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date: 01 February 2023

# Measuring Soil Loss and Subsequent Nutrient and Organic Matter Loss on Farmland

• Vincenzo BagarelloVincenzo BagarelloDepartment of Agricultural and Forestry Sciences, University of Palermo
•  and Vito FerroVito FerroDepartment of Agricultural and Forestry Sciences, University of Palermo

### Summary

Field plots are often used to obtain experimental data (soil loss values corresponding to different climate, soil, topographic, crop, and management conditions) for predicting and evaluating soil erosion and sediment yield. Plots are used to study physical phenomena affecting soil detachment and transport, and their sizes are determined according to the experimental objectives and the type of data to be obtained. Studies on interrill erosion due to rainfall impact and overland flow need small plot width (2–3 m) and length (< 10 m), while studies on rill erosion require plot lengths greater than 6–13 m. Sites must be selected to represent the range of uniform slopes prevailing in the farming area under consideration. Plots equipped to study interrill and rill erosion, like those used for developing the Universal Soil Loss Equation (USLE), measure erosion from the top of a slope where runoff begins; they must be wide enough to minimize the edge or border effects and long enough to develop downslope rills. Experimental stations generally include bounded runoff plots of known rea, slope steepness, slope length, and soil type, from which both runoff and soil loss can be monitored. Once the boundaries defining the plot area are fixed, a collecting equipment must be used to catch the plot runoff. A conveyance system (H-flume or pipe) carries total runoff to a unit sampling the sediment and a storage system, such as a sequence of tanks, in which sediments are accumulated. Simple methods have been developed for estimating the mean sediment concentration of all runoff stored in a tank by using the vertical concentration profile measured on a side of the tank. When a large number of plots are equipped, the sampling of suspension and consequent oven-drying in the laboratory are highly time-consuming. For this purpose, a sampler that can extract a column of suspension, extending from the free surface to the bottom of the tank, can be used. For large plots, or where runoff volumes are high, a divisor that splits the flow into equal parts and passes one part in a storage tank as a sample can be used. Examples of these devices include the Geib multislot divisor and the Coshocton wheel. Specific equipment and procedures must be employed to detect the soil removed by rill and gully erosion. Because most of the soil organic matter is found close to the soil surface, erosion significantly decreases soil organic matter content. Several studies have demonstrated that the soil removed by erosion is 1.3–5 times richer in organic matter than the remaining soil. Soil organic matter facilitates the formation of soil aggregates, increases soil porosity, and improves soil structure, facilitating water infiltration. The removal of organic matter content can influence soil infiltration, soil structure, and soil erodibility.

### Subjects

• Agriculture and the Environment

### Introduction

Measurement is a sequence of steps or operations that produce a value representing the magnitude of a selected entity, whether constant or variable (Toy, Foster, & Renard, 2002). Different experimental methods can be applied to collect soil erosion data, but none has proved to be fully satisfactory under any circumstances (PAP/RAC, 1997; Bonilla et al., 2006). Each method has advantages and disadvantages, and a good knowledge of their feasibility and limitations is necessary to plan experiments properly and also make correct use of the data (Boix-Fayos et al., 2007).

For example, erosion pins are simple and inexpensive tools for measuring soil erosion (e.g., Haigh, 1977; Loughran, 1989; Couper, Stott, & Maddock, 2002) that can be implemented with different materials (Hancock & Lowry, 2015; Hudson, 1983). The pin is inserted vertically into the ground, and the exact height of the exposed length, approximately equal to 50 mm, is recorded after insertion for reference. Over time, repeated measurements of the protruding height of the pin allow one to determine both soil erosion and deposition. Pins are small, have minimal surface exposure, and do not appreciably influence the surrounding land surface. Pins are also relatively inexpensive and lightweight and require little space for storage and transport and little effort to install. However, pin insertion can disturb the soil, and pins may be buried by deposition and/or disturbed by animal and human activity (Lawler, 1991). Because of their small size and surface exposure, pins can be difficult to find, especially when the vegetation is dense. After a fire, they can become blackened and may blend in with the surrounding surface, making them hard to see (Hancock & Lowry, 2015).

The experimental equipment depends on the investigation objectives and the type of data to be obtained. For example, splash erosion is measured by devices (i.e., splash cups), that differ substantially from the plots used to measure rill plus interrill erosion. Moreover, on the plot scale, the rill component can be directly measured (e.g., Bruno, Di Stefano, & Ferro, 2008) or it can be determined by the difference between total soil loss (rill plus interrill) and the interrill component alone (Bagarello & Ferro, 2004; Toy et al., 2002). In other words, two physical quantities (interrill erosion and interrill plus rill erosion) are measured to derive a third physical quantity (rill erosion). For determining the existing relationship between soil loss and a given variable, such as rainfall erosivity, the experiment has to be carried out by maintaining all the other factors influencing the phenomenon (soil, land morphology, vegetative cover) at constant levels.

The spatial scale at which the measurement is carried out (cup, microplot, plot, hillslope, or watershed) and the applied measurement technique (global or distributed) must be chosen according to the considered erosion subprocess (e.g., impact, interrill, rill, and gully); the objectives of the experiment, such as determination of the interrill soil erodibility or the soil erodibility factor of the Universal Soil Loss Equation (USLE); and the type of data that must be collected (e.g., soil loss or sediment yield) (Bagarello & Ferro, 2006). According to Stroosnijder (2005), there are five relevant spatial scales for human-induced water erosion at agricultural scales: (a) the point scale (1 m2) for interrill (splash) erosion; (b) the plot (< 100 m2) for rill erosion; (c) the hillslope (< 500 m2) for sediment deposition; (d) the field (< 1 ha) for channels; and (e) the small watershed (< 50 ha) for spatial interaction effects.

The technique for the experimental evaluation of soil erosion can be based on two antithetical approaches: (a) direct survey of the eroded area at given time intervals to detect the amount of soil removed from the area; or (b) indirect evaluation of the amount of soil that, leaving the eroded area, accumulates in a collecting device (e.g., a sedimentation tank) where the measurement is carried out.

The choice of the technique to be used depends on both the desired spatial resolution and the requested measurement accuracy. For example, plot soil loss in a given temporal interval can potentially be determined by using erosion pins at multiple points or by determining the amount of sediments reaching the base of the plot. The two approaches are very different, and both the quality of the data and the type of collected information (distributed and global) depend on both the technological and procedural aspects of the applied techniques.

Erosion research can be carried out in the field or in a laboratory. Field data are generally representative of the prevailing characteristics in the area of interest in terms of climate, soil, morphology, and land use. Moreover, the natural landscape variability allows for checking the relationships between soil erosion and the factors affecting the phenomenon (e.g., soil type, hillslope morphology). Other advantages of field research are the possibility to conduct measurements at the proper scale, with realistic soil and plant characteristics and temporal changes in environmental variables (Stroosnijder, 2005). However, field data collected with reference to a short temporal interval (i.e., a limited number of natural erosive events) could not be representative of average or extreme conditions for the area of interest. To obtain representative data, a multiyear experiment has to be carried out, although this circumstance is expensive and poses several practical problems. Moreover, this type of experiment does not always guarantee collection of appropriate data for the planned investigation. For example, Toy et al. (2002) cited a five-year period of soil erosion monitoring in Wyoming with only eight events yielding measurable runoff. The practical problems of field experimental activities make this type of data less accurate than those that can be collected in the laboratory, where the experiment can be easily controlled and more advanced equipment can be used. Laboratory measurements can be carried out for specific erosion subprocesses (e.g., interrill erosion) in highly controlled conditions, but on the other hand, studying these subprocesses in the light of the natural variability of the different environmental factors is not possible. Laboratory experiments commonly refer to scale-model studies reproducing the difference in size between experimental and field conditions (Toy et al., 2002). Contrary to field experiments, those carried out in the laboratory are generally fast and repeatable. Soil samples have to be prepared for laboratory runs, and their representativeness of field conditions is rather uncertain.

