over wide areas, such as basins, constitute nonpoint source pollution (Troeh, Hobbs, & Donahue, 1991).

The most costly off-site damages occur when eroded particles, transported along the hillslopes of a watershed, arrive at the river network or are deposited in lakes.

The transported sediments contaminate the water with soil particles, fertilizer, and pesticide chemicals which alter habitat quality. Suspended soil particles alter the biologic nature of water systems by reducing the transmission of sunlight, raising surface water temperature and affecting the respiration and digestion of aquatic life (Uri, 2000). Suspended soil particles raise the treatment costs of using water and can also damage moving parts of hydraulic machines such as pumps and turbines.

Sediment carries a quantity of plant nutrients and other chemicals which is greater than the one dissolved in the water. Several studies demonstrated that most of the nitrogen and phosphorus moving from fields into streams is transported by sediments. Some pesticides are dissolved in water, but many chemicals are adsorbed by soil colloids and transported by sediments.

When eroded soil particles are deposited on the bottom of a river or a lake, they also cause problems for aquatic life by covering food sources, hiding places, and nesting sites.

Siltation is a major problem in reservoirs because it reduces water storage, increases the maintenance cost of dams, and shortens the lifetime of reservoirs.

Reservoir sedimentation is a complex process that varies with basin sediment yield, transport rate, and mode of deposition. Sedimentation reduces storage capacity for flow regulation and with it all water supply and flood control benefits. Sediment control strategies can be executed for reducing sediment inflow by erosion control.

In stream beds, sedimentation reduces the channel conveyance and increases the frequency and severity of flooding because of the reduced channel capacity. Sediment eroded from upland areas and streambeds is transported downstream and is deposited where the flow velocity decreases. This raises the bottom level of a river and reduces channel capacity so that during a flood the water level overtops the banks and the flow floods the surrounding land.

The following discussion deals with the transport of sediments from eroding sources through the hillslopes and the river network to a basin outlet. The basin sediment delivery ratio and its estimate at hillslope scale are presented. The link between the sediment yield spatial distribution and the corresponding distribution of clay, organic matter, and all pollutants adsorbed by soil particles is analyzed. For estimating the basin sediment yield and its spatial distribution inside the basin, an empirical soil erosion model at plot scale is also discussed.

Finally, the estimate of sediment delivery processes coupled with the evaluation of soil loss at hillslope scale is introduced for estimating pollutants enrichment and reservoir sedimentation phenomena.

# Sediment Yield and Sediment Delivery Processes

Sediment yield is the quantity of transported sediments, in a given time interval, from eroding sources through the river network to a basin outlet.

Sediment is eroded and transported on the hillslopes by the process of detachment (separation of soil particles from the mass of soil), entrainment (the detached particles become the sediment load of a flow), transport (movement of eroded soil particles by flow), and deposition (a specific amount of sediment load is transferred from the flow to the soil surface) by water.

The quantity of sediment leaving an area is determined by the amount of sediment made available by detachment process or by transport capacity of the erosive agent (rainfall and runoff). If the amount of sediment produced by soil detachment is less than the flow transport capacity, the amount of sediment leaving the area is controlled by detachment processes; i.e., the process is detachment limited. If the flow transport capacity is less than the detached soil available to be transported, the amount of sediment leaving the area is controlled by transport processes; i.e., the process is transport limited.

In other words, sediment delivery processes in a given area determine the effective quantity of sediments leaving an area and are due to detachment limited or transport limited conditions.

The water erosion process at basin scale is based on a spatial context in which interrill areas, rill, ephemeral gully, permanent gully, and stream channels are present (Ferro, 2006). On interrill areas the soil particles are detached by rainfall impact and are transported by interrill flow, which has the hydraulic characteristics of an overland flow with a very wide rectangular cross-section. Since the overland flow is characterized by low values of both water depth and bottom shear stress, it is not able to detach soil particles and is able to transport only the detached particles. In other words, the sediments delivered from interrill areas to rills are detached by rainfall impact and are transported by interrill overland flow. Sediment delivery processes from interrill areas to rills are controlled by either a detachment-limited or a transport-limited condition. Generally interrill sediment delivery is controlled by the quantity of soil detached particles by rainfall while the flow transport capacity becomes the limiting factor when the interrill slope steepness is low.

The basic principle of detachment- and transport-limiting condition also applies to rill areas (Toy, Foster, & Renard, 2002). Deposition inside a rill occurs when the effective sediment load of the rill flow exceeds its transport capacity, and the deposition rate is proportional to the difference between sediment load and rill flow transport capacity.

Ephemeral gullies are scoured by concentrated flows, but unlike rills, ephemeral channels occur in the same location each season and are strongly affected by landscape configuration. Ephemeral gullies are narrow enough to allow passage of tillage implements and other farm equipment across them during normal farm operations (Di Stefano & Ferro, 2011; Laflen, Watson, & Franti, 1986).

Ephemeral gullies (EG) can vary in length and width, and are mainly located along natural drainage-lines (thalwegs of zero-order basins or hollows) or along linear landscape elements such as, for instance, dead furrows coinciding with parcel borders, tractor tracks, unpaved access roads, etc. (Poesen, Nachtergaele, & van Wesemael, 1996). These erosion features are continuous, temporary channels, which are often refilled by ordinary filling (Capra, Di Stefano, Ferro, & Scicolone, 2009; Capra & Scicolone, 2002; Casalí, Loizu, Campo, De Santisteban, & Álvarez-Mozos, 2006; Casalí, López, & Giràldez, 1999; Poesen, Nachtergaele, Verstraeten, & Valentin, 2003).

Although ephemeral gullies can occur on almost any soil surface, they are normally restricted to cultivated fields that have highly erodible soils, little or no crop residue cover, and where crop harvest disturbs the soil. Ephemeral gully erosion occurs on cultivated land during rainstorms following seedbed preparation, planting and crop establishment periods. Ephemeral gullies can cause large soil losses that contribute to on-site loss of soil productivity, inconvenience to farming operations, off-site sedimentation problems, and nonpoint source pollution (Auzet, Boiffin, Papy, Maucorps, & Ouvry, 1990; Vandaele, 1993). According to Foster (1982), ephemeral gullies facilitate coarse particle and soil aggregate transport in a more efficient way than rills.

The formation of a typical ephemeral gully cross-section is controlled by several factors (Vandaele, Poesen, Marques de Silva, & Desmet, 1996), such as the rainfall intensity, the size of the basin, the morphology of zones of runoff concentration, etc. The mechanism of evolution of an ephemeral gully is strongly affected by processes causing soil stratification. The tilled topsoil is easily erodible while the subsequent soil layer, not worked and compacted, is more resistant to erosion or even nonerodible. The ephemeral gully channel, after having caused the incision of the erodible layer, begins to erode the base of its channel banks and consequently the gully widens. The widening of the ephemeral gully cross-section goes on until the flow shear stress at the channel bank is equal to or exceeds its critical value (Foster, 1982).

If ephemeral gullies are not filled during farm operations, they rapidly evolve into permanent gullies that constitute effective links for transferring runoff and sediment from uplands to valley bottoms, contribute to denudation processes, may generate badlands, and aggravate off-site effects of water erosion (Woodward, 1999).

According to Moges and Holden (2008), gullies can be a natural part of the landscape or can be artifacts arising from agricultural activities. Surface flow is the most common mechanism for gully initiation (Morgan, 1986), and the resulting gully growth is dominated by gully-head retreat upslope.

Permanent gullies are steep-sided channels in which ephemeral flows occur during rainstorms and cannot be eliminated by usual tillage operations.

The mass balance equation describing the relation of sediment yield Ys to upland erosion can be written as follows (Toy et al., 2002):

$Display mathematics$
(1)

in which Air is the interrill and rill erosion on the portion of landscape where overland and rill flow occur, Ach is the water erosion due to concentrated flow (ephemeral and permanent gully), Dup is the deposition on upland areas, and Dval is the sedimentation on the valley floor.

# Sediment Delivery Ratio

In the 1950s, researchers studying sediment deposition in reservoirs concluded that the quantity of sediments deposited into and passed through the reservoirs was smaller than the upland soil erosion. The difference between sediment yield and weight of eroded soil was an order of magnitude, and for overcoming these differences a parameter known as delivery ratio was introduced (Novotny & Chesters, 1989).