The parameters used for modeling specific erosive subprocesses are often represented by derived physical quantities (e.g., soil erodibility) that are not expressive of intrinsic soil properties. This circumstance implies that only an indirect measurement can be carried out. To be clearer, the measurement depends on the mathematical model used to represent the specific subprocess. Therefore, the measured property varies based on the equation used by the simulation model.

In any case, the objective of the researcher should be to obtain accurate measurements—that is, both precise and unbiased (Toy et al., 2002). Precision refers to the degree of conformity among the measured values themselves (small standard deviation), and bias refers to systematic errors in the measured values. Repeated, biased measurements yield a mean value that is not centered on the true value. Statistical analysis of the data cannot replace the ability of the researcher to both detect and explain unexpected measurement results. A discouraged conclusion by Stroosnijder (2005) was that there are currently insufficient empirical data of adequate quality, a lack of funds to improve that situation, and a lack of development of new technologies and equipment, as well as a lack of skilled personnel.

This article first deals with the description of plots used for measuring interrill and rill erosion. Then the equipment used at the plot scale for measuring runoff and to sample sediments is presented. Classic and new techniques for monitoring ephemeral gully (EG) erosion are also introduced. Finally, the nutrient and organic loss associated with soil erosion is discussed.

### Laboratory and Field Equipment to Measure Interrill and Rill Erosion

Plots of given geometry are frequently used for soil erosion measurement (e.g., Bagarello & Ferro, 1999, 2006; Boix-Fayos et al., 2006, 2007; Stroosnijder, 2005; Bonilla et al., 2006). When the objective of the investigation is to study the interrill process, the physical quantity to be determined is how much soil is detached by rain impact and transported by overland flow. Therefore, the measurement area has to be small so that overland flow can occur but rill development is avoided (Toy et al., 2002). Interrill erosion can be measured in the laboratory, using simulated rainfall, or in the field under both simulated and natural rainfall events.

Laboratory measurements are generally carried out using sieved soil, packed to a given bulk density in pans that are then disposed of to the desired steepness. With this aim, different researchers have been using a variety of mesh sizes to sieve the soil. For example, Zhang, Nearing, Miller, Norton, and West (1998) used soil particles smaller than 6 mm in diameter, whereas Grosh and Jarrett (1994) used a 19-mm sieve. Agassi and Bradford (1999) recommend that soil be passed through sieves not smaller than 10 mm, or preferably even 20 mm, since erosion tests conducted on soil passed through larger sieves are more representative of field conditions. Soil samples for laboratory measurements generally have a thickness of about 10 cm (Grosh & Jarrett, 1994; Zhang et al., 1998) with surface areas approximately ranging between 0.20 × 0.40 m2 and 1.25 × 1.78 m2 (Bradford & Huang, 1993; Grosh & Jarrett, 1994; Lattanzi, Meyer, & Baumgardner, 1974; Moldenhauer & Long, 1964; Poesen, Ingelmo-Sanchez, & Mucher, 1990; Zhang et al., 1998). The larger pans have a central test area surrounded by a buffer area of soil, so that any redistribution of splash does not result in a net loss of splashed soil within the test area. To reproduce the erosion subprocess properly, any splash leaving the test area must be balanced by an input of splash from the surrounding areas (Agassi & Bradford, 1999). Generally, the soil pan is placed in the central zone of the area wet by the nozzle used for rainfall simulation. For large pans, multiple nozzles have to be used simultaneously to achieve a satisfactory uniformity distribution of the applied rainfall (Bradford & Huang, 1993).

Total runoff (water plus sediment) is intercepted at the lower end of the pan or the test area through a gutter, and it is conveyed to a container with small volume (i.e., a few liters) since the eroded area is small. The weight of the container after the event is determined, and then the suspension is oven-dried at 105°C. The weight of the oven-dried sediment is the total soil loss that can be referred to the sampled area and expressed, for example, in grams per square meter. The total liquid runoff is determined by subtracting the weight of solid particles from the net weight of the suspension collected during the experiment. This weight is transformed into volume using the specific weight of water. Runoff is generally referred to the sampled area and expressed in millimeters, being equal to the ratio between the volume of water and the surface of the test area. Sampling total runoff during the event at short temporal intervals (e.g., 1 or 2 min) in small containers allows for determining how the liquid runoff and soil loss vary with time.

In the field, microplots can be set by inserting 0.20-m-high sheet metal barriers to a 0.10-m depth (Figure 1). A gutter, leveled with the natural soil surface, is installed at the bottom end of the microplot and connected to a small tank located in a small trench. The tanks are removed after each erosive event, and total runoff and soil loss are determined gravimetrically. The microplot surface varies approximately between 0.04 and 10 m2 (Bagarello & Ferro, 2004, 2006; Chaplot & Le Bissonnais, 2000).

A proper choice of the plot area has to be made since the soil loss data can be expected to vary with the microplot dimensions (Agassi & Bradford, 1999). As an example, Figure 2 shows soil loss values measured in large (0.16 m2) and small (0.04 m2) square microplots by Bagarello and Ferro (2004). During the study period in which different rainfall depths were recorded, mean soil loss values measured in the small microplots ranged from 1.6 to 3.5 times higher than those obtained in the large microplots. This result was interpreted by considering that the factors enhancing water infiltration had a larger impact on runoff in the longer microplots. Therefore, the influence of the microplot dimensions on soil loss has to be considered when the interrill erodibility coefficient is experimentally determined.

According to Chaplot and Le Bissonnais (2000), interrill erodibility should be evaluated on large microplots (10 m2, and 5 m slope length). The reason is that the erosion process is transport-limited (i.e., not all the detached material is transported) in the small microplots and detachment-limited (i.e., overland flow could transport more material than detached) in the large microplots. In other terms, using large microplots allows one to be confident that the measurement is expressive of the interrill erosion subprocess (i.e., transport by runoff of detached sediments by rainfall). Transport-limiting conditions do not tend to dominate if the soil steepness is large (Truman & Bradford, 1995). Therefore, small microplots can also be used for interrill erosion measurement if they are installed with high steepnesses (Bagarello & Ferro, 2004).

Rill plus interrill erosion can be measured on plots approximately 10–200 m long and 2–50 m wide (Brakensiek, Osborn, & Rawls, 1979). In the United States, the standard plot has a length of 22 m and a width of 1.8 m, and hence an area of 39.6 m2. Generally, an experimental plot is a portion of land with a rectangular shape, with the longest side oriented parallel to the maximum steepness, hydraulically disconnected from the surrounding area (Figure 3). Runoff and associated sediments produced in the plot are intercepted by a gutter placed along the lower end of the plot (Figure 4), and then they are transferred to a storage tank or sampling system. In particular, the upper side and the two longest sides of the plot can be separated from the surrounding soil by a 0.25-m-high (aboveground) sheet metal barrier that is inserted into the soil to a 0.20–0.30-m depth. Water and sediment intercepted by the gutter are conveyed to the system used for partitioning and/or storing the mixture, which can be constituted by total collection tanks, flume and samplers, and slot divisors (Bagarello & Ferro, 1998; Brakensiek et al., 1979; Bonilla et al., 2006).

Total collection tanks should be large enough to contain the total runoff (water and sediment) expected in a 24- or 48-h period (Bonilla et al., 2006). The total volume of the water-sediment mixture is easily determined from the known tank geometry by measuring the water depth. The sediment load generally has to be determined by oven-drying laboratory procedures. Total collection devices are suitable for erosion studies if runoff is not excessive (Brakensiek et al., 1979). However, multiple tanks can be used if plots are large and, hence, relatively high runoff volumes are expected. For example, runoff and associated sediment from plots of 22 × 8 m2 to 44 × 8 m2 established at the Sparacia experimental area (in Sicily, southern Italy) are collected into a storage system consisting of three tanks (Figure 5), each with a capacity of approximately 1 m3, that are arranged in series at the base of each plot (Bagarello, Ferro, & Giordano, 2010). A single tank is instead installed at the base of the 11-m-long plots and two tanks are used for the 22 × 2-m2 plots.

Sediment concentration in the stored mixture can be measured by either catching the whole sediment amount, after siphoning the supernatant cleared water, or collecting a sample of the mixed suspension (Pierson, Van Vactor, Blacbum, & Wood, 1994). As reported by Ciesiolka et al. (2004, 2006), data used for calibrating the USLE (Wischmeier & Smith, 1965, 1978) were obtained by stirring the suspension, taking a sample by immersing a collector to a substantial depth beneath the surface of the water in the tank, and oven-drying the sample. This procedure was also adopted worldwide (Hudson, 1971; Edwards, 1987; Rosewell, 1993; Bagarello & Ferro, 2016). If all the sediment is collected for laboratory analysis, the result is accurate, but it requires the collection and oven-drying of a high mud volume. Therefore, this technique becomes cumbersome and time-consuming for increasing amounts of collected runoff and number and size of plots.

The suspended sediment concentration measured on a sample is representative of the whole collected suspension if the water-sediment mixture is well mixed and the measured suspended concentration assumes the same value in each measurement point of the tank, corresponding to the actual. Consequently, the sediment amount is calculated by multiplying the sample concentration by total runoff volume. However, Lang (1992) tested a bottle sampler for sampling clay soil-water mixtures and concluded that the actual suspended particle concentration was underestimated by a factor of 2; consequently, he threw doubt on the reliability of soil loss data from plots collected using a runoff sampling technique. Since in many plots, the runoff and sediment concentration are sampled manually, Zobisch, Klingspor, and Oduor (1996) also verified the accuracy and the repeatability of this sampling procedure by comparing the sampling results of different field workers. The authors showed that the runoff volume was slightly underestimated, while an unacceptably poor accuracy of the soil loss measurements was recognized. Zobisch et al. (1996) concluded that the differences were due to the way that the suspended sediment was stirred just before sampling and the way that the sample was retrieved by plunging a beaker into the suspension.

In fact, the thoroughness of mixing the suspended sediment influences its homogeneity within the tank; moreover, the timing and plunging depth of the sample beaker determine the concentration of suspended sediment. According to Ciesiolka et al. (2004, 2006), the investigations of sampling techniques cast doubt on the correctness of the USLE soil loss database, which has been relied upon to the present day, even to validate process-based erosion technologies (Zhang et al., 1996; Tiwari, Risse, & Nearing, 2000). Consequently, Ciesiolka et al. (2004, 2006) developed a correction for any slight delay between stirring and sampling, tailoring this correction to the soil type involved. A check of the magnitude of errors due to the assumption of a uniform sediment distribution after stirring (complete mixing) the suspension and the actual distribution (incomplete mixing) was also made. Bagarello and Ferro (1998), Bagarello, Di Piazza, and Ferro (2004) evaluated factors affecting the measured sediment concentration and derived calibration curves for the sediment storage tanks.

The plot width, w, generally varies among different investigations. For example, w for an investigation by Bagarello and Ferro (2010), Nearing (2000) varied from 2 to 8 m, whereas Boix-Fayos et al. (2007) used w = 1 and 3 m. Plots varying in width from 1.83 to 39.0 m were considered by Risse, Nearing, Nicks, and Laflen (1993). An effect of plot width on measured soil loss for a given plot length cannot be excluded. For example, it may be suspected that the probability for runoff to become concentrated (higher runoff and soil loss) is higher in a narrow plot than a wider one since surface runoff has less opportunity to deviate from the flow direction of maximum slope. On the other hand, localized areas with relatively low soil erodibility, high roughness, or high infiltration rates, reducing runoff and soil loss, are expected to have a more noticeable effect in the narrow plots than in the larger ones.

Therefore, an improved interpretation of plot soil loss data needs experimental definition of the effect of plot width on soil loss, but this topic does not seem to be largely treated in the scientific literature. Bagarello et al. (2011) empirically established plot width effects on runoff volume and soil loss per unit area, and also on sediment concentration by using data collected, at the temporal scale of the erosive event, on bare plots of different widths (2–8 m) and lengths (11–22 m) set in two Italian installations aimed to monitor soil erosion (Masse, Umbria; Sparacia, Sicily). This investigation showed that, for low-erosivity events, the effect of plot width on the measured variable may vary from negligible to significant. In this last case, a plot of a given width may give both higher and lower results than a plot with a different width, depending on the event. Probably, local soil conditions at the beginning of the rainfall play an important role in determining the hydrological response of a given plot subjected to a low-erosivity event.

Another factor likely affecting the observed discrepancies is that measurement errors increase for decreasing values of the measured variable (Bagarello & Ferro, 2004). For highly erosive events, the importance of local soil conditions is reduced and the plot width effect tends to disappear. In other words, plots differing in width tend to give similar results in terms of the considered variables. Taking into account that a few severe storms generally affect total soil loss per unit area and sampling these events is particularly important to develop effective soil conservation practices, an implication of the investigation by Bagarello et al. (2011) should be that an appropriate sampling scheme for plot runoff, soil loss, and sediment concentration measurements in case of severe storm events may be based on narrow plots, with a substantial reduction of experimental effort.

In addition to total soil loss, erosion measurements can be used to determine the sediment enrichment ratio (SER), defined as the ratio between the amount of sediment of a given size range and the amount of particles of the same size range in the original soil (Di Stefano & Ferro, 2002). The SER concept is important for understanding water pollution. Because of the chemically enriched nature of fine particles due to the large surface area of clay-sized sediments, the concentration of chemicals that are associated with sediment increases as more fine particles are washed downstream (FAO, 1996). According to Defersha and Melesse (2012), the SER is determined separately for coarse, medium, and fine sand, silt, and clay. These authors determined the original soil particle size distribution by pipette method, following the procedure of the U.S. Soil Conservation Service (1967) and the sedimentation time recommended by Tanner and Jackson (1947). The particle sizes of the collected sediment were determined by gently sieving sand-sized particles, followed by drying and weighing. Silt and clay were determined in the suspension passing the sieve by drying pipetted volumes of suspension sampled at fixed depths after different settling times. After the washed sediment size for each sample was estimated, the SER was determined.