The use of the term sediment delivery ratio was probably introduced for the first time by the work of Glymph (1954), which defined the sediment delivery rate as “the percentage relationship between annual sediment yield and annual gross erosion in the watershed, the percentage being derived with both sediment yield and erosion expressed in tons” (Parsons, Wainwright, Brazier, & Powell, 2006). Sediment yield is defined as the amount of sediment leaving the basin while gross erosion is defined as the absolute amount of eroded particles within the basin.

The definition of sediment yield implies the need to establish the time period (event, month, year, multiyear period) in which the quantity of sediments is transferred from the eroding sources through the hillslopes and the channel network to the basin outlet.

For a given time period, the sediment delivery ratio is a mathematical operator representing the sediment transport efficiency of the hillslopes and the channel network (Kirkby & Morgan, 1980; Renfro, 1975; Walling, 1983). According to Meyer and Wischmeier (1969), this mathematical operator can be complex and represents, for each subarea into which the basin is divided, the balance between the sediment transport capacity of the flow, and the sum of the upstream sediment yield and soil erosion by raindrop impact and runoff.

The basin sediment delivery SDRw is the fraction of gross erosion (interrill, rill, ephemeral gully, gully, and stream erosion) that is expected to be delivered to the outlet of the drainage area considered (Glymph, 1954; Maner, 1958; Roehl, 1962; Walling, 1983).

The magnitude of the basin sediment delivery will be influenced by many geomorphological and environmental factors, such as extent and location of sediment sources, slope steepness, slope length, drainage pattern, stream length, land cover and soil texture and structure.

Channel erosion produces sediments which are immediately available since they are inside the stream system and a lot of sediments remain in motion as suspended load and bedload.

A sediment source area which is remote from the stream, even if it is subjected to severe erosion phenomena, has a sediment delivery ratio less than an area close to the stream; in other words, a sediment source area close to the stream, with moderate erosion, can have a contribution to basin sediment yield greater than an area far from the stream and subjected to severe soil loss.

A river system having a high drainage density has the greatest probability of becoming the final recipient of transported eroded material from the hillslopes. The condition of the channels affects the delivery along the river: steep stream slopes provide more efficient transport of eroded material.

The size distribution and density of the sediment are the primary factors which determine whether soil particles are transported or deposited for a given flow condition (Di Stefano & Ferro, 2002; Harmon, Meyer, & Alonso, 1989; Rothon, Meyer, & Whisler, 1982). Sand-size eroded particles need efficient transport systems and relatively high flow velocities. Eroded material having a silt and clay size has a high transportability and can be easily delivered to a downstream point which sand grains cannot reach.

Soil erosion work has directed attention to the properties of the eroded material, including grain size, particle shape, density, organic matter content, mineralogy, and aggregate stability, because of their influence on the sediment delivery processes and the importance of sediment-associated transport in nonpoint pollution problems.

Slattery and Burt (1997) carried out an investigation of sediment delivery from a small agricultural basin and provided information on the size of the eroded particles and transported sediments under natural conditions. These authors, by analyzing the grain size distribution of the sediment collected during storm events, concluded that for increasing flow discharge values the sediment load generally becomes finer and less well aggregated, probably due to the increased flow turbulence, which in turn influences aggregate breakdown. Slattery and Burt (1997) also reported that most of the clay grains seemed to move as individual particles or at least clay-sized aggregates both as suspended sediment in the stream and in the sediment transported by hillslope runoff.

An important characteristic of a basin is its size, which can be indexed by drainage area. Furthermore high relief is often indicative of transport efficiency and high sediment delivery ratio values. The relief-length ratio of the basin is the ratio of the difference between the elevation of the water divide at the headwater of the main channel and the elevation of the basin outlet and the length of the main channel from the headwater to the basin outlet.

Sediment delivery ratio equations have been developed from studies of basins located in particular regions and their predictive ability becomes therefore limited to these investigated regions (Kent Mitchell & Bubenzer, 1980). For this reason, SDRw values reported in literature for given basins and specific time intervals (for example the mean annual value) can vary from 0.1% to 100% (Walling, 1983).

Sediment delivery ratio, generally decreasing with increasing basin size, is indexed by basin area or stream length, and ASCE (1975) suggested the use of the following power function:

$Display mathematics$
(2)

in which K and n are numerical constants and Sw is the basin area.

The available regional relationships (Ferro & Minacapilli, 1995) have the mathematical shape of equation (2) with an exponent n varying between 0.01 and 0.25. ASCE (1975) supports the idea that, even if a wide range of intercept values exists, the value of the exponent equal to 0.125 can be considered typical. The noticeable variability of SDRw for a given Sw is due to the influence of local factors. For example, the SDRw values measured for Blackland Prairie, Texas (Maner, 1962) are greater than those measured for other American basins (Ferro & Minacapilli, 1995), and this difference probably reflects on the high clay content of the soil in the Blackland Prairie region. The clay particles, as individual particles transported in suspended load, are generally not deposited along the hillslope conveyance system or in the channel network (Williams & Berndt, 1972).

The inverse relationship between SDRw and Sw can be explained by the upland theory of Boyce (Richards, 1993). According to this theory, the steeper areas of a basin are the main sediment-producing zones, and since the average slope of both hillslopes and main stream decrease with increasing basin size, the sediment yield per unit area decreases too. Furthermore, large basins have more sediment storage sites located between sediment source areas and the basin outlet.

The wide range of variability of the sediment delivery ratio and the absence of a general predictive equation may also result from the difficulties associated to with both the estimate of gross erosion and the existence of a locally unique relationship between sediment yield and gross erosion.

The sediment delivery ratio is a lumped concept, from a temporal and spatial point of view, and it has a typical black-box nature.

The characteristic temporal lumping of SDRw can be examined from the individual storm to the long period. Piest, Kramer, and Heinemann (1975) demonstrated that at event scale the range of the sediment delivery ratio can be particularly wide. These researchers, studying a small American basin for the period 1965–1971 in which occurred 55 erosion events, documented the lack of a clear relationship between measured sediment yield and estimated basin gross erosion. The wide range of the sediment delivery ratio (0.01–5.54) was justified taking into account the antecedent soil moisture condition and the period of the year in which each erosive event occurred. At annual scale, for the same basin, the sediment delivery ratio varied from 0.06 to 0.72 and was correlated to the annual rainfall and the seasonal distribution of precipitation. This result can be justified taking into account that the estimate of the gross erosion can be more simple and reliable at annual scale that at event scale and that the models used for estimating the gross erosion tend to overestimate the low soil erosion value and underestimate the largest ones (Nearing, 1998).

From a physical point of view, the values of sediment delivery ratio greater than one can be explained as a short-term sediment storage, during the smallest rainfall-runoff event, and a subsequent sediment remobilization during the largest erosion events. Trimble (1975, 1976) demonstrated the existence of attenuation by storage and remobilization within the sediment delivery process over a long time scale. In particular, Trimble demonstrated that only a small fraction of the eroded particles was transported out of the basin area by the river network; most of the transported sediments were accumulated as alluvium in the valley systems.

# Spatial Variability of Sediment Delivery

According to Walling (1983), problems of spatial lumping could be due to the difficulties of representing the sediment delivery characteristics of a basin using a single number. The variability of morphology, soil characteristics, soil condition and land use within a basin can determine variations in sediment delivery response. Burns (1979) suggested that each sediment source within the basin has a different probability that sediments will be exported from the area to contribute to the basin sediment yield. Each sediment source should have a different sediment delivery response depending on its position with respect to the stream and the basin divide.

According to Walling (1983) the sediment delivery ratio is a black-box concept, and “because it subsumes a variety of processes, it is difficult to assess the precise influence of various controlling factors and to forecast changes that might result from changes in catchments condition.”

The sediment delivery process is the result of many processes, each related to environmental variables, and its estimate requires both a detailed description of the movement of the eroded particles from the source area through the basin system to the outlet and that the spatial and temporal variability of the basin system be taken into account.

In reality, sediments are produced from different sources distributed throughout the basin; each source is characterized by its sediment detachment, transport, and storage. Each source area is also characterized by its travel time, i.e., the time that particles eroded from the source area and transported through the hillslope conveyance system take to arrive at the channel network.

Sources of sediments are not necessarily areas involved in intense soil erosion phenomena because of the different flow capacity to transport sediments on hillslopes and channels.