Installing plot borders on three sides of the test area and a gutter at the lower end of the plot implies the construction of a closed system (i.e., not connected to the surrounding ground surface). This closed system may suffer medium- to long-term exhaustion of available material to be eroded (Boix-Fayos et al., 2007). In particular, closed erosion plots show an exhaustion of available material for soil detachment after several years of functioning, probably due to the creation of an armor layer at the soil surface, lack of input of transported material from outside the plot (Morgan, 2005; Ollesch & Vacca, 2002), and a low soil formation rate (Dunjó, Pardini, & Gisbert, 2004). This partial exhaustion of material can be expected to occur a few years after plot installation (4–7 years), and is translated into an increase of the precipitation thresholds for erosion during the years of measurement (Boix-Fayos et al., 2007). Less depletion of material occurs in bounded cultivated plots (Romero-Díaz, Cammeraat, Vacca, & Kosmas, 1999) where new soil material is available after tillage. Erosion measurements in open plots are independent of the detachment-limited conditions over the same time span as in closed plots (Boix-Fayos et al., 2007). In this last case, however, determining the contributing area of the collector using detailed topographic maps can be challenging (Bonilla et al., 2006).

According to Boix-Fayos et al. (2006, 2007), the bigger the plot, the closer its response is to reality due to a better representation of the connections between the different factors of a natural system. Large plots reduce some problems that occur in small plots, such as artificial hydrological disconnection within the system, low energy flows due to the short distances, and induction to a quick response to runoff due to an artificial decrease of concentration times for continuous flow. In contrast, small plots are very suitable to characterizing quickly the hydrological and erosion response of different microenvironments, as well as studying the effect of soil surface components. Direct extrapolation from plots to catchments is not possible since the connectivity of water and sediment fluxes, the different thresholds for geomorphological responses and the nonlinear processes operating at different scales will not be represented (Boix-Fayos et al., 2006). Understanding the physical representativeness of plot data is important to make a proper interpolation and use of the results. With this aim, Boix-Fayos et al. (2006) recommended systems of nested plots (Cammeraat, 2002; Wilcox, Breshears, & Allen, 2003) installed within large measurement areas to identify the main sediment sources and sinks and the geomorphological thresholds involved in the erosion process at different scales within a specific system.

Taking into account that soil loss measurements can vary appreciably between apparently identical plots (Nearing, Govers, & Norton, 1999; Bagarello & Ferro, 2010; Wendt, Alberts, & Hjelmfelt, 1986), the use of replicated plots is recommended to obtain representative soil erosion data for a particular treatment. Boix-Fayos et al. (2007) suggested that the number of replicated plots must be decided according to the natural variability of soil loss and the size of the plot. The total percentage and the spatial pattern of surface components, such as vegetation cover, stones, crusts, and litter, must be considered when using replicated plots. Data obtained from these plots must be interpreted considering not only total coverage, but also the distribution of surface components within the plot, and especially the outlet of the plot. According to Lavee, Imeson, and Sarah (1998), the size of the bare patches between plants is the dominant factor determining the production of runoff at plot scale. Boix-Fayos et al. (2007) suggested that the closer the bare and crusted areas to the outlet of the plot, the higher the soil loss. Therefore, surface components should have a similar spatial pattern in replicated plots.

Redistribution of the eroded soil in a plot can occur if the soil erosion process is transport limited, and it can be checked by the so-called mesh-bag (MB) dynamic method (Hsieh, 1992; Hsieh, Grant, & Bugna, 2009). With this method, the redistribution of eroded soil in a plot can be monitored after one or more runoff events by installing small (e.g., 20 × 20 cm2) nylon sheets. These sheets are installed in intimate contact with the bare ground (i.e., after removing vegetation), so that they allow water but only negligible amounts of soil particles to infiltrate underneath the bag. Mesh bags can be constructed out of two nylon mesh sheets: one with a 4-mm mesh opening on the top to mimic the roughness of a soil surface, and another with a 0.1-mm opening at the bottom to facilitate water infiltration. The top and bottom sheets are aligned and stapled together to form a mesh bag before they are deployed in the field. The bags are secured to the soil with metal nails so that the mesh sheets are in close contact with and conform to the soil surface. Mesh bags are harvested after the event, and the soil on and within the sheets is collected for analysis. The MB and the runoff plot methods assess two mutually exclusive parts of soil erosion: the former allows for assessing the amount of soil left in the plot, while the latter allows for assessing the amount of soil transported out of the plot.

Data collected simultaneously on plots and microplots in a given test area can be used to determine the relative importance of interrill and rill erosion on total soil loss. Bagarello and Ferro (2004) used the data collected at the Sparacia experimental station on 8 × 22 m2 plots, and 0.4 × 0.4 m2 and 0.2 × 0.2 m2 microplots having a common steepness of 14.9%. For a given erosive event, a mean value of soil loss per unit area, μ‎(SLe), was determined by averaging the data collected in all the operating plots of a given surface area, Sp. For each event, soil loss decreased when passing from the smaller (0.04 m2) to the larger (0.16 m2) microplots; the straight line passing through the two (Sp, μ‎(SLe)) data points representative of the microplots was extrapolated to the biggest plot (176 m2) to estimate the expected interrill soil erosion measurement . Depending on the event, total soil loss measured on the biggest plots was 14 to 1,810 times greater than the value estimated by extrapolation. This ratio was considered indicative of the relative influence of the different soil erosion processes acting at different scales. In the microplots, only interrill erosion likely occurred while rills developed in the plots. Processes of soil detachment and transport were more noticeable in the rilled areas than in the nonrilled ones. Interrill soil erosion was a minor or negligible part of rill plus interrill soil erosion (0.1%–7.1%, depending on the event). According to more recent investigations, increasing plot length tends to moderately increase the rate of rill erosion and has a clear decreasing effect on the interrill erosion rate (Bagarello & Ferro, 2010).

Soil loss data acquired in the plots are used for several purposes, including the assessment of models aimed to predict soil erosion. In general, the performances of soil erosion models are evaluated by using a single or a few replicated data for a given treatment. However, plots modeled with identical input parameters yield variable soil loss data (Wendt et al., 1986; Bagarello & Ferro, 2004, 2010). Generally, experimental output variability is not quantitatively taken into account during model evaluation because the knowledge of natural variability between plots subjected to the same treatment is limited (Nearing, 2000). Therefore, it has to be expected that, for a particular treatment, one part of any difference between measured and predicted erosion rates will be due to model error, but another part will be due to the circumstance that the measured sample value will not coincide with the representative mean value (Nearing et al., 1999).

Using many replicated plots within a given treatment reduces this type of uncertainty because it allows for evaluating a more representative soil loss mean value (Wendt et al., 1986). However, equipping and operating many plots with the same treatment at a single experimental station must be considered an exception, being onerous from an economic point of view as well as impractical. Therefore, evaluation of soil erosion models, such as the USLE/Revised Universal Soil Loss Equation (RUSLE) or the Water Erosion Prediction Project (WEPP) (Wischmeier & Smith, 1965, 1978; Renard, Foster, Weesies, McCool, & Yoder, 1997; Flanagan & Nearing, 1995), whose nature is deterministic, commonly ignores the variability of measured data (Nearing, 1998). A limit to the accuracy of deterministic models (whether empirical or process oriented) should be expected since the variation in soil erosion rates is practically random (Nearing, 2000).

Nearing (1998) suggested that the best possible model to predict the erosion is a physical model reproducing the area with similar soil type, land use, size, shape, slope, and erosive inputs. Therefore, for a plot and its replicate, the measured soil loss in a plot is treated as the measure (M), while the measurement in the replicate is used as the predicted soil loss (P). In other terms, the physical model represented by a replicated plot has to be considered the best possible, unbiased, real-world model. Using this concept, Nearing (2000) suggested that the prediction by a soil erosion model has to be considered acceptable if the difference between the model estimation and the corresponding measured value lies within the population of differences between pairs of measured values. In particular, the relative difference, Rdiff, between the measured (M) and the predicted (P) soil loss value is calculated as

$Display mathematics$(1)

The 95% occurrence interval for a given measured value is then estimated by the following relationships:

$Display mathematics$(2a)
$Display mathematics$(2b)

where Rdiff,INF and Rdiff,SUP are the lower and the upper limit of the interval, respectively; and M is expressed in kg/m2. Eq. (2) was empirically developed using data from plots that were mostly 22 m long and 2–8 m wide and with a slope steepness varying from 3% to 16%. Moreover, wide ranges of geographic conditions, rainfall regimes, erosion rates, and soil types were represented in the data set. If the Rdiff value calculated by Eq. (1) falls outside the range of the expected differences according to Eq. (2), the conclusion is that the prediction is not equal to the measured value. The probability of incorrectly rejecting the null hypothesis (PM = 0) is less than 5%. The conclusion by Nearing (2000) was that the results should be generally applicable to the validation of erosion models at the plot scale.

An Italian database was recently developed by considering two stations (Sparacia in Sicily and Masse in Umbria); four plot lengths (λ‎ = 11, 22, 33, and 44 m); and four slope steepness values (s = 14.9, 16.0, 22.0, and 26.0%); and defining a physical model as a plot planimetrically identical to the sampled one (Bagarello et al., 2015). For this database, the premise of the analysis by Nearing (2000)—i.e., that the measured data with greater erosion rates show, on average, less relative difference between replicates—was confirmed only with reference to the highest erosion rates (i.e., M > 1 kg/m2), but also in this particular case, the correspondence of the predicted occurrence interval with the data was not fully satisfactory. From a scientific point of view, the sign of the difference between P and M must be determined to establish how to improve a soil erosion predictive tool. From a practical point of view, however, the absolute PM difference is enough to establish the accuracy level of the predictions. In Italy, the $|P−M|$ values were found to increase with M according to the following relationship (Figure 6):

$Display mathematics$(3)

having a coefficient of determination R2 = 0.72 and a 95% confidence interval of the exponent of 0.88–0.94, denoting a nonlinearity of the relationship. Eq. (3) can be viewed as an alternative approach for applying the physical model concept by Nearing (2000) since it predicts, for a given soil loss value (M), the mean absolute difference associated with the sampling of another identical plot. A soil loss prediction by a model is accurate enough if the absolute difference with the measured value does not exceed the $|P−M|$ value calculated by Eq. (3). Alternatively, the least restrictive criterion, using a relationship enveloping all data points, could be proposed. An intermediate criterion between the suggested regression line and a data-enveloping line could also be developed by carrying out a frequency analysis of the data divided into half-log-cycle intervals, similar to the one carried out by Nearing (2000) to estimate 95% occurrence intervals for the data.

### Rill Measurements

Bounded plots of known geometry (width, slope length, and slope steepness) are generally used for monitoring rill erosion and for measuring rill features.

Accurate ground measurements of rill erosion are based on the assessment of some cross-sectional areas along the rill channel using a microtopographic profiler, or a tape and a ruler. These direct measurements are very simple, low-cost, time-consuming, and widely used (Casali et al., 2006). To measure the rill length, cross-sectional area, and slope, each rill has to be divided into segments and each segment length Lr,s can be measured by a metric rule (Bruno et al., 2008).

Rill sections can be measured along transverse transects with a variable interdistance, preferably established to account the variability of rill depth, rill width, and the appearance of rill tributaries along the rill length (Figure 7). Characterization of cross-sections by a tape and a ruler requires that each rill cross section is assimilated to a simple geometric form. Tape is usually used for the direct measurement of field horizontal distance, while the ruler is used for measuring vertical distances (depth). Generally, researchers employing these methods do not provide information on probable errors associated to the relief of the cross section (Casalì, Loizu, Campo, De Santisteban, & Àlvarez-Mozos, 2006). The end sections of each rill segment can be surveyed by a microtopographic profiler (rillmeter). Figure 8 shows a typical rillmeter that was constructed by 10 pins, each having a diameter of 4 mm and a length approximately equal to 250 mm, installed on an aluminium bar using a cross-interdistance of 10 mm. The pin configuration can be photographed and pin heights can be measured or digitized from these images.

A laser profiler, based on the defect of focus of a laser light beam, can be used for measuring the soil surface height. The laser profiler consists of an aluminum girder supporting a carriage system in which the laser detector is allocated. This nondestructive measurement technique requires no mechanical contact between the laser sensor and the soil surface during the relief (Bertuzzi & Caussignac, 1988).

The accuracy of direct measurements mainly depends on the researcher’s choice (e.g., the used experimental setup and the number of measurements carried out), rather than on the precision of the used equipment. The rill segment volume, Vr,s, is calculated by the following relationship:

$Display mathematics$(4)

in which Ai is the initial cross-sectional area of the rill segment and Ai+1 is the final cross-section. The total volume, V, of a rill is calculated by adding the volumes Vr,s of all segments into which the rill is divided. The total length L is calculated by adding the length Lr,s of all segments into which the rill is divided.

When the rill and interrill erosion have to be compared to establish the weight of the rill component on the total plot soil loss, the total rill volume has to be converted into the weight of the eroded material. To determine the weight of soil corresponding to the total rill volume, soil bulk density is experimentally determined by collecting undisturbed soil samples uniformly distributed on the plot. The sampling can be carried out using cylindric samplers (e.g., having a diameter of 8–10 cm and a height equal to 5 cm) that are oven-dried at 105°C for 48 h.

After each erosive event, the plan of the rill network can be deduced by a photographic relief corrected by using the transverse and longitudinal bands painted on the plot boundaries (Figure 7). Figure 9 shows, as an example, the plan view of a rill network monitored after a rainfall event.

The traditional direct survey method, carried out by rillmeter and topographic instruments, is particularly time-consuming and requires that the operator gets into the plot with consequent alteration of the plot surface. The plan and elevation relief by a low-altitude flight plane is a remote relief method, so it is noninvasive, feasible immediately after an event, and suitable for an automatic extraction of the characteristic features of the rills (Carollo, Di Stefano, Ferro, & Pampalone, 2015a).

The aerial photography is carried out using a photo camera installed onboard a radio-controlled microdrone (Figure 10). This vector has a small weight (less than 1.5 kg at full load) and extremely small dimensions (70 cm), and is able to run automatically in flights that are previously planned by the available maps of the investigated area. In the planning phase, the number of flights and the relative elevation are programmed. Figure 11 shows an example of a flight plane with the followed route. The flight plane follows the classic photogrammetric strips with an overlapping of 80% and a side lapping of 60%. The obtained Digital Elevation Model (DEM) is characterized by a mesh size equal to 1 cm and an elevation resolution equal to 2 mm.