The dependence of the sediment delivery processes on local factors (sediment detachment, flow transport, travel time, etc.) emphasizes the need to use a spatially distributed approach for modeling this phenomenon. Applying a spatially distributed strategy at the basin scale requires the choice of both a soil erosion model to estimate gross erosion and a spatial disaggregation criterion for the sediment delivery processes.

An estimate of soil loss by a physically based model is theoretically preferable to an estimate obtained by using an empirical approach like the Universal Soil Loss Equation (USLE). However, at present, the physically based models are mainly for understanding processes (Quinton, 1994) and give soil loss estimates whose reliability is comparable to, or less than, the one obtained by a simple parametric approach like USLE and its revised version (RUSLE) (Tiwari, Risse, & Nearing, 2000).

A process-oriented model, like the Water Erosion Prediction Project (WEPP) (Nearing, Foster, Lane, & Finkner, 1989), is able to predict spatial and temporal distribution of soil loss and deposition and has the real advantage of providing estimates of when and where erosion is occurring so that conservation measures can be properly designed.

Since the USLE still represents the better agreement between the simplicity of application, in terms of required input data and accuracy of obtainable soil loss estimates (Risse, Nearing, Nicks, & Laflen, 1993), its use at basin scale can be conveniently coupled with a spatial discretization criterion of sediment delivery processes to obtain a soil erosion and deposition spatial distribution (Di Stefano, Ferro, & Porto, 1999a, 1999b; Ferro, 1997; Ferro, Di Stefano, Giordano, & Rizzo, 1998; Ferro & Minacapilli, 1995; Ferro & Porto, 2000).

Applying a sediment delivery model at hillslope scale, such as the Sediment Delivery Distributed (SEDD) model (Ferro & Porto, 2000), also needs the choice of the temporal scale, from the single event to a mean year of a multiyear period.

At mean annual temporal scale, the channel component of the sediment delivery problem, i.e., the mitigation of sediment yield due to sediment transport within the channel network, can be neglected according to Playfair’s law of stream morphology, which establishes that over a long time a stream must essentially transport all sediments delivered to it (Richards, 1993; Walling, 1983). For the floodplain system, Walling, Bradley, and Lambert (1986) measured significant sediment deposits, and Leopold, Wolman, and Miller (1964) suggested that sediments eroded from a drainage basin are only temporarily stored in floodplains.

For a small basin, having an ephemeral channel network and with no well-developed floodplains, the channel sediment delivery component can be neglected at event scale too (Richards, 1993).

For studying the within-basin variability of sediment delivery the basin has first to be divided into elementary units (square [Figure 3a] and triangular cells [Figure 4]), and morphological units (Figure 3b) (Aksoy & Kavvas, 2005) where calculating the variables appearing in the physically based equations (Morgan & Nearing, 2000) or the parameters of the selected empirical model (Nearing et al., 1989; Wischmeier & Smith, 1978). In particular, morphological units areas are characterized by clearly defined aspect, slope length, and slope steepness (Bagarello, Baiamonte, Ferro, & Giordano et al., 1993; Ferro & Porto, 2000) (Figure 5).

Click to view larger

Figure 3. Example of subdivision of a basin are into (a) square cells and (b) morphological units.

Click to view larger

Figure 4. Example of basin area divided into triangular irregular cells.

Click to view larger

Figure 5. Example of basin area divided into morphological units with flow direction information.

A distributed approach allows for within-basin variability of the sediment delivery and, in particular, takes into account the following circumstances (Ferro & Minacapilli, 1995):

1. (1) downstream areas, characterized by a low slope, also have low delivery ratios (Boyce, 1975);

2. (2) much of the predicted sediment yield originates in an area representing a small fraction of the total basin area;

3. (3) steep fallow areas near main channels contribute to both erosion and sediment yield while steep row-cropped fields remote from the channel network are characterized by local erosion but contribute little to sediment yield.

Sediment transport on basin hillslopes is a physical process distinct from transport within the channel network. Therefore hillslope and channel sediment delivery processes have to be considered and modeled separately (Atkinson, 1995).

At the mean annual temporal scale, the sediment delivery problem can be simplified if the channel component is neglected. In this case, the transport capacity of the river flow is not a limiting factor and sediment delivery losses occur at hillslope scale only (Ferro, 1997). The delivery effects into the channel system can be also neglected for small basins in which well-developed floodplains do not exist.

Neglecting the channel component of the sediment delivery, Ferro and Minacapilli (1995) suggested taking into account the within-basin variability of the sediment delivery processes by calculating the sediment delivery ratio SDRi of each morphological unit i into which the basin is divided.

The sediment delivery ratio SDRi of each morphological unit i is a measurement of the probability that the eroded particles arrive from the considered area into the nearest stream reach.

SDRi is dependent on the travel time, tp,i, of each morphological unit and it is, therefore, assumed to decrease both as the length lp,i of the hydraulic path increases and the square root of the slope sp,i of the hydraulic path decreases. According to Ferro and Minacapilli (1995), the probability that the eroded particles arrive from the morphological unit into the nearest stream reach is assumed proportional to the probability of nonexceedance of the travel time tp,i.

To specify the relationship between SDRi and $lp,i/sp,i$, the cumulative frequency distribution function (CFD) of the variable travel time was studied by Ferro and Minacapilli (1995). Since these authors demonstrated that relationship between the logarithm of the cumulative frequency and the variable $−lp,i/sp,i$ is linear, the following equation for calculating the SDRi coefficient of each morphological unit was proposed:

$Display mathematics$
(3)

in which β‎ is a coefficient. Taking into account Chezy’s scheme, the β‎ coefficient lumps together the effects due to roughness and runoff along the hydraulic path. Therefore β‎ is affected by the roughness distribution along the flow path and is time-dependent (i.e., for a given basin β‎ is dependent on the temporal scale (event, annual, mean annual) (Ferro & Porto, 2000).

For evaluating the travel time of the particles eroded from a given morphological unit i, following a Langrangian sequential scheme, the travel times of all morphological areas which are localized along the path p between the ith unit and the nearest stream reach have to be summed. This gives:

$Display mathematics$
(4)

in which Np is the number of morphological units localized along the hydraulic path and λ‎ij and sij are the length and slope of each morphological unit i located along the hydraulic path j.

Equation (3) can be rewritten in the following form:

$Display mathematics$
(5)

In order to estimate the β‎ coefficient of equation (5), the sediment balance equation for the basin outlet has to be applied. The sediment balance equation establishes that the basin sediment yield at the basin outlet Ys (t) is equal to the sum of the sediments produced by all morphological units Nu into which the basin is divided:

$Display mathematics$
(6)

in which Ai is the soil loss (t ha−1) from a morphological unit which can be estimated by a selected erosion model (USLE, RUSLE, etc.) (Renard, Foster, Yoder, & McCool, 1994; Wischmeier & Smith, 1978) and Su,i is the area (ha) of the morphological unit.

The sediment balance equation (6) is based on the hypothesis, supported by Playfair’s law, that sediment yield which arrives from a given morphological unit into a stream reach (SDRiAi Su,i) can be transported to the basin outlet. In other words, the river flow transport capacity Tc is always greater than the actual sediment transport, which is equal to or greater than the hillslope sediment yield Th. An alternative hypothesis is the use of β‎ coefficient to calibrate the model for taking into account the possible case Th > Tc.

Ferro and Minacapilli (1995) demonstrated that the relationship between the basin sediment delivery ratio SDRw and β‎ coefficient is independent of the selected erosion model and it is represented by the following morphological relationship:

$Display mathematics$
(7)

in which λi and si are the slope length and the slope steepness of the i morphological unit, respectively. Equation (7) establishes that both the relationship between the basin sediment delivery ratio SDRw and SDRi is independent of the selected erosion model and β‎ coefficient can be estimated using only morphological data.

# Coupling Sediment Delivery and Soil Loss Estimate

To apply equation (6) for estimating the basin sediment yield and its spatial distribution inside the basin, a soil erosion model at plot scale has to be selected (Bagarello & Ferro, 2006; Renard et al., 1994; Wischmeier & Smith, 1978).