The orthophoto obtained by the DEM can be used to survey the rill features by a manual method. This method is carried out by drawing on the PC screen the rill paths obtained by the visual orthophoto interpretation. This manual method is not applicable for the plots in which rills of limited depth occur and are not detectable.

Carollo et al. (2015a) developed an automatic extraction method of rills from the DEM. Using an appropriate calculation routine, a vector coverage of transects orthogonal to the main flow direction (i.e., the maximum slope steepness path) was generated. The intersection of each plot DEM with the transect coverage allowed for obtaining both the cross-sections and the main rill morphological features.

The automatic method to extract rills from DEM applied the theory of drop analysis by Broscoe (1959). This theory is based on the concept that when the order of the channels within the network increases, the slope of the thalweg decreases, and the length of the channels increases.

For a 44-m-long plot, Figure 12 shows the comparison between the map of rills extracted by the drop analysis (the automatic method, shown in panel (a) and the manual method (b). This comparison shows that the automatic extraction is characterized by a number of detected rills greater than the manual method. Moreover, the rills identified by the automatic method are longer than those determined by the manual method because of the difficulty of identifying rills by orthophotos in the downstream end of the plot. For four rills detected into the plot, Figure 13a shows that the total rill length detected by DEM (the automatic method) is greater than the one determined by the direct (rillmeter) and manual (orthophoto) methods. No differences were observed between the total rill volumes estimated by the three methods (Figure 13b).

Carollo et al. (2015a) also carried out a DEM versus rillmeter comparison in terms of depth and width, verifying that the DEM yielded underestimations of the depth and overestimations of the width. Depth underestimation can be explained by taking into account that each pin of the rillmeter could penetrate the soil of the rill boundary, while the overestimation of the surface width could be due to the difficulties and uncertainties of the field operator to establish the exact width of a small channel like a rill. The cross-sectional area invariance with the relief method can be obviously justified by considering that the depth underestimations are balanced by the width overestimations.

### Runoff and Sediment Concentration Measurements

The runoff rate can be monitored continuously by using a weir or flume in conjunction with a water-level sensor and a data logger (Bonilla et al., 2006). An automated pumping sampler can be used to draw samples from downstream of the weir or flume, communicating with the data logger to tie the sample concentration to the represented flow volume and permitting a mass movement calculation. Such systems are valuable for studies needing time-varying concentration values.

In the 18th century, Giovanni Battista Venturi was the first to observe the effects on pressure and velocity distribution in a conduit due to local contractions (Ferro, 2002). The flume determines a local reduction of the channel width, and the contraction is obtained by locally thickening the channel sidewalls. Measurement channels having a flat bottom and a local diminution of width, named Venturi channels (Cone, 1917), have been proposed and widely applied. In European countries, the use of a long-throated flume with gradual width variation, called a Khafagi flume, is widespread, while in Anglo-Saxon countries, the Parshall flume (Parshall, 1926; Blaisdell, 1994), which consists of a throatless flume with broken plane transitions, is widely employed.

These flumes are all characterized by a particular shape of the cross-sectional area with various degrees of convergence and subsequent divergence. The shape aims to contract the width of the original channel (Figure 14) in order to assure, for a free-flow condition, that the critical depth occurs in the narrow section (Baiamonte & Ferro, 2007). For example, the Endress+Hauser commercializes nine different models of Venturi meters, whose plan configuration follows the shape of the streamlines and determines a gradual contraction from the inlet rectangular section, having width B, to another still rectangular section, having narrow section Bc. For the nine models, characterized by different lengths L of the Venturi meter, and also by different B and Bc values, a laboratory investigation to determine the stage-discharge relationship was carried out. The manufacturing company supplied the pairs (h, Q), where h is the water depth measured in a section of the channel upstream of the Venturi meter and Q is the discharge. The experimental runs were carried out for the free-outflow condition, using a horizontal measurement flume and placing, upstream of the Venturi meter, an inlet reach where the measurement of h was carried out. The inlet reach had a length that was double the Venturi meter length L. The stage-discharge relationship of a generic Endress+Hauser Venturi meter can be expressed by the following equation:

$Display mathematics$(5)

in which Q is measured in m3/s and Bc and h are expressed in meters. The reliability of a single stage-discharge relationship [Eq. (5)] demonstrates that a condition of hydraulic similarity exists among the nine models commercialized by Endress+Hauser.

The Parshall flume introduces a convergent feature with a horizontal bottom, followed by a feature to a constant section (throttling) and tilted in the direction of the motion and a divergent feature in the back slope. The Parshall flumes, as Blaisdell (1994) noticed, are not hydraulically similar, and so a single stage-discharge relationship cannot be established. In any case, the Parshall flumes, realized in fiberglass, cement, or steel, are expensive and not always easy to install when the downstream back slope bottom must be installed in an existing channel.

More recently, another device, a Samani-Magallanez-Baiamonte-Ferro (SMBF) flume, to measure discharge in open-channel flow was proposed by Samani and Magallanez (2000) and subsequently developed by Baiamonte and Ferro (2007) and Carollo, Di Stefano, Ferro, and Pampalone (2016). The measurement principle is based on establishing a channel contraction (Hager, 1986; Samani & Magallanez, 1993) using a cylinder, which is, according to Hager (1985), the simplest body having a streamlined shape Using two semicylinders applied to the walls of a laboratory channel, having a zero slope, the width B of the rectangular cross section is narrowed to the throat width Bc (Figure 15a). Using the dimensional analysis and the incomplete self-similarity hypothesis (Barenblatt, 1979, 1987; Ferro, 1997), Baiamonte and Ferro (2007) deduced the following relationship between h and Q (stage-discharge relationship of the flume):

$Display mathematics$(6)

in which a and n are two numerical constants depending on the contraction ratio Bc/B and g (m/s2) is the acceleration due to gravity.

Recently, Carollo et al. (2016), applying the Bernoulli theorem, theoretically deduced the following new stage-discharge equation for the SMBF flume:

$Display mathematics$(7)

in which α‎ and β‎ are two coefficients equal to 1.085 and 0.243, respectively.

In order to test Eq. (7), field measurements were carried out at the Sparacia experimental station by using an SMBF flume inserted into a field horizontal channel, characterized by a contraction ratio equal to 0.5 (Figure 15b).

Slot samplers offer an alternative to flumes and total collection tanks and can provide a low-cost solution for a wide range of plot sizes (Bonilla et al., 2006). Slot samplers are designed to collect a representative portion of the runoff-sediment mixture. An example is the Coshocton wheel (Figure 16) (Carter & Parson, 1967), which has a water wheel, slightly inclined from the vertical, and a sampling head with a narrow opening (slot). With each revolution of the wheel, the slot cuts across the jet from the flume conveying total runoff and collects a given portion of the runoff, which is then transported to a storage tank.

Another example of slot sampler is the stationary multislot divisor, first suggested by Geib (1933). Runoff is routed to this divisor, and a sample is obtained from a single slot and routed to a storage tank. As an example, the multislot divisor by Pinson, Yoder, Buchanan, Wright, and Wilkerson (2004) is built using a commercially available 19-L bucket with a screwtop lid. A series of 22.5° V-slot weirs are cut with a precision laser into a strip of metal, which is then rolled into a crown and fastened to the top of the lid, from which the center has been removed. The bucket fills completely, and overflowing water-sediment is evenly divided among many slots. Flow from one of the overflowing slots is then collected in another bucket, and more buckets with crowns can be placed in a series to divide runoff for larger storm events or larger plots (Bonilla et al., 2006).

Another sampler is the Fagna-type hydrological unit (Bazzoffi, 1993). Runoff, cleaned of the coarser materials by passing it through a sedimentation tank, falls into a revolving pot supported by two U-shaped forks. When the pot is full, it turns completely upside down. A few cubic centimeters of the outgoing jet are intercepted by a sampling hole and conveyed to a small tank below the hole level. When the pot is empty, two coaxial pivots enable the pot mouth to return to the up position. Both the hydrograph and the runoff volume are measured by the number of times that the pot is emptied. The weight of suspended material is determined by the mean sediment concentration in the small tank and the measured runoff volume.

The suspended sediment concentration also can be measured by infrared turbidity sensors. The excitation radiation is emitted in a pulselike manner into the flow at a defined angle by infrared transmitters. The suspended particles generate a scattered light that it is received by a receiver. The measured signals are processed to produce an output that is proportional to the suspended solid concentration. By coupling this local measurement to the discharge, the temporal pattern of sediment concentration can be determined.

A simple method to measure the sediment concentration is to store all plot runoff or divide it using a sequence of tanks (Figure 5). At first, the water level in the tank is measured. Then, the suspension (water + sediments) is thoroughly mixed (Figure 17) and samples of known volume are collected at different depths along a vertical profile by opening the sampling taps installed at different heights, so as to determine the suspended sediment concentration profile. The samples are oven-dried at 105°C for at least 48 h or the time necessary to obtain a constant sediment weight. Then, a mean concentration, Cm, is determined by integrating the measured sediment concentration profile (Figure 18). The measured mean concentration Cm differs from the actual concentration of the suspension, C, because the manual sampling procedure determines an incomplete mixing condition and sedimentation phenomena take place within the suspension during the sampling time (Lang, 1992; Bagarello & Ferro, 1998; Todisco, Vergni, Mannocchi, & Bomba, 2012). The measured mean concentration Cm is then transformed into the actual concentration C of sediment stored in the tank using the calibration curve of the storage system (Bagarello & Ferro, 1998; Bagarello et al., 2004):

$Display mathematics$(8)

where the coefficient b depends on the eroded soil type (Figure 19), the sampled suspension volume from each location, the water depth inside the tank, the number of sampling locations, and the mixing time before sampling. By this curve, the risk of measuring soil loss values lower than the actual is appreciably reduced. The total runoff volume is deduced from the water-level readings and the accumulated sediments in the tanks. The total weight of the solid particles both suspended and dissolved in the suspension collected in each tank is calculated by the product of the mean concentration of the suspension and the stored volume.

When the number of equipped experimental plots is large, the procedure of collecting the sediments stored into the tanks is highly time-consuming for the field sampling phase and the following laboratory oven-drying.

A quick sampling procedure can be efficiently applied by using a sampler that is constituted by a brass cylinder 120 cm high, with an inner diameter of 4.75 cm (Carollo, Di Stefano, Ferro, Pampalone, & Sanzone, 2015b). It is equipped with a closing valve “guillotine” fitted with a sealing gasket (Figure 20). The valve is controlled from above by means of a knob joined to a drive pin. The use of the sampler is very simple: it is introduced into the suspension collected in the tank and, after the closure of the valve, is extracted.

The sampler allows the extraction of a column of suspension extending from the free surface to the bottom of the tank. The mean concentration in the sampling vertical is established by measuring the weight of the solid material and the collected volume. In other words, the sampler measures the mean concentration along a vertical profile by integrating the sediment concentration.

The sampler was tested with a series of laboratory runs, carried out using a cubic tank having a volume of about 1 m3 (Figure 21). Four values of actual concentration (Ca = 15, 50, 120, and 400 g/l) and three values of water levels inside the tank (h = 53 cm, 65 cm, and 83 cm) were investigated. For each configuration (Ca, h), nine samples were extracted from nine vertical profiles according to the scheme shown in Figure 21. For each sample, the volume was measured by a calibrated beaker and, after oven-drying the suspension at 105°C for at least 48 h, the solid material was weighed by a balance with an accuracy of 0.01 g. Runs were carried out after mixing the suspension manually or using a flat scoop similar to that used in the field, taking care to avoid centrifugal effects. Furthermore, a run of the series with Ca= 50 g/L and h = 65 cm was designed to verify the reliability of the sampler without mixing.

For low concentration values, the runs showed a noticeable spatial variability of the concentration measured in different verticals, whereas this spatial variability considerably decreased as the actual concentration increased, and it became negligible at the highest concentration value. In any case, the mean value of the measured concentration can be considered equal to the actual concentration. Moreover, the statistical analysis allowed one to conclude that the expected value of the mean concentration measured along a given vertical could always be considered equal to the actual concentration, and that the water level into the tank and the sampling vertical did not affect the measurements.

To establish the sampling procedure to be adopted in the field, the margin of error of the concentration estimate for a given sample size was calculated. The analysis established that five samples were sufficient both to ensure a relatively low margin of error and to limit the difficult level of the sampling.

### Measuring Ephemeral Gully (EG) Erosion

According to Nachtergaele and Poesen (1999), the major problem with EG erosion research is carrying out accurate measurements to collect reliable data. The most common way to collect EG erosion data is taking a field survey after a rainfall event in order to measure the EGs’ characteristic parameters, such as length, cross-section, and width.

As discussed with reference to rill measurements, accurate ground measurements of EG erosion are based on the assessment of the vertical surface of some cross-sections along the channel using a topographic profiler or a tape and a ruler. These direct measurements are very simple, low-cost, time-consuming, and widely used (Casalì et al., 2006) and allow for calculating EG volumes through the determination of the cross-sectional areas and the length of reaches. Even in this case, the tape is usually used for the direct measurement of field horizontal distances, while the ruler is used for measuring vertical distances (depths) and, generally, information on probable errors associated with the relief of the cross section is lacking (Casalì et al., 2006).

Field measurement of EG cross sections can be carried out using a pin profiler, that consists of some stainless steel pins having a transverse constant spacing, which are placed perpendicular to the channel axis. The pin configuration can be photographed and pin heights can be measured or digitized from these pictures. Laser profilometers (Giménez et al., 2009) are also used for EG erosion determination since they allow a rapid and detailed measurement of the soil surface height.

Gully length measurement on high-altitude aerial photographs can be combined with field measurements of cross sections to assess three-dimensional (3D) gully erosion (Vandale, Poesen, Marques de Silva, & Desmet, 1996; Nachtergaele & Poesen, 1999; Giménez et al., 2009). Traditional aerial photogrammetry was successfully applied for large-scale and long-term investigations (Martinez-Casanova, Antón-Fernández, & Ramos, 2003; Ionita, 2006), while for both short-term applications at high spatial resolution the use of drones (Carollo et al., 2015a) is diffused. Aerial photography allows rapid and spatially continuous coverage of an area with high resolution. The accuracy of the data obtained by aerial and terrestrial photogrammetry depends on the instruments and the applied technique (Marzolff & Poesen, 2009). In addition, the accuracy of rill and gully measurements depends on the morphology and size of the channels. For example, the relief of the cross-sectional area is difficult if the cross section is narrow and deeply eroded due to the difficulty of measuring heights inside the channel (Daba, Rieger, & Strauss, 2003).