For a basin discretized in Nu morphological units and for each rainfall event, the application of the sediment balance equation at the basin outlet and the USLE, or its revised version RUSLE, leads to the following relationship for calculating the basin sediment yield at event scale Ys:

$Display mathematics$
(8)

in which Re is the event rainfall erosivity factor (MJ mm ha−1 h−1) proposed by Wischmeier and Smith (1978) and, for each morphological unit i, Ki is the soil erodibility factor (t ha MJ−1 mm1 ha−1 h) (Wischmeier et al., 1971), Li (dimensionless) is the slope length factor, Si (dimensionless) is the slope steepness factor, Ci (dimensionless) is the cover and management factor, Pi (dimensionless) is the support practice factor.

Rainfall erosivity is an expression of the ability of the erosive agent (rainfall) to cause soil detachment and its transport. The rainfall erosivity factor of each storm is calculated as:

$Display mathematics$
(9)

in which I30 is the maximum 30-minute rainfall intensity of the storm (mm/h), hj and Ij are the rainfall depth (mm) and intensity (mm/h) for the j storm increment, and n is the number of storm increments.

Erodibility, as a soil characteristic, is a measure of the soil particles’ susceptibility to be detached and transported by the agent of erosion (rainfall and runoff).

The soil erodibility factor Ki has to be estimated by the nomograph of Wischmeier et al. (1971), which uses five parameters for estimating the inherent soil erodibility: percentage f of silt (soil particle diameter ranging from 0.002 to 0.05 mm) plus very fine sand (0.05–0.1 mm); percentage g of sand (0.1–0.2 mm); organic matter content OM expressed as percentage; a structural index SI and a permeability index PI. The nomograph uses a particle size parameter M = f (f + g) that explains 85% of the variation of the soil erodibility factor.

The variables f, g, and OM are quantitative while the structural index and the permeability index are qualitative indexes, having a code varying from 1 to 4 (1, very fine granular; 2, fine granular; 3, medium or coarse granular; 4, blocky, platy, or massive) for SI and from 1 to 6 (1, rapid; 2, moderate to rapid; 3, moderate; 4, slow to moderate; 5, slow; 6, very slow) for PI.

Rosewell and Edwards (Loch & Rosewell, 1992) also developed the following equation, relating soil properties and soil erodibility, which analytically expresses the nomograph of Wischmeier et al. (1971):

$Display mathematics$
(10)

The slope length factor Li is estimated by the following equation (Di Stefano, Ferro, & Porto, 2000; Di Stefano, Ferro, Porto, & Tusa, 2000; Moore & Burch 1986; Moore & Wilson 1992):

$Display mathematics$
(11)

where m is an exponent that, in the RUSLE, is linked at the ratio, F, between rill and interrill erosion:

$Display mathematics$
(12)

$Display mathematics$
(13)

and θ‎ is the slope angle.

Soil loss is much more sensitive to changes in slope steepness than to changes in slope length.

The slope steepness factor Si can be calculated by Nearing’s (1997) equation:

$Display mathematics$
(14)

The crop and management factor Ci represents the ratio of soil loss from a specific cropping or cover condition to the soil loss from a tilled, continuous-fallow condition for the same soil and slope and for the same rainfall. The procedure for calculating the Ci factor requires the knowledge of crop rotation, crop-stage periods, soil loss ratio (SLR) for each crop period, and temporal distribution of rainfall erosivity. The SLR values for most of the crop rotation in the United States are listed in Wischmeier and Smith (1978). The main limitations of this approach are the unavailability of SLRs values for all crop covers or crop rotations and the difficulties of transferring the SLRs values calculated for American conditions to other regions.

To estimate the Ci factor for a forest environment, a procedure, based on the evaluation of nine subfactors, proposed by Dissmeyer and Foster (1981) is available.

The Pi factor mainly represents how surface conditions affect flow paths and flow hydraulics. The erosion control practices usually included in this factor are contouring, contour strip-cropping, and terracing (Wischmeier & Smith, 1978).

# Testing Spatial Variability of Sediment Yield within a Basin

Applying a sediment delivery model at hillslope scale, such as SEDD (Fernandez, Wu, McCool, & Stöckle, 2003; Ferro & Porto, 2000; Fu, Chen, & McCool, 2006; Jain & Kothyari, 2000), allows to obtain the total sediment yield at the basin outlet and its spatial distribution within the basin. The need to quantify the amount of sediment yield in a spatially distributed form has become essential at basin scale for implementing conservation efforts.

At a given temporal scale, the agreement between measured and predicted sediment yield, the former calculated by summation of the sediment yield of each elementary unit into which the basin is divided, does not assure that the calculated spatial distribution of sediment yield is correct.

For testing the internal functioning of a model a field technique, such as the cesium-137 approach capable of monitoring erosion, deposition, storage, and remobilization processes within a basin (Walling & Bradley, 1988), can be used. The radionuclide cesium-137 (137Cs) is a man-made radionuclide which has a half-life of 30 years; it is a fission reaction product of atmospheric thermonuclear weapons test and has been released in significant quantities into the stratosphere. 137Cs fallout reaches the land surfaces with precipitation and is strongly adsorbed on clay and organic particles. 137Cs is adsorbed on sediment particles and it is essentially nonexchangeable by physical and chemical processes and it moves with the sediment particle as a tracer (Ferro et al., 1998).

The 137Cs technique is based on the key assumption that the local fallout distribution is uniform and subsequent redistribution of cesium-137 reflects sediment movement. Measurement of 137Cs input is commonly carried out at undisturbed sites at which no erosion or no depositional processes have occurred and where the original fall-out activity, Csref, will still be found. Where soil erosion occurs, 137Cs will also been lost, leading to a loading less than Csref. Conversely, where deposition takes place, an increase in 137Cs activity will be found. For determining patterns of soil movement from information on 137Cs redistribution, lines of equal 137Cs inventory (mBq cm−2), termed isocaes, can be mapped. If a scale of values of 137Cs inventory is used both to grade erosion severity and soil deposition, the caesiographic map clearly delineates areas of net erosion and net soil deposition. 137Cs data can be used to validate spatially distributed sediment yield models by comparing the caesiographic map with the spatial distribution of sediment yield simulated by the model.

# Sediment Delivery Processes and Clay Enrichment

Some researchers have demonstrated that soil particle aggregates may constitute a considerable fraction of the eroded sediment and their behavior, which is very different from the individual particles (Slattery & Burt, 1997), can appreciably affect sediment delivery processes (Di Stefano & Ferro, 2002). Soil erosion research has directed attention to the properties of the eroded material, because of their influence on the sediment delivery processes and the importance of sediment-associated transport in nonpoint pollution problems (Novotny & Chesters, 1989). The size distribution and density of the sediments are the primary factors which determine whether soil particles are transported or deposited for a given flow condition (Harmon et al., 1989; Rothon et al., 1982). The capacity of the transported particles to carry various contaminants, which contribute to water pollution, is closely related to their specific surface area which is in turn largely dependent on the clay and especially the montmorillonite content of the transported particles (Young & Onstad, 1976).

Slattery and Burt (1997) carried out an investigation of sediment delivery from a small agricultural basin and provided information on the grain sizes of the sediment eroded and transported under natural conditions. These authors compared the effective particle-size distribution (aggregates and individual particles) and the ultimate grain-size distribution (sediments are fully dispersed into its individual particles) of the transported sediments collected during 11 storm events and concluded that for increasing discharge values the sediment load generally becomes finer and less well aggregated, probably due to increased turbulence which in turn influences aggregate breakdown. Slattery and Burt (1997) also reported that most of the clay moves as individual particles or at least clay-sized aggregates both as suspended sediment in the stream and in the sediment transported by hillslope runoff. Since the clay fraction of the sediments arriving at the basin outlet seems to be less sensitive to aggregation processes, the clay enrichment ratio CER, defined as the ratio between the percentage of clay in the sediment and in the original soil, could be used to simply represent delivery processes at basin scale.

Use of the rill‐interrill concept allows the different mechanisms to be distinguished and their link with the size of eroded sediment to be established. Raindrops impact and detach (interrill erosion) both individual particles (sand, silt, and clay) and soil aggregates, which represents clusters of individual particles in which the forces holding the particles together are stronger than the dispersive forces exerted on them by the raindrops. Subsequent raindrop impact will probably break down the detached aggregates further, as they are transported to the rills. In general, no differentiation is made between the particle size of sediment eroded from rill and interrill areas. Particle selectivity largely occurs within the erosion process both because interrill flow does not have sufficient energy to transport many of the aggregates and because the larger particles and aggregates are preferentially deposited during transport (Foster & Meyer, 1975). According to Alberts, Wendt, and Piest (1983), sediment mobilized by interrill erosion will have a percentage of individual clay particles (< 2 µm) larger than interrill plus rill erosion due to flow transport capacity of interrill flow and preferential deposition of large size particles and aggregates. Meyer, Foster, and Nikolov (1975) indicated that particle selectivity is unlikely when rill erosion dominates because of the efficient removal of sediments from rills.

However, when the grain size distribution of eroded sediment is compared with that of the original soil, a considerable enrichment of the finer fraction is generally noticed. The difference of clay content in the sediment Csed and in the original soil Csoil can be due to selective erosion of finer particles or deposition of coarser particles; in other words, the clay enrichment could be attributed to selective erosion or to the conveyance processes.

At the basin scale, the relationship between the grain size distribution of the eroded sediment and the original soil is affected by the potential for selective losses of the coarser fractions in a wide range of depositional environments associated with the transport of eroded sediments from its source to the basin outlet. Size-selective deposition of the eroded sediment occurring throughout the channel network and during the transport from the hillslopes to the stream can result in sediment having particle-size distributions which are enriched in clay fraction with respect to the original soil. For engineering application, selectivity due to particle detachment able to enhance the clay content of eroded sediments can be neglected or, as an alternative, can be considered balanced by selectivity due to aggregate segregation. Walling (1983) suggested that if it is assumed that all clay-size particles have high transportability and move through the conveyance system without deposition, the basin sediment delivery ratio SDRw can be calculated as the ratio between the representative clay content value of the soil covering the basin Csoil,b and Csed. The relationship between clay enrichment and the sediment delivery ratio is more complicated if the clay content of the soils covering the basin is spatially variable, so that a spatially distributed approach has to be adopted.

According to Walling’s (1983) idea of linking the enrichment of fine fraction to the erosion and conveyance process, the delivery ratio SDRi of each morphological unit can be calculated using the following equation:

$Display mathematics$
(15)

in which Csoil,i is the clay content of the soil covering the morphological unit i, which has to be derived from information on the spatial distribution of the clay content of the soil covering the basin, and Csed is the clay content of the sediment arriving at the basin outlet.

The representative clay content at basin scale Csoil,b is a weighted mean value to calculate taking into account the following observations.

1. (a) The clay content Csoil,i spatially varies into a morphological unit having an area equal to Su,i and the area is also an indicator of the transport-limiting case;

2. (b) The transport of Csoil,i along the morphological unit is primarily controlled by the overland flow transport capacity, which is well represented by USLE topographic factors (Moore & Burch, 1986; Moore & Wilson, 1992) or the product $λi0.5si2$.

According to these observations the following expression is used to calculate SDRw:

$Display mathematics$
(16)

Comparing equation (16) with equation (7) gives equation (15), and Di Stefano and Ferro (2002) established that the simple ratio Csoil,i/Csed determined by ultimate grain size distribution can be effectively used for representing the clay enrichment phenomenon.

# Sediment Delivery and Pollutants from Nonpoint Sources

Appreciable enrichment of fine and organic matter fractions are associated with the erosion and conveyance processes. These fractions are also the most chemically active and play a main role in the transport of nutrients, pesticides, and other contaminants.

According to Novotny and Chesters (1989), “Enrichment of sediments and pollutants gives a new ‘quality’ dimension to delivery problems.”

When rainfall reaches the surface horizon of the soil, some pollutants are desorbed and go into solution while others remain adsorbed and move with soil particles.

Deposition and conveyance processes change the qualitative properties of the transported sediments. Detachment of soil particles and pollutants from the original soil is a selective process for fine soil fractions and dissolved pollutants.

In soils, most of the pollutants are adsorbed by clay and organic matter fraction, which are characterized by high surface area, and strong adsorption bonds are formed. Generally the pollutants contained in transported sediments have a concentration higher than that of the original soil. Since the clay fraction of the sediment is the site for most pollutants, the relationship between the grain-size distribution of the eroded sediment and the original soil can be used to explain the increase, or enrichment, in a pollutant content of the sediment with respect to the parent soil.

This difference between pollutant content per gram of sediment PCsed and the pollutant content of the parent soil per gram PCsoil is termed enrichment ratio (ER) and it is defined as follows:

$Display mathematics$
(17)

This enrichment concept may be applied to all pollutants adsorbed by soil particles such as nitrogen, phosphorus, and many pesticides.

The capacity of transported sediments to carry chemicals depends on their specific surface area which is in turn strongly linked to the clay content of the transported individual particles and aggregates.

The effects of particle selectivity within the erosion process (small size particle eroded from interrill areas) and the high transportability of clay particles and small aggregates determine an increase of the clay content of eroded sediment, which can be counteracted by the clay deposited within large aggregates during the conveyance processes. The nutrient enrichment of eroded sediments has been often attributed to a selective erosion process for the finest soil fractions without taking into account that hillslope flow could be unable to transport aggregates having inside a high percentage of primary clay particles.

Since sediments and adsorbed pollutants are produced from different areas distributed throughout the basin, Di Stefano, Ferro, Palazzolo, and Tusa (2000) suggested that improvements in modeling nonpoint pollution phenomena can be obtained by a sediment delivery distributed approach.

Using measurements of weight of chemicals (as an example, nitrogen, phosphorus, and total organic carbon) per kg of soil carried out in samples collected within a basin, the spatial distribution of each chemical concentration can be obtained by a Kriging interpolation procedure (Di Stefano, Ferro, Palazzolo, & Panno, 2005). For a basin divided into morphological units, the overlay of the discretization map of the basin and the spatial distribution of a given chemical concentration allows us to calculate the concentration for each morphological unit (as an example the concentration of nitrogen ni expressed in mg of nitrogen per kg of soil).

For each morphological unit the load of the chemical (the load of nitrogen Ni expressed as g) is then calculated by multiplying the concentration of the chemical (ni expressed as g kg−1) for the corresponding sediment yield Yi (kg).

For a basin divided in Nu morphological units, the total basin load of nitrogen Nb in g is calculated by the following relationship:

$Display mathematics$
(18)

The analysis developed by Di Stefano, Ferro, Palazzolo, et al. (2000) showed that both at morphological unit and basin scale the load of each pollutant X, expressed as g, is related to the sediment yield Y, expressed as kg, by a power relationship:

$Display mathematics$
(19)

in which the values of the coefficient a and n depend on both the considered chemical and the used scale (morphological unit, basin).

The exponent n estimated by Di Stefano, Ferro, Pallazzolo, et al. (2000) for nitrogen, phosphorus, and total organic carbon was generally different from one demonstrating a nonlinear behavior of the basin. For each pollutant the comparison of the n values estimated for the two different scales (morphological unit and basin) underlined the scale shifting. In particular, for phosphorus and total organic carbon the scale shifting from morphological unit to basin scale is obtained by the coefficient a, which becomes a scale factor, because the two values of the exponent n are similar.

For nitrogen, the scale shifting from morphological unit to basin scale is not obtainable by a simple scale factor because of the high spatial variability of the nitrogen load.

Nitrogen and phosphorus have also different adsorption, desorption, and solution characteristics, which affect their mobility and transportability (Di Stefano et al., 2005). In particular, soil nitrogen assumes nitric (NO3 ) and ammoniac (NH4 +) and organic form. The anion NO3 can be transported in solution by hillslope overland flow even if in soils without manuring this anion is negligible. The cation NH4 + is adsorbed into the soil exchange complex. The organic form is characterized by a low mobility and it is preferentially transported by small particles. Soil phosphorus has the phosphate form which is insoluble and precipitates around the soil particles. Phosphorus is characterized by a low mobility even if it can be indifferently transported by small and large particles. Therefore, any nitrogen form is more mobile than phosphorus and this property justifies that the nitrogen load is more spatially variable than the phosphorus load.

The spatial distribution of nitrogen load, phosphorous, and total organic carbon can be deduced using the spatial distribution of sediment yield (kg) and the pollutant load (g per kg of soil) measured on soil samples.