Automatic 3D-photo reconstruction techniques for oblique images from uncalibrated and nonmetric cameras coupled with the availability of photogrammetric software packages allow the use of close-range photogrammetry to investigate soil erosion processes (Castillo et al., 2015). Terrestrial digital photogrammetry is characterized by high spatial resolution (centimeters to millimeters) and minimal impact of the field activity on both the relief and farming operations, while a time-consuming work for post-processing the digital photos is required.

Image-based modeling creates a digital terrain model using a set of photographs taken from the same surface (Frankl et al., 2015). The procedure allows to solve camera model parameters and scene geometry simultaneously using redundant information coming from oblique images and without using control points during the composition of the model (Gòmez-Gutiérrez, Schnabel, Berenguer-Sempere, Lavado-Contador, & Rubio-Delgado, 2014). The resulting point cloud must be scaled and georeferenced using some control points within the monitored area. The main advantage of this technique is that it requires little expertise because the image processing is almost automatic (James & Robson, 2012), and the obtained accuracy is similar to the best available method, such as using a terrestrial laser scanner (Castillo et al., 2012). The methodology is based on semiautomated 3D photo-reconstruction techniques, such as the coupled use of Structure from Motion and MultView-Stereo workflows (Seiz et al., 2006; Javernick, Brasington, & Caruso, 2014) which are integrated in software such as PhotoScan (Agisoft).

According to Frankl et al. (2015), understanding gully erosion processes requires the use of a 3D model that is also able to approximate the 3D topography, including areas into which multiple z-coordinates (elevations) exist for a given couple of x-y plane coordinates (Figure 22).

### Nutrients and Organic Matter Loss

Soil erosion affects both the nutrient content of eroded sediments and soil organic carbon (SOC) dynamics by (a) redistribution within watersheds or transport outside of its boundaries and (b) altering SOC mineralization processes in disturbed sediments (Gregorich, Greer, Anderson, & Liang, 1998; Polyakov & Lal, 2008).

Blanco-Canqui, Gantzer, Anderson, Alberts, and Thompson (2004) suggested using 0.25-L samples from the collected runoff volume that are preliminarily stirred to suspended sediments. The samples are stored in an insulated cooler and quickly transported to the laboratory. Samples are filtered through Whatman #1 filter paper for determination of nitrate (NO3-N), ammonium (NH4-N), and orthophosphate (PO4-P), and then stored at 4°C until analyzed. Total N and P concentrations are determined from unfiltered aliquots. Analysis of N and P can be done using a Lachat flow injection analyzer (Lachat Quik-Chem 800 Zellweger Analytics, Milwaukee, WI). Nutrients are computed as the product of runoff and concentration. Organic N is calculated as the difference of NO3-N and NH4-N from total N. Particulate P is calculated as the difference of total P minus PO4-P.

In the investigation by Cogle, Keating, Langford, Gunton, and Webb (2011), total nitrogen and phosphorus in runoff water were determined. An aliquot (10 mL) of well-mixed, unfiltered water is digested in sulfuric acid and potassium sulfate with mercuric oxide added as a catalyst. The digest is then diluted and analyzed using automated continuous flow colorimetric techniques. During digestion, nitrogenous (except nitrate-N) compounds are converted to ammonium ions, while phosphorous compounds are converted to orthophosphate ions. The total nitrogen in the soil is determined by combustion at 1,300°C in a LECO CNS-2000 analyzer (LECO Corp., St. Joseph, MI). Total phosphorus is determined using wet digestion. An enrichment ratio is determined for nitrogen and phosphorus as the ratio between the nutrient concentration in the sediment and the topsoil.

According to Zheng et al. (2005), nitrogen, phosphorus, and organic matter losses can be determined by using preliminarily mixed runoff samples collected from plots. In particular, after each runoff event, the water level in a container is measured to calculate the runoff volume and four 1-L samples are collected from each container after mixing around with a muddler. After more than 24 h of sedimentation, the clear water is poured out of the bottles. The rest of the samples are dried by air or sunlight, and then the air-dried soil samples are used for the chemical analysis. Organic matter is determined using the method of Walkley and Black (1934), the total nitrogen (Kjeldahl digest) and NH4-N (2.0 M KCl extractant) are determined using an automated ion analyzer, and available phosphorus (0.5 M NaHCO3 extractant) is analyzed with colorimetry.

Water erosion effects on soil organic matter and CO2 emission can be tested with the methodology used by Polyakov and Lal (2008). Immediately following a plot runoff event, the content of the collection tank is stirred and two runoff subsamples are taken and weighted. One of the subsamples is treated with the solution AlK(SO4)2×12H2O allowing coagulation. When the sediments settle, the excess water is decanted and the remaining soil is dried at 45°C and weighed to determine the soil erosion rate and the total sediment balance for the plot. Dried samples are analyzed for SOC concentration by dry combustion at 920°C using the Vario MAX CN macroelemental analyzer. The second subsample is poured through a set of sieves with 1-, 0.5-, 0.25-, 0.1-, and 0.05-mm screen openings. Care must be taken to prevent breaking the aggregates during the sieving. Then, the material remaining on the sieve, as well as the fraction passing through the 0.05-mm sieve is air-dried. Approximately 2 g of material from each fraction are used to determine the total SOC concentration. The remaining aggregates are left intact and used to determine the amount of potentially mineralizable SOC (Jacinthe, Lal, & Kimble, 2002). Then 1 gram of the aggregates is saturated with water, placed into 120-mLvials with airtight rubber stoppers, and incubated at 25°C. Samples of headspace air in the vials are taken using a syringe at increasing time intervals during the following 100 days. The amount of CO2 emitted from the incubated samples is determined using the Shimadzu GC-14A gas chromatograph. The vials are ventilated after each sampling. The SOC pool at the experimental site, used to calculate the enrichment ratio in SOC, is assessed by analyzing core soil samples obtained with an auger of 2 cm and using the known soil bulk density.

Nie et al. (2014) determined SOC concentrations of soil and sediment via the dichromate oxidation method of Walkley and Black (1934). The total organic carbon concentrations for the runoff samples were measured with a Shimadzu TOCTN analyzer. The enrichment ratio of organic carbon is calculated by dividing the SOC content of the sediment by its content in the original soil material.

A very simple check of the noticeable importance of the organic matter content on soil erosion can be made by calculating the soil erodibility factor, K, of the USLE (Wischmeier, Johnson, & Cross, 1971) for the two extreme organic matter values expected in agricultural soils (0% and 4%, respectively). As shown in Figure 23 for 45 soil samples collected in Sicily, the lack of organic matter always determines the most erodible conditions and, considering the multiplicative nature of the model, the mean annual soil loss can even increase by 50% as the organic matter decreases from 4% to 0%. According to Dissmeyer and Foster (1981), soil erosion under permanent forest is expected to be approximately 70% of that occurring under common agricultural conditions due to the particularly high level of soil organic matter.

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