Taking into account that the enrichment ratio of a given pollutant is defined as the load of a given chemical fraction in sediment divided by the load of that fraction in an equal mass of soil, the basin enrichment ratio of the nitrogen ERNb, as an example, can be calculated by the following relationship (Di Stefano, Ferro, Palazzolo, et al., 2000):

$Display mathematics$
(20)

in which Nsed in g is the load of nitrogen in the eroded sediment. Equation (20) clearly demonstrates that the enrichment ratio of a pollutant depends on the load of the pollutant in the eroded sediment and the spatial distribution of both the sediment yield and the pollutant (g per kg of soil) in the matrix soil covering the basin.

Equation (20) can be rewritten in the following form:

$Display mathematics$
(21)

in which the ratio between the basin total load of nitrogen $∑i=1NuniYi$ and the basin sediment yield $∑i=1NuYi$ is termed the pollutant-sediment ratio of the nitrogen.

The definition of pollutant sediment ratio proposed by Di Stefano, Ferro, Palazzolo, et al. (2000) and Di Stefano et al. (2005) allows distinguishing the influence of pollutant load in the eroded sediment from the effects of the spatial distribution of both pollutant content in the matrix soil and of sediment yield.

The pollutant-sediment ratio of the nitrogen PSNb, as an example, is dependent on the soil erosion model applied:

$Display mathematics$
(22)

in which Ri is the rainfall erosivity factor (MJ mm ha−1 h−1) of the morphological unit i. Di Stefano, Ferro, Palazzolo, et al. (2000) and Di Stefano et al. (2005) demonstrated that the pollutant-sediment ratio of the nitrogen PSNb is independent of β‎ coefficient of equation (5) and, according to equation (7), PSNb is also independent of the basin sediment delivery ratio SDRw.

Equation (22) can assume, using only morphological data to weight the nitrogen values of each morphological unit, the following expression:

$Display mathematics$
(23)

Equation (23) is based on the hypotheses that (1) the chemical load (as an example ni) spatially varies into a morphological unit having an area equal to Su,i, and (2) the transport of chemical along the morphological unit is primarily controlled by the overland flow transport capacity which is represented by the product $λi0.5si2$ (Moore & Wilson, 1992) and the sediment delivery ratio of the morphological unit. In conclusion the influence of the sediment delivery processes has to be considered to obtain a reliable estimate of the pollutant-sediment ratio.

# Basin Sediment Yield and Reservoir Sedimentation

Reservoir sedimentation is a complex process varying with basin sediment yield, rate of transportation and mode of deposition. Sedimentation reduces reservoir storage capacity and, besides storage loss, many sediment related problems can occur both upstream and downstream a dam.

The current total large dam (higher than 15 m) reservoir storage capacity for the world is 6100 km3 (ICOLD, 2009). In 2006, the reservoir storage capacity free of sediments was 4100 km3, which means that 33% of the original capacity was used to trap sediments. Without control strategies of sedimentation, the volume of sediment is expected to equal 3900 km3 by 2050 (based on current storage capacity). This means that by 2050 we can roughly estimate that 64% of the world’s current storage capacity could be filled with sediments.

Soil particles are eroded from both the basin hillslopes and the wetted perimeter of the river channels and then these sediments are transported downstream by the river flow.

When a river is dammed, the flow entering the reservoir has its cross-section area enlarged and, as a consequence, the velocity decreases, creating conditions for sediment depositions. The heaviest particles, such as gravel and sand, are the first to settle, while finer particles (silts and clays) enter into the reservoir. The largest and heaviest particles settled near the upstream end of the dam cause the formation of a backwater delta. The finest suspended particles will settle near the dam where the velocities are even lower.

While most of delta deposits gradually reduce the useful capacity of the reservoir, the finest particles reduce the dead storage, which is the quota of reservoir volume designed for storing sediments. The backwater delta will move toward the dam and will be contained in the dead storage too. The sediments reaching the dam pass through spillways and pipes and cause abrasions of the structures.

Each reservoir is characterized by a trap efficiency, which is defined as the proportion of sediments flowing into the dam which is trapped behind in. Most of the large dams have a trap efficiency close to 100%; the dams characterized by a low ratio of storage capacity to mean annual runoff can have trap efficiencies less than 20%.

Knowledge of both the rate and pattern of sediment deposition in a reservoir is required to establish practicable remedial strategies for conserving the reservoir volume. Repeated reservoir capacity surveys are used to determine the total volume occupied by sediment, the sedimentation pattern, and the shift in the stage-area and stage-storage curves.

By converting to sediment mass on the basis of estimated or measured bulk density, and correcting for trap efficiency, the reservoir sedimentation volume can be computed by the basin sediment yield.

For a sustainable use of reservoirs some sediment control strategies should be executed: (1) reduce sediment inflow by erosion control strategies and upstream sediment trapping; (2) route sediments by sediment sluicing and venting the turbid density currents; and (3) removing of sediments by hydraulic flushing, hydraulic dredging, or dry excavation.

# Conclusions

Erosion has been recognized as one of the most significant environmental problems worldwide, particularly in areas where a seasonally climate variability and human pressure act. The negative effects of soil erosion include water pollution, reduction of water storage reservoir capacity, of soil productivity and of crop yield, organic matter loss, and nutrient transport.

Mathematical modeling for soil erosion is important for understanding how landscapes undergo changes as a result of agriculture and other human activities, not simply natural processes. Models are also useful for choosing soil conservation strategies and for designing soil protection works.

Challenges to develop useful equations are many and this result can help to increase the applicability of detailed process-oriented models operating at different spatial and temporal scales. Improvements can derive from the availability of soil loss and sediment yield data, which are useful to verify the applicability of the selected model in a given study area.

Finally, as more research takes place into the design of soil conservation strategies and works, the concept of using long-term soil loss and sediment yield data for a probabilistic representation of the phenomenon should be applied.

Morgan, R. P. C., & Nearing, M. A. (2011). Handbook of erosion modelling. Chichester, U.K.: Wiley-Blackwell.Find this resource:

Toy, D. T., Foster, G. R., & Renard, K. G. (2002). Soil erosion: Processes, prediction, measurement and control. New York: John Wiley.Find this resource:

Zapata, F. (2010). Handbook for the assessment of soil erosion and sedimentation using environmental radionuclides. Dordrecht: Kluwer Academic.Find this resource:

## References

Aksoy, H., & Kavvas, M. L. (2005). A review of hillslope and watershed scale erosion and sediment transport models. Catena, 64, 247–271.Find this resource:

Alberts, E. E., Wendt, R. C., & Piest, R. F. (1983). Physical and chemical properties of eroded soil aggregates. Transactions of the ASAE, 26, 465–471.Find this resource:

American Society of Civil Engineering (ASCE). (1975). Sedimentation Engineering. Manuals and Reports on Engineering Practice, No. 54. New York: ASCE.Find this resource:

Atkinson, E. (1995). Methods for assessing sediment delivery in river systems. Journal of Hydrological Sciences, 40(2), 273–280.Find this resource:

Auzet, A. V., Boiffin, J., Papy, F., Maucorps, J., & Ouvry, J. F. (1990). An approach to the assessment of erosion forms on erosion risk on agricultural land in the Northern Paris basin, France. In J. Boardman, I. D. L. Foster, & J. A. Dearing (Eds.), Soil erosion and agricultural land (pp. 383–400). New York: John Wiley.Find this resource:

Bagarello, V., Baiamonte, G., Ferro, V., & Giordano, G. (1993). Evaluating the topographic factors for watershed soil erosion studies. In R. P. C. Morgan (Ed.), Proceedings of workshop on soil erosion in semi-arid Mediterranean areas (pp. 3–17). Taormina.Find this resource:

Bagarello, V., & Ferro, V. (2006). Erosione e conservazione del suolo. Milan: McGraw-Hill.Find this resource:

Boyce, R. C. (1975). Sediment routing with sediment-delivery ratios. In Present and prospective technology for predicting sediment yields and sources, ARS-S-40 (pp. 61–65). New Orleans, LA: U.S. Department of Agriculture, Agricultural Research Service.Find this resource:

Burns, R. G. (1979). An improved sediment delivery model for Piedmont forests (Unpublished PhD diss.). Georgia Institute of Technology, Atlanta, Georgia.Find this resource:

Capra, A., Di Stefano, C., Ferro, V., & Scicolone, B. (2009). Similarity between morphological characteristics of rills and ephemeral gullies in Sicily, Italy. Hydrological Processes, 23, 3334–3341.Find this resource:

Capra, A., & Scicolone, B. (2002). Ephemeral gully erosion in a wheat-cultivated area in Sicily (Italy). Biosystems Engineering, 83, 119–126.Find this resource:

Casalí J., Loizu, J., Campo, M. A., De Santisteban, L. M., & Álvarez-Mozos, J. (2006). Accuracy of methods for field assessment of rill and ephemeral gully erosion. Catena, 67, 128–138.Find this resource:

Casalí J., López, J. J., & Giràldez, J. V. (1999). Ephemeral gully erosion in southern Navarra (Spain). Catena, 36, 65–84.Find this resource:

Di Stefano, C., & Ferro, V. (2002). Linking clay enrichment and sediment delivery processes. Biosystems Engineering, 81(4), 465–479.Find this resource:

Di Stefano, C., & Ferro, V. (2011). Measurements of rill and gully erosion in Sicily. Hydrological Processes, 25, 2221–2227.Find this resource:

Di Stefano, C., Ferro, V., & Porto, P. (1999a). Modelling sediment delivery processes by a stream tube approach. Journal of Hydrological Sciences, 44(5), 725–742.Find this resource:

Di Stefano, C., Ferro, V., & Porto, P. (1999b). Linking sediment yield and caesium-137 spatial distribution at basin scale. Journal of Agricultural Engineering Research, 74, 41–62.Find this resource:

Di Stefano, C., Ferro, V., & Porto, P. (2000). Length slope factors for applying the Revised Universal Soil Loss Equation at basin scale in Southern Italy. Journal of Agricultural Engineering Research, 75, 349–364.Find this resource:

Di Stefano, C., Ferro, V., Porto, P., & Tusa, G. (2000). Slope curvature influence on soil erosion and deposition processes. Water Resources Research, 36(2), 607–617.Find this resource:

Di Stefano, C., Ferro, V., Palazzolo, E., & Panno, M. (2000). Sediment delivery processes and agricultural non-point pollution in a Sicilian basin. Journal of Agricultural Engineering Research, 77, 103–112.Find this resource:

Di Stefano, C., Ferro, V., Palazzolo, E., & Panno, M. (2005). Sediment delivery processes and chemical transport in a small forested basin. Journal of Hydrological Sciences, 50(4), 697–712.Find this resource:

Dissmeyer, G. E., & Foster, G. R. (1981). Estimating the cover-management factor (C) in the universal soil loss equation for forest conditions. Journal of Soil and Water Conservation, 36, 235–240.Find this resource:

Ellison, W. D. (1947a). Soil erosion studies: Part I. Agricultural Engineering, 28, 145–146.Find this resource:

Ellison, W. D. (1947b). Soil erosion studies: Part II. Agricultural Engineering, 28, 197–201.Find this resource:

Fernandez, C., Wu, J. Q., McCool, D. K., & Stöckle, C. O. (2003). Estimating water erosion and sediment yield with GIS, RUSLE, and SEDD. Journal of Soil and Water Conservation, 58(3), 128–136.Find this resource:

Ferro, V. (1997). Further remarks on a distributed approach to sediment delivery. Journal of Hydrological Sciences, 42(5), 633–648.Find this resource:

Ferro, V. (2006). La sistemazione dei bacini idrografici (2d ed.). Milan: McGraw-Hill.Find this resource:

Ferro, V., Di Stefano, C., Giordano, G., & Rizzo, S. (1998). Sediment delivery processes and the spatial distribution of caesium-137 in a small Sicilian basin. Hydrological Processes, 12, 701–711.Find this resource:

Ferro, V., & Minacapilli, M. (1995). Sediment delivery processes at basin scale. Journal of Hydrological Sciences, 40(6), 703–717.Find this resource:

Ferro, V., & Porto, P. (2000). A sediment delivery distributed (SEDD) model. Journal of Hydrological Engineering, ASCE, 5(4), 411–422.Find this resource:

Ferro, V., Porto, P., & Tusa, G. (1998). Testing a distributed approach for modelling sediment delivery. Journal of Hydrological Sciences, 43(3), 425–442.Find this resource:

Foster, G. R. (1982). Modelling the erosion process. In C. T. Hann, H. P. Johnson, & D. L. Brakensiek (Eds.), Hydraulic modelling of small watersheds, ASAE monograph 5 (pp. 295–380). St. Joseph, MI: American Society of Agricultural Engineers.Find this resource:

Foster, G. R., & Meyer, L. D. (1975). Mathematical simulation of upland erosion using fundamental erosion mechanics. In Proceedings, sediment yield workshop, ARS-S-40 (pp. 190–207). Oxford: USDA Sedimentation Laboratory.Find this resource:

Fu, G., Chen, S., & McCool, D. K. (2006). Modeling the impacts of no-till practice on soil erosion and sediment yield with RUSLE, SEDD and ArcView GIS. Soil & Tillage Research, 85, 38–49.Find this resource:

Glymph, L. M. (1954). Study of sediment yields from watersheds. In Assemblée General de Rome 1954 (vol. 1, pp. 173–191). IAHS Publication no. 36. International Association of Hydrological Sciences.Find this resource:

Harmon, W. C., Meyer, L. D., & Alonso C. V. (1989). A new method for evaluating particle size distribution and aggregated portion of eroded sediment. Transactions of the ASAE, 32, 89–96.Find this resource:

ICOLD. (2009, March). Sedimentation and sustainable use of reservoirs and river systems. ICOLD Bulletin 147.Find this resource:

Jain, M. K., & Kothyari, U. C. (2000). Estimation of soil erosion and sediment yield using GIS. Journal of Hydrological Sciences, 45(5), 771–786.Find this resource:

Kent Mitchell, J., & Bubenzer, G. D. (1980). Soil loss estimation. In M. J. Kirkby & R. P. C. Morgan (Eds.), Soil erosion (pp. 17–62). New York: John Wiley.Find this resource:

Kirkby, M. J., & Morgan, R. P. C. (Eds.). (1980). Soil erosion. New York: John Wiley.Find this resource:

Laflen, J. M., Watson, D. A., & Franti, T. G. (1986). Ephemeral gully erosion. In Proceedings of the Fourth Federal Interagency Sedimentation Conference, Las Vegas, Nevada (pp. 329–337). Washington, DC: U.S. Government Printing Office.Find this resource:

Lal, R. (2001). Soil degradation by erosion. Land Degradation & Development, 12, 519–539.Find this resource:

Leopold, L. B., Wolman, M. G., & Miller, J. P. (1964). Fluvial processes in geomorphology. San Francisco: W. H. Freeman.Find this resource:

Loch, R. J., & Rosewell, C. J. (1992). Laboratory methods for measurements of soil erodibility (K factors) for the Universal Soil Loss Equation. Australian Journal of Soil Research, 30, 233–248.Find this resource:

Maner, S. B. (1958). Factors influencing sediment delivery rates in the Red Hills physiographic area. Transactions of the American Geophys Union, 39, 669–675.Find this resource:

Maner, S. B. (1962). Factors influencing delivery ratios in the Blackland Prairie land resource area. Fort Worth, TX: U.S. Department of Agriculture, Soil Conservation Service.Find this resource:

Meyer, L. D., Foster, G. R., & Nikolov, S. (1975). Effect of flow rate and canopy on rill erosion. Transactions of the ASAE, 18, 905–911.Find this resource:

Meyer, L. D. & Wischmeier, W. H. (1969). Mathematical simulation of the process of soil erosion by water. Transactions of the ASAE, 12, 754–758, 762.Find this resource:

Moges, A., & Holden, H. M. (2008). Estimating the rate and consequences of gully development: A case study of Umbulo Catchment in southern Ethiopia. Land Degradation & Development, 19, 574–586.Find this resource:

Montgomery, D. R. (2007). Soil erosion and agricultural sustainability. Proceedings of the National Academy of Sciences of the United States of America, 104(33), 13268–13272.Find this resource:

Moore, I. D., & Burch, F. J. (1986). Physical basis of the length-slope factor in the Universal Soil Loss Equation. Soil Science Society of America Journal, 50, 1294–1298.Find this resource:

Moore, I. D., & Wilson, J. P. (1992). Length-slope factors for the Revised Universal Soil Loss Equation. Journal of Soil and Water Conservation, 47(5), 423–428.Find this resource:

Morgan, R. P. C. (1986). Soil erosion and conservation. London: Longman.Find this resource:

Morgan, R. P. C., & Nearing, M. A. (2000). Soil erosion models: Present and future. In J. L. Rubio, S. Asins, V. Andreu, J. M. de Paz, & E. Gimeno (Eds.), Proceedings of Third International Congress of the European Society for Soil Conservation: Man and soil at the third millennium (pp. 145–164). Logroño: Geoforma Ediciones.Find this resource:

Nearing, M. A. (1997). A single continuous function for slope steepness influence on soil loss. Soil Science Society America Journal, 61, 917–919.Find this resource:

Nearing, M. A. (1998). Why soil erosion models over-predict small soil losses and under-predict large soil losses. Catena, 32, 15–22.Find this resource:

Nearing, M. A., Foster, G. R., Lane, L. J., & Finkner, S. C. (1989). A process-based soil erosion model for USDA-Water Erosion Prediction Project technology. Transactions of ASAE, 32(5), 1587–1593.Find this resource:

Novotny, V., & Chesters, G. (1989). Delivery of sediment and pollutants from nonpoint sources: A water quality perspective. Journal of Soil and Water Conservation, 44(6), 568–576.Find this resource:

Parsons, A. J., Wainwright, J., Brazier, R. E., & Powell, D. M. (2006). Is sediment delivery a fallacy? Earth Surface Processes and Landforms, 31, 1325–1328.Find this resource:

Piest, R. F., Kramer, L. A., & Heinemann, H. G. (1975). Sediment movement from loessial watershed. In Present and prospective technology for predicting sediment yields and sources, ARS-S-40 (pp. 130–141). New Orleans, LA: U.S. Department of Agriculture, Agricultural Research Service.Find this resource:

Pimentel, D. (2006). Soil erosion: A food and environmental threat. Environment, Development and Sustainability, 8, 119–137.Find this resource:

Pimentel, D., Harvey, C., Resosudarmo, P., Sinclair, K., Kurz, D., McNair, M., Crist, S., Shpritz, L., Fitton, L., Saffouri, R., & Blair, R. (1995). Environmental and economic costs of soil erosion and conservation benefits. Science, 267, 1117–1123.Find this resource:

Poesen, J., Nachtergaele, J., & van Wesemael, B. (1996). Contribution of gully erosion to sediment production in cultivated lands and rangelands. In Erosion and sediment yield: Global and regional perspectives (Proceedings of the Exeter Symposium July 1996) (pp. 251–266). IAHS Publication no. 236. Wallingford, U.K.: International Association of Hydrological Sciences.Find this resource:

Poesen, J., Nachtergaele, J., Verstraeten, G., & Valentin, C. (2003). Gully erosion and environmental change: importance and research needs. Catena, 50, 91–133.Find this resource:

Quinton, J. N. (1994). Validation of physically based erosion models, with particular reference to EUROSEM. In R. J. Rickson (Ed.), Conserving Soil Resources European Perspective (pp. 300–313). Wallingford, U.K.: CAB International.Find this resource:

Renard, K. G., Foster, G. R., Yoder, D. C., & McCool, D. K. (1994). RUSLE revisited: status, questions, answers and the future. Journal of Soil and Water Conservation, 49, 213–220.Find this resource:

Renfro, W. G. (1975). Use of erosion equation and sediment delivery ratios for predicting sediment yield. In Present and prospective technology for predicting sediment yields and sources, ARS-S-40 (pp. 33–45). New Orleans, LA: U.S. Department of Agriculture, Agricultural Research Service.Find this resource:

Richards, K. (1993). Sediment delivery and drainage network. In K. Beven & M. J. Kirkby (Eds.), Channel network hydrology (pp. 221–254). New York: Wiley.Find this resource:

Risse, L. M., Nearing, M. A., Nicks, A., & Laflen, J. M. (1993). Error assessment in the universal soil loss equation. Soil Science Society American Journal, 57, 825–833.Find this resource:

Roehl, J. E. (1962). Sediment sources areas, delivery ratios and influencing morphological factors. In Commission of land erosion (pp. 202–213). IAHS Publication no. 59. Wallingford, U.K.: International Association of Hydrological Sciences.Find this resource:

Rothon, F. E., Meyer, L. D., & Whisler, F. D. (1982). A laboratory method for predicting the size distribution of sediment eroded from surface soils. Soil Science Society America Journal, 46, 1259–1263.Find this resource:

Slattery, M. C., & Burt, T. P. (1997). Particle size characteristics of suspended sediment in hillslope runoff and streamflow. Earth Surface Processes and Landforms, 22, 705–719.Find this resource:

Tiwari, A. K., Risse, L. M., & Nearing, M. A. (2000). Evaluation of WEPP and its comparison with USLE and RUSLE. Transactions of the ASAE, 43, 1129–1135.Find this resource:

Toy, D. T., Foster, G. R., & Renard, K. G. (2002). Soil erosion: Processes, prediction, measurement and control. New York: John Wiley.Find this resource:

Trimble, S. W. (1975). A volumetric estimate of man-induced soil erosion on the southern Piedmont plateau. In Present and prospective technology for predicting sediment yields and sources, ARS-S-40 (pp. 142–152). New Orleans, LA: U.S. Department of Agriculture, Agricultural Research Service.Find this resource:

Trimble, S. W. (1976). Sedimentation in Coon Creek Valley, Wisconsin. In Proceedings of the Third Federal Inter-Agency Sedimentation Conference, (pp. 5:100–5:112). Washington, DC: U.S. Water Resource Council.Find this resource:

Troeh, F. R., Hobbs, J. A., & Donahue, R. L. (1991). Soil and water conservation (2d ed.). Englewood Cliffs, NJ: Prentice-Hall.Find this resource:

Uri, N. D. (2000). Agriculture and the environment: The problem of soil erosion. Journal of Sustainable Agriculture, 16(4), 71–94.Find this resource:

Vandaele, K. (1993). Assessment of factors affecting ephemeral gully erosion in cultivated catchments of the Belgian loam belt. In S. Wicherek (Ed.), Farm land erosion in temperate plains environment and hills (pp. 125–136). Amsterdam: Elsevier.Find this resource:

Vandaele, K., Poesen, J., Marques de Silva, J. R., & Desmet, P. (1996). Rates and predictability of ephemeral gully erosion in two contrasting environments. Geomorphology: Relief, Processes, Environment, 2, 37–58.Find this resource:

Walling, D. E. (1983). The sediment delivery problem. Journal of Hydrology, 65, 209–237.Find this resource:

Walling, D. E., & Bradley, S. B. (1988). The use of 137Cs measurements to investigate sediment delivery from cultivated areas in Devon UK. In M. P. Bordas & D. E. Walling (Eds.), Sediment budgets (pp. 325–335). IAHS Publication no. 174. Wallingford, U.K.: International Association of Hydrological Sciences.Find this resource:

Walling, D. E., Bradley, S. B., & Lambert, C. P. (1986). Conveyance losses of suspended sediment within a floodplain system. In R. F. Hadley (Ed.), Drainage basin sediment delivery (pp. 119–131). IAHS Publication no. 159. Wallingford, U.K.: International Association of Hydrological Sciences.Find this resource:

Williams, J. R., & Berndt, H. D. (1972). Sediment yield computed with Universal Equation. Journal of Hydraulic Engineering, ASCE, 98(2), 2087–2098.Find this resource:

Wischmeier, W. H., Johnson, C., & Cross, B. (1971). A soil erodibility nomograph for farmland and construction sites. Journal of Soil and Water Conservation, 26(3), 189–193.Find this resource:

Wischmeier, W. H., & Smith, D. D. (1978). Predicting rainfall erosion losses. A guide to conservation planning. USDA Agriculture Handbook, 537.Find this resource:

Woodward, D. E. (1999). Method to predict cropland ephemeral gully erosion. Catena, 37, 393–399.Find this resource:

Young, R. A., Olness, A. E., Mutchler, C. K., & Moldenhauer, W. C. (1986). Chemical and physical enrichments of sediment from cropland. Transactions of the ASAE, 29(1), 165–169.Find this resource:

Young, R. A., & Onstad, C. A. (1976). Predicting particle-size composition of eroded soil. Transactions of ASAE, 19, 1071–1075.Find this resource: